LMFDB - Embedded newform 243.3.f.d.53.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [243,3,Mod(26,243)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(243, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([1])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("243.26"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 243 = 3^{5} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	243.f (of order $18$, degree $6$, not minimal)

Newform invariants

comment:select newform

sage:traces = [30,3,0,3,21] 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:	$6.62127042396$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$5$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 27)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			53.2
Character	$\chi$	$=$	243.53
Dual form			243.3.f.d.188.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.663577 + 1.82316i) q^{2} +(0.180586 + 0.151529i) q^{4} +(4.25686 + 0.750600i) q^{5} +(6.80967 - 5.71399i) q^{7} +(-7.11704 + 4.10903i) q^{8} +(-4.19322 + 7.26288i) q^{10} +(7.26396 - 1.28083i) q^{11} +(15.2310 - 5.54364i) q^{13} +(5.89880 + 16.2068i) q^{14} +(-2.60498 - 14.7736i) q^{16} +(9.06825 + 5.23555i) q^{17} +(-8.63742 - 14.9604i) q^{19} +(0.654990 + 0.780587i) q^{20} +(-2.48503 + 14.0933i) q^{22} +(-8.47110 + 10.0955i) q^{23} +(-5.93484 - 2.16011i) q^{25} +31.4473i q^{26} +2.09556 q^{28} +(-14.3092 + 39.3143i) q^{29} +(28.3928 + 23.8244i) q^{31} +(-3.70957 - 0.654097i) q^{32} +(-15.5628 + 13.0587i) q^{34} +(33.2767 - 19.2123i) q^{35} +(-31.9875 + 55.4041i) q^{37} +(33.0069 - 5.82001i) q^{38} +(-33.3805 + 12.1495i) q^{40} +(-8.70442 - 23.9152i) q^{41} +(0.430521 + 2.44161i) q^{43} +(1.50585 + 0.869403i) q^{44} +(-12.7845 - 22.1433i) q^{46} +(-30.0028 - 35.7559i) q^{47} +(5.21313 - 29.5652i) q^{49} +(7.87646 - 9.38679i) q^{50} +(3.59053 + 1.30685i) q^{52} -50.7217i q^{53} +31.8831 q^{55} +(-24.9858 + 68.6478i) q^{56} +(-62.1811 - 52.1761i) q^{58} +(-4.12626 - 0.727571i) q^{59} +(27.8569 - 23.3747i) q^{61} +(-62.2766 + 35.9554i) q^{62} +(33.6571 - 58.2957i) q^{64} +(68.9974 - 12.1661i) q^{65} +(-16.2651 + 5.92003i) q^{67} +(0.844255 + 2.31957i) q^{68} +(12.9455 + 73.4178i) q^{70} +(-51.5041 - 29.7359i) q^{71} +(26.3451 + 45.6310i) q^{73} +(-79.7845 - 95.0834i) q^{74} +(0.707153 - 4.01046i) q^{76} +(42.1465 - 50.2282i) q^{77} +(1.46560 + 0.533436i) q^{79} -64.8443i q^{80} +49.3774 q^{82} +(38.6733 - 106.254i) q^{83} +(34.6725 + 29.0937i) q^{85} +(-4.73713 - 0.835284i) q^{86} +(-46.4349 + 38.9635i) q^{88} +(41.4518 - 23.9322i) q^{89} +(72.0419 - 124.780i) q^{91} +(-3.05952 + 0.539476i) q^{92} +(85.0981 - 30.9732i) q^{94} +(-25.5390 - 70.1678i) q^{95} +(-6.38452 - 36.2084i) q^{97} +(50.4428 + 29.1232i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 3 q^{2} + 3 q^{4} + 21 q^{5} + 3 q^{7} - 9 q^{8} - 3 q^{10} + 57 q^{11} + 3 q^{13} - 114 q^{14} + 27 q^{16} - 9 q^{17} - 3 q^{19} - 183 q^{20} + 75 q^{22} + 48 q^{23} + 21 q^{25} - 12 q^{28} - 78 q^{29}+ \cdots + 882 q^{98}+O(q^{100}) $ 30 * q + 3 * q^2 + 3 * q^4 + 21 * q^5 + 3 * q^7 - 9 * q^8 - 3 * q^10 + 57 * q^11 + 3 * q^13 - 114 * q^14 + 27 * q^16 - 9 * q^17 - 3 * q^19 - 183 * q^20 + 75 * q^22 + 48 * q^23 + 21 * q^25 - 12 * q^28 - 78 * q^29 - 87 * q^31 + 243 * q^32 - 153 * q^34 - 252 * q^35 - 3 * q^37 + 321 * q^38 - 168 * q^40 - 357 * q^41 - 87 * q^43 + 639 * q^44 - 3 * q^46 - 51 * q^47 - 69 * q^49 + 168 * q^50 - 36 * q^52 - 12 * q^55 - 177 * q^56 + 138 * q^58 + 48 * q^59 + 147 * q^61 - 900 * q^62 - 51 * q^64 + 624 * q^65 + 12 * q^67 - 477 * q^68 - 6 * q^70 + 315 * q^71 - 66 * q^73 - 480 * q^74 - 57 * q^76 + 453 * q^77 - 15 * q^79 - 12 * q^82 - 591 * q^83 + 243 * q^85 + 669 * q^86 + 591 * q^88 + 72 * q^89 + 96 * q^91 + 564 * q^92 + 957 * q^94 - 606 * q^95 + 696 * q^97 + 882 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/243\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{11}{18}\right)$

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 $

$2$	−0.663577	+	1.82316i	−0.331789	+	0.911582i	0.655858	+	0.754884i	$0.272307\pi$
$2$	−0.663577	+	1.82316i	−0.331789	+	0.911582i	−0.987647	+	0.156698i	$0.949915\pi$
$3$		0			0
$3$		0			0
$4$	0.180586	+	0.151529i	0.0451464	+	0.0378823i
$5$	4.25686	+	0.750600i	0.851372	+	0.150120i	0.582274	−	0.812993i	$-0.302163\pi$
$5$	4.25686	+	0.750600i	0.851372	+	0.150120i	0.269099	+	0.963113i	$0.413274\pi$
$6$		0			0
$7$	6.80967	−	5.71399i	0.972810	−	0.816284i	−0.0101795	−	0.999948i	$-0.503240\pi$
$7$	6.80967	−	5.71399i	0.972810	−	0.816284i	0.982989	+	0.183664i	$0.0587958\pi$
$8$	−7.11704	+	4.10903i	−0.889630	+	0.513628i
$9$		0			0
$10$	−4.19322	+	7.26288i	−0.419322	+	0.726288i
$11$	7.26396	−	1.28083i	0.660360	−	0.116439i	0.166582	−	0.986028i	$-0.446727\pi$
$11$	7.26396	−	1.28083i	0.660360	−	0.116439i	0.493778	+	0.869588i	$0.335616\pi$
$12$		0			0
$13$	15.2310	−	5.54364i	1.17162	−	0.426434i	0.318383	−	0.947962i	$-0.396860\pi$
$13$	15.2310	−	5.54364i	1.17162	−	0.426434i	0.853234	+	0.521528i	$0.174638\pi$
$14$	5.89880	+	16.2068i	0.421343	+	1.15763i
$15$		0			0
$16$	−2.60498	−	14.7736i	−0.162811	−	0.923348i
$17$	9.06825	+	5.23555i	0.533426	+	0.307974i	0.742411	−	0.669945i	$-0.233682\pi$
$17$	9.06825	+	5.23555i	0.533426	+	0.307974i	−0.208984	+	0.977919i	$0.567016\pi$
$18$		0			0
$19$	−8.63742	−	14.9604i	−0.454601	−	0.787392i	0.544064	−	0.839044i	$-0.316885\pi$
$19$	−8.63742	−	14.9604i	−0.454601	−	0.787392i	−0.998665	+	0.0516517i	$0.983551\pi$
$20$	0.654990	+	0.780587i	0.0327495	+	0.0390293i
$21$		0			0
$22$	−2.48503	+	14.0933i	−0.112956	+	0.640606i
$23$	−8.47110	+	10.0955i	−0.368309	+	0.438933i	−0.918088	−	0.396377i	$-0.870267\pi$
$23$	−8.47110	+	10.0955i	−0.368309	+	0.438933i	0.549779	+	0.835310i	$0.314712\pi$
$24$		0			0
$25$	−5.93484	−	2.16011i	−0.237394	−	0.0864042i
$26$			31.4473i			1.20951i
$27$		0			0
$28$	2.09556			0.0748416
$29$	−14.3092	+	39.3143i	−0.493421	+	1.35566i	0.404109	+	0.914711i	$0.367582\pi$
$29$	−14.3092	+	39.3143i	−0.493421	+	1.35566i	−0.897530	+	0.440953i	$0.854641\pi$
$30$		0			0
$31$	28.3928	+	23.8244i	0.915896	+	0.768528i	0.973232	−	0.229827i	$-0.0738159\pi$
$31$	28.3928	+	23.8244i	0.915896	+	0.768528i	−0.0573351	+	0.998355i	$0.518260\pi$
$32$	−3.70957	−	0.654097i	−0.115924	−	0.0204405i
$33$		0			0
$34$	−15.5628	+	13.0587i	−0.457728	+	0.384080i
$35$	33.2767	−	19.2123i	0.950764	−	0.548924i
$36$		0			0
$37$	−31.9875	+	55.4041i	−0.864528	+	1.49741i	0.00298644	+	0.999996i	$0.499049\pi$
$37$	−31.9875	+	55.4041i	−0.864528	+	1.49741i	−0.867515	+	0.497411i	$0.834284\pi$
$38$	33.0069	−	5.82001i	0.868604	−	0.153158i
$39$		0			0
$40$	−33.3805	+	12.1495i	−0.834513	+	0.303738i
$41$	−8.70442	−	23.9152i	−0.212303	−	0.583297i	0.787136	−	0.616779i	$-0.211563\pi$
$41$	−8.70442	−	23.9152i	−0.212303	−	0.583297i	−0.999439	+	0.0334815i	$0.989341\pi$
$42$		0			0
$43$	0.430521	+	2.44161i	0.0100121	+	0.0567815i	0.989404	−	0.145185i	$-0.0463778\pi$
$43$	0.430521	+	2.44161i	0.0100121	+	0.0567815i	−0.979392	+	0.201967i	$0.935267\pi$
$44$	1.50585	+	0.869403i	0.0342239	+	0.0197592i
$45$		0			0
$46$	−12.7845	−	22.1433i	−0.277923	−	0.481377i
$47$	−30.0028	−	35.7559i	−0.638357	−	0.760765i	0.345752	−	0.938326i	$-0.387624\pi$
$47$	−30.0028	−	35.7559i	−0.638357	−	0.760765i	−0.984110	+	0.177561i	$0.943179\pi$
$48$		0			0
$49$	5.21313	−	29.5652i	0.106390	−	0.603370i
$50$	7.87646	−	9.38679i	0.157529	−	0.187736i
$51$		0			0
$52$	3.59053	+	1.30685i	0.0690486	+	0.0251316i
$53$		−	50.7217i		−	0.957013i	−0.878084	−	0.478507i	$-0.841178\pi$
$53$		−	50.7217i		−	0.957013i	0.878084	−	0.478507i	$-0.158822\pi$
$54$		0			0
$55$	31.8831			0.579692
$56$	−24.9858	+	68.6478i	−0.446174	+	1.22585i
$57$		0			0
$58$	−62.1811	−	52.1761i	−1.07209	−	0.899588i
$59$	−4.12626	−	0.727571i	−0.0699366	−	0.0123317i	0.138570	−	0.990353i	$-0.455749\pi$
$59$	−4.12626	−	0.727571i	−0.0699366	−	0.0123317i	−0.208507	+	0.978021i	$0.566860\pi$
$60$		0			0
$61$	27.8569	−	23.3747i	0.456671	−	0.383192i	−0.385234	−	0.922819i	$-0.625879\pi$
$61$	27.8569	−	23.3747i	0.456671	−	0.383192i	0.841904	+	0.539627i	$0.181435\pi$
$62$	−62.2766	+	35.9554i	−1.00446	+	0.579926i
$63$		0			0
$64$	33.6571	−	58.2957i	0.525892	−	0.910871i
$65$	68.9974	−	12.1661i	1.06150	−	0.187171i
$66$		0			0
$67$	−16.2651	+	5.92003i	−0.242763	+	0.0883586i	−0.460536	−	0.887641i	$-0.652343\pi$
$67$	−16.2651	+	5.92003i	−0.242763	+	0.0883586i	0.217773	+	0.975999i	$0.430121\pi$
$68$	0.844255	+	2.31957i	0.0124155	+	0.0341113i
$69$		0			0
$70$	12.9455	+	73.4178i	0.184936	+	1.04883i
$71$	−51.5041	−	29.7359i	−0.725410	−	0.418815i	0.0913309	−	0.995821i	$-0.470888\pi$
$71$	−51.5041	−	29.7359i	−0.725410	−	0.418815i	−0.816740	+	0.577005i	$0.804221\pi$
$72$		0			0
$73$	26.3451	+	45.6310i	0.360892	+	0.625083i	0.988108	−	0.153762i	$-0.0491391\pi$
$73$	26.3451	+	45.6310i	0.360892	+	0.625083i	−0.627216	+	0.778845i	$0.715806\pi$
$74$	−79.7845	−	95.0834i	−1.07817	−	1.28491i
$75$		0			0
$76$	0.707153	−	4.01046i	0.00930464	−	0.0527692i
$77$	42.1465	−	50.2282i	0.547357	−	0.652315i
$78$		0			0
$79$	1.46560	+	0.533436i	0.0185519	+	0.00675236i	0.351279	−	0.936271i	$-0.385747\pi$
$79$	1.46560	+	0.533436i	0.0185519	+	0.00675236i	−0.332728	+	0.943023i	$0.607969\pi$
$80$		−	64.8443i		−	0.810554i
$81$		0			0
$82$	49.3774			0.602163
$83$	38.6733	−	106.254i	0.465943	−	1.28017i	−0.455007	−	0.890488i	$-0.650363\pi$
$83$	38.6733	−	106.254i	0.465943	−	1.28017i	0.920950	−	0.389680i	$-0.127414\pi$
$84$		0			0
$85$	34.6725	+	29.0937i	0.407911	+	0.342278i
$86$	−4.73713	−	0.835284i	−0.0550829	−	0.00971261i
$87$		0			0
$88$	−46.4349	+	38.9635i	−0.527670	+	0.442768i
$89$	41.4518	−	23.9322i	0.465750	−	0.268901i	−0.248709	−	0.968578i	$-0.580006\pi$
$89$	41.4518	−	23.9322i	0.465750	−	0.268901i	0.714459	+	0.699677i	$0.246673\pi$
$90$		0			0
$91$	72.0419	−	124.780i	0.791670	−	1.37121i
$92$	−3.05952	+	0.539476i	−0.0332556	+	0.00586387i
$93$		0			0
$94$	85.0981	−	30.9732i	0.905299	−	0.329502i
$95$	−25.5390	−	70.1678i	−0.268831	−	0.738608i
$96$		0			0
$97$	−6.38452	−	36.2084i	−0.0658198	−	0.373283i	−0.999870	−	0.0161402i	$-0.994862\pi$
$97$	−6.38452	−	36.2084i	−0.0658198	−	0.373283i	0.934050	−	0.357142i	$-0.116249\pi$
$98$	50.4428	+	29.1232i	0.514722	+	0.297175i
$99$		0			0
$100$	−0.744428	−	1.28939i	−0.00744428	−	0.0128939i
$101$	−54.8285	−	65.3421i	−0.542857	−	0.646952i	0.422969	−	0.906144i	$-0.360988\pi$
$101$	−54.8285	−	65.3421i	−0.542857	−	0.646952i	−0.965826	+	0.259193i	$0.916544\pi$
$102$		0			0
$103$	4.03589	−	22.8887i	0.0391834	−	0.222220i	−0.958928	−	0.283649i	$-0.908455\pi$
$103$	4.03589	−	22.8887i	0.0391834	−	0.222220i	0.998111	+	0.0614294i	$0.0195659\pi$
$104$	−85.6209	+	102.039i	−0.823278	+	0.981145i
$105$		0			0
$106$	92.4740	+	33.6578i	0.872396	+	0.317526i
$107$			95.7625i			0.894977i	0.894290	+	0.447488i	$0.147681\pi$
$107$			95.7625i			0.894977i	−0.894290	+	0.447488i	$0.852319\pi$
$108$		0			0
$109$	−102.160			−0.937249			−0.468625	−	0.883397i	$-0.655250\pi$
$109$	−102.160			−0.937249			−0.468625	+	0.883397i	$0.655250\pi$
$110$	−21.1569	+	58.1281i	−0.192335	+	0.528437i
$111$		0			0
$112$	−102.155	−	85.7183i	−0.912099	−	0.765342i
$113$	−16.0622	−	2.83220i	−0.142144	−	0.0250638i	0.102124	−	0.994772i	$-0.467436\pi$
$113$	−16.0622	−	2.83220i	−0.142144	−	0.0250638i	−0.244267	+	0.969708i	$0.578547\pi$
$114$		0			0
$115$	−43.6380	+	36.6166i	−0.379461	+	0.318405i
$116$	−8.54130	+	4.93132i	−0.0736319	+	0.0425114i
$117$		0			0
$118$	4.06457	−	7.04005i	0.0344455	−	0.0596614i
$119$	91.6676	−	16.1635i	0.770316	−	0.135828i
$120$		0			0
$121$	−62.5782	+	22.7766i	−0.517175	+	0.188236i
$122$	24.1307	+	66.2986i	0.197793	+	0.543431i
$123$		0			0
$124$	1.51724	+	8.60468i	0.0122358	+	0.0693926i
$125$	−117.228	−	67.6816i	−0.937824	−	0.541453i
$126$		0			0
$127$	40.7309	+	70.5479i	0.320715	+	0.555495i	0.980636	−	0.195840i	$-0.0627433\pi$
$127$	40.7309	+	70.5479i	0.320715	+	0.555495i	−0.659920	+	0.751336i	$0.729410\pi$
$128$	74.2636	+	88.5040i	0.580185	+	0.691437i
$129$		0			0
$130$	−23.6043	+	133.867i	−0.181572	+	1.02974i
$131$	93.4951	−	111.423i	0.713703	−	0.850558i	−0.280300	−	0.959913i	$-0.590434\pi$
$131$	93.4951	−	111.423i	0.713703	−	0.850558i	0.994003	+	0.109354i	$0.0348783\pi$
$132$		0			0
$133$	−144.302	−	52.5215i	−1.08498	−	0.394899i
$134$		−	33.5824i		−	0.250615i
$135$		0			0
$136$	−86.0521			−0.632736
$137$	−64.2995	+	176.661i	−0.469339	+	1.28950i	0.448939	+	0.893563i	$0.351802\pi$
$137$	−64.2995	+	176.661i	−0.469339	+	1.28950i	−0.918278	+	0.395936i	$0.870420\pi$
$138$		0			0
$139$	67.3058	+	56.4763i	0.484214	+	0.406304i	0.851947	−	0.523627i	$-0.175422\pi$
$139$	67.3058	+	56.4763i	0.484214	+	0.406304i	−0.367733	+	0.929931i	$0.619866\pi$
$140$	8.92053	+	1.57293i	0.0637181	+	0.0112352i
$141$		0			0
$142$	88.3904	−	74.1683i	0.622467	−	0.522312i
$143$	103.537	−	59.7772i	0.724036	−	0.418022i
$144$		0			0
$145$	−90.4216	+	156.615i	−0.623597	+	1.08010i
$146$	−100.675	+	17.7517i	−0.689554	+	0.121587i
$147$		0			0
$148$	−14.1718	+	5.15812i	−0.0957556	+	0.0348522i
$149$	21.5015	+	59.0748i	0.144305	+	0.396475i	0.990697	−	0.136085i	$-0.0434521\pi$
$149$	21.5015	+	59.0748i	0.144305	+	0.396475i	−0.846392	+	0.532561i	$0.821230\pi$
$150$		0			0
$151$	−20.0380	−	113.641i	−0.132702	−	0.752591i	−0.976432	−	0.215824i	$-0.930756\pi$
$151$	−20.0380	−	113.641i	−0.132702	−	0.752591i	0.843730	−	0.536767i	$-0.180355\pi$
$152$	122.946	+	70.9828i	0.808854	+	0.466992i
$153$		0			0
$154$	63.6068	+	110.170i	0.413031	+	0.715391i
$155$	102.982	+	122.729i	0.664398	+	0.791798i
$156$		0			0
$157$	9.08750	−	51.5377i	0.0578821	−	0.328266i	−0.942093	−	0.335352i	$-0.891145\pi$
$157$	9.08750	−	51.5377i	0.0578821	−	0.328266i	0.999975	+	0.00708651i	$0.00225573\pi$
$158$	−1.94508	+	2.31806i	−0.0123107	+	0.0146713i
$159$		0			0
$160$	−15.3001	−	5.56880i	−0.0956259	−	0.0348050i
$161$			117.151i			0.727643i
$162$		0			0
$163$	−251.388			−1.54226			−0.771128	−	0.636681i	$-0.780307\pi$
$163$	−251.388			−1.54226			−0.771128	+	0.636681i	$0.780307\pi$
$164$	2.05196	−	5.63771i	0.0125120	−	0.0343763i
$165$		0			0
$166$	168.056	+	141.015i	1.01238	+	0.849490i
$167$	8.33626	+	1.46991i	0.0499177	+	0.00880185i	0.198551	−	0.980091i	$-0.436376\pi$
$167$	8.33626	+	1.46991i	0.0499177	+	0.00880185i	−0.148634	+	0.988892i	$0.547487\pi$
$168$		0			0
$169$	71.7908	−	60.2396i	0.424797	−	0.356447i
$170$	−76.0504	+	43.9077i	−0.447355	+	0.258281i
$171$		0			0
$172$	−0.292229	+	0.506155i	−0.00169901	+	0.00294276i
$173$	−192.095	+	33.8715i	−1.11037	+	0.195789i	−0.698611	−	0.715502i	$-0.746198\pi$
$173$	−192.095	+	33.8715i	−1.11037	+	0.195789i	−0.411764	+	0.911291i	$0.635087\pi$
$174$		0			0
$175$	−52.7571	+	19.2020i	−0.301469	+	0.109726i
$176$	−37.8449	−	103.978i	−0.215028	−	0.590785i
$177$		0			0
$178$	16.1259	+	91.4543i	0.0905947	+	0.513788i
$179$	183.204	+	105.773i	1.02349	+	0.590910i	0.915112	−	0.403200i	$-0.132102\pi$
$179$	183.204	+	105.773i	1.02349	+	0.590910i	0.108374	+	0.994110i	$0.465436\pi$
$180$		0			0
$181$	−43.8874	−	76.0153i	−0.242472	−	0.419974i	0.718946	−	0.695066i	$-0.244625\pi$
$181$	−43.8874	−	76.0153i	−0.242472	−	0.419974i	−0.961418	+	0.275092i	$0.911292\pi$
$182$	179.690	+	214.146i	0.987305	+	1.17662i
$183$		0			0
$184$	18.8067	−	106.658i	0.102210	−	0.579662i
$185$	−177.753	+	211.838i	−0.960826	+	1.14507i
$186$		0			0
$187$	72.5772	+	26.4160i	0.388114	+	0.141262i
$188$		−	11.0033i		−	0.0585283i
$189$		0			0
$190$	144.874			0.762497
$191$	109.875	−	301.878i	0.575260	−	1.58051i	−0.220816	−	0.975316i	$-0.570872\pi$
$191$	109.875	−	301.878i	0.575260	−	1.58051i	0.796075	−	0.605197i	$-0.206906\pi$
$192$		0			0
$193$	47.2668	+	39.6615i	0.244906	+	0.205500i	0.756975	−	0.653444i	$-0.226676\pi$
$193$	47.2668	+	39.6615i	0.244906	+	0.205500i	−0.512069	+	0.858944i	$0.671121\pi$
$194$	70.2505	+	12.3871i	0.362116	+	0.0638508i
$195$		0			0
$196$	5.42140	−	4.54910i	0.0276602	−	0.0232097i
$197$	−194.174	+	112.106i	−0.985652	+	0.569067i	−0.903972	−	0.427592i	$-0.859362\pi$
$197$	−194.174	+	112.106i	−0.985652	+	0.569067i	−0.0816805	+	0.996659i	$0.526029\pi$
$198$		0			0
$199$	2.60375	−	4.50982i	0.0130842	−	0.0226624i	−0.859409	−	0.511288i	$-0.829168\pi$
$199$	2.60375	−	4.50982i	0.0130842	−	0.0226624i	0.872493	+	0.488626i	$0.162502\pi$
$200$	51.1145	−	9.01286i	0.255572	−	0.0450643i
$201$		0			0
$202$	155.512	−	56.6019i	0.769863	−	0.280207i
$203$	127.200	+	349.480i	0.626602	+	1.72157i
$204$		0			0
$205$	−19.1028	−	108.337i	−0.0931843	−	0.528474i
$206$	39.0517	+	22.5465i	0.189571	+	0.109449i
$207$		0			0
$208$	−121.576	−	210.576i	−0.584499	−	1.01238i
$209$	−81.9037	−	97.6090i	−0.391884	−	0.467029i
$210$		0			0
$211$	−4.00322	+	22.7034i	−0.0189726	+	0.107599i	−0.992823	−	0.119589i	$-0.961842\pi$
$211$	−4.00322	+	22.7034i	−0.0189726	+	0.107599i	0.973851	+	0.227188i	$0.0729533\pi$
$212$	7.68583	−	9.15961i	0.0362539	−	0.0432057i
$213$		0			0
$214$	−174.591	−	63.5458i	−0.815845	−	0.296943i
$215$			10.7167i			0.0498452i
$216$		0			0
$217$	329.478			1.51833
$218$	67.7912	−	186.255i	0.310969	−	0.854380i
$219$		0			0
$220$	5.75762	+	4.83122i	0.0261710	+	0.0219601i
$221$	167.143	+	29.4718i	0.756302	+	0.133356i
$222$		0			0
$223$	−144.086	+	120.902i	−0.646124	+	0.542163i	−0.905892	−	0.423508i	$-0.860798\pi$
$223$	−144.086	+	120.902i	−0.646124	+	0.542163i	0.259768	+	0.965671i	$0.416354\pi$
$224$	−28.9984	+	16.7422i	−0.129457	+	0.0747421i
$225$		0			0
$226$	15.8221	−	27.4047i	0.0700093	−	0.121260i
$227$	−123.590	+	21.7922i	−0.544447	+	0.0960007i	−0.439106	−	0.898435i	$-0.644705\pi$
$227$	−123.590	+	21.7922i	−0.544447	+	0.0960007i	−0.105341	+	0.994436i	$0.533594\pi$
$228$		0			0
$229$	123.108	−	44.8078i	0.537591	−	0.195667i	−0.0589335	−	0.998262i	$-0.518770\pi$
$229$	123.108	−	44.8078i	0.537591	−	0.195667i	0.596525	+	0.802595i	$0.296548\pi$
$230$	−37.8009	−	103.857i	−0.164352	−	0.451553i
$231$		0			0
$232$	−59.7040	−	338.598i	−0.257345	−	1.45948i
$233$	−352.009	−	203.233i	−1.51077	−	0.872243i	−0.999921	−	0.0125723i	$-0.995998\pi$
$233$	−352.009	−	203.233i	−1.51077	−	0.872243i	−0.510848	−	0.859671i	$-0.670669\pi$
$234$		0			0
$235$	−100.879	−	174.728i	−0.429274	−	0.743524i
$236$	−0.634895	−	0.756638i	−0.00269023	−	0.00320609i
$237$		0			0
$238$	−31.3599	+	177.851i	−0.131764	+	0.747273i
$239$	123.624	−	147.330i	0.517257	−	0.616443i	−0.442673	−	0.896683i	$-0.645970\pi$
$239$	123.624	−	147.330i	0.517257	−	0.616443i	0.959930	+	0.280240i	$0.0904141\pi$
$240$		0			0
$241$	325.853	+	118.601i	1.35209	+	0.492119i	0.913598	−	0.406618i	$-0.133292\pi$
$241$	325.853	+	118.601i	1.35209	+	0.492119i	0.438488	+	0.898737i	$0.355514\pi$
$242$		−	129.204i		−	0.533903i
$243$		0			0
$244$	8.57251			0.0351332
$245$	44.3832	−	121.942i	0.181156	−	0.497722i
$246$		0			0
$247$	−214.492	−	179.980i	−0.868389	−	0.728665i
$248$	−299.968	−	52.8924i	−1.20955	−	0.213276i
$249$		0			0
$250$	201.184	−	168.814i	0.804738	−	0.675255i
$251$	370.198	−	213.734i	1.47489	−	0.851530i	0.475294	−	0.879827i	$-0.342342\pi$
$251$	370.198	−	213.734i	1.47489	−	0.851530i	0.999600	+	0.0282966i	$0.00900829\pi$
$252$		0			0
$253$	−48.6032	+	84.1831i	−0.192107	+	0.332740i
$254$	−155.649	+	27.4450i	−0.612789	+	0.108051i
$255$		0			0
$256$	42.3814	−	15.4256i	0.165552	−	0.0602561i
$257$	−97.1579	−	266.939i	−0.378046	−	1.03867i	−0.972165	−	0.234297i	$-0.924721\pi$
$257$	−97.1579	−	266.939i	−0.378046	−	1.03867i	0.594119	−	0.804377i	$-0.297501\pi$
$258$		0			0
$259$	98.7536	+	560.060i	0.381288	+	2.16239i
$260$	14.3035	+	8.25811i	0.0550133	+	0.0317620i
$261$		0			0
$262$	141.101	+	244.395i	0.538555	+	0.932805i
$263$	222.694	+	265.396i	0.846746	+	1.00911i	0.999782	+	0.0208915i	$0.00665046\pi$
$263$	222.694	+	265.396i	0.846746	+	1.00911i	−0.153036	+	0.988221i	$0.548905\pi$
$264$		0			0
$265$	38.0717	−	215.915i	0.143667	−	0.814775i
$266$	191.511	−	228.234i	0.719965	−	0.858021i
$267$		0			0
$268$	−3.83431	−	1.39557i	−0.0143071	−	0.00520737i
$269$			297.900i			1.10743i	0.832705	+	0.553717i	$0.186791\pi$
$269$			297.900i			1.10743i	−0.832705	+	0.553717i	$0.813209\pi$
$270$		0			0
$271$	368.678			1.36044			0.680218	−	0.733010i	$-0.261885\pi$
$271$	368.678			1.36044			0.680218	+	0.733010i	$0.261885\pi$
$272$	53.7252	−	147.609i	0.197519	−	0.542680i
$273$		0			0
$274$	−279.415	−	234.457i	−1.01976	−	0.855682i
$275$	−45.8772	−	8.08939i	−0.166826	−	0.0294160i
$276$		0			0
$277$	−216.688	+	181.823i	−0.782268	+	0.656401i	−0.943819	−	0.330463i	$-0.892795\pi$
$277$	−216.688	+	181.823i	−0.782268	+	0.656401i	0.161550	+	0.986864i	$0.448351\pi$
$278$	−147.628	+	85.2331i	−0.531036	+	0.306594i
$279$		0			0
$280$	−157.888	+	273.470i	−0.563886	+	0.976678i
$281$	−276.855	+	48.8169i	−0.985248	+	0.173726i	−0.642985	−	0.765879i	$-0.722304\pi$
$281$	−276.855	+	48.8169i	−0.985248	+	0.173726i	−0.342263	+	0.939604i	$0.611193\pi$
$282$		0			0
$283$	−409.918	+	149.198i	−1.44847	+	0.527201i	−0.942165	−	0.335151i	$-0.891213\pi$
$283$	−409.918	+	149.198i	−1.44847	+	0.527201i	−0.506309	+	0.862352i	$0.668991\pi$
$284$	−4.79504	−	13.1743i	−0.0168839	−	0.0463882i
$285$		0			0
$286$	40.2787	+	228.432i	0.140835	+	0.798713i
$287$	−195.925	−	113.118i	−0.682667	−	0.394138i
$288$		0			0
$289$	−89.6779	−	155.327i	−0.310304	−	0.537463i
$290$	−225.533	−	268.780i	−0.777699	−	0.926826i
$291$		0			0
$292$	−2.15690	+	12.2324i	−0.00738663	+	0.0418917i
$293$	−237.292	+	282.794i	−0.809872	+	0.965167i	−0.999862	−	0.0166187i	$-0.994710\pi$
$293$	−237.292	+	282.794i	−0.809872	+	0.965167i	0.189990	+	0.981786i	$0.439154\pi$
$294$		0			0
$295$	−17.0188	−	6.19434i	−0.0576908	−	0.0209977i
$296$		−	525.751i		−	1.77619i
$297$		0			0
$298$	−121.971			−0.409299
$299$	−73.0580	+	200.725i	−0.244341	+	0.671321i
$300$		0			0
$301$	16.8830	+	14.1665i	0.0560897	+	0.0470649i
$302$	220.483	+	38.8772i	0.730078	+	0.128732i
$303$		0			0
$304$	−198.519	+	166.577i	−0.653023	+	0.547951i
$305$	136.128	−	78.5936i	0.446321	−	0.257684i
$306$		0			0
$307$	183.104	−	317.145i	0.596429	−	1.03304i	−0.396915	−	0.917855i	$-0.629919\pi$
$307$	183.104	−	317.145i	0.596429	−	1.03304i	0.993344	−	0.115189i	$-0.0367475\pi$
$308$	15.2221	−	2.68407i	0.0494224	−	0.00871450i
$309$		0			0
$310$	−292.091	+	106.312i	−0.942229	+	0.342943i
$311$	−163.214	−	448.426i	−0.524803	−	1.44189i	−0.865115	−	0.501573i	$-0.832755\pi$
$311$	−163.214	−	448.426i	−0.524803	−	1.44189i	0.340312	−	0.940313i	$-0.389467\pi$
$312$		0			0
$313$	−17.5673	−	99.6288i	−0.0561254	−	0.318303i	0.943800	−	0.330517i	$-0.107223\pi$
$313$	−17.5673	−	99.6288i	−0.0561254	−	0.318303i	−0.999925	+	0.0122141i	$0.996112\pi$
$314$	87.9315	+	50.7673i	0.280037	+	0.161679i
$315$		0			0
$316$	0.183836	+	0.318413i	0.000581759	+	0.00100764i
$317$	238.169	+	283.839i	0.751321	+	0.895390i	0.997266	−	0.0738942i	$-0.0235427\pi$
$317$	238.169	+	283.839i	0.751321	+	0.895390i	−0.245945	+	0.969284i	$0.579098\pi$
$318$		0			0
$319$	−53.5866	+	303.905i	−0.167983	+	0.952680i
$320$	187.030	−	222.894i	0.584469	−	0.696544i
$321$		0			0
$322$	−213.585	−	77.7385i	−0.663307	−	0.241424i
$323$		−	180.887i		−	0.560021i
$324$		0			0
$325$	−102.369			−0.314980
$326$	166.815	−	458.321i	0.511703	−	1.40589i
$327$		0			0
$328$	160.218	+	134.439i	0.488469	+	0.409874i
$329$	−408.618	−	72.0504i	−1.24200	−	0.218998i
$330$		0			0
$331$	273.215	−	229.254i	0.825422	−	0.692611i	−0.128813	−	0.991669i	$-0.541117\pi$
$331$	273.215	−	229.254i	0.825422	−	0.692611i	0.954235	+	0.299058i	$0.0966723\pi$
$332$	23.0844	−	13.3278i	0.0695314	−	0.0401440i
$333$		0			0
$334$	−8.21164	+	14.2230i	−0.0245857	+	0.0425838i
$335$	−73.6820	+	12.9921i	−0.219946	+	0.0387825i
$336$		0			0
$337$	377.038	−	137.231i	1.11881	−	0.407212i	0.284590	−	0.958649i	$-0.408143\pi$
$337$	377.038	−	137.231i	1.11881	−	0.407212i	0.834217	+	0.551437i	$0.185920\pi$
$338$	62.1879	+	170.860i	0.183988	+	0.505503i
$339$		0			0
$340$	1.85281	+	10.5078i	0.00544943	+	0.0309053i
$341$	236.759	+	136.693i	0.694308	+	0.400859i
$342$		0			0
$343$	84.3548	+	146.107i	0.245932	+	0.425967i
$344$	−13.0967	−	15.6080i	−0.0380717	−	0.0453721i
$345$		0			0
$346$	65.7165	−	372.697i	0.189932	−	1.07716i
$347$	−36.8193	+	43.8795i	−0.106107	+	0.126454i	−0.816484	−	0.577367i	$-0.804080\pi$
$347$	−36.8193	+	43.8795i	−0.106107	+	0.126454i	0.710377	+	0.703821i	$0.248524\pi$
$348$		0			0
$349$	−352.495	−	128.298i	−1.01001	−	0.367615i	−0.216576	−	0.976266i	$-0.569489\pi$
$349$	−352.495	−	128.298i	−1.01001	−	0.367615i	−0.793438	+	0.608651i	$0.791711\pi$
$350$		−	108.927i		−	0.311220i
$351$		0			0
$352$	−27.7839			−0.0789316
$353$	−75.2545	+	206.760i	−0.213185	+	0.585722i	−0.999484	−	0.0321247i	$-0.989773\pi$
$353$	−75.2545	+	206.760i	−0.213185	+	0.585722i	0.786298	+	0.617847i	$0.211995\pi$
$354$		0			0
$355$	−196.926	−	165.241i	−0.554721	−	0.465466i
$356$	11.1120	+	1.95935i	0.0312136	+	0.00550379i
$357$		0			0
$358$	−314.411	+	263.822i	−0.878244	+	0.736934i
$359$	−174.426	+	100.705i	−0.485866	+	0.280515i	−0.722858	−	0.690997i	$-0.757172\pi$
$359$	−174.426	+	100.705i	−0.485866	+	0.280515i	0.236992	+	0.971512i	$0.423838\pi$
$360$		0			0
$361$	31.2901	−	54.1960i	0.0866761	−	0.150127i
$362$	167.711	−	29.5720i	0.463290	−	0.0816906i
$363$		0			0
$364$	31.9176	−	11.6171i	0.0876857	−	0.0319150i
$365$	77.8968	+	214.020i	0.213416	+	0.586355i
$366$		0			0
$367$	27.6384	+	156.745i	0.0753089	+	0.427098i	0.999030	+	0.0440325i	$0.0140205\pi$
$367$	27.6384	+	156.745i	0.0753089	+	0.427098i	−0.923721	+	0.383065i	$0.874868\pi$
$368$	171.213	+	98.8500i	0.465253	+	0.268614i
$369$		0			0
$370$	−268.262	−	464.643i	−0.725032	−	1.25579i
$371$	−289.823	−	345.398i	−0.781195	−	0.930992i
$372$		0			0
$373$	−8.96857	+	50.8633i	−0.0240444	+	0.136363i	−0.994467	−	0.105050i	$-0.966500\pi$
$373$	−8.96857	+	50.8633i	−0.0240444	+	0.136363i	0.970423	+	0.241413i	$0.0776108\pi$
$374$	−96.3212	+	114.791i	−0.257543	+	0.306928i
$375$		0			0
$376$	360.453	+	131.194i	0.958653	+	0.348921i
$377$			678.122i			1.79873i
$378$		0			0
$379$	147.231			0.388472			0.194236	−	0.980955i	$-0.437777\pi$
$379$	147.231			0.388472			0.194236	+	0.980955i	$0.437777\pi$
$380$	6.02050	−	16.5412i	0.0158434	−	0.0435295i
$381$		0			0
$382$	477.463	+	400.639i	1.24990	+	1.04879i
$383$	112.007	+	19.7499i	0.292447	+	0.0515663i	0.317947	−	0.948109i	$-0.397007\pi$
$383$	112.007	+	19.7499i	0.292447	+	0.0515663i	−0.0255000	+	0.999675i	$0.508118\pi$
$384$		0			0
$385$	217.113	−	182.180i	0.563930	−	0.473194i
$386$	−103.675	+	59.8566i	−0.268587	+	0.155069i
$387$		0			0
$388$	4.33368	−	7.50616i	0.0111693	−	0.0193458i
$389$	356.902	−	62.9314i	0.917485	−	0.161777i	0.305085	−	0.952325i	$-0.401315\pi$
$389$	356.902	−	62.9314i	0.917485	−	0.161777i	0.612400	+	0.790548i	$0.290204\pi$
$390$		0			0
$391$	−129.673	+	47.1973i	−0.331646	+	0.120709i
$392$	84.3819	+	231.837i	0.215260	+	0.591422i
$393$		0			0
$394$	−75.5387	−	428.401i	−0.191723	−	1.08731i
$395$	5.83848	+	3.37085i	0.0147810	+	0.00853379i
$396$		0			0
$397$	368.516	+	638.289i	0.928252	+	1.60778i	0.786246	+	0.617914i	$0.212022\pi$
$397$	368.516	+	638.289i	0.928252	+	1.60778i	0.142006	+	0.989866i	$0.454645\pi$
$398$	6.49436	+	7.73968i	0.0163175	+	0.0194464i
$399$		0			0
$400$	−16.4523	+	93.3058i	−0.0411308	+	0.233265i
$401$	−142.250	+	169.527i	−0.354739	+	0.422761i	−0.913673	−	0.406451i	$-0.866766\pi$
$401$	−142.250	+	169.527i	−0.354739	+	0.422761i	0.558934	+	0.829212i	$0.311211\pi$
$402$		0			0
$403$	564.525	+	205.470i	1.40081	+	0.509852i
$404$		−	20.1080i		−	0.0497722i
$405$		0			0
$406$	−721.566			−1.77726
$407$	−161.393	+	443.424i	−0.396543	+	1.08949i
$408$		0			0
$409$	341.033	+	286.161i	0.833823	+	0.699660i	0.956165	−	0.292828i	$-0.0945962\pi$
$409$	341.033	+	286.161i	0.833823	+	0.699660i	−0.122343	+	0.992488i	$0.539041\pi$
$410$	210.193	+	37.0626i	0.512665	+	0.0903967i
$411$		0			0
$412$	4.19713	−	3.52181i	0.0101872	−	0.00854807i
$413$	−32.2558	+	18.6229i	−0.0781012	+	0.0450917i
$414$		0			0
$415$	244.381	−	423.280i	0.588870	−	1.01995i
$416$	−60.1266	+	10.6019i	−0.144535	+	0.0254854i
$417$		0			0
$418$	232.307	−	84.5527i	0.555758	−	0.202279i
$419$	197.412	+	542.386i	0.471151	+	1.29448i	0.916828	+	0.399283i	$0.130741\pi$
$419$	197.412	+	542.386i	0.471151	+	1.29448i	−0.445676	+	0.895194i	$0.647037\pi$
$420$		0			0
$421$	−58.3454	−	330.893i	−0.138588	−	0.785970i	−0.972294	−	0.233762i	$-0.924896\pi$
$421$	−58.3454	−	330.893i	−0.138588	−	0.785970i	0.833706	−	0.552208i	$-0.186215\pi$
$422$	−38.7356	−	22.3640i	−0.0917905	−	0.0529953i
$423$		0			0
$424$	208.417	+	360.989i	0.491549	+	0.851388i
$425$	−42.5093	−	50.6606i	−0.100022	−	0.119201i
$426$		0			0
$427$	56.1334	−	318.348i	0.131460	−	0.745546i
$428$	−14.5108	+	17.2933i	−0.0339038	+	0.0404050i
$429$		0			0
$430$	−19.5384	−	7.11138i	−0.0454380	−	0.0165381i
$431$			113.799i			0.264034i	0.991247	+	0.132017i	$0.0421454\pi$
$431$			113.799i			0.264034i	−0.991247	+	0.132017i	$0.957855\pi$
$432$		0			0
$433$	−204.214			−0.471625			−0.235812	−	0.971799i	$-0.575775\pi$
$433$	−204.214			−0.471625			−0.235812	+	0.971799i	$0.575775\pi$
$434$	−218.634	+	600.692i	−0.503765	+	1.38408i
$435$		0			0
$436$	−18.4487	−	15.4803i	−0.0423134	−	0.0355052i
$437$	224.201	+	39.5327i	0.513046	+	0.0904639i
$438$		0			0
$439$	309.361	−	259.584i	0.704694	−	0.591309i	−0.218411	−	0.975857i	$-0.570087\pi$
$439$	309.361	−	259.584i	0.704694	−	0.591309i	0.923105	+	0.384548i	$0.125643\pi$
$440$	−226.913	+	131.008i	−0.515712	+	0.297746i
$441$		0			0
$442$	−164.644	+	285.172i	−0.372498	+	0.645185i
$443$	651.568	−	114.889i	1.47081	−	0.259343i	0.619909	−	0.784674i	$-0.287169\pi$
$443$	651.568	−	114.889i	1.47081	−	0.259343i	0.850898	+	0.525331i	$0.176058\pi$
$444$		0			0
$445$	194.418	−	70.7624i	0.436894	−	0.159017i
$446$	−124.813	−	342.920i	−0.279849	−	0.768879i
$447$		0			0
$448$	−103.908	−	589.291i	−0.231937	−	1.31538i
$449$	−403.851	−	233.164i	−0.899446	−	0.519295i	−0.0224253	−	0.999749i	$-0.507139\pi$
$449$	−403.851	−	233.164i	−0.899446	−	0.519295i	−0.877020	+	0.480453i	$0.840472\pi$
$450$		0			0
$451$	−93.8599	−	162.570i	−0.208115	−	0.360466i
$452$	−2.47145	−	2.94535i	−0.00546780	−	0.00651627i
$453$		0			0
$454$	42.2805	−	239.785i	0.0931289	−	0.528160i
$455$	400.333	−	477.098i	0.879852	−	1.04857i
$456$		0			0
$457$	−802.579	−	292.115i	−1.75619	−	0.639201i	−0.756303	−	0.654222i	$-0.772996\pi$
$457$	−802.579	−	292.115i	−1.75619	−	0.639201i	−0.999887	+	0.0150210i	$0.995218\pi$
$458$			254.180i			0.554979i
$459$		0			0
$460$	−13.4289			−0.0291932
$461$	−28.0154	+	76.9718i	−0.0607710	+	0.166967i	−0.966362	−	0.257184i	$-0.917205\pi$
$461$	−28.0154	+	76.9718i	−0.0607710	+	0.166967i	0.905591	+	0.424151i	$0.139428\pi$
$462$		0			0
$463$	−501.465	−	420.779i	−1.08308	−	0.908810i	−0.0869046	−	0.996217i	$-0.527698\pi$
$463$	−501.465	−	420.779i	−1.08308	−	0.908810i	−0.996173	+	0.0874069i	$0.972142\pi$
$464$	618.087	+	108.985i	1.33208	+	0.234882i
$465$		0			0
$466$	604.112	−	506.910i	1.29638	−	1.08779i
$467$	113.391	−	65.4664i	0.242808	−	0.140185i	−0.373659	−	0.927566i	$-0.621897\pi$
$467$	113.391	−	65.4664i	0.242808	−	0.140185i	0.616466	+	0.787381i	$0.288564\pi$
$468$		0			0
$469$	−76.9332	+	133.252i	−0.164037	+	0.284120i
$470$	385.499	−	67.9739i	0.820212	−	0.144625i
$471$		0			0
$472$	32.3564	−	11.7768i	0.0685516	−	0.0249508i
$473$	6.25457	+	17.1843i	0.0132232	+	0.0363304i
$474$		0			0
$475$	18.9456	+	107.446i	0.0398854	+	0.226201i
$476$	19.0031	+	10.9714i	0.0399225	+	0.0230493i
$477$		0			0
$478$	186.572	+	323.152i	0.390318	+	0.676051i
$479$	101.346	+	120.780i	0.211579	+	0.252150i	0.861388	−	0.507947i	$-0.169596\pi$
$479$	101.346	+	120.780i	0.211579	+	0.252150i	−0.649809	+	0.760098i	$0.725151\pi$
$480$		0			0
$481$	−180.063	+	1021.19i	−0.374351	+	2.12305i
$482$	−432.457	+	515.382i	−0.897214	+	1.06926i
$483$		0			0
$484$	−14.7520	−	5.36931i	−0.0304794	−	0.0110936i
$485$		−	158.926i		−	0.327683i
$486$		0			0
$487$	−698.201			−1.43368			−0.716839	−	0.697239i	$-0.754412\pi$
$487$	−698.201			−1.43368			−0.716839	+	0.697239i	$0.754412\pi$
$488$	−102.211	+	280.824i	−0.209450	+	0.575458i
$489$		0			0
$490$	192.868	+	161.836i	0.393609	+	0.330277i
$491$	−41.5804	−	7.33174i	−0.0846851	−	0.0149323i	0.131145	−	0.991363i	$-0.458135\pi$
$491$	−41.5804	−	7.33174i	−0.0846851	−	0.0149323i	−0.215830	+	0.976431i	$0.569246\pi$
$492$		0			0
$493$	−335.591	+	281.595i	−0.680713	+	0.571186i
$494$	470.466	−	271.623i	0.952359	−	0.549845i
$495$		0			0
$496$	278.009	−	481.525i	0.560501	−	0.970816i
$497$	−520.636	+	91.8022i	−1.04756	+	0.184713i
$498$		0			0
$499$	451.394	−	164.294i	0.904597	−	0.329247i	0.152504	−	0.988303i	$-0.451266\pi$
$499$	451.394	−	164.294i	0.904597	−	0.329247i	0.752094	+	0.659056i	$0.229044\pi$
$500$	−10.9139	−	29.9858i	−0.0218279	−	0.0599716i
$501$		0			0
$502$	144.017	+	816.761i	0.286887	+	1.62701i
$503$	73.7969	+	42.6067i	0.146714	+	0.0847051i	0.571560	−	0.820560i	$-0.306339\pi$
$503$	73.7969	+	42.6067i	0.146714	+	0.0847051i	−0.424846	+	0.905266i	$0.639672\pi$
$504$		0			0
$505$	−184.352	−	319.307i	−0.365053	−	0.632290i
$506$	−121.228	−	144.474i	−0.239580	−	0.285521i
$507$		0			0
$508$	−3.33467	+	18.9119i	−0.00656431	+	0.0372281i
$509$	−255.368	+	304.336i	−0.501706	+	0.597910i	−0.956154	−	0.292863i	$-0.905392\pi$
$509$	−255.368	+	304.336i	−0.501706	+	0.597910i	0.454449	+	0.890773i	$0.349836\pi$
$510$		0			0
$511$	440.137	+	160.197i	0.861324	+	0.313496i
$512$			549.639i			1.07351i
$513$		0			0
$514$	551.146			1.07227
$515$	34.3604	−	94.4045i	0.0667193	−	0.183310i
$516$		0			0
$517$	−263.736	−	221.301i	−0.510129	−	0.428049i
$518$	−1086.61	−	191.599i	−2.09771	−	0.369882i
$519$		0			0
$520$	−441.067	+	370.099i	−0.848206	+	0.711729i
$521$	−19.7109	+	11.3801i	−0.0378328	+	0.0218428i	−0.518797	−	0.854897i	$-0.673620\pi$
$521$	−19.7109	+	11.3801i	−0.0378328	+	0.0218428i	0.480964	+	0.876740i	$0.340287\pi$
$522$		0			0
$523$	−380.270	+	658.647i	−0.727093	+	1.25936i	0.231013	+	0.972951i	$0.425796\pi$
$523$	−380.270	+	658.647i	−0.727093	+	1.25936i	−0.958107	+	0.286412i	$0.907537\pi$
$524$	33.7677	−	5.95416i	0.0644423	−	0.0113629i
$525$		0			0
$526$	−631.636	+	229.897i	−1.20083	+	0.437066i
$527$	132.739	+	364.697i	0.251877	+	0.692025i
$528$		0			0
$529$	61.7010	+	349.924i	0.116637	+	0.661482i
$530$	368.385	+	212.687i	0.695067	+	0.401297i
$531$		0			0
$532$	−18.1003	−	31.3506i	−0.0340231	−	0.0589297i
$533$	−265.154	−	315.999i	−0.497476	−	0.592868i
$534$		0			0
$535$	−71.8793	+	407.648i	−0.134354	+	0.761958i
$536$	91.4342	−	108.967i	0.170586	−	0.203297i
$537$		0			0
$538$	−543.120	−	197.680i	−1.00952	−	0.367434i
$539$		−	221.437i		−	0.410830i
$540$		0			0
$541$	−158.844			−0.293612			−0.146806	−	0.989165i	$-0.546899\pi$
$541$	−158.844			−0.293612			−0.146806	+	0.989165i	$0.546899\pi$
$542$	−244.646	+	672.161i	−0.451377	+	1.24015i
$543$		0			0
$544$	−30.2147	−	25.3531i	−0.0555417	−	0.0466050i
$545$	−434.882	−	76.6814i	−0.797948	−	0.140700i
$546$		0			0
$547$	−504.099	+	422.989i	−0.921570	+	0.773289i	−0.974285	−	0.225320i	$-0.927657\pi$
$547$	−504.099	+	422.989i	−0.921570	+	0.773289i	0.0527145	+	0.998610i	$0.483213\pi$
$548$	−38.3809	+	22.1592i	−0.0700382	+	0.0404366i
$549$		0			0
$550$	45.1914	−	78.2737i	0.0821661	−	0.142316i
$551$	711.753	−	125.501i	1.29175	−	0.227770i
$552$		0			0
$553$	13.0283	−	4.74192i	0.0235594	−	0.00857490i
$554$	−187.704	−	515.712i	−0.338816	−	0.930888i
$555$		0			0
$556$	3.59665	+	20.3976i	0.00646879	+	0.0366863i
$557$	817.907	+	472.219i	1.46842	+	0.847790i	0.999374	−	0.0353864i	$-0.0112662\pi$
$557$	817.907	+	472.219i	1.46842	+	0.847790i	0.469041	+	0.883176i	$0.344600\pi$
$558$		0			0
$559$	20.0927	+	34.8015i	0.0359439	+	0.0622567i
$560$	−370.520	−	441.568i	−0.661643	−	0.788515i
$561$		0			0
$562$	94.7132	−	537.145i	0.168529	−	0.955774i
$563$	680.250	−	810.691i	1.20826	−	1.43995i	0.342479	−	0.939526i	$-0.388734\pi$
$563$	680.250	−	810.691i	1.20826	−	1.43995i	0.865781	−	0.500423i	$-0.166822\pi$
$564$		0			0
$565$	−66.2489	−	24.1126i	−0.117255	−	0.0426772i
$566$		−	846.352i		−	1.49532i
$567$		0			0
$568$	488.742			0.860462
$569$	61.1104	−	167.899i	0.107400	−	0.295078i	−0.874338	−	0.485317i	$-0.838704\pi$
$569$	61.1104	−	167.899i	0.107400	−	0.295078i	0.981738	+	0.190239i	$0.0609264\pi$
$570$		0			0
$571$	461.490	+	387.236i	0.808213	+	0.678171i	0.950181	−	0.311700i	$-0.100898\pi$
$571$	461.490	+	387.236i	0.808213	+	0.678171i	−0.141968	+	0.989871i	$0.545343\pi$
$572$	27.7553	+	4.89401i	0.0485233	+	0.00855596i
$573$		0			0
$574$	336.244	−	282.142i	0.585790	−	0.491536i
$575$	72.0819	−	41.6165i	0.125360	−	0.0723766i
$576$		0			0
$577$	87.1430	−	150.936i	0.151028	−	0.261588i	−0.780578	−	0.625059i	$-0.785075\pi$
$577$	87.1430	−	150.936i	0.151028	−	0.261588i	0.931606	+	0.363471i	$0.118408\pi$
$578$	342.694	−	60.4263i	0.592897	−	0.104544i
$579$		0			0
$580$	−40.0606	+	14.5809i	−0.0690700	+	0.0251394i
$581$	−343.782	−	944.532i	−0.591707	−	1.62570i
$582$		0			0
$583$	−64.9660	−	368.440i	−0.111434	−	0.631973i
$584$	−374.998	−	216.505i	−0.642121	−	0.370728i
$585$		0			0
$586$	−358.118	−	620.279i	−0.611123	−	1.05850i
$587$	−656.356	−	782.215i	−1.11815	−	1.33256i	−0.937088	−	0.349092i	$-0.886490\pi$
$587$	−656.356	−	782.215i	−1.11815	−	1.33256i	−0.181065	−	0.983471i	$-0.557955\pi$
$588$		0			0
$589$	111.183	−	630.550i	0.188766	−	1.07054i
$590$	22.5866	−	26.9176i	0.0382823	−	0.0456231i
$591$		0			0
$592$	901.843	+	328.244i	1.52338	+	0.554466i
$593$		−	848.172i		−	1.43031i	−0.698967	−	0.715153i	$-0.746357\pi$
$593$		−	848.172i		−	1.43031i	0.698967	−	0.715153i	$-0.253643\pi$
$594$		0			0
$595$	402.349			0.676216
$596$	−5.06871	+	13.9262i	−0.00850455	+	0.0233661i
$597$		0			0
$598$	−317.475	−	266.393i	−0.530895	−	0.445474i
$599$	313.067	+	55.2021i	0.522649	+	0.0921571i	0.428747	−	0.903424i	$-0.358955\pi$
$599$	313.067	+	55.2021i	0.522649	+	0.0921571i	0.0939015	+	0.995581i	$0.470066\pi$
$600$		0			0
$601$	−417.180	+	350.055i	−0.694143	+	0.582455i	−0.920101	−	0.391682i	$-0.871893\pi$
$601$	−417.180	+	350.055i	−0.694143	+	0.582455i	0.225958	+	0.974137i	$0.427449\pi$
$602$	−37.0311	+	21.3799i	−0.0615134	+	0.0355148i
$603$		0			0
$604$	13.6014	−	23.5583i	0.0225189	−	0.0390039i
$605$	−283.483	+	49.9857i	−0.468567	+	0.0826210i
$606$		0			0
$607$	−400.257	+	145.682i	−0.659402	+	0.240003i	−0.649978	−	0.759953i	$-0.725222\pi$
$607$	−400.257	+	145.682i	−0.659402	+	0.240003i	−0.00942378	+	0.999956i	$0.503000\pi$
$608$	22.2555	+	61.1465i	0.0366044	+	0.100570i
$609$		0			0
$610$	52.9575	+	300.337i	0.0868155	+	0.492355i
$611$	−655.192	−	378.275i	−1.07233	−	0.619108i
$612$		0			0
$613$	−43.8571	−	75.9627i	−0.0715450	−	0.123920i	0.828034	−	0.560679i	$-0.189460\pi$
$613$	−43.8571	−	75.9627i	−0.0715450	−	0.123920i	−0.899579	+	0.436759i	$0.856126\pi$
$614$	456.703	+	544.278i	0.743817	+	0.886446i
$615$		0			0
$616$	−93.5693	+	530.658i	−0.151898	+	0.861457i
$617$	−443.723	+	528.809i	−0.719163	+	0.857065i	−0.994549	−	0.104269i	$-0.966750\pi$
$617$	−443.723	+	528.809i	−0.719163	+	0.857065i	0.275387	+	0.961334i	$0.411194\pi$
$618$		0			0
$619$	−651.792	−	237.233i	−1.05298	−	0.383252i	−0.243190	−	0.969979i	$-0.578194\pi$
$619$	−651.792	−	237.233i	−1.05298	−	0.383252i	−0.809785	+	0.586727i	$0.800416\pi$
$620$			37.7678i			0.0609158i
$621$		0			0
$622$	925.860			1.48852
$623$	145.525	−	399.825i	0.233587	−	0.641774i
$624$		0			0
$625$	−327.268	−	274.611i	−0.523629	−	0.439377i
$626$	193.297	+	34.0835i	0.308781	+	0.0544464i
$627$		0			0
$628$	9.45055	−	7.92995i	0.0150486	−	0.0126273i
$629$	−580.142	+	334.945i	−0.922324	+	0.532504i
$630$		0			0
$631$	−58.9015	+	102.020i	−0.0933463	+	0.161681i	−0.908917	−	0.416977i	$-0.863090\pi$
$631$	−58.9015	+	102.020i	−0.0933463	+	0.161681i	0.815571	+	0.578657i	$0.196423\pi$
$632$	−12.6227	+	2.22572i	−0.0199726	+	0.00352170i
$633$		0			0
$634$	−675.528	+	245.872i	−1.06550	+	0.387811i
$635$	120.432	+	330.885i	0.189657	+	0.521079i
$636$		0			0
$637$	−84.4972	−	479.207i	−0.132649	−	0.752288i
$638$	−518.510	−	299.362i	−0.812711	−	0.469219i
$639$		0			0
$640$	249.699	+	432.491i	0.390155	+	0.675768i
$641$	−235.696	−	280.891i	−0.367700	−	0.438208i	0.550192	−	0.835038i	$-0.314555\pi$
$641$	−235.696	−	280.891i	−0.367700	−	0.438208i	−0.917892	+	0.396830i	$0.870110\pi$
$642$		0			0
$643$	166.808	−	946.016i	0.259422	−	1.47125i	−0.525041	−	0.851077i	$-0.675950\pi$
$643$	166.808	−	946.016i	0.259422	−	1.47125i	0.784463	−	0.620176i	$-0.212939\pi$
$644$	−17.7517	+	21.1557i	−0.0275648	+	0.0328505i
$645$		0			0
$646$	329.786	+	120.032i	0.510505	+	0.185809i
$647$			181.832i			0.281039i	0.990078	+	0.140519i	$0.0448772\pi$
$647$			181.832i			0.281039i	−0.990078	+	0.140519i	$0.955123\pi$
$648$		0			0
$649$	−30.9049			−0.0476192
$650$	67.9295	−	186.635i	0.104507	−	0.287130i
$651$		0			0
$652$	−45.3970	−	38.0926i	−0.0696273	−	0.0584242i
$653$	867.398	+	152.946i	1.32833	+	0.234220i	0.792378	−	0.610030i	$-0.208843\pi$
$653$	867.398	+	152.946i	1.32833	+	0.234220i	0.535950	+	0.844250i	$0.319954\pi$
$654$		0			0
$655$	481.630	−	404.135i	0.735313	−	0.617001i
$656$	−330.638	+	190.894i	−0.504021	+	0.290997i
$657$		0			0
$658$	402.509	−	697.167i	0.611717	−	1.05952i
$659$	62.7839	−	11.0705i	0.0952715	−	0.0167989i	−0.125809	−	0.992054i	$-0.540153\pi$
$659$	62.7839	−	11.0705i	0.0952715	−	0.0167989i	0.221081	+	0.975256i	$0.429042\pi$
$660$		0			0
$661$	430.936	−	156.848i	0.651945	−	0.237289i	0.00519031	−	0.999987i	$-0.498348\pi$
$661$	430.936	−	156.848i	0.651945	−	0.237289i	0.646755	+	0.762698i	$0.276126\pi$
$662$	236.669	+	650.243i	0.357506	+	0.982240i
$663$		0			0
$664$	161.361	+	915.123i	0.243013	+	1.37820i
$665$	−574.850	−	331.890i	−0.864436	−	0.499082i
$666$		0			0
$667$	−275.681	−	477.493i	−0.413315	−	0.715882i
$668$	1.28267	+	1.52863i	0.00192017	+	0.00228837i
$669$		0			0
$670$	25.2070	−	142.956i	0.0376223	−	0.213367i
$671$	172.412	−	205.473i	0.256948	−	0.306219i
$672$		0			0
$673$	1031.32	+	375.371i	1.53243	+	0.557758i	0.964214	−	0.265124i	$-0.0854129\pi$
$673$	1031.32	+	375.371i	1.53243	+	0.557758i	0.568213	+	0.822882i	$0.307635\pi$
$674$			778.465i			1.15499i
$675$		0			0
$676$	22.0924			0.0326811
$677$	167.823	−	461.089i	0.247892	−	0.681077i	−0.751871	−	0.659310i	$-0.770849\pi$
$677$	167.823	−	461.089i	0.247892	−	0.681077i	0.999763	−	0.0217671i	$-0.00692923\pi$
$678$		0			0
$679$	−250.371	−	210.086i	−0.368735	−	0.309405i
$680$	−366.312	−	64.5907i	−0.538694	−	0.0949863i
$681$		0			0
$682$	−406.322	+	340.944i	−0.595780	+	0.499918i
$683$	684.465	−	395.176i	1.00215	−	0.578589i	0.0932631	−	0.995642i	$-0.470270\pi$
$683$	684.465	−	395.176i	1.00215	−	0.578589i	0.908882	+	0.417053i	$0.136937\pi$
$684$		0			0
$685$	−406.316	+	703.760i	−0.593162	+	1.02739i
$686$	−322.353	+	56.8395i	−0.469902	+	0.0828563i
$687$		0			0
$688$	34.9497	−	12.7207i	0.0507990	−	0.0184893i
$689$	−281.183	−	772.544i	−0.408103	−	1.12125i
$690$		0			0
$691$	−37.4889	−	212.610i	−0.0542531	−	0.307685i	0.945591	−	0.325359i	$-0.105485\pi$
$691$	−37.4889	−	212.610i	−0.0542531	−	0.307685i	−0.999844	+	0.0176740i	$0.994374\pi$
$692$	−39.8221	−	22.9913i	−0.0575464	−	0.0332244i
$693$		0			0
$694$	−55.5671	−	96.2451i	−0.0800679	−	0.138682i
$695$	244.120	+	290.931i	0.351252	+	0.418606i
$696$		0			0
$697$	46.2755	−	262.441i	0.0663924	−	0.376530i
$698$	467.815	−	557.521i	0.670223	−	0.798740i
$699$		0			0
$700$	−12.4368	−	4.52664i	−0.0177669	−	0.00646663i
$701$		−	503.242i		−	0.717891i	−0.933358	−	0.358946i	$-0.883136\pi$
$701$		−	503.242i		−	0.717891i	0.933358	−	0.358946i	$-0.116864\pi$
$702$		0			0
$703$	1105.16			1.57206
$704$	169.817	−	466.567i	0.241217	−	0.662737i
$705$		0			0
$706$	−327.020	−	274.402i	−0.463201	−	0.388672i
$707$	−746.728	−	131.668i	−1.05619	−	0.186235i
$708$		0			0
$709$	987.327	−	828.466i	1.39256	−	1.16850i	0.428273	−	0.903650i	$-0.359122\pi$
$709$	987.327	−	828.466i	1.39256	−	1.16850i	0.964290	−	0.264849i	$-0.0853221\pi$
$710$	431.936	−	249.379i	0.608361	−	0.351237i
$711$		0			0
$712$	−196.676	+	340.653i	−0.276230	+	0.478445i
$713$	−481.036	+	84.8197i	−0.674665	+	0.118962i
$714$		0			0
$715$	485.612	−	176.748i	0.679177	−	0.247200i
$716$	17.0563	+	46.8618i	0.0238217	+	0.0654495i
$717$		0			0
$718$	−67.8563	−	384.832i	−0.0945074	−	0.535978i
$719$	497.326	+	287.131i	0.691691	+	0.399348i	0.804245	−	0.594298i	$-0.202570\pi$
$719$	497.326	+	287.131i	0.691691	+	0.399348i	−0.112554	+	0.993646i	$0.535903\pi$
$720$		0			0
$721$	−103.302	−	178.925i	−0.143277	−	0.248162i
$722$	78.0448	+	93.0102i	0.108095	+	0.128823i
$723$		0			0
$724$	3.59310	−	20.3775i	0.00496285	−	0.0281457i
$725$	169.846	−	202.414i	0.234270	−	0.279192i
$726$		0			0
$727$	−524.941	−	191.063i	−0.722065	−	0.262810i	−0.0452628	−	0.998975i	$-0.514413\pi$
$727$	−524.941	−	191.063i	−0.722065	−	0.262810i	−0.676802	+	0.736165i	$0.736635\pi$
$728$			1184.09i			1.62650i
$729$		0			0
$730$	−441.884			−0.605320
$731$	−8.87909	+	24.3951i	−0.0121465	+	0.0333722i
$732$		0			0
$733$	863.874	+	724.876i	1.17855	+	0.988917i	0.999988	+	0.00498788i	$0.00158770\pi$
$733$	863.874	+	724.876i	1.17855	+	0.988917i	0.178558	+	0.983929i	$0.442857\pi$
$734$	−304.112	−	53.6231i	−0.414321	−	0.0730560i
$735$		0			0
$736$	38.0275	−	31.9089i	0.0516678	−	0.0433545i
$737$	−110.567	+	63.8358i	−0.150023	+	0.0866157i
$738$		0			0
$739$	−163.517	+	283.219i	−0.221268	+	0.383247i	−0.955193	−	0.295983i	$-0.904353\pi$
$739$	−163.517	+	283.219i	−0.221268	+	0.383247i	0.733926	+	0.679230i	$0.237686\pi$
$740$	−64.1992	+	11.3201i	−0.0867557	+	0.0152974i
$741$		0			0
$742$	822.037	−	299.197i	1.10787	−	0.403231i
$743$	127.652	+	350.722i	0.171807	+	0.472034i	0.995474	−	0.0950393i	$-0.0302977\pi$
$743$	127.652	+	350.722i	0.171807	+	0.472034i	−0.823667	+	0.567074i	$0.808075\pi$
$744$		0			0
$745$	47.1873	+	267.612i	0.0633386	+	0.359211i
$746$	−86.7808	−	50.1029i	−0.116328	−	0.0671621i
$747$		0			0
$748$	9.10361	+	15.7679i	0.0121706	+	0.0210801i
$749$	547.186	+	652.111i	0.730555	+	0.870642i
$750$		0			0
$751$	−200.348	+	1136.23i	−0.266774	+	1.51295i	0.497160	+	0.867659i	$0.334376\pi$
$751$	−200.348	+	1136.23i	−0.266774	+	1.51295i	−0.763934	+	0.645294i	$0.776735\pi$
$752$	−450.086	+	536.392i	−0.598519	+	0.713287i
$753$		0			0
$754$	−1236.33	−	449.986i	−1.63969	−	0.596799i
$755$		−	498.796i		−	0.660657i
$756$		0			0
$757$	−372.849			−0.492535			−0.246268	−	0.969202i	$-0.579204\pi$
$757$	−372.849			−0.492535			−0.246268	+	0.969202i	$0.579204\pi$
$758$	−97.6991	+	268.426i	−0.128891	+	0.354124i
$759$		0			0
$760$	470.083	+	394.447i	0.618531	+	0.519009i
$761$	1138.05	+	200.669i	1.49547	+	0.263691i	0.860740	−	0.509046i	$-0.170002\pi$
$761$	1138.05	+	200.669i	1.49547	+	0.263691i	0.634727	+	0.772737i	$0.281113\pi$
$762$		0			0
$763$	−695.677	+	583.742i	−0.911765	+	0.765062i
$764$	65.5851	−	37.8656i	0.0858444	−	0.0495623i
$765$		0			0
$766$	−110.333	+	191.102i	−0.144037	+	0.249480i
$767$	−66.8805	+	11.7928i	−0.0871976	+	0.0153753i
$768$		0			0
$769$	−998.338	+	363.365i	−1.29823	+	0.472517i	−0.896419	−	0.443207i	$-0.853841\pi$
$769$	−998.338	+	363.365i	−1.29823	+	0.472517i	−0.401809	+	0.915723i	$0.631618\pi$
$770$	188.072	+	516.723i	0.244249	+	0.671069i
$771$		0			0
$772$	2.52581	+	14.3246i	0.00327178	+	0.0185552i
$773$	808.848	+	466.989i	1.04638	+	0.604125i	0.921632	−	0.388064i	$-0.126856\pi$
$773$	808.848	+	466.989i	1.04638	+	0.604125i	0.124743	+	0.992189i	$0.460189\pi$
$774$		0			0
$775$	−117.044	−	202.725i	−0.151024	−	0.261581i
$776$	194.220	+	231.463i	0.250284	+	0.298277i
$777$		0			0
$778$	−122.098	+	692.450i	−0.156938	+	0.890039i
$779$	−282.598	+	336.787i	−0.362771	+	0.432333i
$780$		0			0
$781$	−412.210	−	150.032i	−0.527798	−	0.192103i
$782$		−	267.735i		−	0.342372i
$783$		0			0
$784$	−450.363			−0.574443
$785$	77.3684	−	212.568i	0.0985585	−	0.270787i
$786$		0			0
$787$	628.689	+	527.532i	0.798842	+	0.670308i	0.947917	−	0.318518i	$-0.103185\pi$
$787$	628.689	+	527.532i	0.798842	+	0.670308i	−0.149075	+	0.988826i	$0.547630\pi$
$788$	−52.0523	−	9.17823i	−0.0660562	−	0.0116475i
$789$		0			0
$790$	−10.0199	+	8.40768i	−0.0126834	+	0.0106426i
$791$	−125.562	+	72.4931i	−0.158738	+	0.0916473i
$792$		0			0
$793$	294.708	−	510.450i	0.371637	−	0.643694i
$794$	−1408.24	+	248.311i	−1.77361	+	0.312735i
$795$		0			0
$796$	1.15357	−	0.419865i	0.00144921	−	0.000527469i
$797$	11.7271	+	32.2200i	0.0147141	+	0.0404266i	0.946832	−	0.321728i	$-0.104264\pi$
$797$	11.7271	+	32.2200i	0.0147141	+	0.0404266i	−0.932118	+	0.362154i	$0.882041\pi$
$798$		0			0
$799$	−84.8706	−	481.325i	−0.106221	−	0.602409i
$800$	20.6028	+	11.8950i	0.0257535	+	0.0148688i
$801$		0			0
$802$	−214.682	−	371.840i	−0.267683	−	0.463641i
$803$	249.815	+	297.718i	0.311103	+	0.370758i
$804$		0			0
$805$	−87.9332	+	498.694i	−0.109234	+	0.619495i
$806$	−749.212	+	892.877i	−0.929544	+	1.10779i
$807$		0			0
$808$	658.710	+	239.751i	0.815235	+	0.296721i
$809$			521.511i			0.644636i	0.946631	+	0.322318i	$0.104462\pi$
$809$			521.511i			0.644636i	−0.946631	+	0.322318i	$0.895538\pi$
$810$		0			0
$811$	−684.645			−0.844199			−0.422099	−	0.906550i	$-0.638707\pi$
$811$	−684.645			−0.844199			−0.422099	+	0.906550i	$0.638707\pi$
$812$	−29.9859	+	82.3856i	−0.0369284	+	0.101460i
$813$		0			0
$814$	−701.337	−	588.492i	−0.861594	−	0.722963i
$815$	−1070.12	−	188.691i	−1.31303	−	0.231523i
$816$		0			0
$817$	32.8089	−	27.5300i	0.0401578	−	0.0336964i
$818$	−748.021	+	431.870i	−0.914451	+	0.527958i
$819$		0			0
$820$	12.9666	−	22.4588i	0.0158129	−	0.0273887i
$821$	1334.77	−	235.356i	1.62579	−	0.286670i	0.714870	−	0.699257i	$-0.246486\pi$
$821$	1334.77	−	235.356i	1.62579	−	0.286670i	0.910918	+	0.412587i	$0.135375\pi$
$822$		0			0
$823$	611.555	−	222.588i	0.743080	−	0.270459i	0.0573894	−	0.998352i	$-0.481722\pi$
$823$	611.555	−	222.588i	0.743080	−	0.270459i	0.685691	+	0.727893i	$0.259500\pi$
$824$	65.3265	+	179.483i	0.0792798	+	0.217819i
$825$		0			0
$826$	−12.5484	−	71.1653i	−0.0151917	−	0.0861565i
$827$	1042.15	+	601.688i	1.26016	+	0.727555i	0.973106	−	0.230359i	$-0.0739900\pi$
$827$	1042.15	+	601.688i	1.26016	+	0.727555i	0.287056	+	0.957914i	$0.407323\pi$
$828$		0			0
$829$	753.210	+	1304.60i	0.908577	+	1.57370i	0.816043	+	0.577992i	$0.196163\pi$
$829$	753.210	+	1304.60i	0.908577	+	1.57370i	0.0925344	+	0.995709i	$0.470503\pi$
$830$	609.543	+	726.426i	0.734390	+	0.875211i
$831$		0			0
$832$	189.461	−	1074.49i	0.227718	−	1.29145i
$833$	202.064	−	240.810i	0.242574	−	0.289088i
$834$		0			0
$835$	34.3830	+	12.5144i	0.0411773	+	0.0149873i
$836$		−	30.0376i		−	0.0359301i
$837$		0			0
$838$	−1119.86			−1.33635
$839$	20.3353	−	55.8707i	0.0242375	−	0.0665920i	−0.926984	−	0.375101i	$-0.877608\pi$
$839$	20.3353	−	55.8707i	0.0242375	−	0.0665920i	0.951221	+	0.308509i	$0.0998301\pi$
$840$		0			0
$841$	−696.614	−	584.528i	−0.828316	−	0.695039i
$842$	641.990	+	113.200i	0.762458	+	0.134442i
$843$		0			0
$844$	−4.16316	+	3.49330i	−0.00493265	+	0.00413899i
$845$	350.819	−	202.546i	0.415171	−	0.239699i
$846$		0			0
$847$	−295.992	+	512.672i	−0.349459	+	0.605280i
$848$	−749.341	+	132.129i	−0.883656	+	0.155812i
$849$		0			0
$850$	120.571	−	43.8841i	0.141848	−	0.0516284i
$851$	−288.360	−	792.263i	−0.338848	−	0.930979i
$852$		0			0
$853$	−61.0451	−	346.204i	−0.0715652	−	0.405866i	−0.999455	−	0.0330117i	$-0.989490\pi$
$853$	−61.0451	−	346.204i	−0.0715652	−	0.405866i	0.927890	−	0.372855i	$-0.121621\pi$
$854$	543.152	+	313.589i	0.636009	+	0.367200i
$855$		0			0
$856$	−393.491	−	681.546i	−0.459685	−	0.796198i
$857$	795.906	+	948.524i	0.928712	+	1.10680i	0.994049	+	0.108933i	$0.0347434\pi$
$857$	795.906	+	948.524i	0.928712	+	1.10680i	−0.0653368	+	0.997863i	$0.520812\pi$
$858$		0			0
$859$	−46.1722	+	261.855i	−0.0537511	+	0.304837i	−0.999817	−	0.0191371i	$-0.993908\pi$
$859$	−46.1722	+	261.855i	−0.0537511	+	0.304837i	0.946066	+	0.323975i	$0.105019\pi$
$860$	−1.62390	+	1.93529i	−0.00188825	+	0.00225033i
$861$		0			0
$862$	−207.474	−	75.5143i	−0.240689	−	0.0876036i
$863$			297.514i			0.344744i	0.985032	+	0.172372i	$0.0551431\pi$
$863$			297.514i			0.344744i	−0.985032	+	0.172372i	$0.944857\pi$
$864$		0			0
$865$	−843.145			−0.974734
$866$	135.512	−	372.315i	0.156480	−	0.429925i
$867$		0			0
$868$	59.4989	+	49.9255i	0.0685472	+	0.0575179i
$869$	11.3293	+	1.99767i	0.0130372	+	0.00229881i
$870$		0			0
$871$	−214.916	+	180.336i	−0.246747	+	0.207045i
$872$	727.078	−	419.779i	0.833805	−	0.481398i
$873$		0			0
$874$	−220.849	+	382.522i	−0.252688	+	0.437669i
$875$	−1185.02	+	208.950i	−1.35430	+	0.238800i
$876$		0			0
$877$	339.196	−	123.457i	0.386768	−	0.140772i	−0.141315	−	0.989965i	$-0.545133\pi$
$877$	339.196	−	123.457i	0.386768	−	0.140772i	0.528083	+	0.849193i	$0.322911\pi$
$878$	267.980	+	736.270i	0.305217	+	0.838576i
$879$		0			0
$880$	−83.0547	−	471.027i	−0.0943804	−	0.535258i
$881$	−782.766	−	451.930i	−0.888497	−	0.512974i	−0.0150464	−	0.999887i	$-0.504790\pi$
$881$	−782.766	−	451.930i	−0.888497	−	0.512974i	−0.873451	+	0.486913i	$0.838123\pi$
$882$		0			0
$883$	462.202	+	800.558i	0.523445	+	0.906634i	0.999628	+	0.0272872i	$0.00868687\pi$
$883$	462.202	+	800.558i	0.523445	+	0.906634i	−0.476182	+	0.879347i	$0.657980\pi$
$884$	25.7177	+	30.6492i	0.0290925	+	0.0346710i
$885$		0			0
$886$	−222.904	+	1264.15i	−0.251585	+	1.42681i
$887$	−179.583	+	214.019i	−0.202462	+	0.241284i	−0.857716	−	0.514124i	$-0.828117\pi$
$887$	−179.583	+	214.019i	−0.202462	+	0.241284i	0.655254	+	0.755408i	$0.272561\pi$
$888$		0			0
$889$	680.474	+	247.672i	0.765437	+	0.278596i
$890$			401.412i			0.451025i
$891$		0			0
$892$	−44.3400			−0.0497086
$893$	−275.778	+	757.694i	−0.308822	+	0.848482i
$894$		0			0
$895$	700.481	+	587.773i	0.782660	+	0.656730i
$896$	1011.42	+	178.341i	1.12882	+	0.199041i
$897$		0			0
$898$	693.082	−	581.565i	0.771806	−	0.647622i
$899$	−1342.92	+	775.333i	−1.49379	+	0.862440i
$900$		0			0
$901$	265.556	−	459.957i	0.294735	−	0.510496i
$902$	358.675	−	63.2441i	0.397644	−	0.0701154i
$903$		0			0
$904$	125.953	−	45.8432i	0.139329	−	0.0507115i
$905$	−129.766	−	356.528i	−0.143388	−	0.393954i
$906$		0			0
$907$	−102.632	−	582.052i	−0.113155	−	0.641733i	−0.987647	−	0.156694i	$-0.949916\pi$
$907$	−102.632	−	582.052i	−0.113155	−	0.641733i	0.874492	−	0.485039i	$-0.161195\pi$
$908$	−25.6206	−	14.7921i	−0.0282166	−	0.0162908i
$909$		0			0
$910$	604.176	+	1046.46i	0.663930	+	1.14996i
$911$	243.127	+	289.748i	0.266880	+	0.318055i	0.882796	−	0.469757i	$-0.155658\pi$
$911$	243.127	+	289.748i	0.266880	+	0.318055i	−0.615916	+	0.787812i	$0.711214\pi$
$912$		0			0
$913$	144.828	−	821.358i	0.158628	−	0.899626i
$914$	1065.15	−	1269.39i	1.16537	−	1.38883i
$915$		0			0
$916$	29.0213	+	10.5629i	0.0316826	+	0.0115315i
$917$		−	1292.98i		−	1.41002i
$918$		0			0
$919$	86.9159			0.0945766			0.0472883	−	0.998881i	$-0.484942\pi$
$919$	86.9159			0.0945766			0.0472883	+	0.998881i	$0.484942\pi$
$920$	160.115	−	439.912i	0.174038	−	0.478165i
$921$		0			0
$922$	−121.742	−	102.153i	−0.132041	−	0.110796i
$923$	−949.305	−	167.388i	−1.02850	−	0.181352i
$924$		0			0
$925$	309.520	−	259.718i	0.334616	−	0.280776i
$926$	1099.91	−	635.033i	1.18781	−	0.685781i
$927$		0			0
$928$	78.7963	−	136.479i	0.0849098	−	0.147068i
$929$	−665.919	+	117.419i	−0.716813	+	0.126393i	−0.520146	−	0.854077i	$-0.674123\pi$
$929$	−665.919	+	117.419i	−0.716813	+	0.126393i	−0.196666	+	0.980471i	$0.563012\pi$
$930$		0			0
$931$	−487.336	+	177.376i	−0.523454	+	0.190522i
$932$	−32.7721	−	90.0406i	−0.0351632	−	0.0966101i
$933$		0			0
$934$	44.1122	+	250.173i	0.0472293	+	0.267851i
$935$	289.124	+	166.926i	0.309223	+	0.178530i
$936$		0			0
$937$	168.348	+	291.587i	0.179667	+	0.311192i	0.941766	−	0.336268i	$-0.109165\pi$
$937$	168.348	+	291.587i	0.179667	+	0.311192i	−0.762100	+	0.647460i	$0.775831\pi$
$938$	−191.890	−	228.685i	−0.204573	−	0.243801i
$939$		0			0
$940$	8.25908	−	46.8396i	0.00878626	−	0.0498293i
$941$	−151.608	+	180.680i	−0.161114	+	0.192008i	−0.840562	−	0.541716i	$-0.817775\pi$
$941$	−151.608	+	180.680i	−0.161114	+	0.192008i	0.679448	+	0.733724i	$0.262219\pi$
$942$		0			0
$943$	315.171	+	114.713i	0.334222	+	0.121647i
$944$			62.8549i			0.0665836i
$945$		0			0
$946$	−35.4802			−0.0375055
$947$	218.744	−	600.994i	0.230986	−	0.634630i	−0.769003	−	0.639245i	$-0.779247\pi$
$947$	218.744	−	600.994i	0.230986	−	0.634630i	0.999989	+	0.00461549i	$0.00146916\pi$
$948$		0			0
$949$	654.225	+	548.960i	0.689384	+	0.578461i
$950$	−208.463	−	36.7576i	−0.219435	−	0.0386922i
$951$		0			0
$952$	−585.986	+	491.701i	−0.615532	+	0.516493i
$953$	−742.976	+	428.957i	−0.779618	+	0.450112i	−0.836295	−	0.548280i	$-0.815283\pi$
$953$	−742.976	+	428.957i	−0.779618	+	0.450112i	0.0566772	+	0.998393i	$0.481949\pi$
$954$		0			0
$955$	694.310	−	1202.58i	0.727027	−	1.25925i
$956$	44.6496	−	7.87293i	0.0467046	−	0.00823528i
$957$		0			0
$958$	−287.453	+	104.624i	−0.300055	+	0.109211i
$959$	571.583	+	1570.41i	0.596020	+	1.63755i
$960$		0			0
$961$	71.6736	+	406.481i	0.0745823	+	0.422977i
$962$	−1742.31	−	1005.92i	−1.81113	−	1.04566i
$963$		0			0
$964$	40.8728	+	70.7938i	0.0423992	+	0.0734376i
$965$	171.438	+	204.312i	0.177656	+	0.211722i
$966$		0			0
$967$	99.4203	−	563.840i	0.102813	−	0.583082i	−0.889258	−	0.457406i	$-0.848779\pi$
$967$	99.4203	−	563.840i	0.102813	−	0.583082i	0.992071	−	0.125677i	$-0.0401101\pi$
$968$	351.782	−	419.238i	0.363411	−	0.433097i
$969$		0			0
$970$	289.749	+	105.460i	0.298710	+	0.108722i
$971$			140.513i			0.144710i	0.997379	+	0.0723548i	$0.0230514\pi$
$971$			140.513i			0.144710i	−0.997379	+	0.0723548i	$0.976949\pi$
$972$		0			0
$973$	781.035			0.802708
$974$	463.311	−	1272.94i	0.475678	−	1.30692i
$975$		0			0
$976$	−417.895	−	350.655i	−0.428171	−	0.359278i
$977$	1522.14	+	268.395i	1.55798	+	0.274713i	0.885228	−	0.465158i	$-0.154003\pi$
$977$	1522.14	+	268.395i	1.55798	+	0.274713i	0.672748	+	0.739871i	$0.265114\pi$
$978$		0			0
$979$	270.451	−	226.935i	0.276252	−	0.231803i
$980$	26.4927	−	15.2956i	0.0270334	−	0.0156077i
$981$		0			0
$982$	40.9588	−	70.9427i	0.0417095	−	0.0722430i
$983$	−1034.31	+	182.378i	−1.05220	+	0.185532i	−0.672894	−	0.739739i	$-0.734949\pi$
$983$	−1034.31	+	182.378i	−1.05220	+	0.185532i	−0.379308	+	0.925270i	$0.623838\pi$
$984$		0			0
$985$	−910.717	+	331.474i	−0.924585	+	0.336522i
$986$	−290.702	−	798.698i	−0.294830	−	0.810039i
$987$		0			0
$988$	−11.4619	−	65.0037i	−0.0116011	−	0.0657932i
$989$	−28.2961	−	16.3368i	−0.0286109	−	0.0165185i
$990$		0			0
$991$	−255.730	−	442.938i	−0.258053	−	0.446961i	0.707667	−	0.706546i	$-0.249748\pi$
$991$	−255.730	−	442.938i	−0.258053	−	0.446961i	−0.965720	+	0.259585i	$0.916414\pi$
$992$	−89.7415	−	106.950i	−0.0904652	−	0.107812i
$993$		0			0
$994$	178.112	−	1010.12i	0.179187	−	1.01622i
$995$	14.4689	−	17.2433i	0.0145416	−	0.0173300i
$996$		0			0
$997$	−307.012	−	111.743i	−0.307936	−	0.112079i	0.183430	−	0.983033i	$-0.441280\pi$
$997$	−307.012	−	111.743i	−0.307936	−	0.112079i	−0.491366	+	0.870953i	$0.663502\pi$
$998$			931.987i			0.933855i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	243.3.f.d.53.2		30
3.2	odd	2		243.3.f.a.53.4		30
9.2	odd	6		243.3.f.b.215.2		30
9.4	even	3		27.3.f.a.5.2	✓	30
9.5	odd	6		81.3.f.a.44.4		30
9.7	even	3		243.3.f.c.215.4		30
27.2	odd	18		27.3.f.a.11.2	yes	30
27.7	even	9		243.3.f.a.188.4		30
27.11	odd	18		243.3.f.c.26.4		30
27.13	even	9		729.3.b.a.728.9		30
27.14	odd	18		729.3.b.a.728.22		30
27.16	even	9		243.3.f.b.26.2		30
27.20	odd	18	inner	243.3.f.d.188.2		30
27.25	even	9		81.3.f.a.35.4		30
36.31	odd	6		432.3.bc.a.113.1		30
108.83	even	18		432.3.bc.a.65.1		30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.3.f.a.5.2	✓	30	9.4	even	3
27.3.f.a.11.2	yes	30	27.2	odd	18
81.3.f.a.35.4		30	27.25	even	9
81.3.f.a.44.4		30	9.5	odd	6
243.3.f.a.53.4		30	3.2	odd	2
243.3.f.a.188.4		30	27.7	even	9
243.3.f.b.26.2		30	27.16	even	9
243.3.f.b.215.2		30	9.2	odd	6
243.3.f.c.26.4		30	27.11	odd	18
243.3.f.c.215.4		30	9.7	even	3
243.3.f.d.53.2		30	1.1	even	1	trivial
243.3.f.d.188.2		30	27.20	odd	18	inner
432.3.bc.a.65.1		30	108.83	even	18
432.3.bc.a.113.1		30	36.31	odd	6
729.3.b.a.728.9		30	27.13	even	9
729.3.b.a.728.22		30	27.14	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:	\( N \)	\(=\)	\( 243 = 3^{5} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	243.f (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.663577 + 1.82316i) q^{2} +(0.180586 + 0.151529i) q^{4} +(4.25686 + 0.750600i) q^{5} +(6.80967 - 5.71399i) q^{7} +(-7.11704 + 4.10903i) q^{8} +(-4.19322 + 7.26288i) q^{10} +(7.26396 - 1.28083i) q^{11} +(15.2310 - 5.54364i) q^{13} +(5.89880 + 16.2068i) q^{14} +(-2.60498 - 14.7736i) q^{16} +(9.06825 + 5.23555i) q^{17} +(-8.63742 - 14.9604i) q^{19} +(0.654990 + 0.780587i) q^{20} +(-2.48503 + 14.0933i) q^{22} +(-8.47110 + 10.0955i) q^{23} +(-5.93484 - 2.16011i) q^{25} +31.4473i q^{26} +2.09556 q^{28} +(-14.3092 + 39.3143i) q^{29} +(28.3928 + 23.8244i) q^{31} +(-3.70957 - 0.654097i) q^{32} +(-15.5628 + 13.0587i) q^{34} +(33.2767 - 19.2123i) q^{35} +(-31.9875 + 55.4041i) q^{37} +(33.0069 - 5.82001i) q^{38} +(-33.3805 + 12.1495i) q^{40} +(-8.70442 - 23.9152i) q^{41} +(0.430521 + 2.44161i) q^{43} +(1.50585 + 0.869403i) q^{44} +(-12.7845 - 22.1433i) q^{46} +(-30.0028 - 35.7559i) q^{47} +(5.21313 - 29.5652i) q^{49} +(7.87646 - 9.38679i) q^{50} +(3.59053 + 1.30685i) q^{52} -50.7217i q^{53} +31.8831 q^{55} +(-24.9858 + 68.6478i) q^{56} +(-62.1811 - 52.1761i) q^{58} +(-4.12626 - 0.727571i) q^{59} +(27.8569 - 23.3747i) q^{61} +(-62.2766 + 35.9554i) q^{62} +(33.6571 - 58.2957i) q^{64} +(68.9974 - 12.1661i) q^{65} +(-16.2651 + 5.92003i) q^{67} +(0.844255 + 2.31957i) q^{68} +(12.9455 + 73.4178i) q^{70} +(-51.5041 - 29.7359i) q^{71} +(26.3451 + 45.6310i) q^{73} +(-79.7845 - 95.0834i) q^{74} +(0.707153 - 4.01046i) q^{76} +(42.1465 - 50.2282i) q^{77} +(1.46560 + 0.533436i) q^{79} -64.8443i q^{80} +49.3774 q^{82} +(38.6733 - 106.254i) q^{83} +(34.6725 + 29.0937i) q^{85} +(-4.73713 - 0.835284i) q^{86} +(-46.4349 + 38.9635i) q^{88} +(41.4518 - 23.9322i) q^{89} +(72.0419 - 124.780i) q^{91} +(-3.05952 + 0.539476i) q^{92} +(85.0981 - 30.9732i) q^{94} +(-25.5390 - 70.1678i) q^{95} +(-6.38452 - 36.2084i) q^{97} +(50.4428 + 29.1232i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 3 q^{2} + 3 q^{4} + 21 q^{5} + 3 q^{7} - 9 q^{8} - 3 q^{10} + 57 q^{11} + 3 q^{13} - 114 q^{14} + 27 q^{16} - 9 q^{17} - 3 q^{19} - 183 q^{20} + 75 q^{22} + 48 q^{23} + 21 q^{25} - 12 q^{28} - 78 q^{29}+ \cdots + 882 q^{98}+O(q^{100}) \) 30 * q + 3 * q^2 + 3 * q^4 + 21 * q^5 + 3 * q^7 - 9 * q^8 - 3 * q^10 + 57 * q^11 + 3 * q^13 - 114 * q^14 + 27 * q^16 - 9 * q^17 - 3 * q^19 - 183 * q^20 + 75 * q^22 + 48 * q^23 + 21 * q^25 - 12 * q^28 - 78 * q^29 - 87 * q^31 + 243 * q^32 - 153 * q^34 - 252 * q^35 - 3 * q^37 + 321 * q^38 - 168 * q^40 - 357 * q^41 - 87 * q^43 + 639 * q^44 - 3 * q^46 - 51 * q^47 - 69 * q^49 + 168 * q^50 - 36 * q^52 - 12 * q^55 - 177 * q^56 + 138 * q^58 + 48 * q^59 + 147 * q^61 - 900 * q^62 - 51 * q^64 + 624 * q^65 + 12 * q^67 - 477 * q^68 - 6 * q^70 + 315 * q^71 - 66 * q^73 - 480 * q^74 - 57 * q^76 + 453 * q^77 - 15 * q^79 - 12 * q^82 - 591 * q^83 + 243 * q^85 + 669 * q^86 + 591 * q^88 + 72 * q^89 + 96 * q^91 + 564 * q^92 + 957 * q^94 - 606 * q^95 + 696 * q^97 + 882 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more