LMFDB - Embedded newform 513.2.y.c.460.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [513,2,Mod(28,513)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(513, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([0, 8])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("513.28"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 513 = 3^{3} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	513.y (of order $9$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [6,3,0,9,3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$4.09632562369$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			460.1
Root			$0.939693 + 0.342020i$ of defining polynomial
Character	$\chi$	$=$	513.460
Dual form			513.2.y.c.271.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.37939 + 0.866025i) q^{2} +(3.37939 + 2.83564i) q^{4} +(-1.03209 + 0.866025i) q^{5} +(2.43969 - 4.22567i) q^{7} +(3.05303 + 5.28801i) q^{8} +(-3.20574 + 1.16679i) q^{10} +(2.09240 + 3.62414i) q^{11} +(-0.460637 + 2.61240i) q^{13} +(9.46451 - 7.94166i) q^{14} +(1.15270 + 6.53731i) q^{16} +(-6.12449 - 2.22913i) q^{17} +(-2.52094 - 3.55596i) q^{19} -5.94356 q^{20} +(1.84002 + 10.4353i) q^{22} +(1.93969 + 1.62760i) q^{23} +(-0.553033 + 3.13641i) q^{25} +(-3.35844 + 5.81699i) q^{26} +(20.2271 - 7.36208i) q^{28} +(-2.76604 + 1.00676i) q^{29} +(3.16637 - 5.48432i) q^{31} +(-0.798133 + 4.52644i) q^{32} +(-12.6420 - 10.6079i) q^{34} +(1.14156 + 6.47410i) q^{35} -5.24123 q^{37} +(-2.91875 - 10.6442i) q^{38} +(-7.73055 - 2.81369i) q^{40} +(-1.27584 - 7.23567i) q^{41} +(-2.51501 + 2.11035i) q^{43} +(-3.20574 + 18.1806i) q^{44} +(3.20574 + 5.55250i) q^{46} +(1.41875 - 0.516382i) q^{47} +(-8.40420 - 14.5565i) q^{49} +(-4.03209 + 6.98378i) q^{50} +(-8.96451 + 7.52211i) q^{52} +(3.05303 + 2.56180i) q^{53} +(-5.29813 - 1.92836i) q^{55} +29.7939 q^{56} -7.45336 q^{58} +(3.35844 + 1.22237i) q^{59} +(2.28699 + 1.91901i) q^{61} +(12.2836 - 10.3072i) q^{62} +(0.819078 - 1.41868i) q^{64} +(-1.78699 - 3.09516i) q^{65} +(1.37939 - 0.502055i) q^{67} +(-14.3760 - 24.8999i) q^{68} +(-2.89053 + 16.3930i) q^{70} +(-0.343426 + 0.288169i) q^{71} +(-1.54916 - 8.78574i) q^{73} +(-12.4709 - 4.53904i) q^{74} +(1.56418 - 19.1654i) q^{76} +20.4192 q^{77} +(-1.74170 - 9.87765i) q^{79} +(-6.85117 - 5.74881i) q^{80} +(3.23055 - 18.3214i) q^{82} +(-2.29813 + 3.98048i) q^{83} +(8.25150 - 3.00330i) q^{85} +(-7.81180 + 2.84326i) q^{86} +(-12.7763 + 22.1292i) q^{88} +(-3.24035 + 18.3770i) q^{89} +(9.91534 + 8.31996i) q^{91} +(1.93969 + 11.0005i) q^{92} +3.82295 q^{94} +(5.68139 + 1.48686i) q^{95} +(13.6284 + 4.96032i) q^{97} +(-7.39053 - 41.9138i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{2} + 9 q^{4} + 3 q^{5} + 9 q^{7} + 6 q^{8} - 9 q^{10} + 9 q^{11} + 6 q^{13} + 24 q^{14} + 9 q^{16} - 24 q^{17} - 12 q^{19} - 6 q^{20} - 9 q^{22} + 6 q^{23} + 9 q^{25} - 12 q^{26} + 42 q^{28}+ \cdots - 27 q^{98}+O(q^{100}) $ 6 * q + 3 * q^2 + 9 * q^4 + 3 * q^5 + 9 * q^7 + 6 * q^8 - 9 * q^10 + 9 * q^11 + 6 * q^13 + 24 * q^14 + 9 * q^16 - 24 * q^17 - 12 * q^19 - 6 * q^20 - 9 * q^22 + 6 * q^23 + 9 * q^25 - 12 * q^26 + 42 * q^28 - 12 * q^29 + 9 * q^32 - 18 * q^34 + 15 * q^35 - 54 * q^37 - 15 * q^38 - 9 * q^40 - 6 * q^41 + 15 * q^43 - 9 * q^44 + 9 * q^46 + 6 * q^47 - 12 * q^49 - 15 * q^50 - 21 * q^52 + 6 * q^53 - 18 * q^55 + 66 * q^56 - 18 * q^58 + 12 * q^59 + 6 * q^61 + 24 * q^62 - 12 * q^64 - 3 * q^65 - 3 * q^67 - 33 * q^68 - 24 * q^71 - 21 * q^73 - 3 * q^74 - 9 * q^76 + 54 * q^77 + 33 * q^79 - 15 * q^80 - 18 * q^82 + 9 * q^85 - 12 * q^86 - 9 * q^88 + 15 * q^89 + 15 * q^91 + 6 * q^92 - 18 * q^94 - 15 * q^95 + 45 * q^97 - 27 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/513\mathbb{Z}\right)^\times$.

$n$	$191$	$325$
$\chi(n)$	$1$	$e\left(\frac{1}{9}\right)$

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 $

$2$	2.37939	+	0.866025i	1.68248	+	0.612372i	0.993646	−	0.112548i	$-0.0359011\pi$
$2$	2.37939	+	0.866025i	1.68248	+	0.612372i	0.688833	+	0.724920i	$0.258123\pi$
$3$		0			0
$3$		0			0
$4$	3.37939	+	2.83564i	1.68969	+	1.41782i
$5$	−1.03209	+	0.866025i	−0.461564	+	0.387298i	−0.843706	−	0.536805i	$-0.819631\pi$
$5$	−1.03209	+	0.866025i	−0.461564	+	0.387298i	0.382142	+	0.924104i	$0.375187\pi$
$6$		0			0
$7$	2.43969	−	4.22567i	0.922117	−	1.59715i	0.125984	−	0.992032i	$-0.459791\pi$
$7$	2.43969	−	4.22567i	0.922117	−	1.59715i	0.796133	−	0.605121i	$-0.206875\pi$
$8$	3.05303	+	5.28801i	1.07941	+	1.86959i
$9$		0			0
$10$	−3.20574	+	1.16679i	−1.01374	+	0.368972i
$11$	2.09240	+	3.62414i	0.630881	+	1.09272i	0.987372	+	0.158419i	$0.0506398\pi$
$11$	2.09240	+	3.62414i	0.630881	+	1.09272i	−0.356491	+	0.934299i	$0.616027\pi$
$12$		0			0
$13$	−0.460637	+	2.61240i	−0.127758	+	0.724550i	0.851874	+	0.523747i	$0.175466\pi$
$13$	−0.460637	+	2.61240i	−0.127758	+	0.724550i	−0.979632	+	0.200803i	$0.935645\pi$
$14$	9.46451	−	7.94166i	2.52950	−	2.12250i
$15$		0			0
$16$	1.15270	+	6.53731i	0.288176	+	1.63433i
$17$	−6.12449	−	2.22913i	−1.48541	−	0.540644i	−0.533170	−	0.846008i	$-0.678999\pi$
$17$	−6.12449	−	2.22913i	−1.48541	−	0.540644i	−0.952236	+	0.305364i	$0.901222\pi$
$18$		0			0
$19$	−2.52094	−	3.55596i	−0.578344	−	0.815793i
$19$	−2.52094	−	3.55596i	−0.578344	−	0.815793i
$20$	−5.94356			−1.32902
$21$		0			0
$22$	1.84002	+	10.4353i	0.392294	+	2.22481i
$23$	1.93969	+	1.62760i	0.404454	+	0.339377i	0.822212	−	0.569181i	$-0.192740\pi$
$23$	1.93969	+	1.62760i	0.404454	+	0.339377i	−0.417758	+	0.908558i	$0.637184\pi$
$24$		0			0
$25$	−0.553033	+	3.13641i	−0.110607	+	0.627282i
$26$	−3.35844	+	5.81699i	−0.658644	+	1.14081i
$27$		0			0
$28$	20.2271	−	7.36208i	3.82257	−	1.39130i
$29$	−2.76604	+	1.00676i	−0.513642	+	0.186950i	−0.585820	−	0.810442i	$-0.699227\pi$
$29$	−2.76604	+	1.00676i	−0.513642	+	0.186950i	0.0721780	+	0.997392i	$0.477005\pi$
$30$		0			0
$31$	3.16637	−	5.48432i	0.568698	−	0.985013i	−0.427998	−	0.903780i	$-0.640781\pi$
$31$	3.16637	−	5.48432i	0.568698	−	0.985013i	0.996695	−	0.0812332i	$-0.0258859\pi$
$32$	−0.798133	+	4.52644i	−0.141091	+	0.800169i
$33$		0			0
$34$	−12.6420	−	10.6079i	−2.16809	−	1.81924i
$35$	1.14156	+	6.47410i	0.192959	+	1.09432i
$36$		0			0
$37$	−5.24123			−0.861653			−0.430826	−	0.902435i	$-0.641778\pi$
$37$	−5.24123			−0.861653			−0.430826	+	0.902435i	$0.641778\pi$
$38$	−2.91875	−	10.6442i	−0.473483	−	1.72672i
$39$		0			0
$40$	−7.73055	−	2.81369i	−1.22231	−	0.444884i
$41$	−1.27584	−	7.23567i	−0.199253	−	1.13002i	−0.906230	−	0.422785i	$-0.861052\pi$
$41$	−1.27584	−	7.23567i	−0.199253	−	1.13002i	0.706976	−	0.707237i	$-0.250059\pi$
$42$		0			0
$43$	−2.51501	+	2.11035i	−0.383536	+	0.321825i	−0.814089	−	0.580740i	$-0.802763\pi$
$43$	−2.51501	+	2.11035i	−0.383536	+	0.321825i	0.430553	+	0.902565i	$0.358319\pi$
$44$	−3.20574	+	18.1806i	−0.483283	+	2.74083i
$45$		0			0
$46$	3.20574	+	5.55250i	0.472660	+	0.818671i
$47$	1.41875	−	0.516382i	0.206946	−	0.0753221i	−0.236467	−	0.971639i	$-0.575990\pi$
$47$	1.41875	−	0.516382i	0.206946	−	0.0753221i	0.443413	+	0.896317i	$0.353767\pi$
$48$		0			0
$49$	−8.40420	−	14.5565i	−1.20060	−	2.07950i
$50$	−4.03209	+	6.98378i	−0.570223	+	0.987656i
$51$		0			0
$52$	−8.96451	+	7.52211i	−1.24315	+	1.04313i
$53$	3.05303	+	2.56180i	0.419366	+	0.351890i	0.827922	−	0.560843i	$-0.189523\pi$
$53$	3.05303	+	2.56180i	0.419366	+	0.351890i	−0.408556	+	0.912733i	$0.633967\pi$
$54$		0			0
$55$	−5.29813	−	1.92836i	−0.714400	−	0.260020i
$56$	29.7939			3.98137
$57$		0			0
$58$	−7.45336			−0.978675
$59$	3.35844	+	1.22237i	0.437232	+	0.159139i	0.551251	−	0.834339i	$-0.314150\pi$
$59$	3.35844	+	1.22237i	0.437232	+	0.159139i	−0.114020	+	0.993478i	$0.536373\pi$
$60$		0			0
$61$	2.28699	+	1.91901i	0.292819	+	0.245704i	0.777348	−	0.629071i	$-0.216565\pi$
$61$	2.28699	+	1.91901i	0.292819	+	0.245704i	−0.484529	+	0.874775i	$0.661009\pi$
$62$	12.2836	−	10.3072i	1.56002	−	1.30901i
$63$		0			0
$64$	0.819078	−	1.41868i	0.102385	−	0.177336i
$65$	−1.78699	−	3.09516i	−0.221649	−	0.383907i
$66$		0			0
$67$	1.37939	−	0.502055i	0.168519	−	0.0613358i	−0.256383	−	0.966575i	$-0.582531\pi$
$67$	1.37939	−	0.502055i	0.168519	−	0.0613358i	0.424902	+	0.905239i	$0.360309\pi$
$68$	−14.3760	−	24.8999i	−1.74334	−	3.01956i
$69$		0			0
$70$	−2.89053	+	16.3930i	−0.345484	+	1.95934i
$71$	−0.343426	+	0.288169i	−0.0407572	+	0.0341993i	−0.662939	−	0.748674i	$-0.730691\pi$
$71$	−0.343426	+	0.288169i	−0.0407572	+	0.0341993i	0.622182	+	0.782873i	$0.286247\pi$
$72$		0			0
$73$	−1.54916	−	8.78574i	−0.181316	−	1.02829i	−0.930598	−	0.366042i	$-0.880713\pi$
$73$	−1.54916	−	8.78574i	−0.181316	−	1.02829i	0.749282	−	0.662251i	$-0.230399\pi$
$74$	−12.4709	−	4.53904i	−1.44971	−	0.527652i
$75$		0			0
$76$	1.56418	−	19.1654i	0.179423	−	2.19843i
$77$	20.4192			2.32699
$78$		0			0
$79$	−1.74170	−	9.87765i	−0.195956	−	1.11132i	−0.911051	−	0.412295i	$-0.864727\pi$
$79$	−1.74170	−	9.87765i	−0.195956	−	1.11132i	0.715094	−	0.699028i	$-0.246384\pi$
$80$	−6.85117	−	5.74881i	−0.765984	−	0.642737i
$81$		0			0
$82$	3.23055	−	18.3214i	0.356755	−	2.02326i
$83$	−2.29813	+	3.98048i	−0.252253	+	0.436915i	−0.964146	−	0.265373i	$-0.914505\pi$
$83$	−2.29813	+	3.98048i	−0.252253	+	0.436915i	0.711893	+	0.702288i	$0.247838\pi$
$84$		0			0
$85$	8.25150	−	3.00330i	0.895000	−	0.325754i
$86$	−7.81180	+	2.84326i	−0.842368	+	0.306597i
$87$		0			0
$88$	−12.7763	+	22.1292i	−1.36196	+	2.35898i
$89$	−3.24035	+	18.3770i	−0.343477	+	1.94795i	−0.0260804	+	0.999660i	$0.508303\pi$
$89$	−3.24035	+	18.3770i	−0.343477	+	1.94795i	−0.317396	+	0.948293i	$0.602809\pi$
$90$		0			0
$91$	9.91534	+	8.31996i	1.03941	+	0.872169i
$92$	1.93969	+	11.0005i	0.202227	+	1.14689i
$93$		0			0
$94$	3.82295			0.394307
$95$	5.68139	+	1.48686i	0.582898	+	0.152549i
$96$		0			0
$97$	13.6284	+	4.96032i	1.38375	+	0.503644i	0.923313	−	0.384049i	$-0.125471\pi$
$97$	13.6284	+	4.96032i	1.38375	+	0.503644i	0.460437	+	0.887692i	$0.347693\pi$
$98$	−7.39053	−	41.9138i	−0.746556	−	4.23393i
$99$		0			0
$100$	−10.7626	+	9.03093i	−1.07626	+	0.903093i
$101$	−1.76217	+	9.99379i	−0.175343	+	0.994419i	0.762405	+	0.647101i	$0.224019\pi$
$101$	−1.76217	+	9.99379i	−0.175343	+	0.994419i	−0.937747	+	0.347318i	$0.887092\pi$
$102$		0			0
$103$	2.12449	+	3.67972i	0.209332	+	0.362573i	0.951504	−	0.307636i	$-0.0995378\pi$
$103$	2.12449	+	3.67972i	0.209332	+	0.362573i	−0.742172	+	0.670209i	$0.766204\pi$
$104$	−15.2208	+	5.53990i	−1.49252	+	0.543232i
$105$		0			0
$106$	5.04576	+	8.73951i	0.490087	+	0.848856i
$107$	5.57532	−	9.65674i	0.538987	−	0.933552i	−0.459972	−	0.887933i	$-0.652141\pi$
$107$	5.57532	−	9.65674i	0.538987	−	0.933552i	0.998959	−	0.0456191i	$-0.0145260\pi$
$108$		0			0
$109$	−7.86618	+	6.60051i	−0.753444	+	0.632214i	−0.936411	−	0.350905i	$-0.885874\pi$
$109$	−7.86618	+	6.60051i	−0.753444	+	0.632214i	0.182968	+	0.983119i	$0.441430\pi$
$110$	−10.9363	−	9.17664i	−1.04273	−	0.874958i
$111$		0			0
$112$	30.4368	+	11.0781i	2.87600	+	1.04678i
$113$	−2.85710			−0.268773			−0.134387	−	0.990929i	$-0.542906\pi$
$113$	−2.85710			−0.268773			−0.134387	+	0.990929i	$0.542906\pi$
$114$		0			0
$115$	−3.41147			−0.318122
$116$	−12.2023	−	4.44129i	−1.13296	−	0.412363i
$117$		0			0
$118$	6.93242	+	5.81699i	0.638181	+	0.535497i
$119$	−24.3614	+	20.4417i	−2.23321	+	1.87388i
$120$		0			0
$121$	−3.25624	+	5.63998i	−0.296022	+	0.512726i
$122$	3.77972	+	6.54666i	0.342199	+	0.592707i
$123$		0			0
$124$	26.2520	−	9.55493i	2.35750	−	0.858058i
$125$	−5.51367	−	9.54996i	−0.493158	−	0.854174i
$126$		0			0
$127$	−2.92127	+	16.5674i	−0.259221	+	1.47012i	0.525779	+	0.850621i	$0.323774\pi$
$127$	−2.92127	+	16.5674i	−0.259221	+	1.47012i	−0.785000	+	0.619495i	$0.787337\pi$
$128$	10.2194	−	8.57510i	0.903277	−	0.757939i
$129$		0			0
$130$	−1.57145	−	8.91215i	−0.137825	−	0.781647i
$131$	−4.30066	−	1.56531i	−0.375750	−	0.136762i	0.147239	−	0.989101i	$-0.452961\pi$
$131$	−4.30066	−	1.56531i	−0.375750	−	0.136762i	−0.522990	+	0.852339i	$0.675183\pi$
$132$		0			0
$133$	−21.1766	+	1.97724i	−1.83625	+	0.171448i
$134$	3.71688			0.321090
$135$		0			0
$136$	−6.91060	−	39.1919i	−0.592579	−	3.36068i
$137$	−15.5556	−	13.0527i	−1.32900	−	1.11516i	−0.984310	−	0.176448i	$-0.943539\pi$
$137$	−15.5556	−	13.0527i	−1.32900	−	1.11516i	−0.344691	−	0.938716i	$-0.612016\pi$
$138$		0			0
$139$	−2.84642	+	16.1428i	−0.241430	+	1.36922i	0.587209	+	0.809435i	$0.300227\pi$
$139$	−2.84642	+	16.1428i	−0.241430	+	1.36922i	−0.828639	+	0.559783i	$0.810885\pi$
$140$	−14.5005	+	25.1155i	−1.22551	+	2.12265i
$141$		0			0
$142$	−1.06670	+	0.388249i	−0.0895158	+	0.0325811i
$143$	−10.4315	+	3.79677i	−0.872329	+	0.317502i
$144$		0			0
$145$	1.98293	−	3.43453i	0.164673	−	0.285222i
$146$	3.92262	−	22.2463i	0.324638	−	1.84111i
$147$		0			0
$148$	−17.7121	−	14.8622i	−1.45593	−	1.22167i
$149$	0.870767	+	4.93837i	0.0713360	+	0.404567i	0.999477	+	0.0323378i	$0.0102952\pi$
$149$	0.870767	+	4.93837i	0.0713360	+	0.404567i	−0.928141	+	0.372229i	$0.878594\pi$
$150$		0			0
$151$	6.04189			0.491682			0.245841	−	0.969310i	$-0.420936\pi$
$151$	6.04189			0.491682			0.245841	+	0.969310i	$0.420936\pi$
$152$	11.1074	−	24.1872i	0.900930	−	1.96184i
$153$		0			0
$154$	48.5852	+	17.6836i	3.91511	+	1.42498i
$155$	1.48158	+	8.40247i	0.119004	+	0.674902i
$156$		0			0
$157$	10.8289	−	9.08651i	0.864239	−	0.725182i	−0.0986383	−	0.995123i	$-0.531449\pi$
$157$	10.8289	−	9.08651i	0.864239	−	0.725182i	0.962877	+	0.269941i	$0.0870042\pi$
$158$	4.41013	−	25.0111i	0.350851	−	1.98978i
$159$		0			0
$160$	−3.09627	−	5.36289i	−0.244781	−	0.423974i
$161$	11.6099	−	4.22567i	0.914991	−	0.333030i
$162$		0			0
$163$	−0.669778	−	1.16009i	−0.0524610	−	0.0908652i	0.838602	−	0.544744i	$-0.183373\pi$
$163$	−0.669778	−	1.16009i	−0.0524610	−	0.0908652i	−0.891063	+	0.453879i	$0.850040\pi$
$164$	16.2062	−	28.0700i	1.26549	−	2.19190i
$165$		0			0
$166$	−8.91534	+	7.48086i	−0.691965	+	0.580628i
$167$	−2.43763	−	2.04542i	−0.188630	−	0.158279i	0.543582	−	0.839356i	$-0.317068\pi$
$167$	−2.43763	−	2.04542i	−0.188630	−	0.158279i	−0.732212	+	0.681077i	$0.761512\pi$
$168$		0			0
$169$	5.60354	+	2.03952i	0.431042	+	0.156886i
$170$	22.2344			1.70530
$171$		0			0
$172$	−14.4834			−1.10435
$173$	20.5005	+	7.46156i	1.55862	+	0.567292i	0.970420	−	0.241423i	$-0.0776140\pi$
$173$	20.5005	+	7.46156i	1.55862	+	0.567292i	0.588202	+	0.808714i	$0.299836\pi$
$174$		0			0
$175$	11.9042	+	9.98881i	0.899873	+	0.755083i
$176$	−21.2802	+	17.8562i	−1.60405	+	1.34596i
$177$		0			0
$178$	−23.6250	+	40.9196i	−1.77077	+	3.06705i
$179$	4.84002	+	8.38316i	0.361760	+	0.626587i	0.988251	−	0.152842i	$-0.0488426\pi$
$179$	4.84002	+	8.38316i	0.361760	+	0.626587i	−0.626490	+	0.779429i	$0.715509\pi$
$180$		0			0
$181$	5.73308	−	2.08667i	0.426136	−	0.155101i	−0.120044	−	0.992769i	$-0.538304\pi$
$181$	5.73308	−	2.08667i	0.426136	−	0.155101i	0.546180	+	0.837668i	$0.316081\pi$
$182$	16.3871	+	28.3833i	1.21469	+	2.10391i
$183$		0			0
$184$	−2.68479	+	15.2262i	−0.197926	+	1.12249i
$185$	5.40941	−	4.53904i	0.397708	−	0.333717i
$186$		0			0
$187$	−4.73618	−	26.8602i	−0.346344	−	1.96421i
$188$	6.25877	+	2.27801i	0.456468	+	0.166141i
$189$		0			0
$190$	12.2306	+	8.45805i	0.887297	+	0.613611i
$191$	−9.04963			−0.654808			−0.327404	−	0.944884i	$-0.606174\pi$
$191$	−9.04963			−0.654808			−0.327404	+	0.944884i	$0.606174\pi$
$192$		0			0
$193$	2.99747	+	16.9995i	0.215763	+	1.22365i	0.879578	+	0.475755i	$0.157825\pi$
$193$	2.99747	+	16.9995i	0.215763	+	1.22365i	−0.663815	+	0.747897i	$0.731064\pi$
$194$	28.1313	+	23.6050i	2.01971	+	1.69474i
$195$		0			0
$196$	12.8760	−	73.0233i	0.919713	−	5.21595i
$197$	−4.47519	+	7.75125i	−0.318844	+	0.552254i	−0.980247	−	0.197777i	$-0.936628\pi$
$197$	−4.47519	+	7.75125i	−0.318844	+	0.552254i	0.661403	+	0.750030i	$0.269961\pi$
$198$		0			0
$199$	−13.9226	+	5.06742i	−0.986948	+	0.359220i	−0.784538	−	0.620081i	$-0.787100\pi$
$199$	−13.9226	+	5.06742i	−0.986948	+	0.359220i	−0.202410	+	0.979301i	$0.564878\pi$
$200$	−18.2738	+	6.65111i	−1.29215	+	0.470305i
$201$		0			0
$202$	−12.8478	+	22.2530i	−0.903965	+	1.56571i
$203$	−2.49407	+	14.1446i	−0.175049	+	0.992755i
$204$		0			0
$205$	7.58306	+	6.36295i	0.529624	+	0.444407i
$206$	1.86824	+	10.5953i	0.130167	+	0.738211i
$207$		0			0
$208$	−17.6091			−1.22097
$209$	7.61246	−	16.5767i	0.526565	−	1.14664i
$210$		0			0
$211$	19.7690	+	7.19534i	1.36096	+	0.495348i	0.916350	−	0.400378i	$-0.131121\pi$
$211$	19.7690	+	7.19534i	1.36096	+	0.495348i	0.444607	+	0.895726i	$0.353343\pi$
$212$	3.05303	+	17.3146i	0.209683	+	1.18917i
$213$		0			0
$214$	21.6288	−	18.1487i	1.47852	−	1.24062i
$215$	0.768104	−	4.35613i	0.0523842	−	0.297086i
$216$		0			0
$217$	−15.4500	−	26.7601i	−1.04881	−	1.81659i
$218$	−24.4329	+	8.89284i	−1.65480	+	0.602299i
$219$		0			0
$220$	−12.4363	−	21.5403i	−0.838454	−	1.45225i
$221$	8.64455	−	14.9728i	0.581496	−	1.00718i
$222$		0			0
$223$	8.75671	−	7.34775i	0.586393	−	0.492042i	−0.300647	−	0.953736i	$-0.597202\pi$
$223$	8.75671	−	7.34775i	0.586393	−	0.492042i	0.887039	+	0.461694i	$0.152758\pi$
$224$	17.1800	+	14.4158i	1.14789	+	0.963194i
$225$		0			0
$226$	−6.79813	−	2.47432i	−0.452205	−	0.164589i
$227$	−14.1070			−0.936315			−0.468157	−	0.883645i	$-0.655082\pi$
$227$	−14.1070			−0.936315			−0.468157	+	0.883645i	$0.655082\pi$
$228$		0			0
$229$	−10.6108			−0.701182			−0.350591	−	0.936529i	$-0.614019\pi$
$229$	−10.6108			−0.701182			−0.350591	+	0.936529i	$0.614019\pi$
$230$	−8.11721	−	2.95442i	−0.535233	−	0.194809i
$231$		0			0
$232$	−13.7686	−	11.5532i	−0.903951	−	0.758505i
$233$	22.0835	−	18.5303i	1.44674	−	1.21396i	0.511824	−	0.859090i	$-0.328970\pi$
$233$	22.0835	−	18.5303i	1.44674	−	1.21396i	0.934916	−	0.354869i	$-0.115474\pi$
$234$		0			0
$235$	−1.01707	+	1.76162i	−0.0663466	+	0.114916i
$236$	7.88326	+	13.6542i	0.513156	+	0.888813i
$237$		0			0
$238$	−75.6682	+	27.5410i	−4.90484	+	1.78522i
$239$	5.22668	+	9.05288i	0.338086	+	0.585582i	0.984073	−	0.177767i	$-0.0568872\pi$
$239$	5.22668	+	9.05288i	0.338086	+	0.585582i	−0.645987	+	0.763349i	$0.723554\pi$
$240$		0			0
$241$	−1.29679	+	7.35446i	−0.0835335	+	0.473742i	0.914130	+	0.405421i	$0.132875\pi$
$241$	−1.29679	+	7.35446i	−0.0835335	+	0.473742i	−0.997663	+	0.0683207i	$0.978236\pi$
$242$	−12.6322	+	10.5997i	−0.812030	+	0.681374i
$243$		0			0
$244$	2.28699	+	12.9702i	0.146409	+	0.830329i
$245$	21.2802	+	7.74535i	1.35954	+	0.494832i
$246$		0			0
$247$	10.4508	−	4.94772i	0.664971	−	0.314816i
$248$	38.6682			2.45543
$249$		0			0
$250$	−4.84864	−	27.4980i	−0.306655	−	1.73913i
$251$	−15.0929	−	12.6644i	−0.952653	−	0.799371i	0.0270893	−	0.999633i	$-0.491376\pi$
$251$	−15.0929	−	12.6644i	−0.952653	−	0.799371i	−0.979742	+	0.200262i	$0.935821\pi$
$252$		0			0
$253$	−1.84002	+	10.4353i	−0.115681	+	0.656061i
$254$	−21.2986	+	36.8903i	−1.33639	+	2.31470i
$255$		0			0
$256$	28.6634	−	10.4326i	1.79146	−	0.652040i
$257$	6.41787	−	2.33591i	0.400336	−	0.145710i	−0.134003	−	0.990981i	$-0.542783\pi$
$257$	6.41787	−	2.33591i	0.400336	−	0.145710i	0.534338	+	0.845271i	$0.320561\pi$
$258$		0			0
$259$	−12.7870	+	22.1477i	−0.794545	+	1.37619i
$260$	2.73783	−	15.5270i	0.169793	−	0.962943i
$261$		0			0
$262$	−8.87733	−	7.44896i	−0.548443	−	0.460198i
$263$	−2.15405	−	12.2162i	−0.132824	−	0.753284i	−0.976350	−	0.216195i	$-0.930635\pi$
$263$	−2.15405	−	12.2162i	−0.132824	−	0.753284i	0.843526	−	0.537089i	$-0.180476\pi$
$264$		0			0
$265$	−5.36959			−0.329851
$266$	−52.0997	−	13.6349i	−3.19444	−	0.836009i
$267$		0			0
$268$	6.08512	+	2.21480i	0.371708	+	0.135291i
$269$	1.35070	+	7.66020i	0.0823536	+	0.467051i	0.997896	+	0.0648299i	$0.0206505\pi$
$269$	1.35070	+	7.66020i	0.0823536	+	0.467051i	−0.915543	+	0.402221i	$0.868238\pi$
$270$		0			0
$271$	−1.95084	+	1.63695i	−0.118505	+	0.0994374i	−0.700114	−	0.714031i	$-0.746868\pi$
$271$	−1.95084	+	1.63695i	−0.118505	+	0.0994374i	0.581609	+	0.813468i	$0.302423\pi$
$272$	7.51279	−	42.6072i	0.455530	−	2.58344i
$273$		0			0
$274$	−25.7087	−	44.5288i	−1.55312	−	2.69008i
$275$	−12.5239	+	4.55834i	−0.755222	+	0.274878i
$276$		0			0
$277$	12.5963	+	21.8174i	0.756836	+	1.31088i	0.944456	+	0.328637i	$0.106589\pi$
$277$	12.5963	+	21.8174i	0.756836	+	1.31088i	−0.187620	+	0.982242i	$0.560077\pi$
$278$	−20.7528	+	35.9450i	−1.24467	+	2.15584i
$279$		0			0
$280$	−30.7499	+	25.8022i	−1.83766	+	1.54198i
$281$	7.03667	+	5.90447i	0.419773	+	0.352231i	0.828077	−	0.560615i	$-0.189435\pi$
$281$	7.03667	+	5.90447i	0.419773	+	0.352231i	−0.408304	+	0.912846i	$0.633880\pi$
$282$		0			0
$283$	6.83022	+	2.48600i	0.406015	+	0.147777i	0.536951	−	0.843614i	$-0.319576\pi$
$283$	6.83022	+	2.48600i	0.406015	+	0.147777i	−0.130936	+	0.991391i	$0.541798\pi$
$284$	−1.97771			−0.117356
$285$		0			0
$286$	−28.1088			−1.66211
$287$	−33.6883	−	12.2615i	−1.98855	−	0.723775i
$288$		0			0
$289$	19.5175	+	16.3772i	1.14809	+	0.963362i
$290$	7.69253	−	6.45480i	0.451721	−	0.379039i
$291$		0			0
$292$	19.6780	−	34.0833i	1.15157	−	1.99457i
$293$	−10.0039	−	17.3272i	−0.584432	−	1.01227i	−0.994946	−	0.100412i	$-0.967984\pi$
$293$	−10.0039	−	17.3272i	−0.584432	−	1.01227i	0.410514	−	0.911854i	$-0.365349\pi$
$294$		0			0
$295$	−4.52481	+	1.64690i	−0.263445	+	0.0958861i
$296$	−16.0016	−	27.7157i	−0.930077	−	1.61094i
$297$		0			0
$298$	−2.20486	+	12.5044i	−0.127724	+	0.724359i
$299$	−5.14543	+	4.31753i	−0.297568	+	0.249689i
$300$		0			0
$301$	2.78177	+	15.7762i	0.160339	+	0.909327i
$302$	14.3760	+	5.23243i	0.827245	+	0.301092i
$303$		0			0
$304$	20.3405	−	20.5792i	1.16661	−	1.18030i
$305$	−4.02229			−0.230316
$306$		0			0
$307$	−0.102196	−	0.579585i	−0.00583266	−	0.0330787i	0.981753	−	0.190163i	$-0.0609017\pi$
$307$	−0.102196	−	0.579585i	−0.00583266	−	0.0330787i	−0.987585	+	0.157084i	$0.949791\pi$
$308$	69.0044	+	57.9016i	3.93189	+	3.29925i
$309$		0			0
$310$	−3.75150	+	21.2758i	−0.213071	+	1.20838i
$311$	3.59240	−	6.22221i	0.203706	−	0.352829i	−0.746014	−	0.665931i	$-0.768035\pi$
$311$	3.59240	−	6.22221i	0.203706	−	0.352829i	0.949720	+	0.313101i	$0.101368\pi$
$312$		0			0
$313$	11.1903	−	4.07294i	0.632514	−	0.230216i	−0.00581126	−	0.999983i	$-0.501850\pi$
$313$	11.1903	−	4.07294i	0.632514	−	0.230216i	0.638325	+	0.769767i	$0.279628\pi$
$314$	33.6352	−	12.2422i	1.89815	−	0.690868i
$315$		0			0
$316$	22.1236	−	38.3192i	1.24455	−	2.15562i
$317$	−0.651826	+	3.69669i	−0.0366102	+	0.207627i	−0.997626	−	0.0688673i	$-0.978062\pi$
$317$	−0.651826	+	3.69669i	−0.0366102	+	0.207627i	0.961016	+	0.276494i	$0.0891726\pi$
$318$		0			0
$319$	−9.43629	−	7.91799i	−0.528331	−	0.443322i
$320$	0.383256	+	2.17355i	0.0214246	+	0.121505i
$321$		0			0
$322$	31.2841			1.74339
$323$	7.51279	+	27.3979i	0.418023	+	1.52446i
$324$		0			0
$325$	−7.93882	−	2.88949i	−0.440366	−	0.160280i
$326$	−0.588993	−	3.34034i	−0.0326213	−	0.185005i
$327$		0			0
$328$	34.3671	−	28.8374i	1.89761	−	1.59228i
$329$	1.27925	−	7.25498i	0.0705272	−	0.399980i
$330$		0			0
$331$	−4.94222	−	8.56017i	−0.271649	−	0.470510i	0.697635	−	0.716453i	$-0.254236\pi$
$331$	−4.94222	−	8.56017i	−0.271649	−	0.470510i	−0.969284	+	0.245943i	$0.920902\pi$
$332$	−19.0535	+	6.93491i	−1.04570	+	0.380602i
$333$		0			0
$334$	−4.02869	−	6.97789i	−0.220440	−	0.381813i
$335$	−0.988856	+	1.71275i	−0.0540270	+	0.0935774i
$336$		0			0
$337$	24.5594	−	20.6078i	1.33784	−	1.12258i	0.355661	−	0.934615i	$-0.384256\pi$
$337$	24.5594	−	20.6078i	1.33784	−	1.12258i	0.982176	−	0.187964i	$-0.0601888\pi$
$338$	11.5667	+	9.70562i	0.629146	+	0.527916i
$339$		0			0
$340$	36.4013	+	13.2490i	1.97414	+	0.718527i
$341$	26.5012			1.43512
$342$		0			0
$343$	−47.8590			−2.58414
$344$	−18.8380	−	6.85646i	−1.01567	−	0.369675i
$345$		0			0
$346$	42.3166	+	35.5079i	2.27495	+	1.90891i
$347$	15.3498	−	12.8800i	0.824022	−	0.691436i	−0.129889	−	0.991529i	$-0.541462\pi$
$347$	15.3498	−	12.8800i	0.824022	−	0.691436i	0.953910	+	0.300092i	$0.0970175\pi$
$348$		0			0
$349$	−1.63563	+	2.83299i	−0.0875532	+	0.151647i	−0.906476	−	0.422257i	$-0.861238\pi$
$349$	−1.63563	+	2.83299i	−0.0875532	+	0.151647i	0.818923	+	0.573903i	$0.194571\pi$
$350$	19.6741	+	34.0766i	1.05163	+	1.82147i
$351$		0			0
$352$	−18.0744	+	6.57856i	−0.963371	+	0.350638i
$353$	−18.6800	−	32.3548i	−0.994238	−	1.72207i	−0.589949	−	0.807440i	$-0.700852\pi$
$353$	−18.6800	−	32.3548i	−0.994238	−	1.72207i	−0.404289	−	0.914631i	$-0.632481\pi$
$354$		0			0
$355$	0.104885	−	0.594831i	0.00556671	−	0.0315704i
$356$	−63.0608	+	52.9143i	−3.34222	+	2.80445i
$357$		0			0
$358$	4.25624	+	24.1384i	0.224949	+	1.27575i
$359$	−11.0522	−	4.02266i	−0.583310	−	0.212308i	0.0334742	−	0.999440i	$-0.489343\pi$
$359$	−11.0522	−	4.02266i	−0.583310	−	0.212308i	−0.616785	+	0.787132i	$0.711565\pi$
$360$		0			0
$361$	−6.28968	+	17.9287i	−0.331036	+	0.943618i
$362$	15.4483			0.811945
$363$		0			0
$364$	9.91534	+	56.2327i	0.519705	+	2.94740i
$365$	9.20755	+	7.72605i	0.481945	+	0.404400i
$366$		0			0
$367$	0.413534	−	2.34527i	0.0215863	−	0.122422i	−0.972110	−	0.234523i	$-0.924647\pi$
$367$	0.413534	−	2.34527i	0.0215863	−	0.122422i	0.993697	+	0.112102i	$0.0357582\pi$
$368$	−8.40420	+	14.5565i	−0.438099	+	0.758810i
$369$		0			0
$370$	16.8020	−	6.11543i	0.873495	−	0.317926i
$371$	18.2738	−	6.65111i	0.948728	−	0.345309i
$372$		0			0
$373$	8.73530	−	15.1300i	0.452297	−	0.783401i	−0.546232	−	0.837634i	$-0.683938\pi$
$373$	8.73530	−	15.1300i	0.452297	−	0.783401i	0.998528	+	0.0542334i	$0.0172715\pi$
$374$	11.9924	−	68.0124i	0.620113	−	3.51684i
$375$		0			0
$376$	7.06212	+	5.92582i	0.364201	+	0.305601i
$377$	−1.35591	−	7.68977i	−0.0698331	−	0.396043i
$378$		0			0
$379$	10.2199			0.524960			0.262480	−	0.964937i	$-0.415460\pi$
$379$	10.2199			0.524960			0.262480	+	0.964937i	$0.415460\pi$
$380$	14.9834	+	21.1351i	0.768632	+	1.08421i
$381$		0			0
$382$	−21.5326	−	7.83721i	−1.10170	−	0.400987i
$383$	4.10994	+	23.3086i	0.210008	+	1.19101i	0.889362	+	0.457204i	$0.151149\pi$
$383$	4.10994	+	23.3086i	0.210008	+	1.19101i	−0.679354	+	0.733811i	$0.737740\pi$
$384$		0			0
$385$	−21.0744	+	17.6836i	−1.07405	+	0.901238i
$386$	−7.58987	+	43.0443i	−0.386314	+	2.19090i
$387$		0			0
$388$	31.9898	+	55.4079i	1.62404	+	2.81291i
$389$	−13.6775	+	4.97821i	−0.693478	+	0.252405i	−0.664624	−	0.747178i	$-0.731408\pi$
$389$	−13.6775	+	4.97821i	−0.693478	+	0.252405i	−0.0288542	+	0.999584i	$0.509186\pi$
$390$		0			0
$391$	−8.25150	−	14.2920i	−0.417296	−	0.722778i
$392$	51.3166	−	88.8830i	2.59188	−	4.48927i
$393$		0			0
$394$	−17.3610	+	14.5676i	−0.874633	+	0.733904i
$395$	10.3519	+	8.68626i	0.520860	+	0.437053i
$396$		0			0
$397$	1.49747	+	0.545036i	0.0751561	+	0.0273546i	0.379325	−	0.925264i	$-0.376156\pi$
$397$	1.49747	+	0.545036i	0.0751561	+	0.0273546i	−0.304169	+	0.952618i	$0.598379\pi$
$398$	−37.5158			−1.88050
$399$		0			0
$400$	−21.1411			−1.05706
$401$	0.714660	+	0.260115i	0.0356884	+	0.0129895i	0.359803	−	0.933028i	$-0.382844\pi$
$401$	0.714660	+	0.260115i	0.0356884	+	0.0129895i	−0.324114	+	0.946018i	$0.605066\pi$
$402$		0			0
$403$	12.8687	+	10.7981i	0.641036	+	0.537893i
$404$	−34.2939	+	28.7760i	−1.70618	+	1.43166i
$405$		0			0
$406$	−18.1839	+	31.4955i	−0.902453	+	1.56309i
$407$	−10.9667	−	18.9949i	−0.543601	−	0.941544i
$408$		0			0
$409$	−7.38326	+	2.68729i	−0.365078	+	0.132878i	−0.518044	−	0.855354i	$-0.673340\pi$
$409$	−7.38326	+	2.68729i	−0.365078	+	0.132878i	0.152966	+	0.988231i	$0.451118\pi$
$410$	12.5326	+	21.7070i	0.618939	+	1.07203i
$411$		0			0
$412$	−3.25490	+	18.4595i	−0.160357	+	0.909432i
$413$	13.3589	−	11.2095i	0.657349	−	0.551581i
$414$		0			0
$415$	−1.07532	−	6.09845i	−0.0527855	−	0.299361i
$416$	−11.4572	−	4.17009i	−0.561737	−	0.204456i
$417$		0			0
$418$	32.4688	−	32.8498i	1.58810	−	1.60674i
$419$	−6.77930			−0.331191			−0.165595	−	0.986194i	$-0.552955\pi$
$419$	−6.77930			−0.331191			−0.165595	+	0.986194i	$0.552955\pi$
$420$		0			0
$421$	−4.10307	−	23.2697i	−0.199972	−	1.13410i	−0.905159	−	0.425074i	$-0.860248\pi$
$421$	−4.10307	−	23.2697i	−0.199972	−	1.13410i	0.705187	−	0.709021i	$-0.250863\pi$
$422$	40.8068	+	34.2410i	1.98644	+	1.66682i
$423$		0			0
$424$	−4.22580	+	23.9657i	−0.205223	+	1.16388i
$425$	10.3785	−	17.9761i	0.503432	−	0.871969i
$426$		0			0
$427$	13.6887	−	4.98227i	0.662441	−	0.241109i
$428$	46.2242	−	16.8242i	2.23433	−	0.813230i
$429$		0			0
$430$	5.60014	−	9.69972i	0.270063	−	0.467762i
$431$	−3.15729	+	17.9059i	−0.152081	+	0.862496i	0.809325	+	0.587362i	$0.199833\pi$
$431$	−3.15729	+	17.9059i	−0.152081	+	0.862496i	−0.961406	+	0.275134i	$0.911278\pi$
$432$		0			0
$433$	−6.87211	−	5.76639i	−0.330253	−	0.277115i	0.462550	−	0.886593i	$-0.346935\pi$
$433$	−6.87211	−	5.76639i	−0.330253	−	0.277115i	−0.792803	+	0.609478i	$0.791379\pi$
$434$	−13.5865	−	77.0527i	−0.652171	−	3.69865i
$435$		0			0
$436$	−45.2995			−2.16945
$437$	0.897804	−	11.0005i	0.0429478	−	0.526227i
$438$		0			0
$439$	0.337496	+	0.122839i	0.0161078	+	0.00586276i	0.350061	−	0.936727i	$-0.386161\pi$
$439$	0.337496	+	0.122839i	0.0161078	+	0.00586276i	−0.333954	+	0.942589i	$0.608383\pi$
$440$	−5.97818	−	33.9039i	−0.284998	−	1.61631i
$441$		0			0
$442$	33.5355	−	28.1397i	1.59512	−	1.33847i
$443$	2.52910	−	14.3432i	0.120161	−	0.681467i	−0.863904	−	0.503657i	$-0.831988\pi$
$443$	2.52910	−	14.3432i	0.120161	−	0.681467i	0.984065	−	0.177810i	$-0.0569012\pi$
$444$		0			0
$445$	−12.5706	−	21.7729i	−0.595902	−	1.03213i
$446$	27.1989	−	9.89960i	1.28791	−	0.468760i
$447$		0			0
$448$	−3.99660	−	6.92231i	−0.188821	−	0.327048i
$449$	−0.0248149	+	0.0429807i	−0.00117109	+	0.00202839i	−0.866610	−	0.498985i	$-0.833706\pi$
$449$	−0.0248149	+	0.0429807i	−0.00117109	+	0.00202839i	0.865439	+	0.501014i	$0.167039\pi$
$450$		0			0
$451$	23.5535	−	19.7637i	1.10909	−	0.930638i
$452$	−9.65523	−	8.10170i	−0.454144	−	0.381072i
$453$		0			0
$454$	−33.5660	−	12.2170i	−1.57533	−	0.573373i
$455$	−17.4388			−0.817544
$456$		0			0
$457$	35.5303			1.66204			0.831019	−	0.556243i	$-0.187758\pi$
$457$	35.5303			1.66204			0.831019	+	0.556243i	$0.187758\pi$
$458$	−25.2472	−	9.18923i	−1.17972	−	0.429385i
$459$		0			0
$460$	−11.5287	−	9.67372i	−0.537528	−	0.451039i
$461$	−8.85188	+	7.42761i	−0.412273	+	0.345938i	−0.825215	−	0.564819i	$-0.808946\pi$
$461$	−8.85188	+	7.42761i	−0.412273	+	0.345938i	0.412941	+	0.910758i	$0.364501\pi$
$462$		0			0
$463$	6.76739	−	11.7215i	0.314507	−	0.544742i	−0.664825	−	0.746999i	$-0.731494\pi$
$463$	6.76739	−	11.7215i	0.314507	−	0.544742i	0.979333	+	0.202256i	$0.0648274\pi$
$464$	−9.76991	−	16.9220i	−0.453557	−	0.785584i
$465$		0			0
$466$	68.5929	−	24.9658i	3.17751	−	1.15652i
$467$	12.4697	+	21.5982i	0.577030	+	0.999445i	0.995818	+	0.0913611i	$0.0291217\pi$
$467$	12.4697	+	21.5982i	0.577030	+	0.999445i	−0.418788	+	0.908084i	$0.637545\pi$
$468$		0			0
$469$	1.24376	−	7.05369i	0.0574313	−	0.325709i
$470$	−3.94562	+	3.31077i	−0.181998	+	0.152714i
$471$		0			0
$472$	3.78952	+	21.4914i	0.174427	+	0.989222i
$473$	−12.9106	−	4.69907i	−0.593630	−	0.216064i
$474$		0			0
$475$	12.5471	−	5.94015i	0.575701	−	0.272553i
$476$	−140.292			−6.43027
$477$		0			0
$478$	4.59627	+	26.0667i	0.210228	+	1.19226i
$479$	−5.19846	−	4.36203i	−0.237524	−	0.199306i	0.516254	−	0.856436i	$-0.327326\pi$
$479$	−5.19846	−	4.36203i	−0.237524	−	0.199306i	−0.753778	+	0.657129i	$0.771771\pi$
$480$		0			0
$481$	2.41431	−	13.6922i	0.110083	−	0.624311i
$482$	−9.45471	+	16.3760i	−0.430650	+	0.745908i
$483$		0			0
$484$	−26.9971	+	9.82613i	−1.22714	+	0.446642i
$485$	−18.3614	+	6.68302i	−0.833750	+	0.303460i
$486$		0			0
$487$	−16.8097	+	29.1153i	−0.761722	+	1.31934i	0.180240	+	0.983623i	$0.442313\pi$
$487$	−16.8097	+	29.1153i	−0.761722	+	1.31934i	−0.941962	+	0.335719i	$0.891021\pi$
$488$	−3.16550	+	17.9524i	−0.143295	+	0.812668i
$489$		0			0
$490$	43.9261	+	36.8584i	1.98438	+	1.66509i
$491$	−4.97612	−	28.2210i	−0.224569	−	1.27359i	−0.863507	−	0.504336i	$-0.831737\pi$
$491$	−4.97612	−	28.2210i	−0.224569	−	1.27359i	0.638938	−	0.769258i	$-0.279374\pi$
$492$		0			0
$493$	19.1848			0.864040
$494$	29.1514	−	2.72183i	1.31158	−	0.122461i
$495$		0			0
$496$	39.5026	+	14.3778i	1.77372	+	0.645581i
$497$	0.379852	+	2.15425i	0.0170387	+	0.0966312i
$498$		0			0
$499$	−32.2859	+	27.0911i	−1.44531	+	1.21276i	−0.509401	+	0.860529i	$0.670133\pi$
$499$	−32.2859	+	27.0911i	−1.44531	+	1.21276i	−0.935912	+	0.352233i	$0.885422\pi$
$500$	8.44743	−	47.9078i	0.377781	−	2.14250i
$501$		0			0
$502$	−24.9440	−	43.2043i	−1.11331	−	1.92830i
$503$	−17.9804	+	6.54433i	−0.801706	+	0.291797i	−0.710193	−	0.704007i	$-0.751393\pi$
$503$	−17.9804	+	6.54433i	−0.801706	+	0.291797i	−0.0915130	+	0.995804i	$0.529170\pi$
$504$		0			0
$505$	−6.83615	−	11.8406i	−0.304205	−	0.526898i
$506$	−13.4153	+	23.2361i	−0.596385	+	1.03297i
$507$		0			0
$508$	−56.8512	+	47.7038i	−2.52237	+	2.11652i
$509$	−22.2690	−	18.6859i	−0.987058	−	0.828240i	−0.00191863	−	0.999998i	$-0.500611\pi$
$509$	−22.2690	−	18.6859i	−0.987058	−	0.828240i	−0.985139	+	0.171758i	$0.945055\pi$
$510$		0			0
$511$	−40.9051	−	14.8883i	−1.80954	−	0.658617i
$512$	50.5553			2.23425
$513$		0			0
$514$	17.2935			0.762786
$515$	−5.37939	−	1.95794i	−0.237044	−	0.0862770i
$516$		0			0
$517$	4.84002	+	4.06126i	0.212864	+	0.178614i
$518$	−49.6057	+	41.6241i	−2.17955	+	1.82886i
$519$		0			0
$520$	10.9115	−	18.8992i	0.478500	−	0.828786i
$521$	3.48293	+	6.03260i	0.152590	+	0.264293i	0.932179	−	0.361998i	$-0.117905\pi$
$521$	3.48293	+	6.03260i	0.152590	+	0.264293i	−0.779589	+	0.626291i	$0.784572\pi$
$522$		0			0
$523$	15.8148	−	5.75612i	0.691533	−	0.251697i	0.0277414	−	0.999615i	$-0.491169\pi$
$523$	15.8148	−	5.75612i	0.691533	−	0.251697i	0.663791	+	0.747918i	$0.268946\pi$
$524$	−10.0949	−	17.4849i	−0.440999	−	0.763832i
$525$		0			0
$526$	5.45424	−	30.9325i	0.237816	−	1.34872i
$527$	−31.6177	+	26.5304i	−1.37729	+	1.15568i
$528$		0			0
$529$	−2.88057	−	16.3365i	−0.125242	−	0.710283i
$530$	−12.7763	−	4.65020i	−0.554968	−	0.201992i
$531$		0			0
$532$	−77.1708	−	53.3675i	−3.34578	−	2.31377i
$533$	19.4902			0.844214
$534$		0			0
$535$	2.60876	+	14.7950i	0.112786	+	0.639643i
$536$	6.86618	+	5.76141i	0.296574	+	0.248855i
$537$		0			0
$538$	−3.42009	+	19.3963i	−0.147451	+	0.836234i
$539$	35.1698	−	60.9159i	1.51487	−	2.62384i
$540$		0			0
$541$	14.1395	−	5.14636i	0.607905	−	0.221259i	−0.0196816	−	0.999806i	$-0.506265\pi$
$541$	14.1395	−	5.14636i	0.607905	−	0.221259i	0.627586	+	0.778547i	$0.284043\pi$
$542$	−6.05943	+	2.20545i	−0.260275	+	0.0947323i
$543$		0			0
$544$	14.9782	−	25.9430i	0.642184	−	1.11230i
$545$	2.40239	−	13.6246i	0.102907	−	0.583615i
$546$		0			0
$547$	−27.6313	−	23.1855i	−1.18143	−	0.991338i	−0.999968	−	0.00794061i	$-0.997472\pi$
$547$	−27.6313	−	23.1855i	−1.18143	−	0.991338i	−0.181463	−	0.983398i	$-0.558083\pi$
$548$	−15.5556	−	88.2200i	−0.664501	−	3.76857i
$549$		0			0
$550$	−33.7469			−1.43897
$551$	10.5530	+	7.29796i	0.449574	+	0.310903i
$552$		0			0
$553$	−45.9889	−	16.7386i	−1.95565	−	0.711797i
$554$	11.0770	+	62.8206i	0.470615	+	2.66899i
$555$		0			0
$556$	−55.3945	+	46.4815i	−2.34925	+	1.97125i
$557$	5.90151	−	33.4691i	0.250055	−	1.41813i	−0.558398	−	0.829573i	$-0.688584\pi$
$557$	5.90151	−	33.4691i	0.250055	−	1.41813i	0.808454	−	0.588560i	$-0.200305\pi$
$558$		0			0
$559$	−4.35457	−	7.54234i	−0.184179	−	0.319007i
$560$	−41.0073	+	14.9254i	−1.73288	+	0.630715i
$561$		0			0
$562$	11.6295	+	20.1429i	0.490562	+	0.849679i
$563$	−9.14290	+	15.8360i	−0.385327	+	0.667407i	−0.991815	−	0.127687i	$-0.959245\pi$
$563$	−9.14290	+	15.8360i	−0.385327	+	0.667407i	0.606487	+	0.795093i	$0.292578\pi$
$564$		0			0
$565$	2.94878	−	2.47432i	0.124056	−	0.104095i
$566$	14.0988	+	11.8303i	0.592616	+	0.497264i
$567$		0			0
$568$	−2.57233	−	0.936251i	−0.107933	−	0.0392842i
$569$	18.5107			0.776010			0.388005	−	0.921657i	$-0.373164\pi$
$569$	18.5107			0.776010			0.388005	+	0.921657i	$0.373164\pi$
$570$		0			0
$571$	−1.28136			−0.0536234			−0.0268117	−	0.999641i	$-0.508535\pi$
$571$	−1.28136			−0.0536234			−0.0268117	+	0.999641i	$0.508535\pi$
$572$	−46.0185	−	16.7494i	−1.92413	−	0.700326i
$573$		0			0
$574$	−69.5385	−	58.3498i	−2.90248	−	2.43547i
$575$	−6.17752	+	5.18355i	−0.257620	+	0.216169i
$576$		0			0
$577$	−1.08466	+	1.87868i	−0.0451548	+	0.0782104i	−0.887719	−	0.460385i	$-0.847711\pi$
$577$	−1.08466	+	1.87868i	−0.0451548	+	0.0782104i	0.842565	+	0.538595i	$0.181045\pi$
$578$	32.2567	+	55.8703i	1.34170	+	2.32390i
$579$		0			0
$580$	16.4402	−	5.98373i	0.682640	−	0.248461i
$581$	11.2135	+	19.4223i	0.465213	+	0.805773i
$582$		0			0
$583$	−2.89615	+	16.4249i	−0.119946	+	0.680250i
$584$	41.7294	−	35.0151i	1.72678	−	1.44894i
$585$		0			0
$586$	−8.79726	−	49.8917i	−0.363411	−	2.06101i
$587$	31.9111	+	11.6147i	1.31711	+	0.479389i	0.902531	−	0.430624i	$-0.141707\pi$
$587$	31.9111	+	11.6147i	1.31711	+	0.479389i	0.414579	+	0.910013i	$0.363929\pi$
$588$		0			0
$589$	−27.4843	+	2.56617i	−1.13247	+	0.105737i
$590$	−12.1925			−0.501959
$591$		0			0
$592$	−6.04158	−	34.2635i	−0.248308	−	1.40822i
$593$	−21.8576	−	18.3407i	−0.897583	−	0.753161i	0.0721338	−	0.997395i	$-0.477019\pi$
$593$	−21.8576	−	18.3407i	−0.897583	−	0.753161i	−0.969716	+	0.244234i	$0.921464\pi$
$594$		0			0
$595$	7.44016	−	42.1952i	0.305017	−	1.72984i
$596$	−11.0608	+	19.1578i	−0.453067	+	0.784735i
$597$		0			0
$598$	−15.9820	+	5.81699i	−0.653555	+	0.237874i
$599$	13.7618	−	5.00887i	0.562290	−	0.204657i	−0.0452084	−	0.998978i	$-0.514395\pi$
$599$	13.7618	−	5.00887i	0.562290	−	0.204657i	0.607499	+	0.794321i	$0.292173\pi$
$600$		0			0
$601$	−11.8366	+	20.5016i	−0.482826	+	0.836279i	−0.999806	−	0.0197189i	$-0.993723\pi$
$601$	−11.8366	+	20.5016i	−0.482826	+	0.836279i	0.516980	+	0.855998i	$0.327056\pi$
$602$	−7.04370	+	39.9468i	−0.287080	+	1.62811i
$603$		0			0
$604$	20.4179	+	17.1326i	0.830791	+	0.697117i
$605$	−1.52363	−	8.64095i	−0.0619445	−	0.351305i
$606$		0			0
$607$	39.9745			1.62252			0.811258	−	0.584688i	$-0.198783\pi$
$607$	39.9745			1.62252			0.811258	+	0.584688i	$0.198783\pi$
$608$	18.1079	−	8.57277i	0.734371	−	0.347672i
$609$		0			0
$610$	−9.57057	−	3.48340i	−0.387501	−	0.141039i
$611$	0.695470	+	3.94421i	0.0281357	+	0.159566i
$612$		0			0
$613$	−15.1518	+	12.7139i	−0.611977	+	0.513509i	−0.895270	−	0.445524i	$-0.853017\pi$
$613$	−15.1518	+	12.7139i	−0.611977	+	0.513509i	0.283293	+	0.959033i	$0.408573\pi$
$614$	0.258770	−	1.46756i	0.0104431	−	0.0592259i
$615$		0			0
$616$	62.3405	+	107.977i	2.51177	+	4.35052i
$617$	0.881607	−	0.320879i	0.0354922	−	0.0129181i	−0.324213	−	0.945984i	$-0.605099\pi$
$617$	0.881607	−	0.320879i	0.0354922	−	0.0129181i	0.359705	+	0.933066i	$0.382877\pi$
$618$		0			0
$619$	0.750152	+	1.29930i	0.0301512	+	0.0522234i	0.880707	−	0.473661i	$-0.157068\pi$
$619$	0.750152	+	1.29930i	0.0301512	+	0.0522234i	−0.850556	+	0.525884i	$0.823734\pi$
$620$	−18.8195	+	32.5964i	−0.755811	+	1.30910i
$621$		0			0
$622$	13.9363	−	11.6939i	0.558794	−	0.468884i
$623$	69.7495	+	58.5268i	2.79445	+	2.34483i
$624$		0			0
$625$	−1.00253	−	0.364890i	−0.0401010	−	0.0145956i
$626$	30.1533			1.20517
$627$		0			0
$628$	62.3610			2.48848
$629$	32.0998	+	11.6834i	1.27990	+	0.465847i
$630$		0			0
$631$	−25.1989	−	21.1444i	−1.00315	−	0.841746i	−0.0157353	−	0.999876i	$-0.505009\pi$
$631$	−25.1989	−	21.1444i	−1.00315	−	0.841746i	−0.987418	+	0.158130i	$0.949453\pi$
$632$	46.9156	−	39.3669i	1.86620	−	1.56593i
$633$		0			0
$634$	−4.75237	+	8.23135i	−0.188741	+	0.326909i
$635$	−11.3327	−	19.6289i	−0.449726	−	0.778949i
$636$		0			0
$637$	41.8987	−	15.2499i	1.66009	−	0.604223i
$638$	−15.5954	−	27.0120i	−0.617427	−	1.06942i
$639$		0			0
$640$	−3.12108	+	17.7005i	−0.123372	+	0.699675i
$641$	−13.4436	+	11.2805i	−0.530989	+	0.445553i	−0.868443	−	0.495790i	$-0.834879\pi$
$641$	−13.4436	+	11.2805i	−0.530989	+	0.445553i	0.337454	+	0.941342i	$0.390434\pi$
$642$		0			0
$643$	3.59286	+	20.3761i	0.141689	+	0.803556i	0.969966	+	0.243239i	$0.0782099\pi$
$643$	3.59286	+	20.3761i	0.141689	+	0.803556i	−0.828278	+	0.560318i	$0.810679\pi$
$644$	51.2169	+	18.6414i	2.01823	+	0.734576i
$645$		0			0
$646$	−5.85147	+	71.6965i	−0.230223	+	2.82086i
$647$	−36.8462			−1.44857			−0.724286	−	0.689499i	$-0.757831\pi$
$647$	−36.8462			−1.44857			−0.724286	+	0.689499i	$0.757831\pi$
$648$		0			0
$649$	2.59714	+	14.7291i	0.101947	+	0.578169i
$650$	−16.3871	−	13.7504i	−0.642756	−	0.539336i
$651$		0			0
$652$	1.02616	−	5.81964i	0.0401875	−	0.227915i
$653$	−11.4278	+	19.7936i	−0.447206	+	0.774583i	−0.998203	−	0.0599241i	$-0.980914\pi$
$653$	−11.4278	+	19.7936i	−0.447206	+	0.774583i	0.550997	+	0.834507i	$0.314247\pi$
$654$		0			0
$655$	5.79426	−	2.10894i	0.226401	−	0.0824031i
$656$	45.8312	−	16.6812i	1.78941	−	0.651291i
$657$		0			0
$658$	9.32682	−	16.1545i	0.363597	−	0.629769i
$659$	1.81299	−	10.2820i	0.0706239	−	0.400528i	−0.928919	−	0.370284i	$-0.879260\pi$
$659$	1.81299	−	10.2820i	0.0706239	−	0.400528i	0.999543	−	0.0302442i	$-0.00962849\pi$
$660$		0			0
$661$	−18.9322	−	15.8860i	−0.736376	−	0.617893i	0.195486	−	0.980707i	$-0.437372\pi$
$661$	−18.9322	−	15.8860i	−0.736376	−	0.617893i	−0.931862	+	0.362814i	$0.881816\pi$
$662$	−4.34611	−	24.6480i	−0.168917	−	0.957973i
$663$		0			0
$664$	−28.0651			−1.08914
$665$	20.1438	−	20.3802i	0.781144	−	0.790310i
$666$		0			0
$667$	−7.00387	−	2.54920i	−0.271191	−	0.0987054i
$668$	−2.43763	−	13.8245i	−0.0943149	−	0.534886i
$669$		0			0
$670$	−3.83615	+	3.21891i	−0.148203	+	0.124357i
$671$	−2.16947	+	12.3037i	−0.0837516	+	0.474979i
$672$		0			0
$673$	−10.8910	−	18.8638i	−0.419817	−	0.727144i	0.576104	−	0.817377i	$-0.304572\pi$
$673$	−10.8910	−	18.8638i	−0.419817	−	0.727144i	−0.995921	+	0.0902321i	$0.971239\pi$
$674$	76.2832	−	27.7648i	2.93832	−	1.06946i
$675$		0			0
$676$	13.1532	+	22.7820i	0.505891	+	0.876229i
$677$	6.36484	−	11.0242i	0.244621	−	0.423695i	−0.717404	−	0.696657i	$-0.754670\pi$
$677$	6.36484	−	11.0242i	0.244621	−	0.423695i	0.962025	+	0.272962i	$0.0880033\pi$
$678$		0			0
$679$	54.2097	−	45.4873i	2.08038	−	1.74564i
$680$	41.0736	+	34.4648i	1.57510	+	1.32167i
$681$		0			0
$682$	63.0567	+	22.9507i	2.41456	+	0.878829i
$683$	0.706452			0.0270316			0.0135158	−	0.999909i	$-0.495698\pi$
$683$	0.706452			0.0270316			0.0135158	+	0.999909i	$0.495698\pi$
$684$		0			0
$685$	27.3587			1.04532
$686$	−113.875	−	41.4471i	−4.34776	−	1.58246i
$687$		0			0
$688$	−16.6951	−	14.0088i	−0.636493	−	0.534081i
$689$	−8.09879	+	6.79569i	−0.308539	+	0.258895i
$690$		0			0
$691$	2.44650	−	4.23746i	0.0930692	−	0.161201i	−0.815732	−	0.578430i	$-0.803666\pi$
$691$	2.44650	−	4.23746i	0.0930692	−	0.161201i	0.908801	+	0.417229i	$0.136999\pi$
$692$	48.1207	+	83.3474i	1.82927	+	3.16839i
$693$		0			0
$694$	47.6776	−	17.3532i	1.80982	−	0.658719i
$695$	−11.0424	−	19.1259i	−0.418860	−	0.725488i
$696$		0			0
$697$	−8.31537	+	47.1588i	−0.314967	+	1.78627i
$698$	−6.34524	+	5.32429i	−0.240171	+	0.201527i
$699$		0			0
$700$	11.9042	+	67.5121i	0.449936	+	2.55172i
$701$	−43.6391	−	15.8833i	−1.64823	−	0.599905i	−0.659777	−	0.751461i	$-0.729349\pi$
$701$	−43.6391	−	15.8833i	−1.64823	−	0.599905i	−0.988449	+	0.151556i	$0.951572\pi$
$702$		0			0
$703$	13.2128	+	18.6376i	0.498332	+	0.702930i
$704$	6.85534			0.258370
$705$		0			0
$706$	−16.4270	−	93.1619i	−0.618237	−	3.50619i
$707$	37.9313	+	31.8281i	1.42655	+	1.19702i
$708$		0			0
$709$	5.14109	−	29.1566i	0.193078	−	1.09500i	−0.722052	−	0.691839i	$-0.756801\pi$
$709$	5.14109	−	29.1566i	0.193078	−	1.09500i	0.915130	−	0.403160i	$-0.132088\pi$
$710$	0.764700	−	1.32450i	0.0286987	−	0.0497076i
$711$		0			0
$712$	−107.070	+	38.9704i	−4.01263	+	1.46048i
$713$	15.0680	−	5.48432i	0.564303	−	0.205389i
$714$		0			0
$715$	7.47818	−	12.9526i	0.279668	−	0.484399i
$716$	−7.41534	+	42.0545i	−0.277124	+	1.57165i
$717$		0			0
$718$	−22.8136	−	19.1429i	−0.851397	−	0.714407i
$719$	−0.820727	−	4.65457i	−0.0306079	−	0.173586i	0.965672	−	0.259766i	$-0.0836453\pi$
$719$	−0.820727	−	4.65457i	−0.0306079	−	0.173586i	−0.996280	+	0.0861793i	$0.972534\pi$
$720$		0			0
$721$	20.7324			0.772114
$722$	−30.4923	+	37.2124i	−1.13481	+	1.38490i
$723$		0			0
$724$	25.2913	+	9.20529i	0.939945	+	0.342112i
$725$	−1.62789	−	9.23222i	−0.0604583	−	0.342876i
$726$		0			0
$727$	−28.9636	+	24.3034i	−1.07420	+	0.901362i	−0.995427	−	0.0955303i	$-0.969545\pi$
$727$	−28.9636	+	24.3034i	−1.07420	+	0.901362i	−0.0787751	+	0.996892i	$0.525101\pi$
$728$	−13.7242	+	77.8336i	−0.508651	+	2.88470i
$729$		0			0
$730$	15.2173	+	26.3572i	0.563219	+	0.975524i
$731$	20.1074	−	7.31850i	0.743699	−	0.270684i
$732$		0			0
$733$	−11.2010	−	19.4007i	−0.413718	−	0.716581i	0.581575	−	0.813493i	$-0.302437\pi$
$733$	−11.2010	−	19.4007i	−0.413718	−	0.716581i	−0.995293	+	0.0969123i	$0.969103\pi$
$734$	3.01501	−	5.22216i	0.111286	−	0.192753i
$735$		0			0
$736$	−8.91534	+	7.48086i	−0.328624	+	0.275748i
$737$	4.70574	+	3.94858i	0.173338	+	0.145448i
$738$		0			0
$739$	−19.4979	−	7.09667i	−0.717243	−	0.261055i	−0.0424883	−	0.999097i	$-0.513529\pi$
$739$	−19.4979	−	7.09667i	−0.717243	−	0.261055i	−0.674755	+	0.738042i	$0.735751\pi$
$740$	31.1516			1.14515
$741$		0			0
$742$	49.2404			1.80767
$743$	−36.6190	−	13.3282i	−1.34342	−	0.488965i	−0.432533	−	0.901618i	$-0.642380\pi$
$743$	−36.6190	−	13.3282i	−1.34342	−	0.488965i	−0.910889	+	0.412653i	$0.864602\pi$
$744$		0			0
$745$	−5.17546	−	4.34273i	−0.189614	−	0.159105i
$746$	33.8876	−	28.4351i	1.24071	−	1.04108i
$747$		0			0
$748$	60.1605	−	104.201i	2.19969	−	3.80997i
$749$	−27.2041	−	47.1190i	−0.994018	−	1.72169i
$750$		0			0
$751$	28.9206	−	10.5262i	1.05533	−	0.384107i	0.244656	−	0.969610i	$-0.421325\pi$
$751$	28.9206	−	10.5262i	1.05533	−	0.384107i	0.810670	+	0.585503i	$0.199103\pi$
$752$	5.01114	+	8.67956i	0.182738	+	0.316511i
$753$		0			0
$754$	3.43330	−	19.4712i	0.125033	−	0.709099i
$755$	−6.23577	+	5.23243i	−0.226943	+	0.190428i
$756$		0			0
$757$	−0.136812	−	0.775897i	−0.00497250	−	0.0282005i	0.982221	−	0.187731i	$-0.0601132\pi$
$757$	−0.136812	−	0.775897i	−0.00497250	−	0.0282005i	−0.987193	+	0.159530i	$0.949002\pi$
$758$	24.3170	+	8.85067i	0.883234	+	0.321471i
$759$		0			0
$760$	9.48293	+	34.5827i	0.343982	+	1.25445i
$761$	−19.8384			−0.719143			−0.359571	−	0.933118i	$-0.617077\pi$
$761$	−19.8384			−0.719143			−0.359571	+	0.933118i	$0.617077\pi$
$762$		0			0
$763$	8.70052	+	49.3431i	0.314980	+	1.78634i
$764$	−30.5822	−	25.6615i	−1.10642	−	0.928401i
$765$		0			0
$766$	−10.4067	+	59.0195i	−0.376010	+	2.13246i
$767$	−4.74035	+	8.21053i	−0.171164	+	0.296465i
$768$		0			0
$769$	5.31180	−	1.93334i	0.191549	−	0.0697180i	−0.244465	−	0.969658i	$-0.578612\pi$
$769$	5.31180	−	1.93334i	0.191549	−	0.0697180i	0.436013	+	0.899940i	$0.356390\pi$
$770$	−65.4586	+	23.8250i	−2.35897	+	0.858593i
$771$		0			0
$772$	−38.0749	+	65.9477i	−1.37035	+	2.37351i
$773$	5.05216	−	28.6522i	0.181713	−	1.03055i	−0.748392	−	0.663256i	$-0.769174\pi$
$773$	5.05216	−	28.6522i	0.181713	−	1.03055i	0.930106	−	0.367292i	$-0.119715\pi$
$774$		0			0
$775$	15.4500	+	12.9641i	0.554979	+	0.465683i
$776$	15.3776	+	87.2109i	0.552025	+	3.13069i
$777$		0			0
$778$	−36.8553			−1.32133
$779$	−22.5134	+	22.7776i	−0.806627	+	0.816092i
$780$		0			0
$781$	−1.76295	−	0.641660i	−0.0630832	−	0.0229604i
$782$	−7.25624	−	41.1522i	−0.259483	−	1.47160i
$783$		0			0
$784$	85.4728	−	71.7202i	3.05260	−	2.56143i
$785$	−3.30722	+	18.7562i	−0.118040	+	0.669436i
$786$		0			0
$787$	10.9978	+	19.0487i	0.392028	+	0.679013i	0.992717	−	0.120470i	$-0.0384401\pi$
$787$	10.9978	+	19.0487i	0.392028	+	0.679013i	−0.600689	+	0.799483i	$0.705107\pi$
$788$	−37.1031	+	13.5044i	−1.32174	+	0.481076i
$789$		0			0
$790$	17.1086	+	29.6330i	0.608696	+	1.05429i
$791$	−6.97044	+	12.0732i	−0.247840	+	0.429272i
$792$		0			0
$793$	−6.06670	+	5.09057i	−0.215435	+	0.180771i
$794$	3.09105	+	2.59370i	0.109697	+	0.0920470i
$795$		0			0
$796$	−61.4193	−	22.3548i	−2.17695	−	0.792344i
$797$	−45.5280			−1.61268			−0.806342	−	0.591450i	$-0.798556\pi$
$797$	−45.5280			−1.61268			−0.806342	+	0.591450i	$0.798556\pi$
$798$		0			0
$799$	−9.84018			−0.348121
$800$	−13.7554	−	5.00654i	−0.486326	−	0.177008i
$801$		0			0
$802$	1.47519	+	1.23783i	0.0520906	+	0.0437092i
$803$	28.5993	−	23.9976i	1.00925	−	0.846858i
$804$		0			0
$805$	−8.32295	+	14.4158i	−0.293345	+	0.508089i
$806$	21.2682	+	36.8375i	0.749139	+	1.29755i
$807$		0			0
$808$	−58.2272	+	21.1930i	−2.04843	+	0.745566i
$809$	10.2694	+	17.7872i	0.361055	+	0.625365i	0.988135	−	0.153590i	$-0.0490835\pi$
$809$	10.2694	+	17.7872i	0.361055	+	0.625365i	−0.627080	+	0.778955i	$0.715750\pi$
$810$		0			0
$811$	1.67499	−	9.49935i	0.0588169	−	0.333567i	−0.941174	−	0.337924i	$-0.890275\pi$
$811$	1.67499	−	9.49935i	0.0588169	−	0.333567i	0.999991	+	0.00435609i	$0.00138659\pi$
$812$	−48.5374	+	40.7277i	−1.70333	+	1.42926i
$813$		0			0
$814$	−9.64398	−	54.6937i	−0.338021	−	1.91701i
$815$	1.69594	+	0.617271i	0.0594061	+	0.0216220i
$816$		0			0
$817$	13.8445	+	3.62322i	0.484359	+	0.126760i
$818$	−19.8949			−0.695608
$819$		0			0
$820$	7.58306	+	43.0057i	0.264812	+	1.50182i
$821$	5.39621	+	4.52796i	0.188329	+	0.158027i	0.732077	−	0.681221i	$-0.238551\pi$
$821$	5.39621	+	4.52796i	0.188329	+	0.158027i	−0.543748	+	0.839248i	$0.682995\pi$
$822$		0			0
$823$	−5.46316	+	30.9831i	−0.190434	+	1.08000i	0.728339	+	0.685217i	$0.240293\pi$
$823$	−5.46316	+	30.9831i	−0.190434	+	1.08000i	−0.918773	+	0.394787i	$0.870818\pi$
$824$	−12.9722	+	22.4686i	−0.451910	+	0.782731i
$825$		0			0
$826$	41.4937	−	15.1025i	1.44375	−	0.525482i
$827$	34.7790	−	12.6585i	1.20938	−	0.440180i	0.342894	−	0.939374i	$-0.388593\pi$
$827$	34.7790	−	12.6585i	1.20938	−	0.440180i	0.866490	+	0.499194i	$0.166371\pi$
$828$		0			0
$829$	−12.2653	+	21.2442i	−0.425992	+	0.737841i	−0.996513	−	0.0834430i	$-0.973408\pi$
$829$	−12.2653	+	21.2442i	−0.425992	+	0.737841i	0.570520	+	0.821284i	$0.306742\pi$
$830$	2.72281	−	15.4418i	0.0945102	−	0.535994i
$831$		0			0
$832$	3.32888	+	2.79326i	0.115408	+	0.0968389i
$833$	19.0231	+	107.885i	0.659110	+	3.73800i
$834$		0			0
$835$	4.28724			0.148366
$836$	72.7311	−	34.4329i	2.51546	−	1.19089i
$837$		0			0
$838$	−16.1306	−	5.87105i	−0.557222	−	0.202812i
$839$	−3.14527	−	17.8377i	−0.108587	−	0.615826i	−0.989727	−	0.142971i	$-0.954335\pi$
$839$	−3.14527	−	17.8377i	−0.108587	−	0.615826i	0.881140	−	0.472855i	$-0.156777\pi$
$840$		0			0
$841$	−15.5778	+	13.0714i	−0.537167	+	0.450737i
$842$	10.3893	−	58.9209i	0.358041	−	2.03055i
$843$		0			0
$844$	46.4038	+	80.3737i	1.59728	+	2.76658i
$845$	−7.54963	+	2.74784i	−0.259715	+	0.0945286i
$846$		0			0
$847$	15.8885	+	27.5196i	0.545934	+	0.945586i
$848$	−13.2280	+	22.9116i	−0.454252	+	0.786788i
$849$		0			0
$850$	40.2622	−	33.7840i	1.38098	−	1.15878i
$851$	−10.1664	−	8.53060i	−0.348499	−	0.292425i
$852$		0			0
$853$	−52.3478	−	19.0530i	−1.79236	−	0.652364i	−0.999052	−	0.0435374i	$-0.986137\pi$
$853$	−52.3478	−	19.0530i	−1.79236	−	0.652364i	−0.793303	−	0.608826i	$-0.791641\pi$
$854$	36.8854			1.26219
$855$		0			0
$856$	68.0866			2.32715
$857$	47.8141	+	17.4029i	1.63330	+	0.594472i	0.985849	−	0.167637i	$-0.0536136\pi$
$857$	47.8141	+	17.4029i	1.63330	+	0.594472i	0.647449	+	0.762109i	$0.275836\pi$
$858$		0			0
$859$	8.35844	+	7.01356i	0.285186	+	0.239300i	0.774147	−	0.633006i	$-0.218179\pi$
$859$	8.35844	+	7.01356i	0.285186	+	0.239300i	−0.488960	+	0.872306i	$0.662624\pi$
$860$	14.9481	−	12.5430i	0.509728	−	0.427712i
$861$		0			0
$862$	−23.0194	+	39.8707i	−0.784042	+	1.35800i
$863$	9.88120	+	17.1147i	0.336360	+	0.582592i	0.983745	−	0.179571i	$-0.0574708\pi$
$863$	9.88120	+	17.1147i	0.336360	+	0.582592i	−0.647385	+	0.762163i	$0.724138\pi$
$864$		0			0
$865$	−27.6202	+	10.0529i	−0.939115	+	0.341810i
$866$	−11.3576	−	19.6719i	−0.385946	−	0.668478i
$867$		0			0
$868$	23.6707	−	134.243i	0.803436	−	4.55651i
$869$	32.1536	−	26.9801i	1.09074	−	0.915237i
$870$		0			0
$871$	0.676174	+	3.83478i	0.0229113	+	0.129936i
$872$	−58.9193	−	21.4449i	−1.99526	−	0.726215i
$873$		0			0
$874$	11.6630	−	25.3970i	0.394506	−	0.859067i
$875$	−53.8066			−1.81900
$876$		0			0
$877$	0.686137	+	3.89127i	0.0231692	+	0.131399i	0.994198	−	0.107562i	$-0.0343044\pi$
$877$	0.686137	+	3.89127i	0.0231692	+	0.131399i	−0.971029	+	0.238961i	$0.923193\pi$
$878$	0.696652	+	0.584561i	0.0235109	+	0.0197280i
$879$		0			0
$880$	6.49912	−	36.8584i	0.219085	−	1.24249i
$881$	−14.5505	+	25.2022i	−0.490219	+	0.849084i	−0.999937	−	0.0112575i	$-0.996417\pi$
$881$	−14.5505	+	25.2022i	−0.490219	+	0.849084i	0.509718	+	0.860342i	$0.329750\pi$
$882$		0			0
$883$	0.668900	−	0.243460i	0.0225103	−	0.00819308i	−0.330740	−	0.943722i	$-0.607298\pi$
$883$	0.668900	−	0.243460i	0.0225103	−	0.00819308i	0.353251	+	0.935529i	$0.385076\pi$
$884$	71.6708	−	26.0860i	2.41055	−	0.877368i
$885$		0			0
$886$	18.4393	−	31.9378i	0.619480	−	1.07297i
$887$	7.75578	−	43.9852i	0.260414	−	1.47688i	−0.521371	−	0.853330i	$-0.674579\pi$
$887$	7.75578	−	43.9852i	0.260414	−	1.47688i	0.781785	−	0.623548i	$-0.214310\pi$
$888$		0			0
$889$	62.8813	+	52.7636i	2.10897	+	1.76964i
$890$	−11.0544	−	62.6925i	−0.370544	−	2.10146i
$891$		0			0
$892$	50.4279			1.68845
$893$	−5.41282	−	3.74324i	−0.181133	−	0.125263i
$894$		0			0
$895$	−12.2554	−	4.46059i	−0.409652	−	0.149101i
$896$	−11.3033	−	64.1045i	−0.377618	−	2.14158i
$897$		0			0
$898$	−0.0962667	+	0.0807773i	−0.00321246	+	0.00269557i
$899$	−3.23695	+	18.3576i	−0.107958	+	0.612262i
$900$		0			0
$901$	−12.9877	−	22.4953i	−0.432682	−	0.749427i
$902$	73.1587	−	26.6276i	2.43592	−	0.886602i
$903$		0			0
$904$	−8.72281	−	15.1084i	−0.290116	−	0.502496i
$905$	−4.10994	+	7.11862i	−0.136619	+	0.236631i
$906$		0			0
$907$	25.4124	−	21.3235i	0.843805	−	0.708037i	−0.114611	−	0.993410i	$-0.536562\pi$
$907$	25.4124	−	21.3235i	0.843805	−	0.708037i	0.958416	+	0.285374i	$0.0921178\pi$
$908$	−47.6730	−	40.0024i	−1.58208	−	1.32753i
$909$		0			0
$910$	−41.4937	−	15.1025i	−1.37550	−	0.500642i
$911$	−22.7392			−0.753382			−0.376691	−	0.926339i	$-0.622938\pi$
$911$	−22.7392			−0.753382			−0.376691	+	0.926339i	$0.622938\pi$
$912$		0			0
$913$	−19.2344			−0.636566
$914$	84.5404	+	30.7702i	2.79635	+	1.01779i
$915$		0			0
$916$	−35.8580	−	30.0885i	−1.18478	−	0.994151i
$917$	−17.1068	+	14.3543i	−0.564916	+	0.474021i
$918$		0			0
$919$	9.62449	−	16.6701i	0.317482	−	0.549896i	−0.662480	−	0.749080i	$-0.730496\pi$
$919$	9.62449	−	16.6701i	0.317482	−	0.549896i	0.979962	+	0.199184i	$0.0638292\pi$
$920$	−10.4153	−	18.0399i	−0.343384	−	0.594758i
$921$		0			0
$922$	−27.4945	+	10.0072i	−0.905484	+	0.329569i
$923$	−0.594618	−	1.02991i	−0.0195721	−	0.0338998i
$924$		0			0
$925$	2.89858	−	16.4386i	0.0953046	−	0.540499i
$926$	26.2533	−	22.0291i	0.862737	−	0.723922i
$927$		0			0
$928$	−2.34936	−	13.3239i	−0.0771214	−	0.437377i
$929$	−20.0141	−	7.28455i	−0.656643	−	0.238998i	−0.00785641	−	0.999969i	$-0.502501\pi$
$929$	−20.0141	−	7.28455i	−0.656643	−	0.238998i	−0.648786	+	0.760971i	$0.724723\pi$
$930$		0			0
$931$	−30.5758	+	66.5811i	−1.00208	+	2.18211i
$932$	127.174			4.16572
$933$		0			0
$934$	10.9657	+	62.1895i	0.358808	+	2.03490i
$935$	28.1498	+	23.6205i	0.920596	+	0.772472i
$936$		0			0
$937$	−7.99566	+	45.3457i	−0.261207	+	1.48138i	0.518416	+	0.855129i	$0.326522\pi$
$937$	−7.99566	+	45.3457i	−0.261207	+	1.48138i	−0.779623	+	0.626249i	$0.784589\pi$
$938$	9.06805	−	15.7063i	0.296082	−	0.512830i
$939$		0			0
$940$	−8.43242	+	3.06915i	−0.275035	+	0.100105i
$941$	12.5578	−	4.57066i	0.409372	−	0.148999i	−0.129122	−	0.991629i	$-0.541216\pi$
$941$	12.5578	−	4.57066i	0.409372	−	0.148999i	0.538494	+	0.842630i	$0.318994\pi$
$942$		0			0
$943$	9.30200	−	16.1115i	0.302915	−	0.524664i
$944$	−4.11974	+	23.3642i	−0.134086	+	0.760440i
$945$		0			0
$946$	−26.6498	−	22.3618i	−0.866459	−	0.727045i
$947$	9.31743	+	52.8418i	0.302776	+	1.71713i	0.633794	+	0.773502i	$0.281497\pi$
$947$	9.31743	+	52.8418i	0.302776	+	1.71713i	−0.331018	+	0.943624i	$0.607392\pi$
$948$		0			0
$949$	23.6655			0.768215
$950$	34.9987	−	3.26779i	1.13551	−	0.106021i
$951$		0			0
$952$	−182.472	−	66.4144i	−5.91395	−	2.15250i
$953$	−2.07960	−	11.7940i	−0.0673650	−	0.382046i	−0.999786	−	0.0206726i	$-0.993419\pi$
$953$	−2.07960	−	11.7940i	−0.0673650	−	0.382046i	0.932421	−	0.361373i	$-0.117692\pi$
$954$		0			0
$955$	9.34002	−	7.83721i	0.302236	−	0.253606i
$956$	−8.00774	+	45.4142i	−0.258989	+	1.46880i
$957$		0			0
$958$	−8.59152	−	14.8809i	−0.277579	−	0.480782i
$959$	−93.1071	+	33.8882i	−3.00658	+	1.09431i
$960$		0			0
$961$	−4.55185	−	7.88404i	−0.146834	−	0.254324i
$962$	17.6024	−	30.4882i	0.567523	−	0.982978i
$963$		0			0
$964$	−25.2369	+	21.1763i	−0.812827	+	0.682043i
$965$	−17.8157	−	14.9491i	−0.573507	−	0.481229i
$966$		0			0
$967$	39.3435	+	14.3199i	1.26520	+	0.460496i	0.885511	−	0.464618i	$-0.153808\pi$
$967$	39.3435	+	14.3199i	1.26520	+	0.460496i	0.379690	+	0.925114i	$0.376031\pi$
$968$	−39.7657			−1.27812
$969$		0			0
$970$	−49.4766			−1.58860
$971$	13.0471	+	4.74876i	0.418701	+	0.152395i	0.542775	−	0.839878i	$-0.317374\pi$
$971$	13.0471	+	4.74876i	0.418701	+	0.152395i	−0.124074	+	0.992273i	$0.539596\pi$
$972$		0			0
$973$	61.2700	+	51.4116i	1.96423	+	1.64818i
$974$	−65.2115	+	54.7189i	−2.08951	+	1.75331i
$975$		0			0
$976$	−9.90895	+	17.1628i	−0.317178	+	0.549368i
$977$	19.0753	+	33.0394i	0.610274	+	1.05702i	0.991194	+	0.132417i	$0.0422738\pi$
$977$	19.0753	+	33.0394i	0.610274	+	1.05702i	−0.380920	+	0.924608i	$0.624393\pi$
$978$		0			0
$979$	−73.3807	+	26.7084i	−2.34526	+	0.853604i
$980$	49.9509	+	86.5175i	1.59562	+	2.76370i
$981$		0			0
$982$	12.6000	−	71.4580i	0.402081	−	2.28032i
$983$	−15.5405	+	13.0401i	−0.495666	+	0.415913i	−0.856052	−	0.516890i	$-0.827090\pi$
$983$	−15.5405	+	13.0401i	−0.495666	+	0.415913i	0.360385	+	0.932803i	$0.382645\pi$
$984$		0			0
$985$	−2.09399	−	11.8756i	−0.0667200	−	0.378388i
$986$	45.6480	+	16.6145i	1.45373	+	0.529114i
$987$		0			0
$988$	49.3474	+	12.9146i	1.56995	+	0.410868i
$989$	−8.31315			−0.264343
$990$		0			0
$991$	−4.28817	−	24.3194i	−0.136218	−	0.772532i	−0.974004	−	0.226532i	$-0.927261\pi$
$991$	−4.28817	−	24.3194i	−0.136218	−	0.772532i	0.837785	−	0.546000i	$-0.183850\pi$
$992$	22.2973	+	18.7096i	0.707939	+	0.594031i
$993$		0			0
$994$	−0.961819	+	5.45475i	−0.0305071	+	0.173014i
$995$	9.98087	−	17.2874i	0.316415	−	0.548046i
$996$		0			0
$997$	−27.3704	+	9.96200i	−0.866828	+	0.315500i	−0.736882	−	0.676022i	$-0.763703\pi$
$997$	−27.3704	+	9.96200i	−0.866828	+	0.315500i	−0.129946	+	0.991521i	$0.541480\pi$
$998$	−100.282	+	36.4997i	−3.17437	+	1.15538i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	513.2.y.c.460.1	yes	6
3.2	odd	2		513.2.y.a.460.1	yes	6
19.5	even	9	inner	513.2.y.c.271.1	yes	6
19.9	even	9		9747.2.a.u.1.1		3
19.10	odd	18		9747.2.a.bb.1.3		3
57.5	odd	18		513.2.y.a.271.1	✓	6
57.29	even	18		9747.2.a.v.1.1		3
57.47	odd	18		9747.2.a.bd.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
513.2.y.a.271.1	✓	6	57.5	odd	18
513.2.y.a.460.1	yes	6	3.2	odd	2
513.2.y.c.271.1	yes	6	19.5	even	9	inner
513.2.y.c.460.1	yes	6	1.1	even	1	trivial
9747.2.a.u.1.1		3	19.9	even	9
9747.2.a.v.1.1		3	57.29	even	18
9747.2.a.bb.1.3		3	19.10	odd	18
9747.2.a.bd.1.3		3	57.47	odd	18

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 513 = 3^{3} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	513.y (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(2.37939 + 0.866025i) q^{2} +(3.37939 + 2.83564i) q^{4} +(-1.03209 + 0.866025i) q^{5} +(2.43969 - 4.22567i) q^{7} +(3.05303 + 5.28801i) q^{8} +(-3.20574 + 1.16679i) q^{10} +(2.09240 + 3.62414i) q^{11} +(-0.460637 + 2.61240i) q^{13} +(9.46451 - 7.94166i) q^{14} +(1.15270 + 6.53731i) q^{16} +(-6.12449 - 2.22913i) q^{17} +(-2.52094 - 3.55596i) q^{19} -5.94356 q^{20} +(1.84002 + 10.4353i) q^{22} +(1.93969 + 1.62760i) q^{23} +(-0.553033 + 3.13641i) q^{25} +(-3.35844 + 5.81699i) q^{26} +(20.2271 - 7.36208i) q^{28} +(-2.76604 + 1.00676i) q^{29} +(3.16637 - 5.48432i) q^{31} +(-0.798133 + 4.52644i) q^{32} +(-12.6420 - 10.6079i) q^{34} +(1.14156 + 6.47410i) q^{35} -5.24123 q^{37} +(-2.91875 - 10.6442i) q^{38} +(-7.73055 - 2.81369i) q^{40} +(-1.27584 - 7.23567i) q^{41} +(-2.51501 + 2.11035i) q^{43} +(-3.20574 + 18.1806i) q^{44} +(3.20574 + 5.55250i) q^{46} +(1.41875 - 0.516382i) q^{47} +(-8.40420 - 14.5565i) q^{49} +(-4.03209 + 6.98378i) q^{50} +(-8.96451 + 7.52211i) q^{52} +(3.05303 + 2.56180i) q^{53} +(-5.29813 - 1.92836i) q^{55} +29.7939 q^{56} -7.45336 q^{58} +(3.35844 + 1.22237i) q^{59} +(2.28699 + 1.91901i) q^{61} +(12.2836 - 10.3072i) q^{62} +(0.819078 - 1.41868i) q^{64} +(-1.78699 - 3.09516i) q^{65} +(1.37939 - 0.502055i) q^{67} +(-14.3760 - 24.8999i) q^{68} +(-2.89053 + 16.3930i) q^{70} +(-0.343426 + 0.288169i) q^{71} +(-1.54916 - 8.78574i) q^{73} +(-12.4709 - 4.53904i) q^{74} +(1.56418 - 19.1654i) q^{76} +20.4192 q^{77} +(-1.74170 - 9.87765i) q^{79} +(-6.85117 - 5.74881i) q^{80} +(3.23055 - 18.3214i) q^{82} +(-2.29813 + 3.98048i) q^{83} +(8.25150 - 3.00330i) q^{85} +(-7.81180 + 2.84326i) q^{86} +(-12.7763 + 22.1292i) q^{88} +(-3.24035 + 18.3770i) q^{89} +(9.91534 + 8.31996i) q^{91} +(1.93969 + 11.0005i) q^{92} +3.82295 q^{94} +(5.68139 + 1.48686i) q^{95} +(13.6284 + 4.96032i) q^{97} +(-7.39053 - 41.9138i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{2} + 9 q^{4} + 3 q^{5} + 9 q^{7} + 6 q^{8} - 9 q^{10} + 9 q^{11} + 6 q^{13} + 24 q^{14} + 9 q^{16} - 24 q^{17} - 12 q^{19} - 6 q^{20} - 9 q^{22} + 6 q^{23} + 9 q^{25} - 12 q^{26} + 42 q^{28}+ \cdots - 27 q^{98}+O(q^{100}) \) 6 * q + 3 * q^2 + 9 * q^4 + 3 * q^5 + 9 * q^7 + 6 * q^8 - 9 * q^10 + 9 * q^11 + 6 * q^13 + 24 * q^14 + 9 * q^16 - 24 * q^17 - 12 * q^19 - 6 * q^20 - 9 * q^22 + 6 * q^23 + 9 * q^25 - 12 * q^26 + 42 * q^28 - 12 * q^29 + 9 * q^32 - 18 * q^34 + 15 * q^35 - 54 * q^37 - 15 * q^38 - 9 * q^40 - 6 * q^41 + 15 * q^43 - 9 * q^44 + 9 * q^46 + 6 * q^47 - 12 * q^49 - 15 * q^50 - 21 * q^52 + 6 * q^53 - 18 * q^55 + 66 * q^56 - 18 * q^58 + 12 * q^59 + 6 * q^61 + 24 * q^62 - 12 * q^64 - 3 * q^65 - 3 * q^67 - 33 * q^68 - 24 * q^71 - 21 * q^73 - 3 * q^74 - 9 * q^76 + 54 * q^77 + 33 * q^79 - 15 * q^80 - 18 * q^82 + 9 * q^85 - 12 * q^86 - 9 * q^88 + 15 * q^89 + 15 * q^91 + 6 * q^92 - 18 * q^94 - 15 * q^95 + 45 * q^97 - 27 * q^98

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