LMFDB - Embedded newform 504.2.cj.e.37.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [504,2,Mod(37,504)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("504.37"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(504, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 3, 0, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.cj (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [32,-2,0,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(4)] == traces)

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

Self dual:	no
Analytic conductor:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 168)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			37.3
Character	$\chi$	$=$	504.37
Dual form			504.2.cj.e.109.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.10325 - 0.884778i) q^{2} +(0.434335 + 1.95227i) q^{4} +(-0.0402223 - 0.0232224i) q^{5} +(-1.97032 + 1.76574i) q^{7} +(1.24814 - 2.53814i) q^{8} +(0.0238287 + 0.0612079i) q^{10} +(-3.11586 + 1.79894i) q^{11} -6.29415i q^{13} +(3.73605 - 0.204763i) q^{14} +(-3.62271 + 1.69588i) q^{16} +(-0.258110 - 0.447060i) q^{17} +(-2.80834 - 1.62140i) q^{19} +(0.0278663 - 0.0886110i) q^{20} +(5.02925 + 0.772156i) q^{22} +(3.47322 - 6.01578i) q^{23} +(-2.49892 - 4.32826i) q^{25} +(-5.56893 + 6.94404i) q^{26} +(-4.30298 - 3.07967i) q^{28} -2.29579i q^{29} +(-1.05460 - 1.82662i) q^{31} +(5.49724 + 1.33431i) q^{32} +(-0.110788 + 0.721591i) q^{34} +(0.120255 - 0.0252667i) q^{35} +(-1.12720 - 0.650790i) q^{37} +(1.66374 + 4.27357i) q^{38} +(-0.109145 + 0.0731049i) q^{40} -10.1883 q^{41} +9.12162i q^{43} +(-4.86535 - 5.30165i) q^{44} +(-9.15447 + 3.56391i) q^{46} +(2.32465 - 4.02641i) q^{47} +(0.764321 - 6.95815i) q^{49} +(-1.07261 + 6.98616i) q^{50} +(12.2879 - 2.73377i) q^{52} +(-4.91727 + 2.83899i) q^{53} +0.167103 q^{55} +(2.02245 + 7.20484i) q^{56} +(-2.03126 + 2.53284i) q^{58} +(1.42910 - 0.825090i) q^{59} +(-1.10386 - 0.637312i) q^{61} +(-0.452663 + 2.94831i) q^{62} +(-4.88428 - 6.33591i) q^{64} +(-0.146165 + 0.253165i) q^{65} +(-6.72366 + 3.88191i) q^{67} +(0.760675 - 0.698075i) q^{68} +(-0.155028 - 0.0785238i) q^{70} -11.8320 q^{71} +(5.57028 + 9.64802i) q^{73} +(0.667784 + 1.71531i) q^{74} +(1.94564 - 6.18687i) q^{76} +(2.96278 - 9.04630i) q^{77} +(-2.75086 + 4.76463i) q^{79} +(0.185096 + 0.0159156i) q^{80} +(11.2403 + 9.01443i) q^{82} +8.25030i q^{83} +0.0239757i q^{85} +(8.07061 - 10.0635i) q^{86} +(0.676926 + 10.1538i) q^{88} +(7.38218 - 12.7863i) q^{89} +(11.1138 + 12.4015i) q^{91} +(13.2530 + 4.16778i) q^{92} +(-6.12716 + 2.38535i) q^{94} +(0.0753053 + 0.130433i) q^{95} -6.16464 q^{97} +(-6.99966 + 7.00034i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 2 q^{2} - 2 q^{4} + 16 q^{8} + 6 q^{10} - 22 q^{14} - 10 q^{16} + 40 q^{20} - 12 q^{22} + 8 q^{23} + 16 q^{25} - 6 q^{26} - 26 q^{28} - 24 q^{31} + 8 q^{32} - 24 q^{34} + 26 q^{38} - 6 q^{40} - 20 q^{44}+ \cdots + 64 q^{98}+O(q^{100}) $ 32 * q - 2 * q^2 - 2 * q^4 + 16 * q^8 + 6 * q^10 - 22 * q^14 - 10 * q^16 + 40 * q^20 - 12 * q^22 + 8 * q^23 + 16 * q^25 - 6 * q^26 - 26 * q^28 - 24 * q^31 + 8 * q^32 - 24 * q^34 + 26 * q^38 - 6 * q^40 - 20 * q^44 + 16 * q^46 + 24 * q^47 + 8 * q^49 - 52 * q^50 + 44 * q^52 - 64 * q^55 - 40 * q^56 + 34 * q^58 - 100 * q^62 - 20 * q^64 - 16 * q^68 + 38 * q^70 + 80 * q^71 + 8 * q^73 - 10 * q^74 - 32 * q^76 + 8 * q^79 + 56 * q^80 + 22 * q^86 + 50 * q^88 - 64 * q^92 - 48 * q^94 - 24 * q^95 - 48 * q^97 + 64 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$-1$	$1$

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 $

$2$	−1.10325	−	0.884778i	−0.780118	−	0.625633i
$2$	−1.10325	−	0.884778i	−0.780118	−	0.625633i
$3$		0			0
$3$		0			0
$4$	0.434335	+	1.95227i	0.217168	+	0.976134i
$5$	−0.0402223	−	0.0232224i	−0.0179880	−	0.0103854i	0.490979	−	0.871171i	$-0.336639\pi$
$5$	−0.0402223	−	0.0232224i	−0.0179880	−	0.0103854i	−0.508967	+	0.860786i	$0.669972\pi$
$6$		0			0
$7$	−1.97032	+	1.76574i	−0.744711	+	0.667387i
$7$	−1.97032	+	1.76574i	−0.744711	+	0.667387i
$8$	1.24814	−	2.53814i	0.441285	−	0.897367i
$9$		0			0
$10$	0.0238287	+	0.0612079i	0.00753531	+	0.0193556i
$11$	−3.11586	+	1.79894i	−0.939468	+	0.542402i	−0.889793	−	0.456364i	$-0.849152\pi$
$11$	−3.11586	+	1.79894i	−0.939468	+	0.542402i	−0.0496743	+	0.998765i	$0.515818\pi$
$12$		0			0
$13$		−	6.29415i		−	1.74568i	−0.488004	−	0.872842i	$-0.662275\pi$
$13$		−	6.29415i		−	1.74568i	0.488004	−	0.872842i	$-0.337725\pi$
$14$	3.73605	−	0.204763i	0.998501	−	0.0547252i
$15$		0			0
$16$	−3.62271	+	1.69588i	−0.905676	+	0.423970i
$17$	−0.258110	−	0.447060i	−0.0626010	−	0.108428i	0.833026	−	0.553233i	$-0.186606\pi$
$17$	−0.258110	−	0.447060i	−0.0626010	−	0.108428i	−0.895627	+	0.444805i	$0.853273\pi$
$18$		0			0
$19$	−2.80834	−	1.62140i	−0.644278	−	0.371974i	0.141983	−	0.989869i	$-0.454652\pi$
$19$	−2.80834	−	1.62140i	−0.644278	−	0.371974i	−0.786261	+	0.617895i	$0.787986\pi$
$20$	0.0278663	−	0.0886110i	0.00623109	−	0.0198140i
$21$		0			0
$22$	5.02925	+	0.772156i	1.07224	+	0.164624i
$23$	3.47322	−	6.01578i	0.724215	−	1.25438i	−0.235081	−	0.971976i	$-0.575535\pi$
$23$	3.47322	−	6.01578i	0.724215	−	1.25438i	0.959296	−	0.282402i	$-0.0911312\pi$
$24$		0			0
$25$	−2.49892	−	4.32826i	−0.499784	−	0.865652i
$26$	−5.56893	+	6.94404i	−1.09216	+	1.36184i
$27$		0			0
$28$	−4.30298	−	3.07967i	−0.813187	−	0.582003i
$29$		−	2.29579i		−	0.426317i	−0.977018	−	0.213159i	$-0.931625\pi$
$29$		−	2.29579i		−	0.426317i	0.977018	−	0.213159i	$-0.0683751\pi$
$30$		0			0
$31$	−1.05460	−	1.82662i	−0.189411	−	0.328070i	0.755643	−	0.654984i	$-0.227325\pi$
$31$	−1.05460	−	1.82662i	−0.189411	−	0.328070i	−0.945054	+	0.326914i	$0.893991\pi$
$32$	5.49724	+	1.33431i	0.971784	+	0.235874i
$33$		0			0
$34$	−0.110788	+	0.721591i	−0.0190000	+	0.123752i
$35$	0.120255	−	0.0252667i	0.0203269	−	0.00427085i
$36$		0			0
$37$	−1.12720	−	0.650790i	−0.185311	−	0.106989i	0.404475	−	0.914549i	$-0.367454\pi$
$37$	−1.12720	−	0.650790i	−0.185311	−	0.106989i	−0.589785	+	0.807560i	$0.700788\pi$
$38$	1.66374	+	4.27357i	0.269894	+	0.693265i
$39$		0			0
$40$	−0.109145	+	0.0731049i	−0.0172573	+	0.0115589i
$41$	−10.1883			−1.59115			−0.795576	−	0.605854i	$-0.792832\pi$
$41$	−10.1883			−1.59115			−0.795576	+	0.605854i	$0.792832\pi$
$42$		0			0
$43$			9.12162i			1.39103i	0.718510	+	0.695517i	$0.244824\pi$
$43$			9.12162i			1.39103i	−0.718510	+	0.695517i	$0.755176\pi$
$44$	−4.86535	−	5.30165i	−0.733479	−	0.799255i
$45$		0			0
$46$	−9.15447	+	3.56391i	−1.34975	+	0.525470i
$47$	2.32465	−	4.02641i	0.339085	−	0.587313i	−0.645176	−	0.764034i	$-0.723216\pi$
$47$	2.32465	−	4.02641i	0.339085	−	0.587313i	0.984261	+	0.176722i	$0.0565492\pi$
$48$		0			0
$49$	0.764321	−	6.95815i	0.109189	−	0.994021i
$50$	−1.07261	+	6.98616i	−0.151689	+	0.987992i
$51$		0			0
$52$	12.2879	−	2.73377i	1.70402	−	0.379106i
$53$	−4.91727	+	2.83899i	−0.675439	+	0.389965i	−0.798134	−	0.602480i	$-0.794179\pi$
$53$	−4.91727	+	2.83899i	−0.675439	+	0.389965i	0.122696	+	0.992444i	$0.460846\pi$
$54$		0			0
$55$	0.167103			0.0225321
$56$	2.02245	+	7.20484i	0.270261	+	0.962787i
$57$		0			0
$58$	−2.03126	+	2.53284i	−0.266718	+	0.332578i
$59$	1.42910	−	0.825090i	0.186053	−	0.107418i	−0.404081	−	0.914723i	$-0.632409\pi$
$59$	1.42910	−	0.825090i	0.186053	−	0.107418i	0.590133	+	0.807306i	$0.299075\pi$
$60$		0			0
$61$	−1.10386	−	0.637312i	−0.141334	−	0.0815995i	0.427665	−	0.903937i	$-0.359336\pi$
$61$	−1.10386	−	0.637312i	−0.141334	−	0.0815995i	−0.569000	+	0.822338i	$0.692669\pi$
$62$	−0.452663	+	2.94831i	−0.0574882	+	0.374436i
$63$		0			0
$64$	−4.88428	−	6.33591i	−0.610535	−	0.791989i
$65$	−0.146165	+	0.253165i	−0.0181295	+	0.0314013i
$66$		0			0
$67$	−6.72366	+	3.88191i	−0.821426	+	0.474251i	−0.850908	−	0.525315i	$-0.823948\pi$
$67$	−6.72366	+	3.88191i	−0.821426	+	0.474251i	0.0294820	+	0.999565i	$0.490614\pi$
$68$	0.760675	−	0.698075i	0.0922454	−	0.0846540i
$69$		0			0
$70$	−0.155028	−	0.0785238i	−0.0185293	−	0.00938539i
$71$	−11.8320			−1.40420			−0.702099	−	0.712080i	$-0.747753\pi$
$71$	−11.8320			−1.40420			−0.702099	+	0.712080i	$0.747753\pi$
$72$		0			0
$73$	5.57028	+	9.64802i	0.651953	+	1.12921i	0.982649	+	0.185478i	$0.0593832\pi$
$73$	5.57028	+	9.64802i	0.651953	+	1.12921i	−0.330696	+	0.943737i	$0.607283\pi$
$74$	0.667784	+	1.71531i	0.0776283	+	0.199401i
$75$		0			0
$76$	1.94564	−	6.18687i	0.223180	−	0.709683i
$77$	2.96278	−	9.04630i	0.337640	−	1.03092i
$78$		0			0
$79$	−2.75086	+	4.76463i	−0.309496	+	0.536063i	−0.978252	−	0.207419i	$-0.933494\pi$
$79$	−2.75086	+	4.76463i	−0.309496	+	0.536063i	0.668756	+	0.743482i	$0.266827\pi$
$80$	0.185096	+	0.0159156i	0.0206943	+	0.00177942i
$81$		0			0
$82$	11.2403	+	9.01443i	1.24129	+	0.995477i
$83$			8.25030i			0.905588i	0.891615	+	0.452794i	$0.149573\pi$
$83$			8.25030i			0.905588i	−0.891615	+	0.452794i	$0.850427\pi$
$84$		0			0
$85$			0.0239757i			0.00260053i
$86$	8.07061	−	10.0635i	0.870276	−	1.08517i
$87$		0			0
$88$	0.676926	+	10.1538i	0.0721605	+	1.08240i
$89$	7.38218	−	12.7863i	0.782510	−	1.35535i	−0.147966	−	0.988993i	$-0.547273\pi$
$89$	7.38218	−	12.7863i	0.782510	−	1.35535i	0.930475	−	0.366354i	$-0.119394\pi$
$90$		0			0
$91$	11.1138	+	12.4015i	1.16505	+	1.30003i
$92$	13.2530	+	4.16778i	1.38172	+	0.434521i
$93$		0			0
$94$	−6.12716	+	2.38535i	−0.631968	+	0.246030i
$95$	0.0753053	+	0.130433i	0.00772616	+	0.0133821i
$96$		0			0
$97$	−6.16464			−0.625925			−0.312962	−	0.949766i	$-0.601321\pi$
$97$	−6.16464			−0.625925			−0.312962	+	0.949766i	$0.601321\pi$
$98$	−6.99966	+	7.00034i	−0.707072	+	0.707142i
$99$		0			0
$100$	7.36455	−	6.75848i	0.736455	−	0.675848i
$101$	6.93470	−	4.00375i	0.690029	−	0.398388i	−0.113594	−	0.993527i	$-0.536236\pi$
$101$	6.93470	−	4.00375i	0.690029	−	0.398388i	0.803623	+	0.595139i	$0.202903\pi$
$102$		0			0
$103$	6.43821	−	11.1513i	0.634376	−	1.09877i	−0.352271	−	0.935898i	$-0.614591\pi$
$103$	6.43821	−	11.1513i	0.634376	−	1.09877i	0.986647	−	0.162873i	$-0.0520761\pi$
$104$	−15.9754	−	7.85600i	−1.56652	−	0.770344i
$105$		0			0
$106$	7.93686	+	1.21857i	0.770896	+	0.118358i
$107$	−8.84815	−	5.10848i	−0.855383	−	0.493856i	0.00708048	−	0.999975i	$-0.497746\pi$
$107$	−8.84815	−	5.10848i	−0.855383	−	0.493856i	−0.862463	+	0.506119i	$0.831080\pi$
$108$		0			0
$109$	10.1275	−	5.84714i	0.970043	−	0.560054i	0.0707935	−	0.997491i	$-0.477447\pi$
$109$	10.1275	−	5.84714i	0.970043	−	0.560054i	0.899249	+	0.437437i	$0.144114\pi$
$110$	−0.184357	−	0.147849i	−0.0175777	−	0.0140968i
$111$		0			0
$112$	4.14341	−	9.73818i	0.391515	−	0.920172i
$113$	9.08476			0.854623			0.427311	−	0.904105i	$-0.359461\pi$
$113$	9.08476			0.854623			0.427311	+	0.904105i	$0.359461\pi$
$114$		0			0
$115$	−0.279401	+	0.161312i	−0.0260543	+	0.0150425i
$116$	4.48200	−	0.997143i	0.416143	−	0.0925824i
$117$		0			0
$118$	−2.30668	−	0.354151i	−0.212347	−	0.0326023i
$119$	1.29795	+	0.425096i	0.118983	+	0.0389685i
$120$		0			0
$121$	0.972397	−	1.68424i	0.0883997	−	0.153113i
$122$	0.653954	+	1.67979i	0.0592062	+	0.152081i
$123$		0			0
$124$	3.10800	−	2.85222i	0.279107	−	0.256137i
$125$			0.464347i			0.0415324i
$126$		0			0
$127$	14.1059			1.25170			0.625849	−	0.779944i	$-0.284753\pi$
$127$	14.1059			1.25170			0.625849	+	0.779944i	$0.284753\pi$
$128$	−0.217281	+	11.3116i	−0.0192051	+	0.999816i
$129$		0			0
$130$	0.385252	−	0.149982i	0.0337888	−	0.0131543i
$131$	14.8183	+	8.55535i	1.29468	+	0.747484i	0.979480	−	0.201541i	$-0.0645949\pi$
$131$	14.8183	+	8.55535i	1.29468	+	0.747484i	0.315200	+	0.949025i	$0.397928\pi$
$132$		0			0
$133$	8.39630	−	1.76413i	0.728052	−	0.152970i
$134$	10.8525	+	1.66622i	0.937516	+	0.143940i
$135$		0			0
$136$	−1.45686	+	0.0971245i	−0.124925	+	0.00832836i
$137$	−2.48594	−	4.30578i	−0.212388	−	0.367867i	0.740073	−	0.672526i	$-0.234791\pi$
$137$	−2.48594	−	4.30578i	−0.212388	−	0.367867i	−0.952462	+	0.304659i	$0.901458\pi$
$138$		0			0
$139$			5.20468i			0.441455i	0.975335	+	0.220728i	$0.0708432\pi$
$139$			5.20468i			0.441455i	−0.975335	+	0.220728i	$0.929157\pi$
$140$	0.101559	+	0.223797i	0.00858326	+	0.0189143i
$141$		0			0
$142$	13.0537	+	10.4687i	1.09544	+	0.878512i
$143$	11.3228	+	19.6117i	0.946862	+	1.64001i
$144$		0			0
$145$	−0.0533136	+	0.0923419i	−0.00442746	+	0.00766858i
$146$	2.39092	−	15.5727i	0.197874	−	1.28880i
$147$		0			0
$148$	0.780933	−	2.48326i	0.0641923	−	0.204123i
$149$	0.725874	+	0.419084i	0.0594659	+	0.0343327i	0.529438	−	0.848349i	$-0.322403\pi$
$149$	0.725874	+	0.419084i	0.0594659	+	0.0343327i	−0.469972	+	0.882681i	$0.655736\pi$
$150$		0			0
$151$	−3.21803	−	5.57379i	−0.261879	−	0.453588i	0.704862	−	0.709345i	$-0.251009\pi$
$151$	−3.21803	−	5.57379i	−0.261879	−	0.453588i	−0.966741	+	0.255756i	$0.917676\pi$
$152$	−7.62054	+	5.10422i	−0.618108	+	0.414007i
$153$		0			0
$154$	−11.2727	+	7.35896i	−0.908377	+	0.593002i
$155$			0.0979610i			0.00786842i
$156$		0			0
$157$	−4.73349	+	2.73288i	−0.377774	+	0.218108i	−0.676849	−	0.736122i	$-0.736655\pi$
$157$	−4.73349	+	2.73288i	−0.377774	+	0.218108i	0.299075	+	0.954229i	$0.403322\pi$
$158$	7.25054	−	2.82269i	0.576822	−	0.224561i
$159$		0			0
$160$	−0.190126	−	0.181328i	−0.0150308	−	0.0143352i
$161$	3.77897	+	17.9858i	0.297825	+	1.41748i
$162$		0			0
$163$	−13.2105	−	7.62708i	−1.03473	−	0.597399i	−0.116390	−	0.993204i	$-0.537132\pi$
$163$	−13.2105	−	7.62708i	−1.03473	−	0.597399i	−0.918335	+	0.395805i	$0.870466\pi$
$164$	−4.42516	−	19.8904i	−0.345547	−	1.55318i
$165$		0			0
$166$	7.29969	−	9.10217i	0.566566	−	0.706466i
$167$	1.77463			0.137325			0.0686625	−	0.997640i	$-0.478127\pi$
$167$	1.77463			0.137325			0.0686625	+	0.997640i	$0.478127\pi$
$168$		0			0
$169$	−26.6163			−2.04741
$170$	0.0212132	−	0.0264513i	0.00162698	−	0.00202872i
$171$		0			0
$172$	−17.8078	+	3.96184i	−1.35784	+	0.302087i
$173$	2.23631	+	1.29114i	0.170024	+	0.0981633i	0.582597	−	0.812761i	$-0.302037\pi$
$173$	2.23631	+	1.29114i	0.170024	+	0.0981633i	−0.412573	+	0.910924i	$0.635370\pi$
$174$		0			0
$175$	12.5663	+	4.11561i	0.949920	+	0.311111i
$176$	8.23706	−	11.8012i	0.620892	−	0.889546i
$177$		0			0
$178$	−19.4575	+	7.57495i	−1.45840	+	0.567767i
$179$	−17.0438	+	9.84027i	−1.27392	+	0.735496i	−0.975723	−	0.219009i	$-0.929718\pi$
$179$	−17.0438	+	9.84027i	−1.27392	+	0.735496i	−0.298194	+	0.954505i	$0.596384\pi$
$180$		0			0
$181$		−	25.5613i		−	1.89996i	−0.312315	−	0.949979i	$-0.601104\pi$
$181$		−	25.5613i		−	1.89996i	0.312315	−	0.949979i	$-0.398896\pi$
$182$	−1.28881	−	23.5153i	−0.0955329	−	1.74307i
$183$		0			0
$184$	−10.9338	−	16.3241i	−0.806052	−	1.20343i
$185$	0.0302257	+	0.0523525i	0.00222224	+	0.00384903i
$186$		0			0
$187$	1.60847	+	0.928652i	0.117623	+	0.0679098i
$188$	8.87032	+	2.78953i	0.646934	+	0.203447i
$189$		0			0
$190$	0.0323231	−	0.210529i	0.00234496	−	0.0152734i
$191$	−6.98804	+	12.1036i	−0.505637	+	0.875788i	0.494342	+	0.869267i	$0.335409\pi$
$191$	−6.98804	+	12.1036i	−0.505637	+	0.875788i	−0.999979	+	0.00652098i	$0.997924\pi$
$192$		0			0
$193$	9.00706	+	15.6007i	0.648342	+	1.12296i	0.983519	+	0.180806i	$0.0578707\pi$
$193$	9.00706	+	15.6007i	0.648342	+	1.12296i	−0.335176	+	0.942155i	$0.608796\pi$
$194$	6.80116	+	5.45434i	0.488295	+	0.391599i
$195$		0			0
$196$	13.9161	−	1.53001i	0.994010	−	0.109286i
$197$			3.70082i			0.263672i	0.991272	+	0.131836i	$0.0420873\pi$
$197$			3.70082i			0.263672i	−0.991272	+	0.131836i	$0.957913\pi$
$198$		0			0
$199$	0.882192	+	1.52800i	0.0625369	+	0.108317i	0.895599	−	0.444863i	$-0.146748\pi$
$199$	0.882192	+	1.52800i	0.0625369	+	0.108317i	−0.833062	+	0.553180i	$0.813414\pi$
$200$	−14.1047	+	0.940321i	−0.997355	+	0.0664907i
$201$		0			0
$202$	−11.1932	−	1.71852i	−0.787549	−	0.120915i
$203$	4.05377	+	4.52344i	0.284519	+	0.317483i
$204$		0			0
$205$	0.409799	+	0.236597i	0.0286216	+	0.0165247i
$206$	−16.9694	+	6.60633i	−1.18231	+	0.460285i
$207$		0			0
$208$	10.6741	+	22.8019i	0.740117	+	1.58102i
$209$	11.6672			0.807038
$210$		0			0
$211$		−	10.6757i		−	0.734945i	−0.930034	−	0.367473i	$-0.880223\pi$
$211$		−	10.6757i		−	0.734945i	0.930034	−	0.367473i	$-0.119777\pi$
$212$	−7.67821	−	8.36676i	−0.527341	−	0.574631i
$213$		0			0
$214$	5.24188	+	13.4646i	0.358327	+	0.920421i
$215$	0.211825	−	0.366892i	0.0144464	−	0.0250218i
$216$		0			0
$217$	5.30323	+	1.73688i	0.360007	+	0.117907i
$218$	−16.3467	−	2.50975i	−1.10714	−	0.169982i
$219$		0			0
$220$	0.0725787	+	0.326230i	0.00489325	+	0.0219944i
$221$	−2.81386	+	1.62459i	−0.189281	+	0.109281i
$222$		0			0
$223$	−22.2212			−1.48804			−0.744020	−	0.668158i	$-0.767083\pi$
$223$	−22.2212			−1.48804			−0.744020	+	0.668158i	$0.767083\pi$
$224$	−13.1874	+	7.07768i	−0.881117	+	0.472898i
$225$		0			0
$226$	−10.0228	−	8.03800i	−0.666706	−	0.534680i
$227$	17.0728	−	9.85697i	1.13316	−	0.654230i	0.188432	−	0.982086i	$-0.439660\pi$
$227$	17.0728	−	9.85697i	1.13316	−	0.654230i	0.944728	+	0.327856i	$0.106326\pi$
$228$		0			0
$229$	6.06806	+	3.50340i	0.400989	+	0.231511i	0.686911	−	0.726742i	$-0.258966\pi$
$229$	6.06806	+	3.50340i	0.400989	+	0.231511i	−0.285922	+	0.958253i	$0.592300\pi$
$230$	0.450976	+	0.0692397i	0.0297365	+	0.00456553i
$231$		0			0
$232$	−5.82703	−	2.86547i	−0.382563	−	0.188128i
$233$	−12.3717	+	21.4284i	−0.810495	+	1.40382i	0.102023	+	0.994782i	$0.467468\pi$
$233$	−12.3717	+	21.4284i	−0.810495	+	1.40382i	−0.912518	+	0.409036i	$0.865865\pi$
$234$		0			0
$235$	−0.187006	+	0.107968i	−0.0121989	+	0.00704303i
$236$	2.23150	+	2.43162i	0.145259	+	0.158285i
$237$		0			0
$238$	−1.05585	−	1.61739i	−0.0684409	−	0.104840i
$239$	−21.9503			−1.41985			−0.709924	−	0.704278i	$-0.751271\pi$
$239$	−21.9503			−1.41985			−0.709924	+	0.704278i	$0.751271\pi$
$240$		0			0
$241$	7.39162	+	12.8027i	0.476136	+	0.824692i	0.999626	−	0.0273397i	$-0.00870359\pi$
$241$	7.39162	+	12.8027i	0.476136	+	0.824692i	−0.523490	+	0.852032i	$0.675370\pi$
$242$	−2.56298	+	0.997789i	−0.164755	+	0.0641403i
$243$		0			0
$244$	0.764761	−	2.43183i	0.0489588	−	0.155682i
$245$	−0.192327	+	0.262123i	−0.0122873	+	0.0167464i
$246$		0			0
$247$	−10.2053	+	17.6761i	−0.649349	+	1.12471i
$248$	−5.95250	+	0.396836i	−0.377984	+	0.0251991i
$249$		0			0
$250$	0.410844	−	0.512292i	0.0259841	−	0.0324002i
$251$		−	14.4785i		−	0.913876i	−0.889499	−	0.456938i	$-0.848946\pi$
$251$		−	14.4785i		−	0.913876i	0.889499	−	0.456938i	$-0.151054\pi$
$252$		0			0
$253$			24.9925i			1.57126i
$254$	−15.5624	−	12.4806i	−0.976472	−	0.783103i
$255$		0			0
$256$	10.2480	−	12.2873i	0.640499	−	0.767959i
$257$	7.93731	−	13.7478i	0.495116	−	0.857566i	−0.504868	−	0.863196i	$-0.668459\pi$
$257$	7.93731	−	13.7478i	0.495116	−	0.857566i	0.999984	+	0.00563049i	$0.00179225\pi$
$258$		0			0
$259$	3.37007	−	0.708080i	0.209406	−	0.0439980i
$260$	−0.557731	−	0.175395i	−0.0345890	−	0.0108775i
$261$		0			0
$262$	−8.77875	−	22.5496i	−0.542353	−	1.39312i
$263$	0.162710	+	0.281822i	0.0100331	+	0.0173779i	0.870998	−	0.491286i	$-0.163473\pi$
$263$	0.162710	+	0.281822i	0.0100331	+	0.0173779i	−0.860965	+	0.508664i	$0.830140\pi$
$264$		0			0
$265$	0.263712			0.0161997
$266$	−10.8241	−	5.48258i	−0.663669	−	0.336158i
$267$		0			0
$268$	−10.4989	−	11.4403i	−0.641319	−	0.698830i
$269$	−20.3761	+	11.7642i	−1.24235	+	0.717273i	−0.969573	−	0.244803i	$-0.921277\pi$
$269$	−20.3761	+	11.7642i	−1.24235	+	0.717273i	−0.272780	+	0.962076i	$0.587943\pi$
$270$		0			0
$271$	−0.751567	+	1.30175i	−0.0456544	+	0.0790758i	−0.887950	−	0.459941i	$-0.847871\pi$
$271$	−0.751567	+	1.30175i	−0.0456544	+	0.0790758i	0.842295	+	0.539017i	$0.181204\pi$
$272$	1.69322	+	1.18184i	0.102666	+	0.0716598i
$273$		0			0
$274$	−1.06703	+	6.94987i	−0.0644619	+	0.419857i
$275$	15.5726	+	8.99084i	0.939062	+	0.542168i
$276$		0			0
$277$	−12.6685	+	7.31418i	−0.761178	+	0.439466i	−0.829719	−	0.558182i	$-0.811499\pi$
$277$	−12.6685	+	7.31418i	−0.761178	+	0.439466i	0.0685405	+	0.997648i	$0.478166\pi$
$278$	4.60499	−	5.74208i	0.276189	−	0.344387i
$279$		0			0
$280$	0.0859657	−	0.336761i	0.00513743	−	0.0201253i
$281$	−21.3285			−1.27235			−0.636175	−	0.771545i	$-0.719484\pi$
$281$	−21.3285			−1.27235			−0.636175	+	0.771545i	$0.719484\pi$
$282$		0			0
$283$	15.0068	−	8.66416i	0.892059	−	0.515031i	0.0174438	−	0.999848i	$-0.494447\pi$
$283$	15.0068	−	8.66416i	0.892059	−	0.515031i	0.874616	+	0.484817i	$0.161114\pi$
$284$	−5.13905	−	23.0992i	−0.304946	−	1.37068i
$285$		0			0
$286$	4.86007	−	31.6549i	0.287382	−	1.87179i
$287$	20.0743	−	17.9900i	1.18495	−	1.06191i
$288$		0			0
$289$	8.36676	−	14.4917i	0.492162	−	0.852450i
$290$	0.140521	−	0.0547058i	0.00825165	−	0.00321243i
$291$		0			0
$292$	−16.4161	+	15.0652i	−0.960682	+	0.881622i
$293$		−	29.6927i		−	1.73466i	−0.497730	−	0.867332i	$-0.665833\pi$
$293$		−	29.6927i		−	1.73466i	0.497730	−	0.867332i	$-0.334167\pi$
$294$		0			0
$295$	−0.0766421			−0.00446228
$296$	−3.05870	+	2.04871i	−0.177783	+	0.119079i
$297$		0			0
$298$	−0.430027	−	1.10459i	−0.0249108	−	0.0639873i
$299$	−37.8643	−	21.8609i	−2.18975	−	1.26425i
$300$		0			0
$301$	−16.1064	−	17.9725i	−0.928358	−	1.03592i
$302$	−1.38127	+	8.99654i	−0.0794829	+	0.517693i
$303$		0			0
$304$	12.9235	+	1.11124i	0.741213	+	0.0637338i
$305$	0.0295998	+	0.0512683i	0.00169488	+	0.00293562i
$306$		0			0
$307$		−	4.88243i		−	0.278655i	−0.990246	−	0.139327i	$-0.955506\pi$
$307$		−	4.88243i		−	0.278655i	0.990246	−	0.139327i	$-0.0444940\pi$
$308$	18.9476	+	1.85501i	1.07964	+	0.105699i
$309$		0			0
$310$	0.0866738	−	0.108076i	0.00492274	−	0.00613829i
$311$	9.08277	+	15.7318i	0.515036	+	0.892069i	0.999848	+	0.0174504i	$0.00555493\pi$
$311$	9.08277	+	15.7318i	0.515036	+	0.892069i	−0.484811	+	0.874619i	$0.661112\pi$
$312$		0			0
$313$	6.80533	−	11.7872i	0.384660	−	0.666251i	−0.607062	−	0.794655i	$-0.707652\pi$
$313$	6.80533	−	11.7872i	0.384660	−	0.666251i	0.991722	+	0.128404i	$0.0409853\pi$
$314$	7.64023	+	1.17303i	0.431163	+	0.0661978i
$315$		0			0
$316$	−10.4966	−	3.30097i	−0.590482	−	0.185694i
$317$	21.6407	+	12.4943i	1.21546	+	0.701749i	0.963944	−	0.266103i	$-0.0857363\pi$
$317$	21.6407	+	12.4943i	1.21546	+	0.701749i	0.251520	+	0.967852i	$0.419070\pi$
$318$		0			0
$319$	4.13000	+	7.15336i	0.231235	+	0.400511i
$320$	0.0493221	+	0.368269i	0.00275719	+	0.0205869i
$321$		0			0
$322$	11.7443	−	23.1865i	0.654484	−	1.29213i
$323$			1.67400i			0.0931437i
$324$		0			0
$325$	−27.2427	+	15.7286i	−1.51115	+	0.872465i
$326$	7.82624	+	20.1029i	0.433455	+	1.11340i
$327$		0			0
$328$	−12.7165	+	25.8594i	−0.702152	+	1.42785i
$329$	2.52929	+	12.0380i	0.139445	+	0.663679i
$330$		0			0
$331$	−6.34783	−	3.66492i	−0.348908	−	0.201442i	0.315296	−	0.948993i	$-0.397896\pi$
$331$	−6.34783	−	3.66492i	−0.348908	−	0.201442i	−0.664204	+	0.747551i	$0.731229\pi$
$332$	−16.1068	+	3.58340i	−0.883976	+	0.196665i
$333$		0			0
$334$	−1.95787	−	1.57015i	−0.107130	−	0.0859150i
$335$	0.360588			0.0197010
$336$		0			0
$337$	1.49107			0.0812237			0.0406118	−	0.999175i	$-0.487069\pi$
$337$	1.49107			0.0812237			0.0406118	+	0.999175i	$0.487069\pi$
$338$	29.3646	+	23.5495i	1.59722	+	1.28093i
$339$		0			0
$340$	−0.0468070	+	0.0104135i	−0.00253847	+	0.000564751i
$341$	6.57197	+	3.79433i	0.355892	+	0.205474i
$342$		0			0
$343$	10.7803	+	15.0594i	0.582083	+	0.813129i
$344$	23.1519	+	11.3851i	1.24827	+	0.613842i
$345$		0			0
$346$	−1.32485	−	3.40309i	−0.0712244	−	0.182951i
$347$	20.6494	−	11.9219i	1.10852	−	0.640003i	0.170073	−	0.985431i	$-0.445600\pi$
$347$	20.6494	−	11.9219i	1.10852	−	0.640003i	0.938445	+	0.345428i	$0.112266\pi$
$348$		0			0
$349$			11.5733i			0.619504i	0.950817	+	0.309752i	$0.100246\pi$
$349$			11.5733i			0.619504i	−0.950817	+	0.309752i	$0.899754\pi$
$350$	−10.2224	−	15.6589i	−0.546408	−	0.837004i
$351$		0			0
$352$	−19.5290	+	5.73171i	−1.04090	+	0.305501i
$353$	5.01488	+	8.68603i	0.266915	+	0.462311i	0.968064	−	0.250705i	$-0.0806623\pi$
$353$	5.01488	+	8.68603i	0.266915	+	0.462311i	−0.701148	+	0.713015i	$0.747329\pi$
$354$		0			0
$355$	0.475909	+	0.274766i	0.0252586	+	0.0145831i
$356$	28.1687	+	8.85845i	1.49294	+	0.469497i
$357$		0			0
$358$	27.5101	+	4.22371i	1.45396	+	0.223230i
$359$	1.80639	−	3.12876i	0.0953375	−	0.165129i	−0.814412	−	0.580287i	$-0.802940\pi$
$359$	1.80639	−	3.12876i	0.0953375	−	0.165129i	0.909749	+	0.415158i	$0.136274\pi$
$360$		0			0
$361$	−4.24214	−	7.34760i	−0.223271	−	0.386716i
$362$	−22.6161	+	28.2006i	−1.18868	+	1.48219i
$363$		0			0
$364$	−19.3839	+	27.0836i	−1.01599	+	1.41957i
$365$		−	0.517420i		−	0.0270830i
$366$		0			0
$367$	−11.0055	−	19.0620i	−0.574480	−	0.995029i	−0.996098	−	0.0882554i	$-0.971871\pi$
$367$	−11.0055	−	19.0620i	−0.574480	−	0.995029i	0.421617	−	0.906774i	$-0.361463\pi$
$368$	−2.38039	+	27.6836i	−0.124087	+	1.44311i
$369$		0			0
$370$	0.0129737	−	0.0845012i	0.000674471	−	0.00439301i
$371$	4.67568	−	14.2763i	0.242749	−	0.741190i
$372$		0			0
$373$	27.9915	+	16.1609i	1.44934	+	0.836780i	0.998442	−	0.0557935i	$-0.0177688\pi$
$373$	27.9915	+	16.1609i	1.44934	+	0.836780i	0.450903	+	0.892573i	$0.351102\pi$
$374$	−0.952901	−	2.44768i	−0.0492734	−	0.126566i
$375$		0			0
$376$	−7.31809	−	10.9258i	−0.377402	−	0.563456i
$377$	−14.4500			−0.744215
$378$		0			0
$379$		−	16.6668i		−	0.856115i	−0.903751	−	0.428058i	$-0.859198\pi$
$379$		−	16.6668i		−	0.856115i	0.903751	−	0.428058i	$-0.140802\pi$
$380$	−0.221932	+	0.203668i	−0.0113849	+	0.0104479i
$381$		0			0
$382$	18.4186	−	7.17051i	0.942378	−	0.366875i
$383$	12.1998	−	21.1307i	0.623383	−	1.07973i	−0.365468	−	0.930824i	$-0.619091\pi$
$383$	12.1998	−	21.1307i	0.623383	−	1.07973i	0.988851	−	0.148907i	$-0.0475755\pi$
$384$		0			0
$385$	−0.329246	+	0.295060i	−0.0167799	+	0.0150377i
$386$	3.86608	−	25.1808i	0.196778	−	1.28167i
$387$		0			0
$388$	−2.67752	−	12.0350i	−0.135931	−	0.610986i
$389$	7.38356	−	4.26290i	0.374362	−	0.216138i	−0.301001	−	0.953624i	$-0.597321\pi$
$389$	7.38356	−	4.26290i	0.374362	−	0.216138i	0.675362	+	0.737486i	$0.263987\pi$
$390$		0			0
$391$	−3.58589			−0.181346
$392$	−16.7067	−	10.6247i	−0.843818	−	0.536629i
$393$		0			0
$394$	3.27440	−	4.08294i	0.164962	−	0.205696i
$395$	0.221292	−	0.127763i	0.0111344	−	0.00642845i
$396$		0			0
$397$	5.91805	+	3.41679i	0.297019	+	0.171484i	0.641103	−	0.767455i	$-0.278477\pi$
$397$	5.91805	+	3.41679i	0.297019	+	0.171484i	−0.344084	+	0.938939i	$0.611811\pi$
$398$	0.378661	−	2.46632i	0.0189806	−	0.123625i
$399$		0			0
$400$	16.3931	+	11.4421i	0.819653	+	0.572107i
$401$	−5.24408	+	9.08301i	−0.261877	+	0.453584i	−0.966741	−	0.255759i	$-0.917675\pi$
$401$	−5.24408	+	9.08301i	−0.261877	+	0.453584i	0.704864	+	0.709343i	$0.251008\pi$
$402$		0			0
$403$	−11.4970	+	6.63780i	−0.572707	+	0.330652i
$404$	10.8284	+	11.7994i	0.538733	+	0.587044i
$405$		0			0
$406$	−0.470093	−	8.57719i	−0.0233303	−	0.425679i
$407$	4.68294			0.232125
$408$		0			0
$409$	−4.01466	−	6.95360i	−0.198512	−	0.343833i	0.749534	−	0.661966i	$-0.230278\pi$
$409$	−4.01466	−	6.95360i	−0.198512	−	0.343833i	−0.948046	+	0.318133i	$0.896944\pi$
$410$	−0.242775	−	0.623608i	−0.0119898	−	0.0307978i
$411$		0			0
$412$	24.5667	+	7.72571i	1.21031	+	0.380618i
$413$	−1.35888	+	4.14911i	−0.0668663	+	0.204164i
$414$		0			0
$415$	0.191591	−	0.331846i	0.00940485	−	0.0162897i
$416$	8.39833	−	34.6004i	0.411762	−	1.69643i
$417$		0			0
$418$	−12.8719	−	10.3229i	−0.629585	−	0.504909i
$419$			16.7264i			0.817139i	0.912727	+	0.408570i	$0.133972\pi$
$419$			16.7264i			0.817139i	−0.912727	+	0.408570i	$0.866028\pi$
$420$		0			0
$421$			14.7157i			0.717199i	0.933492	+	0.358599i	$0.116746\pi$
$421$			14.7157i			0.717199i	−0.933492	+	0.358599i	$0.883254\pi$
$422$	−9.44562	+	11.7780i	−0.459806	+	0.573344i
$423$		0			0
$424$	1.06828	+	16.0242i	0.0518804	+	0.778202i
$425$	−1.28999	+	2.23434i	−0.0625739	+	0.108381i
$426$		0			0
$427$	3.30028	−	0.693416i	0.159712	−	0.0335568i
$428$	6.13006	−	19.4928i	0.296308	−	0.942218i
$429$		0			0
$430$	−0.558315	+	0.217357i	−0.0269244	+	0.0104819i
$431$	−1.57036	−	2.71995i	−0.0756416	−	0.131015i	0.825723	−	0.564075i	$-0.190767\pi$
$431$	−1.57036	−	2.71995i	−0.0756416	−	0.131015i	−0.901365	+	0.433060i	$0.857434\pi$
$432$		0			0
$433$	33.6748			1.61831			0.809155	−	0.587595i	$-0.199925\pi$
$433$	33.6748			1.61831			0.809155	+	0.587595i	$0.199925\pi$
$434$	−4.31406	−	6.60840i	−0.207081	−	0.317213i
$435$		0			0
$436$	15.8139	+	17.2321i	0.757350	+	0.825266i
$437$	−19.5080	+	11.2629i	−0.933192	+	0.538779i
$438$		0			0
$439$	3.68016	−	6.37423i	0.175645	−	0.304225i	−0.764740	−	0.644340i	$-0.777132\pi$
$439$	3.68016	−	6.37423i	0.175645	−	0.304225i	0.940384	+	0.340114i	$0.110466\pi$
$440$	0.208568	−	0.424130i	0.00994310	−	0.0202196i
$441$		0			0
$442$	4.54180	+	0.697317i	0.216032	+	0.0331680i
$443$	−22.3955	−	12.9300i	−1.06404	−	0.614325i	−0.137494	−	0.990503i	$-0.543905\pi$
$443$	−22.3955	−	12.9300i	−1.06404	−	0.614325i	−0.926547	+	0.376178i	$0.877238\pi$
$444$		0			0
$445$	−0.593857	+	0.342863i	−0.0281515	+	0.0162533i
$446$	24.5156	+	19.6608i	1.16085	+	0.930966i
$447$		0			0
$448$	20.8112	+	3.85941i	0.983236	+	0.182340i
$449$	19.7508			0.932096			0.466048	−	0.884759i	$-0.345677\pi$
$449$	19.7508			0.932096			0.466048	+	0.884759i	$0.345677\pi$
$450$		0			0
$451$	31.7455	−	18.3283i	1.49484	−	0.863044i
$452$	3.94583	+	17.7359i	0.185596	+	0.834227i
$453$		0			0
$454$	−27.5568	−	4.23088i	−1.29331	−	0.198565i
$455$	−0.159032	−	0.756906i	−0.00745555	−	0.0354843i
$456$		0			0
$457$	−1.28552	+	2.22658i	−0.0601339	+	0.104155i	−0.894525	−	0.447018i	$-0.852486\pi$
$457$	−1.28552	+	2.22658i	−0.0601339	+	0.104155i	0.834391	+	0.551173i	$0.185819\pi$
$458$	−3.59488	−	9.23402i	−0.167978	−	0.431478i
$459$		0			0
$460$	−0.436279	−	0.475403i	−0.0203416	−	0.0221658i
$461$			30.2081i			1.40693i	0.710728	+	0.703467i	$0.248366\pi$
$461$			30.2081i			1.40693i	−0.710728	+	0.703467i	$0.751634\pi$
$462$		0			0
$463$	−20.1707			−0.937412			−0.468706	−	0.883354i	$-0.655280\pi$
$463$	−20.1707			−0.937412			−0.468706	+	0.883354i	$0.655280\pi$
$464$	3.89338	+	8.31697i	0.180746	+	0.386106i
$465$		0			0
$466$	32.6084	−	12.6947i	1.51056	−	0.588072i
$467$	7.99333	+	4.61495i	0.369887	+	0.213554i	0.673409	−	0.739270i	$-0.264829\pi$
$467$	7.99333	+	4.61495i	0.369887	+	0.213554i	−0.303522	+	0.952824i	$0.598163\pi$
$468$		0			0
$469$	6.39332	−	19.5208i	0.295216	−	0.901389i
$470$	0.301842	+	0.0463427i	0.0139229	+	0.00213763i
$471$		0			0
$472$	−0.310474	−	4.65707i	−0.0142907	−	0.214359i
$473$	−16.4093	−	28.4217i	−0.754499	−	1.30683i
$474$		0			0
$475$			16.2070i			0.743627i
$476$	−0.266155	+	2.71859i	−0.0121992	+	0.124606i
$477$		0			0
$478$	24.2168	+	19.4212i	1.10765	+	0.888303i
$479$	−19.6055	−	33.9577i	−0.895797	−	1.55157i	−0.832815	−	0.553551i	$-0.813272\pi$
$479$	−19.6055	−	33.9577i	−0.895797	−	1.55157i	−0.0629820	−	0.998015i	$-0.520061\pi$
$480$		0			0
$481$	−4.09617	+	7.09477i	−0.186769	+	0.323494i
$482$	3.17269	−	20.6645i	0.144512	−	0.941243i
$483$		0			0
$484$	3.71044	+	1.16685i	0.168656	+	0.0530389i
$485$	0.247956	+	0.143157i	0.0112591	+	0.00650045i
$486$		0			0
$487$	−3.06454	−	5.30794i	−0.138868	−	0.240526i	0.788201	−	0.615418i	$-0.211013\pi$
$487$	−3.06454	−	5.30794i	−0.138868	−	0.240526i	−0.927068	+	0.374893i	$0.877680\pi$
$488$	−2.99536	+	2.00628i	−0.135593	+	0.0908202i
$489$		0			0
$490$	0.444107	−	0.119021i	0.0200627	−	0.00537684i
$491$			20.5291i			0.926463i	0.886237	+	0.463232i	$0.153310\pi$
$491$			20.5291i			0.926463i	−0.886237	+	0.463232i	$0.846690\pi$
$492$		0			0
$493$	−1.02636	+	0.592567i	−0.0462248	+	0.0266879i
$494$	26.8985	−	10.4718i	1.21022	−	0.471149i
$495$		0			0
$496$	6.91822	+	4.82883i	0.310637	+	0.216821i
$497$	23.3128	−	20.8922i	1.04572	−	0.937143i
$498$		0			0
$499$	−9.57940	−	5.53067i	−0.428833	−	0.247587i	0.270016	−	0.962856i	$-0.412971\pi$
$499$	−9.57940	−	5.53067i	−0.428833	−	0.247587i	−0.698849	+	0.715269i	$0.746304\pi$
$500$	−0.906530	+	0.201682i	−0.0405412	+	0.00901950i
$501$		0			0
$502$	−12.8103	+	15.9735i	−0.571751	+	0.712931i
$503$	−2.64242			−0.117820			−0.0589099	−	0.998263i	$-0.518762\pi$
$503$	−2.64242			−0.117820			−0.0589099	+	0.998263i	$0.518762\pi$
$504$		0			0
$505$	−0.371906			−0.0165496
$506$	22.1128	−	27.5730i	0.983034	−	1.22577i
$507$		0			0
$508$	6.12670	+	27.5385i	0.271828	+	1.22183i
$509$	−28.9903	−	16.7376i	−1.28497	−	0.741880i	−0.307220	−	0.951638i	$-0.599399\pi$
$509$	−28.9903	−	16.7376i	−1.28497	−	0.741880i	−0.977753	+	0.209758i	$0.932732\pi$
$510$		0			0
$511$	−28.0111	−	9.17400i	−1.23914	−	0.405834i
$512$	−22.1777	+	4.48885i	−0.980125	+	0.198381i
$513$		0			0
$514$	−20.9206	+	8.14458i	−0.922770	+	0.359242i
$515$	−0.517919	+	0.299021i	−0.0228222	+	0.0131764i
$516$		0			0
$517$			16.7277i			0.735682i
$518$	−4.34454	−	2.20057i	−0.190888	−	0.0966877i
$519$		0			0
$520$	0.460133	+	0.686973i	0.0201782	+	0.0301258i
$521$	−12.4133	−	21.5005i	−0.543837	−	0.941954i	−0.998679	−	0.0513815i	$-0.983638\pi$
$521$	−12.4133	−	21.5005i	−0.543837	−	0.941954i	0.454842	−	0.890572i	$-0.349696\pi$
$522$		0			0
$523$	−4.00205	−	2.31058i	−0.174997	−	0.101035i	0.409943	−	0.912111i	$-0.365549\pi$
$523$	−4.00205	−	2.31058i	−0.174997	−	0.101035i	−0.584940	+	0.811076i	$0.698882\pi$
$524$	−10.2662	+	32.6452i	−0.448482	+	1.42611i
$525$		0			0
$526$	0.0698396	−	0.454883i	0.00304515	−	0.0198338i
$527$	−0.544406	+	0.942938i	−0.0237147	+	0.0410750i
$528$		0			0
$529$	−12.6264	−	21.8696i	−0.548976	−	0.950854i
$530$	−0.290941	−	0.233326i	−0.0126377	−	0.0101350i
$531$		0			0
$532$	7.09087	+	15.6256i	0.307428	+	0.677456i
$533$			64.1270i			2.77765i
$534$		0			0
$535$	0.237262	+	0.410950i	0.0102577	+	0.0177669i
$536$	1.46073	+	21.9107i	0.0630937	+	0.946400i
$537$		0			0
$538$	32.8887	+	5.04950i	1.41793	+	0.217699i
$539$	10.1358	+	23.0556i	0.436580	+	0.993075i
$540$		0			0
$541$	21.7241	+	12.5424i	0.933992	+	0.539241i	0.888072	−	0.459704i	$-0.152045\pi$
$541$	21.7241	+	12.5424i	0.933992	+	0.539241i	0.0459203	+	0.998945i	$0.485378\pi$
$542$	1.98093	−	0.771192i	0.0850882	−	0.0331255i
$543$		0			0
$544$	−0.822378	−	2.80199i	−0.0352592	−	0.120135i
$545$	−0.543137			−0.0232654
$546$		0			0
$547$		−	38.8014i		−	1.65903i	−0.558487	−	0.829514i	$-0.688618\pi$
$547$		−	38.8014i		−	1.65903i	0.558487	−	0.829514i	$-0.311382\pi$
$548$	7.32630	−	6.72338i	0.312964	−	0.287208i
$549$		0			0
$550$	−9.22561	−	23.6975i	−0.393381	−	1.01046i
$551$	−3.72239	+	6.44736i	−0.158579	+	0.274667i
$552$		0			0
$553$	−2.99303	−	14.2452i	−0.127276	−	0.605766i
$554$	20.4480	+	3.13945i	0.868753	+	0.133382i
$555$		0			0
$556$	−10.1609	+	2.26058i	−0.430920	+	0.0958699i
$557$	27.2335	−	15.7233i	1.15392	−	0.666217i	0.204082	−	0.978954i	$-0.434579\pi$
$557$	27.2335	−	15.7233i	1.15392	−	0.666217i	0.949840	+	0.312737i	$0.101246\pi$
$558$		0			0
$559$	57.4128			2.42830
$560$	−0.392801	+	0.295472i	−0.0165989	+	0.0124860i
$561$		0			0
$562$	23.5307	+	18.8710i	0.992583	+	0.796024i
$563$	9.22107	−	5.32379i	0.388622	−	0.224371i	−0.292941	−	0.956131i	$-0.594634\pi$
$563$	9.22107	−	5.32379i	0.388622	−	0.224371i	0.681563	+	0.731760i	$0.261301\pi$
$564$		0			0
$565$	−0.365410	−	0.210970i	−0.0153729	−	0.00887556i
$566$	−24.2221	−	3.71889i	−1.01813	−	0.156317i
$567$		0			0
$568$	−14.7680	+	30.0312i	−0.619651	+	1.26008i
$569$	13.1394	−	22.7581i	0.550832	−	0.954069i	−0.447383	−	0.894343i	$-0.647644\pi$
$569$	13.1394	−	22.7581i	0.550832	−	0.954069i	0.998215	−	0.0597265i	$-0.0190229\pi$
$570$		0			0
$571$	6.37133	−	3.67849i	0.266632	−	0.153940i	−0.360724	−	0.932673i	$-0.617470\pi$
$571$	6.37133	−	3.67849i	0.266632	−	0.153940i	0.627356	+	0.778733i	$0.284137\pi$
$572$	−33.3694	+	30.6232i	−1.39525	+	1.28042i
$573$		0			0
$574$	−38.0642	+	2.08620i	−1.58877	+	0.0870761i
$575$	−34.7172			−1.44781
$576$		0			0
$577$	6.42935	+	11.1360i	0.267658	+	0.463596i	0.968256	−	0.249959i	$-0.0804171\pi$
$577$	6.42935	+	11.1360i	0.267658	+	0.463596i	−0.700599	+	0.713555i	$0.747084\pi$
$578$	−22.0525	+	8.58524i	−0.917265	+	0.357099i
$579$		0			0
$580$	−0.203432	−	0.0639752i	−0.00844706	−	0.00265642i
$581$	−14.5679	−	16.2557i	−0.604378	−	0.674402i
$582$		0			0
$583$	10.2144	−	17.6918i	0.423035	−	0.732719i
$584$	31.4405	−	2.09605i	1.30102	−	0.0867350i
$585$		0			0
$586$	−26.2714	+	32.7585i	−1.08526	+	1.35324i
$587$		−	7.51402i		−	0.310137i	−0.987904	−	0.155068i	$-0.950440\pi$
$587$		−	7.51402i		−	0.310137i	0.987904	−	0.155068i	$-0.0495598\pi$
$588$		0			0
$589$			6.83969i			0.281825i
$590$	0.0845556	+	0.0678113i	0.00348110	+	0.00279174i
$591$		0			0
$592$	5.18718	+	0.446024i	0.213192	+	0.0183315i
$593$	9.63761	−	16.6928i	0.395769	−	0.685492i	−0.597430	−	0.801921i	$-0.703811\pi$
$593$	9.63761	−	16.6928i	0.395769	−	0.685492i	0.993199	+	0.116429i	$0.0371448\pi$
$594$		0			0
$595$	−0.0423349	−	0.0472398i	−0.00173556	−	0.00193664i
$596$	−0.502891	+	1.59912i	−0.0205992	+	0.0655027i
$597$		0			0
$598$	22.4318	+	57.6196i	0.917304	+	2.35624i
$599$	−7.76773	−	13.4541i	−0.317381	−	0.549720i	0.662560	−	0.749009i	$-0.269470\pi$
$599$	−7.76773	−	13.4541i	−0.317381	−	0.549720i	−0.979941	+	0.199289i	$0.936137\pi$
$600$		0			0
$601$	−44.5011			−1.81524			−0.907620	−	0.419793i	$-0.862103\pi$
$601$	−44.5011			−1.81524			−0.907620	+	0.419793i	$0.862103\pi$
$602$	1.86777	+	34.0788i	0.0761246	+	1.38895i
$603$		0			0
$604$	9.48383	−	8.70335i	0.385892	−	0.354134i
$605$	−0.0782241	+	0.0451627i	−0.00318026	+	0.00183612i
$606$		0			0
$607$	11.9183	−	20.6432i	0.483751	−	0.837881i	−0.516075	−	0.856543i	$-0.672607\pi$
$607$	11.9183	−	20.6432i	0.483751	−	0.837881i	0.999826	+	0.0186624i	$0.00594079\pi$
$608$	−13.2747	−	12.6604i	−0.538360	−	0.513447i
$609$		0			0
$610$	0.0127050	−	0.0827512i	0.000514412	−	0.00335050i
$611$	−25.3428	−	14.6317i	−1.02526	−	0.591935i
$612$		0			0
$613$	−17.7261	+	10.2342i	−0.715950	+	0.413354i	−0.813260	−	0.581900i	$-0.802310\pi$
$613$	−17.7261	+	10.2342i	−0.715950	+	0.413354i	0.0973099	+	0.995254i	$0.468976\pi$
$614$	−4.31986	+	5.38655i	−0.174336	+	0.217384i
$615$		0			0
$616$	−19.2628	−	18.8110i	−0.776119	−	0.757917i
$617$	−19.3039			−0.777146			−0.388573	−	0.921418i	$-0.627032\pi$
$617$	−19.3039			−0.777146			−0.388573	+	0.921418i	$0.627032\pi$
$618$		0			0
$619$	21.1475	−	12.2095i	0.849990	−	0.490742i	−0.0106577	−	0.999943i	$-0.503393\pi$
$619$	21.1475	−	12.2095i	0.849990	−	0.490742i	0.860647	+	0.509201i	$0.170059\pi$
$620$	−0.191246	+	0.0425479i	−0.00768063	+	0.00170877i
$621$		0			0
$622$	3.89857	−	25.3924i	0.156319	−	1.01814i
$623$	8.03205	+	38.2282i	0.321797	+	1.53158i
$624$		0			0
$625$	−12.4838	+	21.6226i	−0.499353	+	0.864905i
$626$	−17.9370	+	6.98304i	−0.716909	+	0.279098i
$627$		0			0
$628$	−7.39124	−	8.05406i	−0.294943	−	0.321392i
$629$			0.671902i			0.0267905i
$630$		0			0
$631$	−20.7613			−0.826494			−0.413247	−	0.910619i	$-0.635605\pi$
$631$	−20.7613			−0.826494			−0.413247	+	0.910619i	$0.635605\pi$
$632$	8.65982	+	12.9290i	0.344469	+	0.514288i
$633$		0			0
$634$	−12.8205	−	32.9316i	−0.509169	−	1.30788i
$635$	−0.567372	−	0.327573i	−0.0225155	−	0.0129993i
$636$		0			0
$637$	−43.7956	−	4.81075i	−1.73525	−	0.190609i
$638$	1.77271	−	11.5461i	0.0701822	−	0.457115i
$639$		0			0
$640$	0.271422	−	0.449934i	0.0107289	−	0.0177852i
$641$	11.0483	+	19.1363i	0.436383	+	0.755838i	0.997407	−	0.0719616i	$-0.0229259\pi$
$641$	11.0483	+	19.1363i	0.436383	+	0.755838i	−0.561024	+	0.827799i	$0.689593\pi$
$642$		0			0
$643$			31.9358i			1.25943i	0.776828	+	0.629713i	$0.216827\pi$
$643$			31.9358i			1.25943i	−0.776828	+	0.629713i	$0.783173\pi$
$644$	−33.4718	+	15.1894i	−1.31897	+	0.598548i
$645$		0			0
$646$	1.48112	−	1.84684i	0.0582738	−	0.0726631i
$647$	1.48741	+	2.57626i	0.0584760	+	0.101283i	0.893781	−	0.448503i	$-0.148043\pi$
$647$	1.48741	+	2.57626i	0.0584760	+	0.101283i	−0.835305	+	0.549786i	$0.814709\pi$
$648$		0			0
$649$	−2.96858	+	5.14173i	−0.116527	+	0.201831i
$650$	43.9719	+	6.75114i	1.72472	+	0.264802i
$651$		0			0
$652$	9.15232	−	29.1031i	0.358433	−	1.13977i
$653$	−14.9217	−	8.61507i	−0.583933	−	0.337134i	0.178762	−	0.983892i	$-0.442791\pi$
$653$	−14.9217	−	8.61507i	−0.583933	−	0.337134i	−0.762695	+	0.646758i	$0.776124\pi$
$654$		0			0
$655$	−0.397351	−	0.688231i	−0.0155258	−	0.0268914i
$656$	36.9094	−	17.2782i	1.44107	−	0.674600i
$657$		0			0
$658$	7.86055	−	15.5189i	0.306436	−	0.604989i
$659$		−	27.7588i		−	1.08133i	−0.841238	−	0.540665i	$-0.818173\pi$
$659$		−	27.7588i		−	1.08133i	0.841238	−	0.540665i	$-0.181827\pi$
$660$		0			0
$661$	−28.3232	+	16.3524i	−1.10164	+	0.636034i	−0.936652	−	0.350261i	$-0.886093\pi$
$661$	−28.3232	+	16.3524i	−1.10164	+	0.636034i	−0.164991	+	0.986295i	$0.552759\pi$
$662$	3.76062	+	9.65975i	0.146161	+	0.375437i
$663$		0			0
$664$	20.9404	+	10.2976i	0.812645	+	0.399623i
$665$	−0.378686	−	0.124024i	−0.0146848	−	0.00480946i
$666$		0			0
$667$	−13.8110	−	7.97377i	−0.534763	−	0.308746i
$668$	0.770785	+	3.46456i	0.0298226	+	0.134048i
$669$		0			0
$670$	−0.397820	−	0.319040i	−0.0153691	−	0.0123256i
$671$	4.58596			0.177039
$672$		0			0
$673$	12.9387			0.498752			0.249376	−	0.968407i	$-0.419775\pi$
$673$	12.9387			0.498752			0.249376	+	0.968407i	$0.419775\pi$
$674$	−1.64503	−	1.31926i	−0.0633640	−	0.0508162i
$675$		0			0
$676$	−11.5604	−	51.9622i	−0.444631	−	1.99855i
$677$	1.12548	+	0.649798i	0.0432558	+	0.0249738i	0.521472	−	0.853268i	$-0.325383\pi$
$677$	1.12548	+	0.649798i	0.0432558	+	0.0249738i	−0.478216	+	0.878242i	$0.658716\pi$
$678$		0			0
$679$	12.1463	−	10.8852i	0.466133	−	0.417734i
$680$	0.0608537	+	0.0299251i	0.00233363	+	0.00114758i
$681$		0			0
$682$	−3.89341	−	10.0008i	−0.149086	−	0.382952i
$683$	16.8225	−	9.71249i	0.643696	−	0.371638i	−0.142341	−	0.989818i	$-0.545463\pi$
$683$	16.8225	−	9.71249i	0.643696	−	0.371638i	0.786037	+	0.618179i	$0.212130\pi$
$684$		0			0
$685$			0.230918i			0.00882291i
$686$	1.43077	−	26.1525i	0.0546271	−	0.998507i
$687$		0			0
$688$	−15.4692	−	33.0449i	−0.589756	−	1.25983i
$689$	17.8690	+	30.9500i	0.680755	+	1.17910i
$690$		0			0
$691$	−11.1725	−	6.45042i	−0.425020	−	0.245386i	0.272203	−	0.962240i	$-0.412248\pi$
$691$	−11.1725	−	6.45042i	−0.425020	−	0.245386i	−0.697223	+	0.716854i	$0.745581\pi$
$692$	−1.54933	+	4.92667i	−0.0588969	+	0.187284i
$693$		0			0
$694$	−33.3298	−	5.11722i	−1.26518	−	0.194247i
$695$	0.120865	−	0.209344i	0.00458467	−	0.00794088i
$696$		0			0
$697$	2.62972	+	4.55480i	0.0996076	+	0.172526i
$698$	10.2398	−	12.7683i	0.387582	−	0.483286i
$699$		0			0
$700$	−2.57680	+	26.3203i	−0.0973940	+	0.994812i
$701$		−	34.3868i		−	1.29877i	−0.760460	−	0.649385i	$-0.775026\pi$
$701$		−	34.3868i		−	1.29877i	0.760460	−	0.649385i	$-0.224974\pi$
$702$		0			0
$703$	2.11038	+	3.65528i	0.0795944	+	0.137862i
$704$	26.6167	+	10.9553i	1.00315	+	0.412893i
$705$		0			0
$706$	2.15253	−	14.0200i	0.0810114	−	0.527648i
$707$	−6.59400	+	20.1336i	−0.247993	+	0.757201i
$708$		0			0
$709$	19.7915	+	11.4266i	0.743284	+	0.429135i	0.823262	−	0.567661i	$-0.192152\pi$
$709$	19.7915	+	11.4266i	0.743284	+	0.429135i	−0.0799779	+	0.996797i	$0.525485\pi$
$710$	−0.281941	−	0.724211i	−0.0105811	−	0.0271791i
$711$		0			0
$712$	−23.2394	−	34.6961i	−0.870934	−	1.30029i
$713$	−14.6514			−0.548699
$714$		0			0
$715$		−	1.05177i		−	0.0393340i
$716$	−26.6136	−	29.0002i	−0.994597	−	1.08379i
$717$		0			0
$718$	−4.76116	+	1.85356i	−0.177685	+	0.0691741i
$719$	−5.21620	+	9.03472i	−0.194531	+	0.336938i	−0.946747	−	0.321979i	$-0.895652\pi$
$719$	−5.21620	+	9.03472i	−0.194531	+	0.336938i	0.752215	+	0.658917i	$0.228985\pi$
$720$		0			0
$721$	7.00498	+	33.3399i	0.260879	+	1.24164i
$722$	−1.82084	+	11.8596i	−0.0677648	+	0.441369i
$723$		0			0
$724$	49.9025	−	11.1022i	1.85461	−	0.412609i
$725$	−9.93677	+	5.73700i	−0.369042	+	0.213067i
$726$		0			0
$727$	−2.48753			−0.0922572			−0.0461286	−	0.998936i	$-0.514688\pi$
$727$	−2.48753			−0.0922572			−0.0461286	+	0.998936i	$0.514688\pi$
$728$	45.3483	−	12.7296i	1.68072	−	0.471791i
$729$		0			0
$730$	−0.457802	+	0.570846i	−0.0169440	+	0.0211279i
$731$	4.07791	−	2.35438i	0.150827	−	0.0870800i
$732$		0			0
$733$	0.674033	+	0.389153i	0.0248960	+	0.0143737i	0.512396	−	0.858749i	$-0.328758\pi$
$733$	0.674033	+	0.389153i	0.0248960	+	0.0143737i	−0.487500	+	0.873123i	$0.662091\pi$
$734$	−4.72385	+	30.7676i	−0.174360	+	1.13565i
$735$		0			0
$736$	27.1200	−	28.4359i	0.999656	−	1.04816i
$737$	13.9667	−	24.1910i	0.514469	−	0.891086i
$738$		0			0
$739$	−22.4331	+	12.9518i	−0.825215	+	0.476438i	−0.852212	−	0.523197i	$-0.824739\pi$
$739$	−22.4331	+	12.9518i	−0.825215	+	0.476438i	0.0269963	+	0.999636i	$0.491406\pi$
$740$	−0.0890781	+	0.0817473i	−0.00327458	+	0.00300509i
$741$		0			0
$742$	−17.7898	+	11.6135i	−0.653086	+	0.426344i
$743$	27.7729			1.01889			0.509445	−	0.860503i	$-0.329851\pi$
$743$	27.7729			1.01889			0.509445	+	0.860503i	$0.329851\pi$
$744$		0			0
$745$	−0.0194642	−	0.0337130i	−0.000713113	−	0.00123515i
$746$	−16.5829	−	42.5958i	−0.607143	−	1.55954i
$747$		0			0
$748$	−1.11436	+	3.54352i	−0.0407451	+	0.129564i
$749$	26.4539	−	5.55819i	0.966606	−	0.203092i
$750$		0			0
$751$	−10.5549	+	18.2816i	−0.385153	+	0.667105i	−0.991790	−	0.127874i	$-0.959185\pi$
$751$	−10.5549	+	18.2816i	−0.385153	+	0.667105i	0.606637	+	0.794979i	$0.292518\pi$
$752$	−1.59322	+	18.5288i	−0.0580986	+	0.675677i
$753$		0			0
$754$	15.9421	+	12.7851i	0.580576	+	0.465605i
$755$			0.298921i			0.0108788i
$756$		0			0
$757$		−	46.6419i		−	1.69523i	−0.530612	−	0.847615i	$-0.678038\pi$
$757$		−	46.6419i		−	1.69523i	0.530612	−	0.847615i	$-0.321962\pi$
$758$	−14.7464	+	18.3877i	−0.535614	+	0.667871i
$759$		0			0
$760$	0.425048	−	0.0283367i	0.0154181	−	0.00102788i
$761$	−12.5114	+	21.6703i	−0.453537	+	0.785550i	−0.998603	−	0.0528439i	$-0.983171\pi$
$761$	−12.5114	+	21.6703i	−0.453537	+	0.785550i	0.545066	+	0.838393i	$0.316505\pi$
$762$		0			0
$763$	−9.62997	+	29.4034i	−0.348628	+	1.06447i
$764$	−26.6647	−	8.38549i	−0.964695	−	0.303376i
$765$		0			0
$766$	−32.1555	+	12.5184i	−1.16183	+	0.452309i
$767$	−5.19324	−	8.99495i	−0.187517	−	0.324789i
$768$		0			0
$769$	1.32800			0.0478891			0.0239445	−	0.999713i	$-0.492377\pi$
$769$	1.32800			0.0478891			0.0239445	+	0.999713i	$0.492377\pi$
$770$	0.624305	−	0.0342165i	0.0224984	−	0.00123308i
$771$		0			0
$772$	−26.5446	+	24.3601i	−0.955363	+	0.876740i
$773$	19.2488	−	11.1133i	0.692332	−	0.399718i	−0.112153	−	0.993691i	$-0.535775\pi$
$773$	19.2488	−	11.1133i	0.692332	−	0.399718i	0.804485	+	0.593973i	$0.202441\pi$
$774$		0			0
$775$	−5.27072	+	9.12915i	−0.189330	+	0.327929i
$776$	−7.69435	+	15.6467i	−0.276211	+	0.561684i
$777$		0			0
$778$	−11.9177	−	1.82975i	−0.427269	−	0.0655999i
$779$	28.6124	+	16.5194i	1.02514	+	0.591867i
$780$		0			0
$781$	36.8668	−	21.2851i	1.31920	−	0.761639i
$782$	3.95615	+	3.17272i	0.141471	+	0.113456i
$783$		0			0
$784$	9.03126	+	26.5035i	0.322545	+	0.946554i
$785$	0.253856			0.00906050
$786$		0			0
$787$	16.5930	−	9.57996i	0.591476	−	0.341489i	−0.174205	−	0.984709i	$-0.555736\pi$
$787$	16.5930	−	9.57996i	0.591476	−	0.341489i	0.765681	+	0.643221i	$0.222402\pi$
$788$	−7.22499	+	1.60740i	−0.257380	+	0.0572611i
$789$		0			0
$790$	−0.357183	−	0.0548394i	−0.0127080	−	0.00195110i
$791$	−17.8999	+	16.0413i	−0.636447	+	0.570364i
$792$		0			0
$793$	−4.01134	+	6.94784i	−0.142447	+	0.246725i
$794$	−3.50601	−	9.00575i	−0.124424	−	0.319602i
$795$		0			0
$796$	−2.59990	+	2.38594i	−0.0921511	+	0.0845674i
$797$		−	35.9779i		−	1.27440i	−0.770697	−	0.637201i	$-0.780092\pi$
$797$		−	35.9779i		−	1.27440i	0.770697	−	0.637201i	$-0.219908\pi$
$798$		0			0
$799$	−2.40006			−0.0849082
$800$	−7.96194	−	27.1278i	−0.281497	−	0.959112i
$801$		0			0
$802$	13.8220	−	5.38101i	0.488071	−	0.190010i
$803$	−34.7125	−	20.0413i	−1.22498	−	0.707241i
$804$		0			0
$805$	0.265674	−	0.811187i	0.00936378	−	0.0285906i
$806$	18.5571	+	2.84913i	0.653646	+	0.100356i
$807$		0			0
$808$	−1.50657	−	22.5985i	−0.0530011	−	0.795012i
$809$	−4.56264	−	7.90272i	−0.160414	−	0.277845i	0.774603	−	0.632447i	$-0.217950\pi$
$809$	−4.56264	−	7.90272i	−0.160414	−	0.277845i	−0.935017	+	0.354603i	$0.884616\pi$
$810$		0			0
$811$			9.64051i			0.338524i	0.985571	+	0.169262i	$0.0541384\pi$
$811$			9.64051i			0.338524i	−0.985571	+	0.169262i	$0.945862\pi$
$812$	−7.07027	+	9.87873i	−0.248118	+	0.346676i
$813$		0			0
$814$	−5.16647	−	4.14336i	−0.181085	−	0.145225i
$815$	0.354237	+	0.613557i	0.0124084	+	0.0214920i
$816$		0			0
$817$	14.7898	−	25.6166i	0.517428	−	0.896212i
$818$	−1.72320	+	11.2237i	−0.0602504	+	0.392426i
$819$		0			0
$820$	−0.283912	+	0.902800i	−0.00991462	+	0.0315271i
$821$	16.6309	+	9.60187i	0.580423	+	0.335107i	0.761301	−	0.648398i	$-0.224561\pi$
$821$	16.6309	+	9.60187i	0.580423	+	0.335107i	−0.180878	+	0.983505i	$0.557894\pi$
$822$		0			0
$823$	0.820157	+	1.42055i	0.0285889	+	0.0495174i	0.879966	−	0.475037i	$-0.157565\pi$
$823$	0.820157	+	1.42055i	0.0285889	+	0.0495174i	−0.851377	+	0.524554i	$0.824232\pi$
$824$	−20.2677	−	30.2595i	−0.706060	−	1.05414i
$825$		0			0
$826$	5.17023	−	3.37520i	0.179895	−	0.117438i
$827$		−	27.3891i		−	0.952412i	−0.879334	−	0.476206i	$-0.842012\pi$
$827$		−	27.3891i		−	0.952412i	0.879334	−	0.476206i	$-0.157988\pi$
$828$		0			0
$829$	15.4922	−	8.94441i	0.538065	−	0.310652i	−0.206229	−	0.978504i	$-0.566119\pi$
$829$	15.4922	−	8.94441i	0.538065	−	0.310652i	0.744294	+	0.667852i	$0.232786\pi$
$830$	−0.504984	+	0.196594i	−0.0175282	+	0.00682389i
$831$		0			0
$832$	−39.8792	+	30.7424i	−1.38256	+	1.06580i
$833$	−3.30799	+	1.45427i	−0.114615	+	0.0503875i
$834$		0			0
$835$	−0.0713797	−	0.0412111i	−0.00247020	−	0.00142617i
$836$	5.06748	+	22.7775i	0.175263	+	0.787777i
$837$		0			0
$838$	14.7992	−	18.4535i	0.511229	−	0.637465i
$839$	−11.0644			−0.381986			−0.190993	−	0.981591i	$-0.561171\pi$
$839$	−11.0644			−0.381986			−0.190993	+	0.981591i	$0.561171\pi$
$840$		0			0
$841$	23.7294			0.818253
$842$	13.0201	−	16.2351i	0.448703	−	0.559499i
$843$		0			0
$844$	20.8418	−	4.63683i	0.717405	−	0.159606i
$845$	1.07057	+	0.618094i	0.0368287	+	0.0212631i
$846$		0			0
$847$	1.05800	+	5.03550i	0.0363533	+	0.173022i
$848$	12.9992	−	18.6239i	0.446396	−	0.639547i
$849$		0			0
$850$	3.40008	−	1.32368i	0.116622	−	0.0454018i
$851$	−7.83002	+	4.52067i	−0.268410	+	0.154966i
$852$		0			0
$853$		−	29.4621i		−	1.00876i	−0.863480	−	0.504382i	$-0.831720\pi$
$853$		−	29.4621i		−	1.00876i	0.863480	−	0.504382i	$-0.168280\pi$
$854$	−4.25456	−	2.15500i	−0.145588	−	0.0737426i
$855$		0			0
$856$	−24.0098	+	16.0817i	−0.820637	+	0.549661i
$857$	8.88103	+	15.3824i	0.303370	+	0.525453i	0.976897	−	0.213710i	$-0.0685548\pi$
$857$	8.88103	+	15.3824i	0.303370	+	0.525453i	−0.673527	+	0.739163i	$0.735221\pi$
$858$		0			0
$859$	−31.7456	−	18.3283i	−1.08314	−	0.625354i	−0.151402	−	0.988472i	$-0.548379\pi$
$859$	−31.7456	−	18.3283i	−1.08314	−	0.625354i	−0.931743	+	0.363118i	$0.881712\pi$
$860$	0.808276	+	0.254186i	0.0275620	+	0.00866766i
$861$		0			0
$862$	−0.674042	+	4.39021i	−0.0229580	+	0.149531i
$863$	−1.57129	+	2.72156i	−0.0534874	+	0.0926429i	−0.891529	−	0.452963i	$-0.850367\pi$
$863$	−1.57129	+	2.72156i	−0.0534874	+	0.0926429i	0.838042	+	0.545606i	$0.183700\pi$
$864$		0			0
$865$	−0.0599664	−	0.103865i	−0.00203892	−	0.00353151i
$866$	−37.1519	−	29.7948i	−1.26247	−	1.01247i
$867$		0			0
$868$	−1.08747	+	11.1077i	−0.0369110	+	0.377020i
$869$		−	19.7946i		−	0.671485i
$870$		0			0
$871$	24.4333	+	42.3197i	0.827891	+	1.43395i
$872$	−2.20022	−	33.0032i	−0.0745090	−	1.11763i
$873$		0			0
$874$	31.4874	+	4.83436i	1.06508	+	0.163525i
$875$	−0.819916	−	0.914912i	−0.0277182	−	0.0309297i
$876$		0			0
$877$	−12.4428	−	7.18384i	−0.420162	−	0.242581i	0.274984	−	0.961449i	$-0.411327\pi$
$877$	−12.4428	−	7.18384i	−0.420162	−	0.242581i	−0.695147	+	0.718868i	$0.744661\pi$
$878$	−9.69993	+	3.77626i	−0.327357	+	0.127443i
$879$		0			0
$880$	−0.605364	+	0.283386i	−0.0204068	+	0.00955294i
$881$	21.4314			0.722043			0.361022	−	0.932557i	$-0.382428\pi$
$881$	21.4314			0.722043			0.361022	+	0.932557i	$0.382428\pi$
$882$		0			0
$883$			29.5761i			0.995316i	0.867373	+	0.497658i	$0.165806\pi$
$883$			29.5761i			0.995316i	−0.867373	+	0.497658i	$0.834194\pi$
$884$	−4.39379	−	4.78780i	−0.147779	−	0.161031i
$885$		0			0
$886$	13.2677	+	34.0801i	0.445736	+	1.14494i
$887$	−1.90744	+	3.30379i	−0.0640456	+	0.110930i	−0.896270	−	0.443508i	$-0.853734\pi$
$887$	−1.90744	+	3.30379i	−0.0640456	+	0.110930i	0.832225	+	0.554439i	$0.187067\pi$
$888$		0			0
$889$	−27.7932	+	24.9074i	−0.932153	+	0.835367i
$890$	0.958532	+	0.147166i	0.0321301	+	0.00493303i
$891$		0			0
$892$	−9.65144	−	43.3817i	−0.323154	−	1.45253i
$893$	−13.0568	+	7.53836i	−0.436930	+	0.252262i
$894$		0			0
$895$	0.914057			0.0305536
$896$	−19.5453	−	22.6712i	−0.652962	−	0.757391i
$897$		0			0
$898$	−21.7901	−	17.4750i	−0.727145	−	0.583150i
$899$	−4.19353	+	2.42114i	−0.139862	+	0.0807494i
$900$		0			0
$901$	2.53840	+	1.46554i	0.0845662	+	0.0488243i
$902$	−51.2397	−	7.86699i	−1.70610	−	0.261942i
$903$		0			0
$904$	11.3391	−	23.0584i	0.377132	−	0.766910i
$905$	−0.593594	+	1.02813i	−0.0197317	+	0.0341763i
$906$		0			0
$907$	4.23020	−	2.44231i	0.140462	−	0.0810955i	−0.428122	−	0.903721i	$-0.640825\pi$
$907$	4.23020	−	2.44231i	0.140462	−	0.0810955i	0.568584	+	0.822625i	$0.307491\pi$
$908$	26.6588	+	29.0494i	0.884702	+	0.964038i
$909$		0			0
$910$	−0.494241	+	0.975767i	−0.0163839	+	0.0323464i
$911$	47.3325			1.56820			0.784098	−	0.620637i	$-0.213126\pi$
$911$	47.3325			1.56820			0.784098	+	0.620637i	$0.213126\pi$
$912$		0			0
$913$	−14.8418	−	25.7068i	−0.491193	−	0.850771i
$914$	3.38828	−	1.31908i	0.112074	−	0.0436314i
$915$		0			0
$916$	−4.20400	+	13.3681i	−0.138904	+	0.441696i
$917$	−44.3033	+	9.30849i	−1.46302	+	0.307394i
$918$		0			0
$919$	15.5826	−	26.9898i	0.514022	−	0.890312i	−0.485846	−	0.874044i	$-0.661488\pi$
$919$	15.5826	−	26.9898i	0.514022	−	0.890312i	0.999868	−	0.0162672i	$-0.00517825\pi$
$920$	0.0607003	+	0.910500i	0.00200123	+	0.0300183i
$921$		0			0
$922$	26.7275	−	33.3272i	0.880223	−	1.09757i
$923$			74.4722i			2.45128i
$924$		0			0
$925$			6.50509i			0.213886i
$926$	22.2534	+	17.8466i	0.731292	+	0.586476i
$927$		0			0
$928$	3.06329	−	12.6205i	0.100557	−	0.414288i
$929$	−14.3019	+	24.7717i	−0.469231	+	0.812733i	−0.999381	−	0.0351712i	$-0.988802\pi$
$929$	−14.3019	+	24.7717i	−0.469231	+	0.812733i	0.530150	+	0.847904i	$0.322136\pi$
$930$		0			0
$931$	−13.4284	+	18.3016i	−0.440098	+	0.599811i
$932$	−47.2074	−	14.8457i	−1.54633	−	0.486288i
$933$		0			0
$934$	−4.73546	−	12.1638i	−0.154949	−	0.398011i
$935$	−0.0431310	−	0.0747050i	−0.00141053	−	0.00244312i
$936$		0			0
$937$	5.62816			0.183864			0.0919320	−	0.995765i	$-0.470696\pi$
$937$	5.62816			0.183864			0.0919320	+	0.995765i	$0.470696\pi$
$938$	−24.3251	+	15.8798i	−0.794242	+	0.518493i
$939$		0			0
$940$	−0.292005	−	0.318191i	−0.00952415	−	0.0103782i
$941$	−29.2442	+	16.8842i	−0.953334	+	0.550408i	−0.894115	−	0.447837i	$-0.852194\pi$
$941$	−29.2442	+	16.8842i	−0.953334	+	0.550408i	−0.0592190	+	0.998245i	$0.518861\pi$
$942$		0			0
$943$	−35.3863	+	61.2909i	−1.15234	+	1.99591i
$944$	−3.77795	+	5.41263i	−0.122962	+	0.176166i
$945$		0			0
$946$	−7.04331	+	45.8749i	−0.228998	+	1.49152i
$947$	−10.1554	−	5.86321i	−0.330005	−	0.190529i	0.325838	−	0.945426i	$-0.394354\pi$
$947$	−10.1554	−	5.86321i	−0.330005	−	0.190529i	−0.655843	+	0.754897i	$0.727687\pi$
$948$		0			0
$949$	60.7261	−	35.0602i	1.97125	−	1.13810i
$950$	14.3396	−	17.8804i	0.465237	−	0.580117i
$951$		0			0
$952$	2.69898	−	2.76380i	0.0874745	−	0.0895753i
$953$	−37.7047			−1.22137			−0.610687	−	0.791872i	$-0.709107\pi$
$953$	−37.7047			−1.22137			−0.610687	+	0.791872i	$0.709107\pi$
$954$		0			0
$955$	0.562150	−	0.324557i	0.0181907	−	0.0105024i
$956$	−9.53380	−	42.8529i	−0.308345	−	1.38596i
$957$		0			0
$958$	−8.41521	+	54.8104i	−0.271883	+	1.77084i
$959$	12.5010	+	4.09423i	0.403678	+	0.132210i
$960$		0			0
$961$	13.2756	−	22.9941i	0.428247	−	0.741745i
$962$	10.7964	−	4.20313i	0.348090	−	0.135514i
$963$		0			0
$964$	−21.7838	+	19.9911i	−0.701609	+	0.643869i
$965$		−	0.836660i		−	0.0269330i
$966$		0			0
$967$	−8.89648			−0.286092			−0.143046	−	0.989716i	$-0.545690\pi$
$967$	−8.89648			−0.286092			−0.143046	+	0.989716i	$0.545690\pi$
$968$	−3.06114	−	4.57025i	−0.0983889	−	0.146893i
$969$		0			0
$970$	−0.146896	−	0.377325i	−0.00471654	−	0.0121152i
$971$	52.8744	+	30.5270i	1.69682	+	0.979659i	0.948745	+	0.316044i	$0.102355\pi$
$971$	52.8744	+	30.5270i	1.69682	+	0.979659i	0.748074	+	0.663615i	$0.230979\pi$
$972$		0			0
$973$	−9.19012	−	10.2549i	−0.294622	−	0.328757i
$974$	−1.31539	+	8.56744i	−0.0421477	+	0.274519i
$975$		0			0
$976$	5.07975	+	0.436787i	0.162599	+	0.0139812i
$977$	23.8132	+	41.2456i	0.761851	+	1.31956i	0.941896	+	0.335906i	$0.109042\pi$
$977$	23.8132	+	41.2456i	0.761851	+	1.31956i	−0.180045	+	0.983658i	$0.557624\pi$
$978$		0			0
$979$			53.1205i			1.69774i
$980$	−0.595270	−	0.261625i	−0.0190152	−	0.00835731i
$981$		0			0
$982$	18.1637	−	22.6487i	0.579626	−	0.722750i
$983$	6.89129	+	11.9361i	0.219798	+	0.380701i	0.954746	−	0.297422i	$-0.0961268\pi$
$983$	6.89129	+	11.9361i	0.219798	+	0.380701i	−0.734948	+	0.678123i	$0.762793\pi$
$984$		0			0
$985$	0.0859417	−	0.148855i	0.00273833	−	0.00474293i
$986$	1.65662	+	0.254346i	0.0527576	+	0.00810003i
$987$		0			0
$988$	−38.9411	−	12.2462i	−1.23888	−	0.389602i
$989$	54.8737	+	31.6813i	1.74488	+	1.00741i
$990$		0			0
$991$	−4.32034	−	7.48305i	−0.137240	−	0.237707i	0.789211	−	0.614122i	$-0.210490\pi$
$991$	−4.32034	−	7.48305i	−0.137240	−	0.237707i	−0.926451	+	0.376415i	$0.877157\pi$
$992$	−3.36011	−	11.4485i	−0.106684	−	0.363491i
$993$		0			0
$994$	−44.2049	+	2.42275i	−1.40209	+	0.0768450i
$995$		−	0.0819463i		−	0.00259787i
$996$		0			0
$997$	−38.0017	+	21.9403i	−1.20353	+	0.694856i	−0.961337	−	0.275374i	$-0.911198\pi$
$997$	−38.0017	+	21.9403i	−1.20353	+	0.694856i	−0.242188	+	0.970229i	$0.577865\pi$
$998$	5.67509	+	14.5774i	0.179642	+	0.461439i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.cj.e.37.3		32
3.2	odd	2		168.2.bc.a.37.14	yes	32
4.3	odd	2		2016.2.cr.e.1297.8		32
7.4	even	3	inner	504.2.cj.e.109.14		32
8.3	odd	2		2016.2.cr.e.1297.9		32
8.5	even	2	inner	504.2.cj.e.37.14		32
12.11	even	2		672.2.bk.a.625.4		32
21.2	odd	6		1176.2.c.e.589.9		16
21.5	even	6		1176.2.c.f.589.9		16
21.11	odd	6		168.2.bc.a.109.3	yes	32
24.5	odd	2		168.2.bc.a.37.3	✓	32
24.11	even	2		672.2.bk.a.625.13		32
28.11	odd	6		2016.2.cr.e.1873.9		32
56.11	odd	6		2016.2.cr.e.1873.8		32
56.53	even	6	inner	504.2.cj.e.109.3		32
84.11	even	6		672.2.bk.a.529.13		32
84.23	even	6		4704.2.c.e.2353.5		16
84.47	odd	6		4704.2.c.f.2353.12		16
168.5	even	6		1176.2.c.f.589.10		16
168.11	even	6		672.2.bk.a.529.4		32
168.53	odd	6		168.2.bc.a.109.14	yes	32
168.107	even	6		4704.2.c.e.2353.12		16
168.131	odd	6		4704.2.c.f.2353.5		16
168.149	odd	6		1176.2.c.e.589.10		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.2.bc.a.37.3	✓	32	24.5	odd	2
168.2.bc.a.37.14	yes	32	3.2	odd	2
168.2.bc.a.109.3	yes	32	21.11	odd	6
168.2.bc.a.109.14	yes	32	168.53	odd	6
504.2.cj.e.37.3		32	1.1	even	1	trivial
504.2.cj.e.37.14		32	8.5	even	2	inner
504.2.cj.e.109.3		32	56.53	even	6	inner
504.2.cj.e.109.14		32	7.4	even	3	inner
672.2.bk.a.529.4		32	168.11	even	6
672.2.bk.a.529.13		32	84.11	even	6
672.2.bk.a.625.4		32	12.11	even	2
672.2.bk.a.625.13		32	24.11	even	2
1176.2.c.e.589.9		16	21.2	odd	6
1176.2.c.e.589.10		16	168.149	odd	6
1176.2.c.f.589.9		16	21.5	even	6
1176.2.c.f.589.10		16	168.5	even	6
2016.2.cr.e.1297.8		32	4.3	odd	2
2016.2.cr.e.1297.9		32	8.3	odd	2
2016.2.cr.e.1873.8		32	56.11	odd	6
2016.2.cr.e.1873.9		32	28.11	odd	6
4704.2.c.e.2353.5		16	84.23	even	6
4704.2.c.e.2353.12		16	168.107	even	6
4704.2.c.f.2353.5		16	168.131	odd	6
4704.2.c.f.2353.12		16	84.47	odd	6

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.cj (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.10325 - 0.884778i) q^{2} +(0.434335 + 1.95227i) q^{4} +(-0.0402223 - 0.0232224i) q^{5} +(-1.97032 + 1.76574i) q^{7} +(1.24814 - 2.53814i) q^{8} +(0.0238287 + 0.0612079i) q^{10} +(-3.11586 + 1.79894i) q^{11} -6.29415i q^{13} +(3.73605 - 0.204763i) q^{14} +(-3.62271 + 1.69588i) q^{16} +(-0.258110 - 0.447060i) q^{17} +(-2.80834 - 1.62140i) q^{19} +(0.0278663 - 0.0886110i) q^{20} +(5.02925 + 0.772156i) q^{22} +(3.47322 - 6.01578i) q^{23} +(-2.49892 - 4.32826i) q^{25} +(-5.56893 + 6.94404i) q^{26} +(-4.30298 - 3.07967i) q^{28} -2.29579i q^{29} +(-1.05460 - 1.82662i) q^{31} +(5.49724 + 1.33431i) q^{32} +(-0.110788 + 0.721591i) q^{34} +(0.120255 - 0.0252667i) q^{35} +(-1.12720 - 0.650790i) q^{37} +(1.66374 + 4.27357i) q^{38} +(-0.109145 + 0.0731049i) q^{40} -10.1883 q^{41} +9.12162i q^{43} +(-4.86535 - 5.30165i) q^{44} +(-9.15447 + 3.56391i) q^{46} +(2.32465 - 4.02641i) q^{47} +(0.764321 - 6.95815i) q^{49} +(-1.07261 + 6.98616i) q^{50} +(12.2879 - 2.73377i) q^{52} +(-4.91727 + 2.83899i) q^{53} +0.167103 q^{55} +(2.02245 + 7.20484i) q^{56} +(-2.03126 + 2.53284i) q^{58} +(1.42910 - 0.825090i) q^{59} +(-1.10386 - 0.637312i) q^{61} +(-0.452663 + 2.94831i) q^{62} +(-4.88428 - 6.33591i) q^{64} +(-0.146165 + 0.253165i) q^{65} +(-6.72366 + 3.88191i) q^{67} +(0.760675 - 0.698075i) q^{68} +(-0.155028 - 0.0785238i) q^{70} -11.8320 q^{71} +(5.57028 + 9.64802i) q^{73} +(0.667784 + 1.71531i) q^{74} +(1.94564 - 6.18687i) q^{76} +(2.96278 - 9.04630i) q^{77} +(-2.75086 + 4.76463i) q^{79} +(0.185096 + 0.0159156i) q^{80} +(11.2403 + 9.01443i) q^{82} +8.25030i q^{83} +0.0239757i q^{85} +(8.07061 - 10.0635i) q^{86} +(0.676926 + 10.1538i) q^{88} +(7.38218 - 12.7863i) q^{89} +(11.1138 + 12.4015i) q^{91} +(13.2530 + 4.16778i) q^{92} +(-6.12716 + 2.38535i) q^{94} +(0.0753053 + 0.130433i) q^{95} -6.16464 q^{97} +(-6.99966 + 7.00034i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 2 q^{2} - 2 q^{4} + 16 q^{8} + 6 q^{10} - 22 q^{14} - 10 q^{16} + 40 q^{20} - 12 q^{22} + 8 q^{23} + 16 q^{25} - 6 q^{26} - 26 q^{28} - 24 q^{31} + 8 q^{32} - 24 q^{34} + 26 q^{38} - 6 q^{40} - 20 q^{44}+ \cdots + 64 q^{98}+O(q^{100}) \) 32 * q - 2 * q^2 - 2 * q^4 + 16 * q^8 + 6 * q^10 - 22 * q^14 - 10 * q^16 + 40 * q^20 - 12 * q^22 + 8 * q^23 + 16 * q^25 - 6 * q^26 - 26 * q^28 - 24 * q^31 + 8 * q^32 - 24 * q^34 + 26 * q^38 - 6 * q^40 - 20 * q^44 + 16 * q^46 + 24 * q^47 + 8 * q^49 - 52 * q^50 + 44 * q^52 - 64 * q^55 - 40 * q^56 + 34 * q^58 - 100 * q^62 - 20 * q^64 - 16 * q^68 + 38 * q^70 + 80 * q^71 + 8 * q^73 - 10 * q^74 - 32 * q^76 + 8 * q^79 + 56 * q^80 + 22 * q^86 + 50 * q^88 - 64 * q^92 - 48 * q^94 - 24 * q^95 - 48 * q^97 + 64 * q^98

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