LMFDB - Embedded newform 243.3.f.b.26.2

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,-3,0,3,6] 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			26.2
Character	$\chi$	$=$	243.26
Dual form			243.3.f.b.215.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.91070 - 0.336907i) q^{2} +(-0.221521 - 0.0806271i) q^{4} +(2.77847 + 3.31125i) q^{5} +(-8.35329 + 3.04035i) q^{7} +(7.11704 + 4.10903i) q^{8} +(-4.19322 - 7.26288i) q^{10} +(4.74121 - 5.65036i) q^{11} +(-2.81458 - 15.9623i) q^{13} +(16.9849 - 2.99490i) q^{14} +(-11.4918 - 9.64276i) q^{16} +(-9.06825 + 5.23555i) q^{17} +(-8.63742 + 14.9604i) q^{19} +(-0.348513 - 0.957532i) q^{20} +(-10.9627 + 9.19876i) q^{22} +(4.50738 - 12.3839i) q^{23} +(1.09671 - 6.21978i) q^{25} +31.4473i q^{26} +2.09556 q^{28} +(-41.2018 - 7.26498i) q^{29} +(-34.8289 - 12.6767i) q^{31} +(-2.42125 - 2.88553i) q^{32} +(19.0905 - 6.94839i) q^{34} +(-33.2767 - 19.2123i) q^{35} +(-31.9875 - 55.4041i) q^{37} +(21.5437 - 25.6748i) q^{38} +(6.16847 + 34.9831i) q^{40} +(-25.0634 + 4.41935i) q^{41} +(1.89923 + 1.59364i) q^{43} +(-1.50585 + 0.869403i) q^{44} +(-12.7845 + 22.1433i) q^{46} +(15.9642 + 43.8612i) q^{47} +(22.9976 - 19.2973i) q^{49} +(-4.19097 + 11.5146i) q^{50} +(-0.663503 + 3.76291i) q^{52} -50.7217i q^{53} +31.8831 q^{55} +(-71.9436 - 12.6856i) q^{56} +(76.2764 + 27.7623i) q^{58} +(-2.69322 - 3.20966i) q^{59} +(-34.1715 + 12.4374i) q^{61} +(62.2766 + 35.9554i) q^{62} +(33.6571 + 58.2957i) q^{64} +(45.0349 - 53.6705i) q^{65} +(3.00568 + 17.0460i) q^{67} +(2.43093 - 0.428639i) q^{68} +(57.1089 + 47.9201i) q^{70} +(51.5041 - 29.7359i) q^{71} +(26.3451 - 45.6310i) q^{73} +(42.4524 + 116.637i) q^{74} +(3.11959 - 2.61764i) q^{76} +(-22.4257 + 61.6140i) q^{77} +(-0.270833 + 1.53597i) q^{79} -64.8443i q^{80} +49.3774 q^{82} +(111.355 + 19.6349i) q^{83} +(-42.5321 - 15.4804i) q^{85} +(-3.09194 - 3.68483i) q^{86} +(56.9609 - 20.7321i) q^{88} +(-41.4518 - 23.9322i) q^{89} +(72.0419 + 124.780i) q^{91} +(-1.99696 + 2.37988i) q^{92} +(-15.7255 - 89.1837i) q^{94} +(-73.5366 + 12.9665i) q^{95} +(-28.1651 - 23.6334i) q^{97} +(-50.4428 + 29.1232i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 3 q^{2} + 3 q^{4} + 6 q^{5} + 3 q^{7} + 9 q^{8} - 3 q^{10} + 51 q^{11} + 3 q^{13} - 129 q^{14} - 9 q^{16} + 9 q^{17} - 3 q^{19} + 30 q^{20} - 33 q^{22} + 168 q^{23} - 6 q^{25} - 12 q^{28} - 246 q^{29}+ \cdots - 882 q^{98}+O(q^{100}) $ 30 * q - 3 * q^2 + 3 * q^4 + 6 * q^5 + 3 * q^7 + 9 * q^8 - 3 * q^10 + 51 * q^11 + 3 * q^13 - 129 * q^14 - 9 * q^16 + 9 * q^17 - 3 * q^19 + 30 * q^20 - 33 * q^22 + 168 * q^23 - 6 * q^25 - 12 * q^28 - 246 * q^29 + 48 * q^31 - 117 * q^32 + 99 * q^34 + 252 * q^35 - 3 * q^37 + 237 * q^38 + 201 * q^40 - 129 * q^41 + 183 * q^43 - 639 * q^44 - 3 * q^46 + 348 * q^47 + 147 * q^49 + 471 * q^50 + 45 * q^52 - 12 * q^55 - 570 * q^56 - 267 * q^58 - 426 * q^59 - 285 * q^61 + 900 * q^62 - 51 * q^64 + 213 * q^65 - 366 * q^67 - 378 * q^68 - 483 * q^70 - 315 * q^71 - 66 * q^73 - 159 * q^74 - 201 * q^76 + 654 * q^77 - 15 * q^79 - 12 * q^82 - 624 * q^83 + 18 * q^85 + 411 * q^86 + 51 * q^88 - 72 * q^89 + 96 * q^91 + 561 * q^92 - 96 * q^94 + 75 * q^95 - 114 * q^97 - 882 * q^98

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{18}\right)$

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 $

$2$	−1.91070	−	0.336907i	−0.955348	−	0.168454i	−0.325820	−	0.945432i	$-0.605640\pi$
$2$	−1.91070	−	0.336907i	−0.955348	−	0.168454i	−0.629527	+	0.776978i	$0.716751\pi$
$3$		0			0
$3$		0			0
$4$	−0.221521	−	0.0806271i	−0.0553803	−	0.0201568i
$5$	2.77847	+	3.31125i	0.555694	+	0.662250i	0.968629	−	0.248510i	$-0.0799409\pi$
$5$	2.77847	+	3.31125i	0.555694	+	0.662250i	−0.412935	+	0.910760i	$0.635496\pi$
$6$		0			0
$7$	−8.35329	+	3.04035i	−1.19333	+	0.434336i	−0.860891	−	0.508790i	$-0.830093\pi$
$7$	−8.35329	+	3.04035i	−1.19333	+	0.434336i	−0.332437	+	0.943126i	$0.607871\pi$
$8$	7.11704	+	4.10903i	0.889630	+	0.513628i
$9$		0			0
$10$	−4.19322	−	7.26288i	−0.419322	−	0.726288i
$11$	4.74121	−	5.65036i	0.431019	−	0.513669i	−0.506197	−	0.862418i	$-0.668949\pi$
$11$	4.74121	−	5.65036i	0.431019	−	0.513669i	0.937216	+	0.348749i	$0.113393\pi$
$12$		0			0
$13$	−2.81458	−	15.9623i	−0.216506	−	1.22787i	−0.878274	−	0.478158i	$-0.841304\pi$
$13$	−2.81458	−	15.9623i	−0.216506	−	1.22787i	0.661767	−	0.749709i	$-0.269807\pi$
$14$	16.9849	−	2.99490i	1.21321	−	0.213921i
$15$		0			0
$16$	−11.4918	−	9.64276i	−0.718237	−	0.602673i
$17$	−9.06825	+	5.23555i	−0.533426	+	0.307974i	−0.742411	−	0.669945i	$-0.766318\pi$
$17$	−9.06825	+	5.23555i	−0.533426	+	0.307974i	0.208984	+	0.977919i	$0.432984\pi$
$18$		0			0
$19$	−8.63742	+	14.9604i	−0.454601	+	0.787392i	−0.998665	−	0.0516517i	$-0.983551\pi$
$19$	−8.63742	+	14.9604i	−0.454601	+	0.787392i	0.544064	+	0.839044i	$0.316885\pi$
$20$	−0.348513	−	0.957532i	−0.0174256	−	0.0478766i
$21$		0			0
$22$	−10.9627	+	9.19876i	−0.498303	+	0.418126i
$23$	4.50738	−	12.3839i	0.195973	−	0.538431i	−0.802316	−	0.596899i	$-0.796399\pi$
$23$	4.50738	−	12.3839i	0.195973	−	0.538431i	0.998289	+	0.0584677i	$0.0186215\pi$
$24$		0			0
$25$	1.09671	−	6.21978i	0.0438686	−	0.248791i
$26$			31.4473i			1.20951i
$27$		0			0
$28$	2.09556			0.0748416
$29$	−41.2018	−	7.26498i	−1.42075	−	0.250517i	−0.590108	−	0.807324i	$-0.700915\pi$
$29$	−41.2018	−	7.26498i	−1.42075	−	0.250517i	−0.830642	+	0.556807i	$0.812026\pi$
$30$		0			0
$31$	−34.8289	−	12.6767i	−1.12351	−	0.408925i	−0.287580	−	0.957757i	$-0.592851\pi$
$31$	−34.8289	−	12.6767i	−1.12351	−	0.408925i	−0.835933	+	0.548831i	$0.815073\pi$
$32$	−2.42125	−	2.88553i	−0.0756640	−	0.0901728i
$33$		0			0
$34$	19.0905	−	6.94839i	0.561487	−	0.204364i
$35$	−33.2767	−	19.2123i	−0.950764	−	0.548924i
$36$		0			0
$37$	−31.9875	−	55.4041i	−0.864528	−	1.49741i	−0.867515	−	0.497411i	$-0.834284\pi$
$37$	−31.9875	−	55.4041i	−0.864528	−	1.49741i	0.00298644	−	0.999996i	$-0.499049\pi$
$38$	21.5437	−	25.6748i	0.566941	−	0.675654i
$39$		0			0
$40$	6.16847	+	34.9831i	0.154212	+	0.874578i
$41$	−25.0634	+	4.41935i	−0.611302	+	0.107789i	−0.470724	−	0.882281i	$-0.656007\pi$
$41$	−25.0634	+	4.41935i	−0.611302	+	0.107789i	−0.140578	+	0.990070i	$0.544896\pi$
$42$		0			0
$43$	1.89923	+	1.59364i	0.0441682	+	0.0370615i	0.664605	−	0.747195i	$-0.268600\pi$
$43$	1.89923	+	1.59364i	0.0441682	+	0.0370615i	−0.620436	+	0.784257i	$0.713044\pi$
$44$	−1.50585	+	0.869403i	−0.0342239	+	0.0197592i
$45$		0			0
$46$	−12.7845	+	22.1433i	−0.277923	+	0.481377i
$47$	15.9642	+	43.8612i	0.339663	+	0.933216i	0.985490	+	0.169733i	$0.0542904\pi$
$47$	15.9642	+	43.8612i	0.339663	+	0.933216i	−0.645827	+	0.763484i	$0.723487\pi$
$48$		0			0
$49$	22.9976	−	19.2973i	0.469339	−	0.393822i
$50$	−4.19097	+	11.5146i	−0.0838195	+	0.230292i
$51$		0			0
$52$	−0.663503	+	3.76291i	−0.0127597	+	0.0723637i
$53$		−	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
$56$	−71.9436	−	12.6856i	−1.28471	−	0.226529i
$57$		0			0
$58$	76.2764	+	27.7623i	1.31511	+	0.478661i
$59$	−2.69322	−	3.20966i	−0.0456479	−	0.0544010i	0.742737	−	0.669583i	$-0.233527\pi$
$59$	−2.69322	−	3.20966i	−0.0456479	−	0.0544010i	−0.788385	+	0.615182i	$0.789083\pi$
$60$		0			0
$61$	−34.1715	+	12.4374i	−0.560189	+	0.203892i	−0.606568	−	0.795032i	$-0.707454\pi$
$61$	−34.1715	+	12.4374i	−0.560189	+	0.203892i	0.0463786	+	0.998924i	$0.485232\pi$
$62$	62.2766	+	35.9554i	1.00446	+	0.579926i
$63$		0			0
$64$	33.6571	+	58.2957i	0.525892	+	0.910871i
$65$	45.0349	−	53.6705i	0.692844	−	0.825700i
$66$		0			0
$67$	3.00568	+	17.0460i	0.0448608	+	0.254419i	0.998988	−	0.0449841i	$-0.0143237\pi$
$67$	3.00568	+	17.0460i	0.0448608	+	0.254419i	−0.954127	+	0.299403i	$0.903213\pi$
$68$	2.43093	−	0.428639i	0.0357490	−	0.00630352i
$69$		0			0
$70$	57.1089	+	47.9201i	0.815842	+	0.684572i
$71$	51.5041	−	29.7359i	0.725410	−	0.418815i	−0.0913309	−	0.995821i	$-0.529112\pi$
$71$	51.5041	−	29.7359i	0.725410	−	0.418815i	0.816740	+	0.577005i	$0.195779\pi$
$72$		0			0
$73$	26.3451	−	45.6310i	0.360892	−	0.625083i	−0.627216	−	0.778845i	$-0.715806\pi$
$73$	26.3451	−	45.6310i	0.360892	−	0.625083i	0.988108	+	0.153762i	$0.0491391\pi$
$74$	42.4524	+	116.637i	0.573681	+	1.57618i
$75$		0			0
$76$	3.11959	−	2.61764i	0.0410472	−	0.0344427i
$77$	−22.4257	+	61.6140i	−0.291243	+	0.800182i
$78$		0			0
$79$	−0.270833	+	1.53597i	−0.00342826	+	0.0194426i	−0.986474	−	0.163918i	$-0.947587\pi$
$79$	−0.270833	+	1.53597i	−0.00342826	+	0.0194426i	0.983046	+	0.183361i	$0.0586977\pi$
$80$		−	64.8443i		−	0.810554i
$81$		0			0
$82$	49.3774			0.602163
$83$	111.355	+	19.6349i	1.34163	+	0.236565i	0.797948	−	0.602726i	$-0.205919\pi$
$83$	111.355	+	19.6349i	1.34163	+	0.236565i	0.543681	+	0.839292i	$0.317030\pi$
$84$		0			0
$85$	−42.5321	−	15.4804i	−0.500377	−	0.182122i
$86$	−3.09194	−	3.68483i	−0.0359528	−	0.0428469i
$87$		0			0
$88$	56.9609	−	20.7321i	0.647283	−	0.235592i
$89$	−41.4518	−	23.9322i	−0.465750	−	0.268901i	0.248709	−	0.968578i	$-0.419994\pi$
$89$	−41.4518	−	23.9322i	−0.465750	−	0.268901i	−0.714459	+	0.699677i	$0.753327\pi$
$90$		0			0
$91$	72.0419	+	124.780i	0.791670	+	1.37121i
$92$	−1.99696	+	2.37988i	−0.0217061	+	0.0258683i
$93$		0			0
$94$	−15.7255	−	89.1837i	−0.167293	−	0.948763i
$95$	−73.5366	+	12.9665i	−0.774069	+	0.136489i
$96$		0			0
$97$	−28.1651	−	23.6334i	−0.290362	−	0.243643i	0.485957	−	0.873983i	$-0.338471\pi$
$97$	−28.1651	−	23.6334i	−0.290362	−	0.243643i	−0.776319	+	0.630340i	$0.782916\pi$
$98$	−50.4428	+	29.1232i	−0.514722	+	0.297175i
$99$		0			0
$100$	−0.744428	+	1.28939i	−0.00744428	+	0.0128939i
$101$	29.1737	+	80.1540i	0.288848	+	0.793604i	0.996228	+	0.0867704i	$0.0276546\pi$
$101$	29.1737	+	80.1540i	0.288848	+	0.793604i	−0.707380	+	0.706833i	$0.750123\pi$
$102$		0			0
$103$	17.8042	−	14.9395i	0.172856	−	0.145044i	−0.552255	−	0.833675i	$-0.686233\pi$
$103$	17.8042	−	14.9395i	0.172856	−	0.145044i	0.725112	+	0.688631i	$0.241788\pi$
$104$	45.5579	−	125.169i	0.438057	−	1.20355i
$105$		0			0
$106$	−17.0885	+	96.9137i	−0.161212	+	0.914280i
$107$			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	$0.655250\pi$
$110$	−60.9188	−	10.7416i	−0.553807	−	0.0976512i
$111$		0			0
$112$	125.312	+	45.6097i	1.11885	+	0.407230i
$113$	−10.4839	−	12.4942i	−0.0927777	−	0.110568i	0.717658	−	0.696396i	$-0.245214\pi$
$113$	−10.4839	−	12.4942i	−0.0927777	−	0.110568i	−0.810436	+	0.585827i	$0.800770\pi$
$114$		0			0
$115$	53.5299	−	19.4833i	0.465477	−	0.169420i
$116$	8.54130	+	4.93132i	0.0736319	+	0.0425114i
$117$		0			0
$118$	4.06457	+	7.04005i	0.0344455	+	0.0596614i
$119$	59.8318	−	71.3048i	0.502788	−	0.599200i
$120$		0			0
$121$	11.5640	+	65.5826i	0.0955701	+	0.542005i
$122$	69.4817	−	12.2515i	0.569522	−	0.100422i
$123$		0			0
$124$	6.69325	+	5.61631i	0.0539778	+	0.0452928i
$125$	117.228	−	67.6816i	0.937824	−	0.541453i
$126$		0			0
$127$	40.7309	−	70.5479i	0.320715	−	0.555495i	−0.659920	−	0.751336i	$-0.729410\pi$
$127$	40.7309	−	70.5479i	0.320715	−	0.555495i	0.980636	+	0.195840i	$0.0627433\pi$
$128$	−39.5149	−	108.566i	−0.308710	−	0.848173i
$129$		0			0
$130$	−104.130	+	87.3754i	−0.800999	+	0.672118i
$131$	−49.7477	+	136.681i	−0.379753	+	1.04336i	0.591705	+	0.806155i	$0.298455\pi$
$131$	−49.7477	+	136.681i	−0.379753	+	1.04336i	−0.971459	+	0.237210i	$0.923767\pi$
$132$		0			0
$133$	26.6659	−	151.230i	0.200495	−	1.13707i
$134$		−	33.5824i		−	0.250615i
$135$		0			0
$136$	−86.0521			−0.632736
$137$	−185.143	−	32.6457i	−1.35141	−	0.238290i	−0.549379	−	0.835574i	$-0.685135\pi$
$137$	−185.143	−	32.6457i	−1.35141	−	0.238290i	−0.802030	+	0.597284i	$0.796247\pi$
$138$		0			0
$139$	−82.5628	−	30.0504i	−0.593977	−	0.216190i	0.0275008	−	0.999622i	$-0.491245\pi$
$139$	−82.5628	−	30.0504i	−0.593977	−	0.216190i	−0.621478	+	0.783432i	$0.713467\pi$
$140$	5.82246	+	6.93894i	0.0415890	+	0.0495639i
$141$		0			0
$142$	−108.427	+	39.4641i	−0.763569	+	0.277916i
$143$	−103.537	−	59.7772i	−0.724036	−	0.418022i
$144$		0			0
$145$	−90.4216	−	156.615i	−0.623597	−	1.08010i
$146$	−65.7109	+	78.3112i	−0.450074	+	0.536378i
$147$		0			0
$148$	2.61885	+	14.8522i	0.0176949	+	0.100353i
$149$	61.9110	−	10.9166i	0.415510	−	0.0732657i	0.0380150	−	0.999277i	$-0.487897\pi$
$149$	61.9110	−	10.9166i	0.415510	−	0.0732657i	0.377495	+	0.926011i	$0.376785\pi$
$150$		0			0
$151$	−88.3972	−	74.1741i	−0.585412	−	0.491219i	0.301307	−	0.953527i	$-0.402577\pi$
$151$	−88.3972	−	74.1741i	−0.585412	−	0.491219i	−0.886719	+	0.462308i	$0.847021\pi$
$152$	−122.946	+	70.9828i	−0.808854	+	0.466992i
$153$		0			0
$154$	63.6068	−	110.170i	0.413031	−	0.715391i
$155$	−54.7954	−	150.549i	−0.353519	−	0.971284i
$156$		0			0
$157$	40.0892	−	33.6389i	0.255346	−	0.214260i	−0.506125	−	0.862460i	$-0.668922\pi$
$157$	40.0892	−	33.6389i	0.255346	−	0.214260i	0.761470	+	0.648200i	$0.224478\pi$
$158$	1.03496	−	2.84352i	0.00655036	−	0.0179970i
$159$		0			0
$160$	2.82735	−	16.0347i	0.0176710	−	0.100217i
$161$			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	$0.780307\pi$
$164$	5.90838	+	1.04181i	0.0360267	+	0.00635248i
$165$		0			0
$166$	−206.151	−	75.0327i	−1.24187	−	0.452004i
$167$	5.44111	+	6.48446i	0.0325815	+	0.0388291i	0.782089	−	0.623167i	$-0.214154\pi$
$167$	5.44111	+	6.48446i	0.0325815	+	0.0388291i	−0.749508	+	0.661996i	$0.769710\pi$
$168$		0			0
$169$	−88.0644	+	32.0528i	−0.521091	+	0.189662i
$170$	76.0504	+	43.9077i	0.447355	+	0.258281i
$171$		0			0
$172$	−0.292229	−	0.506155i	−0.00169901	−	0.00294276i
$173$	−125.381	+	149.423i	−0.724746	+	0.863718i	−0.995083	−	0.0990474i	$-0.968420\pi$
$173$	−125.381	+	149.423i	−0.724746	+	0.863718i	0.270337	+	0.962766i	$0.412865\pi$
$174$		0			0
$175$	9.74912	+	55.2900i	0.0557093	+	0.315943i
$176$	−108.970	+	19.2144i	−0.619148	+	0.109173i
$177$		0			0
$178$	71.1388	+	59.6925i	0.399656	+	0.335351i
$179$	−183.204	+	105.773i	−1.02349	+	0.590910i	−0.915112	−	0.403200i	$-0.867898\pi$
$179$	−183.204	+	105.773i	−1.02349	+	0.590910i	−0.108374	+	0.994110i	$0.534564\pi$
$180$		0			0
$181$	−43.8874	+	76.0153i	−0.242472	+	0.419974i	−0.961418	−	0.275092i	$-0.911292\pi$
$181$	−43.8874	+	76.0153i	−0.242472	+	0.419974i	0.718946	+	0.695066i	$0.244625\pi$
$182$	−95.6108	−	262.689i	−0.525334	−	1.44334i
$183$		0			0
$184$	82.9651	−	69.6160i	0.450897	−	0.378348i
$185$	94.5803	−	259.857i	0.511245	−	1.40463i
$186$		0			0
$187$	−13.4117	+	76.0617i	−0.0717205	+	0.406747i
$188$		−	11.0033i		−	0.0585283i
$189$		0			0
$190$	144.874			0.762497
$191$	316.371	+	55.7848i	1.65639	+	0.292067i	0.922154	−	0.386823i	$-0.126428\pi$
$191$	316.371	+	55.7848i	1.65639	+	0.292067i	0.734240	+	0.678890i	$0.237539\pi$
$192$		0			0
$193$	−57.9813	−	21.1035i	−0.300421	−	0.109344i	0.187412	−	0.982281i	$-0.439990\pi$
$193$	−57.9813	−	21.1035i	−0.300421	−	0.109344i	−0.487833	+	0.872937i	$0.662212\pi$
$194$	45.8528	+	54.6452i	0.236354	+	0.281676i
$195$		0			0
$196$	−6.65034	+	2.42052i	−0.0339303	+	0.0123496i
$197$	194.174	+	112.106i	0.985652	+	0.569067i	0.903972	−	0.427592i	$-0.140638\pi$
$197$	194.174	+	112.106i	0.985652	+	0.569067i	0.0816805	+	0.996659i	$0.473971\pi$
$198$		0			0
$199$	2.60375	+	4.50982i	0.0130842	+	0.0226624i	0.872493	−	0.488626i	$-0.162502\pi$
$199$	2.60375	+	4.50982i	0.0130842	+	0.0226624i	−0.859409	+	0.511288i	$0.829168\pi$
$200$	33.3626	−	39.7600i	0.166813	−	0.198800i
$201$		0			0
$202$	−28.7375	−	162.979i	−0.142265	−	0.806825i
$203$	366.258	−	64.5812i	1.80423	−	0.318134i
$204$		0			0
$205$	−84.2714	−	70.7121i	−0.411080	−	0.344937i
$206$	−39.0517	+	22.5465i	−0.189571	+	0.109449i
$207$		0			0
$208$	−121.576	+	210.576i	−0.584499	+	1.01238i
$209$	43.5800	+	119.735i	0.208517	+	0.572895i
$210$		0			0
$211$	−17.6601	+	14.8186i	−0.0836973	+	0.0702303i	−0.683676	−	0.729785i	$-0.739620\pi$
$211$	−17.6601	+	14.8186i	−0.0836973	+	0.0702303i	0.599979	+	0.800016i	$0.295176\pi$
$212$	−4.08954	+	11.2359i	−0.0192903	+	0.0529996i
$213$		0			0
$214$	32.2631	−	182.973i	0.150762	−	0.855014i
$215$			10.7167i			0.0498452i
$216$		0			0
$217$	329.478			1.51833
$218$	195.197	+	34.4185i	0.895399	+	0.157883i
$219$		0			0
$220$	−7.06277	−	2.57064i	−0.0321035	−	0.0116847i
$221$	109.095	+	130.014i	0.493641	+	0.588299i
$222$		0			0
$223$	176.747	−	64.3308i	0.792589	−	0.288479i	0.0861771	−	0.996280i	$-0.472535\pi$
$223$	176.747	−	64.3308i	0.792589	−	0.288479i	0.706412	+	0.707801i	$0.250313\pi$
$224$	28.9984	+	16.7422i	0.129457	+	0.0747421i
$225$		0			0
$226$	15.8221	+	27.4047i	0.0700093	+	0.121260i
$227$	−80.6673	+	96.1356i	−0.355363	+	0.423505i	−0.913878	−	0.405990i	$-0.866927\pi$
$227$	−80.6673	+	96.1356i	−0.355363	+	0.423505i	0.558515	+	0.829494i	$0.311371\pi$
$228$		0			0
$229$	−22.7495	−	129.019i	−0.0993429	−	0.563401i	−0.993330	−	0.115308i	$-0.963214\pi$
$229$	−22.7495	−	129.019i	−0.0993429	−	0.563401i	0.893987	−	0.448093i	$-0.147897\pi$
$230$	−108.843	+	19.1920i	−0.473232	+	0.0834436i
$231$		0			0
$232$	−263.383	−	221.004i	−1.13527	−	0.952605i
$233$	352.009	−	203.233i	1.51077	−	0.872243i	0.510848	−	0.859671i	$-0.329331\pi$
$233$	352.009	−	203.233i	1.51077	−	0.872243i	0.999921	−	0.0125723i	$-0.00400199\pi$
$234$		0			0
$235$	−100.879	+	174.728i	−0.429274	+	0.743524i
$236$	0.337820	+	0.928154i	0.00143144	+	0.00393285i
$237$		0			0
$238$	−138.343	+	116.084i	−0.581275	+	0.487748i
$239$	−65.7792	+	180.727i	−0.275227	+	0.756179i	0.722660	+	0.691204i	$0.242919\pi$
$239$	−65.7792	+	180.727i	−0.275227	+	0.756179i	−0.997887	+	0.0649757i	$0.979303\pi$
$240$		0			0
$241$	−60.2152	+	341.497i	−0.249855	+	1.41700i	0.559085	+	0.829110i	$0.311152\pi$
$241$	−60.2152	+	341.497i	−0.249855	+	1.41700i	−0.808941	+	0.587890i	$0.799959\pi$
$242$		−	129.204i		−	0.533903i
$243$		0			0
$244$	8.57251			0.0351332
$245$	127.796	+	22.5339i	0.521617	+	0.0919752i
$246$		0			0
$247$	263.113	+	95.7655i	1.06524	+	0.387714i
$248$	−195.790	−	233.333i	−0.789476	−	0.940861i
$249$		0			0
$250$	−246.789	+	89.8240i	−0.987157	+	0.359296i
$251$	−370.198	−	213.734i	−1.47489	−	0.851530i	−0.475294	−	0.879827i	$-0.657658\pi$
$251$	−370.198	−	213.734i	−1.47489	−	0.851530i	−0.999600	+	0.0282966i	$0.990992\pi$
$252$		0			0
$253$	−48.6032	−	84.1831i	−0.192107	−	0.332740i
$254$	−101.592	+	121.073i	−0.399970	+	0.476666i
$255$		0			0
$256$	−7.83177	−	44.4162i	−0.0305928	−	0.173501i
$257$	−279.755	+	49.3284i	−1.08854	+	0.191939i	−0.688990	−	0.724771i	$-0.741945\pi$
$257$	−279.755	+	49.3284i	−1.08854	+	0.191939i	−0.399552	+	0.916711i	$0.630834\pi$
$258$		0			0
$259$	435.649	+	365.553i	1.68204	+	1.41140i
$260$	−14.3035	+	8.25811i	−0.0550133	+	0.0317620i
$261$		0			0
$262$	141.101	−	244.395i	0.538555	−	0.932805i
$263$	−118.493	−	325.557i	−0.450544	−	1.23786i	−0.932342	−	0.361577i	$-0.882238\pi$
$263$	−118.493	−	325.557i	−0.450544	−	1.23786i	0.481798	−	0.876282i	$-0.339984\pi$
$264$		0			0
$265$	167.952	−	140.929i	0.633782	−	0.531806i
$266$	−101.901	+	279.970i	−0.383086	+	1.05252i
$267$		0			0
$268$	0.708552	−	4.01840i	0.00264385	−	0.0149940i
$269$			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	$0.261885\pi$
$272$	154.696	+	27.2770i	0.568734	+	0.100283i
$273$		0			0
$274$	342.753	+	124.752i	1.25092	+	0.455299i
$275$	−29.9442	−	35.6861i	−0.108888	−	0.129768i
$276$		0			0
$277$	265.808	−	96.7461i	0.959594	−	0.349264i	0.185720	−	0.982603i	$-0.440538\pi$
$277$	265.808	−	96.7461i	0.959594	−	0.349264i	0.773874	+	0.633339i	$0.218316\pi$
$278$	147.628	+	85.2331i	0.531036	+	0.306594i
$279$		0			0
$280$	−157.888	−	273.470i	−0.563886	−	0.976678i
$281$	−180.704	+	215.355i	−0.643075	+	0.766387i	−0.984853	−	0.173394i	$-0.944527\pi$
$281$	−180.704	+	215.355i	−0.643075	+	0.766387i	0.341778	+	0.939781i	$0.388971\pi$
$282$		0			0
$283$	75.7498	+	429.598i	0.267667	+	1.51802i	0.761331	+	0.648363i	$0.224546\pi$
$283$	75.7498	+	429.598i	0.267667	+	1.51802i	−0.493664	+	0.869653i	$0.664343\pi$
$284$	−13.8068	+	2.43450i	−0.0486153	+	0.00857219i
$285$		0			0
$286$	177.688	+	149.098i	0.621288	+	0.521323i
$287$	195.925	−	113.118i	0.682667	−	0.394138i
$288$		0			0
$289$	−89.6779	+	155.327i	−0.310304	+	0.537463i
$290$	120.004	+	329.707i	0.413805	+	1.13692i
$291$		0			0
$292$	−9.51509	+	7.98411i	−0.0325859	+	0.0273428i
$293$	126.261	−	346.898i	0.430924	−	1.18395i	−0.514323	−	0.857596i	$-0.671957\pi$
$293$	126.261	−	346.898i	0.430924	−	1.18395i	0.945247	−	0.326356i	$-0.105821\pi$
$294$		0			0
$295$	3.14495	−	17.8359i	0.0106608	−	0.0604606i
$296$		−	525.751i		−	1.77619i
$297$		0			0
$298$	−121.971			−0.409299
$299$	−210.362	−	37.0925i	−0.703552	−	0.124055i
$300$		0			0
$301$	−20.7101	−	7.53785i	−0.0688043	−	0.0250427i
$302$	143.910	+	171.506i	0.476524	+	0.567900i
$303$		0			0
$304$	243.519	−	88.6338i	0.801051	−	0.291559i
$305$	−136.128	−	78.5936i	−0.446321	−	0.257684i
$306$		0			0
$307$	183.104	+	317.145i	0.596429	+	1.03304i	0.993344	+	0.115189i	$0.0367475\pi$
$307$	183.104	+	317.145i	0.596429	+	1.03304i	−0.396915	+	0.917855i	$0.629919\pi$
$308$	9.93552	−	11.8407i	0.0322582	−	0.0384438i
$309$		0			0
$310$	53.9762	+	306.114i	0.174117	+	0.987465i
$311$	−469.956	+	82.8659i	−1.51111	+	0.266450i	−0.866933	−	0.498425i	$-0.833912\pi$
$311$	−469.956	+	82.8659i	−1.51111	+	0.266450i	−0.644179	+	0.764875i	$0.722801\pi$
$312$		0			0
$313$	−77.4975	−	65.0281i	−0.247596	−	0.207758i	0.510540	−	0.859854i	$-0.329445\pi$
$313$	−77.4975	−	65.0281i	−0.247596	−	0.207758i	−0.758136	+	0.652096i	$0.773890\pi$
$314$	−87.9315	+	50.7673i	−0.280037	+	0.161679i
$315$		0			0
$316$	0.183836	−	0.318413i	0.000581759	−	0.00100764i
$317$	−126.727	−	348.179i	−0.399770	−	1.09836i	−0.962397	−	0.271647i	$-0.912432\pi$
$317$	−126.727	−	348.179i	−0.399770	−	1.09836i	0.562627	−	0.826711i	$-0.309791\pi$
$318$		0			0
$319$	−236.396	+	198.360i	−0.741053	+	0.621818i
$320$	−99.5167	+	273.420i	−0.310990	+	0.854437i
$321$		0			0
$322$	39.4689	−	223.839i	0.122574	−	0.695152i
$323$		−	180.887i		−	0.560021i
$324$		0			0
$325$	−102.369			−0.314980
$326$	480.325	+	84.6943i	1.47339	+	0.259798i
$327$		0			0
$328$	−196.536	−	71.5334i	−0.599196	−	0.218090i
$329$	−266.707	−	317.848i	−0.810658	−	0.966105i
$330$		0			0
$331$	−335.147	+	121.984i	−1.01253	+	0.368531i	−0.794404	−	0.607390i	$-0.792217\pi$
$331$	−335.147	+	121.984i	−1.01253	+	0.368531i	−0.218126	+	0.975921i	$0.569994\pi$
$332$	−23.0844	−	13.3278i	−0.0695314	−	0.0401440i
$333$		0			0
$334$	−8.21164	−	14.2230i	−0.0245857	−	0.0425838i
$335$	−48.0925	+	57.3144i	−0.143560	+	0.171088i
$336$		0			0
$337$	−69.6738	−	395.140i	−0.206747	−	1.17252i	−0.894667	−	0.446734i	$-0.852587\pi$
$337$	−69.6738	−	395.140i	−0.206747	−	1.17252i	0.687920	−	0.725787i	$-0.258524\pi$
$338$	179.063	−	31.5736i	0.529772	−	0.0934132i
$339$		0			0
$340$	8.17361	+	6.85847i	0.0240400	+	0.0201720i
$341$	−236.759	+	136.693i	−0.694308	+	0.400859i
$342$		0			0
$343$	84.3548	−	146.107i	0.245932	−	0.425967i
$344$	6.96859	+	19.1460i	0.0202575	+	0.0556571i
$345$		0			0
$346$	289.907	−	243.261i	0.837881	−	0.703065i
$347$	19.5911	−	53.8262i	0.0564586	−	0.155119i	−0.908257	−	0.418413i	$-0.862587\pi$
$347$	19.5911	−	53.8262i	0.0564586	−	0.155119i	0.964716	+	0.263294i	$0.0848089\pi$
$348$		0			0
$349$	65.1384	−	369.418i	0.186643	−	1.05851i	−0.737183	−	0.675693i	$-0.763844\pi$
$349$	65.1384	−	369.418i	0.186643	−	1.05851i	0.923826	−	0.382812i	$-0.125044\pi$
$350$		−	108.927i		−	0.311220i
$351$		0			0
$352$	−27.7839			−0.0789316
$353$	−216.687	−	38.2077i	−0.613843	−	0.108237i	−0.141922	−	0.989878i	$-0.545328\pi$
$353$	−216.687	−	38.2077i	−0.613843	−	0.108237i	−0.471921	+	0.881641i	$0.656439\pi$
$354$		0			0
$355$	241.565	+	87.9226i	0.680466	+	0.247669i
$356$	7.25286	+	8.64362i	0.0203732	+	0.0242798i
$357$		0			0
$358$	385.683	−	140.377i	1.07733	−	0.392114i
$359$	174.426	+	100.705i	0.485866	+	0.280515i	0.722858	−	0.690997i	$-0.242828\pi$
$359$	174.426	+	100.705i	0.485866	+	0.280515i	−0.236992	+	0.971512i	$0.576162\pi$
$360$		0			0
$361$	31.2901	+	54.1960i	0.0866761	+	0.150127i
$362$	109.466	−	130.456i	0.302391	−	0.360376i
$363$		0			0
$364$	−5.89814	−	33.4500i	−0.0162037	−	0.0918956i
$365$	224.295	−	39.5492i	0.614506	−	0.108354i
$366$		0			0
$367$	121.926	+	102.308i	0.332223	+	0.278768i	0.793605	−	0.608433i	$-0.208202\pi$
$367$	121.926	+	102.308i	0.332223	+	0.278768i	−0.461382	+	0.887202i	$0.652646\pi$
$368$	−171.213	+	98.8500i	−0.465253	+	0.268614i
$369$		0			0
$370$	−268.262	+	464.643i	−0.725032	+	1.25579i
$371$	154.212	+	423.693i	0.415665	+	1.14203i
$372$		0			0
$373$	−39.5646	+	33.1987i	−0.106071	+	0.0890044i	−0.694281	−	0.719704i	$-0.744277\pi$
$373$	−39.5646	+	33.1987i	−0.106071	+	0.0890044i	0.588210	+	0.808709i	$0.299833\pi$
$374$	51.2515	−	140.812i	0.137036	−	0.376503i
$375$		0			0
$376$	−66.6091	+	377.759i	−0.177152	+	1.00468i
$377$			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	$0.437777\pi$
$380$	17.3353	+	3.05669i	0.0456193	+	0.00804392i
$381$		0			0
$382$	−585.695	−	213.175i	−1.53323	−	0.558051i
$383$	73.1074	+	87.1261i	0.190881	+	0.227483i	0.852994	−	0.521921i	$-0.174784\pi$
$383$	73.1074	+	87.1261i	0.190881	+	0.227483i	−0.662113	+	0.749404i	$0.730340\pi$
$384$		0			0
$385$	−266.329	+	96.9357i	−0.691763	+	0.251781i
$386$	103.675	+	59.8566i	0.268587	+	0.155069i
$387$		0			0
$388$	4.33368	+	7.50616i	0.0111693	+	0.0193458i
$389$	232.951	−	277.620i	0.598846	−	0.713677i	−0.378434	−	0.925628i	$-0.623537\pi$
$389$	232.951	−	277.620i	0.598846	−	0.713677i	0.977280	+	0.211952i	$0.0679819\pi$
$390$		0			0
$391$	23.9627	+	135.899i	0.0612856	+	0.347568i
$392$	242.968	−	42.8418i	0.619816	−	0.109290i
$393$		0			0
$394$	−333.237	−	279.619i	−0.845779	−	0.709693i
$395$	−5.83848	+	3.37085i	−0.0147810	+	0.00853379i
$396$		0			0
$397$	368.516	−	638.289i	0.928252	−	1.60778i	0.142006	−	0.989866i	$-0.454645\pi$
$397$	368.516	−	638.289i	0.928252	−	1.60778i	0.786246	−	0.617914i	$-0.212022\pi$
$398$	−3.45558	−	9.49412i	−0.00868235	−	0.0238546i
$399$		0			0
$400$	−72.5791	+	60.9011i	−0.181448	+	0.152253i
$401$	75.6898	−	207.956i	0.188753	−	0.518593i	−0.808833	−	0.588038i	$-0.799900\pi$
$401$	75.6898	−	207.956i	0.188753	−	0.518593i	0.997586	+	0.0694446i	$0.0221227\pi$
$402$		0			0
$403$	−104.320	+	591.628i	−0.258859	+	1.46806i
$404$		−	20.1080i		−	0.0497722i
$405$		0			0
$406$	−721.566			−1.77726
$407$	−464.713	−	81.9414i	−1.14180	−	0.201330i
$408$		0			0
$409$	−418.339	−	152.263i	−1.02283	−	0.372281i	−0.224486	−	0.974477i	$-0.572070\pi$
$409$	−418.339	−	152.263i	−1.02283	−	0.372281i	−0.798348	+	0.602196i	$0.794293\pi$
$410$	137.194	+	163.501i	0.334618	+	0.398783i
$411$		0			0
$412$	−5.14854	+	1.87391i	−0.0124964	+	0.00454834i
$413$	32.2558	+	18.6229i	0.0781012	+	0.0450917i
$414$		0			0
$415$	244.381	+	423.280i	0.588870	+	1.01995i
$416$	−39.2448	+	46.7702i	−0.0943385	+	0.112428i
$417$		0			0
$418$	−42.9285	−	243.460i	−0.102700	−	0.582440i
$419$	568.426	−	100.229i	1.35663	−	0.239210i	0.552423	−	0.833564i	$-0.313703\pi$
$419$	568.426	−	100.229i	1.35663	−	0.239210i	0.804203	+	0.594354i	$0.202592\pi$
$420$		0			0
$421$	−257.389	−	215.975i	−0.611376	−	0.513005i	0.283703	−	0.958912i	$-0.408437\pi$
$421$	−257.389	−	215.975i	−0.611376	−	0.513005i	−0.895079	+	0.445907i	$0.852881\pi$
$422$	38.7356	−	22.3640i	0.0917905	−	0.0529953i
$423$		0			0
$424$	208.417	−	360.989i	0.491549	−	0.851388i
$425$	22.6187	+	62.1444i	0.0532205	+	0.146222i
$426$		0			0
$427$	247.631	−	207.787i	0.579932	−	0.486620i
$428$	7.72105	−	21.2134i	0.0180398	−	0.0495640i
$429$		0			0
$430$	3.61054	−	20.4764i	0.00839661	−	0.0476195i
$431$			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	$0.575775\pi$
$434$	−629.531	−	111.003i	−1.45053	−	0.255768i
$435$		0			0
$436$	22.6306	+	8.23687i	0.0519051	+	0.0188919i
$437$	146.337	+	174.398i	0.334867	+	0.399079i
$438$		0			0
$439$	−379.487	+	138.122i	−0.864435	+	0.314629i	−0.735912	−	0.677078i	$-0.763246\pi$
$439$	−379.487	+	138.122i	−0.864435	+	0.314629i	−0.128524	+	0.991706i	$0.541024\pi$
$440$	226.913	+	131.008i	0.515712	+	0.297746i
$441$		0			0
$442$	−164.644	−	285.172i	−0.372498	−	0.645185i
$443$	425.281	−	506.830i	0.960001	−	1.14409i	−0.0295005	−	0.999565i	$-0.509392\pi$
$443$	425.281	−	506.830i	0.960001	−	1.14409i	0.989502	−	0.144520i	$-0.0461639\pi$
$444$		0			0
$445$	−35.9270	−	203.752i	−0.0807348	−	0.457870i
$446$	−359.384	+	63.3690i	−0.805793	+	0.142083i
$447$		0			0
$448$	−458.387	−	384.632i	−1.02318	−	0.858554i
$449$	403.851	−	233.164i	0.899446	−	0.519295i	0.0224253	−	0.999749i	$-0.492861\pi$
$449$	403.851	−	233.164i	0.899446	−	0.519295i	0.877020	+	0.480453i	$0.159528\pi$
$450$		0			0
$451$	−93.8599	+	162.570i	−0.208115	+	0.360466i
$452$	1.31503	+	3.61301i	0.00290936	+	0.00799339i
$453$		0			0
$454$	186.519	−	156.508i	0.410836	−	0.344732i
$455$	−213.013	+	585.247i	−0.468159	+	1.28626i
$456$		0			0
$457$	148.311	−	841.111i	0.324531	−	1.84051i	−0.188421	−	0.982088i	$-0.560337\pi$
$457$	148.311	−	841.111i	0.324531	−	1.84051i	0.512952	−	0.858417i	$-0.328552\pi$
$458$			254.180i			0.554979i
$459$		0			0
$460$	−13.4289			−0.0291932
$461$	−80.6673	−	14.2238i	−0.174983	−	0.0308543i	0.0854699	−	0.996341i	$-0.472761\pi$
$461$	−80.6673	−	14.2238i	−0.174983	−	0.0308543i	−0.260453	+	0.965486i	$0.583872\pi$
$462$		0			0
$463$	615.138	+	223.892i	1.32859	+	0.483568i	0.906201	−	0.422847i	$-0.138969\pi$
$463$	615.138	+	223.892i	1.32859	+	0.483568i	0.422390	+	0.906414i	$0.361191\pi$
$464$	403.428	+	480.786i	0.869456	+	1.03618i
$465$		0			0
$466$	−741.053	+	269.721i	−1.59024	+	0.578801i
$467$	−113.391	−	65.4664i	−0.242808	−	0.140185i	0.373659	−	0.927566i	$-0.378103\pi$
$467$	−113.391	−	65.4664i	−0.242808	−	0.140185i	−0.616466	+	0.787381i	$0.711436\pi$
$468$		0			0
$469$	−76.9332	−	133.252i	−0.164037	−	0.284120i
$470$	251.617	−	299.865i	0.535355	−	0.638011i
$471$		0			0
$472$	−5.97921	−	33.9098i	−0.0126678	−	0.0718428i
$473$	18.0093	−	3.17553i	0.0380747	−	0.00671360i
$474$		0			0
$475$	83.5779	+	70.1301i	0.175953	+	0.147642i
$476$	−19.0031	+	10.9714i	−0.0399225	+	0.0230493i
$477$		0			0
$478$	186.572	−	323.152i	0.390318	−	0.676051i
$479$	−53.9253	−	148.158i	−0.112579	−	0.309308i	0.870589	−	0.492010i	$-0.163738\pi$
$479$	−53.9253	−	148.158i	−0.112579	−	0.309308i	−0.983168	+	0.182702i	$0.941516\pi$
$480$		0			0
$481$	−794.343	+	666.533i	−1.65144	+	1.38572i
$482$	230.106	−	632.210i	0.477397	−	1.31164i
$483$		0			0
$484$	2.72607	−	15.4603i	0.00563237	−	0.0319428i
$485$		−	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	$0.754412\pi$
$488$	−294.306	−	51.8941i	−0.603086	−	0.106340i
$489$		0			0
$490$	−236.588	−	86.1109i	−0.482832	−	0.175737i
$491$	−27.1397	−	32.3438i	−0.0552743	−	0.0658733i	0.737699	−	0.675130i	$-0.235912\pi$
$491$	−27.1397	−	32.3438i	−0.0552743	−	0.0658733i	−0.792973	+	0.609257i	$0.791468\pi$
$492$		0			0
$493$	411.664	−	149.833i	0.835018	−	0.303922i
$494$	−470.466	−	271.623i	−0.952359	−	0.549845i
$495$		0			0
$496$	278.009	+	481.525i	0.560501	+	0.970816i
$497$	−339.821	+	404.983i	−0.683745	+	0.814855i
$498$		0			0
$499$	−83.4143	−	473.066i	−0.167163	−	0.948028i	−0.946806	−	0.321804i	$-0.895711\pi$
$499$	−83.4143	−	473.066i	−0.167163	−	0.948028i	0.779643	−	0.626224i	$-0.215400\pi$
$500$	−31.4254	+	5.54115i	−0.0628509	+	0.0110823i
$501$		0			0
$502$	635.328	+	533.103i	1.26559	+	1.06196i
$503$	−73.7969	+	42.6067i	−0.146714	+	0.0847051i	−0.571560	−	0.820560i	$-0.693661\pi$
$503$	−73.7969	+	42.6067i	−0.146714	+	0.0847051i	0.424846	+	0.905266i	$0.360328\pi$
$504$		0			0
$505$	−184.352	+	319.307i	−0.365053	+	0.632290i
$506$	64.5039	+	177.223i	0.127478	+	0.350243i
$507$		0			0
$508$	−14.7108	+	12.3438i	−0.0289583	+	0.0242989i
$509$	135.879	−	373.323i	0.266952	−	0.733445i	−0.731704	−	0.681622i	$-0.761275\pi$
$509$	135.879	−	373.323i	0.266952	−	0.733445i	0.998656	−	0.0518226i	$-0.0165030\pi$
$510$		0			0
$511$	−81.3340	+	461.268i	−0.159166	+	0.902677i
$512$			549.639i			1.07351i
$513$		0			0
$514$	551.146			1.07227
$515$	98.9369	+	17.4452i	0.192111	+	0.0338743i
$516$		0			0
$517$	323.521	+	117.752i	0.625765	+	0.227760i
$518$	−709.235	−	845.234i	−1.36918	−	1.63173i
$519$		0			0
$520$	541.049	−	196.926i	1.04048	−	0.378703i
$521$	19.7109	+	11.3801i	0.0378328	+	0.0218428i	0.518797	−	0.854897i	$-0.326380\pi$
$521$	19.7109	+	11.3801i	0.0378328	+	0.0218428i	−0.480964	+	0.876740i	$0.659713\pi$
$522$		0			0
$523$	−380.270	−	658.647i	−0.727093	−	1.25936i	−0.958107	−	0.286412i	$-0.907537\pi$
$523$	−380.270	−	658.647i	−0.727093	−	1.25936i	0.231013	−	0.972951i	$-0.425796\pi$
$524$	22.0403	−	26.2666i	0.0420617	−	0.0501272i
$525$		0			0
$526$	116.722	+	661.961i	0.221904	+	1.25848i
$527$	382.207	−	67.3933i	0.725250	−	0.127881i
$528$		0			0
$529$	272.192	+	228.397i	0.514541	+	0.431752i
$530$	−368.385	+	212.687i	−0.695067	+	0.401297i
$531$		0			0
$532$	−18.1003	+	31.3506i	−0.0340231	+	0.0589297i
$533$	141.086	+	387.630i	0.264701	+	0.727261i
$534$		0			0
$535$	−317.094	+	266.073i	−0.592698	+	0.497333i
$536$	−48.6511	+	133.668i	−0.0907670	+	0.249380i
$537$		0			0
$538$	100.365	−	569.195i	0.186551	−	1.05798i
$539$		−	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	$0.546899\pi$
$542$	−704.431	−	124.210i	−1.29969	−	0.229170i
$543$		0			0
$544$	37.0638	+	13.4901i	0.0681320	+	0.0247980i
$545$	−283.849	−	338.278i	−0.520824	−	0.620693i
$546$		0			0
$547$	618.369	−	225.068i	1.13047	−	0.411459i	0.292009	−	0.956416i	$-0.405676\pi$
$547$	618.369	−	225.068i	1.13047	−	0.411459i	0.838464	+	0.544957i	$0.183454\pi$
$548$	38.3809	+	22.1592i	0.0700382	+	0.0404366i
$549$		0			0
$550$	45.1914	+	78.2737i	0.0821661	+	0.142316i
$551$	464.564	−	553.646i	0.843129	−	1.00480i
$552$		0			0
$553$	−2.40754	−	13.6538i	−0.00435359	−	0.0246904i
$554$	−540.472	+	95.2997i	−0.975581	+	0.172021i
$555$		0			0
$556$	15.8665	+	13.3136i	0.0285369	+	0.0239453i
$557$	−817.907	+	472.219i	−1.46842	+	0.847790i	−0.999374	−	0.0353864i	$-0.988734\pi$
$557$	−817.907	+	472.219i	−1.46842	+	0.847790i	−0.469041	+	0.883176i	$0.655400\pi$
$558$		0			0
$559$	20.0927	−	34.8015i	0.0359439	−	0.0622567i
$560$	197.150	+	541.664i	0.352053	+	0.967257i
$561$		0			0
$562$	417.825	−	350.597i	0.743460	−	0.623837i
$563$	−361.954	+	994.460i	−0.642902	+	1.76636i	−0.000488026		1.00000i	$0.500155\pi$
$563$	−361.954	+	994.460i	−0.642902	+	1.76636i	−0.642414	+	0.766358i	$0.722067\pi$
$564$		0			0
$565$	12.2423	−	69.4295i	0.0216678	−	0.122884i
$566$		−	846.352i		−	1.49532i
$567$		0			0
$568$	488.742			0.860462
$569$	175.960	+	31.0266i	0.309245	+	0.0545282i	0.326117	−	0.945329i	$-0.394260\pi$
$569$	175.960	+	31.0266i	0.309245	+	0.0545282i	−0.0168721	+	0.999858i	$0.505371\pi$
$570$		0			0
$571$	−566.101	−	206.044i	−0.991420	−	0.360847i	−0.205150	−	0.978731i	$-0.565768\pi$
$571$	−566.101	−	206.044i	−0.991420	−	0.360847i	−0.786270	+	0.617883i	$0.787990\pi$
$572$	18.1160	+	21.5898i	0.0316713	+	0.0377444i
$573$		0			0
$574$	−412.464	+	150.125i	−0.718578	+	0.261541i
$575$	−72.0819	−	41.6165i	−0.125360	−	0.0723766i
$576$		0			0
$577$	87.1430	+	150.936i	0.151028	+	0.261588i	0.931606	−	0.363471i	$-0.118408\pi$
$577$	87.1430	+	150.936i	0.151028	+	0.261588i	−0.780578	+	0.625059i	$0.785075\pi$
$578$	223.678	−	266.569i	0.386986	−	0.461192i
$579$		0			0
$580$	7.40290	+	41.9839i	0.0127636	+	0.0723861i
$581$	−989.880	+	174.543i	−1.70375	+	0.300417i
$582$		0			0
$583$	−286.596	−	240.482i	−0.491588	−	0.412491i
$584$	374.998	−	216.505i	0.642121	−	0.370728i
$585$		0			0
$586$	−358.118	+	620.279i	−0.611123	+	1.05850i
$587$	349.240	+	959.528i	0.594957	+	1.63463i	0.761178	+	0.648543i	$0.224621\pi$
$587$	349.240	+	959.528i	0.594957	+	1.63463i	−0.166221	+	0.986088i	$0.553157\pi$
$588$		0			0
$589$	490.481	−	411.562i	0.832735	−	0.698747i
$590$	−12.0181	+	33.0194i	−0.0203696	+	0.0559650i
$591$		0			0
$592$	−166.654	+	945.141i	−0.281510	+	1.59652i
$593$		−	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
$596$	−14.5948	−	2.57345i	−0.0244879	−	0.00431787i
$597$		0			0
$598$	389.441	+	141.745i	0.651239	+	0.237032i
$599$	204.340	+	243.523i	0.341135	+	0.406549i	0.909150	−	0.416470i	$-0.136733\pi$
$599$	204.340	+	243.523i	0.341135	+	0.406549i	−0.568015	+	0.823018i	$0.692288\pi$
$600$		0			0
$601$	511.747	−	186.261i	0.851492	−	0.309918i	0.120843	−	0.992672i	$-0.461440\pi$
$601$	511.747	−	186.261i	0.851492	−	0.309918i	0.730648	+	0.682754i	$0.239218\pi$
$602$	37.0311	+	21.3799i	0.0615134	+	0.0355148i
$603$		0			0
$604$	13.6014	+	23.5583i	0.0225189	+	0.0390039i
$605$	−185.030	+	220.511i	−0.305835	+	0.364480i
$606$		0			0
$607$	73.9645	+	419.473i	0.121853	+	0.691060i	0.983128	+	0.182921i	$0.0585553\pi$
$607$	73.9645	+	419.473i	0.121853	+	0.691060i	−0.861275	+	0.508139i	$0.830334\pi$
$608$	64.0821	−	11.2994i	0.105398	−	0.0185846i
$609$		0			0
$610$	233.620	+	196.031i	0.382984	+	0.321362i
$611$	655.192	−	378.275i	1.07233	−	0.619108i
$612$		0			0
$613$	−43.8571	+	75.9627i	−0.0715450	+	0.123920i	−0.899579	−	0.436759i	$-0.856126\pi$
$613$	−43.8571	+	75.9627i	−0.0715450	+	0.123920i	0.828034	+	0.560679i	$0.189460\pi$
$614$	−243.007	−	667.656i	−0.395777	−	1.08739i
$615$		0			0
$616$	−412.778	+	346.362i	−0.670095	+	0.562276i
$617$	236.100	−	648.680i	0.382658	−	1.05135i	−0.587574	−	0.809170i	$-0.699917\pi$
$617$	236.100	−	648.680i	0.382658	−	1.05135i	0.970233	−	0.242175i	$-0.0778608\pi$
$618$		0			0
$619$	120.446	−	683.085i	0.194582	−	1.10353i	−0.718431	−	0.695598i	$-0.755139\pi$
$619$	120.446	−	683.085i	0.194582	−	1.10353i	0.913013	−	0.407931i	$-0.133750\pi$
$620$			37.7678i			0.0609158i
$621$		0			0
$622$	925.860			1.48852
$623$	419.021	+	73.8847i	0.672586	+	0.118595i
$624$		0			0
$625$	401.454	+	146.117i	0.642326	+	0.233788i
$626$	126.166	+	150.358i	0.201543	+	0.240189i
$627$		0			0
$628$	−11.5928	+	4.21944i	−0.0184599	+	0.00671885i
$629$	580.142	+	334.945i	0.922324	+	0.532504i
$630$		0			0
$631$	−58.9015	−	102.020i	−0.0933463	−	0.161681i	0.815571	−	0.578657i	$-0.196423\pi$
$631$	−58.9015	−	102.020i	−0.0933463	−	0.161681i	−0.908917	+	0.416977i	$0.863090\pi$
$632$	−8.23886	+	9.81869i	−0.0130362	+	0.0155359i
$633$		0			0
$634$	124.832	+	707.960i	0.196897	+	1.11666i
$635$	346.771	−	61.1451i	0.546097	−	0.0962916i
$636$		0			0
$637$	−372.757	−	312.780i	−0.585176	−	0.491021i
$638$	518.510	−	299.362i	0.812711	−	0.469219i
$639$		0			0
$640$	249.699	−	432.491i	0.390155	−	0.675768i
$641$	125.411	+	344.564i	0.195649	+	0.537542i	0.998260	−	0.0589610i	$-0.0187788\pi$
$641$	125.411	+	344.564i	0.195649	+	0.537542i	−0.802611	+	0.596503i	$0.796557\pi$
$642$		0			0
$643$	735.870	−	617.468i	1.14443	−	0.960292i	0.144857	−	0.989453i	$-0.453728\pi$
$643$	735.870	−	617.468i	1.14443	−	0.960292i	0.999575	+	0.0291603i	$0.00928333\pi$
$644$	9.44551	−	25.9513i	0.0146669	−	0.0402971i
$645$		0			0
$646$	−60.9420	+	345.619i	−0.0943375	+	0.535014i
$647$			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
$650$	195.595	+	34.4887i	0.300916	+	0.0530596i
$651$		0			0
$652$	55.6876	+	20.2686i	0.0854105	+	0.0310869i
$653$	566.154	+	674.716i	0.867005	+	1.03326i	0.999117	+	0.0420211i	$0.0133797\pi$
$653$	566.154	+	674.716i	0.867005	+	1.03326i	−0.132112	+	0.991235i	$0.542176\pi$
$654$		0			0
$655$	−590.807	+	215.036i	−0.901995	+	0.328299i
$656$	330.638	+	190.894i	0.504021	+	0.290997i
$657$		0			0
$658$	402.509	+	697.167i	0.611717	+	1.05952i
$659$	40.9793	−	48.8372i	0.0621841	−	0.0741081i	−0.734056	−	0.679089i	$-0.762375\pi$
$659$	40.9793	−	48.8372i	0.0621841	−	0.0741081i	0.796240	+	0.604981i	$0.206819\pi$
$660$		0			0
$661$	−79.6337	−	451.625i	−0.120475	−	0.683246i	−0.983893	−	0.178757i	$-0.942792\pi$
$661$	−79.6337	−	451.625i	−0.120475	−	0.683246i	0.863419	−	0.504488i	$-0.168319\pi$
$662$	681.462	−	120.160i	1.02940	−	0.181511i
$663$		0			0
$664$	711.839	+	597.304i	1.07205	+	0.899555i
$665$	574.850	−	331.890i	0.864436	−	0.499082i
$666$		0			0
$667$	−275.681	+	477.493i	−0.413315	+	0.715882i
$668$	−0.682497	−	1.87515i	−0.00102170	−	0.00280710i
$669$		0			0
$670$	111.200	−	93.3077i	0.165970	−	0.139265i
$671$	−91.7387	+	252.050i	−0.136719	+	0.375633i
$672$		0			0
$673$	−190.581	+	1080.84i	−0.283181	+	1.60600i	0.428530	+	0.903527i	$0.359032\pi$
$673$	−190.581	+	1080.84i	−0.283181	+	1.60600i	−0.711711	+	0.702472i	$0.752080\pi$
$674$			778.465i			1.15499i
$675$		0			0
$676$	22.0924			0.0326811
$677$	483.226	+	85.2058i	0.713776	+	0.125858i	0.518732	−	0.854937i	$-0.326404\pi$
$677$	483.226	+	85.2058i	0.713776	+	0.125858i	0.195043	+	0.980795i	$0.437515\pi$
$678$		0			0
$679$	307.125	+	111.785i	0.452320	+	0.164631i
$680$	−239.093	−	284.940i	−0.351608	−	0.419030i
$681$		0			0
$682$	498.427	−	181.413i	0.730832	−	0.266001i
$683$	−684.465	−	395.176i	−1.00215	−	0.578589i	−0.0932631	−	0.995642i	$-0.529730\pi$
$683$	−684.465	−	395.176i	−1.00215	−	0.578589i	−0.908882	+	0.417053i	$0.863063\pi$
$684$		0			0
$685$	−406.316	−	703.760i	−0.593162	−	1.02739i
$686$	−210.401	+	250.746i	−0.306707	+	0.365519i
$687$		0			0
$688$	−6.45845	−	36.6277i	−0.00938728	−	0.0532379i
$689$	−809.634	+	142.760i	−1.17509	+	0.207199i
$690$		0			0
$691$	−165.381	−	138.771i	−0.239336	−	0.200827i	0.515228	−	0.857053i	$-0.327707\pi$
$691$	−165.381	−	138.771i	−0.239336	−	0.200827i	−0.754564	+	0.656226i	$0.772152\pi$
$692$	39.8221	−	22.9913i	0.0575464	−	0.0332244i
$693$		0			0
$694$	−55.5671	+	96.2451i	−0.0800679	+	0.138682i
$695$	−129.894	−	356.880i	−0.186898	−	0.513497i
$696$		0			0
$697$	204.143	−	171.296i	0.292888	−	0.245762i
$698$	−248.919	+	683.900i	−0.356618	+	0.979800i
$699$		0			0
$700$	2.29824	−	13.0339i	0.00328319	−	0.0186199i
$701$		−	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
$704$	488.967	+	86.2181i	0.694556	+	0.122469i
$705$		0			0
$706$	401.150	+	146.007i	0.568201	+	0.206808i
$707$	−487.392	−	580.851i	−0.689381	−	0.821572i
$708$		0			0
$709$	−1211.14	+	440.817i	−1.70823	+	0.621745i	−0.996720	−	0.0809298i	$-0.974211\pi$
$709$	−1211.14	+	440.817i	−1.70823	+	0.621745i	−0.711511	+	0.702675i	$0.751989\pi$
$710$	−431.936	−	249.379i	−0.608361	−	0.351237i
$711$		0			0
$712$	−196.676	−	340.653i	−0.276230	−	0.478445i
$713$	−313.974	+	374.180i	−0.440357	+	0.524797i
$714$		0			0
$715$	−89.7375	−	508.926i	−0.125507	−	0.711785i
$716$	49.1117	−	8.65971i	0.0685917	−	0.0120946i
$717$		0			0
$718$	−299.346	−	251.181i	−0.416917	−	0.349835i
$719$	−497.326	+	287.131i	−0.691691	+	0.399348i	−0.804245	−	0.594298i	$-0.797430\pi$
$719$	−497.326	+	287.131i	−0.691691	+	0.399348i	0.112554	+	0.993646i	$0.464097\pi$
$720$		0			0
$721$	−103.302	+	178.925i	−0.143277	+	0.248162i
$722$	−41.5268	−	114.094i	−0.0575163	−	0.158025i
$723$		0			0
$724$	15.8509	−	13.3005i	0.0218935	−	0.0183708i
$725$	−90.3731	+	248.298i	−0.124653	+	0.342480i
$726$		0			0
$727$	97.0052	−	550.144i	0.133432	−	0.756732i	−0.842506	−	0.538686i	$-0.818921\pi$
$727$	97.0052	−	550.144i	0.133432	−	0.756732i	0.975939	−	0.218045i	$-0.0699681\pi$
$728$			1184.09i			1.62650i
$729$		0			0
$730$	−441.884			−0.605320
$731$	−25.5663	−	4.50803i	−0.0349744	−	0.00616694i
$732$		0			0
$733$	−1059.70	−	385.699i	−1.44570	−	0.526192i	−0.504313	−	0.863521i	$-0.668254\pi$
$733$	−1059.70	−	385.699i	−1.44570	−	0.526192i	−0.941387	+	0.337329i	$0.890477\pi$
$734$	−198.495	−	236.557i	−0.270429	−	0.322285i
$735$		0			0
$736$	−46.6477	+	16.9784i	−0.0633800	+	0.0230684i
$737$	110.567	+	63.8358i	0.150023	+	0.0866157i
$738$		0			0
$739$	−163.517	−	283.219i	−0.221268	−	0.383247i	0.733926	−	0.679230i	$-0.237686\pi$
$739$	−163.517	−	283.219i	−0.221268	−	0.383247i	−0.955193	+	0.295983i	$0.904353\pi$
$740$	−41.9031	+	49.9381i	−0.0566258	+	0.0674839i
$741$		0			0
$742$	−151.906	−	861.504i	−0.204726	−	1.16106i
$743$	367.560	−	64.8107i	0.494697	−	0.0872284i	0.0792668	−	0.996853i	$-0.474742\pi$
$743$	367.560	−	64.8107i	0.494697	−	0.0872284i	0.415430	+	0.909625i	$0.363631\pi$
$744$		0			0
$745$	208.165	+	174.672i	0.279417	+	0.234459i
$746$	86.7808	−	50.1029i	0.116328	−	0.0671621i
$747$		0			0
$748$	9.10361	−	15.7679i	0.0121706	−	0.0210801i
$749$	−291.152	−	799.932i	−0.388720	−	1.06800i
$750$		0			0
$751$	−883.828	+	741.620i	−1.17687	+	0.987510i	−0.176874	+	0.984234i	$0.556598\pi$
$751$	−883.828	+	741.620i	−1.17687	+	0.987510i	−0.999995	+	0.00327622i	$0.998957\pi$
$752$	239.486	−	657.982i	0.318465	−	0.874976i
$753$		0			0
$754$	228.464	−	1295.68i	0.303003	−	1.71841i
$755$		−	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	$0.579204\pi$
$758$	−281.313	−	49.6031i	−0.371126	−	0.0654395i
$759$		0			0
$760$	−576.643	−	209.881i	−0.758740	−	0.276159i
$761$	742.809	+	885.246i	0.976096	+	1.16327i	0.986573	+	0.163321i	$0.0522207\pi$
$761$	742.809	+	885.246i	0.976096	+	1.16327i	−0.0104767	+	0.999945i	$0.503335\pi$
$762$		0			0
$763$	853.374	−	310.603i	1.11845	−	0.407081i
$764$	−65.5851	−	37.8656i	−0.0858444	−	0.0495623i
$765$		0			0
$766$	−110.333	−	191.102i	−0.144037	−	0.249480i
$767$	−43.6532	+	52.0238i	−0.0569142	+	0.0678277i
$768$		0			0
$769$	184.485	+	1046.27i	0.239903	+	1.36056i	0.832038	+	0.554718i	$0.187174\pi$
$769$	184.485	+	1046.27i	0.239903	+	1.36056i	−0.592135	+	0.805839i	$0.701715\pi$
$770$	541.531	−	95.4865i	0.703287	−	0.124009i
$771$		0			0
$772$	11.1426	+	9.34972i	0.0144334	+	0.0121110i
$773$	−808.848	+	466.989i	−1.04638	+	0.604125i	−0.921632	−	0.388064i	$-0.873144\pi$
$773$	−808.848	+	466.989i	−1.04638	+	0.604125i	−0.124743	+	0.992189i	$0.539811\pi$
$774$		0			0
$775$	−117.044	+	202.725i	−0.151024	+	0.261581i
$776$	−103.342	−	283.931i	−0.133173	−	0.365890i
$777$		0			0
$778$	−538.631	+	451.965i	−0.692327	+	0.580932i
$779$	150.367	−	413.131i	0.193026	−	0.530335i
$780$		0			0
$781$	76.1734	−	432.001i	0.0975331	−	0.553138i
$782$		−	267.735i		−	0.342372i
$783$		0			0
$784$	−450.363			−0.574443
$785$	222.773	+	39.2810i	0.283788	+	0.0500395i
$786$		0			0
$787$	−771.201	−	280.694i	−0.979925	−	0.356663i	−0.198114	−	0.980179i	$-0.563482\pi$
$787$	−771.201	−	280.694i	−0.979925	−	0.356663i	−0.781811	+	0.623516i	$0.785704\pi$
$788$	−33.9747	−	40.4895i	−0.0431151	−	0.0513826i
$789$		0			0
$790$	12.2912	−	4.47363i	0.0155585	−	0.00566283i
$791$	125.562	+	72.4931i	0.158738	+	0.0916473i
$792$		0			0
$793$	294.708	+	510.450i	0.371637	+	0.643694i
$794$	−919.166	+	1095.42i	−1.15764	+	1.37962i
$795$		0			0
$796$	−0.213171	−	1.20895i	−0.000267803	−	0.00151879i
$797$	33.7669	−	5.95402i	0.0423675	−	0.00747053i	−0.152424	−	0.988315i	$-0.548708\pi$
$797$	33.7669	−	5.95402i	0.0423675	−	0.00747053i	0.194792	+	0.980845i	$0.437597\pi$
$798$		0			0
$799$	−374.404	−	314.163i	−0.468591	−	0.393195i
$800$	−20.6028	+	11.8950i	−0.0257535	+	0.0148688i
$801$		0			0
$802$	−214.682	+	371.840i	−0.267683	+	0.463641i
$803$	−132.924	−	365.206i	−0.165534	−	0.454802i
$804$		0			0
$805$	−387.915	+	325.499i	−0.481882	+	0.404347i
$806$	398.648	−	1095.28i	0.494600	−	1.35890i
$807$		0			0
$808$	−121.725	+	690.335i	−0.150649	+	0.854374i
$809$			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	$0.638707\pi$
$812$	−86.3409	−	15.2242i	−0.106331	−	0.0187491i
$813$		0			0
$814$	860.317	+	313.130i	1.05690	+	0.384680i
$815$	−698.473	−	832.407i	−0.857022	−	1.02136i
$816$		0			0
$817$	−40.2461	+	14.6484i	−0.0492608	+	0.0179295i
$818$	748.021	+	431.870i	0.914451	+	0.527958i
$819$		0			0
$820$	12.9666	+	22.4588i	0.0158129	+	0.0273887i
$821$	871.211	−	1038.27i	1.06116	−	1.26464i	0.0981483	−	0.995172i	$-0.468708\pi$
$821$	871.211	−	1038.27i	1.06116	−	1.26464i	0.963010	−	0.269467i	$-0.0868475\pi$
$822$		0			0
$823$	−113.011	−	640.916i	−0.137316	−	0.778756i	−0.973219	−	0.229879i	$-0.926167\pi$
$823$	−113.011	−	640.916i	−0.137316	−	0.778756i	0.835903	−	0.548877i	$-0.184944\pi$
$824$	188.100	−	33.1671i	0.228277	−	0.0402514i
$825$		0			0
$826$	−55.3568	−	46.4498i	−0.0670179	−	0.0562347i
$827$	−1042.15	+	601.688i	−1.26016	+	0.727555i	−0.973106	−	0.230359i	$-0.926010\pi$
$827$	−1042.15	+	601.688i	−1.26016	+	0.727555i	−0.287056	+	0.957914i	$0.592677\pi$
$828$		0			0
$829$	753.210	−	1304.60i	0.908577	−	1.57370i	0.0925344	−	0.995709i	$-0.470503\pi$
$829$	753.210	−	1304.60i	0.908577	−	1.57370i	0.816043	−	0.577992i	$-0.196163\pi$
$830$	−324.331	−	891.093i	−0.390761	−	1.07361i
$831$		0			0
$832$	835.802	−	701.321i	1.00457	−	0.842934i
$833$	−107.516	+	295.398i	−0.129071	+	0.354619i
$834$		0			0
$835$	−6.35372	+	36.0338i	−0.00760925	+	0.0431542i
$836$		−	30.0376i		−	0.0359301i
$837$		0			0
$838$	−1119.86			−1.33635
$839$	58.5531	+	10.3245i	0.0697891	+	0.0123057i	0.208434	−	0.978036i	$-0.433163\pi$
$839$	58.5531	+	10.3245i	0.0697891	+	0.0123057i	−0.138645	+	0.990342i	$0.544275\pi$
$840$		0			0
$841$	854.523	+	311.021i	1.01608	+	0.369823i
$842$	419.029	+	499.379i	0.497659	+	0.593087i
$843$		0			0
$844$	5.10687	−	1.85875i	0.00605079	−	0.00220231i
$845$	−350.819	−	202.546i	−0.415171	−	0.239699i
$846$		0			0
$847$	−295.992	−	512.672i	−0.349459	−	0.605280i
$848$	−489.097	+	582.884i	−0.576766	+	0.687363i
$849$		0			0
$850$	−22.2806	−	126.359i	−0.0262124	−	0.148658i
$851$	−830.300	+	146.404i	−0.975675	+	0.172038i
$852$		0			0
$853$	−269.299	−	225.969i	−0.315708	−	0.264910i	0.471138	−	0.882059i	$-0.343843\pi$
$853$	−269.299	−	225.969i	−0.315708	−	0.264910i	−0.786846	+	0.617149i	$0.788288\pi$
$854$	−543.152	+	313.589i	−0.636009	+	0.367200i
$855$		0			0
$856$	−393.491	+	681.546i	−0.459685	+	0.796198i
$857$	−423.493	−	1163.54i	−0.494158	−	1.35769i	−0.896843	−	0.442348i	$-0.854145\pi$
$857$	−423.493	−	1163.54i	−0.494158	−	1.35769i	0.402686	−	0.915338i	$-0.368077\pi$
$858$		0			0
$859$	−203.687	+	170.914i	−0.237121	+	0.198968i	−0.753603	−	0.657330i	$-0.771686\pi$
$859$	−203.687	+	170.914i	−0.237121	+	0.198968i	0.516482	+	0.856298i	$0.327241\pi$
$860$	0.864058	−	2.37398i	0.00100472	−	0.00276044i
$861$		0			0
$862$	38.3396	−	217.435i	0.0444775	−	0.252245i
$863$			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
$866$	390.190	+	68.8010i	0.450566	+	0.0794469i
$867$		0			0
$868$	−72.9862	−	26.5648i	−0.0840855	−	0.0306046i
$869$	7.39469	+	8.81265i	0.00850943	+	0.0101411i
$870$		0			0
$871$	263.634	−	95.9549i	0.302680	−	0.110166i
$872$	−727.078	−	419.779i	−0.833805	−	0.481398i
$873$		0			0
$874$	−220.849	−	382.522i	−0.252688	−	0.437669i
$875$	−773.464	+	921.778i	−0.883959	+	1.05346i
$876$		0			0
$877$	−62.6808	−	355.481i	−0.0714719	−	0.405337i	−0.999464	−	0.0327374i	$-0.989578\pi$
$877$	−62.6808	−	355.481i	−0.0714719	−	0.405337i	0.927992	−	0.372600i	$-0.121534\pi$
$878$	771.618	−	136.057i	0.878837	−	0.154963i
$879$		0			0
$880$	−366.394	−	307.441i	−0.416357	−	0.349365i
$881$	782.766	−	451.930i	0.888497	−	0.512974i	0.0150464	−	0.999887i	$-0.495210\pi$
$881$	782.766	−	451.930i	0.888497	−	0.512974i	0.873451	+	0.486913i	$0.161877\pi$
$882$		0			0
$883$	462.202	−	800.558i	0.523445	−	0.906634i	−0.476182	−	0.879347i	$-0.657980\pi$
$883$	462.202	−	800.558i	0.523445	−	0.906634i	0.999628	−	0.0272872i	$-0.00868687\pi$
$884$	−13.6841	−	37.5968i	−0.0154798	−	0.0425303i
$885$		0			0
$886$	−983.336	+	825.117i	−1.10986	+	0.931283i
$887$	95.5543	−	262.533i	0.107728	−	0.295979i	−0.874102	−	0.485742i	$-0.838550\pi$
$887$	95.5543	−	262.533i	0.107728	−	0.295979i	0.981830	+	0.189763i	$0.0607718\pi$
$888$		0			0
$889$	−125.746	+	713.144i	−0.141447	+	0.802186i
$890$			401.412i			0.451025i
$891$		0			0
$892$	−44.3400			−0.0497086
$893$	−794.071	−	140.016i	−0.889218	−	0.156793i
$894$		0			0
$895$	−859.267	−	312.748i	−0.960075	−	0.349439i
$896$	660.158	+	786.746i	0.736784	+	0.878065i
$897$		0			0
$898$	−850.191	+	309.444i	−0.946760	+	0.344593i
$899$	1342.92	+	775.333i	1.49379	+	0.862440i
$900$		0			0
$901$	265.556	+	459.957i	0.294735	+	0.510496i
$902$	234.109	−	279.000i	0.259544	−	0.309312i
$903$		0			0
$904$	−23.2752	−	132.000i	−0.0257469	−	0.146018i
$905$	−373.646	+	65.8838i	−0.412868	+	0.0727998i
$906$		0			0
$907$	−452.756	−	379.908i	−0.499180	−	0.418862i	0.358123	−	0.933675i	$-0.383417\pi$
$907$	−452.756	−	379.908i	−0.499180	−	0.418862i	−0.857303	+	0.514813i	$0.827861\pi$
$908$	25.6206	−	14.7921i	0.0282166	−	0.0162908i
$909$		0			0
$910$	604.176	−	1046.46i	0.663930	−	1.14996i
$911$	−129.365	−	355.429i	−0.142004	−	0.390152i	0.848219	−	0.529645i	$-0.177675\pi$
$911$	−129.365	−	355.429i	−0.142004	−	0.390152i	−0.990223	+	0.139493i	$0.955453\pi$
$912$		0			0
$913$	638.903	−	536.103i	0.699784	−	0.587189i
$914$	−566.753	+	1557.14i	−0.620079	+	1.70365i
$915$		0			0
$916$	−5.36292	+	30.4146i	−0.00585472	+	0.0332037i
$917$		−	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	$0.484942\pi$
$920$	461.032	+	81.2924i	0.501122	+	0.0883613i
$921$		0			0
$922$	149.338	+	54.3547i	0.161972	+	0.0589531i
$923$	−619.615	−	738.428i	−0.671305	−	0.800031i
$924$		0			0
$925$	−379.682	+	138.193i	−0.410467	+	0.149398i
$926$	−1099.91	−	635.033i	−1.18781	−	0.685781i
$927$		0			0
$928$	78.7963	+	136.479i	0.0849098	+	0.147068i
$929$	−434.648	+	517.993i	−0.467866	+	0.557581i	−0.947445	−	0.319917i	$-0.896345\pi$
$929$	−434.648	+	517.993i	−0.467866	+	0.557581i	0.479579	+	0.877499i	$0.340789\pi$
$930$		0			0
$931$	90.0560	+	510.733i	0.0967304	+	0.548585i
$932$	−94.3635	+	16.6388i	−0.101248	+	0.0178528i
$933$		0			0
$934$	194.600	+	163.289i	0.208351	+	0.174827i
$935$	−289.124	+	166.926i	−0.309223	+	0.178530i
$936$		0			0
$937$	168.348	−	291.587i	0.179667	−	0.311192i	−0.762100	−	0.647460i	$-0.775831\pi$
$937$	168.348	−	291.587i	0.179667	−	0.311192i	0.941766	+	0.336268i	$0.109165\pi$
$938$	102.102	+	280.524i	0.108851	+	0.299066i
$939$		0			0
$940$	36.4347	−	30.5724i	0.0387603	−	0.0325238i
$941$	80.6690	−	221.636i	0.0857269	−	0.235533i	−0.889420	−	0.457090i	$-0.848892\pi$
$941$	80.6690	−	221.636i	0.0857269	−	0.235533i	0.975147	+	0.221557i	$0.0711140\pi$
$942$		0			0
$943$	−58.2413	+	330.303i	−0.0617617	+	0.350268i
$944$			62.8549i			0.0665836i
$945$		0			0
$946$	−35.4802			−0.0375055
$947$	629.848	+	111.059i	0.665098	+	0.117275i	0.495998	−	0.868324i	$-0.334802\pi$
$947$	629.848	+	111.059i	0.665098	+	0.117275i	0.169101	+	0.985599i	$0.445914\pi$
$948$		0			0
$949$	−802.526	−	292.095i	−0.845654	−	0.307793i
$950$	−136.064	−	162.155i	−0.143226	−	0.170690i
$951$		0			0
$952$	718.819	−	261.629i	0.755062	−	0.274820i
$953$	742.976	+	428.957i	0.779618	+	0.450112i	0.836295	−	0.548280i	$-0.184717\pi$
$953$	742.976	+	428.957i	0.779618	+	0.450112i	−0.0566772	+	0.998393i	$0.518051\pi$
$954$		0			0
$955$	694.310	+	1202.58i	0.727027	+	1.25925i
$956$	29.1430	−	34.7312i	0.0304843	−	0.0363297i
$957$		0			0
$958$	53.1191	+	301.253i	0.0554479	+	0.314461i
$959$	1645.81	−	290.200i	1.71617	−	0.302607i
$960$		0			0
$961$	316.186	+	265.312i	0.329018	+	0.276079i
$962$	1742.31	−	1005.92i	1.81113	−	1.04566i
$963$		0			0
$964$	40.8728	−	70.7938i	0.0423992	−	0.0734376i
$965$	−91.2204	−	250.626i	−0.0945289	−	0.259716i
$966$		0			0
$967$	438.590	−	368.021i	0.453557	−	0.380580i	−0.387197	−	0.921997i	$-0.626557\pi$
$967$	438.590	−	368.021i	0.453557	−	0.380580i	0.840754	+	0.541417i	$0.182112\pi$
$968$	−187.179	+	514.271i	−0.193367	+	0.531272i
$969$		0			0
$970$	−53.5434	+	303.660i	−0.0551994	+	0.313051i
$971$			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
$974$	1334.05	+	235.229i	1.36966	+	0.241508i
$975$		0			0
$976$	512.624	+	186.580i	0.525229	+	0.191168i
$977$	993.508	+	1184.02i	1.01690	+	1.21189i	0.977122	+	0.212681i	$0.0682196\pi$
$977$	993.508	+	1184.02i	1.01690	+	1.21189i	0.0397749	+	0.999209i	$0.487336\pi$
$978$		0			0
$979$	−331.757	+	120.750i	−0.338874	+	0.123340i
$980$	−26.4927	−	15.2956i	−0.0270334	−	0.0156077i
$981$		0			0
$982$	40.9588	+	70.9427i	0.0417095	+	0.0722430i
$983$	−675.101	+	804.554i	−0.686776	+	0.818468i	−0.990962	−	0.134145i	$-0.957171\pi$
$983$	−675.101	+	804.554i	−0.686776	+	0.818468i	0.304185	+	0.952613i	$0.401616\pi$
$984$		0			0
$985$	168.294	+	954.441i	0.170856	+	0.968975i
$986$	−837.044	+	147.593i	−0.848929	+	0.149689i
$987$		0			0
$988$	−50.5639	−	42.4281i	−0.0511780	−	0.0429435i
$989$	28.2961	−	16.3368i	0.0286109	−	0.0165185i
$990$		0			0
$991$	−255.730	+	442.938i	−0.258053	+	0.446961i	−0.965720	−	0.259585i	$-0.916414\pi$
$991$	−255.730	+	442.938i	−0.258053	+	0.446961i	0.707667	+	0.706546i	$0.249748\pi$
$992$	47.7504	+	131.193i	0.0481355	+	0.132251i
$993$		0			0
$994$	785.736	−	659.311i	0.790479	−	0.663291i
$995$	−7.69872	+	21.1521i	−0.00773741	+	0.0212584i
$996$		0			0
$997$	56.7335	−	321.752i	0.0569042	−	0.322720i	−0.943046	−	0.332661i	$-0.892053\pi$
$997$	56.7335	−	321.752i	0.0569042	−	0.322720i	0.999951	+	0.00994151i	$0.00316453\pi$
$998$			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.b.26.2		30
3.2	odd	2		243.3.f.c.26.4		30
9.2	odd	6		243.3.f.d.188.2		30
9.4	even	3		81.3.f.a.35.4		30
9.5	odd	6		27.3.f.a.11.2	yes	30
9.7	even	3		243.3.f.a.188.4		30
27.4	even	9		27.3.f.a.5.2	✓	30
27.5	odd	18		243.3.f.a.53.4		30
27.11	odd	18		729.3.b.a.728.22		30
27.13	even	9		243.3.f.c.215.4		30
27.14	odd	18	inner	243.3.f.b.215.2		30
27.16	even	9		729.3.b.a.728.9		30
27.22	even	9		243.3.f.d.53.2		30
27.23	odd	18		81.3.f.a.44.4		30
36.23	even	6		432.3.bc.a.65.1		30
108.31	odd	18		432.3.bc.a.113.1		30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.3.f.a.5.2	✓	30	27.4	even	9
27.3.f.a.11.2	yes	30	9.5	odd	6
81.3.f.a.35.4		30	9.4	even	3
81.3.f.a.44.4		30	27.23	odd	18
243.3.f.a.53.4		30	27.5	odd	18
243.3.f.a.188.4		30	9.7	even	3
243.3.f.b.26.2		30	1.1	even	1	trivial
243.3.f.b.215.2		30	27.14	odd	18	inner
243.3.f.c.26.4		30	3.2	odd	2
243.3.f.c.215.4		30	27.13	even	9
243.3.f.d.53.2		30	27.22	even	9
243.3.f.d.188.2		30	9.2	odd	6
432.3.bc.a.65.1		30	36.23	even	6
432.3.bc.a.113.1		30	108.31	odd	18
729.3.b.a.728.9		30	27.16	even	9
729.3.b.a.728.22		30	27.11	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)

\(f(q)\)	\(=\)	\(q+(-1.91070 - 0.336907i) q^{2} +(-0.221521 - 0.0806271i) q^{4} +(2.77847 + 3.31125i) q^{5} +(-8.35329 + 3.04035i) q^{7} +(7.11704 + 4.10903i) q^{8} +(-4.19322 - 7.26288i) q^{10} +(4.74121 - 5.65036i) q^{11} +(-2.81458 - 15.9623i) q^{13} +(16.9849 - 2.99490i) q^{14} +(-11.4918 - 9.64276i) q^{16} +(-9.06825 + 5.23555i) q^{17} +(-8.63742 + 14.9604i) q^{19} +(-0.348513 - 0.957532i) q^{20} +(-10.9627 + 9.19876i) q^{22} +(4.50738 - 12.3839i) q^{23} +(1.09671 - 6.21978i) q^{25} +31.4473i q^{26} +2.09556 q^{28} +(-41.2018 - 7.26498i) q^{29} +(-34.8289 - 12.6767i) q^{31} +(-2.42125 - 2.88553i) q^{32} +(19.0905 - 6.94839i) q^{34} +(-33.2767 - 19.2123i) q^{35} +(-31.9875 - 55.4041i) q^{37} +(21.5437 - 25.6748i) q^{38} +(6.16847 + 34.9831i) q^{40} +(-25.0634 + 4.41935i) q^{41} +(1.89923 + 1.59364i) q^{43} +(-1.50585 + 0.869403i) q^{44} +(-12.7845 + 22.1433i) q^{46} +(15.9642 + 43.8612i) q^{47} +(22.9976 - 19.2973i) q^{49} +(-4.19097 + 11.5146i) q^{50} +(-0.663503 + 3.76291i) q^{52} -50.7217i q^{53} +31.8831 q^{55} +(-71.9436 - 12.6856i) q^{56} +(76.2764 + 27.7623i) q^{58} +(-2.69322 - 3.20966i) q^{59} +(-34.1715 + 12.4374i) q^{61} +(62.2766 + 35.9554i) q^{62} +(33.6571 + 58.2957i) q^{64} +(45.0349 - 53.6705i) q^{65} +(3.00568 + 17.0460i) q^{67} +(2.43093 - 0.428639i) q^{68} +(57.1089 + 47.9201i) q^{70} +(51.5041 - 29.7359i) q^{71} +(26.3451 - 45.6310i) q^{73} +(42.4524 + 116.637i) q^{74} +(3.11959 - 2.61764i) q^{76} +(-22.4257 + 61.6140i) q^{77} +(-0.270833 + 1.53597i) q^{79} -64.8443i q^{80} +49.3774 q^{82} +(111.355 + 19.6349i) q^{83} +(-42.5321 - 15.4804i) q^{85} +(-3.09194 - 3.68483i) q^{86} +(56.9609 - 20.7321i) q^{88} +(-41.4518 - 23.9322i) q^{89} +(72.0419 + 124.780i) q^{91} +(-1.99696 + 2.37988i) q^{92} +(-15.7255 - 89.1837i) q^{94} +(-73.5366 + 12.9665i) q^{95} +(-28.1651 - 23.6334i) q^{97} +(-50.4428 + 29.1232i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 3 q^{2} + 3 q^{4} + 6 q^{5} + 3 q^{7} + 9 q^{8} - 3 q^{10} + 51 q^{11} + 3 q^{13} - 129 q^{14} - 9 q^{16} + 9 q^{17} - 3 q^{19} + 30 q^{20} - 33 q^{22} + 168 q^{23} - 6 q^{25} - 12 q^{28} - 246 q^{29}+ \cdots - 882 q^{98}+O(q^{100}) \) 30 * q - 3 * q^2 + 3 * q^4 + 6 * q^5 + 3 * q^7 + 9 * q^8 - 3 * q^10 + 51 * q^11 + 3 * q^13 - 129 * q^14 - 9 * q^16 + 9 * q^17 - 3 * q^19 + 30 * q^20 - 33 * q^22 + 168 * q^23 - 6 * q^25 - 12 * q^28 - 246 * q^29 + 48 * q^31 - 117 * q^32 + 99 * q^34 + 252 * q^35 - 3 * q^37 + 237 * q^38 + 201 * q^40 - 129 * q^41 + 183 * q^43 - 639 * q^44 - 3 * q^46 + 348 * q^47 + 147 * q^49 + 471 * q^50 + 45 * q^52 - 12 * q^55 - 570 * q^56 - 267 * q^58 - 426 * q^59 - 285 * q^61 + 900 * q^62 - 51 * q^64 + 213 * q^65 - 366 * q^67 - 378 * q^68 - 483 * q^70 - 315 * q^71 - 66 * q^73 - 159 * q^74 - 201 * q^76 + 654 * q^77 - 15 * q^79 - 12 * q^82 - 624 * q^83 + 18 * q^85 + 411 * q^86 + 51 * q^88 - 72 * q^89 + 96 * q^91 + 561 * q^92 - 96 * q^94 + 75 * q^95 - 114 * q^97 - 882 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more