LMFDB - Embedded newform 189.2.i.b.152.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,2,Mod(143,189)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(189, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 1]))

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

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

chi := DirichletCharacter("189.143");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	189.i (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:	$1.50917259820$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{6})$
Coefficient field:	10.0.288778218147.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + 7x^{8} - 4x^{7} + 34x^{6} - 19x^{5} + 64x^{4} - x^{3} + 64x^{2} - 21x + 9 $ x^10 - x^9 + 7x^8 - 4x^7 + 34x^6 - 19x^5 + 64x^4 - x^3 + 64x^2 - 21*x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			152.1
Root			$1.07065 + 1.85442i$ of defining polynomial
Character	$\chi$	$=$	189.152
Dual form			189.2.i.b.143.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.59354i q^{2} -4.72645 q^{4} +(-0.626493 - 1.08512i) q^{5} +(-1.89735 - 1.84393i) q^{7} +7.07116i q^{8} +O(q^{10})$	\(q-2.59354i q^{2} -4.72645 q^{4} +(-0.626493 - 1.08512i) q^{5} +(-1.89735 - 1.84393i) q^{7} +7.07116i q^{8} +(-2.81429 + 1.62483i) q^{10} +(0.534126 + 0.308378i) q^{11} +(1.06343 + 0.613974i) q^{13} +(-4.78229 + 4.92086i) q^{14} +8.88643 q^{16} +(-2.21501 - 3.83652i) q^{17} +(-1.64679 - 0.950775i) q^{19} +(2.96109 + 5.12875i) q^{20} +(0.799790 - 1.38528i) q^{22} +(4.11267 - 2.37445i) q^{23} +(1.71501 - 2.97049i) q^{25} +(1.59237 - 2.75806i) q^{26} +(8.96773 + 8.71522i) q^{28} +(5.07629 - 2.93080i) q^{29} +2.48089i q^{31} -8.90499i q^{32} +(-9.95016 + 5.74473i) q^{34} +(-0.812198 + 3.21405i) q^{35} +(1.33217 - 2.30738i) q^{37} +(-2.46587 + 4.27102i) q^{38} +(7.67303 - 4.43003i) q^{40} +(2.09966 - 3.63671i) q^{41} +(-2.24637 - 3.89083i) q^{43} +(-2.52452 - 1.45753i) q^{44} +(-6.15823 - 10.6664i) q^{46} -7.61476 q^{47} +(0.199880 + 6.99715i) q^{49} +(-7.70409 - 4.44796i) q^{50} +(-5.02627 - 2.90192i) q^{52} +(2.67782 - 1.54604i) q^{53} -0.772786i q^{55} +(13.0387 - 13.4165i) q^{56} +(-7.60114 - 13.1656i) q^{58} -3.56459 q^{59} +14.4495i q^{61} +6.43428 q^{62} -5.32259 q^{64} -1.53860i q^{65} +13.6129 q^{67} +(10.4692 + 18.1331i) q^{68} +(8.33577 + 2.10647i) q^{70} +10.4095i q^{71} +(9.95016 - 5.74473i) q^{73} +(-5.98429 - 3.45503i) q^{74} +(7.78348 + 4.49379i) q^{76} +(-0.444799 - 1.56999i) q^{77} -4.03185 q^{79} +(-5.56728 - 9.64281i) q^{80} +(-9.43196 - 5.44554i) q^{82} +(4.36775 + 7.56516i) q^{83} +(-2.77538 + 4.80710i) q^{85} +(-10.0910 + 5.82605i) q^{86} +(-2.18059 + 3.77689i) q^{88} +(-0.811226 + 1.40508i) q^{89} +(-0.885586 - 3.12582i) q^{91} +(-19.4383 + 11.2227i) q^{92} +19.7492i q^{94} +2.38261i q^{95} +(8.76527 - 5.06063i) q^{97} +(18.1474 - 0.518397i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 8 q^{4} - 6 q^{7}+O(q^{10}) $ 10 * q - 8 * q^4 - 6 * q^7	$ 10 q - 8 q^{4} - 6 q^{7} - 15 q^{10} + 12 q^{11} - 6 q^{13} - 12 q^{14} + 12 q^{16} - 12 q^{17} + 3 q^{19} - 3 q^{20} + 5 q^{22} + 15 q^{23} + 7 q^{25} + 3 q^{26} + 2 q^{28} + 15 q^{29} - 3 q^{34} - 15 q^{35} + 6 q^{37} - 18 q^{38} + 15 q^{40} - 9 q^{41} + 3 q^{43} + 24 q^{44} - 13 q^{46} - 30 q^{47} + 4 q^{49} - 3 q^{50} - 12 q^{52} - 9 q^{53} + 30 q^{56} + 8 q^{58} + 36 q^{59} + 12 q^{62} + 6 q^{64} + 20 q^{67} + 27 q^{68} + 6 q^{70} + 3 q^{73} + 30 q^{74} - 9 q^{76} - 39 q^{77} - 40 q^{79} - 30 q^{80} + 9 q^{82} - 15 q^{83} + 18 q^{85} - 54 q^{86} - 8 q^{88} + 24 q^{89} - 24 q^{91} - 39 q^{92} - 6 q^{97} + 45 q^{98}+O(q^{100}) $ 10 * q - 8 * q^4 - 6 * q^7 - 15 * q^10 + 12 * q^11 - 6 * q^13 - 12 * q^14 + 12 * q^16 - 12 * q^17 + 3 * q^19 - 3 * q^20 + 5 * q^22 + 15 * q^23 + 7 * q^25 + 3 * q^26 + 2 * q^28 + 15 * q^29 - 3 * q^34 - 15 * q^35 + 6 * q^37 - 18 * q^38 + 15 * q^40 - 9 * q^41 + 3 * q^43 + 24 * q^44 - 13 * q^46 - 30 * q^47 + 4 * q^49 - 3 * q^50 - 12 * q^52 - 9 * q^53 + 30 * q^56 + 8 * q^58 + 36 * q^59 + 12 * q^62 + 6 * q^64 + 20 * q^67 + 27 * q^68 + 6 * q^70 + 3 * q^73 + 30 * q^74 - 9 * q^76 - 39 * q^77 - 40 * q^79 - 30 * q^80 + 9 * q^82 - 15 * q^83 + 18 * q^85 - 54 * q^86 - 8 * q^88 + 24 * q^89 - 24 * q^91 - 39 * q^92 - 6 * q^97 + 45 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/189\mathbb{Z}\right)^\times$.

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$		−	2.59354i		−	1.83391i	−0.398991	−	0.916955i	$-0.630640\pi$
$2$		−	2.59354i		−	1.83391i	0.398991	−	0.916955i	$-0.369360\pi$
$3$		0			0
$3$		0			0
$4$	−4.72645			−2.36322
$5$	−0.626493	−	1.08512i	−0.280176	−	0.485279i	0.691252	−	0.722614i	$-0.257059\pi$
$5$	−0.626493	−	1.08512i	−0.280176	−	0.485279i	−0.971428	+	0.237335i	$0.923726\pi$
$6$		0			0
$7$	−1.89735	−	1.84393i	−0.717131	−	0.696938i
$7$	−1.89735	−	1.84393i	−0.717131	−	0.696938i
$8$			7.07116i			2.50003i
$9$		0			0
$10$	−2.81429	+	1.62483i	−0.889958	+	0.513817i
$11$	0.534126	+	0.308378i	0.161045	+	0.0929794i	0.578357	−	0.815784i	$-0.303694\pi$
$11$	0.534126	+	0.308378i	0.161045	+	0.0929794i	−0.417311	+	0.908764i	$0.637028\pi$
$12$		0			0
$13$	1.06343	+	0.613974i	0.294944	+	0.170286i	0.640169	−	0.768234i	$-0.278864\pi$
$13$	1.06343	+	0.613974i	0.294944	+	0.170286i	−0.345226	+	0.938520i	$0.612198\pi$
$14$	−4.78229	+	4.92086i	−1.27812	+	1.31515i
$15$		0			0
$16$	8.88643			2.22161
$17$	−2.21501	−	3.83652i	−0.537220	−	0.930492i	−0.999052	−	0.0435249i	$-0.986141\pi$
$17$	−2.21501	−	3.83652i	−0.537220	−	0.930492i	0.461833	−	0.886967i	$-0.347192\pi$
$18$		0			0
$19$	−1.64679	−	0.950775i	−0.377800	−	0.218123i	0.299061	−	0.954234i	$-0.403327\pi$
$19$	−1.64679	−	0.950775i	−0.377800	−	0.218123i	−0.676861	+	0.736111i	$0.736660\pi$
$20$	2.96109	+	5.12875i	0.662119	+	1.14682i
$21$		0			0
$22$	0.799790	−	1.38528i	0.170516	−	0.295342i
$23$	4.11267	−	2.37445i	0.857550	−	0.495107i	−0.00564111	−	0.999984i	$-0.501796\pi$
$23$	4.11267	−	2.37445i	0.857550	−	0.495107i	0.863191	+	0.504877i	$0.168462\pi$
$24$		0			0
$25$	1.71501	−	2.97049i	0.343003	−	0.594098i
$26$	1.59237	−	2.75806i	0.312289	−	0.540900i
$27$		0			0
$28$	8.96773	+	8.71522i	1.69474	+	1.64702i
$29$	5.07629	−	2.93080i	0.942643	−	0.544235i	0.0518553	−	0.998655i	$-0.483487\pi$
$29$	5.07629	−	2.93080i	0.942643	−	0.544235i	0.890788	+	0.454419i	$0.150153\pi$
$30$		0			0
$31$			2.48089i			0.445580i	0.974866	+	0.222790i	$0.0715165\pi$
$31$			2.48089i			0.445580i	−0.974866	+	0.222790i	$0.928484\pi$
$32$		−	8.90499i		−	1.57419i
$33$		0			0
$34$	−9.95016	+	5.74473i	−1.70644	+	0.985213i
$35$	−0.812198	+	3.21405i	−0.137287	+	0.543274i
$36$		0			0
$37$	1.33217	−	2.30738i	0.219007	−	0.379331i	−0.735498	−	0.677527i	$-0.763052\pi$
$37$	1.33217	−	2.30738i	0.219007	−	0.379331i	0.954505	+	0.298196i	$0.0963849\pi$
$38$	−2.46587	+	4.27102i	−0.400018	+	0.692851i
$39$		0			0
$40$	7.67303	−	4.43003i	1.21321	−	0.700449i
$41$	2.09966	−	3.63671i	0.327911	−	0.567959i	−0.654186	−	0.756334i	$-0.726989\pi$
$41$	2.09966	−	3.63671i	0.327911	−	0.567959i	0.982097	+	0.188375i	$0.0603220\pi$
$42$		0			0
$43$	−2.24637	−	3.89083i	−0.342568	−	0.593346i	0.642340	−	0.766419i	$-0.277964\pi$
$43$	−2.24637	−	3.89083i	−0.342568	−	0.593346i	−0.984909	+	0.173073i	$0.944630\pi$
$44$	−2.52452	−	1.45753i	−0.380586	−	0.219731i
$45$		0			0
$46$	−6.15823	−	10.6664i	−0.907981	−	1.57267i
$47$	−7.61476			−1.11073			−0.555364	−	0.831608i	$-0.687421\pi$
$47$	−7.61476			−1.11073			−0.555364	+	0.831608i	$0.687421\pi$
$48$		0			0
$49$	0.199880	+	6.99715i	0.0285543	+	0.999592i
$50$	−7.70409	−	4.44796i	−1.08952	−	0.629036i
$51$		0			0
$52$	−5.02627	−	2.90192i	−0.697018	−	0.402424i
$53$	2.67782	−	1.54604i	0.367827	−	0.212365i	−0.304682	−	0.952454i	$-0.598550\pi$
$53$	2.67782	−	1.54604i	0.367827	−	0.212365i	0.672509	+	0.740089i	$0.265217\pi$
$54$		0			0
$55$		−	0.772786i		−	0.104202i
$56$	13.0387	−	13.4165i	1.74237	−	1.79285i
$57$		0			0
$58$	−7.60114	−	13.1656i	−0.998078	−	1.72872i
$59$	−3.56459			−0.464070			−0.232035	−	0.972707i	$-0.574538\pi$
$59$	−3.56459			−0.464070			−0.232035	+	0.972707i	$0.574538\pi$
$60$		0			0
$61$			14.4495i			1.85006i	0.379890	+	0.925032i	$0.375962\pi$
$61$			14.4495i			1.85006i	−0.379890	+	0.925032i	$0.624038\pi$
$62$	6.43428			0.817154
$63$		0			0
$64$	−5.32259			−0.665324
$65$		−	1.53860i		−	0.190840i
$66$		0			0
$67$	13.6129			1.66308			0.831539	−	0.555467i	$-0.187460\pi$
$67$	13.6129			1.66308			0.831539	+	0.555467i	$0.187460\pi$
$68$	10.4692	+	18.1331i	1.26957	+	2.19896i
$69$		0			0
$70$	8.33577	+	2.10647i	0.996316	+	0.251771i
$71$			10.4095i			1.23538i	0.786420	+	0.617692i	$0.211932\pi$
$71$			10.4095i			1.23538i	−0.786420	+	0.617692i	$0.788068\pi$
$72$		0			0
$73$	9.95016	−	5.74473i	1.16458	−	0.672369i	0.212181	−	0.977230i	$-0.431943\pi$
$73$	9.95016	−	5.74473i	1.16458	−	0.672369i	0.952397	+	0.304861i	$0.0986100\pi$
$74$	−5.98429	−	3.45503i	−0.695659	−	0.401639i
$75$		0			0
$76$	7.78348	+	4.49379i	0.892826	+	0.515473i
$77$	−0.444799	−	1.56999i	−0.0506895	−	0.178917i
$78$		0			0
$79$	−4.03185			−0.453618			−0.226809	−	0.973939i	$-0.572829\pi$
$79$	−4.03185			−0.453618			−0.226809	+	0.973939i	$0.572829\pi$
$80$	−5.56728	−	9.64281i	−0.622441	−	1.07810i
$81$		0			0
$82$	−9.43196	−	5.44554i	−1.04159	−	0.601360i
$83$	4.36775	+	7.56516i	0.479422	+	0.830384i	0.999721	−	0.0236001i	$-0.00751285\pi$
$83$	4.36775	+	7.56516i	0.479422	+	0.830384i	−0.520299	+	0.853984i	$0.674180\pi$
$84$		0			0
$85$	−2.77538	+	4.80710i	−0.301032	+	0.521403i
$86$	−10.0910	+	5.82605i	−1.08814	+	0.628240i
$87$		0			0
$88$	−2.18059	+	3.77689i	−0.232451	+	0.402618i
$89$	−0.811226	+	1.40508i	−0.0859897	+	0.148939i	−0.905813	−	0.423679i	$-0.860739\pi$
$89$	−0.811226	+	1.40508i	−0.0859897	+	0.148939i	0.819823	+	0.572617i	$0.194072\pi$
$90$		0			0
$91$	−0.885586	−	3.12582i	−0.0928346	−	0.327675i
$92$	−19.4383	+	11.2227i	−2.02658	+	1.17005i
$93$		0			0
$94$			19.7492i			2.03697i
$95$			2.38261i			0.244451i
$96$		0			0
$97$	8.76527	−	5.06063i	0.889979	−	0.513829i	0.0160431	−	0.999871i	$-0.494893\pi$
$97$	8.76527	−	5.06063i	0.889979	−	0.513829i	0.873936	+	0.486042i	$0.161560\pi$
$98$	18.1474	−	0.518397i	1.83316	−	0.0523660i
$99$		0			0
$100$	−8.10593	+	14.0399i	−0.810593	+	1.40399i
$101$	0.856611	−	1.48369i	0.0852360	−	0.147633i	−0.820256	−	0.571997i	$-0.806169\pi$
$101$	0.856611	−	1.48369i	0.0852360	−	0.147633i	0.905492	+	0.424364i	$0.139502\pi$
$102$		0			0
$103$	−6.41315	+	3.70263i	−0.631906	+	0.364831i	−0.781490	−	0.623918i	$-0.785540\pi$
$103$	−6.41315	+	3.70263i	−0.631906	+	0.364831i	0.149584	+	0.988749i	$0.452207\pi$
$104$	−4.34151	+	7.51971i	−0.425720	+	0.737368i
$105$		0			0
$106$	−4.00972	−	6.94503i	−0.389458	−	0.674561i
$107$	−0.131657	−	0.0760123i	−0.0127278	−	0.00734839i	0.493623	−	0.869676i	$-0.335672\pi$
$107$	−0.131657	−	0.0760123i	−0.0127278	−	0.00734839i	−0.506350	+	0.862328i	$0.669006\pi$
$108$		0			0
$109$	2.70051	+	4.67742i	0.258662	+	0.448016i	0.965884	−	0.258976i	$-0.0833851\pi$
$109$	2.70051	+	4.67742i	0.258662	+	0.448016i	−0.707222	+	0.706992i	$0.750052\pi$
$110$	−2.00425			−0.191098
$111$		0			0
$112$	−16.8607	−	16.3859i	−1.59318	−	1.54832i
$113$	5.60391	+	3.23542i	0.527171	+	0.304362i	0.739864	−	0.672757i	$-0.234890\pi$
$113$	5.60391	+	3.23542i	0.527171	+	0.304362i	−0.212693	+	0.977119i	$0.568223\pi$
$114$		0			0
$115$	−5.15311	−	2.97515i	−0.480530	−	0.277434i
$116$	−23.9928	+	13.8523i	−2.22768	+	1.28615i
$117$		0			0
$118$			9.24490i			0.851062i
$119$	−2.87159	+	11.3635i	−0.263238	+	1.04169i
$120$		0			0
$121$	−5.30981	−	9.19685i	−0.482710	−	0.836078i
$122$	37.4752			3.39285
$123$		0			0
$124$		−	11.7258i		−	1.05301i
$125$	−10.5627			−0.944757
$126$		0			0
$127$	−2.93175			−0.260151			−0.130075	−	0.991504i	$-0.541522\pi$
$127$	−2.93175			−0.260151			−0.130075	+	0.991504i	$0.541522\pi$
$128$		−	4.00562i		−	0.354050i
$129$		0			0
$130$	−3.99042			−0.349983
$131$	−8.11382	−	14.0535i	−0.708908	−	1.22786i	−0.965263	−	0.261281i	$-0.915855\pi$
$131$	−8.11382	−	14.0535i	−0.708908	−	1.22786i	0.256355	−	0.966583i	$-0.417478\pi$
$132$		0			0
$133$	1.37138	+	4.84051i	0.118914	+	0.419726i
$134$		−	35.3055i		−	3.04993i
$135$		0			0
$136$	27.1286	−	15.6627i	2.32626	−	1.34307i
$137$	15.0711	+	8.70129i	1.28761	+	0.743402i	0.978227	−	0.207536i	$-0.0665445\pi$
$137$	15.0711	+	8.70129i	1.28761	+	0.743402i	0.309382	+	0.950938i	$0.399878\pi$
$138$		0			0
$139$	−5.45273	−	3.14813i	−0.462494	−	0.267021i	0.250598	−	0.968091i	$-0.419373\pi$
$139$	−5.45273	−	3.14813i	−0.462494	−	0.267021i	−0.713092	+	0.701070i	$0.752706\pi$
$140$	3.83881	−	15.1911i	0.324439	−	1.28388i
$141$		0			0
$142$	26.9975			2.26558
$143$	0.378672	+	0.655879i	0.0316661	+	0.0548474i
$144$		0			0
$145$	−6.36052	−	3.67225i	−0.528212	−	0.304963i
$146$	−14.8992	−	25.8061i	−1.23306	−	2.13573i
$147$		0			0
$148$	−6.29642	+	10.9057i	−0.517563	+	0.896445i
$149$	9.20319	−	5.31346i	0.753954	−	0.435296i	−0.0731665	−	0.997320i	$-0.523310\pi$
$149$	9.20319	−	5.31346i	0.753954	−	0.435296i	0.827121	+	0.562024i	$0.189977\pi$
$150$		0			0
$151$	−4.74465	+	8.21798i	−0.386114	+	0.668770i	−0.991923	−	0.126841i	$-0.959516\pi$
$151$	−4.74465	+	8.21798i	−0.386114	+	0.668770i	0.605809	+	0.795610i	$0.292850\pi$
$152$	6.72308	−	11.6447i	0.545314	−	0.944511i
$153$		0			0
$154$	−4.07183	+	1.15360i	−0.328117	+	0.0929600i
$155$	2.69205	−	1.55426i	0.216231	−	0.124841i
$156$		0			0
$157$		−	23.8116i		−	1.90037i	−0.311688	−	0.950185i	$-0.600894\pi$
$157$		−	23.8116i		−	1.90037i	0.311688	−	0.950185i	$-0.399106\pi$
$158$			10.4568i			0.831895i
$159$		0			0
$160$	−9.66295	+	5.57891i	−0.763924	+	0.441051i
$161$	−12.1815	−	3.07829i	−0.960035	−	0.242603i
$162$		0			0
$163$	−4.41101	+	7.64009i	−0.345497	+	0.598418i	−0.985444	−	0.170001i	$-0.945623\pi$
$163$	−4.41101	+	7.64009i	−0.345497	+	0.598418i	0.639947	+	0.768419i	$0.278956\pi$
$164$	−9.92392	+	17.1887i	−0.774928	+	1.34221i
$165$		0			0
$166$	19.6205	−	11.3279i	1.52285	−	0.879217i
$167$	−11.0335	+	19.1106i	−0.853800	+	1.47883i	0.0239535	+	0.999713i	$0.492375\pi$
$167$	−11.0335	+	19.1106i	−0.853800	+	1.47883i	−0.877754	+	0.479112i	$0.840959\pi$
$168$		0			0
$169$	−5.74607	−	9.95249i	−0.442005	−	0.765576i
$170$	12.4674	+	7.19806i	0.956206	+	0.552066i
$171$		0			0
$172$	10.6174	+	18.3898i	0.809566	+	1.40221i
$173$	−4.06750			−0.309246			−0.154623	−	0.987974i	$-0.549416\pi$
$173$	−4.06750			−0.309246			−0.154623	+	0.987974i	$0.549416\pi$
$174$		0			0
$175$	−8.73135	+	2.47371i	−0.660028	+	0.186995i
$176$	4.74647	+	2.74038i	0.357779	+	0.206564i
$177$		0			0
$178$	3.64414	+	2.10395i	0.273140	+	0.157697i
$179$	7.20787	−	4.16146i	0.538741	−	0.311042i	−0.205827	−	0.978588i	$-0.565989\pi$
$179$	7.20787	−	4.16146i	0.538741	−	0.311042i	0.744569	+	0.667546i	$0.232655\pi$
$180$		0			0
$181$			12.6701i			0.941763i	0.882196	+	0.470881i	$0.156064\pi$
$181$			12.6701i			0.941763i	−0.882196	+	0.470881i	$0.843936\pi$
$182$	−8.10693	+	2.29680i	−0.600926	+	0.170250i
$183$		0			0
$184$	16.7901	+	29.0813i	1.23778	+	2.14390i
$185$	−3.33837			−0.245442
$186$		0			0
$187$		−	2.73225i		−	0.199802i
$188$	35.9908			2.62490
$189$		0			0
$190$	6.17941			0.448301
$191$		−	3.80050i		−	0.274995i	−0.990502	−	0.137497i	$-0.956094\pi$
$191$		−	3.80050i		−	0.274995i	0.990502	−	0.137497i	$-0.0439059\pi$
$192$		0			0
$193$	6.78897			0.488680			0.244340	−	0.969690i	$-0.421429\pi$
$193$	6.78897			0.488680			0.244340	+	0.969690i	$0.421429\pi$
$194$	−13.1250	−	22.7331i	−0.942317	−	1.63214i
$195$		0			0
$196$	−0.944723	−	33.0717i	−0.0674802	−	2.36226i
$197$		−	6.41453i		−	0.457017i	−0.973542	−	0.228508i	$-0.926615\pi$
$197$		−	6.41453i		−	0.457017i	0.973542	−	0.228508i	$-0.0733848\pi$
$198$		0			0
$199$	−13.8921	+	8.02063i	−0.984788	+	0.568568i	−0.903712	−	0.428140i	$-0.859169\pi$
$199$	−13.8921	+	8.02063i	−0.984788	+	0.568568i	−0.0810756	+	0.996708i	$0.525836\pi$
$200$	21.0048	+	12.1271i	1.48526	+	0.857518i
$201$		0			0
$202$	−3.84802	−	2.22166i	−0.270746	−	0.156315i
$203$	−15.0357	−	3.79955i	−1.05530	−	0.266676i
$204$		0			0
$205$	−5.26168			−0.367491
$206$	9.60292	+	16.6327i	0.669067	+	1.15886i
$207$		0			0
$208$	9.45013	+	5.45604i	0.655249	+	0.378308i
$209$	−0.586396	−	1.01567i	−0.0405619	−	0.0702552i
$210$		0			0
$211$	−4.06070	+	7.03333i	−0.279550	+	0.484194i	−0.971273	−	0.237968i	$-0.923519\pi$
$211$	−4.06070	+	7.03333i	−0.279550	+	0.484194i	0.691723	+	0.722163i	$0.256852\pi$
$212$	−12.6566	+	7.30728i	−0.869257	+	0.501866i
$213$		0			0
$214$	−0.197141	+	0.341458i	−0.0134763	+	0.0233416i
$215$	−2.81467	+	4.87515i	−0.191959	+	0.332483i
$216$		0			0
$217$	4.57457	−	4.70711i	0.310542	−	0.319540i
$218$	12.1311	−	7.00388i	0.821620	−	0.474363i
$219$		0			0
$220$			3.65253i			0.246254i
$221$		−	5.43985i		−	0.365924i
$222$		0			0
$223$	6.96205	−	4.01954i	0.466213	−	0.269168i	−0.248440	−	0.968647i	$-0.579918\pi$
$223$	6.96205	−	4.01954i	0.466213	−	0.269168i	0.714653	+	0.699479i	$0.246585\pi$
$224$	−16.4201	+	16.8959i	−1.09712	+	1.12890i
$225$		0			0
$226$	8.39118	−	14.5340i	0.558173	−	0.966784i
$227$	10.4117	−	18.0336i	0.691048	−	1.19693i	−0.280447	−	0.959870i	$-0.590483\pi$
$227$	10.4117	−	18.0336i	0.691048	−	1.19693i	0.971495	−	0.237061i	$-0.0761840\pi$
$228$		0			0
$229$	5.21276	−	3.00959i	0.344469	−	0.198879i	−0.317777	−	0.948165i	$-0.602936\pi$
$229$	5.21276	−	3.00959i	0.344469	−	0.198879i	0.662247	+	0.749286i	$0.269603\pi$
$230$	−7.71617	+	13.3648i	−0.508789	+	0.881248i
$231$		0			0
$232$	20.7241	+	35.8952i	1.36061	+	2.35664i
$233$	−18.2156	−	10.5168i	−1.19335	−	0.688978i	−0.234282	−	0.972169i	$-0.575274\pi$
$233$	−18.2156	−	10.5168i	−1.19335	−	0.688978i	−0.959064	+	0.283191i	$0.908607\pi$
$234$		0			0
$235$	4.77059	+	8.26291i	0.311199	+	0.539013i
$236$	16.8478			1.09670
$237$		0			0
$238$	29.4718	+	7.44759i	1.91037	+	0.482755i
$239$	7.51079	+	4.33636i	0.485832	+	0.280496i	0.722844	−	0.691011i	$-0.242835\pi$
$239$	7.51079	+	4.33636i	0.485832	+	0.280496i	−0.237011	+	0.971507i	$0.576168\pi$
$240$		0			0
$241$	7.33797	+	4.23658i	0.472680	+	0.272902i	0.717361	−	0.696702i	$-0.245350\pi$
$241$	7.33797	+	4.23658i	0.472680	+	0.272902i	−0.244681	+	0.969604i	$0.578683\pi$
$242$	−23.8524	+	13.7712i	−1.53329	+	0.885246i
$243$		0			0
$244$		−	68.2946i		−	4.37211i
$245$	7.46750	−	4.60055i	0.477081	−	0.293919i
$246$		0			0
$247$	−1.16750	−	2.02217i	−0.0742864	−	0.128668i
$248$	−17.5427			−1.11396
$249$		0			0
$250$			27.3948i			1.73260i
$251$	23.4435			1.47974			0.739871	−	0.672749i	$-0.234887\pi$
$251$	23.4435			1.47974			0.739871	+	0.672749i	$0.234887\pi$
$252$		0			0
$253$	2.92891			0.184139
$254$			7.60361i			0.477093i
$255$		0			0
$256$	−21.0339			−1.31462
$257$	12.2585	+	21.2324i	0.764665	+	1.32444i	0.940423	+	0.340005i	$0.110429\pi$
$257$	12.2585	+	21.2324i	0.764665	+	1.32444i	−0.175758	+	0.984433i	$0.556238\pi$
$258$		0			0
$259$	−6.78223	+	1.92150i	−0.421427	+	0.119396i
$260$			7.27212i			0.450998i
$261$		0			0
$262$	−36.4484	+	21.0435i	−2.25179	+	1.30007i
$263$	−9.14036	−	5.27719i	−0.563619	−	0.325406i	0.190978	−	0.981594i	$-0.438834\pi$
$263$	−9.14036	−	5.27719i	−0.563619	−	0.325406i	−0.754597	+	0.656189i	$0.772167\pi$
$264$		0			0
$265$	−3.35527	−	1.93716i	−0.206112	−	0.118999i
$266$	12.5541	−	3.55673i	0.769739	−	0.218077i
$267$		0			0
$268$	−64.3406			−3.93023
$269$	1.14451	+	1.98235i	0.0697821	+	0.120866i	0.898805	−	0.438348i	$-0.144436\pi$
$269$	1.14451	+	1.98235i	0.0697821	+	0.120866i	−0.829023	+	0.559214i	$0.811103\pi$
$270$		0			0
$271$	−20.9239	−	12.0804i	−1.27103	−	0.733831i	−0.295851	−	0.955234i	$-0.595603\pi$
$271$	−20.9239	−	12.0804i	−1.27103	−	0.733831i	−0.975182	+	0.221403i	$0.928936\pi$
$272$	−19.6836	−	34.0929i	−1.19349	−	2.06719i
$273$		0			0
$274$	22.5672	−	39.0875i	1.36333	−	2.36136i
$275$	1.83207	−	1.05774i	0.110478	−	0.0637844i
$276$		0			0
$277$	5.68551	−	9.84760i	0.341609	−	0.591685i	−0.643122	−	0.765763i	$-0.722361\pi$
$277$	5.68551	−	9.84760i	0.341609	−	0.591685i	0.984732	+	0.174079i	$0.0556947\pi$
$278$	−8.16481	+	14.1419i	−0.489693	+	0.848173i
$279$		0			0
$280$	−22.7271	−	5.74318i	−1.35820	−	0.343221i
$281$	−17.6382	+	10.1834i	−1.05221	+	0.607492i	−0.923267	−	0.384160i	$-0.874491\pi$
$281$	−17.6382	+	10.1834i	−1.05221	+	0.607492i	−0.128941	+	0.991652i	$0.541158\pi$
$282$		0			0
$283$		−	12.1611i		−	0.722903i	−0.932391	−	0.361451i	$-0.882281\pi$
$283$		−	12.1611i		−	0.722903i	0.932391	−	0.361451i	$-0.117719\pi$
$284$		−	49.2001i		−	2.91949i
$285$		0			0
$286$	1.70105	−	0.982101i	0.100585	−	0.0580729i
$287$	−10.6896	+	3.02851i	−0.630988	+	0.178767i
$288$		0			0
$289$	−1.31257	+	2.27345i	−0.0772103	+	0.133732i
$290$	−9.52411	+	16.4962i	−0.559275	+	0.968693i
$291$		0			0
$292$	−47.0289	+	27.1522i	−2.75216	+	1.58896i
$293$	13.4674	−	23.3262i	0.786773	−	1.36273i	−0.141161	−	0.989987i	$-0.545083\pi$
$293$	13.4674	−	23.3262i	0.786773	−	1.36273i	0.927934	−	0.372745i	$-0.121583\pi$
$294$		0			0
$295$	2.23319	+	3.86799i	0.130021	+	0.225203i
$296$	16.3159	+	9.41996i	0.948340	+	0.547524i
$297$		0			0
$298$	−13.7807	−	23.8688i	−0.798293	−	1.38268i
$299$	5.83140			0.337239
$300$		0			0
$301$	−2.91224	+	11.5244i	−0.167859	+	0.664256i
$302$	21.3137	+	12.3054i	1.22646	+	0.708099i
$303$		0			0
$304$	−14.6341	−	8.44899i	−0.839322	−	0.484583i
$305$	15.6793	−	9.05248i	0.897797	−	0.518343i
$306$		0			0
$307$			21.3700i			1.21965i	0.792536	+	0.609825i	$0.208760\pi$
$307$			21.3700i			1.21965i	−0.792536	+	0.609825i	$0.791240\pi$
$308$	2.10232	+	7.42048i	0.119791	+	0.422821i
$309$		0			0
$310$	−4.03103	−	6.98195i	−0.228947	−	0.396548i
$311$	−16.2312			−0.920385			−0.460192	−	0.887819i	$-0.652220\pi$
$311$	−16.2312			−0.920385			−0.460192	+	0.887819i	$0.652220\pi$
$312$		0			0
$313$			14.0805i			0.795880i	0.917412	+	0.397940i	$0.130275\pi$
$313$			14.0805i			0.795880i	−0.917412	+	0.397940i	$0.869725\pi$
$314$	−61.7562			−3.48511
$315$		0			0
$316$	19.0563			1.07200
$317$			20.2968i			1.13998i	0.821651	+	0.569991i	$0.193053\pi$
$317$			20.2968i			1.13998i	−0.821651	+	0.569991i	$0.806947\pi$
$318$		0			0
$319$	3.61517			0.202411
$320$	3.33456	+	5.77563i	0.186408	+	0.322868i
$321$		0			0
$322$	−7.98366	+	31.5931i	−0.444912	+	1.76062i
$323$			8.42392i			0.468720i
$324$		0			0
$325$	3.64761	−	2.10595i	0.202333	−	0.116817i
$326$	19.8149	+	11.4401i	1.09744	+	0.633610i
$327$		0			0
$328$	25.7158	+	14.8470i	1.41991	+	0.819788i
$329$	14.4479	+	14.0410i	0.796537	+	0.774108i
$330$		0			0
$331$	26.4682			1.45482			0.727411	−	0.686202i	$-0.240723\pi$
$331$	26.4682			1.45482			0.727411	+	0.686202i	$0.240723\pi$
$332$	−20.6439	−	35.7563i	−1.13298	−	1.96238i
$333$		0			0
$334$	49.5642	+	28.6159i	2.71203	+	1.56579i
$335$	−8.52836	−	14.7716i	−0.465954	−	0.807057i
$336$		0			0
$337$	−1.73659	+	3.00785i	−0.0945979	+	0.163848i	−0.909441	−	0.415834i	$-0.863490\pi$
$337$	−1.73659	+	3.00785i	−0.0945979	+	0.163848i	0.814843	+	0.579682i	$0.196823\pi$
$338$	−25.8122	+	14.9027i	−1.40400	+	0.810598i
$339$		0			0
$340$	13.1177	−	22.7205i	0.711407	−	1.23219i
$341$	−0.765051	+	1.32511i	−0.0414298	+	0.0717585i
$342$		0			0
$343$	12.5230	−	13.6446i	0.676177	−	0.736739i
$344$	27.5127	−	15.8844i	1.48338	−	0.856432i
$345$		0			0
$346$			10.5492i			0.567130i
$347$		−	9.40810i		−	0.505053i	−0.967590	−	0.252527i	$-0.918738\pi$
$347$		−	9.40810i		−	0.505053i	0.967590	−	0.252527i	$-0.0812615\pi$
$348$		0			0
$349$	12.3253	−	7.11603i	0.659759	−	0.380912i	−0.132426	−	0.991193i	$-0.542277\pi$
$349$	12.3253	−	7.11603i	0.659759	−	0.380912i	0.792185	+	0.610281i	$0.208943\pi$
$350$	6.41566	+	22.6451i	0.342931	+	1.21043i
$351$		0			0
$352$	2.74610	−	4.75639i	0.146368	−	0.253516i
$353$	−8.58262	+	14.8655i	−0.456807	+	0.791213i	−0.998790	−	0.0491765i	$-0.984340\pi$
$353$	−8.58262	+	14.8655i	−0.456807	+	0.791213i	0.541983	+	0.840389i	$0.317674\pi$
$354$		0			0
$355$	11.2956	−	6.52149i	0.599506	−	0.346125i
$356$	3.83422	−	6.64106i	0.203213	−	0.351975i
$357$		0			0
$358$	−10.7929	−	18.6939i	−0.570424	−	0.988003i
$359$	24.4705	+	14.1281i	1.29150	+	0.745650i	0.978921	−	0.204241i	$-0.0654725\pi$
$359$	24.4705	+	14.1281i	1.29150	+	0.745650i	0.312583	+	0.949890i	$0.398806\pi$
$360$		0			0
$361$	−7.69205	−	13.3230i	−0.404845	−	0.701212i
$362$	32.8605			1.72711
$363$		0			0
$364$	4.18568	+	14.7740i	0.219389	+	0.774369i
$365$	−12.4674	−	7.19806i	−0.652574	−	0.376764i
$366$		0			0
$367$	19.9796	+	11.5352i	1.04293	+	0.602133i	0.920661	−	0.390364i	$-0.127651\pi$
$367$	19.9796	+	11.5352i	1.04293	+	0.602133i	0.122265	+	0.992498i	$0.460984\pi$
$368$	36.5469	−	21.1004i	1.90514	−	1.09993i
$369$		0			0
$370$			8.65820i			0.450118i
$371$	−7.93154	−	2.00432i	−0.411785	−	0.104059i
$372$		0			0
$373$	6.93635	+	12.0141i	0.359150	+	0.622067i	0.987819	−	0.155607i	$-0.0497332\pi$
$373$	6.93635	+	12.0141i	0.359150	+	0.622067i	−0.628669	+	0.777673i	$0.716400\pi$
$374$	−7.08619			−0.366418
$375$		0			0
$376$		−	53.8452i		−	2.77685i
$377$	7.19773			0.370702
$378$		0			0
$379$	22.7814			1.17020			0.585101	−	0.810961i	$-0.301055\pi$
$379$	22.7814			1.17020			0.585101	+	0.810961i	$0.301055\pi$
$380$		−	11.2613i		−	0.577693i
$381$		0			0
$382$	−9.85676			−0.504316
$383$	7.61598	+	13.1913i	0.389158	+	0.674042i	0.992337	−	0.123564i	$-0.0394325\pi$
$383$	7.61598	+	13.1913i	0.389158	+	0.674042i	−0.603178	+	0.797606i	$0.706099\pi$
$384$		0			0
$385$	−1.42496	+	1.46625i	−0.0726226	+	0.0747268i
$386$		−	17.6075i		−	0.896196i
$387$		0			0
$388$	−41.4286	+	23.9188i	−2.10322	+	1.21429i
$389$	−12.2525	−	7.07396i	−0.621224	−	0.358664i	0.156121	−	0.987738i	$-0.450101\pi$
$389$	−12.2525	−	7.07396i	−0.621224	−	0.358664i	−0.777346	+	0.629074i	$0.783434\pi$
$390$		0			0
$391$	−18.2192	−	10.5189i	−0.921386	−	0.531962i
$392$	−49.4779	+	1.41338i	−2.49901	+	0.0713866i
$393$		0			0
$394$	−16.6363			−0.838127
$395$	2.52592	+	4.37503i	0.127093	+	0.220131i
$396$		0			0
$397$	8.40688	+	4.85371i	0.421929	+	0.243601i	0.695902	−	0.718136i	$-0.255005\pi$
$397$	8.40688	+	4.85371i	0.421929	+	0.243601i	−0.273973	+	0.961737i	$0.588338\pi$
$398$	20.8018	+	36.0298i	1.04270	+	1.80601i
$399$		0			0
$400$	15.2403	−	26.3970i	0.762017	−	1.31985i
$401$	7.56156	−	4.36567i	0.377606	−	0.218011i	−0.299170	−	0.954200i	$-0.596710\pi$
$401$	7.56156	−	4.36567i	0.377606	−	0.218011i	0.676776	+	0.736189i	$0.263376\pi$
$402$		0			0
$403$	−1.52320	+	2.63826i	−0.0758760	+	0.131421i
$404$	−4.04873	+	7.01261i	−0.201432	+	0.348890i
$405$		0			0
$406$	−9.85428	+	38.9956i	−0.489060	+	1.93532i
$407$	1.42309	−	0.821622i	0.0705400	−	0.0407263i
$408$		0			0
$409$			14.8918i			0.736353i	0.929756	+	0.368176i	$0.120018\pi$
$409$			14.8918i			0.736353i	−0.929756	+	0.368176i	$0.879982\pi$
$410$			13.6464i			0.673946i
$411$		0			0
$412$	30.3114	−	17.5003i	1.49334	−	0.862178i
$413$	6.76327	+	6.57283i	0.332799	+	0.323428i
$414$		0			0
$415$	5.47272	−	9.47903i	0.268645	−	0.465307i
$416$	5.46743	−	9.46987i	0.268063	−	0.464299i
$417$		0			0
$418$	−2.63418	+	1.52084i	−0.128842	+	0.0743868i
$419$	−2.13859	+	3.70414i	−0.104477	+	0.180959i	−0.913524	−	0.406784i	$-0.866650\pi$
$419$	−2.13859	+	3.70414i	−0.104477	+	0.180959i	0.809048	+	0.587743i	$0.199983\pi$
$420$		0			0
$421$	5.76681	+	9.98841i	0.281057	+	0.486805i	0.971645	−	0.236443i	$-0.0759816\pi$
$421$	5.76681	+	9.98841i	0.281057	+	0.486805i	−0.690588	+	0.723248i	$0.742648\pi$
$422$	18.2412	+	10.5316i	0.887969	+	0.512669i
$423$		0			0
$424$	10.9323	+	18.9353i	0.530919	+	0.919578i
$425$	−15.1951			−0.737072
$426$		0			0
$427$	26.6437	−	27.4157i	1.28938	−	1.32674i
$428$	0.622271	+	0.359268i	0.0300786	+	0.0173659i
$429$		0			0
$430$	12.6439	+	7.29996i	0.609743	+	0.352035i
$431$	−14.4497	+	8.34254i	−0.696018	+	0.401846i	−0.805863	−	0.592103i	$-0.798298\pi$
$431$	−14.4497	+	8.34254i	−0.696018	+	0.401846i	0.109845	+	0.993949i	$0.464965\pi$
$432$		0			0
$433$			12.3503i			0.593516i	0.954953	+	0.296758i	$0.0959055\pi$
$433$			12.3503i			0.593516i	−0.954953	+	0.296758i	$0.904094\pi$
$434$	−12.2081	−	11.8643i	−0.586007	−	0.569506i
$435$		0			0
$436$	−12.7638	−	22.1076i	−0.611276	−	1.05876i
$437$	−9.03027			−0.431976
$438$		0			0
$439$		−	22.1346i		−	1.05643i	−0.849112	−	0.528213i	$-0.822862\pi$
$439$		−	22.1346i		−	1.05643i	0.849112	−	0.528213i	$-0.177138\pi$
$440$	5.46449			0.260509
$441$		0			0
$442$	−14.1085			−0.671071
$443$		−	4.88329i		−	0.232012i	−0.993248	−	0.116006i	$-0.962991\pi$
$443$		−	4.88329i		−	0.232012i	0.993248	−	0.116006i	$-0.0370092\pi$
$444$		0			0
$445$	2.03291			0.0963690
$446$	−10.4248	−	18.0563i	−0.493630	−	0.854993i
$447$		0			0
$448$	10.0988	+	9.81446i	0.477124	+	0.463690i
$449$			12.4409i			0.587121i	0.955941	+	0.293560i	$0.0948401\pi$
$449$			12.4409i			0.587121i	−0.955941	+	0.293560i	$0.905160\pi$
$450$		0			0
$451$	2.24296	−	1.29498i	0.105617	−	0.0609780i
$452$	−26.4866	−	15.2920i	−1.24582	−	0.719277i
$453$		0			0
$454$	−46.7708	−	27.0031i	−2.19506	−	1.26732i
$455$	−2.83707	+	2.91927i	−0.133004	+	0.136857i
$456$		0			0
$457$	−10.7755			−0.504056			−0.252028	−	0.967720i	$-0.581098\pi$
$457$	−10.7755			−0.504056			−0.252028	+	0.967720i	$0.581098\pi$
$458$	−7.80549	−	13.5195i	−0.364727	−	0.631725i
$459$		0			0
$460$	24.3559	+	14.0619i	1.13560	+	0.655639i
$461$	−0.333303	−	0.577297i	−0.0155235	−	0.0268874i	0.858159	−	0.513383i	$-0.171608\pi$
$461$	−0.333303	−	0.577297i	−0.0155235	−	0.0268874i	−0.873683	+	0.486496i	$0.838275\pi$
$462$		0			0
$463$	−20.7892	+	36.0079i	−0.966155	+	1.67343i	−0.259677	+	0.965696i	$0.583616\pi$
$463$	−20.7892	+	36.0079i	−0.966155	+	1.67343i	−0.706479	+	0.707734i	$0.749717\pi$
$464$	45.1101	−	26.0443i	2.09418	−	1.20908i
$465$		0			0
$466$	−27.2757	+	47.2429i	−1.26352	+	2.18849i
$467$	19.6568	−	34.0465i	0.909606	−	1.57548i	0.0949943	−	0.995478i	$-0.469717\pi$
$467$	19.6568	−	34.0465i	0.909606	−	1.57548i	0.814612	−	0.580006i	$-0.196950\pi$
$468$		0			0
$469$	−25.8284	−	25.1011i	−1.19264	−	1.15906i
$470$	21.4302	−	12.3727i	0.988500	−	0.570711i
$471$		0			0
$472$		−	25.2057i		−	1.16019i
$473$		−	2.77093i		−	0.127407i
$474$		0			0
$475$	−5.64854	+	3.26119i	−0.259173	+	0.149633i
$476$	13.5724	−	53.7092i	0.622091	−	2.46176i
$477$		0			0
$478$	11.2465	−	19.4795i	0.514403	−	0.890973i
$479$	19.0577	−	33.0088i	0.870767	−	1.50821i	0.00956182	−	0.999954i	$-0.496956\pi$
$479$	19.0577	−	33.0088i	0.870767	−	1.50821i	0.861205	−	0.508258i	$-0.169710\pi$
$480$		0			0
$481$	2.83335	−	1.63583i	0.129189	−	0.0745875i
$482$	10.9877	−	19.0313i	0.500477	−	0.866852i
$483$		0			0
$484$	25.0965	+	43.4685i	1.14075	+	1.97584i
$485$	−10.9828	−	6.34090i	−0.498701	−	0.287925i
$486$		0			0
$487$	−3.80277	−	6.58659i	−0.172320	−	0.298467i	0.766911	−	0.641754i	$-0.221793\pi$
$487$	−3.80277	−	6.58659i	−0.172320	−	0.298467i	−0.939231	+	0.343287i	$0.888460\pi$
$488$	−102.174			−4.62521
$489$		0			0
$490$	−11.9317	−	19.3673i	−0.539020	−	0.874923i
$491$	−3.33297	−	1.92429i	−0.150415	−	0.0868420i	0.422904	−	0.906175i	$-0.361011\pi$
$491$	−3.33297	−	1.92429i	−0.150415	−	0.0868420i	−0.573318	+	0.819333i	$0.694344\pi$
$492$		0			0
$493$	−22.4881	−	12.9835i	−1.01281	−	0.584748i
$494$	−5.24459	+	3.02797i	−0.235965	+	0.136235i
$495$		0			0
$496$			22.0462i			0.989904i
$497$	19.1944	−	19.7505i	0.860986	−	0.885932i
$498$		0			0
$499$	16.0794	+	27.8503i	0.719812	+	1.24675i	0.961074	+	0.276291i	$0.0891053\pi$
$499$	16.0794	+	27.8503i	0.719812	+	1.24675i	−0.241262	+	0.970460i	$0.577561\pi$
$500$	49.9241			2.23267
$501$		0			0
$502$		−	60.8017i		−	2.71371i
$503$	−0.425693			−0.0189807			−0.00949035	−	0.999955i	$-0.503021\pi$
$503$	−0.425693			−0.0189807			−0.00949035	+	0.999955i	$0.503021\pi$
$504$		0			0
$505$	−2.14664			−0.0955243
$506$		−	7.59624i		−	0.337694i
$507$		0			0
$508$	13.8568			0.614794
$509$	12.8963	+	22.3370i	0.571617	+	0.990071i	0.996400	+	0.0847751i	$0.0270172\pi$
$509$	12.8963	+	22.3370i	0.571617	+	0.990071i	−0.424783	+	0.905295i	$0.639649\pi$
$510$		0			0
$511$	−29.4718	−	7.44759i	−1.30376	−	0.329462i
$512$			46.5411i			2.05684i
$513$		0			0
$514$	55.0670	−	31.7929i	2.42890	−	1.40233i
$515$	8.03558	+	4.63934i	0.354090	+	0.204434i
$516$		0			0
$517$	−4.06724	−	2.34822i	−0.178877	−	0.103275i
$518$	4.98347	+	17.5900i	0.218961	+	0.772859i
$519$		0			0
$520$	10.8797			0.477106
$521$	−9.07174	−	15.7127i	−0.397440	−	0.688386i	0.595969	−	0.803007i	$-0.296768\pi$
$521$	−9.07174	−	15.7127i	−0.397440	−	0.688386i	−0.993409	+	0.114621i	$0.963435\pi$
$522$		0			0
$523$	12.0723	+	6.96997i	0.527887	+	0.304776i	0.740155	−	0.672436i	$-0.234752\pi$
$523$	12.0723	+	6.96997i	0.527887	+	0.304776i	−0.212269	+	0.977211i	$0.568085\pi$
$524$	38.3495	+	66.4234i	1.67531	+	2.90172i
$525$		0			0
$526$	−13.6866	+	23.7059i	−0.596764	+	1.03363i
$527$	9.51796	−	5.49520i	0.414609	−	0.239375i
$528$		0			0
$529$	−0.223990	+	0.387962i	−0.00973870	+	0.0168679i
$530$	−5.02411	+	8.70202i	−0.218234	+	0.377992i
$531$		0			0
$532$	−6.48177	−	22.8784i	−0.281020	−	0.991906i
$533$	4.46569	−	2.57827i	0.193431	−	0.111677i
$534$		0			0
$535$			0.190485i			0.00823537i
$536$			96.2587i			4.15774i
$537$		0			0
$538$	5.14131	−	2.96834i	0.221658	−	0.127974i
$539$	−2.05100	+	3.79900i	−0.0883430	+	0.163634i
$540$		0			0
$541$	−14.8576	+	25.7341i	−0.638779	+	1.10640i	0.346922	+	0.937894i	$0.387227\pi$
$541$	−14.8576	+	25.7341i	−0.638779	+	1.10640i	−0.985701	+	0.168503i	$0.946107\pi$
$542$	−31.3310	+	54.2668i	−1.34578	+	2.33096i
$543$		0			0
$544$	−34.1641	+	19.7247i	−1.46478	+	0.845688i
$545$	3.38370	−	5.86074i	0.144942	−	0.251046i
$546$		0			0
$547$	−9.13516	−	15.8226i	−0.390591	−	0.676524i	0.601937	−	0.798544i	$-0.294396\pi$
$547$	−9.13516	−	15.8226i	−0.390591	−	0.676524i	−0.992528	+	0.122020i	$0.961063\pi$
$548$	−71.2327	−	41.1262i	−3.04291	−	1.75683i
$549$		0			0
$550$	−2.74330	−	4.75154i	−0.116975	−	0.202606i
$551$	−11.1461			−0.474841
$552$		0			0
$553$	7.64983	+	7.43442i	0.325304	+	0.316144i
$554$	−25.5401	−	14.7456i	−1.08510	−	0.626481i
$555$		0			0
$556$	25.7720	+	14.8795i	1.09298	+	0.631031i
$557$	−0.359456	+	0.207532i	−0.0152307	+	0.00879343i	−0.507596	−	0.861595i	$-0.669466\pi$
$557$	−0.359456	+	0.207532i	−0.0152307	+	0.00879343i	0.492365	+	0.870389i	$0.336132\pi$
$558$		0			0
$559$		−	5.51686i		−	0.233338i
$560$	−7.21754	+	28.5614i	−0.304997	+	1.20694i
$561$		0			0
$562$	26.4111	+	45.7454i	1.11409	+	1.92965i
$563$	−3.65925			−0.154219			−0.0771095	−	0.997023i	$-0.524569\pi$
$563$	−3.65925			−0.154219			−0.0771095	+	0.997023i	$0.524569\pi$
$564$		0			0
$565$		−	8.10786i		−	0.341100i
$566$	−31.5403			−1.32574
$567$		0			0
$568$	−73.6074			−3.08850
$569$			35.1828i			1.47494i	0.675380	+	0.737470i	$0.263980\pi$
$569$			35.1828i			1.47494i	−0.675380	+	0.737470i	$0.736020\pi$
$570$		0			0
$571$	−10.0536			−0.420730			−0.210365	−	0.977623i	$-0.567465\pi$
$571$	−10.0536			−0.420730			−0.210365	+	0.977623i	$0.567465\pi$
$572$	−1.78977	−	3.09998i	−0.0748342	−	0.129617i
$573$		0			0
$574$	7.85456	+	27.7239i	0.327843	+	1.15717i
$575$		−	16.2888i		−	0.679292i
$576$		0			0
$577$	0.0597672	−	0.0345066i	0.00248814	−	0.00143653i	−0.498755	−	0.866743i	$-0.666209\pi$
$577$	0.0597672	−	0.0345066i	0.00248814	−	0.00143653i	0.501244	+	0.865306i	$0.332876\pi$
$578$	5.89627	+	3.40421i	0.245253	+	0.141597i
$579$		0			0
$580$	30.0627	+	17.3567i	1.24828	+	0.720697i
$581$	5.66244	−	22.4076i	0.234918	−	0.929622i
$582$		0			0
$583$	1.90706			0.0789823
$584$	40.6219	+	70.3591i	1.68094	+	2.91148i
$585$		0			0
$586$	−60.4974	−	34.9282i	−2.49913	−	1.44287i
$587$	−11.4799	−	19.8838i	−0.473827	−	0.820693i	0.525724	−	0.850655i	$-0.323795\pi$
$587$	−11.4799	−	19.8838i	−0.473827	−	0.820693i	−0.999551	+	0.0299626i	$0.990461\pi$
$588$		0			0
$589$	2.35877	−	4.08550i	0.0971913	−	0.168340i
$590$	10.0318	−	5.79186i	0.413003	−	0.238447i
$591$		0			0
$592$	11.8382	−	20.5044i	0.486547	−	0.842725i
$593$	14.3970	−	24.9363i	0.591213	−	1.02401i	−0.402856	−	0.915263i	$-0.631982\pi$
$593$	14.3970	−	24.9363i	0.591213	−	1.02401i	0.994069	−	0.108748i	$-0.0346843\pi$
$594$		0			0
$595$	14.1298	−	4.00316i	0.579265	−	0.164114i
$596$	−43.4984	+	25.1138i	−1.78176	+	1.02870i
$597$		0			0
$598$		−	15.1240i		−	0.618465i
$599$			38.2885i			1.56442i	0.623012	+	0.782212i	$0.285909\pi$
$599$			38.2885i			1.56442i	−0.623012	+	0.782212i	$0.714091\pi$
$600$		0			0
$601$	−26.7618	+	15.4509i	−1.09164	+	0.630257i	−0.934012	−	0.357242i	$-0.883717\pi$
$601$	−26.7618	+	15.4509i	−1.09164	+	0.630257i	−0.157625	+	0.987499i	$0.550384\pi$
$602$	29.8890	+	7.55302i	1.21819	+	0.307838i
$603$		0			0
$604$	22.4254	−	38.8419i	0.912475	−	1.58045i
$605$	−6.65311	+	11.5235i	−0.270487	+	0.468498i
$606$		0			0
$607$	28.7339	−	16.5895i	1.16627	−	0.673349i	0.213475	−	0.976949i	$-0.431522\pi$
$607$	28.7339	−	16.5895i	1.16627	−	0.673349i	0.952800	+	0.303600i	$0.0981886\pi$
$608$	−8.46664	+	14.6647i	−0.343368	+	0.594730i
$609$		0			0
$610$	−23.4780	−	40.6650i	−0.950595	−	1.64648i
$611$	−8.09780	−	4.67527i	−0.327602	−	0.189141i
$612$		0			0
$613$	−2.01164	−	3.48426i	−0.0812492	−	0.140728i	0.822538	−	0.568711i	$-0.192558\pi$
$613$	−2.01164	−	3.48426i	−0.0812492	−	0.140728i	−0.903787	+	0.427983i	$0.859224\pi$
$614$	55.4239			2.23673
$615$		0			0
$616$	11.1016	−	3.14524i	0.447298	−	0.126725i
$617$	−27.1191	−	15.6572i	−1.09177	−	0.630336i	−0.157726	−	0.987483i	$-0.550416\pi$
$617$	−27.1191	−	15.6572i	−1.09177	−	0.630336i	−0.934048	+	0.357147i	$0.883749\pi$
$618$		0			0
$619$	12.0646	+	6.96550i	0.484917	+	0.279967i	0.722463	−	0.691409i	$-0.243010\pi$
$619$	12.0646	+	6.96550i	0.484917	+	0.279967i	−0.237546	+	0.971376i	$0.576343\pi$
$620$	−12.7238	+	7.34612i	−0.511002	+	0.295027i
$621$		0			0
$622$			42.0962i			1.68790i
$623$	4.13005	−	1.17010i	0.165467	−	0.0468790i
$624$		0			0
$625$	−1.95762	−	3.39069i	−0.0783047	−	0.135628i
$626$	36.5185			1.45957
$627$		0			0
$628$			112.544i			4.49100i
$629$	−11.8031			−0.470620
$630$		0			0
$631$	−4.61815			−0.183846			−0.0919229	−	0.995766i	$-0.529301\pi$
$631$	−4.61815			−0.183846			−0.0919229	+	0.995766i	$0.529301\pi$
$632$		−	28.5098i		−	1.13406i
$633$		0			0
$634$	52.6406			2.09063
$635$	1.83672	+	3.18129i	0.0728879	+	0.126246i
$636$		0			0
$637$	−4.08351	+	7.56373i	−0.161794	+	0.299686i
$638$		−	9.37609i		−	0.371203i
$639$		0			0
$640$	−4.34657	+	2.50949i	−0.171813	+	0.0991964i
$641$	−36.7821	−	21.2362i	−1.45281	−	0.838779i	−0.454167	−	0.890917i	$-0.650063\pi$
$641$	−36.7821	−	21.2362i	−1.45281	−	0.838779i	−0.998640	+	0.0521380i	$0.983396\pi$
$642$		0			0
$643$	3.13514	+	1.81008i	0.123638	+	0.0713825i	0.560544	−	0.828125i	$-0.310592\pi$
$643$	3.13514	+	1.81008i	0.123638	+	0.0713825i	−0.436905	+	0.899507i	$0.643926\pi$
$644$	57.5751	+	14.5494i	2.26878	+	0.573325i
$645$		0			0
$646$	21.8478			0.859589
$647$	6.00617	+	10.4030i	0.236127	+	0.408984i	0.959600	−	0.281369i	$-0.0907886\pi$
$647$	6.00617	+	10.4030i	0.236127	+	0.408984i	−0.723473	+	0.690353i	$0.757455\pi$
$648$		0			0
$649$	−1.90394	−	1.09924i	−0.0747361	−	0.0431489i
$650$	−5.46186	−	9.46022i	−0.214232	−	0.371060i
$651$		0			0
$652$	20.8484	−	36.1105i	0.816486	−	1.41420i
$653$	−39.9950	+	23.0911i	−1.56512	+	0.903625i	−0.568400	+	0.822752i	$0.692437\pi$
$653$	−39.9950	+	23.0911i	−1.56512	+	0.903625i	−0.996724	+	0.0808728i	$0.974229\pi$
$654$		0			0
$655$	−10.1665	+	17.6089i	−0.397238	+	0.688036i
$656$	18.6584	−	32.3174i	0.728490	−	1.26178i
$657$		0			0
$658$	36.4160	−	37.4711i	1.41964	−	1.46078i
$659$	16.3479	−	9.43847i	0.636824	−	0.367671i	−0.146566	−	0.989201i	$-0.546822\pi$
$659$	16.3479	−	9.43847i	0.636824	−	0.367671i	0.783390	+	0.621530i	$0.213489\pi$
$660$		0			0
$661$		−	3.32787i		−	0.129439i	−0.997903	−	0.0647195i	$-0.979385\pi$
$661$		−	3.32787i		−	0.129439i	0.997903	−	0.0647195i	$-0.0206153\pi$
$662$		−	68.6463i		−	2.66801i
$663$		0			0
$664$	−53.4944	+	30.8850i	−2.07599	+	1.19857i
$665$	4.39336	−	4.52066i	0.170367	−	0.175304i
$666$		0			0
$667$	13.9181	−	24.1068i	0.538909	−	0.933418i
$668$	52.1494	−	90.3254i	2.01772	−	3.49480i
$669$		0			0
$670$	−38.3106	+	22.1187i	−1.48007	+	0.854518i
$671$	−4.45589	+	7.71783i	−0.172018	+	0.297944i
$672$		0			0
$673$	−16.3678	−	28.3499i	−0.630934	−	1.09281i	−0.987361	−	0.158487i	$-0.949339\pi$
$673$	−16.3678	−	28.3499i	−0.630934	−	1.09281i	0.356427	−	0.934323i	$-0.383995\pi$
$674$	7.80099	+	4.50390i	0.300483	+	0.173484i
$675$		0			0
$676$	27.1585	+	47.0399i	1.04456	+	1.80923i
$677$	33.8456			1.30079			0.650396	−	0.759596i	$-0.274603\pi$
$677$	33.8456			1.30079			0.650396	+	0.759596i	$0.274603\pi$
$678$		0			0
$679$	−25.9622	−	6.56071i	−0.996339	−	0.251777i
$680$	−33.9917	−	19.6251i	−1.30352	−	0.752590i
$681$		0			0
$682$	3.43672	+	1.98419i	0.131599	+	0.0759785i
$683$	4.79617	−	2.76907i	0.183520	−	0.105956i	−0.405425	−	0.914128i	$-0.632877\pi$
$683$	4.79617	−	2.76907i	0.183520	−	0.105956i	0.588946	+	0.808173i	$0.299543\pi$
$684$		0			0
$685$		−	21.8052i		−	0.833133i
$686$	−35.3878	−	32.4788i	−1.35111	−	1.24005i
$687$		0			0
$688$	−19.9622	−	34.5756i	−0.761052	−	1.31818i
$689$	3.79691			0.144651
$690$		0			0
$691$			14.2510i			0.542134i	0.962561	+	0.271067i	$0.0873764\pi$
$691$			14.2510i			0.542134i	−0.962561	+	0.271067i	$0.912624\pi$
$692$	19.2248			0.730818
$693$		0			0
$694$	−24.4003			−0.926222
$695$			7.88913i			0.299252i
$696$		0			0
$697$	−18.6031			−0.704642
$698$	−18.4557	−	31.9662i	−0.698559	−	1.20994i
$699$		0			0
$700$	41.2683	−	11.6919i	1.55979	−	0.441910i
$701$			18.6105i			0.702908i	0.936205	+	0.351454i	$0.114313\pi$
$701$			18.6105i			0.702908i	−0.936205	+	0.351454i	$0.885687\pi$
$702$		0			0
$703$	−4.38760	+	2.53318i	−0.165482	+	0.0955408i
$704$	−2.84293	−	1.64137i	−0.107147	−	0.0618614i
$705$		0			0
$706$	38.5544	+	22.2594i	1.45101	+	0.837743i
$707$	−4.36111	+	1.23556i	−0.164017	+	0.0464681i
$708$		0			0
$709$	−13.4947			−0.506803			−0.253401	−	0.967361i	$-0.581549\pi$
$709$	−13.4947			−0.506803			−0.253401	+	0.967361i	$0.581549\pi$
$710$	−16.9137	−	29.2955i	−0.634762	−	1.09944i
$711$		0			0
$712$	−9.93557	−	5.73630i	−0.372351	−	0.214977i
$713$	5.89074	+	10.2031i	0.220610	+	0.382107i
$714$		0			0
$715$	0.474470	−	0.821807i	0.0177442	−	0.0307338i
$716$	−34.0676	+	19.6689i	−1.27317	+	0.735063i
$717$		0			0
$718$	36.6417	−	63.4652i	1.36745	−	2.36850i
$719$	−18.8692	+	32.6824i	−0.703702	+	1.21885i	0.263456	+	0.964671i	$0.415137\pi$
$719$	−18.8692	+	32.6824i	−0.703702	+	1.21885i	−0.967158	+	0.254176i	$0.918196\pi$
$720$		0			0
$721$	18.9954	+	4.80017i	0.707424	+	0.178768i
$722$	−34.5538	+	19.9496i	−1.28596	+	0.742449i
$723$		0			0
$724$		−	59.8847i		−	2.22560i
$725$		−	20.1054i		−	0.746697i
$726$		0			0
$727$	−1.98480	+	1.14592i	−0.0736121	+	0.0424999i	−0.536354	−	0.843993i	$-0.680199\pi$
$727$	−1.98480	+	1.14592i	−0.0736121	+	0.0424999i	0.462742	+	0.886493i	$0.346866\pi$
$728$	22.1031	−	6.26211i	0.819197	−	0.232089i
$729$		0			0
$730$	−18.6685	+	32.3347i	−0.690950	+	1.19676i
$731$	−9.95149	+	17.2365i	−0.368069	+	0.637514i
$732$		0			0
$733$	−21.4678	+	12.3944i	−0.792930	+	0.457798i	−0.840993	−	0.541046i	$-0.818028\pi$
$733$	−21.4678	+	12.3944i	−0.792930	+	0.457798i	0.0480633	+	0.998844i	$0.484695\pi$
$734$	29.9170	−	51.8178i	1.10426	−	1.91263i
$735$		0			0
$736$	−21.1444	−	36.6232i	−0.779394	−	1.34995i
$737$	7.27099	+	4.19791i	0.267830	+	0.154632i
$738$		0			0
$739$	8.10081	+	14.0310i	0.297993	+	0.516139i	0.975677	−	0.219214i	$-0.0703494\pi$
$739$	8.10081	+	14.0310i	0.297993	+	0.516139i	−0.677684	+	0.735354i	$0.737016\pi$
$740$	15.7786			0.580035
$741$		0			0
$742$	−5.19828	+	20.5708i	−0.190835	+	0.755177i
$743$	18.8312	+	10.8722i	0.690848	+	0.398862i	0.803930	−	0.594724i	$-0.202739\pi$
$743$	18.8312	+	10.8722i	0.690848	+	0.398862i	−0.113081	+	0.993586i	$0.536072\pi$
$744$		0			0
$745$	−11.5315	−	6.65769i	−0.422480	−	0.243919i
$746$	31.1591	−	17.9897i	1.14081	−	0.658649i
$747$		0			0
$748$			12.9138i			0.472176i
$749$	0.109639	+	0.386988i	0.00400612	+	0.0141402i
$750$		0			0
$751$	3.78997	+	6.56443i	0.138298	+	0.239539i	0.926853	−	0.375426i	$-0.122503\pi$
$751$	3.78997	+	6.56443i	0.138298	+	0.239539i	−0.788554	+	0.614965i	$0.789170\pi$
$752$	−67.6680			−2.46760
$753$		0			0
$754$		−	18.6676i		−	0.679834i
$755$	11.8900			0.432720
$756$		0			0
$757$	10.3436			0.375944			0.187972	−	0.982174i	$-0.439809\pi$
$757$	10.3436			0.375944			0.187972	+	0.982174i	$0.439809\pi$
$758$		−	59.0844i		−	2.14604i
$759$		0			0
$760$	−16.8478			−0.611135
$761$	17.2169	+	29.8206i	0.624114	+	1.08100i	0.988711	+	0.149832i	$0.0478732\pi$
$761$	17.2169	+	29.8206i	0.624114	+	1.08100i	−0.364598	+	0.931165i	$0.618793\pi$
$762$		0			0
$763$	3.50100	−	13.8542i	0.126745	−	0.501557i
$764$			17.9629i			0.649874i
$765$		0			0
$766$	34.2121	−	19.7523i	1.23613	−	0.713681i
$767$	−3.79070	−	2.18856i	−0.136874	−	0.0790245i
$768$		0			0
$769$	12.9344	+	7.46765i	0.466425	+	0.269290i	0.714742	−	0.699388i	$-0.246544\pi$
$769$	12.9344	+	7.46765i	0.466425	+	0.269290i	−0.248317	+	0.968679i	$0.579877\pi$
$770$	3.80277	+	3.69569i	0.137042	+	0.133183i
$771$		0			0
$772$	−32.0877			−1.15486
$773$	19.9924	+	34.6278i	0.719076	+	1.24548i	0.961366	+	0.275272i	$0.0887680\pi$
$773$	19.9924	+	34.6278i	0.719076	+	1.24548i	−0.242290	+	0.970204i	$0.577899\pi$
$774$		0			0
$775$	7.36945	+	4.25476i	0.264719	+	0.152835i
$776$	35.7845	+	61.9806i	1.28459	+	2.22497i
$777$		0			0
$778$	−18.3466	+	31.7772i	−0.657758	+	1.13927i
$779$	−6.91539	+	3.99260i	−0.247770	+	0.143050i
$780$		0			0
$781$	−3.21007	+	5.56000i	−0.114865	+	0.198952i
$782$	−27.2811	+	47.2523i	−0.975571	+	1.68974i
$783$		0			0
$784$	1.77622	+	62.1796i	0.0634364	+	2.22070i
$785$	−25.8383	+	14.9178i	−0.922209	+	0.532438i
$786$		0			0
$787$			2.24117i			0.0798892i	0.999202	+	0.0399446i	$0.0127181\pi$
$787$			2.24117i			0.0798892i	−0.999202	+	0.0399446i	$0.987282\pi$
$788$			30.3180i			1.08003i
$789$		0			0
$790$	11.3468	−	6.55108i	0.403701	−	0.233077i
$791$	−4.66671	−	16.4719i	−0.165929	−	0.585674i
$792$		0			0
$793$	−8.87159	+	15.3660i	−0.315039	+	0.545664i
$794$	12.5883	−	21.8036i	0.446742	−	0.773780i
$795$		0			0
$796$	65.6605	−	37.9091i	2.32727	−	1.34365i
$797$	−22.1077	+	38.2916i	−0.783094	+	1.35636i	0.147037	+	0.989131i	$0.453026\pi$
$797$	−22.1077	+	38.2916i	−0.783094	+	1.35636i	−0.930131	+	0.367227i	$0.880307\pi$
$798$		0			0
$799$	16.8668	+	29.2142i	0.596705	+	1.03352i
$800$	−26.4522	−	15.2722i	−0.935226	−	0.539953i
$801$		0			0
$802$	−11.3225	−	19.6112i	−0.399812	−	0.692495i
$803$	7.08619			0.250066
$804$		0			0
$805$	4.29130	+	15.1468i	0.151249	+	0.533856i
$806$	6.84243	+	3.95048i	0.241014	+	0.139150i
$807$		0			0
$808$	10.4914	+	6.05723i	0.369087	+	0.213093i
$809$	4.31478	−	2.49114i	0.151699	−	0.0875837i	−0.422229	−	0.906489i	$-0.638752\pi$
$809$	4.31478	−	2.49114i	0.151699	−	0.0875837i	0.573928	+	0.818906i	$0.305419\pi$
$810$		0			0
$811$		−	36.5749i		−	1.28432i	−0.766571	−	0.642160i	$-0.778039\pi$
$811$		−	36.5749i		−	1.28432i	0.766571	−	0.642160i	$-0.221961\pi$
$812$	71.0653	+	17.9584i	2.49390	+	0.630215i
$813$		0			0
$814$	−2.13091	−	3.69084i	−0.0746883	−	0.129364i
$815$	11.0539			0.387200
$816$		0			0
$817$			8.54318i			0.298888i
$818$	38.6225			1.35040
$819$		0			0
$820$	24.8690			0.868465
$821$			40.2294i			1.40402i	0.712169	+	0.702008i	$0.247713\pi$
$821$			40.2294i			1.40402i	−0.712169	+	0.702008i	$0.752287\pi$
$822$		0			0
$823$	−35.8032			−1.24802			−0.624011	−	0.781416i	$-0.714498\pi$
$823$	−35.8032			−1.24802			−0.624011	+	0.781416i	$0.714498\pi$
$824$	−26.1819	−	45.3483i	−0.912089	−	1.57978i
$825$		0			0
$826$	17.0469	−	17.5408i	0.593138	−	0.610323i
$827$		−	32.0733i		−	1.11530i	−0.830077	−	0.557648i	$-0.811704\pi$
$827$		−	32.0733i		−	1.11530i	0.830077	−	0.557648i	$-0.188296\pi$
$828$		0			0
$829$	−14.0640	+	8.11986i	−0.488463	+	0.282014i	−0.723937	−	0.689866i	$-0.757669\pi$
$829$	−14.0640	+	8.11986i	−0.488463	+	0.282014i	0.235474	+	0.971881i	$0.424336\pi$
$830$	−24.5842	−	14.1937i	−0.853332	−	0.492671i
$831$		0			0
$832$	−5.66023	−	3.26793i	−0.196233	−	0.113295i
$833$	26.4019	−	16.2656i	0.914773	−	0.563570i
$834$		0			0
$835$	27.6497			0.956857
$836$	2.77157	+	4.80050i	0.0958568	+	0.166029i
$837$		0			0
$838$	9.60684	+	5.54651i	0.331863	+	0.191601i
$839$	−1.35145	−	2.34077i	−0.0466571	−	0.0808125i	0.841754	−	0.539862i	$-0.181523\pi$
$839$	−1.35145	−	2.34077i	−0.0466571	−	0.0808125i	−0.888411	+	0.459049i	$0.848190\pi$
$840$		0			0
$841$	2.67914	−	4.64041i	0.0923842	−	0.160014i
$842$	25.9053	−	14.9565i	0.892757	−	0.515434i
$843$		0			0
$844$	19.1927	−	33.2427i	0.660639	−	1.14426i
$845$	−7.19974	+	12.4703i	−0.247679	+	0.428992i
$846$		0			0
$847$	−6.88375	+	27.2405i	−0.236528	+	0.935996i
$848$	23.7962	−	13.7388i	0.817166	−	0.471791i
$849$		0			0
$850$			39.4092i			1.35172i
$851$		−	12.6526i		−	0.433727i
$852$		0			0
$853$	41.3187	−	23.8554i	1.41473	−	0.816793i	0.418897	−	0.908034i	$-0.362417\pi$
$853$	41.3187	−	23.8554i	1.41473	−	0.816793i	0.995829	+	0.0912411i	$0.0290834\pi$
$854$	−71.1037	−	69.1015i	−2.43312	−	2.36461i
$855$		0			0
$856$	0.537495	−	0.930969i	0.0183712	−	0.0318199i
$857$	−8.93973	+	15.4841i	−0.305375	+	0.528926i	−0.977345	−	0.211653i	$-0.932115\pi$
$857$	−8.93973	+	15.4841i	−0.305375	+	0.528926i	0.671969	+	0.740579i	$0.265449\pi$
$858$		0			0
$859$	29.1901	−	16.8529i	0.995953	−	0.575014i	0.0889047	−	0.996040i	$-0.471663\pi$
$859$	29.1901	−	16.8529i	0.995953	−	0.575014i	0.907048	+	0.421026i	$0.138330\pi$
$860$	13.3034	−	23.0422i	0.453642	−	0.785731i
$861$		0			0
$862$	21.6367	+	37.4759i	0.736950	+	1.27643i
$863$	−16.4318	−	9.48693i	−0.559347	−	0.322939i	0.193537	−	0.981093i	$-0.438004\pi$
$863$	−16.4318	−	9.48693i	−0.559347	−	0.322939i	−0.752883	+	0.658154i	$0.771338\pi$
$864$		0			0
$865$	2.54826	+	4.41371i	0.0866434	+	0.150071i
$866$	32.0309			1.08846
$867$		0			0
$868$	−21.6215	+	22.2479i	−0.733881	+	0.755144i
$869$	−2.15351	−	1.24333i	−0.0730530	−	0.0421772i
$870$		0			0
$871$	14.4764	+	8.35795i	0.490514	+	0.283198i
$872$	−33.0748	+	19.0957i	−1.12005	+	0.646663i
$873$		0			0
$874$			23.4204i			0.792206i
$875$	20.0411	+	19.4768i	0.677514	+	0.658437i
$876$		0			0
$877$	−18.6188	−	32.2487i	−0.628712	−	1.08896i	−0.987810	−	0.155662i	$-0.950249\pi$
$877$	−18.6188	−	32.2487i	−0.628712	−	1.08896i	0.359098	−	0.933300i	$-0.383084\pi$
$878$	−57.4070			−1.93739
$879$		0			0
$880$		−	6.86730i		−	0.231497i
$881$	−4.71527			−0.158862			−0.0794308	−	0.996840i	$-0.525310\pi$
$881$	−4.71527			−0.158862			−0.0794308	+	0.996840i	$0.525310\pi$
$882$		0			0
$883$	30.1766			1.01552			0.507762	−	0.861497i	$-0.330473\pi$
$883$	30.1766			1.01552			0.507762	+	0.861497i	$0.330473\pi$
$884$			25.7112i			0.864760i
$885$		0			0
$886$	−12.6650			−0.425490
$887$	−19.2217	−	33.2930i	−0.645402	−	1.11787i	−0.984208	−	0.177013i	$-0.943356\pi$
$887$	−19.2217	−	33.2930i	−0.645402	−	1.11787i	0.338806	−	0.940856i	$-0.389977\pi$
$888$		0			0
$889$	5.56255	+	5.40592i	0.186562	+	0.181309i
$890$		−	5.27243i		−	0.176732i
$891$		0			0
$892$	−32.9058	+	18.9981i	−1.10177	+	0.636105i
$893$	12.5399	+	7.23993i	0.419632	+	0.242275i
$894$		0			0
$895$	−9.03135	−	5.21425i	−0.301885	−	0.174293i
$896$	−7.38607	+	7.60007i	−0.246751	+	0.253901i
$897$		0			0
$898$	32.2659			1.07673
$899$	7.27098	+	12.5937i	0.242501	+	0.420023i
$900$		0			0
$901$	−11.8628	−	6.84900i	−0.395208	−	0.228173i
$902$	−3.35857	−	5.81721i	−0.111828	−	0.193692i
$903$		0			0
$904$	−22.8781	+	39.6261i	−0.760916	+	1.31794i
$905$	13.7486	−	7.93774i	0.457018	−	0.263859i
$906$		0			0
$907$	−21.7951	+	37.7503i	−0.723695	+	1.25348i	0.235814	+	0.971798i	$0.424224\pi$
$907$	−21.7951	+	37.7503i	−0.723695	+	1.25348i	−0.959509	+	0.281678i	$0.909109\pi$
$908$	−49.2103	+	85.2348i	−1.63310	+	2.82862i
$909$		0			0
$910$	7.57123	+	7.35804i	0.250984	+	0.243917i
$911$	1.67736	−	0.968423i	0.0555734	−	0.0320853i	−0.471956	−	0.881622i	$-0.656452\pi$
$911$	1.67736	−	0.968423i	0.0555734	−	0.0320853i	0.527529	+	0.849537i	$0.323119\pi$
$912$		0			0
$913$			5.38766i			0.178306i
$914$			27.9467i			0.924393i
$915$		0			0
$916$	−24.6379	+	14.2247i	−0.814058	+	0.469997i
$917$	−10.5189	+	41.6258i	−0.347366	+	1.37460i
$918$		0			0
$919$	4.61421	−	7.99205i	0.152209	−	0.263634i	−0.779830	−	0.625991i	$-0.784695\pi$
$919$	4.61421	−	7.99205i	0.152209	−	0.263634i	0.932039	+	0.362357i	$0.118028\pi$
$920$	21.0377	−	36.4384i	0.693594	−	1.20134i
$921$		0			0
$922$	−1.49724	+	0.864434i	−0.0493091	+	0.0284686i
$923$	−6.39118	+	11.0698i	−0.210368	+	0.364368i
$924$		0			0
$925$	−4.56937	−	7.91438i	−0.150240	−	0.260223i
$926$	93.3880	+	53.9176i	3.06892	+	1.77184i
$927$		0			0
$928$	−26.0987	−	45.2043i	−0.856732	−	1.48390i
$929$	−53.3699			−1.75101			−0.875504	−	0.483211i	$-0.839471\pi$
$929$	−53.3699			−1.75101			−0.875504	+	0.483211i	$0.839471\pi$
$930$		0			0
$931$	6.32355	−	11.7129i	0.207246	−	0.383874i
$932$	86.0952	+	49.7071i	2.82014	+	1.62821i
$933$		0			0
$934$	−88.3010	−	50.9806i	−2.88930	−	1.66814i
$935$	−2.96481	+	1.71173i	−0.0969595	+	0.0559796i
$936$		0			0
$937$			28.6378i			0.935555i	0.883846	+	0.467778i	$0.154945\pi$
$937$			28.6378i			0.935555i	−0.883846	+	0.467778i	$0.845055\pi$
$938$	−65.1008	+	66.9870i	−2.12562	+	2.18720i
$939$		0			0
$940$	−22.5480	−	39.0542i	−0.735433	−	1.27381i
$941$	1.37662			0.0448764			0.0224382	−	0.999748i	$-0.492857\pi$
$941$	1.37662			0.0448764			0.0224382	+	0.999748i	$0.492857\pi$
$942$		0			0
$943$		−	19.9421i		−	0.649404i
$944$	−31.6764			−1.03098
$945$		0			0
$946$	−7.18651			−0.233653
$947$		−	54.2801i		−	1.76387i	−0.471374	−	0.881933i	$-0.656242\pi$
$947$		−	54.2801i		−	1.76387i	0.471374	−	0.881933i	$-0.343758\pi$
$948$		0			0
$949$	14.1085			0.457980
$950$	8.45802	+	14.6497i	0.274414	+	0.475300i
$951$		0			0
$952$	−80.3533	−	20.3055i	−2.60427	−	0.658104i
$953$			11.2998i			0.366036i	0.983110	+	0.183018i	$0.0585867\pi$
$953$			11.2998i			0.366036i	−0.983110	+	0.183018i	$0.941413\pi$
$954$		0			0
$955$	−4.12399	+	2.38099i	−0.133449	+	0.0770469i
$956$	−35.4994	−	20.4956i	−1.14813	−	0.662874i
$957$		0			0
$958$	−85.6097	−	49.4268i	−2.76592	−	1.59691i
$959$	−12.5506	−	44.2994i	−0.405280	−	1.43050i
$960$		0			0
$961$	24.8452			0.801458
$962$	−4.24260	−	7.34839i	−0.136787	−	0.236922i
$963$		0			0
$964$	−34.6825	−	20.0240i	−1.11705	−	0.644928i
$965$	−4.25324	−	7.36682i	−0.136917	−	0.237146i
$966$		0			0
$967$	5.93412	−	10.2782i	0.190829	−	0.330525i	−0.754696	−	0.656074i	$-0.772216\pi$
$967$	5.93412	−	10.2782i	0.190829	−	0.330525i	0.945525	+	0.325549i	$0.105549\pi$
$968$	65.0324	−	37.5465i	2.09022	−	1.20679i
$969$		0			0
$970$	−16.4454	+	28.4842i	−0.528029	+	0.914573i
$971$	28.0837	−	48.6424i	0.901249	−	1.56101i	0.0753736	−	0.997155i	$-0.475985\pi$
$971$	28.0837	−	48.6424i	0.901249	−	1.56101i	0.825875	−	0.563853i	$-0.190682\pi$
$972$		0			0
$973$	4.54081	+	16.0275i	0.145572	+	0.513819i
$974$	−17.0826	+	9.86263i	−0.547361	+	0.316019i
$975$		0			0
$976$			128.404i			4.11011i
$977$		−	21.6651i		−	0.693129i	−0.938026	−	0.346565i	$-0.887348\pi$
$977$		−	21.6651i		−	0.693129i	0.938026	−	0.346565i	$-0.112652\pi$
$978$		0			0
$979$	−0.866594	+	0.500328i	−0.0276964	+	0.0159906i
$980$	−35.2948	+	21.7443i	−1.12745	+	0.694596i
$981$		0			0
$982$	−4.99072	+	8.64419i	−0.159260	+	0.275847i
$983$	9.70006	−	16.8010i	0.309384	−	0.535869i	−0.668844	−	0.743403i	$-0.733211\pi$
$983$	9.70006	−	16.8010i	0.309384	−	0.535869i	0.978228	+	0.207534i	$0.0665438\pi$
$984$		0			0
$985$	−6.96052	+	4.01866i	−0.221781	+	0.128045i
$986$	−33.6733	+	58.3238i	−1.07238	+	1.85741i
$987$		0			0
$988$	5.51814	+	9.55771i	0.175556	+	0.304071i
$989$	−18.4771	−	10.6678i	−0.587539	−	0.339216i
$990$		0			0
$991$	−12.6630	−	21.9330i	−0.402254	−	0.696725i	0.591743	−	0.806126i	$-0.298440\pi$
$991$	−12.6630	−	21.9330i	−0.402254	−	0.696725i	−0.993998	+	0.109402i	$0.965107\pi$
$992$	22.0923			0.701430
$993$		0			0
$994$	−51.2238	−	49.7814i	−1.62472	−	1.57897i
$995$	17.4066	+	10.0497i	0.551828	+	0.318598i
$996$		0			0
$997$	4.82016	+	2.78292i	0.152656	+	0.0881360i	0.574382	−	0.818587i	$-0.305242\pi$
$997$	4.82016	+	2.78292i	0.152656	+	0.0881360i	−0.421726	+	0.906723i	$0.638576\pi$
$998$	72.2309	−	41.7025i	2.28643	−	1.32007i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.2.i.b.152.1		10
3.2	odd	2		63.2.i.b.5.5	✓	10
4.3	odd	2		3024.2.ca.b.2609.2		10
7.2	even	3		1323.2.o.c.881.1		10
7.3	odd	6		189.2.s.b.17.5		10
7.4	even	3		1323.2.s.b.962.5		10
7.5	odd	6		1323.2.o.d.881.1		10
7.6	odd	2		1323.2.i.b.1097.1		10
9.2	odd	6		189.2.s.b.89.5		10
9.4	even	3		567.2.p.c.404.5		10
9.5	odd	6		567.2.p.d.404.1		10
9.7	even	3		63.2.s.b.47.1	yes	10
12.11	even	2		1008.2.ca.b.257.1		10
21.2	odd	6		441.2.o.d.293.5		10
21.5	even	6		441.2.o.c.293.5		10
21.11	odd	6		441.2.s.b.374.1		10
21.17	even	6		63.2.s.b.59.1	yes	10
21.20	even	2		441.2.i.b.68.5		10
28.3	even	6		3024.2.df.b.17.2		10
36.7	odd	6		1008.2.df.b.929.1		10
36.11	even	6		3024.2.df.b.1601.2		10
63.2	odd	6		1323.2.o.d.440.1		10
63.11	odd	6		1323.2.i.b.521.5		10
63.16	even	3		441.2.o.c.146.5		10
63.20	even	6		1323.2.s.b.656.5		10
63.25	even	3		441.2.i.b.227.1		10
63.31	odd	6		567.2.p.d.80.1		10
63.34	odd	6		441.2.s.b.362.1		10
63.38	even	6	inner	189.2.i.b.143.5		10
63.47	even	6		1323.2.o.c.440.1		10
63.52	odd	6		63.2.i.b.38.1	yes	10
63.59	even	6		567.2.p.c.80.5		10
63.61	odd	6		441.2.o.d.146.5		10
84.59	odd	6		1008.2.df.b.689.1		10
252.115	even	6		1008.2.ca.b.353.1		10
252.227	odd	6		3024.2.ca.b.2033.2		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.i.b.5.5	✓	10	3.2	odd	2
63.2.i.b.38.1	yes	10	63.52	odd	6
63.2.s.b.47.1	yes	10	9.7	even	3
63.2.s.b.59.1	yes	10	21.17	even	6
189.2.i.b.143.5		10	63.38	even	6	inner
189.2.i.b.152.1		10	1.1	even	1	trivial
189.2.s.b.17.5		10	7.3	odd	6
189.2.s.b.89.5		10	9.2	odd	6
441.2.i.b.68.5		10	21.20	even	2
441.2.i.b.227.1		10	63.25	even	3
441.2.o.c.146.5		10	63.16	even	3
441.2.o.c.293.5		10	21.5	even	6
441.2.o.d.146.5		10	63.61	odd	6
441.2.o.d.293.5		10	21.2	odd	6
441.2.s.b.362.1		10	63.34	odd	6
441.2.s.b.374.1		10	21.11	odd	6
567.2.p.c.80.5		10	63.59	even	6
567.2.p.c.404.5		10	9.4	even	3
567.2.p.d.80.1		10	63.31	odd	6
567.2.p.d.404.1		10	9.5	odd	6
1008.2.ca.b.257.1		10	12.11	even	2
1008.2.ca.b.353.1		10	252.115	even	6
1008.2.df.b.689.1		10	84.59	odd	6
1008.2.df.b.929.1		10	36.7	odd	6
1323.2.i.b.521.5		10	63.11	odd	6
1323.2.i.b.1097.1		10	7.6	odd	2
1323.2.o.c.440.1		10	63.47	even	6
1323.2.o.c.881.1		10	7.2	even	3
1323.2.o.d.440.1		10	63.2	odd	6
1323.2.o.d.881.1		10	7.5	odd	6
1323.2.s.b.656.5		10	63.20	even	6
1323.2.s.b.962.5		10	7.4	even	3
3024.2.ca.b.2033.2		10	252.227	odd	6
3024.2.ca.b.2609.2		10	4.3	odd	2
3024.2.df.b.17.2		10	28.3	even	6
3024.2.df.b.1601.2		10	36.11	even	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 189 = 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	189.i (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-2.59354i q^{2} -4.72645 q^{4} +(-0.626493 - 1.08512i) q^{5} +(-1.89735 - 1.84393i) q^{7} +7.07116i q^{8} +O(q^{10})\)	\(q-2.59354i q^{2} -4.72645 q^{4} +(-0.626493 - 1.08512i) q^{5} +(-1.89735 - 1.84393i) q^{7} +7.07116i q^{8} +(-2.81429 + 1.62483i) q^{10} +(0.534126 + 0.308378i) q^{11} +(1.06343 + 0.613974i) q^{13} +(-4.78229 + 4.92086i) q^{14} +8.88643 q^{16} +(-2.21501 - 3.83652i) q^{17} +(-1.64679 - 0.950775i) q^{19} +(2.96109 + 5.12875i) q^{20} +(0.799790 - 1.38528i) q^{22} +(4.11267 - 2.37445i) q^{23} +(1.71501 - 2.97049i) q^{25} +(1.59237 - 2.75806i) q^{26} +(8.96773 + 8.71522i) q^{28} +(5.07629 - 2.93080i) q^{29} +2.48089i q^{31} -8.90499i q^{32} +(-9.95016 + 5.74473i) q^{34} +(-0.812198 + 3.21405i) q^{35} +(1.33217 - 2.30738i) q^{37} +(-2.46587 + 4.27102i) q^{38} +(7.67303 - 4.43003i) q^{40} +(2.09966 - 3.63671i) q^{41} +(-2.24637 - 3.89083i) q^{43} +(-2.52452 - 1.45753i) q^{44} +(-6.15823 - 10.6664i) q^{46} -7.61476 q^{47} +(0.199880 + 6.99715i) q^{49} +(-7.70409 - 4.44796i) q^{50} +(-5.02627 - 2.90192i) q^{52} +(2.67782 - 1.54604i) q^{53} -0.772786i q^{55} +(13.0387 - 13.4165i) q^{56} +(-7.60114 - 13.1656i) q^{58} -3.56459 q^{59} +14.4495i q^{61} +6.43428 q^{62} -5.32259 q^{64} -1.53860i q^{65} +13.6129 q^{67} +(10.4692 + 18.1331i) q^{68} +(8.33577 + 2.10647i) q^{70} +10.4095i q^{71} +(9.95016 - 5.74473i) q^{73} +(-5.98429 - 3.45503i) q^{74} +(7.78348 + 4.49379i) q^{76} +(-0.444799 - 1.56999i) q^{77} -4.03185 q^{79} +(-5.56728 - 9.64281i) q^{80} +(-9.43196 - 5.44554i) q^{82} +(4.36775 + 7.56516i) q^{83} +(-2.77538 + 4.80710i) q^{85} +(-10.0910 + 5.82605i) q^{86} +(-2.18059 + 3.77689i) q^{88} +(-0.811226 + 1.40508i) q^{89} +(-0.885586 - 3.12582i) q^{91} +(-19.4383 + 11.2227i) q^{92} +19.7492i q^{94} +2.38261i q^{95} +(8.76527 - 5.06063i) q^{97} +(18.1474 - 0.518397i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 8 q^{4} - 6 q^{7}+O(q^{10}) \) 10 * q - 8 * q^4 - 6 * q^7	\( 10 q - 8 q^{4} - 6 q^{7} - 15 q^{10} + 12 q^{11} - 6 q^{13} - 12 q^{14} + 12 q^{16} - 12 q^{17} + 3 q^{19} - 3 q^{20} + 5 q^{22} + 15 q^{23} + 7 q^{25} + 3 q^{26} + 2 q^{28} + 15 q^{29} - 3 q^{34} - 15 q^{35} + 6 q^{37} - 18 q^{38} + 15 q^{40} - 9 q^{41} + 3 q^{43} + 24 q^{44} - 13 q^{46} - 30 q^{47} + 4 q^{49} - 3 q^{50} - 12 q^{52} - 9 q^{53} + 30 q^{56} + 8 q^{58} + 36 q^{59} + 12 q^{62} + 6 q^{64} + 20 q^{67} + 27 q^{68} + 6 q^{70} + 3 q^{73} + 30 q^{74} - 9 q^{76} - 39 q^{77} - 40 q^{79} - 30 q^{80} + 9 q^{82} - 15 q^{83} + 18 q^{85} - 54 q^{86} - 8 q^{88} + 24 q^{89} - 24 q^{91} - 39 q^{92} - 6 q^{97} + 45 q^{98}+O(q^{100}) \) 10 * q - 8 * q^4 - 6 * q^7 - 15 * q^10 + 12 * q^11 - 6 * q^13 - 12 * q^14 + 12 * q^16 - 12 * q^17 + 3 * q^19 - 3 * q^20 + 5 * q^22 + 15 * q^23 + 7 * q^25 + 3 * q^26 + 2 * q^28 + 15 * q^29 - 3 * q^34 - 15 * q^35 + 6 * q^37 - 18 * q^38 + 15 * q^40 - 9 * q^41 + 3 * q^43 + 24 * q^44 - 13 * q^46 - 30 * q^47 + 4 * q^49 - 3 * q^50 - 12 * q^52 - 9 * q^53 + 30 * q^56 + 8 * q^58 + 36 * q^59 + 12 * q^62 + 6 * q^64 + 20 * q^67 + 27 * q^68 + 6 * q^70 + 3 * q^73 + 30 * q^74 - 9 * q^76 - 39 * q^77 - 40 * q^79 - 30 * q^80 + 9 * q^82 - 15 * q^83 + 18 * q^85 - 54 * q^86 - 8 * q^88 + 24 * q^89 - 24 * q^91 - 39 * q^92 - 6 * q^97 + 45 * q^98

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