LMFDB - Embedded newform 378.2.v.b.67.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("378.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.01834519640$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$12$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			67.3
Character	$\chi$	$=$	378.67
Dual form			378.2.v.b.79.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.766044 - 0.642788i) q^{2} +(-1.42742 + 0.981051i) q^{3} +(0.173648 - 0.984808i) q^{4} +(0.343656 - 1.94897i) q^{5} +(-0.462863 + 1.66906i) q^{6} +(1.84248 + 1.89876i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(1.07508 - 2.80075i) q^{9} +O(q^{10})$	\(q+(0.766044 - 0.642788i) q^{2} +(-1.42742 + 0.981051i) q^{3} +(0.173648 - 0.984808i) q^{4} +(0.343656 - 1.94897i) q^{5} +(-0.462863 + 1.66906i) q^{6} +(1.84248 + 1.89876i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(1.07508 - 2.80075i) q^{9} +(-0.989519 - 1.71390i) q^{10} +(0.568823 + 3.22596i) q^{11} +(0.718277 + 1.57610i) q^{12} +(1.17085 - 6.64020i) q^{13} +(2.63192 + 0.270209i) q^{14} +(1.42150 + 3.11915i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(0.298584 + 0.517162i) q^{17} +(-0.976729 - 2.83655i) q^{18} +(4.15869 - 7.20307i) q^{19} +(-1.85969 - 0.676871i) q^{20} +(-4.49277 - 0.902766i) q^{21} +(2.50935 + 2.10559i) q^{22} +(0.380241 + 0.319060i) q^{23} +(1.56333 + 0.745660i) q^{24} +(1.01807 + 0.370549i) q^{25} +(-3.37132 - 5.83929i) q^{26} +(1.21308 + 5.05257i) q^{27} +(2.18985 - 1.48477i) q^{28} +(0.221437 + 1.25583i) q^{29} +(3.09388 + 1.47569i) q^{30} +(-0.261547 + 1.48331i) q^{31} +(-0.939693 + 0.342020i) q^{32} +(-3.97678 - 4.04677i) q^{33} +(0.561154 + 0.204243i) q^{34} +(4.33380 - 2.93842i) q^{35} +(-2.57152 - 1.54509i) q^{36} -0.542374 q^{37} +(-1.44430 - 8.19103i) q^{38} +(4.84307 + 10.6270i) q^{39} +(-1.85969 + 0.676871i) q^{40} +(0.421633 - 2.39120i) q^{41} +(-4.02195 + 2.19634i) q^{42} +(-2.94820 + 2.47384i) q^{43} +3.27572 q^{44} +(-5.08912 - 3.05779i) q^{45} +0.496369 q^{46} +(-0.157691 - 0.894312i) q^{47} +(1.67688 - 0.433678i) q^{48} +(-0.210549 + 6.99683i) q^{49} +(1.01807 - 0.370549i) q^{50} +(-0.933568 - 0.445284i) q^{51} +(-6.33600 - 2.30612i) q^{52} +(-5.09597 + 8.82648i) q^{53} +(4.17700 + 3.09074i) q^{54} +6.48278 q^{55} +(0.723132 - 2.54501i) q^{56} +(1.13035 + 14.3617i) q^{57} +(0.976863 + 0.819685i) q^{58} +(-12.6532 + 4.60539i) q^{59} +(3.31861 - 0.858265i) q^{60} +(1.27613 + 7.23729i) q^{61} +(0.753095 + 1.30440i) q^{62} +(7.29875 - 3.11901i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-12.5392 - 4.56389i) q^{65} +(-5.64760 - 0.543778i) q^{66} +(-2.08879 - 1.75271i) q^{67} +(0.561154 - 0.204243i) q^{68} +(-0.855779 - 0.0823984i) q^{69} +(1.43110 - 5.03667i) q^{70} +(-1.32437 + 2.29388i) q^{71} +(-2.96306 + 0.469329i) q^{72} -1.35179 q^{73} +(-0.415482 + 0.348631i) q^{74} +(-1.81675 + 0.469852i) q^{75} +(-6.37149 - 5.34631i) q^{76} +(-5.07726 + 7.02381i) q^{77} +(10.5409 + 5.02771i) q^{78} +(5.44325 - 4.56743i) q^{79} +(-0.989519 + 1.71390i) q^{80} +(-6.68841 - 6.02206i) q^{81} +(-1.21404 - 2.10278i) q^{82} +(-1.31290 - 7.44583i) q^{83} +(-1.66921 + 4.26775i) q^{84} +(1.11054 - 0.404205i) q^{85} +(-0.668303 + 3.79014i) q^{86} +(-1.54812 - 1.57536i) q^{87} +(2.50935 - 2.10559i) q^{88} +(-8.63183 + 14.9508i) q^{89} +(-5.86401 + 0.928819i) q^{90} +(14.7654 - 10.0113i) q^{91} +(0.380241 - 0.319060i) q^{92} +(-1.08186 - 2.37390i) q^{93} +(-0.695651 - 0.583721i) q^{94} +(-12.6094 - 10.5806i) q^{95} +(1.00580 - 1.41009i) q^{96} +(-6.38539 + 5.35798i) q^{97} +(4.33619 + 5.49522i) q^{98} +(9.64663 + 1.87503i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 3 q^{6} + 6 q^{7} - 36 q^{8} + 24 q^{9}+O(q^{10}) $ 72 * q + 3 * q^6 + 6 * q^7 - 36 * q^8 + 24 * q^9	$ 72 q + 3 q^{6} + 6 q^{7} - 36 q^{8} + 24 q^{9} - 6 q^{10} + 12 q^{11} - 12 q^{13} - 3 q^{14} - 6 q^{15} - 12 q^{17} - 18 q^{19} - 30 q^{21} - 6 q^{22} + 30 q^{23} + 6 q^{25} - 18 q^{26} - 6 q^{27} + 3 q^{29} + 3 q^{30} + 9 q^{31} - 18 q^{33} + 9 q^{34} - 18 q^{35} + 9 q^{36} - 24 q^{39} - 6 q^{41} + 12 q^{42} + 24 q^{43} + 51 q^{45} + 45 q^{47} - 6 q^{48} - 12 q^{49} + 6 q^{50} - 51 q^{51} + 6 q^{52} - 15 q^{53} + 27 q^{54} + 72 q^{55} - 3 q^{56} - 63 q^{57} + 3 q^{58} - 30 q^{59} - 3 q^{60} + 9 q^{61} - 24 q^{62} - 39 q^{63} - 36 q^{64} + 9 q^{65} - 6 q^{67} + 9 q^{68} - 21 q^{69} - 33 q^{70} + 12 q^{71} - 12 q^{72} + 132 q^{73} - 18 q^{74} - 30 q^{75} - 33 q^{77} + 30 q^{78} - 9 q^{79} - 6 q^{80} + 36 q^{81} - 33 q^{82} - 18 q^{83} + 15 q^{84} + 21 q^{85} - 12 q^{86} - 39 q^{87} - 6 q^{88} - 36 q^{89} + 69 q^{90} + 39 q^{91} + 30 q^{92} - 66 q^{93} - 9 q^{94} - 33 q^{95} - 48 q^{97} - 12 q^{98} - 54 q^{99}+O(q^{100}) $ 72 * q + 3 * q^6 + 6 * q^7 - 36 * q^8 + 24 * q^9 - 6 * q^10 + 12 * q^11 - 12 * q^13 - 3 * q^14 - 6 * q^15 - 12 * q^17 - 18 * q^19 - 30 * q^21 - 6 * q^22 + 30 * q^23 + 6 * q^25 - 18 * q^26 - 6 * q^27 + 3 * q^29 + 3 * q^30 + 9 * q^31 - 18 * q^33 + 9 * q^34 - 18 * q^35 + 9 * q^36 - 24 * q^39 - 6 * q^41 + 12 * q^42 + 24 * q^43 + 51 * q^45 + 45 * q^47 - 6 * q^48 - 12 * q^49 + 6 * q^50 - 51 * q^51 + 6 * q^52 - 15 * q^53 + 27 * q^54 + 72 * q^55 - 3 * q^56 - 63 * q^57 + 3 * q^58 - 30 * q^59 - 3 * q^60 + 9 * q^61 - 24 * q^62 - 39 * q^63 - 36 * q^64 + 9 * q^65 - 6 * q^67 + 9 * q^68 - 21 * q^69 - 33 * q^70 + 12 * q^71 - 12 * q^72 + 132 * q^73 - 18 * q^74 - 30 * q^75 - 33 * q^77 + 30 * q^78 - 9 * q^79 - 6 * q^80 + 36 * q^81 - 33 * q^82 - 18 * q^83 + 15 * q^84 + 21 * q^85 - 12 * q^86 - 39 * q^87 - 6 * q^88 - 36 * q^89 + 69 * q^90 + 39 * q^91 + 30 * q^92 - 66 * q^93 - 9 * q^94 - 33 * q^95 - 48 * q^97 - 12 * q^98 - 54 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.766044	−	0.642788i	0.541675	−	0.454519i
$2$	0.766044	−	0.642788i	0.541675	−	0.454519i
$3$	−1.42742	+	0.981051i	−0.824124	+	0.566410i
$3$	−1.42742	+	0.981051i	−0.824124	+	0.566410i
$4$	0.173648	−	0.984808i	0.0868241	−	0.492404i
$5$	0.343656	−	1.94897i	0.153688	−	0.871606i	−0.806288	−	0.591523i	$-0.798527\pi$
$5$	0.343656	−	1.94897i	0.153688	−	0.871606i	0.959976	−	0.280083i	$-0.0903621\pi$
$6$	−0.462863	+	1.66906i	−0.188963	+	0.681390i
$7$	1.84248	+	1.89876i	0.696391	+	0.717662i
$7$	1.84248	+	1.89876i	0.696391	+	0.717662i
$8$	−0.500000	−	0.866025i	−0.176777	−	0.306186i
$9$	1.07508	−	2.80075i	0.358360	−	0.933584i
$10$	−0.989519	−	1.71390i	−0.312913	−	0.541982i
$11$	0.568823	+	3.22596i	0.171507	+	0.972663i	0.942099	+	0.335335i	$0.108849\pi$
$11$	0.568823	+	3.22596i	0.171507	+	0.972663i	−0.770592	+	0.637328i	$0.780040\pi$
$12$	0.718277	+	1.57610i	0.207349	+	0.454980i
$13$	1.17085	−	6.64020i	0.324734	−	1.84166i	−0.186803	−	0.982397i	$-0.559813\pi$
$13$	1.17085	−	6.64020i	0.324734	−	1.84166i	0.511537	−	0.859261i	$-0.329076\pi$
$14$	2.63192	+	0.270209i	0.703409	+	0.0722165i
$15$	1.42150	+	3.11915i	0.367029	+	0.805362i
$16$	−0.939693	−	0.342020i	−0.234923	−	0.0855050i
$17$	0.298584	+	0.517162i	0.0724172	+	0.125430i	0.899960	−	0.435972i	$-0.143595\pi$
$17$	0.298584	+	0.517162i	0.0724172	+	0.125430i	−0.827543	+	0.561402i	$0.810262\pi$
$18$	−0.976729	−	2.83655i	−0.230217	−	0.668581i
$19$	4.15869	−	7.20307i	0.954070	−	1.65250i	0.217586	−	0.976041i	$-0.430182\pi$
$19$	4.15869	−	7.20307i	0.954070	−	1.65250i	0.736483	−	0.676456i	$-0.236485\pi$
$20$	−1.85969	−	0.676871i	−0.415839	−	0.151353i
$21$	−4.49277	−	0.902766i	−0.980404	−	0.197000i
$22$	2.50935	+	2.10559i	0.534995	+	0.448914i
$23$	0.380241	+	0.319060i	0.0792857	+	0.0665286i	0.681569	−	0.731754i	$-0.261298\pi$
$23$	0.380241	+	0.319060i	0.0792857	+	0.0665286i	−0.602283	+	0.798282i	$0.705742\pi$
$24$	1.56333	+	0.745660i	0.319113	+	0.152207i
$25$	1.01807	+	0.370549i	0.203615	+	0.0741097i
$26$	−3.37132	−	5.83929i	−0.661169	−	1.14518i
$27$	1.21308	+	5.05257i	0.233458	+	0.972367i
$28$	2.18985	−	1.48477i	0.413843	−	0.280595i
$29$	0.221437	+	1.25583i	0.0411198	+	0.233202i	0.998441	−	0.0558258i	$-0.0177792\pi$
$29$	0.221437	+	1.25583i	0.0411198	+	0.233202i	−0.957321	+	0.289028i	$0.906668\pi$
$30$	3.09388	+	1.47569i	0.564863	+	0.269423i
$31$	−0.261547	+	1.48331i	−0.0469753	+	0.266410i	−0.999245	−	0.0388474i	$-0.987631\pi$
$31$	−0.261547	+	1.48331i	−0.0469753	+	0.266410i	0.952270	+	0.305257i	$0.0987425\pi$
$32$	−0.939693	+	0.342020i	−0.166116	+	0.0604612i
$33$	−3.97678	−	4.04677i	−0.692269	−	0.704452i
$34$	0.561154	+	0.204243i	0.0962371	+	0.0350274i
$35$	4.33380	−	2.93842i	0.732546	−	0.496683i
$36$	−2.57152	−	1.54509i	−0.428586	−	0.257515i
$37$	−0.542374			−0.0891657			−0.0445828	−	0.999006i	$-0.514196\pi$
$37$	−0.542374			−0.0891657			−0.0445828	+	0.999006i	$0.514196\pi$
$38$	−1.44430	−	8.19103i	−0.234296	−	1.32876i
$39$	4.84307	+	10.6270i	0.775512	+	1.70169i
$40$	−1.85969	+	0.676871i	−0.294042	+	0.107023i
$41$	0.421633	−	2.39120i	0.0658480	−	0.373442i	−0.934020	−	0.357220i	$-0.883725\pi$
$41$	0.421633	−	2.39120i	0.0658480	−	0.373442i	0.999868	−	0.0162228i	$-0.00516412\pi$
$42$	−4.02195	+	2.19634i	−0.620601	+	0.338903i
$43$	−2.94820	+	2.47384i	−0.449597	+	0.377256i	−0.839286	−	0.543690i	$-0.817027\pi$
$43$	−2.94820	+	2.47384i	−0.449597	+	0.377256i	0.389689	+	0.920946i	$0.372582\pi$
$44$	3.27572			0.493834
$45$	−5.08912	−	3.05779i	−0.758642	−	0.455829i
$46$	0.496369			0.0731856
$47$	−0.157691	−	0.894312i	−0.0230016	−	0.130449i	0.971145	−	0.238491i	$-0.0766528\pi$
$47$	−0.157691	−	0.894312i	−0.0230016	−	0.130449i	−0.994146	+	0.108043i	$0.965542\pi$
$48$	1.67688	−	0.433678i	0.242037	−	0.0625960i
$49$	−0.210549	+	6.99683i	−0.0300784	+	0.999548i
$50$	1.01807	−	0.370549i	0.143977	−	0.0524035i
$51$	−0.933568	−	0.445284i	−0.130726	−	0.0623522i
$52$	−6.33600	−	2.30612i	−0.878645	−	0.319801i
$53$	−5.09597	+	8.82648i	−0.699985	+	1.21241i	0.268486	+	0.963284i	$0.413477\pi$
$53$	−5.09597	+	8.82648i	−0.699985	+	1.21241i	−0.968471	+	0.249127i	$0.919856\pi$
$54$	4.17700	+	3.09074i	0.568418	+	0.420596i
$55$	6.48278			0.874138
$56$	0.723132	−	2.54501i	0.0966326	−	0.340091i
$57$	1.13035	+	14.3617i	0.149719	+	1.90226i
$58$	0.976863	+	0.819685i	0.128268	+	0.107630i
$59$	−12.6532	+	4.60539i	−1.64731	+	0.599570i	−0.988294	−	0.152562i	$-0.951248\pi$
$59$	−12.6532	+	4.60539i	−1.64731	+	0.599570i	−0.659012	+	0.752132i	$0.729025\pi$
$60$	3.31861	−	0.858265i	0.428430	−	0.110802i
$61$	1.27613	+	7.23729i	0.163392	+	0.926639i	0.950707	+	0.310090i	$0.100359\pi$
$61$	1.27613	+	7.23729i	0.163392	+	0.926639i	−0.787316	+	0.616550i	$0.788530\pi$
$62$	0.753095	+	1.30440i	0.0956432	+	0.165659i
$63$	7.29875	−	3.11901i	0.919556	−	0.392958i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	−12.5392	−	4.56389i	−1.55529	−	0.566081i
$66$	−5.64760	−	0.543778i	−0.695172	−	0.0669344i
$67$	−2.08879	−	1.75271i	−0.255187	−	0.214127i	0.506215	−	0.862407i	$-0.331044\pi$
$67$	−2.08879	−	1.75271i	−0.255187	−	0.214127i	−0.761402	+	0.648280i	$0.775489\pi$
$68$	0.561154	−	0.204243i	0.0680499	−	0.0247681i
$69$	−0.855779	−	0.0823984i	−0.103024	−	0.00991961i
$70$	1.43110	−	5.03667i	0.171050	−	0.601997i
$71$	−1.32437	+	2.29388i	−0.157174	+	0.272233i	−0.933848	−	0.357669i	$-0.883572\pi$
$71$	−1.32437	+	2.29388i	−0.157174	+	0.272233i	0.776675	+	0.629902i	$0.216905\pi$
$72$	−2.96306	+	0.469329i	−0.349200	+	0.0553109i
$73$	−1.35179			−0.158216			−0.0791078	−	0.996866i	$-0.525207\pi$
$73$	−1.35179			−0.158216			−0.0791078	+	0.996866i	$0.525207\pi$
$74$	−0.415482	+	0.348631i	−0.0482988	+	0.0405275i
$75$	−1.81675	+	0.469852i	−0.209780	+	0.0542538i
$76$	−6.37149	−	5.34631i	−0.730860	−	0.613264i
$77$	−5.07726	+	7.02381i	−0.578608	+	0.800438i
$78$	10.5409	+	5.02771i	1.19353	+	0.569276i
$79$	5.44325	−	4.56743i	0.612413	−	0.513876i	−0.282995	−	0.959121i	$-0.591328\pi$
$79$	5.44325	−	4.56743i	0.612413	−	0.513876i	0.895408	+	0.445246i	$0.146884\pi$
$80$	−0.989519	+	1.71390i	−0.110632	+	0.191619i
$81$	−6.68841	−	6.02206i	−0.743156	−	0.669118i
$82$	−1.21404	−	2.10278i	−0.134069	−	0.232214i
$83$	−1.31290	−	7.44583i	−0.144110	−	0.817286i	−0.968078	−	0.250650i	$-0.919356\pi$
$83$	−1.31290	−	7.44583i	−0.144110	−	0.817286i	0.823968	−	0.566636i	$-0.191755\pi$
$84$	−1.66921	+	4.26775i	−0.182126	+	0.465650i
$85$	1.11054	−	0.404205i	0.120455	−	0.0438422i
$86$	−0.668303	+	3.79014i	−0.0720650	+	0.408701i
$87$	−1.54812	−	1.57536i	−0.165976	−	0.168897i
$88$	2.50935	−	2.10559i	0.267498	−	0.224457i
$89$	−8.63183	+	14.9508i	−0.914973	+	1.58478i	−0.108031	+	0.994148i	$0.534455\pi$
$89$	−8.63183	+	14.9508i	−0.914973	+	1.58478i	−0.806942	+	0.590631i	$0.798879\pi$
$90$	−5.86401	+	0.928819i	−0.618121	+	0.0979061i
$91$	14.7654	−	10.0113i	1.54783	−	1.04947i
$92$	0.380241	−	0.319060i	0.0396428	−	0.0332643i
$93$	−1.08186	−	2.37390i	−0.112184	−	0.246162i
$94$	−0.695651	−	0.583721i	−0.0717509	−	0.0602062i
$95$	−12.6094	−	10.5806i	−1.29370	−	1.08554i
$96$	1.00580	−	1.41009i	0.102654	−	0.143917i
$97$	−6.38539	+	5.35798i	−0.648338	+	0.544020i	−0.906566	−	0.422064i	$-0.861306\pi$
$97$	−6.38539	+	5.35798i	−0.648338	+	0.544020i	0.258228	+	0.966084i	$0.416861\pi$
$98$	4.33619	+	5.49522i	0.438021	+	0.555101i
$99$	9.64663	+	1.87503i	0.969523	+	0.188448i
$100$	0.541706	−	0.938262i	0.0541706	−	0.0938262i
$101$	12.9695	−	10.8827i	1.29051	−	1.08287i	0.298810	−	0.954313i	$-0.403410\pi$
$101$	12.9695	−	10.8827i	1.29051	−	1.08287i	0.991702	−	0.128556i	$-0.0410342\pi$
$102$	−1.00138	+	0.258978i	−0.0991512	+	0.0256427i
$103$	−2.74718	+	15.5800i	−0.270688	+	1.53515i	0.481647	+	0.876365i	$0.340039\pi$
$103$	−2.74718	+	15.5800i	−0.270688	+	1.53515i	−0.752335	+	0.658781i	$0.771072\pi$
$104$	−6.33600	+	2.30612i	−0.621296	+	0.226133i
$105$	−3.30343	+	8.44604i	−0.322382	+	0.824250i
$106$	1.76981	+	10.0371i	0.171899	+	0.974890i
$107$	1.44677	+	2.50589i	0.139865	+	0.242253i	0.927445	−	0.373959i	$-0.122000\pi$
$107$	1.44677	+	2.50589i	0.139865	+	0.242253i	−0.787580	+	0.616212i	$0.788667\pi$
$108$	5.18646	−	0.317284i	0.499067	−	0.0305307i
$109$	9.97350	−	17.2746i	0.955288	−	1.65461i	0.221580	−	0.975142i	$-0.428878\pi$
$109$	9.97350	−	17.2746i	0.955288	−	1.65461i	0.733708	−	0.679465i	$-0.237788\pi$
$110$	4.96610	−	4.16705i	0.473499	−	0.397313i
$111$	0.774197	−	0.532096i	0.0734836	−	0.0505043i
$112$	−1.08195	−	2.41441i	−0.102235	−	0.228140i
$113$	5.52639	+	4.63719i	0.519879	+	0.436230i	0.864590	−	0.502479i	$-0.167578\pi$
$113$	5.52639	+	4.63719i	0.519879	+	0.436230i	−0.344710	+	0.938709i	$0.612023\pi$
$114$	10.0974	+	10.2751i	0.945712	+	0.962355i
$115$	0.752511	−	0.631431i	0.0701720	−	0.0588813i
$116$	1.27520			0.118400
$117$	−17.3388	−	10.4180i	−1.60297	−	0.963143i
$118$	−6.73263	+	11.6613i	−0.619789	+	1.07351i
$119$	−0.431831	+	1.51980i	−0.0395859	+	0.139320i
$120$	1.99052	−	2.79063i	0.181709	−	0.254748i
$121$	0.253373	−	0.0922203i	0.0230339	−	0.00838367i
$122$	5.62961	+	4.72380i	0.509681	+	0.427673i
$123$	1.74404	+	3.82690i	0.157255	+	0.345060i
$124$	1.41536	+	0.515148i	0.127103	+	0.0462616i
$125$	6.01965	−	10.4263i	0.538414	−	0.932560i
$126$	3.58631	−	7.08085i	0.319494	−	0.630812i
$127$	4.51749	+	7.82452i	0.400862	+	0.694314i	0.993830	−	0.110912i	$-0.0353772\pi$
$127$	4.51749	+	7.82452i	0.400862	+	0.694314i	−0.592968	+	0.805226i	$0.702044\pi$
$128$	0.173648	+	0.984808i	0.0153485	+	0.0870455i
$129$	1.78138	−	6.42355i	0.156842	−	0.565562i
$130$	−12.5392	+	4.56389i	−1.09976	+	0.400279i
$131$	10.6528	+	8.93879i	0.930743	+	0.780986i	0.975951	−	0.217992i	$-0.0699505\pi$
$131$	10.6528	+	8.93879i	0.930743	+	0.780986i	−0.0452078	+	0.998978i	$0.514395\pi$
$132$	−4.67585	+	3.21365i	−0.406980	+	0.279712i
$133$	21.3392	−	5.37515i	1.85034	−	0.466085i
$134$	−2.72673			−0.235553
$135$	10.2642	−	0.627917i	0.883401	−	0.0540425i
$136$	0.298584	−	0.517162i	0.0256033	−	0.0443463i
$137$	−10.5182	−	3.82831i	−0.898630	−	0.327075i	−0.148927	−	0.988848i	$-0.547582\pi$
$137$	−10.5182	−	3.82831i	−0.898630	−	0.327075i	−0.749704	+	0.661774i	$0.769804\pi$
$138$	−0.708529	+	0.486963i	−0.0603140	+	0.0414531i
$139$	4.89594	−	1.78198i	0.415268	−	0.151145i	−0.125932	−	0.992039i	$-0.540192\pi$
$139$	4.89594	−	1.78198i	0.415268	−	0.151145i	0.541200	+	0.840894i	$0.317970\pi$
$140$	−2.14122	−	4.77821i	−0.180966	−	0.403832i
$141$	1.10246	+	1.12186i	0.0928437	+	0.0944776i
$142$	0.459949	+	2.60850i	0.0385981	+	0.218900i
$143$	22.0870			1.84701
$144$	−1.96816	+	2.26415i	−0.164013	+	0.188679i
$145$	2.52368			0.209580
$146$	−1.03553	+	0.868917i	−0.0857015	+	0.0719121i
$147$	−6.56370	−	10.1940i	−0.541365	−	0.840788i
$148$	−0.0941822	+	0.534134i	−0.00774173	+	0.0439055i
$149$	10.8595	−	3.95254i	0.889647	−	0.323805i	0.143550	−	0.989643i	$-0.454148\pi$
$149$	10.8595	−	3.95254i	0.889647	−	0.323805i	0.746096	+	0.665838i	$0.231926\pi$
$150$	−1.08970	+	1.52771i	−0.0889734	+	0.124737i
$151$	2.86385	+	16.2417i	0.233057	+	1.32173i	0.846668	+	0.532122i	$0.178605\pi$
$151$	2.86385	+	16.2417i	0.233057	+	1.32173i	−0.613611	+	0.789609i	$0.710284\pi$
$152$	−8.31739			−0.674629
$153$	1.76944	−	0.280268i	0.143051	−	0.0226583i
$154$	0.625412	+	8.64416i	0.0503971	+	0.696566i
$155$	2.80104	+	1.01950i	0.224985	+	0.0818879i
$156$	11.3066	−	2.92413i	0.905251	−	0.234118i
$157$	−13.0535	+	4.75108i	−1.04178	+	0.379178i	−0.805555	−	0.592520i	$-0.798133\pi$
$157$	−13.0535	+	4.75108i	−1.04178	+	0.379178i	−0.236226	+	0.971698i	$0.575911\pi$
$158$	1.23388	−	6.99770i	0.0981625	−	0.556707i
$159$	−1.38511	−	17.5985i	−0.109846	−	1.39565i
$160$	0.343656	+	1.94897i	0.0271684	+	0.154080i
$161$	0.0947684	+	1.30985i	0.00746880	+	0.103230i
$162$	−8.99452	−	0.313941i	−0.706676	−	0.0246655i
$163$	−6.51673	−	11.2873i	−0.510430	−	0.884091i	−0.999927	−	0.0120856i	$-0.996153\pi$
$163$	−6.51673	−	11.2873i	−0.510430	−	0.884091i	0.489497	−	0.872005i	$-0.337180\pi$
$164$	−2.28166	−	0.830455i	−0.178167	−	0.0648476i
$165$	−9.25368	+	6.35993i	−0.720398	+	0.495120i
$166$	−5.79183	−	4.85992i	−0.449533	−	0.377203i
$167$	−17.4447	−	14.6378i	−1.34991	−	1.13271i	−0.978959	−	0.204057i	$-0.934587\pi$
$167$	−17.4447	−	14.6378i	−1.34991	−	1.13271i	−0.370952	−	0.928652i	$-0.620968\pi$
$168$	1.46457	+	4.34224i	0.112994	+	0.335011i
$169$	−30.5053	−	11.1030i	−2.34656	−	0.854079i
$170$	0.590908	−	1.02348i	0.0453206	−	0.0784976i
$171$	−15.7031	−	19.3913i	−1.20084	−	1.48289i
$172$	1.92430	+	3.33299i	0.146727	+	0.254138i
$173$	−13.2652	−	4.82813i	−1.00853	−	0.367076i	−0.215664	−	0.976468i	$-0.569192\pi$
$173$	−13.2652	−	4.82813i	−1.00853	−	0.367076i	−0.792869	+	0.609392i	$0.791414\pi$
$174$	−2.19855	−	0.211687i	−0.166672	−	0.0160479i
$175$	1.17220	+	2.61580i	0.0886098	+	0.197736i
$176$	0.568823	−	3.22596i	0.0428767	−	0.243166i
$177$	13.5434	−	18.9873i	1.01798	−	1.42717i
$178$	2.99780	+	17.0014i	0.224695	+	1.27431i
$179$	−0.00802956	−	0.0139076i	−0.000600158	−	0.00103950i	0.865725	−	0.500520i	$-0.166858\pi$
$179$	−0.00802956	−	0.0139076i	−0.000600158	−	0.00103950i	−0.866325	+	0.499480i	$0.833524\pi$
$180$	−3.89506	+	4.48083i	−0.290320	+	0.333981i
$181$	−1.97514	−	3.42105i	−0.146811	−	0.254285i	0.783236	−	0.621725i	$-0.213568\pi$
$181$	−1.97514	−	3.42105i	−0.146811	−	0.254285i	−0.930047	+	0.367440i	$0.880234\pi$
$182$	4.87581	−	17.1601i	0.361419	−	1.27199i
$183$	−8.92172	−	9.07873i	−0.659512	−	0.671119i
$184$	0.0861936	−	0.488828i	0.00635428	−	0.0360369i
$185$	−0.186390	+	1.05707i	−0.0137037	+	0.0777174i
$186$	−2.35467	−	1.12311i	−0.172653	−	0.0823502i
$187$	−1.49850	+	1.25739i	−0.109581	+	0.0919496i
$188$	−0.908108			−0.0662306
$189$	−7.35851	+	11.6126i	−0.535253	+	0.844692i
$190$	−16.4604			−1.19416
$191$	−13.6974	+	11.4935i	−0.991110	+	0.831640i	−0.985728	−	0.168345i	$-0.946158\pi$
$191$	−13.6974	+	11.4935i	−0.991110	+	0.831640i	−0.00538196	+	0.999986i	$0.501713\pi$
$192$	−0.135903	−	1.72671i	−0.00980792	−	0.124615i
$193$	0.278012	−	1.57668i	0.0200117	−	0.113492i	−0.973166	−	0.230106i	$-0.926093\pi$
$193$	0.278012	−	1.57668i	0.0200117	−	0.113492i	0.993177	+	0.116614i	$0.0372039\pi$
$194$	−1.44745	+	8.20889i	−0.103921	+	0.589364i
$195$	22.3761	−	5.78696i	1.60239	−	0.414413i
$196$	6.85397	+	1.42234i	0.489570	+	0.101596i
$197$	9.50079	+	16.4558i	0.676903	+	1.17243i	0.975909	+	0.218179i	$0.0700118\pi$
$197$	9.50079	+	16.4558i	0.676903	+	1.17243i	−0.299006	+	0.954251i	$0.596655\pi$
$198$	8.59500	−	4.76438i	0.610820	−	0.338590i
$199$	4.16219	+	7.20912i	0.295050	+	0.511041i	0.974996	−	0.222220i	$-0.0713305\pi$
$199$	4.16219	+	7.20912i	0.295050	+	0.511041i	−0.679947	+	0.733261i	$0.737997\pi$
$200$	−0.188132	−	1.06695i	−0.0133030	−	0.0754449i
$201$	4.70109	+	0.452643i	0.331589	+	0.0319270i
$202$	2.93994	−	16.6733i	0.206854	−	1.17313i
$203$	−1.97652	+	2.73429i	−0.138725	+	0.191910i
$204$	−0.600632	+	0.842062i	−0.0420526	+	0.0589561i
$205$	−4.51548	−	1.64350i	−0.315375	−	0.114787i
$206$	7.91019	+	13.7008i	0.551129	+	0.954583i
$207$	1.30240	−	0.721945i	0.0905228	−	0.0501786i
$208$	−3.37132	+	5.83929i	−0.233759	+	0.404882i
$209$	25.6024	+	9.31849i	1.77095	+	0.644574i
$210$	2.89844	+	8.59345i	0.200011	+	0.593005i
$211$	3.59633	+	3.01768i	0.247581	+	0.207745i	0.758130	−	0.652103i	$-0.226113\pi$
$211$	3.59633	+	3.01768i	0.247581	+	0.207745i	−0.510549	+	0.859849i	$0.670558\pi$
$212$	7.80748	+	6.55125i	0.536220	+	0.449942i
$213$	−0.359971	−	4.57361i	−0.0246648	−	0.313379i
$214$	2.71905	+	0.989652i	0.185870	+	0.0676512i
$215$	3.80827	+	6.59611i	0.259722	+	0.449851i
$216$	3.76911	−	3.57684i	0.256455	−	0.243373i
$217$	−3.29834	+	2.23635i	−0.223906	+	0.151813i
$218$	−3.46376	−	19.6440i	−0.234595	−	1.33046i
$219$	1.92958	−	1.32618i	0.130389	−	0.0896149i
$220$	1.12572	−	6.38429i	0.0758962	−	0.430429i
$221$	3.78365	−	1.37714i	0.254516	−	0.0926363i
$222$	0.251045	−	0.905254i	0.0168490	−	0.0607567i
$223$	1.46317	+	0.532550i	0.0979810	+	0.0356622i	0.390546	−	0.920584i	$-0.372286\pi$
$223$	1.46317	+	0.532550i	0.0979810	+	0.0356622i	−0.292565	+	0.956246i	$0.594509\pi$
$224$	−2.38078	−	1.15408i	−0.159072	−	0.0771104i
$225$	2.13233	−	2.45300i	0.142155	−	0.163533i
$226$	7.21419			0.479881
$227$	0.778222	+	4.41352i	0.0516524	+	0.292935i	0.999681	−	0.0252492i	$-0.00803792\pi$
$227$	0.778222	+	4.41352i	0.0516524	+	0.292935i	−0.948029	+	0.318185i	$0.896927\pi$
$228$	14.3398	+	1.38071i	0.949678	+	0.0914394i
$229$	17.3045	−	6.29834i	1.14352	−	0.416206i	0.300335	−	0.953834i	$-0.402902\pi$
$229$	17.3045	−	6.29834i	1.14352	−	0.416206i	0.843182	+	0.537628i	$0.180679\pi$
$230$	0.170580	−	0.967409i	0.0112477	−	0.0637891i
$231$	0.356691	−	15.0070i	0.0234686	−	0.987389i
$232$	0.976863	−	0.819685i	0.0641342	−	0.0538150i
$233$	10.4132			0.682190			0.341095	−	0.940029i	$-0.389202\pi$
$233$	10.4132			0.682190			0.341095	+	0.940029i	$0.389202\pi$
$234$	−19.9788	+	3.16451i	−1.30606	+	0.206871i
$235$	−1.79718			−0.117235
$236$	2.33822	+	13.2607i	0.152205	+	0.863197i
$237$	−3.28895	+	11.8598i	−0.213640	+	0.770374i
$238$	0.646105	+	1.44181i	0.0418808	+	0.0934585i
$239$	−9.03426	+	3.28820i	−0.584378	+	0.212696i	−0.617255	−	0.786763i	$-0.711755\pi$
$239$	−9.03426	+	3.28820i	−0.584378	+	0.212696i	0.0328769	+	0.999459i	$0.489533\pi$
$240$	−0.268956	−	3.41723i	−0.0173610	−	0.220581i
$241$	−26.8336	−	9.76662i	−1.72850	−	0.629123i	−0.729979	−	0.683469i	$-0.760470\pi$
$241$	−26.8336	−	9.76662i	−1.72850	−	0.629123i	−0.998522	+	0.0543459i	$0.982693\pi$
$242$	0.134817	−	0.233510i	0.00866637	−	0.0150106i
$243$	15.4551	+	2.03437i	0.991448	+	0.130505i
$244$	7.34893			0.470467
$245$	13.5643	+	2.81486i	0.866589	+	0.179835i
$246$	3.79589	+	1.81053i	0.242017	+	0.115435i
$247$	−42.9606	−	36.0482i	−2.73352	−	2.29369i
$248$	1.41536	−	0.515148i	0.0898752	−	0.0327119i
$249$	9.17880	+	9.34034i	0.581683	+	0.591920i
$250$	−2.09060	−	11.8564i	−0.132221	−	0.749864i
$251$	−3.73667	−	6.47211i	−0.235857	−	0.408516i	0.723665	−	0.690152i	$-0.242456\pi$
$251$	−3.73667	−	6.47211i	−0.235857	−	0.408516i	−0.959521	+	0.281636i	$0.909123\pi$
$252$	−1.80421	−	7.72948i	−0.113654	−	0.486911i
$253$	−0.812984	+	1.40813i	−0.0511119	+	0.0885284i
$254$	8.49010	+	3.09015i	0.532717	+	0.193893i
$255$	−1.18867	+	1.66647i	−0.0744375	+	0.104359i
$256$	0.766044	+	0.642788i	0.0478778	+	0.0401742i
$257$	−26.1959	+	9.53453i	−1.63406	+	0.594748i	−0.985985	−	0.166832i	$-0.946646\pi$
$257$	−26.1959	+	9.53453i	−1.63406	+	0.594748i	−0.648071	+	0.761580i	$0.724424\pi$
$258$	−2.76436	−	6.06577i	−0.172102	−	0.377638i
$259$	−0.999312	−	1.02984i	−0.0620942	−	0.0639909i
$260$	−6.67196	+	11.5562i	−0.413777	+	0.716683i
$261$	3.75533	+	0.729929i	0.232449	+	0.0451815i
$262$	13.9063			0.859134
$263$	9.37802	−	7.86909i	0.578273	−	0.485229i	−0.306106	−	0.951997i	$-0.599026\pi$
$263$	9.37802	−	7.86909i	0.578273	−	0.485229i	0.884380	+	0.466768i	$0.154582\pi$
$264$	−1.51621	+	5.46738i	−0.0933164	+	0.336494i
$265$	15.4513	+	12.9652i	0.949165	+	0.796444i
$266$	12.8917	−	17.8342i	0.790439	−	1.09348i
$267$	−2.34618	−	29.8094i	−0.143584	−	1.82430i
$268$	−2.08879	+	1.75271i	−0.127593	+	0.107064i
$269$	11.6402	−	20.1614i	0.709713	−	1.22926i	−0.255250	−	0.966875i	$-0.582158\pi$
$269$	11.6402	−	20.1614i	0.709713	−	1.22926i	0.964963	−	0.262384i	$-0.0845088\pi$
$270$	7.45921	−	7.07871i	0.453953	−	0.430796i
$271$	10.0745	+	17.4496i	0.611985	+	1.05999i	0.990905	+	0.134560i	$0.0429621\pi$
$271$	10.0745	+	17.4496i	0.611985	+	1.05999i	−0.378920	+	0.925429i	$0.623705\pi$
$272$	−0.103697	−	0.588095i	−0.00628756	−	0.0356585i
$273$	−11.2549	+	28.7759i	−0.681177	+	1.74160i
$274$	−10.5182	+	3.82831i	−0.635428	+	0.231277i
$275$	−0.616270	+	3.49504i	−0.0371625	+	0.210759i
$276$	−0.229751	+	0.828469i	−0.0138294	+	0.0498680i
$277$	−7.84259	+	6.58072i	−0.471216	+	0.395397i	−0.847238	−	0.531214i	$-0.821736\pi$
$277$	−7.84259	+	6.58072i	−0.471216	+	0.395397i	0.376022	+	0.926611i	$0.377292\pi$
$278$	2.60507	−	4.51212i	0.156242	−	0.270619i
$279$	3.87319	+	2.32720i	0.231882	+	0.139326i
$280$	−4.71164	−	2.28397i	−0.281575	−	0.136493i
$281$	13.9814	−	11.7318i	0.834061	−	0.699860i	−0.122158	−	0.992511i	$-0.538982\pi$
$281$	13.9814	−	11.7318i	0.834061	−	0.699860i	0.956220	+	0.292650i	$0.0945372\pi$
$282$	1.56565	+	0.150748i	0.0932330	+	0.00897691i
$283$	5.95618	+	4.99782i	0.354058	+	0.297090i	0.802417	−	0.596764i	$-0.203547\pi$
$283$	5.95618	+	4.99782i	0.354058	+	0.297090i	−0.448359	+	0.893853i	$0.647991\pi$
$284$	2.02905	+	1.70258i	0.120402	+	0.101029i
$285$	28.3790	+	2.73247i	1.68103	+	0.161857i
$286$	16.9196	−	14.1972i	1.00048	−	0.839501i
$287$	5.31715	−	3.60515i	0.313862	−	0.212805i
$288$	−0.0523315	+	2.99954i	−0.00308366	+	0.176750i
$289$	8.32170	−	14.4136i	0.489512	−	0.847859i
$290$	1.93325	−	1.62219i	0.113524	−	0.0952581i
$291$	3.85821	−	13.9125i	0.226172	−	0.815565i
$292$	−0.234737	+	1.33126i	−0.0137369	+	0.0779060i
$293$	−15.8822	+	5.78065i	−0.927849	+	0.337709i	−0.761357	−	0.648333i	$-0.775466\pi$
$293$	−15.8822	+	5.78065i	−0.927849	+	0.337709i	−0.166492	+	0.986043i	$0.553244\pi$
$294$	−11.5807	−	3.59000i	−0.675398	−	0.209373i
$295$	4.62742	+	26.2434i	0.269419	+	1.52795i
$296$	0.271187	+	0.469709i	0.0157624	+	0.0273013i
$297$	−15.6093	+	6.78737i	−0.905746	+	0.393843i
$298$	5.77823	−	10.0082i	0.334724	−	0.579759i
$299$	2.56382	−	2.15130i	0.148270	−	0.124413i
$300$	0.147238	+	1.87074i	0.00850081	+	0.108007i
$301$	−10.1292	−	1.03993i	−0.583838	−	0.0599405i
$302$	12.6338	+	10.6010i	0.726994	+	0.610020i
$303$	−7.83649	+	28.2579i	−0.450195	+	1.62338i
$304$	−6.37149	+	5.34631i	−0.365430	+	0.306632i
$305$	14.5438			0.832776
$306$	1.17532	−	1.35207i	0.0671886	−	0.0772929i
$307$	−9.92235	+	17.1860i	−0.566298	+	0.980858i	0.430629	+	0.902529i	$0.358292\pi$
$307$	−9.92235	+	17.1860i	−0.566298	+	0.980858i	−0.996928	+	0.0783287i	$0.975042\pi$
$308$	6.03545	+	6.21980i	0.343902	+	0.354406i
$309$	−11.3634	−	24.9344i	−0.646442	−	1.41847i
$310$	2.80104	−	1.01950i	0.159089	−	0.0579035i
$311$	17.6693	+	14.8263i	1.00194	+	0.840724i	0.987251	−	0.159168i	$-0.0508813\pi$
$311$	17.6693	+	14.8263i	1.00194	+	0.840724i	0.0146842	+	0.999892i	$0.495326\pi$
$312$	6.78174	−	9.50774i	0.383941	−	0.538270i
$313$	−7.28068	−	2.64995i	−0.411528	−	0.149784i	0.127956	−	0.991780i	$-0.459158\pi$
$313$	−7.28068	−	2.64995i	−0.411528	−	0.149784i	−0.539484	+	0.841996i	$0.681381\pi$
$314$	−6.94562	+	12.0302i	−0.391964	+	0.678901i
$315$	−3.57059	−	15.2969i	−0.201180	−	0.861884i
$316$	−3.55283	−	6.15368i	−0.199862	−	0.346171i
$317$	4.86439	+	27.5873i	0.273212	+	1.54946i	0.744586	+	0.667527i	$0.232647\pi$
$317$	4.86439	+	27.5873i	0.273212	+	1.54946i	−0.471374	+	0.881933i	$0.656242\pi$
$318$	−12.3732	−	12.5909i	−0.693853	−	0.706064i
$319$	−3.92530	+	1.42869i	−0.219774	+	0.0799914i
$320$	1.51603	+	1.27210i	0.0847487	+	0.0711126i
$321$	−4.52356	−	2.15760i	−0.252481	−	0.120426i
$322$	0.914549	+	0.942484i	0.0509658	+	0.0525226i
$323$	4.96687			0.276364
$324$	−7.09200	+	5.54107i	−0.394000	+	0.307837i
$325$	3.65252	−	6.32636i	0.202606	−	0.350923i
$326$	−12.2475	−	4.45771i	−0.678324	−	0.246890i
$327$	2.71085	+	34.4427i	0.149910	+	1.90469i
$328$	−2.28166	+	0.830455i	−0.125983	+	0.0458542i
$329$	1.40754	−	1.94717i	0.0776000	−	0.107351i
$330$	−3.00064	+	10.8201i	−0.165180	+	0.595629i
$331$	1.77095	+	10.0435i	0.0973400	+	0.552043i	0.994005	+	0.109333i	$0.0348715\pi$
$331$	1.77095	+	10.0435i	0.0973400	+	0.552043i	−0.896665	+	0.442709i	$0.854017\pi$
$332$	−7.56069			−0.414947
$333$	−0.583095	+	1.51905i	−0.0319534	+	0.0832436i
$334$	−22.7724			−1.24605
$335$	−4.13380	+	3.46867i	−0.225854	+	0.189514i
$336$	3.91306	+	2.38494i	0.213475	+	0.130109i
$337$	0.475096	−	2.69440i	0.0258801	−	0.146774i	−0.969130	−	0.246552i	$-0.920702\pi$
$337$	0.475096	−	2.69440i	0.0258801	−	0.146774i	0.995010	+	0.0997786i	$0.0318135\pi$
$338$	−30.5053	+	11.1030i	−1.65927	+	0.603925i
$339$	−12.4378	−	1.19757i	−0.675530	−	0.0650432i
$340$	−0.205220	−	1.16386i	−0.0111296	−	0.0631193i
$341$	−4.93386			−0.267184
$342$	−24.4938	−	4.76089i	−1.32447	−	0.257439i
$343$	−13.6732	+	12.4917i	−0.738284	+	0.674490i
$344$	3.61651	+	1.31630i	0.194989	+	0.0709702i
$345$	−0.454686	+	1.63957i	−0.0244795	+	0.0882716i
$346$	−13.2652	+	4.82813i	−0.713141	+	0.259562i
$347$	0.422470	−	2.39594i	0.0226794	−	0.128621i	−0.971366	−	0.237588i	$-0.923643\pi$
$347$	0.422470	−	2.39594i	0.0226794	−	0.128621i	0.994045	+	0.108967i	$0.0347543\pi$
$348$	−1.82026	+	1.25104i	−0.0975760	+	0.0670627i
$349$	−0.745200	−	4.22624i	−0.0398896	−	0.226225i	0.958345	−	0.285612i	$-0.0921968\pi$
$349$	−0.745200	−	4.22624i	−0.0398896	−	0.226225i	−0.998235	+	0.0593863i	$0.981086\pi$
$350$	2.57936	+	1.25035i	0.137873	+	0.0668338i
$351$	34.9704	−	2.13933i	1.86658	−	0.114189i
$352$	−1.63786	−	2.83686i	−0.0872983	−	0.151205i
$353$	20.4486	+	7.44269i	1.08837	+	0.396134i	0.823017	−	0.568017i	$-0.192289\pi$
$353$	20.4486	+	7.44269i	1.08837	+	0.396134i	0.265353	+	0.964151i	$0.414511\pi$
$354$	−1.82996	−	23.2506i	−0.0972614	−	1.23576i
$355$	4.01557	+	3.36946i	0.213124	+	0.178833i
$356$	13.2247	+	11.0969i	0.700910	+	0.588133i
$357$	−0.874592	−	2.59304i	−0.0462883	−	0.137238i
$358$	−0.0150906	−	0.00549254i	−0.000797565	−	0.000290290i
$359$	14.5206	−	25.1504i	0.766369	−	1.32739i	−0.173151	−	0.984895i	$-0.555395\pi$
$359$	14.5206	−	25.1504i	0.766369	−	1.32739i	0.939520	−	0.342495i	$-0.111272\pi$
$360$	−0.103566	+	5.93621i	−0.00545841	+	0.312866i
$361$	−25.0894	−	43.4562i	−1.32050	−	2.28717i
$362$	−3.71206	−	1.35108i	−0.195101	−	0.0710111i
$363$	−0.271198	+	0.380210i	−0.0142342	+	0.0199558i
$364$	−7.29519	−	16.2795i	−0.382372	−	0.853277i
$365$	−0.464553	+	2.63461i	−0.0243158	+	0.137902i
$366$	−12.6701	−	1.21994i	−0.662278	−	0.0637673i
$367$	3.74342	+	21.2300i	0.195405	+	1.10820i	0.911841	+	0.410543i	$0.134661\pi$
$367$	3.74342	+	21.2300i	0.195405	+	1.10820i	−0.716437	+	0.697652i	$0.754228\pi$
$368$	−0.248185	−	0.429868i	−0.0129375	−	0.0224084i
$369$	−6.24386	−	3.75162i	−0.325042	−	0.195301i
$370$	0.536689	+	0.929572i	0.0279011	+	0.0483262i
$371$	−26.1485	+	6.58659i	−1.35756	+	0.341959i
$372$	−2.52570	+	0.653202i	−0.130951	+	0.0338669i
$373$	0.155952	−	0.884448i	0.00807489	−	0.0457950i	−0.980504	−	0.196499i	$-0.937043\pi$
$373$	0.155952	−	0.884448i	0.00807489	−	0.0457950i	0.988579	+	0.150704i	$0.0481540\pi$
$374$	−0.339683	+	1.92644i	−0.0175646	+	0.0996137i
$375$	1.63617	+	20.7884i	0.0844915	+	1.07351i
$376$	−0.695651	+	0.583721i	−0.0358755	+	0.0301031i
$377$	8.59823			0.442831
$378$	1.82748	+	13.6257i	0.0939955	+	0.700832i
$379$	−24.5625			−1.26169			−0.630845	−	0.775909i	$-0.717291\pi$
$379$	−24.5625			−1.26169			−0.630845	+	0.775909i	$0.717291\pi$
$380$	−12.6094	+	10.5806i	−0.646849	+	0.542771i
$381$	−14.1246	−	6.73703i	−0.723627	−	0.345148i
$382$	−3.10495	+	17.6091i	−0.158863	+	0.900958i
$383$	−1.57542	+	8.93463i	−0.0805000	+	0.456538i	0.917737	+	0.397188i	$0.130014\pi$
$383$	−1.57542	+	8.93463i	−0.0805000	+	0.456538i	−0.998237	+	0.0593501i	$0.981097\pi$
$384$	−1.21402	−	1.23538i	−0.0619525	−	0.0630428i
$385$	11.9444	+	12.3092i	0.608742	+	0.627336i
$386$	−0.800503	−	1.38651i	−0.0407445	−	0.0705716i
$387$	3.75904	+	10.9168i	0.191083	+	0.554930i
$388$	4.16777	+	7.21878i	0.211586	+	0.366478i
$389$	5.43970	+	30.8501i	0.275804	+	1.56416i	0.736397	+	0.676550i	$0.236526\pi$
$389$	5.43970	+	30.8501i	0.275804	+	1.56416i	−0.460593	+	0.887611i	$0.652363\pi$
$390$	13.4213	−	18.8162i	0.679615	−	0.952794i
$391$	−0.0514720	+	0.291912i	−0.00260305	+	0.0147626i
$392$	6.16471	−	3.31608i	0.311365	−	0.167487i
$393$	−23.9755	−	2.30848i	−1.20941	−	0.116447i
$394$	17.8556	+	6.49892i	0.899554	+	0.327411i
$395$	−7.03118	−	12.1784i	−0.353777	−	0.612760i
$396$	3.52166	−	9.17448i	0.176970	−	0.461035i
$397$	−1.92238	+	3.32966i	−0.0964814	+	0.167111i	−0.910226	−	0.414112i	$-0.864092\pi$
$397$	−1.92238	+	3.32966i	−0.0964814	+	0.167111i	0.813745	+	0.581223i	$0.197425\pi$
$398$	7.82235	+	2.84710i	0.392099	+	0.142712i
$399$	−25.1867	+	28.6074i	−1.26091	+	1.43216i
$400$	−0.829942	−	0.696404i	−0.0414971	−	0.0348202i
$401$	7.36725	+	6.18186i	0.367903	+	0.308707i	0.807931	−	0.589277i	$-0.200587\pi$
$401$	7.36725	+	6.18186i	0.367903	+	0.308707i	−0.440028	+	0.897984i	$0.645032\pi$
$402$	3.89220	−	2.67506i	0.194125	−	0.133420i
$403$	9.54322	+	3.47345i	0.475382	+	0.173025i
$404$	−8.46523	−	14.6622i	−0.421161	−	0.729472i
$405$	−14.0353	+	10.9660i	−0.697421	+	0.544905i
$406$	0.243466	+	3.36508i	0.0120830	+	0.167006i
$407$	−0.308515	−	1.74968i	−0.0152925	−	0.0867282i
$408$	0.0811566	+	1.03114i	0.00401785	+	0.0510488i
$409$	−0.857938	+	4.86561i	−0.0424223	+	0.240589i	−0.998644	−	0.0520535i	$-0.983423\pi$
$409$	−0.857938	+	4.86561i	−0.0424223	+	0.240589i	0.956222	+	0.292642i	$0.0945345\pi$
$410$	−4.51548	+	1.64350i	−0.223004	+	0.0811667i
$411$	18.7697	−	4.85426i	0.925841	−	0.239443i
$412$	14.8663	+	5.41089i	0.732410	+	0.266575i
$413$	−32.0578	−	15.5400i	−1.57746	−	0.764674i
$414$	0.533636	−	1.39021i	0.0262268	−	0.0683249i
$415$	−14.9629			−0.734500
$416$	1.17085	+	6.64020i	0.0574054	+	0.325562i
$417$	−5.24037	+	7.34680i	−0.256622	+	0.359774i
$418$	25.6024	−	9.31849i	1.25225	−	0.455782i
$419$	4.41265	−	25.0254i	0.215572	−	1.22257i	−0.664339	−	0.747431i	$-0.731287\pi$
$419$	4.41265	−	25.0254i	0.215572	−	1.22257i	0.879911	−	0.475138i	$-0.157602\pi$
$420$	7.74409	+	4.71989i	0.377873	+	0.230307i
$421$	11.3843	−	9.55254i	0.554836	−	0.465562i	−0.321739	−	0.946828i	$-0.604267\pi$
$421$	11.3843	−	9.55254i	0.554836	−	0.465562i	0.876575	+	0.481266i	$0.159823\pi$
$422$	4.69467			0.228533
$423$	−2.67427	−	0.519803i	−0.130028	−	0.0252737i
$424$	10.1919			0.494964
$425$	0.112347	+	0.637149i	0.00544961	+	0.0309063i
$426$	−3.21561	−	3.27220i	−0.155797	−	0.158539i
$427$	−11.3906	+	15.7576i	−0.551230	+	0.762564i
$428$	2.71905	−	0.989652i	0.131430	−	0.0478366i
$429$	−31.5275	+	21.6685i	−1.52216	+	1.04616i
$430$	7.15720	+	2.60501i	0.345151	+	0.125625i
$431$	−4.89865	+	8.48471i	−0.235960	+	0.408694i	−0.959551	−	0.281534i	$-0.909157\pi$
$431$	−4.89865	+	8.48471i	−0.235960	+	0.408694i	0.723591	+	0.690228i	$0.242490\pi$
$432$	0.588155	−	5.16276i	0.0282976	−	0.248393i
$433$	27.3619			1.31493			0.657464	−	0.753486i	$-0.271629\pi$
$433$	27.3619			1.31493			0.657464	+	0.753486i	$0.271629\pi$
$434$	−1.08917	+	3.83327i	−0.0522820	+	0.184003i
$435$	−3.60236	+	2.47585i	−0.172720	+	0.118708i
$436$	−15.2803	−	12.8217i	−0.731793	−	0.614047i
$437$	3.87951	−	1.41203i	0.185582	−	0.0675465i
$438$	0.625696	−	2.25623i	0.0298969	−	0.107807i
$439$	−5.61740	−	31.8579i	−0.268104	−	1.52049i	−0.760049	−	0.649866i	$-0.774825\pi$
$439$	−5.61740	−	31.8579i	−0.268104	−	1.52049i	0.491945	−	0.870626i	$-0.336286\pi$
$440$	−3.24139	−	5.61425i	−0.154527	−	0.267649i
$441$	19.3700	+	8.11185i	0.922382	+	0.386278i
$442$	2.01324	−	3.48703i	0.0957601	−	0.165861i
$443$	−28.6959	−	10.4445i	−1.36338	−	0.496231i	−0.446285	−	0.894891i	$-0.647253\pi$
$443$	−28.6959	−	10.4445i	−1.36338	−	0.496231i	−0.917099	+	0.398660i	$0.869475\pi$
$444$	−0.389574	−	0.854833i	−0.0184884	−	0.0405686i
$445$	26.1722	+	21.9611i	1.24068	+	1.04106i
$446$	1.46317	−	0.532550i	0.0692830	−	0.0252170i
$447$	−11.6235	+	16.2957i	−0.549773	+	0.770760i
$448$	−2.56561	+	0.646255i	−0.121214	+	0.0305327i
$449$	−5.77134	+	9.99626i	−0.272366	+	0.471753i	−0.969467	−	0.245221i	$-0.921140\pi$
$449$	−5.77134	+	9.99626i	−0.272366	+	0.471753i	0.697101	+	0.716973i	$0.254473\pi$
$450$	0.0566966	−	3.24974i	0.00267270	−	0.153194i
$451$	7.95374			0.374527
$452$	5.52639	−	4.63719i	0.259940	−	0.218115i
$453$	−20.0219	−	20.3742i	−0.940709	−	0.957264i
$454$	3.43311	+	2.88072i	0.161124	+	0.135199i
$455$	−14.4375	−	32.2177i	−0.676838	−	1.51039i
$456$	11.8724	−	8.15977i	0.555978	−	0.382116i
$457$	−9.68142	+	8.12368i	−0.452878	+	0.380010i	−0.840503	−	0.541808i	$-0.817740\pi$
$457$	−9.68142	+	8.12368i	−0.452878	+	0.380010i	0.387625	+	0.921817i	$0.373296\pi$
$458$	9.20756	−	15.9480i	0.430241	−	0.745199i
$459$	−2.25079	+	2.13597i	−0.105058	+	0.0996988i
$460$	−0.491166	−	0.850725i	−0.0229008	−	0.0396653i
$461$	−3.47332	−	19.6982i	−0.161768	−	0.917434i	−0.952334	−	0.305057i	$-0.901324\pi$
$461$	−3.47332	−	19.6982i	−0.161768	−	0.917434i	0.790566	−	0.612377i	$-0.209787\pi$
$462$	−9.37308	−	11.7253i	−0.436075	−	0.545511i
$463$	12.0406	−	4.38242i	0.559574	−	0.203668i	−0.0467212	−	0.998908i	$-0.514877\pi$
$463$	12.0406	−	4.38242i	0.559574	−	0.203668i	0.606295	+	0.795240i	$0.292655\pi$
$464$	0.221437	−	1.25583i	0.0102799	−	0.0583005i
$465$	−4.99845	+	1.29271i	−0.231798	+	0.0599480i
$466$	7.97695	−	6.69346i	0.369525	−	0.310069i
$467$	13.8762	−	24.0342i	0.642112	−	1.11217i	−0.342849	−	0.939391i	$-0.611392\pi$
$467$	13.8762	−	24.0342i	0.642112	−	1.11217i	0.984961	−	0.172780i	$-0.0552748\pi$
$468$	−13.2706	+	15.2663i	−0.613432	+	0.705685i
$469$	−0.520596	−	7.19543i	−0.0240389	−	0.332254i
$470$	−1.37672	+	1.15520i	−0.0635033	+	0.0532856i
$471$	13.9718	−	19.5879i	0.643787	−	0.902565i
$472$	10.3150	+	8.65530i	0.474786	+	0.398392i
$473$	−9.65750	−	8.10360i	−0.444052	−	0.372604i
$474$	5.10382	+	11.1992i	0.234426	+	0.514396i
$475$	6.90294	−	5.79226i	0.316729	−	0.265767i
$476$	1.42172	+	0.689180i	0.0651645	+	0.0315885i
$477$	19.2422	+	23.7617i	0.881039	+	1.08797i
$478$	−4.80703	+	8.32602i	−0.219869	+	0.380823i
$479$	−10.9401	+	9.17986i	−0.499867	+	0.419438i	−0.857547	−	0.514406i	$-0.828012\pi$
$479$	−10.9401	+	9.17986i	−0.499867	+	0.419438i	0.357680	+	0.933844i	$0.383568\pi$
$480$	−2.40258	−	2.44486i	−0.109662	−	0.111592i
$481$	−0.635036	+	3.60147i	−0.0289551	+	0.164213i
$482$	−26.8336	+	9.76662i	−1.22224	+	0.444857i
$483$	−1.42030	−	1.77673i	−0.0646259	−	0.0808441i
$484$	−0.0468215	−	0.265538i	−0.00212825	−	0.0120699i
$485$	8.24816	+	14.2862i	0.374530	+	0.648705i
$486$	13.1470	−	8.37595i	0.596360	−	0.379941i
$487$	−18.8491	+	32.6476i	−0.854134	+	1.47940i	0.0233124	+	0.999728i	$0.492579\pi$
$487$	−18.8491	+	32.6476i	−0.854134	+	1.47940i	−0.877446	+	0.479675i	$0.840755\pi$
$488$	5.62961	−	4.72380i	0.254840	−	0.213836i
$489$	20.3756	+	9.71854i	0.921415	+	0.439488i
$490$	12.2002	−	6.56264i	0.551148	−	0.296470i
$491$	−9.35212	−	7.84736i	−0.422055	−	0.354146i	0.406889	−	0.913478i	$-0.366614\pi$
$491$	−9.35212	−	7.84736i	−0.422055	−	0.354146i	−0.828944	+	0.559331i	$0.811058\pi$
$492$	4.07161	−	1.05301i	0.183562	−	0.0474733i
$493$	−0.583351	+	0.489489i	−0.0262728	+	0.0220455i
$494$	−56.0811			−2.52321
$495$	6.96950	−	18.1566i	0.313256	−	0.816081i
$496$	0.753095	−	1.30440i	0.0338150	−	0.0585693i
$497$	−6.79563	+	1.71176i	−0.304826	+	0.0767830i
$498$	13.0352	+	1.25509i	0.584122	+	0.0562421i
$499$	−4.29316	+	1.56258i	−0.192188	+	0.0699508i	−0.436321	−	0.899791i	$-0.643719\pi$
$499$	−4.29316	+	1.56258i	−0.192188	+	0.0699508i	0.244133	+	0.969742i	$0.421497\pi$
$500$	−9.22264	−	7.73871i	−0.412449	−	0.346086i
$501$	39.2614	+	3.78028i	1.75407	+	0.168890i
$502$	−7.02265	−	2.55604i	−0.313436	−	0.114081i
$503$	−2.44425	+	4.23357i	−0.108984	+	0.188766i	−0.915359	−	0.402639i	$-0.868093\pi$
$503$	−2.44425	+	4.23357i	−0.108984	+	0.188766i	0.806375	+	0.591405i	$0.201426\pi$
$504$	−6.35052	−	4.76140i	−0.282874	−	0.212090i
$505$	−16.7530	−	29.0171i	−0.745499	−	1.29124i
$506$	0.282346	+	1.60127i	0.0125518	+	0.0711850i
$507$	54.4366	−	14.0785i	2.41762	−	0.625249i
$508$	8.49010	−	3.09015i	0.376687	−	0.137103i
$509$	4.68933	+	3.93481i	0.207851	+	0.174407i	0.740770	−	0.671758i	$-0.234461\pi$
$509$	4.68933	+	3.93481i	0.207851	+	0.174407i	−0.532920	+	0.846166i	$0.678905\pi$
$510$	0.160612	+	2.04066i	0.00711201	+	0.0903617i
$511$	−2.49065	−	2.56673i	−0.110180	−	0.113545i
$512$	1.00000			0.0441942
$513$	41.4388	+	12.2742i	1.82957	+	0.541917i
$514$	−13.9386	+	24.1423i	−0.614803	+	1.06487i
$515$	29.4209	+	10.7083i	1.29644	+	0.471866i
$516$	−6.01663	−	2.86975i	−0.264867	−	0.126334i
$517$	2.79531	−	1.01741i	0.122938	−	0.0447457i
$518$	−1.42748	−	0.146554i	−0.0627200	−	0.00643923i
$519$	23.6717	−	6.12202i	1.03907	−	0.268727i
$520$	2.31715	+	13.1412i	0.101614	+	0.576279i
$521$	17.2963			0.757763			0.378881	−	0.925445i	$-0.376309\pi$
$521$	17.2963			0.757763			0.378881	+	0.925445i	$0.376309\pi$
$522$	3.34594	−	1.85472i	0.146448	−	0.0811790i
$523$	34.1662			1.49398			0.746991	−	0.664834i	$-0.231498\pi$
$523$	34.1662			1.49398			0.746991	+	0.664834i	$0.231498\pi$
$524$	10.6528	−	8.93879i	0.465371	−	0.390493i
$525$	−4.23946	−	2.58387i	−0.185025	−	0.112770i
$526$	2.12582	−	12.0561i	0.0926903	−	0.525673i
$527$	−0.845205	+	0.307629i	−0.0368177	+	0.0134005i
$528$	2.35288	+	5.16286i	0.102396	+	0.224684i
$529$	−3.95112	−	22.4079i	−0.171788	−	0.974258i
$530$	20.1702			0.876139
$531$	−0.704657	+	40.3896i	−0.0305795	+	1.75276i
$532$	−1.58798	−	21.9484i	−0.0688478	−	0.951582i
$533$	−15.3844	−	5.59945i	−0.666370	−	0.242539i
$534$	−20.9584	−	21.3272i	−0.906957	−	0.922918i
$535$	5.38109	−	1.95856i	0.232645	−	0.0846758i
$536$	−0.473491	+	2.68530i	−0.0204517	+	0.115987i
$537$	0.0251057	+	0.0119747i	0.00108339	+	0.000516744i
$538$	−4.04259	−	22.9266i	−0.174288	−	0.988438i
$539$	−22.6913	+	3.30074i	−0.977382	+	0.142173i
$540$	1.16398	−	10.2173i	0.0500897	−	0.439682i
$541$	14.2140	+	24.6193i	0.611107	+	1.05847i	0.991054	+	0.133460i	$0.0426087\pi$
$541$	14.2140	+	24.6193i	0.611107	+	1.05847i	−0.379948	+	0.925008i	$0.624058\pi$
$542$	18.9340	+	6.89140i	0.813283	+	0.296011i
$543$	6.17559	+	2.94557i	0.265020	+	0.126407i
$544$	−0.457457	−	0.383852i	−0.0196133	−	0.0164575i
$545$	−30.2403	−	25.3746i	−1.29535	−	1.08693i
$546$	9.87504	+	29.2781i	0.422613	+	1.25299i
$547$	12.8925	+	4.69250i	0.551245	+	0.200637i	0.602599	−	0.798044i	$-0.294132\pi$
$547$	12.8925	+	4.69250i	0.551245	+	0.200637i	−0.0513547	+	0.998680i	$0.516354\pi$
$548$	−5.59662	+	9.69362i	−0.239076	+	0.414091i
$549$	21.6418	+	4.20654i	0.923648	+	0.179531i
$550$	1.77448	+	3.07349i	0.0756640	+	0.131054i
$551$	9.96672	+	3.62759i	0.424596	+	0.154540i
$552$	0.356530	+	0.782325i	0.0151749	+	0.0332980i
$553$	18.7015	+	1.92001i	0.795268	+	0.0816473i
$554$	−1.77777	+	10.0822i	−0.0755303	+	0.428353i
$555$	−0.770982	−	1.69175i	−0.0327264	−	0.0718106i
$556$	−0.904733	−	5.13100i	−0.0383692	−	0.217603i
$557$	−8.78728	−	15.2200i	−0.372329	−	0.644893i	0.617594	−	0.786497i	$-0.288107\pi$
$557$	−8.78728	−	15.2200i	−0.372329	−	0.644893i	−0.989923	+	0.141604i	$0.954774\pi$
$558$	4.46293	−	0.706899i	0.188931	−	0.0299254i
$559$	12.9749	+	22.4731i	0.548778	+	0.950512i
$560$	−5.07744	+	1.27896i	−0.214561	+	0.0540460i
$561$	0.905433	−	3.26494i	0.0382274	−	0.137846i
$562$	3.16933	−	17.9742i	0.133690	−	0.758194i
$563$	4.65361	−	26.3919i	0.196126	−	1.11229i	−0.714679	−	0.699452i	$-0.753427\pi$
$563$	4.65361	−	26.3919i	0.196126	−	1.11229i	0.910806	−	0.412835i	$-0.135461\pi$
$564$	1.29626	−	0.890900i	0.0545822	−	0.0375136i
$565$	10.9369	−	9.17718i	0.460120	−	0.386087i
$566$	7.77524			0.326818
$567$	−0.888819	−	23.7952i	−0.0373269	−	0.999303i
$568$	2.64874			0.111139
$569$	1.94865	−	1.63511i	0.0816917	−	0.0685475i	−0.601027	−	0.799228i	$-0.705242\pi$
$569$	1.94865	−	1.63511i	0.0816917	−	0.0685475i	0.682719	+	0.730681i	$0.260797\pi$
$570$	23.4960	−	16.1485i	0.984139	−	0.676386i
$571$	3.72221	−	21.1097i	0.155770	−	0.883414i	−0.802309	−	0.596909i	$-0.796395\pi$
$571$	3.72221	−	21.1097i	0.155770	−	0.883414i	0.958079	−	0.286505i	$-0.0924936\pi$
$572$	3.83537	−	21.7514i	0.160365	−	0.909474i
$573$	8.27632	−	29.8439i	0.345748	−	1.24675i
$574$	1.75583	−	6.17951i	0.0732868	−	0.257928i
$575$	0.268886	+	0.465724i	0.0112133	+	0.0194220i
$576$	1.88798	+	2.33142i	0.0786659	+	0.0971426i
$577$	3.93668	+	6.81854i	0.163886	+	0.283859i	0.936259	−	0.351310i	$-0.114264\pi$
$577$	3.93668	+	6.81854i	0.163886	+	0.283859i	−0.772373	+	0.635169i	$0.780930\pi$
$578$	−2.89009	−	16.3905i	−0.120212	−	0.681757i
$579$	1.14996	+	2.52334i	0.0477909	+	0.104866i
$580$	0.438232	−	2.48534i	0.0181966	−	0.103198i
$581$	11.7188	−	16.2117i	0.486179	−	0.672573i
$582$	−5.98722	−	13.1376i	−0.248178	−	0.544571i
$583$	−31.3726	−	11.4187i	−1.29932	−	0.472913i
$584$	0.675897	+	1.17069i	0.0279688	+	0.0484434i
$585$	−26.2629	+	30.2126i	−1.08584	+	1.24914i
$586$	−8.45075	+	14.6371i	−0.349097	+	0.604654i
$587$	−38.9778	−	14.1868i	−1.60879	−	0.585550i	−0.627586	−	0.778547i	$-0.715957\pi$
$587$	−38.9778	−	14.1868i	−1.60879	−	0.585550i	−0.981199	+	0.192997i	$0.938179\pi$
$588$	−11.1789	+	4.69382i	−0.461011	+	0.193570i
$589$	9.59667	+	8.05256i	0.395424	+	0.331800i
$590$	20.4137	+	17.1292i	0.840420	+	0.705196i
$591$	−29.7057	−	14.1687i	−1.22193	−	0.582823i
$592$	0.509665	+	0.185503i	0.0209471	+	0.00762412i
$593$	4.52774	+	7.84227i	0.185932	+	0.322043i	0.943890	−	0.330260i	$-0.107136\pi$
$593$	4.52774	+	7.84227i	0.185932	+	0.322043i	−0.757958	+	0.652303i	$0.773803\pi$
$594$	−7.59461	+	15.2329i	−0.311611	+	0.625014i
$595$	2.81364	+	1.36391i	0.115348	+	0.0559150i
$596$	−2.00676	−	11.3809i	−0.0822000	−	0.466180i
$597$	−13.0137	−	6.20716i	−0.532616	−	0.254042i
$598$	0.581172	−	3.29599i	0.0237659	−	0.134783i
$599$	25.9231	−	9.43522i	1.05919	−	0.385513i	0.247065	−	0.968999i	$-0.420534\pi$
$599$	25.9231	−	9.43522i	1.05919	−	0.385513i	0.812123	+	0.583486i	$0.198312\pi$
$600$	1.31528	+	1.33843i	0.0536960	+	0.0546410i
$601$	−24.5814	−	8.94690i	−1.00270	−	0.364952i	−0.212073	−	0.977254i	$-0.568021\pi$
$601$	−24.5814	−	8.94690i	−1.00270	−	0.364952i	−0.790624	+	0.612302i	$0.790244\pi$
$602$	−8.42788	+	5.71430i	−0.343495	+	0.232897i
$603$	−7.15451	+	3.96589i	−0.291354	+	0.161504i
$604$	16.4923			0.671060
$605$	−0.0926615	−	0.525509i	−0.00376722	−	0.0213650i
$606$	12.1608	+	26.6840i	0.493997	+	1.08397i
$607$	−10.2567	+	3.73312i	−0.416305	+	0.151523i	−0.541676	−	0.840587i	$-0.682210\pi$
$607$	−10.2567	+	3.73312i	−0.416305	+	0.151523i	0.125371	+	0.992110i	$0.459988\pi$
$608$	−1.44430	+	8.19103i	−0.0585740	+	0.332190i
$609$	0.138856	−	5.84207i	0.00562673	−	0.236733i
$610$	11.1412	−	9.34858i	0.451094	−	0.378513i
$611$	−6.12304			−0.247712
$612$	0.0312507	−	1.79123i	0.00126323	−	0.0724062i
$613$	−0.382093			−0.0154326			−0.00771630	−	0.999970i	$-0.502456\pi$
$613$	−0.382093			−0.0154326			−0.00771630	+	0.999970i	$0.502456\pi$
$614$	3.44600	+	19.5432i	0.139069	+	0.788700i
$615$	8.05786	−	2.08394i	0.324924	−	0.0840326i
$616$	8.62143	+	0.885131i	0.347367	+	0.0356630i
$617$	25.9351	−	9.43961i	1.04411	−	0.380024i	0.237672	−	0.971345i	$-0.423616\pi$
$617$	25.9351	−	9.43961i	1.04411	−	0.380024i	0.806436	+	0.591321i	$0.201393\pi$
$618$	−24.7324	−	11.7966i	−0.994884	−	0.474530i
$619$	−6.72202	−	2.44661i	−0.270181	−	0.0983377i	0.203377	−	0.979100i	$-0.434808\pi$
$619$	−6.72202	−	2.44661i	−0.270181	−	0.0983377i	−0.473558	+	0.880763i	$0.657030\pi$
$620$	1.49040	−	2.58145i	0.0598560	−	0.103674i
$621$	−1.15081	+	2.30824i	−0.0461803	+	0.0926264i
$622$	23.0657			0.924849
$623$	−44.2918	+	11.1567i	−1.77451	+	0.446985i
$624$	−0.916341	−	11.6426i	−0.0366830	−	0.466076i
$625$	−14.1022	−	11.8332i	−0.564089	−	0.473327i
$626$	−7.28068	+	2.64995i	−0.290994	+	0.105913i
$627$	−45.6873	+	11.8158i	−1.82458	+	0.471876i
$628$	2.41219	+	13.6802i	0.0962568	+	0.545899i
$629$	−0.161944	−	0.280495i	−0.00645713	−	0.0111841i
$630$	−12.5679	−	9.42299i	−0.500717	−	0.375421i
$631$	4.02933	−	6.97900i	0.160405	−	0.277830i	−0.774609	−	0.632440i	$-0.782053\pi$
$631$	4.02933	−	6.97900i	0.160405	−	0.277830i	0.935014	+	0.354611i	$0.115387\pi$
$632$	−6.67713	−	2.43028i	−0.265602	−	0.0966712i
$633$	−8.09398	−	0.779327i	−0.321707	−	0.0309754i
$634$	21.4591	+	18.0064i	0.852252	+	0.715124i
$635$	16.8022	−	6.11551i	0.666776	−	0.242687i
$636$	−17.5717	−	1.69189i	−0.696763	−	0.0670876i
$637$	46.2138	+	9.59029i	1.83106	+	0.379981i
$638$	−2.08861	+	3.61757i	−0.0826888	+	0.143221i
$639$	5.00077	+	6.17533i	0.197827	+	0.244292i
$640$	1.97904			0.0782283
$641$	14.7929	−	12.4127i	0.584283	−	0.490272i	−0.302067	−	0.953287i	$-0.597677\pi$
$641$	14.7929	−	12.4127i	0.584283	−	0.490272i	0.886351	+	0.463015i	$0.153232\pi$
$642$	−4.85213	+	1.25487i	−0.191498	+	0.0495257i
$643$	25.5593	+	21.4468i	1.00796	+	0.845780i	0.988067	−	0.154022i	$-0.0492228\pi$
$643$	25.5593	+	21.4468i	1.00796	+	0.845780i	0.0198936	+	0.999802i	$0.493667\pi$
$644$	1.30640	+	0.134124i	0.0514795	+	0.00528521i
$645$	−11.9071	−	5.67935i	−0.468843	−	0.223624i
$646$	3.80484	−	3.19264i	0.149700	−	0.125613i
$647$	−13.1461	+	22.7697i	−0.516827	+	0.895170i	0.482982	+	0.875630i	$0.339554\pi$
$647$	−13.1461	+	22.7697i	−0.516827	+	0.895170i	−0.999809	+	0.0195402i	$0.993780\pi$
$648$	−1.87105	+	8.80336i	−0.0735020	+	0.345829i
$649$	−22.0542	−	38.1990i	−0.865704	−	1.49944i
$650$	−1.26851	−	7.19407i	−0.0497550	−	0.282174i
$651$	2.51415	−	6.42805i	0.0985374	−	0.251935i
$652$	−12.2475	+	4.45771i	−0.479647	+	0.174577i
$653$	−2.34264	+	13.2858i	−0.0916748	+	0.519913i	0.904041	+	0.427446i	$0.140587\pi$
$653$	−2.34264	+	13.2858i	−0.0916748	+	0.519913i	−0.995716	+	0.0924676i	$0.970525\pi$
$654$	24.2160	+	24.6421i	0.946919	+	0.963584i
$655$	21.0824	−	17.6902i	0.823756	−	0.691213i
$656$	−1.21404	+	2.10278i	−0.0474004	+	0.0820999i
$657$	−1.45329	+	3.78604i	−0.0566981	+	0.147707i
$658$	−0.173379	−	2.39636i	−0.00675902	−	0.0934200i
$659$	9.39594	−	7.88413i	0.366014	−	0.307122i	−0.441168	−	0.897424i	$-0.645436\pi$
$659$	9.39594	−	7.88413i	0.366014	−	0.307122i	0.807182	+	0.590302i	$0.200991\pi$
$660$	4.65643	+	10.2175i	0.181251	+	0.397715i
$661$	12.6624	+	10.6250i	0.492510	+	0.413265i	0.854925	−	0.518752i	$-0.173603\pi$
$661$	12.6624	+	10.6250i	0.492510	+	0.413265i	−0.362415	+	0.932017i	$0.618048\pi$
$662$	7.81248	+	6.55545i	0.303641	+	0.254785i
$663$	−4.04984	+	5.67771i	−0.157283	+	0.220504i
$664$	−5.79183	+	4.85992i	−0.224767	+	0.188601i
$665$	−3.14268	−	43.4366i	−0.121868	−	1.68440i
$666$	0.529752	+	1.53847i	0.0205275	+	0.0596145i
$667$	−0.316486	+	0.548170i	−0.0122544	+	0.0212252i
$668$	−17.4447	+	14.6378i	−0.674955	+	0.566355i
$669$	−2.61102	+	0.675268i	−0.100948	+	0.0261074i
$670$	−0.937057	+	5.31431i	−0.0362017	+	0.205310i
$671$	−22.6213	+	8.23347i	−0.873285	+	0.317850i
$672$	4.53059	−	0.688296i	0.174771	−	0.0265516i
$673$	−3.81185	−	21.6181i	−0.146936	−	0.833315i	−0.965792	−	0.259317i	$-0.916503\pi$
$673$	−3.81185	−	21.6181i	−0.146936	−	0.833315i	0.818856	−	0.573998i	$-0.194608\pi$
$674$	−1.36798	−	2.36942i	−0.0526928	−	0.0912666i
$675$	−0.637214	+	5.59339i	−0.0245264	+	0.215290i
$676$	−16.2315	+	28.1138i	−0.624290	+	1.08130i
$677$	13.6785	−	11.4776i	0.525706	−	0.441120i	−0.340910	−	0.940096i	$-0.610735\pi$
$677$	13.6785	−	11.4776i	0.525706	−	0.441120i	0.866616	+	0.498976i	$0.166291\pi$
$678$	−10.2977	+	7.07749i	−0.395481	+	0.271809i
$679$	−21.9384	−	2.25234i	−0.841919	−	0.0864368i
$680$	−0.905324	−	0.759657i	−0.0347176	−	0.0291315i
$681$	−5.44074	−	5.53649i	−0.208489	−	0.212159i
$682$	−3.77956	+	3.17143i	−0.144727	+	0.121440i
$683$	−22.2530			−0.851488			−0.425744	−	0.904844i	$-0.639988\pi$
$683$	−22.2530			−0.851488			−0.425744	+	0.904844i	$0.639988\pi$
$684$	−21.8235	+	12.0972i	−0.834444	+	0.462549i
$685$	−11.0759	+	19.1840i	−0.423189	+	0.732985i
$686$	−2.44476	+	18.3582i	−0.0933412	+	0.700919i
$687$	−18.5219	+	25.9670i	−0.706656	+	0.990704i
$688$	3.61651	−	1.31630i	0.137878	−	0.0501835i
$689$	52.6430	+	44.1727i	2.00554	+	1.68285i
$690$	0.705587	+	1.54825i	0.0268612	+	0.0589409i
$691$	−29.9930	−	10.9166i	−1.14099	−	0.415285i	−0.298718	−	0.954342i	$-0.596559\pi$
$691$	−29.9930	−	10.9166i	−1.14099	−	0.415285i	−0.842270	+	0.539056i	$0.818781\pi$
$692$	−7.05826	+	12.2253i	−0.268315	+	0.464735i
$693$	14.2135	+	21.7713i	0.539926	+	0.827024i
$694$	−1.21645	−	2.10696i	−0.0461759	−	0.0799790i
$695$	−1.79050	−	10.1544i	−0.0679175	−	0.385180i
$696$	−0.590245	+	2.12839i	−0.0223732	+	0.0806764i
$697$	1.36253	−	0.495920i	0.0516095	−	0.0187843i
$698$	−3.28743	−	2.75848i	−0.124431	−	0.104410i
$699$	−14.8640	+	10.2159i	−0.562209	+	0.386399i
$700$	2.77961	−	0.700160i	0.105059	−	0.0264636i
$701$	−26.6856			−1.00790			−0.503950	−	0.863733i	$-0.668121\pi$
$701$	−26.6856			−1.00790			−0.503950	+	0.863733i	$0.668121\pi$
$702$	25.4137	−	24.1173i	0.959179	−	0.910250i
$703$	−2.25557	+	3.90675i	−0.0850703	+	0.147346i
$704$	−3.07817	−	1.12036i	−0.116013	−	0.0422253i
$705$	2.56534	−	1.76312i	0.0966162	−	0.0664031i
$706$	20.4486	−	7.44269i	0.769594	−	0.280109i
$707$	44.5596	+	4.57477i	1.67584	+	0.172052i
$708$	−16.3470	−	16.6347i	−0.614359	−	0.625171i
$709$	0.249226	+	1.41343i	0.00935986	+	0.0530824i	0.989130	−	0.147044i	$-0.0469759\pi$
$709$	0.249226	+	1.41343i	0.00935986	+	0.0530824i	−0.979770	+	0.200126i	$0.935865\pi$
$710$	5.24196			0.196727
$711$	−6.94030	−	20.1555i	−0.260281	−	0.755891i
$712$	17.2637			0.646983
$713$	−0.572715	+	0.480565i	−0.0214484	+	0.0179973i
$714$	−2.33675	−	1.42421i	−0.0874508	−	0.0532997i
$715$	7.59033	−	43.0469i	0.283862	−	1.60986i
$716$	−0.0150906	+	0.00549254i	−0.000563964	+	0.000205266i
$717$	9.66983	−	13.5567i	0.361127	−	0.506285i
$718$	−5.04296	−	28.6000i	−0.188202	−	1.06734i
$719$	−41.1637			−1.53515			−0.767573	−	0.640962i	$-0.778536\pi$
$719$	−41.1637			−1.53515			−0.767573	+	0.640962i	$0.778536\pi$
$720$	3.73638	+	4.61397i	0.139247	+	0.171953i
$721$	−34.6443	+	23.4896i	−1.29022	+	0.874800i
$722$	−47.1527	−	17.1622i	−1.75484	−	0.638711i
$723$	47.8844	−	12.3840i	1.78084	−	0.460565i
$724$	−3.71206	+	1.35108i	−0.137958	+	0.0502124i
$725$	−0.239907	+	1.36058i	−0.00890993	+	0.0505307i
$726$	0.0366440	+	0.465580i	0.00135999	+	0.0172793i
$727$	−3.36954	−	19.1096i	−0.124969	−	0.708737i	−0.981326	−	0.192352i	$-0.938389\pi$
$727$	−3.36954	−	19.1096i	−0.124969	−	0.708737i	0.856357	−	0.516385i	$-0.172723\pi$
$728$	−16.0527	−	7.78155i	−0.594952	−	0.288403i
$729$	−24.0569	+	12.2584i	−0.890995	+	0.454013i
$730$	1.33763	+	2.31684i	0.0495078	+	0.0857500i
$731$	−2.15966	−	0.786052i	−0.0798779	−	0.0290732i
$732$	−10.4900	+	7.20967i	−0.387723	+	0.266477i
$733$	−18.4826	−	15.5088i	−0.682672	−	0.572830i	0.234114	−	0.972209i	$-0.424781\pi$
$733$	−18.4826	−	15.5088i	−0.682672	−	0.572830i	−0.916786	+	0.399379i	$0.869226\pi$
$734$	16.5140	+	13.8569i	0.609542	+	0.511467i
$735$	−22.1235	+	9.28924i	−0.816037	+	0.342639i
$736$	−0.466434	−	0.169768i	−0.0171930	−	0.00625774i
$737$	4.46600	−	7.73534i	0.164507	−	0.284935i
$738$	−7.19457	+	1.13957i	−0.264836	+	0.0419482i
$739$	−19.8802	−	34.4335i	−0.731304	−	1.26666i	−0.956326	−	0.292302i	$-0.905579\pi$
$739$	−19.8802	−	34.4335i	−0.731304	−	1.26666i	0.225022	−	0.974354i	$-0.427755\pi$
$740$	1.00865	+	0.367117i	0.0370785	+	0.0134955i
$741$	96.6881	+	9.30959i	3.55193	+	0.341996i
$742$	−15.7972	+	21.8536i	−0.579932	+	0.802270i
$743$	0.703175	−	3.98791i	0.0257970	−	0.146302i	−0.969189	−	0.246320i	$-0.920779\pi$
$743$	0.703175	−	3.98791i	0.0257970	−	0.146302i	0.994986	+	0.100017i	$0.0318899\pi$
$744$	−1.51493	+	2.12387i	−0.0555400	+	0.0778648i
$745$	−3.97145	−	22.5232i	−0.145503	−	0.825187i
$746$	−0.449046	−	0.777771i	−0.0164407	−	0.0284762i
$747$	−22.2654	−	4.32775i	−0.814648	−	0.158344i
$748$	0.978078	+	1.69408i	0.0357621	+	0.0619417i
$749$	−2.09242	+	7.36411i	−0.0764552	+	0.269079i
$750$	14.6159	+	14.8731i	0.533697	+	0.543089i
$751$	−2.84153	+	16.1151i	−0.103689	+	0.588050i	0.888047	+	0.459753i	$0.152062\pi$
$751$	−2.84153	+	16.1151i	−0.103689	+	0.588050i	−0.991736	+	0.128297i	$0.959049\pi$
$752$	−0.157691	+	0.894312i	−0.00575041	+	0.0326122i
$753$	11.6833	+	5.57258i	0.425763	+	0.203076i
$754$	6.58662	−	5.52683i	0.239871	−	0.201275i
$755$	32.6388			1.18785
$756$	10.1584	+	9.26323i	0.369457	+	0.336900i
$757$	14.9344			0.542799			0.271400	−	0.962467i	$-0.412514\pi$
$757$	14.9344			0.542799			0.271400	+	0.962467i	$0.412514\pi$
$758$	−18.8159	+	15.7884i	−0.683426	+	0.573462i
$759$	−0.220973	−	2.80758i	−0.00802082	−	0.101909i
$760$	−2.85832	+	16.2103i	−0.103682	+	0.588011i
$761$	5.62078	−	31.8770i	0.203753	−	1.15554i	−0.695637	−	0.718394i	$-0.744878\pi$
$761$	5.62078	−	31.8770i	0.203753	−	1.15554i	0.899390	−	0.437147i	$-0.144011\pi$
$762$	−15.1506	+	3.91827i	−0.548847	+	0.141944i
$763$	51.1762	−	12.8908i	1.85270	−	0.466680i
$764$	8.94035	+	15.4851i	0.323451	+	0.560233i
$765$	0.0618462	−	3.54491i	0.00223606	−	0.128167i
$766$	4.53623	+	7.85698i	0.163901	+	0.283884i
$767$	15.7657	+	89.4119i	0.569268	+	3.22848i
$768$	−1.72408	−	0.166002i	−0.0622123	−	0.00599009i
$769$	1.34579	−	7.63237i

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)

\(f(q)\)	\(=\)	\(q+(0.766044 - 0.642788i) q^{2} +(-1.42742 + 0.981051i) q^{3} +(0.173648 - 0.984808i) q^{4} +(0.343656 - 1.94897i) q^{5} +(-0.462863 + 1.66906i) q^{6} +(1.84248 + 1.89876i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(1.07508 - 2.80075i) q^{9} +O(q^{10})\)	\(q+(0.766044 - 0.642788i) q^{2} +(-1.42742 + 0.981051i) q^{3} +(0.173648 - 0.984808i) q^{4} +(0.343656 - 1.94897i) q^{5} +(-0.462863 + 1.66906i) q^{6} +(1.84248 + 1.89876i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(1.07508 - 2.80075i) q^{9} +(-0.989519 - 1.71390i) q^{10} +(0.568823 + 3.22596i) q^{11} +(0.718277 + 1.57610i) q^{12} +(1.17085 - 6.64020i) q^{13} +(2.63192 + 0.270209i) q^{14} +(1.42150 + 3.11915i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(0.298584 + 0.517162i) q^{17} +(-0.976729 - 2.83655i) q^{18} +(4.15869 - 7.20307i) q^{19} +(-1.85969 - 0.676871i) q^{20} +(-4.49277 - 0.902766i) q^{21} +(2.50935 + 2.10559i) q^{22} +(0.380241 + 0.319060i) q^{23} +(1.56333 + 0.745660i) q^{24} +(1.01807 + 0.370549i) q^{25} +(-3.37132 - 5.83929i) q^{26} +(1.21308 + 5.05257i) q^{27} +(2.18985 - 1.48477i) q^{28} +(0.221437 + 1.25583i) q^{29} +(3.09388 + 1.47569i) q^{30} +(-0.261547 + 1.48331i) q^{31} +(-0.939693 + 0.342020i) q^{32} +(-3.97678 - 4.04677i) q^{33} +(0.561154 + 0.204243i) q^{34} +(4.33380 - 2.93842i) q^{35} +(-2.57152 - 1.54509i) q^{36} -0.542374 q^{37} +(-1.44430 - 8.19103i) q^{38} +(4.84307 + 10.6270i) q^{39} +(-1.85969 + 0.676871i) q^{40} +(0.421633 - 2.39120i) q^{41} +(-4.02195 + 2.19634i) q^{42} +(-2.94820 + 2.47384i) q^{43} +3.27572 q^{44} +(-5.08912 - 3.05779i) q^{45} +0.496369 q^{46} +(-0.157691 - 0.894312i) q^{47} +(1.67688 - 0.433678i) q^{48} +(-0.210549 + 6.99683i) q^{49} +(1.01807 - 0.370549i) q^{50} +(-0.933568 - 0.445284i) q^{51} +(-6.33600 - 2.30612i) q^{52} +(-5.09597 + 8.82648i) q^{53} +(4.17700 + 3.09074i) q^{54} +6.48278 q^{55} +(0.723132 - 2.54501i) q^{56} +(1.13035 + 14.3617i) q^{57} +(0.976863 + 0.819685i) q^{58} +(-12.6532 + 4.60539i) q^{59} +(3.31861 - 0.858265i) q^{60} +(1.27613 + 7.23729i) q^{61} +(0.753095 + 1.30440i) q^{62} +(7.29875 - 3.11901i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-12.5392 - 4.56389i) q^{65} +(-5.64760 - 0.543778i) q^{66} +(-2.08879 - 1.75271i) q^{67} +(0.561154 - 0.204243i) q^{68} +(-0.855779 - 0.0823984i) q^{69} +(1.43110 - 5.03667i) q^{70} +(-1.32437 + 2.29388i) q^{71} +(-2.96306 + 0.469329i) q^{72} -1.35179 q^{73} +(-0.415482 + 0.348631i) q^{74} +(-1.81675 + 0.469852i) q^{75} +(-6.37149 - 5.34631i) q^{76} +(-5.07726 + 7.02381i) q^{77} +(10.5409 + 5.02771i) q^{78} +(5.44325 - 4.56743i) q^{79} +(-0.989519 + 1.71390i) q^{80} +(-6.68841 - 6.02206i) q^{81} +(-1.21404 - 2.10278i) q^{82} +(-1.31290 - 7.44583i) q^{83} +(-1.66921 + 4.26775i) q^{84} +(1.11054 - 0.404205i) q^{85} +(-0.668303 + 3.79014i) q^{86} +(-1.54812 - 1.57536i) q^{87} +(2.50935 - 2.10559i) q^{88} +(-8.63183 + 14.9508i) q^{89} +(-5.86401 + 0.928819i) q^{90} +(14.7654 - 10.0113i) q^{91} +(0.380241 - 0.319060i) q^{92} +(-1.08186 - 2.37390i) q^{93} +(-0.695651 - 0.583721i) q^{94} +(-12.6094 - 10.5806i) q^{95} +(1.00580 - 1.41009i) q^{96} +(-6.38539 + 5.35798i) q^{97} +(4.33619 + 5.49522i) q^{98} +(9.64663 + 1.87503i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 3 q^{6} + 6 q^{7} - 36 q^{8} + 24 q^{9}+O(q^{10}) \) 72 * q + 3 * q^6 + 6 * q^7 - 36 * q^8 + 24 * q^9	\( 72 q + 3 q^{6} + 6 q^{7} - 36 q^{8} + 24 q^{9} - 6 q^{10} + 12 q^{11} - 12 q^{13} - 3 q^{14} - 6 q^{15} - 12 q^{17} - 18 q^{19} - 30 q^{21} - 6 q^{22} + 30 q^{23} + 6 q^{25} - 18 q^{26} - 6 q^{27} + 3 q^{29} + 3 q^{30} + 9 q^{31} - 18 q^{33} + 9 q^{34} - 18 q^{35} + 9 q^{36} - 24 q^{39} - 6 q^{41} + 12 q^{42} + 24 q^{43} + 51 q^{45} + 45 q^{47} - 6 q^{48} - 12 q^{49} + 6 q^{50} - 51 q^{51} + 6 q^{52} - 15 q^{53} + 27 q^{54} + 72 q^{55} - 3 q^{56} - 63 q^{57} + 3 q^{58} - 30 q^{59} - 3 q^{60} + 9 q^{61} - 24 q^{62} - 39 q^{63} - 36 q^{64} + 9 q^{65} - 6 q^{67} + 9 q^{68} - 21 q^{69} - 33 q^{70} + 12 q^{71} - 12 q^{72} + 132 q^{73} - 18 q^{74} - 30 q^{75} - 33 q^{77} + 30 q^{78} - 9 q^{79} - 6 q^{80} + 36 q^{81} - 33 q^{82} - 18 q^{83} + 15 q^{84} + 21 q^{85} - 12 q^{86} - 39 q^{87} - 6 q^{88} - 36 q^{89} + 69 q^{90} + 39 q^{91} + 30 q^{92} - 66 q^{93} - 9 q^{94} - 33 q^{95} - 48 q^{97} - 12 q^{98} - 54 q^{99}+O(q^{100}) \) 72 * q + 3 * q^6 + 6 * q^7 - 36 * q^8 + 24 * q^9 - 6 * q^10 + 12 * q^11 - 12 * q^13 - 3 * q^14 - 6 * q^15 - 12 * q^17 - 18 * q^19 - 30 * q^21 - 6 * q^22 + 30 * q^23 + 6 * q^25 - 18 * q^26 - 6 * q^27 + 3 * q^29 + 3 * q^30 + 9 * q^31 - 18 * q^33 + 9 * q^34 - 18 * q^35 + 9 * q^36 - 24 * q^39 - 6 * q^41 + 12 * q^42 + 24 * q^43 + 51 * q^45 + 45 * q^47 - 6 * q^48 - 12 * q^49 + 6 * q^50 - 51 * q^51 + 6 * q^52 - 15 * q^53 + 27 * q^54 + 72 * q^55 - 3 * q^56 - 63 * q^57 + 3 * q^58 - 30 * q^59 - 3 * q^60 + 9 * q^61 - 24 * q^62 - 39 * q^63 - 36 * q^64 + 9 * q^65 - 6 * q^67 + 9 * q^68 - 21 * q^69 - 33 * q^70 + 12 * q^71 - 12 * q^72 + 132 * q^73 - 18 * q^74 - 30 * q^75 - 33 * q^77 + 30 * q^78 - 9 * q^79 - 6 * q^80 + 36 * q^81 - 33 * q^82 - 18 * q^83 + 15 * q^84 + 21 * q^85 - 12 * q^86 - 39 * q^87 - 6 * q^88 - 36 * q^89 + 69 * q^90 + 39 * q^91 + 30 * q^92 - 66 * q^93 - 9 * q^94 - 33 * q^95 - 48 * q^97 - 12 * q^98 - 54 * q^99

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