LMFDB - Embedded newform 378.2.v.b.79.3

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			79.3
Character	$\chi$	$=$	378.79
Dual form			378.2.v.b.67.3

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

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

Coefficient data

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

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

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

$2$	0.766044	+	0.642788i	0.541675	+	0.454519i
$2$	0.766044	+	0.642788i	0.541675	+	0.454519i
$3$	−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	0.959976	+	0.280083i	$0.0903621\pi$
$5$	0.343656	+	1.94897i	0.153688	+	0.871606i	−0.806288	+	0.591523i	$0.798527\pi$
$6$	−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	−0.770592	−	0.637328i	$-0.780040\pi$
$11$	0.568823	−	3.22596i	0.171507	−	0.972663i	0.942099	−	0.335335i	$-0.108849\pi$
$12$	0.718277	−	1.57610i	0.207349	−	0.454980i
$13$	1.17085	+	6.64020i	0.324734	+	1.84166i	0.511537	+	0.859261i	$0.329076\pi$
$13$	1.17085	+	6.64020i	0.324734	+	1.84166i	−0.186803	+	0.982397i	$0.559813\pi$
$14$	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	−0.827543	−	0.561402i	$-0.810262\pi$
$17$	0.298584	−	0.517162i	0.0724172	−	0.125430i	0.899960	+	0.435972i	$0.143595\pi$
$18$	−0.976729	+	2.83655i	−0.230217	+	0.668581i
$19$	4.15869	+	7.20307i	0.954070	+	1.65250i	0.736483	+	0.676456i	$0.236485\pi$
$19$	4.15869	+	7.20307i	0.954070	+	1.65250i	0.217586	+	0.976041i	$0.430182\pi$
$20$	−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	−0.602283	−	0.798282i	$-0.705742\pi$
$23$	0.380241	−	0.319060i	0.0792857	−	0.0665286i	0.681569	+	0.731754i	$0.261298\pi$
$24$	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	−0.957321	−	0.289028i	$-0.906668\pi$
$29$	0.221437	−	1.25583i	0.0411198	−	0.233202i	0.998441	+	0.0558258i	$0.0177792\pi$
$30$	3.09388	−	1.47569i	0.564863	−	0.269423i
$31$	−0.261547	−	1.48331i	−0.0469753	−	0.266410i	0.952270	−	0.305257i	$-0.0987425\pi$
$31$	−0.261547	−	1.48331i	−0.0469753	−	0.266410i	−0.999245	+	0.0388474i	$0.987631\pi$
$32$	−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	0.999868	+	0.0162228i	$0.00516412\pi$
$41$	0.421633	+	2.39120i	0.0658480	+	0.373442i	−0.934020	+	0.357220i	$0.883725\pi$
$42$	−4.02195	−	2.19634i	−0.620601	−	0.338903i
$43$	−2.94820	−	2.47384i	−0.449597	−	0.377256i	0.389689	−	0.920946i	$-0.372582\pi$
$43$	−2.94820	−	2.47384i	−0.449597	−	0.377256i	−0.839286	+	0.543690i	$0.817027\pi$
$44$	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	−0.994146	−	0.108043i	$-0.965542\pi$
$47$	−0.157691	+	0.894312i	−0.0230016	+	0.130449i	0.971145	+	0.238491i	$0.0766528\pi$
$48$	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	−0.968471	−	0.249127i	$-0.919856\pi$
$53$	−5.09597	−	8.82648i	−0.699985	−	1.21241i	0.268486	−	0.963284i	$-0.413477\pi$
$54$	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	−0.659012	−	0.752132i	$-0.729025\pi$
$59$	−12.6532	−	4.60539i	−1.64731	−	0.599570i	−0.988294	+	0.152562i	$0.951248\pi$
$60$	3.31861	+	0.858265i	0.428430	+	0.110802i
$61$	1.27613	−	7.23729i	0.163392	−	0.926639i	−0.787316	−	0.616550i	$-0.788530\pi$
$61$	1.27613	−	7.23729i	0.163392	−	0.926639i	0.950707	−	0.310090i	$-0.100359\pi$
$62$	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	−0.761402	−	0.648280i	$-0.775489\pi$
$67$	−2.08879	+	1.75271i	−0.255187	+	0.214127i	0.506215	+	0.862407i	$0.331044\pi$
$68$	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	0.776675	−	0.629902i	$-0.216905\pi$
$71$	−1.32437	−	2.29388i	−0.157174	−	0.272233i	−0.933848	+	0.357669i	$0.883572\pi$
$72$	−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	0.895408	−	0.445246i	$-0.146884\pi$
$79$	5.44325	+	4.56743i	0.612413	+	0.513876i	−0.282995	+	0.959121i	$0.591328\pi$
$80$	−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	0.823968	+	0.566636i	$0.191755\pi$
$83$	−1.31290	+	7.44583i	−0.144110	+	0.817286i	−0.968078	+	0.250650i	$0.919356\pi$
$84$	−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	−0.806942	−	0.590631i	$-0.798879\pi$
$89$	−8.63183	−	14.9508i	−0.914973	−	1.58478i	−0.108031	−	0.994148i	$-0.534455\pi$
$90$	−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	0.258228	−	0.966084i	$-0.416861\pi$
$97$	−6.38539	−	5.35798i	−0.648338	−	0.544020i	−0.906566	+	0.422064i	$0.861306\pi$
$98$	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	0.991702	+	0.128556i	$0.0410342\pi$
$101$	12.9695	+	10.8827i	1.29051	+	1.08287i	0.298810	+	0.954313i	$0.403410\pi$
$102$	−1.00138	−	0.258978i	−0.0991512	−	0.0256427i
$103$	−2.74718	−	15.5800i	−0.270688	−	1.53515i	−0.752335	−	0.658781i	$-0.771072\pi$
$103$	−2.74718	−	15.5800i	−0.270688	−	1.53515i	0.481647	−	0.876365i	$-0.340039\pi$
$104$	−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	−0.787580	−	0.616212i	$-0.788667\pi$
$107$	1.44677	−	2.50589i	0.139865	−	0.242253i	0.927445	+	0.373959i	$0.122000\pi$
$108$	5.18646	+	0.317284i	0.499067	+	0.0305307i
$109$	9.97350	+	17.2746i	0.955288	+	1.65461i	0.733708	+	0.679465i	$0.237788\pi$
$109$	9.97350	+	17.2746i	0.955288	+	1.65461i	0.221580	+	0.975142i	$0.428878\pi$
$110$	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	−0.344710	−	0.938709i	$-0.612023\pi$
$113$	5.52639	−	4.63719i	0.519879	−	0.436230i	0.864590	+	0.502479i	$0.167578\pi$
$114$	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	−0.592968	−	0.805226i	$-0.702044\pi$
$127$	4.51749	−	7.82452i	0.400862	−	0.694314i	0.993830	+	0.110912i	$0.0353772\pi$
$128$	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	−0.0452078	−	0.998978i	$-0.514395\pi$
$131$	10.6528	−	8.93879i	0.930743	−	0.780986i	0.975951	+	0.217992i	$0.0699505\pi$
$132$	−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	−0.749704	−	0.661774i	$-0.769804\pi$
$137$	−10.5182	+	3.82831i	−0.898630	+	0.327075i	−0.148927	+	0.988848i	$0.547582\pi$
$138$	−0.708529	−	0.486963i	−0.0603140	−	0.0414531i
$139$	4.89594	+	1.78198i	0.415268	+	0.151145i	0.541200	−	0.840894i	$-0.317970\pi$
$139$	4.89594	+	1.78198i	0.415268	+	0.151145i	−0.125932	+	0.992039i	$0.540192\pi$
$140$	−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	0.746096	−	0.665838i	$-0.231926\pi$
$149$	10.8595	+	3.95254i	0.889647	+	0.323805i	0.143550	+	0.989643i	$0.454148\pi$
$150$	−1.08970	−	1.52771i	−0.0889734	−	0.124737i
$151$	2.86385	−	16.2417i	0.233057	−	1.32173i	−0.613611	−	0.789609i	$-0.710284\pi$
$151$	2.86385	−	16.2417i	0.233057	−	1.32173i	0.846668	−	0.532122i	$-0.178605\pi$
$152$	−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	−0.236226	−	0.971698i	$-0.575911\pi$
$157$	−13.0535	−	4.75108i	−1.04178	−	0.379178i	−0.805555	+	0.592520i	$0.798133\pi$
$158$	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	0.489497	+	0.872005i	$0.337180\pi$
$163$	−6.51673	+	11.2873i	−0.510430	+	0.884091i	−0.999927	+	0.0120856i	$0.996153\pi$
$164$	−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	−0.370952	+	0.928652i	$0.620968\pi$
$167$	−17.4447	+	14.6378i	−1.34991	+	1.13271i	−0.978959	+	0.204057i	$0.934587\pi$
$168$	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	−0.792869	−	0.609392i	$-0.791414\pi$
$173$	−13.2652	+	4.82813i	−1.00853	+	0.367076i	−0.215664	+	0.976468i	$0.569192\pi$
$174$	−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	−0.866325	−	0.499480i	$-0.833524\pi$
$179$	−0.00802956	+	0.0139076i	−0.000600158	+	0.00103950i	0.865725	+	0.500520i	$0.166858\pi$
$180$	−3.89506	−	4.48083i	−0.290320	−	0.333981i
$181$	−1.97514	+	3.42105i	−0.146811	+	0.254285i	−0.930047	−	0.367440i	$-0.880234\pi$
$181$	−1.97514	+	3.42105i	−0.146811	+	0.254285i	0.783236	+	0.621725i	$0.213568\pi$
$182$	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	−0.00538196	−	0.999986i	$-0.501713\pi$
$191$	−13.6974	−	11.4935i	−0.991110	−	0.831640i	−0.985728	+	0.168345i	$0.946158\pi$
$192$	−0.135903	+	1.72671i	−0.00980792	+	0.124615i
$193$	0.278012	+	1.57668i	0.0200117	+	0.113492i	0.993177	−	0.116614i	$-0.0372039\pi$
$193$	0.278012	+	1.57668i	0.0200117	+	0.113492i	−0.973166	+	0.230106i	$0.926093\pi$
$194$	−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	−0.299006	−	0.954251i	$-0.596655\pi$
$197$	9.50079	−	16.4558i	0.676903	−	1.17243i	0.975909	−	0.218179i	$-0.0700118\pi$
$198$	8.59500	+	4.76438i	0.610820	+	0.338590i
$199$	4.16219	−	7.20912i	0.295050	−	0.511041i	−0.679947	−	0.733261i	$-0.737997\pi$
$199$	4.16219	−	7.20912i	0.295050	−	0.511041i	0.974996	+	0.222220i	$0.0713305\pi$
$200$	−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	−0.510549	−	0.859849i	$-0.670558\pi$
$211$	3.59633	−	3.01768i	0.247581	−	0.207745i	0.758130	+	0.652103i	$0.226113\pi$
$212$	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	−0.292565	−	0.956246i	$-0.594509\pi$
$223$	1.46317	−	0.532550i	0.0979810	−	0.0356622i	0.390546	+	0.920584i	$0.372286\pi$
$224$	−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	−0.948029	−	0.318185i	$-0.896927\pi$
$227$	0.778222	−	4.41352i	0.0516524	−	0.292935i	0.999681	+	0.0252492i	$0.00803792\pi$
$228$	14.3398	−	1.38071i	0.949678	−	0.0914394i
$229$	17.3045	+	6.29834i	1.14352	+	0.416206i	0.843182	−	0.537628i	$-0.180679\pi$
$229$	17.3045	+	6.29834i	1.14352	+	0.416206i	0.300335	+	0.953834i	$0.402902\pi$
$230$	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	0.0328769	−	0.999459i	$-0.489533\pi$
$239$	−9.03426	−	3.28820i	−0.584378	−	0.212696i	−0.617255	+	0.786763i	$0.711755\pi$
$240$	−0.268956	+	3.41723i	−0.0173610	+	0.220581i
$241$	−26.8336	+	9.76662i	−1.72850	+	0.629123i	−0.998522	−	0.0543459i	$-0.982693\pi$
$241$	−26.8336	+	9.76662i	−1.72850	+	0.629123i	−0.729979	+	0.683469i	$0.760470\pi$
$242$	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	−0.959521	−	0.281636i	$-0.909123\pi$
$251$	−3.73667	+	6.47211i	−0.235857	+	0.408516i	0.723665	+	0.690152i	$0.242456\pi$
$252$	−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	−0.648071	−	0.761580i	$-0.724424\pi$
$257$	−26.1959	−	9.53453i	−1.63406	−	0.594748i	−0.985985	+	0.166832i	$0.946646\pi$
$258$	−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	0.884380	−	0.466768i	$-0.154582\pi$
$263$	9.37802	+	7.86909i	0.578273	+	0.485229i	−0.306106	+	0.951997i	$0.599026\pi$
$264$	−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	0.964963	+	0.262384i	$0.0845088\pi$
$269$	11.6402	+	20.1614i	0.709713	+	1.22926i	−0.255250	+	0.966875i	$0.582158\pi$
$270$	7.45921	+	7.07871i	0.453953	+	0.430796i
$271$	10.0745	−	17.4496i	0.611985	−	1.05999i	−0.378920	−	0.925429i	$-0.623705\pi$
$271$	10.0745	−	17.4496i	0.611985	−	1.05999i	0.990905	−	0.134560i	$-0.0429621\pi$
$272$	−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	0.376022	−	0.926611i	$-0.377292\pi$
$277$	−7.84259	−	6.58072i	−0.471216	−	0.395397i	−0.847238	+	0.531214i	$0.821736\pi$
$278$	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	0.956220	−	0.292650i	$-0.0945372\pi$
$281$	13.9814	+	11.7318i	0.834061	+	0.699860i	−0.122158	+	0.992511i	$0.538982\pi$
$282$	1.56565	−	0.150748i	0.0932330	−	0.00897691i
$283$	5.95618	−	4.99782i	0.354058	−	0.297090i	−0.448359	−	0.893853i	$-0.647991\pi$
$283$	5.95618	−	4.99782i	0.354058	−	0.297090i	0.802417	+	0.596764i	$0.203547\pi$
$284$	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	−0.166492	−	0.986043i	$-0.553244\pi$
$293$	−15.8822	−	5.78065i	−0.927849	−	0.337709i	−0.761357	+	0.648333i	$0.775466\pi$
$294$	−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	−0.996928	−	0.0783287i	$-0.975042\pi$
$307$	−9.92235	−	17.1860i	−0.566298	−	0.980858i	0.430629	−	0.902529i	$-0.358292\pi$
$308$	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	0.0146842	−	0.999892i	$-0.495326\pi$
$311$	17.6693	−	14.8263i	1.00194	−	0.840724i	0.987251	+	0.159168i	$0.0508813\pi$
$312$	6.78174	+	9.50774i	0.383941	+	0.538270i
$313$	−7.28068	+	2.64995i	−0.411528	+	0.149784i	−0.539484	−	0.841996i	$-0.681381\pi$
$313$	−7.28068	+	2.64995i	−0.411528	+	0.149784i	0.127956	+	0.991780i	$0.459158\pi$
$314$	−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	−0.471374	−	0.881933i	$-0.656242\pi$
$317$	4.86439	−	27.5873i	0.273212	−	1.54946i	0.744586	−	0.667527i	$-0.232647\pi$
$318$	−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	−0.896665	−	0.442709i	$-0.854017\pi$
$331$	1.77095	−	10.0435i	0.0973400	−	0.552043i	0.994005	−	0.109333i	$-0.0348715\pi$
$332$	−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	0.995010	−	0.0997786i	$-0.0318135\pi$
$337$	0.475096	+	2.69440i	0.0258801	+	0.146774i	−0.969130	+	0.246552i	$0.920702\pi$
$338$	−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	0.994045	−	0.108967i	$-0.0347543\pi$
$347$	0.422470	+	2.39594i	0.0226794	+	0.128621i	−0.971366	+	0.237588i	$0.923643\pi$
$348$	−1.82026	−	1.25104i	−0.0975760	−	0.0670627i
$349$	−0.745200	+	4.22624i	−0.0398896	+	0.226225i	−0.998235	−	0.0593863i	$-0.981086\pi$
$349$	−0.745200	+	4.22624i	−0.0398896	+	0.226225i	0.958345	+	0.285612i	$0.0921968\pi$
$350$	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	0.265353	−	0.964151i	$-0.414511\pi$
$353$	20.4486	−	7.44269i	1.08837	−	0.396134i	0.823017	+	0.568017i	$0.192289\pi$
$354$	−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	0.939520	+	0.342495i	$0.111272\pi$
$359$	14.5206	+	25.1504i	0.766369	+	1.32739i	−0.173151	+	0.984895i	$0.555395\pi$
$360$	−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	−0.716437	−	0.697652i	$-0.754228\pi$
$367$	3.74342	−	21.2300i	0.195405	−	1.10820i	0.911841	−	0.410543i	$-0.134661\pi$
$368$	−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	0.988579	−	0.150704i	$-0.0481540\pi$
$373$	0.155952	+	0.884448i	0.00807489	+	0.0457950i	−0.980504	+	0.196499i	$0.937043\pi$
$374$	−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	−0.998237	−	0.0593501i	$-0.981097\pi$
$383$	−1.57542	−	8.93463i	−0.0805000	−	0.456538i	0.917737	−	0.397188i	$-0.130014\pi$
$384$	−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	−0.460593	−	0.887611i	$-0.652363\pi$
$389$	5.43970	−	30.8501i	0.275804	−	1.56416i	0.736397	−	0.676550i	$-0.236526\pi$
$390$	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	0.813745	−	0.581223i	$-0.197425\pi$
$397$	−1.92238	−	3.32966i	−0.0964814	−	0.167111i	−0.910226	+	0.414112i	$0.864092\pi$
$398$	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	−0.440028	−	0.897984i	$-0.645032\pi$
$401$	7.36725	−	6.18186i	0.367903	−	0.308707i	0.807931	+	0.589277i	$0.200587\pi$
$402$	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	0.956222	−	0.292642i	$-0.0945345\pi$
$409$	−0.857938	−	4.86561i	−0.0424223	−	0.240589i	−0.998644	+	0.0520535i	$0.983423\pi$
$410$	−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	0.879911	+	0.475138i	$0.157602\pi$
$419$	4.41265	+	25.0254i	0.215572	+	1.22257i	−0.664339	+	0.747431i	$0.731287\pi$
$420$	7.74409	−	4.71989i	0.377873	−	0.230307i
$421$	11.3843	+	9.55254i	0.554836	+	0.465562i	0.876575	−	0.481266i	$-0.159823\pi$
$421$	11.3843	+	9.55254i	0.554836	+	0.465562i	−0.321739	+	0.946828i	$0.604267\pi$
$422$	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	0.723591	−	0.690228i	$-0.242490\pi$
$431$	−4.89865	−	8.48471i	−0.235960	−	0.408694i	−0.959551	+	0.281534i	$0.909157\pi$
$432$	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	0.491945	+	0.870626i	$0.336286\pi$
$439$	−5.61740	+	31.8579i	−0.268104	+	1.52049i	−0.760049	+	0.649866i	$0.774825\pi$
$440$	−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	−0.917099	−	0.398660i	$-0.869475\pi$
$443$	−28.6959	+	10.4445i	−1.36338	+	0.496231i	−0.446285	+	0.894891i	$0.647253\pi$
$444$	−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	0.697101	−	0.716973i	$-0.254473\pi$
$449$	−5.77134	−	9.99626i	−0.272366	−	0.471753i	−0.969467	+	0.245221i	$0.921140\pi$
$450$	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	0.387625	−	0.921817i	$-0.373296\pi$
$457$	−9.68142	−	8.12368i	−0.452878	−	0.380010i	−0.840503	+	0.541808i	$0.817740\pi$
$458$	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	0.790566	+	0.612377i	$0.209787\pi$
$461$	−3.47332	+	19.6982i	−0.161768	+	0.917434i	−0.952334	+	0.305057i	$0.901324\pi$
$462$	−9.37308	+	11.7253i	−0.436075	+	0.545511i
$463$	12.0406	+	4.38242i	0.559574	+	0.203668i	0.606295	−	0.795240i	$-0.292655\pi$
$463$	12.0406	+	4.38242i	0.559574	+	0.203668i	−0.0467212	+	0.998908i	$0.514877\pi$
$464$	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	0.984961	+	0.172780i	$0.0552748\pi$
$467$	13.8762	+	24.0342i	0.642112	+	1.11217i	−0.342849	+	0.939391i	$0.611392\pi$
$468$	−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	0.357680	−	0.933844i	$-0.383568\pi$
$479$	−10.9401	−	9.17986i	−0.499867	−	0.419438i	−0.857547	+	0.514406i	$0.828012\pi$
$480$	−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	−0.877446	−	0.479675i	$-0.840755\pi$
$487$	−18.8491	−	32.6476i	−0.854134	−	1.47940i	0.0233124	−	0.999728i	$-0.492579\pi$
$488$	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	−0.828944	−	0.559331i	$-0.811058\pi$
$491$	−9.35212	+	7.84736i	−0.422055	+	0.354146i	0.406889	+	0.913478i	$0.366614\pi$
$492$	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	0.244133	−	0.969742i	$-0.421497\pi$
$499$	−4.29316	−	1.56258i	−0.192188	−	0.0699508i	−0.436321	+	0.899791i	$0.643719\pi$
$500$	−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	0.806375	−	0.591405i	$-0.201426\pi$
$503$	−2.44425	−	4.23357i	−0.108984	−	0.188766i	−0.915359	+	0.402639i	$0.868093\pi$
$504$	−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	−0.532920	−	0.846166i	$-0.678905\pi$
$509$	4.68933	−	3.93481i	0.207851	−	0.174407i	0.740770	+	0.671758i	$0.234461\pi$
$510$	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	−0.379948	−	0.925008i	$-0.624058\pi$
$541$	14.2140	−	24.6193i	0.611107	−	1.05847i	0.991054	−	0.133460i	$-0.0426087\pi$
$542$	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	−0.0513547	−	0.998680i	$-0.516354\pi$
$547$	12.8925	−	4.69250i	0.551245	−	0.200637i	0.602599	+	0.798044i	$0.294132\pi$
$548$	−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	−0.989923	−	0.141604i	$-0.954774\pi$
$557$	−8.78728	+	15.2200i	−0.372329	+	0.644893i	0.617594	+	0.786497i	$0.288107\pi$
$558$	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	0.910806	+	0.412835i	$0.135461\pi$
$563$	4.65361	+	26.3919i	0.196126	+	1.11229i	−0.714679	+	0.699452i	$0.753427\pi$
$564$	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	0.682719	−	0.730681i	$-0.260797\pi$
$569$	1.94865	+	1.63511i	0.0816917	+	0.0685475i	−0.601027	+	0.799228i	$0.705242\pi$
$570$	23.4960	+	16.1485i	0.984139	+	0.676386i
$571$	3.72221	+	21.1097i	0.155770	+	0.883414i	0.958079	+	0.286505i	$0.0924936\pi$
$571$	3.72221	+	21.1097i	0.155770	+	0.883414i	−0.802309	+	0.596909i	$0.796395\pi$
$572$	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	−0.772373	−	0.635169i	$-0.780930\pi$
$577$	3.93668	−	6.81854i	0.163886	−	0.283859i	0.936259	+	0.351310i	$0.114264\pi$
$578$	−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	−0.981199	−	0.192997i	$-0.938179\pi$
$587$	−38.9778	+	14.1868i	−1.60879	+	0.585550i	−0.627586	+	0.778547i	$0.715957\pi$
$588$	−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	−0.757958	−	0.652303i	$-0.773803\pi$
$593$	4.52774	−	7.84227i	0.185932	−	0.322043i	0.943890	+	0.330260i	$0.107136\pi$
$594$	−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	0.812123	−	0.583486i	$-0.198312\pi$
$599$	25.9231	+	9.43522i	1.05919	+	0.385513i	0.247065	+	0.968999i	$0.420534\pi$
$600$	1.31528	−	1.33843i	0.0536960	−	0.0546410i
$601$	−24.5814	+	8.94690i	−1.00270	+	0.364952i	−0.790624	−	0.612302i	$-0.790244\pi$
$601$	−24.5814	+	8.94690i	−1.00270	+	0.364952i	−0.212073	+	0.977254i	$0.568021\pi$
$602$	−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	0.125371	−	0.992110i	$-0.459988\pi$
$607$	−10.2567	−	3.73312i	−0.416305	−	0.151523i	−0.541676	+	0.840587i	$0.682210\pi$
$608$	−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	0.806436	−	0.591321i	$-0.201393\pi$
$617$	25.9351	+	9.43961i	1.04411	+	0.380024i	0.237672	+	0.971345i	$0.423616\pi$
$618$	−24.7324	+	11.7966i	−0.994884	+	0.474530i
$619$	−6.72202	+	2.44661i	−0.270181	+	0.0983377i	−0.473558	−	0.880763i	$-0.657030\pi$
$619$	−6.72202	+	2.44661i	−0.270181	+	0.0983377i	0.203377	+	0.979100i	$0.434808\pi$
$620$	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	0.935014	−	0.354611i	$-0.115387\pi$
$631$	4.02933	+	6.97900i	0.160405	+	0.277830i	−0.774609	+	0.632440i	$0.782053\pi$
$632$	−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	0.886351	−	0.463015i	$-0.153232\pi$
$641$	14.7929	+	12.4127i	0.584283	+	0.490272i	−0.302067	+	0.953287i	$0.597677\pi$
$642$	−4.85213	−	1.25487i	−0.191498	−	0.0495257i
$643$	25.5593	−	21.4468i	1.00796	−	0.845780i	0.0198936	−	0.999802i	$-0.493667\pi$
$643$	25.5593	−	21.4468i	1.00796	−	0.845780i	0.988067	+	0.154022i	$0.0492228\pi$
$644$	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	−0.999809	−	0.0195402i	$-0.993780\pi$
$647$	−13.1461	−	22.7697i	−0.516827	−	0.895170i	0.482982	−	0.875630i	$-0.339554\pi$
$648$	−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	−0.995716	−	0.0924676i	$-0.970525\pi$
$653$	−2.34264	−	13.2858i	−0.0916748	−	0.519913i	0.904041	−	0.427446i	$-0.140587\pi$
$654$	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	0.807182	−	0.590302i	$-0.200991\pi$
$659$	9.39594	+	7.88413i	0.366014	+	0.307122i	−0.441168	+	0.897424i	$0.645436\pi$
$660$	4.65643	−	10.2175i	0.181251	−	0.397715i
$661$	12.6624	−	10.6250i	0.492510	−	0.413265i	−0.362415	−	0.932017i	$-0.618048\pi$
$661$	12.6624	−	10.6250i	0.492510	−	0.413265i	0.854925	+	0.518752i	$0.173603\pi$
$662$	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	0.818856	+	0.573998i	$0.194608\pi$
$673$	−3.81185	+	21.6181i	−0.146936	+	0.833315i	−0.965792	+	0.259317i	$0.916503\pi$
$674$	−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	0.866616	−	0.498976i	$-0.166291\pi$
$677$	13.6785	+	11.4776i	0.525706	+	0.441120i	−0.340910	+	0.940096i	$0.610735\pi$
$678$	−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	−0.842270	−	0.539056i	$-0.818781\pi$
$691$	−29.9930	+	10.9166i	−1.14099	+	0.415285i	−0.298718	+	0.954342i	$0.596559\pi$
$692$	−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	−0.979770	−	0.200126i	$-0.935865\pi$
$709$	0.249226	−	1.41343i	0.00935986	−	0.0530824i	0.989130	+	0.147044i	$0.0469759\pi$
$710$	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	0.856357	+	0.516385i	$0.172723\pi$
$727$	−3.36954	+	19.1096i	−0.124969	+	0.708737i	−0.981326	+	0.192352i	$0.938389\pi$
$728$	−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	−0.916786	−	0.399379i	$-0.869226\pi$
$733$	−18.4826	+	15.5088i	−0.682672	+	0.572830i	0.234114	+	0.972209i	$0.424781\pi$
$734$	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	0.225022	+	0.974354i	$0.427755\pi$
$739$	−19.8802	+	34.4335i	−0.731304	+	1.26666i	−0.956326	+	0.292302i	$0.905579\pi$
$740$	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	0.994986	−	0.100017i	$-0.0318899\pi$
$743$	0.703175	+	3.98791i	0.0257970	+	0.146302i	−0.969189	+	0.246320i	$0.920779\pi$
$744$	−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	−0.991736	−	0.128297i	$-0.959049\pi$
$751$	−2.84153	−	16.1151i	−0.103689	−	0.588050i	0.888047	−	0.459753i	$-0.152062\pi$
$752$	−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	0.899390	+	0.437147i	$0.144011\pi$
$761$	5.62078	+	31.8770i	0.203753	+	1.15554i	−0.695637	+	0.718394i	$0.744878\pi$
$762$	−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

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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