LMFDB - Embedded newform 3276.2.x.k.2557.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3276,2,Mod(2557,3276)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3276, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2, 4]))

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

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

chi := DirichletCharacter("3276.2557");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3276 = 2^{2} \cdot 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3276.x (of order $3$, degree $2$, 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:	$26.1589917022$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$9$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - x^{17} + 19 x^{16} - 16 x^{15} + 244 x^{14} - 181 x^{13} + 1600 x^{12} - 607 x^{11} + \cdots + 1296 $ x^18 - x^17 + 19x^16 - 16x^15 + 244x^14 - 181x^13 + 1600x^12 - 607x^11 + 7069x^10 - 1482x^9 + 17139x^8 + 5442x^7 + 25305x^6 + 13059x^5 + 28116x^4 + 18981x^3 + 15021x^2 + 4644x + 1296
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 3^{3} $
Twist minimal:	no (minimal twist has level 364)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			2557.1
Root			$-0.520270 - 0.901135i$ of defining polynomial
Character	$\chi$	$=$	3276.2557
Dual form			3276.2.x.k.2629.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.59004 + 2.75404i) q^{5} +(2.63951 - 0.181658i) q^{7} +1.70494 q^{11} +(-2.78983 - 2.28404i) q^{13} +(-1.40001 + 2.42488i) q^{17} +5.48910 q^{19} +(2.73500 + 4.73716i) q^{23} +(-2.55648 - 4.42795i) q^{25} +(-3.81432 + 6.60660i) q^{29} +(1.25981 + 2.18206i) q^{31} +(-3.69664 + 7.55814i) q^{35} +(-3.95043 - 6.84235i) q^{37} +(4.19364 - 7.26359i) q^{41} +(5.61467 + 9.72490i) q^{43} +(3.12503 - 5.41272i) q^{47} +(6.93400 - 0.958974i) q^{49} +(-0.921060 - 1.59532i) q^{53} +(-2.71093 + 4.69547i) q^{55} +(-1.34710 + 2.33325i) q^{59} -6.77693 q^{61} +(10.7263 - 4.05157i) q^{65} +3.58333 q^{67} +(2.00501 + 3.47278i) q^{71} +(5.85146 + 10.1350i) q^{73} +(4.50020 - 0.309716i) q^{77} +(-6.62195 + 11.4695i) q^{79} -8.55336 q^{83} +(-4.45215 - 7.71134i) q^{85} +(0.105061 + 0.181971i) q^{89} +(-7.77869 - 5.52195i) q^{91} +(-8.72791 + 15.1172i) q^{95} +(6.33077 + 10.9652i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + q^{7} + 4 q^{11} + 4 q^{13} + 6 q^{17} + 2 q^{19} - 6 q^{23} - 5 q^{25} - 2 q^{29} + 7 q^{31} + 3 q^{35} - 8 q^{37} - 7 q^{41} - 2 q^{43} + 12 q^{47} + 9 q^{49} - 13 q^{53} - q^{55} + 8 q^{59}+ \cdots - 24 q^{97}+O(q^{100}) $ 18 * q + q^7 + 4 * q^11 + 4 * q^13 + 6 * q^17 + 2 * q^19 - 6 * q^23 - 5 * q^25 - 2 * q^29 + 7 * q^31 + 3 * q^35 - 8 * q^37 - 7 * q^41 - 2 * q^43 + 12 * q^47 + 9 * q^49 - 13 * q^53 - q^55 + 8 * q^59 + 2 * q^61 - 10 * q^65 - 58 * q^67 - 7 * q^71 + 9 * q^73 + 31 * q^77 - 2 * q^79 + 30 * q^83 - 46 * q^85 - 13 * q^89 - 14 * q^91 + 14 * q^95 - 24 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3276\mathbb{Z}\right)^\times$.

$n$	$1639$	$2017$	$2341$	$2549$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$1$

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			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−1.59004	+	2.75404i	−0.711089	+	1.23164i	0.253359	+	0.967372i	$0.418464\pi$
$5$	−1.59004	+	2.75404i	−0.711089	+	1.23164i	−0.964449	+	0.264270i	$0.914869\pi$
$6$		0			0
$7$	2.63951	−	0.181658i	0.997640	−	0.0686602i
$7$	2.63951	−	0.181658i	0.997640	−	0.0686602i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	1.70494			0.514059			0.257029	−	0.966404i	$-0.417256\pi$
$11$	1.70494			0.514059			0.257029	+	0.966404i	$0.417256\pi$
$12$		0			0
$13$	−2.78983	−	2.28404i	−0.773760	−	0.633479i
$13$	−2.78983	−	2.28404i	−0.773760	−	0.633479i
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−1.40001	+	2.42488i	−0.339552	+	0.588121i	−0.984348	−	0.176233i	$-0.943609\pi$
$17$	−1.40001	+	2.42488i	−0.339552	+	0.588121i	0.644797	+	0.764354i	$0.276942\pi$
$18$		0			0
$19$	5.48910			1.25929			0.629643	−	0.776885i	$-0.283201\pi$
$19$	5.48910			1.25929			0.629643	+	0.776885i	$0.283201\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	2.73500	+	4.73716i	0.570287	+	0.987766i	0.996536	+	0.0831603i	$0.0265014\pi$
$23$	2.73500	+	4.73716i	0.570287	+	0.987766i	−0.426249	+	0.904606i	$0.640165\pi$
$24$		0			0
$25$	−2.55648	−	4.42795i	−0.511296	−	0.885590i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−3.81432	+	6.60660i	−0.708302	+	1.22682i	0.257185	+	0.966362i	$0.417205\pi$
$29$	−3.81432	+	6.60660i	−0.708302	+	1.22682i	−0.965487	+	0.260453i	$0.916128\pi$
$30$		0			0
$31$	1.25981	+	2.18206i	0.226269	+	0.391909i	0.956699	−	0.291078i	$-0.0940140\pi$
$31$	1.25981	+	2.18206i	0.226269	+	0.391909i	−0.730431	+	0.682987i	$0.760681\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−3.69664	+	7.55814i	−0.624846	+	1.27756i
$36$		0			0
$37$	−3.95043	−	6.84235i	−0.649447	−	1.12487i	−0.983255	−	0.182234i	$-0.941667\pi$
$37$	−3.95043	−	6.84235i	−0.649447	−	1.12487i	0.333808	−	0.942641i	$-0.391666\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	4.19364	−	7.26359i	0.654936	−	1.13438i	−0.326974	−	0.945033i	$-0.606029\pi$
$41$	4.19364	−	7.26359i	0.654936	−	1.13438i	0.981910	−	0.189349i	$-0.0606379\pi$
$42$		0			0
$43$	5.61467	+	9.72490i	0.856230	+	1.48303i	0.875499	+	0.483219i	$0.160533\pi$
$43$	5.61467	+	9.72490i	0.856230	+	1.48303i	−0.0192697	+	0.999814i	$0.506134\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	3.12503	−	5.41272i	0.455833	−	0.789526i	−0.542903	−	0.839796i	$-0.682675\pi$
$47$	3.12503	−	5.41272i	0.455833	−	0.789526i	0.998736	+	0.0502697i	$0.0160081\pi$
$48$		0			0
$49$	6.93400	−	0.958974i	0.990572	−	0.136996i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−0.921060	−	1.59532i	−0.126517	−	0.219134i	0.795808	−	0.605549i	$-0.207047\pi$
$53$	−0.921060	−	1.59532i	−0.126517	−	0.219134i	−0.922325	+	0.386415i	$0.873713\pi$
$54$		0			0
$55$	−2.71093	+	4.69547i	−0.365542	+	0.633137i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−1.34710	+	2.33325i	−0.175378	+	0.303764i	−0.940292	−	0.340369i	$-0.889448\pi$
$59$	−1.34710	+	2.33325i	−0.175378	+	0.303764i	0.764914	+	0.644132i	$0.222781\pi$
$60$		0			0
$61$	−6.77693			−0.867697			−0.433848	−	0.900986i	$-0.642845\pi$
$61$	−6.77693			−0.867697			−0.433848	+	0.900986i	$0.642845\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	10.7263	−	4.05157i	1.33043	−	0.502536i
$66$		0			0
$67$	3.58333			0.437773			0.218887	−	0.975750i	$-0.429757\pi$
$67$	3.58333			0.437773			0.218887	+	0.975750i	$0.429757\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	2.00501	+	3.47278i	0.237951	+	0.412143i	0.960126	−	0.279567i	$-0.0901909\pi$
$71$	2.00501	+	3.47278i	0.237951	+	0.412143i	−0.722175	+	0.691710i	$0.756858\pi$
$72$		0			0
$73$	5.85146	+	10.1350i	0.684862	+	1.18622i	0.973480	+	0.228771i	$0.0734709\pi$
$73$	5.85146	+	10.1350i	0.684862	+	1.18622i	−0.288618	+	0.957444i	$0.593196\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	4.50020	−	0.309716i	0.512846	−	0.0352954i
$78$		0			0
$79$	−6.62195	+	11.4695i	−0.745027	+	1.29043i	0.205155	+	0.978730i	$0.434230\pi$
$79$	−6.62195	+	11.4695i	−0.745027	+	1.29043i	−0.950182	+	0.311696i	$0.899103\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−8.55336			−0.938853			−0.469426	−	0.882972i	$-0.655539\pi$
$83$	−8.55336			−0.938853			−0.469426	+	0.882972i	$0.655539\pi$
$84$		0			0
$85$	−4.45215	−	7.71134i	−0.482903	−	0.836413i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	0.105061	+	0.181971i	0.0111364	+	0.0192889i	0.871540	−	0.490325i	$-0.163122\pi$
$89$	0.105061	+	0.181971i	0.0111364	+	0.0192889i	−0.860403	+	0.509613i	$0.829788\pi$
$90$		0			0
$91$	−7.77869	−	5.52195i	−0.815429	−	0.578858i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−8.72791	+	15.1172i	−0.895464	+	1.55099i
$96$		0			0
$97$	6.33077	+	10.9652i	0.642792	+	1.11335i	0.984807	+	0.173654i	$0.0555574\pi$
$97$	6.33077	+	10.9652i	0.642792	+	1.11335i	−0.342015	+	0.939695i	$0.611109\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−11.5539			−1.14965			−0.574826	−	0.818276i	$-0.694930\pi$
$101$	−11.5539			−1.14965			−0.574826	+	0.818276i	$0.694930\pi$
$102$		0			0
$103$	6.10134	−	10.5678i	0.601183	−	1.04128i	−0.391459	−	0.920195i	$-0.628030\pi$
$103$	6.10134	−	10.5678i	0.601183	−	1.04128i	0.992642	−	0.121084i	$-0.0386370\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−1.13656	−	1.96858i	−0.109875	−	0.190310i	0.805844	−	0.592128i	$-0.201712\pi$
$107$	−1.13656	−	1.96858i	−0.109875	−	0.190310i	−0.915720	+	0.401818i	$0.868379\pi$
$108$		0			0
$109$	2.42607	+	4.20208i	0.232376	+	0.402487i	0.958507	−	0.285070i	$-0.0920168\pi$
$109$	2.42607	+	4.20208i	0.232376	+	0.402487i	−0.726131	+	0.687556i	$0.758683\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	0.333301	+	0.577294i	0.0313543	+	0.0543072i	0.881277	−	0.472601i	$-0.156685\pi$
$113$	0.333301	+	0.577294i	0.0313543	+	0.0543072i	−0.849922	+	0.526908i	$0.823351\pi$
$114$		0			0
$115$	−17.3951			−1.62210
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−3.25483	+	6.65482i	−0.298370	+	0.610046i
$120$		0			0
$121$	−8.09318			−0.735743
$122$		0			0
$123$		0			0
$124$		0			0
$125$	0.359215			0.0321292
$126$		0			0
$127$	−9.03831	+	15.6548i	−0.802020	+	1.38914i	0.116264	+	0.993218i	$0.462908\pi$
$127$	−9.03831	+	15.6548i	−0.802020	+	1.38914i	−0.918284	+	0.395922i	$0.870425\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	9.35254	−	16.1991i	0.817135	−	1.41532i	−0.0906496	−	0.995883i	$-0.528894\pi$
$131$	9.35254	−	16.1991i	0.817135	−	1.41532i	0.907785	−	0.419437i	$-0.137772\pi$
$132$		0			0
$133$	14.4885	−	0.997137i	1.25631	−	0.0864628i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−11.2574	+	19.4984i	−0.961786	+	1.66586i	−0.243775	+	0.969832i	$0.578386\pi$
$137$	−11.2574	+	19.4984i	−0.961786	+	1.66586i	−0.718012	+	0.696031i	$0.754948\pi$
$138$		0			0
$139$	3.61314	+	6.25815i	0.306463	+	0.530809i	0.977586	−	0.210537i	$-0.0675212\pi$
$139$	3.61314	+	6.25815i	0.306463	+	0.530809i	−0.671123	+	0.741346i	$0.734188\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−4.75650	−	3.89415i	−0.397758	−	0.325646i
$144$		0			0
$145$	−12.1299	−	21.0096i	−1.00733	−	1.74475i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	7.49862			0.614311			0.307155	−	0.951659i	$-0.400623\pi$
$149$	7.49862			0.614311			0.307155	+	0.951659i	$0.400623\pi$
$150$		0			0
$151$	0.992571	+	1.71918i	0.0807743	+	0.139905i	0.903583	−	0.428414i	$-0.140927\pi$
$151$	0.992571	+	1.71918i	0.0807743	+	0.139905i	−0.822808	+	0.568319i	$0.807594\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−8.01261			−0.643589
$156$		0			0
$157$	−2.01235	−	3.48549i	−0.160603	−	0.278172i	0.774482	−	0.632596i	$-0.218010\pi$
$157$	−2.01235	−	3.48549i	−0.160603	−	0.278172i	−0.935085	+	0.354424i	$0.884677\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	8.07960	+	12.0069i	0.636761	+	0.946279i
$162$		0			0
$163$	−3.98715			−0.312298			−0.156149	−	0.987734i	$-0.549908\pi$
$163$	−3.98715			−0.312298			−0.156149	+	0.987734i	$0.549908\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	1.98915	−	3.44532i	0.153925	−	0.266607i	−0.778742	−	0.627345i	$-0.784142\pi$
$167$	1.98915	−	3.44532i	0.153925	−	0.266607i	0.932667	+	0.360738i	$0.117475\pi$
$168$		0			0
$169$	2.56631	+	12.7442i	0.197409	+	0.980321i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−22.7206			−1.72741			−0.863706	−	0.503996i	$-0.831863\pi$
$173$	−22.7206			−1.72741			−0.863706	+	0.503996i	$0.831863\pi$
$174$		0			0
$175$	−7.55222	−	11.2232i	−0.570894	−	0.848395i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	4.13020			0.308706			0.154353	−	0.988016i	$-0.450671\pi$
$179$	4.13020			0.308706			0.154353	+	0.988016i	$0.450671\pi$
$180$		0			0
$181$	2.63446			0.195818			0.0979091	−	0.995195i	$-0.468785\pi$
$181$	2.63446			0.195818			0.0979091	+	0.995195i	$0.468785\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	25.1254			1.84726
$186$		0			0
$187$	−2.38693	+	4.13428i	−0.174550	+	0.302329i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	4.68011			0.338641			0.169320	−	0.985561i	$-0.445843\pi$
$191$	4.68011			0.338641			0.169320	+	0.985561i	$0.445843\pi$
$192$		0			0
$193$	−17.9366			−1.29110			−0.645551	−	0.763717i	$-0.723372\pi$
$193$	−17.9366			−1.29110			−0.645551	+	0.763717i	$0.723372\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−11.3526	+	19.6632i	−0.808838	+	1.40095i	0.104832	+	0.994490i	$0.466570\pi$
$197$	−11.3526	+	19.6632i	−0.808838	+	1.40095i	−0.913669	+	0.406458i	$0.866764\pi$
$198$		0			0
$199$	3.97980	−	6.89322i	0.282121	−	0.488648i	−0.689786	−	0.724013i	$-0.742295\pi$
$199$	3.97980	−	6.89322i	0.282121	−	0.488648i	0.971907	+	0.235366i	$0.0756287\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−8.86779	+	18.1311i	−0.622397	+	1.27255i
$204$		0			0
$205$	13.3361	+	23.0989i	0.931436	+	1.61329i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	9.35859			0.647347
$210$		0			0
$211$	−5.08147	+	8.80136i	−0.349823	+	0.605911i	−0.986218	−	0.165453i	$-0.947092\pi$
$211$	−5.08147	+	8.80136i	−0.349823	+	0.605911i	0.636395	+	0.771363i	$0.280425\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−35.7103			−2.43542
$216$		0			0
$217$	3.72167	+	5.53070i	0.252643	+	0.375448i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	9.44432	−	3.56734i	0.635294	−	0.239965i
$222$		0			0
$223$	1.33387	−	2.31033i	0.0893224	−	0.154711i	−0.817902	−	0.575357i	$-0.804863\pi$
$223$	1.33387	−	2.31033i	0.0893224	−	0.154711i	0.907225	+	0.420646i	$0.138197\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−12.5757	+	21.7817i	−0.834677	+	1.44570i	0.0596159	+	0.998221i	$0.481012\pi$
$227$	−12.5757	+	21.7817i	−0.834677	+	1.44570i	−0.894293	+	0.447482i	$0.852321\pi$
$228$		0			0
$229$	6.15374	−	10.6586i	0.406651	−	0.704339i	−0.587862	−	0.808962i	$-0.700030\pi$
$229$	6.15374	−	10.6586i	0.406651	−	0.704339i	0.994512	+	0.104622i	$0.0333633\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−10.5720	+	18.3112i	−0.692594	+	1.19961i	0.278391	+	0.960468i	$0.410199\pi$
$233$	−10.5720	+	18.3112i	−0.692594	+	1.19961i	−0.970985	+	0.239141i	$0.923134\pi$
$234$		0			0
$235$	9.93788	+	17.2129i	0.648276	+	1.12285i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	27.3984			1.77225			0.886127	−	0.463443i	$-0.153386\pi$
$239$	27.3984			1.77225			0.886127	+	0.463443i	$0.153386\pi$
$240$		0			0
$241$	−8.57805	+	14.8576i	−0.552561	+	0.957064i	0.445528	+	0.895268i	$0.353016\pi$
$241$	−8.57805	+	14.8576i	−0.552561	+	0.957064i	−0.998089	+	0.0617955i	$0.980317\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−8.38432	+	20.6213i	−0.535654	+	1.31745i
$246$		0			0
$247$	−15.3137	−	12.5373i	−0.974385	−	0.797731i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	13.4469	+	23.2907i	0.848759	+	1.47009i	0.882317	+	0.470656i	$0.155983\pi$
$251$	13.4469	+	23.2907i	0.848759	+	1.47009i	−0.0335582	+	0.999437i	$0.510684\pi$
$252$		0			0
$253$	4.66301	+	8.07658i	0.293161	+	0.507770i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−5.65006	−	9.78619i	−0.352441	−	0.610446i	0.634235	−	0.773140i	$-0.281315\pi$
$257$	−5.65006	−	9.78619i	−0.352441	−	0.610446i	−0.986677	+	0.162694i	$0.947982\pi$
$258$		0			0
$259$	−11.6702	−	17.3428i	−0.725148	−	1.07763i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	0.997479			0.0615072			0.0307536	−	0.999527i	$-0.490209\pi$
$263$	0.997479			0.0615072			0.0307536	+	0.999527i	$0.490209\pi$
$264$		0			0
$265$	5.85810			0.359860
$266$		0			0
$267$		0			0
$268$		0			0
$269$	6.56406	−	11.3693i	0.400218	−	0.693198i	−0.593534	−	0.804809i	$-0.702268\pi$
$269$	6.56406	−	11.3693i	0.400218	−	0.693198i	0.993752	+	0.111611i	$0.0356010\pi$
$270$		0			0
$271$	−3.22120	−	5.57928i	−0.195674	−	0.338917i	0.751447	−	0.659793i	$-0.229356\pi$
$271$	−3.22120	−	5.57928i	−0.195674	−	0.338917i	−0.947121	+	0.320876i	$0.896023\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−4.35864	−	7.54939i	−0.262836	−	0.455246i
$276$		0			0
$277$	11.9907	−	20.7685i	0.720451	−	1.24786i	−0.240369	−	0.970682i	$-0.577268\pi$
$277$	11.9907	−	20.7685i	0.720451	−	1.24786i	0.960819	−	0.277175i	$-0.0893983\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	10.3602			0.618035			0.309018	−	0.951056i	$-0.400000\pi$
$281$	10.3602			0.618035			0.309018	+	0.951056i	$0.400000\pi$
$282$		0			0
$283$	29.9130			1.77814			0.889071	−	0.457769i	$-0.151351\pi$
$283$	29.9130			1.77814			0.889071	+	0.457769i	$0.151351\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	9.74965	−	19.9341i	0.575504	−	1.17667i
$288$		0			0
$289$	4.57996	+	7.93272i	0.269409	+	0.466631i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−0.184399	−	0.319389i	−0.0107727	−	0.0186589i	0.860589	−	0.509300i	$-0.170096\pi$
$293$	−0.184399	−	0.319389i	−0.0107727	−	0.0186589i	−0.871362	+	0.490642i	$0.836762\pi$
$294$		0			0
$295$	−4.28391	−	7.41995i	−0.249419	−	0.432006i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	3.18968	−	19.4627i	0.184464	−	1.12556i
$300$		0			0
$301$	16.5866	+	24.6490i	0.956034	+	1.42074i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	10.7756	−	18.6639i	0.617010	−	1.06869i
$306$		0			0
$307$	−13.8684			−0.791511			−0.395756	−	0.918356i	$-0.629517\pi$
$307$	−13.8684			−0.791511			−0.395756	+	0.918356i	$0.629517\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−0.590595	−	1.02294i	−0.0334895	−	0.0580056i	0.848795	−	0.528722i	$-0.177329\pi$
$311$	−0.590595	−	1.02294i	−0.0334895	−	0.0580056i	−0.882284	+	0.470717i	$0.843995\pi$
$312$		0			0
$313$	5.29311	−	9.16793i	0.299184	−	0.518202i	−0.676765	−	0.736199i	$-0.736619\pi$
$313$	5.29311	−	9.16793i	0.299184	−	0.518202i	0.975950	+	0.217997i	$0.0699522\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	4.24444	−	7.35159i	0.238392	−	0.412906i	−0.721861	−	0.692038i	$-0.756713\pi$
$317$	4.24444	−	7.35159i	0.238392	−	0.412906i	0.960253	+	0.279131i	$0.0900465\pi$
$318$		0			0
$319$	−6.50319	+	11.2639i	−0.364109	+	0.630655i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−7.68478	+	13.3104i	−0.427592	+	0.740612i
$324$		0			0
$325$	−2.98148	+	18.1923i	−0.165383	+	1.00913i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	7.26529	−	14.8546i	0.400548	−	0.818960i
$330$		0			0
$331$	4.34420			0.238779			0.119389	−	0.992848i	$-0.461906\pi$
$331$	4.34420			0.238779			0.119389	+	0.992848i	$0.461906\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−5.69765	+	9.86862i	−0.311296	+	0.539180i
$336$		0			0
$337$	8.59397			0.468143			0.234072	−	0.972219i	$-0.424795\pi$
$337$	8.59397			0.468143			0.234072	+	0.972219i	$0.424795\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	2.14790	+	3.72027i	0.116315	+	0.201464i
$342$		0			0
$343$	18.1281	−	3.79083i	0.978828	−	0.204686i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	10.4098	−	18.0304i	0.558829	−	0.967920i	−0.438765	−	0.898602i	$-0.644584\pi$
$347$	10.4098	−	18.0304i	0.558829	−	0.967920i	0.997595	−	0.0693188i	$-0.0220826\pi$
$348$		0			0
$349$	−0.115786	+	0.200546i	−0.00619786	+	0.0107350i	−0.869108	−	0.494623i	$-0.835306\pi$
$349$	−0.115786	+	0.200546i	−0.00619786	+	0.0107350i	0.862910	+	0.505358i	$0.168640\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	18.1994			0.968659			0.484329	−	0.874886i	$-0.339064\pi$
$353$	18.1994			0.968659			0.484329	+	0.874886i	$0.339064\pi$
$354$		0			0
$355$	−12.7522			−0.676817
$356$		0			0
$357$		0			0
$358$		0			0
$359$	2.27149	−	3.93434i	0.119885	−	0.207646i	−0.799837	−	0.600217i	$-0.795081\pi$
$359$	2.27149	−	3.93434i	0.119885	−	0.207646i	0.919722	+	0.392571i	$0.128414\pi$
$360$		0			0
$361$	11.1302			0.585800
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−37.2163			−1.94799
$366$		0			0
$367$	10.0228			0.523185			0.261592	−	0.965178i	$-0.415752\pi$
$367$	10.0228			0.523185			0.261592	+	0.965178i	$0.415752\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−2.72095	−	4.04355i	−0.141265	−	0.209931i
$372$		0			0
$373$	8.43135			0.436559			0.218279	−	0.975886i	$-0.429956\pi$
$373$	8.43135			0.436559			0.218279	+	0.975886i	$0.429956\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	25.7311	−	9.71923i	1.32522	−	0.500566i
$378$		0			0
$379$	−5.15804	+	8.93398i	−0.264951	+	0.458908i	−0.967551	−	0.252677i	$-0.918689\pi$
$379$	−5.15804	+	8.93398i	−0.264951	+	0.458908i	0.702600	+	0.711585i	$0.252022\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	2.19625			0.112223			0.0561116	−	0.998425i	$-0.482130\pi$
$383$	2.19625			0.112223			0.0561116	+	0.998425i	$0.482130\pi$
$384$		0			0
$385$	−6.30255	+	12.8862i	−0.321208	+	0.656741i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−16.3977	−	28.4017i	−0.831398	−	1.44002i	−0.896930	−	0.442173i	$-0.854208\pi$
$389$	−16.3977	−	28.4017i	−0.831398	−	1.44002i	0.0655315	−	0.997851i	$-0.479126\pi$
$390$		0			0
$391$	−15.3161			−0.774568
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−21.0584	−	36.4742i	−1.05956	−	1.83521i
$396$		0			0
$397$	−5.51695			−0.276888			−0.138444	−	0.990370i	$-0.544210\pi$
$397$	−5.51695			−0.276888			−0.138444	+	0.990370i	$0.544210\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−9.66790	−	16.7453i	−0.482792	−	0.836220i	0.517013	−	0.855977i	$-0.327044\pi$
$401$	−9.66790	−	16.7453i	−0.482792	−	0.836220i	−0.999805	+	0.0197577i	$0.993711\pi$
$402$		0			0
$403$	1.46925	−	8.96502i	0.0731884	−	0.446580i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−6.73525	−	11.6658i	−0.333854	−	0.578252i
$408$		0			0
$409$	18.0322	−	31.2326i	0.891633	−	1.54435i	0.0537150	−	0.998556i	$-0.482894\pi$
$409$	18.0322	−	31.2326i	0.891633	−	1.54435i	0.837918	−	0.545797i	$-0.183773\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−3.13184	+	6.40335i	−0.154108	+	0.315088i
$414$		0			0
$415$	13.6002	−	23.5563i	0.667608	−	1.15633i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	4.22915	−	7.32510i	0.206607	−	0.357854i	−0.744036	−	0.668139i	$-0.767091\pi$
$419$	4.22915	−	7.32510i	0.206607	−	0.357854i	0.950644	+	0.310285i	$0.100424\pi$
$420$		0			0
$421$	−40.2697			−1.96262			−0.981312	−	0.192424i	$-0.938365\pi$
$421$	−40.2697			−1.96262			−0.981312	+	0.192424i	$0.938365\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	14.3164			0.694445
$426$		0			0
$427$	−17.8878	+	1.23108i	−0.865649	+	0.0595762i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	13.0760			0.629847			0.314924	−	0.949117i	$-0.398021\pi$
$431$	13.0760			0.629847			0.314924	+	0.949117i	$0.398021\pi$
$432$		0			0
$433$	9.78438	+	16.9470i	0.470207	+	0.814423i	0.999420	−	0.0340664i	$-0.0108458\pi$
$433$	9.78438	+	16.9470i	0.470207	+	0.814423i	−0.529212	+	0.848490i	$0.677512\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	15.0127	+	26.0027i	0.718154	+	1.24388i
$438$		0			0
$439$	−7.19768	−	12.4667i	−0.343527	−	0.595006i	0.641558	−	0.767074i	$-0.278288\pi$
$439$	−7.19768	−	12.4667i	−0.343527	−	0.595006i	−0.985085	+	0.172069i	$0.944955\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	4.31882	−	7.48041i	0.205193	−	0.355405i	−0.745001	−	0.667063i	$-0.767551\pi$
$443$	4.31882	−	7.48041i	0.205193	−	0.355405i	0.950194	+	0.311658i	$0.100884\pi$
$444$		0			0
$445$	−0.668206			−0.0316760
$446$		0			0
$447$		0			0
$448$		0			0
$449$	11.4447	+	19.8228i	0.540110	+	0.935498i	0.998897	+	0.0469519i	$0.0149507\pi$
$449$	11.4447	+	19.8228i	0.540110	+	0.935498i	−0.458787	+	0.888546i	$0.651716\pi$
$450$		0			0
$451$	7.14990	−	12.3840i	0.336676	−	0.583140i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	27.5761	−	12.6427i	1.29279	−	0.592697i
$456$		0			0
$457$	12.9024	+	22.3476i	0.603548	+	1.04538i	0.992279	+	0.124024i	$0.0395800\pi$
$457$	12.9024	+	22.3476i	0.603548	+	1.04538i	−0.388732	+	0.921351i	$0.627087\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	3.84106	+	6.65291i	0.178896	+	0.309857i	0.941503	−	0.337005i	$-0.109414\pi$
$461$	3.84106	+	6.65291i	0.178896	+	0.309857i	−0.762607	+	0.646862i	$0.776081\pi$
$462$		0			0
$463$	7.95930			0.369900			0.184950	−	0.982748i	$-0.440788\pi$
$463$	7.95930			0.369900			0.184950	+	0.982748i	$0.440788\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	10.7578	−	18.6330i	0.497810	−	0.862233i	−0.502186	−	0.864759i	$-0.667471\pi$
$467$	10.7578	−	18.6330i	0.497810	−	0.862233i	0.999997	+	0.00252639i	$0.000804175\pi$
$468$		0			0
$469$	9.45822	−	0.650939i	0.436740	−	0.0300576i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	9.57269	+	16.5804i	0.440153	+	0.762367i
$474$		0			0
$475$	−14.0328	−	24.3055i	−0.643867	−	1.11521i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−33.5009			−1.53070			−0.765348	−	0.643617i	$-0.777433\pi$
$479$	−33.5009			−1.53070			−0.765348	+	0.643617i	$0.777433\pi$
$480$		0			0
$481$	−4.60717	+	28.1119i	−0.210069	+	1.28179i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−40.2648			−1.82833
$486$		0			0
$487$	−7.62298	+	13.2034i	−0.345430	+	0.598303i	−0.985432	−	0.170071i	$-0.945600\pi$
$487$	−7.62298	+	13.2034i	−0.345430	+	0.598303i	0.640001	+	0.768374i	$0.278934\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−10.9575	+	18.9790i	−0.494507	+	0.856510i	−0.999980	−	0.00633175i	$-0.997985\pi$
$491$	−10.9575	+	18.9790i	−0.494507	+	0.856510i	0.505473	+	0.862842i	$0.331318\pi$
$492$		0			0
$493$	−10.6802	−	18.4986i	−0.481010	−	0.833134i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	5.92310	+	8.80220i	0.265687	+	0.394833i
$498$		0			0
$499$	18.1564	−	31.4478i	0.812791	−	1.40780i	−0.0981123	−	0.995175i	$-0.531280\pi$
$499$	18.1564	−	31.4478i	0.812791	−	1.40780i	0.910903	−	0.412620i	$-0.135386\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−13.2906	−	23.0199i	−0.592597	−	1.02641i	−0.993881	−	0.110454i	$-0.964769\pi$
$503$	−13.2906	−	23.0199i	−0.592597	−	1.02641i	0.401285	−	0.915953i	$-0.368564\pi$
$504$		0			0
$505$	18.3711	−	31.8198i	0.817505	−	1.41596i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	17.5859	+	30.4597i	0.779483	+	1.35010i	0.932240	+	0.361841i	$0.117852\pi$
$509$	17.5859	+	30.4597i	0.779483	+	1.35010i	−0.152757	+	0.988264i	$0.548815\pi$
$510$		0			0
$511$	17.2861	+	25.6885i	0.764692	+	1.13639i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	19.4028	+	33.6066i	0.854989	+	1.48089i
$516$		0			0
$517$	5.32800	−	9.22836i	0.234325	−	0.405863i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	3.80745	+	6.59470i	0.166807	+	0.288919i	0.937296	−	0.348535i	$-0.113321\pi$
$521$	3.80745	+	6.59470i	0.166807	+	0.288919i	−0.770488	+	0.637454i	$0.779988\pi$
$522$		0			0
$523$	−19.0037	−	32.9154i	−0.830975	−	1.43929i	−0.897266	−	0.441490i	$-0.854450\pi$
$523$	−19.0037	−	32.9154i	−0.830975	−	1.43929i	0.0662915	−	0.997800i	$-0.478883\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−7.05497			−0.307319
$528$		0			0
$529$	−3.46046	+	5.99369i	−0.150455	+	0.260595i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−28.2899	+	10.6858i	−1.22537	+	0.462852i
$534$		0			0
$535$	7.22872			0.312525
$536$		0			0
$537$		0			0
$538$		0			0
$539$	11.8221	−	1.63499i	0.509212	−	0.0704242i
$540$		0			0
$541$	4.45613	−	7.71824i	0.191584	−	0.331833i	−0.754191	−	0.656655i	$-0.771971\pi$
$541$	4.45613	−	7.71824i	0.191584	−	0.331833i	0.945775	+	0.324822i	$0.105304\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−15.4303			−0.660960
$546$		0			0
$547$	−16.7066			−0.714321			−0.357161	−	0.934043i	$-0.616255\pi$
$547$	−16.7066			−0.714321			−0.357161	+	0.934043i	$0.616255\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−20.9372	+	36.2643i	−0.891955	+	1.54491i
$552$		0			0
$553$	−15.3951	+	31.4769i	−0.654668	+	1.33853i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	36.6524			1.55301			0.776507	−	0.630109i	$-0.216990\pi$
$557$	36.6524			1.55301			0.776507	+	0.630109i	$0.216990\pi$
$558$		0			0
$559$	6.54808	−	39.9550i	0.276954	−	1.68992i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−1.96094	+	3.39646i	−0.0826440	+	0.143144i	−0.904385	−	0.426718i	$-0.859670\pi$
$563$	−1.96094	+	3.39646i	−0.0826440	+	0.143144i	0.821741	+	0.569861i	$0.193003\pi$
$564$		0			0
$565$	−2.11985			−0.0891828
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−1.00915	−	1.74790i	−0.0423058	−	0.0732757i	0.844097	−	0.536190i	$-0.180137\pi$
$569$	−1.00915	−	1.74790i	−0.0423058	−	0.0732757i	−0.886403	+	0.462914i	$0.846804\pi$
$570$		0			0
$571$	−2.78183	−	4.81827i	−0.116416	−	0.201639i	0.801929	−	0.597420i	$-0.203807\pi$
$571$	−2.78183	−	4.81827i	−0.116416	−	0.201639i	−0.918345	+	0.395781i	$0.870474\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	13.9839	−	24.2209i	0.583171	−	1.01008i
$576$		0			0
$577$	0.540691	+	0.936505i	0.0225093	+	0.0389872i	0.877061	−	0.480380i	$-0.159501\pi$
$577$	0.540691	+	0.936505i	0.0225093	+	0.0389872i	−0.854551	+	0.519367i	$0.826168\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−22.5766	+	1.55378i	−0.936637	+	0.0644618i
$582$		0			0
$583$	−1.57035	−	2.71993i	−0.0650374	−	0.112648i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	11.3515	−	19.6613i	0.468526	−	0.811510i	−0.530827	−	0.847480i	$-0.678119\pi$
$587$	11.3515	−	19.6613i	0.468526	−	0.811510i	0.999353	+	0.0359699i	$0.0114520\pi$
$588$		0			0
$589$	6.91522	+	11.9775i	0.284937	+	0.493525i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	11.0275	−	19.1002i	0.452846	−	0.784352i	−0.545716	−	0.837970i	$-0.683742\pi$
$593$	11.0275	−	19.1002i	0.452846	−	0.784352i	0.998561	+	0.0536184i	$0.0170755\pi$
$594$		0			0
$595$	−13.1523	−	19.5454i	−0.539192	−	0.801282i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	3.08142	+	5.33717i	0.125903	+	0.218071i	0.922086	−	0.386986i	$-0.126484\pi$
$599$	3.08142	+	5.33717i	0.125903	+	0.218071i	−0.796182	+	0.605057i	$0.793150\pi$
$600$		0			0
$601$	−9.13735	+	15.8264i	−0.372720	+	0.645571i	−0.989983	−	0.141187i	$-0.954908\pi$
$601$	−9.13735	+	15.8264i	−0.372720	+	0.645571i	0.617263	+	0.786757i	$0.288242\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	12.8685	−	22.2889i	0.523179	−	0.906173i
$606$		0			0
$607$	14.9078			0.605088			0.302544	−	0.953135i	$-0.402164\pi$
$607$	14.9078			0.605088			0.302544	+	0.953135i	$0.402164\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−21.0812	+	7.96286i	−0.852853	+	0.322143i
$612$		0			0
$613$	4.64348			0.187548			0.0937742	−	0.995593i	$-0.470107\pi$
$613$	4.64348			0.187548			0.0937742	+	0.995593i	$0.470107\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	5.34393	+	9.25597i	0.215139	+	0.372631i	0.953315	−	0.301976i	$-0.0976463\pi$
$617$	5.34393	+	9.25597i	0.215139	+	0.372631i	−0.738177	+	0.674607i	$0.764313\pi$
$618$		0			0
$619$	10.2913	+	17.8250i	0.413642	+	0.716448i	0.995285	−	0.0969957i	$-0.0309233\pi$
$619$	10.2913	+	17.8250i	0.413642	+	0.716448i	−0.581643	+	0.813444i	$0.697590\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	0.310366	+	0.461229i	0.0124345	+	0.0184787i
$624$		0			0
$625$	12.2112	−	21.1505i	0.488449	−	0.846019i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	22.1225			0.882083
$630$		0			0
$631$	−21.9750	−	38.0619i	−0.874812	−	1.51522i	−0.856963	−	0.515379i	$-0.827651\pi$
$631$	−21.9750	−	38.0619i	−0.874812	−	1.51522i	−0.0178498	−	0.999841i	$-0.505682\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−28.7426	−	49.7837i	−1.14062	−	1.97560i
$636$		0			0
$637$	−21.5350	−	13.1622i	−0.853249	−	0.521504i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	24.3981	−	42.2587i	0.963666	−	1.66912i	0.250509	−	0.968114i	$-0.419402\pi$
$641$	24.3981	−	42.2587i	0.963666	−	1.66912i	0.713157	−	0.701005i	$-0.247265\pi$
$642$		0			0
$643$	−2.08350	−	3.60873i	−0.0821653	−	0.142315i	0.822014	−	0.569467i	$-0.192850\pi$
$643$	−2.08350	−	3.60873i	−0.0821653	−	0.142315i	−0.904180	+	0.427152i	$0.859517\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−16.2616			−0.639310			−0.319655	−	0.947534i	$-0.603567\pi$
$647$	−16.2616			−0.639310			−0.319655	+	0.947534i	$0.603567\pi$
$648$		0			0
$649$	−2.29673	+	3.97806i	−0.0901546	+	0.156152i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	3.91378	+	6.77886i	0.153158	+	0.265277i	0.932387	−	0.361462i	$-0.117722\pi$
$653$	3.91378	+	6.77886i	0.153158	+	0.265277i	−0.779229	+	0.626740i	$0.784389\pi$
$654$		0			0
$655$	29.7419	+	51.5145i	1.16211	+	2.01284i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−20.3114	−	35.1805i	−0.791221	−	1.37044i	−0.925211	−	0.379453i	$-0.876112\pi$
$659$	−20.3114	−	35.1805i	−0.791221	−	1.37044i	0.133990	−	0.990983i	$-0.457221\pi$
$660$		0			0
$661$	−30.8684			−1.20064			−0.600320	−	0.799760i	$-0.704960\pi$
$661$	−30.8684			−1.20064			−0.600320	+	0.799760i	$0.704960\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−20.2912	+	41.4874i	−0.786860	+	1.60881i
$666$		0			0
$667$	−41.7287			−1.61574
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−11.5543			−0.446047
$672$		0			0
$673$	−13.5310	+	23.4364i	−0.521581	+	0.903405i	0.478104	+	0.878303i	$0.341324\pi$
$673$	−13.5310	+	23.4364i	−0.521581	+	0.903405i	−0.999685	+	0.0251020i	$0.992009\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	8.42360	−	14.5901i	0.323745	−	0.560743i	−0.657512	−	0.753444i	$-0.728391\pi$
$677$	8.42360	−	14.5901i	0.323745	−	0.560743i	0.981258	+	0.192701i	$0.0617246\pi$
$678$		0			0
$679$	18.7020	+	27.7927i	0.717718	+	1.06659i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	9.89038	−	17.1306i	0.378445	−	0.655486i	−0.612391	−	0.790555i	$-0.709792\pi$
$683$	9.89038	−	17.1306i	0.378445	−	0.655486i	0.990836	+	0.135069i	$0.0431256\pi$
$684$		0			0
$685$	−35.7996	−	62.0067i	−1.36783	−	2.36915i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−1.07418	+	6.55442i	−0.0409230	+	0.249704i
$690$		0			0
$691$	4.64021	+	8.03707i	0.176522	+	0.305745i	0.940687	−	0.339276i	$-0.110182\pi$
$691$	4.64021	+	8.03707i	0.176522	+	0.305745i	−0.764165	+	0.645021i	$0.776849\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−22.9802			−0.871690
$696$		0			0
$697$	11.7422	+	20.3382i	0.444769	+	0.770363i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−34.6015			−1.30688			−0.653441	−	0.756977i	$-0.726675\pi$
$701$	−34.6015			−1.30688			−0.653441	+	0.756977i	$0.726675\pi$
$702$		0			0
$703$	−21.6843	−	37.5583i	−0.817839	−	1.41654i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−30.4965	+	2.09885i	−1.14694	+	0.0789353i
$708$		0			0
$709$	−15.1165			−0.567711			−0.283855	−	0.958867i	$-0.591614\pi$
$709$	−15.1165			−0.567711			−0.283855	+	0.958867i	$0.591614\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−6.89116	+	11.9358i	−0.258076	+	0.447001i
$714$		0			0
$715$	18.2877	−	6.90769i	0.683920	−	0.258333i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	21.2760			0.793460			0.396730	−	0.917935i	$-0.370145\pi$
$719$	21.2760			0.793460			0.396730	+	0.917935i	$0.370145\pi$
$720$		0			0
$721$	14.1848	−	29.0022i	0.528270	−	1.08010i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	39.0049			1.44861
$726$		0			0
$727$	10.5609			0.391684			0.195842	−	0.980635i	$-0.437256\pi$
$727$	10.5609			0.391684			0.195842	+	0.980635i	$0.437256\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−31.4423			−1.16294
$732$		0			0
$733$	−4.40828	+	7.63536i	−0.162824	+	0.282019i	−0.935880	−	0.352318i	$-0.885393\pi$
$733$	−4.40828	+	7.63536i	−0.162824	+	0.282019i	0.773057	+	0.634337i	$0.218727\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	6.10936			0.225041
$738$		0			0
$739$	29.0768			1.06961			0.534803	−	0.844977i	$-0.320386\pi$
$739$	29.0768			1.06961			0.534803	+	0.844977i	$0.320386\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	19.3225	−	33.4675i	0.708872	−	1.22780i	−0.256404	−	0.966570i	$-0.582538\pi$
$743$	19.3225	−	33.4675i	0.708872	−	1.22780i	0.965276	−	0.261233i	$-0.0841290\pi$
$744$		0			0
$745$	−11.9231	+	20.6515i	−0.436830	+	0.756611i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−3.35757	−	4.98962i	−0.122683	−	0.182317i
$750$		0			0
$751$	20.1942	+	34.9775i	0.736898	+	1.27635i	0.953885	+	0.300171i	$0.0970437\pi$
$751$	20.1942	+	34.9775i	0.736898	+	1.27635i	−0.216987	+	0.976174i	$0.569623\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−6.31293			−0.229751
$756$		0			0
$757$	11.2192	−	19.4322i	0.407768	−	0.706275i	−0.586871	−	0.809680i	$-0.699641\pi$
$757$	11.2192	−	19.4322i	0.407768	−	0.706275i	0.994639	+	0.103405i	$0.0329739\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	17.1650			0.622231			0.311115	−	0.950372i	$-0.399297\pi$
$761$	17.1650			0.622231			0.311115	+	0.950372i	$0.399297\pi$
$762$		0			0
$763$	7.16698	+	10.6507i	0.259462	+	0.385582i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	9.08744	−	3.43254i	0.328128	−	0.123942i
$768$		0			0
$769$	21.4658	−	37.1798i	0.774076	−	1.34074i	−0.161236	−	0.986916i	$-0.551548\pi$
$769$	21.4658	−	37.1798i	0.774076	−	1.34074i	0.935312	−	0.353823i	$-0.115119\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	3.36534	−	5.82893i	0.121043	−	0.209652i	−0.799136	−	0.601150i	$-0.794710\pi$
$773$	3.36534	−	5.82893i	0.121043	−	0.209652i	0.920179	+	0.391498i	$0.128043\pi$
$774$		0			0
$775$	6.44136	−	11.1568i	0.231380	−	0.400762i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	23.0193	−	39.8706i	0.824752	−	1.42851i
$780$		0			0
$781$	3.41842	+	5.92088i	0.122321	+	0.211866i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	12.7989			0.456811
$786$		0			0
$787$	−19.1240	+	33.1238i	−0.681699	+	1.18074i	0.292764	+	0.956185i	$0.405425\pi$
$787$	−19.1240	+	33.1238i	−0.681699	+	1.18074i	−0.974462	+	0.224552i	$0.927908\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	0.984620	+	1.46323i	0.0350091	+	0.0520263i
$792$		0			0
$793$	18.9065	+	15.4788i	0.671389	+	0.549668i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	21.3120	+	36.9134i	0.754909	+	1.30754i	0.945420	+	0.325855i	$0.105652\pi$
$797$	21.3120	+	36.9134i	0.754909	+	1.30754i	−0.190511	+	0.981685i	$0.561015\pi$
$798$		0			0
$799$	8.75014	+	15.1557i	0.309558	+	0.536170i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	9.97640	+	17.2796i	0.352059	+	0.609785i
$804$		0			0
$805$	−45.9145	+	3.15995i	−1.61827	+	0.111374i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	37.4897			1.31807			0.659033	−	0.752114i	$-0.270966\pi$
$809$	37.4897			1.31807			0.659033	+	0.752114i	$0.270966\pi$
$810$		0			0
$811$	−25.4069			−0.892156			−0.446078	−	0.894994i	$-0.647180\pi$
$811$	−25.4069			−0.892156			−0.446078	+	0.894994i	$0.647180\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	6.33975	−	10.9808i	0.222072	−	0.384640i
$816$		0			0
$817$	30.8195	+	53.3809i	1.07824	+	1.86756i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−0.0406154	−	0.0703480i	−0.00141749	−	0.00245516i	0.865316	−	0.501227i	$-0.167118\pi$
$821$	−0.0406154	−	0.0703480i	−0.00141749	−	0.00245516i	−0.866733	+	0.498772i	$0.833785\pi$
$822$		0			0
$823$	0.624767	−	1.08213i	0.0217780	−	0.0377206i	−0.854931	−	0.518742i	$-0.826401\pi$
$823$	0.624767	−	1.08213i	0.0217780	−	0.0377206i	0.876709	+	0.481021i	$0.159734\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−32.9535			−1.14591			−0.572954	−	0.819588i	$-0.694202\pi$
$827$	−32.9535			−1.14591			−0.572954	+	0.819588i	$0.694202\pi$
$828$		0			0
$829$	−17.2241			−0.598218			−0.299109	−	0.954219i	$-0.596689\pi$
$829$	−17.2241			−0.598218			−0.299109	+	0.954219i	$0.596689\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−7.38225	+	18.1567i	−0.255780	+	0.629093i
$834$		0			0
$835$	6.32569	+	10.9564i	0.218909	+	0.379162i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−14.7357	−	25.5229i	−0.508731	−	0.881149i	−0.999949	−	0.0101117i	$-0.996781\pi$
$839$	−14.7357	−	25.5229i	−0.508731	−	0.881149i	0.491217	−	0.871037i	$-0.336552\pi$
$840$		0			0
$841$	−14.5981	−	25.2847i	−0.503383	−	0.871886i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−39.1785	−	13.1961i	−1.34778	−	0.453959i
$846$		0			0
$847$	−21.3620	+	1.47019i	−0.734007	+	0.0505163i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	21.6089	−	37.4276i	0.740742	−	1.28300i
$852$		0			0
$853$	17.8668			0.611747			0.305873	−	0.952072i	$-0.401052\pi$
$853$	17.8668			0.611747			0.305873	+	0.952072i	$0.401052\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	10.0807	+	17.4603i	0.344351	+	0.596433i	0.985236	−	0.171204i	$-0.0547657\pi$
$857$	10.0807	+	17.4603i	0.344351	+	0.596433i	−0.640885	+	0.767637i	$0.721432\pi$
$858$		0			0
$859$	−5.98669	+	10.3692i	−0.204263	+	0.353794i	−0.949898	−	0.312561i	$-0.898813\pi$
$859$	−5.98669	+	10.3692i	−0.204263	+	0.353794i	0.745635	+	0.666355i	$0.232146\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	19.8505	−	34.3821i	0.675719	−	1.17038i	−0.300540	−	0.953769i	$-0.597167\pi$
$863$	19.8505	−	34.3821i	0.675719	−	1.17038i	0.976258	−	0.216610i	$-0.0694999\pi$
$864$		0			0
$865$	36.1267	−	62.5732i	1.22834	−	2.12755i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−11.2900	+	19.5549i	−0.382988	+	0.663355i
$870$		0			0
$871$	−9.99688	−	8.18447i	−0.338731	−	0.277320i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	0.948152	−	0.0652543i	0.0320534	−	0.00220600i
$876$		0			0
$877$	−45.6656			−1.54202			−0.771010	−	0.636823i	$-0.780248\pi$
$877$	−45.6656			−1.54202			−0.771010	+	0.636823i	$0.780248\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	16.6420	−	28.8249i	0.560685	−	0.971134i	−0.436752	−	0.899582i	$-0.643871\pi$
$881$	16.6420	−	28.8249i	0.560685	−	0.971134i	0.997437	−	0.0715523i	$-0.0227953\pi$
$882$		0			0
$883$	32.3115			1.08737			0.543685	−	0.839289i	$-0.317029\pi$
$883$	32.3115			1.08737			0.543685	+	0.839289i	$0.317029\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−16.7530	−	29.0170i	−0.562509	−	0.974295i	−0.997277	−	0.0737520i	$-0.976503\pi$
$887$	−16.7530	−	29.0170i	−0.562509	−	0.974295i	0.434767	−	0.900543i	$-0.356831\pi$
$888$		0			0
$889$	−21.0129	+	42.9629i	−0.704749	+	1.44093i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	17.1536	−	29.7109i	0.574024	−	0.994239i
$894$		0			0
$895$	−6.56721	+	11.3747i	−0.219517	+	0.380215i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−19.2213			−0.641066
$900$		0			0
$901$	5.15796			0.171837
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−4.18891	+	7.25541i	−0.139244	+	0.241178i
$906$		0			0
$907$	−38.8901			−1.29133			−0.645663	−	0.763623i	$-0.723419\pi$
$907$	−38.8901			−1.29133			−0.645663	+	0.763623i	$0.723419\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	41.0133			1.35883			0.679415	−	0.733754i	$-0.262234\pi$
$911$	41.0133			1.35883			0.679415	+	0.733754i	$0.262234\pi$
$912$		0			0
$913$	−14.5830			−0.482626
$914$		0			0
$915$		0			0
$916$		0			0
$917$	21.7434	−	44.4565i	0.718031	−	1.46808i
$918$		0			0
$919$	23.9148			0.788875			0.394438	−	0.918923i	$-0.370939\pi$
$919$	23.9148			0.788875			0.394438	+	0.918923i	$0.370939\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	2.33833	−	14.2680i	0.0769671	−	0.469637i
$924$		0			0
$925$	−20.1984	+	34.9846i	−0.664119	+	1.15029i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	15.4825			0.507964			0.253982	−	0.967209i	$-0.418260\pi$
$929$	15.4825			0.507964			0.253982	+	0.967209i	$0.418260\pi$
$930$		0			0
$931$	38.0614	−	5.26390i	1.24741	−	0.172517i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−7.59064	−	13.1474i	−0.248241	−	0.429965i
$936$		0			0
$937$	38.8172			1.26810			0.634052	−	0.773290i	$-0.281391\pi$
$937$	38.8172			1.26810			0.634052	+	0.773290i	$0.281391\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−2.64172	−	4.57560i	−0.0861177	−	0.149160i	0.819749	−	0.572723i	$-0.194113\pi$
$941$	−2.64172	−	4.57560i	−0.0861177	−	0.149160i	−0.905867	+	0.423562i	$0.860779\pi$
$942$		0			0
$943$	45.8784			1.49401
$944$		0			0
$945$		0			0
$946$		0			0
$947$	3.98486	+	6.90198i	0.129491	+	0.224284i	0.923479	−	0.383648i	$-0.125332\pi$
$947$	3.98486	+	6.90198i	0.129491	+	0.224284i	−0.793989	+	0.607932i	$0.791999\pi$
$948$		0			0
$949$	6.82424	−	41.6400i	0.221524	−	1.35169i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	8.48138	+	14.6902i	0.274739	+	0.475862i	0.970069	−	0.242829i	$-0.0780752\pi$
$953$	8.48138	+	14.6902i	0.274739	+	0.475862i	−0.695330	+	0.718690i	$0.744742\pi$
$954$		0			0
$955$	−7.44157	+	12.8892i	−0.240804	+	0.417084i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−26.1720	+	53.5112i	−0.845138	+	1.72797i
$960$		0			0
$961$	12.3258	−	21.3488i	0.397605	−	0.688672i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	28.5199	−	49.3980i	0.918089	−	1.59018i
$966$		0			0
$967$	21.4177			0.688746			0.344373	−	0.938833i	$-0.388092\pi$
$967$	21.4177			0.688746			0.344373	+	0.938833i	$0.388092\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	16.9302			0.543318			0.271659	−	0.962394i	$-0.412428\pi$
$971$	16.9302			0.543318			0.271659	+	0.962394i	$0.412428\pi$
$972$		0			0
$973$	10.6738	+	15.8621i	0.342185	+	0.508515i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−40.8774			−1.30778			−0.653891	−	0.756588i	$-0.726865\pi$
$977$	−40.8774			−1.30778			−0.653891	+	0.756588i	$0.726865\pi$
$978$		0			0
$979$	0.179123	+	0.310250i	0.00572479	+	0.00991562i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−4.26867	−	7.39355i	−0.136149	−	0.235817i	0.789887	−	0.613253i	$-0.210139\pi$
$983$	−4.26867	−	7.39355i	−0.136149	−	0.235817i	−0.926036	+	0.377435i	$0.876806\pi$
$984$		0			0
$985$	−36.1022	−	62.5308i	−1.15031	−	1.99240i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−30.7123	+	53.1952i	−0.976593	+	1.69151i
$990$		0			0
$991$	35.1748			1.11736			0.558682	−	0.829382i	$-0.311307\pi$
$991$	35.1748			1.11736			0.558682	+	0.829382i	$0.311307\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	12.6561	+	21.9211i	0.401226	+	0.694944i
$996$		0			0
$997$	20.3109	−	35.1795i	0.643252	−	1.11414i	−0.341450	−	0.939900i	$-0.610918\pi$
$997$	20.3109	−	35.1795i	0.643252	−	1.11414i	0.984702	−	0.174245i	$-0.0557485\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3276.2.x.k.2557.1		18
3.2	odd	2		364.2.l.a.9.3	yes	18
7.4	even	3		3276.2.u.k.1621.1		18
13.3	even	3		3276.2.u.k.289.1		18
21.2	odd	6		2548.2.k.h.1569.7		18
21.5	even	6		2548.2.k.i.1569.3		18
21.11	odd	6		364.2.i.a.165.7	✓	18
21.17	even	6		2548.2.i.n.165.3		18
21.20	even	2		2548.2.l.n.373.7		18
39.29	odd	6		364.2.i.a.289.7	yes	18
91.81	even	3	inner	3276.2.x.k.2629.1		18
273.68	even	6		2548.2.k.i.393.3		18
273.107	odd	6		2548.2.k.h.393.7		18
273.146	even	6		2548.2.i.n.1745.3		18
273.185	even	6		2548.2.l.n.1537.7		18
273.263	odd	6		364.2.l.a.81.3	yes	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
364.2.i.a.165.7	✓	18	21.11	odd	6
364.2.i.a.289.7	yes	18	39.29	odd	6
364.2.l.a.9.3	yes	18	3.2	odd	2
364.2.l.a.81.3	yes	18	273.263	odd	6
2548.2.i.n.165.3		18	21.17	even	6
2548.2.i.n.1745.3		18	273.146	even	6
2548.2.k.h.393.7		18	273.107	odd	6
2548.2.k.h.1569.7		18	21.2	odd	6
2548.2.k.i.393.3		18	273.68	even	6
2548.2.k.i.1569.3		18	21.5	even	6
2548.2.l.n.373.7		18	21.20	even	2
2548.2.l.n.1537.7		18	273.185	even	6
3276.2.u.k.289.1		18	13.3	even	3
3276.2.u.k.1621.1		18	7.4	even	3
3276.2.x.k.2557.1		18	1.1	even	1	trivial
3276.2.x.k.2629.1		18	91.81	even	3	inner

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:	\( N \)	\(=\)	\( 3276 = 2^{2} \cdot 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3276.x (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.59004 + 2.75404i) q^{5} +(2.63951 - 0.181658i) q^{7} +1.70494 q^{11} +(-2.78983 - 2.28404i) q^{13} +(-1.40001 + 2.42488i) q^{17} +5.48910 q^{19} +(2.73500 + 4.73716i) q^{23} +(-2.55648 - 4.42795i) q^{25} +(-3.81432 + 6.60660i) q^{29} +(1.25981 + 2.18206i) q^{31} +(-3.69664 + 7.55814i) q^{35} +(-3.95043 - 6.84235i) q^{37} +(4.19364 - 7.26359i) q^{41} +(5.61467 + 9.72490i) q^{43} +(3.12503 - 5.41272i) q^{47} +(6.93400 - 0.958974i) q^{49} +(-0.921060 - 1.59532i) q^{53} +(-2.71093 + 4.69547i) q^{55} +(-1.34710 + 2.33325i) q^{59} -6.77693 q^{61} +(10.7263 - 4.05157i) q^{65} +3.58333 q^{67} +(2.00501 + 3.47278i) q^{71} +(5.85146 + 10.1350i) q^{73} +(4.50020 - 0.309716i) q^{77} +(-6.62195 + 11.4695i) q^{79} -8.55336 q^{83} +(-4.45215 - 7.71134i) q^{85} +(0.105061 + 0.181971i) q^{89} +(-7.77869 - 5.52195i) q^{91} +(-8.72791 + 15.1172i) q^{95} +(6.33077 + 10.9652i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + q^{7} + 4 q^{11} + 4 q^{13} + 6 q^{17} + 2 q^{19} - 6 q^{23} - 5 q^{25} - 2 q^{29} + 7 q^{31} + 3 q^{35} - 8 q^{37} - 7 q^{41} - 2 q^{43} + 12 q^{47} + 9 q^{49} - 13 q^{53} - q^{55} + 8 q^{59}+ \cdots - 24 q^{97}+O(q^{100}) \) 18 * q + q^7 + 4 * q^11 + 4 * q^13 + 6 * q^17 + 2 * q^19 - 6 * q^23 - 5 * q^25 - 2 * q^29 + 7 * q^31 + 3 * q^35 - 8 * q^37 - 7 * q^41 - 2 * q^43 + 12 * q^47 + 9 * q^49 - 13 * q^53 - q^55 + 8 * q^59 + 2 * q^61 - 10 * q^65 - 58 * q^67 - 7 * q^71 + 9 * q^73 + 31 * q^77 - 2 * q^79 + 30 * q^83 - 46 * q^85 - 13 * q^89 - 14 * q^91 + 14 * q^95 - 24 * q^97

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