LMFDB - Embedded newform 378.2.v.b.79.12

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			79.12
Character	$\chi$	$=$	378.79
Dual form			378.2.v.b.67.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.766044 + 0.642788i) q^{2} +(1.72085 - 0.196628i) q^{3} +(0.173648 + 0.984808i) q^{4} +(0.683660 + 3.87723i) q^{5} +(1.44464 + 0.955517i) q^{6} +(-1.15546 - 2.38011i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(2.92267 - 0.676737i) q^{9} +O(q^{10})$	\(q+(0.766044 + 0.642788i) q^{2} +(1.72085 - 0.196628i) q^{3} +(0.173648 + 0.984808i) q^{4} +(0.683660 + 3.87723i) q^{5} +(1.44464 + 0.955517i) q^{6} +(-1.15546 - 2.38011i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(2.92267 - 0.676737i) q^{9} +(-1.96852 + 3.40958i) q^{10} +(0.286164 - 1.62291i) q^{11} +(0.492464 + 1.66057i) q^{12} +(-0.258932 - 1.46848i) q^{13} +(0.644767 - 2.56598i) q^{14} +(1.93885 + 6.53772i) q^{15} +(-0.939693 + 0.342020i) q^{16} +(-3.00147 + 5.19869i) q^{17} +(2.67390 + 1.36025i) q^{18} +(-1.99659 - 3.45820i) q^{19} +(-3.69961 + 1.34655i) q^{20} +(-2.45638 - 3.86862i) q^{21} +(1.26240 - 1.05928i) q^{22} +(2.26978 - 1.90457i) q^{23} +(-0.690142 + 1.58862i) q^{24} +(-9.86707 + 3.59132i) q^{25} +(0.745566 - 1.29136i) q^{26} +(4.89643 - 1.73925i) q^{27} +(2.14330 - 1.55121i) q^{28} +(0.387255 - 2.19623i) q^{29} +(-2.71712 + 6.25446i) q^{30} +(-0.174681 - 0.990665i) q^{31} +(-0.939693 - 0.342020i) q^{32} +(0.173335 - 2.84907i) q^{33} +(-5.64091 + 2.05312i) q^{34} +(8.43828 - 6.10718i) q^{35} +(1.17397 + 2.76076i) q^{36} +11.5523 q^{37} +(0.693410 - 3.93252i) q^{38} +(-0.734329 - 2.47612i) q^{39} +(-3.69961 - 1.34655i) q^{40} +(0.699279 + 3.96581i) q^{41} +(0.605004 - 4.54246i) q^{42} +(-3.28674 - 2.75790i) q^{43} +1.64795 q^{44} +(4.62198 + 10.8692i) q^{45} +2.96298 q^{46} +(1.57235 - 8.91722i) q^{47} +(-1.54982 + 0.773337i) q^{48} +(-4.32981 + 5.50025i) q^{49} +(-9.86707 - 3.59132i) q^{50} +(-4.14288 + 9.53636i) q^{51} +(1.40121 - 0.509997i) q^{52} +(-5.68396 - 9.84491i) q^{53} +(4.86885 + 1.81502i) q^{54} +6.48805 q^{55} +(2.63896 + 0.189393i) q^{56} +(-4.11583 - 5.55847i) q^{57} +(1.70836 - 1.43349i) q^{58} +(1.81067 + 0.659030i) q^{59} +(-6.10172 + 3.04466i) q^{60} +(-0.132304 + 0.750333i) q^{61} +(0.502974 - 0.871176i) q^{62} +(-4.98775 - 6.17433i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(5.51661 - 2.00788i) q^{65} +(1.96413 - 2.07109i) q^{66} +(-10.5823 + 8.87960i) q^{67} +(-5.64091 - 2.05312i) q^{68} +(3.53146 - 3.72379i) q^{69} +(10.3897 + 0.745647i) q^{70} +(0.162856 + 0.282076i) q^{71} +(-0.875266 + 2.86948i) q^{72} +0.342964 q^{73} +(8.84957 + 7.42567i) q^{74} +(-16.2736 + 8.12028i) q^{75} +(3.05896 - 2.56677i) q^{76} +(-4.19336 + 1.19412i) q^{77} +(1.02909 - 2.36884i) q^{78} +(-10.5479 - 8.85072i) q^{79} +(-1.96852 - 3.40958i) q^{80} +(8.08405 - 3.95576i) q^{81} +(-2.01349 + 3.48747i) q^{82} +(-2.11023 + 11.9677i) q^{83} +(3.38330 - 3.09084i) q^{84} +(-22.2085 - 8.08324i) q^{85} +(-0.745043 - 4.22535i) q^{86} +(0.234568 - 3.85554i) q^{87} +(1.26240 + 1.05928i) q^{88} +(3.33906 + 5.78343i) q^{89} +(-3.44596 + 11.2973i) q^{90} +(-3.19595 + 2.31306i) q^{91} +(2.26978 + 1.90457i) q^{92} +(-0.495393 - 1.67044i) q^{93} +(6.93636 - 5.82030i) q^{94} +(12.0433 - 10.1055i) q^{95} +(-1.68432 - 0.403796i) q^{96} +(-4.05678 - 3.40404i) q^{97} +(-6.85232 + 1.43029i) q^{98} +(-0.261923 - 4.93691i) 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
$3$	1.72085	−	0.196628i	0.993535	−	0.113523i
$3$	1.72085	−	0.196628i	0.993535	−	0.113523i
$4$	0.173648	+	0.984808i	0.0868241	+	0.492404i
$5$	0.683660	+	3.87723i	0.305742	+	1.73395i	0.619990	+	0.784610i	$0.287137\pi$
$5$	0.683660	+	3.87723i	0.305742	+	1.73395i	−0.314248	+	0.949341i	$0.601752\pi$
$6$	1.44464	+	0.955517i	0.589772	+	0.390088i
$7$	−1.15546	−	2.38011i	−0.436724	−	0.899596i
$7$	−1.15546	−	2.38011i	−0.436724	−	0.899596i
$8$	−0.500000	+	0.866025i	−0.176777	+	0.306186i
$9$	2.92267	−	0.676737i	0.974225	−	0.225579i
$10$	−1.96852	+	3.40958i	−0.622501	+	1.07820i
$11$	0.286164	−	1.62291i	0.0862815	−	0.489327i	−0.910791	−	0.412867i	$-0.864527\pi$
$11$	0.286164	−	1.62291i	0.0862815	−	0.489327i	0.997073	−	0.0764596i	$-0.0243616\pi$
$12$	0.492464	+	1.66057i	0.142162	+	0.479364i
$13$	−0.258932	−	1.46848i	−0.0718149	−	0.407282i	−0.999430	−	0.0337461i	$-0.989256\pi$
$13$	−0.258932	−	1.46848i	−0.0718149	−	0.407282i	0.927616	−	0.373536i	$-0.121855\pi$
$14$	0.644767	−	2.56598i	0.172321	−	0.685788i
$15$	1.93885	+	6.53772i	0.500610	+	1.68803i
$16$	−0.939693	+	0.342020i	−0.234923	+	0.0855050i
$17$	−3.00147	+	5.19869i	−0.727963	+	1.26087i	0.229780	+	0.973243i	$0.426199\pi$
$17$	−3.00147	+	5.19869i	−0.727963	+	1.26087i	−0.957743	+	0.287626i	$0.907134\pi$
$18$	2.67390	+	1.36025i	0.630244	+	0.320614i
$19$	−1.99659	−	3.45820i	−0.458050	−	0.793366i	0.540808	−	0.841146i	$-0.318119\pi$
$19$	−1.99659	−	3.45820i	−0.458050	−	0.793366i	−0.998858	+	0.0477802i	$0.984785\pi$
$20$	−3.69961	+	1.34655i	−0.827258	+	0.301097i
$21$	−2.45638	−	3.86862i	−0.536026	−	0.844202i
$22$	1.26240	−	1.05928i	0.269145	−	0.225840i
$23$	2.26978	−	1.90457i	0.473281	−	0.397130i	−0.374708	−	0.927143i	$-0.622257\pi$
$23$	2.26978	−	1.90457i	0.473281	−	0.397130i	0.847990	+	0.530012i	$0.177813\pi$
$24$	−0.690142	+	1.58862i	−0.140875	+	0.324275i
$25$	−9.86707	+	3.59132i	−1.97341	+	0.718264i
$26$	0.745566	−	1.29136i	0.146217	−	0.253256i
$27$	4.89643	−	1.73925i	0.942318	−	0.334718i
$28$	2.14330	−	1.55121i	0.405046	−	0.293151i
$29$	0.387255	−	2.19623i	0.0719114	−	0.407830i	−0.927509	−	0.373800i	$-0.878055\pi$
$29$	0.387255	−	2.19623i	0.0719114	−	0.407830i	0.999421	−	0.0340301i	$-0.0108342\pi$
$30$	−2.71712	+	6.25446i	−0.496076	+	1.14190i
$31$	−0.174681	−	0.990665i	−0.0313736	−	0.177929i	0.965094	−	0.261903i	$-0.0843499\pi$
$31$	−0.174681	−	0.990665i	−0.0313736	−	0.177929i	−0.996468	+	0.0839738i	$0.973239\pi$
$32$	−0.939693	−	0.342020i	−0.166116	−	0.0604612i
$33$	0.173335	−	2.84907i	0.0301737	−	0.495959i
$34$	−5.64091	+	2.05312i	−0.967409	+	0.352108i
$35$	8.43828	−	6.10718i	1.42633	−	1.03230i
$36$	1.17397	+	2.76076i	0.195662	+	0.460126i
$37$	11.5523			1.89919			0.949593	−	0.313485i	$-0.101497\pi$
$37$	11.5523			1.89919			0.949593	+	0.313485i	$0.101497\pi$
$38$	0.693410	−	3.93252i	0.112486	−	0.637939i
$39$	−0.734329	−	2.47612i	−0.117587	−	0.396497i
$40$	−3.69961	−	1.34655i	−0.584960	−	0.212908i
$41$	0.699279	+	3.96581i	0.109209	+	0.619355i	0.989455	+	0.144838i	$0.0462662\pi$
$41$	0.699279	+	3.96581i	0.109209	+	0.619355i	−0.880246	+	0.474517i	$0.842623\pi$
$42$	0.605004	−	4.54246i	0.0933541	−	0.700917i
$43$	−3.28674	−	2.75790i	−0.501223	−	0.420576i	0.356805	−	0.934179i	$-0.383866\pi$
$43$	−3.28674	−	2.75790i	−0.501223	−	0.420576i	−0.858028	+	0.513603i	$0.828310\pi$
$44$	1.64795			0.248438
$45$	4.62198	+	10.8692i	0.689005	+	1.62029i
$46$	2.96298			0.436868
$47$	1.57235	−	8.91722i	0.229350	−	1.30071i	−0.624841	−	0.780752i	$-0.714836\pi$
$47$	1.57235	−	8.91722i	0.229350	−	1.30071i	0.854192	−	0.519958i	$-0.174052\pi$
$48$	−1.54982	+	0.773337i	−0.223698	+	0.111622i
$49$	−4.32981	+	5.50025i	−0.618544	+	0.785750i
$50$	−9.86707	−	3.59132i	−1.39541	−	0.507889i
$51$	−4.14288	+	9.53636i	−0.580119	+	1.33536i
$52$	1.40121	−	0.509997i	0.194312	−	0.0707239i
$53$	−5.68396	−	9.84491i	−0.780752	−	1.35230i	−0.931504	−	0.363730i	$-0.881503\pi$
$53$	−5.68396	−	9.84491i	−0.780752	−	1.35230i	0.150753	−	0.988572i	$-0.451830\pi$
$54$	4.86885	+	1.81502i	0.662566	+	0.246994i
$55$	6.48805			0.874849
$56$	2.63896	+	0.189393i	0.352646	+	0.0253087i
$57$	−4.11583	−	5.55847i	−0.545155	−	0.736238i
$58$	1.70836	−	1.43349i	0.224319	−	0.188226i
$59$	1.81067	+	0.659030i	0.235729	+	0.0857984i	0.457184	−	0.889372i	$-0.348858\pi$
$59$	1.81067	+	0.659030i	0.235729	+	0.0857984i	−0.221455	+	0.975171i	$0.571080\pi$
$60$	−6.10172	+	3.04466i	−0.787729	+	0.393064i
$61$	−0.132304	+	0.750333i	−0.0169398	+	0.0960703i	−0.992105	−	0.125406i	$-0.959977\pi$
$61$	−0.132304	+	0.750333i	−0.0169398	+	0.0960703i	0.975166	+	0.221477i	$0.0710877\pi$
$62$	0.502974	−	0.871176i	0.0638777	−	0.110639i
$63$	−4.98775	−	6.17433i	−0.628397	−	0.777893i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	5.51661	−	2.00788i	0.684251	−	0.249047i
$66$	1.96413	−	2.07109i	0.241767	−	0.254934i
$67$	−10.5823	+	8.87960i	−1.29283	+	1.08482i	−0.301496	+	0.953467i	$0.597486\pi$
$67$	−10.5823	+	8.87960i	−1.29283	+	1.08482i	−0.991336	+	0.131348i	$0.958070\pi$
$68$	−5.64091	−	2.05312i	−0.684061	−	0.248978i
$69$	3.53146	−	3.72379i	0.425138	−	0.448291i
$70$	10.3897	+	0.745647i	1.24181	+	0.0891219i
$71$	0.162856	+	0.282076i	0.0193275	+	0.0334762i	0.875527	−	0.483168i	$-0.160514\pi$
$71$	0.162856	+	0.282076i	0.0193275	+	0.0334762i	−0.856200	+	0.516645i	$0.827181\pi$
$72$	−0.875266	+	2.86948i	−0.103151	+	0.338171i
$73$	0.342964			0.0401409			0.0200705	−	0.999799i	$-0.493611\pi$
$73$	0.342964			0.0401409			0.0200705	+	0.999799i	$0.493611\pi$
$74$	8.84957	+	7.42567i	1.02874	+	0.863217i
$75$	−16.2736	+	8.12028i	−1.87912	+	0.937649i
$76$	3.05896	−	2.56677i	0.350887	−	0.294429i
$77$	−4.19336	+	1.19412i	−0.477878	+	0.136082i
$78$	1.02909	−	2.36884i	0.116522	−	0.268218i
$79$	−10.5479	−	8.85072i	−1.18673	−	0.995783i	−0.999910	−	0.0133887i	$-0.995738\pi$
$79$	−10.5479	−	8.85072i	−1.18673	−	0.995783i	−0.186818	−	0.982395i	$-0.559817\pi$
$80$	−1.96852	−	3.40958i	−0.220087	−	0.381203i
$81$	8.08405	−	3.95576i	0.898228	−	0.439529i
$82$	−2.01349	+	3.48747i	−0.222353	+	0.385127i
$83$	−2.11023	+	11.9677i	−0.231628	+	1.31363i	0.617972	+	0.786200i	$0.287955\pi$
$83$	−2.11023	+	11.9677i	−0.231628	+	1.31363i	−0.849600	+	0.527428i	$0.823157\pi$
$84$	3.38330	−	3.09084i	0.369148	−	0.337238i
$85$	−22.2085	−	8.08324i	−2.40885	−	0.876751i
$86$	−0.745043	−	4.22535i	−0.0803400	−	0.455631i
$87$	0.234568	−	3.85554i	0.0251483	−	0.413357i
$88$	1.26240	+	1.05928i	0.134573	+	0.112920i
$89$	3.33906	+	5.78343i	0.353940	+	0.613042i	0.986936	−	0.161113i	$-0.0515084\pi$
$89$	3.33906	+	5.78343i	0.353940	+	0.613042i	−0.632996	+	0.774155i	$0.718175\pi$
$90$	−3.44596	+	11.2973i	−0.363236	+	1.19084i
$91$	−3.19595	+	2.31306i	−0.335026	+	0.242474i
$92$	2.26978	+	1.90457i	0.236641	+	0.198565i
$93$	−0.495393	−	1.67044i	−0.0513699	−	0.173217i
$94$	6.93636	−	5.82030i	0.715431	−	0.600318i
$95$	12.0433	−	10.1055i	1.23561	−	1.03680i
$96$	−1.68432	−	0.403796i	−0.171906	−	0.0412123i
$97$	−4.05678	−	3.40404i	−0.411903	−	0.345628i	0.413170	−	0.910654i	$-0.364422\pi$
$97$	−4.05678	−	3.40404i	−0.411903	−	0.345628i	−0.825073	+	0.565026i	$0.808866\pi$
$98$	−6.85232	+	1.43029i	−0.692189	+	0.144481i
$99$	−0.261923	−	4.93691i	−0.0263243	−	0.496178i
$100$	−5.25016	−	9.09354i	−0.525016	−	0.909354i
$101$	7.95501	+	6.67504i	0.791553	+	0.664192i	0.946129	−	0.323789i	$-0.104957\pi$
$101$	7.95501	+	6.67504i	0.791553	+	0.664192i	−0.154577	+	0.987981i	$0.549401\pi$
$102$	−9.30348	+	4.64229i	−0.921182	+	0.459655i
$103$	2.55123	+	14.4687i	0.251380	+	1.42565i	0.805197	+	0.593008i	$0.202060\pi$
$103$	2.55123	+	14.4687i	0.251380	+	1.42565i	−0.553817	+	0.832639i	$0.686829\pi$
$104$	1.40121	+	0.509997i	0.137399	+	0.0500093i
$105$	13.3202	−	12.1688i	1.29992	−	1.18755i
$106$	1.97402	−	11.1952i	0.191734	−	1.08738i
$107$	6.80229	−	11.7819i	0.657602	−	1.13900i	−0.323632	−	0.946183i	$-0.604904\pi$
$107$	6.80229	−	11.7819i	0.657602	−	1.13900i	0.981235	−	0.192818i	$-0.0617626\pi$
$108$	2.56308	+	4.52003i	0.246632	+	0.434940i
$109$	−4.78613	−	8.28982i	−0.458428	−	0.794021i	0.540450	−	0.841376i	$-0.318254\pi$
$109$	−4.78613	−	8.28982i	−0.458428	−	0.794021i	−0.998878	+	0.0473552i	$0.984921\pi$
$110$	4.97014	+	4.17044i	0.473884	+	0.397636i
$111$	19.8798	−	2.27151i	1.88691	−	0.215602i
$112$	1.89982	+	1.84138i	0.179517	+	0.173994i
$113$	1.41520	−	1.18749i	0.133131	−	0.111710i	−0.573791	−	0.819002i	$-0.694528\pi$
$113$	1.41520	−	1.18749i	0.133131	−	0.111710i	0.706922	+	0.707292i	$0.250083\pi$
$114$	0.420012	−	6.90364i	0.0393377	−	0.646585i
$115$	8.93621	+	7.49837i	0.833306	+	0.699227i
$116$	2.23011			0.207061
$117$	−1.75055	−	4.11665i	−0.161838	−	0.380585i
$118$	0.963437	+	1.66872i	0.0886916	+	0.153618i
$119$	15.8415	+	1.13691i	1.45219	+	0.104221i
$120$	−6.63126	−	1.58976i	−0.605348	−	0.145125i
$121$	7.78466	+	2.83338i	0.707696	+	0.257580i
$122$	−0.583656	+	0.489745i	−0.0528417	+	0.0443395i
$123$	1.98315	+	6.68708i	0.178814	+	0.602954i
$124$	0.945282	−	0.344054i	0.0848888	−	0.0308970i
$125$	−10.8275	−	18.7538i	−0.968440	−	1.67739i
$126$	0.147947	−	7.93587i	0.0131801	−	0.706984i
$127$	4.80221	−	8.31767i	0.426127	−	0.738074i	−0.570398	−	0.821369i	$-0.693211\pi$
$127$	4.80221	−	8.31767i	0.426127	−	0.738074i	0.996525	+	0.0832946i	$0.0265443\pi$
$128$	0.173648	−	0.984808i	0.0153485	−	0.0870455i
$129$	−6.19827	−	4.09968i	−0.545728	−	0.360956i
$130$	5.51661	+	2.00788i	0.483838	+	0.176103i
$131$	−10.0888	+	8.46551i	−0.881462	+	0.739635i	−0.966479	−	0.256745i	$-0.917350\pi$
$131$	−10.0888	+	8.46551i	−0.881462	+	0.739635i	0.0850168	+	0.996380i	$0.472906\pi$
$132$	2.83588	−	0.324034i	0.246832	−	0.0282035i
$133$	−5.92390	+	8.74793i	−0.513667	+	0.758542i
$134$	−13.8142			−1.19336
$135$	10.0910	+	17.7955i	0.868491	+	1.53160i
$136$	−3.00147	−	5.19869i	−0.257374	−	0.445784i
$137$	−18.3480	+	6.67813i	−1.56758	+	0.570551i	−0.972456	−	0.233085i	$-0.925118\pi$
$137$	−18.3480	+	6.67813i	−1.56758	+	0.570551i	−0.595120	+	0.803636i	$0.702896\pi$
$138$	5.09886	−	0.582607i	0.434044	−	0.0495948i
$139$	−4.31051	−	1.56890i	−0.365613	−	0.133072i	0.152680	−	0.988276i	$-0.451210\pi$
$139$	−4.31051	−	1.56890i	−0.365613	−	0.133072i	−0.518292	+	0.855204i	$0.673432\pi$
$140$	7.47969	+	7.24958i	0.632149	+	0.612701i
$141$	0.952400	−	15.6544i	0.0802066	−	1.31834i
$142$	−0.0565595	+	0.320765i	−0.00474636	+	0.0269180i
$143$	−2.45731			−0.205491
$144$	−2.51496	+	1.63554i	−0.209580	+	0.136295i
$145$	8.78005			0.729143
$146$	0.262726	+	0.220453i	0.0217433	+	0.0182448i
$147$	−6.36947	+	10.3165i	−0.525345	+	0.850890i
$148$	2.00604	+	11.3768i	0.164895	+	0.935167i
$149$	−7.10884	−	2.58740i	−0.582379	−	0.211968i	0.0339955	−	0.999422i	$-0.489177\pi$
$149$	−7.10884	−	2.58740i	−0.582379	−	0.211968i	−0.616374	+	0.787454i	$0.711399\pi$
$150$	−17.6859	−	4.23999i	−1.44405	−	0.346194i
$151$	−3.56606	+	20.2241i	−0.290202	+	1.64582i	0.395886	+	0.918300i	$0.370438\pi$
$151$	−3.56606	+	20.2241i	−0.290202	+	1.64582i	−0.686088	+	0.727518i	$0.740674\pi$
$152$	3.99319			0.323890
$153$	−5.25416	+	17.2253i	−0.424774	+	1.39258i
$154$	−3.97986	−	1.78069i	−0.320707	−	0.143492i
$155$	3.72162	−	1.35456i	0.298927	−	0.108801i
$156$	2.31099	−	1.15315i	0.185027	−	0.0923256i
$157$	−6.63254	−	2.41405i	−0.529334	−	0.192662i	0.0635069	−	0.997981i	$-0.479772\pi$
$157$	−6.63254	−	2.41405i	−0.529334	−	0.192662i	−0.592841	+	0.805320i	$0.701994\pi$
$158$	−2.39101	−	13.5601i	−0.190218	−	1.07878i
$159$	−11.7170	−	15.8240i	−0.929222	−	1.25493i
$160$	0.683660	−	3.87723i	0.0540481	−	0.306522i
$161$	−7.15572	−	3.20165i	−0.563950	−	0.252326i
$162$	8.73546	+	2.16604i	0.686323	+	0.170180i
$163$	−0.867735	+	1.50296i	−0.0679662	+	0.117721i	−0.898006	−	0.439983i	$-0.854984\pi$
$163$	−0.867735	+	1.50296i	−0.0679662	+	0.117721i	0.830040	+	0.557704i	$0.188318\pi$
$164$	−3.78413	+	1.37731i	−0.295491	+	0.107550i
$165$	11.1650	−	1.27573i	0.869193	−	0.0993158i
$166$	−9.30923	+	7.81137i	−0.722537	+	0.606280i
$167$	−0.597809	+	0.501622i	−0.0462599	+	0.0388166i	−0.665624	−	0.746287i	$-0.731835\pi$
$167$	−0.597809	+	0.501622i	−0.0462599	+	0.0388166i	0.619365	+	0.785103i	$0.287390\pi$
$168$	4.57851	−	0.192978i	0.353240	−	0.0148886i
$169$	10.1266	−	3.68579i	0.778971	−	0.283522i
$170$	−11.8169	−	20.4675i	−0.906315	−	1.56978i
$171$	−8.17569	−	8.75603i	−0.625210	−	0.669590i
$172$	2.14527	−	3.71571i	0.163575	−	0.283320i
$173$	13.1810	−	4.79750i	1.00214	−	0.364747i	0.211728	−	0.977329i	$-0.432091\pi$
$173$	13.1810	−	4.79750i	1.00214	−	0.364747i	0.790408	+	0.612581i	$0.209869\pi$
$174$	2.65798	−	2.80274i	0.201501	−	0.212475i
$175$	19.9488	+	19.3350i	1.50798	+	1.46159i
$176$	0.286164	+	1.62291i	0.0215704	+	0.122332i
$177$	3.24548	+	0.778065i	0.243945	+	0.0584829i
$178$	−1.15964	+	6.57667i	−0.0869190	+	0.492942i
$179$	−11.9414	+	20.6831i	−0.892542	+	1.54593i	−0.0557253	+	0.998446i	$0.517747\pi$
$179$	−11.9414	+	20.6831i	−0.892542	+	1.54593i	−0.836817	+	0.547483i	$0.815586\pi$
$180$	−9.90150	+	6.43919i	−0.738014	+	0.479949i
$181$	−12.6683	+	21.9421i	−0.941624	+	1.63094i	−0.179249	+	0.983804i	$0.557367\pi$
$181$	−12.6683	+	21.9421i	−0.941624	+	1.63094i	−0.762374	+	0.647136i	$0.775966\pi$
$182$	−3.93504	−	0.282409i	−0.291685	−	0.0209336i
$183$	−0.0801391	+	1.31723i	−0.00592405	+	0.0973723i
$184$	0.514517	+	2.91797i	0.0379307	+	0.215116i
$185$	7.89785	+	44.7909i	0.580661	+	3.29309i
$186$	0.694246	−	1.59807i	0.0509046	−	0.117176i
$187$	7.57812	+	6.35880i	0.554167	+	0.465001i
$188$	9.05478			0.660388
$189$	−9.79723	−	9.64439i	−0.712644	−	0.701526i
$190$	15.7214			1.14055
$191$	18.7546	+	15.7370i	1.35704	+	1.13869i	0.976885	+	0.213766i	$0.0685729\pi$
$191$	18.7546	+	15.7370i	1.35704	+	1.13869i	0.380152	+	0.924924i	$0.375872\pi$
$192$	−1.03071	−	1.39199i	−0.0743852	−	0.100458i
$193$	−2.41439	−	13.6927i	−0.173791	−	0.985620i	−0.939530	−	0.342468i	$-0.888737\pi$
$193$	−2.41439	−	13.6927i	−0.173791	−	0.985620i	0.765738	−	0.643152i	$-0.222374\pi$
$194$	−0.919597	−	5.21529i	−0.0660232	−	0.374436i
$195$	9.09847	−	4.53999i	0.651555	−	0.325115i
$196$	−6.16855	−	3.30892i	−0.440611	−	0.236352i
$197$	−6.22118	+	10.7754i	−0.443241	+	0.767716i	−0.997928	−	0.0643433i	$-0.979505\pi$
$197$	−6.22118	+	10.7754i	−0.443241	+	0.767716i	0.554687	+	0.832059i	$0.312838\pi$
$198$	2.97274	−	3.95025i	0.211263	−	0.280732i
$199$	9.61869	−	16.6601i	0.681851	−	1.18100i	−0.292565	−	0.956246i	$-0.594509\pi$
$199$	9.61869	−	16.6601i	0.681851	−	1.18100i	0.974415	−	0.224754i	$-0.0721580\pi$
$200$	1.82336	−	10.3408i	0.128931	−	0.731204i
$201$	−16.4646	+	17.3613i	−1.16132	+	1.22457i
$202$	1.80325	+	10.2268i	0.126876	+	0.719552i
$203$	−5.67472	+	1.61596i	−0.398287	+	0.113418i
$204$	−10.1109	−	2.42396i	−0.707904	−	0.169711i
$205$	−14.8983	+	5.42253i	−1.04054	+	0.378726i
$206$	−7.34597	+	12.7236i	−0.511818	+	0.886495i
$207$	5.34493	−	7.10248i	0.371498	−	0.493656i
$208$	0.745566	+	1.29136i	0.0516957	+	0.0895395i
$209$	−6.18372	+	2.25069i	−0.427737	+	0.155683i
$210$	18.0258	−	0.759762i	1.24390	−	0.0524286i
$211$	7.78357	−	6.53119i	0.535843	−	0.449626i	−0.334270	−	0.942477i	$-0.608490\pi$
$211$	7.78357	−	6.53119i	0.535843	−	0.449626i	0.870114	+	0.492851i	$0.164045\pi$
$212$	8.70833	−	7.30716i	0.598091	−	0.501858i
$213$	0.335716	+	0.453389i	0.0230029	+	0.0310657i
$214$	12.7841	−	4.65304i	0.873905	−	0.318075i
$215$	8.44600	−	14.6289i	0.576013	−	0.997683i
$216$	−0.941984	+	5.11006i	−0.0640939	+	0.347695i
$217$	−2.15605	+	1.56044i	−0.146362	+	0.105929i
$218$	1.66221	−	9.42684i	0.112579	−	0.638466i
$219$	0.590191	−	0.0674365i	0.0398814	−	0.00455693i
$220$	1.12664	+	6.38948i	0.0759579	+	0.430779i
$221$	8.41134	+	3.06148i	0.565808	+	0.205937i
$222$	16.6889	+	11.0384i	1.12009	+	0.740850i
$223$	6.14714	−	2.23738i	0.411643	−	0.149826i	−0.127894	−	0.991788i	$-0.540822\pi$
$223$	6.14714	−	2.23738i	0.411643	−	0.149826i	0.539537	+	0.841962i	$0.318599\pi$
$224$	0.271736	+	2.63176i	0.0181561	+	0.175842i
$225$	−26.4078	+	17.1737i	−1.76052	+	1.14491i
$226$	1.84741			0.122888
$227$	−2.26294	+	12.8338i	−0.150197	+	0.851808i	0.812850	+	0.582473i	$0.197915\pi$
$227$	−2.26294	+	12.8338i	−0.150197	+	0.851808i	−0.963047	+	0.269335i	$0.913196\pi$
$228$	4.75932	−	5.01852i	0.315194	−	0.332359i
$229$	9.46418	+	3.44468i	0.625411	+	0.227631i	0.635233	−	0.772321i	$-0.280904\pi$
$229$	9.46418	+	3.44468i	0.625411	+	0.227631i	−0.00982197	+	0.999952i	$0.503126\pi$
$230$	2.02568	+	11.4882i	0.133569	+	0.757508i
$231$	−6.98136	+	2.87943i	−0.459340	+	0.189453i
$232$	1.70836	+	1.43349i	0.112160	+	0.0941131i
$233$	1.90776			0.124982			0.0624908	−	0.998046i	$-0.480096\pi$
$233$	1.90776			0.124982			0.0624908	+	0.998046i	$0.480096\pi$
$234$	1.30514	−	4.27877i	0.0853194	−	0.279712i
$235$	35.6491			2.32549
$236$	−0.334598	+	1.89760i	−0.0217805	+	0.123523i
$237$	−19.8916	−	13.1568i	−1.29210	−	0.854624i
$238$	11.4045	+	11.0537i	0.739245	+	0.716503i
$239$	−6.84005	−	2.48957i	−0.442446	−	0.161037i	0.111184	−	0.993800i	$-0.464536\pi$
$239$	−6.84005	−	2.48957i	−0.442446	−	0.161037i	−0.553630	+	0.832763i	$0.686758\pi$
$240$	−4.05796	−	5.48032i	−0.261940	−	0.353753i
$241$	10.8972	−	3.96625i	0.701949	−	0.255489i	0.0337062	−	0.999432i	$-0.489269\pi$
$241$	10.8972	−	3.96625i	0.701949	−	0.255489i	0.668243	+	0.743943i	$0.267047\pi$
$242$	4.14213	+	7.17438i	0.266266	+	0.461187i
$243$	13.1337	−	8.39685i	0.842525	−	0.538658i
$244$	−0.761908			−0.0487762
$245$	−24.2859	−	13.0274i	−1.55157	−	0.832288i
$246$	−2.77919	+	6.39734i	−0.177195	+	0.407880i
$247$	−4.56131	+	3.82739i	−0.290229	+	0.243531i
$248$	0.945282	+	0.344054i	0.0600254	+	0.0218475i
$249$	−1.27821	+	21.0096i	−0.0810031	+	1.33143i
$250$	3.76035	−	21.3260i	0.237825	−	1.34877i
$251$	6.61645	−	11.4600i	0.417627	−	0.723351i	−0.578074	−	0.815985i	$-0.696195\pi$
$251$	6.61645	−	11.4600i	0.417627	−	0.723351i	0.995700	+	0.0926340i	$0.0295287\pi$
$252$	5.21442	−	5.98413i	0.328477	−	0.376965i
$253$	−2.44143	−	4.22867i	−0.153491	−	0.265854i
$254$	9.02520	−	3.28491i	0.566292	−	0.206113i
$255$	−39.8070	−	9.54325i	−2.49281	−	0.597622i
$256$	0.766044	−	0.642788i	0.0478778	−	0.0401742i
$257$	−15.7880	−	5.74638i	−0.984831	−	0.358449i	−0.201115	−	0.979568i	$-0.564456\pi$
$257$	−15.7880	−	5.74638i	−0.984831	−	0.358449i	−0.783717	+	0.621118i	$0.786679\pi$
$258$	−2.11293	−	7.12471i	−0.131545	−	0.443565i
$259$	−13.3483	−	27.4957i	−0.829420	−	1.70850i
$260$	2.93532	+	5.08413i	0.182041	+	0.315304i
$261$	−0.354451	−	6.68094i	−0.0219400	−	0.413540i
$262$	−13.1700			−0.813645
$263$	3.51508	+	2.94950i	0.216749	+	0.181874i	0.744697	−	0.667403i	$-0.232594\pi$
$263$	3.51508	+	2.94950i	0.216749	+	0.181874i	−0.527948	+	0.849277i	$0.677038\pi$
$264$	2.38070	+	1.57464i	0.146522	+	0.0969127i
$265$	34.2851	−	28.7686i	2.10612	−	1.76724i
$266$	−10.1610	+	2.89350i	−0.623013	+	0.177412i
$267$	6.88323	+	9.29588i	0.421247	+	0.568899i
$268$	−10.5823	−	8.87960i	−0.646416	−	0.542408i
$269$	10.3614	+	17.9465i	0.631748	+	1.09422i	0.987194	+	0.159523i	$0.0509957\pi$
$269$	10.3614	+	17.9465i	0.631748	+	1.09422i	−0.355446	+	0.934697i	$0.615671\pi$
$270$	−3.70863	+	20.1185i	−0.225700	+	1.22437i
$271$	3.94725	−	6.83683i	0.239778	−	0.415308i	−0.720872	−	0.693068i	$-0.756259\pi$
$271$	3.94725	−	6.83683i	0.239778	−	0.415308i	0.960651	+	0.277760i	$0.0895920\pi$
$272$	1.04240	−	5.91174i	0.0632047	−	0.358452i
$273$	−5.04494	+	4.60885i	−0.305334	+	0.278940i
$274$	−18.3480	−	6.67813i	−1.10844	−	0.403441i
$275$	3.00481	+	17.0411i	0.181197	+	1.02762i
$276$	4.28045	+	2.83118i	0.257653	+	0.170417i
$277$	−3.21955	−	2.70152i	−0.193444	−	0.162319i	0.540921	−	0.841073i	$-0.318076\pi$
$277$	−3.21955	−	2.70152i	−0.193444	−	0.162319i	−0.734365	+	0.678754i	$0.762520\pi$
$278$	−2.29357	−	3.97259i	−0.137559	−	0.238260i
$279$	−1.18096	−	2.77718i	−0.0707020	−	0.166265i
$280$	1.06984	+	10.3614i	0.0639349	+	0.619209i
$281$	6.32170	+	5.30454i	0.377121	+	0.316442i	0.811571	−	0.584254i	$-0.198613\pi$
$281$	6.32170	+	5.30454i	0.377121	+	0.316442i	−0.434450	+	0.900696i	$0.643057\pi$
$282$	10.7920	−	11.3798i	0.642656	−	0.677655i
$283$	−10.6237	+	8.91432i	−0.631512	+	0.529901i	−0.901398	−	0.432991i	$-0.857458\pi$
$283$	−10.6237	+	8.91432i	−0.631512	+	0.529901i	0.269886	+	0.962892i	$0.413014\pi$
$284$	−0.249511	+	0.209364i	−0.0148057	+	0.0124235i
$285$	18.7377	−	19.7581i	1.10992	−	1.17037i
$286$	−1.88241	−	1.57953i	−0.111309	−	0.0933995i
$287$	8.63106	−	6.24670i	0.509475	−	0.368731i
$288$	−2.97787	−	0.363689i	−0.175473	−	0.0214306i
$289$	−9.51761	−	16.4850i	−0.559859	−	0.969705i
$290$	6.72591	+	5.64371i	0.394959	+	0.331410i
$291$	−7.65045	−	5.06018i	−0.448478	−	0.296633i
$292$	0.0595551	+	0.337754i	0.00348520	+	0.0197656i
$293$	4.43361	+	1.61370i	0.259014	+	0.0942736i	0.468264	−	0.883589i	$-0.344880\pi$
$293$	4.43361	+	1.61370i	0.259014	+	0.0942736i	−0.209249	+	0.977862i	$0.567102\pi$
$294$	−11.5106	+	3.80867i	−0.671312	+	0.222126i
$295$	−1.31733	+	7.47094i	−0.0766978	+	0.434975i
$296$	−5.77615	+	10.0046i	−0.335732	+	0.581505i
$297$	−1.42147	−	8.44419i	−0.0824819	−	0.489982i
$298$	−3.78253	−	6.55154i	−0.219116	−	0.379520i
$299$	−3.38454	−	2.83996i	−0.195733	−	0.164239i
$300$	−10.8228	−	14.6163i	−0.624855	−	0.843874i
$301$	−2.76639	+	11.0094i	−0.159452	+	0.634573i
$302$	−15.7316	+	13.2004i	−0.905252	+	0.759596i
$303$	15.0019	+	9.92259i	0.861837	+	0.570038i
$304$	3.05896	+	2.56677i	0.175443	+	0.147214i
$305$	−2.99967			−0.171760
$306$	−15.0971	+	9.81803i	−0.863045	+	0.561259i
$307$	9.95456	+	17.2418i	0.568137	+	0.984042i	0.996750	+	0.0805537i	$0.0256688\pi$
$307$	9.95456	+	17.2418i	0.568137	+	0.984042i	−0.428614	+	0.903488i	$0.640998\pi$
$308$	−1.90415	−	3.92230i	−0.108499	−	0.223494i
$309$	7.23525	+	24.3969i	0.411599	+	1.38789i
$310$	3.72162	+	1.35456i	0.211374	+	0.0769337i
$311$	−10.3028	+	8.64509i	−0.584219	+	0.490218i	−0.886330	−	0.463055i	$-0.846753\pi$
$311$	−10.3028	+	8.64509i	−0.584219	+	0.490218i	0.302111	+	0.953273i	$0.402309\pi$
$312$	2.51155	+	0.602114i	0.142188	+	0.0340880i
$313$	−9.21049	+	3.35234i	−0.520608	+	0.189486i	−0.588940	−	0.808177i	$-0.700454\pi$
$313$	−9.21049	+	3.35234i	−0.520608	+	0.189486i	0.0683321	+	0.997663i	$0.478232\pi$
$314$	−3.52910	−	6.11258i	−0.199159	−	0.344953i
$315$	20.5294	−	23.5598i	1.15670	−	1.32744i
$316$	6.88463	−	11.9245i	0.387291	−	0.670808i
$317$	−5.63135	+	31.9370i	−0.316288	+	1.79376i	0.248617	+	0.968602i	$0.420024\pi$
$317$	−5.63135	+	31.9370i	−0.316288	+	1.79376i	−0.564905	+	0.825156i	$0.691087\pi$
$318$	1.19570	−	19.6535i	0.0670516	−	1.10211i
$319$	−3.45348	−	1.25696i	−0.193358	−	0.0703764i
$320$	3.01595	−	2.53068i	0.168597	−	0.141469i
$321$	9.38909	−	21.6125i	0.524048	−	1.20629i
$322$	−3.42362	−	7.05222i	−0.190791	−	0.393005i
$323$	23.9708			1.33377
$324$	5.29945	+	7.27433i	0.294414	+	0.404129i
$325$	7.82867	+	13.5597i	0.434257	+	0.752155i
$326$	−1.63081	+	0.593565i	−0.0903221	+	0.0328746i
$327$	−9.86625	−	13.3245i	−0.545605	−	0.736846i
$328$	−3.78413	−	1.37731i	−0.208944	−	0.0760493i
$329$	−23.0407	+	6.56116i	−1.27028	+	0.361729i
$330$	9.37290	+	6.19945i	0.515961	+	0.341268i
$331$	−1.74452	+	9.89365i	−0.0958874	+	0.543804i	0.898584	+	0.438801i	$0.144597\pi$
$331$	−1.74452	+	9.89365i	−0.0958874	+	0.543804i	−0.994472	+	0.105004i	$0.966515\pi$
$332$	−12.1523			−0.666946
$333$	33.7636	−	7.81787i	1.85023	−	0.428417i
$334$	−0.780385			−0.0427007
$335$	−41.6629	−	34.9594i	−2.27629	−	1.91003i
$336$	3.63139	+	2.79518i	0.198108	+	0.152490i
$337$	−3.78662	−	21.4750i	−0.206270	−	1.16982i	−0.895429	−	0.445205i	$-0.853131\pi$
$337$	−3.78662	−	21.4750i	−0.206270	−	1.16982i	0.689158	−	0.724611i	$-0.257980\pi$
$338$	10.1266	+	3.68579i	0.550816	+	0.200481i
$339$	2.20185	−	2.32177i	0.119588	−	0.126101i
$340$	4.10397	−	23.2748i	0.222569	−	1.26225i
$341$	−1.65775			−0.0897723
$342$	−0.634672	−	11.9627i	−0.0343191	−	0.646871i
$343$	18.0941	+	3.95007i	0.976990	+	0.213284i
$344$	4.03178	−	1.46745i	0.217379	−	0.0791195i
$345$	16.8523	+	11.1465i	0.907298	+	0.600107i
$346$	13.1810	+	4.79750i	0.708616	+	0.257915i
$347$	−4.11547	−	23.3400i	−0.220930	−	1.25296i	−0.870314	−	0.492497i	$-0.836084\pi$
$347$	−4.11547	−	23.3400i	−0.220930	−	1.25296i	0.649384	−	0.760461i	$-0.275027\pi$
$348$	3.83770	−	0.438503i	0.205722	−	0.0235062i
$349$	0.965025	−	5.47293i	0.0516566	−	0.292959i	−0.948025	−	0.318196i	$-0.896923\pi$
$349$	0.965025	−	5.47293i	0.0516566	−	0.292959i	0.999681	+	0.0252370i	$0.00803404\pi$
$350$	2.85331	+	27.6343i	0.152516	+	1.47712i
$351$	−3.82189	−	6.73995i	−0.203997	−	0.359752i
$352$	−0.823975	+	1.42717i	−0.0439180	+	0.0760682i
$353$	3.36025	−	1.22303i	0.178848	−	0.0650953i	−0.251044	−	0.967976i	$-0.580774\pi$
$353$	3.36025	−	1.22303i	0.178848	−	0.0650953i	0.429892	+	0.902880i	$0.358552\pi$
$354$	1.98605	+	2.68219i	0.105557	+	0.142557i
$355$	−0.982334	+	0.824276i	−0.0521369	+	0.0437480i
$356$	−5.11574	+	4.29262i	−0.271134	+	0.227508i
$357$	27.4845	−	1.15843i	1.45463	−	0.0613108i
$358$	−22.4425	+	8.16840i	−1.18612	+	0.431713i
$359$	−5.28790	−	9.15890i	−0.279084	−	0.483388i	0.692073	−	0.721827i	$-0.256698\pi$
$359$	−5.28790	−	9.15890i	−0.279084	−	0.483388i	−0.971157	+	0.238439i	$0.923364\pi$
$360$	−11.7240	−	1.43186i	−0.617910	−	0.0754656i
$361$	1.52723	−	2.64523i	0.0803803	−	0.139223i
$362$	−23.8085	+	8.66559i	−1.25135	+	0.455454i
$363$	13.9534	+	3.34516i	0.732363	+	0.175575i
$364$	−2.83289	−	2.74573i	−0.148484	−	0.143916i
$365$	0.234471	+	1.32975i	0.0122728	+	0.0696024i
$366$	−0.908088	+	0.957543i	−0.0474665	+	0.0500516i
$367$	1.66632	−	9.45015i	0.0869810	−	0.493294i	−0.909930	−	0.414761i	$-0.863865\pi$
$367$	1.66632	−	9.45015i	0.0869810	−	0.493294i	0.996912	−	0.0785331i	$-0.0250236\pi$
$368$	−1.48149	+	2.56602i	−0.0772281	+	0.133763i
$369$	4.72758	+	11.1175i	0.246108	+	0.578756i
$370$	−22.7410	+	39.3885i	−1.18225	+	2.04771i
$371$	−16.8643	+	24.9038i	−0.875552	+	1.29294i
$372$	1.55904	−	0.777936i	0.0808325	−	0.0403341i
$373$	−5.23559	−	29.6925i	−0.271089	−	1.53742i	−0.751118	−	0.660168i	$-0.770485\pi$
$373$	−5.23559	−	29.6925i	−0.271089	−	1.53742i	0.480029	−	0.877252i	$-0.340626\pi$
$374$	1.71782	+	9.74225i	0.0888264	+	0.503760i
$375$	−22.3200	−	30.1435i	−1.15260	−	1.55660i
$376$	6.93636	+	5.82030i	0.357716	+	0.300159i
$377$	−3.32539			−0.171266
$378$	−1.30582	−	13.6856i	−0.0671643	−	0.703910i
$379$	−3.98054			−0.204467			−0.102233	−	0.994760i	$-0.532599\pi$
$379$	−3.98054			−0.204467			−0.102233	+	0.994760i	$0.532599\pi$
$380$	12.0433	+	10.1055i	0.617806	+	0.518401i
$381$	6.62841	−	15.2577i	0.339584	−	0.781678i
$382$	4.25133	+	24.1105i	0.217517	+	1.23360i
$383$	0.601075	+	3.40887i	0.0307135	+	0.174185i	0.996306	−	0.0858753i	$-0.0273687\pi$
$383$	0.601075	+	3.40887i	0.0307135	+	0.174185i	−0.965592	+	0.260060i	$0.916258\pi$
$384$	0.105182	−	1.72885i	0.00536755	−	0.0882252i
$385$	−7.49670	−	15.4423i	−0.382067	−	0.787010i
$386$	6.95195	−	12.0411i	0.353845	−	0.612878i
$387$	−11.4724	−	5.83619i	−0.583177	−	0.296670i
$388$	2.64787	−	4.58625i	0.134425	−	0.232832i
$389$	4.67788	−	26.5296i	0.237178	−	1.34510i	−0.600801	−	0.799399i	$-0.705152\pi$
$389$	4.67788	−	26.5296i	0.237178	−	1.34510i	0.837979	−	0.545703i	$-0.183737\pi$
$390$	9.88808	+	2.37055i	0.500702	+	0.120037i
$391$	3.08861	+	17.5164i	0.156198	+	0.885841i
$392$	−2.59845	−	6.49985i	−0.131242	−	0.328292i
$393$	−15.6968	+	16.5516i	−0.791798	+	0.834920i
$394$	−11.6920	+	4.25554i	−0.589035	+	0.214391i
$395$	27.1051	−	46.9474i	1.36381	−	2.36218i
$396$	4.81642	−	1.11523i	0.242034	−	0.0560424i
$397$	−5.73774	−	9.93805i	−0.287969	−	0.498776i	0.685356	−	0.728208i	$-0.259647\pi$
$397$	−5.73774	−	9.93805i	−0.287969	−	0.498776i	−0.973325	+	0.229432i	$0.926313\pi$
$398$	18.0772	−	6.57957i	0.906129	−	0.329804i
$399$	−8.47407	+	16.2187i	−0.424234	+	0.811951i
$400$	8.04371	−	6.74947i	0.402185	−	0.337474i
$401$	−6.93235	+	5.81693i	−0.346185	+	0.290484i	−0.799256	−	0.600991i	$-0.794773\pi$
$401$	−6.93235	+	5.81693i	−0.346185	+	0.290484i	0.453071	+	0.891474i	$0.350328\pi$
$402$	−23.7722	+	2.71626i	−1.18565	+	0.135475i
$403$	−1.40954	+	0.513030i	−0.0702141	+	0.0255559i
$404$	−5.19226	+	8.99326i	−0.258325	+	0.447431i
$405$	20.8642	+	28.6393i	1.03675	+	1.42310i
$406$	−5.38581	−	2.40975i	−0.267293	−	0.119594i
$407$	3.30585	−	18.7484i	0.163865	−	0.929323i
$408$	−6.18730	−	8.35602i	−0.306317	−	0.413685i
$409$	−6.46292	−	36.6530i	−0.319571	−	1.81237i	−0.545364	−	0.838200i	$-0.683608\pi$
$409$	−6.46292	−	36.6530i	−0.319571	−	1.81237i	0.225793	−	0.974175i	$-0.427503\pi$
$410$	−14.8983	−	5.42253i	−0.735774	−	0.267800i
$411$	−30.2611	+	15.0998i	−1.49267	+	0.744820i
$412$	−13.8059	+	5.02494i	−0.680168	+	0.247561i
$413$	−0.523601	−	5.07107i	−0.0257647	−	0.249531i
$414$	8.65984	−	2.00516i	0.425608	−	0.0985483i
$415$	−47.8443			−2.34858
$416$	−0.258932	+	1.46848i	−0.0126952	+	0.0719980i
$417$	−7.72624	−	1.85227i	−0.378356	−	0.0907062i
$418$	−6.18372	−	2.25069i	−0.302455	−	0.110085i
$419$	2.25461	+	12.7865i	0.110145	+	0.624662i	0.989040	+	0.147647i	$0.0471700\pi$
$419$	2.25461	+	12.7865i	0.110145	+	0.624662i	−0.878895	+	0.477015i	$0.841719\pi$
$420$	14.2969	+	11.0047i	0.697619	+	0.536977i
$421$	5.20931	+	4.37113i	0.253886	+	0.213036i	0.760844	−	0.648935i	$-0.224785\pi$
$421$	5.20931	+	4.37113i	0.253886	+	0.213036i	−0.506957	+	0.861971i	$0.669230\pi$
$422$	10.1607			0.494617
$423$	−1.43916	−	27.1262i	−0.0699741	−	1.31892i
$424$	11.3679			0.552075
$425$	10.9455	−	62.0751i	0.530935	−	3.01108i
$426$	−0.0342591	+	0.563110i	−0.00165986	+	0.0272828i
$427$	1.93875	−	0.552085i	0.0938225	−	0.0267173i
$428$	12.7841	+	4.65304i	0.617944	+	0.224913i
$429$	−4.22867	+	0.483177i	−0.204162	+	0.0233280i
$430$	15.8733	−	5.77741i	0.765478	−	0.278611i
$431$	7.27375	+	12.5985i	0.350364	+	0.606848i	0.986313	−	0.164883i	$-0.0527245\pi$
$431$	7.27375	+	12.5985i	0.350364	+	0.606848i	−0.635949	+	0.771731i	$0.719391\pi$
$432$	−4.00628	+	3.30903i	−0.192752	+	0.159206i
$433$	9.39529			0.451509			0.225755	−	0.974184i	$-0.427515\pi$
$433$	9.39529			0.451509			0.225755	+	0.974184i	$0.427515\pi$
$434$	−2.65466	−	0.190519i	−0.127428	−	0.00914521i
$435$	15.1092	−	1.72641i	0.724430	−	0.0827748i
$436$	7.33278	−	6.15293i	0.351176	−	0.294672i
$437$	−11.1182	−	4.04670i	−0.531856	−	0.193580i
$438$	0.495460	+	0.327708i	0.0236740	+	0.0156585i
$439$	−1.22261	+	6.93376i	−0.0583520	+	0.330930i	−0.999984	−	0.00571438i	$-0.998181\pi$
$439$	−1.22261	+	6.93376i	−0.0583520	+	0.330930i	0.941632	+	0.336645i	$0.109292\pi$
$440$	−3.24403	+	5.61882i	−0.154653	+	0.267867i
$441$	−8.93240	+	19.0056i	−0.425353	+	0.905028i
$442$	4.47558	+	7.75194i	0.212882	+	0.368722i
$443$	−5.43053	+	1.97655i	−0.258012	+	0.0939088i	−0.467788	−	0.883841i	$-0.654949\pi$
$443$	−5.43053	+	1.97655i	−0.258012	+	0.0939088i	0.209776	+	0.977750i	$0.432727\pi$
$444$	5.68909	+	19.1834i	0.269992	+	0.910402i
$445$	−20.1409	+	16.9002i	−0.954770	+	0.801147i
$446$	6.14714	+	2.23738i	0.291076	+	0.105943i
$447$	−12.7420	−	3.05475i	−0.602677	−	0.144485i
$448$	−1.48350	+	2.19071i	−0.0700888	+	0.103501i
$449$	12.3215	+	21.3415i	0.581488	+	1.00717i	0.995303	+	0.0968063i	$0.0308628\pi$
$449$	12.3215	+	21.3415i	0.581488	+	1.00717i	−0.413815	+	0.910361i	$0.635804\pi$
$450$	−31.2686	−	3.81885i	−1.47402	−	0.180022i
$451$	6.63628			0.312490
$452$	1.41520	+	1.18749i	0.0665653	+	0.0558549i
$453$	−2.16003	+	35.5040i	−0.101487	+	1.66812i
$454$	−9.98291	+	8.37665i	−0.468521	+	0.393136i
$455$	−11.1532	−	10.8101i	−0.522870	−	0.506784i
$456$	6.87169	−	0.785174i	0.321796	−	0.0367691i
$457$	−2.80407	−	2.35289i	−0.131169	−	0.110064i	0.574843	−	0.818264i	$-0.305063\pi$
$457$	−2.80407	−	2.35289i	−0.131169	−	0.110064i	−0.706012	+	0.708200i	$0.749508\pi$
$458$	5.03578	+	8.72223i	0.235307	+	0.407563i
$459$	−5.65467	+	30.6753i	−0.263937	+	1.43180i
$460$	−5.83270	+	10.1025i	−0.271951	+	0.471033i
$461$	1.56879	−	8.89702i	0.0730656	−	0.414376i	−0.926234	−	0.376950i	$-0.876973\pi$
$461$	1.56879	−	8.89702i	0.0730656	−	0.414376i	0.999299	−	0.0374261i	$-0.0119159\pi$
$462$	−7.19890	−	2.28176i	−0.334923	−	0.106157i
$463$	15.3762	+	5.59649i	0.714594	+	0.260091i	0.673629	−	0.739070i	$-0.264735\pi$
$463$	15.3762	+	5.59649i	0.714594	+	0.260091i	0.0409649	+	0.999161i	$0.486957\pi$
$464$	0.387255	+	2.19623i	0.0179779	+	0.101957i
$465$	6.13801	−	3.06277i	0.284643	−	0.142033i
$466$	1.46143	+	1.22629i	0.0676995	+	0.0568066i
$467$	2.72352	+	4.71728i	0.126030	+	0.218290i	0.922135	−	0.386868i	$-0.126443\pi$
$467$	2.72352	+	4.71728i	0.126030	+	0.218290i	−0.796105	+	0.605158i	$0.793110\pi$
$468$	3.75013	−	2.43880i	0.173350	−	0.112734i
$469$	33.3618	+	14.9269i	1.54051	+	0.689261i
$470$	27.3088	+	22.9148i	1.25966	+	1.05698i
$471$	−11.8883	−	2.85008i	−0.547784	−	0.131325i
$472$	−1.47607	+	1.23857i	−0.0679417	+	0.0570098i
$473$	−5.41638	+	4.54488i	−0.249045	+	0.208974i
$474$	−6.78087	−	22.8648i	−0.311456	−	1.05021i
$475$	32.1200	+	26.9519i	1.47377	+	1.23664i
$476$	1.63121	+	15.7983i	0.0747665	+	0.724113i
$477$	−23.2748	−	24.9269i	−1.06568	−	1.14132i
$478$	−3.63951	−	6.30382i	−0.166468	−	0.288330i
$479$	−20.8734	−	17.5148i	−0.953729	−	0.800274i	0.0261924	−	0.999657i	$-0.491662\pi$
$479$	−20.8734	−	17.5148i	−0.953729	−	0.800274i	−0.979922	+	0.199383i	$0.936106\pi$
$480$	0.414106	−	6.80657i	0.0189013	−	0.310676i
$481$	−2.99126	−	16.9643i	−0.136390	−	0.773505i
$482$	10.8972	+	3.96625i	0.496353	+	0.180658i
$483$	−12.9435	−	4.10256i	−0.588949	−	0.186673i
$484$	−1.43855	+	8.15840i	−0.0653885	+	0.370837i
$485$	10.4248	−	18.0563i	0.473366	−	0.819893i
$486$	15.4584	+	2.00980i	0.701205	+	0.0911662i
$487$	−16.3844	−	28.3786i	−0.742448	−	1.28596i	−0.951378	−	0.308027i	$-0.900331\pi$
$487$	−16.3844	−	28.3786i	−0.742448	−	1.28596i	0.208930	−	0.977931i	$-0.433002\pi$
$488$	−0.583656	−	0.489745i	−0.0264209	−	0.0221697i
$489$	−1.19772	+	2.75700i	−0.0541628	+	0.124676i
$490$	−10.2302	−	25.5902i	−0.462154	−	1.15605i
$491$	4.38515	−	3.67958i	0.197899	−	0.166057i	−0.538453	−	0.842655i	$-0.680991\pi$
$491$	4.38515	−	3.67958i	0.197899	−	0.166057i	0.736352	+	0.676598i	$0.236547\pi$
$492$	−6.24112	+	3.11422i	−0.281371	+	0.140400i
$493$	10.2552	+	8.60514i	0.461871	+	0.387556i
$494$	−5.95437			−0.267900
$495$	18.9625	−	4.39070i	0.852299	−	0.197348i
$496$	0.502974	+	0.871176i	0.0225842	+	0.0391170i
$497$	0.483195	−	0.713544i	0.0216743	−	0.0320068i
$498$	−14.4839	+	15.2727i	−0.649039	+	0.684386i
$499$	6.69966	+	2.43848i	0.299918	+	0.109161i	0.487596	−	0.873069i	$-0.337874\pi$
$499$	6.69966	+	2.43848i	0.299918	+	0.109161i	−0.187678	+	0.982231i	$0.560096\pi$
$500$	16.5887	−	13.9196i	0.741868	−	0.622501i
$501$	−0.930109	+	0.980763i	−0.0415542	+	0.0438173i
$502$	12.4349	−	4.52592i	0.554995	−	0.202002i
$503$	−11.8867	−	20.5883i	−0.530001	−	0.917989i	−0.999387	−	0.0349962i	$-0.988858\pi$
$503$	−11.8867	−	20.5883i	−0.530001	−	0.917989i	0.469386	−	0.882993i	$-0.344475\pi$
$504$	7.84100	−	1.23235i	0.349266	−	0.0548933i
$505$	−20.4422	+	35.4069i	−0.909664	+	1.57558i
$506$	0.847898	−	4.80867i	0.0376937	−	0.213771i
$507$	16.7017	−	8.33388i	0.741749	−	0.370121i
$508$	9.02520	+	3.28491i	0.400429	+	0.145744i
$509$	26.0114	−	21.8262i	1.15294	−	0.967429i	0.153153	−	0.988203i	$-0.451057\pi$
$509$	26.0114	−	21.8262i	1.15294	−	0.967429i	0.999784	+	0.0207735i	$0.00661289\pi$
$510$	−24.3597	−	32.8980i	−1.07866	−	1.45675i
$511$	−0.396283	−	0.816291i	−0.0175305	−	0.0361106i
$512$	1.00000			0.0441942
$513$	−15.7908	−	13.4603i	−0.697183	−	0.594286i
$514$	−8.40064	−	14.5503i	−0.370537	−	0.641788i
$515$	−54.3545	+	19.7834i	−2.39514	+	0.871761i
$516$	2.96107	−	6.81601i	0.130354	−	0.300058i
$517$	−14.0219	−	5.10356i	−0.616684	−	0.224455i
$518$	7.44854	−	29.6430i	0.327270	−	1.30244i
$519$	21.7393	−	10.8476i	0.954249	−	0.476155i
$520$	−1.01943	+	5.78146i	−0.0447049	+	0.253534i
$521$	23.9856			1.05083			0.525414	−	0.850847i	$-0.323911\pi$
$521$	23.9856			1.05083			0.525414	+	0.850847i	$0.323911\pi$
$522$	4.02290	−	5.34573i	0.176078	−	0.233976i
$523$	−34.1029			−1.49122			−0.745608	−	0.666385i	$-0.767841\pi$
$523$	−34.1029			−1.49122			−0.745608	+	0.666385i	$0.767841\pi$
$524$	−10.0888	−	8.46551i	−0.440731	−	0.369817i
$525$	38.1307	+	29.3503i	1.66416	+	1.28095i
$526$	0.796803	+	4.51890i	0.0347423	+	0.197033i
$527$	5.67446	+	2.06534i	0.247184	+	0.0899674i
$528$	0.811556	+	2.73653i	0.0353185	+	0.119092i
$529$	−2.46940	+	14.0047i	−0.107365	+	0.608899i
$530$	44.7560			1.94408
$531$	5.73799	+	0.700782i	0.249007	+	0.0304114i
$532$	−9.64370	−	4.31484i	−0.418108	−	0.187072i
$533$	5.64264	−	2.05375i	0.244410	−	0.0889579i
$534$	−0.702419	+	11.5455i	−0.0303966	+	0.499623i
$535$	50.3317	+	18.3192i	2.17603	+	0.792009i
$536$	−2.39881	−	13.6043i	−0.103613	−	0.587618i
$537$	−16.4825	+	37.9406i	−0.711273	+	1.63726i
$538$	−3.59849	+	20.4081i	−0.155142	+	0.879854i
$539$	7.68740	+	8.60088i	0.331120	+	0.370466i
$540$	−15.7729	+	13.0278i	−0.678758	+	0.560628i
$541$	−2.94791	+	5.10593i	−0.126740	+	0.219521i	−0.922412	−	0.386208i	$-0.873785\pi$
$541$	−2.94791	+	5.10593i	−0.126740	+	0.219521i	0.795671	+	0.605728i	$0.207118\pi$
$542$	7.41839	−	2.70007i	0.318647	−	0.115978i
$543$	−17.4858	+	40.2500i	−0.750387	+	1.72729i
$544$	4.59851	−	3.85861i	0.197160	−	0.165437i
$545$	28.8695	−	24.2244i	1.23663	−	1.03766i
$546$	−6.82716	+	0.287755i	−0.292176	+	0.0123148i
$547$	25.5550	−	9.30125i	1.09265	−	0.397693i	0.268049	−	0.963405i	$-0.413621\pi$
$547$	25.5550	−	9.30125i	1.09265	−	0.397693i	0.824602	+	0.565713i	$0.191399\pi$
$548$	−9.76278	−	16.9096i	−0.417045	−	0.722343i
$549$	0.121097	+	2.28252i	0.00516828	+	0.0974154i
$550$	−8.65200	+	14.9857i	−0.368922	+	0.638992i
$551$	−8.36820	+	3.04578i	−0.356497	+	0.129754i
$552$	1.45916	+	4.92023i	0.0621061	+	0.209419i
$553$	−8.87797	+	35.3317i	−0.377530	+	1.50246i
$554$	−0.729812	−	4.13897i	−0.0310067	−	0.175848i
$555$	22.3982	+	75.5257i	0.950751	+	3.20589i
$556$	0.796550	−	4.51746i	0.0337812	−	0.191583i
$557$	17.2425	−	29.8650i	0.730590	−	1.26542i	−0.226042	−	0.974118i	$-0.572579\pi$
$557$	17.2425	−	29.8650i	0.730590	−	1.26542i	0.956631	−	0.291301i	$-0.0940882\pi$
$558$	0.880472	−	2.88655i	0.0372733	−	0.122197i
$559$	−3.19887	+	5.54061i	−0.135298	+	0.234343i
$560$	−5.84061	+	8.62493i	−0.246811	+	0.364470i
$561$	14.2912	+	9.45249i	0.603373	+	0.399084i
$562$	1.43301	+	8.12702i	0.0604480	+	0.342818i
$563$	−2.86326	−	16.2384i	−0.120672	−	0.684365i	−0.983785	−	0.179354i	$-0.942599\pi$
$563$	−2.86326	−	16.2384i	−0.120672	−	0.684365i	0.863113	−	0.505012i	$-0.168512\pi$
$564$	15.5820	−	1.78043i	0.656118	−	0.0749695i
$565$	5.57170	+	4.67521i	0.234403	+	0.196688i
$566$	−13.8682			−0.582925
$567$	−18.7560	−	14.6702i	−0.787676	−	0.616089i
$568$	−0.325713			−0.0136666
$569$	11.9495	+	10.0268i	0.500949	+	0.420346i	0.857931	−	0.513765i	$-0.171750\pi$
$569$	11.9495	+	10.0268i	0.500949	+	0.420346i	−0.356982	+	0.934111i	$0.616194\pi$
$570$	27.0542	−	3.09126i	1.13317	−	0.129479i
$571$	−3.48176	−	19.7461i	−0.145707	−	0.826347i	−0.966797	−	0.255547i	$-0.917744\pi$
$571$	−3.48176	−	19.7461i	−0.145707	−	0.826347i	0.821089	−	0.570800i	$-0.193367\pi$
$572$	−0.426707	−	2.41998i	−0.0178415	−	0.101184i
$573$	35.3683	+	23.3934i	1.47753	+	0.977273i
$574$	10.6271	+	0.762682i	0.443566	+	0.0318337i
$575$	−15.5561	+	26.9440i	−0.648736	+	1.12364i
$576$	−2.04741	−	2.19274i	−0.0853087	−	0.0913642i
$577$	16.2379	−	28.1249i	0.675995	−	1.17086i	−0.300183	−	0.953882i	$-0.597048\pi$
$577$	16.2379	−	28.1249i	0.675995	−	1.17086i	0.976177	−	0.216975i	$-0.0696191\pi$
$578$	3.30543	−	18.7460i	0.137488	−	0.779732i
$579$	−6.84717	−	23.0883i	−0.284559	−	0.959519i
$580$	1.52464	+	8.64666i	0.0633072	+	0.359033i
$581$	30.9227	−	8.80568i	1.28289	−	0.365321i
$582$	−2.60797	−	8.79394i	−0.108104	−	0.364521i
$583$	−17.6040	+	6.40732i	−0.729082	+	0.265364i
$584$	−0.171482	+	0.297016i	−0.00709598	+	0.0122906i
$585$	14.7644	−	9.60167i	0.610434	−	0.396980i
$586$	2.35908	+	4.08604i	0.0974526	+	0.168793i
$587$	−10.5599	+	3.84350i	−0.435855	+	0.158638i	−0.550623	−	0.834754i	$-0.685610\pi$
$587$	−10.5599	+	3.84350i	−0.435855	+	0.158638i	0.114768	+	0.993392i	$0.463387\pi$
$588$	−11.2658	−	4.48126i	−0.464594	−	0.184804i
$589$	−3.07715	+	2.58204i	−0.126792	+	0.106391i
$590$	−5.81136	+	4.87631i	−0.239250	+	0.200754i
$591$	−8.58700	+	19.7662i	−0.353222	+	0.813071i
$592$	−10.8556	+	3.95112i	−0.446163	+	0.162390i
$593$	−16.0355	+	27.7743i	−0.658498	+	1.14055i	0.322506	+	0.946567i	$0.395475\pi$
$593$	−16.0355	+	27.7743i	−0.658498	+	1.14055i	−0.981004	+	0.193985i	$0.937859\pi$
$594$	4.33892	−	7.38233i	0.178028	−	0.302901i
$595$	6.42215	+	62.1985i	0.263283	+	2.54989i
$596$	1.31366	−	7.45014i	0.0538096	−	0.305169i
$597$	13.2765	−	30.5608i	0.543372	−	1.25077i
$598$	−0.767212	−	4.35108i	−0.0313736	−	0.177929i
$599$	30.0687	+	10.9441i	1.22857	+	0.447164i	0.873108	−	0.487526i	$-0.162101\pi$
$599$	30.0687	+	10.9441i	1.22857	+	0.447164i	0.355464	+	0.934690i	$0.384323\pi$
$600$	1.10444	−	18.1535i	0.0450888	−	0.741114i
$601$	23.5574	−	8.57420i	0.960928	−	0.349749i	0.186531	−	0.982449i	$-0.440276\pi$
$601$	23.5574	−	8.57420i	0.960928	−	0.349749i	0.774397	+	0.632700i	$0.218053\pi$
$602$	−9.19591	+	6.65551i	−0.374797	+	0.271258i
$603$	−24.9194	+	33.1136i	−1.01480	+	1.34849i
$604$	−20.5361			−0.835604
$605$	−5.66362	+	32.1200i	−0.230259	+	1.30586i
$606$	5.11400	+	17.2442i	0.207742	+	0.700497i
$607$	−8.92003	−	3.24663i	−0.362053	−	0.131776i	0.154587	−	0.987979i	$-0.450595\pi$
$607$	−8.92003	−	3.24663i	−0.362053	−	0.131776i	−0.516640	+	0.856203i	$0.672817\pi$
$608$	0.693410	+	3.93252i	0.0281215	+	0.159485i
$609$	−9.44762	+	3.89664i	−0.382837	+	0.157900i
$610$	−2.29788	−	1.92815i	−0.0930384	−	0.0780685i
$611$	−13.5019			−0.546227
$612$	−17.8760	−	2.18320i	−0.722594	−	0.0882506i
$613$	−4.39195			−0.177389			−0.0886945	−	0.996059i	$-0.528269\pi$
$613$	−4.39195			−0.177389			−0.0886945	+	0.996059i	$0.528269\pi$
$614$	−3.45718	+	19.6067i	−0.139521	+	0.791260i
$615$	−24.5716	+	12.2608i	−0.990821	+	0.494404i
$616$	1.06254	−	4.22861i	0.0428111	−	0.170376i
$617$	6.80897	+	2.47826i	0.274119	+	0.0997710i	0.475422	−	0.879758i	$-0.342295\pi$
$617$	6.80897	+	2.47826i	0.274119	+	0.0997710i	−0.201303	+	0.979529i	$0.564518\pi$
$618$	−10.1395	+	23.3399i	−0.407871	+	0.938867i
$619$	−4.08391	+	1.48642i	−0.164146	+	0.0597443i	−0.422786	−	0.906229i	$-0.638948\pi$
$619$	−4.08391	+	1.48642i	−0.164146	+	0.0597443i	0.258640	+	0.965974i	$0.416726\pi$
$620$	1.98023	+	3.42986i	0.0795280	+	0.137746i
$621$	7.80129	−	13.2733i	0.313055	−	0.532639i
$622$	−13.4494			−0.539270
$623$	9.90701	−	14.6299i	0.396916	−	0.586133i
$624$	1.53693	+	2.07564i	0.0615263	+	0.0830920i
$625$	25.0918	−	21.0545i	1.00367	−	0.842181i
$626$	−9.21049	−	3.35234i	−0.368125	−	0.133987i
$627$	−10.1987	+	5.08900i	−0.407298	+	0.203235i
$628$	1.22564	−	6.95097i	0.0489085	−	0.277374i
$629$	−34.6738	+	60.0569i	−1.38254	+	2.39462i
$630$	30.8704	−	4.85182i	1.22990	−	0.193301i
$631$	6.75224	+	11.6952i	0.268802	+	0.465579i	0.968553	−	0.248808i	$-0.0800388\pi$
$631$	6.75224	+	11.6952i	0.268802	+	0.465579i	−0.699750	+	0.714387i	$0.746705\pi$
$632$	12.9389	−	4.70937i	0.514681	−	0.187329i
$633$	12.1102	−	12.7697i	0.481336	−	0.507550i
$634$	−24.8425	+	20.8454i	−0.986623	+	0.827875i
$635$	35.5326	+	12.9328i	1.41007	+	0.513223i
$636$	13.5490	−	14.2869i	0.537252	−	0.566511i
$637$	9.19812	+	4.93404i	0.364443	+	0.195494i
$638$	−1.83756	−	3.18274i	−0.0727496	−	0.126006i
$639$	0.666867	+	0.714204i	0.0263809	+	0.0282535i
$640$	3.93704			0.155625
$641$	33.1873	+	27.8475i	1.31082	+	1.09991i	0.988165	+	0.153393i	$0.0490199\pi$
$641$	33.1873	+	27.8475i	1.31082	+	1.09991i	0.322655	+	0.946517i	$0.395425\pi$
$642$	21.0847	−	10.5209i	0.832146	−	0.415228i
$643$	−22.2887	+	18.7024i	−0.878979	+	0.737551i	−0.965969	−	0.258659i	$-0.916720\pi$
$643$	−22.2887	+	18.7024i	−0.878979	+	0.737551i	0.0869902	+	0.996209i	$0.472275\pi$
$644$	1.91043	−	7.60297i	0.0752816	−	0.299599i
$645$	11.6579	−	26.8349i	0.459028	−	1.05662i
$646$	18.3627	+	15.4082i	0.722472	+	0.606226i
$647$	−19.7654	−	34.2347i	−0.777058	−	1.34590i	−0.933630	−	0.358238i	$-0.883378\pi$
$647$	−19.7654	−	34.2347i	−0.777058	−	1.34590i	0.156572	−	0.987667i	$-0.449956\pi$
$648$	−0.616235	+	8.97888i	−0.0242080	+	0.352724i
$649$	1.58770	−	2.74997i	0.0623225	−	0.107946i
$650$	−2.71887	+	15.4195i	−0.106643	+	0.604802i
$651$	−3.40342	+	3.10922i	−0.133391	+	0.121860i
$652$	−1.63081	−	0.593565i	−0.0638674	−	0.0232458i
$653$	−4.14180	−	23.4893i	−0.162081	−	0.919208i	−0.952023	−	0.306026i	$-0.901000\pi$
$653$	−4.14180	−	23.4893i	−0.162081	−	0.919208i	0.789942	−	0.613182i	$-0.210111\pi$
$654$	1.00683	−	16.5490i	0.0393702	−	0.647119i
$655$	−39.7200	−	33.3291i	−1.55199	−	1.30227i
$656$	−2.01349	−	3.48747i	−0.0786137	−	0.136163i
$657$	1.00237	−	0.232097i	0.0391063	−	0.00905495i
$658$	−21.8676	−	9.78414i	−0.852490	−	0.381425i
$659$	2.79688	+	2.34686i	0.108951	+	0.0914208i	0.695636	−	0.718395i	$-0.255123\pi$
$659$	2.79688	+	2.34686i	0.108951	+	0.0914208i	−0.586685	+	0.809815i	$0.699567\pi$
$660$	3.19513	+	10.7738i	0.124370	+	0.419371i
$661$	−28.1784	+	23.6445i	−1.09601	+	0.919665i	−0.997151	−	0.0754361i	$-0.975965\pi$
$661$	−28.1784	+	23.6445i	−1.09601	+	0.919665i	−0.0988633	+	0.995101i	$0.531521\pi$
$662$	−7.69589	+	6.45762i	−0.299109	+	0.250983i
$663$	15.0767	+	3.61445i	0.585529	+	0.140374i
$664$	−9.30923	−	7.81137i	−0.361268	−	0.303140i
$665$	−37.9677	−	16.9877i	−1.47232	−	0.658755i
$666$	30.8897	+	15.7140i	1.19695	+	0.608905i
$667$	−3.30389	−	5.72251i	−0.127927	−	0.221577i
$668$	−0.597809	−	0.501622i	−0.0231299	−	0.0194083i
$669$	10.1384	−	5.05890i	0.391973	−	0.195588i
$670$	−9.44422	−	53.5608i	−0.364862	−	2.06924i
$671$	1.17987	+	0.429436i	0.0455482	+	0.0165782i
$672$	0.985096	+	4.47544i	0.0380009	+	0.172644i
$673$	0.548582	−	3.11116i	0.0211463	−	0.119927i	−0.972407	−	0.233289i	$-0.925051\pi$
$673$	0.548582	−	3.11116i	0.0211463	−	0.119927i	0.993554	+	0.113363i	$0.0361622\pi$
$674$	10.9031	−	18.8848i	0.419973	−	0.727414i
$675$	−42.0672	+	34.7459i	−1.61917	+	1.33737i
$676$	5.38826	+	9.33275i	0.207241	+	0.358952i
$677$	13.1853	+	11.0638i	0.506753	+	0.425217i	0.859985	−	0.510319i	$-0.170473\pi$
$677$	13.1853	+	11.0638i	0.506753	+	0.425217i	−0.353232	+	0.935536i	$0.614917\pi$
$678$	3.17912	−	0.363253i	0.122093	−	0.0139507i
$679$	−3.41452	+	13.5888i	−0.131037	+	0.521491i
$680$	18.1046	−	15.1915i	0.694278	−	0.582568i
$681$	−1.37071	+	22.5300i	−0.0525256	+	0.863352i
$682$	−1.26991	−	1.06558i	−0.0486274	−	0.0408033i
$683$	40.9382			1.56646			0.783228	−	0.621735i	$-0.213572\pi$
$683$	40.9382			1.56646			0.783228	+	0.621735i	$0.213572\pi$
$684$	7.20331	−	9.57195i	0.275426	−	0.365993i
$685$	−38.4365	−	66.5739i	−1.46858	−	2.54366i
$686$	11.3218	+	14.6566i	0.432270	+	0.559592i
$687$	16.9638	+	4.06686i	0.647209	+	0.155161i
$688$	4.03178	+	1.46745i	0.153710	+	0.0559459i
$689$	−12.9853	+	10.8959i	−0.494699	+	0.415102i
$690$	5.74479	+	19.3712i	0.218700	+	0.737448i
$691$	26.2119	−	9.54036i	0.997149	−	0.362933i	0.208665	−	0.977987i	$-0.433088\pi$
$691$	26.2119	−	9.54036i	0.997149	−	0.362933i	0.788484	+	0.615055i	$0.210866\pi$
$692$	7.01348	+	12.1477i	0.266612	+	0.461786i
$693$	−11.4477	+	6.32782i	−0.434863	+	0.240374i
$694$	11.8500	−	20.5249i	0.449821	−	0.779113i
$695$	3.13605	−	17.7854i	0.118957	−	0.674640i
$696$	3.22171	+	2.13091i	0.122119	+	0.0807720i
$697$	−22.7159	−	8.26791i	−0.860426	−	0.313169i
$698$	4.25718	−	3.57220i	0.161137	−	0.135210i
$699$	3.28298	−	0.375120i	0.124174	−	0.0141883i
$700$	−15.5772	+	23.0032i	−0.588764	+	0.869438i
$701$	−3.10143			−0.117139			−0.0585697	−	0.998283i	$-0.518654\pi$
$701$	−3.10143			−0.117139			−0.0585697	+	0.998283i	$0.518654\pi$
$702$	1.40462	−	7.61976i	0.0530140	−	0.287589i
$703$	−23.0652	−	39.9502i	−0.869922	−	1.50675i
$704$	−1.54857	+	0.563632i	−0.0583638	+	0.0212427i
$705$	61.3468	−	7.00961i	2.31045	−	0.263997i
$706$	3.36025	+	1.22303i	0.126465	+	0.0460293i
$707$	6.69559	−	26.6465i	0.251814	−	1.00215i
$708$	−0.202673	+	3.33128i	−0.00761690	+	0.125197i
$709$	−5.76735	+	32.7082i	−0.216597	+	1.22838i	0.661516	+	0.749931i	$0.269913\pi$
$709$	−5.76735	+	32.7082i	−0.216597	+	1.22838i	−0.878113	+	0.478453i	$0.841198\pi$
$710$	−1.28235			−0.0481256
$711$	−36.8176	−	18.7296i	−1.38077	−	0.702416i
$712$	−6.67813			−0.250273
$713$	−2.28328	−	1.91590i	−0.0855094	−	0.0717509i
$714$	21.7990	+	16.7793i	0.815806	+	0.627949i
$715$	−1.67997	−	9.52756i	−0.0628272	−	0.356311i
$716$	−22.4425	−	8.16840i	−0.838715	−	0.305267i
$717$	−12.2602	−	2.93925i	−0.457867	−	0.109768i
$718$	1.83647	−	10.4151i	0.0685363	−	0.388689i
$719$	−1.66693			−0.0621659			−0.0310829	−	0.999517i	$-0.509896\pi$
$719$	−1.66693			−0.0621659			−0.0310829	+	0.999517i	$0.509896\pi$
$720$	−8.06074	−	8.63292i	−0.300406	−	0.321730i
$721$	31.4893	−	22.7903i	1.17272	−	0.848754i
$722$	2.87025	−	1.04468i	0.106819	−	0.0388791i
$723$	17.9726	−	8.96803i	0.668407	−	0.333525i
$724$	−23.8085	−	8.66559i	−0.884837	−	0.322054i
$725$	4.06630	+	23.0611i	0.151019	+	0.856468i
$726$	8.53869	+	11.5316i	0.316900	+	0.427978i
$727$	3.81640	−	21.6439i	0.141543	−	0.802728i	−0.828536	−	0.559936i	$-0.810826\pi$
$727$	3.81640	−	21.6439i	0.141543	−	0.802728i	0.970078	−	0.242792i	$-0.0780632\pi$
$728$	−0.405194	−	3.92430i	−0.0150175	−	0.145444i
$729$	20.9500	−	17.0322i	0.775928	−	0.630822i
$730$	−0.675133	+	1.16936i	−0.0249878	+	0.0432801i
$731$	24.2025	−	8.80899i	0.895162	−	0.325812i
$732$	−1.31113	+	0.149813i	−0.0484609	+	0.00553724i
$733$	−36.2119	+	30.3854i	−1.33752	+	1.12231i	−0.355262	+	0.934767i	$0.615608\pi$
$733$	−36.2119	+	30.3854i	−1.33752	+	1.12231i	−0.982256	+	0.187544i	$0.939947\pi$
$734$	7.35091	−	6.16815i	0.271327	−	0.227671i
$735$	−44.3540	−	17.6429i	−1.63602	−	0.650769i
$736$	−2.78429	+	1.01340i	−0.102630	+	0.0373544i
$737$	11.3826	+	19.7152i	0.419282	+	0.726217i
$738$	−3.52469	+	11.5554i	−0.129745	+	0.425359i
$739$	−13.2412	+	22.9344i	−0.487084	+	0.843654i	−0.999890	−	0.0148505i	$-0.995273\pi$
$739$	−13.2412	+	22.9344i	−0.487084	+	0.843654i	0.512806	+	0.858505i	$0.328606\pi$
$740$	−42.7390	+	15.5557i	−1.57112	+	0.571840i
$741$	−7.09677	+	7.48327i	−0.260706	+	0.274905i
$742$	−28.9267	+	8.23728i	−1.06193	+	0.302400i
$743$	−0.664390	−	3.76794i	−0.0243741	−	0.138232i	0.970192	−	0.242336i	$-0.0779137\pi$
$743$	−0.664390	−	3.76794i	−0.0243741	−	0.138232i	−0.994566	+	0.104104i	$0.966803\pi$
$744$	1.69434	+	0.406198i	0.0621176	+	0.0148919i
$745$	5.17194	−	29.3315i	0.189485	−	1.07462i
$746$	15.0753	−	26.1112i	0.551945	−	0.955998i
$747$	1.93148	+	36.4058i	0.0706691	+	1.33202i
$748$	−4.94627	+	8.56719i	−0.180853	+	0.313247i
$749$	−35.9020	−	2.57661i	−1.31183	−	0.0941472i
$750$	2.27771	−	37.4383i	0.0831704	−	1.36705i
$751$	−3.12695	−	17.7338i	−0.114104	−	0.647117i	−0.987190	−	0.159550i	$-0.948996\pi$
$751$	−3.12695	−	17.7338i	−0.114104	−	0.647117i	0.873086	−	0.487567i	$-0.162115\pi$
$752$	1.57235	+	8.91722i	0.0573376	+	0.325177i
$753$	9.13258	−	21.0220i	0.332810	−	0.766085i
$754$	−2.54740	−	2.13752i	−0.0927707	−	0.0778439i
$755$	−80.8517			−2.94249
$756$	7.79660	−	11.3231i	0.283559	−	0.411818i
$757$	7.06319			0.256716			0.128358	−	0.991728i	$-0.459029\pi$
$757$	7.06319			0.256716			0.128358	+	0.991728i	$0.459029\pi$
$758$	−3.04927	−	2.55864i	−0.110755	−	0.0929341i
$759$	−5.03281	−	6.79687i	−0.182679	−	0.246711i
$760$	2.72998	+	15.4825i	0.0990270	+	0.561610i
$761$	2.97048	+	16.8465i	0.107680	+	0.610684i	0.990116	+	0.140251i	$0.0447910\pi$
$761$	2.97048	+	16.8465i	0.107680	+	0.610684i	−0.882436	+	0.470433i	$0.844098\pi$
$762$	14.8851	−	7.42745i	0.539232	−	0.269068i
$763$	−14.2005	+	20.9701i	−0.514091	+	0.759168i
$764$	−12.2412	+	21.2024i	−0.442872	+	0.767076i
$765$	−70.3785	−	8.59535i	−2.54454	−	0.310766i
$766$	−1.73073	+	2.99771i	−0.0625337	+	0.108312i
$767$	0.498930	−	2.82957i	0.0180153	−	0.102170i
$768$	1.19186	−	1.25677i	0.0430075	−	0.0453498i
$769$	−4.29109	−	24.3360i	−0.154741	−

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)

\(f(q)\)	\(=\)	\(q+(0.766044 + 0.642788i) q^{2} +(1.72085 - 0.196628i) q^{3} +(0.173648 + 0.984808i) q^{4} +(0.683660 + 3.87723i) q^{5} +(1.44464 + 0.955517i) q^{6} +(-1.15546 - 2.38011i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(2.92267 - 0.676737i) q^{9} +O(q^{10})\)	\(q+(0.766044 + 0.642788i) q^{2} +(1.72085 - 0.196628i) q^{3} +(0.173648 + 0.984808i) q^{4} +(0.683660 + 3.87723i) q^{5} +(1.44464 + 0.955517i) q^{6} +(-1.15546 - 2.38011i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(2.92267 - 0.676737i) q^{9} +(-1.96852 + 3.40958i) q^{10} +(0.286164 - 1.62291i) q^{11} +(0.492464 + 1.66057i) q^{12} +(-0.258932 - 1.46848i) q^{13} +(0.644767 - 2.56598i) q^{14} +(1.93885 + 6.53772i) q^{15} +(-0.939693 + 0.342020i) q^{16} +(-3.00147 + 5.19869i) q^{17} +(2.67390 + 1.36025i) q^{18} +(-1.99659 - 3.45820i) q^{19} +(-3.69961 + 1.34655i) q^{20} +(-2.45638 - 3.86862i) q^{21} +(1.26240 - 1.05928i) q^{22} +(2.26978 - 1.90457i) q^{23} +(-0.690142 + 1.58862i) q^{24} +(-9.86707 + 3.59132i) q^{25} +(0.745566 - 1.29136i) q^{26} +(4.89643 - 1.73925i) q^{27} +(2.14330 - 1.55121i) q^{28} +(0.387255 - 2.19623i) q^{29} +(-2.71712 + 6.25446i) q^{30} +(-0.174681 - 0.990665i) q^{31} +(-0.939693 - 0.342020i) q^{32} +(0.173335 - 2.84907i) q^{33} +(-5.64091 + 2.05312i) q^{34} +(8.43828 - 6.10718i) q^{35} +(1.17397 + 2.76076i) q^{36} +11.5523 q^{37} +(0.693410 - 3.93252i) q^{38} +(-0.734329 - 2.47612i) q^{39} +(-3.69961 - 1.34655i) q^{40} +(0.699279 + 3.96581i) q^{41} +(0.605004 - 4.54246i) q^{42} +(-3.28674 - 2.75790i) q^{43} +1.64795 q^{44} +(4.62198 + 10.8692i) q^{45} +2.96298 q^{46} +(1.57235 - 8.91722i) q^{47} +(-1.54982 + 0.773337i) q^{48} +(-4.32981 + 5.50025i) q^{49} +(-9.86707 - 3.59132i) q^{50} +(-4.14288 + 9.53636i) q^{51} +(1.40121 - 0.509997i) q^{52} +(-5.68396 - 9.84491i) q^{53} +(4.86885 + 1.81502i) q^{54} +6.48805 q^{55} +(2.63896 + 0.189393i) q^{56} +(-4.11583 - 5.55847i) q^{57} +(1.70836 - 1.43349i) q^{58} +(1.81067 + 0.659030i) q^{59} +(-6.10172 + 3.04466i) q^{60} +(-0.132304 + 0.750333i) q^{61} +(0.502974 - 0.871176i) q^{62} +(-4.98775 - 6.17433i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(5.51661 - 2.00788i) q^{65} +(1.96413 - 2.07109i) q^{66} +(-10.5823 + 8.87960i) q^{67} +(-5.64091 - 2.05312i) q^{68} +(3.53146 - 3.72379i) q^{69} +(10.3897 + 0.745647i) q^{70} +(0.162856 + 0.282076i) q^{71} +(-0.875266 + 2.86948i) q^{72} +0.342964 q^{73} +(8.84957 + 7.42567i) q^{74} +(-16.2736 + 8.12028i) q^{75} +(3.05896 - 2.56677i) q^{76} +(-4.19336 + 1.19412i) q^{77} +(1.02909 - 2.36884i) q^{78} +(-10.5479 - 8.85072i) q^{79} +(-1.96852 - 3.40958i) q^{80} +(8.08405 - 3.95576i) q^{81} +(-2.01349 + 3.48747i) q^{82} +(-2.11023 + 11.9677i) q^{83} +(3.38330 - 3.09084i) q^{84} +(-22.2085 - 8.08324i) q^{85} +(-0.745043 - 4.22535i) q^{86} +(0.234568 - 3.85554i) q^{87} +(1.26240 + 1.05928i) q^{88} +(3.33906 + 5.78343i) q^{89} +(-3.44596 + 11.2973i) q^{90} +(-3.19595 + 2.31306i) q^{91} +(2.26978 + 1.90457i) q^{92} +(-0.495393 - 1.67044i) q^{93} +(6.93636 - 5.82030i) q^{94} +(12.0433 - 10.1055i) q^{95} +(-1.68432 - 0.403796i) q^{96} +(-4.05678 - 3.40404i) q^{97} +(-6.85232 + 1.43029i) q^{98} +(-0.261923 - 4.93691i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 3 q^{6} + 6 q^{7} - 36 q^{8} + 24 q^{9}+O(q^{10}) \) 72 * q + 3 * q^6 + 6 * q^7 - 36 * q^8 + 24 * q^9	\( 72 q + 3 q^{6} + 6 q^{7} - 36 q^{8} + 24 q^{9} - 6 q^{10} + 12 q^{11} - 12 q^{13} - 3 q^{14} - 6 q^{15} - 12 q^{17} - 18 q^{19} - 30 q^{21} - 6 q^{22} + 30 q^{23} + 6 q^{25} - 18 q^{26} - 6 q^{27} + 3 q^{29} + 3 q^{30} + 9 q^{31} - 18 q^{33} + 9 q^{34} - 18 q^{35} + 9 q^{36} - 24 q^{39} - 6 q^{41} + 12 q^{42} + 24 q^{43} + 51 q^{45} + 45 q^{47} - 6 q^{48} - 12 q^{49} + 6 q^{50} - 51 q^{51} + 6 q^{52} - 15 q^{53} + 27 q^{54} + 72 q^{55} - 3 q^{56} - 63 q^{57} + 3 q^{58} - 30 q^{59} - 3 q^{60} + 9 q^{61} - 24 q^{62} - 39 q^{63} - 36 q^{64} + 9 q^{65} - 6 q^{67} + 9 q^{68} - 21 q^{69} - 33 q^{70} + 12 q^{71} - 12 q^{72} + 132 q^{73} - 18 q^{74} - 30 q^{75} - 33 q^{77} + 30 q^{78} - 9 q^{79} - 6 q^{80} + 36 q^{81} - 33 q^{82} - 18 q^{83} + 15 q^{84} + 21 q^{85} - 12 q^{86} - 39 q^{87} - 6 q^{88} - 36 q^{89} + 69 q^{90} + 39 q^{91} + 30 q^{92} - 66 q^{93} - 9 q^{94} - 33 q^{95} - 48 q^{97} - 12 q^{98} - 54 q^{99}+O(q^{100}) \) 72 * q + 3 * q^6 + 6 * q^7 - 36 * q^8 + 24 * q^9 - 6 * q^10 + 12 * q^11 - 12 * q^13 - 3 * q^14 - 6 * q^15 - 12 * q^17 - 18 * q^19 - 30 * q^21 - 6 * q^22 + 30 * q^23 + 6 * q^25 - 18 * q^26 - 6 * q^27 + 3 * q^29 + 3 * q^30 + 9 * q^31 - 18 * q^33 + 9 * q^34 - 18 * q^35 + 9 * q^36 - 24 * q^39 - 6 * q^41 + 12 * q^42 + 24 * q^43 + 51 * q^45 + 45 * q^47 - 6 * q^48 - 12 * q^49 + 6 * q^50 - 51 * q^51 + 6 * q^52 - 15 * q^53 + 27 * q^54 + 72 * q^55 - 3 * q^56 - 63 * q^57 + 3 * q^58 - 30 * q^59 - 3 * q^60 + 9 * q^61 - 24 * q^62 - 39 * q^63 - 36 * q^64 + 9 * q^65 - 6 * q^67 + 9 * q^68 - 21 * q^69 - 33 * q^70 + 12 * q^71 - 12 * q^72 + 132 * q^73 - 18 * q^74 - 30 * q^75 - 33 * q^77 + 30 * q^78 - 9 * q^79 - 6 * q^80 + 36 * q^81 - 33 * q^82 - 18 * q^83 + 15 * q^84 + 21 * q^85 - 12 * q^86 - 39 * q^87 - 6 * q^88 - 36 * q^89 + 69 * q^90 + 39 * q^91 + 30 * q^92 - 66 * q^93 - 9 * q^94 - 33 * q^95 - 48 * q^97 - 12 * q^98 - 54 * q^99

Introduction

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