LMFDB - Embedded newform 378.2.w.b.25.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [378,2,Mod(25,378)]

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([10, 12]))

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

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

chi := DirichletCharacter("378.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 378 = 2 \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	378.w (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			25.10
Character	$\chi$	$=$	378.25
Dual form			378.2.w.b.121.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.939693 - 0.342020i) q^{2} +(1.47894 - 0.901527i) q^{3} +(0.766044 - 0.642788i) q^{4} +(1.05304 + 0.383275i) q^{5} +(1.08140 - 1.35298i) q^{6} +(1.66470 + 2.05639i) q^{7} +(0.500000 - 0.866025i) q^{8} +(1.37450 - 2.66660i) q^{9} +O(q^{10})$	\(q+(0.939693 - 0.342020i) q^{2} +(1.47894 - 0.901527i) q^{3} +(0.766044 - 0.642788i) q^{4} +(1.05304 + 0.383275i) q^{5} +(1.08140 - 1.35298i) q^{6} +(1.66470 + 2.05639i) q^{7} +(0.500000 - 0.866025i) q^{8} +(1.37450 - 2.66660i) q^{9} +1.12062 q^{10} +(-4.85062 + 1.76548i) q^{11} +(0.553440 - 1.64125i) q^{12} +(0.104655 + 0.593530i) q^{13} +(2.26764 + 1.36302i) q^{14} +(1.90291 - 0.382505i) q^{15} +(0.173648 - 0.984808i) q^{16} -2.64369 q^{17} +(0.379575 - 2.97589i) q^{18} -2.99705 q^{19} +(1.05304 - 0.383275i) q^{20} +(4.31588 + 1.54050i) q^{21} +(-3.95426 + 3.31802i) q^{22} +(0.455644 + 2.58409i) q^{23} +(-0.0412776 - 1.73156i) q^{24} +(-2.86823 - 2.40673i) q^{25} +(0.301343 + 0.521941i) q^{26} +(-0.371217 - 5.18288i) q^{27} +(2.59706 + 0.505239i) q^{28} +(0.657346 - 3.72799i) q^{29} +(1.65733 - 1.01027i) q^{30} +(1.70206 - 1.42820i) q^{31} +(-0.173648 - 0.984808i) q^{32} +(-5.58213 + 6.98400i) q^{33} +(-2.48426 + 0.904196i) q^{34} +(0.964836 + 2.80351i) q^{35} +(-0.661130 - 2.92624i) q^{36} +(0.637238 - 1.10373i) q^{37} +(-2.81630 + 1.02505i) q^{38} +(0.689861 + 0.783442i) q^{39} +(0.858447 - 0.720322i) q^{40} +(-1.28984 - 7.31506i) q^{41} +(4.58249 - 0.0285242i) q^{42} +(4.79067 + 4.01985i) q^{43} +(-2.58096 + 4.47036i) q^{44} +(2.46945 - 2.28123i) q^{45} +(1.31197 + 2.27241i) q^{46} +(-6.40954 - 5.37824i) q^{47} +(-0.631016 - 1.61302i) q^{48} +(-1.45752 + 6.84658i) q^{49} +(-3.51840 - 1.28059i) q^{50} +(-3.90985 + 2.38336i) q^{51} +(0.461684 + 0.387399i) q^{52} +(-6.05084 + 10.4804i) q^{53} +(-2.12148 - 4.74335i) q^{54} -5.78457 q^{55} +(2.61324 - 0.413479i) q^{56} +(-4.43244 + 2.70192i) q^{57} +(-0.657346 - 3.72799i) q^{58} +(0.0893074 + 0.506487i) q^{59} +(1.21185 - 1.51618i) q^{60} +(7.91024 + 6.63748i) q^{61} +(1.11094 - 1.92421i) q^{62} +(7.77172 - 1.61259i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-0.117279 + 0.665123i) q^{65} +(-2.85681 + 8.47201i) q^{66} +(12.7733 + 4.64911i) q^{67} +(-2.02519 + 1.69933i) q^{68} +(3.00349 + 3.41092i) q^{69} +(1.86551 + 2.30444i) q^{70} +(4.45463 + 7.71565i) q^{71} +(-1.62209 - 2.52365i) q^{72} +(-4.04838 - 7.01200i) q^{73} +(0.221311 - 1.25511i) q^{74} +(-6.41165 - 0.973611i) q^{75} +(-2.29587 + 1.92646i) q^{76} +(-11.7054 - 7.03579i) q^{77} +(0.916210 + 0.500248i) q^{78} +(10.6914 - 3.89135i) q^{79} +(0.560311 - 0.970488i) q^{80} +(-5.22151 - 7.33047i) q^{81} +(-3.71395 - 6.43276i) q^{82} +(-1.31934 + 7.48238i) q^{83} +(4.29637 - 1.59411i) q^{84} +(-2.78392 - 1.01326i) q^{85} +(5.87662 + 2.13892i) q^{86} +(-2.38871 - 6.10607i) q^{87} +(-0.896359 + 5.08350i) q^{88} -6.65883 q^{89} +(1.54029 - 2.98825i) q^{90} +(-1.04631 + 1.20326i) q^{91} +(2.01006 + 1.68664i) q^{92} +(1.22968 - 3.64666i) q^{93} +(-7.86246 - 2.86170i) q^{94} +(-3.15601 - 1.14869i) q^{95} +(-1.14465 - 1.29992i) q^{96} +(6.73681 + 5.65286i) q^{97} +(0.972048 + 6.93218i) q^{98} +(-1.95934 + 15.3613i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 3 q^{6} + 3 q^{7} + 36 q^{8}+O(q^{10}) $ 72 * q + 3 * q^6 + 3 * q^7 + 36 * q^8	$ 72 q + 3 q^{6} + 3 q^{7} + 36 q^{8} - 12 q^{10} - 6 q^{11} + 12 q^{13} - 3 q^{14} - 6 q^{15} + 24 q^{17} - 36 q^{19} + 18 q^{21} + 6 q^{22} - 6 q^{23} + 30 q^{25} - 18 q^{26} + 6 q^{27} + 3 q^{29} + 15 q^{30} - 9 q^{31} - 18 q^{33} - 9 q^{34} + 9 q^{35} - 3 q^{36} + 51 q^{39} - 6 q^{41} - 27 q^{42} - 24 q^{43} + 18 q^{45} + 27 q^{47} + 6 q^{48} - 69 q^{49} + 6 q^{50} + 6 q^{51} - 6 q^{52} - 15 q^{53} + 45 q^{54} - 72 q^{55} + 6 q^{56} + 57 q^{57} - 3 q^{58} + 15 q^{59} - 33 q^{60} - 18 q^{61} - 24 q^{62} - 12 q^{63} - 36 q^{64} - 90 q^{65} - 36 q^{66} - 66 q^{67} - 18 q^{68} - 39 q^{69} - 12 q^{70} + 12 q^{71} + 30 q^{73} + 9 q^{74} - 21 q^{75} - 87 q^{77} + 6 q^{78} - 45 q^{79} - 6 q^{80} - 24 q^{81} + 33 q^{82} + 18 q^{83} + 6 q^{84} + 51 q^{85} - 12 q^{86} - 18 q^{87} - 12 q^{88} + 72 q^{89} - 69 q^{90} - 30 q^{91} + 12 q^{92} - 48 q^{93} + 21 q^{95} + 48 q^{97} + 6 q^{98} + 90 q^{99}+O(q^{100}) $ 72 * q + 3 * q^6 + 3 * q^7 + 36 * q^8 - 12 * q^10 - 6 * q^11 + 12 * q^13 - 3 * q^14 - 6 * q^15 + 24 * q^17 - 36 * q^19 + 18 * q^21 + 6 * q^22 - 6 * q^23 + 30 * q^25 - 18 * q^26 + 6 * q^27 + 3 * q^29 + 15 * q^30 - 9 * q^31 - 18 * q^33 - 9 * q^34 + 9 * q^35 - 3 * q^36 + 51 * q^39 - 6 * q^41 - 27 * q^42 - 24 * q^43 + 18 * q^45 + 27 * q^47 + 6 * q^48 - 69 * q^49 + 6 * q^50 + 6 * q^51 - 6 * q^52 - 15 * q^53 + 45 * q^54 - 72 * q^55 + 6 * q^56 + 57 * q^57 - 3 * q^58 + 15 * q^59 - 33 * q^60 - 18 * q^61 - 24 * q^62 - 12 * q^63 - 36 * q^64 - 90 * q^65 - 36 * q^66 - 66 * q^67 - 18 * q^68 - 39 * q^69 - 12 * q^70 + 12 * q^71 + 30 * q^73 + 9 * q^74 - 21 * q^75 - 87 * q^77 + 6 * q^78 - 45 * q^79 - 6 * q^80 - 24 * q^81 + 33 * q^82 + 18 * q^83 + 6 * q^84 + 51 * q^85 - 12 * q^86 - 18 * q^87 - 12 * q^88 + 72 * q^89 - 69 * q^90 - 30 * q^91 + 12 * q^92 - 48 * q^93 + 21 * q^95 + 48 * q^97 + 6 * q^98 + 90 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$29$	$325$
$\chi(n)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	0.939693	−	0.342020i	0.664463	−	0.241845i
$2$	0.939693	−	0.342020i	0.664463	−	0.241845i
$3$	1.47894	−	0.901527i	0.853864	−	0.520497i
$3$	1.47894	−	0.901527i	0.853864	−	0.520497i
$4$	0.766044	−	0.642788i	0.383022	−	0.321394i
$5$	1.05304	+	0.383275i	0.470934	+	0.171406i	0.566575	−	0.824010i	$-0.308268\pi$
$5$	1.05304	+	0.383275i	0.470934	+	0.171406i	−0.0956413	+	0.995416i	$0.530490\pi$
$6$	1.08140	−	1.35298i	0.441481	−	0.552353i
$7$	1.66470	+	2.05639i	0.629199	+	0.777244i
$7$	1.66470	+	2.05639i	0.629199	+	0.777244i
$8$	0.500000	−	0.866025i	0.176777	−	0.306186i
$9$	1.37450	−	2.66660i	0.458166	−	0.888867i
$10$	1.12062			0.354372
$11$	−4.85062	+	1.76548i	−1.46252	+	0.532313i	−0.946058	−	0.323998i	$-0.894973\pi$
$11$	−4.85062	+	1.76548i	−1.46252	+	0.532313i	−0.516460	+	0.856311i	$0.672751\pi$
$12$	0.553440	−	1.64125i	0.159764	−	0.473788i
$13$	0.104655	+	0.593530i	0.0290261	+	0.164615i	0.995875	−	0.0907329i	$-0.0289210\pi$
$13$	0.104655	+	0.593530i	0.0290261	+	0.164615i	−0.966849	+	0.255348i	$0.917810\pi$
$14$	2.26764	+	1.36302i	0.606052	+	0.364282i
$15$	1.90291	−	0.382505i	0.491330	−	0.0987624i
$16$	0.173648	−	0.984808i	0.0434120	−	0.246202i
$17$	−2.64369			−0.641190			−0.320595	−	0.947216i	$-0.603883\pi$
$17$	−2.64369			−0.641190			−0.320595	+	0.947216i	$0.603883\pi$
$18$	0.379575	−	2.97589i	0.0894667	−	0.701424i
$19$	−2.99705			−0.687570			−0.343785	−	0.939048i	$-0.611709\pi$
$19$	−2.99705			−0.687570			−0.343785	+	0.939048i	$0.611709\pi$
$20$	1.05304	−	0.383275i	0.235467	−	0.0857030i
$21$	4.31588	+	1.54050i	0.941803	+	0.336164i
$22$	−3.95426	+	3.31802i	−0.843052	+	0.707405i
$23$	0.455644	+	2.58409i	0.0950083	+	0.538819i	0.994745	+	0.102385i	$0.0326475\pi$
$23$	0.455644	+	2.58409i	0.0950083	+	0.538819i	−0.899736	+	0.436434i	$0.856241\pi$
$24$	−0.0412776	−	1.73156i	−0.00842576	−	0.353453i
$25$	−2.86823	−	2.40673i	−0.573645	−	0.481346i
$26$	0.301343	+	0.521941i	0.0590982	+	0.102361i
$27$	−0.371217	−	5.18288i	−0.0714408	−	0.997445i
$28$	2.59706	+	0.505239i	0.490799	+	0.0954811i
$29$	0.657346	−	3.72799i	0.122066	−	0.692271i	−0.860941	−	0.508704i	$-0.830125\pi$
$29$	0.657346	−	3.72799i	0.122066	−	0.692271i	0.983007	−	0.183566i	$-0.0587643\pi$
$30$	1.65733	−	1.01027i	0.302585	−	0.184449i
$31$	1.70206	−	1.42820i	0.305699	−	0.256512i	−0.477013	−	0.878896i	$-0.658280\pi$
$31$	1.70206	−	1.42820i	0.305699	−	0.256512i	0.782712	+	0.622385i	$0.213836\pi$
$32$	−0.173648	−	0.984808i	−0.0306970	−	0.174091i
$33$	−5.58213	+	6.98400i	−0.971724	+	1.21576i
$34$	−2.48426	+	0.904196i	−0.426047	+	0.155068i
$35$	0.964836	+	2.80351i	0.163087	+	0.473879i
$36$	−0.661130	−	2.92624i	−0.110188	−	0.487707i
$37$	0.637238	−	1.10373i	0.104761	−	0.181452i	−0.808879	−	0.587975i	$-0.799925\pi$
$37$	0.637238	−	1.10373i	0.104761	−	0.181452i	0.913641	+	0.406523i	$0.133259\pi$
$38$	−2.81630	+	1.02505i	−0.456865	+	0.166285i
$39$	0.689861	+	0.783442i	0.110466	+	0.125451i
$40$	0.858447	−	0.720322i	0.135732	−	0.113893i
$41$	−1.28984	−	7.31506i	−0.201440	−	1.14242i	−0.902945	−	0.429756i	$-0.858600\pi$
$41$	−1.28984	−	7.31506i	−0.201440	−	1.14242i	0.701505	−	0.712664i	$-0.252512\pi$
$42$	4.58249	−	0.0285242i	0.707093	−	0.00440138i
$43$	4.79067	+	4.01985i	0.730570	+	0.613021i	0.930287	−	0.366833i	$-0.119558\pi$
$43$	4.79067	+	4.01985i	0.730570	+	0.613021i	−0.199717	+	0.979854i	$0.564002\pi$
$44$	−2.58096	+	4.47036i	−0.389095	+	0.673932i
$45$	2.46945	−	2.28123i	0.368123	−	0.340065i
$46$	1.31197	+	2.27241i	0.193440	+	0.335048i
$47$	−6.40954	−	5.37824i	−0.934927	−	0.784497i	0.0417680	−	0.999127i	$-0.486701\pi$
$47$	−6.40954	−	5.37824i	−0.934927	−	0.784497i	−0.976695	+	0.214630i	$0.931145\pi$
$48$	−0.631016	−	1.61302i	−0.0910794	−	0.232819i
$49$	−1.45752	+	6.84658i	−0.208217	+	0.978083i
$50$	−3.51840	−	1.28059i	−0.497577	−	0.181103i
$51$	−3.90985	+	2.38336i	−0.547488	+	0.333737i
$52$	0.461684	+	0.387399i	0.0640241	+	0.0537226i
$53$	−6.05084	+	10.4804i	−0.831146	+	1.43959i	0.0659834	+	0.997821i	$0.478982\pi$
$53$	−6.05084	+	10.4804i	−0.831146	+	1.43959i	−0.897130	+	0.441767i	$0.854352\pi$
$54$	−2.12148	−	4.74335i	−0.288697	−	0.645488i
$55$	−5.78457			−0.779991
$56$	2.61324	−	0.413479i	0.349209	−	0.0552534i
$57$	−4.43244	+	2.70192i	−0.587091	+	0.357878i
$58$	−0.657346	−	3.72799i	−0.0863137	−	0.489509i
$59$	0.0893074	+	0.506487i	0.0116268	+	0.0659390i	0.990069	−	0.140581i	$-0.0448971\pi$
$59$	0.0893074	+	0.506487i	0.0116268	+	0.0659390i	−0.978442	+	0.206520i	$0.933786\pi$
$60$	1.21185	−	1.51618i	0.156449	−	0.195739i
$61$	7.91024	+	6.63748i	1.01280	+	0.849843i	0.988706	−	0.149867i	$-0.0478846\pi$
$61$	7.91024	+	6.63748i	1.01280	+	0.849843i	0.0240968	+	0.999710i	$0.492329\pi$
$62$	1.11094	−	1.92421i	0.141090	−	0.244374i
$63$	7.77172	−	1.61259i	0.979144	−	0.203167i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	−0.117279	+	0.665123i	−0.0145467	+	0.0824983i
$66$	−2.85681	+	8.47201i	−0.351650	+	1.04283i
$67$	12.7733	+	4.64911i	1.56051	+	0.567979i	0.970853	−	0.239674i	$-0.0770406\pi$
$67$	12.7733	+	4.64911i	1.56051	+	0.567979i	0.589657	+	0.807654i	$0.299263\pi$
$68$	−2.02519	+	1.69933i	−0.245590	+	0.206074i
$69$	3.00349	+	3.41092i	0.361578	+	0.410627i
$70$	1.86551	+	2.30444i	0.222971	+	0.275434i
$71$	4.45463	+	7.71565i	0.528668	+	0.915679i	0.999441	+	0.0334252i	$0.0106416\pi$
$71$	4.45463	+	7.71565i	0.528668	+	0.915679i	−0.470774	+	0.882254i	$0.656025\pi$
$72$	−1.62209	−	2.52365i	−0.191166	−	0.297415i
$73$	−4.04838	−	7.01200i	−0.473827	−	0.820693i	0.525724	−	0.850655i	$-0.323795\pi$
$73$	−4.04838	−	7.01200i	−0.473827	−	0.820693i	−0.999551	+	0.0299626i	$0.990461\pi$
$74$	0.221311	−	1.25511i	0.0257268	−	0.145904i
$75$	−6.41165	−	0.973611i	−0.740354	−	0.112423i
$76$	−2.29587	+	1.92646i	−0.263354	+	0.220981i
$77$	−11.7054	−	7.03579i	−1.33395	−	0.801803i
$78$	0.916210	+	0.500248i	0.103740	+	0.0566420i
$79$	10.6914	−	3.89135i	1.20288	−	0.437811i	0.338648	−	0.940913i	$-0.390030\pi$
$79$	10.6914	−	3.89135i	1.20288	−	0.437811i	0.864227	+	0.503102i	$0.167808\pi$
$80$	0.560311	−	0.970488i	0.0626447	−	0.108504i
$81$	−5.22151	−	7.33047i	−0.580168	−	0.814497i
$82$	−3.71395	−	6.43276i	−0.410137	−	0.710379i
$83$	−1.31934	+	7.48238i	−0.144817	+	0.821297i	0.822697	+	0.568480i	$0.192468\pi$
$83$	−1.31934	+	7.48238i	−0.144817	+	0.821297i	−0.967514	+	0.252817i	$0.918643\pi$
$84$	4.29637	−	1.59411i	0.468773	−	0.173931i
$85$	−2.78392	−	1.01326i	−0.301958	−	0.109904i
$86$	5.87662	+	2.13892i	0.633693	+	0.230645i
$87$	−2.38871	−	6.10607i	−0.256097	−	0.654640i
$88$	−0.896359	+	5.08350i	−0.0955522	+	0.541903i
$89$	−6.65883			−0.705834			−0.352917	−	0.935655i	$-0.614810\pi$
$89$	−6.65883			−0.705834			−0.352917	+	0.935655i	$0.614810\pi$
$90$	1.54029	−	2.98825i	0.162361	−	0.314989i
$91$	−1.04631	+	1.20326i	−0.109683	+	0.126136i
$92$	2.01006	+	1.68664i	0.209563	+	0.175845i
$93$	1.22968	−	3.64666i	0.127512	−	0.378141i
$94$	−7.86246	−	2.86170i	−0.810951	−	0.295162i
$95$	−3.15601	−	1.14869i	−0.323800	−	0.117854i
$96$	−1.14465	−	1.29992i	−0.116825	−	0.132672i
$97$	6.73681	+	5.65286i	0.684020	+	0.573961i	0.917178	−	0.398478i	$-0.130462\pi$
$97$	6.73681	+	5.65286i	0.684020	+	0.573961i	−0.233158	+	0.972439i	$0.574906\pi$
$98$	0.972048	+	6.93218i	0.0981917	+	0.700256i
$99$	−1.95934	+	15.3613i	−0.196921	+	1.54387i
$100$	−3.74421			−0.374421
$101$	2.75295	−	15.6128i	0.273929	−	1.55353i	−0.468415	−	0.883508i	$-0.655175\pi$
$101$	2.75295	−	15.6128i	0.273929	−	1.55353i	0.742344	−	0.670019i	$-0.233714\pi$
$102$	−2.85890	+	3.57687i	−0.283073	+	0.354163i
$103$	−4.60200	−	1.67499i	−0.453449	−	0.165042i	0.105191	−	0.994452i	$-0.466454\pi$
$103$	−4.60200	−	1.67499i	−0.453449	−	0.165042i	−0.558640	+	0.829410i	$0.688677\pi$
$104$	0.566339	+	0.206131i	0.0555341	+	0.0202128i
$105$	3.95437	+	3.27638i	0.385907	+	0.319742i
$106$	−2.10143	+	11.9178i	−0.204109	+	1.15756i
$107$	4.11549	+	7.12824i	0.397860	+	0.689113i	0.993462	−	0.114167i	$-0.0364198\pi$
$107$	4.11549	+	7.12824i	0.397860	+	0.689113i	−0.595602	+	0.803280i	$0.703086\pi$
$108$	−3.61586	−	3.73170i	−0.347936	−	0.359083i
$109$	−2.87374	+	4.97746i	−0.275254	+	0.476754i	−0.970199	−	0.242309i	$-0.922095\pi$
$109$	−2.87374	+	4.97746i	−0.275254	+	0.476754i	0.694945	+	0.719063i	$0.255429\pi$
$110$	−5.43572	+	1.97844i	−0.518275	+	0.188637i
$111$	−0.0526074	−	2.20683i	−0.00499327	−	0.209463i
$112$	2.31423	−	1.28232i	0.218674	−	0.121168i
$113$	−8.95106	+	7.51083i	−0.842045	+	0.706560i	−0.958023	−	0.286692i	$-0.907444\pi$
$113$	−8.95106	+	7.51083i	−0.842045	+	0.706560i	0.115978	+	0.993252i	$0.463000\pi$
$114$	−3.24102	+	4.05496i	−0.303549	+	0.379781i
$115$	−0.510605	+	2.89578i	−0.0476142	+	0.270033i
$116$	−1.89275	−	3.27834i	−0.175738	−	0.304386i
$117$	1.72655	+	0.536732i	0.159620	+	0.0496209i
$118$	0.257150	+	0.445398i	0.0236726	+	0.0410022i
$119$	−4.40097	−	5.43648i	−0.403436	−	0.498361i
$120$	0.620197	−	1.83922i	0.0566160	−	0.167897i
$121$	11.9851	−	10.0567i	1.08956	−	0.914247i
$122$	9.70335	+	3.53173i	0.878500	+	0.319748i
$123$	−8.50232	−	9.65567i	−0.766628	−	0.870622i
$124$	0.385826	−	2.18813i	0.0346482	−	0.196499i
$125$	−4.89948	−	8.48614i	−0.438223	−	0.759024i
$126$	6.75149	−	4.17342i	0.601470	−	0.371798i
$127$	−4.86585	+	8.42790i	−0.431775	+	0.747856i	−0.997026	−	0.0770629i	$-0.975446\pi$
$127$	−4.86585	+	8.42790i	−0.431775	+	0.747856i	0.565252	+	0.824919i	$0.308779\pi$
$128$	−0.766044	−	0.642788i	−0.0677094	−	0.0568149i
$129$	10.7091	+	1.62618i	0.942883	+	0.143177i
$130$	0.117279	+	0.665123i	0.0102861	+	0.0583351i
$131$	−1.98840	−	11.2768i	−0.173728	−	0.985259i	−0.939602	−	0.342269i	$-0.888805\pi$
$131$	−1.98840	−	11.2768i	−0.173728	−	0.985259i	0.765874	−	0.642990i	$-0.222306\pi$
$132$	0.213072	+	8.93818i	0.0185455	+	0.777968i
$133$	−4.98920	−	6.16311i	−0.432618	−	0.534410i
$134$	13.5931			1.17426
$135$	1.59556	−	5.60006i	0.137324	−	0.481976i
$136$	−1.32185	+	2.28950i	−0.113347	+	0.196323i
$137$	2.98311	+	2.50313i	0.254865	+	0.213857i	0.761264	−	0.648442i	$-0.224579\pi$
$137$	2.98311	+	2.50313i	0.254865	+	0.213857i	−0.506399	+	0.862299i	$0.669024\pi$
$138$	3.98896	+	2.17796i	0.339563	+	0.185400i
$139$	15.4258	+	5.61455i	1.30840	+	0.476220i	0.899724	−	0.436459i	$-0.143768\pi$
$139$	15.4258	+	5.61455i	1.30840	+	0.476220i	0.408678	+	0.912678i	$0.365990\pi$
$140$	2.54117	+	1.52743i	0.214768	+	0.129091i
$141$	−14.3279	−	2.17570i	−1.20663	−	0.183227i
$142$	6.82489	+	5.72677i	0.572732	+	0.480580i
$143$	−1.55551	−	2.69422i	−0.130078	−	0.225302i
$144$	−2.38741	−	1.81667i	−0.198951	−	0.151389i
$145$	2.12106	−	3.67378i	0.176144	−	0.305091i
$146$	−6.20248	−	5.20450i	−0.513321	−	0.430727i
$147$	4.01680	+	11.4396i	0.331300	+	0.943525i
$148$	−0.221311	−	1.25511i	−0.0181916	−	0.103170i
$149$	17.9483	−	15.0604i	1.47038	−	1.23380i	0.554599	−	0.832118i	$-0.312872\pi$
$149$	17.9483	−	15.0604i	1.47038	−	1.23380i	0.915781	−	0.401678i	$-0.131573\pi$
$150$	−6.35798	+	1.27802i	−0.519127	+	0.104350i
$151$	−16.9367	+	6.16445i	−1.37829	+	0.501656i	−0.921659	−	0.388001i	$-0.873166\pi$
$151$	−16.9367	+	6.16445i	−1.37829	+	0.501656i	−0.456630	+	0.889657i	$0.650944\pi$
$152$	−1.49852	+	2.59552i	−0.121546	+	0.210524i
$153$	−3.63375	+	7.04967i	−0.293771	+	0.569932i
$154$	−13.4058	−	2.60800i	−1.08027	−	0.210159i
$155$	2.33973	−	0.851593i	0.187932	−	0.0684016i
$156$	1.03205	+	0.156717i	0.0826302	+	0.0125474i
$157$	−2.75251	−	15.6103i	−0.219675	−	1.24584i	−0.872608	−	0.488421i	$-0.837573\pi$
$157$	−2.75251	−	15.6103i	−0.219675	−	1.24584i	0.652934	−	0.757415i	$-0.273538\pi$
$158$	8.71570	−	7.31334i	0.693384	−	0.581818i
$159$	0.499528	+	20.9548i	0.0396152	+	1.66182i
$160$	0.194594	−	1.10360i	0.0153840	−	0.0872471i
$161$	−4.55539	+	5.23872i	−0.359015	+	0.412869i
$162$	−7.41378	−	5.10253i	−0.582482	−	0.400893i
$163$	1.27712	+	2.21203i	0.100032	+	0.173260i	0.911697	−	0.410862i	$-0.134772\pi$
$163$	1.27712	+	2.21203i	0.100032	+	0.173260i	−0.811666	+	0.584122i	$0.801439\pi$
$164$	−5.69011	−	4.77457i	−0.444323	−	0.372831i
$165$	−8.55500	+	5.21495i	−0.666006	+	0.405983i
$166$	1.31934	+	7.48238i	0.102401	+	0.580745i
$167$	2.58990	−	2.17318i	0.200412	−	0.168166i	−0.537058	−	0.843545i	$-0.680464\pi$
$167$	2.58990	−	2.17318i	0.200412	−	0.168166i	0.737471	+	0.675379i	$0.236020\pi$
$168$	3.49205	−	2.96742i	0.269418	−	0.228941i
$169$	11.8747	−	4.32203i	0.913437	−	0.332464i
$170$	−2.96258			−0.227220
$171$	−4.11944	+	7.99192i	−0.315021	+	0.611158i
$172$	6.25377			0.476846
$173$	1.66576	−	9.44701i	0.126646	−	0.718243i	−0.853671	−	0.520812i	$-0.825629\pi$
$173$	1.66576	−	9.44701i	0.126646	−	0.718243i	0.980317	−	0.197430i	$-0.0632597\pi$
$174$	−4.33306	−	4.92084i	−0.328488	−	0.373048i
$175$	0.174434	−	9.90470i	0.0131859	−	0.748725i
$176$	0.896359	+	5.08350i	0.0675656	+	0.383183i
$177$	0.588692	+	0.668549i	0.0442488	+	0.0502512i
$178$	−6.25725	+	2.27745i	−0.469001	+	0.170702i
$179$	5.50864			0.411735			0.205868	−	0.978580i	$-0.433998\pi$
$179$	5.50864			0.411735			0.205868	+	0.978580i	$0.433998\pi$
$180$	0.425361	−	3.33485i	0.0317045	−	0.248565i
$181$	3.22516	−	5.58614i	0.239724	−	0.415214i	−0.720911	−	0.693028i	$-0.756276\pi$
$181$	3.22516	−	5.58614i	0.239724	−	0.415214i	0.960635	+	0.277813i	$0.0896097\pi$
$182$	−0.571670	+	1.48856i	−0.0423750	+	0.110339i
$183$	17.6826	+	2.68511i	1.30714	+	0.198489i
$184$	2.46571	+	0.897444i	0.181774	+	0.0661604i
$185$	1.09407	−	0.918034i	0.0804376	−	0.0674952i
$186$	−0.0917140	−	3.84732i	−0.00672480	−	0.282099i
$187$	12.8236	−	4.66739i	0.937751	−	0.341314i
$188$	−8.36706			−0.610231
$189$	10.0401	−	9.39132i	0.730308	−	0.683118i
$190$	−3.35856			−0.243655
$191$	−6.56732	+	2.39031i	−0.475194	+	0.172957i	−0.568504	−	0.822681i	$-0.692478\pi$
$191$	−6.56732	+	2.39031i	−0.475194	+	0.172957i	0.0933096	+	0.995637i	$0.470255\pi$
$192$	−1.52021	−	0.830032i	−0.109712	−	0.0599024i
$193$	18.0880	−	15.1776i	1.30200	−	1.09251i	0.312206	−	0.950014i	$-0.398932\pi$
$193$	18.0880	−	15.1776i	1.30200	−	1.09251i	0.989796	−	0.142494i	$-0.0455123\pi$
$194$	8.26392	+	3.00782i	0.593315	+	0.215949i
$195$	0.426178	+	1.08940i	0.0305192	+	0.0780138i
$196$	3.28437	+	6.18166i	0.234598	+	0.441547i
$197$	1.11178	−	1.92566i	0.0792112	−	0.137198i	−0.823699	−	0.567028i	$-0.808093\pi$
$197$	1.11178	−	1.92566i	0.0792112	−	0.137198i	0.902910	+	0.429830i	$0.141427\pi$
$198$	3.41271	+	15.1051i	0.242530	+	1.07347i
$199$	−26.0446			−1.84626			−0.923128	−	0.384494i	$-0.874376\pi$
$199$	−26.0446			−1.84626			−0.923128	+	0.384494i	$0.874376\pi$
$200$	−3.51840	+	1.28059i	−0.248789	+	0.0905516i
$201$	23.0822	−	4.63977i	1.62809	−	0.327264i
$202$	−2.75295	−	15.6128i	−0.193697	−	1.09851i
$203$	8.76051	−	4.85424i	0.614867	−	0.340701i
$204$	−1.46312	+	4.33896i	−0.102439	+	0.303788i
$205$	1.44543	−	8.19742i	0.100953	−	0.572533i
$206$	−4.89735			−0.341214
$207$	7.51700	+	2.33680i	0.522468	+	0.162419i
$208$	0.602686			0.0417887
$209$	14.5375	−	5.29123i	1.00558	−	0.366002i
$210$	4.83648	+	1.72632i	0.333749	+	0.119127i
$211$	−8.51422	+	7.14428i	−0.586143	+	0.491833i	−0.886958	−	0.461850i	$-0.847186\pi$
$211$	−8.51422	+	7.14428i	−0.586143	+	0.491833i	0.300815	+	0.953683i	$0.402741\pi$
$212$	2.10143	+	11.9178i	0.144327	+	0.818519i
$213$	13.5440	+	7.39498i	0.928018	+	0.506695i
$214$	6.30530	+	5.29077i	0.431021	+	0.361670i
$215$	3.50406	+	6.06921i	0.238975	+	0.413917i
$216$	−4.67411	−	2.26995i	−0.318033	−	0.154451i
$217$	5.77036	+	1.12258i	0.391718	+	0.0762057i
$218$	−0.998038	+	5.66016i	−0.0675957	+	0.383354i
$219$	−12.3088	−	6.72057i	−0.831752	−	0.454134i
$220$	−4.43124	+	3.71825i	−0.298754	+	0.250684i
$221$	−0.276676	−	1.56911i	−0.0186113	−	0.105550i
$222$	−0.804215	−	2.05575i	−0.0539754	−	0.137973i
$223$	−5.60165	+	2.03883i	−0.375114	+	0.136530i	−0.522695	−	0.852520i	$-0.675073\pi$
$223$	−5.60165	+	2.03883i	−0.375114	+	0.136530i	0.147581	+	0.989050i	$0.452851\pi$
$224$	1.73608	−	1.99650i	0.115997	−	0.133397i
$225$	−10.3602	+	4.34037i	−0.690677	+	0.289358i
$226$	−5.84239	+	10.1193i	−0.388630	+	0.673127i
$227$	28.1085	−	10.2306i	1.86563	−	0.679032i	0.891501	−	0.453018i	$-0.149653\pi$
$227$	28.1085	−	10.2306i	1.86563	−	0.679032i	0.974124	−	0.226014i	$-0.0725694\pi$
$228$	−1.65868	+	4.91891i	−0.109849	+	0.325762i
$229$	13.0824	−	10.9774i	0.864507	−	0.725408i	−0.0984269	−	0.995144i	$-0.531381\pi$
$229$	13.0824	−	10.9774i	0.864507	−	0.725408i	0.962934	+	0.269737i	$0.0869366\pi$
$230$	0.510605	+	2.89578i	0.0336683	+	0.190942i
$231$	−23.6545	+	0.147240i	−1.55635	+	0.00968767i
$232$	−2.89986	−	2.43327i	−0.190385	−	0.159752i
$233$	−8.86543	+	15.3554i	−0.580794	+	1.00596i	0.414592	+	0.910008i	$0.363924\pi$
$233$	−8.86543	+	15.3554i	−0.580794	+	1.00596i	−0.995386	+	0.0959568i	$0.969409\pi$
$234$	1.80600	−	0.0861535i	0.118062	−	0.00563203i
$235$	−4.68816	−	8.12013i	−0.305822	−	0.529699i
$236$	0.393977	+	0.330586i	0.0256457	+	0.0215193i
$237$	12.3037	−	15.3936i	0.799212	−	0.999924i
$238$	−5.99494	−	3.60340i	−0.388594	−	0.233574i
$239$	26.9037	+	9.79215i	1.74026	+	0.633402i	0.999273	−	0.0381217i	$-0.0121374\pi$
$239$	26.9037	+	9.79215i	1.74026	+	0.633402i	0.740983	+	0.671523i	$0.234360\pi$
$240$	−0.0462566	−	1.94042i	−0.00298585	−	0.125254i
$241$	−19.8464	−	16.6531i	−1.27842	−	1.07272i	−0.993460	−	0.114182i	$-0.963575\pi$
$241$	−19.8464	−	16.6531i	−1.27842	−	1.07272i	−0.284959	−	0.958540i	$-0.591980\pi$
$242$	7.82273	−	13.5494i	0.502864	−	0.870987i
$243$	−14.3309	−	6.13397i	−0.919327	−	0.393494i
$244$	10.3261			0.661060
$245$	−4.15895	+	6.65109i	−0.265706	+	0.424923i
$246$	−11.2920	−	6.16540i	−0.719951	−	0.393091i
$247$	−0.313657	−	1.77884i	−0.0199575	−	0.113185i
$248$	−0.385826	−	2.18813i	−0.0244999	−	0.138946i
$249$	4.79434	+	12.2554i	0.303829	+	0.776653i
$250$	−7.50643	−	6.29865i	−0.474749	−	0.398361i
$251$	−5.23039	+	9.05930i	−0.330139	+	0.571818i	−0.982539	−	0.186057i	$-0.940429\pi$
$251$	−5.23039	+	9.05930i	−0.330139	+	0.571818i	0.652400	+	0.757875i	$0.273762\pi$
$252$	4.91693	−	6.23088i	0.309737	−	0.392508i
$253$	−6.77231	−	11.7300i	−0.425772	−	0.737458i
$254$	−1.68989	+	9.58386i	−0.106033	+	0.601345i
$255$	−5.03071	+	1.01123i	−0.315036	+	0.0633254i
$256$	−0.939693	−	0.342020i	−0.0587308	−	0.0213763i
$257$	−15.1896	+	12.7456i	−0.947504	+	0.795050i	−0.978875	−	0.204458i	$-0.934457\pi$
$257$	−15.1896	+	12.7456i	−0.947504	+	0.795050i	0.0313717	+	0.999508i	$0.490012\pi$
$258$	10.6194	−	2.13462i	0.661137	−	0.132895i
$259$	3.33052	−	0.526969i	0.206948	−	0.0327443i
$260$	0.337692	+	0.584899i	0.0209427	+	0.0362739i
$261$	−9.03754	−	6.87700i	−0.559410	−	0.425675i
$262$	−5.72538	−	9.91665i	−0.353715	−	0.612653i
$263$	3.06783	−	17.3986i	0.189171	−	1.07284i	−0.731308	−	0.682048i	$-0.761090\pi$
$263$	3.06783	−	17.3986i	0.189171	−	1.07284i	0.920479	−	0.390793i	$-0.127799\pi$
$264$	3.25726	+	8.32626i	0.200470	+	0.512446i
$265$	−10.3886	+	8.71711i	−0.638169	+	0.535488i
$266$	−6.79622	−	4.08502i	−0.416703	−	0.250469i
$267$	−9.84797	+	6.00311i	−0.602686	+	0.367384i
$268$	12.7733	−	4.64911i	0.780255	−	0.283990i
$269$	−6.67615	+	11.5634i	−0.407052	+	0.705035i	−0.994558	−	0.104185i	$-0.966777\pi$
$269$	−6.67615	+	11.5634i	−0.407052	+	0.705035i	0.587506	+	0.809220i	$0.300110\pi$
$270$	−0.415995	−	5.80805i	−0.0253166	−	0.353466i
$271$	4.05289	+	7.01982i	0.246196	+	0.426423i	0.962467	−	0.271398i	$-0.0874861\pi$
$271$	4.05289	+	7.01982i	0.246196	+	0.426423i	−0.716271	+	0.697822i	$0.754153\pi$
$272$	−0.459072	+	2.60353i	−0.0278354	+	0.157862i
$273$	−0.462651	+	2.72283i	−0.0280009	+	0.164793i
$274$	3.65933	+	1.33189i	0.221068	+	0.0804623i
$275$	18.1617	+	6.61033i	1.09519	+	0.398618i
$276$	4.49330	+	0.682310i	0.270465	+	0.0410702i
$277$	2.61254	−	14.8164i	0.156972	−	0.890233i	−0.799989	−	0.600015i	$-0.795161\pi$
$277$	2.61254	−	14.8164i	0.156972	−	0.890233i	0.956961	−	0.290218i	$-0.0937277\pi$
$278$	16.4158			0.984556
$279$	−1.46895	−	6.50177i	−0.0879439	−	0.389251i
$280$	2.91033	+	0.566182i	0.173925	+	0.0338358i
$281$	−2.50620	−	2.10295i	−0.149507	−	0.125451i	0.564966	−	0.825114i	$-0.308889\pi$
$281$	−2.50620	−	2.10295i	−0.149507	−	0.125451i	−0.714473	+	0.699663i	$0.753334\pi$
$282$	−14.2080	+	2.85595i	−0.846073	+	0.170069i
$283$	−16.8169	−	6.12085i	−0.999661	−	0.363847i	−0.210207	−	0.977657i	$-0.567414\pi$
$283$	−16.8169	−	6.12085i	−0.999661	−	0.363847i	−0.789454	+	0.613810i	$0.789636\pi$
$284$	8.37197	+	3.04715i	0.496785	+	0.180815i
$285$	−5.70312	+	1.14639i	−0.337823	+	0.0679060i
$286$	−2.38318	−	1.99972i	−0.140920	−	0.118246i
$287$	12.8954	−	14.8298i	0.761194	−	0.875378i
$288$	−2.86477	−	0.890567i	−0.168808	−	0.0524771i
$289$	−10.0109			−0.588876
$290$	0.736636	−	4.17767i	0.0432568	−	0.245321i
$291$	15.0595	+	2.28679i	0.882804	+	0.134054i
$292$	−7.60847	−	2.76926i	−0.445252	−	0.162058i
$293$	3.22137	+	1.17248i	0.188195	+	0.0684973i	0.434398	−	0.900721i	$-0.356961\pi$
$293$	3.22137	+	1.17248i	0.188195	+	0.0684973i	−0.246204	+	0.969218i	$0.579183\pi$
$294$	7.68714	+	9.37592i	0.448323	+	0.546815i
$295$	−0.100080	+	0.567581i	−0.00582688	+	0.0330459i
$296$	−0.637238	−	1.10373i	−0.0370387	−	0.0641529i
$297$	10.9509	+	24.4848i	0.635436	+	1.42075i
$298$	11.7149	−	20.2908i	0.678626	−	1.17542i
$299$	−1.48605	+	0.540876i	−0.0859402	+	0.0312797i
$300$	−5.53744	+	3.37550i	−0.319704	+	0.194885i
$301$	−0.291348	+	16.5434i	−0.0167930	+	0.953544i
$302$	−13.8069	+	11.5854i	−0.794499	+	0.666664i
$303$	−10.0039	−	25.5721i	−0.574708	−	1.46908i
$304$	−0.520432	+	2.95151i	−0.0298488	+	0.169281i
$305$	5.78583	+	10.0213i	0.331295	+	0.573820i
$306$	−1.00348	+	7.86734i	−0.0573651	+	0.449746i
$307$	13.2876	+	23.0148i	0.758362	+	1.31352i	0.943685	+	0.330844i	$0.107334\pi$
$307$	13.2876	+	23.0148i	0.758362	+	1.31352i	−0.185323	+	0.982678i	$0.559333\pi$
$308$	−13.4894	+	2.13435i	−0.768628	+	0.121616i
$309$	−8.31611	+	1.67162i	−0.473087	+	0.0950954i
$310$	1.90737	−	1.60047i	0.108331	−	0.0909006i
$311$	−1.15766	−	0.421354i	−0.0656449	−	0.0238928i	0.308989	−	0.951066i	$-0.400009\pi$
$311$	−1.15766	−	0.421354i	−0.0656449	−	0.0238928i	−0.374634	+	0.927173i	$0.622232\pi$
$312$	1.02341	−	0.205716i	0.0579393	−	0.0116464i
$313$	−1.95122	+	11.0659i	−0.110290	+	0.625483i	0.878685	+	0.477401i	$0.158421\pi$
$313$	−1.95122	+	11.0659i	−0.110290	+	0.625483i	−0.988975	+	0.148082i	$0.952690\pi$
$314$	−7.92555	−	13.7275i	−0.447265	−	0.774685i
$315$	8.80200	+	1.28059i	0.495936	+	0.0721529i
$316$	5.68877	−	9.85324i	0.320018	−	0.554288i
$317$	−5.10082	−	4.28010i	−0.286491	−	0.240394i	0.488204	−	0.872729i	$-0.337652\pi$
$317$	−5.10082	−	4.28010i	−0.286491	−	0.240394i	−0.774695	+	0.632335i	$0.782097\pi$
$318$	7.63635	+	19.5202i	0.428225	+	1.09464i
$319$	3.39317	+	19.2436i	0.189981	+	1.07744i
$320$	−0.194594	−	1.10360i	−0.0108781	−	0.0616930i
$321$	12.5128	+	6.83198i	0.698399	+	0.381324i
$322$	−2.48892	+	6.48082i	−0.138702	+	0.361162i
$323$	7.92327			0.440862
$324$	−8.71185	−	2.25915i	−0.483991	−	0.125508i
$325$	1.12829	−	1.95425i	0.0625862	−	0.108403i
$326$	1.95666	+	1.64183i	0.108369	+	0.0909326i
$327$	0.237242	+	9.95209i	0.0131195	+	0.550352i
$328$	−6.97995	−	2.54049i	−0.385403	−	0.140275i
$329$	0.389801	−	22.1337i	0.0214904	−	1.22027i
$330$	−6.25546	+	7.82643i	−0.344352	+	0.430831i
$331$	−8.72601	−	7.32200i	−0.479625	−	0.402453i	0.370666	−	0.928766i	$-0.379130\pi$
$331$	−8.72601	−	7.32200i	−0.479625	−	0.402453i	−0.850291	+	0.526313i	$0.823574\pi$
$332$	3.79890	+	6.57989i	0.208492	+	0.361118i
$333$	−2.06732	−	3.21633i	−0.113288	−	0.176254i
$334$	1.69044	−	2.92792i	0.0924966	−	0.160209i
$335$	11.6689	+	9.79141i	0.637543	+	0.534962i
$336$	2.26654	−	3.98281i	0.123650	−	0.217280i
$337$	−3.92790	−	22.2762i	−0.213967	−	1.21346i	−0.882691	−	0.469954i	$-0.844270\pi$
$337$	−3.92790	−	22.2762i	−0.213967	−	1.21346i	0.668724	−	0.743510i	$-0.266841\pi$
$338$	9.68033	−	8.12276i	0.526540	−	0.441820i
$339$	−6.46682	+	19.1777i	−0.351230	+	1.04159i
$340$	−2.78392	+	1.01326i	−0.150979	+	0.0549519i
$341$	−5.73459	+	9.93260i	−0.310546	+	0.537881i
$342$	−1.13760	+	8.91888i	−0.0615146	+	0.482278i
$343$	−16.5056	+	8.40029i	−0.891219	+	0.453573i
$344$	5.87662	−	2.13892i	0.316846	−	0.115323i
$345$	1.85548	+	4.74300i	0.0998955	+	0.255355i
$346$	−1.66576	−	9.44701i	−0.0895519	−	0.507874i
$347$	−9.29490	+	7.79935i	−0.498976	+	0.418691i	−0.857230	−	0.514933i	$-0.827817\pi$
$347$	−9.29490	+	7.79935i	−0.498976	+	0.418691i	0.358254	+	0.933624i	$0.383372\pi$
$348$	−5.75477	−	3.14209i	−0.308488	−	0.168434i
$349$	−6.08774	+	34.5253i	−0.325869	+	1.84810i	0.177625	+	0.984098i	$0.443159\pi$
$349$	−6.08774	+	34.5253i	−0.325869	+	1.84810i	−0.503494	+	0.863999i	$0.667953\pi$
$350$	−3.22369	−	9.36703i	−0.172314	−	0.500689i
$351$	3.03734	−	0.762744i	0.162121	−	0.0407122i
$352$	2.58096	+	4.47036i	0.137566	+	0.238271i
$353$	24.3664	+	20.4459i	1.29689	+	1.08822i	0.990673	+	0.136263i	$0.0435093\pi$
$353$	24.3664	+	20.4459i	1.29689	+	1.08822i	0.306222	+	0.951960i	$0.400935\pi$
$354$	0.781847	+	0.426886i	0.0415547	+	0.0226887i
$355$	1.73369	+	9.83225i	0.0920147	+	0.521841i
$356$	−5.10096	+	4.28021i	−0.270350	+	0.226851i
$357$	−11.4099	−	4.07261i	−0.603874	−	0.215545i
$358$	5.17643	−	1.88407i	0.273583	−	0.0995760i
$359$	−7.01075			−0.370013			−0.185007	−	0.982737i	$-0.559231\pi$
$359$	−7.01075			−0.370013			−0.185007	+	0.982737i	$0.559231\pi$
$360$	−0.740878	−	3.27922i	−0.0390477	−	0.172830i
$361$	−10.0177			−0.527248
$362$	1.12009	−	6.35232i	0.0588704	−	0.333870i
$363$	8.65882	−	25.6781i	0.454470	−	1.34775i
$364$	−0.0280777	+	1.59431i	−0.00147167	+	0.0835645i
$365$	−1.57558	−	8.93557i	−0.0824697	−	0.467709i
$366$	17.5346	−	3.52463i	0.916547	−	0.184235i
$367$	−20.3936	+	7.42267i	−1.06454	+	0.387460i	−0.814132	−	0.580680i	$-0.802787\pi$
$367$	−20.3936	+	7.42267i	−1.06454	+	0.387460i	−0.250407	+	0.968141i	$0.580564\pi$
$368$	2.62395			0.136783
$369$	−21.2792	−	6.61504i	−1.10775	−	0.344365i
$370$	0.714104	−	1.23686i	0.0371245	−	0.0643015i
$371$	−31.6246	+	5.00379i	−1.64187	+	0.259784i
$372$	−1.40204	−	3.58393i	−0.0726926	−	0.185818i
$373$	−27.2366	−	9.91330i	−1.41026	−	0.513291i	−0.479051	−	0.877787i	$-0.659019\pi$
$373$	−27.2366	−	9.91330i	−1.41026	−	0.513291i	−0.931205	+	0.364496i	$0.881241\pi$
$374$	10.4539	−	8.77183i	0.540556	−	0.453580i
$375$	−14.8965	−	8.13344i	−0.769252	−	0.420009i
$376$	−7.86246	+	2.86170i	−0.405476	+	0.147581i
$377$	2.28147			0.117502
$378$	6.22256	−	12.2589i	0.320054	−	0.630528i
$379$	−12.4747			−0.640781			−0.320390	−	0.947286i	$-0.603814\pi$
$379$	−12.4747			−0.640781			−0.320390	+	0.947286i	$0.603814\pi$
$380$	−3.15601	+	1.14869i	−0.161900	+	0.0589268i
$381$	0.401702	+	16.8510i	0.0205798	+	0.863304i
$382$	−5.35372	+	4.49231i	−0.273920	+	0.229846i
$383$	0.656200	+	0.238837i	0.0335303	+	0.0122040i	0.358731	−	0.933441i	$-0.383210\pi$
$383$	0.656200	+	0.238837i	0.0335303	+	0.0122040i	−0.325201	+	0.945645i	$0.605432\pi$
$384$	−1.71242	−	0.260032i	−0.0873866	−	0.0132697i
$385$	−9.62960	−	11.8954i	−0.490770	−	0.606244i
$386$	11.8061	−	20.4488i	0.600914	−	1.04081i
$387$	17.3041	−	7.24952i	0.879616	−	0.368514i
$388$	8.79428			0.446462
$389$	−36.1319	+	13.1509i	−1.83196	+	0.666779i	−0.839631	+	0.543158i	$0.817228\pi$
$389$	−36.1319	+	13.1509i	−1.83196	+	0.666779i	−0.992330	+	0.123621i	$0.960549\pi$
$390$	0.773074	+	0.877943i	0.0391461	+	0.0444564i
$391$	−1.20458	−	6.83153i	−0.0609184	−	0.345485i
$392$	5.20055	+	4.68554i	0.262668	+	0.236655i
$393$	−13.1071	−	14.8851i	−0.661164	−	0.750852i
$394$	0.386118	−	2.18978i	0.0194523	−	0.110320i
$395$	12.7499			0.641519
$396$	8.37313	+	13.0269i	0.420765	+	0.654626i
$397$	19.4509			0.976210			0.488105	−	0.872785i	$-0.337688\pi$
$397$	19.4509			0.976210			0.488105	+	0.872785i	$0.337688\pi$
$398$	−24.4740	+	8.90779i	−1.22677	+	0.446507i
$399$	−12.9349	−	4.61695i	−0.647555	−	0.231136i
$400$	−2.86823	+	2.40673i	−0.143411	+	0.120336i
$401$	5.04822	+	28.6299i	0.252096	+	1.42971i	0.803418	+	0.595416i	$0.203013\pi$
$401$	5.04822	+	28.6299i	0.252096	+	1.42971i	−0.551321	+	0.834293i	$0.685876\pi$
$402$	20.1033	−	12.2545i	1.00266	−	0.611201i
$403$	1.02581	+	0.860754i	0.0510991	+	0.0428772i
$404$	−7.92680	−	13.7296i	−0.394373	−	0.683074i
$405$	−2.68887	−	9.72056i	−0.133611	−	0.483019i
$406$	6.57194	−	7.55777i	0.326160	−	0.375086i
$407$	−1.14239	+	6.47881i	−0.0566261	+	0.321142i
$408$	0.109125	+	4.57771i	0.00540251	+	0.226630i
$409$	20.2133	−	16.9610i	0.999482	−	0.838665i	0.0125698	−	0.999921i	$-0.495999\pi$
$409$	20.2133	−	16.9610i	0.999482	−	0.838665i	0.986913	+	0.161256i	$0.0515544\pi$
$410$	−1.44543	−	8.19742i	−0.0713845	−	0.404842i
$411$	6.66847	+	1.01261i	0.328931	+	0.0499483i
$412$	−4.60200	+	1.67499i	−0.226724	+	0.0825209i
$413$	−0.892868	+	1.02680i	−0.0439351	+	0.0505257i
$414$	7.86291	−	0.375092i	0.386441	−	0.0184348i
$415$	−4.25714	+	7.37357i	−0.208975	+	0.361955i
$416$	0.566339	−	0.206131i	0.0277671	−	0.0101064i
$417$	27.8755	−	5.60326i	1.36507	−	0.274393i
$418$	11.8511	−	9.94426i	0.579657	−	0.486390i
$419$	2.69402	+	15.2786i	0.131612	+	0.746407i	0.977159	+	0.212507i	$0.0681629\pi$
$419$	2.69402	+	15.2786i	0.131612	+	0.746407i	−0.845548	+	0.533900i	$0.820726\pi$
$420$	5.13524	−	0.0319649i	0.250574	−	0.00155973i
$421$	−8.53996	−	7.16588i	−0.416212	−	0.349244i	0.410508	−	0.911857i	$-0.365352\pi$
$421$	−8.53996	−	7.16588i	−0.416212	−	0.349244i	−0.826720	+	0.562613i	$0.809796\pi$
$422$	−5.55726	+	9.62546i	−0.270523	+	0.468560i
$423$	−23.1515	+	9.69929i	−1.12567	+	0.471596i
$424$	6.05084	+	10.4804i	0.293855	+	0.508971i
$425$	7.58271	+	6.36265i	0.367816	+	0.308634i
$426$	15.2564	+	2.31669i	0.739175	+	0.112244i
$427$	−0.481068	+	27.3160i	−0.0232805	+	1.32192i
$428$	7.73460	+	2.81516i	0.373866	+	0.136076i
$429$	−4.72941	−	2.58224i	−0.228338	−	0.124672i
$430$	5.36853	+	4.50473i	0.258894	+	0.217237i
$431$	−2.96018	+	5.12719i	−0.142587	+	0.246968i	−0.928470	−	0.371407i	$-0.878875\pi$
$431$	−2.96018	+	5.12719i	−0.142587	+	0.246968i	0.785883	+	0.618375i	$0.212209\pi$
$432$	−5.16860	−	0.534419i	−0.248674	−	0.0257123i
$433$	−38.0048			−1.82639			−0.913197	−	0.407518i	$-0.866394\pi$
$433$	−38.0048			−1.82639			−0.913197	+	0.407518i	$0.866394\pi$
$434$	5.80631	−	0.918701i	0.278712	−	0.0440990i
$435$	−0.175105	−	7.34548i	−0.00839563	−	0.352189i
$436$	0.998038	+	5.66016i	0.0477974	+	0.271072i
$437$	−1.36559	−	7.74463i	−0.0653249	−	0.370476i
$438$	−13.8651	−	2.10541i	−0.662498	−	0.100601i
$439$	−5.64899	−	4.74007i	−0.269612	−	0.226231i	0.497951	−	0.867205i	$-0.334086\pi$
$439$	−5.64899	−	4.74007i	−0.269612	−	0.226231i	−0.767562	+	0.640974i	$0.778530\pi$
$440$	−2.89228	+	5.00958i	−0.137884	+	0.238823i
$441$	16.2537	+	13.2972i	0.773987	+	0.633202i
$442$	−0.796658	−	1.37985i	−0.0378931	−	0.0656329i
$443$	0.114242	−	0.647897i	0.00542779	−	0.0307825i	−0.981974	−	0.189018i	$-0.939469\pi$
$443$	0.114242	−	0.647897i	0.00542779	−	0.0307825i	0.987401	+	0.158236i	$0.0505806\pi$
$444$	−1.45882	−	1.65672i	−0.0692327	−	0.0786242i
$445$	−7.01202	−	2.55217i	−0.332401	−	0.120984i
$446$	−4.56651	+	3.83175i	−0.216230	+	0.181439i
$447$	12.9670	−	38.4542i	0.613318	−	1.81882i
$448$	0.948538	−	2.46987i	0.0448142	−	0.116691i
$449$	−15.3893	−	26.6550i	−0.726264	−	1.25793i	−0.958452	−	0.285255i	$-0.907922\pi$
$449$	−15.3893	−	26.6550i	−0.726264	−	1.25793i	0.232188	−	0.972671i	$-0.425412\pi$
$450$	−8.25087	+	7.62200i	−0.388950	+	0.359304i
$451$	19.1711	+	33.2054i	0.902734	+	1.56358i
$452$	−2.02904	+	11.5073i	−0.0954381	+	0.541256i
$453$	−19.4909	+	24.3857i	−0.915760	+	1.14574i
$454$	22.9142	−	19.2273i	1.07542	−	0.902383i
$455$	−1.56299	+	0.866060i	−0.0732741	+	0.0406015i
$456$	0.123711	+	5.18956i	0.00579330	+	0.243024i
$457$	1.48946	−	0.542120i	0.0696742	−	0.0253593i	−0.306948	−	0.951726i	$-0.599308\pi$
$457$	1.48946	−	0.542120i	0.0696742	−	0.0253593i	0.376622	+	0.926367i	$0.377086\pi$
$458$	8.53891	−	14.7898i	0.398997	−	0.691083i
$459$	0.981384	+	13.7019i	0.0458071	+	0.639551i
$460$	1.47023	+	2.54651i	0.0685498	+	0.118732i
$461$	−0.684017	+	3.87925i	−0.0318579	+	0.180675i	−0.996585	−	0.0825786i	$-0.973684\pi$
$461$	−0.684017	+	3.87925i	−0.0318579	+	0.180675i	0.964727	+	0.263253i	$0.0847956\pi$
$462$	−22.1776	+	8.22866i	−1.03179	+	0.382832i
$463$	18.3792	+	6.68950i	0.854156	+	0.310887i	0.731734	−	0.681591i	$-0.238712\pi$
$463$	18.3792	+	6.68950i	0.854156	+	0.310887i	0.122422	+	0.992478i	$0.460934\pi$
$464$	−3.55721	−	1.29472i	−0.165139	−	0.0601058i
$465$	2.69258	−	3.36878i	0.124865	−	0.156223i
$466$	−3.07893	+	17.4615i	−0.142629	+	0.808888i
$467$	1.78120			0.0824240			0.0412120	−	0.999150i	$-0.486878\pi$
$467$	1.78120			0.0824240			0.0412120	+	0.999150i	$0.486878\pi$
$468$	1.66762	−	0.698647i	0.0770858	−	0.0322950i
$469$	11.7034	+	34.0064i	0.540413	+	1.57027i
$470$	−7.18267	−	6.02698i	−0.331312	−	0.278004i
$471$	−18.1439	−	20.6051i	−0.836026	−	0.949434i
$472$	0.483285	+	0.175901i	0.0222450	+	0.00809651i
$473$	−30.3347	−	11.0409i	−1.39479	−	0.507662i
$474$	6.29678	−	18.6734i	0.289221	−	0.857698i
$475$	8.59621	+	7.21308i	0.394421	+	0.330959i
$476$	−6.86583	−	1.33570i	−0.314695	−	0.0612215i
$477$	19.6301	+	30.5404i	0.898798	+	1.39835i
$478$	28.6303			1.30952
$479$	0.978080	−	5.54697i	0.0446896	−	0.253448i	−0.954276	−	0.298928i	$-0.903371\pi$
$479$	0.978080	−	5.54697i	0.0446896	−	0.253448i	0.998965	+	0.0454808i	$0.0144820\pi$
$480$	−0.707131	−	1.80758i	−0.0322760	−	0.0825044i
$481$	0.721786	+	0.262709i	0.0329106	+	0.0119785i
$482$	−24.3452	−	8.86093i	−1.10889	−	0.403605i
$483$	−2.01427	+	11.8545i	−0.0916526	+	0.539400i
$484$	2.71681	−	15.4078i	0.123491	−	0.700354i
$485$	4.92754	+	8.53474i	0.223748	+	0.387543i
$486$	−15.5646	−	0.862589i	−0.706023	−	0.0391278i
$487$	13.7227	−	23.7683i	0.621833	−	1.07705i	−0.367311	−	0.930098i	$-0.619722\pi$
$487$	13.7227	−	23.7683i	0.621833	−	1.07705i	0.989144	−	0.146948i	$-0.0469451\pi$
$488$	9.70335	−	3.53173i	0.439250	−	0.159874i
$489$	3.88298	+	2.12010i	0.175595	+	0.0958741i
$490$	−1.63333	+	7.67243i	−0.0737863	+	0.346605i
$491$	5.42602	−	4.55297i	0.244873	−	0.205473i	−0.512088	−	0.858933i	$-0.671128\pi$
$491$	5.42602	−	4.55297i	0.244873	−	0.205473i	0.756961	+	0.653460i	$0.226683\pi$
$492$	−12.7197	−	1.93149i	−0.573448	−	0.0870783i
$493$	−1.73782	+	9.85567i	−0.0782675	+	0.443877i
$494$	−0.903139	−	1.56428i	−0.0406341	−	0.0703804i
$495$	−7.95088	+	15.4251i	−0.357366	+	0.693308i
$496$	−1.11094	−	1.92421i	−0.0498827	−	0.0863994i
$497$	−8.45078	+	22.0048i	−0.379069	+	0.987049i
$498$	8.69679	+	9.87652i	0.389712	+	0.442578i
$499$	5.56106	−	4.66628i	0.248947	−	0.208891i	−0.509772	−	0.860310i	$-0.670270\pi$
$499$	5.56106	−	4.66628i	0.248947	−	0.208891i	0.758719	+	0.651418i	$0.225826\pi$
$500$	−9.20800	−	3.35144i	−0.411794	−	0.149881i
$501$	1.87111	−	5.54886i	0.0835950	−	0.247905i
$502$	−1.81649	+	10.3019i	−0.0810741	+	0.459794i
$503$	−11.6839	−	20.2370i	−0.520957	−	0.902324i	−0.999703	−	0.0243707i	$-0.992242\pi$
$503$	−11.6839	−	20.2370i	−0.520957	−	0.902324i	0.478746	−	0.877954i	$-0.341092\pi$
$504$	2.48931	−	7.53680i	0.110883	−	0.335716i
$505$	8.88295	−	15.3857i	0.395286	−	0.684656i
$506$	−10.3758	−	8.70632i	−0.461260	−	0.387043i
$507$	13.6655	−	17.0973i	0.606904	−	0.759320i
$508$	1.68989	+	9.58386i	0.0749769	+	0.425215i
$509$	−2.96741	−	16.8290i	−0.131528	−	0.745933i	−0.977215	−	0.212253i	$-0.931920\pi$
$509$	−2.96741	−	16.8290i	−0.131528	−	0.745933i	0.845687	−	0.533680i	$-0.179191\pi$
$510$	−4.38147	+	2.67085i	−0.194015	+	0.118267i
$511$	7.68009	−	19.9980i	0.339747	−	0.884658i
$512$	−1.00000			−0.0441942
$513$	1.11256	+	15.5333i	0.0491205	+	0.685813i
$514$	−9.91433	+	17.1721i	−0.437303	+	0.757430i
$515$	−4.20411	−	3.52767i	−0.185255	−	0.155448i
$516$	9.24893	−	5.63794i	0.407161	−	0.248197i
$517$	40.5854	+	14.7719i	1.78495	+	0.649667i
$518$	2.94943	−	1.63429i	0.129590	−	0.0718067i
$519$	−6.05318	−	15.4732i	−0.265705	−	0.679200i
$520$	0.517374	+	0.434128i	0.0226883	+	0.0190378i
$521$	−6.12276	−	10.6049i	−0.268243	−	0.464611i	0.700165	−	0.713981i	$-0.253110\pi$
$521$	−6.12276	−	10.6049i	−0.268243	−	0.464611i	−0.968408	+	0.249370i	$0.919776\pi$
$522$	−10.8446	−	3.37124i	−0.474655	−	0.147555i
$523$	19.5283	−	33.8239i	0.853911	−	1.47902i	−0.0237408	−	0.999718i	$-0.507558\pi$
$523$	19.5283	−	33.8239i	0.853911	−	1.47902i	0.877652	−	0.479299i	$-0.159109\pi$
$524$	−8.77180	−	7.36041i	−0.383198	−	0.321541i
$525$	−8.67138	−	14.8057i	−0.378450	−	0.646172i
$526$	−3.06783	−	17.3986i	−0.133764	−	0.758613i
$527$	−4.49972	+	3.77572i	−0.196011	+	0.164473i
$528$	5.90857	+	6.71008i	0.257138	+	0.292019i
$529$	15.1430	−	5.51162i	0.658393	−	0.239636i
$530$	−6.78070	+	11.7445i	−0.294535	+	0.510150i
$531$	1.47335	+	0.458019i	0.0639380	+	0.0198763i
$532$	−7.78352	−	1.51422i	−0.337458	−	0.0656499i
$533$	4.20671	−	1.53112i	0.182213	−	0.0663201i
$534$	−7.20088	+	9.00929i	−0.311613	+	0.389870i
$535$	1.60170	+	9.08370i	0.0692476	+	0.392722i
$536$	10.4129	−	8.73747i	0.449769	−	0.377401i
$537$	8.14693	−	4.96619i	0.351566	−	0.214307i
$538$	−2.31860	+	13.1495i	−0.0999621	+	0.566913i
$539$	−5.01764	−	35.7834i	−0.216125	−	1.54130i
$540$	−2.37738	−	5.31550i	−0.102306	−	0.228743i
$541$	17.0963	+	29.6117i	0.735029	+	1.27311i	0.954711	+	0.297536i	$0.0961647\pi$
$541$	17.0963	+	29.6117i	0.735029	+	1.27311i	−0.219682	+	0.975572i	$0.570502\pi$
$542$	6.20939	+	5.21030i	0.266716	+	0.223801i
$543$	−0.266254	−	11.1691i	−0.0114260	−	0.479312i
$544$	0.459072	+	2.60353i	0.0196826	+	0.111625i
$545$	−4.93390	+	4.14003i	−0.211345	+	0.177340i
$546$	0.496511	+	2.71686i	0.0212487	+	0.116271i
$547$	7.53875	−	2.74388i	0.322334	−	0.117320i	−0.175785	−	0.984429i	$-0.556246\pi$
$547$	7.53875	−	2.74388i	0.322334	−	0.117320i	0.498119	+	0.867109i	$0.334024\pi$
$548$	3.89418			0.166351
$549$	28.5721	−	11.9702i	1.21943	−	0.510878i
$550$	19.3273			0.824119
$551$	−1.97010	+	11.1730i	−0.0839289	+	0.475984i
$552$	4.45569	−	0.895639i	0.189647	−	0.0381209i
$553$	25.8002	+	15.5078i	1.09713	+	0.659458i
$554$	−2.61254	−	14.8164i	−0.110996	−	0.629490i
$555$	0.790427	−	2.34405i	0.0335517	−	0.0994992i
$556$	15.4258	−	5.61455i	0.654201	−	0.238110i
$557$	43.5419			1.84493			0.922465	−	0.386080i	$-0.126171\pi$
$557$	43.5419			1.84493			0.922465	+	0.386080i	$0.126171\pi$
$558$	−3.60410	−	5.60725i	−0.152574	−	0.237374i
$559$	−1.88453	+	3.26410i	−0.0797071	+	0.138057i
$560$	2.92846	−	0.463354i	0.123750	−	0.0195803i
$561$	14.7574	−	18.4635i	0.623059	−	0.779532i
$562$	−3.07430	−	1.11896i	−0.129682	−	0.0472003i
$563$	1.45872	−	1.22401i	0.0614777	−	0.0515859i	−0.611531	−	0.791220i	$-0.709446\pi$
$563$	1.45872	−	1.22401i	0.0614777	−	0.0515859i	0.673009	+	0.739635i	$0.265002\pi$
$564$	−12.3743	+	7.54313i	−0.521054	+	0.317623i
$565$	−12.3046	+	4.47849i	−0.517656	+	0.188412i
$566$	−17.8962			−0.752233
$567$	6.38208	−	22.9406i	0.268022	−	0.963413i
$568$	8.90927			0.373825
$569$	5.22117	−	1.90035i	0.218883	−	0.0796669i	−0.230251	−	0.973131i	$-0.573955\pi$
$569$	5.22117	−	1.90035i	0.218883	−	0.0796669i	0.449134	+	0.893464i	$0.351733\pi$
$570$	−4.96709	+	3.02783i	−0.208048	+	0.126822i
$571$	−31.2810	+	26.2479i	−1.30907	+	1.09844i	−0.320567	+	0.947226i	$0.603874\pi$
$571$	−31.2810	+	26.2479i	−1.30907	+	1.09844i	−0.988501	+	0.151213i	$0.951682\pi$
$572$	−2.92340	−	1.06403i	−0.122234	−	0.0444894i
$573$	−7.55771	+	9.45572i	−0.315728	+	0.395018i
$574$	7.04565	−	18.3460i	0.294080	−	0.765747i
$575$	4.91230	−	8.50836i	0.204857	−	0.354823i
$576$	−2.99659	+	0.142949i	−0.124858	+	0.00595622i
$577$	11.6803			0.486258			0.243129	−	0.969994i	$-0.421826\pi$
$577$	11.6803			0.486258			0.243129	+	0.969994i	$0.421826\pi$
$578$	−9.40716	+	3.42393i	−0.391286	+	0.142417i
$579$	13.0679	−	38.7535i	0.543084	−	1.61054i
$580$	−0.736636	−	4.17767i	−0.0305872	−	0.173468i
$581$	−17.5830	+	9.74285i	−0.729467	+	0.404202i
$582$	14.9334	−	3.00178i	0.619011	−	0.124428i
$583$	10.8474	−	61.5189i	0.449255	−	2.54785i
$584$	−8.09676			−0.335046
$585$	1.61242	+	1.22695i	0.0666652	+	0.0507280i
$586$	3.42811			0.141614
$587$	36.7835	−	13.3881i	1.51822	−	0.552586i	0.557515	−	0.830167i	$-0.311755\pi$
$587$	36.7835	−	13.3881i	1.51822	−	0.552586i	0.960702	+	0.277581i	$0.0895327\pi$
$588$	10.4303	+	6.18132i	0.430138	+	0.254913i
$589$	−5.10115	+	4.28037i	−0.210189	+	0.176370i
$590$	0.100080	+	0.567581i	0.00412022	+	0.0233669i
$591$	−0.0917835	−	3.85023i	−0.00377547	−	0.158377i
$592$	−0.976306	−	0.819218i	−0.0401259	−	0.0336696i
$593$	14.5294	+	25.1657i	0.596651	+	1.03343i	0.993312	+	0.115464i	$0.0368356\pi$
$593$	14.5294	+	25.1657i	0.596651	+	1.03343i	−0.396661	+	0.917965i	$0.629831\pi$
$594$	18.6648	+	19.2627i	0.765825	+	0.790360i
$595$	−2.55073	−	7.41161i	−0.104570	−	0.303846i
$596$	4.06854	−	23.0739i	0.166654	−	0.945142i
$597$	−38.5183	+	23.4799i	−1.57645	+	0.960970i
$598$	−1.21144	+	1.01652i	−0.0495393	+	0.0415684i
$599$	−0.126122	−	0.715272i	−0.00515319	−	0.0292252i	0.982123	−	0.188242i	$-0.0602788\pi$
$599$	−0.126122	−	0.715272i	−0.00515319	−	0.0292252i	−0.987276	+	0.159016i	$0.949168\pi$
$600$	−4.04900	+	5.06585i	−0.165300	+	0.206812i
$601$	−17.0343	+	6.19997i	−0.694843	+	0.252902i	−0.665207	−	0.746659i	$-0.731657\pi$
$601$	−17.0343	+	6.19997i	−0.694843	+	0.252902i	−0.0296356	+	0.999561i	$0.509435\pi$
$602$	5.38439	+	15.6453i	0.219451	+	0.637656i
$603$	29.9542	−	27.6712i	1.21983	−	1.12686i
$604$	−9.01183	+	15.6089i	−0.366686	+	0.635119i
$605$	16.4753	−	5.99652i	0.669817	−	0.243793i
$606$	−18.1468	−	20.6084i	−0.737161	−	0.837159i
$607$	−13.0651	+	10.9630i	−0.530298	+	0.444973i	−0.868204	−	0.496207i	$-0.834726\pi$
$607$	−13.0651	+	10.9630i	−0.530298	+	0.444973i	0.337906	+	0.941180i	$0.390281\pi$
$608$	0.520432	+	2.95151i	0.0211063	+	0.119700i
$609$	8.58000	−	15.0769i	0.347679	−	0.610949i
$610$	8.86440	+	7.43811i	0.358909	+	0.301160i
$611$	2.52135	−	4.36711i	0.102003	−	0.176674i
$612$	1.74783	+	7.73609i	0.0706516	+	0.312713i
$613$	15.7854	+	27.3411i	0.637567	+	1.10430i	0.985965	+	0.166951i	$0.0533922\pi$
$613$	15.7854	+	27.3411i	0.637567	+	1.10430i	−0.348399	+	0.937346i	$0.613274\pi$
$614$	20.3578	+	17.0822i	0.821572	+	0.689381i
$615$	−5.25250	−	13.4265i	−0.211801	−	0.541411i
$616$	−11.9459	+	6.61926i	−0.481313	+	0.266698i
$617$	−3.94892	−	1.43729i	−0.158978	−	0.0578631i	0.261306	−	0.965256i	$-0.415847\pi$
$617$	−3.94892	−	1.43729i	−0.158978	−	0.0578631i	−0.420283	+	0.907393i	$0.638069\pi$
$618$	−7.24286	+	4.41509i	−0.291351	+	0.177601i
$619$	11.9965	+	10.0662i	0.482179	+	0.404597i	0.851214	−	0.524819i	$-0.175867\pi$
$619$	11.9965	+	10.0662i	0.482179	+	0.404597i	−0.369034	+	0.929416i	$0.620312\pi$
$620$	1.24495	−	2.15631i	0.0499982	−	0.0865994i
$621$	13.2239	−	3.32080i	0.530655	−	0.133259i
$622$	−1.23196			−0.0493970
$623$	−11.0850	−	13.6932i	−0.444110	−	0.548606i
$624$	0.891333	−	0.543337i	0.0356819	−	0.0217509i
$625$	1.34405	+	7.62251i	0.0537621	+	0.304900i
$626$	1.95122	+	11.0659i	0.0779865	+	0.442284i
$627$	16.7299	−	20.9314i	0.668128	−	0.835919i
$628$	−12.1426	−	10.1889i	−0.484544	−	0.406581i
$629$	−1.68466	+	2.91792i	−0.0671719	+	0.116345i
$630$	8.70916	−	1.80710i	0.346981	−	0.0719967i
$631$	−15.8522	−	27.4568i	−0.631065	−	1.09304i	−0.987334	−	0.158653i	$-0.949285\pi$
$631$	−15.8522	−	27.4568i	−0.631065	−	1.09304i	0.356269	−	0.934383i	$-0.384049\pi$
$632$	1.97569	−	11.2047i	0.0785887	−	0.445699i
$633$	−6.15122	+	18.2417i	−0.244489	+	0.725044i
$634$	−6.25709	−	2.27739i	−0.248501	−	0.0904468i
$635$	−8.35415	+	7.00997i	−0.331524	+	0.278182i
$636$	13.8521	+	15.7312i	0.549272	+	0.623782i
$637$	−4.21618	−	0.148550i	−0.167051	−	0.00588577i
$638$	9.77024	+	16.9226i	0.386808	+	0.669970i
$639$	26.6974	−	1.27357i	1.05613	−	0.0503818i
$640$	−0.560311	−	0.970488i	−0.0221482	−	0.0383619i
$641$	−4.44897	+	25.2314i	−0.175724	+	0.996579i	0.761581	+	0.648069i	$0.224423\pi$
$641$	−4.44897	+	25.2314i	−0.175724	+	0.996579i	−0.937305	+	0.348510i	$0.886688\pi$
$642$	14.0949	+	2.14032i	0.556282	+	0.0844715i
$643$	−18.0253	+	15.1250i	−0.710849	+	0.596474i	−0.924837	−	0.380363i	$-0.875799\pi$
$643$	−18.0253	+	15.1250i	−0.710849	+	0.596474i	0.213988	+	0.976836i	$0.431355\pi$
$644$	−0.122244	+	6.94124i	−0.00481707	+	0.273523i
$645$	10.6538	+	5.81696i	0.419494	+	0.229043i
$646$	7.44544	−	2.70992i	0.292937	−	0.106620i
$647$	−1.47298	+	2.55128i	−0.0579089	+	0.100301i	−0.893527	−	0.449010i	$-0.851777\pi$
$647$	−1.47298	+	2.55128i	−0.0579089	+	0.100301i	0.835618	+	0.549312i	$0.185110\pi$
$648$	−8.95913	+	0.856721i	−0.351948	+	0.0336552i
$649$	−1.32739	−	2.29911i	−0.0521047	−	0.0902479i
$650$	0.391851	−	2.22230i	0.0153697	−	0.0871656i
$651$	9.54603	−	3.54192i	0.374138	−	0.138819i
$652$	2.40020	+	0.873600i	0.0939990	+	0.0342128i
$653$	1.03048	+	0.375063i	0.0403256	+	0.0146773i	0.362104	−	0.932138i	$-0.382058\pi$
$653$	1.03048	+	0.375063i	0.0403256	+	0.0146773i	−0.321779	+	0.946815i	$0.604281\pi$
$654$	3.62675	+	9.27076i	0.141817	+	0.362515i
$655$	2.22825	−	12.6370i	0.0870650	−	0.493770i
$656$	−7.42791			−0.290011
$657$	−24.2627	+	1.15743i	−0.946578	+	0.0451555i
$658$	−7.20389	−	20.9322i	−0.280837	−	0.816023i
$659$	10.9898	+	9.22156i	0.428103	+	0.359221i	0.831235	−	0.555921i	$-0.187634\pi$
$659$	10.9898	+	9.22156i	0.428103	+	0.359221i	−0.403133	+	0.915142i	$0.632079\pi$
$660$	−3.20141	+	9.49393i	−0.124615	+	0.369551i
$661$	−12.7687	−	4.64743i	−0.496646	−	0.180764i	0.0815391	−	0.996670i	$-0.474016\pi$
$661$	−12.7687	−	4.64743i	−0.496646	−	0.180764i	−0.578185	+	0.815906i	$0.696239\pi$
$662$	−10.7040	−	3.89595i	−0.416024	−	0.151420i
$663$	−1.82378	−	2.07118i	−0.0708298	−	0.0804380i
$664$	5.82026	+	4.88377i	0.225870	+	0.189527i
$665$	−2.89166	−	8.40224i	−0.112134	−	0.325825i
$666$	−3.04270	−	2.31530i	−0.117902	−	0.0897160i
$667$	9.93297			0.384606
$668$	0.587083	−	3.32951i	0.0227149	−	0.128823i
$669$	−6.44641	+	8.06534i	−0.249233	+	0.311824i
$670$	14.3141	+	5.20990i	0.553001	+	0.201276i
$671$	−50.0880	−	18.2305i	−1.93362	−	0.703782i
$672$	0.767650	−	4.51782i	0.0296127	−	0.174279i
$673$	0.0937793	−	0.531849i	0.00361492	−	0.0205013i	−0.982947	−	0.183889i	$-0.941131\pi$
$673$	0.0937793	−	0.531849i	0.00361492	−	0.0205013i	0.986562	+	0.163388i	$0.0522423\pi$
$674$	−11.3099	−	19.5894i	−0.435643	−	0.754556i
$675$	−11.4090	+	15.7591i	−0.439134	+	0.606567i
$676$	6.31838	−	10.9438i	0.243015	−	0.420914i
$677$	35.0616	−	12.7614i	1.34753	−	0.490460i	0.435353	−	0.900260i	$-0.356624\pi$
$677$	35.0616	−	12.7614i	1.34753	−	0.490460i	0.912176	+	0.409800i	$0.134401\pi$
$678$	0.482320	+	20.2329i	0.0185234	+	0.777039i
$679$	−0.409705	+	23.2639i	−0.0157230	+	0.892786i
$680$	−2.26947	+	1.90431i	−0.0870302	+	0.0730270i
$681$	32.3474	−	40.4710i	1.23956	−	1.55085i
$682$	−1.99160	+	11.2949i	−0.0762624	+	0.432506i
$683$	15.1796	+	26.2919i	0.580832	+	1.00603i	0.995381	+	0.0960038i	$0.0306061\pi$
$683$	15.1796	+	26.2919i	0.580832	+	1.00603i	−0.414549	+	0.910027i	$0.636061\pi$
$684$	1.98144	+	8.77009i	0.0757622	+	0.335333i
$685$	2.18195	+	3.77925i	0.0833681	+	0.144398i
$686$	−12.6371	+	13.5389i	−0.482488	+	0.516919i
$687$	9.45154	−	28.0290i	0.360599	−	1.06937i
$688$	4.79067	−	4.01985i	0.182643	−	0.153255i
$689$	−6.85365	−	2.49453i	−0.261103	−	0.0950339i
$690$	3.36578	+	3.82235i	0.128133	+	0.145515i
$691$	−0.441628	+	2.50460i	−0.0168003	+	0.0952793i	−0.992055	−	0.125805i	$-0.959849\pi$
$691$	−0.441628	+	2.50460i	−0.0168003	+	0.0952793i	0.975255	+	0.221085i	$0.0709597\pi$
$692$	−4.79637	−	8.30756i	−0.182331	−	0.315806i
$693$	−34.8507	+	21.5429i	−1.32387	+	0.818346i
$694$	−6.06682	+	10.5080i	−0.230293	+	0.398880i
$695$	14.0921	+	11.8247i	0.534545	+	0.448536i
$696$	−6.48237	−	0.984350i	−0.245714	−	0.0373117i
$697$	3.40995	+	19.3388i	0.129161	+	0.732508i
$698$	6.08774	+	34.5253i	0.230424	+	1.30680i
$699$	0.731888	+	30.7020i	0.0276825	+	1.16126i
$700$	−6.23299	−	7.69956i	−0.235585	−	0.291016i
$701$	2.52102			0.0952176			0.0476088	−	0.998866i	$-0.484840\pi$
$701$	2.52102			0.0952176			0.0476088	+	0.998866i	$0.484840\pi$
$702$	2.59329	−	1.75558i	0.0978775	−	0.0662599i
$703$	−1.90983	+	3.30793i	−0.0720307	+	0.124761i
$704$	3.95426	+	3.31802i	0.149032	+	0.125053i
$705$	−14.2540	−	7.78264i	−0.536837	−	0.293111i
$706$	29.8899	+	10.8790i	1.12492	+	0.409437i
$707$	36.6888	−	20.3295i	1.37983	−	0.764568i
$708$	0.880699	+	0.133734i	0.0330987	+	0.00502605i
$709$	11.8924	+	9.97888i	0.446627	+	0.374765i	0.838183	−	0.545390i	$-0.183618\pi$
$709$	11.8924	+	9.97888i	0.446627	+	0.374765i	−0.391555	+	0.920155i	$0.628063\pi$
$710$	4.99196	+	8.64633i	0.187345	+	0.324491i
$711$	4.31863	−	33.8583i	0.161961	−	1.26979i
$712$	−3.32941	+	5.76671i	−0.124775	+	0.216117i
$713$	4.46612	+	3.74752i	0.167257	+	0.140346i
$714$	−12.1147	+	0.0754092i	−0.453381	+	0.00282212i
$715$	−0.605386	−	3.43331i	−0.0226401	−	0.128399i
$716$	4.21987	−	3.54089i	0.157704	−	0.132329i
$717$	48.6167	−	9.77247i	1.81563	−	0.364959i
$718$	−6.58795	+	2.39782i	−0.245860	+	0.0894857i
$719$	24.3791	−	42.2258i	0.909185	−	1.57476i	0.0939869	−	0.995573i	$-0.470039\pi$
$719$	24.3791	−	42.2258i	0.909185	−	1.57476i	0.815198	−	0.579182i	$-0.196628\pi$
$720$	−1.81776	−	2.82806i	−0.0677437	−	0.105396i
$721$	−4.21653	−	12.2519i	−0.157032	−	0.456285i
$722$	−9.41357	+	3.42626i	−0.350337	+	0.127512i
$723$	−44.3648	−	6.73680i	−1.64994	−	0.250544i
$724$	−1.12009	−	6.35232i	−0.0416276	−	0.236082i
$725$	−10.8577	+	9.11068i	−0.403244	+	0.338362i
$726$	−0.645808	−	27.0910i	−0.0239682	−	1.00544i
$727$	−2.96761	+	16.8302i	−0.110063	+	0.624196i	0.879014	+	0.476795i	$0.158202\pi$
$727$	−2.96761	+	16.8302i	−0.110063	+	0.624196i	−0.989077	+	0.147401i	$0.952909\pi$
$728$	0.518901	+	1.50776i	0.0192318	+	0.0558814i
$729$	−26.7244	+	3.84795i	−0.989792	+	0.142517i
$730$	−4.53671	−	7.85781i	−0.167911	−	0.290830i
$731$	−12.6651	−	10.6272i	−0.468434	−	0.393063i
$732$	15.2716	−	9.30925i	0.564455	−	0.344080i
$733$	−2.40832	−	13.6583i	−0.0889533	−	0.504479i	−0.996433	−	0.0843840i	$-0.973108\pi$
$733$	−2.40832	−	13.6583i	−0.0889533	−	0.504479i	0.907480	−	0.420095i	$-0.138003\pi$
$734$	−16.6250	+	13.9501i	−0.613641	+	0.514906i
$735$	−0.154681	+	13.5859i	−0.00570548	+	0.501125i
$736$	2.46571	−	0.897444i	0.0908871	−	0.0330802i
$737$	−70.1665			−2.58462
$738$	−22.2584	+	1.06181i	−0.819343	+	0.0390859i
$739$	−16.7741			−0.617043			−0.308522	−	0.951217i	$-0.599834\pi$
$739$	−16.7741			−0.617043			−0.308522	+	0.951217i	$0.599834\pi$
$740$	0.248006	−	1.40651i	0.00911687	−	0.0517043i
$741$	−2.06755	−	2.34801i	−0.0759532	−	0.0862564i
$742$	−28.0060	+	15.5183i	−1.02813	+	0.569694i
$743$	4.66137	+	26.4359i	0.171009	+	0.969840i	0.942650	+	0.333782i	$0.108325\pi$
$743$	4.66137	+	26.4359i	0.171009	+	0.969840i	−0.771641	+	0.636058i	$0.780564\pi$
$744$	−2.54327	−	2.88826i	−0.0932406	−	0.105889i
$745$	24.6725	−	8.98007i	0.903932	−	0.329004i
$746$	−28.9845			−1.06120
$747$	18.1391	+	13.8027i	0.663674	+	0.505014i
$748$	6.82327	−	11.8183i	0.249483	−	0.432118i
$749$	−7.80740	+	20.3295i	−0.285276	+	0.742823i
$750$	−16.7799	−	2.54804i	−0.612716	−	0.0930411i
$751$	−29.1441	−	10.6076i	−1.06348	−	0.387076i	−0.249747	−	0.968311i	$-0.580347\pi$
$751$	−29.1441	−	10.6076i	−1.06348	−	0.387076i	−0.813736	+	0.581235i	$0.802570\pi$
$752$	−6.40954	+	5.37824i	−0.233732	+	0.196124i
$753$	0.431796	+	18.1134i	0.0157355	+	0.660091i
$754$	2.14388	−	0.780308i	0.0780755	−	0.0284171i
$755$	−20.1977			−0.735070
$756$	1.65451	−	13.6478i	0.0601741	−	0.496366i
$757$	25.4715			0.925779			0.462889	−	0.886416i	$-0.346813\pi$
$757$	25.4715			0.925779			0.462889	+	0.886416i	$0.346813\pi$
$758$	−11.7224	+	4.26659i	−0.425775	+	0.154969i
$759$	−20.5907	−	11.2425i	−0.747396	−	0.408076i
$760$	−2.57280	+	2.15884i	−0.0933254	+	0.0783093i
$761$	−44.6880	−	16.2651i	−1.61994	−	0.589610i	−0.636569	−	0.771220i	$-0.719647\pi$
$761$	−44.6880	−	16.2651i	−1.61994	−	0.589610i	−0.983371	+	0.181610i	$0.941869\pi$
$762$	6.14087	+	15.6974i	0.222460	+	0.568656i
$763$	−15.0195	+	2.37646i	−0.543744	+	0.0860336i
$764$	−3.49440	+	6.05247i	−0.126423	+	0.218971i
$765$	−6.52845	+	6.03086i	−0.236037	+	0.218046i
$766$	0.698314			0.0252311
$767$	−0.291269	+	0.106013i	−0.0105171	+	0.00382791i
$768$	−1.69808	+	0.341333i	−0.0612744	+	0.0123168i
$769$	−0.310303	−	1.75981i	−0.0111898	−	0.0634605i	0.978702	−	0.205288i	$-0.0658132\pi$
$769$	−0.310303	−	1.75981i	−0.0111898	−	0.0634605i	−0.989891	+	0.141828i	$0.954702\pi$
$770$	−13.1173	−	7.88446i	−0.472715	−	0.284136i
$771$	−10.9740	+	32.5438i	−0.395218	+	1.17204i
$772$	4.10021	−	23.2535i	0.147570	−	0.836910i
$773$	−5.41978			−0.194936			−0.0974680	−	0.995239i	$-0.531074\pi$
$773$	−5.41978			−0.194936			−0.0974680	+	0.995239i	$0.531074\pi$
$774$	13.7810	−	12.7307i	0.495349	−	0.457594i
$775$	−8.31918			−0.298834
$776$	8.26392	−	3.00782i	0.296658	−	0.107975i
$777$	4.45054	−	3.78190i	0.159662	−	0.135675i
$778$	−29.4550	+	24.7157i	−1.05601	+	0.886100i
$779$	3.86572	+	21.9236i	0.138504	+	0.785494i
$780$	1.02673	+	0.560590i	0.0367627	+	0.0200723i
$781$	−35.2296	−	29.5611i	−1.26061	−	1.05778i
$782$	−3.46846	−	6.00754i	−0.124032	−	0.214829i
$783$	−19.5657	−	2.02305i	−0.699223	−	0.0722977i
$784$	6.48947	+	2.62427i	0.231767	+	0.0937240i
$785$	3.08453	−	17.4932i	0.110092	−	0.624360i
$786$	−17.4076	−	9.50450i	−0.620909	−	0.339014i
$787$	−9.89296	+	8.30118i	−0.352646	+	0.295905i	−0.801852	−	0.597523i	$-0.796152\pi$
$787$	−9.89296	+	8.30118i	−0.352646	+	0.295905i	0.449206	+	0.893428i	$0.351707\pi$
$788$	−0.386118	−	2.18978i	−0.0137549	−	0.0780078i
$789$	−11.1481	−	28.4971i	−0.396884	−	1.01452i
$790$	11.9810	−	4.36073i	0.426265	−	0.155148i
$791$	−30.3461	−	5.90360i	−1.07898	−	0.209908i
$792$	12.3236	+	9.37750i	0.437901	+	0.333215i
$793$	−3.11169	+	5.38961i	−0.110499	+	0.191391i
$794$	18.2778	−	6.65258i	0.648656	−	0.236091i
$795$	−7.50542	+	22.2577i	−0.266190	+	0.789398i
$796$	−19.9513	+	16.7412i	−0.707157	+	0.593375i
$797$	3.71226	+	21.0533i	0.131495	+	0.745746i	0.977237	+	0.212153i	$0.0680474\pi$
$797$	3.71226	+	21.0533i	0.131495	+	0.745746i	−0.845741	+	0.533593i	$0.820841\pi$
$798$	−13.7339	+	0.0854884i	−0.486176	+	0.00302626i
$799$	16.9449	+	14.2184i	0.599466	+	0.503011i
$800$	−1.87210	+	3.24258i	−0.0661888	+	0.114642i
$801$	−9.15255	+	17.7564i	−0.323389	+	0.627392i
$802$	14.5358	+	25.1767i	0.513276	+	0.889021i
$803$	32.0167	+	26.8652i	1.12985	+	0.948053i
$804$	14.6996	−	18.3912i	0.518416	−	0.648609i
$805$	−6.80488	+	3.77062i	−0.239841	+	0.132897i
$806$	1.25834	+	0.457998i	0.0443231	+	0.0161323i
$807$	0.551151	+	23.1203i	0.0194014	+	0.813873i
$808$	−12.1446	−	10.1905i	−0.427244	−	0.358501i
$809$	−6.95161	+	12.0405i	−0.244406	+	0.423323i	−0.961964	−	0.273175i	$-0.911926\pi$
$809$	−6.95161	+	12.0405i	−0.244406	+	0.423323i	0.717559	+	0.696498i	$0.245260\pi$
$810$	−5.85134	−	8.21469i	−0.205595	−	0.288635i
$811$	−53.1335			−1.86577			−0.932885	−	0.360173i	$-0.882718\pi$
$811$	−53.1335			−1.86577			−0.932885	+	0.360173i	$0.882718\pi$
$812$	3.59069	−	9.34971i	0.126009	−	0.328111i
$813$	12.3225	+	6.72806i	0.432170	+	0.235963i
$814$	1.14239	+	6.47881i	0.0400407	+	0.227082i
$815$	0.497039	+	2.81885i	0.0174105	+	0.0987400i
$816$	1.66821	+	4.26432i	0.0583991	+	0.149281i
$817$	−14.3579	−	12.0477i	−0.502318	−	0.421495i
$818$	13.1933	−	22.8514i	0.461292	−	0.798982i
$819$	1.77047	+	4.44398i	0.0618652	+	0.155285i
$820$	−4.16194	−	7.20869i	−0.145341	−	0.251738i
$821$	4.05151	−	22.9772i	0.141399	−	0.801911i	−0.828790	−	0.559560i	$-0.810970\pi$
$821$	4.05151	−	22.9772i	0.141399	−	0.801911i	0.970189	−	0.242351i	$-0.0779186\pi$
$822$	6.61265	−	1.32921i	0.230643	−	0.0463615i
$823$	2.79349	+	1.01675i	0.0973750	+	0.0354416i	0.390248	−	0.920710i	$-0.372389\pi$
$823$	2.79349	+	1.01675i	0.0973750	+	0.0354416i	−0.292873	+	0.956151i	$0.594611\pi$
$824$	−3.75159	+	3.14795i	−0.130693	+	0.109664i
$825$	32.8194	−	6.59704i	1.14262	−	0.229679i
$826$	−0.487834	+	1.27026i	−0.0169739	+	0.0441979i
$827$	7.25985	+	12.5744i	0.252450	+	0.437256i	0.964200	−	0.265177i	$-0.0854304\pi$
$827$	7.25985	+	12.5744i	0.252450	+	0.437256i	−0.711750	+	0.702433i	$0.752097\pi$
$828$	7.26043	−	3.04174i	0.252317	−	0.105708i
$829$	13.3745	+	23.1653i	0.464516	+	0.804565i	0.999180	−	0.0404998i	$-0.0128950\pi$
$829$	13.3745	+	23.1653i	0.464516	+	0.804565i	−0.534664	+	0.845065i	$0.679562\pi$
$830$	−1.47849	+	8.38492i	−0.0513190	+	0.291045i
$831$	−9.49364	−	24.2678i	−0.329331	−	0.841841i
$832$	0.461684	−	0.387399i	0.0160060	−	0.0134306i
$833$	3.85323	−	18.1002i	0.133507	−	0.627136i
$834$	24.2780	−	14.7993i	0.840677	−	0.512458i
$835$	3.56020	−	1.29581i	0.123206	−	0.0448432i
$836$	7.73526	−	13.3979i	0.267530	−	0.463375i
$837$	−8.03400	−	8.29139i	−0.277696	−	0.286592i
$838$	7.75713	+	13.4357i	0.267966	+	0.464130i
$839$	5.00728	−	28.3977i	0.172870	−	0.980397i	−0.767703	−	0.640806i	$-0.778600\pi$
$839$	5.00728	−	28.3977i	0.172870	−	0.980397i	0.940573	−	0.339591i	$-0.110289\pi$
$840$	4.81461	−	1.78639i	0.166120	−	0.0616364i
$841$	13.7853	+	5.01742i	0.475354	+	0.173015i
$842$	−10.4758	−	3.81289i	−0.361021	−	0.131401i
$843$	−5.60237	−	0.850721i	−0.192956	−	0.0293004i
$844$	−1.93002	+	10.9457i	−0.0664339	+	0.376766i
$845$	14.1610			0.487155
$846$	−18.4380	+	17.0326i	−0.633910	+	0.585594i
$847$	40.6323	+	7.90469i	1.39614	+	0.271608i
$848$	9.27042	+	7.77881i	0.318348	+	0.267125i
$849$	−30.3892	+	6.10855i	−1.04296	+	0.209645i
$850$	9.30157	+	3.38550i	0.319041	+	0.116122i
$851$	3.14248	+	1.14377i	0.107723	+	0.0392080i
$852$	15.1287	−	3.04102i	0.518300	−	0.104184i
$853$	−3.86423	−	3.24248i	−0.132309	−	0.111020i	0.574232	−	0.818693i	$-0.305301\pi$
$853$	−3.86423	−	3.24248i	−0.132309	−	0.111020i	−0.706541	+	0.707672i	$0.749745\pi$
$854$	8.89058	+	25.8332i	0.304229	+	0.883994i
$855$	−7.40104	+	6.83694i	−0.253110	+	0.233819i
$856$	8.23098			0.281329
$857$	−4.09858	+	23.2442i	−0.140005	+	0.794007i	0.831238	+	0.555916i	$0.187633\pi$
$857$	−4.09858	+	23.2442i	−0.140005	+	0.794007i	−0.971243	+	0.238090i	$0.923479\pi$
$858$	−5.32737	−	0.808963i	−0.181873	−	0.0276175i
$859$	−24.5491	−	8.93513i	−0.837603	−	0.304863i	−0.112628	−	0.993637i	$-0.535927\pi$
$859$	−24.5491	−	8.93513i	−0.837603	−	0.304863i	−0.724976	+	0.688775i	$0.758149\pi$
$860$	6.58548	+	2.39692i	0.224563	+	0.0817342i
$861$	5.70203	−	33.5580i	0.194325	−	1.14365i
$862$	−1.02806	+	5.83042i	−0.0350159	+	0.198585i
$863$	14.8762	+	25.7664i	0.506393	+	0.877099i	0.999973	+	0.00739799i	$0.00235488\pi$
$863$	14.8762	+	25.7664i	0.506393	+	0.877099i	−0.493579	+	0.869701i	$0.664312\pi$
$864$	−5.03967	+	1.26557i	−0.171453	+	0.0430557i
$865$	5.37492	−	9.30964i	0.182753	−	0.316537i
$866$	−35.7128	+	12.9984i	−1.21357	+	0.441704i
$867$	−14.8055	+	9.02509i	−0.502820	+	0.306508i
$868$	5.14194	−	2.84917i	0.174529	−	0.0967072i
$869$	−44.9898	+	37.7509i	−1.52617	+	1.28061i
$870$	−2.67685	−	6.84260i	−0.0907536	−	0.231986i
$871$	−1.42259	+	8.06790i	−0.0482026	+	0.273370i
$872$	2.87374	+	4.97746i	0.0973170	+	0.168558i
$873$	24.3336	−	10.1945i	0.823569	−	0.345033i
$874$	−3.93205	−	6.81051i	−0.133004	−	0.230369i
$875$	9.29468	−	24.2022i	0.314218	−	0.818183i
$876$	−13.7490	+	2.76369i	−0.464535	+	0.0933764i
$877$	−22.8311	+	19.1576i	−0.770952	+	0.646905i	−0.940952	−	0.338539i	$-0.890067\pi$
$877$	−22.8311	+	19.1576i	−0.770952	+	0.646905i	0.170001	+	0.985444i	$0.445623\pi$
$878$	−6.92951	−	2.52214i	−0.233860	−	0.0851180i
$879$	5.82123	−	1.17013i	0.196345	−	0.0394674i
$880$	−1.00448	+	5.69669i	−0.0338610	+	0.192035i
$881$	11.4018	+	19.7485i	0.384136	+	0.665344i	0.991649	−	0.128966i	$-0.0411659\pi$
$881$	11.4018	+	19.7485i	0.384136	+	0.665344i	−0.607513	+	0.794310i	$0.707833\pi$
$882$	19.8214	+	6.93621i	0.667422	+	0.233554i
$883$	13.5538	−	23.4758i	0.456121	−	0.790025i	−0.542631	−	0.839971i	$-0.682572\pi$
$883$	13.5538	−	23.4758i	0.456121	−	0.790025i	0.998752	+	0.0499466i	$0.0159051\pi$
$884$	−1.22055	−	1.02416i	−0.0410516	−	0.0344463i
$885$	0.363678	+	0.929640i	0.0122249	+	0.0312495i
$886$	−0.114242	−	0.647897i	−0.00383803	−	0.0217665i
$887$	2.25808	+	12.8062i	0.0758189	+	0.429990i	0.998963	+	0.0455355i	$0.0144994\pi$
$887$	2.25808	+	12.8062i	0.0758189	+	0.429990i	−0.923144	+	0.384455i	$0.874389\pi$
$888$	−1.93748	−	1.05786i	−0.0650174	−	0.0354993i
$889$	−25.4313	+	4.02385i	−0.852939	+	0.134956i
$890$	−7.46203			−0.250128
$891$	38.2694	+	26.3389i	1.28207	+	0.882386i
$892$	−2.98058	+	5.16251i	−0.0997971	+	0.172854i
$893$	19.2097	+	16.1188i	0.642828	+	0.539397i
$894$	−0.967127	−	40.5701i	−0.0323456	−	1.35687i
$895$	5.80083	+	2.11133i	0.193900	+	0.0705739i
$896$	0.0465876	−	2.64534i	0.00155638	−	0.0883746i
$897$	−1.71015	+	2.13963i	−0.0571003	+	0.0714402i
$898$	−23.5777	−	19.7840i	−0.786798	−	0.660202i
$899$	−4.20547	−	7.28409i	−0.140260	−	0.242938i
$900$	−5.14640	+	9.98430i	−0.171547	+	0.332810i
$901$	15.9966	−	27.7068i	0.532922	−	0.923049i
$902$	29.3719	+	24.6459i	0.977977	+	0.820620i
$903$	14.4834	+	24.7292i	0.481977	+	0.822937i
$904$	2.02904	+	11.5073i	0.0674849	+	0.382726i
$905$	5.53725	−	4.64630i	0.184064	−	0.154448i
$906$	−9.97501	+	29.5813i	−0.331397	+	0.982774i
$907$	−2.34737	+	0.854372i	−0.0779431	+	0.0283690i	−0.380697	−	0.924700i	$-0.624316\pi$
$907$	−2.34737	+	0.854372i	−0.0779431	+	0.0283690i	0.302754	+	0.953069i	$0.402094\pi$
$908$	14.9562	−	25.9049i	0.496339	−	0.859685i
$909$	−37.8490	−	28.8007i	−1.25537	−	0.955260i
$910$	−1.17252	+	1.34840i	−0.0388686	+	0.0446992i
$911$	−25.5853	+	9.31230i	−0.847680	+	0.308530i	−0.729094	−	0.684413i	$-0.760058\pi$
$911$	−25.5853	+	9.31230i	−0.847680	+	0.308530i	−0.118586	+	0.992944i	$0.537836\pi$
$912$	1.89119	+	4.83428i	0.0626234	+	0.160079i
$913$	−6.81036	−	38.6235i	−0.225390	−	1.27825i
$914$	1.21422	−	1.01885i	0.0401629	−	0.0337007i
$915$	17.5914	+	9.60484i	0.581553	+	0.317526i
$916$	2.96553	−	16.8184i	0.0979839	−	0.555695i
$917$	19.8795	−	22.8615i	0.656477	−	0.754953i
$918$	5.60854	+	12.5399i	0.185109	+	0.413880i
$919$	−6.83377	−	11.8364i	−0.225425	−	0.390448i	0.731022	−	0.682354i	$-0.239044\pi$
$919$	−6.83377	−	11.8364i	−0.225425	−	0.390448i	−0.956447	+	0.291906i	$0.905710\pi$
$920$	2.25252	+	1.89009i	0.0742634	+	0.0623144i
$921$	40.3999	+	22.0582i	1.33122	+	0.726843i
$922$	0.684017	+	3.87925i	0.0225269	+	0.127756i
$923$	−4.11327	+	3.45144i	−0.135390	+	0.113606i
$924$	−18.0257	+	15.3176i	−0.593003	+	0.503911i
$925$	−4.48412	+	1.63209i	−0.147437	+	0.0536627i
$926$	19.5588			0.642742
$927$	−10.7920	+	9.96942i	−0.354455	+	0.327439i
$928$	−3.78550			−0.124265
$929$	0.369460	−	2.09531i	0.0121216	−	0.0687450i	−0.978147	−	0.207915i	$-0.933332\pi$
$929$	0.369460	−	2.09531i	0.0121216	−	0.0687450i	0.990269	+	0.139170i	$0.0444434\pi$
$930$	1.37800	−	4.08653i	0.0451865	−	0.134003i
$931$	4.36825	−	20.5195i	0.143164	−	0.672500i
$932$	3.07893	+	17.4615i	0.100854	+	0.571970i
$933$	−2.09197	+	0.420507i	−0.0684879	+	0.0137668i
$934$	1.67378	−	0.609205i	0.0547677	−	0.0199338i
$935$	15.2926			0.500122
$936$	1.32810	−	1.22687i	0.0434103	−	0.0401016i
$937$	6.97571	−	12.0823i	0.227886	−	0.394711i	−0.729295	−	0.684199i	$-0.760152\pi$
$937$	6.97571	−	12.0823i	0.227886	−	0.394711i	0.957182	+	0.289488i	$0.0934852\pi$
$938$	22.6285	+	27.9528i	0.738846	+	0.912690i
$939$	7.09050	+	18.1249i	0.231390	+	0.591483i
$940$	−8.81085	−	3.20689i	−0.287378	−	0.104597i
$941$	30.9245	−	25.9487i	1.00811	−	0.845904i	0.0200223	−	0.999800i	$-0.493626\pi$
$941$	30.9245	−	25.9487i	1.00811	−	0.845904i	0.988087	+	0.153895i	$0.0491818\pi$
$942$	−24.0970	−	13.1569i	−0.785124	−	0.428676i
$943$	18.3150	−	6.66613i	0.596419	−	0.217079i
$944$	0.514301			0.0167391
$945$	14.1721	−	6.04133i	0.461017	−	0.196525i
$946$	−32.2815			−1.04956
$947$	−29.0204	+	10.5626i	−0.943036	+	0.343237i	−0.767364	−	0.641212i	$-0.778432\pi$
$947$	−29.0204	+	10.5626i	−0.943036	+	0.343237i	−0.175672	+	0.984449i	$0.556210\pi$
$948$	−0.469638	−	19.7009i	−0.0152531	−	0.639855i
$949$	3.73815	−	3.13668i	0.121345	−	0.101821i
$950$	10.5448	+	3.83800i	0.342119	+	0.124521i
$951$	−11.4024	−	1.73146i	−0.369748	−	0.0561464i
$952$	−6.90861	+	1.09311i	−0.223909	+	0.0354279i
$953$	7.46826	−	12.9354i	0.241921	−	0.419019i	−0.719341	−	0.694657i	$-0.755556\pi$
$953$	7.46826	−	12.9354i	0.241921	−	0.419019i	0.961261	+	0.275639i	$0.0888893\pi$
$954$	28.8916	+	21.9847i	0.935402	+	0.711781i
$955$	−7.83180			−0.253431
$956$	26.9037	−	9.79215i	0.870128	−	0.316701i
$957$	22.3669	+	25.4010i	0.723020	+	0.821099i
$958$	−0.978080	−	5.54697i	−0.0316003	−	0.179214i
$959$	−0.181421	+	10.3014i	−0.00585837	+	0.332651i
$960$	−1.28272	−	1.45672i	−0.0413995	−	0.0470154i
$961$	−4.52583	+	25.6673i	−0.145995	+	0.827977i
$962$	0.768109			0.0247648
$963$	24.6649	−	1.17661i	0.794815	−	0.0379158i
$964$	−25.9076			−0.834429
$965$	24.8646	−	9.04997i	0.800420	−	0.291329i
$966$	2.16169	+	11.8285i	0.0695513	+	0.380577i
$967$	33.5206	−	28.1271i	1.07795	−	0.904507i	0.0822010	−	0.996616i	$-0.473805\pi$
$967$	33.5206	−	28.1271i	1.07795	−	0.904507i	0.995749	+	0.0921084i	$0.0293606\pi$
$968$	−2.71681	−	15.4078i	−0.0873215	−	0.495225i
$969$	11.7180	−	7.14304i	0.376436	−	0.229468i
$970$	7.54942	+	6.33472i	0.242397	+	0.203396i
$971$	−14.6996	−	25.4605i	−0.471733	−	0.817066i	0.527744	−	0.849404i	$-0.323038\pi$
$971$	−14.6996	−	25.4605i	−0.471733	−	0.817066i	−0.999477	+	0.0323377i	$0.989705\pi$
$972$	−14.9209	+	4.51283i	−0.478589	+	0.144749i
$973$	14.1337	+	41.0682i	0.453107	+	1.31659i
$974$	4.76583	−	27.0284i	0.152707	−	0.866044i
$975$	−0.0931462	−	3.90740i	−0.00298307	−	0.125137i
$976$	7.91024	−	6.63748i	0.253201	−	0.212461i
$977$	−6.71358	−	38.0746i	−0.214786	−	1.21811i	−0.881277	−	0.472600i	$-0.843315\pi$
$977$	−6.71358	−	38.0746i	−0.214786	−	1.21811i	0.666491	−	0.745513i	$-0.267796\pi$
$978$	4.37393	+	0.664182i	0.139863	+	0.0212382i
$979$	32.2995	−	11.7560i	1.03230	−	0.375725i
$980$	1.08930	+	7.76836i	0.0347964	+	0.248151i
$981$	9.32294	+	14.5046i	0.297659	+	0.463097i
$982$	3.54158	−	6.13420i	0.113016	−	0.195750i
$983$	−3.10337	+	1.12954i	−0.0989823	+	0.0360266i	−0.391037	−	0.920375i	$-0.627883\pi$
$983$	−3.10337	+	1.12954i	−0.0989823	+	0.0360266i	0.292054	+	0.956402i	$0.405661\pi$
$984$	−12.6132	+	2.53539i	−0.402095	+	0.0808252i
$985$	1.90881	−	1.60168i	0.0608198	−	0.0510339i
$986$	1.73782	+	9.85567i	0.0553435	+	0.313868i
$987$	−19.3777	−	33.0858i	−0.616798	−	1.05313i
$988$	−1.38369	−	1.16105i	−0.0440210	−	0.0369380i
$989$	−8.20479	+	14.2111i	−0.260897	+	0.451887i
$990$	−2.19568	+	17.2142i	−0.0697833	+	0.547105i
$991$	−7.06324	−	12.2339i	−0.224371	−	0.388622i	0.731759	−	0.681563i	$-0.238699\pi$
$991$	−7.06324	−	12.2339i	−0.224371	−	0.388622i	−0.956131	+	0.292941i	$0.905366\pi$
$992$	−1.70206	−	1.42820i	−0.0540404	−	0.0453453i
$993$	−19.5062	−	2.96202i	−0.619010	−	0.0939969i
$994$	−0.415061	+	23.5680i	−0.0131650	+	0.747533i
$995$	−27.4261	−	9.98227i	−0.869465	−	0.316459i
$996$	11.5503	+	6.30642i	0.365985	+	0.199827i
$997$	−6.20703	−	5.20832i	−0.196579	−	0.164949i	0.539185	−	0.842187i	$-0.318732\pi$
$997$	−6.20703	−	5.20832i	−0.196579	−	0.164949i	−0.735764	+	0.677238i	$0.763177\pi$
$998$	3.62972	−	6.28686i	0.114897	−	0.199007i
$999$	−5.95704	−	2.89300i	−0.188473	−	0.0915306i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	378.2.w.b.25.10	yes	72
7.2	even	3		378.2.v.a.79.7	yes	72
27.13	even	9		378.2.v.a.67.7	✓	72
189.121	even	9	inner	378.2.w.b.121.10	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
378.2.v.a.67.7	✓	72	27.13	even	9
378.2.v.a.79.7	yes	72	7.2	even	3
378.2.w.b.25.10	yes	72	1.1	even	1	trivial
378.2.w.b.121.10	yes	72	189.121	even	9	inner

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

\(f(q)\)	\(=\)	\(q+(0.939693 - 0.342020i) q^{2} +(1.47894 - 0.901527i) q^{3} +(0.766044 - 0.642788i) q^{4} +(1.05304 + 0.383275i) q^{5} +(1.08140 - 1.35298i) q^{6} +(1.66470 + 2.05639i) q^{7} +(0.500000 - 0.866025i) q^{8} +(1.37450 - 2.66660i) q^{9} +O(q^{10})\)	\(q+(0.939693 - 0.342020i) q^{2} +(1.47894 - 0.901527i) q^{3} +(0.766044 - 0.642788i) q^{4} +(1.05304 + 0.383275i) q^{5} +(1.08140 - 1.35298i) q^{6} +(1.66470 + 2.05639i) q^{7} +(0.500000 - 0.866025i) q^{8} +(1.37450 - 2.66660i) q^{9} +1.12062 q^{10} +(-4.85062 + 1.76548i) q^{11} +(0.553440 - 1.64125i) q^{12} +(0.104655 + 0.593530i) q^{13} +(2.26764 + 1.36302i) q^{14} +(1.90291 - 0.382505i) q^{15} +(0.173648 - 0.984808i) q^{16} -2.64369 q^{17} +(0.379575 - 2.97589i) q^{18} -2.99705 q^{19} +(1.05304 - 0.383275i) q^{20} +(4.31588 + 1.54050i) q^{21} +(-3.95426 + 3.31802i) q^{22} +(0.455644 + 2.58409i) q^{23} +(-0.0412776 - 1.73156i) q^{24} +(-2.86823 - 2.40673i) q^{25} +(0.301343 + 0.521941i) q^{26} +(-0.371217 - 5.18288i) q^{27} +(2.59706 + 0.505239i) q^{28} +(0.657346 - 3.72799i) q^{29} +(1.65733 - 1.01027i) q^{30} +(1.70206 - 1.42820i) q^{31} +(-0.173648 - 0.984808i) q^{32} +(-5.58213 + 6.98400i) q^{33} +(-2.48426 + 0.904196i) q^{34} +(0.964836 + 2.80351i) q^{35} +(-0.661130 - 2.92624i) q^{36} +(0.637238 - 1.10373i) q^{37} +(-2.81630 + 1.02505i) q^{38} +(0.689861 + 0.783442i) q^{39} +(0.858447 - 0.720322i) q^{40} +(-1.28984 - 7.31506i) q^{41} +(4.58249 - 0.0285242i) q^{42} +(4.79067 + 4.01985i) q^{43} +(-2.58096 + 4.47036i) q^{44} +(2.46945 - 2.28123i) q^{45} +(1.31197 + 2.27241i) q^{46} +(-6.40954 - 5.37824i) q^{47} +(-0.631016 - 1.61302i) q^{48} +(-1.45752 + 6.84658i) q^{49} +(-3.51840 - 1.28059i) q^{50} +(-3.90985 + 2.38336i) q^{51} +(0.461684 + 0.387399i) q^{52} +(-6.05084 + 10.4804i) q^{53} +(-2.12148 - 4.74335i) q^{54} -5.78457 q^{55} +(2.61324 - 0.413479i) q^{56} +(-4.43244 + 2.70192i) q^{57} +(-0.657346 - 3.72799i) q^{58} +(0.0893074 + 0.506487i) q^{59} +(1.21185 - 1.51618i) q^{60} +(7.91024 + 6.63748i) q^{61} +(1.11094 - 1.92421i) q^{62} +(7.77172 - 1.61259i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-0.117279 + 0.665123i) q^{65} +(-2.85681 + 8.47201i) q^{66} +(12.7733 + 4.64911i) q^{67} +(-2.02519 + 1.69933i) q^{68} +(3.00349 + 3.41092i) q^{69} +(1.86551 + 2.30444i) q^{70} +(4.45463 + 7.71565i) q^{71} +(-1.62209 - 2.52365i) q^{72} +(-4.04838 - 7.01200i) q^{73} +(0.221311 - 1.25511i) q^{74} +(-6.41165 - 0.973611i) q^{75} +(-2.29587 + 1.92646i) q^{76} +(-11.7054 - 7.03579i) q^{77} +(0.916210 + 0.500248i) q^{78} +(10.6914 - 3.89135i) q^{79} +(0.560311 - 0.970488i) q^{80} +(-5.22151 - 7.33047i) q^{81} +(-3.71395 - 6.43276i) q^{82} +(-1.31934 + 7.48238i) q^{83} +(4.29637 - 1.59411i) q^{84} +(-2.78392 - 1.01326i) q^{85} +(5.87662 + 2.13892i) q^{86} +(-2.38871 - 6.10607i) q^{87} +(-0.896359 + 5.08350i) q^{88} -6.65883 q^{89} +(1.54029 - 2.98825i) q^{90} +(-1.04631 + 1.20326i) q^{91} +(2.01006 + 1.68664i) q^{92} +(1.22968 - 3.64666i) q^{93} +(-7.86246 - 2.86170i) q^{94} +(-3.15601 - 1.14869i) q^{95} +(-1.14465 - 1.29992i) q^{96} +(6.73681 + 5.65286i) q^{97} +(0.972048 + 6.93218i) q^{98} +(-1.95934 + 15.3613i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 3 q^{6} + 3 q^{7} + 36 q^{8}+O(q^{10}) \) 72 * q + 3 * q^6 + 3 * q^7 + 36 * q^8	\( 72 q + 3 q^{6} + 3 q^{7} + 36 q^{8} - 12 q^{10} - 6 q^{11} + 12 q^{13} - 3 q^{14} - 6 q^{15} + 24 q^{17} - 36 q^{19} + 18 q^{21} + 6 q^{22} - 6 q^{23} + 30 q^{25} - 18 q^{26} + 6 q^{27} + 3 q^{29} + 15 q^{30} - 9 q^{31} - 18 q^{33} - 9 q^{34} + 9 q^{35} - 3 q^{36} + 51 q^{39} - 6 q^{41} - 27 q^{42} - 24 q^{43} + 18 q^{45} + 27 q^{47} + 6 q^{48} - 69 q^{49} + 6 q^{50} + 6 q^{51} - 6 q^{52} - 15 q^{53} + 45 q^{54} - 72 q^{55} + 6 q^{56} + 57 q^{57} - 3 q^{58} + 15 q^{59} - 33 q^{60} - 18 q^{61} - 24 q^{62} - 12 q^{63} - 36 q^{64} - 90 q^{65} - 36 q^{66} - 66 q^{67} - 18 q^{68} - 39 q^{69} - 12 q^{70} + 12 q^{71} + 30 q^{73} + 9 q^{74} - 21 q^{75} - 87 q^{77} + 6 q^{78} - 45 q^{79} - 6 q^{80} - 24 q^{81} + 33 q^{82} + 18 q^{83} + 6 q^{84} + 51 q^{85} - 12 q^{86} - 18 q^{87} - 12 q^{88} + 72 q^{89} - 69 q^{90} - 30 q^{91} + 12 q^{92} - 48 q^{93} + 21 q^{95} + 48 q^{97} + 6 q^{98} + 90 q^{99}+O(q^{100}) \) 72 * q + 3 * q^6 + 3 * q^7 + 36 * q^8 - 12 * q^10 - 6 * q^11 + 12 * q^13 - 3 * q^14 - 6 * q^15 + 24 * q^17 - 36 * q^19 + 18 * q^21 + 6 * q^22 - 6 * q^23 + 30 * q^25 - 18 * q^26 + 6 * q^27 + 3 * q^29 + 15 * q^30 - 9 * q^31 - 18 * q^33 - 9 * q^34 + 9 * q^35 - 3 * q^36 + 51 * q^39 - 6 * q^41 - 27 * q^42 - 24 * q^43 + 18 * q^45 + 27 * q^47 + 6 * q^48 - 69 * q^49 + 6 * q^50 + 6 * q^51 - 6 * q^52 - 15 * q^53 + 45 * q^54 - 72 * q^55 + 6 * q^56 + 57 * q^57 - 3 * q^58 + 15 * q^59 - 33 * q^60 - 18 * q^61 - 24 * q^62 - 12 * q^63 - 36 * q^64 - 90 * q^65 - 36 * q^66 - 66 * q^67 - 18 * q^68 - 39 * q^69 - 12 * q^70 + 12 * q^71 + 30 * q^73 + 9 * q^74 - 21 * q^75 - 87 * q^77 + 6 * q^78 - 45 * q^79 - 6 * q^80 - 24 * q^81 + 33 * q^82 + 18 * q^83 + 6 * q^84 + 51 * q^85 - 12 * q^86 - 18 * q^87 - 12 * q^88 + 72 * q^89 - 69 * q^90 - 30 * q^91 + 12 * q^92 - 48 * q^93 + 21 * q^95 + 48 * q^97 + 6 * q^98 + 90 * q^99

Introduction

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