LMFDB - Embedded newform 729.2.c.c.487.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [729,2,Mod(244,729)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(729, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("729.244");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$5.82109430735$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\zeta_{36})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{6} + 1 $ x^12 - x^6 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			487.4
Root			$-0.342020 + 0.939693i$ of defining polynomial
Character	$\chi$	$=$	729.487
Dual form			729.2.c.c.244.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.342020 - 0.592396i) q^{2} +(0.766044 + 1.32683i) q^{4} +(0.524005 + 0.907604i) q^{5} +(0.0603074 - 0.104455i) q^{7} +2.41609 q^{8} +O(q^{10})$	\(q+(0.342020 - 0.592396i) q^{2} +(0.766044 + 1.32683i) q^{4} +(0.524005 + 0.907604i) q^{5} +(0.0603074 - 0.104455i) q^{7} +2.41609 q^{8} +0.716881 q^{10} +(-2.71686 + 4.70574i) q^{11} +(2.28699 + 3.96118i) q^{13} +(-0.0412527 - 0.0714517i) q^{14} +(-0.705737 + 1.22237i) q^{16} -4.77833 q^{17} -0.588526 q^{19} +(-0.802823 + 1.39053i) q^{20} +(1.85844 + 3.21891i) q^{22} +(-3.89798 - 6.75150i) q^{23} +(1.95084 - 3.37895i) q^{25} +3.12879 q^{26} +0.184793 q^{28} +(2.53487 - 4.39053i) q^{29} +(4.37939 + 7.58532i) q^{31} +(2.89884 + 5.02094i) q^{32} +(-1.63429 + 2.83067i) q^{34} +0.126406 q^{35} -2.18479 q^{37} +(-0.201288 + 0.348641i) q^{38} +(1.26604 + 2.19285i) q^{40} +(3.77920 + 6.54576i) q^{41} +(0.652704 - 1.13052i) q^{43} -8.32494 q^{44} -5.33275 q^{46} +(1.20805 - 2.09240i) q^{47} +(3.49273 + 6.04958i) q^{49} +(-1.33445 - 2.31134i) q^{50} +(-3.50387 + 6.06888i) q^{52} +3.04628 q^{53} -5.69459 q^{55} +(0.145708 - 0.252374i) q^{56} +(-1.73396 - 3.00330i) q^{58} +(-0.0219501 - 0.0380187i) q^{59} +(5.10607 - 8.84397i) q^{61} +5.99135 q^{62} +1.14290 q^{64} +(-2.39679 + 4.15136i) q^{65} +(0.929892 + 1.61062i) q^{67} +(-3.66041 - 6.34002i) q^{68} +(0.0432332 - 0.0748822i) q^{70} +6.51038 q^{71} +12.2344 q^{73} +(-0.747243 + 1.29426i) q^{74} +(-0.450837 - 0.780873i) q^{76} +(0.327693 + 0.567581i) q^{77} +(-0.351167 + 0.608239i) q^{79} -1.47924 q^{80} +5.17024 q^{82} +(3.38830 - 5.86871i) q^{83} +(-2.50387 - 4.33683i) q^{85} +(-0.446476 - 0.773318i) q^{86} +(-6.56418 + 11.3695i) q^{88} -6.85565 q^{89} +0.551689 q^{91} +(5.97205 - 10.3439i) q^{92} +(-0.826352 - 1.43128i) q^{94} +(-0.308391 - 0.534148i) q^{95} +(4.51367 - 7.81791i) q^{97} +4.77833 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 12 q^{7}+O(q^{10}) $ 12 * q + 12 * q^7	$ 12 q + 12 q^{7} - 24 q^{10} + 12 q^{13} + 12 q^{16} - 48 q^{19} + 6 q^{22} - 12 q^{28} + 30 q^{31} - 12 q^{37} + 6 q^{40} + 12 q^{43} + 12 q^{46} + 6 q^{49} + 6 q^{52} - 60 q^{55} - 30 q^{58} + 12 q^{61} + 12 q^{64} - 6 q^{67} - 30 q^{70} + 24 q^{73} + 18 q^{76} + 48 q^{79} - 24 q^{82} + 18 q^{85} - 42 q^{88} - 12 q^{94} + 12 q^{97}+O(q^{100}) $ 12 * q + 12 * q^7 - 24 * q^10 + 12 * q^13 + 12 * q^16 - 48 * q^19 + 6 * q^22 - 12 * q^28 + 30 * q^31 - 12 * q^37 + 6 * q^40 + 12 * q^43 + 12 * q^46 + 6 * q^49 + 6 * q^52 - 60 * q^55 - 30 * q^58 + 12 * q^61 + 12 * q^64 - 6 * q^67 - 30 * q^70 + 24 * q^73 + 18 * q^76 + 48 * q^79 - 24 * q^82 + 18 * q^85 - 42 * q^88 - 12 * q^94 + 12 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	0.342020	−	0.592396i	0.241845	−	0.418887i	−0.719395	−	0.694601i	$-0.755581\pi$
$2$	0.342020	−	0.592396i	0.241845	−	0.418887i	0.961240	+	0.275714i	$0.0889142\pi$
$3$		0			0
$3$		0			0
$4$	0.766044	+	1.32683i	0.383022	+	0.663414i
$5$	0.524005	+	0.907604i	0.234342	+	0.405893i	0.959081	−	0.283131i	$-0.0913730\pi$
$5$	0.524005	+	0.907604i	0.234342	+	0.405893i	−0.724739	+	0.689023i	$0.758040\pi$
$6$		0			0
$7$	0.0603074	−	0.104455i	0.0227940	−	0.0394804i	−0.854403	−	0.519610i	$-0.826077\pi$
$7$	0.0603074	−	0.104455i	0.0227940	−	0.0394804i	0.877197	+	0.480130i	$0.159410\pi$
$8$	2.41609			0.854217
$9$		0			0
$10$	0.716881			0.226698
$11$	−2.71686	+	4.70574i	−0.819164	+	1.41883i	0.0871355	+	0.996196i	$0.472229\pi$
$11$	−2.71686	+	4.70574i	−0.819164	+	1.41883i	−0.906299	+	0.422637i	$0.861105\pi$
$12$		0			0
$13$	2.28699	+	3.96118i	0.634297	+	1.09863i	0.986664	+	0.162772i	$0.0520435\pi$
$13$	2.28699	+	3.96118i	0.634297	+	1.09863i	−0.352367	+	0.935862i	$0.614623\pi$
$14$	−0.0412527	−	0.0714517i	−0.0110252	−	0.0190963i
$15$		0			0
$16$	−0.705737	+	1.22237i	−0.176434	+	0.305593i
$17$	−4.77833			−1.15892			−0.579458	−	0.815002i	$-0.696736\pi$
$17$	−4.77833			−1.15892			−0.579458	+	0.815002i	$0.696736\pi$
$18$		0			0
$19$	−0.588526			−0.135017			−0.0675085	−	0.997719i	$-0.521505\pi$
$19$	−0.588526			−0.135017			−0.0675085	+	0.997719i	$0.521505\pi$
$20$	−0.802823	+	1.39053i	−0.179517	+	0.310932i
$21$		0			0
$22$	1.85844	+	3.21891i	0.396221	+	0.686275i
$23$	−3.89798	−	6.75150i	−0.812785	−	1.40778i	−0.910908	−	0.412610i	$-0.864617\pi$
$23$	−3.89798	−	6.75150i	−0.812785	−	1.40778i	0.0981231	−	0.995174i	$-0.468716\pi$
$24$		0			0
$25$	1.95084	−	3.37895i	0.390167	−	0.675790i
$26$	3.12879			0.613605
$27$		0			0
$28$	0.184793			0.0349225
$29$	2.53487	−	4.39053i	0.470714	−	0.815301i	−0.528725	−	0.848793i	$-0.677330\pi$
$29$	2.53487	−	4.39053i	0.470714	−	0.815301i	0.999439	+	0.0334924i	$0.0106630\pi$
$30$		0			0
$31$	4.37939	+	7.58532i	0.786561	+	1.36236i	0.928062	+	0.372425i	$0.121474\pi$
$31$	4.37939	+	7.58532i	0.786561	+	1.36236i	−0.141501	+	0.989938i	$0.545193\pi$
$32$	2.89884	+	5.02094i	0.512448	+	0.887586i
$33$		0			0
$34$	−1.63429	+	2.83067i	−0.280278	+	0.485455i
$35$	0.126406			0.0213664
$36$		0			0
$37$	−2.18479			−0.359178			−0.179589	−	0.983742i	$-0.557477\pi$
$37$	−2.18479			−0.359178			−0.179589	+	0.983742i	$0.557477\pi$
$38$	−0.201288	+	0.348641i	−0.0326532	+	0.0565570i
$39$		0			0
$40$	1.26604	+	2.19285i	0.200179	+	0.346721i
$41$	3.77920	+	6.54576i	0.590211	+	1.02228i	0.994204	+	0.107514i	$0.0342889\pi$
$41$	3.77920	+	6.54576i	0.590211	+	1.02228i	−0.403992	+	0.914762i	$0.632378\pi$
$42$		0			0
$43$	0.652704	−	1.13052i	0.0995364	−	0.172402i	−0.811956	−	0.583718i	$-0.801597\pi$
$43$	0.652704	−	1.13052i	0.0995364	−	0.172402i	0.911493	+	0.411316i	$0.134931\pi$
$44$	−8.32494			−1.25503
$45$		0			0
$46$	−5.33275			−0.786271
$47$	1.20805	−	2.09240i	0.176212	−	0.305207i	−0.764368	−	0.644780i	$-0.776949\pi$
$47$	1.20805	−	2.09240i	0.176212	−	0.305207i	0.940580	+	0.339572i	$0.110282\pi$
$48$		0			0
$49$	3.49273	+	6.04958i	0.498961	+	0.864226i
$50$	−1.33445	−	2.31134i	−0.188720	−	0.326872i
$51$		0			0
$52$	−3.50387	+	6.06888i	−0.485899	+	0.841602i
$53$	3.04628			0.418439			0.209219	−	0.977869i	$-0.432908\pi$
$53$	3.04628			0.418439			0.209219	+	0.977869i	$0.432908\pi$
$54$		0			0
$55$	−5.69459			−0.767859
$56$	0.145708	−	0.252374i	0.0194711	−	0.0337249i
$57$		0			0
$58$	−1.73396	−	3.00330i	−0.227680	−	0.394352i
$59$	−0.0219501	−	0.0380187i	−0.00285766	−	0.00494961i	0.864593	−	0.502473i	$-0.167576\pi$
$59$	−0.0219501	−	0.0380187i	−0.00285766	−	0.00494961i	−0.867451	+	0.497523i	$0.834243\pi$
$60$		0			0
$61$	5.10607	−	8.84397i	0.653765	−	1.13235i	−0.328437	−	0.944526i	$-0.606522\pi$
$61$	5.10607	−	8.84397i	0.653765	−	1.13235i	0.982202	−	0.187828i	$-0.0601448\pi$
$62$	5.99135			0.760902
$63$		0			0
$64$	1.14290			0.142863
$65$	−2.39679	+	4.15136i	−0.297285	+	0.514913i
$66$		0			0
$67$	0.929892	+	1.61062i	0.113604	+	0.196769i	0.917221	−	0.398379i	$-0.130427\pi$
$67$	0.929892	+	1.61062i	0.113604	+	0.196769i	−0.803617	+	0.595147i	$0.797094\pi$
$68$	−3.66041	−	6.34002i	−0.443890	−	0.768841i
$69$		0			0
$70$	0.0432332	−	0.0748822i	0.00516736	−	0.00895013i
$71$	6.51038			0.772640			0.386320	−	0.922365i	$-0.373746\pi$
$71$	6.51038			0.772640			0.386320	+	0.922365i	$0.373746\pi$
$72$		0			0
$73$	12.2344			1.43193			0.715965	−	0.698136i	$-0.245987\pi$
$73$	12.2344			1.43193			0.715965	+	0.698136i	$0.245987\pi$
$74$	−0.747243	+	1.29426i	−0.0868652	+	0.150455i
$75$		0			0
$76$	−0.450837	−	0.780873i	−0.0517145	−	0.0895722i
$77$	0.327693	+	0.567581i	0.0373441	+	0.0646819i
$78$		0			0
$79$	−0.351167	+	0.608239i	−0.0395093	+	0.0684322i	−0.885104	−	0.465394i	$-0.845913\pi$
$79$	−0.351167	+	0.608239i	−0.0395093	+	0.0684322i	0.845595	+	0.533826i	$0.179246\pi$
$80$	−1.47924			−0.165384
$81$		0			0
$82$	5.17024			0.570958
$83$	3.38830	−	5.86871i	0.371914	−	0.644174i	−0.617946	−	0.786221i	$-0.712035\pi$
$83$	3.38830	−	5.86871i	0.371914	−	0.644174i	0.989860	+	0.142046i	$0.0453682\pi$
$84$		0			0
$85$	−2.50387	−	4.33683i	−0.271583	−	0.470395i
$86$	−0.446476	−	0.773318i	−0.0481447	−	0.0833891i
$87$		0			0
$88$	−6.56418	+	11.3695i	−0.699744	+	1.21199i
$89$	−6.85565			−0.726697			−0.363349	−	0.931653i	$-0.618367\pi$
$89$	−6.85565			−0.726697			−0.363349	+	0.931653i	$0.618367\pi$
$90$		0			0
$91$	0.551689			0.0578327
$92$	5.97205	−	10.3439i	0.622629	−	1.07843i
$93$		0			0
$94$	−0.826352	−	1.43128i	−0.0852317	−	0.147626i
$95$	−0.308391	−	0.534148i	−0.0316402	−	0.0548025i
$96$		0			0
$97$	4.51367	−	7.81791i	0.458294	−	0.793788i	−0.540577	−	0.841294i	$-0.681794\pi$
$97$	4.51367	−	7.81791i	0.458294	−	0.793788i	0.998871	+	0.0475063i	$0.0151274\pi$
$98$	4.77833			0.482684
$99$		0			0
$100$	5.97771			0.597771
$101$	6.49605	−	11.2515i	0.646382	−	1.11957i	−0.337599	−	0.941290i	$-0.609615\pi$
$101$	6.49605	−	11.2515i	0.646382	−	1.11957i	0.983981	−	0.178276i	$-0.0570519\pi$
$102$		0			0
$103$	−4.53596	−	7.85651i	−0.446941	−	0.774125i	0.551244	−	0.834344i	$-0.314153\pi$
$103$	−4.53596	−	7.85651i	−0.446941	−	0.774125i	−0.998185	+	0.0602191i	$0.980820\pi$
$104$	5.52557	+	9.57057i	0.541827	+	0.938472i
$105$		0			0
$106$	1.04189	−	1.80460i	0.101197	−	0.175279i
$107$	−11.3865			−1.10077			−0.550386	−	0.834911i	$-0.685519\pi$
$107$	−11.3865			−1.10077			−0.550386	+	0.834911i	$0.685519\pi$
$108$		0			0
$109$	2.89899			0.277672			0.138836	−	0.990315i	$-0.455664\pi$
$109$	2.89899			0.277672			0.138836	+	0.990315i	$0.455664\pi$
$110$	−1.94767	+	3.37346i	−0.185703	+	0.321646i
$111$		0			0
$112$	0.0851223	+	0.147436i	0.00804330	+	0.0139314i
$113$	−5.79006	−	10.0287i	−0.544683	−	0.943419i	−0.998627	−	0.0523888i	$-0.983316\pi$
$113$	−5.79006	−	10.0287i	−0.544683	−	0.943419i	0.453943	−	0.891031i	$-0.350017\pi$
$114$		0			0
$115$	4.08512	−	7.07564i	0.380940	−	0.659807i
$116$	7.76730			0.721176
$117$		0			0
$118$	−0.0300295			−0.00276444
$119$	−0.288169	+	0.499123i	−0.0264164	+	0.0457545i
$120$		0			0
$121$	−9.26264	−	16.0434i	−0.842058	−	1.45849i
$122$	−3.49276	−	6.04963i	−0.316219	−	0.547708i
$123$		0			0
$124$	−6.70961	+	11.6214i	−0.602541	+	1.04363i
$125$	9.32905			0.834415
$126$		0			0
$127$	−15.4192			−1.36823			−0.684117	−	0.729372i	$-0.739812\pi$
$127$	−15.4192			−1.36823			−0.684117	+	0.729372i	$0.739812\pi$
$128$	−5.40679	+	9.36484i	−0.477897	+	0.827742i
$129$		0			0
$130$	1.63950	+	2.83970i	0.143794	+	0.249058i
$131$	6.67804	+	11.5667i	0.583463	+	1.01059i	0.995065	+	0.0992240i	$0.0316360\pi$
$131$	6.67804	+	11.5667i	0.583463	+	1.01059i	−0.411602	+	0.911364i	$0.635031\pi$
$132$		0			0
$133$	−0.0354925	+	0.0614747i	−0.00307759	+	0.00533054i
$134$	1.27217			0.109899
$135$		0			0
$136$	−11.5449			−0.989965
$137$	−9.81180	+	16.9945i	−0.838279	+	1.45194i	0.0530541	+	0.998592i	$0.483104\pi$
$137$	−9.81180	+	16.9945i	−0.838279	+	1.45194i	−0.891333	+	0.453350i	$0.850229\pi$
$138$		0			0
$139$	−8.15317	−	14.1217i	−0.691543	−	1.19779i	−0.971332	−	0.237726i	$-0.923598\pi$
$139$	−8.15317	−	14.1217i	−0.691543	−	1.19779i	0.279789	−	0.960061i	$-0.409735\pi$
$140$	0.0968323	+	0.167718i	0.00818382	+	0.0141748i
$141$		0			0
$142$	2.22668	−	3.85673i	0.186859	−	0.323649i
$143$	−24.8537			−2.07837
$144$		0			0
$145$	5.31315			0.441233
$146$	4.18442	−	7.24763i	0.346305	−	0.599818i
$147$		0			0
$148$	−1.67365	−	2.89884i	−0.137573	−	0.238283i
$149$	5.52385	+	9.56758i	0.452531	+	0.783807i	0.998543	−	0.0539709i	$-0.0171878\pi$
$149$	5.52385	+	9.56758i	0.452531	+	0.783807i	−0.546011	+	0.837778i	$0.683854\pi$
$150$		0			0
$151$	3.40033	−	5.88954i	0.276715	−	0.479284i	−0.693851	−	0.720118i	$-0.744088\pi$
$151$	3.40033	−	5.88954i	0.276715	−	0.479284i	0.970566	+	0.240834i	$0.0774209\pi$
$152$	−1.42193			−0.115334
$153$		0			0
$154$	0.448311			0.0361259
$155$	−4.58964	+	7.94949i	−0.368649	+	0.638519i
$156$		0			0
$157$	−8.44356	−	14.6247i	−0.673870	−	1.16718i	−0.976798	−	0.214163i	$-0.931298\pi$
$157$	−8.44356	−	14.6247i	−0.673870	−	1.16718i	0.302928	−	0.953013i	$-0.402036\pi$
$158$	0.240212	+	0.416060i	0.0191103	+	0.0330999i
$159$		0			0
$160$	−3.03802	+	5.26200i	−0.240176	+	0.415998i
$161$	−0.940307			−0.0741066
$162$		0			0
$163$	8.41147			0.658838			0.329419	−	0.944184i	$-0.393147\pi$
$163$	8.41147			0.658838			0.329419	+	0.944184i	$0.393147\pi$
$164$	−5.79006	+	10.0287i	−0.452128	+	0.783109i
$165$		0			0
$166$	−2.31773	−	4.01443i	−0.179891	−	0.311580i
$167$	−1.31250	−	2.27332i	−0.101564	−	0.175915i	0.810765	−	0.585372i	$-0.199051\pi$
$167$	−1.31250	−	2.27332i	−0.101564	−	0.175915i	−0.912329	+	0.409457i	$0.865718\pi$
$168$		0			0
$169$	−3.96064	+	6.86002i	−0.304664	+	0.527694i
$170$	−3.42550			−0.262724
$171$		0			0
$172$	2.00000			0.152499
$173$	6.55163	−	11.3478i	0.498112	−	0.862754i	−0.501886	−	0.864934i	$-0.667360\pi$
$173$	6.55163	−	11.3478i	0.498112	−	0.862754i	0.999998	+	0.00217926i	$0.000693680\pi$
$174$		0			0
$175$	−0.235300	−	0.407551i	−0.0177870	−	0.0308080i
$176$	−3.83478	−	6.64203i	−0.289057	−	0.500662i
$177$		0			0
$178$	−2.34477	+	4.06126i	−0.175748	+	0.304404i
$179$	22.0988			1.65174			0.825872	−	0.563857i	$-0.190683\pi$
$179$	22.0988			1.65174			0.825872	+	0.563857i	$0.190683\pi$
$180$		0			0
$181$	−2.05913			−0.153054			−0.0765268	−	0.997068i	$-0.524383\pi$
$181$	−2.05913			−0.153054			−0.0765268	+	0.997068i	$0.524383\pi$
$182$	0.188689	−	0.326819i	0.0139865	−	0.0242254i
$183$		0			0
$184$	−9.41787	−	16.3122i	−0.694295	−	1.20255i
$185$	−1.14484	−	1.98293i	−0.0841705	−	0.145788i
$186$		0			0
$187$	12.9820	−	22.4856i	0.949341	−	1.64431i
$188$	3.70167			0.269972
$189$		0			0
$190$	−0.421903			−0.0306081
$191$	−1.97459	+	3.42009i	−0.142876	+	0.247469i	−0.928579	−	0.371136i	$-0.878968\pi$
$191$	−1.97459	+	3.42009i	−0.142876	+	0.247469i	0.785702	+	0.618605i	$0.212302\pi$
$192$		0			0
$193$	4.22328	+	7.31493i	0.303998	+	0.526540i	0.977038	−	0.213066i	$-0.0683450\pi$
$193$	4.22328	+	7.31493i	0.303998	+	0.526540i	−0.673040	+	0.739606i	$0.735012\pi$
$194$	−3.08753	−	5.34776i	−0.221672	−	0.383947i
$195$		0			0
$196$	−5.35117	+	9.26849i	−0.382226	+	0.662035i
$197$	2.29498			0.163511			0.0817553	−	0.996652i	$-0.473947\pi$
$197$	2.29498			0.163511			0.0817553	+	0.996652i	$0.473947\pi$
$198$		0			0
$199$	−23.5030			−1.66608			−0.833042	−	0.553210i	$-0.813403\pi$
$199$	−23.5030			−1.66608			−0.833042	+	0.553210i	$0.813403\pi$
$200$	4.71340	−	8.16385i	0.333288	−	0.577271i
$201$		0			0
$202$	−4.44356	−	7.69648i	−0.312648	−	0.541522i
$203$	−0.305743	−	0.529563i	−0.0214590	−	0.0371680i
$204$		0			0
$205$	−3.96064	+	6.86002i	−0.276623	+	0.479125i
$206$	−6.20556			−0.432362
$207$		0			0
$208$	−6.45605			−0.447647
$209$	1.59894	−	2.76945i	0.110601	−	0.191567i
$210$		0			0
$211$	0.833626	+	1.44388i	0.0573892	+	0.0994010i	0.893293	−	0.449475i	$-0.148389\pi$
$211$	0.833626	+	1.44388i	0.0573892	+	0.0994010i	−0.835904	+	0.548876i	$0.815056\pi$
$212$	2.33359	+	4.04189i	0.160271	+	0.277598i
$213$		0			0
$214$	−3.89440	+	6.74530i	−0.266216	+	0.461099i
$215$	1.36808			0.0933023
$216$		0			0
$217$	1.05644			0.0717156
$218$	0.991511	−	1.71735i	0.0671536	−	0.116313i
$219$		0			0
$220$	−4.36231	−	7.55574i	−0.294107	−	0.509408i
$221$	−10.9280	−	18.9278i	−0.735096	−	1.27322i
$222$		0			0
$223$	4.90033	−	8.48762i	0.328150	−	0.568373i	−0.653995	−	0.756499i	$-0.726908\pi$
$223$	4.90033	−	8.48762i	0.328150	−	0.568373i	0.982145	+	0.188126i	$0.0602414\pi$
$224$	0.699287			0.0467231
$225$		0			0
$226$	−7.92127			−0.526915
$227$	−7.74038	+	13.4067i	−0.513747	+	0.889836i	0.486126	+	0.873889i	$0.338410\pi$
$227$	−7.74038	+	13.4067i	−0.513747	+	0.889836i	−0.999873	+	0.0159469i	$0.994924\pi$
$228$		0			0
$229$	5.62701	+	9.74627i	0.371843	+	0.644052i	0.989849	−	0.142122i	$-0.0453925\pi$
$229$	5.62701	+	9.74627i	0.371843	+	0.644052i	−0.618006	+	0.786174i	$0.712059\pi$
$230$	−2.79439	−	4.84002i	−0.184257	−	0.319142i
$231$		0			0
$232$	6.12449	−	10.6079i	0.402092	−	0.696444i
$233$	5.23476			0.342940			0.171470	−	0.985189i	$-0.445148\pi$
$233$	5.23476			0.342940			0.171470	+	0.985189i	$0.445148\pi$
$234$		0			0
$235$	2.53209			0.165175
$236$	0.0336295	−	0.0582480i	0.00218909	−	0.00379162i
$237$		0			0
$238$	0.197119	+	0.341420i	0.0127773	+	0.0221310i
$239$	5.15490	+	8.92855i	0.333443	+	0.577540i	0.983184	−	0.182615i	$-0.0584563\pi$
$239$	5.15490	+	8.92855i	0.333443	+	0.577540i	−0.649742	+	0.760155i	$0.725123\pi$
$240$		0			0
$241$	−5.37211	+	9.30477i	−0.346048	+	0.599373i	−0.985544	−	0.169422i	$-0.945810\pi$
$241$	−5.37211	+	9.30477i	−0.346048	+	0.599373i	0.639496	+	0.768795i	$0.279143\pi$
$242$	−12.6720			−0.814590
$243$		0			0
$244$	15.6459			1.00163
$245$	−3.66041	+	6.34002i	−0.233855	+	0.405049i
$246$		0			0
$247$	−1.34595	−	2.33126i	−0.0856409	−	0.148334i
$248$	10.5810	+	18.3268i	0.671894	+	1.16375i
$249$		0			0
$250$	3.19072	−	5.52649i	0.201799	−	0.349526i
$251$	15.0729			0.951392			0.475696	−	0.879610i	$-0.342196\pi$
$251$	15.0729			0.951392			0.475696	+	0.879610i	$0.342196\pi$
$252$		0			0
$253$	42.3610			2.66321
$254$	−5.27368	+	9.13429i	−0.330900	+	0.573136i
$255$		0			0
$256$	4.84137	+	8.38549i	0.302585	+	0.524093i
$257$	1.66122	+	2.87733i	0.103624	+	0.179483i	0.913175	−	0.407567i	$-0.133623\pi$
$257$	1.66122	+	2.87733i	0.103624	+	0.179483i	−0.809551	+	0.587050i	$0.800289\pi$
$258$		0			0
$259$	−0.131759	+	0.228213i	−0.00818711	+	0.0141805i
$260$	−7.34419			−0.455467
$261$		0			0
$262$	9.13610			0.564430
$263$	−4.41934	+	7.65451i	−0.272508	+	0.471998i	−0.969503	−	0.245078i	$-0.921186\pi$
$263$	−4.41934	+	7.65451i	−0.272508	+	0.471998i	0.696995	+	0.717076i	$0.254520\pi$
$264$		0			0
$265$	1.59627	+	2.76481i	0.0980579	+	0.169841i
$266$	0.0242783	+	0.0420512i	0.00148860	+	0.00257832i
$267$		0			0
$268$	−1.42468	+	2.46761i	−0.0870261	+	0.150734i
$269$	8.09267			0.493419			0.246709	−	0.969090i	$-0.420651\pi$
$269$	8.09267			0.493419			0.246709	+	0.969090i	$0.420651\pi$
$270$		0			0
$271$	−19.0000			−1.15417			−0.577084	−	0.816685i	$-0.695809\pi$
$271$	−19.0000			−1.15417			−0.577084	+	0.816685i	$0.695809\pi$
$272$	3.37225	−	5.84090i	0.204472	−	0.354157i
$273$		0			0
$274$	6.71167	+	11.6249i	0.405467	+	0.702289i
$275$	10.6003	+	18.3603i	0.639222	+	1.10716i
$276$		0			0
$277$	2.11468	−	3.66274i	0.127059	−	0.220073i	−0.795477	−	0.605984i	$-0.792780\pi$
$277$	2.11468	−	3.66274i	0.127059	−	0.220073i	0.922536	+	0.385911i	$0.126113\pi$
$278$	−11.1542			−0.668984
$279$		0			0
$280$	0.305407			0.0182516
$281$	−3.65106	+	6.32383i	−0.217804	+	0.377248i	−0.954136	−	0.299372i	$-0.903223\pi$
$281$	−3.65106	+	6.32383i	−0.217804	+	0.377248i	0.736332	+	0.676620i	$0.236556\pi$
$282$		0			0
$283$	−8.01027	−	13.8742i	−0.476161	−	0.824735i	0.523466	−	0.852047i	$-0.324639\pi$
$283$	−8.01027	−	13.8742i	−0.476161	−	0.824735i	−0.999627	+	0.0273116i	$0.991305\pi$
$284$	4.98724	+	8.63816i	0.295938	+	0.512580i
$285$		0			0
$286$	−8.50047	+	14.7232i	−0.502643	+	0.870603i
$287$	0.911654			0.0538132
$288$		0			0
$289$	5.83244			0.343085
$290$	1.81720	−	3.14749i	0.106710	−	0.184827i
$291$		0			0
$292$	9.37211	+	16.2330i	0.548461	+	0.949963i
$293$	−9.00227	−	15.5924i	−0.525918	−	0.910918i	−0.999544	−	0.0301913i	$-0.990388\pi$
$293$	−9.00227	−	15.5924i	−0.525918	−	0.910918i	0.473626	−	0.880726i	$-0.342945\pi$
$294$		0			0
$295$	0.0230039	−	0.0398440i	0.00133934	−	0.00231981i
$296$	−5.27866			−0.306816
$297$		0			0
$298$	7.55707			0.437769
$299$	17.8293	−	30.8812i	1.03109	−	1.78591i
$300$		0			0
$301$	−0.0787257	−	0.136357i	−0.00453767	−	0.00785948i
$302$	−2.32596	−	4.02869i	−0.133844	−	0.231825i
$303$		0			0
$304$	0.415345	−	0.719398i	0.0238216	−	0.0412603i
$305$	10.7024			0.612819
$306$		0			0
$307$	−13.5107			−0.771098			−0.385549	−	0.922687i	$-0.625988\pi$
$307$	−13.5107			−0.771098			−0.385549	+	0.922687i	$0.625988\pi$
$308$	−0.502055	+	0.869585i	−0.0286072	+	0.0495492i
$309$		0			0
$310$	3.13950	+	5.43777i	0.178312	+	0.308845i
$311$	−8.21113	−	14.2221i	−0.465611	−	0.806461i	0.533618	−	0.845725i	$-0.320832\pi$
$311$	−8.21113	−	14.2221i	−0.465611	−	0.806461i	−0.999229	+	0.0392643i	$0.987499\pi$
$312$		0			0
$313$	9.78240	−	16.9436i	0.552934	−	0.957710i	−0.445127	−	0.895467i	$-0.646841\pi$
$313$	9.78240	−	16.9436i	0.552934	−	0.957710i	0.998061	−	0.0622425i	$-0.0198252\pi$
$314$	−11.5515			−0.651887
$315$		0			0
$316$	−1.07604			−0.0605318
$317$	12.1893	−	21.1125i	0.684619	−	1.18579i	−0.288938	−	0.957348i	$-0.593302\pi$
$317$	12.1893	−	21.1125i	0.684619	−	1.18579i	0.973557	−	0.228446i	$-0.0733645\pi$
$318$		0			0
$319$	13.7738	+	23.8569i	0.771184	+	1.33573i
$320$	0.598887	+	1.03730i	0.0334788	+	0.0579870i
$321$		0			0
$322$	−0.321604	+	0.557035i	−0.0179223	+	0.0310423i
$323$	2.81217			0.156473
$324$		0			0
$325$	17.8462			0.989927
$326$	2.87689	−	4.98293i	0.159336	−	0.275979i
$327$		0			0
$328$	9.13088	+	15.8152i	0.504169	+	0.873246i
$329$	−0.145708	−	0.252374i	−0.00803315	−	0.0139138i
$330$		0			0
$331$	−14.2494	+	24.6807i	−0.783220	+	1.35658i	0.146837	+	0.989161i	$0.453091\pi$
$331$	−14.2494	+	24.6807i	−0.783220	+	1.35658i	−0.930057	+	0.367416i	$0.880243\pi$
$332$	10.3824			0.569806
$333$		0			0
$334$	−1.79561			−0.0982512
$335$	−0.974537	+	1.68795i	−0.0532446	+	0.0922224i
$336$		0			0
$337$	8.72328	+	15.1092i	0.475187	+	0.823048i	0.999596	−	0.0284181i	$-0.00904699\pi$
$337$	8.72328	+	15.1092i	0.475187	+	0.823048i	−0.524409	+	0.851467i	$0.675714\pi$
$338$	2.70924	+	4.69253i	0.147363	+	0.255240i
$339$		0			0
$340$	3.83615	−	6.64441i	0.208045	−	0.360344i
$341$	−47.5927			−2.57729
$342$		0			0
$343$	1.68685			0.0910814
$344$	1.57699	−	2.73143i	0.0850257	−	0.147269i
$345$		0			0
$346$	−4.48158	−	7.76233i	−0.240931	−	0.417305i
$347$	−12.5945	−	21.8143i	−0.676109	−	1.17105i	−0.976144	−	0.217126i	$-0.930332\pi$
$347$	−12.5945	−	21.8143i	−0.676109	−	1.17105i	0.300035	−	0.953928i	$-0.403002\pi$
$348$		0			0
$349$	5.92602	−	10.2642i	0.317213	−	0.549428i	−0.662693	−	0.748891i	$-0.730586\pi$
$349$	5.92602	−	10.2642i	0.317213	−	0.549428i	0.979905	+	0.199463i	$0.0639198\pi$
$350$	−0.321909			−0.0172068
$351$		0			0
$352$	−31.5030			−1.67912
$353$	4.19875	−	7.27244i	0.223477	−	0.387073i	−0.732385	−	0.680891i	$-0.761593\pi$
$353$	4.19875	−	7.27244i	0.223477	−	0.387073i	0.955861	+	0.293818i	$0.0949260\pi$
$354$		0			0
$355$	3.41147	+	5.90885i	0.181062	+	0.313609i
$356$	−5.25173	−	9.09627i	−0.278341	−	0.482101i
$357$		0			0
$358$	7.55825	−	13.0913i	0.399466	−	0.691895i
$359$	2.64025			0.139347			0.0696735	−	0.997570i	$-0.477804\pi$
$359$	2.64025			0.139347			0.0696735	+	0.997570i	$0.477804\pi$
$360$		0			0
$361$	−18.6536			−0.981770
$362$	−0.704262	+	1.21982i	−0.0370152	+	0.0641122i
$363$		0			0
$364$	0.422618	+	0.731997i	0.0221512	+	0.0383671i
$365$	6.41090	+	11.1040i	0.335562	+	0.581210i
$366$		0			0
$367$	−4.59879	+	7.96534i	−0.240055	+	0.415788i	−0.960730	−	0.277486i	$-0.910499\pi$
$367$	−4.59879	+	7.96534i	−0.240055	+	0.415788i	0.720675	+	0.693273i	$0.243832\pi$
$368$	11.0038			0.573612
$369$		0			0
$370$	−1.56624			−0.0814248
$371$	0.183713	−	0.318201i	0.00953791	−	0.0165201i
$372$		0			0
$373$	13.3956	+	23.2018i	0.693597	+	1.20135i	0.970651	+	0.240491i	$0.0773084\pi$
$373$	13.3956	+	23.2018i	0.693597	+	1.20135i	−0.277054	+	0.960854i	$0.589358\pi$
$374$	−8.88024	−	15.3810i	−0.459186	−	0.795334i
$375$		0			0
$376$	2.91875	−	5.05542i	0.150523	−	0.260713i
$377$	23.1889			1.19429
$378$		0			0
$379$	−27.1242			−1.39328			−0.696639	−	0.717422i	$-0.745322\pi$
$379$	−27.1242			−1.39328			−0.696639	+	0.717422i	$0.745322\pi$
$380$	0.472482	−	0.818363i	0.0242378	−	0.0419811i
$381$		0			0
$382$	1.35070	+	2.33948i	0.0691078	+	0.119698i
$383$	17.2134	+	29.8145i	0.879564	+	1.52345i	0.851820	+	0.523834i	$0.175499\pi$
$383$	17.2134	+	29.8145i	0.879564	+	1.52345i	0.0277437	+	0.999615i	$0.491168\pi$
$384$		0			0
$385$	−0.343426	+	0.594831i	−0.0175026	+	0.0303154i
$386$	5.77778			0.294081
$387$		0			0
$388$	13.8307			0.702147
$389$	0.378297	−	0.655230i	0.0191804	−	0.0332215i	−0.856276	−	0.516519i	$-0.827228\pi$
$389$	0.378297	−	0.655230i	0.0191804	−	0.0332215i	0.875456	+	0.483297i	$0.160561\pi$
$390$		0			0
$391$	18.6258	+	32.2609i	0.941949	+	1.63150i
$392$	8.43874	+	14.6163i	0.426221	+	0.738236i
$393$		0			0
$394$	0.784930	−	1.35954i	0.0395442	−	0.0684925i
$395$	−0.736053			−0.0370348
$396$		0			0
$397$	7.00774			0.351708			0.175854	−	0.984416i	$-0.443731\pi$
$397$	7.00774			0.351708			0.175854	+	0.984416i	$0.443731\pi$
$398$	−8.03850	+	13.9231i	−0.402933	+	0.697901i
$399$		0			0
$400$	2.75356	+	4.76930i	0.137678	+	0.238465i
$401$	−4.72540	−	8.18463i	−0.235975	−	0.408721i	0.723580	−	0.690240i	$-0.242495\pi$
$401$	−4.72540	−	8.18463i	−0.235975	−	0.408721i	−0.959556	+	0.281519i	$0.909162\pi$
$402$		0			0
$403$	−20.0312	+	34.6951i	−0.997826	+	1.72828i
$404$	19.9051			0.990314
$405$		0			0
$406$	−0.418281			−0.0207590
$407$	5.93577	−	10.2811i	0.294225	−	0.509613i
$408$		0			0
$409$	−2.75877	−	4.77833i	−0.136412	−	0.236273i	0.789724	−	0.613463i	$-0.210224\pi$
$409$	−2.75877	−	4.77833i	−0.136412	−	0.236273i	−0.926136	+	0.377189i	$0.876891\pi$
$410$	2.70924	+	4.69253i	0.133800	+	0.231748i
$411$		0			0
$412$	6.94949	−	12.0369i	0.342377	−	0.593014i
$413$	−0.00529501			−0.000260550
$414$		0			0
$415$	7.10195			0.348621
$416$	−13.2592	+	22.9657i	−0.650088	+	1.12599i
$417$		0			0
$418$	−1.09374	−	1.89441i	−0.0534966	−	0.0926588i
$419$	−0.233189	−	0.403895i	−0.0113920	−	0.0197316i	0.860273	−	0.509833i	$-0.170293\pi$
$419$	−0.233189	−	0.403895i	−0.0113920	−	0.0197316i	−0.871665	+	0.490102i	$0.836960\pi$
$420$		0			0
$421$	1.20708	−	2.09073i	0.0588295	−	0.101896i	−0.835111	−	0.550082i	$-0.814596\pi$
$421$	1.20708	−	2.09073i	0.0588295	−	0.101896i	0.893940	+	0.448186i	$0.147930\pi$
$422$	1.14047			0.0555171
$423$		0			0
$424$	7.36009			0.357438
$425$	−9.32174	+	16.1457i	−0.452171	+	0.783183i
$426$		0			0
$427$	−0.615867	−	1.06671i	−0.0298039	−	0.0516219i
$428$	−8.72254	−	15.1079i	−0.421620	−	0.730267i
$429$		0			0
$430$	0.467911	−	0.810446i	0.0225647	−	0.0390832i
$431$	−12.0992			−0.582796			−0.291398	−	0.956602i	$-0.594120\pi$
$431$	−12.0992			−0.582796			−0.291398	+	0.956602i	$0.594120\pi$
$432$		0			0
$433$	33.3509			1.60274			0.801371	−	0.598167i	$-0.204104\pi$
$433$	33.3509			1.60274			0.801371	+	0.598167i	$0.204104\pi$
$434$	0.361323	−	0.625829i	0.0173440	−	0.0300408i
$435$		0			0
$436$	2.22075	+	3.84645i	0.106355	+	0.184212i
$437$	2.29406	+	3.97343i	0.109740	+	0.190075i
$438$		0			0
$439$	4.52229	−	7.83283i	0.215837	−	0.373841i	−0.737694	−	0.675135i	$-0.764085\pi$
$439$	4.52229	−	7.83283i	0.215837	−	0.373841i	0.953531	+	0.301294i	$0.0974187\pi$
$440$	−13.7587			−0.655918
$441$		0			0
$442$	−14.9504			−0.711117
$443$	2.33856	−	4.05051i	0.111108	−	0.192445i	−0.805109	−	0.593127i	$-0.797893\pi$
$443$	2.33856	−	4.05051i	0.111108	−	0.192445i	0.916217	+	0.400681i	$0.131227\pi$
$444$		0			0
$445$	−3.59240	−	6.22221i	−0.170296	−	0.294961i
$446$	−3.35202	−	5.80587i	−0.158723	−	0.274916i
$447$		0			0
$448$	0.0689255	−	0.119382i	0.00325642	−	0.00564029i
$449$	−26.7069			−1.26037			−0.630187	−	0.776443i	$-0.717022\pi$
$449$	−26.7069			−1.26037			−0.630187	+	0.776443i	$0.717022\pi$
$450$		0			0
$451$	−41.0702			−1.93392
$452$	8.87089	−	15.3648i	0.417252	−	0.722701i
$453$		0			0
$454$	5.29473	+	9.17074i	0.248494	+	0.430404i
$455$	0.289088	+	0.500715i	0.0135527	+	0.0234739i
$456$		0			0
$457$	0.328878	−	0.569633i	0.0153843	−	0.0266463i	−0.858231	−	0.513264i	$-0.828436\pi$
$457$	0.328878	−	0.569633i	0.0153843	−	0.0266463i	0.873615	+	0.486618i	$0.161770\pi$
$458$	7.69820			0.359713
$459$		0			0
$460$	12.5175			0.583633
$461$	−10.3519	+	17.9299i	−0.482134	+	0.835081i	−0.999790	−	0.0205082i	$-0.993472\pi$
$461$	−10.3519	+	17.9299i	−0.482134	+	0.835081i	0.517655	+	0.855589i	$0.326805\pi$
$462$		0			0
$463$	12.4119	+	21.4981i	0.576832	+	0.999102i	0.995840	+	0.0911195i	$0.0290445\pi$
$463$	12.4119	+	21.4981i	0.576832	+	0.999102i	−0.419008	+	0.907982i	$0.637622\pi$
$464$	3.57791	+	6.19712i	0.166100	+	0.287694i
$465$		0			0
$466$	1.79039	−	3.10105i	0.0829383	−	0.143653i
$467$	26.6729			1.23428			0.617138	−	0.786855i	$-0.288292\pi$
$467$	26.6729			1.23428			0.617138	+	0.786855i	$0.288292\pi$
$468$		0			0
$469$	0.224318			0.0103580
$470$	0.866025	−	1.50000i	0.0399468	−	0.0691898i
$471$		0			0
$472$	−0.0530334	−	0.0918566i	−0.00244106	−	0.00422804i
$473$	3.54661	+	6.14290i	0.163073	+	0.282451i
$474$		0			0
$475$	−1.14812	+	1.98860i	−0.0526793	+	0.0912432i
$476$	−0.883000			−0.0404722
$477$		0			0
$478$	7.05232			0.322566
$479$	1.61327	−	2.79426i	0.0737121	−	0.127673i	−0.826813	−	0.562476i	$-0.809849\pi$
$479$	1.61327	−	2.79426i	0.0737121	−	0.127673i	0.900525	+	0.434803i	$0.143182\pi$
$480$		0			0
$481$	−4.99660	−	8.65436i	−0.227825	−	0.394605i
$482$	3.67474	+	6.36484i	0.167380	+	0.289910i
$483$		0			0
$484$	14.1912	−	24.5799i	0.645054	−	1.11727i
$485$	9.46075			0.429590
$486$		0			0
$487$	−7.77930			−0.352514			−0.176257	−	0.984344i	$-0.556399\pi$
$487$	−7.77930			−0.352514			−0.176257	+	0.984344i	$0.556399\pi$
$488$	12.3367	−	21.3678i	0.558457	−	0.967276i
$489$		0			0
$490$	2.50387	+	4.33683i	0.113113	+	0.195918i
$491$	−8.52298	−	14.7622i	−0.384637	−	0.666210i	0.607082	−	0.794639i	$-0.292340\pi$
$491$	−8.52298	−	14.7622i	−0.384637	−	0.666210i	−0.991719	+	0.128429i	$0.959007\pi$
$492$		0			0
$493$	−12.1125	+	20.9794i	−0.545518	+	0.944865i
$494$	−1.84137			−0.0828472
$495$		0			0
$496$	−12.3628			−0.555105
$497$	0.392624	−	0.680045i	0.0176116	−	0.0305042i
$498$		0			0
$499$	−3.96538	−	6.86825i	−0.177515	−	0.307465i	0.763514	−	0.645792i	$-0.223472\pi$
$499$	−3.96538	−	6.86825i	−0.177515	−	0.307465i	−0.941029	+	0.338327i	$0.890139\pi$
$500$	7.14647	+	12.3780i	0.319600	+	0.553563i
$501$		0			0
$502$	5.15523	−	8.92912i	0.230089	−	0.398526i
$503$	24.9496			1.11245			0.556224	−	0.831032i	$-0.312250\pi$
$503$	24.9496			1.11245			0.556224	+	0.831032i	$0.312250\pi$
$504$		0			0
$505$	13.6159			0.605898
$506$	14.4883	−	25.0945i	0.644085	−	1.11559i
$507$		0			0
$508$	−11.8118	−	20.4586i	−0.524064	−	0.907706i
$509$	20.2345	+	35.0472i	0.896878	+	1.55344i	0.831463	+	0.555580i	$0.187504\pi$
$509$	20.2345	+	35.0472i	0.896878	+	1.55344i	0.0654147	+	0.997858i	$0.479163\pi$
$510$		0			0
$511$	0.737826	−	1.27795i	0.0326395	−	0.0565333i
$512$	−15.0038			−0.663080
$513$		0			0
$514$	2.27269			0.100244
$515$	4.75373	−	8.23371i	0.209475	−	0.362820i
$516$		0			0
$517$	6.56418	+	11.3695i	0.288692	+	0.500030i
$518$	0.0901285	+	0.156107i	0.00396002	+	0.00685896i
$519$		0			0
$520$	−5.79086	+	10.0301i	−0.253946	+	0.439847i
$521$	25.3674			1.11137			0.555684	−	0.831394i	$-0.312457\pi$
$521$	25.3674			1.11137			0.555684	+	0.831394i	$0.312457\pi$
$522$		0			0
$523$	12.7219			0.556291			0.278146	−	0.960539i	$-0.410280\pi$
$523$	12.7219			0.556291			0.278146	+	0.960539i	$0.410280\pi$
$524$	−10.2314	+	17.7212i	−0.446959	+	0.774155i
$525$		0			0
$526$	3.02300	+	5.23600i	0.131809	+	0.228300i
$527$	−20.9262	−	36.2452i	−0.911557	−	1.57886i
$528$		0			0
$529$	−18.8885	+	32.7158i	−0.821238	+	1.42243i
$530$	2.18382			0.0948591
$531$		0			0
$532$	−0.108755			−0.00471514
$533$	−17.2860	+	29.9402i	−0.748738	+	1.29685i
$534$		0			0
$535$	−5.96657	−	10.3344i	−0.257957	−	0.446795i
$536$	2.24670	+	3.89141i	0.0970429	+	0.168083i
$537$		0			0
$538$	2.76786	−	4.79407i	0.119331	−	0.206687i
$539$	−37.9570			−1.63492
$540$		0			0
$541$	2.09327			0.0899969			0.0449984	−	0.998987i	$-0.485672\pi$
$541$	2.09327			0.0899969			0.0449984	+	0.998987i	$0.485672\pi$
$542$	−6.49838	+	11.2555i	−0.279129	+	0.483466i
$543$		0			0
$544$	−13.8516	−	23.9917i	−0.593884	−	1.02864i
$545$	1.51908	+	2.63113i	0.0650704	+	0.112705i
$546$		0			0
$547$	−1.72550	+	2.98865i	−0.0737770	+	0.127786i	−0.900554	−	0.434745i	$-0.856839\pi$
$547$	−1.72550	+	2.98865i	−0.0737770	+	0.127786i	0.826777	+	0.562530i	$0.190172\pi$
$548$	−30.0651			−1.28432
$549$		0			0
$550$	14.5021			0.618370
$551$	−1.49184	+	2.58394i	−0.0635545	+	0.110080i
$552$		0			0
$553$	0.0423559	+	0.0733626i	0.00180116	+	0.00311969i
$554$	−1.44653	−	2.50546i	−0.0614572	−	0.106447i
$555$		0			0
$556$	12.4914	−	21.6357i	0.529753	−	0.917558i
$557$	−11.1003			−0.470337			−0.235168	−	0.971955i	$-0.575564\pi$
$557$	−11.1003			−0.470337			−0.235168	+	0.971955i	$0.575564\pi$
$558$		0			0
$559$	5.97090			0.252542
$560$	−0.0892091	+	0.154515i	−0.00376977	+	0.00652944i
$561$		0			0
$562$	2.49747	+	4.32575i	0.105350	+	0.182471i
$563$	−12.1553	−	21.0537i	−0.512286	−	0.887306i	−0.999899	−	0.0142457i	$-0.995465\pi$
$563$	−12.1553	−	21.0537i	−0.512286	−	0.887306i	0.487612	−	0.873060i	$-0.337868\pi$
$564$		0			0
$565$	6.06805	−	10.5102i	0.255285	−	0.442166i
$566$	−10.9587			−0.460628
$567$		0			0
$568$	15.7297			0.660002
$569$	−21.3820	+	37.0347i	−0.896379	+	1.55257i	−0.0642907	+	0.997931i	$0.520478\pi$
$569$	−21.3820	+	37.0347i	−0.896379	+	1.55257i	−0.832088	+	0.554643i	$0.812855\pi$
$570$		0			0
$571$	−9.01414	−	15.6129i	−0.377230	−	0.653381i	0.613428	−	0.789751i	$-0.289790\pi$
$571$	−9.01414	−	15.6129i	−0.377230	−	0.653381i	−0.990658	+	0.136369i	$0.956457\pi$
$572$	−19.0390	−	32.9766i	−0.796062	−	1.37882i
$573$		0			0
$574$	0.311804	−	0.540060i	0.0130144	−	0.0225417i
$575$	−30.4173			−1.26849
$576$		0			0
$577$	25.2763			1.05227			0.526133	−	0.850402i	$-0.323641\pi$
$577$	25.2763			1.05227			0.526133	+	0.850402i	$0.323641\pi$
$578$	1.99481	−	3.45512i	0.0829733	−	0.143714i
$579$		0			0
$580$	4.07011	+	7.04963i	0.169002	+	0.292720i
$581$	−0.408679	−	0.707853i	−0.0169549	−	0.0293667i
$582$		0			0
$583$	−8.27631	+	14.3350i	−0.342770	+	0.593695i
$584$	29.5595			1.22318
$585$		0			0
$586$	−12.3158			−0.508763
$587$	−14.2827	+	24.7383i	−0.589508	+	1.02106i	0.404788	+	0.914410i	$0.367345\pi$
$587$	−14.2827	+	24.7383i	−0.589508	+	1.02106i	−0.994297	+	0.106648i	$0.965988\pi$
$588$		0			0
$589$	−2.57738	−	4.46416i	−0.106199	−	0.183942i
$590$	−0.0157356	−	0.0272549i	−0.000647825	−	0.00112207i
$591$		0			0
$592$	1.54189	−	2.67063i	0.0633713	−	0.109762i
$593$	20.6009			0.845977			0.422989	−	0.906135i	$-0.360981\pi$
$593$	20.6009			0.845977			0.422989	+	0.906135i	$0.360981\pi$
$594$		0			0
$595$	−0.604007			−0.0247619
$596$	−8.46302	+	14.6584i	−0.346659	+	0.600431i
$597$		0			0
$598$	−12.1959	−	21.1240i	−0.498729	−	0.863824i
$599$	7.23740	+	12.5355i	0.295712	+	0.512189i	0.975150	−	0.221544i	$-0.0711097\pi$
$599$	7.23740	+	12.5355i	0.295712	+	0.512189i	−0.679438	+	0.733733i	$0.737776\pi$
$600$		0			0
$601$	6.67752	−	11.5658i	0.272382	−	0.471779i	−0.697090	−	0.716984i	$-0.745522\pi$
$601$	6.67752	−	11.5658i	0.272382	−	0.471779i	0.969471	+	0.245205i	$0.0788553\pi$
$602$	−0.107703			−0.00438965
$603$		0			0
$604$	10.4192			0.423952
$605$	9.70735	−	16.8136i	0.394660	−	0.683571i
$606$		0			0
$607$	−15.6065	−	27.0313i	−0.633450	−	1.09717i	−0.986841	−	0.161692i	$-0.948305\pi$
$607$	−15.6065	−	27.0313i	−0.633450	−	1.09717i	0.353392	−	0.935475i	$-0.385028\pi$
$608$	−1.70604	−	2.95496i	−0.0691892	−	0.119839i
$609$		0			0
$610$	3.66044	−	6.34008i	0.148207	−	0.256702i
$611$	11.0511			0.447082
$612$		0			0
$613$	30.0651			1.21432			0.607159	−	0.794580i	$-0.292309\pi$
$613$	30.0651			1.21432			0.607159	+	0.794580i	$0.292309\pi$
$614$	−4.62094	+	8.00371i	−0.186486	+	0.323003i
$615$		0			0
$616$	0.791737	+	1.37133i	0.0319000	+	0.0552524i
$617$	21.0768	+	36.5061i	0.848521	+	1.46968i	0.882528	+	0.470261i	$0.155840\pi$
$617$	21.0768	+	36.5061i	0.848521	+	1.46968i	−0.0340062	+	0.999422i	$0.510827\pi$
$618$		0			0
$619$	−5.80541	+	10.0553i	−0.233339	+	0.404155i	−0.958789	−	0.284120i	$-0.908299\pi$
$619$	−5.80541	+	10.0553i	−0.233339	+	0.404155i	0.725450	+	0.688275i	$0.241632\pi$
$620$	−14.0635			−0.564803
$621$		0			0
$622$	−11.2335			−0.450422
$623$	−0.413446	+	0.716110i	−0.0165644	+	0.0286903i
$624$		0			0
$625$	−4.86571	−	8.42767i	−0.194629	−	0.337107i
$626$	−6.69156	−	11.5901i	−0.267448	−	0.463234i
$627$		0			0
$628$	12.9363	−	22.4063i	0.516214	−	0.894109i
$629$	10.4397			0.416257
$630$		0			0
$631$	−29.3105			−1.16683			−0.583415	−	0.812174i	$-0.698284\pi$
$631$	−29.3105			−1.16683			−0.583415	+	0.812174i	$0.698284\pi$
$632$	−0.848451	+	1.46956i	−0.0337496	+	0.0584560i
$633$		0			0
$634$	−8.33796	−	14.4418i	−0.331143	−	0.573556i
$635$	−8.07975	−	13.9945i	−0.320635	−	0.555356i
$636$		0			0
$637$	−15.9757	+	27.6706i	−0.632978	+	1.09635i
$638$	18.8436			0.746027
$639$		0			0
$640$	−11.3327			−0.447966
$641$	15.5489	−	26.9315i	0.614146	−	1.06373i	−0.376388	−	0.926462i	$-0.622834\pi$
$641$	15.5489	−	26.9315i	0.614146	−	1.06373i	0.990534	−	0.137270i	$-0.0438327\pi$
$642$		0			0
$643$	−21.0360	−	36.4354i	−0.829577	−	1.43687i	−0.898370	−	0.439239i	$-0.855248\pi$
$643$	−21.0360	−	36.4354i	−0.829577	−	1.43687i	0.0687930	−	0.997631i	$-0.478085\pi$
$644$	−0.720317	−	1.24763i	−0.0283845	−	0.0491634i
$645$		0			0
$646$	0.961819	−	1.66592i	0.0378423	−	0.0655447i
$647$	4.66717			0.183485			0.0917427	−	0.995783i	$-0.470756\pi$
$647$	4.66717			0.183485			0.0917427	+	0.995783i	$0.470756\pi$
$648$		0			0
$649$	0.238541			0.00936356
$650$	6.10375	−	10.5720i	0.239409	−	0.414668i
$651$		0			0
$652$	6.44356	+	11.1606i	0.252349	+	0.437082i
$653$	−1.56206	−	2.70557i	−0.0611283	−	0.105877i	0.833842	−	0.552004i	$-0.186137\pi$
$653$	−1.56206	−	2.70557i	−0.0611283	−	0.105877i	−0.894970	+	0.446126i	$0.852803\pi$
$654$		0			0
$655$	−6.99866	+	12.1220i	−0.273460	+	0.473647i
$656$	−10.6685			−0.416534
$657$		0			0
$658$	−0.199340			−0.00777110
$659$	18.7146	−	32.4146i	0.729017	−	1.26269i	−0.228282	−	0.973595i	$-0.573311\pi$
$659$	18.7146	−	32.4146i	0.729017	−	1.26269i	0.957299	−	0.289100i	$-0.0933559\pi$
$660$		0			0
$661$	−13.2502	−	22.9499i	−0.515371	−	0.892649i	−0.999841	−	0.0178410i	$-0.994321\pi$
$661$	−13.2502	−	22.9499i	−0.515371	−	0.892649i	0.484470	−	0.874808i	$-0.339013\pi$
$662$	9.74719	+	16.8826i	0.378835	+	0.656162i
$663$		0			0
$664$	8.18644	−	14.1793i	0.317696	−	0.550265i
$665$	−0.0743929			−0.00288483
$666$		0			0
$667$	−39.5235			−1.53036
$668$	2.01087	−	3.48293i	0.0778028	−	0.134758i
$669$		0			0
$670$	0.666623	+	1.15462i	0.0257539	+	0.0446070i
$671$	27.7449	+	48.0556i	1.07108	+	1.85517i
$672$		0			0
$673$	−0.860500	+	1.49043i	−0.0331698	+	0.0574519i	−0.882134	−	0.470999i	$-0.843894\pi$
$673$	−0.860500	+	1.49043i	−0.0331698	+	0.0574519i	0.848964	+	0.528451i	$0.177227\pi$
$674$	11.9341			0.459686
$675$		0			0
$676$	−12.1361			−0.466773
$677$	−14.1396	+	24.4905i	−0.543429	+	0.941247i	0.455275	+	0.890351i	$0.349541\pi$
$677$	−14.1396	+	24.4905i	−0.543429	+	0.941247i	−0.998704	+	0.0508957i	$0.983792\pi$
$678$		0			0
$679$	−0.544415	−	0.942955i	−0.0208927	−	0.0361873i
$680$	−6.04958	−	10.4782i	−0.231991	−	0.401820i
$681$		0			0
$682$	−16.2777	+	28.1937i	−0.623304	+	1.07959i
$683$	−24.7139			−0.945651			−0.472825	−	0.881156i	$-0.656766\pi$
$683$	−24.7139			−0.945651			−0.472825	+	0.881156i	$0.656766\pi$
$684$		0			0
$685$	−20.5657			−0.785777
$686$	0.576937	−	0.999285i	0.0220276	−	0.0381529i
$687$		0			0
$688$	0.921274	+	1.59569i	0.0351233	+	0.0608353i
$689$	6.96681	+	12.0669i	0.265414	+	0.459711i
$690$		0			0
$691$	21.8862	−	37.9081i	0.832592	−	1.44209i	−0.0633838	−	0.997989i	$-0.520189\pi$
$691$	21.8862	−	37.9081i	0.832592	−	1.44209i	0.895976	−	0.444103i	$-0.146477\pi$
$692$	20.0754			0.763151
$693$		0			0
$694$	−17.2303			−0.654053
$695$	8.54461	−	14.7997i	0.324115	−	0.561384i
$696$		0			0
$697$	−18.0582	−	31.2778i	−0.684005	−	1.18473i
$698$	−4.05364	−	7.02111i	−0.153432	−	0.265753i
$699$		0			0
$700$	0.360500	−	0.624404i	0.0136256	−	0.0236003i
$701$	−14.6504			−0.553338			−0.276669	−	0.960965i	$-0.589231\pi$
$701$	−14.6504			−0.553338			−0.276669	+	0.960965i	$0.589231\pi$
$702$		0			0
$703$	1.28581			0.0484951
$704$	−3.10511	+	5.37820i	−0.117028	+	0.202699i
$705$		0			0
$706$	−2.87211	−	4.97464i	−0.108093	−	0.187223i
$707$	−0.783520	−	1.35710i	−0.0294673	−	0.0510389i
$708$		0			0
$709$	−2.53684	+	4.39393i	−0.0952729	+	0.165018i	−0.909722	−	0.415217i	$-0.863706\pi$
$709$	−2.53684	+	4.39393i	−0.0952729	+	0.165018i	0.814450	+	0.580234i	$0.197039\pi$
$710$	4.66717			0.175156
$711$		0			0
$712$	−16.5639			−0.620757
$713$	34.1415	−	59.1348i	1.27861	−	2.21462i
$714$		0			0
$715$	−13.0235	−	22.5573i	−0.487050	−	0.843596i
$716$	16.9287	+	29.3214i	0.632655	+	1.09579i
$717$		0			0
$718$	0.903018	−	1.56407i	0.0337003	−	0.0583707i
$719$	−5.33717			−0.199043			−0.0995213	−	0.995035i	$-0.531731\pi$
$719$	−5.33717			−0.199043			−0.0995213	+	0.995035i	$0.531731\pi$
$720$		0			0
$721$	−1.09421			−0.0407504
$722$	−6.37992	+	11.0503i	−0.237436	+	0.411251i
$723$		0			0
$724$	−1.57738	−	2.73210i	−0.0586229	−	0.101538i
$725$	−9.89025	−	17.1304i	−0.367315	−	0.636208i
$726$		0			0
$727$	−18.5599	+	32.1467i	−0.688348	+	1.19225i	0.284023	+	0.958817i	$0.408331\pi$
$727$	−18.5599	+	32.1467i	−0.688348	+	1.19225i	−0.972372	+	0.233437i	$0.925003\pi$
$728$	1.33293			0.0494017
$729$		0			0
$730$	8.77063			0.324616
$731$	−3.11883	+	5.40198i	−0.115354	+	0.199799i
$732$		0			0
$733$	−14.9731	−	25.9342i	−0.553045	−	0.957902i	−0.998053	−	0.0623753i	$-0.980132\pi$
$733$	−14.9731	−	25.9342i	−0.553045	−	0.957902i	0.445008	−	0.895527i	$-0.353201\pi$
$734$	3.14576	+	5.44862i	0.116112	+	0.201112i
$735$		0			0
$736$	22.5993	−	39.1431i	0.833020	−	1.44283i
$737$	−10.1055			−0.372243
$738$		0			0
$739$	−28.6100			−1.05244			−0.526218	−	0.850350i	$-0.676390\pi$
$739$	−28.6100			−1.05244			−0.526218	+	0.850350i	$0.676390\pi$
$740$	1.75400	−	3.03802i	0.0644784	−	0.111680i
$741$		0			0
$742$	−0.125667	−	0.217662i	−0.00461339	−	0.00799062i
$743$	−24.8218	−	42.9926i	−0.910624	−	1.57725i	−0.813185	−	0.582005i	$-0.802269\pi$
$743$	−24.8218	−	42.9926i	−0.910624	−	1.57725i	−0.0974381	−	0.995242i	$-0.531065\pi$
$744$		0			0
$745$	−5.78905	+	10.0269i	−0.212094	+	0.367358i
$746$	18.3262			0.670971
$747$		0			0
$748$	39.7793			1.45448
$749$	−0.686688	+	1.18938i	−0.0250910	+	0.0434589i
$750$		0			0
$751$	15.8118	+	27.3868i	0.576981	+	0.999360i	0.995823	+	0.0913013i	$0.0291026\pi$
$751$	15.8118	+	27.3868i	0.576981	+	0.999360i	−0.418842	+	0.908059i	$0.637564\pi$
$752$	1.70513	+	2.95336i	0.0621795	+	0.107698i
$753$		0			0
$754$	7.93107	−	13.7370i	0.288833	−	0.500273i
$755$	7.12716			0.259384
$756$		0			0
$757$	3.04189			0.110559			0.0552797	−	0.998471i	$-0.482395\pi$
$757$	3.04189			0.110559			0.0552797	+	0.998471i	$0.482395\pi$
$758$	−9.27704	+	16.0683i	−0.336957	+	0.583627i
$759$		0			0
$760$	−0.745100	−	1.29055i	−0.0270276	−	0.0468132i
$761$	−18.9642	−	32.8469i	−0.687450	−	1.19070i	−0.972660	−	0.232234i	$-0.925397\pi$
$761$	−18.9642	−	32.8469i	−0.687450	−	1.19070i	0.285210	−	0.958465i	$-0.407937\pi$
$762$		0			0
$763$	0.174830	−	0.302815i	0.00632928	−	0.0109626i
$764$	−6.05050			−0.218899
$765$		0			0
$766$	23.5493			0.850872
$767$	0.100399	−	0.173897i	0.00362521	−	0.00627904i
$768$		0			0
$769$	10.1939	+	17.6563i	0.367601	+	0.636703i	0.989190	−	0.146640i	$-0.0468460\pi$
$769$	10.1939	+	17.6563i	0.367601	+	0.636703i	−0.621589	+	0.783343i	$0.713513\pi$
$770$	0.234917	+	0.406889i	0.00846583	+	0.0146632i
$771$		0			0
$772$	−6.47044	+	11.2071i	−0.232876	+	0.403353i
$773$	24.4664			0.879994			0.439997	−	0.897999i	$-0.354979\pi$
$773$	24.4664			0.879994			0.439997	+	0.897999i	$0.354979\pi$
$774$		0			0
$775$	34.1739			1.22756
$776$	10.9054	−	18.8888i	0.391482	−	0.678068i
$777$		0			0
$778$	−0.258770	−	0.448204i	−0.00927737	−	0.0160689i
$779$	−2.22415	−	3.85235i	−0.0796886	−	0.138025i
$780$		0			0
$781$	−17.6878	+	30.6361i	−0.632919	+	1.09625i
$782$	25.4816			0.911221
$783$		0			0
$784$	−9.85978			−0.352135
$785$	8.84894	−	15.3268i	0.315832	−	0.547038i
$786$		0			0

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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(0.342020 - 0.592396i) q^{2} +(0.766044 + 1.32683i) q^{4} +(0.524005 + 0.907604i) q^{5} +(0.0603074 - 0.104455i) q^{7} +2.41609 q^{8} +O(q^{10})\)	\(q+(0.342020 - 0.592396i) q^{2} +(0.766044 + 1.32683i) q^{4} +(0.524005 + 0.907604i) q^{5} +(0.0603074 - 0.104455i) q^{7} +2.41609 q^{8} +0.716881 q^{10} +(-2.71686 + 4.70574i) q^{11} +(2.28699 + 3.96118i) q^{13} +(-0.0412527 - 0.0714517i) q^{14} +(-0.705737 + 1.22237i) q^{16} -4.77833 q^{17} -0.588526 q^{19} +(-0.802823 + 1.39053i) q^{20} +(1.85844 + 3.21891i) q^{22} +(-3.89798 - 6.75150i) q^{23} +(1.95084 - 3.37895i) q^{25} +3.12879 q^{26} +0.184793 q^{28} +(2.53487 - 4.39053i) q^{29} +(4.37939 + 7.58532i) q^{31} +(2.89884 + 5.02094i) q^{32} +(-1.63429 + 2.83067i) q^{34} +0.126406 q^{35} -2.18479 q^{37} +(-0.201288 + 0.348641i) q^{38} +(1.26604 + 2.19285i) q^{40} +(3.77920 + 6.54576i) q^{41} +(0.652704 - 1.13052i) q^{43} -8.32494 q^{44} -5.33275 q^{46} +(1.20805 - 2.09240i) q^{47} +(3.49273 + 6.04958i) q^{49} +(-1.33445 - 2.31134i) q^{50} +(-3.50387 + 6.06888i) q^{52} +3.04628 q^{53} -5.69459 q^{55} +(0.145708 - 0.252374i) q^{56} +(-1.73396 - 3.00330i) q^{58} +(-0.0219501 - 0.0380187i) q^{59} +(5.10607 - 8.84397i) q^{61} +5.99135 q^{62} +1.14290 q^{64} +(-2.39679 + 4.15136i) q^{65} +(0.929892 + 1.61062i) q^{67} +(-3.66041 - 6.34002i) q^{68} +(0.0432332 - 0.0748822i) q^{70} +6.51038 q^{71} +12.2344 q^{73} +(-0.747243 + 1.29426i) q^{74} +(-0.450837 - 0.780873i) q^{76} +(0.327693 + 0.567581i) q^{77} +(-0.351167 + 0.608239i) q^{79} -1.47924 q^{80} +5.17024 q^{82} +(3.38830 - 5.86871i) q^{83} +(-2.50387 - 4.33683i) q^{85} +(-0.446476 - 0.773318i) q^{86} +(-6.56418 + 11.3695i) q^{88} -6.85565 q^{89} +0.551689 q^{91} +(5.97205 - 10.3439i) q^{92} +(-0.826352 - 1.43128i) q^{94} +(-0.308391 - 0.534148i) q^{95} +(4.51367 - 7.81791i) q^{97} +4.77833 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 12 q^{7}+O(q^{10}) \) 12 * q + 12 * q^7	\( 12 q + 12 q^{7} - 24 q^{10} + 12 q^{13} + 12 q^{16} - 48 q^{19} + 6 q^{22} - 12 q^{28} + 30 q^{31} - 12 q^{37} + 6 q^{40} + 12 q^{43} + 12 q^{46} + 6 q^{49} + 6 q^{52} - 60 q^{55} - 30 q^{58} + 12 q^{61} + 12 q^{64} - 6 q^{67} - 30 q^{70} + 24 q^{73} + 18 q^{76} + 48 q^{79} - 24 q^{82} + 18 q^{85} - 42 q^{88} - 12 q^{94} + 12 q^{97}+O(q^{100}) \) 12 * q + 12 * q^7 - 24 * q^10 + 12 * q^13 + 12 * q^16 - 48 * q^19 + 6 * q^22 - 12 * q^28 + 30 * q^31 - 12 * q^37 + 6 * q^40 + 12 * q^43 + 12 * q^46 + 6 * q^49 + 6 * q^52 - 60 * q^55 - 30 * q^58 + 12 * q^61 + 12 * q^64 - 6 * q^67 - 30 * q^70 + 24 * q^73 + 18 * q^76 + 48 * q^79 - 24 * q^82 + 18 * q^85 - 42 * q^88 - 12 * q^94 + 12 * q^97

Introduction

L-functions

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