LMFDB - Embedded newform 378.2.u.e.169.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [378,2,Mod(43,378)]

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([4, 0]))

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

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

chi := DirichletCharacter("378.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 378 = 2 \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	378.u (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:	$36$
Relative dimension:	$6$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			169.5
Character	$\chi$	$=$	378.169
Dual form			378.2.u.e.85.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.939693 - 0.342020i) q^{2} +(1.28430 - 1.16214i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-0.345781 - 1.96102i) q^{5} +(0.809368 - 1.53131i) q^{6} +(0.766044 + 0.642788i) q^{7} +(0.500000 - 0.866025i) q^{8} +(0.298838 - 2.98508i) q^{9} +O(q^{10})$	\(q+(0.939693 - 0.342020i) q^{2} +(1.28430 - 1.16214i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-0.345781 - 1.96102i) q^{5} +(0.809368 - 1.53131i) q^{6} +(0.766044 + 0.642788i) q^{7} +(0.500000 - 0.866025i) q^{8} +(0.298838 - 2.98508i) q^{9} +(-0.995637 - 1.72449i) q^{10} +(-0.732484 + 4.15412i) q^{11} +(0.236816 - 1.71578i) q^{12} +(-2.94847 - 1.07316i) q^{13} +(0.939693 + 0.342020i) q^{14} +(-2.72308 - 2.11669i) q^{15} +(0.173648 - 0.984808i) q^{16} +(2.40789 + 4.17059i) q^{17} +(-0.740141 - 2.90727i) q^{18} +(1.91945 - 3.32458i) q^{19} +(-1.52540 - 1.27997i) q^{20} +(1.73084 - 0.0647244i) q^{21} +(0.732484 + 4.15412i) q^{22} +(-7.32143 + 6.14341i) q^{23} +(-0.364298 - 1.69331i) q^{24} +(0.972422 - 0.353933i) q^{25} -3.13770 q^{26} +(-3.08530 - 4.18102i) q^{27} +1.00000 q^{28} +(6.42350 - 2.33796i) q^{29} +(-3.28280 - 1.05769i) q^{30} +(1.95298 - 1.63874i) q^{31} +(-0.173648 - 0.984808i) q^{32} +(3.88697 + 6.18638i) q^{33} +(3.68910 + 3.09552i) q^{34} +(0.995637 - 1.72449i) q^{35} +(-1.68985 - 2.47879i) q^{36} +(1.96163 + 3.39764i) q^{37} +(0.666617 - 3.78058i) q^{38} +(-5.03387 + 2.04830i) q^{39} +(-1.87118 - 0.681056i) q^{40} +(-2.70961 - 0.986218i) q^{41} +(1.60432 - 0.652804i) q^{42} +(-0.641085 + 3.63578i) q^{43} +(2.10910 + 3.65307i) q^{44} +(-5.95714 + 0.446155i) q^{45} +(-4.77872 + 8.27699i) q^{46} +(8.79161 + 7.37704i) q^{47} +(-0.921473 - 1.46659i) q^{48} +(0.173648 + 0.984808i) q^{49} +(0.792726 - 0.665176i) q^{50} +(7.93927 + 2.55796i) q^{51} +(-2.94847 + 1.07316i) q^{52} -12.9026 q^{53} +(-4.32922 - 2.87364i) q^{54} +8.39960 q^{55} +(0.939693 - 0.342020i) q^{56} +(-1.39850 - 6.50043i) q^{57} +(5.23649 - 4.39393i) q^{58} +(-0.543969 - 3.08500i) q^{59} +(-3.44658 + 0.128884i) q^{60} +(-3.30626 - 2.77428i) q^{61} +(1.27472 - 2.20787i) q^{62} +(2.14770 - 2.09461i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-1.08496 + 6.15309i) q^{65} +(5.76842 + 4.48387i) q^{66} +(13.4552 + 4.89729i) q^{67} +(4.52535 + 1.64709i) q^{68} +(-2.26336 + 16.3985i) q^{69} +(0.345781 - 1.96102i) q^{70} +(-3.02959 - 5.24740i) q^{71} +(-2.43573 - 1.75134i) q^{72} +(4.22982 - 7.32626i) q^{73} +(3.00539 + 2.52182i) q^{74} +(0.837558 - 1.58465i) q^{75} +(-0.666617 - 3.78058i) q^{76} +(-3.23133 + 2.71141i) q^{77} +(-4.02973 + 3.64646i) q^{78} +(-13.3291 + 4.85141i) q^{79} -1.99127 q^{80} +(-8.82139 - 1.78411i) q^{81} -2.88351 q^{82} +(-3.32011 + 1.20842i) q^{83} +(1.28430 - 1.16214i) q^{84} +(7.34601 - 6.16403i) q^{85} +(0.641085 + 3.63578i) q^{86} +(5.53263 - 10.4677i) q^{87} +(3.23133 + 2.71141i) q^{88} +(-5.49875 + 9.52411i) q^{89} +(-5.44528 + 2.45671i) q^{90} +(-1.56885 - 2.71732i) q^{91} +(-1.65963 + 9.41225i) q^{92} +(0.603748 - 4.37428i) q^{93} +(10.7845 + 3.92524i) q^{94} +(-7.18329 - 2.61450i) q^{95} +(-1.36751 - 1.06298i) q^{96} +(0.904341 - 5.12877i) q^{97} +(0.500000 + 0.866025i) q^{98} +(12.1815 + 3.42793i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 3 q^{3} + 3 q^{5} + 6 q^{6} + 18 q^{8} + 3 q^{9}+O(q^{10}) $ 36 * q + 3 * q^3 + 3 * q^5 + 6 * q^6 + 18 * q^8 + 3 * q^9	$ 36 q + 3 q^{3} + 3 q^{5} + 6 q^{6} + 18 q^{8} + 3 q^{9} - 3 q^{10} + 9 q^{13} - 6 q^{15} + 6 q^{18} - 15 q^{19} - 6 q^{20} + 3 q^{21} - 3 q^{24} - 3 q^{25} - 18 q^{26} - 30 q^{27} + 36 q^{28} - 6 q^{29} - 9 q^{30} + 60 q^{33} + 9 q^{34} + 3 q^{35} - 27 q^{37} + 15 q^{38} + 6 q^{39} - 3 q^{40} - 9 q^{41} - 6 q^{43} + 9 q^{44} + 42 q^{45} - 9 q^{46} + 36 q^{47} + 3 q^{48} - 15 q^{50} - 36 q^{51} + 9 q^{52} - 42 q^{53} - 27 q^{54} + 30 q^{55} - 18 q^{57} - 21 q^{58} + 12 q^{59} + 24 q^{60} + 3 q^{61} + 18 q^{62} + 12 q^{63} - 18 q^{64} - 84 q^{65} + 18 q^{66} - 69 q^{67} + 9 q^{68} - 48 q^{69} - 3 q^{70} + 12 q^{71} + 6 q^{72} - 12 q^{73} + 9 q^{75} - 15 q^{76} + 9 q^{77} - 48 q^{78} - 51 q^{79} - 6 q^{80} - 69 q^{81} + 15 q^{83} + 3 q^{84} - 12 q^{85} + 6 q^{86} + 84 q^{87} - 9 q^{88} - 3 q^{89} + 6 q^{90} - 9 q^{91} + 18 q^{92} - 21 q^{93} + 9 q^{94} - 75 q^{95} - 42 q^{97} + 18 q^{98} + 39 q^{99}+O(q^{100}) $ 36 * q + 3 * q^3 + 3 * q^5 + 6 * q^6 + 18 * q^8 + 3 * q^9 - 3 * q^10 + 9 * q^13 - 6 * q^15 + 6 * q^18 - 15 * q^19 - 6 * q^20 + 3 * q^21 - 3 * q^24 - 3 * q^25 - 18 * q^26 - 30 * q^27 + 36 * q^28 - 6 * q^29 - 9 * q^30 + 60 * q^33 + 9 * q^34 + 3 * q^35 - 27 * q^37 + 15 * q^38 + 6 * q^39 - 3 * q^40 - 9 * q^41 - 6 * q^43 + 9 * q^44 + 42 * q^45 - 9 * q^46 + 36 * q^47 + 3 * q^48 - 15 * q^50 - 36 * q^51 + 9 * q^52 - 42 * q^53 - 27 * q^54 + 30 * q^55 - 18 * q^57 - 21 * q^58 + 12 * q^59 + 24 * q^60 + 3 * q^61 + 18 * q^62 + 12 * q^63 - 18 * q^64 - 84 * q^65 + 18 * q^66 - 69 * q^67 + 9 * q^68 - 48 * q^69 - 3 * q^70 + 12 * q^71 + 6 * q^72 - 12 * q^73 + 9 * q^75 - 15 * q^76 + 9 * q^77 - 48 * q^78 - 51 * q^79 - 6 * q^80 - 69 * q^81 + 15 * q^83 + 3 * q^84 - 12 * q^85 + 6 * q^86 + 84 * q^87 - 9 * q^88 - 3 * q^89 + 6 * q^90 - 9 * q^91 + 18 * q^92 - 21 * q^93 + 9 * q^94 - 75 * q^95 - 42 * q^97 + 18 * q^98 + 39 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$29$	$325$
$\chi(n)$	$e\left(\frac{8}{9}\right)$	$1$

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 $

$2$	0.939693	−	0.342020i	0.664463	−	0.241845i
$2$	0.939693	−	0.342020i	0.664463	−	0.241845i
$3$	1.28430	−	1.16214i	0.741489	−	0.670965i
$3$	1.28430	−	1.16214i	0.741489	−	0.670965i
$4$	0.766044	−	0.642788i	0.383022	−	0.321394i
$5$	−0.345781	−	1.96102i	−0.154638	−	0.876995i	−0.959116	−	0.283013i	$-0.908666\pi$
$5$	−0.345781	−	1.96102i	−0.154638	−	0.876995i	0.804478	−	0.593982i	$-0.202445\pi$
$6$	0.809368	−	1.53131i	0.330423	−	0.625157i
$7$	0.766044	+	0.642788i	0.289538	+	0.242951i
$7$	0.766044	+	0.642788i	0.289538	+	0.242951i
$8$	0.500000	−	0.866025i	0.176777	−	0.306186i
$9$	0.298838	−	2.98508i	0.0996128	−	0.995026i
$10$	−0.995637	−	1.72449i	−0.314848	−	0.545333i
$11$	−0.732484	+	4.15412i	−0.220852	+	1.25251i	0.649605	+	0.760272i	$0.274934\pi$
$11$	−0.732484	+	4.15412i	−0.220852	+	1.25251i	−0.870458	+	0.492243i	$0.836177\pi$
$12$	0.236816	−	1.71578i	0.0683630	−	0.495304i
$13$	−2.94847	−	1.07316i	−0.817758	−	0.297640i	−0.100934	−	0.994893i	$-0.532183\pi$
$13$	−2.94847	−	1.07316i	−0.817758	−	0.297640i	−0.716825	+	0.697253i	$0.754405\pi$
$14$	0.939693	+	0.342020i	0.251143	+	0.0914087i
$15$	−2.72308	−	2.11669i	−0.703095	−	0.546526i
$16$	0.173648	−	0.984808i	0.0434120	−	0.246202i
$17$	2.40789	+	4.17059i	0.583999	+	1.01152i	0.994999	+	0.0998807i	$0.0318461\pi$
$17$	2.40789	+	4.17059i	0.583999	+	1.01152i	−0.411001	+	0.911635i	$0.634821\pi$
$18$	−0.740141	−	2.90727i	−0.174453	−	0.685249i
$19$	1.91945	−	3.32458i	0.440352	−	0.762712i	−0.557364	−	0.830268i	$-0.688187\pi$
$19$	1.91945	−	3.32458i	0.440352	−	0.762712i	0.997715	+	0.0675569i	$0.0215204\pi$
$20$	−1.52540	−	1.27997i	−0.341091	−	0.286209i
$21$	1.73084	−	0.0647244i	0.377700	−	0.0141240i
$22$	0.732484	+	4.15412i	0.156166	+	0.885662i
$23$	−7.32143	+	6.14341i	−1.52662	+	1.28099i	−0.709068	+	0.705140i	$0.750884\pi$
$23$	−7.32143	+	6.14341i	−1.52662	+	1.28099i	−0.817556	+	0.575849i	$0.804672\pi$
$24$	−0.364298	−	1.69331i	−0.0743621	−	0.345645i
$25$	0.972422	−	0.353933i	0.194484	−	0.0707866i
$26$	−3.13770			−0.615353
$27$	−3.08530	−	4.18102i	−0.593766	−	0.804638i
$28$	1.00000			0.188982
$29$	6.42350	−	2.33796i	1.19281	−	0.434149i	0.332103	−	0.943243i	$-0.392242\pi$
$29$	6.42350	−	2.33796i	1.19281	−	0.434149i	0.860711	+	0.509094i	$0.170020\pi$
$30$	−3.28280	−	1.05769i	−0.599355	−	0.193106i
$31$	1.95298	−	1.63874i	0.350766	−	0.294327i	−0.450332	−	0.892861i	$-0.648694\pi$
$31$	1.95298	−	1.63874i	0.350766	−	0.294327i	0.801097	+	0.598534i	$0.204250\pi$
$32$	−0.173648	−	0.984808i	−0.0306970	−	0.174091i
$33$	3.88697	+	6.18638i	0.676634	+	1.07691i
$34$	3.68910	+	3.09552i	0.632675	+	0.530878i
$35$	0.995637	−	1.72449i	0.168293	−	0.291493i
$36$	−1.68985	−	2.47879i	−0.281641	−	0.413132i
$37$	1.96163	+	3.39764i	0.322490	+	0.558568i	0.981001	−	0.194002i	$-0.0621469\pi$
$37$	1.96163	+	3.39764i	0.322490	+	0.558568i	−0.658511	+	0.752571i	$0.728814\pi$
$38$	0.666617	−	3.78058i	0.108140	−	0.613290i
$39$	−5.03387	+	2.04830i	−0.806065	+	0.327990i
$40$	−1.87118	−	0.681056i	−0.295860	−	0.107684i
$41$	−2.70961	−	0.986218i	−0.423170	−	0.154021i	0.121652	−	0.992573i	$-0.461181\pi$
$41$	−2.70961	−	0.986218i	−0.423170	−	0.154021i	−0.544822	+	0.838551i	$0.683403\pi$
$42$	1.60432	−	0.652804i	0.247552	−	0.100730i
$43$	−0.641085	+	3.63578i	−0.0977646	+	0.554451i	0.896100	+	0.443851i	$0.146388\pi$
$43$	−0.641085	+	3.63578i	−0.0977646	+	0.554451i	−0.993865	+	0.110599i	$0.964723\pi$
$44$	2.10910	+	3.65307i	0.317959	+	0.550722i
$45$	−5.95714	+	0.446155i	−0.888037	+	0.0665089i
$46$	−4.77872	+	8.27699i	−0.704584	+	1.22038i
$47$	8.79161	+	7.37704i	1.28239	+	1.07605i	0.992910	+	0.118867i	$0.0379261\pi$
$47$	8.79161	+	7.37704i	1.28239	+	1.07605i	0.289478	+	0.957185i	$0.406518\pi$
$48$	−0.921473	−	1.46659i	−0.133003	−	0.211684i
$49$	0.173648	+	0.984808i	0.0248069	+	0.140687i
$50$	0.792726	−	0.665176i	0.112108	−	0.0940701i
$51$	7.93927	+	2.55796i	1.11172	+	0.358185i
$52$	−2.94847	+	1.07316i	−0.408879	+	0.148820i
$53$	−12.9026			−1.77231			−0.886155	−	0.463389i	$-0.846633\pi$
$53$	−12.9026			−1.77231			−0.886155	+	0.463389i	$0.846633\pi$
$54$	−4.32922	−	2.87364i	−0.589133	−	0.391053i
$55$	8.39960			1.13260
$56$	0.939693	−	0.342020i	0.125572	−	0.0457044i
$57$	−1.39850	−	6.50043i	−0.185236	−	0.861003i
$58$	5.23649	−	4.39393i	0.687584	−	0.576952i
$59$	−0.543969	−	3.08500i	−0.0708188	−	0.401633i	−0.999525	−	0.0308169i	$-0.990189\pi$
$59$	−0.543969	−	3.08500i	−0.0708188	−	0.401633i	0.928706	−	0.370816i	$-0.120922\pi$
$60$	−3.44658	+	0.128884i	−0.444951	+	0.0166388i
$61$	−3.30626	−	2.77428i	−0.423323	−	0.355210i	0.406102	−	0.913828i	$-0.366888\pi$
$61$	−3.30626	−	2.77428i	−0.423323	−	0.355210i	−0.829426	+	0.558617i	$0.811332\pi$
$62$	1.27472	−	2.20787i	0.161889	−	0.280400i
$63$	2.14770	−	2.09461i	0.270584	−	0.263896i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	−1.08496	+	6.15309i	−0.134572	+	0.763197i
$66$	5.76842	+	4.48387i	0.710043	+	0.551927i
$67$	13.4552	+	4.89729i	1.64381	+	0.598299i	0.987700	−	0.156364i	$-0.0499772\pi$
$67$	13.4552	+	4.89729i	1.64381	+	0.598299i	0.656113	+	0.754663i	$0.272199\pi$
$68$	4.52535	+	1.64709i	0.548779	+	0.199739i
$69$	−2.26336	+	16.3985i	−0.272477	+	1.97415i
$70$	0.345781	−	1.96102i	0.0413287	−	0.234387i
$71$	−3.02959	−	5.24740i	−0.359546	−	0.622752i	0.628339	−	0.777940i	$-0.283735\pi$
$71$	−3.02959	−	5.24740i	−0.359546	−	0.622752i	−0.987885	+	0.155188i	$0.950402\pi$
$72$	−2.43573	−	1.75134i	−0.287054	−	0.206398i
$73$	4.22982	−	7.32626i	0.495063	−	0.857474i	−0.504921	−	0.863166i	$-0.668478\pi$
$73$	4.22982	−	7.32626i	0.495063	−	0.857474i	0.999984	+	0.00569131i	$0.00181161\pi$
$74$	3.00539	+	2.52182i	0.349369	+	0.293156i
$75$	0.837558	−	1.58465i	0.0967129	−	0.182980i
$76$	−0.666617	−	3.78058i	−0.0764663	−	0.433662i
$77$	−3.23133	+	2.71141i	−0.368245	+	0.308994i
$78$	−4.02973	+	3.64646i	−0.456278	+	0.412880i
$79$	−13.3291	+	4.85141i	−1.49964	+	0.545826i	−0.955969	−	0.293469i	$-0.905190\pi$
$79$	−13.3291	+	4.85141i	−1.49964	+	0.545826i	−0.543676	+	0.839295i	$0.682968\pi$
$80$	−1.99127			−0.222631
$81$	−8.82139	−	1.78411i	−0.980155	−	0.198235i
$82$	−2.88351			−0.318430
$83$	−3.32011	+	1.20842i	−0.364429	+	0.132641i	−0.517743	−	0.855536i	$-0.673228\pi$
$83$	−3.32011	+	1.20842i	−0.364429	+	0.132641i	0.153314	+	0.988178i	$0.451005\pi$
$84$	1.28430	−	1.16214i	0.140128	−	0.126800i
$85$	7.34601	−	6.16403i	0.796786	−	0.668583i
$86$	0.641085	+	3.63578i	0.0691300	+	0.392056i
$87$	5.53263	−	10.4677i	0.593160	−	1.12225i
$88$	3.23133	+	2.71141i	0.344461	+	0.289037i
$89$	−5.49875	+	9.52411i	−0.582866	+	1.00955i	0.412271	+	0.911061i	$0.364736\pi$
$89$	−5.49875	+	9.52411i	−0.582866	+	1.00955i	−0.995138	+	0.0984930i	$0.968598\pi$
$90$	−5.44528	+	2.45671i	−0.573983	+	0.258960i
$91$	−1.56885	−	2.71732i	−0.164460	−	0.284853i
$92$	−1.65963	+	9.41225i	−0.173029	+	0.981295i
$93$	0.603748	−	4.37428i	0.0626057	−	0.453592i
$94$	10.7845	+	3.92524i	1.11234	+	0.404858i
$95$	−7.18329	−	2.61450i	−0.736990	−	0.268242i
$96$	−1.36751	−	1.06298i	−0.139570	−	0.108490i
$97$	0.904341	−	5.12877i	0.0918219	−	0.520748i	−0.903853	−	0.427843i	$-0.859274\pi$
$97$	0.904341	−	5.12877i	0.0918219	−	0.520748i	0.995675	−	0.0929049i	$-0.0296152\pi$
$98$	0.500000	+	0.866025i	0.0505076	+	0.0874818i
$99$	12.1815	+	3.42793i	1.22429	+	0.344520i
$100$	0.517415	−	0.896189i	0.0517415	−	0.0896189i
$101$	7.18558	+	6.02942i	0.714992	+	0.599949i	0.925995	−	0.377536i	$-0.123229\pi$
$101$	7.18558	+	6.02942i	0.714992	+	0.599949i	−0.211003	+	0.977485i	$0.567673\pi$
$102$	8.33535	−	0.311698i	0.825322	−	0.0308627i
$103$	0.416602	+	2.36267i	0.0410490	+	0.232801i	0.998429	−	0.0560307i	$-0.0178445\pi$
$103$	0.416602	+	2.36267i	0.0410490	+	0.232801i	−0.957380	+	0.288831i	$0.906733\pi$
$104$	−2.40361	+	2.01687i	−0.235694	+	0.197771i
$105$	−0.725418	−	3.37184i	−0.0707935	−	0.329058i
$106$	−12.1245	+	4.41295i	−1.17763	+	0.428624i
$107$	−2.57323			−0.248764			−0.124382	−	0.992234i	$-0.539695\pi$
$107$	−2.57323			−0.248764			−0.124382	+	0.992234i	$0.539695\pi$
$108$	−5.05098	−	1.21966i	−0.486031	−	0.117362i
$109$	−14.9444			−1.43141			−0.715707	−	0.698401i	$-0.753895\pi$
$109$	−14.9444			−1.43141			−0.715707	+	0.698401i	$0.753895\pi$
$110$	7.89304	−	2.87283i	0.752572	−	0.273914i
$111$	6.46786	+	2.08388i	0.613902	+	0.197793i
$112$	0.766044	−	0.642788i	0.0723844	−	0.0607377i
$113$	0.800361	+	4.53907i	0.0752916	+	0.427000i	0.999032	+	0.0439816i	$0.0140043\pi$
$113$	0.800361	+	4.53907i	0.0752916	+	0.427000i	−0.923741	+	0.383018i	$0.874885\pi$
$114$	−3.53744	−	5.63009i	−0.331312	−	0.527306i
$115$	14.5790	+	12.2332i	1.35950	+	1.14075i
$116$	3.41787	−	5.91993i	0.317342	−	0.549652i
$117$	−4.08457	+	8.48072i	−0.377619	+	0.784042i
$118$	−1.56630	−	2.71291i	−0.144189	−	0.249743i
$119$	−0.836251	+	4.74262i	−0.0766590	+	0.434755i
$120$	−3.19464	+	1.29991i	−0.291630	+	0.118665i
$121$	−6.38358	−	2.32343i	−0.580325	−	0.211221i
$122$	−4.05573	−	1.47616i	−0.367188	−	0.133646i
$123$	−4.62607	+	1.88236i	−0.417119	+	0.169727i
$124$	0.442705	−	2.51070i	0.0397560	−	0.225468i
$125$	−6.00850	−	10.4070i	−0.537416	−	0.930833i
$126$	1.30177	−	2.70285i	0.115971	−	0.240789i
$127$	−0.115845	+	0.200649i	−0.0102795	+	0.0178047i	−0.871119	−	0.491071i	$-0.836605\pi$
$127$	−0.115845	+	0.200649i	−0.0102795	+	0.0178047i	0.860840	+	0.508876i	$0.169939\pi$
$128$	−0.766044	−	0.642788i	−0.0677094	−	0.0568149i
$129$	3.40195	+	5.41445i	0.299525	+	0.476716i
$130$	1.08496	+	6.15309i	0.0951569	+	0.539662i
$131$	−1.90708	+	1.60023i	−0.166623	+	0.139813i	−0.722286	−	0.691594i	$-0.756909\pi$
$131$	−1.90708	+	1.60023i	−0.166623	+	0.139813i	0.555664	+	0.831407i	$0.312464\pi$
$132$	6.95412	+	2.24055i	0.605278	+	0.195015i
$133$	3.60738	−	1.31298i	0.312800	−	0.113850i
$134$	14.3187			1.23695
$135$	−7.13224	+	7.49605i	−0.613845	+	0.645157i
$136$	4.81578			0.412950
$137$	−12.4836	+	4.54367i	−1.06655	+	0.388192i	−0.814885	−	0.579622i	$-0.803200\pi$
$137$	−12.4836	+	4.54367i	−1.06655	+	0.388192i	−0.251664	+	0.967815i	$0.580978\pi$
$138$	3.48176	+	16.1837i	0.296387	+	1.37765i
$139$	10.6429	−	8.93049i	0.902723	−	0.757474i	−0.0679979	−	0.997685i	$-0.521661\pi$
$139$	10.6429	−	8.93049i	0.902723	−	0.757474i	0.970721	+	0.240211i	$0.0772167\pi$
$140$	−0.345781	−	1.96102i	−0.0292238	−	0.165737i
$141$	19.8642	−	0.742818i	1.67287	−	0.0625566i
$142$	−4.64160	−	3.89476i	−0.389514	−	0.326841i
$143$	6.61772	−	11.4622i	0.553402	−	0.958520i
$144$	−2.88784	−	0.812652i	−0.240653	−	0.0677210i
$145$	−6.80592	−	11.7882i	−0.565201	−	0.978957i
$146$	1.46900	−	8.33112i	0.121575	−	0.689488i
$147$	1.36751	+	1.06298i	0.112790	+	0.0876732i
$148$	3.68665	+	1.34183i	0.303041	+	0.110298i
$149$	−15.5460	−	5.65827i	−1.27358	−	0.463544i	−0.385273	−	0.922803i	$-0.625893\pi$
$149$	−15.5460	−	5.65827i	−1.27358	−	0.463544i	−0.888303	+	0.459259i	$0.848115\pi$
$150$	0.245065	−	1.77555i	0.0200094	−	0.144973i
$151$	−0.633504	+	3.59278i	−0.0515538	+	0.292376i	−0.999674	−	0.0255363i	$-0.991871\pi$
$151$	−0.633504	+	3.59278i	−0.0515538	+	0.292376i	0.948120	+	0.317912i	$0.102982\pi$
$152$	−1.91945	−	3.32458i	−0.155688	−	0.269659i
$153$	13.1691	−	5.94141i	1.06466	−	0.480334i
$154$	−2.10910	+	3.65307i	−0.169956	+	0.294373i
$155$	−3.88892	−	3.26319i	−0.312365	−	0.262106i
$156$	−2.53955	+	4.80480i	−0.203327	+	0.384692i
$157$	−3.49091	−	19.7979i	−0.278605	−	1.58005i	−0.727272	−	0.686349i	$-0.759212\pi$
$157$	−3.49091	−	19.7979i	−0.278605	−	1.58005i	0.448667	−	0.893699i	$-0.351899\pi$
$158$	−10.8660	+	9.11767i	−0.864453	+	0.725363i
$159$	−16.5708	+	14.9947i	−1.31415	+	1.18916i
$160$	−1.87118	+	0.681056i	−0.147930	+	0.0538422i
$161$	−9.55745			−0.753232
$162$	−8.89960	+	1.34058i	−0.699218	+	0.105326i
$163$	7.11284			0.557121			0.278560	−	0.960419i	$-0.410143\pi$
$163$	7.11284			0.557121			0.278560	+	0.960419i	$0.410143\pi$
$164$	−2.70961	+	0.986218i	−0.211585	+	0.0770107i
$165$	10.7876	−	9.76156i	0.839812	−	0.759936i
$166$	−2.70658	+	2.27109i	−0.210071	+	0.176270i
$167$	−1.10586	−	6.27164i	−0.0855740	−	0.485314i	−0.997231	−	0.0743628i	$-0.976308\pi$
$167$	−1.10586	−	6.27164i	−0.0855740	−	0.485314i	0.911657	−	0.410951i	$-0.134803\pi$
$168$	0.809368	−	1.53131i	0.0624441	−	0.118143i
$169$	−2.41677	−	2.02791i	−0.185905	−	0.155993i
$170$	4.79477	−	8.30478i	0.367742	−	0.636947i
$171$	−9.35054	−	6.72322i	−0.715053	−	0.514137i
$172$	1.84593	+	3.19725i	0.140751	+	0.243788i
$173$	2.48335	−	14.0838i	0.188805	−	1.07077i	−0.732162	−	0.681130i	$-0.761489\pi$
$173$	2.48335	−	14.0838i	0.188805	−	1.07077i	0.920968	−	0.389639i	$-0.127400\pi$
$174$	1.61882	−	11.7287i	0.122722	−	0.889148i
$175$	0.972422	+	0.353933i	0.0735082	+	0.0267548i
$176$	3.96382	+	1.44271i	0.298784	+	0.108748i
$177$	−4.28384	−	3.32989i	−0.321993	−	0.250290i
$178$	−1.90970	+	10.8304i	−0.143138	+	0.811775i
$179$	4.01855	+	6.96034i	0.300361	+	0.520240i	0.976218	−	0.216793i	$-0.0695596\pi$
$179$	4.01855	+	6.96034i	0.300361	+	0.520240i	−0.675857	+	0.737033i	$0.736226\pi$
$180$	−4.27665	+	4.17095i	−0.318763	+	0.310884i
$181$	3.12783	−	5.41756i	0.232490	−	0.402684i	−0.726050	−	0.687642i	$-0.758646\pi$
$181$	3.12783	−	5.41756i	0.232490	−	0.402684i	0.958540	+	0.284957i	$0.0919794\pi$
$182$	−2.40361	−	2.01687i	−0.178168	−	0.149501i
$183$	−7.47034	+	0.279351i	−0.552223	+	0.0206503i
$184$	1.65963	+	9.41225i	0.122350	+	0.693880i
$185$	5.98455	−	5.02163i	0.439993	−	0.369198i
$186$	−0.928755	−	4.31697i	−0.0680996	−	0.316536i
$187$	−19.0889	+	6.94778i	−1.39592	+	0.508072i
$188$	11.4766			0.837019
$189$	0.324034	−	5.18604i	0.0235700	−	0.377229i
$190$	−7.64429			−0.554575
$191$	15.5697	−	5.66692i	1.12659	−	0.410044i	0.289535	−	0.957167i	$-0.406499\pi$
$191$	15.5697	−	5.66692i	1.12659	−	0.410044i	0.837052	+	0.547123i	$0.184277\pi$
$192$	−1.64860	−	0.531161i	−0.118977	−	0.0383333i
$193$	1.28175	−	1.07552i	0.0922623	−	0.0774173i	−0.595490	−	0.803363i	$-0.703042\pi$
$193$	1.28175	−	1.07552i	0.0922623	−	0.0774173i	0.687752	+	0.725946i	$0.258598\pi$
$194$	−0.904341	−	5.12877i	−0.0649279	−	0.368224i
$195$	5.75738	+	9.16327i	0.412294	+	0.656195i
$196$	0.766044	+	0.642788i	0.0547175	+	0.0459134i
$197$	9.89335	−	17.1358i	0.704872	−	1.22087i	−0.261865	−	0.965104i	$-0.584338\pi$
$197$	9.89335	−	17.1358i	0.704872	−	1.22087i	0.966738	−	0.255770i	$-0.0823290\pi$
$198$	12.6193	−	0.945111i	0.896813	−	0.0671661i
$199$	3.24186	+	5.61507i	0.229809	+	0.398041i	0.957751	−	0.287597i	$-0.0928564\pi$
$199$	3.24186	+	5.61507i	0.229809	+	0.398041i	−0.727942	+	0.685639i	$0.759523\pi$
$200$	0.179696	−	1.01911i	0.0127065	−	0.0720619i
$201$	22.9718	−	9.34730i	1.62031	−	0.659308i
$202$	8.81442	+	3.20819i	0.620180	+	0.225727i
$203$	6.42350	+	2.33796i	0.450841	+	0.164093i
$204$	7.72606	−	3.14376i	0.540932	−	0.220107i
$205$	−0.997062	+	5.65462i	−0.0696378	+	0.394936i
$206$	1.19956	+	2.07770i	0.0835772	+	0.144760i
$207$	16.1506	+	23.6909i	1.12255	+	1.64663i
$208$	−1.56885	+	2.71732i	−0.108780	+	0.188413i
$209$	12.4048	+	10.4088i	0.858055	+	0.719994i
$210$	−1.83491	−	2.92038i	−0.126621	−	0.201526i
$211$	−2.59732	−	14.7301i	−0.178807	−	1.01406i	−0.933657	−	0.358168i	$-0.883402\pi$
$211$	−2.59732	−	14.7301i	−0.178807	−	1.01406i	0.754850	−	0.655897i	$-0.227710\pi$
$212$	−9.88397	+	8.29364i	−0.678834	+	0.569609i
$213$	−9.98913	−	3.21840i	−0.684444	−	0.220521i
$214$	−2.41805	+	0.880098i	−0.165294	+	0.0601622i
$215$	7.35151			0.501369
$216$	−5.16352	+	0.581435i	−0.351333	+	0.0395616i
$217$	2.54943			0.173067
$218$	−14.0431	+	5.11129i	−0.951122	+	0.346180i
$219$	−3.08183	−	14.3248i	−0.208251	−	0.967978i
$220$	6.43447	−	5.39916i	0.433812	−	0.364011i
$221$	−2.62390	−	14.8809i	−0.176503	−	1.00100i
$222$	6.79053	−	0.253930i	0.455751	−	0.0170427i
$223$	−0.443833	−	0.372420i	−0.0297213	−	0.0249391i	0.627806	−	0.778370i	$-0.283953\pi$
$223$	−0.443833	−	0.372420i	−0.0297213	−	0.0249391i	−0.657527	+	0.753431i	$0.728398\pi$
$224$	0.500000	−	0.866025i	0.0334077	−	0.0578638i
$225$	−0.765920	−	3.00853i	−0.0510613	−	0.200568i
$226$	2.30455	+	3.99159i	0.153296	+	0.265517i
$227$	−0.723065	+	4.10071i	−0.0479915	+	0.272173i	−0.999356	−	0.0358955i	$-0.988572\pi$
$227$	−0.723065	+	4.10071i	−0.0479915	+	0.272173i	0.951364	+	0.308069i	$0.0996828\pi$
$228$	−5.24971	−	4.08068i	−0.347671	−	0.270249i
$229$	−17.0564	−	6.20804i	−1.12712	−	0.410239i	−0.289875	−	0.957065i	$-0.593614\pi$
$229$	−17.0564	−	6.20804i	−1.12712	−	0.410239i	−0.837246	+	0.546826i	$0.815836\pi$
$230$	17.8838	+	6.50915i	1.17922	+	0.429201i
$231$	−0.998940	+	7.23753i	−0.0657254	+	0.476195i
$232$	1.18701	−	6.73190i	0.0779313	−	0.441971i
$233$	−3.42350	−	5.92968i	−0.224281	−	0.388466i	0.731822	−	0.681495i	$-0.238670\pi$
$233$	−3.42350	−	5.92968i	−0.224281	−	0.388466i	−0.956104	+	0.293029i	$0.905337\pi$
$234$	−0.937664	+	9.36627i	−0.0612970	+	0.612292i
$235$	11.4266	−	19.7914i	0.745386	−	1.29105i
$236$	−2.39971	−	2.01359i	−0.156208	−	0.131074i
$237$	−11.4805	+	21.7210i	−0.745741	+	1.41093i
$238$	0.836251	+	4.74262i	0.0542061	+	0.307418i
$239$	16.7002	−	14.0132i	1.08025	−	0.906436i	0.0843066	−	0.996440i	$-0.473132\pi$
$239$	16.7002	−	14.0132i	1.08025	−	0.906436i	0.995941	+	0.0900041i	$0.0286880\pi$
$240$	−2.55739	+	2.31415i	−0.165079	+	0.149378i
$241$	−18.6479	+	6.78727i	−1.20121	+	0.437206i	−0.863648	−	0.504096i	$-0.831826\pi$
$241$	−18.6479	+	6.78727i	−1.20121	+	0.437206i	−0.337566	+	0.941302i	$0.609604\pi$
$242$	−6.79326			−0.436688
$243$	−13.4027	+	7.96041i	−0.859783	+	0.510660i
$244$	−4.31601			−0.276305
$245$	1.87118	−	0.681056i	0.119546	−	0.0435110i
$246$	−3.70328	+	3.35105i	−0.236113	+	0.213655i
$247$	−9.22723	+	7.74256i	−0.587115	+	0.492648i
$248$	−0.442705	−	2.51070i	−0.0281118	−	0.159430i
$249$	−2.85964	+	5.41041i	−0.181223	+	0.342871i
$250$	−9.20555	−	7.72438i	−0.582210	−	0.488532i
$251$	9.21668	−	15.9638i	0.581752	−	1.00762i	−0.413520	−	0.910495i	$-0.635701\pi$
$251$	9.21668	−	15.9638i	0.581752	−	1.00762i	0.995272	−	0.0971284i	$-0.0309658\pi$
$252$	0.298838	−	2.98508i	0.0188250	−	0.188042i
$253$	−20.1576	−	34.9141i	−1.26730	−	2.19503i
$254$	−0.0402324	+	0.228169i	−0.00252441	+	0.0143166i
$255$	2.27096	−	16.4536i	0.142213	−	1.03036i
$256$	−0.939693	−	0.342020i	−0.0587308	−	0.0213763i
$257$	12.3404	+	4.49155i	0.769775	+	0.280175i	0.696902	−	0.717166i	$-0.254561\pi$
$257$	12.3404	+	4.49155i	0.769775	+	0.280175i	0.0728728	+	0.997341i	$0.476783\pi$
$258$	5.04864	+	3.92438i	0.314315	+	0.244321i
$259$	−0.681266	+	3.86365i	−0.0423318	+	0.240076i
$260$	3.12401	+	5.41094i	0.193743	+	0.335572i
$261$	−5.05942	−	19.8733i	−0.313170	−	1.23013i
$262$	−1.24476	+	2.15599i	−0.0769015	+	0.133197i
$263$	−2.32786	−	1.95331i	−0.143542	−	0.120446i	0.568189	−	0.822898i	$-0.307644\pi$
$263$	−2.32786	−	1.95331i	−0.143542	−	0.120446i	−0.711731	+	0.702452i	$0.752089\pi$
$264$	7.30104	−	0.273021i	0.449348	−	0.0168033i
$265$	4.46148	+	25.3023i	0.274066	+	1.55431i
$266$	2.94077	−	2.46760i	0.180310	−	0.151298i
$267$	4.00637	+	18.6221i	0.245186	+	1.13966i
$268$	13.4552	−	4.89729i	0.821906	−	0.299149i
$269$	−8.06042			−0.491453			−0.245726	−	0.969339i	$-0.579026\pi$
$269$	−8.06042			−0.491453			−0.245726	+	0.969339i	$0.579026\pi$
$270$	−4.13831	+	9.48335i	−0.251849	+	0.577138i
$271$	−27.8884			−1.69410			−0.847049	−	0.531514i	$-0.821623\pi$
$271$	−27.8884			−1.69410			−0.847049	+	0.531514i	$0.821623\pi$
$272$	4.52535	−	1.64709i	0.274390	−	0.0998697i
$273$	−5.17279	−	1.66662i	−0.313072	−	0.100869i
$274$	−10.1768	+	8.53931i	−0.614800	+	0.515879i
$275$	0.757996	+	4.29881i	0.0457089	+	0.259228i
$276$	8.80694	+	14.0169i	0.530115	+	0.843716i
$277$	16.9720	+	14.2412i	1.01975	+	0.855670i	0.989596	−	0.143876i	$-0.0459565\pi$
$277$	16.9720	+	14.2412i	1.01975	+	0.855670i	0.0301517	+	0.999545i	$0.490401\pi$
$278$	6.94669	−	12.0320i	0.416635	−	0.721632i
$279$	−4.30816	−	6.31952i	−0.257923	−	0.378340i
$280$	−0.995637	−	1.72449i	−0.0595007	−	0.103058i
$281$	−4.29854	+	24.3782i	−0.256429	+	1.45428i	0.535948	+	0.844251i	$0.319954\pi$
$281$	−4.29854	+	24.3782i	−0.256429	+	1.45428i	−0.792378	+	0.610031i	$0.791157\pi$
$282$	18.4122	−	7.49199i	1.09643	−	0.446141i
$283$	2.32117	+	0.844837i	0.137979	+	0.0502203i	0.410087	−	0.912047i	$-0.365498\pi$
$283$	2.32117	+	0.844837i	0.137979	+	0.0502203i	−0.272108	+	0.962267i	$0.587721\pi$
$284$	−5.69376	−	2.07236i	−0.337863	−	0.122972i
$285$	−12.2639	+	4.99022i	−0.726451	+	0.295595i
$286$	2.29831	−	13.0344i	0.135902	−	0.770739i
$287$	−1.44175	−	2.49719i	−0.0851040	−	0.147405i
$288$	−2.99162	+	0.224055i	−0.176283	+	0.0132026i
$289$	−3.09586	+	5.36219i	−0.182109	+	0.315423i
$290$	−10.4273	−	8.74952i	−0.612311	−	0.513790i
$291$	−4.79893	−	7.63784i	−0.281318	−	0.447738i
$292$	−1.46900	−	8.33112i	−0.0859668	−	0.487542i
$293$	−2.84696	+	2.38889i	−0.166321	+	0.139560i	−0.722149	−	0.691737i	$-0.756846\pi$
$293$	−2.84696	+	2.38889i	−0.166321	+	0.139560i	0.555828	+	0.831297i	$0.312401\pi$
$294$	1.64860	+	0.531161i	0.0961480	+	0.0309780i
$295$	−5.86166	+	2.13347i	−0.341279	+	0.124215i
$296$	3.92326			0.228035
$297$	19.6284	−	9.75417i	1.13896	−	0.565994i
$298$	−16.5437			−0.958350
$299$	28.1798	−	10.2566i	1.62968	−	0.593156i
$300$	−0.376987	−	1.75228i	−0.0217654	−	0.101168i
$301$	−2.82813	+	2.37308i	−0.163011	+	0.136782i
$302$	0.633504	+	3.59278i	0.0364540	+	0.206741i
$303$	16.2355	−	0.607122i	0.932704	−	0.0348782i
$304$	−2.94077	−	2.46760i	−0.168664	−	0.141526i
$305$	−4.29718	+	7.44294i	−0.246056	+	0.426181i
$306$	10.3428	−	10.0872i	0.591260	−	0.576647i
$307$	6.65403	+	11.5251i	0.379765	+	0.657773i	0.991028	−	0.133655i	$-0.0426714\pi$
$307$	6.65403	+	11.5251i	0.379765	+	0.657773i	−0.611263	+	0.791428i	$0.709338\pi$
$308$	−0.732484	+	4.15412i	−0.0417371	+	0.236703i
$309$	3.28080	+	2.55022i	0.186638	+	0.145077i
$310$	−4.77046	−	1.73631i	−0.270944	−	0.0986156i
$311$	−22.5284	−	8.19968i	−1.27747	−	0.464961i	−0.387875	−	0.921712i	$-0.626791\pi$
$311$	−22.5284	−	8.19968i	−1.27747	−	0.464961i	−0.889595	+	0.456751i	$0.849013\pi$
$312$	−0.743058	+	5.38361i	−0.0420674	+	0.304787i
$313$	3.36727	−	19.0967i	0.190329	−	1.07941i	−0.728586	−	0.684954i	$-0.759822\pi$
$313$	3.36727	−	19.0967i	0.190329	−	1.07941i	0.918915	−	0.394455i	$-0.129067\pi$
$314$	−10.0517	−	17.4100i	−0.567249	−	0.982504i
$315$	−4.85021	−	3.48740i	−0.273279	−	0.196493i
$316$	−7.09228	+	12.2842i	−0.398972	+	0.691040i
$317$	16.9321	+	14.2077i	0.951003	+	0.797986i	0.979466	−	0.201608i	$-0.0646168\pi$
$317$	16.9321	+	14.2077i	0.951003	+	0.797986i	−0.0284630	+	0.999595i	$0.509061\pi$
$318$	−10.4430	+	19.7580i	−0.585612	+	1.10797i
$319$	5.00707	+	28.3965i	0.280342	+	1.58990i
$320$	−1.52540	+	1.27997i	−0.0852727	+	0.0715523i
$321$	−3.30480	+	2.99047i	−0.184456	+	0.166912i
$322$	−8.98106	+	3.26884i	−0.500495	+	0.182165i
$323$	18.4873			1.02866
$324$	−7.90438	+	4.30357i	−0.439132	+	0.239087i
$325$	−3.24698			−0.180110
$326$	6.68388	−	2.43273i	0.370186	−	0.134737i
$327$	−19.1931	+	17.3676i	−1.06138	+	0.960428i
$328$	−2.20889	+	1.85348i	−0.121966	+	0.102341i
$329$	1.99290	+	11.3023i	0.109872	+	0.623115i
$330$	6.79837	−	12.8624i	0.374238	−	0.708054i
$331$	23.0051	+	19.3035i	1.26447	+	1.06102i	0.995191	+	0.0979570i	$0.0312308\pi$
$331$	23.0051	+	19.3035i	1.26447	+	1.06102i	0.269282	+	0.963061i	$0.413214\pi$
$332$	−1.76659	+	3.05983i	−0.0969543	+	0.167930i
$333$	10.7284	−	4.84027i	0.587914	−	0.265245i
$334$	−3.18420	−	5.51519i	−0.174231	−	0.301778i
$335$	4.95114	−	28.0793i	0.270510	−	1.53414i
$336$	0.236816	−	1.71578i	0.0129194	−	0.0936037i
$337$	9.17740	+	3.34030i	0.499925	+	0.181958i	0.579660	−	0.814858i	$-0.303185\pi$
$337$	9.17740	+	3.34030i	0.499925	+	0.181958i	−0.0797353	+	0.996816i	$0.525407\pi$
$338$	−2.96460	−	1.07903i	−0.161253	−	0.0586913i
$339$	6.30296	+	4.89938i	0.342330	+	0.266098i
$340$	1.66520	−	9.44385i	0.0903084	−	0.512164i
$341$	5.37702	+	9.31327i	0.291182	+	0.504342i
$342$	−11.0861	−	3.11969i	−0.599468	−	0.168693i
$343$	−0.500000	+	0.866025i	−0.0269975	+	0.0467610i
$344$	2.82813	+	2.37308i	0.152483	+	0.127948i
$345$	32.9405	−	1.23180i	1.77346	−	0.0663180i
$346$	−2.48335	−	14.0838i	−0.133506	−	0.757148i
$347$	8.49829	−	7.13091i	0.456212	−	0.382807i	−0.385523	−	0.922698i	$-0.625979\pi$
$347$	8.49829	−	7.13091i	0.456212	−	0.382807i	0.841735	+	0.539891i	$0.181535\pi$
$348$	−2.49025	−	11.5750i	−0.133492	−	0.620486i
$349$	−2.83368	+	1.03138i	−0.151684	+	0.0552083i	−0.416746	−	0.909023i	$-0.636830\pi$
$349$	−2.83368	+	1.03138i	−0.151684	+	0.0552083i	0.265063	+	0.964231i	$0.414607\pi$
$350$	1.03483			0.0553140
$351$	4.61002	+	15.6386i	0.246065	+	0.834728i
$352$	4.21821			0.224831
$353$	−1.42784	+	0.519691i	−0.0759963	+	0.0276604i	−0.379739	−	0.925094i	$-0.623986\pi$
$353$	−1.42784	+	0.519691i	−0.0759963	+	0.0276604i	0.303742	+	0.952754i	$0.401764\pi$
$354$	−5.16438	−	1.66391i	−0.274484	−	0.0884360i
$355$	−9.24269	+	7.75554i	−0.490551	+	0.411621i
$356$	1.90970	+	10.8304i	0.101214	+	0.574011i
$357$	4.43761	+	7.06277i	0.234863	+	0.373802i
$358$	6.15678	+	5.16615i	0.325396	+	0.273040i
$359$	−16.3279	+	28.2808i	−0.861756	+	1.49261i	0.00847612	+	0.999964i	$0.497302\pi$
$359$	−16.3279	+	28.2808i	−0.861756	+	1.49261i	−0.870232	+	0.492642i	$0.836031\pi$
$360$	−2.59219	+	5.38211i	−0.136620	+	0.283662i
$361$	2.13143	+	3.69175i	0.112181	+	0.194303i
$362$	1.08628	−	6.16063i	0.0570938	−	0.323795i
$363$	−10.8986	+	4.43467i	−0.572027	+	0.232760i
$364$	−2.94847	−	1.07316i	−0.154542	−	0.0562486i
$365$	−15.8296	−	5.76149i	−0.828557	−	0.301570i
$366$	−6.92428	+	2.81751i	−0.361938	+	0.147274i
$367$	−3.74664	+	21.2483i	−0.195573	+	1.10915i	0.716027	+	0.698072i	$0.245959\pi$
$367$	−3.74664	+	21.2483i	−0.195573	+	1.10915i	−0.911600	+	0.411078i	$0.865152\pi$
$368$	4.77872	+	8.27699i	0.249108	+	0.431468i
$369$	−3.75367	+	7.79368i	−0.195408	+	0.405723i
$370$	3.90614	−	6.76563i	0.203070	−	0.351728i
$371$	−9.88397	−	8.29364i	−0.513150	−	0.430584i
$372$	−2.34924	−	3.73897i	−0.121802	−	0.193857i
$373$	0.115680	+	0.656051i	0.00598966	+	0.0339690i	0.987656	−	0.156638i	$-0.0500655\pi$
$373$	0.115680	+	0.656051i	0.00598966	+	0.0339690i	−0.981666	+	0.190607i	$0.938954\pi$
$374$	−15.5614	+	13.0576i	−0.804660	+	0.675190i
$375$	−19.8112	−	6.38297i	−1.02304	−	0.329615i
$376$	10.7845	−	3.92524i	0.556168	−	0.202429i
$377$	−21.4485			−1.10465
$378$	−1.46924	−	4.98411i	−0.0755694	−	0.256355i
$379$	−15.2472			−0.783194			−0.391597	−	0.920137i	$-0.628077\pi$
$379$	−15.2472			−0.783194			−0.391597	+	0.920137i	$0.628077\pi$
$380$	−7.18329	+	2.61450i	−0.368495	+	0.134121i
$381$	0.0844041	+	0.392321i	0.00432415	+	0.0200992i
$382$	12.6926	−	10.6503i	0.649408	−	0.544918i
$383$	4.37705	+	24.8235i	0.223657	+	1.26842i	0.865236	+	0.501365i	$0.167169\pi$
$383$	4.37705	+	24.8235i	0.223657	+	1.26842i	−0.641579	+	0.767057i	$0.721720\pi$
$384$	−1.73084	+	0.0647244i	−0.0883266	+	0.00330295i
$385$	6.43447	+	5.39916i	0.327931	+	0.275167i
$386$	0.836602	−	1.44904i	0.0425819	−	0.0737541i
$387$	10.6615	+	3.00020i	0.541954	+	0.152509i
$388$	−2.60395	−	4.51017i	−0.132195	−	0.228969i
$389$	0.349868	−	1.98420i	0.0177390	−	0.100603i	−0.974653	−	0.223723i	$-0.928179\pi$
$389$	0.349868	−	1.98420i	0.0177390	−	0.100603i	0.992392	+	0.123120i	$0.0392900\pi$
$390$	8.54419	+	6.64152i	0.432652	+	0.336306i
$391$	−43.2508	−	15.7420i	−2.18729	−	0.796108i
$392$	0.939693	+	0.342020i	0.0474616	+	0.0172746i
$393$	−0.589559	+	4.27148i	−0.0297393	+	0.215468i
$394$	3.43593	−	19.4861i	0.173099	−	0.981696i
$395$	14.1227	+	24.4612i	0.710589	+	1.23078i
$396$	11.5350	−	5.20416i	0.579655	−	0.261519i
$397$	−4.45763	+	7.72084i	−0.223722	+	0.387498i	−0.955935	−	0.293578i	$-0.905154\pi$
$397$	−4.45763	+	7.72084i	−0.223722	+	0.387498i	0.732213	+	0.681075i	$0.238487\pi$
$398$	4.96682	+	4.16765i	0.248964	+	0.208906i
$399$	3.10708	−	5.87856i	0.155548	−	0.294296i
$400$	−0.179696	−	1.01911i	−0.00898482	−	0.0509554i
$401$	17.1219	−	14.3670i	0.855029	−	0.717454i	−0.105862	−	0.994381i	$-0.533760\pi$
$401$	17.1219	−	14.3670i	0.855029	−	0.717454i	0.960891	+	0.276926i	$0.0893158\pi$
$402$	18.3895	−	16.6404i	0.917184	−	0.829949i
$403$	−7.51693	+	2.73594i	−0.374445	+	0.136287i
$404$	9.38011			0.466678
$405$	−0.448412	+	17.9159i	−0.0222818	+	0.890246i
$406$	6.83575			0.339252
$407$	−15.5511	+	5.66013i	−0.770838	+	0.280562i
$408$	6.18489	−	5.59663i	0.306198	−	0.277075i
$409$	−27.7545	+	23.2888i	−1.37237	+	1.15156i	−0.400432	+	0.916327i	$0.631140\pi$
$409$	−27.7545	+	23.2888i	−1.37237	+	1.15156i	−0.971940	+	0.235230i	$0.924416\pi$
$410$	0.997062	+	5.65462i	0.0492414	+	0.279262i
$411$	−10.7523	+	20.3432i	−0.530372	+	1.00346i
$412$	1.83783	+	1.54212i	0.0905433	+	0.0759749i
$413$	1.56630	−	2.71291i	0.0770724	−	0.133493i
$414$	23.2794	+	16.7384i	1.14412	+	0.822645i
$415$	3.51777	+	6.09295i	0.172680	+	0.299091i
$416$	−0.544855	+	3.09003i	−0.0267137	+	0.151501i
$417$	3.29018	−	23.8380i	0.161121	−	1.16735i
$418$	15.2167	+	5.53842i	0.744272	+	0.270893i
$419$	8.99414	+	3.27360i	0.439392	+	0.159926i	0.552238	−	0.833687i	$-0.313774\pi$
$419$	8.99414	+	3.27360i	0.439392	+	0.159926i	−0.112845	+	0.993613i	$0.535996\pi$
$420$	−2.72308	−	2.11669i	−0.132873	−	0.103284i
$421$	−0.604337	+	3.42737i	−0.0294536	+	0.167040i	−0.995987	−	0.0895027i	$-0.971472\pi$
$421$	−0.604337	+	3.42737i	−0.0294536	+	0.167040i	0.966533	+	0.256542i	$0.0825833\pi$
$422$	−7.47869	−	12.9535i	−0.364057	−	0.630565i
$423$	24.6483	−	24.0391i	1.19844	−	1.16882i
$424$	−6.45130	+	11.1740i	−0.313303	+	0.542657i
$425$	3.81759	+	3.20334i	0.185180	+	0.155385i
$426$	−10.4875	+	0.392176i	−0.508120	+	0.0190010i
$427$	−0.749468	−	4.25044i	−0.0362693	−	0.205693i
$428$	−1.97121	+	1.65404i	−0.0952821	+	0.0799512i
$429$	−4.82165	−	22.4117i	−0.232792	−	1.08205i
$430$	6.90816	−	2.51436i	0.333141	−	0.121253i
$431$	−10.6786			−0.514369			−0.257185	−	0.966362i	$-0.582795\pi$
$431$	−10.6786			−0.514369			−0.257185	+	0.966362i	$0.582795\pi$
$432$	−4.65326	+	2.31240i	−0.223880	+	0.111255i
$433$	20.8128			1.00020			0.500100	−	0.865967i	$-0.333296\pi$
$433$	20.8128			1.00020			0.500100	+	0.865967i	$0.333296\pi$
$434$	2.39568	−	0.871958i	0.114997	−	0.0418553i
$435$	−22.4404	−	7.23008i	−1.07594	−	0.346656i
$436$	−11.4481	+	9.60608i	−0.548263	+	0.460048i
$437$	6.37116	+	36.1327i	0.304774	+	1.72846i
$438$	−7.79534	−	12.4068i	−0.372476	−	0.592821i
$439$	8.38159	+	7.03299i	0.400032	+	0.335666i	0.820506	−	0.571638i	$-0.193692\pi$
$439$	8.38159	+	7.03299i	0.400032	+	0.335666i	−0.420474	+	0.907304i	$0.638136\pi$
$440$	4.19980	−	7.27427i	0.200218	−	0.346787i
$441$	2.99162	−	0.224055i	0.142458	−	0.0106693i
$442$	−7.55522	−	13.0860i	−0.359365	−	0.622439i
$443$	−2.82949	+	16.0469i	−0.134433	+	0.762409i	0.840819	+	0.541316i	$0.182074\pi$
$443$	−2.82949	+	16.0469i	−0.134433	+	0.762409i	−0.975253	+	0.221093i	$0.929037\pi$
$444$	6.29416	−	2.56111i	0.298708	−	0.121545i
$445$	20.5784	+	7.48991i	0.975508	+	0.355056i
$446$	−0.544442	−	0.198161i	−0.0257801	−	0.00938318i
$447$	−26.5414	+	10.7998i	−1.25536	+	0.510812i
$448$	0.173648	−	0.984808i	0.00820411	−	0.0465278i
$449$	8.37532	+	14.5065i	0.395256	+	0.684603i	0.993134	−	0.116984i	$-0.0373226\pi$
$449$	8.37532	+	14.5065i	0.395256	+	0.684603i	−0.597878	+	0.801587i	$0.703989\pi$
$450$	−1.74871	−	2.56513i	−0.0824348	−	0.120921i
$451$	6.08161	−	10.5337i	0.286372	−	0.496011i
$452$	3.53077	+	2.96267i	0.166073	+	0.139352i
$453$	3.36172	+	5.35042i	0.157947	+	0.251385i
$454$	0.723065	+	4.10071i	0.0339351	+	0.192456i
$455$	−4.78625	+	4.01614i	−0.224383	+	0.188280i
$456$	−6.32879	−	2.03907i	−0.296373	−	0.0954884i
$457$	−2.65348	+	0.965787i	−0.124125	+	0.0451776i	−0.403336	−	0.915052i	$-0.632149\pi$
$457$	−2.65348	+	0.965787i	−0.124125	+	0.0451776i	0.279211	+	0.960230i	$0.409927\pi$
$458$	−18.1511			−0.848144
$459$	10.0083	−	22.9349i	0.467145	−	1.07051i
$460$	19.0315			0.887348
$461$	−26.7219	+	9.72597i	−1.24456	+	0.452984i	−0.878561	−	0.477631i	$-0.841496\pi$
$461$	−26.7219	+	9.72597i	−1.24456	+	0.452984i	−0.366001	+	0.930614i	$0.619273\pi$
$462$	1.53669	+	7.14272i	0.0714931	+	0.332309i
$463$	22.9982	−	19.2978i	1.06882	−	0.896846i	0.0738742	−	0.997268i	$-0.476464\pi$
$463$	22.9982	−	19.2978i	1.06882	−	0.896846i	0.994945	+	0.100422i	$0.0320192\pi$
$464$	−1.18701	−	6.73190i	−0.0551058	−	0.312520i
$465$	−8.78682	+	0.328581i	−0.407479	+	0.0152376i
$466$	−5.24511	−	4.40117i	−0.242975	−	0.203880i
$467$	19.3297	−	33.4801i	0.894473	−	1.54927i	0.0600181	−	0.998197i	$-0.480884\pi$
$467$	19.3297	−	33.4801i	0.894473	−	1.54927i	0.834455	−	0.551076i	$-0.185783\pi$
$468$	2.32234	+	9.12211i	0.107350	+	0.421670i
$469$	7.15935	+	12.4004i	0.330588	+	0.572596i
$470$	3.96840	−	22.5059i	0.183049	−	1.03812i
$471$	−27.4915	−	21.3695i	−1.26674	−	0.984655i
$472$	−2.94367	−	1.07141i	−0.135494	−	0.0493156i
$473$	−14.6339	−	5.32629i	−0.672866	−	0.244903i
$474$	−3.35914	+	24.3377i	−0.154290	+	1.11787i
$475$	0.689836	−	3.91225i	0.0316518	−	0.179507i
$476$	2.40789	+	4.17059i	0.110365	+	0.191159i
$477$	−3.85579	+	38.5153i	−0.176545	+	1.76349i
$478$	10.9003	−	18.8799i	0.498568	−	0.863545i
$479$	−31.1099	−	26.1043i	−1.42145	−	1.19274i	−0.950558	−	0.310547i	$-0.899488\pi$
$479$	−31.1099	−	26.1043i	−1.42145	−	1.19274i	−0.470892	−	0.882191i	$-0.656068\pi$
$480$	−1.61167	+	3.04927i	−0.0735624	+	0.139179i
$481$	−2.13761	−	12.1230i	−0.0974664	−	0.552760i
$482$	−15.2019	+	12.7559i	−0.692426	+	0.581015i
$483$	−12.2746	+	11.1071i	−0.558514	+	0.505392i
$484$	−6.38358	+	2.32343i	−0.290163	+	0.105611i
$485$	−10.3703			−0.470893
$486$	−9.87178	+	12.0643i	−0.447793	+	0.547249i
$487$	14.9795			0.678786			0.339393	−	0.940645i	$-0.389778\pi$
$487$	14.9795			0.678786			0.339393	+	0.940645i	$0.389778\pi$
$488$	−4.05573	+	1.47616i	−0.183594	+	0.0668228i
$489$	9.13500	−	8.26615i	0.413099	−	0.373808i
$490$	1.52540	−	1.27997i	0.0689107	−	0.0578230i
$491$	−5.56364	−	31.5530i	−0.251083	−	1.42396i	−0.805929	−	0.592012i	$-0.798334\pi$
$491$	−5.56364	−	31.5530i	−0.251083	−	1.42396i	0.554846	−	0.831953i	$-0.312777\pi$
$492$	−2.33382	+	4.41556i	−0.105217	+	0.199069i
$493$	25.2178	+	21.1602i	1.13575	+	0.953008i
$494$	−6.02265	+	10.4315i	−0.270972	+	0.469337i
$495$	2.51012	−	25.0735i	0.112822	−	1.12697i
$496$	−1.27472	−	2.20787i	−0.0572365	−	0.0991365i
$497$	1.05216	−	5.96712i	0.0471960	−	0.267662i
$498$	−0.836715	+	6.06218i	−0.0374941	+	0.271653i
$499$	25.7673	+	9.37852i	1.15350	+	0.419840i	0.846772	−	0.531956i	$-0.178543\pi$
$499$	25.7673	+	9.37852i	1.15350	+	0.419840i	0.306730	+	0.951797i	$0.400765\pi$
$500$	−11.2923	−	4.11005i	−0.505006	−	0.183807i
$501$	−8.70881	−	6.76948i	−0.389081	−	0.302438i
$502$	3.20092	−	18.1533i	0.142864	−	0.810222i
$503$	4.22896	+	7.32477i	0.188560	+	0.326595i	0.944770	−	0.327733i	$-0.106285\pi$
$503$	4.22896	+	7.32477i	0.188560	+	0.326595i	−0.756210	+	0.654328i	$0.772951\pi$
$504$	−0.740141	−	2.90727i	−0.0329685	−	0.129500i
$505$	9.33918	−	16.1759i	0.415588	−	0.719820i
$506$	−30.8833	−	25.9142i	−1.37293	−	1.15203i
$507$	−5.46057	+	0.204197i	−0.242512	+	0.00906869i
$508$	0.0402324	+	0.228169i	0.00178503	+	0.0101234i
$509$	24.2929	−	20.3842i	1.07676	−	0.903512i	0.0811158	−	0.996705i	$-0.474152\pi$
$509$	24.2929	−	20.3842i	1.07676	−	0.903512i	0.995648	+	0.0931925i	$0.0297072\pi$
$510$	−3.49345	−	16.2380i	−0.154693	−	0.719031i
$511$	7.94946	−	2.89337i	0.351664	−	0.127995i
$512$	−1.00000			−0.0441942
$513$	−19.8222	+	2.23207i	−0.875172	+	0.0985482i
$514$	13.1324			0.579246
$515$	4.48919	−	1.63393i	0.197817	−	0.0719996i
$516$	6.08639	+	1.96098i	0.267938	+	0.0863271i
$517$	−37.0848	+	31.1179i	−1.63099	+	1.36856i
$518$	0.681266	+	3.86365i	0.0299331	+	0.169759i
$519$	−13.1780	−	20.9738i	−0.578451	−	0.920646i
$520$	4.78625	+	4.01614i	0.209891	+	0.176120i
$521$	2.95473	−	5.11774i	0.129449	−	0.224212i	−0.794014	−	0.607899i	$-0.792012\pi$
$521$	2.95473	−	5.11774i	0.129449	−	0.224212i	0.923463	+	0.383687i	$0.125346\pi$
$522$	−11.5514	−	16.9444i	−0.505590	−	0.741636i
$523$	20.3093	+	35.1768i	0.888065	+	1.53817i	0.842160	+	0.539228i	$0.181284\pi$
$523$	20.3093	+	35.1768i	0.888065	+	1.53817i	0.0459053	+	0.998946i	$0.485383\pi$
$524$	−0.432300	+	2.45170i	−0.0188851	+	0.107103i
$525$	1.66020	−	0.675541i	0.0724571	−	0.0294830i
$526$	−2.85555	−	1.03933i	−0.124508	−	0.0453172i
$527$	11.5371	+	4.19916i	0.502563	+	0.182918i
$528$	6.76736	−	2.75366i	0.294512	−	0.119838i
$529$	11.8680	−	67.3065i	0.515998	−	2.92637i
$530$	12.8463	+	22.2505i	0.558008	+	0.966498i
$531$	−9.37153	+	0.701874i	−0.406690	+	0.0304587i
$532$	1.91945	−	3.32458i	0.0832186	−	0.144139i
$533$	6.93084	+	5.81567i	0.300208	+	0.251904i
$534$	10.1339	+	16.1288i	0.438537	+	0.697963i
$535$	0.889775	+	5.04617i	0.0384683	+	0.218165i
$536$	10.9688	−	9.20389i	0.473779	−	0.397547i
$537$	13.2499	+	4.26900i	0.571777	+	0.184221i
$538$	−7.57432	+	2.75683i	−0.326552	+	0.118855i
$539$	−4.21821			−0.181691
$540$	−0.645241	+	10.3268i	−0.0277667	+	0.444396i
$541$	23.5328			1.01175			0.505876	−	0.862606i	$-0.331169\pi$
$541$	23.5328			1.01175			0.505876	+	0.862606i	$0.331169\pi$
$542$	−26.2065	+	9.53839i	−1.12567	+	0.409709i
$543$	−2.27893	−	10.5928i	−0.0977982	−	0.454579i
$544$	3.68910	−	3.09552i	0.158169	−	0.132719i
$545$	5.16749	+	29.3063i	0.221351	+	1.25534i
$546$	−5.43085	+	0.203085i	−0.232419	+	0.00869126i
$547$	28.2501	+	23.7046i	1.20789	+	1.01354i	0.999369	+	0.0355184i	$0.0113082\pi$
$547$	28.2501	+	23.7046i	1.20789	+	1.01354i	0.208517	+	0.978019i	$0.433136\pi$
$548$	−6.64241	+	11.5050i	−0.283750	+	0.491469i
$549$	−9.26948	+	9.04038i	−0.395612	+	0.385834i
$550$	2.18256	+	3.78031i	0.0930648	+	0.161193i
$551$	4.55683	−	25.8431i	0.194127	−	1.10095i
$552$	13.0699	+	10.1594i	0.556290	+	0.432412i
$553$	−13.3291	−	4.85141i	−0.566813	−	0.206303i
$554$	20.8192	+	7.57758i	0.884524	+	0.321940i
$555$	1.85007	−	13.4042i	0.0785313	−	0.568976i
$556$	2.41256	−	13.6823i	0.102315	−	0.580259i
$557$	−0.403316	−	0.698565i	−0.0170891	−	0.0295991i	0.857354	−	0.514727i	$-0.172107\pi$
$557$	−0.403316	−	0.698565i	−0.0170891	−	0.0295991i	−0.874443	+	0.485127i	$0.838773\pi$
$558$	−6.20975	−	4.46493i	−0.262879	−	0.189015i
$559$	5.79197	−	10.0320i	0.244974	−	0.424308i
$560$	−1.52540	−	1.27997i	−0.0644601	−	0.0540884i
$561$	−16.4414	+	31.1070i	−0.694159	+	1.31334i
$562$	4.29854	+	24.3782i	0.181323	+	1.02833i
$563$	9.77502	−	8.20221i	0.411968	−	0.345682i	−0.413130	−	0.910672i	$-0.635564\pi$
$563$	9.77502	−	8.20221i	0.411968	−	0.345682i	0.825098	+	0.564990i	$0.191120\pi$
$564$	14.7394	−	13.3375i	0.620641	−	0.561610i
$565$	8.62447	−	3.13905i	0.362834	−	0.132061i
$566$	2.47014			0.103828
$567$	−5.61077	−	7.03699i	−0.235630	−	0.295526i
$568$	−6.05918			−0.254237
$569$	32.8022	−	11.9390i	1.37514	−	0.500509i	0.454437	−	0.890779i	$-0.349840\pi$
$569$	32.8022	−	11.9390i	1.37514	−	0.500509i	0.920701	+	0.390269i	$0.127618\pi$
$570$	−9.81754	+	8.88378i	−0.411212	+	0.372100i
$571$	21.5165	−	18.0545i	0.900437	−	0.755557i	−0.0698384	−	0.997558i	$-0.522248\pi$
$571$	21.5165	−	18.0545i	0.900437	−	0.755557i	0.970276	+	0.242002i	$0.0778039\pi$
$572$	−2.29831	−	13.0344i	−0.0960972	−	0.544995i
$573$	13.4104	−	25.3723i	0.560227	−	1.05994i
$574$	−2.20889	−	1.85348i	−0.0921975	−	0.0773629i
$575$	−4.94517	+	8.56528i	−0.206228	+	0.357197i
$576$	−2.73457	+	1.23374i	−0.113941	+	0.0514057i
$577$	−8.77144	−	15.1926i	−0.365160	−	0.632475i	0.623642	−	0.781710i	$-0.285652\pi$
$577$	−8.77144	−	15.1926i	−0.365160	−	0.632475i	−0.988802	+	0.149235i	$0.952319\pi$
$578$	−1.07518	+	6.09766i	−0.0447216	+	0.253629i
$579$	0.396242	−	2.87086i	0.0164673	−	0.119309i
$580$	−12.7909	−	4.65552i	−0.531115	−	0.193310i
$581$	−3.32011	−	1.20842i	−0.137741	−	0.0501337i
$582$	−7.12182	−	5.53589i	−0.295209	−	0.229470i
$583$	9.45095	−	53.5990i	0.391418	−	2.21984i
$584$	−4.22982	−	7.32626i	−0.175031	−	0.303163i
$585$	18.0432	+	5.07746i	0.745996	+	0.209927i
$586$	−1.85822	+	3.21854i	−0.0767625	+	0.132957i
$587$	4.52083	+	3.79343i	0.186595	+	0.156572i	0.731300	−	0.682056i	$-0.238914\pi$
$587$	4.52083	+	3.79343i	0.186595	+	0.156572i	−0.544705	+	0.838628i	$0.683358\pi$
$588$	1.73084	−	0.0647244i	0.0713787	−	0.00266919i
$589$	−1.69950	−	9.63833i	−0.0700266	−	0.397140i
$590$	−4.77847	+	4.00961i	−0.196727	+	0.165073i
$591$	−7.20827	−	33.5050i	−0.296508	−	1.37821i
$592$	3.68665	−	1.34183i	0.151521	−	0.0551490i
$593$	−44.9986			−1.84787			−0.923935	−	0.382549i	$-0.875046\pi$
$593$	−44.9986			−1.84787			−0.923935	+	0.382549i	$0.875046\pi$
$594$	15.1085	−	15.8792i	0.619911	−	0.651533i
$595$	9.58953			0.393132
$596$	−15.5460	+	5.65827i	−0.636788	+	0.231772i
$597$	10.6890	+	3.44390i	0.437473	+	0.140950i
$598$	22.9724	−	19.2762i	0.939412	−	0.788260i
$599$	−0.678064	−	3.84549i	−0.0277049	−	0.157122i	0.967817	−	0.251656i	$-0.0809751\pi$
$599$	−0.678064	−	3.84549i	−0.0277049	−	0.157122i	−0.995522	+	0.0945335i	$0.969864\pi$
$600$	−0.953569	−	1.51767i	−0.0389293	−	0.0619587i
$601$	−8.71747	−	7.31483i	−0.355593	−	0.298378i	0.447438	−	0.894315i	$-0.352336\pi$
$601$	−8.71747	−	7.31483i	−0.355593	−	0.298378i	−0.803031	+	0.595937i	$0.796781\pi$
$602$	−1.84593	+	3.19725i	−0.0752346	+	0.130310i
$603$	18.6397	−	38.7013i	0.759068	−	1.57604i
$604$	1.82410	+	3.15944i	0.0742216	+	0.128556i
$605$	−2.34898	+	13.3217i	−0.0954997	+	0.541606i
$606$	15.0487	−	6.12337i	0.611312	−	0.248745i
$607$	−23.7800	−	8.65520i	−0.965199	−	0.351304i	−0.189130	−	0.981952i	$-0.560567\pi$
$607$	−23.7800	−	8.65520i	−0.965199	−	0.351304i	−0.776069	+	0.630648i	$0.782789\pi$
$608$	−3.60738	−	1.31298i	−0.146299	−	0.0532484i
$609$	10.9667	−	4.46240i	0.444395	−	0.180826i
$610$	−1.49240	+	8.46380i	−0.0604253	+	0.342689i
$611$	−18.0051	−	31.1857i	−0.728408	−	1.26164i
$612$	6.26905	−	13.0163i	0.253411	−	0.526153i
$613$	−4.60737	+	7.98020i	−0.186090	+	0.322317i	−0.943943	−	0.330108i	$-0.892915\pi$
$613$	−4.60737	+	7.98020i	−0.186090	+	0.322317i	0.757853	+	0.652425i	$0.226248\pi$
$614$	10.1946	+	8.55425i	0.411419	+	0.345222i
$615$	5.29096	+	8.42094i	0.213352	+	0.339565i
$616$	0.732484	+	4.15412i	0.0295126	+	0.167374i
$617$	1.17930	−	0.989546i	0.0474767	−	0.0398376i	−0.618741	−	0.785595i	$-0.712357\pi$
$617$	1.17930	−	0.989546i	0.0474767	−	0.0398376i	0.666217	+	0.745758i	$0.267912\pi$
$618$	3.95517	+	1.27432i	0.159100	+	0.0512606i
$619$	−35.2378	+	12.8255i	−1.41633	+	0.515501i	−0.932980	−	0.359928i	$-0.882801\pi$
$619$	−35.2378	+	12.8255i	−1.41633	+	0.515501i	−0.483347	+	0.875429i	$0.660579\pi$
$620$	−5.07662			−0.203882
$621$	48.2745	+	11.6568i	1.93719	+	0.467772i
$622$	−23.9743			−0.961280
$623$	−10.3343	+	3.76137i	−0.414034	+	0.150696i
$624$	1.14306	+	5.31308i	0.0457589	+	0.212693i
$625$	−14.3671	+	12.0555i	−0.574686	+	0.482219i
$626$	−3.36727	−	19.0967i	−0.134583	−	0.763258i
$627$	28.0280	−	1.04810i	1.11933	−	0.0418570i
$628$	−15.4001	−	12.9222i	−0.614530	−	0.515652i
$629$	−9.44676	+	16.3623i	−0.376667	+	0.652407i
$630$	−5.75047	−	1.61821i	−0.229104	−	0.0644711i
$631$	1.93172	+	3.34585i	0.0769008	+	0.133196i	0.901911	−	0.431921i	$-0.142164\pi$
$631$	1.93172	+	3.34585i	0.0769008	+	0.133196i	−0.825011	+	0.565117i	$0.808831\pi$
$632$	−2.46312	+	13.9691i	−0.0979778	+	0.555660i
$633$	−20.4543	−	15.8994i	−0.812985	−	0.631945i
$634$	20.7703	+	7.55978i	0.824895	+	0.300237i
$635$	0.433533	+	0.157793i	0.0172043	+	0.00626184i
$636$	−3.05555	+	22.1381i	−0.121160	+	0.877833i
$637$	0.544855	−	3.09003i	0.0215879	−	0.122431i
$638$	14.4173	+	24.9715i	0.570786	+	0.988631i
$639$	−16.5693	+	7.47543i	−0.655470	+	0.295724i
$640$	−0.995637	+	1.72449i	−0.0393560	+	0.0681666i
$641$	−2.79632	−	2.34639i	−0.110448	−	0.0926767i	0.585891	−	0.810390i	$-0.300745\pi$
$641$	−2.79632	−	2.34639i	−0.110448	−	0.0926767i	−0.696339	+	0.717713i	$0.745189\pi$
$642$	−2.08269	+	3.94043i	−0.0821973	+	0.155516i
$643$	−6.56477	−	37.2307i	−0.258889	−	1.46823i	−0.785889	−	0.618368i	$-0.787794\pi$
$643$	−6.56477	−	37.2307i	−0.258889	−	1.46823i	0.526999	−	0.849866i	$-0.323317\pi$
$644$	−7.32143	+	6.14341i	−0.288505	+	0.242084i
$645$	9.44152	−	8.54352i	0.371760	−	0.336401i
$646$	17.3724	−	6.32302i	0.683506	−	0.248776i
$647$	39.0162			1.53388			0.766942	−	0.641716i	$-0.221777\pi$
$647$	39.0162			1.53388			0.766942	+	0.641716i	$0.221777\pi$
$648$	−5.95578	+	6.74749i	−0.233965	+	0.265067i
$649$	13.2139			0.518692
$650$	−3.05117	+	1.11053i	−0.119677	+	0.0435587i
$651$	3.27423	−	2.96281i	0.128327	−	0.116122i
$652$	5.44875	−	4.57205i	0.213390	−	0.179055i
$653$	−0.395201	−	2.24130i	−0.0154654	−	0.0877087i	0.976098	−	0.217330i	$-0.0697349\pi$
$653$	−0.395201	−	2.24130i	−0.0154654	−	0.0877087i	−0.991564	+	0.129622i	$0.958624\pi$
$654$	−12.0955	+	22.8846i	−0.472972	+	0.894858i
$655$	3.79752	+	3.18650i	0.148381	+	0.124507i
$656$	−1.44175	+	2.49719i	−0.0562910	+	0.0974989i
$657$	−20.6054	−	14.8157i	−0.803895	−	0.578016i
$658$	5.73832	+	9.93905i	0.223703	+	0.387465i
$659$	−1.41477	+	8.02357i	−0.0551117	+	0.312554i	−0.999885	−	0.0151709i	$-0.995171\pi$
$659$	−1.41477	+	8.02357i	−0.0551117	+	0.312554i	0.944773	+	0.327725i	$0.106282\pi$
$660$	1.98916	−	14.4119i	0.0774281	−	0.560983i
$661$	44.6728	+	16.2596i	1.73757	+	0.632424i	0.999122	−	0.0418870i	$-0.0133369\pi$
$661$	44.6728	+	16.2596i	1.73757	+	0.632424i	0.738448	+	0.674311i	$0.235559\pi$
$662$	28.2199	+	10.2712i	1.09680	+	0.399201i
$663$	−20.6636	−	16.0621i	−0.802508	−	0.623801i
$664$	−0.613531	+	3.47951i	−0.0238096	+	0.135031i
$665$	−3.82215	−	6.62015i	−0.148217	−	0.256719i
$666$	8.42596	−	8.21770i	0.326499	−	0.318430i
$667$	−32.6661	+	56.5794i	−1.26484	+	2.19076i
$668$	−4.87847	−	4.09352i	−0.188754	−	0.158383i
$669$	−1.00282	+	0.0375002i	−0.0387713	+	0.00144984i
$670$	−4.95114	−	28.0793i	−0.191279	−	1.08480i
$671$	13.9465	−	11.7025i	0.538398	−	0.451770i
$672$	−0.364298	−	1.69331i	−0.0140531	−	0.0653207i
$673$	−11.1024	+	4.04094i	−0.427966	+	0.155767i	−0.547017	−	0.837121i	$-0.684237\pi$
$673$	−11.1024	+	4.04094i	−0.427966	+	0.155767i	0.119052	+	0.992888i	$0.462015\pi$
$674$	9.76639			0.376187
$675$	−4.48001	−	2.97373i	−0.172436	−	0.114459i
$676$	−3.15486			−0.121341
$677$	−6.34762	+	2.31035i	−0.243959	+	0.0887938i	−0.461106	−	0.887345i	$-0.652547\pi$
$677$	−6.34762	+	2.31035i	−0.243959	+	0.0887938i	0.217147	+	0.976139i	$0.430325\pi$
$678$	7.59853	+	2.44817i	0.291820	+	0.0940215i
$679$	3.98948	−	3.34757i	0.153102	−	0.128468i
$680$	−1.66520	−	9.44385i	−0.0638577	−	0.362155i
$681$	3.83699	+	6.10683i	0.147034	+	0.234014i
$682$	8.23807	+	6.91256i	0.315452	+	0.264696i
$683$	−9.89398	+	17.1369i	−0.378583	+	0.655725i	−0.990856	−	0.134921i	$-0.956922\pi$
$683$	−9.89398	+	17.1369i	−0.378583	+	0.655725i	0.612274	+	0.790646i	$0.290255\pi$
$684$	−11.4845	+	0.860125i	−0.439122	+	0.0328877i
$685$	13.2268	+	22.9096i	0.505372	+	0.875330i
$686$	−0.173648	+	0.984808i	−0.00662992	+	0.0376001i
$687$	−29.1202	+	11.8491i	−1.11100	+	0.452071i
$688$	3.46922	+	1.26269i	0.132263	+	0.0481397i
$689$	38.0430	+	13.8465i	1.44932	+	0.527510i
$690$	30.5326	−	12.4238i	1.16236	−	0.472967i
$691$	8.03633	−	45.5763i	0.305716	−	1.73380i	−0.314397	−	0.949292i	$-0.601802\pi$
$691$	8.03633	−	45.5763i	0.305716	−	1.73380i	0.620113	−	0.784512i	$-0.287087\pi$
$692$	−7.15052	−	12.3851i	−0.271822	−	0.470809i
$693$	7.12813	+	10.4561i	0.270775	+	0.397193i
$694$	5.54686	−	9.60745i	0.210556	−	0.364694i
$695$	−21.1930	−	17.7830i	−0.803897	−	0.674549i
$696$	−6.29896	−	10.0252i	−0.238761	−	0.380006i
$697$	−2.41134	−	13.6754i	−0.0913359	−	0.517991i
$698$	−2.31004	+	1.93835i	−0.0874363	+	0.0733678i
$699$	−11.2879	−	3.63687i	−0.426949	−	0.137559i
$700$	0.972422	−	0.353933i	0.0367541	−	0.0133774i
$701$	22.5588			0.852034			0.426017	−	0.904715i	$-0.359916\pi$
$701$	22.5588			0.852034			0.426017	+	0.904715i	$0.359916\pi$
$702$	9.68072	+	13.1188i	0.365375	+	0.495136i
$703$	15.0610			0.568035
$704$	3.96382	−	1.44271i	0.149392	−	0.0543742i
$705$	−8.32535	−	38.6973i	−0.313551	−	1.45743i
$706$	−1.16399	+	0.976700i	−0.0438072	+	0.0367586i
$707$	1.62884	+	9.23760i	0.0612588	+	0.347416i
$708$	−5.42202	+	0.202755i	−0.203772	+	0.00762001i
$709$	−21.3008	−	17.8735i	−0.799970	−	0.671254i	0.148222	−	0.988954i	$-0.452645\pi$
$709$	−21.3008	−	17.8735i	−0.799970	−	0.671254i	−0.948191	+	0.317700i	$0.897090\pi$
$710$	−6.03274	+	10.4490i	−0.226405	+	0.392144i
$711$	10.4986	+	41.2383i	0.393728	+	1.54656i
$712$	5.49875	+	9.52411i	0.206074	+	0.356931i
$713$	−4.23113	+	23.9959i	−0.158457	+	0.898654i
$714$	6.58560	+	5.11908i	0.246460	+	0.191577i
$715$	−24.7660	−	9.01408i	−0.926195	−	0.337107i
$716$	7.55241	+	2.74885i	0.282247	+	0.102729i
$717$	5.16274	−	37.4051i	0.192806	−	1.39692i
$718$	−5.67064	+	32.1598i	−0.211626	+	1.20019i
$719$	−0.132486	−	0.229472i	−0.00494089	−	0.00855787i	0.863544	−	0.504273i	$-0.168239\pi$
$719$	−0.132486	−	0.229472i	−0.00494089	−	0.00855787i	−0.868485	+	0.495715i	$0.834906\pi$
$720$	−0.595069	+	5.94411i	−0.0221769	+	0.221524i
$721$	−1.19956	+	2.07770i	−0.0446739	+	0.0773774i
$722$	3.26555	+	2.74012i	0.121531	+	0.101977i
$723$	−16.0616	+	30.3884i	−0.597338	+	1.13016i
$724$	−1.08628	−	6.16063i	−0.0403714	−	0.228958i
$725$	5.41887	−	4.54697i	0.201252	−	0.168870i
$726$	−8.72457	+	7.89476i	−0.323799	+	0.293002i
$727$	6.72977	−	2.44943i	0.249593	−	0.0908445i	−0.214194	−	0.976791i	$-0.568712\pi$
$727$	6.72977	−	2.44943i	0.249593	−	0.0908445i	0.463787	+	0.885947i	$0.346490\pi$
$728$	−3.13770			−0.116291
$729$	−7.96188	+	25.7994i	−0.294885	+	0.955533i
$730$	−16.8455			−0.623478
$731$	−16.7070	+	6.08084i	−0.617930	+	0.224908i
$732$	−5.54305	+	5.01583i	−0.204877	+	0.185391i
$733$	3.74011	−	3.13833i	0.138144	−	0.115917i	−0.571097	−	0.820882i	$-0.693482\pi$
$733$	3.74011	−	3.13833i	0.138144	−	0.115917i	0.709241	+	0.704966i	$0.249038\pi$
$734$	3.74664	+	21.2483i	0.138291	+	0.784288i
$735$	1.61167	−	3.04927i	0.0594474	−	0.112474i
$736$	7.32143	+	6.14341i	0.269872	+	0.226449i
$737$	−30.1996	+	52.3073i	−1.11242	+	1.92676i
$738$	−0.861702	+	8.60750i	−0.0317197	+	0.316846i
$739$	8.06520	+	13.9693i	0.296683	+	0.513871i	0.975375	−	0.220553i	$-0.0707861\pi$
$739$	8.06520	+	13.9693i	0.296683	+	0.513871i	−0.678692	+	0.734423i	$0.737453\pi$
$740$	1.35659	−	7.69359i	0.0498691	−	0.282822i
$741$	−2.85252	+	20.6671i	−0.104790	+	0.759226i
$742$	−12.1245	−	4.41295i	−0.445104	−	0.162005i
$743$	−11.3963	−	4.14791i	−0.418089	−	0.152172i	0.124405	−	0.992231i	$-0.460298\pi$
$743$	−11.3963	−	4.14791i	−0.418089	−	0.152172i	−0.542494	+	0.840060i	$0.682520\pi$
$744$	−3.48636	−	2.71000i	−0.127816	−	0.0993535i
$745$	−5.72049	+	32.4425i	−0.209583	+	1.18860i
$746$	0.333086	+	0.576922i	0.0121951	+	0.0211226i
$747$	2.61505	+	10.2719i	0.0956798	+	0.375829i
$748$	−10.1570	+	17.5924i	−0.371376	+	0.643242i
$749$	−1.97121	−	1.65404i	−0.0720265	−	0.0604374i
$750$	−20.7995	+	0.777793i	−0.759491	+	0.0284010i
$751$	−5.84605	−	33.1546i	−0.213326	−	1.20983i	−0.883789	−	0.467886i	$-0.845016\pi$
$751$	−5.84605	−	33.1546i	−0.213326	−	1.20983i	0.670463	−	0.741943i	$-0.266095\pi$
$752$	8.79161	−	7.37704i	0.320597	−	0.269013i
$753$	−6.71524	−	31.2133i	−0.244717	−	1.13748i
$754$	−20.1550	+	7.33582i	−0.734002	+	0.267155i
$755$	7.26457			0.264385
$756$	−3.08530	−	4.18102i	−0.112211	−	0.152062i
$757$	11.3405			0.412177			0.206089	−	0.978533i	$-0.433927\pi$
$757$	11.3405			0.412177			0.206089	+	0.978533i	$0.433927\pi$
$758$	−14.3276	+	5.21484i	−0.520404	+	0.189411i
$759$	−66.4636	−	21.4139i	−2.41248	−	0.777276i
$760$	−5.85587	+	4.91366i	−0.212415	+	0.178237i
$761$	1.28146	+	7.26754i	0.0464530	+	0.263448i	0.999185	−	0.0403638i	$-0.0128517\pi$
$761$	1.28146	+	7.26754i	0.0464530	+	0.263448i	−0.952732	+	0.303812i	$0.901741\pi$
$762$	0.213496	+	0.339793i	0.00773413	+	0.0123094i
$763$	−11.4481	−	9.60608i	−0.414448	−	0.347763i
$764$	8.28449	−	14.3492i	0.299722	−	0.519134i
$765$	−16.2049	−	23.7705i	−0.585888	−	0.859423i
$766$	12.6032	+	21.8294i	0.455373	+	0.788729i
$767$	−1.70681	+	9.67980i	−0.0616293	+	0.349517i
$768$	−1.60432	+	0.652804i	−0.0578910	+	0.0235560i
$769$	−4.66553	−	1.69811i	−0.168243	−	0.0612356i	0.256525	−	0.966538i	$-0.417422\pi$
$769$	−4.66553	−	1.69811i	−0.168243	−	0.0612356i	−0.424769	+	0.905302i	$0.639645\pi$
$770$	7.89304	+	2.87283i	0.284446	+	0.103530i
$771$	21.0686	−	8.57289i	0.758768	−	0.308745i
$772$	0.290549	−	1.64779i	0.0104571	−	0.0593051i
$773$	9.78671	+	16.9511i	0.352003	+	0.609688i	0.986600	−	0.163155i	$-0.0521672\pi$
$773$	9.78671	+	16.9511i	0.352003	+	0.609688i	−0.634597	+	0.772843i	$0.718834\pi$
$774$	11.0447	−	0.827181i	0.396992	−	0.0297324i
$775$	1.31912	−	2.28478i	0.0473840	−	0.0820715i
$776$	−3.98948	−	3.34757i	−0.143214	−	0.120171i
$777$	3.61518	+	5.75381i	0.129694	+	0.206417i
$778$	−0.349868	−	1.98420i	−0.0125434	−	0.0711370i
$779$	−8.47972	+	7.11533i	−0.303817	+	0.254933i
$780$	10.3004	+	3.31870i	0.368815	+	0.118829i
$781$	24.0175	−	8.74164i	0.859412	−	0.312801i
$782$	−46.0266			−1.64591
$783$	−29.5935	−	19.6435i	−1.05758	−	0.702001i
$784$	1.00000			0.0357143
$785$	−37.6171	+	13.6915i	−1.34261	+	0.488671i
$786$	0.906928	+	4.21552i	0.0323490	+	0.150363i
$787$	−30.7286	+	25.7844i	−1.09536	+	0.919114i	−0.997104	−	0.0760477i	$-0.975770\pi$
$787$	−30.7286	+	25.7844i	−1.09536	+	0.919114i	−0.0982529	+	0.995161i	$0.531325\pi$
$788$	−3.43593	−	19.4861i	−0.122400	−	0.694164i
$789$	−5.25970	+	0.196685i	−0.187250	+	0.00700218i
$790$	21.6372	+	18.1558i	0.769817	+	0.645953i
$791$	−2.30455	+	3.99159i	−0.0819403	+	0.141925i
$792$	9.05942	−	8.83551i	0.321913	−	0.313956i
$793$	6.77117	+	11.7280i	0.240451	+	0.416474i
$794$	−1.54812	+	8.77981i	−0.0549407	+	0.311584i
$795$	35.1348	+	27.3108i	1.24610	+	0.968614i
$796$	6.09270	+	2.21756i	0.215950	+	0.0785994i
$797$	−5.57055	−	2.02752i	−0.197319	−	0.0718183i	0.241470	−	0.970408i	$-0.422370\pi$
$797$	−5.57055	−	2.02752i	−0.197319	−	0.0718183i	−0.438789	+	0.898590i	$0.644593\pi$
$798$	0.909113	−	6.58672i	0.0321823	−	0.233167i
$799$	−9.59735	+	54.4293i	−0.339530	+	1.92557i
$800$	−0.517415	−	0.896189i	−0.0182934	−	0.0316851i
$801$	26.7870	+	19.2604i	0.946472	+	0.680532i
$802$	11.1756	−	19.3566i	0.394622	−	0.683506i
$803$	27.3359	+	22.9376i	0.964664	+	0.809449i
$804$	11.5891	−	21.9264i	0.408716	−	0.773286i
$805$	3.30478	+	18.7424i	0.116478	+	0.660581i
$806$	−6.12786	+	5.14188i	−0.215845	+	0.181115i
$807$	−10.3520	+	9.36738i	−0.364407	+	0.329747i
$808$	8.81442	−	3.20819i	0.310090	−	0.112864i
$809$	48.0120			1.68801			0.844005	−	0.536335i	$-0.180192\pi$
$809$	48.0120			1.68801			0.844005	+	0.536335i	$0.180192\pi$
$810$	5.70621	+	16.9888i	0.200496	+	0.596924i
$811$	7.41369			0.260330			0.130165	−	0.991492i	$-0.458449\pi$
$811$	7.41369			0.260330			0.130165	+	0.991492i	$0.458449\pi$
$812$	6.42350	−	2.33796i	0.225421	−	0.0820464i
$813$	−35.8170	+	32.4103i	−1.25616	+	1.13668i
$814$	−12.6773	+	10.6376i	−0.444341	+	0.372846i
$815$	−2.45949	−	13.9484i	−0.0861520	−	0.488592i
$816$	3.89773	−	7.37447i	0.136448	−	0.258158i
$817$	10.8569	+	9.11003i	0.379835	+	0.318719i
$818$	−18.1155	+	31.3769i	−0.633392	+	1.09707i
$819$	−8.58026	+	3.87109i	−0.299819	+	0.135267i
$820$	2.87093	+	4.97259i	0.100257	+	0.173650i
$821$	1.44030	−	8.16834i	0.0502668	−	0.285077i	−0.949304	−	0.314358i	$-0.898211\pi$
$821$	1.44030	−	8.16834i	0.0502668	−	0.285077i	0.999571	+	0.0292811i	$0.00932179\pi$
$822$	−3.14606	+	22.7939i	−0.109731	+	0.795028i
$823$	−21.0910	−	7.67651i	−0.735187	−	0.267586i	−0.0528283	−	0.998604i	$-0.516824\pi$
$823$	−21.0910	−	7.67651i	−0.735187	−	0.267586i	−0.682359	+	0.731017i	$0.739046\pi$
$824$	2.25443	+	0.820546i	0.0785368	+	0.0285851i
$825$	5.96933	+	4.64005i	0.207826	+	0.161546i
$826$	0.543969	−	3.08500i	0.0189271	−	0.107341i
$827$	−5.69499	−	9.86402i	−0.198034	−	0.343006i	0.749857	−	0.661600i	$-0.230122\pi$
$827$	−5.69499	−	9.86402i	−0.198034	−	0.343006i	−0.947891	+	0.318595i	$0.896789\pi$
$828$	27.6003	+	7.76688i	0.959178	+	0.269918i
$829$	−26.0641	+	45.1443i	−0.905242	+	1.56793i	−0.0846510	+	0.996411i	$0.526978\pi$
$829$	−26.0641	+	45.1443i	−0.905242	+	1.56793i	−0.820591	+	0.571515i	$0.806356\pi$
$830$	5.38953	+	4.52235i	0.187073	+	0.156973i
$831$	38.3474	−	1.43399i	1.33026	−	0.0497446i
$832$	0.544855	+	3.09003i	0.0188895	+	0.107127i
$833$	−3.68910	+	3.09552i	−0.127820	+	0.107254i
$834$	−5.06134	−	23.5257i	−0.175260	−	0.814630i
$835$	−11.9164	+	4.33723i	−0.412385	+	0.150096i
$836$	16.1933			0.560056
$837$	−12.8771	−	3.10944i	−0.445099	−	0.107478i
$838$	9.57136			0.330637
$839$	19.2368	−	7.00161i	0.664127	−	0.241722i	0.0121098	−	0.999927i	$-0.496145\pi$
$839$	19.2368	−	7.00161i	0.664127	−	0.241722i	0.652017	+	0.758204i	$0.273923\pi$
$840$	−3.28280	−	1.05769i	−0.113268	−	0.0364937i
$841$	13.5800	−	11.3950i	0.468276	−	0.392930i
$842$	0.604337	+	3.42737i	0.0208268	+	0.118115i
$843$	22.8104	+	36.3044i	0.785632	+	1.25039i
$844$	−11.4580	−	9.61442i	−0.394401	−	0.330942i
$845$	−3.14110	+	5.44054i	−0.108057	+	0.187160i
$846$	14.9400	−	31.0196i	0.513647	−	1.06648i
$847$	−3.39663	−	5.88314i	−0.116710	−	0.202147i
$848$	−2.24051	+	12.7066i	−0.0769396	+	0.436346i
$849$	3.96289	−	1.61251i	0.136006	−	0.0553414i
$850$	4.68297	+	1.70446i	0.160625	+	0.0584626i
$851$	−35.2350	−	12.8245i	−1.20784	−	0.439618i
$852$	−9.72087	+	3.95545i	−0.333031	+	0.135512i
$853$	6.10602	−	34.6289i	0.209066	−	1.18567i	−0.681846	−	0.731496i	$-0.738822\pi$
$853$	6.10602	−	34.6289i	0.209066	−	1.18567i	0.890912	−	0.454176i	$-0.150066\pi$
$854$	−2.15801	−	3.73778i	−0.0738455	−	0.127904i
$855$	−9.95114	+	20.6614i	−0.340322	+	0.706604i
$856$	−1.28662	+	2.22849i	−0.0439757	+	0.0761681i
$857$	−3.74755	−	3.14457i	−0.128014	−	0.107416i	0.576533	−	0.817074i	$-0.304405\pi$
$857$	−3.74755	−	3.14457i	−0.128014	−	0.107416i	−0.704547	+	0.709658i	$0.748850\pi$
$858$	−12.1961	−	19.4110i	−0.416369	−	0.662680i
$859$	8.60985	+	48.8289i	0.293764	+	1.66602i	0.672182	+	0.740386i	$0.265357\pi$
$859$	8.60985	+	48.8289i	0.293764	+	1.66602i	−0.378418	+	0.925635i	$0.623532\pi$
$860$	5.63158	−	4.72546i	0.192035	−	0.161137i
$861$	−4.75374	−	1.53161i	−0.162007	−	0.0521971i
$862$	−10.0346	+	3.65229i	−0.341779	+	0.124398i
$863$	11.9171			0.405662			0.202831	−	0.979214i	$-0.434986\pi$
$863$	11.9171			0.405662			0.202831	+	0.979214i	$0.434986\pi$
$864$	−3.58175	+	3.76445i	−0.121853	+	0.128069i
$865$	−28.4773			−0.968256
$866$	19.5577	−	7.11841i	0.664596	−	0.241893i
$867$	2.25563	+	10.4845i	0.0766054	+	0.356072i
$868$	1.95298	−	1.63874i	0.0662885	−	0.0556226i
$869$	−10.3900	−	58.9244i	−0.352456	−	1.99887i
$870$	−23.5599	+	0.881018i	−0.798756	+	0.0298693i
$871$	−34.4167	−	28.8790i	−1.16616	−	0.978528i
$872$	−7.47220	+	12.9422i	−0.253041	+	0.438279i
$873$	−15.0395	−	4.23220i	−0.509011	−	0.143238i
$874$	18.3450	+	31.7745i	0.620530	+	1.07479i
$875$	2.08673	−	11.8344i	0.0705443	−	0.400077i
$876$	−11.5686	−	8.99244i	−0.390867	−	0.303826i
$877$	20.8442	+	7.58668i	0.703860	+	0.256184i	0.669058	−	0.743210i	$-0.266698\pi$
$877$	20.8442	+	7.58668i	0.703860	+	0.256184i	0.0348017	+	0.999394i	$0.488920\pi$
$878$	10.2815	+	3.74218i	0.346985	+	0.126292i
$879$	−0.880115	+	6.37662i	−0.0296855	+	0.215078i
$880$	1.45858	−	8.27199i	0.0491686	−	0.278849i
$881$	8.25657	+	14.3008i	0.278171	+	0.481806i	0.970930	−	0.239363i	$-0.0769385\pi$
$881$	8.25657	+	14.3008i	0.278171	+	0.481806i	−0.692759	+	0.721169i	$0.743605\pi$
$882$	2.73457	−	1.23374i	0.0920779	−	0.0415421i
$883$	−5.81322	+	10.0688i	−0.195630	+	0.338842i	−0.947107	−	0.320918i	$-0.896009\pi$
$883$	−5.81322	+	10.0688i	−0.195630	+	0.338842i	0.751477	+	0.659760i	$0.229342\pi$
$884$	−11.5753	−	9.71281i	−0.389319	−	0.326677i
$885$	−5.04871	+	9.55211i	−0.169711	+	0.321091i
$886$	2.82949	+	16.0469i	0.0950587	+	0.539105i
$887$	13.4711	−	11.3036i	0.452314	−	0.379537i	−0.387980	−	0.921668i	$-0.626827\pi$
$887$	13.4711	−	11.3036i	0.452314	−	0.379537i	0.840294	+	0.542131i	$0.182382\pi$
$888$	5.03863	−	4.55939i	0.169085	−	0.153003i
$889$	−0.217717	+	0.0792424i	−0.00730198	+	0.00265770i
$890$	21.8990			0.734057
$891$	13.8729	−	35.3383i	0.464761	−	1.18388i
$892$	−0.579383			−0.0193992
$893$	41.4006	−	15.0686i	1.38542	−	0.504251i
$894$	−21.2470	+	19.2262i	−0.710606	+	0.643019i
$895$	12.2598	−	10.2872i	0.409801	−	0.343864i
$896$	−0.173648	−	0.984808i	−0.00580118	−	0.0329001i
$897$	24.2716	−	45.9216i	0.810406	−	1.53328i
$898$	12.8317	+	10.7671i	0.428200	+	0.359303i
$899$	8.71364	−	15.0925i	0.290616	−	0.503362i
$900$	−2.52057	−	1.81234i	−0.0840191	−	0.0604113i
$901$	−31.0681	−	53.8114i	−1.03503	−	1.79272i
$902$	2.11212	−	11.9784i	0.0703260	−	0.398838i
$903$	−0.874294	+	6.33444i	−0.0290947	+	0.210797i
$904$	4.33113	+	1.57640i	0.144051	+	0.0524304i
$905$	−11.7055	−	4.26045i	−0.389104	−	0.141622i
$906$	4.98894	+	3.87797i	0.165746	+	0.128837i
$907$	−5.78835	+	32.8274i	−0.192199	+	1.09001i	0.724152	+	0.689640i	$0.242231\pi$
$907$	−5.78835	+	32.8274i	−0.192199	+	1.09001i	−0.916351	+	0.400375i	$0.868880\pi$
$908$	2.08198	+	3.60610i	0.0690930	+	0.119673i
$909$	20.1456	−	19.6477i	0.668188	−	0.651673i
$910$	−3.12401	+	5.41094i	−0.103560	+	0.179371i
$911$	−24.7659	−	20.7810i	−0.820530	−	0.688507i	0.132566	−	0.991174i	$-0.457678\pi$
$911$	−24.7659	−	20.7810i	−0.820530	−	0.688507i	−0.953096	+	0.302668i	$0.902123\pi$
$912$	−6.64452	+	0.248470i	−0.220022	+	0.00822767i
$913$	−2.58800	−	14.6773i	−0.0856503	−	0.485747i
$914$	−2.16314	+	1.81509i	−0.0715502	+	0.0600377i
$915$	3.13091	+	14.5529i	0.103505	+	0.481104i
$916$	−17.0564	+	6.20804i	−0.563561	+	0.205119i
$917$	−2.48952			−0.0822111
$918$	1.56048	−	24.9748i	0.0515034	−	0.824292i
$919$	46.0285			1.51834			0.759170	−	0.650892i	$-0.225605\pi$
$919$	46.0285			1.51834			0.759170	+	0.650892i	$0.225605\pi$
$920$	17.8838	−	6.50915i	0.589610	−	0.214600i
$921$	21.9396	+	7.06873i	0.722934	+	0.232922i
$922$	−21.7839	+	18.2788i	−0.717414	+	0.601982i
$923$	3.30137	+	18.7230i	0.108666	+	0.616276i
$924$	3.88697	+	6.18638i	0.127872	+	0.203517i
$925$	3.11007	+	2.60966i	0.102258	+	0.0858049i
$926$	15.0110	−	25.9999i	0.493293	−	0.854409i
$927$	7.17725	−	0.537534i	0.235732	−	0.0176549i
$928$	−3.41787	−	5.91993i	−0.112197	−	0.194331i
$929$	6.73699	−	38.2074i	0.221033	−	1.25354i	−0.649091	−	0.760711i	$-0.724851\pi$
$929$	6.73699	−	38.2074i	0.221033	−	1.25354i	0.870124	−	0.492832i	$-0.164038\pi$
$930$	−8.14453	+	3.31404i	−0.267070	+	0.108672i
$931$	3.60738	+	1.31298i	0.118227	+	0.0430312i
$932$	−6.43408	−	2.34181i	−0.210755	−	0.0767087i
$933$	−38.4624	+	15.6505i	−1.25920	+	0.512374i
$934$	6.71314	−	38.0721i	0.219661	−	1.24576i
$935$	20.2253	+	35.0313i	0.661438	+	1.14564i
$936$	5.30223	+	7.77770i	0.173309	+	0.254222i
$937$	12.5136	−	21.6743i	0.408803	−	0.708068i	−0.585953	−	0.810345i	$-0.699280\pi$
$937$	12.5136	−	21.6743i	0.408803	−	0.708068i	0.994756	+	0.102278i	$0.0326130\pi$
$938$	10.9688	+	9.20389i	0.358143	+	0.300518i
$939$	−17.8686	−	28.4391i	−0.583119	−	0.928075i
$940$	−3.96840	−	22.5059i	−0.129435	−	0.734062i
$941$	30.3153	−	25.4376i	0.988251	−	0.829241i	0.00293766	−	0.999996i	$-0.499065\pi$
$941$	30.3153	−	25.4376i	0.988251	−	0.829241i	0.985314	+	0.170754i	$0.0546205\pi$
$942$	−33.1423	−	10.6781i	−1.07983	−	0.347912i
$943$	25.8970	−	9.42572i	0.843321	−	0.306944i
$944$	−3.13259			−0.101957
$945$	−10.2820	+	1.15780i	−0.334473	+	0.0376631i
$946$	−15.5730			−0.506323
$947$	22.8636	−	8.32168i	0.742968	−	0.270418i	0.0573246	−	0.998356i	$-0.481743\pi$
$947$	22.8636	−	8.32168i	0.742968	−	0.270418i	0.685644	+	0.727937i	$0.259521\pi$
$948$	5.16742	+	24.0188i	0.167830	+	0.780095i
$949$	−20.3337	+	17.0620i	−0.660060	+	0.553856i
$950$	−0.689836	−	3.91225i	−0.0223812	−	0.126930i
$951$	38.2573	−	1.43062i	1.24058	−	0.0463912i
$952$	3.68910	+	3.09552i	0.119564	+	0.100326i
$953$	−20.5313	+	35.5612i	−0.665073	+	1.15194i	0.314193	+	0.949359i	$0.398266\pi$
$953$	−20.5313	+	35.5612i	−0.665073	+	1.15194i	−0.979266	+	0.202581i	$0.935067\pi$
$954$	9.54975	+	37.5113i	0.309185	+	1.21447i
$955$	−16.4967	−	28.5731i	−0.533820	−	0.924603i
$956$	3.78563	−	21.4694i	0.122436	−	0.694370i
$957$	39.4314	+	30.6506i	1.27464	+	0.990794i
$958$	−38.1620	−	13.8898i	−1.23296	−	0.448760i
$959$	−12.4836	−	4.54367i	−0.403118	−	0.146723i
$960$	−0.471566	+	3.41660i	−0.0152197	+	0.110270i
$961$	−4.25445	+	24.1282i	−0.137240	+	0.778328i
$962$	−6.15499	−	10.6608i	−0.198445	−	0.343717i
$963$	−0.768981	+	7.68130i	−0.0247801	+	0.247527i
$964$	−9.92232	+	17.1860i	−0.319576	+	0.553522i
$965$	−2.55231	−	2.14165i	−0.0821619	−	0.0689420i
$966$	−7.73549	+	14.6355i	−0.248885	+	0.470888i
$967$	6.07381	+	34.4463i	0.195321	+	1.10772i	0.911961	+	0.410276i	$0.134568\pi$
$967$	6.07381	+	34.4463i	0.195321	+	1.10772i	−0.716641	+	0.697442i	$0.754321\pi$
$968$	−5.20394	+	4.36663i	−0.167261	+	0.140349i
$969$	23.7432	−	21.4849i	0.762740	−	0.690194i
$970$	−9.74493	+	3.54686i	−0.312891	+	0.113883i
$971$	6.86625			0.220349			0.110174	−	0.993912i	$-0.464859\pi$
$971$	6.86625			0.220349			0.110174	+	0.993912i	$0.464859\pi$
$972$	−5.15020	+	14.7131i	−0.165193	+	0.471923i
$973$	13.8934			0.445401
$974$	14.0761	−	5.12329i	0.451028	−	0.164161i
$975$	−4.17009	+	3.77346i	−0.133550	+	0.120848i
$976$	−3.30626	+	2.77428i	−0.105831	+	0.0888026i
$977$	−5.55072	−	31.4797i	−0.177583	−	1.00712i	−0.935120	−	0.354331i	$-0.884708\pi$
$977$	−5.55072	−	31.4797i	−0.177583	−	1.00712i	0.757537	−	0.652793i	$-0.226403\pi$
$978$	5.75690	−	10.8920i	0.184085	−	0.348288i
$979$	−35.5366	−	29.8187i	−1.13575	−	0.953011i
$980$	0.995637	−	1.72449i	0.0318044	−	0.0550869i
$981$	−4.46596	+	44.6102i	−0.142587	+	1.42429i
$982$	−16.0199	−	27.7472i	−0.511214	−	0.885449i
$983$	−8.84923	+	50.1865i	−0.282247	+	1.60070i	0.432711	+	0.901532i	$0.357557\pi$
$983$	−8.84923	+	50.1865i	−0.282247	+	1.60070i	−0.714958	+	0.699167i	$0.753554\pi$
$984$	−0.682862	+	4.94748i	−0.0217688	+	0.157720i
$985$	−37.0246	−	13.4758i	−1.17970	−	0.429376i
$986$	30.9342	+	11.2591i	0.985144	+	0.358563i
$987$	15.6944	+	12.1994i	0.499557	+	0.388313i
$988$	−2.09164	+	11.8623i	−0.0665440	+	0.377390i
$989$	−17.6424	−	30.5575i	−0.560996	−	0.971673i
$990$	−6.21689	−	24.4199i	−0.197586	−	0.776114i
$991$	−20.9279	+	36.2482i	−0.664796	+	1.15146i	0.314545	+	0.949243i	$0.398148\pi$
$991$	−20.9279	+	36.2482i	−0.664796	+	1.15146i	−0.979341	+	0.202218i	$0.935185\pi$
$992$	−1.95298	−	1.63874i	−0.0620072	−	0.0520302i
$993$	51.9788	−	1.94374i	1.64950	−	0.0616826i
$994$	−1.05216	−	5.96712i	−0.0333726	−	0.189266i
$995$	9.89029	−	8.29894i	0.313543	−	0.263094i
$996$	1.28713	+	5.98276i	0.0407844	+	0.189571i
$997$	46.2449	−	16.8318i	1.46459	−	0.533067i	0.517964	−	0.855403i	$-0.326690\pi$
$997$	46.2449	−	16.8318i	1.46459	−	0.533067i	0.946625	+	0.322336i	$0.104468\pi$
$998$	27.4210			0.867996
$999$	8.15340	−	18.6843i	0.257962	−	0.591146i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	378.2.u.e.169.5	yes	36
27.4	even	9	inner	378.2.u.e.85.5	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
378.2.u.e.85.5	✓	36	27.4	even	9	inner
378.2.u.e.169.5	yes	36	1.1	even	1	trivial

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.u (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.939693 - 0.342020i) q^{2} +(1.28430 - 1.16214i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-0.345781 - 1.96102i) q^{5} +(0.809368 - 1.53131i) q^{6} +(0.766044 + 0.642788i) q^{7} +(0.500000 - 0.866025i) q^{8} +(0.298838 - 2.98508i) q^{9} +O(q^{10})\)	\(q+(0.939693 - 0.342020i) q^{2} +(1.28430 - 1.16214i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-0.345781 - 1.96102i) q^{5} +(0.809368 - 1.53131i) q^{6} +(0.766044 + 0.642788i) q^{7} +(0.500000 - 0.866025i) q^{8} +(0.298838 - 2.98508i) q^{9} +(-0.995637 - 1.72449i) q^{10} +(-0.732484 + 4.15412i) q^{11} +(0.236816 - 1.71578i) q^{12} +(-2.94847 - 1.07316i) q^{13} +(0.939693 + 0.342020i) q^{14} +(-2.72308 - 2.11669i) q^{15} +(0.173648 - 0.984808i) q^{16} +(2.40789 + 4.17059i) q^{17} +(-0.740141 - 2.90727i) q^{18} +(1.91945 - 3.32458i) q^{19} +(-1.52540 - 1.27997i) q^{20} +(1.73084 - 0.0647244i) q^{21} +(0.732484 + 4.15412i) q^{22} +(-7.32143 + 6.14341i) q^{23} +(-0.364298 - 1.69331i) q^{24} +(0.972422 - 0.353933i) q^{25} -3.13770 q^{26} +(-3.08530 - 4.18102i) q^{27} +1.00000 q^{28} +(6.42350 - 2.33796i) q^{29} +(-3.28280 - 1.05769i) q^{30} +(1.95298 - 1.63874i) q^{31} +(-0.173648 - 0.984808i) q^{32} +(3.88697 + 6.18638i) q^{33} +(3.68910 + 3.09552i) q^{34} +(0.995637 - 1.72449i) q^{35} +(-1.68985 - 2.47879i) q^{36} +(1.96163 + 3.39764i) q^{37} +(0.666617 - 3.78058i) q^{38} +(-5.03387 + 2.04830i) q^{39} +(-1.87118 - 0.681056i) q^{40} +(-2.70961 - 0.986218i) q^{41} +(1.60432 - 0.652804i) q^{42} +(-0.641085 + 3.63578i) q^{43} +(2.10910 + 3.65307i) q^{44} +(-5.95714 + 0.446155i) q^{45} +(-4.77872 + 8.27699i) q^{46} +(8.79161 + 7.37704i) q^{47} +(-0.921473 - 1.46659i) q^{48} +(0.173648 + 0.984808i) q^{49} +(0.792726 - 0.665176i) q^{50} +(7.93927 + 2.55796i) q^{51} +(-2.94847 + 1.07316i) q^{52} -12.9026 q^{53} +(-4.32922 - 2.87364i) q^{54} +8.39960 q^{55} +(0.939693 - 0.342020i) q^{56} +(-1.39850 - 6.50043i) q^{57} +(5.23649 - 4.39393i) q^{58} +(-0.543969 - 3.08500i) q^{59} +(-3.44658 + 0.128884i) q^{60} +(-3.30626 - 2.77428i) q^{61} +(1.27472 - 2.20787i) q^{62} +(2.14770 - 2.09461i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-1.08496 + 6.15309i) q^{65} +(5.76842 + 4.48387i) q^{66} +(13.4552 + 4.89729i) q^{67} +(4.52535 + 1.64709i) q^{68} +(-2.26336 + 16.3985i) q^{69} +(0.345781 - 1.96102i) q^{70} +(-3.02959 - 5.24740i) q^{71} +(-2.43573 - 1.75134i) q^{72} +(4.22982 - 7.32626i) q^{73} +(3.00539 + 2.52182i) q^{74} +(0.837558 - 1.58465i) q^{75} +(-0.666617 - 3.78058i) q^{76} +(-3.23133 + 2.71141i) q^{77} +(-4.02973 + 3.64646i) q^{78} +(-13.3291 + 4.85141i) q^{79} -1.99127 q^{80} +(-8.82139 - 1.78411i) q^{81} -2.88351 q^{82} +(-3.32011 + 1.20842i) q^{83} +(1.28430 - 1.16214i) q^{84} +(7.34601 - 6.16403i) q^{85} +(0.641085 + 3.63578i) q^{86} +(5.53263 - 10.4677i) q^{87} +(3.23133 + 2.71141i) q^{88} +(-5.49875 + 9.52411i) q^{89} +(-5.44528 + 2.45671i) q^{90} +(-1.56885 - 2.71732i) q^{91} +(-1.65963 + 9.41225i) q^{92} +(0.603748 - 4.37428i) q^{93} +(10.7845 + 3.92524i) q^{94} +(-7.18329 - 2.61450i) q^{95} +(-1.36751 - 1.06298i) q^{96} +(0.904341 - 5.12877i) q^{97} +(0.500000 + 0.866025i) q^{98} +(12.1815 + 3.42793i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 3 q^{3} + 3 q^{5} + 6 q^{6} + 18 q^{8} + 3 q^{9}+O(q^{10}) \) 36 * q + 3 * q^3 + 3 * q^5 + 6 * q^6 + 18 * q^8 + 3 * q^9	\( 36 q + 3 q^{3} + 3 q^{5} + 6 q^{6} + 18 q^{8} + 3 q^{9} - 3 q^{10} + 9 q^{13} - 6 q^{15} + 6 q^{18} - 15 q^{19} - 6 q^{20} + 3 q^{21} - 3 q^{24} - 3 q^{25} - 18 q^{26} - 30 q^{27} + 36 q^{28} - 6 q^{29} - 9 q^{30} + 60 q^{33} + 9 q^{34} + 3 q^{35} - 27 q^{37} + 15 q^{38} + 6 q^{39} - 3 q^{40} - 9 q^{41} - 6 q^{43} + 9 q^{44} + 42 q^{45} - 9 q^{46} + 36 q^{47} + 3 q^{48} - 15 q^{50} - 36 q^{51} + 9 q^{52} - 42 q^{53} - 27 q^{54} + 30 q^{55} - 18 q^{57} - 21 q^{58} + 12 q^{59} + 24 q^{60} + 3 q^{61} + 18 q^{62} + 12 q^{63} - 18 q^{64} - 84 q^{65} + 18 q^{66} - 69 q^{67} + 9 q^{68} - 48 q^{69} - 3 q^{70} + 12 q^{71} + 6 q^{72} - 12 q^{73} + 9 q^{75} - 15 q^{76} + 9 q^{77} - 48 q^{78} - 51 q^{79} - 6 q^{80} - 69 q^{81} + 15 q^{83} + 3 q^{84} - 12 q^{85} + 6 q^{86} + 84 q^{87} - 9 q^{88} - 3 q^{89} + 6 q^{90} - 9 q^{91} + 18 q^{92} - 21 q^{93} + 9 q^{94} - 75 q^{95} - 42 q^{97} + 18 q^{98} + 39 q^{99}+O(q^{100}) \) 36 * q + 3 * q^3 + 3 * q^5 + 6 * q^6 + 18 * q^8 + 3 * q^9 - 3 * q^10 + 9 * q^13 - 6 * q^15 + 6 * q^18 - 15 * q^19 - 6 * q^20 + 3 * q^21 - 3 * q^24 - 3 * q^25 - 18 * q^26 - 30 * q^27 + 36 * q^28 - 6 * q^29 - 9 * q^30 + 60 * q^33 + 9 * q^34 + 3 * q^35 - 27 * q^37 + 15 * q^38 + 6 * q^39 - 3 * q^40 - 9 * q^41 - 6 * q^43 + 9 * q^44 + 42 * q^45 - 9 * q^46 + 36 * q^47 + 3 * q^48 - 15 * q^50 - 36 * q^51 + 9 * q^52 - 42 * q^53 - 27 * q^54 + 30 * q^55 - 18 * q^57 - 21 * q^58 + 12 * q^59 + 24 * q^60 + 3 * q^61 + 18 * q^62 + 12 * q^63 - 18 * q^64 - 84 * q^65 + 18 * q^66 - 69 * q^67 + 9 * q^68 - 48 * q^69 - 3 * q^70 + 12 * q^71 + 6 * q^72 - 12 * q^73 + 9 * q^75 - 15 * q^76 + 9 * q^77 - 48 * q^78 - 51 * q^79 - 6 * q^80 - 69 * q^81 + 15 * q^83 + 3 * q^84 - 12 * q^85 + 6 * q^86 + 84 * q^87 - 9 * q^88 - 3 * q^89 + 6 * q^90 - 9 * q^91 + 18 * q^92 - 21 * q^93 + 9 * q^94 - 75 * q^95 - 42 * q^97 + 18 * q^98 + 39 * q^99

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