LMFDB - Embedded newform 756.2.bb.a.611.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(611,756)]

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, 5, 2]))

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

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

chi := DirichletCharacter("756.611");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.bb (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:	$88$
Relative dimension:	$44$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 252)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			611.8
Character	$\chi$	$=$	756.611
Dual form			756.2.bb.a.683.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.24253 + 0.675360i) q^{2} +(1.08778 - 1.67831i) q^{4} +(1.44577 - 0.834716i) q^{5} +(0.369619 + 2.61981i) q^{7} +(-0.218133 + 2.82000i) q^{8} +O(q^{10})$	\(q+(-1.24253 + 0.675360i) q^{2} +(1.08778 - 1.67831i) q^{4} +(1.44577 - 0.834716i) q^{5} +(0.369619 + 2.61981i) q^{7} +(-0.218133 + 2.82000i) q^{8} +(-1.23268 + 2.01358i) q^{10} +(-2.77302 + 4.80301i) q^{11} +(-0.458226 + 0.793672i) q^{13} +(-2.22858 - 3.00557i) q^{14} +(-1.63348 - 3.65127i) q^{16} +(0.105306 - 0.0607985i) q^{17} +(-6.59665 - 3.80857i) q^{19} +(0.171761 - 3.33445i) q^{20} +(0.201807 - 7.84068i) q^{22} +(2.15326 + 3.72955i) q^{23} +(-1.10650 + 1.91651i) q^{25} +(0.0333475 - 1.29563i) q^{26} +(4.79892 + 2.22943i) q^{28} +(0.684776 - 0.395356i) q^{29} +2.70618i q^{31} +(4.49557 + 3.43363i) q^{32} +(-0.0897854 + 0.146664i) q^{34} +(2.72118 + 3.47911i) q^{35} +(-4.12969 + 7.15284i) q^{37} +(10.7687 + 0.277170i) q^{38} +(2.03853 + 4.25916i) q^{40} +(1.71368 + 0.989393i) q^{41} +(10.5968 - 6.11808i) q^{43} +(5.04453 + 9.87860i) q^{44} +(-5.19429 - 3.17987i) q^{46} -4.39151 q^{47} +(-6.72676 + 1.93666i) q^{49} +(0.0805256 - 3.12861i) q^{50} +(0.833582 + 1.63239i) q^{52} +(-2.75730 + 1.59193i) q^{53} +9.25874i q^{55} +(-7.46849 + 0.470860i) q^{56} +(-0.583850 + 0.953714i) q^{58} -8.64223 q^{59} +3.83447 q^{61} +(-1.82764 - 3.36252i) q^{62} +(-7.90484 - 1.23027i) q^{64} +1.52996i q^{65} +1.61932i q^{67} +(0.0125106 - 0.242872i) q^{68} +(-5.73081 - 2.48514i) q^{70} +10.7356 q^{71} +(-1.05389 - 1.82540i) q^{73} +(0.300539 - 11.6767i) q^{74} +(-13.5677 + 6.92836i) q^{76} +(-13.6079 - 5.48949i) q^{77} +10.9432i q^{79} +(-5.40941 - 3.91540i) q^{80} +(-2.79750 - 0.0720033i) q^{82} +(-0.658615 - 1.14075i) q^{83} +(0.101499 - 0.175801i) q^{85} +(-9.03500 + 14.7586i) q^{86} +(-12.9396 - 8.86761i) q^{88} +(8.14004 + 4.69966i) q^{89} +(-2.24863 - 0.907109i) q^{91} +(8.60163 + 0.443079i) q^{92} +(5.45659 - 2.96585i) q^{94} -12.7163 q^{95} +(3.33897 + 5.78326i) q^{97} +(7.05029 - 6.94935i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q - 2 q^{4} + 6 q^{5}+O(q^{10}) $ 88 * q - 2 * q^4 + 6 * q^5	$ 88 q - 2 q^{4} + 6 q^{5} + 2 q^{10} - 4 q^{13} + 18 q^{14} - 2 q^{16} + 6 q^{20} - 6 q^{22} + 30 q^{25} - 6 q^{26} + 24 q^{29} - 4 q^{34} - 4 q^{37} + 45 q^{38} - 4 q^{40} + 12 q^{41} - 57 q^{44} - 6 q^{46} - 2 q^{49} - 9 q^{50} - 7 q^{52} + 24 q^{56} + 5 q^{58} - 4 q^{61} - 8 q^{64} + 12 q^{68} - 27 q^{70} - 4 q^{73} - 51 q^{74} - 6 q^{76} + 30 q^{77} + 87 q^{80} - 4 q^{82} - 14 q^{85} - 81 q^{86} + 9 q^{88} + 60 q^{89} - 24 q^{92} - 18 q^{94} - 4 q^{97} - 57 q^{98}+O(q^{100}) $ 88 * q - 2 * q^4 + 6 * q^5 + 2 * q^10 - 4 * q^13 + 18 * q^14 - 2 * q^16 + 6 * q^20 - 6 * q^22 + 30 * q^25 - 6 * q^26 + 24 * q^29 - 4 * q^34 - 4 * q^37 + 45 * q^38 - 4 * q^40 + 12 * q^41 - 57 * q^44 - 6 * q^46 - 2 * q^49 - 9 * q^50 - 7 * q^52 + 24 * q^56 + 5 * q^58 - 4 * q^61 - 8 * q^64 + 12 * q^68 - 27 * q^70 - 4 * q^73 - 51 * q^74 - 6 * q^76 + 30 * q^77 + 87 * q^80 - 4 * q^82 - 14 * q^85 - 81 * q^86 + 9 * q^88 + 60 * q^89 - 24 * q^92 - 18 * q^94 - 4 * q^97 - 57 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−1.24253	+	0.675360i	−0.878604	+	0.477552i
$2$	−1.24253	+	0.675360i	−0.878604	+	0.477552i
$3$		0			0
$3$		0			0
$4$	1.08778	−	1.67831i	0.543889	−	0.839157i
$5$	1.44577	−	0.834716i	0.646569	−	0.373297i	−0.140572	−	0.990070i	$-0.544894\pi$
$5$	1.44577	−	0.834716i	0.646569	−	0.373297i	0.787140	+	0.616774i	$0.211561\pi$
$6$		0			0
$7$	0.369619	+	2.61981i	0.139703	+	0.990193i
$7$	0.369619	+	2.61981i	0.139703	+	0.990193i
$8$	−0.218133	+	2.82000i	−0.0771217	+	0.997022i
$9$		0			0
$10$	−1.23268	+	2.01358i	−0.389809	+	0.636750i
$11$	−2.77302	+	4.80301i	−0.836096	+	1.44816i	0.0570382	+	0.998372i	$0.481834\pi$
$11$	−2.77302	+	4.80301i	−0.836096	+	1.44816i	−0.893135	+	0.449789i	$0.851499\pi$
$12$		0			0
$13$	−0.458226	+	0.793672i	−0.127089	+	0.220125i	−0.922548	−	0.385883i	$-0.873897\pi$
$13$	−0.458226	+	0.793672i	−0.127089	+	0.220125i	0.795458	+	0.606008i	$0.207230\pi$
$14$	−2.22858	−	3.00557i	−0.595612	−	0.803272i
$15$		0			0
$16$	−1.63348	−	3.65127i	−0.408370	−	0.912816i
$17$	0.105306	−	0.0607985i	0.0255405	−	0.0147458i	−0.487175	−	0.873304i	$-0.661973\pi$
$17$	0.105306	−	0.0607985i	0.0255405	−	0.0147458i	0.512716	+	0.858558i	$0.328639\pi$
$18$		0			0
$19$	−6.59665	−	3.80857i	−1.51337	−	0.873747i	−0.999877	−	0.0156555i	$-0.995016\pi$
$19$	−6.59665	−	3.80857i	−1.51337	−	0.873747i	−0.513497	−	0.858092i	$-0.671650\pi$
$20$	0.171761	−	3.33445i	0.0384069	−	0.745605i
$21$		0			0
$22$	0.201807	−	7.84068i	0.0430254	−	1.67164i
$23$	2.15326	+	3.72955i	0.448985	+	0.777666i	0.998320	−	0.0579367i	$-0.0184522\pi$
$23$	2.15326	+	3.72955i	0.448985	+	0.777666i	−0.549335	+	0.835602i	$0.685119\pi$
$24$		0			0
$25$	−1.10650	+	1.91651i	−0.221299	+	0.383302i
$26$	0.0333475	−	1.29563i	0.00653999	−	0.254094i
$27$		0			0
$28$	4.79892	+	2.22943i	0.906911	+	0.421323i
$29$	0.684776	−	0.395356i	0.127160	−	0.0734157i	−0.435071	−	0.900396i	$-0.643277\pi$
$29$	0.684776	−	0.395356i	0.127160	−	0.0734157i	0.562231	+	0.826980i	$0.309943\pi$
$30$		0			0
$31$			2.70618i			0.486044i	0.970021	+	0.243022i	$0.0781387\pi$
$31$			2.70618i			0.486044i	−0.970021	+	0.243022i	$0.921861\pi$
$32$	4.49557	+	3.43363i	0.794712	+	0.606986i
$33$		0			0
$34$	−0.0897854	+	0.146664i	−0.0153981	+	0.0251526i
$35$	2.72118	+	3.47911i	0.459963	+	0.588077i
$36$		0			0
$37$	−4.12969	+	7.15284i	−0.678917	+	1.17592i	0.296390	+	0.955067i	$0.404217\pi$
$37$	−4.12969	+	7.15284i	−0.678917	+	1.17592i	−0.975307	+	0.220852i	$0.929116\pi$
$38$	10.7687	+	0.277170i	1.74692	+	0.0449629i
$39$		0			0
$40$	2.03853	+	4.25916i	0.322320	+	0.673432i
$41$	1.71368	+	0.989393i	0.267632	+	0.154517i	0.627811	−	0.778366i	$-0.283951\pi$
$41$	1.71368	+	0.989393i	0.267632	+	0.154517i	−0.360179	+	0.932883i	$0.617284\pi$
$42$		0			0
$43$	10.5968	−	6.11808i	1.61600	−	0.932998i	0.628060	−	0.778165i	$-0.283849\pi$
$43$	10.5968	−	6.11808i	1.61600	−	0.932998i	0.987941	−	0.154834i	$-0.0494842\pi$
$44$	5.04453	+	9.87860i	0.760492	+	1.48926i
$45$		0			0
$46$	−5.19429	−	3.17987i	−0.765856	−	0.468846i
$47$	−4.39151			−0.640567			−0.320284	−	0.947322i	$-0.603778\pi$
$47$	−4.39151			−0.640567			−0.320284	+	0.947322i	$0.603778\pi$
$48$		0			0
$49$	−6.72676	+	1.93666i	−0.960966	+	0.276665i
$50$	0.0805256	−	3.12861i	0.0113880	−	0.442452i
$51$		0			0
$52$	0.833582	+	1.63239i	0.115597	+	0.226371i
$53$	−2.75730	+	1.59193i	−0.378744	+	0.218668i	−0.677272	−	0.735733i	$-0.736838\pi$
$53$	−2.75730	+	1.59193i	−0.378744	+	0.218668i	0.298528	+	0.954401i	$0.403505\pi$
$54$		0			0
$55$			9.25874i			1.24845i
$56$	−7.46849	+	0.470860i	−0.998018	+	0.0629213i
$57$		0			0
$58$	−0.583850	+	0.953714i	−0.0766633	+	0.125229i
$59$	−8.64223			−1.12512			−0.562561	−	0.826756i	$-0.690184\pi$
$59$	−8.64223			−1.12512			−0.562561	+	0.826756i	$0.690184\pi$
$60$		0			0
$61$	3.83447			0.490953			0.245477	−	0.969403i	$-0.421056\pi$
$61$	3.83447			0.490953			0.245477	+	0.969403i	$0.421056\pi$
$62$	−1.82764	−	3.36252i	−0.232111	−	0.427040i
$63$		0			0
$64$	−7.90484	−	1.23027i	−0.988104	−	0.153784i
$65$			1.52996i			0.189768i
$66$		0			0
$67$			1.61932i			0.197831i	0.995096	+	0.0989155i	$0.0315374\pi$
$67$			1.61932i			0.197831i	−0.995096	+	0.0989155i	$0.968463\pi$
$68$	0.0125106	−	0.242872i	0.00151713	−	0.0294526i
$69$		0			0
$70$	−5.73081	−	2.48514i	−0.684963	−	0.297031i
$71$	10.7356			1.27408			0.637041	−	0.770830i	$-0.280158\pi$
$71$	10.7356			1.27408			0.637041	+	0.770830i	$0.280158\pi$
$72$		0			0
$73$	−1.05389	−	1.82540i	−0.123349	−	0.213647i	0.797737	−	0.603005i	$-0.206030\pi$
$73$	−1.05389	−	1.82540i	−0.123349	−	0.213647i	−0.921086	+	0.389358i	$0.872697\pi$
$74$	0.300539	−	11.6767i	0.0349370	−	1.35738i
$75$		0			0
$76$	−13.5677	+	6.92836i	−1.55632	+	0.794738i
$77$	−13.6079	−	5.48949i	−1.55077	−	0.625585i
$78$		0			0
$79$			10.9432i			1.23121i	0.788055	+	0.615604i	$0.211088\pi$
$79$			10.9432i			1.23121i	−0.788055	+	0.615604i	$0.788912\pi$
$80$	−5.40941	−	3.91540i	−0.604790	−	0.437755i
$81$		0			0
$82$	−2.79750	−	0.0720033i	−0.308932	−	0.00795143i
$83$	−0.658615	−	1.14075i	−0.0722924	−	0.125214i	0.827613	−	0.561299i	$-0.189698\pi$
$83$	−0.658615	−	1.14075i	−0.0722924	−	0.125214i	−0.899906	+	0.436085i	$0.856365\pi$
$84$		0			0
$85$	0.101499	−	0.175801i	0.0110091	−	0.0190683i
$86$	−9.03500	+	14.7586i	−0.974269	+	1.59146i
$87$		0			0
$88$	−12.9396	−	8.86761i	−1.37937	−	0.945291i
$89$	8.14004	+	4.69966i	0.862843	+	0.498163i	0.864963	−	0.501835i	$-0.167342\pi$
$89$	8.14004	+	4.69966i	0.862843	+	0.498163i	−0.00212043	+	0.999998i	$0.500675\pi$
$90$		0			0
$91$	−2.24863	−	0.907109i	−0.235721	−	0.0950908i
$92$	8.60163	+	0.443079i	0.896782	+	0.0461942i
$93$		0			0
$94$	5.45659	−	2.96585i	0.562805	−	0.305904i
$95$	−12.7163			−1.30467
$96$		0			0
$97$	3.33897	+	5.78326i	0.339021	+	0.587201i	0.984249	−	0.176789i	$-0.0565710\pi$
$97$	3.33897	+	5.78326i	0.339021	+	0.587201i	−0.645228	+	0.763990i	$0.723238\pi$
$98$	7.05029	−	6.94935i	0.712186	−	0.701990i
$99$		0			0
$100$	2.01288	+	3.94178i	0.201288	+	0.394178i
$101$	−8.90218	−	5.13967i	−0.885800	−	0.511417i	−0.0132334	−	0.999912i	$-0.504212\pi$
$101$	−8.90218	−	5.13967i	−0.885800	−	0.511417i	−0.872566	+	0.488496i	$0.837546\pi$
$102$		0			0
$103$	9.12176	−	5.26645i	0.898793	−	0.518919i	0.0219848	−	0.999758i	$-0.493001\pi$
$103$	9.12176	−	5.26645i	0.898793	−	0.518919i	0.876808	+	0.480840i	$0.159668\pi$
$104$	−2.13820	−	1.46533i	−0.209668	−	0.143687i
$105$		0			0
$106$	2.35091	−	3.84019i	0.228341	−	0.372993i
$107$	−2.93403	+	5.08188i	−0.283643	+	0.491284i	−0.972279	−	0.233823i	$-0.924876\pi$
$107$	−2.93403	+	5.08188i	−0.283643	+	0.491284i	0.688636	+	0.725107i	$0.258210\pi$
$108$		0			0
$109$	4.50624	+	7.80503i	0.431619	+	0.747586i	0.997013	−	0.0772348i	$-0.0246091\pi$
$109$	4.50624	+	7.80503i	0.431619	+	0.747586i	−0.565394	+	0.824821i	$0.691276\pi$
$110$	−6.25298	−	11.5043i	−0.596198	−	1.09689i
$111$		0			0
$112$	8.96184	−	5.62898i	0.846815	−	0.531888i
$113$	−6.14559	−	3.54816i	−0.578129	−	0.333783i	0.182261	−	0.983250i	$-0.441659\pi$
$113$	−6.14559	−	3.54816i	−0.578129	−	0.333783i	−0.760389	+	0.649468i	$0.774992\pi$
$114$		0			0
$115$	6.22624	+	3.59472i	0.580600	+	0.335209i
$116$	0.0813529	−	1.57933i	0.00755343	−	0.146637i
$117$		0			0
$118$	10.7383	−	5.83661i	0.988536	−	0.537304i
$119$	0.198203	+	0.253409i	0.0181693	+	0.0232300i
$120$		0			0
$121$	−9.87926	−	17.1114i	−0.898114	−	1.55558i
$122$	−4.76445	+	2.58965i	−0.431353	+	0.234455i
$123$		0			0
$124$	4.54182	+	2.94372i	0.407867	+	0.264354i
$125$			12.0416i			1.07703i
$126$		0			0
$127$		−	6.84278i		−	0.607198i	−0.952800	−	0.303599i	$-0.901812\pi$
$127$		−	6.84278i		−	0.607198i	0.952800	−	0.303599i	$-0.0981884\pi$
$128$	10.6529	−	3.80996i	0.941592	−	0.336756i
$129$		0			0
$130$	−1.03327	−	1.90102i	−0.0906239	−	0.166731i
$131$	9.98967	+	17.3026i	0.872801	+	1.51174i	0.859087	+	0.511830i	$0.171032\pi$
$131$	9.98967	+	17.3026i	0.872801	+	1.51174i	0.0137143	+	0.999906i	$0.495634\pi$
$132$		0			0
$133$	7.53948	−	18.6896i	0.653756	−	1.62060i
$134$	−1.09362	−	2.01205i	−0.0944745	−	0.173815i
$135$		0			0
$136$	0.148481	+	0.310226i	0.0127322	+	0.0266016i
$137$	−1.38190	−	0.797841i	−0.118064	−	0.0681642i	0.439805	−	0.898093i	$-0.355047\pi$
$137$	−1.38190	−	0.797841i	−0.118064	−	0.0681642i	−0.557869	+	0.829929i	$0.688381\pi$
$138$		0			0
$139$	7.13703	+	4.12056i	0.605355	+	0.349502i	0.771145	−	0.636659i	$-0.219684\pi$
$139$	7.13703	+	4.12056i	0.605355	+	0.349502i	−0.165791	+	0.986161i	$0.553018\pi$
$140$	8.79908	−	0.782494i	0.743658	−	0.0661328i
$141$		0			0
$142$	−13.3394	+	7.25040i	−1.11941	+	0.608440i
$143$	−2.54134	−	4.40173i	−0.212518	−	0.368091i
$144$		0			0
$145$	0.660020	−	1.14319i	0.0548117	−	0.0949366i
$146$	2.54230	+	1.55636i	0.210402	+	0.128805i
$147$		0			0
$148$	7.51252	+	14.7116i	0.617526	+	1.20929i
$149$	0.780447	−	0.450591i	0.0639367	−	0.0369139i	−0.467691	−	0.883892i	$-0.654914\pi$
$149$	0.780447	−	0.450591i	0.0639367	−	0.0369139i	0.531628	+	0.846978i	$0.321581\pi$
$150$		0			0
$151$	0.786634	+	0.454163i	0.0640154	+	0.0369593i	0.531666	−	0.846954i	$-0.321566\pi$
$151$	0.786634	+	0.454163i	0.0640154	+	0.0369593i	−0.467651	+	0.883913i	$0.654899\pi$
$152$	12.1791	−	17.7718i	0.987859	−	1.44148i
$153$		0			0
$154$	20.6157	−	2.36937i	1.66126	−	0.190929i
$155$	2.25889	+	3.91252i	0.181439	+	0.314261i
$156$		0			0
$157$	−8.28886			−0.661523			−0.330762	−	0.943714i	$-0.607306\pi$
$157$	−8.28886			−0.661523			−0.330762	+	0.943714i	$0.607306\pi$
$158$	−7.39061	−	13.5973i	−0.587966	−	1.08174i
$159$		0			0
$160$	9.36568	+	1.21172i	0.740422	+	0.0957947i
$161$	−8.97482	+	7.01963i	−0.707315	+	0.553225i
$162$		0			0
$163$	10.3387	+	5.96905i	0.809789	+	0.467532i	0.846883	−	0.531780i	$-0.178477\pi$
$163$	10.3387	+	5.96905i	0.809789	+	0.467532i	−0.0370935	+	0.999312i	$0.511810\pi$
$164$	3.52461	−	1.79985i	0.275226	−	0.140545i
$165$		0			0
$166$	1.58877	+	0.972624i	0.123313	+	0.0754902i
$167$	12.2867	−	21.2811i	0.950771	−	1.64678i	0.207010	−	0.978339i	$-0.433627\pi$
$167$	12.2867	−	21.2811i	0.950771	−	1.64678i	0.743761	−	0.668445i	$-0.233040\pi$
$168$		0			0
$169$	6.08006	+	10.5310i	0.467697	+	0.810074i
$170$	−0.00738662	+	0.286988i	−0.000566528	+	0.0220109i
$171$		0			0
$172$	1.25893	−	24.4399i	0.0959922	−	1.86353i
$173$		−	9.08081i		−	0.690401i	−0.938529	−	0.345201i	$-0.887811\pi$
$173$		−	9.08081i		−	0.690401i	0.938529	−	0.345201i	$-0.112189\pi$
$174$		0			0
$175$	−5.42986	−	2.19043i	−0.410459	−	0.165581i
$176$	22.0667	+	2.27941i	1.66334	+	0.171817i
$177$		0			0
$178$	−13.2882	−	0.342019i	−0.995995	−	0.0256354i
$179$	−3.23833	−	5.60895i	−0.242044	−	0.419233i	0.719252	−	0.694749i	$-0.244485\pi$
$179$	−3.23833	−	5.60895i	−0.242044	−	0.419233i	−0.961296	+	0.275516i	$0.911151\pi$
$180$		0			0
$181$	10.1548			0.754801			0.377400	−	0.926050i	$-0.376818\pi$
$181$	10.1548			0.754801			0.377400	+	0.926050i	$0.376818\pi$
$182$	3.40663	−	0.391525i	0.252516	−	0.0290218i
$183$		0			0
$184$	−10.9870	+	5.25866i	−0.809976	+	0.387673i
$185$			13.7885i			1.01375i
$186$		0			0
$187$			0.674381i			0.0493156i
$188$	−4.77698	+	7.37033i	−0.348397	+	0.537537i
$189$		0			0
$190$	15.8005	−	8.58810i	1.14629	−	0.623046i
$191$	6.01862			0.435492			0.217746	−	0.976005i	$-0.430130\pi$
$191$	6.01862			0.435492			0.217746	+	0.976005i	$0.430130\pi$
$192$		0			0
$193$	15.1995			1.09408			0.547040	−	0.837106i	$-0.315754\pi$
$193$	15.1995			1.09408			0.547040	+	0.837106i	$0.315754\pi$
$194$	−8.05456	−	4.93089i	−0.578283	−	0.354017i
$195$		0			0
$196$	−4.06690	+	13.3963i	−0.290493	+	0.956877i
$197$		−	12.5929i		−	0.897208i	−0.893731	−	0.448604i	$-0.851921\pi$
$197$		−	12.5929i		−	0.897208i	0.893731	−	0.448604i	$-0.148079\pi$
$198$		0			0
$199$	4.98014	−	2.87528i	0.353033	−	0.203824i	−0.312987	−	0.949757i	$-0.601330\pi$
$199$	4.98014	−	2.87528i	0.353033	−	0.203824i	0.666020	+	0.745934i	$0.267996\pi$
$200$	−5.16320	−	3.53838i	−0.365093	−	0.250201i
$201$		0			0
$202$	14.5324	+	0.374041i	1.02249	+	0.0263174i
$203$	1.28886	+	1.64785i	0.0904604	+	0.115656i
$204$		0			0
$205$	3.30345			0.230723
$206$	−7.77734	+	12.7042i	−0.541873	+	0.885144i
$207$		0			0
$208$	3.64641	+	0.376660i	0.252833	+	0.0261167i
$209$	36.5852	−	21.1225i	2.53065	−	1.46107i
$210$		0			0
$211$	−10.7631	−	6.21407i	−0.740961	−	0.427794i	0.0814576	−	0.996677i	$-0.474042\pi$
$211$	−10.7631	−	6.21407i	−0.740961	−	0.427794i	−0.822419	+	0.568883i	$0.807376\pi$
$212$	−0.327573	+	6.35928i	−0.0224978	+	0.436757i
$213$		0			0
$214$	0.213525	−	8.29593i	0.0145962	−	0.567098i
$215$	10.2137	−	17.6907i	0.696570	−	1.20650i
$216$		0			0
$217$	−7.08966	+	1.00025i	−0.481278	+	0.0679017i
$218$	−10.8704	−	6.65468i	−0.736233	−	0.450712i
$219$		0			0
$220$	15.5391	+	10.0714i	1.04764	+	0.679017i
$221$			0.111438i			0.00749613i
$222$		0			0
$223$	−6.62650	+	3.82581i	−0.443743	+	0.256195i	−0.705184	−	0.709024i	$-0.749136\pi$
$223$	−6.62650	+	3.82581i	−0.443743	+	0.256195i	0.261441	+	0.965219i	$0.415802\pi$
$224$	−7.33380	+	13.0467i	−0.490010	+	0.871717i
$225$		0			0
$226$	10.0324	+	0.258218i	0.667344	+	0.0171764i
$227$	10.8950	−	18.8708i	0.723130	−	1.25250i	−0.236609	−	0.971605i	$-0.576036\pi$
$227$	10.8950	−	18.8708i	0.723130	−	1.25250i	0.959739	−	0.280893i	$-0.0906305\pi$
$228$		0			0
$229$	−12.8433	−	22.2453i	−0.848711	−	1.47001i	−0.882359	−	0.470577i	$-0.844046\pi$
$229$	−12.8433	−	22.2453i	−0.848711	−	1.47001i	0.0336474	−	0.999434i	$-0.489288\pi$
$230$	−10.1640	−	0.261607i	−0.670197	−	0.0172498i
$231$		0			0
$232$	0.965533	+	2.01731i	0.0633903	+	0.132443i
$233$	−1.90679	−	1.10089i	−0.124918	−	0.0721214i	0.436239	−	0.899831i	$-0.356310\pi$
$233$	−1.90679	−	1.10089i	−0.124918	−	0.0721214i	−0.561157	+	0.827709i	$0.689644\pi$
$234$		0			0
$235$	−6.34911	+	3.66566i	−0.414171	+	0.239121i
$236$	−9.40082	+	14.5044i	−0.611941	+	0.944154i
$237$		0			0
$238$	−0.417417	−	0.181011i	−0.0270571	−	0.0117332i
$239$	−2.99588	+	5.18902i	−0.193787	+	0.335650i	−0.946502	−	0.322697i	$-0.895411\pi$
$239$	−2.99588	+	5.18902i	−0.193787	+	0.335650i	0.752715	+	0.658347i	$0.228744\pi$
$240$		0			0
$241$	−5.52182	+	9.56407i	−0.355692	+	0.616076i	−0.987236	−	0.159264i	$-0.949088\pi$
$241$	−5.52182	+	9.56407i	−0.355692	+	0.616076i	0.631544	+	0.775340i	$0.282421\pi$
$242$	23.8316	+	14.5894i	1.53196	+	0.937842i
$243$		0			0
$244$	4.17105	−	6.43544i	0.267024	−	0.411987i
$245$	−8.10880	+	8.41491i	−0.518052	+	0.537609i
$246$		0			0
$247$	6.04552	−	3.49038i	0.384667	−	0.222088i
$248$	−7.63143	−	0.590307i	−0.484596	−	0.0374845i
$249$		0			0
$250$	−8.13242	−	14.9621i	−0.514340	−	0.946286i
$251$	−17.4191			−1.09948			−0.549742	−	0.835335i	$-0.685274\pi$
$251$	−17.4191			−1.09948			−0.549742	+	0.835335i	$0.685274\pi$
$252$		0			0
$253$	−23.8841			−1.50158
$254$	4.62134	+	8.50238i	0.289969	+	0.533487i
$255$		0			0
$256$	−10.6635	+	11.9285i	−0.666468	+	0.745534i
$257$	9.53973	−	5.50777i	0.595072	−	0.343565i	−0.172028	−	0.985092i	$-0.555032\pi$
$257$	9.53973	−	5.50777i	0.595072	−	0.343565i	0.767100	+	0.641527i	$0.221699\pi$
$258$		0			0
$259$	−20.2655	−	8.17517i	−1.25923	−	0.507980i
$260$	2.56775	+	1.66425i	0.159245	+	0.103213i
$261$		0			0
$262$	−24.0980	−	14.7524i	−1.48878	−	0.911409i
$263$	−2.71131	+	4.69613i	−0.167187	+	0.289576i	−0.937430	−	0.348175i	$-0.886802\pi$
$263$	−2.71131	+	4.69613i	−0.167187	+	0.289576i	0.770243	+	0.637751i	$0.220135\pi$
$264$		0			0
$265$	−2.65762	+	4.60313i	−0.163256	+	0.282768i
$266$	3.25419	+	28.3144i	0.199527	+	1.73607i
$267$		0			0
$268$	2.71772	+	1.76146i	0.166011	+	0.107598i
$269$	13.3178	−	7.68901i	0.811998	−	0.468807i	−0.0356515	−	0.999364i	$-0.511351\pi$
$269$	13.3178	−	7.68901i	0.811998	−	0.468807i	0.847649	+	0.530557i	$0.178017\pi$
$270$		0			0
$271$	−9.75508	−	5.63210i	−0.592579	−	0.342126i	0.173538	−	0.984827i	$-0.444480\pi$
$271$	−9.75508	−	5.63210i	−0.592579	−	0.342126i	−0.766117	+	0.642702i	$0.777814\pi$
$272$	−0.394007	−	0.285187i	−0.0238902	−	0.0172920i
$273$		0			0
$274$	2.25589	+	0.0580631i	0.136283	+	0.00350772i
$275$	−6.13667	−	10.6290i	−0.370055	−	0.640954i
$276$		0			0
$277$	14.7410	−	25.5322i	0.885701	−	1.53408i	0.0407927	−	0.999168i	$-0.487012\pi$
$277$	14.7410	−	25.5322i	0.885701	−	1.53408i	0.844908	−	0.534911i	$-0.179655\pi$
$278$	−11.6509	−	0.299875i	−0.698772	−	0.0179853i
$279$		0			0
$280$	−10.4047	+	6.91482i	−0.621799	+	0.413240i
$281$	−9.71995	+	5.61182i	−0.579844	+	0.334773i	−0.761071	−	0.648668i	$-0.775326\pi$
$281$	−9.71995	+	5.61182i	−0.579844	+	0.334773i	0.181228	+	0.983441i	$0.441993\pi$
$282$		0			0
$283$		−	14.8448i		−	0.882429i	−0.897402	−	0.441215i	$-0.854548\pi$
$283$		−	14.8448i		−	0.882429i	0.897402	−	0.441215i	$-0.145452\pi$
$284$	11.6780	−	18.0177i	0.692959	−	1.06916i
$285$		0			0
$286$	6.13045	+	3.75298i	0.362501	+	0.221918i
$287$	−1.95861	+	4.85520i	−0.115613	+	0.286594i
$288$		0			0
$289$	−8.49261	+	14.7096i	−0.499565	+	0.865272i
$290$	−0.0480331	+	1.86620i	−0.00282060	+	0.109587i
$291$		0			0
$292$	−4.21000	−	0.216861i	−0.246371	−	0.0126908i
$293$	15.3131	+	8.84101i	0.894600	+	0.516497i	0.875444	−	0.483319i	$-0.160569\pi$
$293$	15.3131	+	8.84101i	0.894600	+	0.516497i	0.0191554	+	0.999817i	$0.493902\pi$
$294$		0			0
$295$	−12.4947	+	7.21381i	−0.727469	+	0.420004i
$296$	−19.2702	−	13.2060i	−1.12006	−	0.767584i
$297$		0			0
$298$	−0.665420	+	1.08696i	−0.0385467	+	0.0629658i
$299$	−3.94672			−0.228245
$300$		0			0
$301$	19.9450	+	25.5003i	1.14961	+	1.46981i
$302$	−1.28414	−	0.0330518i	−0.0738941	−	0.00190192i
$303$		0			0
$304$	−3.13063	+	30.3073i	−0.179554	+	1.73825i
$305$	5.54376	−	3.20069i	0.317435	−	0.183271i
$306$		0			0
$307$		−	11.5845i		−	0.661160i	−0.943778	−	0.330580i	$-0.892756\pi$
$307$		−	11.5845i		−	0.661160i	0.943778	−	0.330580i	$-0.107244\pi$
$308$	−24.0155	+	16.8670i	−1.36841	+	0.961087i
$309$		0			0
$310$	−5.44910	−	3.33586i	−0.309488	−	0.189464i
$311$	28.8259			1.63457			0.817283	−	0.576237i	$-0.195479\pi$
$311$	28.8259			1.63457			0.817283	+	0.576237i	$0.195479\pi$
$312$		0			0
$313$	20.5997			1.16436			0.582182	−	0.813058i	$-0.302199\pi$
$313$	20.5997			1.16436			0.582182	+	0.813058i	$0.302199\pi$
$314$	10.2992	−	5.59797i	0.581217	−	0.315912i
$315$		0			0
$316$	18.3662	+	11.9038i	1.03318	+	0.669640i
$317$			26.5881i			1.49334i	0.665196	+	0.746669i	$0.268348\pi$
$317$			26.5881i			1.49334i	−0.665196	+	0.746669i	$0.731652\pi$
$318$		0			0
$319$			4.38532i			0.245531i
$320$	−12.4555	+	4.81961i	−0.696284	+	0.269424i
$321$		0			0
$322$	6.41073	−	14.7834i	0.357256	−	0.823845i
$323$	−0.926223			−0.0515364
$324$		0			0
$325$	−1.01405	−	1.75639i	−0.0562495	−	0.0974270i
$326$	−16.8774	−	0.434399i	−0.934754	−	0.0240591i
$327$		0			0
$328$	−3.16390	+	4.61676i	−0.174697	+	0.254918i
$329$	−1.62318	−	11.5049i	−0.0894890	−	0.634285i
$330$		0			0
$331$			4.00276i			0.220012i	0.993931	+	0.110006i	$0.0350870\pi$
$331$			4.00276i			0.220012i	−0.993931	+	0.110006i	$0.964913\pi$
$332$	−2.63097	−	0.135524i	−0.144393	−	0.00743785i
$333$		0			0
$334$	−0.894166	+	34.7405i	−0.0489266	+	1.90091i
$335$	1.35167	+	2.34116i	0.0738496	+	0.127911i
$336$		0			0
$337$	−5.34969	+	9.26594i	−0.291416	+	0.504748i	−0.974145	−	0.225924i	$-0.927460\pi$
$337$	−5.34969	+	9.26594i	−0.291416	+	0.504748i	0.682729	+	0.730672i	$0.260793\pi$
$338$	−14.6669	−	8.97885i	−0.797772	−	0.488385i
$339$		0			0
$340$	−0.184642	−	0.361580i	−0.0100136	−	0.0196094i
$341$	−12.9978	−	7.50428i	−0.703870	−	0.406380i
$342$		0			0
$343$	−7.56001	−	16.9070i	−0.408202	−	0.912892i
$344$	14.9415	+	31.2176i	0.805591	+	1.68314i
$345$		0			0
$346$	6.13282	+	11.2832i	0.329702	+	0.606589i
$347$	−21.8111			−1.17088			−0.585442	−	0.810715i	$-0.699079\pi$
$347$	−21.8111			−1.17088			−0.585442	+	0.810715i	$0.699079\pi$
$348$		0			0
$349$	−8.16332	−	14.1393i	−0.436972	−	0.756859i	0.560482	−	0.828167i	$-0.310616\pi$
$349$	−8.16332	−	14.1393i	−0.436972	−	0.756859i	−0.997454	+	0.0713082i	$0.977283\pi$
$350$	8.22611	−	0.945431i	0.439704	−	0.0505354i
$351$		0			0
$352$	−28.9581	+	12.0707i	−1.54347	+	0.643373i
$353$	22.2690	+	12.8570i	1.18526	+	0.684309i	0.957225	−	0.289344i	$-0.0934372\pi$
$353$	22.2690	+	12.8570i	1.18526	+	0.684309i	0.228033	+	0.973653i	$0.426771\pi$
$354$		0			0
$355$	15.5212	−	8.96119i	0.823782	−	0.475611i
$356$	16.7421	−	8.54937i	0.887327	−	0.453116i
$357$		0			0
$358$	7.81179	+	4.78227i	0.412866	+	0.252751i
$359$	−4.17336	+	7.22847i	−0.220261	+	0.381504i	−0.954887	−	0.296969i	$-0.904024\pi$
$359$	−4.17336	+	7.22847i	−0.220261	+	0.381504i	0.734626	+	0.678472i	$0.237358\pi$
$360$		0			0
$361$	19.5105	+	33.7932i	1.02687	+	1.77859i
$362$	−12.6177	+	6.85815i	−0.663171	+	0.360456i
$363$		0			0
$364$	−3.96843	+	2.78718i	−0.208002	+	0.146088i
$365$	−3.04738	−	1.75941i	−0.159507	−	0.0920915i
$366$		0			0
$367$	−19.3372	−	11.1643i	−1.00939	−	0.582773i	−0.0983793	−	0.995149i	$-0.531366\pi$
$367$	−19.3372	−	11.1643i	−1.00939	−	0.582773i	−0.911014	+	0.412375i	$0.864699\pi$
$368$	10.1003	−	13.9543i	0.526514	−	0.727417i
$369$		0			0
$370$	−9.31219	−	17.1327i	−0.484118	−	0.890684i
$371$	−5.18969	−	6.63518i	−0.269435	−	0.344482i
$372$		0			0
$373$	−8.08131	−	13.9972i	−0.418434	−	0.724749i	0.577348	−	0.816498i	$-0.304088\pi$
$373$	−8.08131	−	13.9972i	−0.418434	−	0.724749i	−0.995782	+	0.0917488i	$0.970754\pi$
$374$	−0.455450	−	0.837941i	−0.0235508	−	0.0433289i
$375$		0			0
$376$	0.957933	−	12.3841i	0.0494016	−	0.638659i
$377$			0.724650i			0.0373214i
$378$		0			0
$379$		−	0.319037i		−	0.0163878i	−0.999966	−	0.00819391i	$-0.997392\pi$
$379$		−	0.319037i		−	0.0163878i	0.999966	−	0.00819391i	$-0.00260823\pi$
$380$	−13.8325	+	21.3420i	−0.709594	+	1.09482i
$381$		0			0
$382$	−7.47834	+	4.06474i	−0.382625	+	0.207970i
$383$	5.49219	+	9.51276i	0.280638	+	0.486079i	0.971542	−	0.236867i	$-0.0761207\pi$
$383$	5.49219	+	9.51276i	0.280638	+	0.486079i	−0.690904	+	0.722946i	$0.742787\pi$
$384$		0			0
$385$	−24.2561	+	3.42220i	−1.23620	+	0.174412i
$386$	−18.8858	+	10.2651i	−0.961263	+	0.522480i
$387$		0			0
$388$	13.3382	+	0.687063i	0.677143	+	0.0348804i
$389$	−11.2151	−	6.47504i	−0.568628	−	0.328298i	0.187973	−	0.982174i	$-0.439808\pi$
$389$	−11.2151	−	6.47504i	−0.568628	−	0.328298i	−0.756601	+	0.653876i	$0.773142\pi$
$390$		0			0
$391$	0.453502	+	0.261830i	0.0229346	+	0.0132413i
$392$	−3.99405	−	19.3919i	−0.201730	−	0.979441i
$393$		0			0
$394$	8.50475	+	15.6471i	0.428463	+	0.788290i
$395$	9.13449	+	15.8214i	0.459606	+	0.796061i
$396$		0			0
$397$	10.3112	−	17.8595i	0.517504	−	0.896343i	−0.482290	−	0.876012i	$-0.660195\pi$
$397$	10.3112	−	17.8595i	0.517504	−	0.896343i	0.999793	−	0.0203308i	$-0.00647195\pi$
$398$	−4.24614	+	6.93602i	−0.212840	+	0.347671i
$399$		0			0
$400$	8.80512	+	0.909535i	0.440256	+	0.0454768i
$401$	−11.7822	+	6.80244i	−0.588374	+	0.339698i	−0.764454	−	0.644678i	$-0.776991\pi$
$401$	−11.7822	+	6.80244i	−0.588374	+	0.339698i	0.176080	+	0.984376i	$0.443658\pi$
$402$		0			0
$403$	−2.14782	−	1.24004i	−0.106990	−	0.0617709i
$404$	−18.3096	+	9.34983i	−0.910936	+	0.465171i
$405$		0			0
$406$	−2.71435	−	1.17706i	−0.134711	−	0.0584167i
$407$	−22.9034	−	39.6699i	−1.13528	−	1.96636i
$408$		0			0
$409$	−0.261553			−0.0129330			−0.00646648	−	0.999979i	$-0.502058\pi$
$409$	−0.261553			−0.0129330			−0.00646648	+	0.999979i	$0.502058\pi$
$410$	−4.10465	+	2.23102i	−0.202714	+	0.110182i
$411$		0			0
$412$	1.08368	−	21.0379i	0.0533893	−	1.03646i
$413$	−3.19433	−	22.6410i	−0.157183	−	1.11409i
$414$		0			0
$415$	−1.90441	−	1.09951i	−0.0934840	−	0.0539730i
$416$	−4.78517	+	1.99463i	−0.234612	+	0.0977946i
$417$		0			0
$418$	−31.1931	+	50.9536i	−1.52570	+	2.49222i
$419$	−0.252372	+	0.437122i	−0.0123292	+	0.0213548i	−0.872124	−	0.489285i	$-0.837258\pi$
$419$	−0.252372	+	0.437122i	−0.0123292	+	0.0213548i	0.859795	+	0.510639i	$0.170591\pi$
$420$		0			0
$421$	0.908510	+	1.57359i	0.0442781	+	0.0766919i	0.887315	−	0.461164i	$-0.152568\pi$
$421$	0.908510	+	1.57359i	0.0442781	+	0.0766919i	−0.843037	+	0.537856i	$0.819235\pi$
$422$	17.5702	+	0.452230i	0.855305	+	0.0220142i
$423$		0			0
$424$	−3.88778	−	8.12285i	−0.188807	−	0.394480i
$425$			0.269093i			0.0130529i
$426$		0			0
$427$	1.41729	+	10.0456i	0.0685875	+	0.486139i
$428$	5.33743	+	10.4522i	0.257995	+	0.505225i
$429$		0			0
$430$	−0.743306	+	28.8792i	−0.0358454	+	1.39268i
$431$	−1.15815	−	2.00597i	−0.0557860	−	0.0966241i	0.836784	−	0.547533i	$-0.184433\pi$
$431$	−1.15815	−	2.00597i	−0.0557860	−	0.0966241i	−0.892570	+	0.450909i	$0.851100\pi$
$432$		0			0
$433$	15.5029			0.745021			0.372510	−	0.928028i	$-0.378497\pi$
$433$	15.5029			0.745021			0.372510	+	0.928028i	$0.378497\pi$
$434$	8.13361	−	6.03092i	0.390426	−	0.289494i
$435$		0			0
$436$	18.0011	+	0.927254i	0.862095	+	0.0444074i
$437$		−	32.8034i		−	1.56920i
$438$		0			0
$439$			13.3854i			0.638850i	0.947612	+	0.319425i	$0.103490\pi$
$439$			13.3854i			0.638850i	−0.947612	+	0.319425i	$0.896510\pi$
$440$	−26.1097	−	2.01964i	−1.24473	−	0.0962824i
$441$		0			0
$442$	−0.0752607	−	0.138465i	−0.00357979	−	0.00658612i
$443$	29.1467			1.38480			0.692401	−	0.721513i	$-0.256553\pi$
$443$	29.1467			1.38480			0.692401	+	0.721513i	$0.256553\pi$
$444$		0			0
$445$	15.6915			0.743849
$446$	5.64984	−	9.22897i	0.267528	−	0.437004i
$447$		0			0
$448$	0.301297	−	21.1639i	0.0142350	−	0.999899i
$449$			7.62756i			0.359967i	0.983670	+	0.179984i	$0.0576044\pi$
$449$			7.62756i			0.359967i	−0.983670	+	0.179984i	$0.942396\pi$
$450$		0			0
$451$	−9.50412	+	5.48721i	−0.447532	+	0.258383i
$452$	−12.6400	+	6.45463i	−0.594534	+	0.303600i
$453$		0			0
$454$	−0.792890	+	30.8057i	−0.0372122	+	1.44578i
$455$	−4.00819	+	0.565501i	−0.187907	+	0.0265111i
$456$		0			0
$457$	−2.52928			−0.118315			−0.0591574	−	0.998249i	$-0.518841\pi$
$457$	−2.52928			−0.118315			−0.0591574	+	0.998249i	$0.518841\pi$
$458$	30.9819	+	18.9667i	1.44769	+	0.886254i
$459$		0			0
$460$	12.8058	−	6.53933i	0.597075	−	0.304898i
$461$	−28.7899	+	16.6219i	−1.34088	+	0.774158i	−0.986937	−	0.161108i	$-0.948493\pi$
$461$	−28.7899	+	16.6219i	−1.34088	+	0.774158i	−0.353945	+	0.935266i	$0.615160\pi$
$462$		0			0
$463$	−14.0141	−	8.09107i	−0.651292	−	0.376024i	0.137659	−	0.990480i	$-0.456042\pi$
$463$	−14.0141	−	8.09107i	−0.651292	−	0.376024i	−0.788951	+	0.614456i	$0.789376\pi$
$464$	−2.56212	−	1.85450i	−0.118943	−	0.0860928i
$465$		0			0
$466$	3.11274	+	0.0801172i	0.144195	+	0.00371136i
$467$	−14.6712	+	25.4112i	−0.678900	+	1.17589i	0.296412	+	0.955060i	$0.404210\pi$
$467$	−14.6712	+	25.4112i	−0.678900	+	1.17589i	−0.975312	+	0.220830i	$0.929124\pi$
$468$		0			0
$469$	−4.24229	+	0.598530i	−0.195891	+	0.0276375i
$470$	5.41334	−	8.84265i	0.249699	−	0.407881i
$471$		0			0
$472$	1.88515	−	24.3711i	0.0867713	−	1.12177i
$473$			67.8622i			3.12031i
$474$		0			0
$475$	14.5983	−	8.42835i	0.669818	−	0.386719i
$476$	0.640902	−	0.0569947i	0.0293757	−	0.00261235i
$477$		0			0
$478$	0.218026	−	8.47082i	0.00997227	−	0.387446i
$479$	−17.1697	+	29.7387i	−0.784501	+	1.35880i	0.144795	+	0.989462i	$0.453748\pi$
$479$	−17.1697	+	29.7387i	−0.784501	+	1.35880i	−0.929296	+	0.369335i	$0.879586\pi$
$480$		0			0
$481$	−3.78467	−	6.55524i	−0.172566	−	0.298893i
$482$	0.401852	−	15.6129i	0.0183038	−	0.711148i
$483$		0			0
$484$	−39.4647	−	2.03287i	−1.79385	−	0.0924031i
$485$	9.65476	+	5.57418i	0.438400	+	0.253110i
$486$		0			0
$487$	−25.7769	+	14.8823i	−1.16806	+	0.674382i	−0.953223	−	0.302267i	$-0.902257\pi$
$487$	−25.7769	+	14.8823i	−1.16806	+	0.674382i	−0.214841	+	0.976649i	$0.568923\pi$
$488$	−0.836424	+	10.8132i	−0.0378631	+	0.489491i
$489$		0			0
$490$	4.39236	−	15.9322i	0.198427	−	0.719742i
$491$	16.8442	−	29.1751i	0.760170	−	1.31665i	−0.182593	−	0.983189i	$-0.558449\pi$
$491$	16.8442	−	29.1751i	0.760170	−	1.31665i	0.942763	−	0.333464i	$-0.108218\pi$
$492$		0			0
$493$	0.0480741	−	0.0832668i	0.00216515	−	0.00375015i
$494$	−5.15449	+	8.41981i	−0.231911	+	0.378825i
$495$		0			0
$496$	9.88098	−	4.42049i	0.443669	−	0.198486i
$497$	3.96808	+	28.1252i	0.177993	+	1.26159i
$498$		0			0
$499$	−27.4308	+	15.8372i	−1.22797	+	0.708969i	−0.966605	−	0.256271i	$-0.917506\pi$
$499$	−27.4308	+	15.8372i	−1.22797	+	0.708969i	−0.261365	+	0.965240i	$0.584173\pi$
$500$	20.2096	+	13.0986i	0.903801	+	0.585787i
$501$		0			0
$502$	21.6438	−	11.7642i	0.966011	−	0.525060i
$503$	−20.0868			−0.895625			−0.447813	−	0.894127i	$-0.647797\pi$
$503$	−20.0868			−0.895625			−0.447813	+	0.894127i	$0.647797\pi$
$504$		0			0
$505$	−17.1607			−0.763640
$506$	29.6768	−	16.1304i	1.31929	−	0.717082i
$507$		0			0
$508$	−11.4843	−	7.44342i	−0.509535	−	0.330248i
$509$	35.9131	−	20.7344i	1.59182	−	0.919038i	0.598826	−	0.800879i	$-0.295634\pi$
$509$	35.9131	−	20.7344i	1.59182	−	0.919038i	0.992995	−	0.118159i	$-0.0376992\pi$
$510$		0			0
$511$	4.39265	−	3.43570i	0.194319	−	0.151986i
$512$	5.19368	−	22.0233i	0.229530	−	0.973302i
$513$		0			0
$514$	−8.13371	+	13.2863i	−0.358762	+	0.586035i
$515$	8.79198	−	15.2282i	0.387421	−	0.671033i
$516$		0			0
$517$	12.1777	−	21.0924i	0.535576	−	0.927645i
$518$	30.7017	−	3.52856i	1.34895	−	0.155036i
$519$		0			0
$520$	−4.31448	−	0.333734i	−0.189203	−	0.0146352i
$521$	3.10992	−	1.79551i	0.136248	−	0.0786628i	−0.430327	−	0.902673i	$-0.641602\pi$
$521$	3.10992	−	1.79551i	0.136248	−	0.0786628i	0.566575	+	0.824010i	$0.308268\pi$
$522$		0			0
$523$	24.9616	+	14.4116i	1.09149	+	0.630174i	0.933974	−	0.357342i	$-0.116317\pi$
$523$	24.9616	+	14.4116i	1.09149	+	0.630174i	0.157519	+	0.987516i	$0.449650\pi$
$524$	39.9058	+	2.05559i	1.74329	+	0.0897987i
$525$		0			0
$526$	0.197317	−	7.66622i	0.00860341	−	0.334263i
$527$	0.164532	+	0.284977i	0.00716711	+	0.0124138i
$528$		0			0
$529$	2.22695	−	3.85720i	0.0968241	−	0.167704i
$530$	0.193409	−	7.51439i	0.00840114	−	0.326404i
$531$		0			0
$532$	−23.1658	−	32.9838i	−1.00437	−	1.43003i
$533$	−1.57051	+	0.906732i	−0.0680262	+	0.0392749i
$534$		0			0
$535$			9.79632i			0.423532i
$536$	−4.56648	−	0.353226i	−0.197242	−	0.0152571i
$537$		0			0
$538$	−11.3549	+	18.5481i	−0.489544	+	0.799666i
$539$	9.35165	−	37.6791i	0.402804	−	1.62295i
$540$		0			0
$541$	1.44238	−	2.49828i	0.0620128	−	0.107409i	−0.833352	−	0.552742i	$-0.813581\pi$
$541$	1.44238	−	2.49828i	0.0620128	−	0.107409i	0.895365	+	0.445333i	$0.146915\pi$
$542$	15.9247	+	0.409877i	0.684025	+	0.0176057i
$543$		0			0
$544$	0.682171	+	0.0882583i	0.0292478	+	0.00378404i
$545$	13.0300	+	7.52286i	0.558143	+	0.322244i
$546$		0			0
$547$	19.3894	−	11.1945i	0.829030	−	0.478641i	−0.0244906	−	0.999700i	$-0.507796\pi$
$547$	19.3894	−	11.1945i	0.829030	−	0.478641i	0.853520	+	0.521059i	$0.174463\pi$
$548$	−2.84223	+	1.45139i	−0.121414	+	0.0620004i
$549$		0			0
$550$	14.8034	+	9.06246i	0.631221	+	0.386424i
$551$	−6.02297			−0.256587
$552$		0			0
$553$	−28.6691	+	4.04482i	−1.21913	+	0.172003i
$554$	−1.07278	+	41.6800i	−0.0455781	+	1.77082i
$555$		0			0
$556$	14.6791	−	7.49592i	0.622533	−	0.317898i
$557$	−5.45852	+	3.15148i	−0.231285	+	0.133532i	−0.611165	−	0.791503i	$-0.709299\pi$
$557$	−5.45852	+	3.15148i	−0.231285	+	0.133532i	0.379880	+	0.925036i	$0.375965\pi$
$558$		0			0
$559$			11.2139i			0.474296i
$560$	8.25818	−	15.6188i	0.348972	−	0.660015i
$561$		0			0
$562$	8.28737	−	13.5373i	0.349581	−	0.571038i
$563$	−2.66254			−0.112213			−0.0561064	−	0.998425i	$-0.517869\pi$
$563$	−2.66254			−0.112213			−0.0561064	+	0.998425i	$0.517869\pi$
$564$		0			0
$565$	−11.8468			−0.498400
$566$	10.0256	+	18.4451i	0.421405	+	0.775305i
$567$		0			0
$568$	−2.34179	+	30.2745i	−0.0982594	+	1.27029i
$569$		−	28.2525i		−	1.18441i	−0.805788	−	0.592204i	$-0.798258\pi$
$569$		−	28.2525i		−	1.18441i	0.805788	−	0.592204i	$-0.201742\pi$
$570$		0			0
$571$		−	31.6930i		−	1.32631i	−0.748482	−	0.663155i	$-0.769217\pi$
$571$		−	31.6930i		−	1.32631i	0.748482	−	0.663155i	$-0.230783\pi$
$572$	−10.1519	−	0.522935i	−0.424472	−	0.0218650i
$573$		0			0
$574$	−0.845373	−	7.35552i	−0.0352852	−	0.307013i
$575$	−9.53030			−0.397441
$576$		0			0
$577$	2.73814	+	4.74260i	0.113990	+	0.197437i	0.917376	−	0.398022i	$-0.130303\pi$
$577$	2.73814	+	4.74260i	0.113990	+	0.197437i	−0.803385	+	0.595459i	$0.796970\pi$
$578$	0.618052	−	24.0128i	0.0257076	−	0.998799i
$579$		0			0
$580$	−1.20067	−	2.35126i	−0.0498553	−	0.0976306i
$581$	2.74512	−	2.14709i	0.113887	−	0.0890762i
$582$		0			0
$583$		−	17.6578i		−	0.731310i
$584$	5.37752	−	2.57381i	0.222523	−	0.106505i
$585$		0			0
$586$	−24.9979	−	0.643407i	−1.03265	−	0.0265789i
$587$	20.5491	+	35.5920i	0.848151	+	1.46904i	0.882857	+	0.469643i	$0.155617\pi$
$587$	20.5491	+	35.5920i	0.848151	+	1.46904i	−0.0347057	+	0.999398i	$0.511049\pi$
$588$		0			0
$589$	10.3067	−	17.8517i	0.424679	−	0.735566i
$590$	10.6531	−	17.4018i	0.438583	−	0.716421i
$591$		0			0
$592$	32.8627	+	3.39459i	1.35065	+	0.139517i
$593$	6.86958	+	3.96615i	0.282100	+	0.162870i	0.634374	−	0.773027i	$-0.281258\pi$
$593$	6.86958	+	3.96615i	0.282100	+	0.162870i	−0.352274	+	0.935897i	$0.614591\pi$
$594$		0			0
$595$	0.498082	+	0.200928i	0.0204194	+	0.00823725i
$596$	0.0927188	−	1.79998i	0.00379791	−	0.0737300i
$597$		0			0
$598$	4.90393	−	2.66546i	0.200537	−	0.108999i
$599$	0.552652			0.0225807			0.0112904	−	0.999936i	$-0.496406\pi$
$599$	0.552652			0.0225807			0.0112904	+	0.999936i	$0.496406\pi$
$600$		0			0
$601$	11.6785	+	20.2278i	0.476376	+	0.825108i	0.999634	−	0.0270668i	$-0.00861669\pi$
$601$	11.6785	+	20.2278i	0.476376	+	0.825108i	−0.523257	+	0.852175i	$0.675283\pi$
$602$	−42.0041	−	18.2149i	−1.71196	−	0.742384i
$603$		0			0
$604$	1.61791	−	0.826191i	0.0658319	−	0.0336172i
$605$	−28.5663	−	16.4928i	−1.16139	−	0.670526i
$606$		0			0
$607$	28.7687	−	16.6096i	1.16769	−	0.674165i	0.214553	−	0.976712i	$-0.431170\pi$
$607$	28.7687	−	16.6096i	1.16769	−	0.674165i	0.953134	+	0.302548i	$0.0978372\pi$
$608$	−16.5785	−	39.7722i	−0.672345	−	1.61297i
$609$		0			0
$610$	−4.72669	+	7.72100i	−0.191378	+	0.312614i
$611$	2.01230	−	3.48541i	0.0814091	−	0.141005i
$612$		0			0
$613$	−14.8721	−	25.7592i	−0.600677	−	1.04040i	−0.992719	−	0.120456i	$-0.961564\pi$
$613$	−14.8721	−	25.7592i	−0.600677	−	1.04040i	0.392041	−	0.919948i	$-0.371769\pi$
$614$	7.82368	+	14.3941i	0.315738	+	0.580897i
$615$		0			0
$616$	18.4487	−	37.1769i	0.743320	−	1.49790i
$617$	−1.33304	−	0.769632i	−0.0536663	−	0.0309842i	0.472927	−	0.881102i	$-0.343197\pi$
$617$	−1.33304	−	0.769632i	−0.0536663	−	0.0309842i	−0.526593	+	0.850117i	$0.676531\pi$
$618$		0			0
$619$	12.0846	+	6.97703i	0.485720	+	0.280431i	0.722797	−	0.691060i	$-0.242856\pi$
$619$	12.0846	+	6.97703i	0.485720	+	0.280431i	−0.237077	+	0.971491i	$0.576189\pi$
$620$	9.02360	+	0.464815i	0.362397	+	0.0186674i
$621$		0			0
$622$	−35.8171	+	19.4678i	−1.43614	+	0.780589i
$623$	−9.30347	+	23.0624i	−0.372736	+	0.923976i
$624$		0			0
$625$	4.51885	+	7.82687i	0.180754	+	0.313075i
$626$	−25.5958	+	13.9122i	−1.02302	+	0.556044i
$627$		0			0
$628$	−9.01644	+	13.9113i	−0.359795	+	0.555122i
$629$			1.00432i			0.0400447i
$630$		0			0
$631$			32.8617i			1.30820i	0.756407	+	0.654102i	$0.226953\pi$
$631$			32.8617i			1.30820i	−0.756407	+	0.654102i	$0.773047\pi$
$632$	−30.8599	−	2.38708i	−1.22754	−	0.0949528i
$633$		0			0
$634$	−17.9566	−	33.0366i	−0.713146	−	1.31205i
$635$	−5.71178	−	9.89309i	−0.226665	−	0.392595i
$636$		0			0
$637$	1.54531	−	6.22627i	0.0612274	−	0.246694i
$638$	−2.96167	−	5.44890i	−0.117254	−	0.215724i
$639$		0			0
$640$	12.2214	−	14.4005i	0.483094	−	0.569229i
$641$	15.7982	+	9.12111i	0.623993	+	0.360262i	0.778422	−	0.627742i	$-0.216021\pi$
$641$	15.7982	+	9.12111i	0.623993	+	0.360262i	−0.154429	+	0.988004i	$0.549354\pi$
$642$		0			0
$643$	0.902277	+	0.520930i	0.0355823	+	0.0205435i	0.517686	−	0.855571i	$-0.326794\pi$
$643$	0.902277	+	0.520930i	0.0355823	+	0.0205435i	−0.482103	+	0.876114i	$0.660127\pi$
$644$	2.01854	+	22.6984i	0.0795417	+	0.894441i
$645$		0			0
$646$	1.15086	−	0.625534i	0.0452801	−	0.0246113i
$647$	−2.46961	−	4.27748i	−0.0970902	−	0.168165i	0.813389	−	0.581720i	$-0.197620\pi$
$647$	−2.46961	−	4.27748i	−0.0970902	−	0.168165i	−0.910479	+	0.413555i	$0.864287\pi$
$648$		0			0
$649$	23.9651	−	41.5087i	0.940711	−	1.62936i
$650$	2.44619	+	1.49752i	0.0959474	+	0.0587377i
$651$		0			0
$652$	21.2641	−	10.8586i	0.832768	−	0.425255i
$653$	−0.0167205	+	0.00965359i	−0.000654324	+	0.000377774i	−0.500327	−	0.865836i	$-0.666787\pi$
$653$	−0.0167205	+	0.00965359i	−0.000654324	+	0.000377774i	0.499673	+	0.866214i	$0.333454\pi$
$654$		0			0
$655$	28.8855	+	16.6771i	1.12865	+	0.651627i
$656$	0.813276	−	7.87325i	0.0317531	−	0.307399i
$657$		0			0
$658$	9.78680	+	13.1990i	0.381529	+	0.514550i
$659$	5.49141	+	9.51140i	0.213915	+	0.370512i	0.952936	−	0.303170i	$-0.0980451\pi$
$659$	5.49141	+	9.51140i	0.213915	+	0.370512i	−0.739021	+	0.673682i	$0.764712\pi$
$660$		0			0
$661$	−0.611207			−0.0237732			−0.0118866	−	0.999929i	$-0.503784\pi$
$661$	−0.611207			−0.0237732			−0.0118866	+	0.999929i	$0.503784\pi$
$662$	−2.70331	−	4.97357i	−0.105067	−	0.193303i
$663$		0			0
$664$	3.36060	−	1.60846i	0.130417	−	0.0624204i
$665$	−4.70019	−	33.3143i	−0.182266	−	1.29187i
$666$		0			0
$667$	2.94900	+	1.70261i	0.114186	+	0.0659252i
$668$	−22.3513	−	43.7700i	−0.864797	−	1.69351i
$669$		0			0
$670$	−3.26062	−	1.99611i	−0.125969	−	0.0771163i
$671$	−10.6330	+	18.4170i	−0.410484	+	0.710979i
$672$		0			0
$673$	11.2929	+	19.5598i	0.435308	+	0.753976i	0.997321	−	0.0731525i	$-0.0233060\pi$
$673$	11.2929	+	19.5598i	0.435308	+	0.753976i	−0.562012	+	0.827129i	$0.689973\pi$
$674$	0.389325	−	15.1262i	0.0149962	−	0.582640i
$675$		0			0
$676$	24.2880	+	1.25110i	0.934155	+	0.0481193i
$677$		−	22.6286i		−	0.869686i	−0.900506	−	0.434843i	$-0.856804\pi$
$677$		−	22.6286i		−	0.869686i	0.900506	−	0.434843i	$-0.143196\pi$
$678$		0			0
$679$	−13.9169	+	10.8850i	−0.534080	+	0.417729i
$680$	0.473620	+	0.324576i	0.0181625	+	0.0124469i
$681$		0			0
$682$	21.2183	+	0.546126i	0.812490	+	0.0209122i
$683$	20.8314	+	36.0811i	0.797093	+	1.38060i	0.921502	+	0.388374i	$0.126963\pi$
$683$	20.8314	+	36.0811i	0.797093	+	1.38060i	−0.124409	+	0.992231i	$0.539704\pi$
$684$		0			0
$685$	−2.66388			−0.101782
$686$	20.8119	+	15.9018i	0.794601	+	0.607132i
$687$		0			0
$688$	−39.6484	−	28.6981i	−1.51158	−	1.09410i
$689$		−	2.91785i		−	0.111161i
$690$		0			0
$691$			36.1647i			1.37577i	0.725820	+	0.687885i	$0.241461\pi$
$691$			36.1647i			1.37577i	−0.725820	+	0.687885i	$0.758539\pi$
$692$	−15.2405	−	9.87790i	−0.579355	−	0.375501i
$693$		0			0
$694$	27.1011	−	14.7304i	1.02874	−	0.559157i
$695$	13.7580			0.521871
$696$		0			0
$697$	0.240614			0.00911392
$698$	19.6923	+	12.0553i	0.745365	+	0.456302i
$699$		0			0
$700$	−9.58271	+	6.73032i	−0.362192	+	0.254382i
$701$		−	8.15056i		−	0.307842i	−0.988083	−	0.153921i	$-0.950810\pi$
$701$		−	8.15056i		−	0.307842i	0.988083	−	0.153921i	$-0.0491902\pi$
$702$		0			0
$703$	54.4842	−	31.4565i	2.05491	−	1.18640i
$704$	27.8293	−	34.5554i	1.04885	−	1.30236i
$705$		0			0
$706$	−36.3531	−	0.935672i	−1.36817	−	0.0352145i
$707$	10.1745	−	25.2217i	0.382653	−	0.948559i
$708$		0			0
$709$	21.6576			0.813367			0.406683	−	0.913569i	$-0.366685\pi$
$709$	21.6576			0.813367			0.406683	+	0.913569i	$0.366685\pi$
$710$	−13.2336	+	21.6170i	−0.496649	+	0.811272i
$711$		0			0
$712$	−15.0287	+	21.9298i	−0.563223	+	0.821854i
$713$	−10.0928	+	5.82710i	−0.377980	+	0.218227i
$714$		0			0
$715$	−7.34840	−	4.24260i	−0.274814	−	0.158664i
$716$	−12.9362	−	0.666355i	−0.483447	−	0.0249029i
$717$		0			0
$718$	0.303717	−	11.8001i	0.0113346	−	0.440377i
$719$	16.3507	−	28.3202i	0.609778	−	1.05617i	−0.381498	−	0.924370i	$-0.624592\pi$
$719$	16.3507	−	28.3202i	0.609778	−	1.05617i	0.991277	−	0.131798i	$-0.0420749\pi$
$720$		0			0
$721$	17.1686	+	21.9506i	0.639394	+	0.817485i
$722$	−47.0650	−	28.8125i	−1.75158	−	1.07229i
$723$		0			0
$724$	11.0462	−	17.0430i	0.410528	−	0.633397i
$725$			1.74984i			0.0649874i
$726$		0			0
$727$	39.0531	−	22.5473i	1.44840	−	0.836233i	0.450013	−	0.893022i	$-0.351419\pi$
$727$	39.0531	−	22.5473i	1.44840	−	0.836233i	0.998386	+	0.0567887i	$0.0180861\pi$
$728$	3.04855	−	6.14329i	0.112987	−	0.227685i
$729$		0			0
$730$	4.97470	+	0.128041i	0.184122	+	0.00473902i
$731$	0.743940	−	1.28854i	0.0275156	−	0.0476585i
$732$		0			0
$733$	25.3912	+	43.9789i	0.937846	+	1.62440i	0.769479	+	0.638672i	$0.220516\pi$
$733$	25.3912	+	43.9789i	0.937846	+	1.62440i	0.168367	+	0.985724i	$0.446151\pi$
$734$	31.5671	+	0.812487i	1.16516	+	0.0299894i
$735$		0			0
$736$	−3.12578	+	24.1600i	−0.115218	+	0.890549i
$737$	−7.77759	−	4.49039i	−0.286491	−	0.165406i
$738$		0			0
$739$	−14.8941	+	8.59913i	−0.547890	+	0.316324i	−0.748270	−	0.663394i	$-0.769115\pi$
$739$	−14.8941	+	8.59913i	−0.547890	+	0.316324i	0.200381	+	0.979718i	$0.435782\pi$
$740$	23.1414	+	14.9988i	0.850695	+	0.551367i
$741$		0			0
$742$	10.9295	+	4.73953i	0.401235	+	0.173993i
$743$	−25.7102	+	44.5314i	−0.943217	+	1.63370i	−0.183933	+	0.982939i	$0.558883\pi$
$743$	−25.7102	+	44.5314i	−0.943217	+	1.63370i	−0.759283	+	0.650760i	$0.774450\pi$
$744$		0			0
$745$	0.752232	−	1.30290i	0.0275596	−	0.0477347i
$746$	19.4945	+	11.9342i	0.713743	+	0.436944i
$747$		0			0
$748$	1.13182	+	0.733577i	0.0413836	+	0.0268222i
$749$	−14.3980	−	5.80822i	−0.526092	−	0.212228i
$750$		0			0
$751$	14.6956	−	8.48454i	0.536252	−	0.309605i	−0.207307	−	0.978276i	$-0.566470\pi$
$751$	14.6956	−	8.48454i	0.536252	−	0.309605i	0.743558	+	0.668671i	$0.233136\pi$
$752$	7.17344	+	16.0346i	0.261588	+	0.584720i
$753$		0			0
$754$	−0.489400	−	0.900402i	−0.0178229	−	0.0327907i
$755$	1.51639			0.0551871
$756$		0			0
$757$	−26.0926			−0.948353			−0.474177	−	0.880430i	$-0.657254\pi$
$757$	−26.0926			−0.948353			−0.474177	+	0.880430i	$0.657254\pi$
$758$	0.215465	+	0.396414i	0.00782603	+	0.0143984i
$759$		0			0
$760$	2.77385	−	35.8601i	0.100618	−	1.30078i
$761$	12.0058	−	6.93152i	0.435208	−	0.251268i	−0.266355	−	0.963875i	$-0.585819\pi$
$761$	12.0058	−	6.93152i	0.435208	−	0.251268i	0.701563	+	0.712608i	$0.252486\pi$
$762$		0			0
$763$	−18.7821	+	14.6903i	−0.679957	+	0.531826i
$764$	6.54692	−	10.1011i	0.236859	−	0.365446i
$765$		0			0
$766$	−13.2488	−	8.11071i	−0.478697	−	0.293052i
$767$	3.96010	−	6.85909i	0.142991	−	0.247667i
$768$		0			0
$769$	−15.6264	+	27.0657i	−0.563501	+	0.976013i	0.433686	+	0.901064i	$0.357213\pi$
$769$	−15.6264	+	27.0657i	−0.563501	+	0.976013i	−0.997187	+	0.0749490i	$0.976121\pi$
$770$	27.8278	−	20.6338i	1.00284	−	0.743590i
$771$		0			0
$772$	16.5336	−	25.5095i	0.595058	−	0.918106i
$773$	−23.3161	+	13.4616i	−0.838622	+	0.484179i	−0.856796	−	0.515656i	$-0.827548\pi$
$773$	−23.3161	+	13.4616i	−0.838622	+	0.484179i	0.0181735	+	0.999835i	$0.494215\pi$
$774$		0			0
$775$	−5.18641	−	2.99438i	−0.186302	−	0.107561i
$776$	−17.0371	+	8.15437i	−0.611598	+	0.292725i
$777$		0			0
$778$	18.3081	+	0.471223i	0.656378	+	0.0168942i
$779$	−7.53635	−	13.0533i	−0.270018	−	0.467685i
$780$		0			0
$781$	−29.7700	+	51.5632i	−1.06526	+	1.84508i
$782$	−0.740321	−	0.0190547i	−0.0264738	−	0.000681396i
$783$		0			0
$784$	18.0593	+	21.3977i	0.644975	+	0.764204i
$785$	−11.9838	+	6.91885i	−0.427720	+	0.246944i
$786$		0			0
$787$			41.9215i			1.49434i	0.664633	+	0.747170i	$0.268588\pi$
$787$			41.9215i			1.49434i	−0.664633	+	0.747170i	$0.731412\pi$
$788$	−21.1349	−	13.6983i	−0.752898	−	0.487981i
$789$		0			0
$790$	−22.0350	−	13.4895i	−0.783972	−	0.479936i
$791$	7.02396	−	17.4117i	0.249743	−	0.619090i
$792$		0			0
$793$	−1.75705	+	3.04331i	−0.0623948	+	0.108071i
$794$	−0.750399	+	29.1548i	−0.0266307	+	1.03466i
$795$		0			0
$796$	0.591651	−	11.4859i	0.0209705	−	0.407107i
$797$	−38.7013	−	22.3442i	−1.37087	−	0.791473i	−0.379833	−	0.925055i	$-0.624019\pi$
$797$	−38.7013	−	22.3442i	−1.37087	−	0.791473i	−0.991038	+	0.133583i	$0.957352\pi$
$798$		0			0
$799$	−0.462452	+	0.266997i	−0.0163604	+	0.00944567i
$800$	−11.5549	+	4.81650i	−0.408528	+	0.170289i
$801$		0			0
$802$	10.0456	−	16.4095i	0.354724	−	0.579439i
$803$	11.6899			0.412527
$804$		0			0
$805$	−7.11614	+	17.6402i	−0.250811	+	0.621736i
$806$	3.50621	+	0.0902444i	0.123501	+	0.00317872i
$807$		0			0
$808$	16.4358	−	23.9830i	0.578208	−	0.843720i
$809$	−30.1213	+	17.3905i	−1.05901	+	0.611418i	−0.925158	−	0.379583i	$-0.876067\pi$
$809$	−30.1213	+	17.3905i	−1.05901	+	0.611418i	−0.133850	+	0.991002i	$0.542734\pi$
$810$		0			0
$811$		−	16.9568i		−	0.595433i	−0.954654	−	0.297717i	$-0.903775\pi$
$811$		−	16.9568i		−	0.595433i	0.954654	−	0.297717i	$-0.0962251\pi$
$812$	4.16761	−	0.370621i	0.146254	−	0.0130062i
$813$		0			0
$814$	55.2497	+	33.8231i	1.93650	+	1.18550i
$815$	19.9299			0.698112
$816$		0			0
$817$	−93.2047			−3.26082
$818$	0.324988	−	0.176642i	0.0113629	−	0.00617616i
$819$		0			0
$820$	3.59342	−	5.54423i	0.125488	−	0.193613i
$821$		−	48.1235i		−	1.67952i	−0.542957	−	0.839761i	$-0.682695\pi$
$821$		−	48.1235i		−	1.67952i	0.542957	−	0.839761i	$-0.317305\pi$
$822$		0			0
$823$			43.4575i			1.51483i	0.652932	+	0.757417i	$0.273539\pi$
$823$			43.4575i			1.51483i	−0.652932	+	0.757417i	$0.726461\pi$
$824$	12.8616	+	26.8722i	0.448057	+	0.936136i
$825$		0			0
$826$	19.2599	+	25.9748i	0.670136	+	0.903779i
$827$	22.3765			0.778107			0.389054	−	0.921215i	$-0.372802\pi$
$827$	22.3765			0.778107			0.389054	+	0.921215i	$0.372802\pi$
$828$		0			0
$829$	−19.6304	−	34.0009i	−0.681793	−	1.18090i	−0.974433	−	0.224678i	$-0.927867\pi$
$829$	−19.6304	−	34.0009i	−0.681793	−	1.18090i	0.292640	−	0.956223i	$-0.405466\pi$
$830$	3.10887	+	0.0800174i	0.107910	+	0.00277744i
$831$		0			0
$832$	4.59864	−	5.71010i	0.159429	−	0.197962i
$833$	−0.590623	+	0.612919i	−0.0204639	+	0.0212364i
$834$		0			0
$835$		−	41.0235i		−	1.41968i
$836$	4.34640	−	84.3781i	0.150324	−	2.91828i
$837$		0			0
$838$	0.0183665	−	0.713581i	0.000634459	−	0.0246502i
$839$	13.5646	+	23.4946i	0.468302	+	0.811123i	0.999344	−	0.0362228i	$-0.0115326\pi$
$839$	13.5646	+	23.4946i	0.468302	+	0.811123i	−0.531042	+	0.847346i	$0.678199\pi$
$840$		0			0
$841$	−14.1874	+	24.5733i	−0.489220	+	0.847354i
$842$	−2.19159	−	1.34166i	−0.0755272	−	0.0462367i
$843$		0			0
$844$	−22.1370	+	11.3043i	−0.761987	+	0.389110i
$845$	17.5807	+	10.1502i	0.604796	+	0.349179i
$846$		0			0
$847$	41.1769	−	32.2064i	1.41486	−	1.10663i
$848$	10.3165	+	7.46725i	0.354272	+	0.256426i
$849$		0			0
$850$	−0.181735	−	0.334357i	−0.00623346	−	0.0114684i
$851$	−35.5692			−1.21930
$852$		0			0
$853$	−7.93576	−	13.7451i	−0.271715	−	0.470625i	0.697586	−	0.716501i	$-0.254258\pi$
$853$	−7.93576	−	13.7451i	−0.271715	−	0.470625i	−0.969301	+	0.245877i	$0.920924\pi$
$854$	−8.54540	−	11.5248i	−0.292417	−	0.394369i
$855$		0			0
$856$	−13.6909	−	9.38249i	−0.467946	−	0.320687i
$857$	9.83574	+	5.67867i	0.335982	+	0.193980i	0.658494	−	0.752586i	$-0.271194\pi$
$857$	9.83574	+	5.67867i	0.335982	+	0.193980i	−0.322512	+	0.946566i	$0.604527\pi$
$858$		0			0
$859$	−32.7534	+	18.9102i	−1.11753	+	0.645206i	−0.940769	−	0.339047i	$-0.889895\pi$
$859$	−32.7534	+	18.9102i	−1.11753	+	0.645206i	−0.176761	+	0.984254i	$0.556562\pi$
$860$	−18.5803	−	36.3854i	−0.633582	−	1.24073i
$861$		0			0
$862$	2.79379	+	1.71032i	0.0951568	+	0.0582536i
$863$	−6.51097	+	11.2773i	−0.221636	+	0.383885i	−0.955305	−	0.295622i	$-0.904473\pi$
$863$	−6.51097	+	11.2773i	−0.221636	+	0.383885i	0.733669	+	0.679507i	$0.237806\pi$
$864$		0			0
$865$	−7.57990	−	13.1288i	−0.257724	−	0.446392i
$866$	−19.2628	+	10.4700i	−0.654578	+	0.355786i
$867$		0			0
$868$	−6.03323	+	12.9867i	−0.204781	+	0.440799i
$869$	−52.5604	−	30.3457i	−1.78299	−	1.02941i
$870$		0			0
$871$	−1.28521	−	0.742014i	−0.0435475	−	0.0251422i
$872$	−22.9932	+	11.0051i	−0.778647	+	0.372679i
$873$		0			0
$874$	22.1541	+	40.7593i	0.749374	+	1.37870i
$875$	−31.5467	+	4.45080i	−1.06647	+	0.150465i
$876$		0			0
$877$	3.29142	+	5.70090i	0.111143	+	0.192506i	0.916231	−	0.400649i	$-0.131215\pi$
$877$	3.29142	+	5.70090i	0.111143	+	0.192506i	−0.805088	+	0.593155i	$0.797882\pi$
$878$	−9.03996	−	16.6318i	−0.305084	−	0.561296i
$879$		0			0
$880$	33.8061	−	15.1240i	1.13960	−	0.509829i
$881$		−	5.82071i		−	0.196105i	−0.995181	−	0.0980524i	$-0.968739\pi$
$881$		−	5.82071i		−	0.196105i	0.995181	−	0.0980524i	$-0.0312613\pi$
$882$		0			0
$883$			36.2156i			1.21875i	0.792881	+	0.609376i	$0.208580\pi$
$883$			36.2156i			1.21875i	−0.792881	+	0.609376i	$0.791420\pi$
$884$	0.187028	+	0.121220i	0.00629043	+	0.00407706i
$885$		0			0
$886$	−36.2157	+	19.6845i	−1.21669	+	0.661314i
$887$	6.19468	+	10.7295i	0.207997	+	0.360261i	0.951083	−	0.308934i	$-0.0999723\pi$
$887$	6.19468	+	10.7295i	0.207997	+	0.360261i	−0.743086	+	0.669195i	$0.766639\pi$
$888$		0			0
$889$	17.9268	−	2.52922i	0.601244	−	0.0848273i
$890$	−19.4972	+	10.5974i	−0.653549	+	0.355227i
$891$		0			0
$892$	−0.787242	+	15.2830i	−0.0263588	+	0.511712i
$893$	28.9692	+	16.7254i	0.969418	+	0.559694i
$894$		0			0
$895$	−9.36376	−	5.40617i	−0.312996	−	0.180708i
$896$	13.9189	+	26.5003i	0.464996	+	0.885313i
$897$		0			0
$898$	−5.15135	−	9.47750i	−0.171903	−	0.316268i
$899$	1.06990	+	1.85313i	0.0356833	+	0.0618053i
$900$		0			0
$901$	−0.193574	+	0.335279i	−0.00644887	+	0.0111698i
$902$	8.10335	−	13.2367i	0.269812	−	0.440735i
$903$		0			0
$904$	11.3464	−	16.5566i	0.377375	−	0.550665i
$905$	14.6815	−	8.47639i	0.488031	−	0.281765i
$906$		0			0
$907$	−5.21971	−	3.01360i	−0.173318	−	0.100065i	0.410832	−	0.911711i	$-0.365238\pi$
$907$	−5.21971	−	3.01360i	−0.173318	−	0.100065i	−0.584149	+	0.811646i	$0.698572\pi$
$908$	−19.8197	−	38.8125i	−0.657740	−	1.28804i
$909$		0			0
$910$	4.59839	−	3.40962i	0.152435	−	0.113028i
$911$	12.7116	+	22.0171i	0.421153	+	0.729458i	0.996053	−	0.0887660i	$-0.0282923\pi$
$911$	12.7116	+	22.0171i	0.421153	+	0.729458i	−0.574900	+	0.818224i	$0.694959\pi$
$912$		0			0
$913$	7.30541			0.241774
$914$	3.14272	−	1.70818i	0.103952	−	0.0565015i
$915$		0			0
$916$	−51.3053	−	2.64279i	−1.69518	−	0.0873202i
$917$	−41.6371	+	32.5663i	−1.37498	+	1.07544i
$918$		0			0
$919$	−19.2980	−	11.1417i	−0.636583	−	0.367532i	0.146714	−	0.989179i	$-0.453130\pi$
$919$	−19.2980	−	11.1417i	−0.636583	−	0.367532i	−0.783297	+	0.621647i	$0.786464\pi$
$920$	−11.4953	+	16.7739i	−0.378988	+	0.553019i
$921$		0			0
$922$	24.5467	−	40.0968i	0.808403	−	1.32052i
$923$	−4.91934	+	8.52055i	−0.161922	+	0.280457i
$924$		0			0
$925$	−9.13898	−	15.8292i	−0.300488	−	0.520460i
$926$	22.8774	+	0.588829i	0.751799	+	0.0193501i
$927$		0			0
$928$	4.43597	+	0.573919i	0.145618	+	0.0188398i
$929$			33.6630i			1.10445i	0.833697	+	0.552223i	$0.186220\pi$
$929$			33.6630i			1.10445i	−0.833697	+	0.552223i	$0.813780\pi$
$930$		0			0
$931$	51.7500	+	12.8439i	1.69604	+	0.420943i
$932$	−3.92180	+	2.00267i	−0.128463	+	0.0655998i
$933$		0			0
$934$	1.06770	−	41.4826i	0.0349361	−	1.35735i
$935$	0.562917	+	0.975001i	0.0184094	+	0.0318859i
$936$		0			0
$937$	24.2247			0.791387			0.395693	−	0.918383i	$-0.370504\pi$
$937$	24.2247			0.791387			0.395693	+	0.918383i	$0.370504\pi$
$938$	4.86697	−	3.60877i	0.158912	−	0.117830i
$939$		0			0
$940$	−0.754288	+	14.6432i	−0.0246022	+	0.477610i
$941$			21.3140i			0.694817i	0.937714	+	0.347408i	$0.112938\pi$
$941$			21.3140i			0.694817i	−0.937714	+	0.347408i	$0.887062\pi$
$942$		0			0
$943$			8.52167i			0.277504i
$944$	14.1169	+	31.5551i	0.459466	+	1.02703i
$945$		0			0
$946$	−45.8314	−	84.3210i	−1.49011	−	2.74151i
$947$	−35.2301			−1.14482			−0.572412	−	0.819966i	$-0.693992\pi$
$947$	−35.2301			−1.14482			−0.572412	+	0.819966i	$0.693992\pi$
$948$		0			0
$949$	1.93169			0.0627053
$950$	−12.4467	+	20.3316i	−0.403826	+	0.659645i
$951$		0			0
$952$	−0.757850	+	0.503657i	−0.0245620	+	0.0163236i
$953$		−	11.4706i		−	0.371569i	−0.982590	−	0.185785i	$-0.940517\pi$
$953$		−	11.4706i		−	0.371569i	0.982590	−	0.185785i	$-0.0594827\pi$
$954$		0			0
$955$	8.70155	−	5.02384i	0.281576	−	0.162568i
$956$	5.44995	+	10.6725i	0.176264	+	0.345174i
$957$		0			0
$958$	1.24953	−	48.5470i	0.0403703	−	1.56848i
$959$	1.57941	−	3.91521i	0.0510019	−	0.126429i
$960$		0			0
$961$	23.6766			0.763761
$962$	9.12972	+	5.58909i	0.294354	+	0.180199i
$963$		0			0
$964$	10.0450	+	19.6709i	0.323528	+	0.633558i
$965$	21.9749	−	12.6872i	0.707398	−	0.408417i
$966$		0			0
$967$	−8.24220	−	4.75864i	−0.265051	−	0.153027i	0.361585	−	0.932339i	$-0.382236\pi$
$967$	−8.24220	−	4.75864i	−0.265051	−	0.153027i	−0.626637	+	0.779312i	$0.715569\pi$
$968$	50.4091	−	24.1270i	1.62021	−	0.775471i
$969$		0			0
$970$	−15.7609	−	0.405662i	−0.506053	−	0.0130250i
$971$	−29.2431	+	50.6506i	−0.938457	+	1.62545i	−0.170106	+	0.985426i	$0.554411\pi$
$971$	−29.2431	+	50.6506i	−0.938457	+	1.62545i	−0.768351	+	0.640029i	$0.778922\pi$
$972$		0			0
$973$	−8.15710	+	20.2207i	−0.261505	+	0.648245i
$974$	21.9778	−	35.9005i	0.704213	−	1.15033i
$975$		0			0
$976$	−6.26352	−	14.0007i	−0.200490	−	0.448150i
$977$		−	5.31916i		−	0.170175i	−0.996373	−	0.0850875i	$-0.972883\pi$
$977$		−	5.31916i		−	0.170175i	0.996373	−	0.0850875i	$-0.0271170\pi$
$978$		0			0
$979$	−45.1450	+	26.0645i	−1.44284	+	0.833024i
$980$	5.30229	+	22.7627i	0.169375	+	0.727127i
$981$		0			0
$982$	−1.22584	+	47.6269i	−0.0391182	+	1.51984i
$983$	−0.398423	+	0.690088i	−0.0127077	+	0.0220104i	−0.872309	−	0.488954i	$-0.837378\pi$
$983$	−0.398423	+	0.690088i	−0.0127077	+	0.0220104i	0.859602	+	0.510965i	$0.170712\pi$
$984$		0			0
$985$	−10.5115	−	18.2065i	−0.334925	−	0.580106i
$986$	−0.00349860	+	0.135929i	−0.000111418	+	0.00432886i
$987$		0			0
$988$	0.718220	−	13.9430i	0.0228496	−	0.443587i
$989$	45.6354	+	26.3476i	1.45112	+	0.837806i
$990$		0			0
$991$	−12.7041	+	7.33474i	−0.403560	+	0.232996i	−0.688019	−	0.725693i	$-0.741519\pi$
$991$	−12.7041	+	7.33474i	−0.403560	+	0.232996i	0.284459	+	0.958688i	$0.408186\pi$
$992$	−9.29202	+	12.1658i	−0.295022	+	0.386265i
$993$		0			0
$994$	−23.9251	−	32.2666i	−0.758859	−	1.02344i
$995$	4.80009	−	8.31401i	0.152173	−	0.263572i
$996$		0			0
$997$	10.1764	−	17.6260i	0.322289	−	0.558221i	−0.658671	−	0.752431i	$-0.728881\pi$
$997$	10.1764	−	17.6260i	0.322289	−	0.558221i	0.980960	+	0.194210i	$0.0622144\pi$
$998$	23.3879	−	38.2038i	0.740330	−	1.20932i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.bb.a.611.8		88
3.2	odd	2		252.2.bb.a.23.37	yes	88
4.3	odd	2	inner	756.2.bb.a.611.37		88
7.4	even	3		756.2.o.a.179.21		88
9.2	odd	6		756.2.o.a.359.7		88
9.7	even	3		252.2.o.a.191.38	yes	88
12.11	even	2		252.2.bb.a.23.8	yes	88
21.11	odd	6		252.2.o.a.95.24	✓	88
28.11	odd	6		756.2.o.a.179.7		88
36.7	odd	6		252.2.o.a.191.24	yes	88
36.11	even	6		756.2.o.a.359.21		88
63.11	odd	6	inner	756.2.bb.a.683.37		88
63.25	even	3		252.2.bb.a.11.8	yes	88
84.11	even	6		252.2.o.a.95.38	yes	88
252.11	even	6	inner	756.2.bb.a.683.8		88
252.151	odd	6		252.2.bb.a.11.37	yes	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.o.a.95.24	✓	88	21.11	odd	6
252.2.o.a.95.38	yes	88	84.11	even	6
252.2.o.a.191.24	yes	88	36.7	odd	6
252.2.o.a.191.38	yes	88	9.7	even	3
252.2.bb.a.11.8	yes	88	63.25	even	3
252.2.bb.a.11.37	yes	88	252.151	odd	6
252.2.bb.a.23.8	yes	88	12.11	even	2
252.2.bb.a.23.37	yes	88	3.2	odd	2
756.2.o.a.179.7		88	28.11	odd	6
756.2.o.a.179.21		88	7.4	even	3
756.2.o.a.359.7		88	9.2	odd	6
756.2.o.a.359.21		88	36.11	even	6
756.2.bb.a.611.8		88	1.1	even	1	trivial
756.2.bb.a.611.37		88	4.3	odd	2	inner
756.2.bb.a.683.8		88	252.11	even	6	inner
756.2.bb.a.683.37		88	63.11	odd	6	inner

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.bb (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.24253 + 0.675360i) q^{2} +(1.08778 - 1.67831i) q^{4} +(1.44577 - 0.834716i) q^{5} +(0.369619 + 2.61981i) q^{7} +(-0.218133 + 2.82000i) q^{8} +O(q^{10})\)	\(q+(-1.24253 + 0.675360i) q^{2} +(1.08778 - 1.67831i) q^{4} +(1.44577 - 0.834716i) q^{5} +(0.369619 + 2.61981i) q^{7} +(-0.218133 + 2.82000i) q^{8} +(-1.23268 + 2.01358i) q^{10} +(-2.77302 + 4.80301i) q^{11} +(-0.458226 + 0.793672i) q^{13} +(-2.22858 - 3.00557i) q^{14} +(-1.63348 - 3.65127i) q^{16} +(0.105306 - 0.0607985i) q^{17} +(-6.59665 - 3.80857i) q^{19} +(0.171761 - 3.33445i) q^{20} +(0.201807 - 7.84068i) q^{22} +(2.15326 + 3.72955i) q^{23} +(-1.10650 + 1.91651i) q^{25} +(0.0333475 - 1.29563i) q^{26} +(4.79892 + 2.22943i) q^{28} +(0.684776 - 0.395356i) q^{29} +2.70618i q^{31} +(4.49557 + 3.43363i) q^{32} +(-0.0897854 + 0.146664i) q^{34} +(2.72118 + 3.47911i) q^{35} +(-4.12969 + 7.15284i) q^{37} +(10.7687 + 0.277170i) q^{38} +(2.03853 + 4.25916i) q^{40} +(1.71368 + 0.989393i) q^{41} +(10.5968 - 6.11808i) q^{43} +(5.04453 + 9.87860i) q^{44} +(-5.19429 - 3.17987i) q^{46} -4.39151 q^{47} +(-6.72676 + 1.93666i) q^{49} +(0.0805256 - 3.12861i) q^{50} +(0.833582 + 1.63239i) q^{52} +(-2.75730 + 1.59193i) q^{53} +9.25874i q^{55} +(-7.46849 + 0.470860i) q^{56} +(-0.583850 + 0.953714i) q^{58} -8.64223 q^{59} +3.83447 q^{61} +(-1.82764 - 3.36252i) q^{62} +(-7.90484 - 1.23027i) q^{64} +1.52996i q^{65} +1.61932i q^{67} +(0.0125106 - 0.242872i) q^{68} +(-5.73081 - 2.48514i) q^{70} +10.7356 q^{71} +(-1.05389 - 1.82540i) q^{73} +(0.300539 - 11.6767i) q^{74} +(-13.5677 + 6.92836i) q^{76} +(-13.6079 - 5.48949i) q^{77} +10.9432i q^{79} +(-5.40941 - 3.91540i) q^{80} +(-2.79750 - 0.0720033i) q^{82} +(-0.658615 - 1.14075i) q^{83} +(0.101499 - 0.175801i) q^{85} +(-9.03500 + 14.7586i) q^{86} +(-12.9396 - 8.86761i) q^{88} +(8.14004 + 4.69966i) q^{89} +(-2.24863 - 0.907109i) q^{91} +(8.60163 + 0.443079i) q^{92} +(5.45659 - 2.96585i) q^{94} -12.7163 q^{95} +(3.33897 + 5.78326i) q^{97} +(7.05029 - 6.94935i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q - 2 q^{4} + 6 q^{5}+O(q^{10}) \) 88 * q - 2 * q^4 + 6 * q^5	\( 88 q - 2 q^{4} + 6 q^{5} + 2 q^{10} - 4 q^{13} + 18 q^{14} - 2 q^{16} + 6 q^{20} - 6 q^{22} + 30 q^{25} - 6 q^{26} + 24 q^{29} - 4 q^{34} - 4 q^{37} + 45 q^{38} - 4 q^{40} + 12 q^{41} - 57 q^{44} - 6 q^{46} - 2 q^{49} - 9 q^{50} - 7 q^{52} + 24 q^{56} + 5 q^{58} - 4 q^{61} - 8 q^{64} + 12 q^{68} - 27 q^{70} - 4 q^{73} - 51 q^{74} - 6 q^{76} + 30 q^{77} + 87 q^{80} - 4 q^{82} - 14 q^{85} - 81 q^{86} + 9 q^{88} + 60 q^{89} - 24 q^{92} - 18 q^{94} - 4 q^{97} - 57 q^{98}+O(q^{100}) \) 88 * q - 2 * q^4 + 6 * q^5 + 2 * q^10 - 4 * q^13 + 18 * q^14 - 2 * q^16 + 6 * q^20 - 6 * q^22 + 30 * q^25 - 6 * q^26 + 24 * q^29 - 4 * q^34 - 4 * q^37 + 45 * q^38 - 4 * q^40 + 12 * q^41 - 57 * q^44 - 6 * q^46 - 2 * q^49 - 9 * q^50 - 7 * q^52 + 24 * q^56 + 5 * q^58 - 4 * q^61 - 8 * q^64 + 12 * q^68 - 27 * q^70 - 4 * q^73 - 51 * q^74 - 6 * q^76 + 30 * q^77 + 87 * q^80 - 4 * q^82 - 14 * q^85 - 81 * q^86 + 9 * q^88 + 60 * q^89 - 24 * q^92 - 18 * q^94 - 4 * q^97 - 57 * q^98

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