LMFDB - Embedded newform 729.2.e.t.325.1

Error: no document with id 221756686 found in table mf_hecke_traces.

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [729,2,Mod(82,729)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("729.82"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(729, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([8])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 729 = 3^{6} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	729.e (of order $9$, degree $6$, not minimal)

Newform invariants

comment:select newform

sage:traces = [12,3,0,-3,6,0,6,6,0,-6,-15,0,-3,-21,0,9,-9,0,-12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(19)] == traces)

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

Self dual:	no
Analytic conductor:	$5.82109430735$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 18x^{10} + 105x^{8} + 266x^{6} + 306x^{4} + 132x^{2} + 1 $ x^12 + 18x^10 + 105x^8 + 266x^6 + 306x^4 + 132*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			325.1
Root			$-3.10658i$ of defining polynomial
Character	$\chi$	$=$	729.325
Dual form			729.2.e.t.406.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.62787 + 1.36594i) q^{2} +(0.436855 - 2.47753i) q^{4} +(1.94605 - 0.708303i) q^{5} +(0.841963 + 4.77501i) q^{7} +(0.547989 + 0.949144i) q^{8} +(-2.20040 + 3.81121i) q^{10} +(-3.89924 - 1.41921i) q^{11} +(-0.931522 - 0.781640i) q^{13} +(-7.89299 - 6.62301i) q^{14} +(2.53953 + 0.924313i) q^{16} +(-1.18182 + 2.04697i) q^{17} +(0.919003 + 1.59176i) q^{19} +(-0.904700 - 5.13081i) q^{20} +(8.28601 - 3.01586i) q^{22} +(-0.747307 + 4.23819i) q^{23} +(-0.544815 + 0.457154i) q^{25} +2.58407 q^{26} +12.1980 q^{28} +(2.28421 - 1.91668i) q^{29} +(0.255886 - 1.45120i) q^{31} +(-7.45634 + 2.71388i) q^{32} +(-0.872200 - 4.94649i) q^{34} +(5.02066 + 8.69603i) q^{35} +(-4.48554 + 7.76918i) q^{37} +(-3.67027 - 1.33587i) q^{38} +(1.73869 + 1.45894i) q^{40} +(1.73166 + 1.45304i) q^{41} +(5.15408 + 1.87593i) q^{43} +(-5.21953 + 9.04050i) q^{44} +(-4.57260 - 7.91998i) q^{46} +(1.24734 + 7.07400i) q^{47} +(-15.5140 + 5.64663i) q^{49} +(0.262440 - 1.48837i) q^{50} +(-2.34347 + 1.96641i) q^{52} -6.32803 q^{53} -8.59334 q^{55} +(-4.07079 + 3.41580i) q^{56} +(-1.10031 + 6.24019i) q^{58} +(-0.246441 + 0.0896971i) q^{59} +(-0.773708 - 4.38792i) q^{61} +(1.56571 + 2.71188i) q^{62} +(5.72840 - 9.92188i) q^{64} +(-2.36642 - 0.861308i) q^{65} +(3.16461 + 2.65542i) q^{67} +(4.55514 + 3.82222i) q^{68} +(-20.0512 - 7.29805i) q^{70} +(-1.54276 + 2.67213i) q^{71} +(-6.38003 - 11.0505i) q^{73} +(-3.31040 - 18.7742i) q^{74} +(4.34510 - 1.58149i) q^{76} +(3.49372 - 19.8139i) q^{77} +(3.48735 - 2.92623i) q^{79} +5.59674 q^{80} -4.80368 q^{82} +(-6.47542 + 5.43352i) q^{83} +(-0.850000 + 4.82059i) q^{85} +(-10.9526 + 3.98641i) q^{86} +(-0.789708 - 4.47866i) q^{88} +(-8.48158 - 14.6905i) q^{89} +(2.94803 - 5.10614i) q^{91} +(10.1738 + 3.70295i) q^{92} +(-11.6932 - 9.81174i) q^{94} +(2.91587 + 2.44671i) q^{95} +(4.80161 + 1.74764i) q^{97} +(17.5417 - 30.3831i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 3 q^{2} - 3 q^{4} + 6 q^{5} + 6 q^{7} + 6 q^{8} - 6 q^{10} - 15 q^{11} - 3 q^{13} - 21 q^{14} + 9 q^{16} - 9 q^{17} - 12 q^{19} - 3 q^{20} + 33 q^{22} + 15 q^{23} - 12 q^{25} - 48 q^{26} + 6 q^{28}+ \cdots + 18 q^{98}+O(q^{100}) $ 12 * q + 3 * q^2 - 3 * q^4 + 6 * q^5 + 6 * q^7 + 6 * q^8 - 6 * q^10 - 15 * q^11 - 3 * q^13 - 21 * q^14 + 9 * q^16 - 9 * q^17 - 12 * q^19 - 3 * q^20 + 33 * q^22 + 15 * q^23 - 12 * q^25 - 48 * q^26 + 6 * q^28 - 6 * q^29 - 12 * q^31 - 27 * q^32 + 27 * q^34 + 30 * q^35 - 3 * q^37 - 39 * q^38 + 24 * q^40 - 39 * q^41 + 24 * q^43 - 33 * q^44 + 3 * q^46 - 42 * q^47 - 30 * q^49 - 15 * q^50 - 45 * q^52 + 18 * q^53 + 30 * q^55 + 12 * q^56 - 30 * q^58 + 15 * q^59 - 3 * q^61 - 30 * q^62 - 6 * q^64 - 6 * q^65 - 3 * q^67 + 36 * q^68 - 75 * q^70 - 12 * q^73 + 60 * q^74 + 30 * q^76 + 33 * q^77 + 33 * q^79 + 42 * q^80 - 42 * q^82 - 33 * q^83 - 18 * q^85 - 30 * q^86 - 42 * q^88 - 9 * q^89 - 18 * q^91 + 33 * q^92 - 66 * q^94 + 12 * q^95 + 15 * q^97 + 18 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/729\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{7}{9}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.62787	+	1.36594i	−1.15108	+	0.965867i	−0.999744	−	0.0226162i	$-0.992800\pi$
$2$	−1.62787	+	1.36594i	−1.15108	+	0.965867i	−0.151331	+	0.988483i	$0.548356\pi$
$3$		0			0
$3$		0			0
$4$	0.436855	−	2.47753i	0.218427	−	1.23876i
$5$	1.94605	−	0.708303i	0.870299	−	0.316763i	0.132011	−	0.991248i	$-0.457857\pi$
$5$	1.94605	−	0.708303i	0.870299	−	0.316763i	0.738288	+	0.674485i	$0.235634\pi$
$6$		0			0
$7$	0.841963	+	4.77501i	0.318232	+	1.80478i	0.553495	+	0.832853i	$0.313294\pi$
$7$	0.841963	+	4.77501i	0.318232	+	1.80478i	−0.235263	+	0.971932i	$0.575595\pi$
$8$	0.547989	+	0.949144i	0.193743	+	0.335573i
$9$		0			0
$10$	−2.20040	+	3.81121i	−0.695829	+	1.20521i
$11$	−3.89924	−	1.41921i	−1.17567	−	0.427908i	−0.320997	−	0.947080i	$-0.604018\pi$
$11$	−3.89924	−	1.41921i	−1.17567	−	0.427908i	−0.854669	+	0.519173i	$0.826240\pi$
$12$		0			0
$13$	−0.931522	−	0.781640i	−0.258358	−	0.216788i	0.504404	−	0.863468i	$-0.331712\pi$
$13$	−0.931522	−	0.781640i	−0.258358	−	0.216788i	−0.762761	+	0.646680i	$0.776157\pi$
$14$	−7.89299	−	6.62301i	−2.10949	−	1.77007i
$15$		0			0
$16$	2.53953	+	0.924313i	0.634882	+	0.231078i
$17$	−1.18182	+	2.04697i	−0.286633	+	0.496463i	−0.973004	−	0.230789i	$-0.925869\pi$
$17$	−1.18182	+	2.04697i	−0.286633	+	0.496463i	0.686371	+	0.727252i	$0.259203\pi$
$18$		0			0
$19$	0.919003	+	1.59176i	0.210834	+	0.365175i	0.951976	−	0.306174i	$-0.0990488\pi$
$19$	0.919003	+	1.59176i	0.210834	+	0.365175i	−0.741142	+	0.671348i	$0.765715\pi$
$20$	−0.904700	−	5.13081i	−0.202297	−	1.14728i
$21$		0			0
$22$	8.28601	−	3.01586i	1.76658	−	0.642983i
$23$	−0.747307	+	4.23819i	−0.155824	+	0.883723i	0.802204	+	0.597050i	$0.203661\pi$
$23$	−0.747307	+	4.23819i	−0.155824	+	0.883723i	−0.958028	+	0.286673i	$0.907451\pi$
$24$		0			0
$25$	−0.544815	+	0.457154i	−0.108963	+	0.0914309i
$26$	2.58407			0.506777
$27$		0			0
$28$	12.1980			2.30521
$29$	2.28421	−	1.91668i	0.424167	−	0.355918i	−0.405579	−	0.914060i	$-0.632930\pi$
$29$	2.28421	−	1.91668i	0.424167	−	0.355918i	0.829745	+	0.558142i	$0.188486\pi$
$30$		0			0
$31$	0.255886	−	1.45120i	0.0459584	−	0.260643i	−0.953168	−	0.302443i	$-0.902198\pi$
$31$	0.255886	−	1.45120i	0.0459584	−	0.260643i	0.999126	+	0.0417995i	$0.0133091\pi$
$32$	−7.45634	+	2.71388i	−1.31811	+	0.479752i
$33$		0			0
$34$	−0.872200	−	4.94649i	−0.149581	−	0.848316i
$35$	5.02066	+	8.69603i	0.848646	+	1.46990i
$36$		0			0
$37$	−4.48554	+	7.76918i	−0.737418	+	1.27725i	0.216236	+	0.976341i	$0.430622\pi$
$37$	−4.48554	+	7.76918i	−0.737418	+	1.27725i	−0.953654	+	0.300905i	$0.902711\pi$
$38$	−3.67027	−	1.33587i	−0.595396	−	0.216706i
$39$		0			0
$40$	1.73869	+	1.45894i	0.274912	+	0.230678i
$41$	1.73166	+	1.45304i	0.270440	+	0.226926i	0.767914	−	0.640553i	$-0.221295\pi$
$41$	1.73166	+	1.45304i	0.270440	+	0.226926i	−0.497474	+	0.867479i	$0.665739\pi$
$42$		0			0
$43$	5.15408	+	1.87593i	0.785990	+	0.286077i	0.703668	−	0.710529i	$-0.251544\pi$
$43$	5.15408	+	1.87593i	0.785990	+	0.286077i	0.0823218	+	0.996606i	$0.473766\pi$
$44$	−5.21953	+	9.04050i	−0.786874	+	1.36291i
$45$		0			0
$46$	−4.57260	−	7.91998i	−0.674194	−	1.16774i
$47$	1.24734	+	7.07400i	0.181943	+	1.03185i	0.929821	+	0.368013i	$0.119962\pi$
$47$	1.24734	+	7.07400i	0.181943	+	1.03185i	−0.747878	+	0.663836i	$0.768927\pi$
$48$		0			0
$49$	−15.5140	+	5.64663i	−2.21628	+	0.806661i
$50$	0.262440	−	1.48837i	0.0371147	−	0.210488i
$51$		0			0
$52$	−2.34347	+	1.96641i	−0.324981	+	0.272692i
$53$	−6.32803			−0.869222			−0.434611	−	0.900618i	$-0.643114\pi$
$53$	−6.32803			−0.869222			−0.434611	+	0.900618i	$0.643114\pi$
$54$		0			0
$55$	−8.59334			−1.15873
$56$	−4.07079	+	3.41580i	−0.543982	+	0.456455i
$57$		0			0
$58$	−1.10031	+	6.24019i	−0.144478	+	0.819377i
$59$	−0.246441	+	0.0896971i	−0.0320839	+	0.0116776i	−0.358012	−	0.933717i	$-0.616545\pi$
$59$	−0.246441	+	0.0896971i	−0.0320839	+	0.0116776i	0.325928	+	0.945394i	$0.394323\pi$
$60$		0			0
$61$	−0.773708	−	4.38792i	−0.0990631	−	0.561815i	−0.993426	−	0.114473i	$-0.963482\pi$
$61$	−0.773708	−	4.38792i	−0.0990631	−	0.561815i	0.894363	−	0.447342i	$-0.147629\pi$
$62$	1.56571	+	2.71188i	0.198845	+	0.344410i
$63$		0			0
$64$	5.72840	−	9.92188i	0.716050	−	1.24024i
$65$	−2.36642	−	0.861308i	−0.293519	−	0.106832i
$66$		0			0
$67$	3.16461	+	2.65542i	0.386619	+	0.324411i	0.815294	−	0.579047i	$-0.196575\pi$
$67$	3.16461	+	2.65542i	0.386619	+	0.324411i	−0.428676	+	0.903458i	$0.641020\pi$
$68$	4.55514	+	3.82222i	0.552392	+	0.463512i
$69$		0			0
$70$	−20.0512	−	7.29805i	−2.39658	−	0.872284i
$71$	−1.54276	+	2.67213i	−0.183091	+	0.317124i	−0.942932	−	0.332986i	$-0.891944\pi$
$71$	−1.54276	+	2.67213i	−0.183091	+	0.317124i	0.759840	+	0.650110i	$0.225277\pi$
$72$		0			0
$73$	−6.38003	−	11.0505i	−0.746726	−	1.29337i	−0.949384	−	0.314118i	$-0.898291\pi$
$73$	−6.38003	−	11.0505i	−0.746726	−	1.29337i	0.202658	−	0.979250i	$-0.435042\pi$
$74$	−3.31040	−	18.7742i	−0.384826	−	2.18245i
$75$		0			0
$76$	4.34510	−	1.58149i	0.498417	−	0.181409i
$77$	3.49372	−	19.8139i	0.398146	−	2.25800i
$78$		0			0
$79$	3.48735	−	2.92623i	0.392357	−	0.329227i	−0.425174	−	0.905112i	$-0.639787\pi$
$79$	3.48735	−	2.92623i	0.392357	−	0.329227i	0.817531	+	0.575885i	$0.195342\pi$
$80$	5.59674			0.625734
$81$		0			0
$82$	−4.80368			−0.530478
$83$	−6.47542	+	5.43352i	−0.710769	+	0.596406i	−0.924815	−	0.380417i	$-0.875780\pi$
$83$	−6.47542	+	5.43352i	−0.710769	+	0.596406i	0.214045	+	0.976824i	$0.431336\pi$
$84$		0			0
$85$	−0.850000	+	4.82059i	−0.0921954	+	0.522866i
$86$	−10.9526	+	3.98641i	−1.18105	+	0.429866i
$87$		0			0
$88$	−0.789708	−	4.47866i	−0.0841831	−	0.477426i
$89$	−8.48158	−	14.6905i	−0.899046	−	1.55719i	−0.828716	−	0.559670i	$-0.810928\pi$
$89$	−8.48158	−	14.6905i	−0.899046	−	1.55719i	−0.0703304	−	0.997524i	$-0.522405\pi$
$90$		0			0
$91$	2.94803	−	5.10614i	0.309038	−	0.535269i
$92$	10.1738	+	3.70295i	1.06069	+	0.386059i
$93$		0			0
$94$	−11.6932	−	9.81174i	−1.20606	−	1.01200i
$95$	2.91587	+	2.44671i	0.299162	+	0.251027i
$96$		0			0
$97$	4.80161	+	1.74764i	0.487530	+	0.177446i	0.574077	−	0.818801i	$-0.305361\pi$
$97$	4.80161	+	1.74764i	0.487530	+	0.177446i	−0.0865469	+	0.996248i	$0.527583\pi$
$98$	17.5417	−	30.3831i	1.77198	−	3.06916i
$99$		0			0
$100$	0.894607	+	1.54951i	0.0894607	+	0.154951i
$101$	3.22636	+	18.2976i	0.321035	+	1.82068i	0.536186	+	0.844100i	$0.319864\pi$
$101$	3.22636	+	18.2976i	0.321035	+	1.82068i	−0.215151	+	0.976581i	$0.569025\pi$
$102$		0			0
$103$	−8.46266	+	3.08015i	−0.833850	+	0.303497i	−0.723438	−	0.690389i	$-0.757439\pi$
$103$	−8.46266	+	3.08015i	−0.833850	+	0.303497i	−0.110412	+	0.993886i	$0.535217\pi$
$104$	0.231425	−	1.31248i	0.0226931	−	0.128699i
$105$		0			0
$106$	10.3012	−	8.64372i	1.00054	−	0.839552i
$107$	7.42680			0.717976			0.358988	−	0.933342i	$-0.383122\pi$
$107$	7.42680			0.717976			0.358988	+	0.933342i	$0.383122\pi$
$108$		0			0
$109$	−5.62396			−0.538678			−0.269339	−	0.963045i	$-0.586805\pi$
$109$	−5.62396			−0.538678			−0.269339	+	0.963045i	$0.586805\pi$
$110$	13.9888	−	11.7380i	1.33378	−	1.11918i
$111$		0			0
$112$	−2.27541	+	12.9045i	−0.215006	+	1.21936i
$113$	2.25777	−	0.821761i	0.212393	−	0.0773048i	−0.233632	−	0.972325i	$-0.575061\pi$
$113$	2.25777	−	0.821761i	0.212393	−	0.0773048i	0.446026	+	0.895020i	$0.352839\pi$
$114$		0			0
$115$	1.54763	+	8.77703i	0.144317	+	0.818463i
$116$	−3.75075	−	6.49649i	−0.348249	−	0.603184i
$117$		0			0
$118$	0.278652	−	0.482639i	0.0256520	−	0.0444305i
$119$	−10.7694	−	3.91972i	−0.987225	−	0.359321i
$120$		0			0
$121$	4.76346	+	3.99702i	0.433042	+	0.363365i
$122$	7.25313	+	6.08610i	0.656668	+	0.551010i
$123$		0			0
$124$	−3.48360	−	1.26793i	−0.312837	−	0.113863i
$125$	−5.91378	+	10.2430i	−0.528945	+	0.916159i
$126$		0			0
$127$	4.61735	+	7.99748i	0.409723	+	0.709662i	0.994859	−	0.101274i	$-0.0322919\pi$
$127$	4.61735	+	7.99748i	0.409723	+	0.709662i	−0.585135	+	0.810936i	$0.698959\pi$
$128$	1.47189	+	8.34752i	0.130098	+	0.737824i
$129$		0			0
$130$	5.02872	−	1.83030i	0.441048	−	0.160528i
$131$	−2.66359	+	15.1060i	−0.232719	+	1.31981i	0.614646	+	0.788803i	$0.289299\pi$
$131$	−2.66359	+	15.1060i	−0.232719	+	1.31981i	−0.847365	+	0.531011i	$0.821812\pi$
$132$		0			0
$133$	−6.82691	+	5.72845i	−0.591968	+	0.496720i
$134$	−8.77871			−0.758365
$135$		0			0
$136$	−2.59049			−0.222133
$137$	−2.79144	+	2.34230i	−0.238489	+	0.200116i	−0.754197	−	0.656649i	$-0.771974\pi$
$137$	−2.79144	+	2.34230i	−0.238489	+	0.200116i	0.515708	+	0.856765i	$0.327529\pi$
$138$		0			0
$139$	2.30527	−	13.0739i	0.195531	−	1.10891i	−0.716130	−	0.697967i	$-0.754088\pi$
$139$	2.30527	−	13.0739i	0.195531	−	1.10891i	0.911661	−	0.410943i	$-0.134801\pi$
$140$	23.7380	−	8.63991i	2.00622	−	0.730206i
$141$		0			0
$142$	−1.13858	−	6.45719i	−0.0955472	−	0.541875i
$143$	2.52292	+	4.36983i	0.210977	+	0.365423i
$144$		0			0
$145$	3.08759	−	5.34786i	0.256410	−	0.444115i
$146$	25.4802	+	9.27405i	2.10876	+	0.767526i
$147$		0			0
$148$	17.2888	+	14.5071i	1.42113	+	1.19247i
$149$	6.82621	+	5.72787i	0.559225	+	0.469245i	0.878051	−	0.478568i	$-0.158844\pi$
$149$	6.82621	+	5.72787i	0.559225	+	0.469245i	−0.318826	+	0.947813i	$0.603288\pi$
$150$		0			0
$151$	0.669440	+	0.243656i	0.0544783	+	0.0198285i	0.369116	−	0.929384i	$-0.379661\pi$
$151$	0.669440	+	0.243656i	0.0544783	+	0.0198285i	−0.314637	+	0.949212i	$0.601883\pi$
$152$	−1.00721	+	1.74453i	−0.0816953	+	0.141500i
$153$		0			0
$154$	21.3773	+	37.0265i	1.72263	+	2.98368i
$155$	−0.529924	−	3.00535i	−0.0425645	−	0.241395i
$156$		0			0
$157$	12.9847	−	4.72605i	1.03629	−	0.377180i	0.232820	−	0.972520i	$-0.425205\pi$
$157$	12.9847	−	4.72605i	1.03629	−	0.377180i	0.803474	+	0.595340i	$0.202983\pi$
$158$	−1.67987	+	9.52702i	−0.133643	+	0.757929i
$159$		0			0
$160$	−12.5881	+	10.5627i	−0.995179	+	0.835054i
$161$	−20.8666			−1.64452
$162$		0			0
$163$	−1.19321			−0.0934597			−0.0467298	−	0.998908i	$-0.514880\pi$
$163$	−1.19321			−0.0934597			−0.0467298	+	0.998908i	$0.514880\pi$
$164$	4.35642	−	3.65547i	0.340180	−	0.285445i
$165$		0			0
$166$	3.11924	−	17.6901i	0.242100	−	1.37302i
$167$	22.4928	−	8.18670i	1.74054	−	0.633506i	0.741255	−	0.671223i	$-0.234231\pi$
$167$	22.4928	−	8.18670i	1.74054	−	0.633506i	0.999288	+	0.0377169i	$0.0120085\pi$
$168$		0			0
$169$	−2.00065	−	11.3463i	−0.153896	−	0.872790i
$170$	−5.20096	−	9.00832i	−0.398895	−	0.690907i
$171$		0			0
$172$	6.89926	−	11.9499i	0.526063	−	0.911169i
$173$	8.58879	+	3.12607i	0.652994	+	0.237670i	0.647209	−	0.762313i	$-0.275936\pi$
$173$	8.58879	+	3.12607i	0.652994	+	0.237670i	0.00578525	+	0.999983i	$0.498158\pi$
$174$		0			0
$175$	−2.64163	−	2.21659i	−0.199689	−	0.167559i
$176$	−8.59045	−	7.20824i	−0.647530	−	0.543342i
$177$		0			0
$178$	33.8733	+	12.3289i	2.53891	+	0.924088i
$179$	−5.30038	+	9.18052i	−0.396169	+	0.686184i	−0.993250	−	0.115997i	$-0.962994\pi$
$179$	−5.30038	+	9.18052i	−0.396169	+	0.686184i	0.597081	+	0.802181i	$0.296327\pi$
$180$		0			0
$181$	0.731460	+	1.26693i	0.0543690	+	0.0941699i	0.891929	−	0.452176i	$-0.149352\pi$
$181$	0.731460	+	1.26693i	0.0543690	+	0.0941699i	−0.837560	+	0.546345i	$0.816019\pi$
$182$	2.17569	+	12.3389i	0.161273	+	0.914624i
$183$		0			0
$184$	−4.43217	+	1.61318i	−0.326744	+	0.118925i
$185$	−3.22614	+	18.2963i	−0.237190	+	1.34517i
$186$		0			0
$187$	7.51328	−	6.30439i	0.549425	−	0.461023i
$188$	18.0709			1.31796
$189$		0			0
$190$	−8.08871			−0.586817
$191$	9.51601	−	7.98488i	0.688555	−	0.577766i	−0.229937	−	0.973205i	$-0.573852\pi$
$191$	9.51601	−	7.98488i	0.688555	−	0.577766i	0.918492	+	0.395439i	$0.129408\pi$
$192$		0			0
$193$	3.60725	−	20.4577i	0.259655	−	1.47258i	−0.524179	−	0.851608i	$-0.675628\pi$
$193$	3.60725	−	20.4577i	0.259655	−	1.47258i	0.783834	−	0.620970i	$-0.213261\pi$
$194$	−10.2036	+	3.71380i	−0.732574	+	0.266635i
$195$		0			0
$196$	7.21231	+	40.9031i	0.515165	+	2.92165i
$197$	7.09433	+	12.2877i	0.505450	+	0.875465i	0.999980	+	0.00630469i	$0.00200686\pi$
$197$	7.09433	+	12.2877i	0.505450	+	0.875465i	−0.494530	+	0.869161i	$0.664660\pi$
$198$		0			0
$199$	−10.1643	+	17.6051i	−0.720529	+	1.24799i	0.240259	+	0.970709i	$0.422768\pi$
$199$	−10.1643	+	17.6051i	−0.720529	+	1.24799i	−0.960788	+	0.277284i	$0.910566\pi$
$200$	−0.732458	−	0.266593i	−0.0517926	−	0.0188510i
$201$		0			0
$202$	−30.2456	−	25.3790i	−2.12807	−	1.78566i
$203$	11.0754	+	9.29334i	0.777339	+	0.652265i
$204$		0			0
$205$	4.39909	+	1.60114i	0.307246	+	0.111828i
$206$	9.56876	−	16.5736i	0.666687	−	1.15474i
$207$		0			0
$208$	−1.64315	−	2.84601i	−0.113932	−	0.197336i
$209$	−1.32438	−	7.51092i	−0.0916091	−	0.519541i
$210$		0			0
$211$	9.26849	−	3.37345i	0.638069	−	0.232238i	−0.00267052	−	0.999996i	$-0.500850\pi$
$211$	9.26849	−	3.37345i	0.638069	−	0.232238i	0.640740	+	0.767758i	$0.278628\pi$
$212$	−2.76443	+	15.6779i	−0.189862	+	1.07676i
$213$		0			0
$214$	−12.0898	+	10.1446i	−0.826445	+	0.693470i
$215$	11.3588			0.774665
$216$		0			0
$217$	7.14494			0.485030
$218$	9.15506	−	7.68201i	0.620059	−	0.520291i
$219$		0			0
$220$	−3.75404	+	21.2902i	−0.253098	+	1.43539i
$221$	2.70088	−	0.983041i	0.181681	−	0.0661265i
$222$		0			0
$223$	2.61712	+	14.8424i	0.175255	+	0.993922i	0.937849	+	0.347044i	$0.112815\pi$
$223$	2.61712	+	14.8424i	0.175255	+	0.993922i	−0.762594	+	0.646878i	$0.776074\pi$
$224$	−19.2368	−	33.3191i	−1.28531	−	2.22623i
$225$		0			0
$226$	−2.55287	+	4.42170i	−0.169814	+	0.294127i
$227$	21.3240	+	7.76131i	1.41533	+	0.515136i	0.932688	−	0.360684i	$-0.117457\pi$
$227$	21.3240	+	7.76131i	1.41533	+	0.515136i	0.482637	+	0.875820i	$0.339679\pi$
$228$		0			0
$229$	6.67738	+	5.60299i	0.441254	+	0.370256i	0.836178	−	0.548458i	$-0.184785\pi$
$229$	6.67738	+	5.60299i	0.441254	+	0.370256i	−0.394925	+	0.918714i	$0.629229\pi$
$230$	−14.5083	−	12.1739i	−0.956646	−	0.802721i
$231$		0			0
$232$	3.07092	+	1.11772i	0.201616	+	0.0733822i
$233$	11.7945	−	20.4286i	0.772682	−	1.33832i	−0.163406	−	0.986559i	$-0.552248\pi$
$233$	11.7945	−	20.4286i	0.772682	−	1.33832i	0.936088	−	0.351766i	$-0.114419\pi$
$234$		0			0
$235$	7.43792	+	12.8829i	0.485196	+	0.840385i
$236$	0.114568	+	0.649748i	0.00745775	+	0.0422950i
$237$		0			0
$238$	22.8852	−	8.32953i	1.48343	−	0.539923i
$239$	1.72858	−	9.80329i	0.111813	−	0.634122i	−0.876466	−	0.481463i	$-0.840105\pi$
$239$	1.72858	−	9.80329i	0.111813	−	0.634122i	0.988279	−	0.152658i	$-0.0487834\pi$
$240$		0			0
$241$	4.37676	−	3.67253i	0.281932	−	0.236569i	−0.490845	−	0.871247i	$-0.663312\pi$
$241$	4.37676	−	3.67253i	0.281932	−	0.236569i	0.772776	+	0.634678i	$0.218867\pi$
$242$	−13.2140			−0.849427
$243$		0			0
$244$	−11.2092			−0.717594
$245$	−26.1914	+	21.9772i	−1.67331	+	1.40407i
$246$		0			0
$247$	0.388111	−	2.20109i	0.0246949	−	0.140052i
$248$	1.51762	−	0.552369i	0.0963690	−	0.0350754i
$249$		0			0
$250$	−4.36446	−	24.7521i	−0.276033	−	1.56546i
$251$	3.64483	+	6.31303i	0.230060	+	0.398475i	0.957825	−	0.287351i	$-0.0927745\pi$
$251$	3.64483	+	6.31303i	0.230060	+	0.398475i	−0.727766	+	0.685826i	$0.759441\pi$
$252$		0			0
$253$	8.92881	−	15.4651i	0.561349	−	0.972285i
$254$	−18.4405	−	6.71180i	−1.15706	−	0.421136i
$255$		0			0
$256$	3.75456	+	3.15045i	0.234660	+	0.196903i
$257$	−17.8052	−	14.9404i	−1.11066	−	0.931954i	−0.112564	−	0.993644i	$-0.535906\pi$
$257$	−17.8052	−	14.9404i	−1.11066	−	0.931954i	−0.998095	+	0.0616904i	$0.980351\pi$
$258$		0			0
$259$	−40.8746	−	14.8771i	−2.53982	−	0.924420i
$260$	−3.16770	+	5.48661i	−0.196452	+	0.340265i
$261$		0			0
$262$	−16.2979	−	28.2288i	−1.00689	−	1.74398i
$263$	−4.75789	−	26.9833i	−0.293384	−	1.66386i	−0.673698	−	0.739007i	$-0.735295\pi$
$263$	−4.75789	−	26.9833i	−0.293384	−	1.66386i	0.380314	−	0.924858i	$-0.375816\pi$
$264$		0			0
$265$	−12.3146	+	4.48216i	−0.756483	+	0.275337i
$266$	3.28855	−	18.6503i	0.201634	−	1.14352i
$267$		0			0
$268$	7.96136	−	6.68037i	0.486317	−	0.408069i
$269$	9.41973			0.574331			0.287166	−	0.957881i	$-0.407287\pi$
$269$	9.41973			0.574331			0.287166	+	0.957881i	$0.407287\pi$
$270$		0			0
$271$	26.2797			1.59638			0.798189	−	0.602408i	$-0.205792\pi$
$271$	26.2797			1.59638			0.798189	+	0.602408i	$0.205792\pi$
$272$	−4.89331	+	4.10597i	−0.296700	+	0.248961i
$273$		0			0
$274$	1.34465	−	7.62590i	0.0812334	−	0.460697i
$275$	2.77317	−	1.00935i	0.167228	−	0.0608661i
$276$		0			0
$277$	0.0650854	+	0.369118i	0.00391060	+	0.0221781i	0.986701	−	0.162548i	$-0.0519713\pi$
$277$	0.0650854	+	0.369118i	0.00391060	+	0.0221781i	−0.982790	+	0.184726i	$0.940860\pi$
$278$	14.1054	+	24.4314i	0.845989	+	1.46530i
$279$		0			0
$280$	−5.50253	+	9.53065i	−0.328839	+	0.569566i
$281$	−13.1384	−	4.78198i	−0.783771	−	0.285269i	−0.0810267	−	0.996712i	$-0.525820\pi$
$281$	−13.1384	−	4.78198i	−0.783771	−	0.285269i	−0.702744	+	0.711443i	$0.748042\pi$
$282$		0			0
$283$	11.9211	+	10.0030i	0.708636	+	0.594616i	0.924216	−	0.381870i	$-0.124720\pi$
$283$	11.9211	+	10.0030i	0.708636	+	0.594616i	−0.215580	+	0.976486i	$0.569164\pi$
$284$	5.94632	+	4.98955i	0.352849	+	0.296075i
$285$		0			0
$286$	−10.0759	−	3.66733i	−0.595801	−	0.216854i
$287$	−5.48027	+	9.49211i	−0.323490	+	0.560301i
$288$		0			0
$289$	5.70661	+	9.88413i	0.335683	+	0.581420i
$290$	2.27868	+	12.9231i	0.133809	+	0.758868i
$291$		0			0
$292$	−30.1652	+	10.9792i	−1.76528	+	0.642510i
$293$	4.27595	−	24.2501i	0.249804	−	1.41671i	−0.559263	−	0.828990i	$-0.688916\pi$
$293$	4.27595	−	24.2501i	0.249804	−	1.41671i	0.809066	−	0.587717i	$-0.199973\pi$
$294$		0			0
$295$	−0.416053	+	0.349110i	−0.0242235	+	0.0203259i
$296$	−9.83210			−0.571479
$297$		0			0
$298$	−18.9361			−1.09694
$299$	4.00887	−	3.36384i	0.231839	−	0.194536i
$300$		0			0
$301$	−4.61805	+	26.1903i	−0.266180	+	1.50958i
$302$	−1.42258	+	0.517777i	−0.0818603	+	0.0297947i
$303$		0			0
$304$	0.862551	+	4.89177i	0.0494707	+	0.280562i
$305$	−4.61365	−	7.99107i	−0.264177	−	0.457567i
$306$		0			0
$307$	10.1956	−	17.6593i	0.581893	−	1.00787i	−0.413362	−	0.910567i	$-0.635646\pi$
$307$	10.1956	−	17.6593i	0.581893	−	1.00787i	0.995255	−	0.0973012i	$-0.0310210\pi$
$308$	−47.5631	−	17.3116i	−2.71016	−	0.986418i
$309$		0			0
$310$	4.96778	+	4.16846i	0.282151	+	0.236753i
$311$	16.9901	+	14.2564i	0.963421	+	0.808406i	0.981506	−	0.191430i	$-0.0613125\pi$
$311$	16.9901	+	14.2564i	0.963421	+	0.808406i	−0.0180851	+	0.999836i	$0.505757\pi$
$312$		0			0
$313$	10.4983	+	3.82106i	0.593398	+	0.215979i	0.621223	−	0.783634i	$-0.286636\pi$
$313$	10.4983	+	3.82106i	0.593398	+	0.215979i	−0.0278253	+	0.999613i	$0.508858\pi$
$314$	−14.6819	+	25.4298i	−0.828547	+	1.43508i
$315$		0			0
$316$	−5.72635	−	9.91833i	−0.322132	−	0.557950i
$317$	4.37883	+	24.8336i	0.245939	+	1.39479i	0.818301	+	0.574790i	$0.194916\pi$
$317$	4.37883	+	24.8336i	0.245939	+	1.39479i	−0.572361	+	0.820002i	$0.693973\pi$
$318$		0			0
$319$	−11.6268	+	4.23182i	−0.650978	+	0.236937i
$320$	4.12004	−	23.3659i	0.230317	−	1.30619i
$321$		0			0
$322$	33.9680	−	28.5026i	1.89296	−	1.58839i
$323$	−4.34438			−0.241728
$324$		0			0
$325$	0.864837			0.0479725
$326$	1.94239	−	1.62986i	0.107579	−	0.0902696i
$327$		0			0
$328$	−0.430211	+	2.43985i	−0.0237544	+	0.134718i
$329$	−32.7282	+	11.9121i	−1.80437	+	0.656735i
$330$		0			0
$331$	−4.54362	−	25.7682i	−0.249740	−	1.41635i	−0.809221	−	0.587504i	$-0.800111\pi$
$331$	−4.54362	−	25.7682i	−0.249740	−	1.41635i	0.559481	−	0.828843i	$-0.311000\pi$
$332$	10.6329	+	18.4167i	0.583555	+	1.01075i
$333$		0			0
$334$	−25.4327	+	44.0507i	−1.39161	+	2.41035i
$335$	8.03932	+	2.92607i	0.439235	+	0.159869i
$336$		0			0
$337$	8.38516	+	7.03599i	0.456769	+	0.383275i	0.841940	−	0.539570i	$-0.181413\pi$
$337$	8.38516	+	7.03599i	0.456769	+	0.383275i	−0.385172	+	0.922845i	$0.625858\pi$
$338$	18.7551	+	15.7374i	1.02015	+	0.856004i
$339$		0			0
$340$	11.5718	+	4.21180i	0.627570	+	0.228417i
$341$	−3.05732	+	5.29543i	−0.165563	+	0.286763i
$342$		0			0
$343$	−23.0545	−	39.9316i	−1.24483	−	2.15611i
$344$	1.04385	+	5.91996i	0.0562805	+	0.319183i
$345$		0			0
$346$	−18.2514	+	6.64298i	−0.981203	+	0.357129i
$347$	0.610092	−	3.46000i	0.0327514	−	0.185743i	−0.964043	−	0.265746i	$-0.914382\pi$
$347$	0.610092	−	3.46000i	0.0327514	−	0.185743i	0.996795	+	0.0800030i	$0.0254930\pi$
$348$		0			0
$349$	−22.3661	+	18.7674i	−1.19723	+	1.00459i	−0.197524	+	0.980298i	$0.563290\pi$
$349$	−22.3661	+	18.7674i	−1.19723	+	1.00459i	−0.999705	+	0.0242965i	$0.992265\pi$
$350$	7.32796			0.391696
$351$		0			0
$352$	32.9256			1.75494
$353$	−19.2100	+	16.1191i	−1.02244	+	0.857931i	−0.989932	−	0.141540i	$-0.954795\pi$
$353$	−19.2100	+	16.1191i	−1.02244	+	0.857931i	−0.0325100	+	0.999471i	$0.510350\pi$
$354$		0			0
$355$	−1.10960	+	6.29283i	−0.0588912	+	0.333989i
$356$	−40.1014	+	14.5957i	−2.12537	+	0.773572i
$357$		0			0
$358$	−3.91176	−	22.1847i	−0.206743	−	1.17250i
$359$	−2.10362	−	3.64358i	−0.111025	−	0.192301i	0.805159	−	0.593059i	$-0.202080\pi$
$359$	−2.10362	−	3.64358i	−0.111025	−	0.192301i	−0.916184	+	0.400758i	$0.868747\pi$
$360$		0			0
$361$	7.81087	−	13.5288i	0.411098	−	0.712043i
$362$	−2.92127	−	1.06325i	−0.153538	−	0.0558834i
$363$		0			0
$364$	−11.3627	−	9.53447i	−0.595569	−	0.499742i
$365$	−20.2430	−	16.9859i	−1.05957	−	0.889081i
$366$		0			0
$367$	−16.4415	−	5.98420i	−0.858237	−	0.312373i	−0.124843	−	0.992177i	$-0.539843\pi$
$367$	−16.4415	−	5.98420i	−0.858237	−	0.312373i	−0.733394	+	0.679804i	$0.762065\pi$
$368$	−5.81522	+	10.0723i	−0.303139	+	0.525053i
$369$		0			0
$370$	−19.7400	−	34.1907i	−1.02623	−	1.77749i
$371$	−5.32797	−	30.2164i	−0.276614	−	1.56876i
$372$		0			0
$373$	27.8662	−	10.1425i	1.44286	−	0.525157i	0.502270	−	0.864711i	$-0.332499\pi$
$373$	27.8662	−	10.1425i	1.44286	−	0.525157i	0.940586	+	0.339554i	$0.110276\pi$
$374$	−3.61918	+	20.5254i	−0.187144	+	1.06134i
$375$		0			0
$376$	−6.03072	+	5.06038i	−0.311011	+	0.260969i
$377$	−3.62594			−0.186745
$378$		0			0
$379$	20.9523			1.07625			0.538124	−	0.842865i	$-0.319133\pi$
$379$	20.9523			1.07625			0.538124	+	0.842865i	$0.319133\pi$
$380$	7.33560	−	6.15530i	0.376308	−	0.315760i
$381$		0			0
$382$	−4.58391	+	25.9966i	−0.234533	+	1.33010i
$383$	−9.29993	+	3.38490i	−0.475204	+	0.172960i	−0.568508	−	0.822678i	$-0.692479\pi$
$383$	−9.29993	+	3.38490i	−0.475204	+	0.172960i	0.0933043	+	0.995638i	$0.470257\pi$
$384$		0			0
$385$	−7.23528	−	41.0333i	−0.368744	−	2.09125i
$386$	22.0719	+	38.2297i	1.12343	+	1.94584i
$387$		0			0
$388$	6.42745	−	11.1327i	0.326304	−	0.565175i
$389$	19.8414	+	7.22167i	1.00600	+	0.366153i	0.791895	−	0.610658i	$-0.209095\pi$
$389$	19.8414	+	7.22167i	1.00600	+	0.366153i	0.214104	+	0.976811i	$0.431317\pi$
$390$		0			0
$391$	−7.79227	−	6.53849i	−0.394072	−	0.330665i
$392$	−13.8609	−	11.6307i	−0.700083	−	0.587440i
$393$		0			0
$394$	−28.3330	−	10.3124i	−1.42739	−	0.519529i
$395$	4.71388	−	8.16468i	0.237181	−	0.410810i
$396$		0			0
$397$	4.88955	+	8.46894i	0.245399	+	0.425044i	0.962244	−	0.272189i	$-0.0877476\pi$
$397$	4.88955	+	8.46894i	0.245399	+	0.425044i	−0.716845	+	0.697233i	$0.754414\pi$
$398$	−7.50142	−	42.5426i	−0.376012	−	2.13247i
$399$		0			0
$400$	−1.80613	+	0.657377i	−0.0903064	+	0.0328688i
$401$	−3.32351	+	18.8486i	−0.165968	+	0.941252i	0.782092	+	0.623163i	$0.214153\pi$
$401$	−3.32351	+	18.8486i	−0.165968	+	0.941252i	−0.948061	+	0.318090i	$0.896959\pi$
$402$		0			0
$403$	−1.37268	+	1.15181i	−0.0683780	+	0.0573759i
$404$	46.7423			2.32552
$405$		0			0
$406$	−30.7234			−1.52478
$407$	28.5163	−	23.9280i	1.41350	−	1.18607i
$408$		0			0
$409$	2.60395	−	14.7677i	0.128757	−	0.730218i	−0.850248	−	0.526382i	$-0.823548\pi$
$409$	2.60395	−	14.7677i	0.128757	−	0.730218i	0.979005	−	0.203836i	$-0.0653408\pi$
$410$	−9.34819	+	3.40246i	−0.461674	+	0.168036i
$411$		0			0
$412$	3.93421	+	22.3120i	0.193825	+	1.09924i
$413$	−0.635799	−	1.10124i	−0.0312856	−	0.0541883i
$414$		0			0
$415$	−8.75289	+	15.1604i	−0.429662	+	0.744197i
$416$	9.06702	+	3.30013i	0.444547	+	0.161802i
$417$		0			0
$418$	12.4154	+	10.4177i	0.607257	+	0.509549i
$419$	4.45210	+	3.73575i	0.217499	+	0.182504i	0.745027	−	0.667034i	$-0.232437\pi$
$419$	4.45210	+	3.73575i	0.217499	+	0.182504i	−0.527528	+	0.849538i	$0.676881\pi$
$420$		0			0
$421$	12.5106	+	4.55349i	0.609730	+	0.221924i	0.628385	−	0.777902i	$-0.283716\pi$
$421$	12.5106	+	4.55349i	0.609730	+	0.221924i	−0.0186551	+	0.999826i	$0.505938\pi$
$422$	−10.4799	+	18.1518i	−0.510154	+	0.883613i
$423$		0			0
$424$	−3.46769	−	6.00621i	−0.168406	−	0.291687i
$425$	−0.291908	−	1.65549i	−0.0141596	−	0.0803033i
$426$		0			0
$427$	20.3009	−	7.38893i	0.982430	−	0.357575i
$428$	3.24444	−	18.4001i	0.156826	−	0.889403i
$429$		0			0
$430$	−18.4906	+	15.5155i	−0.891697	+	0.748223i
$431$	−36.4166			−1.75413			−0.877064	−	0.480374i	$-0.840501\pi$
$431$	−36.4166			−1.75413			−0.877064	+	0.480374i	$0.840501\pi$
$432$		0			0
$433$	−10.8761			−0.522674			−0.261337	−	0.965248i	$-0.584163\pi$
$433$	−10.8761			−0.522674			−0.261337	+	0.965248i	$0.584163\pi$
$434$	−11.6310	+	9.75957i	−0.558306	+	0.468475i
$435$		0			0
$436$	−2.45686	+	13.9335i	−0.117662	+	0.667295i
$437$	−7.43296	+	2.70537i	−0.355567	+	0.129416i
$438$		0			0
$439$	1.64154	+	9.30965i	0.0783465	+	0.444325i	0.998595	+	0.0529907i	$0.0168754\pi$
$439$	1.64154	+	9.30965i	0.0783465	+	0.444325i	−0.920248	+	0.391335i	$0.872014\pi$
$440$	−4.70906	−	8.15632i	−0.224495	−	0.388837i
$441$		0			0
$442$	−3.05390	+	5.28951i	−0.145259	+	0.251596i
$443$	−15.5274	−	5.65151i	−0.737729	−	0.268511i	−0.0542962	−	0.998525i	$-0.517292\pi$
$443$	−15.5274	−	5.65151i	−0.737729	−	0.268511i	−0.683433	+	0.730013i	$0.739514\pi$
$444$		0			0
$445$	−26.9109	−	22.5809i	−1.27570	−	1.07044i
$446$	−24.5342	−	20.5866i	−1.16173	−	0.974806i
$447$		0			0
$448$	52.2002	+	18.9993i	2.46623	+	0.897633i
$449$	2.37181	−	4.10809i	0.111933	−	0.193873i	−0.804617	−	0.593794i	$-0.797629\pi$
$449$	2.37181	−	4.10809i	0.111933	−	0.193873i	0.916549	+	0.399921i	$0.130963\pi$
$450$		0			0
$451$	−4.69001	−	8.12334i	−0.220844	−	0.382513i
$452$	−1.04962	−	5.95268i	−0.0493699	−	0.279990i
$453$		0			0
$454$	−45.3142	+	16.4930i	−2.12670	+	0.774055i
$455$	2.12031	−	12.0249i	0.0994017	−	0.563735i
$456$		0			0
$457$	−17.1659	+	14.4039i	−0.802989	+	0.673788i	−0.948923	−	0.315506i	$-0.897826\pi$
$457$	−17.1659	+	14.4039i	−0.802989	+	0.673788i	0.145934	+	0.989294i	$0.453381\pi$
$458$	−18.5232			−0.865534
$459$		0			0
$460$	22.4214			1.04540
$461$	−11.4311	+	9.59184i	−0.532400	+	0.446737i	−0.868929	−	0.494936i	$-0.835191\pi$
$461$	−11.4311	+	9.59184i	−0.532400	+	0.446737i	0.336529	+	0.941673i	$0.390747\pi$
$462$		0			0
$463$	−2.57818	+	14.6216i	−0.119818	+	0.679524i	0.864433	+	0.502748i	$0.167678\pi$
$463$	−2.57818	+	14.6216i	−0.119818	+	0.679524i	−0.984251	+	0.176776i	$0.943433\pi$
$464$	7.57242	−	2.75614i	0.351541	−	0.127950i
$465$		0			0
$466$	8.70450	+	49.3657i	0.403228	+	2.28682i
$467$	7.67571	+	13.2947i	0.355190	+	0.615206i	0.987150	−	0.159794i	$-0.0510830\pi$
$467$	7.67571	+	13.2947i	0.355190	+	0.615206i	−0.631961	+	0.775000i	$0.717750\pi$
$468$		0			0
$469$	−10.0152	+	17.3468i	−0.462458	+	0.801001i
$470$	−29.7052	−	10.8118i	−1.37020	−	0.498711i
$471$		0			0
$472$	−0.220182	−	0.184755i	−0.0101347	−	0.00850403i
$473$	−17.4347	−	14.6294i	−0.801647	−	0.672662i
$474$		0			0
$475$	−1.22837	−	0.447089i	−0.0563614	−	0.0205139i
$476$	−14.4159	+	24.9690i	−0.660750	+	1.14445i
$477$		0			0
$478$	10.5768	+	18.3196i	0.483772	+	0.837918i
$479$	1.81438	+	10.2899i	0.0829012	+	0.470156i	0.997790	+	0.0664497i	$0.0211672\pi$
$479$	1.81438	+	10.2899i	0.0829012	+	0.470156i	−0.914889	+	0.403706i	$0.867722\pi$
$480$		0			0
$481$	10.2511	−	3.73109i	0.467409	−	0.170123i
$482$	−2.10830	+	11.9568i	−0.0960306	+	0.544617i
$483$		0			0
$484$	11.9837	−	10.0555i	0.544712	−	0.457068i
$485$	10.5820			0.480505
$486$		0			0
$487$	−16.1649			−0.732500			−0.366250	−	0.930516i	$-0.619359\pi$
$487$	−16.1649			−0.732500			−0.366250	+	0.930516i	$0.619359\pi$
$488$	3.74078	−	3.13889i	0.169337	−	0.142091i
$489$		0			0
$490$	12.6165	−	71.5519i	0.569957	−	3.23239i
$491$	10.1274	−	3.68607i	0.457043	−	0.166350i	−0.103231	−	0.994657i	$-0.532918\pi$
$491$	10.1274	−	3.68607i	0.457043	−	0.166350i	0.560274	+	0.828307i	$0.310696\pi$
$492$		0			0
$493$	1.22386	+	6.94087i	0.0551200	+	0.312601i
$494$	2.37477	+	4.11322i	0.106846	+	0.185062i
$495$		0			0
$496$	1.99119	−	3.44885i	0.0894071	−	0.154858i
$497$	−14.0584	−	5.11684i	−0.630605	−	0.229522i
$498$		0			0
$499$	−14.6982	−	12.3333i	−0.657983	−	0.552114i	0.251498	−	0.967858i	$-0.419077\pi$
$499$	−14.6982	−	12.3333i	−0.657983	−	0.552114i	−0.909482	+	0.415744i	$0.863521\pi$
$500$	22.7938	+	19.1263i	1.01937	+	0.855352i
$501$		0			0
$502$	−14.5565	−	5.29815i	−0.649690	−	0.236468i
$503$	6.01253	−	10.4140i	0.268086	−	0.464338i	−0.700282	−	0.713866i	$-0.746942\pi$
$503$	6.01253	−	10.4140i	0.268086	−	0.464338i	0.968367	+	0.249529i	$0.0802757\pi$
$504$		0			0
$505$	19.2389	+	33.3228i	0.856120	+	1.48284i
$506$	6.58959	+	37.3714i	0.292943	+	1.66136i
$507$		0			0
$508$	21.8311	−	7.94586i	0.968598	−	0.352541i
$509$	−2.59657	+	14.7259i	−0.115091	+	0.652712i	0.871615	+	0.490192i	$0.163073\pi$
$509$	−2.59657	+	14.7259i	−0.115091	+	0.652712i	−0.986705	+	0.162520i	$0.948038\pi$
$510$		0			0
$511$	47.3947	−	39.7689i	2.09662	−	1.75927i
$512$	−27.3678			−1.20950
$513$		0			0
$514$	49.3922			2.17860
$515$	−14.2870	+	11.9883i	−0.629562	+	0.528266i
$516$		0			0
$517$	5.17581	−	29.3535i	0.227632	−	1.29097i
$518$	86.8597	−	31.6143i	3.81640	−	1.38905i
$519$		0			0
$520$	−0.479268	−	2.71806i	−0.0210173	−	0.119195i
$521$	−18.7094	−	32.4056i	−0.819673	−	1.41972i	−0.905923	−	0.423442i	$-0.860822\pi$
$521$	−18.7094	−	32.4056i	−0.819673	−	1.41972i	0.0862502	−	0.996274i	$-0.472512\pi$
$522$		0			0
$523$	4.22489	−	7.31773i	0.184742	−	0.319982i	−0.758748	−	0.651385i	$-0.774188\pi$
$523$	4.22489	−	7.31773i	0.184742	−	0.319982i	0.943489	+	0.331403i	$0.107522\pi$
$524$	36.2619	+	13.1982i	1.58411	+	0.576568i
$525$		0			0
$526$	44.6029	+	37.4263i	1.94478	+	1.63186i
$527$	2.66815	+	2.23885i	0.116227	+	0.0975256i
$528$		0			0
$529$	4.20916	+	1.53201i	0.183007	+	0.0666091i
$530$	13.9242	−	24.1175i	0.604829	−	1.04760i
$531$		0			0
$532$	11.2100	+	19.4163i	0.486017	+	0.841805i
$533$	−0.477330	−	2.70707i	−0.0206754	−	0.117256i
$534$		0			0
$535$	14.4529	−	5.26043i	0.624854	−	0.227428i
$536$	−0.786209	+	4.45881i	−0.0339591	+	0.192591i
$537$		0			0
$538$	−15.3341	+	12.8668i	−0.661098	+	0.554727i
$539$	68.5065			2.95078
$540$		0			0
$541$	12.6259			0.542828			0.271414	−	0.962463i	$-0.412509\pi$
$541$	12.6259			0.542828			0.271414	+	0.962463i	$0.412509\pi$
$542$	−42.7798	+	35.8965i	−1.83755	+	1.54189i
$543$		0			0
$544$	3.25680	−	18.4702i	0.139634	−	0.791904i
$545$	−10.9445	+	3.98347i	−0.468811	+	0.170633i
$546$		0			0
$547$	5.45169	+	30.9181i	0.233098	+	1.32196i	0.846583	+	0.532256i	$0.178656\pi$
$547$	5.45169	+	30.9181i	0.233098	+	1.32196i	−0.613486	+	0.789706i	$0.710233\pi$
$548$	4.58365	+	7.93912i	0.195804	+	0.339142i
$549$		0			0
$550$	−3.13563	+	5.43107i	−0.133704	+	0.231582i
$551$	5.15008	+	1.87448i	0.219401	+	0.0798554i
$552$		0			0
$553$	16.9090	+	14.1883i	0.719044	+	0.603349i
$554$	−0.610144	−	0.511971i	−0.0259225	−	0.0217516i
$555$		0			0
$556$	−31.3838	−	11.4228i	−1.33097	−	0.484433i
$557$	7.96515	−	13.7960i	0.337494	−	0.584557i	−0.646467	−	0.762942i	$-0.723754\pi$
$557$	7.96515	−	13.7960i	0.337494	−	0.584557i	0.983961	+	0.178385i	$0.0570874\pi$
$558$		0			0
$559$	−3.33484	−	5.77610i	−0.141048	−	0.244303i
$560$	4.71225	+	26.7245i	0.199129	+	1.12932i
$561$		0			0
$562$	27.9195	−	10.1619i	1.17771	−	0.428652i
$563$	−4.31704	+	24.4832i	−0.181942	+	1.03184i	0.747881	+	0.663833i	$0.231072\pi$
$563$	−4.31704	+	24.4832i	−0.181942	+	1.03184i	−0.929822	+	0.368009i	$0.880040\pi$
$564$		0			0
$565$	3.81167	−	3.19837i	0.160358	−	0.134557i
$566$	−33.0695			−1.39001
$567$		0			0
$568$	−3.38165			−0.141891
$569$	14.7004	−	12.3351i	0.616273	−	0.517114i	−0.280357	−	0.959896i	$-0.590453\pi$
$569$	14.7004	−	12.3351i	0.616273	−	0.517114i	0.896629	+	0.442782i	$0.146008\pi$
$570$		0			0
$571$	−3.53882	+	20.0696i	−0.148095	+	0.839888i	0.816735	+	0.577013i	$0.195782\pi$
$571$	−3.53882	+	20.0696i	−0.148095	+	0.839888i	−0.964830	+	0.262875i	$0.915329\pi$
$572$	11.9285	−	4.34162i	0.498756	−	0.181532i
$573$		0			0
$574$	−4.04452	−	22.9376i	−0.168815	−	0.957398i
$575$	−1.53036	−	2.65066i	−0.0638205	−	0.110540i
$576$		0			0
$577$	−11.6495	+	20.1776i	−0.484976	+	0.840004i	−0.999851	−	0.0172619i	$-0.994505\pi$
$577$	−11.6495	+	20.1776i	−0.484976	+	0.840004i	0.514875	+	0.857265i	$0.327838\pi$
$578$	−22.7907	−	8.29515i	−0.947970	−	0.345033i
$579$		0			0
$580$	−11.9006	−	9.98581i	−0.494147	−	0.414638i
$581$	−31.3972	−	26.3454i	−1.30257	−	1.09299i
$582$		0			0
$583$	24.6745	+	8.98079i	1.02191	+	0.371946i
$584$	6.99237	−	12.1111i	0.289346	−	0.501163i
$585$		0			0
$586$	26.1636	+	45.3167i	1.08081	+	1.87201i
$587$	−6.40923	−	36.3485i	−0.264537	−	1.50026i	−0.770350	−	0.637621i	$-0.779918\pi$
$587$	−6.40923	−	36.3485i	−0.264537	−	1.50026i	0.505813	−	0.862643i	$-0.331193\pi$
$588$		0			0
$589$	2.54512	−	0.926348i	0.104870	−	0.0381695i
$590$	0.200415	−	1.13661i	0.00825094	−	0.0467934i
$591$		0			0
$592$	−18.5723	+	15.5840i	−0.763318	+	0.640500i
$593$	4.36830			0.179385			0.0896923	−	0.995970i	$-0.471412\pi$
$593$	4.36830			0.179385			0.0896923	+	0.995970i	$0.471412\pi$
$594$		0			0
$595$	−23.7340			−0.973000
$596$	17.1730	−	14.4099i	0.703434	−	0.590251i
$597$		0			0
$598$	−1.93109	+	10.9518i	−0.0789682	+	0.447851i
$599$	29.3237	−	10.6729i	1.19813	−	0.436085i	0.335561	−	0.942019i	$-0.391074\pi$
$599$	29.3237	−	10.6729i	1.19813	−	0.436085i	0.862572	+	0.505934i	$0.168852\pi$
$600$		0			0
$601$	7.62960	+	43.2696i	0.311218	+	1.76500i	0.592686	+	0.805433i	$0.298067\pi$
$601$	7.62960	+	43.2696i	0.311218	+	1.76500i	−0.281468	+	0.959571i	$0.590821\pi$
$602$	−28.2568	−	48.9422i	−1.15166	−	1.99474i
$603$		0			0
$604$	0.896114	−	1.55211i	0.0364623	−	0.0631546i
$605$	12.1010	+	4.40441i	0.491977	+	0.179065i
$606$		0			0
$607$	13.2975	+	11.1579i	0.539729	+	0.452886i	0.871445	−	0.490493i	$-0.163183\pi$
$607$	13.2975	+	11.1579i	0.539729	+	0.452886i	−0.331716	+	0.943379i	$0.607628\pi$
$608$	−11.1723	−	9.37463i	−0.453095	−	0.380192i
$609$		0			0
$610$	18.4257	+	6.70642i	0.746036	+	0.271535i
$611$	4.36740	−	7.56456i	0.176686	−	0.306029i
$612$		0			0
$613$	0.599024	+	1.03754i	0.0241944	+	0.0419059i	0.877869	−	0.478901i	$-0.158965\pi$
$613$	0.599024	+	1.03754i	0.0241944	+	0.0419059i	−0.853675	+	0.520807i	$0.825631\pi$
$614$	7.52449	+	42.6735i	0.303664	+	1.72216i
$615$		0			0
$616$	20.7207	−	7.54173i	0.834862	−	0.303865i
$617$	4.51723	−	25.6185i	0.181857	−	1.03136i	−0.748070	−	0.663619i	$-0.769020\pi$
$617$	4.51723	−	25.6185i	0.181857	−	1.03136i	0.929927	−	0.367743i	$-0.119869\pi$
$618$		0			0
$619$	7.37804	−	6.19091i	0.296549	−	0.248834i	−0.482357	−	0.875974i	$-0.660219\pi$
$619$	7.37804	−	6.19091i	0.296549	−	0.248834i	0.778906	+	0.627141i	$0.215775\pi$
$620$	−7.67733			−0.308329
$621$		0			0
$622$	−47.1311			−1.88978
$623$	63.0063	−	52.8685i	2.52429	−	2.11813i
$624$		0			0
$625$	−3.63587	+	20.6201i	−0.145435	+	0.824802i
$626$	−22.3092	+	8.11987i	−0.891653	+	0.324535i
$627$		0			0
$628$	−6.03648	−	34.2346i	−0.240882	−	1.36611i
$629$	−10.6022	−	18.3635i	−0.422737	−	0.732202i
$630$		0			0
$631$	7.08366	−	12.2693i	0.281996	−	0.488431i	−0.689880	−	0.723924i	$-0.742337\pi$
$631$	7.08366	−	12.2693i	0.281996	−	0.488431i	0.971876	+	0.235492i	$0.0756702\pi$
$632$	4.68844	+	1.70645i	0.186496	+	0.0678791i
$633$		0			0
$634$	−41.0494	−	34.4445i	−1.63028	−	1.36797i
$635$	14.6502	+	12.2930i	0.581376	+	0.487833i
$636$		0			0
$637$	18.8652	+	6.86638i	0.747468	+	0.272056i
$638$	13.1465	−	22.7704i	0.520476	−	0.901490i
$639$		0			0
$640$	8.77695	+	15.2021i	0.346939	+	0.600917i
$641$	3.85515	+	21.8636i	0.152269	+	0.863561i	0.961240	+	0.275713i	$0.0889138\pi$
$641$	3.85515	+	21.8636i	0.152269	+	0.863561i	−0.808971	+	0.587849i	$0.799975\pi$
$642$		0			0
$643$	−20.2380	+	7.36602i	−0.798107	+	0.290487i	−0.708702	−	0.705508i	$-0.750719\pi$
$643$	−20.2380	+	7.36602i	−0.798107	+	0.290487i	−0.0894054	+	0.995995i	$0.528497\pi$
$644$	−9.11568	+	51.6976i	−0.359208	+	2.03717i
$645$		0			0
$646$	7.07207	−	5.93417i	0.278247	−	0.233477i
$647$	13.4037			0.526952			0.263476	−	0.964666i	$-0.415131\pi$
$647$	13.4037			0.526952			0.263476	+	0.964666i	$0.415131\pi$
$648$		0			0
$649$	1.08823			0.0427168
$650$	−1.40784	+	1.18132i	−0.0552200	+	0.0463351i
$651$		0			0
$652$	−0.521261	+	2.95622i	−0.0204142	+	0.115774i
$653$	17.7704	−	6.46790i	0.695409	−	0.253108i	0.0299599	−	0.999551i	$-0.490462\pi$
$653$	17.7704	−	6.46790i	0.695409	−	0.253108i	0.665450	+	0.746443i	$0.268240\pi$
$654$		0			0
$655$	5.51614	+	31.2836i	0.215533	+	1.22235i
$656$	3.05455	+	5.29063i	0.119260	+	0.206564i
$657$		0			0
$658$	37.0059	−	64.0962i	1.44264	−	2.49873i
$659$	0.0264819	+	0.00963862i	0.00103159	+	0.000375467i	0.342536	−	0.939505i	$-0.388714\pi$
$659$	0.0264819	+	0.00963862i	0.00103159	+	0.000375467i	−0.341504	+	0.939880i	$0.610936\pi$
$660$		0			0
$661$	−34.5040	−	28.9523i	−1.34205	−	1.12611i	−0.981095	−	0.193529i	$-0.938007\pi$
$661$	−34.5040	−	28.9523i	−1.34205	−	1.12611i	−0.360954	−	0.932583i	$-0.617549\pi$
$662$	42.5943	+	35.7408i	1.65547	+	1.38911i
$663$		0			0
$664$	−8.70565	−	3.16860i	−0.337845	−	0.122965i
$665$	−9.22800	+	15.9834i	−0.357846	+	0.619808i
$666$		0			0
$667$	6.41623	+	11.1132i	0.248438	+	0.430306i
$668$	−10.4567	−	59.3029i	−0.404582	−	2.29450i
$669$		0			0
$670$	−17.0838	+	6.21799i	−0.660005	+	0.240222i
$671$	−3.21049	+	18.2076i	−0.123940	+	0.702897i
$672$		0			0
$673$	−7.47636	+	6.27341i	−0.288192	+	0.241822i	−0.775409	−	0.631459i	$-0.782456\pi$
$673$	−7.47636	+	6.27341i	−0.288192	+	0.241822i	0.487217	+	0.873281i	$0.338012\pi$
$674$	−23.2607			−0.895968
$675$		0			0
$676$	−28.9847			−1.11480
$677$	31.3165	−	26.2776i	1.20359	−	1.00993i	0.204070	−	0.978956i	$-0.434583\pi$
$677$	31.3165	−	26.2776i	1.20359	−	1.00993i	0.999520	−	0.0309756i	$-0.00986142\pi$
$678$		0			0
$679$	−4.30224	+	24.3992i	−0.165105	+	0.936356i
$680$	−5.04122	+	1.83486i	−0.193322	+	0.0703635i
$681$		0			0
$682$	−2.25634	−	12.7964i	−0.0863999	−	0.489998i
$683$	22.0126	+	38.1269i	0.842287	+	1.45888i	0.887957	+	0.459927i	$0.152125\pi$
$683$	22.0126	+	38.1269i	0.842287	+	1.45888i	−0.0456696	+	0.998957i	$0.514542\pi$
$684$		0			0
$685$	−3.77322	+	6.53541i	−0.144167	+	0.249705i
$686$	92.0740	+	33.5122i	3.51540	+	1.27950i
$687$		0			0
$688$	11.3550	+	9.52797i	0.432905	+	0.363250i
$689$	5.89470	+	4.94624i	0.224570	+	0.188437i
$690$		0			0
$691$	−20.2519	−	7.37108i	−0.770418	−	0.280409i	−0.0732468	−	0.997314i	$-0.523336\pi$
$691$	−20.2519	−	7.37108i	−0.770418	−	0.280409i	−0.697171	+	0.716905i	$0.745558\pi$
$692$	11.4970	−	19.9133i	0.437049	−	0.756991i
$693$		0			0
$694$	3.73302	+	6.46577i	0.141703	+	0.245437i
$695$	−4.77408	−	27.0752i	−0.181091	−	1.02702i
$696$		0			0
$697$	−5.02084	+	1.82743i	−0.190178	+	0.0692190i
$698$	10.7739	−	61.1016i	0.407796	−	2.31273i
$699$		0			0
$700$	−6.64568	+	5.57639i	−0.251183	+	0.210768i
$701$	−12.8521			−0.485419			−0.242709	−	0.970099i	$-0.578036\pi$
$701$	−12.8521			−0.485419			−0.242709	+	0.970099i	$0.578036\pi$
$702$		0			0
$703$	−16.4889			−0.621891
$704$	−36.4177	+	30.5580i	−1.37254	+	1.15170i
$705$		0			0
$706$	9.25353	−	52.4794i	0.348261	−	1.97509i
$707$	−84.6548	+	30.8118i	−3.18377	+	1.15880i
$708$		0			0
$709$	−8.63235	−	48.9565i	−0.324195	−	1.83860i	−0.515276	−	0.857025i	$-0.672310\pi$
$709$	−8.63235	−	48.9565i	−0.324195	−	1.83860i	0.191081	−	0.981574i	$-0.438801\pi$
$710$	−6.78937	−	11.7595i	−0.254800	−	0.441327i
$711$		0			0
$712$	9.29562	−	16.1005i	0.348368	−	0.603392i
$713$	5.95923	+	2.16898i	0.223175	+	0.0812290i
$714$		0			0
$715$	8.00489	+	6.71690i	0.299366	+	0.251198i
$716$	20.4295	+	17.1424i	0.763486	+	0.640641i
$717$		0			0
$718$	8.40133	+	3.05784i	0.313535	+	0.114117i
$719$	2.81873	−	4.88218i	0.105121	−	0.182075i	−0.808667	−	0.588267i	$-0.799810\pi$
$719$	2.81873	−	4.88218i	0.105121	−	0.182075i	0.913788	+	0.406192i	$0.133144\pi$
$720$		0			0
$721$	−21.8330	−	37.8159i	−0.813104	−	1.40834i
$722$	5.76453	+	32.6923i	0.214534	+	1.21668i
$723$		0			0
$724$	3.45839	−	1.25875i	0.128530	−	0.0467811i
$725$	−0.368254	+	2.08847i	−0.0136766	+	0.0775638i
$726$		0			0
$727$	−34.7894	+	29.1917i	−1.29027	+	1.08266i	−0.298525	+	0.954402i	$0.596495\pi$
$727$	−34.7894	+	29.1917i	−1.29027	+	1.08266i	−0.991741	+	0.128260i	$0.959061\pi$
$728$	6.46195			0.239496
$729$		0			0
$730$	56.1546			2.07837
$731$	−9.93117	+	8.33324i	−0.367317	+	0.308216i
$732$		0			0
$733$	−4.45700	+	25.2769i	−0.164623	+	0.933624i	0.784829	+	0.619712i	$0.212751\pi$
$733$	−4.45700	+	25.2769i	−0.164623	+	0.933624i	−0.949452	+	0.313912i	$0.898360\pi$
$734$	34.9386	−	12.7166i	1.28961	−	0.469378i
$735$		0			0
$736$	−5.92978	−	33.6295i	−0.218575	−	1.23960i
$737$	−8.57098	−	14.8454i	−0.315716	−	0.546837i
$738$		0			0
$739$	7.22763	−	12.5186i	0.265873	−	0.460505i	−0.701919	−	0.712256i	$-0.747673\pi$
$739$	7.22763	−	12.5186i	0.265873	−	0.460505i	0.967792	+	0.251752i	$0.0810066\pi$
$740$	43.9203	+	15.9857i	1.61454	+	0.587645i
$741$		0			0
$742$	49.9471	+	41.9106i	1.83362	+	1.53859i
$743$	26.6535	+	22.3650i	0.977824	+	0.820492i	0.983760	−	0.179491i	$-0.0574450\pi$
$743$	26.6535	+	22.3650i	0.977824	+	0.820492i	−0.00593583	+	0.999982i	$0.501889\pi$
$744$		0			0
$745$	17.3412	+	6.31168i	0.635332	+	0.231242i
$746$	−31.5084	+	54.5742i	−1.15360	+	1.99810i
$747$		0			0
$748$	−12.3371	−	21.3685i	−0.451089	−	0.781308i
$749$	6.25310	+	35.4631i	0.228483	+	1.29579i
$750$		0			0
$751$	−17.0258	+	6.19687i	−0.621279	+	0.226127i	−0.633431	−	0.773799i	$-0.718354\pi$
$751$	−17.0258	+	6.19687i	−0.621279	+	0.226127i	0.0121520	+	0.999926i	$0.496132\pi$
$752$	−3.37094	+	19.1176i	−0.122926	+	0.697146i
$753$		0			0
$754$	5.90254	−	4.95282i	0.214958	−	0.180371i
$755$	1.47535			0.0536933
$756$		0			0
$757$	−37.0045			−1.34495			−0.672475	−	0.740120i	$-0.734769\pi$
$757$	−37.0045			−1.34495			−0.672475	+	0.740120i	$0.734769\pi$
$758$	−34.1076	+	28.6197i	−1.23884	+	1.03951i
$759$		0			0
$760$	−0.724413	+	4.10835i	−0.0262772	+	0.149026i
$761$	11.6939	−	4.25624i	0.423905	−	0.154289i	−0.121254	−	0.992621i	$-0.538692\pi$
$761$	11.6939	−	4.25624i	0.423905	−	0.154289i	0.545159	+	0.838333i	$0.316469\pi$
$762$		0			0
$763$	−4.73517	−	26.8545i	−0.171425	−	0.972197i
$764$	−15.6257	−	27.0644i	−0.565316	−	0.979156i
$765$		0			0
$766$	10.5155	−	18.2133i	0.379939	−	0.658074i
$767$	0.299676	+	0.109073i	0.0108207	+	0.00393840i
$768$		0			0
$769$	−31.3202	−	26.2807i	−1.12943	−	0.947707i	−0.130391	−	0.991463i	$-0.541623\pi$
$769$	−31.3202	−	26.2807i	−1.12943	−	0.947707i	−0.999042	+	0.0437551i	$0.986068\pi$
$770$	67.8272	+	56.9138i	2.44432	+	2.05103i
$771$		0			0
$772$	−49.1087	−	17.8741i	−1.76746	−	0.643303i
$773$	18.2081	−	31.5374i	0.654900	−	1.13432i	−0.327019	−	0.945018i	$-0.606044\pi$
$773$	18.2081	−	31.5374i	0.654900	−	1.13432i	0.981919	−	0.189302i	$-0.0606226\pi$
$774$		0			0
$775$	0.524012	+	0.907615i	0.0188231	+	0.0326025i
$776$	0.972463	+	5.51511i	0.0349094	+	0.197981i
$777$		0			0
$778$	−42.1635	+	15.3463i	−1.51164	+	0.550190i
$779$	−0.721484	+	4.09174i	−0.0258498	+	0.146602i
$780$		0			0
$781$	9.80789	−	8.22980i	0.350954	−	0.294485i
$782$	21.6160			0.772985
$783$		0			0
$784$	−44.6174			−1.59348
$785$	21.9214	−	18.3942i	0.782409	−	0.656519i
$786$		0			0
$787$	3.18595	−	18.0684i	0.113567	−	0.644070i	−0.873883	−	0.486136i	$-0.838406\pi$
$787$	3.18595	−	18.0684i	0.113567	−	0.644070i	0.987450	−	0.157933i	$-0.0504831\pi$
$788$	33.5424	−	12.2084i	1.19490	−	0.434908i
$789$		0			0
$790$	3.47891	+	19.7299i	0.123774	+	0.701958i
$791$	5.82488	+	10.0890i	0.207109	+	0.358723i
$792$		0			0
$793$	−2.70904	+	4.69220i	−0.0962009	+	0.166625i
$794$	−19.5276	−	7.10747i	−0.693009	−	0.252235i
$795$		0			0
$796$	39.1768	+	32.8733i	1.38859	+	1.16516i
$797$	2.65429	+	2.22721i	0.0940196	+	0.0788918i	0.688586	−	0.725155i	$-0.258232\pi$
$797$	2.65429	+	2.22721i	0.0940196	+	0.0788918i	−0.594566	+	0.804047i	$0.702676\pi$
$798$		0			0
$799$	−15.9544	−	5.80693i	−0.564426	−	0.205434i
$800$	2.82166	−	4.88726i	0.0997608	−	0.172791i
$801$		0			0
$802$	−20.3358	−	35.2227i	−0.718083	−	1.24376i
$803$	9.19428	+	52.1433i	0.324459	+	1.84010i
$804$		0			0
$805$	−40.6074	+	14.7799i	−1.43122	+	0.520922i
$806$	0.661226	−	3.75000i	0.0232907	−	0.132088i
$807$		0			0
$808$	−15.5991	+	13.0892i	−0.548773	+	0.460475i
$809$	−24.8406			−0.873348			−0.436674	−	0.899620i	$-0.643844\pi$
$809$	−24.8406			−0.873348			−0.436674	+	0.899620i	$0.643844\pi$
$810$		0			0
$811$	−40.3286			−1.41613			−0.708063	−	0.706149i	$-0.750431\pi$
$811$	−40.3286			−1.41613			−0.708063	+	0.706149i	$0.750431\pi$
$812$	27.8628	−	23.3797i	0.977794	−	0.820466i
$813$		0			0
$814$	−13.7364	+	77.9033i	−0.481462	+	2.73051i
$815$	−2.32205	+	0.845157i	−0.0813379	+	0.0296046i
$816$		0			0
$817$	1.75058	+	9.92805i	0.0612451	+	0.347338i
$818$	15.9330	+	27.5968i	0.557084	+	0.964898i
$819$		0			0
$820$	5.88862	−	10.1994i	0.205640	−	0.356178i
$821$	−37.7584	−	13.7429i	−1.31778	−	0.479631i	−0.415031	−	0.909807i	$-0.636229\pi$
$821$	−37.7584	−	13.7429i	−1.31778	−	0.479631i	−0.902745	+	0.430176i	$0.858452\pi$
$822$		0			0
$823$	−36.7359	−	30.8251i	−1.28053	−	1.07450i	−0.993170	−	0.116675i	$-0.962776\pi$
$823$	−36.7359	−	30.8251i	−1.28053	−	1.07450i	−0.287364	−	0.957821i	$-0.592779\pi$
$824$	−7.56095	−	6.34439i	−0.263398	−	0.221017i
$825$		0			0
$826$	2.53922	+	0.924200i	0.0883507	+	0.0321570i
$827$	2.50024	−	4.33054i	0.0869419	−	0.150588i	−0.819275	−	0.573401i	$-0.805624\pi$
$827$	2.50024	−	4.33054i	0.0869419	−	0.150588i	0.906217	+	0.422813i	$0.138957\pi$
$828$		0			0
$829$	−14.8519	−	25.7242i	−0.515826	−	0.893438i	−0.999831	−	0.0183722i	$-0.994152\pi$
$829$	−14.8519	−	25.7242i	−0.515826	−	0.893438i	0.484005	−	0.875065i	$-0.339182\pi$
$830$	−6.45976	−	36.6351i	−0.224222	−	1.27162i
$831$		0			0
$832$	−13.0915	+	4.76490i	−0.453865	+	0.165193i
$833$	6.77624	−	38.4299i	0.234783	−	1.33152i
$834$		0			0
$835$	37.9734	−	31.8634i	1.31412	−	1.10268i
$836$	−19.1871			−0.663599
$837$		0			0
$838$	−12.3502			−0.426632
$839$	−19.8440	+	16.6511i	−0.685092	+	0.574860i	−0.917489	−	0.397761i	$-0.869787\pi$
$839$	−19.8440	+	16.6511i	−0.685092	+	0.574860i	0.232398	+	0.972621i	$0.425343\pi$
$840$		0			0
$841$	−3.49185	+	19.8033i	−0.120409	+	0.682871i
$842$	−26.5854	+	9.67630i	−0.916194	+	0.333467i
$843$		0			0
$844$	−4.30884	−	24.4366i	−0.148316	−	0.841144i
$845$	−11.9300	−	20.6633i	−0.410403	−	0.710840i
$846$		0			0
$847$	−15.0751	+	26.1109i	−0.517988	+	0.897182i
$848$	−16.0702	−	5.84908i	−0.551853	−	0.200858i
$849$		0			0
$850$	2.73650	+	2.29619i	0.0938611	+	0.0787588i
$851$	−29.5752	−	24.8165i	−1.01382	−	0.850700i
$852$		0			0
$853$	4.69063	+	1.70725i	0.160604	+	0.0584551i	0.421071	−	0.907028i	$-0.361654\pi$
$853$	4.69063	+	1.70725i	0.160604	+	0.0584551i	−0.260467	+	0.965483i	$0.583877\pi$
$854$	−22.9543	+	39.7580i	−0.785481	+	1.36049i
$855$		0			0
$856$	4.06980	+	7.04911i	0.139103	+	0.240934i
$857$	−2.54968	−	14.4599i	−0.0870954	−	0.493942i	−0.996885	−	0.0788722i	$-0.974868\pi$
$857$	−2.54968	−	14.4599i	−0.0870954	−	0.493942i	0.909789	−	0.415070i	$-0.136243\pi$
$858$		0			0
$859$	16.4304	−	5.98017i	0.560598	−	0.204041i	−0.0461511	−	0.998934i	$-0.514696\pi$
$859$	16.4304	−	5.98017i	0.560598	−	0.204041i	0.606749	+	0.794894i	$0.292473\pi$
$860$	4.96215	−	28.1418i	0.169208	−	0.959626i
$861$		0			0
$862$	59.2814	−	49.7430i	2.01913	−	1.69425i
$863$	6.33263			0.215565			0.107783	−	0.994174i	$-0.465625\pi$
$863$	6.33263			0.215565			0.107783	+	0.994174i	$0.465625\pi$
$864$		0			0
$865$	18.9284			0.643585
$866$	17.7049	−	14.8562i	0.601637	−	0.504833i
$867$		0			0
$868$	3.12130	−	17.7018i	0.105944	−	0.600838i
$869$	−17.7509	+	6.46082i	−0.602160	+	0.219168i
$870$		0			0
$871$	−0.872319	−	4.94717i	−0.0295574	−	0.167628i
$872$	−3.08187	−	5.33795i	−0.104365	−	0.180766i
$873$		0			0
$874$	8.40448	−	14.5570i	0.284286	−	0.492397i
$875$	−53.8895	−	19.6142i	−1.82180	−	0.663080i
$876$		0			0
$877$	24.9202	+	20.9105i	0.841495	+	0.706098i	0.957899	−	0.287104i	$-0.0926925\pi$
$877$	24.9202	+	20.9105i	0.841495	+	0.706098i	−0.116405	+	0.993202i	$0.537137\pi$
$878$	−15.3887	−	12.9126i	−0.519342	−	0.435780i
$879$		0			0
$880$	−21.8230	−	7.94294i	−0.735655	−	0.267756i
$881$	16.6800	−	28.8906i	0.561963	−	0.973348i	−0.435363	−	0.900255i	$-0.643380\pi$
$881$	16.6800	−	28.8906i	0.561963	−	0.973348i	0.997325	−	0.0730926i	$-0.0232869\pi$
$882$		0			0
$883$	27.4256	+	47.5025i	0.922944	+	1.59859i	0.794835	+	0.606826i	$0.207557\pi$
$883$	27.4256	+	47.5025i	0.922944	+	1.59859i	0.128109	+	0.991760i	$0.459109\pi$
$884$	−1.25562	−	7.12096i	−0.0422310	−	0.239504i
$885$		0			0
$886$	32.9962	−	12.0096i	1.10853	−	0.403471i
$887$	3.65490	−	20.7280i	0.122720	−	0.695978i	−0.859917	−	0.510435i	$-0.829485\pi$
$887$	3.65490	−	20.7280i	0.122720	−	0.695978i	0.982636	−	0.185543i	$-0.0594044\pi$
$888$		0			0
$889$	−34.3004	+	28.7815i	−1.15040	+	0.965299i
$890$	74.6516			2.50233
$891$		0			0
$892$	37.9158			1.26951
$893$	−10.1138	+	8.48649i	−0.338446	+	0.283990i
$894$		0			0
$895$	−3.81219	+	21.6200i	−0.127427	+	0.722677i
$896$	−38.6202	+	14.0566i	−1.29021	+	0.469598i
$897$		0			0
$898$	1.75043	+	9.92718i	0.0584126	+	0.331274i
$899$	−2.19698	−	3.80529i	−0.0732735	−	0.126914i
$900$		0			0
$901$	7.47859	−	12.9533i	0.249148	−	0.431537i
$902$	18.7307	+	6.81742i	0.623665	+	0.226995i
$903$		0			0
$904$	2.01720	+	1.69263i	0.0670911	+	0.0562962i
$905$	2.32082	+	1.94740i	0.0771468	+	0.0647339i
$906$		0			0
$907$	−13.9432	−	5.07491i	−0.462976	−	0.168509i	0.0999919	−	0.994988i	$-0.468118\pi$
$907$	−13.9432	−	5.07491i	−0.462976	−	0.168509i	−0.562968	+	0.826479i	$0.690341\pi$
$908$	28.5444	−	49.4403i	0.947278	−	1.64073i
$909$		0			0
$910$	12.9737	+	22.4711i	0.430074	+	0.744911i
$911$	3.13080	+	17.7556i	0.103728	+	0.588270i	0.991721	+	0.128413i	$0.0409883\pi$
$911$	3.13080	+	17.7556i	0.103728	+	0.588270i	−0.887993	+	0.459857i	$0.847901\pi$
$912$		0			0
$913$	32.9605	−	11.9967i	1.09083	−	0.397031i
$914$	8.26892	−	46.8954i	0.273512	−	1.55116i
$915$		0			0
$916$	16.7986	−	14.0957i	0.555041	−	0.465735i
$917$	−74.3738			−2.45604
$918$		0			0
$919$	13.4881			0.444932			0.222466	−	0.974940i	$-0.428589\pi$
$919$	13.4881			0.444932			0.222466	+	0.974940i	$0.428589\pi$
$920$	−7.48259	+	6.27864i	−0.246694	+	0.207001i
$921$		0			0
$922$	5.50642	−	31.2285i	0.181344	−	1.02846i
$923$	3.52575	−	1.28327i	0.116052	−	0.0422393i
$924$		0			0
$925$	−1.10793	−	6.28336i	−0.0364284	−	0.206595i
$926$	−15.7753	−	27.3237i	−0.518410	−	0.897912i
$927$		0			0
$928$	−11.8302	+	20.4905i	−0.388344	+	0.672632i
$929$	35.3523	+	12.8672i	1.15987	+	0.422159i	0.849052	−	0.528310i	$-0.177174\pi$
$929$	35.3523	+	12.8672i	1.15987	+	0.422159i	0.310820	+	0.950469i	$0.399396\pi$
$930$		0			0
$931$	−23.2455	−	19.5053i	−0.761839	−	0.639259i
$932$	−45.4600	−	38.1455i	−1.48909	−	1.24950i
$933$		0			0
$934$	−30.6549	−	11.1575i	−1.00306	−	0.365083i
$935$	10.1558	−	17.5903i	0.332129	−	0.575265i
$936$		0			0
$937$	−2.07229	−	3.58931i	−0.0676988	−	0.117258i	0.830189	−	0.557482i	$-0.188232\pi$
$937$	−2.07229	−	3.58931i	−0.0676988	−	0.117258i	−0.897888	+	0.440224i	$0.854899\pi$
$938$	−7.39135	−	41.9185i	−0.241336	−	1.36869i
$939$		0			0
$940$	35.1669	−	12.7997i	1.14702	−	0.417480i
$941$	−0.613035	+	3.47669i	−0.0199844	+	0.113337i	−0.993168	−	0.116692i	$-0.962771\pi$
$941$	−0.613035	+	3.47669i	−0.0199844	+	0.113337i	0.973184	+	0.230029i	$0.0738821\pi$
$942$		0			0
$943$	−7.45233	+	6.25325i	−0.242681	+	0.203634i
$944$	−0.708752			−0.0230679
$945$		0			0
$946$	48.3643			1.57246
$947$	−10.9200	+	9.16299i	−0.354853	+	0.297757i	−0.802735	−	0.596335i	$-0.796623\pi$
$947$	−10.9200	+	9.16299i	−0.354853	+	0.297757i	0.447882	+	0.894093i	$0.352178\pi$
$948$		0			0
$949$	−2.69440	+	15.2807i	−0.0874639	+	0.496033i
$950$	2.61032	−	0.950077i	0.0846898	−	0.0308246i
$951$		0			0
$952$	−2.18110	−	12.3696i	−0.0706899	−	0.400902i
$953$	−5.82130	−	10.0828i	−0.188570	−	0.326613i	0.756204	−	0.654336i	$-0.227052\pi$
$953$	−5.82130	−	10.0828i	−0.188570	−	0.326613i	−0.944774	+	0.327723i	$0.893719\pi$
$954$		0			0
$955$	12.8629	−	22.2792i	0.416233	−	0.720938i
$956$	−23.5328	−	8.56523i	−0.761104	−	0.277019i
$957$		0			0
$958$	−17.0089	−	14.2722i	−0.549534	−	0.461114i
$959$	−13.5348	−	11.3570i	−0.437061	−	0.366738i
$960$		0			0
$961$	27.0900	+	9.85994i	0.873870	+	0.318063i
$962$	−11.5909	+	20.0761i	−0.373707	+	0.647279i
$963$		0			0
$964$	−7.18680	−	12.4479i	−0.231471	−	0.400920i
$965$	−7.47039	−	42.3667i	−0.240480	−	1.36383i
$966$		0			0
$967$	−27.3151	+	9.94189i	−0.878395	+	0.319709i	−0.741562	−	0.670885i	$-0.765915\pi$
$967$	−27.3151	+	9.94189i	−0.878395	+	0.319709i	−0.136833	+	0.990594i	$0.543692\pi$
$968$	−1.18342	+	6.71153i	−0.0380367	+	0.215717i
$969$		0			0
$970$	−17.2261	+	14.4544i	−0.553098	+	0.464104i
$971$	47.5792			1.52689			0.763444	−	0.645874i	$-0.223507\pi$
$971$	47.5792			1.52689			0.763444	+	0.645874i	$0.223507\pi$
$972$		0			0
$973$	64.3687			2.06357
$974$	26.3143	−	22.0803i	0.843163	−	0.707498i
$975$		0			0
$976$	2.09095	−	11.8584i	0.0669298	−	0.379578i
$977$	−5.74744	+	2.09190i	−0.183877	+	0.0669258i	−0.432318	−	0.901721i	$-0.642304\pi$
$977$	−5.74744	+	2.09190i	−0.183877	+	0.0669258i	0.248441	+	0.968647i	$0.420082\pi$
$978$		0			0
$979$	12.2228	+	69.3191i	0.390643	+	2.21545i
$980$	43.0073	+	74.4908i	1.37382	+	2.37952i
$981$		0			0
$982$	−11.4511	+	19.8339i	−0.365419	+	0.632924i
$983$	−10.0094	−	3.64313i	−0.319251	−	0.116198i	0.177424	−	0.984135i	$-0.443224\pi$
$983$	−10.0094	−	3.64313i	−0.319251	−	0.116198i	−0.496675	+	0.867937i	$0.665446\pi$
$984$		0			0
$985$	22.5093	+	18.8876i	0.717208	+	0.601809i
$986$	−11.4731	−	9.62708i	−0.365378	−	0.306589i
$987$		0			0
$988$	−5.28371	−	1.92311i	−0.168097	−	0.0611824i
$989$	−11.8022	+	20.4421i	−0.375289	+	0.650020i
$990$		0			0
$991$	−11.9928	−	20.7721i	−0.380964	−	0.659849i	0.610236	−	0.792219i	$-0.291074\pi$
$991$	−11.9928	−	20.7721i	−0.380964	−	0.659849i	−0.991200	+	0.132371i	$0.957741\pi$
$992$	2.03042	+	11.5151i	0.0644659	+	0.365604i
$993$		0			0
$994$	29.8745	−	10.8734i	0.947561	−	0.344884i
$995$	−7.31048	+	41.4598i	−0.231758	+	1.31436i
$996$		0			0
$997$	3.30485	−	2.77310i	0.104666	−	0.0878250i	−0.588953	−	0.808167i	$-0.700460\pi$
$997$	3.30485	−	2.77310i	0.104666	−	0.0878250i	0.693619	+	0.720342i	$0.256015\pi$
$998$	40.7733			1.29066
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	729.2.e.t.325.1		12
3.2	odd	2		729.2.e.k.325.2		12
9.2	odd	6		729.2.e.l.568.1		12
9.4	even	3		729.2.e.j.82.1		12
9.5	odd	6		729.2.e.u.82.2		12
9.7	even	3		729.2.e.s.568.2		12
27.2	odd	18		729.2.e.l.163.1		12
27.4	even	9		729.2.a.b.1.2	✓	6
27.5	odd	18		729.2.c.a.244.2		12
27.7	even	9		729.2.e.j.649.1		12
27.11	odd	18		729.2.e.k.406.2		12
27.13	even	9		729.2.c.d.487.5		12
27.14	odd	18		729.2.c.a.487.2		12
27.16	even	9	inner	729.2.e.t.406.1		12
27.20	odd	18		729.2.e.u.649.2		12
27.22	even	9		729.2.c.d.244.5		12
27.23	odd	18		729.2.a.e.1.5	yes	6
27.25	even	9		729.2.e.s.163.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
729.2.a.b.1.2	✓	6	27.4	even	9
729.2.a.e.1.5	yes	6	27.23	odd	18
729.2.c.a.244.2		12	27.5	odd	18
729.2.c.a.487.2		12	27.14	odd	18
729.2.c.d.244.5		12	27.22	even	9
729.2.c.d.487.5		12	27.13	even	9
729.2.e.j.82.1		12	9.4	even	3
729.2.e.j.649.1		12	27.7	even	9
729.2.e.k.325.2		12	3.2	odd	2
729.2.e.k.406.2		12	27.11	odd	18
729.2.e.l.163.1		12	27.2	odd	18
729.2.e.l.568.1		12	9.2	odd	6
729.2.e.s.163.2		12	27.25	even	9
729.2.e.s.568.2		12	9.7	even	3
729.2.e.t.325.1		12	1.1	even	1	trivial
729.2.e.t.406.1		12	27.16	even	9	inner
729.2.e.u.82.2		12	9.5	odd	6
729.2.e.u.649.2		12	27.20	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:	\( N \)	\(=\)	\( 729 = 3^{6} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	729.e (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.62787 + 1.36594i) q^{2} +(0.436855 - 2.47753i) q^{4} +(1.94605 - 0.708303i) q^{5} +(0.841963 + 4.77501i) q^{7} +(0.547989 + 0.949144i) q^{8} +(-2.20040 + 3.81121i) q^{10} +(-3.89924 - 1.41921i) q^{11} +(-0.931522 - 0.781640i) q^{13} +(-7.89299 - 6.62301i) q^{14} +(2.53953 + 0.924313i) q^{16} +(-1.18182 + 2.04697i) q^{17} +(0.919003 + 1.59176i) q^{19} +(-0.904700 - 5.13081i) q^{20} +(8.28601 - 3.01586i) q^{22} +(-0.747307 + 4.23819i) q^{23} +(-0.544815 + 0.457154i) q^{25} +2.58407 q^{26} +12.1980 q^{28} +(2.28421 - 1.91668i) q^{29} +(0.255886 - 1.45120i) q^{31} +(-7.45634 + 2.71388i) q^{32} +(-0.872200 - 4.94649i) q^{34} +(5.02066 + 8.69603i) q^{35} +(-4.48554 + 7.76918i) q^{37} +(-3.67027 - 1.33587i) q^{38} +(1.73869 + 1.45894i) q^{40} +(1.73166 + 1.45304i) q^{41} +(5.15408 + 1.87593i) q^{43} +(-5.21953 + 9.04050i) q^{44} +(-4.57260 - 7.91998i) q^{46} +(1.24734 + 7.07400i) q^{47} +(-15.5140 + 5.64663i) q^{49} +(0.262440 - 1.48837i) q^{50} +(-2.34347 + 1.96641i) q^{52} -6.32803 q^{53} -8.59334 q^{55} +(-4.07079 + 3.41580i) q^{56} +(-1.10031 + 6.24019i) q^{58} +(-0.246441 + 0.0896971i) q^{59} +(-0.773708 - 4.38792i) q^{61} +(1.56571 + 2.71188i) q^{62} +(5.72840 - 9.92188i) q^{64} +(-2.36642 - 0.861308i) q^{65} +(3.16461 + 2.65542i) q^{67} +(4.55514 + 3.82222i) q^{68} +(-20.0512 - 7.29805i) q^{70} +(-1.54276 + 2.67213i) q^{71} +(-6.38003 - 11.0505i) q^{73} +(-3.31040 - 18.7742i) q^{74} +(4.34510 - 1.58149i) q^{76} +(3.49372 - 19.8139i) q^{77} +(3.48735 - 2.92623i) q^{79} +5.59674 q^{80} -4.80368 q^{82} +(-6.47542 + 5.43352i) q^{83} +(-0.850000 + 4.82059i) q^{85} +(-10.9526 + 3.98641i) q^{86} +(-0.789708 - 4.47866i) q^{88} +(-8.48158 - 14.6905i) q^{89} +(2.94803 - 5.10614i) q^{91} +(10.1738 + 3.70295i) q^{92} +(-11.6932 - 9.81174i) q^{94} +(2.91587 + 2.44671i) q^{95} +(4.80161 + 1.74764i) q^{97} +(17.5417 - 30.3831i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 3 q^{2} - 3 q^{4} + 6 q^{5} + 6 q^{7} + 6 q^{8} - 6 q^{10} - 15 q^{11} - 3 q^{13} - 21 q^{14} + 9 q^{16} - 9 q^{17} - 12 q^{19} - 3 q^{20} + 33 q^{22} + 15 q^{23} - 12 q^{25} - 48 q^{26} + 6 q^{28}+ \cdots + 18 q^{98}+O(q^{100}) \) 12 * q + 3 * q^2 - 3 * q^4 + 6 * q^5 + 6 * q^7 + 6 * q^8 - 6 * q^10 - 15 * q^11 - 3 * q^13 - 21 * q^14 + 9 * q^16 - 9 * q^17 - 12 * q^19 - 3 * q^20 + 33 * q^22 + 15 * q^23 - 12 * q^25 - 48 * q^26 + 6 * q^28 - 6 * q^29 - 12 * q^31 - 27 * q^32 + 27 * q^34 + 30 * q^35 - 3 * q^37 - 39 * q^38 + 24 * q^40 - 39 * q^41 + 24 * q^43 - 33 * q^44 + 3 * q^46 - 42 * q^47 - 30 * q^49 - 15 * q^50 - 45 * q^52 + 18 * q^53 + 30 * q^55 + 12 * q^56 - 30 * q^58 + 15 * q^59 - 3 * q^61 - 30 * q^62 - 6 * q^64 - 6 * q^65 - 3 * q^67 + 36 * q^68 - 75 * q^70 - 12 * q^73 + 60 * q^74 + 30 * q^76 + 33 * q^77 + 33 * q^79 + 42 * q^80 - 42 * q^82 - 33 * q^83 - 18 * q^85 - 30 * q^86 - 42 * q^88 - 9 * q^89 - 18 * q^91 + 33 * q^92 - 66 * q^94 + 12 * q^95 + 15 * q^97 + 18 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more