LMFDB - Embedded newform 513.2.y.a.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.a.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	−0.688833	−	0.724920i	$-0.741877\pi$
$2$	−2.37939	−	0.866025i	−1.68248	−	0.612372i	−0.993646	+	0.112548i	$0.964099\pi$
$3$		0			0
$3$		0			0
$4$	3.37939	+	2.83564i	1.68969	+	1.41782i
$5$	1.03209	−	0.866025i	0.461564	−	0.387298i	−0.382142	−	0.924104i	$-0.624813\pi$
$5$	1.03209	−	0.866025i	0.461564	−	0.387298i	0.843706	+	0.536805i	$0.180369\pi$
$6$		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	$-0.949360\pi$
$11$	−2.09240	−	3.62414i	−0.630881	−	1.09272i	0.356491	−	0.934299i	$-0.383973\pi$
$12$		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	0.952236	−	0.305364i	$-0.0987783\pi$
$17$	6.12449	+	2.22913i	1.48541	+	0.540644i	0.533170	+	0.846008i	$0.321001\pi$
$18$		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	0.417758	−	0.908558i	$-0.362816\pi$
$23$	−1.93969	−	1.62760i	−0.404454	−	0.339377i	−0.822212	+	0.569181i	$0.807260\pi$
$24$		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	−0.0721780	−	0.997392i	$-0.522995\pi$
$29$	2.76604	−	1.00676i	0.513642	−	0.186950i	0.585820	+	0.810442i	$0.300773\pi$
$30$		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	$0.138948\pi$
$41$	1.27584	+	7.23567i	0.199253	+	1.13002i	−0.706976	+	0.707237i	$0.749941\pi$
$42$		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	−0.443413	−	0.896317i	$-0.646233\pi$
$47$	−1.41875	+	0.516382i	−0.206946	+	0.0753221i	0.236467	+	0.971639i	$0.424010\pi$
$48$		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	0.408556	−	0.912733i	$-0.366033\pi$
$53$	−3.05303	−	2.56180i	−0.419366	−	0.351890i	−0.827922	+	0.560843i	$0.810477\pi$
$54$		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	0.114020	−	0.993478i	$-0.463627\pi$
$59$	−3.35844	−	1.22237i	−0.437232	−	0.159139i	−0.551251	+	0.834339i	$0.685850\pi$
$60$		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	−0.622182	−	0.782873i	$-0.713753\pi$
$71$	0.343426	−	0.288169i	0.0407572	−	0.0341993i	0.662939	+	0.748674i	$0.269309\pi$
$72$		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	−0.711893	−	0.702288i	$-0.752162\pi$
$83$	2.29813	−	3.98048i	0.252253	−	0.436915i	0.964146	+	0.265373i	$0.0854952\pi$
$84$		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	$-0.491697\pi$
$89$	3.24035	−	18.3770i	0.343477	−	1.94795i	0.317396	−	0.948293i	$-0.397191\pi$
$90$		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	$-0.775981\pi$
$101$	1.76217	−	9.99379i	0.175343	−	0.994419i	0.937747	−	0.347318i	$-0.112908\pi$
$102$		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	$0.347859\pi$
$107$	−5.57532	+	9.65674i	−0.538987	+	0.933552i	−0.998959	+	0.0456191i	$0.985474\pi$
$108$		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	$-0.457094\pi$
$113$	2.85710			0.268773			0.134387	+	0.990929i	$0.457094\pi$
$114$		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	0.522990	−	0.852339i	$-0.324817\pi$
$131$	4.30066	+	1.56531i	0.375750	+	0.136762i	−0.147239	+	0.989101i	$0.547039\pi$
$132$		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	$0.0564608\pi$
$137$	15.5556	+	13.0527i	1.32900	+	1.11516i	0.344691	+	0.938716i	$0.387984\pi$
$138$		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	$-0.989705\pi$
$149$	−0.870767	−	4.93837i	−0.0713360	−	0.404567i	0.928141	−	0.372229i	$-0.121406\pi$
$150$		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	0.732212	−	0.681077i	$-0.238488\pi$
$167$	2.43763	+	2.04542i	0.188630	+	0.158279i	−0.543582	+	0.839356i	$0.682932\pi$
$168$		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	−0.588202	−	0.808714i	$-0.700164\pi$
$173$	−20.5005	−	7.46156i	−1.55862	−	0.567292i	−0.970420	+	0.241423i	$0.922386\pi$
$174$		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	0.626490	−	0.779429i	$-0.284491\pi$
$179$	−4.84002	−	8.38316i	−0.361760	−	0.626587i	−0.988251	+	0.152842i	$0.951157\pi$
$180$		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	$-0.393826\pi$
$191$	9.04963			0.654808			0.327404	+	0.944884i	$0.393826\pi$
$192$		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	−0.661403	−	0.750030i	$-0.730039\pi$
$197$	4.47519	−	7.75125i	0.318844	−	0.552254i	0.980247	+	0.197777i	$0.0633721\pi$
$198$		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	$-0.344918\pi$
$227$	14.1070			0.936315			0.468157	+	0.883645i	$0.344918\pi$
$228$		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	$0.671030\pi$
$233$	−22.0835	+	18.5303i	−1.44674	+	1.21396i	−0.934916	+	0.354869i	$0.884526\pi$
$234$		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	0.645987	−	0.763349i	$-0.276446\pi$
$239$	−5.22668	−	9.05288i	−0.338086	−	0.585582i	−0.984073	+	0.177767i	$0.943113\pi$
$240$		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	0.979742	−	0.200262i	$-0.0641794\pi$
$251$	15.0929	+	12.6644i	0.952653	+	0.799371i	−0.0270893	+	0.999633i	$0.508624\pi$
$252$		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	−0.534338	−	0.845271i	$-0.679439\pi$
$257$	−6.41787	+	2.33591i	−0.400336	+	0.145710i	0.134003	+	0.990981i	$0.457217\pi$
$258$		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	$0.0693648\pi$
$263$	2.15405	+	12.2162i	0.132824	+	0.753284i	−0.843526	+	0.537089i	$0.819524\pi$
$264$		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	$-0.979350\pi$
$269$	−1.35070	−	7.66020i	−0.0823536	−	0.467051i	0.915543	−	0.402221i	$-0.131762\pi$
$270$		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	0.408304	−	0.912846i	$-0.366120\pi$
$281$	−7.03667	−	5.90447i	−0.419773	−	0.352231i	−0.828077	+	0.560615i	$0.810565\pi$
$282$		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	$0.0320161\pi$
$293$	10.0039	+	17.3272i	0.584432	+	1.01227i	−0.410514	+	0.911854i	$0.634651\pi$
$294$		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	−0.949720	−	0.313101i	$-0.898632\pi$
$311$	−3.59240	+	6.22221i	−0.203706	+	0.352829i	0.746014	+	0.665931i	$0.231965\pi$
$312$		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	−0.961016	−	0.276494i	$-0.910827\pi$
$317$	0.651826	−	3.69669i	0.0366102	−	0.207627i	0.997626	+	0.0688673i	$0.0219385\pi$
$318$		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	−0.953910	−	0.300092i	$-0.902983\pi$
$347$	−15.3498	+	12.8800i	−0.824022	+	0.691436i	0.129889	+	0.991529i	$0.458538\pi$
$348$		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	$0.299148\pi$
$353$	18.6800	+	32.3548i	0.994238	+	1.72207i	0.404289	+	0.914631i	$0.367519\pi$
$354$		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	0.616785	−	0.787132i	$-0.288435\pi$
$359$	11.0522	+	4.02266i	0.583310	+	0.212308i	−0.0334742	+	0.999440i	$0.510657\pi$
$360$		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	$-0.848851\pi$
$383$	−4.10994	−	23.3086i	−0.210008	−	1.19101i	0.679354	−	0.733811i	$-0.262260\pi$
$384$		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	0.0288542	−	0.999584i	$-0.490814\pi$
$389$	13.6775	−	4.97821i	0.693478	−	0.252405i	0.664624	+	0.747178i	$0.268592\pi$
$390$		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	0.324114	−	0.946018i	$-0.394934\pi$
$401$	−0.714660	−	0.260115i	−0.0356884	−	0.0129895i	−0.359803	+	0.933028i	$0.617156\pi$
$402$		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	$-0.447045\pi$
$419$	6.77930			0.331191			0.165595	+	0.986194i	$0.447045\pi$
$420$		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	$-0.800167\pi$
$431$	3.15729	−	17.9059i	0.152081	−	0.862496i	0.961406	−	0.275134i	$-0.0887223\pi$
$432$		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	$0.168012\pi$
$443$	−2.52910	+	14.3432i	−0.120161	+	0.681467i	−0.984065	+	0.177810i	$0.943099\pi$
$444$		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	−0.865439	−	0.501014i	$-0.832961\pi$
$449$	0.0248149	−	0.0429807i	0.00117109	−	0.00202839i	0.866610	+	0.498985i	$0.166294\pi$
$450$		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	−0.412941	−	0.910758i	$-0.635499\pi$
$461$	8.85188	−	7.42761i	0.412273	−	0.345938i	0.825215	+	0.564819i	$0.191054\pi$
$462$		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	$-0.970878\pi$
$467$	−12.4697	−	21.5982i	−0.577030	−	0.999445i	0.418788	−	0.908084i	$-0.362455\pi$
$468$		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	0.753778	−	0.657129i	$-0.228229\pi$
$479$	5.19846	+	4.36203i	0.237524	+	0.199306i	−0.516254	+	0.856436i	$0.672674\pi$
$480$		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	$0.168263\pi$
$491$	4.97612	+	28.2210i	0.224569	+	1.27359i	−0.638938	+	0.769258i	$0.720626\pi$
$492$		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	0.0915130	−	0.995804i	$-0.470830\pi$
$503$	17.9804	−	6.54433i	0.801706	−	0.291797i	0.710193	+	0.704007i	$0.248607\pi$
$504$		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	0.985139	−	0.171758i	$-0.0549448\pi$
$509$	22.2690	+	18.6859i	0.987058	+	0.828240i	0.00191863	+	0.999998i	$0.499389\pi$
$510$		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	0.779589	−	0.626291i	$-0.215428\pi$
$521$	−3.48293	−	6.03260i	−0.152590	−	0.264293i	−0.932179	+	0.361998i	$0.882095\pi$
$522$		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	$0.311416\pi$
$557$	−5.90151	+	33.4691i	−0.250055	+	1.41813i	−0.808454	+	0.588560i	$0.799695\pi$
$558$		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	−0.606487	−	0.795093i	$-0.707422\pi$
$563$	9.14290	−	15.8360i	0.385327	−	0.667407i	0.991815	+	0.127687i	$0.0407552\pi$
$564$		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	$-0.626836\pi$
$569$	−18.5107			−0.776010			−0.388005	+	0.921657i	$0.626836\pi$
$570$		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	−0.414579	−	0.910013i	$-0.636071\pi$
$587$	−31.9111	−	11.6147i	−1.31711	−	0.479389i	−0.902531	+	0.430624i	$0.858293\pi$
$588$		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	0.969716	−	0.244234i	$-0.0785364\pi$
$593$	21.8576	+	18.3407i	0.897583	+	0.753161i	−0.0721338	+	0.997395i	$0.522981\pi$
$594$		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	−0.607499	−	0.794321i	$-0.707827\pi$
$599$	−13.7618	+	5.00887i	−0.562290	+	0.204657i	0.0452084	+	0.998978i	$0.485605\pi$
$600$		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	−0.359705	−	0.933066i	$-0.617123\pi$
$617$	−0.881607	+	0.320879i	−0.0354922	+	0.0129181i	0.324213	+	0.945984i	$0.394901\pi$
$618$		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	−0.337454	−	0.941342i	$-0.609566\pi$
$641$	13.4436	−	11.2805i	0.530989	−	0.445553i	0.868443	+	0.495790i	$0.165121\pi$
$642$		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	$-0.242169\pi$
$647$	36.8462			1.44857			0.724286	+	0.689499i	$0.242169\pi$
$648$		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	−0.550997	−	0.834507i	$-0.685753\pi$
$653$	11.4278	−	19.7936i	0.447206	−	0.774583i	0.998203	+	0.0599241i	$0.0190859\pi$
$654$		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	$0.120740\pi$
$659$	−1.81299	+	10.2820i	−0.0706239	+	0.400528i	−0.999543	+	0.0302442i	$0.990372\pi$
$660$		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	−0.962025	−	0.272962i	$-0.911997\pi$
$677$	−6.36484	+	11.0242i	−0.244621	+	0.423695i	0.717404	+	0.696657i	$0.245330\pi$
$678$		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	$-0.504302\pi$
$683$	−0.706452			−0.0270316			−0.0135158	+	0.999909i	$0.504302\pi$
$684$		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	0.988449	−	0.151556i	$-0.0484285\pi$
$701$	43.6391	+	15.8833i	1.64823	+	0.599905i	0.659777	+	0.751461i	$0.270651\pi$
$702$		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	0.996280	−	0.0861793i	$-0.0274658\pi$
$719$	0.820727	+	4.65457i	0.0306079	+	0.173586i	−0.965672	+	0.259766i	$0.916355\pi$
$720$		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	0.910889	−	0.412653i	$-0.135398\pi$
$743$	36.6190	+	13.3282i	1.34342	+	0.488965i	0.432533	+	0.901618i	$0.357620\pi$
$744$		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	$-0.382923\pi$
$761$	19.8384			0.719143			0.359571	+	0.933118i	$0.382923\pi$
$762$		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	$0.230826\pi$
$773$	−5.05216	+	28.6522i	−0.181713	+	1.03055i	−0.930106	+	0.367292i	$0.880285\pi$
$774$		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	$-0.201444\pi$
$797$	45.5280			1.61268			0.806342	+	0.591450i	$0.201444\pi$
$798$		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	0.627080	−	0.778955i	$-0.284250\pi$
$809$	−10.2694	−	17.7872i	−0.361055	−	0.625365i	−0.988135	+	0.153590i	$0.950917\pi$
$810$		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	0.543748	−	0.839248i	$-0.317005\pi$
$821$	−5.39621	−	4.52796i	−0.188329	−	0.158027i	−0.732077	+	0.681221i	$0.761449\pi$
$822$		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	−0.866490	−	0.499194i	$-0.833629\pi$
$827$	−34.7790	+	12.6585i	−1.20938	+	0.440180i	−0.342894	+	0.939374i	$0.611407\pi$
$828$		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	$0.0456655\pi$
$839$	3.14527	+	17.8377i	0.108587	+	0.615826i	−0.881140	+	0.472855i	$0.843223\pi$
$840$		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	−0.647449	−	0.762109i	$-0.724164\pi$
$857$	−47.8141	−	17.4029i	−1.63330	−	0.594472i	−0.985849	+	0.167637i	$0.946386\pi$
$858$		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	0.647385	−	0.762163i	$-0.275862\pi$
$863$	−9.88120	−	17.1147i	−0.336360	−	0.582592i	−0.983745	+	0.179571i	$0.942529\pi$
$864$		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	−0.509718	−	0.860342i	$-0.670250\pi$
$881$	14.5505	−	25.2022i	0.490219	−	0.849084i	0.999937	+	0.0112575i	$0.00358345\pi$
$882$		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	$0.325421\pi$
$887$	−7.75578	+	43.9852i	−0.260414	+	1.47688i	−0.781785	+	0.623548i	$0.785690\pi$
$888$		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	$-0.377062\pi$
$911$	22.7392			0.753382			0.376691	+	0.926339i	$0.377062\pi$
$912$		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	0.648786	−	0.760971i	$-0.275277\pi$
$929$	20.0141	+	7.28455i	0.656643	+	0.238998i	0.00785641	+	0.999969i	$0.497499\pi$
$930$		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	−0.538494	−	0.842630i	$-0.681006\pi$
$941$	−12.5578	+	4.57066i	−0.409372	+	0.148999i	0.129122	+	0.991629i	$0.458784\pi$
$942$		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	$-0.718503\pi$
$947$	−9.31743	−	52.8418i	−0.302776	−	1.71713i	0.331018	−	0.943624i	$-0.392608\pi$
$948$		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	$0.00658077\pi$
$953$	2.07960	+	11.7940i	0.0673650	+	0.382046i	−0.932421	+	0.361373i	$0.882308\pi$
$954$		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	0.124074	−	0.992273i	$-0.460404\pi$
$971$	−13.0471	−	4.74876i	−0.418701	−	0.152395i	−0.542775	+	0.839878i	$0.682626\pi$
$972$		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	$-0.957726\pi$
$977$	−19.0753	−	33.0394i	−0.610274	−	1.05702i	0.380920	−	0.924608i	$-0.375607\pi$
$978$		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	−0.360385	−	0.932803i	$-0.617355\pi$
$983$	15.5405	−	13.0401i	0.495666	−	0.415913i	0.856052	+	0.516890i	$0.172910\pi$
$984$		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.a.460.1	yes	6
3.2	odd	2		513.2.y.c.460.1	yes	6
19.5	even	9	inner	513.2.y.a.271.1	✓	6
19.9	even	9		9747.2.a.bd.1.3		3
19.10	odd	18		9747.2.a.v.1.1		3
57.5	odd	18		513.2.y.c.271.1	yes	6
57.29	even	18		9747.2.a.bb.1.3		3
57.47	odd	18		9747.2.a.u.1.1		3

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

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more