LMFDB - Embedded newform 756.2.n.b.19.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(19,756)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(756, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 4, 5]))

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

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

chi := DirichletCharacter("756.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.n (of order $6$, degree $2$, not 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:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$84$
Relative dimension:	$42$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 252)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			19.15
Character	$\chi$	$=$	756.19
Dual form			756.2.n.b.199.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.687840 - 1.23567i) q^{2} +(-1.05375 + 1.69988i) q^{4} +2.80831i q^{5} +(0.514387 + 2.59527i) q^{7} +(2.82531 + 0.132842i) q^{8} +O(q^{10})$	\(q+(-0.687840 - 1.23567i) q^{2} +(-1.05375 + 1.69988i) q^{4} +2.80831i q^{5} +(0.514387 + 2.59527i) q^{7} +(2.82531 + 0.132842i) q^{8} +(3.47014 - 1.93167i) q^{10} -3.74301i q^{11} +(0.529793 - 0.305876i) q^{13} +(2.85307 - 2.42074i) q^{14} +(-1.77921 - 3.58252i) q^{16} +(-3.82616 + 2.20903i) q^{17} +(0.594752 - 1.03014i) q^{19} +(-4.77380 - 2.95927i) q^{20} +(-4.62512 + 2.57459i) q^{22} +7.18760i q^{23} -2.88661 q^{25} +(-0.742374 - 0.444255i) q^{26} +(-4.95369 - 1.86037i) q^{28} +(-4.31175 + 7.46818i) q^{29} +(2.00598 - 3.47446i) q^{31} +(-3.20299 + 4.66271i) q^{32} +(5.36142 + 3.20840i) q^{34} +(-7.28832 + 1.44456i) q^{35} +(-4.72127 + 8.17748i) q^{37} +(-1.68201 - 0.0263447i) q^{38} +(-0.373063 + 7.93434i) q^{40} +(-3.44593 + 1.98951i) q^{41} +(1.57801 + 0.911063i) q^{43} +(6.36269 + 3.94421i) q^{44} +(8.88149 - 4.94392i) q^{46} +(-1.21129 - 2.09802i) q^{47} +(-6.47081 + 2.66994i) q^{49} +(1.98553 + 3.56690i) q^{50} +(-0.0383173 + 1.22290i) q^{52} +(-0.171887 - 0.297717i) q^{53} +10.5115 q^{55} +(1.10854 + 7.40075i) q^{56} +(12.1940 + 0.190990i) q^{58} +(6.51230 - 11.2796i) q^{59} +(1.88297 - 1.08713i) q^{61} +(-5.67307 - 0.0888554i) q^{62} +(7.96471 + 0.750641i) q^{64} +(0.858996 + 1.48782i) q^{65} +(-12.7435 - 7.35746i) q^{67} +(0.276727 - 8.83181i) q^{68} +(6.79819 + 8.01232i) q^{70} +5.36830i q^{71} +(-1.51244 + 0.873205i) q^{73} +(13.3521 + 0.209130i) q^{74} +(1.12440 + 2.09652i) q^{76} +(9.71411 - 1.92536i) q^{77} +(-8.54069 + 4.93097i) q^{79} +(10.0608 - 4.99657i) q^{80} +(4.82861 + 2.88956i) q^{82} +(-2.17733 + 3.77124i) q^{83} +(-6.20366 - 10.7451i) q^{85} +(0.0403558 - 2.57656i) q^{86} +(0.497231 - 10.5752i) q^{88} +(-0.865286 - 0.499573i) q^{89} +(1.06635 + 1.21762i) q^{91} +(-12.2181 - 7.57396i) q^{92} +(-1.75928 + 2.93986i) q^{94} +(2.89296 + 1.67025i) q^{95} +(5.76933 + 3.33092i) q^{97} +(7.75004 + 6.15929i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84 q + q^{2} + q^{4} + 16 q^{8}+O(q^{10}) $ 84 * q + q^2 + q^4 + 16 * q^8	$ 84 q + q^{2} + q^{4} + 16 q^{8} - 18 q^{10} - 18 q^{13} + 25 q^{14} - 7 q^{16} - 6 q^{17} - 24 q^{20} + 6 q^{22} - 32 q^{25} + 30 q^{26} - 4 q^{28} - 10 q^{29} - 9 q^{32} + 24 q^{34} + 2 q^{37} + 6 q^{41} + 13 q^{44} + 10 q^{46} + 2 q^{49} + 17 q^{50} + 2 q^{53} + 32 q^{56} + 26 q^{58} - 24 q^{61} - 8 q^{64} - 50 q^{65} - 4 q^{70} + 30 q^{73} - 46 q^{74} - 46 q^{77} - 3 q^{80} - 18 q^{82} - 50 q^{85} - 18 q^{86} - 2 q^{88} + 102 q^{89} - 28 q^{92} + 3 q^{94} - 6 q^{97} - 21 q^{98}+O(q^{100}) $ 84 * q + q^2 + q^4 + 16 * q^8 - 18 * q^10 - 18 * q^13 + 25 * q^14 - 7 * q^16 - 6 * q^17 - 24 * q^20 + 6 * q^22 - 32 * q^25 + 30 * q^26 - 4 * q^28 - 10 * q^29 - 9 * q^32 + 24 * q^34 + 2 * q^37 + 6 * q^41 + 13 * q^44 + 10 * q^46 + 2 * q^49 + 17 * q^50 + 2 * q^53 + 32 * q^56 + 26 * q^58 - 24 * q^61 - 8 * q^64 - 50 * q^65 - 4 * q^70 + 30 * q^73 - 46 * q^74 - 46 * q^77 - 3 * q^80 - 18 * q^82 - 50 * q^85 - 18 * q^86 - 2 * q^88 + 102 * q^89 - 28 * q^92 + 3 * q^94 - 6 * q^97 - 21 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$-1$

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 $

$2$	−0.687840	−	1.23567i	−0.486376	−	0.873750i
$2$	−0.687840	−	1.23567i	−0.486376	−	0.873750i
$3$		0			0
$3$		0			0
$4$	−1.05375	+	1.69988i	−0.526877	+	0.849942i
$5$			2.80831i			1.25592i	0.778248	+	0.627958i	$0.216109\pi$
$5$			2.80831i			1.25592i	−0.778248	+	0.627958i	$0.783891\pi$
$6$		0			0
$7$	0.514387	+	2.59527i	0.194420	+	0.980918i
$7$	0.514387	+	2.59527i	0.194420	+	0.980918i
$8$	2.82531	+	0.132842i	0.998896	+	0.0469669i
$9$		0			0
$10$	3.47014	−	1.93167i	1.09736	−	0.610847i
$11$		−	3.74301i		−	1.12856i	−0.825583	−	0.564280i	$-0.809154\pi$
$11$		−	3.74301i		−	1.12856i	0.825583	−	0.564280i	$-0.190846\pi$
$12$		0			0
$13$	0.529793	−	0.305876i	0.146938	−	0.0848348i	−0.424728	−	0.905321i	$-0.639630\pi$
$13$	0.529793	−	0.305876i	0.146938	−	0.0848348i	0.571667	+	0.820486i	$0.306297\pi$
$14$	2.85307	−	2.42074i	0.762516	−	0.646970i
$15$		0			0
$16$	−1.77921	−	3.58252i	−0.444802	−	0.895629i
$17$	−3.82616	+	2.20903i	−0.927980	+	0.535770i	−0.886172	−	0.463356i	$-0.846645\pi$
$17$	−3.82616	+	2.20903i	−0.927980	+	0.535770i	−0.0418081	+	0.999126i	$0.513312\pi$
$18$		0			0
$19$	0.594752	−	1.03014i	0.136445	−	0.236330i	−0.789703	−	0.613489i	$-0.789765\pi$
$19$	0.594752	−	1.03014i	0.136445	−	0.236330i	0.926149	+	0.377159i	$0.123099\pi$
$20$	−4.77380	−	2.95927i	−1.06745	−	0.661712i
$21$		0			0
$22$	−4.62512	+	2.57459i	−0.986079	+	0.548905i
$23$			7.18760i			1.49872i	0.662164	+	0.749359i	$0.269638\pi$
$23$			7.18760i			1.49872i	−0.662164	+	0.749359i	$0.730362\pi$
$24$		0			0
$25$	−2.88661			−0.577323
$26$	−0.742374	−	0.444255i	−0.145592	−	0.0871256i
$27$		0			0
$28$	−4.95369	−	1.86037i	−0.936159	−	0.351577i
$29$	−4.31175	+	7.46818i	−0.800673	+	1.38681i	0.118501	+	0.992954i	$0.462191\pi$
$29$	−4.31175	+	7.46818i	−0.800673	+	1.38681i	−0.919174	+	0.393852i	$0.871142\pi$
$30$		0			0
$31$	2.00598	−	3.47446i	0.360284	−	0.624031i	−0.627723	−	0.778437i	$-0.716013\pi$
$31$	2.00598	−	3.47446i	0.360284	−	0.624031i	0.988008	+	0.154406i	$0.0493463\pi$
$32$	−3.20299	+	4.66271i	−0.566214	+	0.824258i
$33$		0			0
$34$	5.36142	+	3.20840i	0.919476	+	0.550237i
$35$	−7.28832	+	1.44456i	−1.23195	+	0.244175i
$36$		0			0
$37$	−4.72127	+	8.17748i	−0.776172	+	1.34437i	0.157962	+	0.987445i	$0.449508\pi$
$37$	−4.72127	+	8.17748i	−0.776172	+	1.34437i	−0.934134	+	0.356923i	$0.883826\pi$
$38$	−1.68201	−	0.0263447i	−0.272857	−	0.00427368i
$39$		0			0
$40$	−0.373063	+	7.93434i	−0.0589864	+	1.25453i
$41$	−3.44593	+	1.98951i	−0.538163	+	0.310709i	−0.744334	−	0.667807i	$-0.767233\pi$
$41$	−3.44593	+	1.98951i	−0.538163	+	0.310709i	0.206171	+	0.978516i	$0.433900\pi$
$42$		0			0
$43$	1.57801	+	0.911063i	0.240644	+	0.138936i	0.615473	−	0.788158i	$-0.288965\pi$
$43$	1.57801	+	0.911063i	0.240644	+	0.138936i	−0.374829	+	0.927094i	$0.622299\pi$
$44$	6.36269	+	3.94421i	0.959211	+	0.594612i
$45$		0			0
$46$	8.88149	−	4.94392i	1.30950	−	0.728941i
$47$	−1.21129	−	2.09802i	−0.176685	−	0.306028i	0.764058	−	0.645148i	$-0.223204\pi$
$47$	−1.21129	−	2.09802i	−0.176685	−	0.306028i	−0.940743	+	0.339120i	$0.889871\pi$
$48$		0			0
$49$	−6.47081	+	2.66994i	−0.924402	+	0.381420i
$50$	1.98553	+	3.56690i	0.280796	+	0.504435i
$51$		0			0
$52$	−0.0383173	+	1.22290i	−0.00531366	+	0.169586i
$53$	−0.171887	−	0.297717i	−0.0236105	−	0.0408946i	0.853979	−	0.520308i	$-0.174183\pi$
$53$	−0.171887	−	0.297717i	−0.0236105	−	0.0408946i	−0.877589	+	0.479413i	$0.840849\pi$
$54$		0			0
$55$	10.5115			1.41738
$56$	1.10854	+	7.40075i	0.148135	+	0.988967i
$57$		0			0
$58$	12.1940	+	0.190990i	1.60115	+	0.0250783i
$59$	6.51230	−	11.2796i	0.847830	−	1.46848i	−0.0353111	−	0.999376i	$-0.511242\pi$
$59$	6.51230	−	11.2796i	0.847830	−	1.46848i	0.883141	−	0.469108i	$-0.155424\pi$
$60$		0			0
$61$	1.88297	−	1.08713i	0.241090	−	0.139193i	−0.374588	−	0.927192i	$-0.622216\pi$
$61$	1.88297	−	1.08713i	0.241090	−	0.139193i	0.615678	+	0.787998i	$0.288882\pi$
$62$	−5.67307	−	0.0888554i	−0.720480	−	0.0112847i
$63$		0			0
$64$	7.96471	+	0.750641i	0.995588	+	0.0938301i
$65$	0.858996	+	1.48782i	0.106545	+	0.184542i
$66$		0			0
$67$	−12.7435	−	7.35746i	−1.55686	−	0.898856i	−0.997554	−	0.0698982i	$-0.977733\pi$
$67$	−12.7435	−	7.35746i	−1.55686	−	0.898856i	−0.559311	−	0.828958i	$-0.688934\pi$
$68$	0.276727	−	8.83181i	0.0335581	−	1.07101i
$69$		0			0
$70$	6.79819	+	8.01232i	0.812539	+	0.957655i
$71$			5.36830i			0.637100i	0.947906	+	0.318550i	$0.103196\pi$
$71$			5.36830i			0.637100i	−0.947906	+	0.318550i	$0.896804\pi$
$72$		0			0
$73$	−1.51244	+	0.873205i	−0.177017	+	0.102201i	−0.585890	−	0.810390i	$-0.699255\pi$
$73$	−1.51244	+	0.873205i	−0.177017	+	0.102201i	0.408873	+	0.912591i	$0.365922\pi$
$74$	13.3521	+	0.209130i	1.55215	+	0.0243109i
$75$		0			0
$76$	1.12440	+	2.09652i	0.128977	+	0.240488i
$77$	9.71411	−	1.92536i	1.10703	−	0.219415i
$78$		0			0
$79$	−8.54069	+	4.93097i	−0.960903	+	0.554777i	−0.896451	−	0.443143i	$-0.853863\pi$
$79$	−8.54069	+	4.93097i	−0.960903	+	0.554777i	−0.0644519	+	0.997921i	$0.520530\pi$
$80$	10.0608	−	4.99657i	1.12483	−	0.558634i
$81$		0			0
$82$	4.82861	+	2.88956i	0.533231	+	0.319099i
$83$	−2.17733	+	3.77124i	−0.238993	+	0.413947i	−0.960425	−	0.278537i	$-0.910150\pi$
$83$	−2.17733	+	3.77124i	−0.238993	+	0.413947i	0.721433	+	0.692484i	$0.243484\pi$
$84$		0			0
$85$	−6.20366	−	10.7451i	−0.672881	−	1.16546i
$86$	0.0403558	−	2.57656i	0.00435168	−	0.277837i
$87$		0			0
$88$	0.497231	−	10.5752i	0.0530050	−	1.12732i
$89$	−0.865286	−	0.499573i	−0.0917201	−	0.0529546i	0.453438	−	0.891288i	$-0.350197\pi$
$89$	−0.865286	−	0.499573i	−0.0917201	−	0.0529546i	−0.545159	+	0.838333i	$0.683531\pi$
$90$		0			0
$91$	1.06635	+	1.21762i	0.111784	+	0.127641i
$92$	−12.2181	−	7.57396i	−1.27382	−	0.789640i
$93$		0			0
$94$	−1.75928	+	2.93986i	−0.181456	+	0.303223i
$95$	2.89296	+	1.67025i	0.296811	+	0.171364i
$96$		0			0
$97$	5.76933	+	3.33092i	0.585787	+	0.338204i	0.763430	−	0.645891i	$-0.223514\pi$
$97$	5.76933	+	3.33092i	0.585787	+	0.338204i	−0.177643	+	0.984095i	$0.556847\pi$
$98$	7.75004	+	6.15929i	0.782873	+	0.622182i
$99$		0			0
$100$	3.04178	−	4.90691i	0.304178	−	0.490691i
$101$			7.12000i			0.708467i	0.935157	+	0.354233i	$0.115258\pi$
$101$			7.12000i			0.708467i	−0.935157	+	0.354233i	$0.884742\pi$
$102$		0			0
$103$	10.7313			1.05738			0.528692	−	0.848814i	$-0.322683\pi$
$103$	10.7313			1.05738			0.528692	+	0.848814i	$0.322683\pi$
$104$	1.53746	−	0.793815i	0.150760	−	0.0778399i
$105$		0			0
$106$	−0.249649	+	0.417177i	−0.0242480	+	0.0405198i
$107$	12.5172	+	7.22680i	1.21008	+	0.698641i	0.962777	−	0.270296i	$-0.0871217\pi$
$107$	12.5172	+	7.22680i	1.21008	+	0.698641i	0.247305	+	0.968938i	$0.420455\pi$
$108$		0			0
$109$	0.384805	+	0.666502i	0.0368577	+	0.0638394i	0.883866	−	0.467741i	$-0.154932\pi$
$109$	0.384805	+	0.666502i	0.0368577	+	0.0638394i	−0.847008	+	0.531580i	$0.821599\pi$
$110$	−7.23026	−	12.9888i	−0.689378	−	1.23843i
$111$		0			0
$112$	8.38238	−	6.46032i	0.792061	−	0.610443i
$113$	−3.50852	−	6.07693i	−0.330054	−	0.571670i	0.652468	−	0.757816i	$-0.273734\pi$
$113$	−3.50852	−	6.07693i	−0.330054	−	0.571670i	−0.982522	+	0.186146i	$0.940400\pi$
$114$		0			0
$115$	−20.1850			−1.88226
$116$	−8.15151	−	15.1991i	−0.756848	−	1.41120i
$117$		0			0
$118$	−18.4173	−	0.288464i	−1.69545	−	0.0265553i
$119$	−7.70116	−	8.79361i	−0.705964	−	0.806109i
$120$		0			0
$121$	−3.01014			−0.273649
$122$	−2.63852	−	1.57896i	−0.238881	−	0.142952i
$123$		0			0
$124$	3.79237	+	7.07115i	0.340565	+	0.635008i
$125$			5.93505i			0.530847i
$126$		0			0
$127$			17.0935i			1.51680i	0.651789	+	0.758401i	$0.274019\pi$
$127$			17.0935i			1.51680i	−0.651789	+	0.758401i	$0.725981\pi$
$128$	−4.55090	−	10.3581i	−0.402246	−	0.915532i
$129$		0			0
$130$	1.24761	−	2.08482i	0.109422	−	0.182851i
$131$	15.7650			1.37739			0.688696	−	0.725050i	$-0.258183\pi$
$131$	15.7650			1.37739			0.688696	+	0.725050i	$0.258183\pi$
$132$		0			0
$133$	2.97942	+	1.01365i	0.258349	+	0.0878945i
$134$	−0.325901	+	20.8075i	−0.0281535	+	1.79749i
$135$		0			0
$136$	−11.1035	+	5.73292i	−0.952120	+	0.491594i
$137$	3.01262			0.257385			0.128693	−	0.991685i	$-0.458922\pi$
$137$	3.01262			0.257385			0.128693	+	0.991685i	$0.458922\pi$
$138$		0			0
$139$	−1.85082	−	3.20571i	−0.156984	−	0.271905i	0.776796	−	0.629753i	$-0.216844\pi$
$139$	−1.85082	−	3.20571i	−0.156984	−	0.271905i	−0.933780	+	0.357848i	$0.883510\pi$
$140$	5.22451	−	13.9115i	0.441551	−	1.17574i
$141$		0			0
$142$	6.63344	−	3.69253i	0.556666	−	0.309870i
$143$	−1.14490	−	1.98302i	−0.0957412	−	0.165829i
$144$		0			0
$145$	−20.9730	−	12.1088i	−1.74171	−	1.00558i
$146$	2.11930	+	1.26824i	0.175395	+	0.104961i
$147$		0			0
$148$	−8.92570	−	16.6426i	−0.733688	−	1.36802i
$149$	11.3003			0.925759			0.462880	−	0.886421i	$-0.346816\pi$
$149$	11.3003			0.925759			0.462880	+	0.886421i	$0.346816\pi$
$150$		0			0
$151$		−	4.88431i		−	0.397480i	−0.980052	−	0.198740i	$-0.936315\pi$
$151$		−	4.88431i		−	0.397480i	0.980052	−	0.198740i	$-0.0636849\pi$
$152$	1.81720	−	2.83145i	0.147395	−	0.229661i
$153$		0			0
$154$	−9.06085	−	10.6791i	−0.730144	−	0.860545i
$155$	9.75736	+	5.63341i	0.783730	+	0.452487i
$156$		0			0
$157$	10.0956	+	5.82872i	0.805720	+	0.465183i	0.845467	−	0.534027i	$-0.179322\pi$
$157$	10.0956	+	5.82872i	0.805720	+	0.465183i	−0.0397471	+	0.999210i	$0.512655\pi$
$158$	11.9677	+	7.16174i	0.952097	+	0.569758i
$159$		0			0
$160$	−13.0943	−	8.99500i	−1.03520	−	0.711117i
$161$	−18.6537	+	3.69721i	−1.47012	+	0.291381i
$162$		0			0
$163$	8.82016	+	5.09232i	0.690848	+	0.398861i	0.803930	−	0.594724i	$-0.202739\pi$
$163$	8.82016	+	5.09232i	0.690848	+	0.398861i	−0.113081	+	0.993586i	$0.536072\pi$
$164$	0.249227	−	7.95412i	0.0194613	−	0.621112i
$165$		0			0
$166$	6.15765	+	0.0964453i	0.477926	+	0.00748561i
$167$	−7.03763	−	12.1895i	−0.544588	−	0.943254i	−0.998633	−	0.0522750i	$-0.983353\pi$
$167$	−7.03763	−	12.1895i	−0.544588	−	0.943254i	0.454045	−	0.890979i	$-0.349981\pi$
$168$		0			0
$169$	−6.31288	+	10.9342i	−0.485606	+	0.841094i
$170$	−9.01020	+	15.0565i	−0.691051	+	1.15478i
$171$		0			0
$172$	−3.21153	+	1.72239i	−0.244877	+	0.131331i
$173$	13.8484	−	7.99539i	1.05288	−	0.607878i	0.129423	−	0.991590i	$-0.458688\pi$
$173$	13.8484	−	7.99539i	1.05288	−	0.607878i	0.923453	+	0.383711i	$0.125354\pi$
$174$		0			0
$175$	−1.48484	−	7.49153i	−0.112243	−	0.566306i
$176$	−13.4094	+	6.65960i	−1.01077	+	0.501986i
$177$		0			0
$178$	−0.0221287	+	1.41283i	−0.00165862	+	0.105896i
$179$	1.34673	−	0.777533i	0.100659	−	0.0581156i	−0.448825	−	0.893619i	$-0.648157\pi$
$179$	1.34673	−	0.777533i	0.100659	−	0.0581156i	0.549484	+	0.835504i	$0.314824\pi$
$180$		0			0
$181$		−	11.7809i		−	0.875665i	−0.899056	−	0.437833i	$-0.855746\pi$
$181$		−	11.7809i		−	0.875665i	0.899056	−	0.437833i	$-0.144254\pi$
$182$	0.771092	−	2.15518i	0.0571572	−	0.159752i
$183$		0			0
$184$	−0.954818	+	20.3072i	−0.0703901	+	1.49706i
$185$	−22.9649	−	13.2588i	−1.68841	−	0.974806i
$186$		0			0
$187$	8.26845	+	14.3214i	0.604649	+	1.04728i
$188$	4.84279	+	0.151739i	0.353197	+	0.0110667i
$189$		0			0
$190$	0.0739842	−	4.72360i	0.00536738	−	0.342686i
$191$	−12.5480	+	7.24457i	−0.907939	+	0.524199i	−0.879767	−	0.475404i	$-0.842302\pi$
$191$	−12.5480	+	7.24457i	−0.907939	+	0.524199i	−0.0281715	+	0.999603i	$0.508968\pi$
$192$		0			0
$193$	4.60711	−	7.97975i	0.331627	−	0.574395i	−0.651204	−	0.758903i	$-0.725736\pi$
$193$	4.60711	−	7.97975i	0.331627	−	0.574395i	0.982831	+	0.184508i	$0.0590690\pi$
$194$	0.147544	−	9.42012i	0.0105931	−	0.676325i
$195$		0			0
$196$	2.28005	−	13.8131i	0.162861	−	0.986649i
$197$	9.54933			0.680361			0.340181	−	0.940360i	$-0.389512\pi$
$197$	9.54933			0.680361			0.340181	+	0.940360i	$0.389512\pi$
$198$		0			0
$199$	−8.38058	−	14.5156i	−0.594084	−	1.02898i	−0.993675	−	0.112290i	$-0.964181\pi$
$199$	−8.38058	−	14.5156i	−0.594084	−	1.02898i	0.399592	−	0.916693i	$-0.369152\pi$
$200$	−8.15557	−	0.383465i	−0.576686	−	0.0271151i
$201$		0			0
$202$	8.79796	−	4.89742i	0.619023	−	0.344581i
$203$	−21.5998	−	7.34862i	−1.51601	−	0.515772i
$204$		0			0
$205$	−5.58715	−	9.67723i	−0.390224	−	0.675887i
$206$	−7.38140	−	13.2603i	−0.514286	−	0.923889i
$207$		0			0
$208$	−2.03842	−	1.35377i	−0.141339	−	0.0938674i
$209$	−3.85583	−	2.22616i	−0.266713	−	0.153987i
$210$		0			0
$211$	7.48353	−	4.32062i	0.515187	−	0.297443i	−0.219776	−	0.975550i	$-0.570533\pi$
$211$	7.48353	−	4.32062i	0.515187	−	0.297443i	0.734963	+	0.678107i	$0.237199\pi$
$212$	0.687210	+	0.0215324i	0.0471978	+	0.00147885i
$213$		0			0
$214$	0.320113	−	20.4380i	0.0218825	−	1.39711i
$215$	−2.55855	+	4.43153i	−0.174491	+	0.302228i
$216$		0			0
$217$	10.0490	+	3.41883i	0.682170	+	0.232086i
$218$	0.558892	−	0.933939i	0.0378529	−	0.0632543i
$219$		0			0
$220$	−11.0766	+	17.8684i	−0.746783	+	1.20469i
$221$	−1.35138	+	2.34066i	−0.0909038	+	0.157450i
$222$		0			0
$223$	9.83962	−	17.0427i	0.658909	−	1.14126i	−0.321989	−	0.946743i	$-0.604351\pi$
$223$	9.83962	−	17.0427i	0.658909	−	1.14126i	0.980898	−	0.194521i	$-0.0623153\pi$
$224$	−13.7485	−	5.91418i	−0.918613	−	0.395158i
$225$		0			0
$226$	−5.09578	+	8.51532i	−0.338966	+	0.566431i
$227$	−11.9748			−0.794797			−0.397398	−	0.917646i	$-0.630087\pi$
$227$	−11.9748			−0.794797			−0.397398	+	0.917646i	$0.630087\pi$
$228$		0			0
$229$			2.74118i			0.181142i	0.995890	+	0.0905710i	$0.0288692\pi$
$229$			2.74118i			0.181142i	−0.995890	+	0.0905710i	$0.971131\pi$
$230$	13.8841	+	24.9420i	0.915488	+	1.64463i
$231$		0			0
$232$	−13.1741	+	20.5271i	−0.864923	+	1.34767i
$233$	8.10740	−	14.0424i	0.531133	−	0.919950i	−0.468206	−	0.883619i	$-0.655100\pi$
$233$	8.10740	−	14.0424i	0.531133	−	0.919950i	0.999340	−	0.0363310i	$-0.0115671\pi$
$234$		0			0
$235$	5.89189	−	3.40169i	0.384345	−	0.221902i
$236$	12.3117	+	22.9561i	0.801424	+	1.49432i
$237$		0			0
$238$	−5.56882	+	15.5647i	−0.360973	+	1.00891i
$239$	3.45217	−	1.99311i	0.223302	−	0.128924i	−0.384176	−	0.923260i	$-0.625514\pi$
$239$	3.45217	−	1.99311i	0.223302	−	0.128924i	0.607478	+	0.794336i	$0.292181\pi$
$240$		0			0
$241$		−	11.2442i		−	0.724304i	−0.932119	−	0.362152i	$-0.882042\pi$
$241$		−	11.2442i		−	0.724304i	0.932119	−	0.362152i	$-0.117958\pi$
$242$	2.07050	+	3.71954i	0.133096	+	0.239101i
$243$		0			0
$244$	−0.136186	+	4.34641i	−0.00871842	+	0.278250i
$245$	−7.49802	−	18.1721i	−0.479031	−	1.16097i
$246$		0			0
$247$		−	0.727682i		−	0.0463013i
$248$	6.12906	−	9.54992i	0.389196	−	0.606421i
$249$		0			0
$250$	7.33375	−	4.08236i	0.463827	−	0.258191i
$251$	10.3057			0.650492			0.325246	−	0.945629i	$-0.394553\pi$
$251$	10.3057			0.650492			0.325246	+	0.945629i	$0.394553\pi$
$252$		0			0
$253$	26.9033			1.69139
$254$	21.1219	−	11.7576i	1.32530	−	0.737736i
$255$		0			0
$256$	−9.66884	+	12.7481i	−0.604302	+	0.796755i
$257$			24.2317i			1.51153i	0.654842	+	0.755766i	$0.272735\pi$
$257$			24.2317i			1.51153i	−0.654842	+	0.755766i	$0.727265\pi$
$258$		0			0
$259$	−23.6513	−	8.04656i	−1.46962	−	0.499989i
$260$	−3.43430	−	0.107607i	−0.212986	−	0.00667350i
$261$		0			0
$262$	−10.8438	−	19.4803i	−0.669931	−	1.20350i
$263$			7.36871i			0.454374i	0.973851	+	0.227187i	$0.0729528\pi$
$263$			7.36871i			0.454374i	−0.973851	+	0.227187i	$0.927047\pi$
$264$		0			0
$265$	0.836082	−	0.482712i	0.0513601	−	0.0296528i
$266$	−0.796830	−	4.37881i	−0.0488568	−	0.268482i
$267$		0			0
$268$	25.9353	−	13.9095i	1.58425	−	0.849658i
$269$	26.6977	−	15.4139i	1.62778	−	0.939802i	0.643032	−	0.765839i	$-0.277676\pi$
$269$	26.6977	−	15.4139i	1.62778	−	0.939802i	0.984752	−	0.173963i	$-0.0556573\pi$
$270$		0			0
$271$	−9.52600	+	16.4995i	−0.578664	+	1.00227i	0.416969	+	0.908920i	$0.363092\pi$
$271$	−9.52600	+	16.4995i	−0.578664	+	1.00227i	−0.995633	+	0.0933541i	$0.970241\pi$
$272$	14.7214	+	9.77695i	0.892618	+	0.592815i
$273$		0			0
$274$	−2.07220	−	3.72260i	−0.125186	−	0.224890i
$275$			10.8046i			0.651544i
$276$		0			0
$277$	−0.251302			−0.0150993			−0.00754964	−	0.999972i	$-0.502403\pi$
$277$	−0.251302			−0.0150993			−0.00754964	+	0.999972i	$0.502403\pi$
$278$	−2.68813	+	4.49201i	−0.161223	+	0.269413i
$279$		0			0
$280$	−20.7836	+	3.11312i	−1.24206	+	0.186045i
$281$	5.87455	−	10.1750i	0.350447	−	0.606991i	−0.635881	−	0.771787i	$-0.719363\pi$
$281$	5.87455	−	10.1750i	0.350447	−	0.606991i	0.986328	+	0.164796i	$0.0526965\pi$
$282$		0			0
$283$	4.35446	−	7.54215i	0.258846	−	0.448334i	−0.707087	−	0.707126i	$-0.749991\pi$
$283$	4.35446	−	7.54215i	0.258846	−	0.448334i	0.965933	+	0.258792i	$0.0833245\pi$
$284$	−9.12548	−	5.65686i	−0.541498	−	0.335673i
$285$		0			0
$286$	−1.66285	+	2.77872i	−0.0983265	+	0.164309i
$287$	−6.93584	−	7.91972i	−0.409409	−	0.467486i
$288$		0			0
$289$	1.25967	−	2.18181i	0.0740983	−	0.128342i
$290$	−0.536361	+	34.2445i	−0.0314962	+	2.01091i
$291$		0			0
$292$	0.109387	−	3.49111i	0.00640139	−	0.204302i
$293$	10.0622	−	5.80944i	0.587842	−	0.339391i	−0.176402	−	0.984318i	$-0.556446\pi$
$293$	10.0622	−	5.80944i	0.587842	−	0.339391i	0.764244	+	0.644927i	$0.223112\pi$
$294$		0			0
$295$	31.6767	+	18.2886i	1.84429	+	1.06480i
$296$	−14.4253	+	22.4767i	−0.838456	+	1.30643i
$297$		0			0
$298$	−7.77281	−	13.9635i	−0.450267	−	0.808882i
$299$	2.19852	+	3.80794i	0.127143	+	0.220219i
$300$		0			0
$301$	−1.55274	+	4.56399i	−0.0894987	+	0.263064i
$302$	−6.03539	+	3.35962i	−0.347298	+	0.193325i
$303$		0			0
$304$	−4.74868	−	0.297874i	−0.272356	−	0.0170842i
$305$	3.05301	+	5.28797i	0.174815	+	0.302789i
$306$		0			0
$307$	23.8074			1.35876			0.679380	−	0.733787i	$-0.262249\pi$
$307$	23.8074			1.35876			0.679380	+	0.733787i	$0.262249\pi$
$308$	−6.96340	+	18.5417i	−0.396776	+	1.05651i
$309$		0			0
$310$	0.249534	−	15.9317i	0.0141726	−	0.904862i
$311$	−11.9820	+	20.7534i	−0.679436	+	1.17682i	0.295714	+	0.955276i	$0.404442\pi$
$311$	−11.9820	+	20.7534i	−0.679436	+	1.17682i	−0.975151	+	0.221542i	$0.928891\pi$
$312$		0			0
$313$	8.92829	−	5.15475i	0.504657	−	0.291364i	−0.225978	−	0.974132i	$-0.572558\pi$
$313$	8.92829	−	5.15475i	0.504657	−	0.291364i	0.730635	+	0.682769i	$0.239224\pi$
$314$	0.258185	−	16.4841i	0.0145702	−	0.930252i
$315$		0			0
$316$	0.617706	−	19.7142i	0.0347487	−	1.10901i
$317$	−6.38693	−	11.0625i	−0.358726	−	0.621331i	0.629023	−	0.777387i	$-0.283455\pi$
$317$	−6.38693	−	11.0625i	−0.358726	−	0.621331i	−0.987748	+	0.156056i	$0.950122\pi$
$318$		0			0
$319$	27.9535	+	16.1390i	1.56509	+	0.903608i
$320$	−2.10803	+	22.3674i	−0.117843	+	1.25037i
$321$		0			0
$322$	17.3993	+	20.5067i	0.969625	+	1.14280i
$323$			5.25531i			0.292413i
$324$		0			0
$325$	−1.52931	+	0.882946i	−0.0848307	+	0.0489771i
$326$	0.225566	−	14.4015i	0.0124929	−	0.797625i
$327$		0			0
$328$	−10.0001	+	5.16320i	−0.552162	+	0.285090i
$329$	4.82185	−	4.22282i	0.265837	−	0.232812i
$330$		0			0
$331$	−16.4410	+	9.49224i	−0.903682	+	0.521741i	−0.878393	−	0.477939i	$-0.841384\pi$
$331$	−16.4410	+	9.49224i	−0.903682	+	0.521741i	−0.0252888	+	0.999680i	$0.508051\pi$
$332$	−4.11630	−	7.67515i	−0.225911	−	0.421229i
$333$		0			0
$334$	−10.2215	+	17.0806i	−0.559293	+	0.934610i
$335$	20.6620	−	35.7877i	1.12889	−	1.95529i
$336$		0			0
$337$	9.58901	+	16.6086i	0.522347	+	0.904731i	0.999662	+	0.0259987i	$0.00827657\pi$
$337$	9.58901	+	16.6086i	0.522347	+	0.904731i	−0.477315	+	0.878732i	$0.658390\pi$
$338$	17.8533	+	0.279631i	0.971093	+	0.0152099i
$339$		0			0
$340$	24.8025	+	0.777136i	1.34510	+	0.0421461i
$341$	−13.0049	−	7.50840i	−0.704257	−	0.406603i
$342$		0			0
$343$	−10.2577	−	15.4201i	−0.553864	−	0.832607i
$344$	4.33732	+	2.78366i	0.233853	+	0.150085i
$345$		0			0
$346$	−19.4051	−	11.6125i	−1.04323	−	0.624292i
$347$	23.8689	+	13.7807i	1.28135	+	0.739789i	0.977095	−	0.212802i	$-0.0682589\pi$
$347$	23.8689	+	13.7807i	1.28135	+	0.739789i	0.304256	+	0.952590i	$0.401592\pi$
$348$		0			0
$349$	−15.9615	−	9.21538i	−0.854400	−	0.493288i	0.00773296	−	0.999970i	$-0.497538\pi$
$349$	−15.9615	−	9.21538i	−0.854400	−	0.493288i	−0.862133	+	0.506682i	$0.830872\pi$
$350$	−8.23572	+	6.98774i	−0.440218	+	0.373510i
$351$		0			0
$352$	17.4526	+	11.9888i	0.930225	+	0.639007i
$353$			18.8651i			1.00409i	0.864842	+	0.502044i	$0.167418\pi$
$353$			18.8651i			1.00409i	−0.864842	+	0.502044i	$0.832582\pi$
$354$		0			0
$355$	−15.0759			−0.800143
$356$	1.76101	−	0.944458i	0.0933335	−	0.0500562i
$357$		0			0
$358$	−1.88711	−	1.12929i	−0.0997366	−	0.0596848i
$359$	−10.1985	−	5.88809i	−0.538254	−	0.310761i	0.206117	−	0.978527i	$-0.433917\pi$
$359$	−10.1985	−	5.88809i	−0.538254	−	0.310761i	−0.744371	+	0.667766i	$0.767251\pi$
$360$		0			0
$361$	8.79254	+	15.2291i	0.462765	+	0.801533i
$362$	−14.5573	+	8.10335i	−0.765112	+	0.425903i
$363$		0			0
$364$	−3.19347	+	0.529602i	−0.167383	+	0.0277587i
$365$	−2.45223	−	4.24739i	−0.128356	−	0.222319i
$366$		0			0
$367$	−22.7984			−1.19007			−0.595034	−	0.803701i	$-0.702861\pi$
$367$	−22.7984			−1.19007			−0.595034	+	0.803701i	$0.702861\pi$
$368$	25.7497	−	12.7882i	1.34230	−	0.666633i
$369$		0			0
$370$	−0.587302	+	37.4969i	−0.0305324	+	1.94937i
$371$	0.684238	−	0.599234i	0.0355239	−	0.0311107i
$372$		0			0
$373$	4.99355			0.258556			0.129278	−	0.991608i	$-0.458734\pi$
$373$	4.99355			0.258556			0.129278	+	0.991608i	$0.458734\pi$
$374$	12.0091	−	20.0679i	0.620976	−	1.03768i
$375$		0			0
$376$	−3.14357	−	6.08846i	−0.162117	−	0.313988i
$377$			5.27545i			0.271700i
$378$		0			0
$379$			32.2808i			1.65815i	0.559135	+	0.829077i	$0.311133\pi$
$379$			32.2808i			1.65815i	−0.559135	+	0.829077i	$0.688867\pi$
$380$	−5.88769	+	3.15766i	−0.302032	+	0.161984i
$381$		0			0
$382$	17.5829	+	10.5220i	0.899618	+	0.538354i
$383$	−17.6430			−0.901518			−0.450759	−	0.892646i	$-0.648847\pi$
$383$	−17.6430			−0.901518			−0.450759	+	0.892646i	$0.648847\pi$
$384$		0			0
$385$	5.40700	+	27.2803i	0.275566	+	1.39033i
$386$	−13.0293	−	0.204073i	−0.663173	−	0.0103871i
$387$		0			0
$388$	−11.7416	+	6.29722i	−0.596091	+	0.319693i
$389$	−15.5105			−0.786414			−0.393207	−	0.919450i	$-0.628634\pi$
$389$	−15.5105			−0.786414			−0.393207	+	0.919450i	$0.628634\pi$
$390$		0			0
$391$	−15.8777	−	27.5009i	−0.802968	−	1.39078i
$392$	−18.6367	+	6.68380i	−0.941296	+	0.337583i
$393$		0			0
$394$	−6.56841	−	11.7998i	−0.330912	−	0.594466i
$395$	−13.8477	−	23.9849i	−0.696753	−	1.20681i
$396$		0			0
$397$	29.6794	+	17.1354i	1.48957	+	0.860002i	0.999929	−	0.0119229i	$-0.00379527\pi$
$397$	29.6794	+	17.1354i	1.48957	+	0.860002i	0.489639	+	0.871925i	$0.337129\pi$
$398$	−12.1720	+	20.3400i	−0.610125	+	1.01955i
$399$		0			0
$400$	5.13589	+	10.3413i	0.256794	+	0.517067i
$401$	−6.84901			−0.342023			−0.171012	−	0.985269i	$-0.554704\pi$
$401$	−6.84901			−0.342023			−0.171012	+	0.985269i	$0.554704\pi$
$402$		0			0
$403$		−	2.45432i		−	0.122259i
$404$	−12.1032	−	7.50273i	−0.602156	−	0.373275i
$405$		0			0
$406$	5.77675	+	31.7449i	0.286695	+	1.57547i
$407$	30.6084	+	17.6718i	1.51720	+	0.875957i
$408$		0			0
$409$	29.6195	+	17.1008i	1.46459	+	0.845582i	0.999218	−	0.0395332i	$-0.0125871\pi$
$409$	29.6195	+	17.1008i	1.46459	+	0.845582i	0.465372	+	0.885115i	$0.345920\pi$
$410$	−8.11479	+	13.5603i	−0.400761	+	0.669693i
$411$		0			0
$412$	−11.3081	+	18.2419i	−0.557111	+	0.898715i
$413$	32.6235	+	11.0991i	1.60530	+	0.546149i
$414$		0			0
$415$	−10.5908	−	6.11461i	−0.519883	−	0.300154i
$416$	−0.270712	+	3.44999i	−0.0132727	+	0.169150i
$417$		0			0
$418$	−0.0986086	+	6.29577i	−0.00482311	+	0.307936i
$419$	−10.0572	−	17.4195i	−0.491325	−	0.851000i	0.508625	−	0.860988i	$-0.330154\pi$
$419$	−10.0572	−	17.4195i	−0.491325	−	0.851000i	−0.999950	+	0.00998821i	$0.996821\pi$
$420$		0			0
$421$	3.04994	−	5.28265i	0.148645	−	0.257461i	−0.782082	−	0.623176i	$-0.785842\pi$
$421$	3.04994	−	5.28265i	0.148645	−	0.257461i	0.930727	+	0.365715i	$0.119175\pi$
$422$	−10.4863	−	6.27527i	−0.510466	−	0.305475i
$423$		0			0
$424$	−0.446084	−	0.863975i	−0.0216637	−	0.0419583i
$425$	11.0446	−	6.37663i	0.535744	−	0.309312i
$426$		0			0
$427$	3.78998	+	4.32761i	0.183410	+	0.209428i
$428$	−25.4747	+	13.6625i	−1.23137	+	0.660402i
$429$		0			0
$430$	7.23578	+	0.113332i	0.348940	+	0.00546534i
$431$	23.2792	−	13.4402i	1.12132	−	0.647393i	0.179581	−	0.983743i	$-0.442526\pi$
$431$	23.2792	−	13.4402i	1.12132	−	0.647393i	0.941737	+	0.336350i	$0.109193\pi$
$432$		0			0
$433$			16.0304i			0.770372i	0.922839	+	0.385186i	$0.125863\pi$
$433$			16.0304i			0.770372i	−0.922839	+	0.385186i	$0.874137\pi$
$434$	−2.68755	−	14.7688i	−0.129006	−	0.708927i
$435$		0			0
$436$	−1.53847	−	0.0482048i	−0.0736792	−	0.00230859i
$437$	7.40424	+	4.27484i	0.354193	+	0.204493i
$438$		0			0
$439$	−9.84469	−	17.0515i	−0.469861	−	0.813824i	0.529545	−	0.848282i	$-0.322363\pi$
$439$	−9.84469	−	17.0515i	−0.469861	−	0.813824i	−0.999406	+	0.0344581i	$0.989029\pi$
$440$	29.6983	+	1.39638i	1.41581	+	0.0665698i
$441$		0			0
$442$	3.82182	+	0.0598599i	0.181785	+	0.00284724i
$443$	−6.23901	+	3.60210i	−0.296424	+	0.171141i	−0.640835	−	0.767678i	$-0.721412\pi$
$443$	−6.23901	+	3.60210i	−0.296424	+	0.171141i	0.344411	+	0.938819i	$0.388079\pi$
$444$		0			0
$445$	1.40296	−	2.42999i	0.0665065	−	0.115193i
$446$	−27.8272	−	0.435849i	−1.31766	−	0.0206380i
$447$		0			0
$448$	2.14882	+	21.0567i	0.101522	+	0.994833i
$449$	−6.42464			−0.303198			−0.151599	−	0.988442i	$-0.548442\pi$
$449$	−6.42464			−0.303198			−0.151599	+	0.988442i	$0.548442\pi$
$450$		0			0
$451$	7.44675	+	12.8981i	0.350654	+	0.607350i
$452$	14.0272	+	0.439515i	0.659784	+	0.0206730i
$453$		0			0
$454$	8.23676	+	14.7969i	0.386570	+	0.694453i
$455$	−3.41944	+	2.99464i	−0.160306	+	0.140391i
$456$		0			0
$457$	18.2190	+	31.5563i	0.852250	+	1.47614i	0.879173	+	0.476504i	$0.158096\pi$
$457$	18.2190	+	31.5563i	0.852250	+	1.47614i	−0.0269221	+	0.999638i	$0.508571\pi$
$458$	3.38718	−	1.88549i	0.158273	−	0.0881031i
$459$		0			0
$460$	21.2700	−	34.3122i	0.991720	−	1.59981i
$461$	−1.90388	−	1.09920i	−0.0886725	−	0.0511951i	0.455008	−	0.890487i	$-0.349636\pi$
$461$	−1.90388	−	1.09920i	−0.0886725	−	0.0511951i	−0.543681	+	0.839292i	$0.682970\pi$
$462$		0			0
$463$	2.98183	−	1.72156i	0.138577	−	0.0800077i	−0.429108	−	0.903253i	$-0.641172\pi$
$463$	2.98183	−	1.72156i	0.138577	−	0.0800077i	0.567686	+	0.823245i	$0.307839\pi$
$464$	34.4264	+	2.15949i	1.59820	+	0.100252i
$465$		0			0
$466$	−22.9284	−	0.359120i	−1.06214	−	0.0166359i
$467$	−0.234638	+	0.406404i	−0.0108577	+	0.0188061i	−0.871403	−	0.490567i	$-0.836790\pi$
$467$	−0.234638	+	0.406404i	−0.0108577	+	0.0188061i	0.860545	+	0.509374i	$0.170123\pi$
$468$		0			0
$469$	12.5395	−	36.8573i	0.579019	−	1.70191i
$470$	−8.25603	−	4.94061i	−0.380822	−	0.227893i
$471$		0			0
$472$	19.8977	−	31.0033i	0.915864	−	1.42704i
$473$	3.41012	−	5.90650i	0.156797	−	0.271581i
$474$		0			0
$475$	−1.71682	+	2.97362i	−0.0787731	+	0.136439i
$476$	23.0632	−	3.82478i	1.05710	−	0.175309i
$477$		0			0
$478$	−4.83736	−	2.89480i	−0.221256	−	0.132405i
$479$	7.51654			0.343440			0.171720	−	0.985146i	$-0.445068\pi$
$479$	7.51654			0.343440			0.171720	+	0.985146i	$0.445068\pi$
$480$		0			0
$481$			5.77649i			0.263385i
$482$	−13.8941	+	7.73423i	−0.632861	+	0.352284i
$483$		0			0
$484$	3.17195	−	5.11689i	0.144179	−	0.232586i
$485$	−9.35427	+	16.2021i	−0.424756	+	0.735698i
$486$		0			0
$487$	11.0384	−	6.37304i	0.500199	−	0.288790i	−0.228597	−	0.973521i	$-0.573414\pi$
$487$	11.0384	−	6.37304i	0.500199	−	0.288790i	0.728796	+	0.684731i	$0.240080\pi$
$488$	5.46439	−	2.82135i	0.247361	−	0.127716i
$489$		0			0
$490$	−17.2972	+	21.7645i	−0.781408	+	0.983221i
$491$	16.7854	−	9.69106i	0.757515	−	0.437351i	−0.0708879	−	0.997484i	$-0.522583\pi$
$491$	16.7854	−	9.69106i	0.757515	−	0.437351i	0.828403	+	0.560133i	$0.189250\pi$
$492$		0			0
$493$		−	38.0993i		−	1.71590i
$494$	−0.899174	+	0.500528i	−0.0404557	+	0.0225198i
$495$		0			0
$496$	−16.0164	−	1.00467i	−0.719155	−	0.0451109i
$497$	−13.9322	+	2.76138i	−0.624943	+	0.123865i
$498$		0			0
$499$		−	21.0692i		−	0.943189i	−0.881816	−	0.471594i	$-0.843679\pi$
$499$		−	21.0692i		−	0.943189i	0.881816	−	0.471594i	$-0.156321\pi$
$500$	−10.0889	−	6.25408i	−0.451189	−	0.279691i
$501$		0			0
$502$	−7.08869	−	12.7345i	−0.316384	−	0.568367i
$503$	−29.8779			−1.33219			−0.666095	−	0.745867i	$-0.732035\pi$
$503$	−29.8779			−1.33219			−0.666095	+	0.745867i	$0.732035\pi$
$504$		0			0
$505$	−19.9952			−0.889774
$506$	−18.5051	−	33.2435i	−0.822654	−	1.47786i
$507$		0			0
$508$	−29.0569	−	18.0123i	−1.28919	−	0.799167i
$509$			34.5494i			1.53138i	0.643213	+	0.765688i	$0.277601\pi$
$509$			34.5494i			1.53138i	−0.643213	+	0.765688i	$0.722399\pi$
$510$		0			0
$511$	−3.04418	−	3.47601i	−0.134666	−	0.153770i
$512$	22.4030	+	3.17884i	0.990083	+	0.140486i
$513$		0			0
$514$	29.9423	−	16.6675i	1.32070	−	0.735173i
$515$			30.1368i			1.32798i
$516$		0			0
$517$	−7.85291	+	4.53388i	−0.345371	+	0.199400i
$518$	6.32541	+	34.7599i	0.277922	+	1.52726i
$519$		0			0
$520$	2.22928	+	4.31767i	0.0977604	+	0.189342i
$521$	−6.83068	+	3.94369i	−0.299257	+	0.172776i	−0.642109	−	0.766613i	$-0.721940\pi$
$521$	−6.83068	+	3.94369i	−0.299257	+	0.172776i	0.342852	+	0.939389i	$0.388607\pi$
$522$		0			0
$523$	8.08449	−	14.0027i	0.353510	−	0.612297i	−0.633352	−	0.773864i	$-0.718321\pi$
$523$	8.08449	−	14.0027i	0.353510	−	0.612297i	0.986862	+	0.161567i	$0.0516547\pi$
$524$	−16.6124	+	26.7986i	−0.725716	+	1.17070i
$525$		0			0
$526$	9.10528	−	5.06849i	0.397009	−	0.220997i
$527$			17.7251i			0.772118i
$528$		0			0
$529$	−28.6616			−1.24616
$530$	−1.17156	−	0.701091i	−0.0508894	−	0.0304535i
$531$		0			0
$532$	−4.86266	+	3.99653i	−0.210823	+	0.173272i
$533$	−1.21709	+	2.10805i	−0.0527178	+	0.0913099i
$534$		0			0
$535$	−20.2951	+	35.1522i	−0.877434	+	1.51976i
$536$	−35.0269	−	22.4799i	−1.51293	−	0.970985i
$537$		0			0
$538$	−37.4102	−	22.3872i	−1.61287	−	0.965179i
$539$	9.99362	+	24.2203i	0.430456	+	1.04324i
$540$		0			0
$541$	15.1006	−	26.1550i	0.649224	−	1.12449i	−0.334084	−	0.942543i	$-0.608427\pi$
$541$	15.1006	−	26.1550i	0.649224	−	1.12449i	0.983308	−	0.181946i	$-0.0582397\pi$
$542$	26.9403	+	0.421957i	1.15719	+	0.0181246i
$543$		0			0
$544$	1.95508	−	24.9158i	0.0838233	−	1.06826i
$545$	−1.87175	+	1.08065i	−0.0801768	+	0.0462901i
$546$		0			0
$547$	5.67357	+	3.27564i	0.242584	+	0.140056i	0.616364	−	0.787461i	$-0.288605\pi$
$547$	5.67357	+	3.27564i	0.242584	+	0.140056i	−0.373780	+	0.927518i	$0.621938\pi$
$548$	−3.17455	+	5.12110i	−0.135610	+	0.218762i
$549$		0			0
$550$	13.3509	−	7.43185i	0.569286	−	0.316895i
$551$	5.12885	+	8.88343i	0.218496	+	0.378447i
$552$		0			0
$553$	−17.1904	−	19.6289i	−0.731010	−	0.834707i
$554$	0.172855	+	0.310526i	0.00734393	+	0.0131930i
$555$		0			0
$556$	7.39963	+	0.231853i	0.313814	+	0.00983276i
$557$	−0.158409	−	0.274372i	−0.00671199	−	0.0116255i	0.862650	−	0.505801i	$-0.168803\pi$
$557$	−0.158409	−	0.274372i	−0.00671199	−	0.0116255i	−0.869362	+	0.494176i	$0.835470\pi$
$558$		0			0
$559$	1.11469			0.0471463
$560$	18.1426	+	23.5403i	0.766664	+	0.994761i
$561$		0			0
$562$	−16.6137	−	0.260215i	−0.700807	−	0.0109765i
$563$	3.36690	−	5.83164i	0.141898	−	0.245774i	−0.786313	−	0.617828i	$-0.788013\pi$
$563$	3.36690	−	5.83164i	0.141898	−	0.245774i	0.928211	+	0.372053i	$0.121346\pi$
$564$		0			0
$565$	17.0659	−	9.85302i	0.717969	−	0.414519i
$566$	−12.3148	−	0.192882i	−0.517628	−	0.00810744i
$567$		0			0
$568$	−0.713138	+	15.1671i	−0.0299226	+	0.636397i
$569$	1.67784	+	2.90610i	0.0703387	+	0.121830i	0.899050	−	0.437846i	$-0.144259\pi$
$569$	1.67784	+	2.90610i	0.0703387	+	0.121830i	−0.828711	+	0.559677i	$0.810925\pi$
$570$		0			0
$571$	−20.8972	−	12.0650i	−0.874520	−	0.504904i	−0.00567203	−	0.999984i	$-0.501805\pi$
$571$	−20.8972	−	12.0650i	−0.874520	−	0.504904i	−0.868847	+	0.495080i	$0.835139\pi$
$572$	4.57735	+	0.143422i	0.191389	+	0.00599678i
$573$		0			0
$574$	−5.01540	+	14.0179i	−0.209339	+	0.585095i
$575$		−	20.7478i		−	0.865244i
$576$		0			0
$577$	−32.0115	+	18.4819i	−1.33266	+	0.769410i	−0.985706	−	0.168473i	$-0.946116\pi$
$577$	−32.0115	+	18.4819i	−1.33266	+	0.769410i	−0.346951	+	0.937883i	$0.612783\pi$
$578$	−3.56245	−	0.0557975i	−0.148178	−	0.00232087i
$579$		0			0
$580$	42.6838	−	22.8920i	1.77235	−	0.950537i
$581$	−10.9074	−	3.71086i	−0.452513	−	0.153953i
$582$		0			0
$583$	−1.11436	+	0.643375i	−0.0461520	+	0.0266459i
$584$	−4.38909	+	2.26616i	−0.181622	+	0.0937742i
$585$		0			0
$586$	−14.0997	−	8.43763i	−0.582455	−	0.348555i
$587$	7.18018	−	12.4364i	0.296358	−	0.513307i	−0.678942	−	0.734192i	$-0.737561\pi$
$587$	7.18018	−	12.4364i	0.296358	−	0.513307i	0.975300	+	0.220885i	$0.0708945\pi$
$588$		0			0
$589$	−2.38612	−	4.13288i	−0.0983184	−	0.170292i
$590$	0.810098	−	51.7216i	0.0333512	−	2.12934i
$591$		0			0
$592$	37.6961	+	2.36458i	1.54930	+	0.0971838i
$593$	−29.2573	−	16.8917i	−1.20146	−	0.693660i	−0.240577	−	0.970630i	$-0.577336\pi$
$593$	−29.2573	−	16.8917i	−1.20146	−	0.693660i	−0.960879	+	0.276970i	$0.910670\pi$
$594$		0			0
$595$	24.6952	−	21.6273i	1.01240	−	0.886631i
$596$	−11.9078	+	19.2092i	−0.487761	+	0.786841i
$597$		0			0
$598$	3.19313	−	5.33589i	0.130577	−	0.218201i
$599$	25.4130	+	14.6722i	1.03835	+	0.599490i	0.919365	−	0.393406i	$-0.128703\pi$
$599$	25.4130	+	14.6722i	1.03835	+	0.599490i	0.118983	+	0.992896i	$0.462037\pi$
$600$		0			0
$601$	2.28904	+	1.32158i	0.0933717	+	0.0539082i	0.545959	−	0.837812i	$-0.316166\pi$
$601$	2.28904	+	1.32158i	0.0933717	+	0.0539082i	−0.452587	+	0.891720i	$0.649499\pi$
$602$	6.70761	−	1.22061i	0.273382	−	0.0497485i
$603$		0			0
$604$	8.30277	+	5.14686i	0.337835	+	0.209423i
$605$		−	8.45342i		−	0.343680i
$606$		0			0
$607$	−14.2928			−0.580128			−0.290064	−	0.957007i	$-0.593677\pi$
$607$	−14.2928			−0.580128			−0.290064	+	0.957007i	$0.593677\pi$
$608$	2.89826	+	6.07269i	0.117540	+	0.246280i
$609$		0			0
$610$	4.43420	−	7.40979i	0.179535	−	0.300014i
$611$	−1.28347	−	0.741011i	−0.0519236	−	0.0299781i
$612$		0			0
$613$	−8.49136	−	14.7075i	−0.342963	−	0.594029i	0.642019	−	0.766689i	$-0.278097\pi$
$613$	−8.49136	−	14.7075i	−0.342963	−	0.594029i	−0.984981	+	0.172660i	$0.944764\pi$
$614$	−16.3757	−	29.4181i	−0.660868	−	1.18722i
$615$		0			0
$616$	27.7011	−	4.14927i	1.11611	−	0.167179i
$617$	−6.62896	−	11.4817i	−0.266872	−	0.462235i	0.701181	−	0.712984i	$-0.252657\pi$
$617$	−6.62896	−	11.4817i	−0.266872	−	0.462235i	−0.968052	+	0.250748i	$0.919323\pi$
$618$		0			0
$619$	40.3420			1.62148			0.810741	−	0.585405i	$-0.199064\pi$
$619$	40.3420			1.62148			0.810741	+	0.585405i	$0.199064\pi$
$620$	−19.8580	+	10.6501i	−0.797516	+	0.427720i
$621$		0			0
$622$	33.8860	+	0.530746i	1.35871	+	0.0212810i
$623$	0.851433	−	2.50262i	0.0341119	−	0.100265i
$624$		0			0
$625$	−31.1005			−1.24402
$626$	−12.5108	−	7.48677i	−0.500032	−	0.299231i
$627$		0			0
$628$	−20.5465	+	11.0194i	−0.819894	+	0.439721i
$629$		−	41.7178i		−	1.66340i
$630$		0			0
$631$		−	10.1900i		−	0.405658i	−0.979214	−	0.202829i	$-0.934986\pi$
$631$		−	10.1900i		−	0.405658i	0.979214	−	0.202829i	$-0.0650136\pi$
$632$	−24.7851	+	12.7969i	−0.985898	+	0.509035i
$633$		0			0
$634$	−9.27638	+	15.5013i	−0.368412	+	0.615637i
$635$	−48.0038			−1.90497
$636$		0			0
$637$	−2.61152	+	3.39378i	−0.103472	+	0.134467i
$638$	0.714880	−	45.6423i	0.0283024	−	1.80699i
$639$		0			0
$640$	29.0887	−	12.7803i	1.14983	−	0.505187i
$641$	12.6080			0.497985			0.248992	−	0.968505i	$-0.419901\pi$
$641$	12.6080			0.497985			0.248992	+	0.968505i	$0.419901\pi$
$642$		0			0
$643$	20.9389	+	36.2672i	0.825749	+	1.43024i	0.901345	+	0.433101i	$0.142581\pi$
$643$	20.9389	+	36.2672i	0.825749	+	1.43024i	−0.0755963	+	0.997139i	$0.524086\pi$
$644$	13.3716	−	35.6051i	0.526915	−	1.40304i
$645$		0			0
$646$	6.49382	−	3.61481i	0.255496	−	0.142223i
$647$	4.79985	+	8.31358i	0.188702	+	0.326841i	0.944818	−	0.327597i	$-0.106239\pi$
$647$	4.79985	+	8.31358i	0.188702	+	0.326841i	−0.756116	+	0.654438i	$0.772905\pi$
$648$		0			0
$649$	−42.2198	−	24.3756i	−1.65727	−	0.956827i
$650$	2.14295	+	1.28239i	0.0840533	+	0.0502996i
$651$		0			0
$652$	−17.9506	+	9.62720i	−0.703001	+	0.377030i
$653$	−5.72076			−0.223871			−0.111935	−	0.993715i	$-0.535705\pi$
$653$	−5.72076			−0.223871			−0.111935	+	0.993715i	$0.535705\pi$
$654$		0			0
$655$			44.2730i			1.72989i
$656$	13.2585	+	8.80534i	0.517656	+	0.343791i
$657$		0			0
$658$	−8.53466	−	3.05358i	−0.332716	−	0.119041i
$659$	−29.4052	−	16.9771i	−1.14546	−	0.661334i	−0.197686	−	0.980265i	$-0.563343\pi$
$659$	−29.4052	−	16.9771i	−1.14546	−	0.661334i	−0.947778	+	0.318932i	$0.896676\pi$
$660$		0			0
$661$	−33.9178	−	19.5825i	−1.31925	−	0.761669i	−0.335642	−	0.941990i	$-0.608953\pi$
$661$	−33.9178	−	19.5825i	−1.31925	−	0.761669i	−0.983608	+	0.180321i	$0.942286\pi$
$662$	23.0381	+	13.7865i	0.895400	+	0.535829i
$663$		0			0
$664$	−6.65259	+	10.3657i	−0.258171	+	0.402266i
$665$	−2.84664	+	8.36714i	−0.110388	+	0.324464i
$666$		0			0
$667$	−53.6783	−	30.9912i	−2.07843	−	1.19998i
$668$	28.1367	+	0.881608i	1.08864	+	0.0341104i
$669$		0			0
$670$	−58.4339	−	0.915231i	−2.25750	−	0.0353584i
$671$	−4.06916	−	7.04799i	−0.157088	−	0.272085i
$672$		0			0
$673$	−4.87986	+	8.45217i	−0.188105	+	0.325807i	−0.944618	−	0.328171i	$-0.893568\pi$
$673$	−4.87986	+	8.45217i	−0.188105	+	0.325807i	0.756513	+	0.653978i	$0.226901\pi$
$674$	13.9271	−	23.2729i	0.536451	−	0.896439i
$675$		0			0
$676$	−11.9347	−	22.2531i	−0.459027	−	0.855890i
$677$	24.3548	−	14.0612i	0.936031	−	0.540418i	0.0473170	−	0.998880i	$-0.484933\pi$
$677$	24.3548	−	14.0612i	0.936031	−	0.540418i	0.888714	+	0.458462i	$0.151600\pi$
$678$		0			0
$679$	−5.67697	+	16.6863i	−0.217862	+	0.640363i
$680$	−16.0998	−	31.1822i	−0.617400	−	1.19578i
$681$		0			0
$682$	−0.332587	+	21.2344i	−0.0127354	+	0.813106i
$683$	12.9477	−	7.47537i	0.495431	−	0.286037i	−0.231394	−	0.972860i	$-0.574329\pi$
$683$	12.9477	−	7.47537i	0.495431	−	0.286037i	0.726825	+	0.686823i	$0.240995\pi$
$684$		0			0
$685$			8.46037i			0.323254i
$686$	−11.9985	+	23.2817i	−0.458104	+	0.888899i
$687$		0			0
$688$	0.456294	−	7.27420i	0.0173960	−	0.277326i
$689$	−0.182129	−	0.105152i	−0.00693856	−	0.00400598i
$690$		0			0
$691$	6.93133	+	12.0054i	0.263680	+	0.456708i	0.967217	−	0.253951i	$-0.0817303\pi$
$691$	6.93133	+	12.0054i	0.263680	+	0.456708i	−0.703537	+	0.710659i	$0.748397\pi$
$692$	−1.00159	+	31.9659i	−0.0380747	+	1.21516i
$693$		0			0
$694$	0.610422	−	38.9730i	0.0231713	−	1.47940i
$695$	9.00262	−	5.19767i	0.341489	−	0.197159i
$696$		0			0
$697$	8.78978	−	15.2243i	0.332937	−	0.576663i
$698$	−0.408198	+	26.0618i	−0.0154505	+	0.986455i
$699$		0			0
$700$	14.2994	+	5.37018i	0.540466	+	0.202974i
$701$	23.4800			0.886829			0.443414	−	0.896317i	$-0.353767\pi$
$701$	23.4800			0.886829			0.443414	+	0.896317i	$0.353767\pi$
$702$		0			0
$703$	5.61597	+	9.72714i	0.211810	+	0.366866i
$704$	2.80966	−	29.8120i	0.105893	−	1.12358i
$705$		0			0
$706$	23.3110	−	12.9762i	0.877322	−	0.488364i
$707$	−18.4783	+	3.66243i	−0.694948	+	0.137740i
$708$		0			0
$709$	−10.9448	−	18.9570i	−0.411042	−	0.711945i	0.583962	−	0.811781i	$-0.301502\pi$
$709$	−10.9448	−	18.9570i	−0.411042	−	0.711945i	−0.995004	+	0.0998359i	$0.968168\pi$
$710$	10.3698	+	18.6288i	0.389170	+	0.699125i
$711$		0			0
$712$	−2.37833	−	1.52639i	−0.0891318	−	0.0572040i
$713$	24.9730	+	14.4182i	0.935246	+	0.539965i
$714$		0			0
$715$	5.56894	−	3.21523i	0.208267	−	0.120243i
$716$	−0.0974021	+	3.10861i	−0.00364009	+	0.116174i
$717$		0			0
$718$	−0.260815	+	16.6520i	−0.00973351	+	0.621446i
$719$	−0.739214	+	1.28036i	−0.0275680	+	0.0477492i	−0.879480	−	0.475935i	$-0.842110\pi$
$719$	−0.739214	+	1.28036i	−0.0275680	+	0.0477492i	0.851912	+	0.523685i	$0.175443\pi$
$720$		0			0
$721$	5.52002	+	27.8505i	0.205576	+	1.03721i
$722$	12.7703	−	21.3399i	0.475261	−	0.794187i
$723$		0			0
$724$	20.0261	+	12.4141i	0.744264	+	0.461368i
$725$	12.4464	−	21.5577i	0.462247	−	0.800635i
$726$		0			0
$727$	21.0883	−	36.5260i	0.782121	−	1.35467i	−0.148583	−	0.988900i	$-0.547471\pi$
$727$	21.0883	−	36.5260i	0.782121	−	1.35467i	0.930704	−	0.365773i	$-0.119195\pi$
$728$	2.85101	+	3.58179i	0.105665	+	0.132750i
$729$		0			0
$730$	−3.56162	+	5.95167i	−0.131822	+	0.220281i
$731$	−8.05028			−0.297750
$732$		0			0
$733$			40.2452i			1.48649i	0.669020	+	0.743244i	$0.266714\pi$
$733$			40.2452i			1.48649i	−0.669020	+	0.743244i	$0.733286\pi$
$734$	15.6816	+	28.1713i	0.578820	+	1.03982i
$735$		0			0
$736$	−33.5137	−	23.0218i	−1.23533	−	0.848596i
$737$	−27.5390	+	47.6990i	−1.01441	+	1.75702i
$738$		0			0
$739$	−24.9157	+	14.3851i	−0.916540	+	0.529165i	−0.882530	−	0.470257i	$-0.844161\pi$
$739$	−24.9157	+	14.3851i	−0.916540	+	0.529165i	−0.0340104	+	0.999421i	$0.510828\pi$
$740$	46.7377	−	25.0662i	1.71811	−	0.921450i
$741$		0			0
$742$	−1.21110	−	0.433315i	−0.0444609	−	0.0159075i
$743$	17.6335	−	10.1807i	0.646910	−	0.373494i	−0.140361	−	0.990100i	$-0.544826\pi$
$743$	17.6335	−	10.1807i	0.646910	−	0.373494i	0.787272	+	0.616606i	$0.211493\pi$
$744$		0			0
$745$			31.7348i			1.16267i
$746$	−3.43476	−	6.17037i	−0.125756	−	0.225913i
$747$		0			0
$748$	−33.0576	−	1.03579i	−1.20870	−	0.0378724i
$749$	−12.3168	+	36.2028i	−0.450046	+	1.32282i
$750$		0			0
$751$			4.56051i			0.166415i	0.996532	+	0.0832077i	$0.0265165\pi$
$751$			4.56051i			0.166415i	−0.996532	+	0.0832077i	$0.973484\pi$
$752$	−5.36105	+	8.07229i	−0.195497	+	0.294366i
$753$		0			0
$754$	6.51871	−	3.62867i	0.237397	−	0.132148i
$755$	13.7167			0.499201
$756$		0			0
$757$	−33.7462			−1.22653			−0.613264	−	0.789878i	$-0.710144\pi$
$757$	−33.7462			−1.22653			−0.613264	+	0.789878i	$0.710144\pi$
$758$	39.8884	−	22.2040i	1.44881	−	0.806486i
$759$		0			0
$760$	7.95161	+	5.10327i	0.288435	+	0.185115i
$761$		−	45.0168i		−	1.63186i	−0.578152	−	0.815929i	$-0.696226\pi$
$761$		−	45.0168i		−	1.63186i	0.578152	−	0.815929i	$-0.303774\pi$
$762$		0			0
$763$	−1.53181	+	1.34151i	−0.0554553	+	0.0485660i
$764$	0.907532	−	28.9641i	0.0328334	−	1.04788i
$765$		0			0
$766$	12.1356	+	21.8010i	0.438477	+	0.787701i
$767$		−	7.96784i		−	0.287702i
$768$		0			0
$769$	16.8566	−	9.73214i	0.607863	−	0.350950i	−0.164265	−	0.986416i	$-0.552525\pi$
$769$	16.8566	−	9.73214i	0.607863	−	0.350950i	0.772129	+	0.635466i	$0.219192\pi$
$770$	29.9902	−	25.4457i	1.08077	−	0.916999i
$771$		0			0
$772$	8.70989	+	16.2402i	0.313476	+	0.584499i
$773$	1.15063	−	0.664319i	0.0413855	−	0.0238939i	−0.479165	−	0.877725i	$-0.659060\pi$
$773$	1.15063	−	0.664319i	0.0413855	−	0.0238939i	0.520550	+	0.853831i	$0.325727\pi$
$774$		0			0
$775$	−5.79049	+	10.0294i	−0.208000	+	0.360267i
$776$	15.8576	+	10.1773i	0.569256	+	0.365343i
$777$		0			0
$778$	10.6687	+	19.1658i	0.382493	+	0.687129i
$779$			4.73305i			0.169579i
$780$		0			0
$781$	20.0936			0.719006
$782$	−23.0607	+	38.5357i	−0.824650	+	1.37804i
$783$		0			0
$784$	21.0780	+	18.4314i	0.752787	+	0.658265i
$785$	−16.3689	+	28.3517i	−0.584230	+	1.01192i
$786$		0			0
$787$	17.2452	−	29.8695i	0.614724	−	1.06473i	−0.375709	−	0.926738i	$-0.622601\pi$
$787$	17.2452	−	29.8695i	0.614724	−	1.06473i	0.990433	−	0.137995i	$-0.0440658\pi$
$788$	−10.0626	+	16.2327i	−0.358467	+	0.578268i
$789$		0			0
$790$	−20.1124	+	33.6089i	−0.715567	+	1.19575i
$791$	13.9665	−	12.2314i	0.496592	−	0.434900i
$792$		0			0
$793$	0.665057	−	1.15191i	0.0236169	−	0.0409056i
$794$	0.759019	−	48.4604i	0.0269366	−	1.71979i
$795$		0			0
$796$	33.5059	+	1.04984i	1.18758	+	0.0372106i
$797$	−18.1134	+	10.4578i	−0.641608	+	0.370433i	−0.785234	−	0.619199i	$-0.787457\pi$
$797$	−18.1134	+	10.4578i	−0.641608	+	0.370433i	0.143625	+	0.989632i	$0.454124\pi$
$798$		0			0
$799$	9.26920	+	5.35157i	0.327921	+	0.189325i
$800$	9.24580	−	13.4594i	0.326888	−	0.475863i
$801$		0			0
$802$	4.71102	+	8.46311i	0.166352	+	0.298843i
$803$	3.26842	+	5.66106i	0.115340	+	0.199775i
$804$		0			0
$805$	−10.3829	−	52.3855i	−0.365949	−	1.84635i
$806$	−3.03273	+	1.68818i	−0.106823	+	0.0594637i
$807$		0			0
$808$	−0.945839	+	20.1162i	−0.0332745	+	0.707685i
$809$	−1.33919	−	2.31955i	−0.0470835	−	0.0815510i	0.841523	−	0.540221i	$-0.181659\pi$
$809$	−1.33919	−	2.31955i	−0.0470835	−	0.0815510i	−0.888607	+	0.458670i	$0.848326\pi$
$810$		0			0
$811$	−4.16084			−0.146107			−0.0730534	−	0.997328i	$-0.523274\pi$
$811$	−4.16084			−0.146107			−0.0730534	+	0.997328i	$0.523274\pi$
$812$	35.2527	−	28.9735i	1.23713	−	1.01677i
$813$		0			0
$814$	0.782776	−	49.9772i	0.0274363	−	1.75170i
$815$	−14.3008	+	24.7698i	−0.500936	+	0.867647i
$816$		0			0
$817$	1.87705	−	1.08371i	0.0656695	−	0.0379143i
$818$	0.757487	−	48.3625i	0.0264849	−	1.69096i
$819$		0			0
$820$	22.3376	+	0.699906i	0.780064	+	0.0244418i
$821$	5.82911	+	10.0963i	0.203437	+	0.352364i	0.949634	−	0.313362i	$-0.101455\pi$
$821$	5.82911	+	10.0963i	0.203437	+	0.352364i	−0.746196	+	0.665726i	$0.768122\pi$
$822$		0			0
$823$	21.1757	+	12.2258i	0.738138	+	0.426164i	0.821392	−	0.570364i	$-0.193198\pi$
$823$	21.1757	+	12.2258i	0.738138	+	0.426164i	−0.0832536	+	0.996528i	$0.526531\pi$
$824$	30.3191	+	1.42557i	1.05622	+	0.0496620i
$825$		0			0
$826$	−8.72498	−	47.9462i	−0.303581	−	1.66826i
$827$			1.50378i			0.0522917i	0.999658	+	0.0261458i	$0.00832343\pi$
$827$			1.50378i			0.0522917i	−0.999658	+	0.0261458i	$0.991677\pi$
$828$		0			0
$829$	−41.9427	+	24.2157i	−1.45673	+	0.841044i	−0.998849	−	0.0479683i	$-0.984725\pi$
$829$	−41.9427	+	24.2157i	−1.45673	+	0.841044i	−0.457883	+	0.889013i	$0.651392\pi$
$830$	−0.270848	+	17.2926i	−0.00940129	+	0.600235i
$831$		0			0
$832$	4.44925	−	2.03853i	0.154250	−	0.0706733i
$833$	18.8604	−	24.5099i	0.653473	−	0.849217i
$834$		0			0
$835$	34.2320	−	19.7638i	1.18465	−	0.683956i
$836$	7.84731	−	4.20863i	0.271405	−	0.145559i
$837$		0			0
$838$	−14.6070	+	24.4092i	−0.504592	+	0.843201i
$839$	−5.29494	+	9.17110i	−0.182801	+	0.316621i	−0.942833	−	0.333264i	$-0.891850\pi$
$839$	−5.29494	+	9.17110i	−0.182801	+	0.316621i	0.760032	+	0.649886i	$0.225183\pi$
$840$		0			0
$841$	−22.6825	−	39.2872i	−0.782154	−	1.35473i
$842$	−8.62548	−	0.135098i	−0.297254	−	0.00465579i
$843$		0			0
$844$	−0.541246	+	17.2740i	−0.0186305	+	0.594595i
$845$	−30.7067	−	17.7285i	−1.05634	−	0.609880i
$846$		0			0
$847$	−1.54838	−	7.81212i	−0.0532029	−	0.268428i
$848$	−0.760753	+	1.14549i	−0.0261244	+	0.0393362i
$849$		0			0
$850$	−15.4763	−	9.26142i	−0.530834	−	0.317664i
$851$	−58.7764	−	33.9346i	−2.01483	−	1.16326i
$852$		0			0
$853$	32.3692	+	18.6884i	1.10830	+	0.639877i	0.938389	−	0.345582i	$-0.112318\pi$
$853$	32.3692	+	18.6884i	1.10830	+	0.639877i	0.169912	+	0.985459i	$0.445652\pi$
$854$	2.74059	−	7.65986i	0.0937811	−	0.262115i
$855$		0			0
$856$	34.4049	+	22.0807i	1.17593	+	0.754704i
$857$			6.87661i			0.234900i	0.993079	+	0.117450i	$0.0374721\pi$
$857$			6.87661i			0.234900i	−0.993079	+	0.117450i	$0.962528\pi$
$858$		0			0
$859$	8.64934			0.295112			0.147556	−	0.989054i	$-0.452859\pi$
$859$	8.64934			0.295112			0.147556	+	0.989054i	$0.452859\pi$
$860$	−4.83701	−	9.01898i	−0.164941	−	0.307545i
$861$		0			0
$862$	−32.6200	−	19.5206i	−1.11104	−	0.664874i
$863$	−26.5454	−	15.3260i	−0.903617	−	0.521703i	−0.0252448	−	0.999681i	$-0.508037\pi$
$863$	−26.5454	−	15.3260i	−0.903617	−	0.521703i	−0.878372	+	0.477978i	$0.841370\pi$
$864$		0			0
$865$	22.4535	+	38.8907i	0.763443	+	1.32232i
$866$	19.8083	−	11.0263i	0.673112	−	0.374690i
$867$		0			0
$868$	−16.4008	+	13.4795i	−0.556679	+	0.457524i
$869$	18.4567	+	31.9679i	0.626100	+	1.08444i
$870$		0			0
$871$	−9.00188			−0.305017
$872$	0.998653	+	1.93419i	0.0338187	+	0.0655000i
$873$		0			0
$874$	0.189355	−	12.0896i	0.00640504	−	0.408936i
$875$	−15.4030	+	3.05291i	−0.520717	+	0.103207i
$876$		0			0
$877$	43.3101			1.46248			0.731239	−	0.682122i	$-0.238942\pi$
$877$	43.3101			1.46248			0.731239	+	0.682122i	$0.238942\pi$
$878$	−14.2984	+	23.8935i	−0.482549	+	0.806366i
$879$		0			0
$880$	−18.7022	−	37.6578i	−0.630452	−	1.26944i
$881$			16.8008i			0.566034i	0.959115	+	0.283017i	$0.0913353\pi$
$881$			16.8008i			0.566034i	−0.959115	+	0.283017i	$0.908665\pi$
$882$		0			0
$883$		−	12.8684i		−	0.433055i	−0.976277	−	0.216527i	$-0.930527\pi$
$883$		−	12.8684i		−	0.433055i	0.976277	−	0.216527i	$-0.0694731\pi$
$884$	−2.55483	−	4.76367i	−0.0859283	−	0.160220i
$885$		0			0
$886$	8.74243	+	5.23169i	0.293708	+	0.175762i
$887$	48.9052			1.64208			0.821039	−	0.570873i	$-0.193395\pi$
$887$	48.9052			1.64208			0.821039	+	0.570873i	$0.193395\pi$
$888$		0			0
$889$	−44.3621	+	8.79266i	−1.48786	+	0.294896i
$890$	−3.96767	−	0.0621444i	−0.132997	−	0.00208308i
$891$		0			0
$892$	18.6021	+	34.6850i	0.622844	+	1.16134i
$893$	−2.88167			−0.0964315
$894$		0			0
$895$	2.18356	+	3.78203i	0.0729882	+	0.126419i
$896$	24.5410	−	17.1388i	0.819857	−	0.572568i
$897$		0			0
$898$	4.41912	+	7.93873i	0.147468	+	0.264919i
$899$	17.2986	+	29.9620i	0.576940	+	0.999289i
$900$		0			0
$901$	1.31533	+	0.759408i	0.0438201	+	0.0252996i
$902$	10.8157	−	18.0736i	0.360122	−	0.601784i
$903$		0			0
$904$	−9.10537	−	17.6353i	−0.302840	−	0.586541i
$905$	33.0844			1.09976
$906$		0			0
$907$		−	3.89966i		−	0.129486i	−0.997902	−	0.0647431i	$-0.979377\pi$
$907$		−	3.89966i		−	0.129486i	0.997902	−	0.0647431i	$-0.0206228\pi$
$908$	12.6185	−	20.3558i	0.418760	−	0.675531i
$909$		0			0
$910$	6.05241	+	2.16547i	0.200635	+	0.0717845i
$911$	19.4469	+	11.2277i	0.644305	+	0.371990i	0.786271	−	0.617882i	$-0.212009\pi$
$911$	19.4469	+	11.2277i	0.644305	+	0.371990i	−0.141966	+	0.989872i	$0.545342\pi$
$912$		0			0
$913$	14.1158	+	8.14976i	0.467165	+	0.269718i
$914$	26.4613	−	44.2184i	0.875263	−	1.46261i
$915$		0			0
$916$	−4.65968	−	2.88852i	−0.153960	−	0.0954395i
$917$	8.10930	+	40.9143i	0.267793	+	1.35111i
$918$		0			0
$919$	27.1929	+	15.6998i	0.897012	+	0.517890i	0.876229	−	0.481894i	$-0.160051\pi$
$919$	27.1929	+	15.6998i	0.897012	+	0.517890i	0.0207822	+	0.999784i	$0.493384\pi$
$920$	−57.0288	−	2.68143i	−1.88019	−	0.0884040i
$921$		0			0
$922$	−0.0486896	+	3.10864i	−0.00160351	+	0.102378i
$923$	1.64203	+	2.84409i	0.0540482	+	0.0936143i
$924$		0			0
$925$	13.6285	−	23.6052i	0.448101	−	0.776135i
$926$	−4.17830	−	2.50039i	−0.137307	−	0.0821681i
$927$		0			0
$928$	−21.0114	−	44.0250i	−0.689734	−	1.44519i
$929$	−21.7375	+	12.5502i	−0.713186	+	0.411758i	−0.812239	−	0.583324i	$-0.801752\pi$
$929$	−21.7375	+	12.5502i	−0.713186	+	0.411758i	0.0990538	+	0.995082i	$0.468418\pi$
$930$		0			0
$931$	−1.09811	+	8.25380i	−0.0359892	+	0.270507i
$932$	15.3273	+	28.5789i	0.502062	+	0.936133i
$933$		0			0
$934$	0.663574	+	0.0103933i	0.0217128	+	0.000340081i
$935$	−40.2189	+	23.2204i	−1.31530	+	0.759387i
$936$		0			0
$937$		−	19.0090i		−	0.620996i	−0.950574	−	0.310498i	$-0.899504\pi$
$937$		−	19.0090i		−	0.620996i	0.950574	−	0.310498i	$-0.100496\pi$
$938$	−54.1686	+	9.85729i	−1.76867	+	0.321852i
$939$		0			0
$940$	−0.426131	+	13.6001i	−0.0138989	+	0.443585i
$941$	32.3963	+	18.7040i	1.05609	+	0.609734i	0.924348	−	0.381550i	$-0.124610\pi$
$941$	32.3963	+	18.7040i	1.05609	+	0.609734i	0.131742	+	0.991284i	$0.457943\pi$
$942$		0			0
$943$	−14.2998	−	24.7679i	−0.465665	−	0.806555i
$944$	−51.9962	−	3.26160i	−1.69233	−	0.106156i
$945$		0			0
$946$	−9.64409	−	0.151052i	−0.313556	−	0.00491113i
$947$	−23.5502	+	13.5967i	−0.765279	+	0.441834i	−0.831188	−	0.555992i	$-0.812339\pi$
$947$	−23.5502	+	13.5967i	−0.765279	+	0.441834i	0.0659089	+	0.997826i	$0.479005\pi$
$948$		0			0
$949$	−0.534185	+	0.925236i	−0.0173404	+	0.0300344i
$950$	4.85530	+	0.0760470i	0.157527	+	0.00246729i
$951$		0			0
$952$	−20.5900	−	25.8677i	−0.667325	−	0.838376i
$953$	−25.8339			−0.836841			−0.418420	−	0.908253i	$-0.637416\pi$
$953$	−25.8339			−0.836841			−0.418420	+	0.908253i	$0.637416\pi$
$954$		0			0
$955$	−20.3450	−	35.2386i	−0.658349	−	1.14029i
$956$	−0.249678	+	7.96853i	−0.00807518	+	0.257721i
$957$		0			0
$958$	−5.17018	−	9.28795i	−0.167041	−	0.300080i
$959$	1.54965	+	7.81854i	0.0500408	+	0.252474i
$960$		0			0
$961$	7.45210	+	12.9074i	0.240390	+	0.416368i
$962$	7.13783	−	3.97330i	0.230133	−	0.128104i
$963$		0			0
$964$	19.1139	+	11.8486i	0.615617	+	0.381619i
$965$	22.4096	+	12.9382i	0.721392	+	0.416496i
$966$		0			0
$967$	−38.1504	+	22.0262i	−1.22683	+	0.708313i	−0.966366	−	0.257169i	$-0.917210\pi$
$967$	−38.1504	+	22.0262i	−1.22683	+	0.708313i	−0.260468	+	0.965482i	$0.583877\pi$
$968$	−8.50457	−	0.399875i	−0.273347	−	0.0128525i
$969$		0			0
$970$	26.4546	+	0.414350i	0.849407	+	0.0133040i
$971$	17.9137	−	31.0274i	0.574877	−	0.995716i	−0.421178	−	0.906978i	$-0.638383\pi$
$971$	17.9137	−	31.0274i	0.574877	−	0.995716i	0.996055	−	0.0887384i	$-0.0282835\pi$
$972$		0			0
$973$	7.36763	−	6.45233i	0.236195	−	0.206852i
$974$	−15.4676	−	9.25621i	−0.495615	−	0.296588i
$975$		0			0
$976$	−7.24488	−	4.81154i	−0.231903	−	0.154014i
$977$	−19.8906	+	34.4515i	−0.636355	+	1.10220i	0.349871	+	0.936798i	$0.386225\pi$
$977$	−19.8906	+	34.4515i	−0.636355	+	1.10220i	−0.986226	+	0.165402i	$0.947108\pi$
$978$		0			0
$979$	−1.86991	+	3.23877i	−0.0597625	+	0.103512i
$980$	38.7915	+	6.40310i	1.23915	+	0.204539i
$981$		0			0
$982$	−23.5206	−	14.0753i	−0.750573	−	0.449161i
$983$	2.89853			0.0924488			0.0462244	−	0.998931i	$-0.485281\pi$
$983$	2.89853			0.0924488			0.0462244	+	0.998931i	$0.485281\pi$
$984$		0			0
$985$			26.8175i			0.854476i
$986$	−47.0781	+	26.2062i	−1.49927	+	0.834575i
$987$		0			0
$988$	1.23697	+	0.766797i	0.0393534	+	0.0243951i
$989$	−6.54835	+	11.3421i	−0.208226	+	0.360657i
$990$		0			0
$991$	−35.6534	+	20.5845i	−1.13257	+	0.653888i	−0.944579	−	0.328283i	$-0.893530\pi$
$991$	−35.6534	+	20.5845i	−1.13257	+	0.653888i	−0.187988	+	0.982171i	$0.560197\pi$
$992$	9.77524	+	20.4820i	0.310364	+	0.650303i
$993$		0			0
$994$	12.9952	+	15.3161i	0.412184	+	0.485799i
$995$	40.7643	−	23.5353i	1.29232	−	0.746119i
$996$		0			0
$997$		−	25.6576i		−	0.812585i	−0.913743	−	0.406292i	$-0.866821\pi$
$997$		−	25.6576i		−	0.812585i	0.913743	−	0.406292i	$-0.133179\pi$
$998$	−26.0346	+	14.4923i	−0.824111	+	0.458745i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.n.b.19.15		84
3.2	odd	2		252.2.n.b.187.28	yes	84
4.3	odd	2	inner	756.2.n.b.19.14		84
7.3	odd	6		756.2.bj.b.451.42		84
9.4	even	3		756.2.bj.b.523.42		84
9.5	odd	6		252.2.bj.b.103.1	yes	84
12.11	even	2		252.2.n.b.187.29	yes	84
21.17	even	6		252.2.bj.b.115.1	yes	84
28.3	even	6		756.2.bj.b.451.41		84
36.23	even	6		252.2.bj.b.103.2	yes	84
36.31	odd	6		756.2.bj.b.523.41		84
63.31	odd	6	inner	756.2.n.b.199.14		84
63.59	even	6		252.2.n.b.31.29	yes	84
84.59	odd	6		252.2.bj.b.115.2	yes	84
252.31	even	6	inner	756.2.n.b.199.15		84
252.59	odd	6		252.2.n.b.31.28	✓	84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.n.b.31.28	✓	84	252.59	odd	6
252.2.n.b.31.29	yes	84	63.59	even	6
252.2.n.b.187.28	yes	84	3.2	odd	2
252.2.n.b.187.29	yes	84	12.11	even	2
252.2.bj.b.103.1	yes	84	9.5	odd	6
252.2.bj.b.103.2	yes	84	36.23	even	6
252.2.bj.b.115.1	yes	84	21.17	even	6
252.2.bj.b.115.2	yes	84	84.59	odd	6
756.2.n.b.19.14		84	4.3	odd	2	inner
756.2.n.b.19.15		84	1.1	even	1	trivial
756.2.n.b.199.14		84	63.31	odd	6	inner
756.2.n.b.199.15		84	252.31	even	6	inner
756.2.bj.b.451.41		84	28.3	even	6
756.2.bj.b.451.42		84	7.3	odd	6
756.2.bj.b.523.41		84	36.31	odd	6
756.2.bj.b.523.42		84	9.4	even	3

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:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.n (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.687840 - 1.23567i) q^{2} +(-1.05375 + 1.69988i) q^{4} +2.80831i q^{5} +(0.514387 + 2.59527i) q^{7} +(2.82531 + 0.132842i) q^{8} +O(q^{10})\)	\(q+(-0.687840 - 1.23567i) q^{2} +(-1.05375 + 1.69988i) q^{4} +2.80831i q^{5} +(0.514387 + 2.59527i) q^{7} +(2.82531 + 0.132842i) q^{8} +(3.47014 - 1.93167i) q^{10} -3.74301i q^{11} +(0.529793 - 0.305876i) q^{13} +(2.85307 - 2.42074i) q^{14} +(-1.77921 - 3.58252i) q^{16} +(-3.82616 + 2.20903i) q^{17} +(0.594752 - 1.03014i) q^{19} +(-4.77380 - 2.95927i) q^{20} +(-4.62512 + 2.57459i) q^{22} +7.18760i q^{23} -2.88661 q^{25} +(-0.742374 - 0.444255i) q^{26} +(-4.95369 - 1.86037i) q^{28} +(-4.31175 + 7.46818i) q^{29} +(2.00598 - 3.47446i) q^{31} +(-3.20299 + 4.66271i) q^{32} +(5.36142 + 3.20840i) q^{34} +(-7.28832 + 1.44456i) q^{35} +(-4.72127 + 8.17748i) q^{37} +(-1.68201 - 0.0263447i) q^{38} +(-0.373063 + 7.93434i) q^{40} +(-3.44593 + 1.98951i) q^{41} +(1.57801 + 0.911063i) q^{43} +(6.36269 + 3.94421i) q^{44} +(8.88149 - 4.94392i) q^{46} +(-1.21129 - 2.09802i) q^{47} +(-6.47081 + 2.66994i) q^{49} +(1.98553 + 3.56690i) q^{50} +(-0.0383173 + 1.22290i) q^{52} +(-0.171887 - 0.297717i) q^{53} +10.5115 q^{55} +(1.10854 + 7.40075i) q^{56} +(12.1940 + 0.190990i) q^{58} +(6.51230 - 11.2796i) q^{59} +(1.88297 - 1.08713i) q^{61} +(-5.67307 - 0.0888554i) q^{62} +(7.96471 + 0.750641i) q^{64} +(0.858996 + 1.48782i) q^{65} +(-12.7435 - 7.35746i) q^{67} +(0.276727 - 8.83181i) q^{68} +(6.79819 + 8.01232i) q^{70} +5.36830i q^{71} +(-1.51244 + 0.873205i) q^{73} +(13.3521 + 0.209130i) q^{74} +(1.12440 + 2.09652i) q^{76} +(9.71411 - 1.92536i) q^{77} +(-8.54069 + 4.93097i) q^{79} +(10.0608 - 4.99657i) q^{80} +(4.82861 + 2.88956i) q^{82} +(-2.17733 + 3.77124i) q^{83} +(-6.20366 - 10.7451i) q^{85} +(0.0403558 - 2.57656i) q^{86} +(0.497231 - 10.5752i) q^{88} +(-0.865286 - 0.499573i) q^{89} +(1.06635 + 1.21762i) q^{91} +(-12.2181 - 7.57396i) q^{92} +(-1.75928 + 2.93986i) q^{94} +(2.89296 + 1.67025i) q^{95} +(5.76933 + 3.33092i) q^{97} +(7.75004 + 6.15929i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q + q^{2} + q^{4} + 16 q^{8}+O(q^{10}) \) 84 * q + q^2 + q^4 + 16 * q^8	\( 84 q + q^{2} + q^{4} + 16 q^{8} - 18 q^{10} - 18 q^{13} + 25 q^{14} - 7 q^{16} - 6 q^{17} - 24 q^{20} + 6 q^{22} - 32 q^{25} + 30 q^{26} - 4 q^{28} - 10 q^{29} - 9 q^{32} + 24 q^{34} + 2 q^{37} + 6 q^{41} + 13 q^{44} + 10 q^{46} + 2 q^{49} + 17 q^{50} + 2 q^{53} + 32 q^{56} + 26 q^{58} - 24 q^{61} - 8 q^{64} - 50 q^{65} - 4 q^{70} + 30 q^{73} - 46 q^{74} - 46 q^{77} - 3 q^{80} - 18 q^{82} - 50 q^{85} - 18 q^{86} - 2 q^{88} + 102 q^{89} - 28 q^{92} + 3 q^{94} - 6 q^{97} - 21 q^{98}+O(q^{100}) \) 84 * q + q^2 + q^4 + 16 * q^8 - 18 * q^10 - 18 * q^13 + 25 * q^14 - 7 * q^16 - 6 * q^17 - 24 * q^20 + 6 * q^22 - 32 * q^25 + 30 * q^26 - 4 * q^28 - 10 * q^29 - 9 * q^32 + 24 * q^34 + 2 * q^37 + 6 * q^41 + 13 * q^44 + 10 * q^46 + 2 * q^49 + 17 * q^50 + 2 * q^53 + 32 * q^56 + 26 * q^58 - 24 * q^61 - 8 * q^64 - 50 * q^65 - 4 * q^70 + 30 * q^73 - 46 * q^74 - 46 * q^77 - 3 * q^80 - 18 * q^82 - 50 * q^85 - 18 * q^86 - 2 * q^88 + 102 * q^89 - 28 * q^92 + 3 * q^94 - 6 * q^97 - 21 * q^98

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