LMFDB - Embedded newform 378.2.u.a.169.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([4, 0]))

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

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

chi := DirichletCharacter("378.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.01834519640$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			169.1
Root			$0.939693 - 0.342020i$ of defining polynomial
Character	$\chi$	$=$	378.169
Dual form			378.2.u.a.85.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.939693 + 0.342020i) q^{2} +(0.592396 + 1.62760i) q^{3} +(0.766044 - 0.642788i) q^{4} +(0.152704 + 0.866025i) q^{5} +(-1.11334 - 1.32683i) q^{6} +(0.766044 + 0.642788i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-2.29813 + 1.92836i) q^{9} +O(q^{10})$	\(q+(-0.939693 + 0.342020i) q^{2} +(0.592396 + 1.62760i) q^{3} +(0.766044 - 0.642788i) q^{4} +(0.152704 + 0.866025i) q^{5} +(-1.11334 - 1.32683i) q^{6} +(0.766044 + 0.642788i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-2.29813 + 1.92836i) q^{9} +(-0.439693 - 0.761570i) q^{10} +(-0.358441 + 2.03282i) q^{11} +(1.50000 + 0.866025i) q^{12} +(-0.326352 - 0.118782i) q^{13} +(-0.939693 - 0.342020i) q^{14} +(-1.31908 + 0.761570i) q^{15} +(0.173648 - 0.984808i) q^{16} +(1.70574 + 2.95442i) q^{17} +(1.50000 - 2.59808i) q^{18} +(1.02094 - 1.76833i) q^{19} +(0.673648 + 0.565258i) q^{20} +(-0.592396 + 1.62760i) q^{21} +(-0.358441 - 2.03282i) q^{22} +(-4.36231 + 3.66041i) q^{23} +(-1.70574 - 0.300767i) q^{24} +(3.97178 - 1.44561i) q^{25} +0.347296 q^{26} +(-4.50000 - 2.59808i) q^{27} +1.00000 q^{28} +(-1.78699 + 0.650411i) q^{29} +(0.979055 - 1.16679i) q^{30} +(-2.03209 + 1.70513i) q^{31} +(0.173648 + 0.984808i) q^{32} +(-3.52094 + 0.620838i) q^{33} +(-2.61334 - 2.19285i) q^{34} +(-0.439693 + 0.761570i) q^{35} +(-0.520945 + 2.95442i) q^{36} +(-0.226682 - 0.392624i) q^{37} +(-0.354570 + 2.01087i) q^{38} -0.601535i q^{39} +(-0.826352 - 0.300767i) q^{40} +(-5.06418 - 1.84321i) q^{41} -1.73205i q^{42} +(-0.336152 + 1.90641i) q^{43} +(1.03209 + 1.78763i) q^{44} +(-2.02094 - 1.69577i) q^{45} +(2.84730 - 4.93166i) q^{46} +(2.04916 + 1.71945i) q^{47} +(1.70574 - 0.300767i) q^{48} +(0.173648 + 0.984808i) q^{49} +(-3.23783 + 2.71686i) q^{50} +(-3.79813 + 4.52644i) q^{51} +(-0.326352 + 0.118782i) q^{52} +10.0915 q^{53} +(5.11721 + 0.902302i) q^{54} -1.81521 q^{55} +(-0.939693 + 0.342020i) q^{56} +(3.48293 + 0.614134i) q^{57} +(1.45677 - 1.22237i) q^{58} +(0.177519 + 1.00676i) q^{59} +(-0.520945 + 1.43128i) q^{60} +(-2.62449 - 2.20220i) q^{61} +(1.32635 - 2.29731i) q^{62} -3.00000 q^{63} +(-0.500000 - 0.866025i) q^{64} +(0.0530334 - 0.300767i) q^{65} +(3.09627 - 1.78763i) q^{66} +(10.0706 + 3.66539i) q^{67} +(3.20574 + 1.16679i) q^{68} +(-8.54189 - 4.93166i) q^{69} +(0.152704 - 0.866025i) q^{70} +(2.87211 + 4.97464i) q^{71} +(-0.520945 - 2.95442i) q^{72} +(6.20961 - 10.7554i) q^{73} +(0.347296 + 0.291416i) q^{74} +(4.70574 + 5.60808i) q^{75} +(-0.354570 - 2.01087i) q^{76} +(-1.58125 + 1.32683i) q^{77} +(0.205737 + 0.565258i) q^{78} +(6.33750 - 2.30666i) q^{79} +0.879385 q^{80} +(1.56283 - 8.86327i) q^{81} +5.38919 q^{82} +(3.41147 - 1.24168i) q^{83} +(0.592396 + 1.62760i) q^{84} +(-2.29813 + 1.92836i) q^{85} +(-0.336152 - 1.90641i) q^{86} +(-2.11721 - 2.52319i) q^{87} +(-1.58125 - 1.32683i) q^{88} +(9.38326 - 16.2523i) q^{89} +(2.47906 + 0.902302i) q^{90} +(-0.173648 - 0.300767i) q^{91} +(-0.988856 + 5.60808i) q^{92} +(-3.97906 - 2.29731i) q^{93} +(-2.51367 - 0.914901i) q^{94} +(1.68732 + 0.614134i) q^{95} +(-1.50000 + 0.866025i) q^{96} +(-1.24376 + 7.05369i) q^{97} +(-0.500000 - 0.866025i) q^{98} +(-3.09627 - 5.36289i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{5} - 3 q^{8}+O(q^{10}) $ 6 * q + 3 * q^5 - 3 * q^8	$ 6 q + 3 q^{5} - 3 q^{8} + 3 q^{10} + 6 q^{11} + 9 q^{12} - 3 q^{13} + 9 q^{15} + 9 q^{18} + 3 q^{19} + 3 q^{20} + 6 q^{22} + 6 q^{23} + 9 q^{25} - 27 q^{27} + 6 q^{28} - 3 q^{29} + 9 q^{30} - 3 q^{31} - 18 q^{33} - 9 q^{34} + 3 q^{35} + 12 q^{37} - 18 q^{38} - 6 q^{40} - 12 q^{41} - 6 q^{43} - 3 q^{44} - 9 q^{45} + 15 q^{46} + 24 q^{47} - 9 q^{51} - 3 q^{52} - 18 q^{55} + 24 q^{58} - 24 q^{59} - 3 q^{61} + 9 q^{62} - 18 q^{63} - 3 q^{64} - 12 q^{65} - 9 q^{66} + 3 q^{67} + 9 q^{68} - 45 q^{69} + 3 q^{70} - 12 q^{71} + 3 q^{73} + 18 q^{75} - 18 q^{76} - 12 q^{77} - 9 q^{78} + 33 q^{79} - 6 q^{80} + 24 q^{82} - 6 q^{86} + 18 q^{87} - 12 q^{88} + 21 q^{89} + 18 q^{90} - 12 q^{92} - 27 q^{93} + 6 q^{94} - 12 q^{95} - 9 q^{96} - 15 q^{97} - 3 q^{98} + 9 q^{99}+O(q^{100}) $ 6 * q + 3 * q^5 - 3 * q^8 + 3 * q^10 + 6 * q^11 + 9 * q^12 - 3 * q^13 + 9 * q^15 + 9 * q^18 + 3 * q^19 + 3 * q^20 + 6 * q^22 + 6 * q^23 + 9 * q^25 - 27 * q^27 + 6 * q^28 - 3 * q^29 + 9 * q^30 - 3 * q^31 - 18 * q^33 - 9 * q^34 + 3 * q^35 + 12 * q^37 - 18 * q^38 - 6 * q^40 - 12 * q^41 - 6 * q^43 - 3 * q^44 - 9 * q^45 + 15 * q^46 + 24 * q^47 - 9 * q^51 - 3 * q^52 - 18 * q^55 + 24 * q^58 - 24 * q^59 - 3 * q^61 + 9 * q^62 - 18 * q^63 - 3 * q^64 - 12 * q^65 - 9 * q^66 + 3 * q^67 + 9 * q^68 - 45 * q^69 + 3 * q^70 - 12 * q^71 + 3 * q^73 + 18 * q^75 - 18 * q^76 - 12 * q^77 - 9 * q^78 + 33 * q^79 - 6 * q^80 + 24 * q^82 - 6 * q^86 + 18 * q^87 - 12 * q^88 + 21 * q^89 + 18 * q^90 - 12 * q^92 - 27 * q^93 + 6 * q^94 - 12 * q^95 - 9 * q^96 - 15 * q^97 - 3 * q^98 + 9 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−0.939693	+	0.342020i	−0.664463	+	0.241845i
$2$	−0.939693	+	0.342020i	−0.664463	+	0.241845i
$3$	0.592396	+	1.62760i	0.342020	+	0.939693i
$3$	0.592396	+	1.62760i	0.342020	+	0.939693i
$4$	0.766044	−	0.642788i	0.383022	−	0.321394i
$5$	0.152704	+	0.866025i	0.0682911	+	0.387298i	0.999726	+	0.0233912i	$0.00744633\pi$
$5$	0.152704	+	0.866025i	0.0682911	+	0.387298i	−0.931435	+	0.363907i	$0.881443\pi$
$6$	−1.11334	−	1.32683i	−0.454519	−	0.541675i
$7$	0.766044	+	0.642788i	0.289538	+	0.242951i
$7$	0.766044	+	0.642788i	0.289538	+	0.242951i
$8$	−0.500000	+	0.866025i	−0.176777	+	0.306186i
$9$	−2.29813	+	1.92836i	−0.766044	+	0.642788i
$10$	−0.439693	−	0.761570i	−0.139043	−	0.240830i
$11$	−0.358441	+	2.03282i	−0.108074	+	0.612918i	0.881874	+	0.471485i	$0.156282\pi$
$11$	−0.358441	+	2.03282i	−0.108074	+	0.612918i	−0.989948	+	0.141433i	$0.954829\pi$
$12$	1.50000	+	0.866025i	0.433013	+	0.250000i
$13$	−0.326352	−	0.118782i	−0.0905137	−	0.0329443i	0.296366	−	0.955074i	$-0.404225\pi$
$13$	−0.326352	−	0.118782i	−0.0905137	−	0.0329443i	−0.386880	+	0.922130i	$0.626447\pi$
$14$	−0.939693	−	0.342020i	−0.251143	−	0.0914087i
$15$	−1.31908	+	0.761570i	−0.340584	+	0.196637i
$16$	0.173648	−	0.984808i	0.0434120	−	0.246202i
$17$	1.70574	+	2.95442i	0.413702	+	0.716553i	0.995291	−	0.0969297i	$-0.0309022\pi$
$17$	1.70574	+	2.95442i	0.413702	+	0.716553i	−0.581589	+	0.813483i	$0.697569\pi$
$18$	1.50000	−	2.59808i	0.353553	−	0.612372i
$19$	1.02094	−	1.76833i	0.234221	−	0.405682i	−0.724825	−	0.688933i	$-0.758079\pi$
$19$	1.02094	−	1.76833i	0.234221	−	0.405682i	0.959046	+	0.283251i	$0.0914128\pi$
$20$	0.673648	+	0.565258i	0.150632	+	0.126396i
$21$	−0.592396	+	1.62760i	−0.129271	+	0.355170i
$22$	−0.358441	−	2.03282i	−0.0764198	−	0.433398i
$23$	−4.36231	+	3.66041i	−0.909605	+	0.763249i	−0.972044	−	0.234800i	$-0.924557\pi$
$23$	−4.36231	+	3.66041i	−0.909605	+	0.763249i	0.0624390	+	0.998049i	$0.480112\pi$
$24$	−1.70574	−	0.300767i	−0.348182	−	0.0613939i
$25$	3.97178	−	1.44561i	0.794356	−	0.289122i
$26$	0.347296			0.0681104
$27$	−4.50000	−	2.59808i	−0.866025	−	0.500000i
$28$	1.00000			0.188982
$29$	−1.78699	+	0.650411i	−0.331836	+	0.120778i	−0.502564	−	0.864540i	$-0.667610\pi$
$29$	−1.78699	+	0.650411i	−0.331836	+	0.120778i	0.170729	+	0.985318i	$0.445388\pi$
$30$	0.979055	−	1.16679i	0.178750	−	0.213026i
$31$	−2.03209	+	1.70513i	−0.364974	+	0.306249i	−0.806770	−	0.590866i	$-0.798786\pi$
$31$	−2.03209	+	1.70513i	−0.364974	+	0.306249i	0.441796	+	0.897116i	$0.354342\pi$
$32$	0.173648	+	0.984808i	0.0306970	+	0.174091i
$33$	−3.52094	+	0.620838i	−0.612918	+	0.108074i
$34$	−2.61334	−	2.19285i	−0.448184	−	0.376071i
$35$	−0.439693	+	0.761570i	−0.0743216	+	0.128729i
$36$	−0.520945	+	2.95442i	−0.0868241	+	0.492404i
$37$	−0.226682	−	0.392624i	−0.0372662	−	0.0645470i	0.846791	−	0.531926i	$-0.178532\pi$
$37$	−0.226682	−	0.392624i	−0.0372662	−	0.0645470i	−0.884057	+	0.467379i	$0.845198\pi$
$38$	−0.354570	+	2.01087i	−0.0575189	+	0.326206i
$39$		−	0.601535i		−	0.0963227i
$40$	−0.826352	−	0.300767i	−0.130658	−	0.0475555i
$41$	−5.06418	−	1.84321i	−0.790892	−	0.287861i	−0.0851850	−	0.996365i	$-0.527148\pi$
$41$	−5.06418	−	1.84321i	−0.790892	−	0.287861i	−0.705707	+	0.708504i	$0.749370\pi$
$42$		−	1.73205i		−	0.267261i
$43$	−0.336152	+	1.90641i	−0.0512627	+	0.290725i	−0.999652	−	0.0263835i	$-0.991601\pi$
$43$	−0.336152	+	1.90641i	−0.0512627	+	0.290725i	0.948389	+	0.317109i	$0.102712\pi$
$44$	1.03209	+	1.78763i	0.155593	+	0.269495i
$45$	−2.02094	−	1.69577i	−0.301265	−	0.252791i
$46$	2.84730	−	4.93166i	0.419811	−	0.727134i
$47$	2.04916	+	1.71945i	0.298901	+	0.250808i	0.779887	−	0.625921i	$-0.215277\pi$
$47$	2.04916	+	1.71945i	0.298901	+	0.250808i	−0.480986	+	0.876728i	$0.659721\pi$
$48$	1.70574	−	0.300767i	0.246202	−	0.0434120i
$49$	0.173648	+	0.984808i	0.0248069	+	0.140687i
$50$	−3.23783	+	2.71686i	−0.457898	+	0.384222i
$51$	−3.79813	+	4.52644i	−0.531845	+	0.633828i
$52$	−0.326352	+	0.118782i	−0.0452569	+	0.0164721i
$53$	10.0915			1.38618			0.693088	−	0.720853i	$-0.256250\pi$
$53$	10.0915			1.38618			0.693088	+	0.720853i	$0.256250\pi$
$54$	5.11721	+	0.902302i	0.696364	+	0.122788i
$55$	−1.81521			−0.244763
$56$	−0.939693	+	0.342020i	−0.125572	+	0.0457044i
$57$	3.48293	+	0.614134i	0.461325	+	0.0813440i
$58$	1.45677	−	1.22237i	0.191283	−	0.160505i
$59$	0.177519	+	1.00676i	0.0231109	+	0.131069i	0.994180	−	0.107729i	$-0.0343579\pi$
$59$	0.177519	+	1.00676i	0.0231109	+	0.131069i	−0.971069	+	0.238798i	$0.923247\pi$
$60$	−0.520945	+	1.43128i	−0.0672537	+	0.184778i
$61$	−2.62449	−	2.20220i	−0.336031	−	0.281963i	0.459121	−	0.888374i	$-0.348164\pi$
$61$	−2.62449	−	2.20220i	−0.336031	−	0.281963i	−0.795152	+	0.606410i	$0.792609\pi$
$62$	1.32635	−	2.29731i	0.168447	−	0.291759i
$63$	−3.00000			−0.377964
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	0.0530334	−	0.300767i	0.00657799	−	0.0373056i
$66$	3.09627	−	1.78763i	0.381124	−	0.220042i
$67$	10.0706	+	3.66539i	1.23032	+	0.447799i	0.873706	−	0.486455i	$-0.161710\pi$
$67$	10.0706	+	3.66539i	1.23032	+	0.447799i	0.356611	+	0.934253i	$0.383932\pi$
$68$	3.20574	+	1.16679i	0.388753	+	0.141494i
$69$	−8.54189	−	4.93166i	−1.02832	−	0.593702i
$70$	0.152704	−	0.866025i	0.0182516	−	0.103510i
$71$	2.87211	+	4.97464i	0.340857	+	0.590381i	0.984592	−	0.174867i	$-0.0559495\pi$
$71$	2.87211	+	4.97464i	0.340857	+	0.590381i	−0.643735	+	0.765248i	$0.722616\pi$
$72$	−0.520945	−	2.95442i	−0.0613939	−	0.348182i
$73$	6.20961	−	10.7554i	0.726780	−	1.25882i	−0.231458	−	0.972845i	$-0.574350\pi$
$73$	6.20961	−	10.7554i	0.726780	−	1.25882i	0.958237	−	0.285974i	$-0.0923172\pi$
$74$	0.347296	+	0.291416i	0.0403724	+	0.0338765i
$75$	4.70574	+	5.60808i	0.543372	+	0.647565i
$76$	−0.354570	−	2.01087i	−0.0406720	−	0.230662i
$77$	−1.58125	+	1.32683i	−0.180200	+	0.151206i
$78$	0.205737	+	0.565258i	0.0232951	+	0.0640029i
$79$	6.33750	−	2.30666i	0.713024	−	0.259520i	0.0400627	−	0.999197i	$-0.487244\pi$
$79$	6.33750	−	2.30666i	0.713024	−	0.259520i	0.672961	+	0.739678i	$0.265022\pi$
$80$	0.879385			0.0983183
$81$	1.56283	−	8.86327i	0.173648	−	0.984808i
$82$	5.38919			0.595136
$83$	3.41147	−	1.24168i	0.374458	−	0.136292i	−0.147934	−	0.988997i	$-0.547262\pi$
$83$	3.41147	−	1.24168i	0.374458	−	0.136292i	0.522392	+	0.852706i	$0.325040\pi$
$84$	0.592396	+	1.62760i	0.0646357	+	0.177585i
$85$	−2.29813	+	1.92836i	−0.249268	+	0.209160i
$86$	−0.336152	−	1.90641i	−0.0362482	−	0.205574i
$87$	−2.11721	−	2.52319i	−0.226989	−	0.270515i
$88$	−1.58125	−	1.32683i	−0.168562	−	0.141440i
$89$	9.38326	−	16.2523i	0.994623	−	1.72274i	0.407625	−	0.913149i	$-0.366357\pi$
$89$	9.38326	−	16.2523i	0.994623	−	1.72274i	0.586998	−	0.809588i	$-0.300310\pi$
$90$	2.47906	+	0.902302i	0.261315	+	0.0951110i
$91$	−0.173648	−	0.300767i	−0.0182033	−	0.0315290i
$92$	−0.988856	+	5.60808i	−0.103095	+	0.584683i
$93$	−3.97906	−	2.29731i	−0.412609	−	0.238220i
$94$	−2.51367	−	0.914901i	−0.259265	−	0.0943649i
$95$	1.68732	+	0.614134i	0.173115	+	0.0630088i
$96$	−1.50000	+	0.866025i	−0.153093	+	0.0883883i
$97$	−1.24376	+	7.05369i	−0.126284	+	0.716194i	0.854253	+	0.519858i	$0.174015\pi$
$97$	−1.24376	+	7.05369i	−0.126284	+	0.716194i	−0.980537	+	0.196335i	$0.937096\pi$
$98$	−0.500000	−	0.866025i	−0.0505076	−	0.0874818i
$99$	−3.09627	−	5.36289i	−0.311187	−	0.538991i
$100$	2.11334	−	3.66041i	0.211334	−	0.366041i
$101$	−1.91147	−	1.60392i	−0.190199	−	0.159596i	0.542716	−	0.839916i	$-0.317396\pi$
$101$	−1.91147	−	1.60392i	−0.190199	−	0.159596i	−0.732915	+	0.680321i	$0.761841\pi$
$102$	2.02094	−	5.55250i	0.200103	−	0.549779i
$103$	0.176174	+	0.999135i	0.0173590	+	0.0984477i	0.992256	−	0.124207i	$-0.0396388\pi$
$103$	0.176174	+	0.999135i	0.0173590	+	0.0984477i	−0.974897	+	0.222655i	$0.928528\pi$
$104$	0.266044	−	0.223238i	0.0260878	−	0.0218903i
$105$	−1.50000	−	0.264490i	−0.146385	−	0.0258116i
$106$	−9.48293	+	3.45150i	−0.921063	+	0.335240i
$107$	11.3131			1.09368			0.546842	−	0.837236i	$-0.315830\pi$
$107$	11.3131			1.09368			0.546842	+	0.837236i	$0.315830\pi$
$108$	−5.11721	+	0.902302i	−0.492404	+	0.0868241i
$109$	12.7588			1.22207			0.611034	−	0.791604i	$-0.290754\pi$
$109$	12.7588			1.22207			0.611034	+	0.791604i	$0.290754\pi$
$110$	1.70574	−	0.620838i	0.162636	−	0.0591945i
$111$	0.504748	−	0.601535i	0.0479085	−	0.0570952i
$112$	0.766044	−	0.642788i	0.0723844	−	0.0607377i
$113$	−3.15910	−	17.9161i	−0.297183	−	1.68541i	−0.658194	−	0.752848i	$-0.728680\pi$
$113$	−3.15910	−	17.9161i	−0.297183	−	1.68541i	0.361011	−	0.932561i	$-0.382432\pi$
$114$	−3.48293	+	0.614134i	−0.326206	+	0.0575189i
$115$	−3.83615	−	3.21891i	−0.357723	−	0.300165i
$116$	−0.950837	+	1.64690i	−0.0882830	+	0.152911i
$117$	0.979055	−	0.356347i	0.0905137	−	0.0329443i
$118$	−0.511144	−	0.885328i	−0.0470547	−	0.0815010i
$119$	−0.592396	+	3.35965i	−0.0543049	+	0.307978i
$120$		−	1.52314i		−	0.139043i
$121$	6.33275	+	2.30493i	0.575704	+	0.209539i
$122$	3.21941	+	1.17177i	0.291471	+	0.106087i
$123$		−	9.33434i		−	0.841649i
$124$	−0.460637	+	2.61240i	−0.0413664	+	0.234601i
$125$	4.05690	+	7.02676i	0.362861	+	0.628493i
$126$	2.81908	−	1.02606i	0.251143	−	0.0914087i
$127$	6.14156	−	10.6375i	0.544975	−	0.943925i	−0.453633	−	0.891188i	$-0.649872\pi$
$127$	6.14156	−	10.6375i	0.544975	−	0.943925i	0.998608	−	0.0527364i	$-0.0167943\pi$
$128$	0.766044	+	0.642788i	0.0677094	+	0.0568149i
$129$	−3.30200	+	0.582232i	−0.290725	+	0.0512627i
$130$	0.0530334	+	0.300767i	0.00465134	+	0.0263791i
$131$	1.70574	−	1.43128i	0.149031	−	0.125052i	−0.565224	−	0.824938i	$-0.691210\pi$
$131$	1.70574	−	1.43128i	0.149031	−	0.125052i	0.714255	+	0.699886i	$0.246766\pi$
$132$	−2.29813	+	2.73881i	−0.200027	+	0.238383i
$133$	1.91875	−	0.698367i	0.166377	−	0.0605561i
$134$	−10.7169			−0.925798
$135$	1.56283	−	4.29385i	0.134507	−	0.369556i
$136$	−3.41147			−0.292531
$137$	6.01842	−	2.19053i	0.514188	−	0.187149i	−0.0718764	−	0.997414i	$-0.522899\pi$
$137$	6.01842	−	2.19053i	0.514188	−	0.187149i	0.586065	+	0.810264i	$0.300676\pi$
$138$	9.71348	+	1.71275i	0.826866	+	0.145799i
$139$	−16.7815	+	14.0814i	−1.42339	+	1.19437i	−0.473897	+	0.880580i	$0.657153\pi$
$139$	−16.7815	+	14.0814i	−1.42339	+	1.19437i	−0.949494	+	0.313786i	$0.898403\pi$
$140$	0.152704	+	0.866025i	0.0129058	+	0.0731925i
$141$	−1.58466	+	4.35381i	−0.133452	+	0.366657i
$142$	−4.40033	−	3.69232i	−0.369267	−	0.309852i
$143$	0.358441	−	0.620838i	0.0299743	−	0.0519170i
$144$	1.50000	+	2.59808i	0.125000	+	0.216506i
$145$	−0.836152	−	1.44826i	−0.0694386	−	0.120271i
$146$	−2.15657	+	12.2305i	−0.178479	+	1.01221i
$147$	−1.50000	+	0.866025i	−0.123718	+	0.0714286i
$148$	−0.426022	−	0.155059i	−0.0350188	−	0.0127458i
$149$	−20.7528	−	7.55342i	−1.70014	−	0.618800i	−0.704298	−	0.709905i	$-0.748738\pi$
$149$	−20.7528	−	7.55342i	−1.70014	−	0.618800i	−0.995841	+	0.0911048i	$0.970960\pi$
$150$	−6.34002	−	3.66041i	−0.517661	−	0.298872i
$151$	−3.12361	+	17.7149i	−0.254196	+	1.44161i	0.543933	+	0.839128i	$0.316934\pi$
$151$	−3.12361	+	17.7149i	−0.254196	+	1.44161i	−0.798129	+	0.602487i	$0.794177\pi$
$152$	1.02094	+	1.76833i	0.0828095	+	0.143430i
$153$	−9.61721	−	3.50038i	−0.777505	−	0.282989i
$154$	1.03209	−	1.78763i	0.0831681	−	0.144051i
$155$	−1.78699	−	1.49946i	−0.143534	−	0.120440i
$156$	−0.386659	−	0.460802i	−0.0309575	−	0.0368937i
$157$	3.40554	+	19.3138i	0.271792	+	1.54141i	0.748971	+	0.662603i	$0.230548\pi$
$157$	3.40554	+	19.3138i	0.271792	+	1.54141i	−0.477179	+	0.878806i	$0.658341\pi$
$158$	−5.16637	+	4.33510i	−0.411015	+	0.344882i
$159$	5.97818	+	16.4249i	0.474100	+	1.30258i
$160$	−0.826352	+	0.300767i	−0.0653288	+	0.0237778i
$161$	−5.69459			−0.448797
$162$	1.56283	+	8.86327i	0.122788	+	0.696364i
$163$	8.96585			0.702260			0.351130	−	0.936327i	$-0.385798\pi$
$163$	8.96585			0.702260			0.351130	+	0.936327i	$0.385798\pi$
$164$	−5.06418	+	1.84321i	−0.395446	+	0.143931i
$165$	−1.07532	−	2.95442i	−0.0837137	−	0.230002i
$166$	−2.78106	+	2.33359i	−0.215852	+	0.181121i
$167$	−0.273785	−	1.55271i	−0.0211861	−	0.120153i	0.972381	−	0.233401i	$-0.0749855\pi$
$167$	−0.273785	−	1.55271i	−0.0211861	−	0.120153i	−0.993567	+	0.113248i	$0.963874\pi$
$168$	−1.11334	−	1.32683i	−0.0858961	−	0.102367i
$169$	−9.86618	−	8.27871i	−0.758937	−	0.636824i
$170$	1.50000	−	2.59808i	0.115045	−	0.199263i
$171$	1.06371	+	6.03260i	0.0813440	+	0.461325i
$172$	0.967911	+	1.67647i	0.0738025	+	0.127830i
$173$	3.33363	−	18.9059i	0.253451	−	1.43739i	−0.546567	−	0.837415i	$-0.684066\pi$
$173$	3.33363	−	18.9059i	0.253451	−	1.43739i	0.800018	−	0.599976i	$-0.204823\pi$
$174$	2.85251	+	1.64690i	0.216248	+	0.124851i
$175$	3.97178	+	1.44561i	0.300238	+	0.109278i
$176$	1.93969	+	0.705990i	0.146210	+	0.0532160i
$177$	−1.53343	+	0.885328i	−0.115260	+	0.0665453i
$178$	−3.25877	+	18.4814i	−0.244255	+	1.38524i
$179$	8.03596	+	13.9187i	0.600636	+	1.04033i	0.992725	+	0.120404i	$0.0384191\pi$
$179$	8.03596	+	13.9187i	0.600636	+	1.04033i	−0.392089	+	0.919927i	$0.628248\pi$
$180$	−2.63816			−0.196637
$181$	−11.1630	+	19.3348i	−0.829737	+	1.43715i	0.0685074	+	0.997651i	$0.478176\pi$
$181$	−11.1630	+	19.3348i	−0.829737	+	1.43715i	−0.898244	+	0.439496i	$0.855157\pi$
$182$	0.266044	+	0.223238i	0.0197205	+	0.0165475i
$183$	2.02956	−	5.57618i	0.150030	−	0.412203i
$184$	−0.988856	−	5.60808i	−0.0728994	−	0.413433i
$185$	0.305407	−	0.256267i	0.0224540	−	0.0188411i
$186$	4.52481	+	0.797847i	0.331776	+	0.0585010i
$187$	−6.61721	+	2.40847i	−0.483898	+	0.176125i
$188$	2.67499			0.195094
$189$	−1.77719	−	4.88279i	−0.129271	−	0.355170i
$190$	−1.79561			−0.130267
$191$	−13.3157	+	4.84651i	−0.963488	+	0.350681i	−0.775400	−	0.631471i	$-0.782452\pi$
$191$	−13.3157	+	4.84651i	−0.963488	+	0.350681i	−0.188089	+	0.982152i	$0.560229\pi$
$192$	1.11334	−	1.32683i	0.0803485	−	0.0957556i
$193$	7.43242	−	6.23654i	0.534997	−	0.448916i	−0.334826	−	0.942280i	$-0.608677\pi$
$193$	7.43242	−	6.23654i	0.534997	−	0.448916i	0.869823	+	0.493364i	$0.164233\pi$
$194$	−1.24376	−	7.05369i	−0.0892965	−	0.506425i
$195$	0.520945	−	0.0918566i	0.0373056	−	0.00657799i
$196$	0.766044	+	0.642788i	0.0547175	+	0.0459134i
$197$	2.96198	−	5.13030i	0.211032	−	0.365519i	−0.741005	−	0.671499i	$-0.765651\pi$
$197$	2.96198	−	5.13030i	0.211032	−	0.365519i	0.952038	+	0.305980i	$0.0989841\pi$
$198$	4.74376	+	3.98048i	0.337124	+	0.282881i
$199$	−9.23308	−	15.9922i	−0.654516	−	1.13365i	−0.982015	−	0.188803i	$-0.939539\pi$
$199$	−9.23308	−	15.9922i	−0.654516	−	1.13365i	0.327499	−	0.944851i	$-0.393794\pi$
$200$	−0.733956	+	4.16247i	−0.0518985	+	0.294331i
$201$			18.5622i			1.30928i
$202$	2.34477	+	0.853427i	0.164977	+	0.0600469i
$203$	−1.78699	−	0.650411i	−0.125422	−	0.0456499i
$204$			5.90885i			0.413702i
$205$	0.822948	−	4.66717i	0.0574772	−	0.325969i
$206$	−0.507274	−	0.878624i	−0.0353435	−	0.0612167i
$207$	2.96657	−	16.8242i	0.206191	−	1.16937i
$208$	−0.173648	+	0.300767i	−0.0120403	+	0.0208545i
$209$	3.22874	+	2.70924i	0.223337	+	0.187402i
$210$	1.50000	−	0.264490i	0.103510	−	0.0182516i
$211$	3.21823	+	18.2515i	0.221552	+	1.25648i	0.869168	+	0.494516i	$0.164655\pi$
$211$	3.21823	+	18.2515i	0.221552	+	1.25648i	−0.647617	+	0.761966i	$0.724234\pi$
$212$	7.73055	−	6.48670i	0.530936	−	0.445509i
$213$	−6.39528	+	7.62159i	−0.438197	+	0.522223i
$214$	−10.6309	+	3.86932i	−0.726712	+	0.264502i
$215$	−1.70233			−0.116098
$216$	4.50000	−	2.59808i	0.306186	−	0.176777i
$217$	−2.65270			−0.180077
$218$	−11.9893	+	4.36376i	−0.812019	+	0.295551i
$219$	21.1839	+	3.73530i	1.43148	+	0.252408i
$220$	−1.39053	+	1.16679i	−0.0937495	+	0.0786652i
$221$	−0.205737	−	1.16679i	−0.0138394	−	0.0784870i
$222$	−0.268571	+	0.737892i	−0.0180253	+	0.0495241i
$223$	−8.05169	−	6.75617i	−0.539181	−	0.452427i	0.332077	−	0.943252i	$-0.392251\pi$
$223$	−8.05169	−	6.75617i	−0.539181	−	0.452427i	−0.871258	+	0.490826i	$0.836695\pi$
$224$	−0.500000	+	0.866025i	−0.0334077	+	0.0578638i
$225$	−6.34002	+	10.9812i	−0.422668	+	0.732083i
$226$	9.09627	+	15.7552i	0.605075	+	1.04802i
$227$	−2.22328	+	12.6088i	−0.147564	+	0.836878i	0.817708	+	0.575633i	$0.195244\pi$
$227$	−2.22328	+	12.6088i	−0.147564	+	0.836878i	−0.965272	+	0.261245i	$0.915867\pi$
$228$	3.06283	−	1.76833i	0.202841	−	0.117110i
$229$	−9.75624	−	3.55098i	−0.644711	−	0.234656i	−0.00108918	−	0.999999i	$-0.500347\pi$
$229$	−9.75624	−	3.55098i	−0.644711	−	0.234656i	−0.643622	+	0.765344i	$0.722569\pi$
$230$	4.70574	+	1.71275i	0.310287	+	0.112935i
$231$	−3.09627	−	1.78763i	−0.203719	−	0.117617i
$232$	0.330222	−	1.87278i	0.0216802	−	0.122954i
$233$	2.00134	+	3.46643i	0.131112	+	0.227093i	0.924106	−	0.382137i	$-0.124812\pi$
$233$	2.00134	+	3.46643i	0.131112	+	0.227093i	−0.792993	+	0.609230i	$0.791478\pi$
$234$	−0.798133	+	0.669713i	−0.0521756	+	0.0437805i
$235$	−1.17617	+	2.03719i	−0.0767252	+	0.132892i
$236$	0.783119	+	0.657115i	0.0509767	+	0.0427745i
$237$	7.50862	+	8.94842i	0.487737	+	0.581263i
$238$	−0.592396	−	3.35965i	−0.0383993	−	0.217774i
$239$	16.3537	−	13.7224i	1.05783	−	0.887627i	0.0639371	−	0.997954i	$-0.479634\pi$
$239$	16.3537	−	13.7224i	1.05783	−	0.887627i	0.993895	+	0.110327i	$0.0351898\pi$
$240$	0.520945	+	1.43128i	0.0336268	+	0.0923889i
$241$	5.34642	−	1.94594i	0.344393	−	0.125349i	−0.164032	−	0.986455i	$-0.552450\pi$
$241$	5.34642	−	1.94594i	0.344393	−	0.125349i	0.508425	+	0.861106i	$0.330228\pi$
$242$	−6.73917			−0.433210
$243$	15.3516	−	2.70691i	0.984808	−	0.173648i
$244$	−3.42602			−0.219329
$245$	−0.826352	+	0.300767i	−0.0527937	+	0.0192153i
$246$	3.19253	+	8.77141i	0.203548	+	0.559245i
$247$	−0.543233	+	0.455827i	−0.0345651	+	0.0290036i
$248$	−0.460637	−	2.61240i	−0.0292505	−	0.165888i
$249$	4.04189	+	4.81694i	0.256144	+	0.305261i
$250$	−6.21554	−	5.21546i	−0.393105	−	0.329854i
$251$	6.46451	−	11.1969i	0.408036	−	0.706739i	−0.586634	−	0.809853i	$-0.699547\pi$
$251$	6.46451	−	11.1969i	0.408036	−	0.706739i	0.994670	+	0.103113i	$0.0328804\pi$
$252$	−2.29813	+	1.92836i	−0.144769	+	0.121475i
$253$	−5.87733	−	10.1798i	−0.369504	−	0.640000i
$254$	−2.13294	+	12.0965i	−0.133833	+	0.759003i
$255$	−4.50000	−	2.59808i	−0.281801	−	0.162698i
$256$	−0.939693	−	0.342020i	−0.0587308	−	0.0213763i
$257$	−27.5107	−	10.0131i	−1.71607	−	0.624599i	−0.718585	−	0.695439i	$-0.755210\pi$
$257$	−27.5107	−	10.0131i	−1.71607	−	0.624599i	−0.997488	+	0.0708401i	$0.977432\pi$
$258$	2.90373	−	1.67647i	0.180779	−	0.104373i
$259$	0.0787257	−	0.446476i	0.00489178	−	0.0277426i
$260$	−0.152704	−	0.264490i	−0.00947028	−	0.0164030i
$261$	2.85251	−	4.94069i	0.176566	−	0.305821i
$262$	−1.11334	+	1.92836i	−0.0687824	+	0.119135i
$263$	−5.35117	−	4.49016i	−0.329967	−	0.276875i	0.462719	−	0.886505i	$-0.346874\pi$
$263$	−5.35117	−	4.49016i	−0.329967	−	0.276875i	−0.792686	+	0.609630i	$0.791318\pi$
$264$	1.22281	−	3.35965i	0.0752588	−	0.206772i
$265$	1.54101	+	8.73951i	0.0946636	+	0.536864i
$266$	−1.56418	+	1.31250i	−0.0959059	+	0.0804746i
$267$	32.0107	+	5.64436i	1.95903	+	0.345429i
$268$	10.0706	−	3.66539i	0.615158	−	0.223899i
$269$	−18.9786			−1.15715			−0.578574	−	0.815630i	$-0.696391\pi$
$269$	−18.9786			−1.15715			−0.578574	+	0.815630i	$0.696391\pi$
$270$			4.56942i			0.278086i
$271$	−28.8033			−1.74968			−0.874839	−	0.484413i	$-0.839033\pi$
$271$	−28.8033			−1.74968			−0.874839	+	0.484413i	$0.839033\pi$
$272$	3.20574	−	1.16679i	0.194376	−	0.0707472i
$273$	0.386659	−	0.460802i	0.0234017	−	0.0278890i
$274$	−4.90626	+	4.11684i	−0.296398	+	0.248707i
$275$	1.51501	+	8.59208i	0.0913588	+	0.518122i
$276$	−9.71348	+	1.71275i	−0.584683	+	0.103095i
$277$	−18.0326	−	15.1311i	−1.08347	−	0.909140i	−0.0872669	−	0.996185i	$-0.527813\pi$
$277$	−18.0326	−	15.1311i	−1.08347	−	0.909140i	−0.996204	+	0.0870446i	$0.972258\pi$
$278$	10.9534	−	18.9718i	0.656939	−	1.13785i
$279$	1.38191	−	7.83721i	0.0827329	−	0.469201i
$280$	−0.439693	−	0.761570i	−0.0262767	−	0.0455125i
$281$	3.93464	−	22.3145i	0.234721	−	1.33117i	−0.608480	−	0.793570i	$-0.708220\pi$
$281$	3.93464	−	22.3145i	0.234721	−	1.33117i	0.843201	−	0.537599i	$-0.180669\pi$
$282$		−	4.63322i		−	0.275904i
$283$	8.45811	+	3.07850i	0.502783	+	0.182998i	0.580945	−	0.813943i	$-0.302683\pi$
$283$	8.45811	+	3.07850i	0.502783	+	0.182998i	−0.0781626	+	0.996941i	$0.524905\pi$
$284$	5.39780	+	1.96464i	0.320301	+	0.116580i
$285$			3.11008i			0.184225i
$286$	−0.124485	+	0.705990i	−0.00736096	+	0.0417461i
$287$	−2.69459	−	4.66717i	−0.159057	−	0.275494i
$288$	−2.29813	−	1.92836i	−0.135419	−	0.113630i
$289$	2.68092	−	4.64349i	0.157701	−	0.273147i
$290$	1.28106	+	1.07494i	0.0752264	+	0.0631224i
$291$	−12.2173	+	2.15425i	−0.716194	+	0.126284i
$292$	−2.15657	−	12.2305i	−0.126204	−	0.715738i
$293$	6.99067	−	5.86587i	0.408399	−	0.342688i	−0.415330	−	0.909671i	$-0.636334\pi$
$293$	6.99067	−	5.86587i	0.408399	−	0.342688i	0.823729	+	0.566983i	$0.191890\pi$
$294$	1.11334	−	1.32683i	0.0649314	−	0.0773822i
$295$	−0.844770	+	0.307471i	−0.0491844	+	0.0179017i
$296$	0.453363			0.0263512
$297$	6.89440	−	8.21643i	0.400054	−	0.476765i
$298$	22.0847			1.27933
$299$	1.85844	−	0.676417i	0.107476	−	0.0391182i
$300$	7.20961	+	1.27125i	0.416247	+	0.0733956i
$301$	−1.48293	+	1.24432i	−0.0854744	+	0.0717216i
$302$	−3.12361	−	17.7149i	−0.179743	−	1.01938i
$303$	1.47818	−	4.06126i	0.0849191	−	0.233313i
$304$	−1.56418	−	1.31250i	−0.0897117	−	0.0752771i
$305$	1.50640	−	2.60916i	0.0862560	−	0.149400i
$306$	10.2344			0.585063
$307$	−5.69712	−	9.86770i	−0.325152	−	0.563179i	0.656391	−	0.754421i	$-0.272082\pi$
$307$	−5.69712	−	9.86770i	−0.325152	−	0.563179i	−0.981543	+	0.191241i	$0.938749\pi$
$308$	−0.358441	+	2.03282i	−0.0204241	+	0.115831i
$309$	−1.52182	+	0.878624i	−0.0865734	+	0.0499832i
$310$	2.19207	+	0.797847i	0.124501	+	0.0453147i
$311$	−2.13903	−	0.778544i	−0.121293	−	0.0441472i	0.280660	−	0.959807i	$-0.409447\pi$
$311$	−2.13903	−	0.778544i	−0.121293	−	0.0441472i	−0.401954	+	0.915660i	$0.631669\pi$
$312$	0.520945	+	0.300767i	0.0294927	+	0.0170276i
$313$	−0.253718	+	1.43891i	−0.0143410	+	0.0813318i	−0.991138	−	0.132834i	$-0.957592\pi$
$313$	−0.253718	+	1.43891i	−0.0143410	+	0.0813318i	0.976797	+	0.214166i	$0.0687033\pi$
$314$	−9.80587	−	16.9843i	−0.553377	−	0.958478i
$315$	−0.458111	−	2.59808i	−0.0258116	−	0.146385i
$316$	3.37211	−	5.84067i	0.189696	−	0.328563i
$317$	−0.320422	−	0.268866i	−0.0179967	−	0.0151010i	0.633745	−	0.773542i	$-0.281517\pi$
$317$	−0.320422	−	0.268866i	−0.0179967	−	0.0151010i	−0.651742	+	0.758441i	$0.725961\pi$
$318$	−11.2353	−	13.3897i	−0.630044	−	0.750858i
$319$	−0.681637	−	3.86576i	−0.0381644	−	0.216441i
$320$	0.673648	−	0.565258i	0.0376581	−	0.0315989i
$321$	6.70187	+	18.4132i	0.374062	+	1.02773i
$322$	5.35117	−	1.94767i	0.298209	−	0.108539i
$323$	6.96585			0.387590
$324$	−4.50000	−	7.79423i	−0.250000	−	0.433013i
$325$	−1.46791			−0.0814251
$326$	−8.42514	+	3.06650i	−0.466626	+	0.169838i
$327$	7.55825	+	20.7661i	0.417972	+	1.14837i
$328$	4.12836	−	3.46410i	0.227950	−	0.191273i
$329$	0.464508	+	2.63435i	0.0256091	+	0.145237i
$330$	2.02094	+	2.40847i	0.111249	+	0.132582i
$331$	8.74170	+	7.33515i	0.480487	+	0.403177i	0.850603	−	0.525809i	$-0.176237\pi$
$331$	8.74170	+	7.33515i	0.480487	+	0.403177i	−0.370115	+	0.928986i	$0.620682\pi$
$332$	1.81521	−	3.14403i	0.0996225	−	0.172551i
$333$	1.27807	+	0.465178i	0.0700376	+	0.0254916i
$334$	0.788333	+	1.36543i	0.0431357	+	0.0747132i
$335$	−1.63651	+	9.28109i	−0.0894119	+	0.507080i
$336$	1.50000	+	0.866025i	0.0818317	+	0.0472456i
$337$	23.4047	+	8.51860i	1.27493	+	0.464038i	0.888753	−	0.458386i	$-0.151572\pi$
$337$	23.4047	+	8.51860i	1.27493	+	0.464038i	0.386180	+	0.922423i	$0.373794\pi$
$338$	12.1027	+	4.40501i	0.658298	+	0.239601i
$339$	27.2888	−	15.7552i	1.48212	−	0.855705i
$340$	−0.520945	+	2.95442i	−0.0282522	+	0.160226i
$341$	−2.73783	−	4.74205i	−0.148262	−	0.256797i
$342$	−3.06283	−	5.30498i	−0.165619	−	0.286861i
$343$	−0.500000	+	0.866025i	−0.0269975	+	0.0467610i
$344$	−1.48293	−	1.24432i	−0.0799540	−	0.0670894i
$345$	2.96657	−	8.15058i	0.159715	−	0.438812i
$346$	3.33363	+	18.9059i	0.179217	+	1.01639i
$347$	−9.02481	+	7.57272i	−0.484477	+	0.406525i	−0.852042	−	0.523473i	$-0.824636\pi$
$347$	−9.02481	+	7.57272i	−0.484477	+	0.406525i	0.367565	+	0.929998i	$0.380192\pi$
$348$	−3.24376	−	0.571962i	−0.173884	−	0.0306604i
$349$	21.8332	−	7.94664i	1.16871	−	0.425374i	0.316506	−	0.948591i	$-0.397490\pi$
$349$	21.8332	−	7.94664i	1.16871	−	0.425374i	0.852200	+	0.523217i	$0.175268\pi$
$350$	−4.22668			−0.225926
$351$	1.15998	+	1.38241i	0.0619150	+	0.0737875i
$352$	−2.06418			−0.110021
$353$	−9.70486	+	3.53228i	−0.516538	+	0.188004i	−0.587117	−	0.809502i	$-0.699737\pi$
$353$	−9.70486	+	3.53228i	−0.516538	+	0.188004i	0.0705798	+	0.997506i	$0.477515\pi$
$354$	1.13816	−	1.35640i	0.0604923	−	0.0720919i
$355$	−3.86959	+	3.24697i	−0.205376	+	0.172331i
$356$	−3.25877	−	18.4814i	−0.172714	−	0.979513i
$357$	−5.81908	+	1.02606i	−0.307978	+	0.0543049i
$358$	−12.3118	−	10.3308i	−0.650699	−	0.546001i
$359$	−2.58512	+	4.47756i	−0.136438	+	0.236317i	−0.926146	−	0.377166i	$-0.876899\pi$
$359$	−2.58512	+	4.47756i	−0.136438	+	0.236317i	0.789708	+	0.613483i	$0.210232\pi$
$360$	2.47906	−	0.902302i	0.130658	−	0.0475555i
$361$	7.41534	+	12.8438i	0.390281	+	0.675987i
$362$	3.87686	−	21.9868i	0.203763	−	1.15560i
$363$			11.6726i			0.612652i
$364$	−0.326352	−	0.118782i	−0.0171055	−	0.00622589i
$365$	10.2626	+	3.73530i	0.537171	+	0.195514i
$366$			5.93404i			0.310177i
$367$	2.55216	−	14.4740i	0.133221	−	0.755536i	−0.842860	−	0.538133i	$-0.819130\pi$
$367$	2.55216	−	14.4740i	0.133221	−	0.755536i	0.976082	−	0.217404i	$-0.0697589\pi$
$368$	2.84730	+	4.93166i	0.148426	+	0.257081i
$369$	15.1925	−	5.52963i	0.790892	−	0.287861i
$370$	−0.199340	+	0.345268i	−0.0103632	+	0.0179496i
$371$	7.73055	+	6.48670i	0.401350	+	0.336773i
$372$	−4.52481	+	0.797847i	−0.234601	+	0.0413664i
$373$	−1.91740	−	10.8741i	−0.0992794	−	0.563042i	−0.993352	−	0.115119i	$-0.963275\pi$
$373$	−1.91740	−	10.8741i	−0.0992794	−	0.563042i	0.894072	−	0.447923i	$-0.147836\pi$
$374$	5.39440	−	4.52644i	0.278938	−	0.234057i
$375$	−9.03343	+	10.7656i	−0.466484	+	0.555935i
$376$	−2.51367	+	0.914901i	−0.129633	+	0.0471824i
$377$	0.660444			0.0340146
$378$	3.34002	+	3.98048i	0.171792	+	0.204734i
$379$	−4.77332			−0.245189			−0.122594	−	0.992457i	$-0.539121\pi$
$379$	−4.77332			−0.245189			−0.122594	+	0.992457i	$0.539121\pi$
$380$	1.68732	−	0.614134i	0.0865576	−	0.0315044i
$381$	20.9518	+	3.69436i	1.07339	+	0.189268i
$382$	10.8550	−	9.10846i	0.555392	−	0.466029i
$383$	3.23355	+	18.3383i	0.165226	+	0.937046i	0.948831	+	0.315785i	$0.102268\pi$
$383$	3.23355	+	18.3383i	0.165226	+	0.937046i	−0.783604	+	0.621260i	$0.786621\pi$
$384$	−0.592396	+	1.62760i	−0.0302306	+	0.0830579i
$385$	−1.39053	−	1.16679i	−0.0708680	−	0.0594653i
$386$	−4.85117	+	8.40247i	−0.246918	+	0.427674i
$387$	−2.90373	−	5.02941i	−0.147605	−	0.255659i
$388$	3.58125	+	6.20291i	0.181811	+	0.314905i
$389$	0.400492	−	2.27130i	0.0203057	−	0.115160i	−0.972970	−	0.230931i	$-0.925823\pi$
$389$	0.400492	−	2.27130i	0.0203057	−	0.115160i	0.993276	+	0.115771i	$0.0369340\pi$
$390$	−0.458111	+	0.264490i	−0.0231973	+	0.0133930i
$391$	−18.2554	−	6.64441i	−0.923214	−	0.336022i
$392$	−0.939693	−	0.342020i	−0.0474616	−	0.0172746i
$393$	3.34002	+	1.92836i	0.168482	+	0.0972730i
$394$	−1.02869	+	5.83396i	−0.0518244	+	0.293911i
$395$	2.96538	+	5.13620i	0.149205	+	0.258430i
$396$	−5.81908	−	2.11797i	−0.292420	−	0.106432i
$397$	−13.6224	+	23.5947i	−0.683690	+	1.18419i	0.290157	+	0.956979i	$0.406293\pi$
$397$	−13.6224	+	23.5947i	−0.683690	+	1.18419i	−0.973847	+	0.227207i	$0.927041\pi$
$398$	14.1459	+	11.8698i	0.709070	+	0.594980i
$399$	2.27332	+	2.70924i	0.113808	+	0.135631i
$400$	−0.733956	−	4.16247i	−0.0366978	−	0.208123i
$401$	−22.0385	+	18.4925i	−1.10055	+	0.923471i	−0.997462	−	0.0712017i	$-0.977317\pi$
$401$	−22.0385	+	18.4925i	−1.10055	+	0.923471i	−0.103088	+	0.994672i	$0.532872\pi$
$402$	−6.34864	−	17.4427i	−0.316641	−	0.869965i
$403$	0.865715	−	0.315094i	0.0431243	−	0.0156960i
$404$	−2.49525			−0.124143
$405$	7.91447			0.393273
$406$	1.90167			0.0943785
$407$	0.879385	−	0.320070i	0.0435895	−	0.0158653i
$408$	−2.02094	−	5.55250i	−0.100052	−	0.274890i
$409$	24.2160	−	20.3196i	1.19740	−	1.00474i	0.197704	−	0.980262i	$-0.436652\pi$
$409$	24.2160	−	20.3196i	1.19740	−	1.00474i	0.999700	−	0.0244798i	$-0.00779293\pi$
$410$	0.822948	+	4.66717i	0.0406425	+	0.230495i
$411$	7.13058	+	8.49789i	0.351725	+	0.419170i
$412$	0.777189	+	0.652139i	0.0382893	+	0.0321286i
$413$	−0.511144	+	0.885328i	−0.0251518	+	0.0435641i
$414$	2.96657	+	16.8242i	0.145799	+	0.826866i
$415$	1.59627	+	2.76481i	0.0783576	+	0.135719i
$416$	0.0603074	−	0.342020i	0.00295681	−	0.0167689i
$417$	−32.8601	−	18.9718i	−1.60917	−	0.929052i
$418$	−3.96064	−	1.44155i	−0.193721	−	0.0705087i
$419$	−0.118089	−	0.0429807i	−0.00576900	−	0.00209975i	0.339134	−	0.940738i	$-0.389866\pi$
$419$	−0.118089	−	0.0429807i	−0.00576900	−	0.00209975i	−0.344903	+	0.938638i	$0.612088\pi$
$420$	−1.31908	+	0.761570i	−0.0643644	+	0.0371608i
$421$	−5.13176	+	29.1037i	−0.250107	+	1.41843i	0.558221	+	0.829692i	$0.311484\pi$
$421$	−5.13176	+	29.1037i	−0.250107	+	1.41843i	−0.808328	+	0.588733i	$0.799627\pi$
$422$	−9.26651	−	16.0501i	−0.451087	−	0.781305i
$423$	−8.02498			−0.390188
$424$	−5.04576	+	8.73951i	−0.245044	+	0.424428i
$425$	11.0458	+	9.26849i	0.535798	+	0.449588i
$426$	3.40286	−	9.34927i	0.164869	−	0.452974i
$427$	−0.594922	−	3.37397i	−0.0287903	−	0.163278i
$428$	8.66637	−	7.27195i	0.418905	−	0.351503i
$429$	1.22281	+	0.215615i	0.0590379	+	0.0104100i
$430$	1.59967	−	0.582232i	0.0771429	−	0.0280777i
$431$	−9.25578			−0.445835			−0.222918	−	0.974837i	$-0.571558\pi$
$431$	−9.25578			−0.445835			−0.222918	+	0.974837i	$0.571558\pi$
$432$	−3.34002	+	3.98048i	−0.160697	+	0.191511i
$433$	−4.85978			−0.233546			−0.116773	−	0.993159i	$-0.537255\pi$
$433$	−4.85978			−0.233546			−0.116773	+	0.993159i	$0.537255\pi$
$434$	2.49273	−	0.907278i	0.119655	−	0.0435507i
$435$	1.86184	−	2.21886i	0.0892686	−	0.106386i
$436$	9.77379	−	8.20118i	0.468079	−	0.392765i
$437$	2.01913	+	11.4511i	0.0965883	+	0.547779i
$438$	−21.1839	+	3.73530i	−1.01221	+	0.178479i
$439$	−22.7931	−	19.1257i	−1.08786	−	0.912820i	−0.0913077	−	0.995823i	$-0.529105\pi$
$439$	−22.7931	−	19.1257i	−1.08786	−	0.912820i	−0.996549	+	0.0830022i	$0.973549\pi$
$440$	0.907604	−	1.57202i	0.0432683	−	0.0749429i
$441$	−2.29813	−	1.92836i	−0.109435	−	0.0918268i
$442$	0.592396	+	1.02606i	0.0281774	+	0.0488047i
$443$	−3.69547	+	20.9581i	−0.175577	+	0.995747i	0.761899	+	0.647696i	$0.224267\pi$
$443$	−3.69547	+	20.9581i	−0.175577	+	0.995747i	−0.937476	+	0.348051i	$0.886844\pi$
$444$		−	0.785248i		−	0.0372662i
$445$	15.5077	+	5.64436i	0.735137	+	0.267568i
$446$	9.87686	+	3.59488i	0.467683	+	0.170223i
$447$		−	38.2518i		−	1.80925i
$448$	0.173648	−	0.984808i	0.00820411	−	0.0465278i
$449$	5.89171	+	10.2047i	0.278047	+	0.481592i	0.970899	−	0.239488i	$-0.0769795\pi$
$449$	5.89171	+	10.2047i	0.278047	+	0.481592i	−0.692852	+	0.721080i	$0.743646\pi$
$450$	2.20187	−	12.4874i	0.103797	−	0.588662i
$451$	5.56212	−	9.63387i	0.261910	−	0.453641i
$452$	−13.9363	−	11.6939i	−0.655508	−	0.550036i
$453$	−30.6830	+	5.41025i	−1.44161	+	0.254196i
$454$	−2.22328	−	12.6088i	−0.104344	−	0.591762i
$455$	0.233956	−	0.196312i	0.0109680	−	0.00920325i
$456$	−2.27332	+	2.70924i	−0.106458	+	0.126872i
$457$	36.1117	−	13.1436i	1.68924	−	0.614832i	0.694707	−	0.719293i	$-0.255534\pi$
$457$	36.1117	−	13.1436i	1.68924	−	0.614832i	0.994529	+	0.104461i	$0.0333117\pi$
$458$	10.3824			0.485137
$459$		−	17.7265i		−	0.827404i
$460$	−5.00774			−0.233487
$461$	23.0736	−	8.39809i	1.07464	−	0.391138i	0.256732	−	0.966483i	$-0.417354\pi$
$461$	23.0736	−	8.39809i	1.07464	−	0.391138i	0.817911	+	0.575345i	$0.195132\pi$
$462$	3.52094	+	0.620838i	0.163809	+	0.0288840i
$463$	−5.23964	+	4.39658i	−0.243507	+	0.204326i	−0.756370	−	0.654144i	$-0.773029\pi$
$463$	−5.23964	+	4.39658i	−0.243507	+	0.204326i	0.512864	+	0.858470i	$0.328585\pi$
$464$	0.330222	+	1.87278i	0.0153302	+	0.0869418i
$465$	1.38191	−	3.79677i	0.0640846	−	0.176071i
$466$	−3.06624	−	2.57288i	−0.142041	−	0.119186i
$467$	−0.979055	+	1.69577i	−0.0453053	+	0.0784711i	−0.887789	−	0.460251i	$-0.847759\pi$
$467$	−0.979055	+	1.69577i	−0.0453053	+	0.0784711i	0.842484	+	0.538722i	$0.181093\pi$
$468$	0.520945	−	0.902302i	0.0240807	−	0.0417089i
$469$	5.35844	+	9.28109i	0.247430	+	0.428561i
$470$	0.408481	−	2.31661i	0.0188418	−	0.106857i
$471$	−29.4176	+	16.9843i	−1.35549	+	0.782594i
$472$	−0.960637	−	0.349643i	−0.0442169	−	0.0160936i
$473$	−3.75490	−	1.36667i	−0.172650	−	0.0628396i
$474$	−10.1163	−	5.84067i	−0.464659	−	0.268271i
$475$	1.49866	−	8.49930i	0.0687630	−	0.389975i
$476$	1.70574	+	2.95442i	0.0781823	+	0.135416i
$477$	−23.1917	+	19.4601i	−1.06187	+	0.891017i
$478$	−10.6741	+	18.4881i	−0.488223	+	0.845626i
$479$	−12.6138	−	10.5842i	−0.576340	−	0.483606i	0.307403	−	0.951579i	$-0.400540\pi$
$479$	−12.6138	−	10.5842i	−0.576340	−	0.483606i	−0.883743	+	0.467973i	$0.844984\pi$
$480$	−0.979055	−	1.16679i	−0.0446876	−	0.0532566i
$481$	0.0273411	+	0.155059i	0.00124665	+	0.00707010i
$482$	−4.35844	+	3.65717i	−0.198522	+	0.166579i
$483$	−3.37346	−	9.26849i	−0.153498	−	0.421731i
$484$	6.33275	−	2.30493i	0.287852	−	0.104770i
$485$	−6.29860			−0.286005
$486$	−13.5000	+	7.79423i	−0.612372	+	0.353553i
$487$	−7.53714			−0.341540			−0.170770	−	0.985311i	$-0.554626\pi$
$487$	−7.53714			−0.341540			−0.170770	+	0.985311i	$0.554626\pi$
$488$	3.21941	−	1.17177i	0.145736	−	0.0530435i
$489$	5.31134	+	14.5928i	0.240187	+	0.659908i
$490$	0.673648	−	0.565258i	0.0304323	−	0.0255358i
$491$	1.03667	+	5.87927i	0.0467845	+	0.265328i	0.999223	−	0.0394014i	$-0.0125451\pi$
$491$	1.03667	+	5.87927i	0.0467845	+	0.265328i	−0.952439	+	0.304729i	$0.901434\pi$
$492$	−6.00000	−	7.15052i	−0.270501	−	0.322370i
$493$	−4.96972	−	4.17009i	−0.223825	−	0.187811i
$494$	0.354570	−	0.614134i	0.0159529	−	0.0276312i
$495$	4.17159	−	3.50038i	0.187499	−	0.157330i
$496$	1.32635	+	2.29731i	0.0595550	+	0.103152i
$497$	−0.997474	+	5.65695i	−0.0447428	+	0.253749i
$498$	−5.44562	−	3.14403i	−0.244024	−	0.140887i
$499$	−35.9111	−	13.0706i	−1.60760	−	0.585119i	−0.626637	−	0.779312i	$-0.715569\pi$
$499$	−35.9111	−	13.0706i	−1.60760	−	0.585119i	−0.980963	+	0.194193i	$0.937791\pi$
$500$	7.62449	+	2.77509i	0.340977	+	0.124106i
$501$	2.36500	−	1.36543i	0.105660	−	0.0610031i
$502$	−2.24510	+	12.7326i	−0.100204	+	0.568283i
$503$	−5.44222	−	9.42620i	−0.242657	−	0.420293i	0.718814	−	0.695203i	$-0.244685\pi$
$503$	−5.44222	−	9.42620i	−0.242657	−	0.420293i	−0.961470	+	0.274909i	$0.911352\pi$
$504$	1.50000	−	2.59808i	0.0668153	−	0.115728i
$505$	1.09714	−	1.90031i	0.0488223	−	0.0845626i
$506$	9.00459	+	7.55574i	0.400303	+	0.335894i
$507$	7.62970	−	20.9624i	0.338847	−	0.930974i
$508$	−2.13294	−	12.0965i	−0.0946340	−	0.536696i
$509$	−1.55644	+	1.30601i	−0.0689879	+	0.0578877i	−0.676630	−	0.736324i	$-0.736560\pi$
$509$	−1.55644	+	1.30601i	−0.0689879	+	0.0578877i	0.607642	+	0.794211i	$0.292116\pi$
$510$	5.11721	+	0.902302i	0.226594	+	0.0399546i
$511$	11.6702	−	4.24762i	0.516261	−	0.187904i
$512$	1.00000			0.0441942
$513$	−9.18850	+	5.30498i	−0.405682	+	0.234221i
$514$	29.2763			1.29132
$515$	−0.838374	+	0.305143i	−0.0369432	+	0.0134462i
$516$	−2.15523	+	2.56850i	−0.0948787	+	0.113072i
$517$	−4.22984	+	3.54925i	−0.186028	+	0.156096i
$518$	0.0787257	+	0.446476i	0.00345901	+	0.0196170i
$519$	32.7460	−	5.77401i	1.43739	−	0.253451i
$520$	0.233956	+	0.196312i	0.0102596	+	0.00860885i
$521$	−17.9534	+	31.0961i	−0.786551	+	1.36235i	0.141517	+	0.989936i	$0.454802\pi$
$521$	−17.9534	+	31.0961i	−0.786551	+	1.36235i	−0.928068	+	0.372411i	$0.878531\pi$
$522$	−0.990667	+	5.61835i	−0.0433603	+	0.245908i
$523$	4.68139	+	8.10840i	0.204703	+	0.354556i	0.950038	−	0.312134i	$-0.101044\pi$
$523$	4.68139	+	8.10840i	0.204703	+	0.354556i	−0.745335	+	0.666690i	$0.767711\pi$
$524$	0.386659	−	2.19285i	0.0168913	−	0.0957952i
$525$			7.32083i			0.319507i
$526$	6.56418	+	2.38917i	0.286212	+	0.104173i
$527$	−8.50387	−	3.09516i	−0.370434	−	0.134827i
$528$			3.57526i			0.155593i
$529$	1.63722	−	9.28515i	0.0711836	−	0.403702i
$530$	−4.43717	−	7.68540i	−0.192738	−	0.333832i
$531$	−2.34936	−	1.97134i	−0.101953	−	0.0855490i
$532$	1.02094	−	1.76833i	0.0442636	−	0.0766667i
$533$	1.43376	+	1.20307i	0.0621032	+	0.0521107i
$534$	−32.0107	+	5.64436i	−1.38524	+	0.244255i
$535$	1.72756	+	9.79747i	0.0746889	+	0.423582i
$536$	−8.20961	+	6.88868i	−0.354601	+	0.297546i
$537$	−17.8935	+	21.3247i	−0.772162	+	0.920227i
$538$	17.8341	−	6.49108i	0.768882	−	0.279850i
$539$	−2.06418			−0.0889104
$540$	−1.56283	−	4.29385i	−0.0672537	−	0.184778i
$541$	−2.66313			−0.114497			−0.0572485	−	0.998360i	$-0.518233\pi$
$541$	−2.66313			−0.114497			−0.0572485	+	0.998360i	$0.518233\pi$
$542$	27.0663	−	9.85133i	1.16260	−	0.423151i
$543$	−38.0822	−	6.71492i	−1.63426	−	0.288165i
$544$	−2.61334	+	2.19285i	−0.112046	+	0.0940178i
$545$	1.94831	+	11.0494i	0.0834565	+	0.473305i
$546$	−0.205737	+	0.565258i	−0.00880473	+	0.0241908i
$547$	−11.3543	−	9.52741i	−0.485476	−	0.407363i	0.366926	−	0.930250i	$-0.380410\pi$
$547$	−11.3543	−	9.52741i	−0.485476	−	0.407363i	−0.852402	+	0.522888i	$0.824855\pi$
$548$	3.20233	−	5.54660i	0.136797	−	0.236939i
$549$	10.2781			0.438657
$550$	−4.36231	−	7.55574i	−0.186010	−	0.322178i
$551$	−0.674277	+	3.82402i	−0.0287252	+	0.162909i
$552$	8.54189	−	4.93166i	0.363567	−	0.209905i
$553$	6.33750	+	2.30666i	0.269498	+	0.0980892i
$554$	22.1202	+	8.05110i	0.939797	+	0.342058i
$555$	0.598021	+	0.345268i	0.0253846	+	0.0146558i
$556$	−3.80406	+	21.5739i	−0.161328	+	0.914938i
$557$	8.58512	+	14.8699i	0.363763	+	0.630057i	0.988577	−	0.150717i	$-0.0481584\pi$
$557$	8.58512	+	14.8699i	0.363763	+	0.630057i	−0.624814	+	0.780774i	$0.714825\pi$
$558$	1.38191	+	7.83721i	0.0585010	+	0.331776i
$559$	0.336152	−	0.582232i	0.0142177	−	0.0246258i
$560$	0.673648	+	0.565258i	0.0284668	+	0.0238865i
$561$	−7.84002	−	9.34337i	−0.331006	−	0.394478i
$562$	3.93464	+	22.3145i	0.165973	+	0.941278i
$563$	18.5458	−	15.5617i	0.781611	−	0.655849i	−0.162043	−	0.986784i	$-0.551808\pi$
$563$	18.5458	−	15.5617i	0.781611	−	0.655849i	0.943654	+	0.330935i	$0.107364\pi$
$564$	1.58466	+	4.35381i	0.0667260	+	0.183328i
$565$	15.0334	−	5.47172i	0.632461	−	0.230197i
$566$	−9.00093			−0.378337
$567$	6.89440	−	5.78509i	0.289538	−	0.242951i
$568$	−5.74422			−0.241022
$569$	10.7674	−	3.91901i	0.451392	−	0.164293i	−0.106312	−	0.994333i	$-0.533904\pi$
$569$	10.7674	−	3.91901i	0.451392	−	0.164293i	0.557705	+	0.830039i	$0.311682\pi$
$570$	−1.06371	−	2.92252i	−0.0445539	−	0.122411i
$571$	−8.05169	+	6.75617i	−0.336953	+	0.282737i	−0.795526	−	0.605920i	$-0.792805\pi$
$571$	−8.05169	+	6.75617i	−0.336953	+	0.282737i	0.458573	+	0.888657i	$0.348361\pi$
$572$	−0.124485	−	0.705990i	−0.00520499	−	0.0295189i
$573$	−15.7763	−	18.8015i	−0.659065	−	0.785443i
$574$	4.12836	+	3.46410i	0.172314	+	0.144589i
$575$	−12.0346	+	20.8446i	−0.501878	+	0.869278i
$576$	2.81908	+	1.02606i	0.117462	+	0.0427525i
$577$	−2.52822	−	4.37900i	−0.105251	−	0.182300i	0.808590	−	0.588373i	$-0.200231\pi$
$577$	−2.52822	−	4.37900i	−0.105251	−	0.182300i	−0.913841	+	0.406073i	$0.866898\pi$
$578$	−0.931074	+	5.28039i	−0.0387276	+	0.219635i
$579$	14.5535	+	8.40247i	0.604823	+	0.349195i
$580$	−1.57145	−	0.571962i	−0.0652510	−	0.0237494i
$581$	3.41147	+	1.24168i	0.141532	+	0.0515134i
$582$	10.7438	−	6.20291i	0.445343	−	0.257119i
$583$	−3.61721	+	20.5142i	−0.149810	+	0.849612i
$584$	6.20961	+	10.7554i	0.256955	+	0.445060i
$585$	0.458111	+	0.793471i	0.0189406	+	0.0328060i
$586$	−4.56283	+	7.90306i	−0.188489	+	0.326472i
$587$	13.4684	+	11.3013i	0.555899	+	0.466455i	0.876933	−	0.480613i	$-0.159586\pi$
$587$	13.4684	+	11.3013i	0.555899	+	0.466455i	−0.321033	+	0.947068i	$0.604030\pi$
$588$	−0.592396	+	1.62760i	−0.0244300	+	0.0671209i
$589$	0.940570	+	5.33424i	0.0387555	+	0.219793i
$590$	0.688663	−	0.577857i	0.0283518	−	0.0237900i
$591$	10.1047	+	1.78174i	0.415653	+	0.0732908i
$592$	−0.426022	+	0.155059i	−0.0175094	+	0.00637290i
$593$	12.7041			0.521694			0.260847	−	0.965380i	$-0.415998\pi$
$593$	12.7041			0.521694			0.260847	+	0.965380i	$0.415998\pi$
$594$	−3.66843	+	10.0789i	−0.150518	+	0.413544i
$595$	−3.00000			−0.122988
$596$	−20.7528	+	7.55342i	−0.850069	+	0.309400i
$597$	20.5591	−	24.5014i	0.841429	−	1.00278i
$598$	−1.51501	+	1.27125i	−0.0619536	+	0.0519852i
$599$	6.82594	+	38.7118i	0.278900	+	1.58172i	0.726293	+	0.687385i	$0.241242\pi$
$599$	6.82594	+	38.7118i	0.278900	+	1.58172i	−0.447393	+	0.894338i	$0.647647\pi$
$600$	−7.20961	+	1.27125i	−0.294331	+	0.0518985i
$601$	25.5881	+	21.4710i	1.04376	+	0.875819i	0.992424	−	0.122862i	$-0.0392072\pi$
$601$	25.5881	+	21.4710i	1.04376	+	0.875819i	0.0513372	+	0.998681i	$0.483652\pi$
$602$	0.967911	−	1.67647i	0.0394491	−	0.0683279i
$603$	−30.2117	+	10.9962i	−1.23032	+	0.447799i
$604$	8.99407	+	15.5782i	0.365964	+	0.633867i
$605$	−1.02910	+	5.83629i	−0.0418387	+	0.237279i
$606$			4.32190i			0.175565i
$607$	−38.8482	−	14.1396i	−1.57680	−	0.573909i	−0.602296	−	0.798273i	$-0.705747\pi$
$607$	−38.8482	−	14.1396i	−1.57680	−	0.573909i	−0.974505	+	0.224364i	$0.927969\pi$
$608$	1.91875	+	0.698367i	0.0778155	+	0.0283225i
$609$		−	3.29380i		−	0.133471i
$610$	−0.523166	+	2.96702i	−0.0211824	+	0.120131i
$611$	−0.464508	−	0.804551i	−0.0187920	−	0.0325486i
$612$	−9.61721	+	3.50038i	−0.388753	+	0.141494i
$613$	−3.52528	+	6.10597i	−0.142385	+	0.246618i	−0.928394	−	0.371597i	$-0.878810\pi$
$613$	−3.52528	+	6.10597i	−0.142385	+	0.246618i	0.786009	+	0.618215i	$0.212144\pi$
$614$	8.72849	+	7.32407i	0.352253	+	0.295576i
$615$	8.08378	−	1.42539i	0.325969	−	0.0574772i
$616$	−0.358441	−	2.03282i	−0.0144420	−	0.0819046i
$617$	33.8011	−	28.3625i	1.36078	−	1.14183i	0.385042	−	0.922899i	$-0.374187\pi$
$617$	33.8011	−	28.3625i	1.36078	−	1.14183i	0.975740	−	0.218933i	$-0.0702575\pi$
$618$	1.12954	−	1.34613i	0.0454367	−	0.0541493i
$619$	36.0621	−	13.1255i	1.44946	−	0.527560i	0.507019	−	0.861935i	$-0.330747\pi$
$619$	36.0621	−	13.1255i	1.44946	−	0.527560i	0.942440	+	0.334375i	$0.108525\pi$
$620$	−2.33275			−0.0936854
$621$	29.1404	−	5.13824i	1.16937	−	0.206191i
$622$	2.27631			0.0912718
$623$	17.6348	−	6.41852i	0.706521	−	0.257153i
$624$	−0.592396	−	0.104455i	−0.0237148	−	0.00418156i
$625$	10.7233	−	8.99790i	0.428931	−	0.359916i
$626$	−0.253718	−	1.43891i	−0.0101406	−	0.0575103i
$627$	−2.49684	+	6.86002i	−0.0997144	+	0.273963i
$628$	15.0235	+	12.6062i	0.599502	+	0.503042i
$629$	0.773318	−	1.33943i	0.0308342	−	0.0534064i
$630$	1.31908	+	2.28471i	0.0525533	+	0.0910250i
$631$	−16.6755	−	28.8827i	−0.663840	−	1.14980i	−0.979599	−	0.200964i	$-0.935592\pi$
$631$	−16.6755	−	28.8827i	−0.663840	−	1.14980i	0.315759	−	0.948839i	$-0.397741\pi$
$632$	−1.17112	+	6.64176i	−0.0465847	+	0.264195i
$633$	−27.7995	+	16.0501i	−1.10493	+	0.637933i
$634$	0.393056	+	0.143061i	0.0156102	+	0.00568166i
$635$	10.1502	+	3.69436i	0.402798	+	0.146606i
$636$	15.1373	+	8.73951i	0.600232	+	0.346544i
$637$	0.0603074	−	0.342020i	0.00238947	−	0.0135513i
$638$	1.96270	+	3.39949i	0.0777039	+	0.134587i
$639$	−16.1934	−	5.89392i	−0.640601	−	0.233160i
$640$	−0.439693	+	0.761570i	−0.0173804	+	0.0301037i
$641$	−31.3601	−	26.3142i	−1.23865	−	1.03935i	−0.997628	−	0.0688300i	$-0.978073\pi$
$641$	−31.3601	−	26.3142i	−1.23865	−	1.03935i	−0.241021	−	0.970520i	$-0.577482\pi$
$642$	−12.5954	−	15.0106i	−0.497100	−	0.592421i
$643$	−6.21869	−	35.2680i	−0.245241	−	1.39083i	−0.819932	−	0.572461i	$-0.805989\pi$
$643$	−6.21869	−	35.2680i	−0.245241	−	1.39083i	0.574690	−	0.818371i	$-0.305123\pi$
$644$	−4.36231	+	3.66041i	−0.171899	+	0.144241i
$645$	−1.00846	−	2.77071i	−0.0397079	−	0.109097i
$646$	−6.54576	+	2.38246i	−0.257539	+	0.0937367i
$647$	−34.1388			−1.34213			−0.671067	−	0.741397i	$-0.734164\pi$
$647$	−34.1388			−1.34213			−0.671067	+	0.741397i	$0.734164\pi$
$648$	6.89440	+	5.78509i	0.270838	+	0.227260i
$649$	−2.11019			−0.0828320
$650$	1.37939	−	0.502055i	0.0541039	−	0.0196922i
$651$	−1.57145	−	4.31753i	−0.0615900	−	0.169217i
$652$	6.86824	−	5.76314i	0.268981	−	0.225702i
$653$	6.90003	+	39.1320i	0.270019	+	1.53135i	0.754352	+	0.656470i	$0.227951\pi$
$653$	6.90003	+	39.1320i	0.270019	+	1.53135i	−0.484334	+	0.874883i	$0.660938\pi$
$654$	−14.2049	−	16.9287i	−0.555454	−	0.661964i
$655$	1.50000	+	1.25865i	0.0586098	+	0.0491795i
$656$	−2.69459	+	4.66717i	−0.105206	+	0.182222i
$657$	6.46972	+	36.6916i	0.252408	+	1.43148i
$658$	−1.33750	−	2.31661i	−0.0521410	−	0.0903109i
$659$	2.76563	−	15.6847i	0.107734	−	0.610989i	−0.882359	−	0.470576i	$-0.844046\pi$
$659$	2.76563	−	15.6847i	0.107734	−	0.610989i	0.990093	−	0.140412i	$-0.0448428\pi$
$660$	−2.72281	−	1.57202i	−0.105985	−	0.0611906i
$661$	6.12836	+	2.23054i	0.238365	+	0.0867579i	0.458441	−	0.888725i	$-0.348408\pi$
$661$	6.12836	+	2.23054i	0.238365	+	0.0867579i	−0.220075	+	0.975483i	$0.570630\pi$
$662$	−10.7233	−	3.90295i	−0.416772	−	0.151693i
$663$	1.77719	−	1.02606i	0.0690203	−	0.0398489i
$664$	−0.630415	+	3.57526i	−0.0244648	+	0.138747i
$665$	0.897804	+	1.55504i	0.0348153	+	0.0603019i
$666$	−1.36009			−0.0527024
$667$	5.41463	−	9.37841i	0.209655	−	0.363134i
$668$	−1.20780	−	1.01346i	−0.0467310	−	0.0392120i
$669$	6.22652	−	17.1072i	0.240731	−	0.661403i
$670$	−1.63651	−	9.28109i	−0.0632238	−	0.358560i
$671$	5.41740	−	4.54574i	0.209137	−	0.175486i
$672$	−1.70574	−	0.300767i	−0.0658002	−	0.0116024i
$673$	−15.3500	+	5.58694i	−0.591698	+	0.215361i	−0.620476	−	0.784225i	$-0.713061\pi$
$673$	−15.3500	+	5.58694i	−0.591698	+	0.215361i	0.0287778	+	0.999586i	$0.490838\pi$
$674$	−24.9067			−0.959371
$675$	−21.6288	−	3.81374i	−0.832494	−	0.146791i
$676$	−12.8794			−0.495361
$677$	1.68092	−	0.611806i	0.0646031	−	0.0235136i	−0.309516	−	0.950894i	$-0.600167\pi$
$677$	1.68092	−	0.611806i	0.0646031	−	0.0235136i	0.374120	+	0.927380i	$0.377945\pi$
$678$	−20.2545	+	24.1384i	−0.777869	+	0.927028i
$679$	−5.48680	+	4.60397i	−0.210564	+	0.176684i
$680$	−0.520945	−	2.95442i	−0.0199773	−	0.113297i
$681$	−21.8391	+	3.85083i	−0.836878	+	0.147564i
$682$	4.19459	+	3.51968i	0.160619	+	0.134776i
$683$	−7.89306	+	13.6712i	−0.302019	+	0.523113i	−0.976593	−	0.215094i	$-0.930994\pi$
$683$	−7.89306	+	13.6712i	−0.302019	+	0.523113i	0.674574	+	0.738207i	$0.264327\pi$
$684$	4.69253	+	3.93750i	0.179423	+	0.150554i
$685$	2.81608	+	4.87760i	0.107597	+	0.186364i
$686$	0.173648	−	0.984808i	0.00662992	−	0.0376001i
$687$		−	17.9828i		−	0.686087i
$688$	1.81908	+	0.662090i	0.0693517	+	0.0252420i
$689$	−3.29339	−	1.19869i	−0.125468	−	0.0456666i
$690$			8.67366i			0.330201i
$691$	−2.74376	+	15.5606i	−0.104377	+	0.591954i	0.887090	+	0.461597i	$0.152723\pi$
$691$	−2.74376	+	15.5606i	−0.104377	+	0.591954i	−0.991467	+	0.130357i	$0.958388\pi$
$692$	−9.59879	−	16.6256i	−0.364891	−	0.632010i
$693$	1.07532	−	6.09845i	0.0408481	−	0.231661i
$694$	5.89053	−	10.2027i	0.223601	−	0.387289i
$695$	−14.7574	−	12.3830i	−0.559781	−	0.469712i
$696$	3.24376	−	0.571962i	0.122954	−	0.0216802i
$697$	−3.19253	−	18.1058i	−0.120926	−	0.685804i
$698$	−17.7986	+	14.9348i	−0.673687	+	0.565290i
$699$	−4.45636	+	5.31088i	−0.168555	+	0.200876i
$700$	3.97178	−	1.44561i	0.150119	−	0.0546389i
$701$	29.6705			1.12064			0.560321	−	0.828276i	$-0.310678\pi$
$701$	29.6705			1.12064			0.560321	+	0.828276i	$0.310678\pi$
$702$	−1.56283	−	0.902302i	−0.0589854	−	0.0340552i
$703$	−0.925717			−0.0349141
$704$	1.93969	−	0.705990i	0.0731049	−	0.0266080i
$705$	−4.01249	−	0.707510i	−0.151119	−	0.0266464i
$706$	7.91147	−	6.63852i	0.297752	−	0.249844i
$707$	−0.433296	−	2.45734i	−0.0162958	−	0.0924179i
$708$	−0.605600	+	1.66387i	−0.0227598	+	0.0625322i
$709$	−8.70574	−	7.30498i	−0.326951	−	0.274344i	0.464505	−	0.885570i	$-0.346232\pi$
$709$	−8.70574	−	7.30498i	−0.326951	−	0.274344i	−0.791456	+	0.611226i	$0.790677\pi$
$710$	2.52569	−	4.37463i	0.0947875	−	0.164177i
$711$	−10.1163	+	17.5220i	−0.379392	+	0.657126i
$712$	9.38326	+	16.2523i	0.351652	+	0.609080i
$713$	2.62314	−	14.8766i	0.0982374	−	0.557132i
$714$	5.11721	−	2.95442i	0.191507	−	0.110567i
$715$	0.592396	+	0.215615i	0.0221544	+	0.00806353i
$716$	15.1027	+	5.49692i	0.564413	+	0.205430i
$717$	32.0223	+	18.4881i	1.19590	+	0.690451i
$718$	0.897804	−	5.09170i	0.0335057	−	0.190020i
$719$	−19.5940	−	33.9379i	−0.730735	−	1.26567i	−0.956570	−	0.291504i	$-0.905844\pi$
$719$	−19.5940	−	33.9379i	−0.730735	−	1.26567i	0.225835	−	0.974166i	$-0.427489\pi$
$720$	−2.02094	+	1.69577i	−0.0753162	+	0.0631978i
$721$	−0.507274	+	0.878624i	−0.0188919	+	0.0327217i
$722$	−11.3610	−	9.53298i	−0.422811	−	0.354781i
$723$	6.33440	+	7.54904i	0.235579	+	0.280752i
$724$	3.87686	+	21.9868i	0.144082	+	0.817132i
$725$	−6.15729	+	5.16658i	−0.228676	+	0.191882i
$726$	−3.99226	−	10.9686i	−0.148167	−	0.407084i
$727$	41.9752	−	15.2777i	1.55678	−	0.566620i	0.586781	−	0.809746i	$-0.300395\pi$
$727$	41.9752	−	15.2777i	1.55678	−	0.566620i	0.969995	+	0.243126i	$0.0781728\pi$
$728$	0.347296			0.0128717
$729$	13.5000	+	23.3827i	0.500000	+	0.866025i
$730$	−10.9213			−0.404214
$731$	−6.20574	+	2.25870i	−0.229527	+	0.0835412i
$732$	−2.02956	−	5.57618i	−0.0750148	−	0.206101i
$733$	25.5633	−	21.4502i	0.944202	−	0.792280i	−0.0341096	−	0.999418i	$-0.510860\pi$
$733$	25.5633	−	21.4502i	0.944202	−	0.792280i	0.978312	+	0.207139i	$0.0664151\pi$
$734$	2.55216	+	14.4740i	0.0942018	+	0.534245i
$735$	−0.979055	−	1.16679i	−0.0361130	−	0.0430378i
$736$	−4.36231	−	3.66041i	−0.160797	−	0.134925i
$737$	−11.0608	+	19.1578i	−0.407429	+	0.705687i
$738$	−12.3851	+	10.3923i	−0.455901	+	0.382546i
$739$	3.22921	+	5.59315i	0.118788	+	0.205747i	0.919288	−	0.393586i	$-0.128766\pi$
$739$	3.22921	+	5.59315i	0.118788	+	0.205747i	−0.800499	+	0.599334i	$0.795432\pi$
$740$	0.0692302	−	0.392624i	0.00254495	−	0.0144331i
$741$	−1.06371	−	0.614134i	−0.0390764	−	0.0225608i
$742$	−9.48293	−	3.45150i	−0.348129	−	0.126709i
$743$	16.5342	+	6.01796i	0.606581	+	0.220777i	0.627007	−	0.779014i	$-0.284280\pi$
$743$	16.5342	+	6.01796i	0.606581	+	0.220777i	−0.0204255	+	0.999791i	$0.506502\pi$
$744$	3.97906	−	2.29731i	0.145879	−	0.0842234i
$745$	3.37242	−	19.1259i	0.123556	−	0.700720i
$746$	5.52094	+	9.56256i	0.202136	+	0.350110i
$747$	−5.44562	+	9.43209i	−0.199245	+	0.345102i
$748$	−3.52094	+	6.09845i	−0.128738	+	0.222982i
$749$	8.66637	+	7.27195i	0.316662	+	0.265711i
$750$	4.80659	−	13.2060i	0.175512	−	0.482215i
$751$	−2.54024	−	14.4064i	−0.0926947	−	0.525698i	−0.995429	−	0.0955001i	$-0.969555\pi$
$751$	−2.54024	−	14.4064i	−0.0926947	−	0.525698i	0.902735	−	0.430198i	$-0.141556\pi$
$752$	2.04916	−	1.71945i	0.0747253	−	0.0627020i
$753$	22.0535	+	3.88863i	0.803674	+	0.141709i
$754$	−0.620615	+	0.225885i	−0.0226015	+	0.00822626i
$755$	−15.8185			−0.575694
$756$	−4.50000	−	2.59808i	−0.163663	−	0.0944911i
$757$	−14.7692			−0.536796			−0.268398	−	0.963308i	$-0.586494\pi$
$757$	−14.7692			−0.536796			−0.268398	+	0.963308i	$0.586494\pi$
$758$	4.48545	−	1.63257i	0.162919	−	0.0592977i
$759$	13.0869	−	15.5964i	0.475026	−	0.566113i
$760$	−1.37551	+	1.15419i	−0.0498952	+	0.0418670i
$761$	−3.67768	−	20.8572i	−0.133316	−	0.756072i	−0.976018	−	0.217691i	$-0.930147\pi$
$761$	−3.67768	−	20.8572i	−0.133316	−	0.756072i	0.842702	−	0.538380i	$-0.180964\pi$
$762$	−20.9518	+	3.69436i	−0.759003	+	0.133833i
$763$	9.77379	+	8.20118i	0.353835	+	0.296903i
$764$	−7.08512	+	12.2718i	−0.256331	+	0.443978i
$765$	1.56283	−	8.86327i	0.0565044	−	0.320452i
$766$ </

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-0.939693 + 0.342020i) q^{2} +(0.592396 + 1.62760i) q^{3} +(0.766044 - 0.642788i) q^{4} +(0.152704 + 0.866025i) q^{5} +(-1.11334 - 1.32683i) q^{6} +(0.766044 + 0.642788i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-2.29813 + 1.92836i) q^{9} +O(q^{10})\)	\(q+(-0.939693 + 0.342020i) q^{2} +(0.592396 + 1.62760i) q^{3} +(0.766044 - 0.642788i) q^{4} +(0.152704 + 0.866025i) q^{5} +(-1.11334 - 1.32683i) q^{6} +(0.766044 + 0.642788i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-2.29813 + 1.92836i) q^{9} +(-0.439693 - 0.761570i) q^{10} +(-0.358441 + 2.03282i) q^{11} +(1.50000 + 0.866025i) q^{12} +(-0.326352 - 0.118782i) q^{13} +(-0.939693 - 0.342020i) q^{14} +(-1.31908 + 0.761570i) q^{15} +(0.173648 - 0.984808i) q^{16} +(1.70574 + 2.95442i) q^{17} +(1.50000 - 2.59808i) q^{18} +(1.02094 - 1.76833i) q^{19} +(0.673648 + 0.565258i) q^{20} +(-0.592396 + 1.62760i) q^{21} +(-0.358441 - 2.03282i) q^{22} +(-4.36231 + 3.66041i) q^{23} +(-1.70574 - 0.300767i) q^{24} +(3.97178 - 1.44561i) q^{25} +0.347296 q^{26} +(-4.50000 - 2.59808i) q^{27} +1.00000 q^{28} +(-1.78699 + 0.650411i) q^{29} +(0.979055 - 1.16679i) q^{30} +(-2.03209 + 1.70513i) q^{31} +(0.173648 + 0.984808i) q^{32} +(-3.52094 + 0.620838i) q^{33} +(-2.61334 - 2.19285i) q^{34} +(-0.439693 + 0.761570i) q^{35} +(-0.520945 + 2.95442i) q^{36} +(-0.226682 - 0.392624i) q^{37} +(-0.354570 + 2.01087i) q^{38} -0.601535i q^{39} +(-0.826352 - 0.300767i) q^{40} +(-5.06418 - 1.84321i) q^{41} -1.73205i q^{42} +(-0.336152 + 1.90641i) q^{43} +(1.03209 + 1.78763i) q^{44} +(-2.02094 - 1.69577i) q^{45} +(2.84730 - 4.93166i) q^{46} +(2.04916 + 1.71945i) q^{47} +(1.70574 - 0.300767i) q^{48} +(0.173648 + 0.984808i) q^{49} +(-3.23783 + 2.71686i) q^{50} +(-3.79813 + 4.52644i) q^{51} +(-0.326352 + 0.118782i) q^{52} +10.0915 q^{53} +(5.11721 + 0.902302i) q^{54} -1.81521 q^{55} +(-0.939693 + 0.342020i) q^{56} +(3.48293 + 0.614134i) q^{57} +(1.45677 - 1.22237i) q^{58} +(0.177519 + 1.00676i) q^{59} +(-0.520945 + 1.43128i) q^{60} +(-2.62449 - 2.20220i) q^{61} +(1.32635 - 2.29731i) q^{62} -3.00000 q^{63} +(-0.500000 - 0.866025i) q^{64} +(0.0530334 - 0.300767i) q^{65} +(3.09627 - 1.78763i) q^{66} +(10.0706 + 3.66539i) q^{67} +(3.20574 + 1.16679i) q^{68} +(-8.54189 - 4.93166i) q^{69} +(0.152704 - 0.866025i) q^{70} +(2.87211 + 4.97464i) q^{71} +(-0.520945 - 2.95442i) q^{72} +(6.20961 - 10.7554i) q^{73} +(0.347296 + 0.291416i) q^{74} +(4.70574 + 5.60808i) q^{75} +(-0.354570 - 2.01087i) q^{76} +(-1.58125 + 1.32683i) q^{77} +(0.205737 + 0.565258i) q^{78} +(6.33750 - 2.30666i) q^{79} +0.879385 q^{80} +(1.56283 - 8.86327i) q^{81} +5.38919 q^{82} +(3.41147 - 1.24168i) q^{83} +(0.592396 + 1.62760i) q^{84} +(-2.29813 + 1.92836i) q^{85} +(-0.336152 - 1.90641i) q^{86} +(-2.11721 - 2.52319i) q^{87} +(-1.58125 - 1.32683i) q^{88} +(9.38326 - 16.2523i) q^{89} +(2.47906 + 0.902302i) q^{90} +(-0.173648 - 0.300767i) q^{91} +(-0.988856 + 5.60808i) q^{92} +(-3.97906 - 2.29731i) q^{93} +(-2.51367 - 0.914901i) q^{94} +(1.68732 + 0.614134i) q^{95} +(-1.50000 + 0.866025i) q^{96} +(-1.24376 + 7.05369i) q^{97} +(-0.500000 - 0.866025i) q^{98} +(-3.09627 - 5.36289i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{5} - 3 q^{8}+O(q^{10}) \) 6 * q + 3 * q^5 - 3 * q^8	\( 6 q + 3 q^{5} - 3 q^{8} + 3 q^{10} + 6 q^{11} + 9 q^{12} - 3 q^{13} + 9 q^{15} + 9 q^{18} + 3 q^{19} + 3 q^{20} + 6 q^{22} + 6 q^{23} + 9 q^{25} - 27 q^{27} + 6 q^{28} - 3 q^{29} + 9 q^{30} - 3 q^{31} - 18 q^{33} - 9 q^{34} + 3 q^{35} + 12 q^{37} - 18 q^{38} - 6 q^{40} - 12 q^{41} - 6 q^{43} - 3 q^{44} - 9 q^{45} + 15 q^{46} + 24 q^{47} - 9 q^{51} - 3 q^{52} - 18 q^{55} + 24 q^{58} - 24 q^{59} - 3 q^{61} + 9 q^{62} - 18 q^{63} - 3 q^{64} - 12 q^{65} - 9 q^{66} + 3 q^{67} + 9 q^{68} - 45 q^{69} + 3 q^{70} - 12 q^{71} + 3 q^{73} + 18 q^{75} - 18 q^{76} - 12 q^{77} - 9 q^{78} + 33 q^{79} - 6 q^{80} + 24 q^{82} - 6 q^{86} + 18 q^{87} - 12 q^{88} + 21 q^{89} + 18 q^{90} - 12 q^{92} - 27 q^{93} + 6 q^{94} - 12 q^{95} - 9 q^{96} - 15 q^{97} - 3 q^{98} + 9 q^{99}+O(q^{100}) \) 6 * q + 3 * q^5 - 3 * q^8 + 3 * q^10 + 6 * q^11 + 9 * q^12 - 3 * q^13 + 9 * q^15 + 9 * q^18 + 3 * q^19 + 3 * q^20 + 6 * q^22 + 6 * q^23 + 9 * q^25 - 27 * q^27 + 6 * q^28 - 3 * q^29 + 9 * q^30 - 3 * q^31 - 18 * q^33 - 9 * q^34 + 3 * q^35 + 12 * q^37 - 18 * q^38 - 6 * q^40 - 12 * q^41 - 6 * q^43 - 3 * q^44 - 9 * q^45 + 15 * q^46 + 24 * q^47 - 9 * q^51 - 3 * q^52 - 18 * q^55 + 24 * q^58 - 24 * q^59 - 3 * q^61 + 9 * q^62 - 18 * q^63 - 3 * q^64 - 12 * q^65 - 9 * q^66 + 3 * q^67 + 9 * q^68 - 45 * q^69 + 3 * q^70 - 12 * q^71 + 3 * q^73 + 18 * q^75 - 18 * q^76 - 12 * q^77 - 9 * q^78 + 33 * q^79 - 6 * q^80 + 24 * q^82 - 6 * q^86 + 18 * q^87 - 12 * q^88 + 21 * q^89 + 18 * q^90 - 12 * q^92 - 27 * q^93 + 6 * q^94 - 12 * q^95 - 9 * q^96 - 15 * q^97 - 3 * q^98 + 9 * q^99

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