LMFDB - Embedded newform 1620.2.r.h.109.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1620,2,Mod(109,1620)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1620, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 3]))

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

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

chi := DirichletCharacter("1620.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1620 = 2^{2} \cdot 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1620.r (of order $6$, 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:	$12.9357651274$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 3x^{14} - 11x^{12} - 90x^{10} - 450x^{8} - 2250x^{6} - 6875x^{4} + 46875x^{2} + 390625 $ x^16 + 3x^14 - 11x^12 - 90x^10 - 450x^8 - 2250x^6 - 6875x^4 + 46875*x^2 + 390625
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			109.6
Root			$-1.02733 + 1.98610i$ of defining polynomial
Character	$\chi$	$=$	1620.109
Dual form			1620.2.r.h.1189.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.02733 + 1.98610i) q^{5} +(1.10979 - 0.640739i) q^{7} +O(q^{10})$	$q+(1.02733 + 1.98610i) q^{5} +(1.10979 - 0.640739i) q^{7} +(-2.07237 - 3.58945i) q^{11} +(-5.64823 - 3.26101i) q^{13} +5.98507i q^{17} -7.17891 q^{19} +(-6.52202 - 3.76549i) q^{23} +(-2.88918 + 4.08076i) q^{25} +(2.59808 + 4.50000i) q^{29} +(-2.58945 + 4.48507i) q^{31} +(2.41269 + 1.54591i) q^{35} -5.24054i q^{37} +(-0.340322 + 0.589454i) q^{41} +(-1.10979 + 0.640739i) q^{43} +(4.59980 - 2.65570i) q^{47} +(-2.67891 + 4.64001i) q^{49} -2.21958i q^{53} +(5.00000 - 7.80350i) q^{55} +(-3.80442 + 6.58945i) q^{59} +(1.08945 + 1.88699i) q^{61} +(0.674082 - 14.5681i) q^{65} +(-13.5161 - 7.80350i) q^{67} +5.50603 q^{71} -7.80350i q^{73} +(-4.59980 - 2.65570i) q^{77} +(3.00000 + 5.19615i) q^{79} +(8.44423 - 4.87528i) q^{83} +(-11.8869 + 6.14865i) q^{85} +10.0215 q^{89} -8.35782 q^{91} +(-7.37512 - 14.2580i) q^{95} +(-12.4063 + 7.16276i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q+O(q^{10}) $ 16 * q	$ 16 q - 24 q^{19} - 6 q^{25} + 4 q^{31} + 48 q^{49} + 80 q^{55} - 28 q^{61} + 48 q^{79} - 22 q^{85} + 48 q^{91}+O(q^{100}) $ 16 * q - 24 * q^19 - 6 * q^25 + 4 * q^31 + 48 * q^49 + 80 * q^55 - 28 * q^61 + 48 * q^79 - 22 * q^85 + 48 * q^91

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1620\mathbb{Z}\right)^\times$.

$n$	$811$	$1297$	$1541$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{3}\right)$

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			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	1.02733	+	1.98610i	0.459436	+	0.888211i
$5$	1.02733	+	1.98610i	0.459436	+	0.888211i
$6$		0			0
$7$	1.10979	−	0.640739i	0.419462	−	0.242176i	−0.275385	−	0.961334i	$-0.588805\pi$
$7$	1.10979	−	0.640739i	0.419462	−	0.242176i	0.694847	+	0.719158i	$0.255472\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−2.07237	−	3.58945i	−0.624844	−	1.08226i	−0.988571	−	0.150756i	$-0.951829\pi$
$11$	−2.07237	−	3.58945i	−0.624844	−	1.08226i	0.363727	−	0.931505i	$-0.381504\pi$
$12$		0			0
$13$	−5.64823	−	3.26101i	−1.56654	−	0.904441i	−0.996568	−	0.0827757i	$-0.973621\pi$
$13$	−5.64823	−	3.26101i	−1.56654	−	0.904441i	−0.569970	−	0.821666i	$-0.693045\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$			5.98507i			1.45159i	0.687909	+	0.725797i	$0.258529\pi$
$17$			5.98507i			1.45159i	−0.687909	+	0.725797i	$0.741471\pi$
$18$		0			0
$19$	−7.17891			−1.64695			−0.823477	−	0.567349i	$-0.807969\pi$
$19$	−7.17891			−1.64695			−0.823477	+	0.567349i	$0.807969\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−6.52202	−	3.76549i	−1.35993	−	0.785159i	−0.370320	−	0.928904i	$-0.620752\pi$
$23$	−6.52202	−	3.76549i	−1.35993	−	0.785159i	−0.989615	+	0.143745i	$0.954085\pi$
$24$		0			0
$25$	−2.88918	+	4.08076i	−0.577836	+	0.816153i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	2.59808	+	4.50000i	0.482451	+	0.835629i	0.999797	−	0.0201471i	$-0.00641344\pi$
$29$	2.59808	+	4.50000i	0.482451	+	0.835629i	−0.517346	+	0.855776i	$0.673080\pi$
$30$		0			0
$31$	−2.58945	+	4.48507i	−0.465080	+	0.805542i	−0.999205	−	0.0398636i	$-0.987308\pi$
$31$	−2.58945	+	4.48507i	−0.465080	+	0.805542i	0.534125	+	0.845405i	$0.320641\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	2.41269	+	1.54591i	0.407820	+	0.261306i
$36$		0			0
$37$		−	5.24054i		−	0.861540i	−0.902462	−	0.430770i	$-0.858242\pi$
$37$		−	5.24054i		−	0.861540i	0.902462	−	0.430770i	$-0.141758\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−0.340322	+	0.589454i	−0.0531493	+	0.0920573i	−0.891376	−	0.453265i	$-0.850259\pi$
$41$	−0.340322	+	0.589454i	−0.0531493	+	0.0920573i	0.838227	+	0.545322i	$0.183593\pi$
$42$		0			0
$43$	−1.10979	+	0.640739i	−0.169242	+	0.0977117i	−0.582228	−	0.813025i	$-0.697819\pi$
$43$	−1.10979	+	0.640739i	−0.169242	+	0.0977117i	0.412987	+	0.910737i	$0.364486\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	4.59980	−	2.65570i	0.670950	−	0.387373i	−0.125486	−	0.992095i	$-0.540049\pi$
$47$	4.59980	−	2.65570i	0.670950	−	0.387373i	0.796437	+	0.604722i	$0.206716\pi$
$48$		0			0
$49$	−2.67891	+	4.64001i	−0.382701	+	0.662858i
$50$		0			0
$51$		0			0
$52$		0			0
$53$		−	2.21958i		−	0.304883i	−0.988312	−	0.152442i	$-0.951286\pi$
$53$		−	2.21958i		−	0.304883i	0.988312	−	0.152442i	$-0.0487136\pi$
$54$		0			0
$55$	5.00000	−	7.80350i	0.674200	−	1.05222i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−3.80442	+	6.58945i	−0.495294	+	0.857874i	−0.999985	−	0.00542586i	$-0.998273\pi$
$59$	−3.80442	+	6.58945i	−0.495294	+	0.857874i	0.504692	+	0.863300i	$0.331606\pi$
$60$		0			0
$61$	1.08945	+	1.88699i	0.139490	+	0.241604i	0.927304	−	0.374310i	$-0.122120\pi$
$61$	1.08945	+	1.88699i	0.139490	+	0.241604i	−0.787813	+	0.615914i	$0.788787\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	0.674082	−	14.5681i	0.0836096	−	1.80695i
$66$		0			0
$67$	−13.5161	−	7.80350i	−1.65125	−	0.953349i	−0.976560	−	0.215246i	$-0.930945\pi$
$67$	−13.5161	−	7.80350i	−1.65125	−	0.953349i	−0.674689	−	0.738103i	$-0.735722\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	5.50603			0.653446			0.326723	−	0.945120i	$-0.394056\pi$
$71$	5.50603			0.653446			0.326723	+	0.945120i	$0.394056\pi$
$72$		0			0
$73$		−	7.80350i		−	0.913330i	−0.889639	−	0.456665i	$-0.849044\pi$
$73$		−	7.80350i		−	0.913330i	0.889639	−	0.456665i	$-0.150956\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−4.59980	−	2.65570i	−0.524196	−	0.302645i
$78$		0			0
$79$	3.00000	+	5.19615i	0.337526	+	0.584613i	0.983967	−	0.178352i	$-0.0570765\pi$
$79$	3.00000	+	5.19615i	0.337526	+	0.584613i	−0.646440	+	0.762964i	$0.723743\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	8.44423	−	4.87528i	0.926875	−	0.535132i	0.0410532	−	0.999157i	$-0.486929\pi$
$83$	8.44423	−	4.87528i	0.926875	−	0.535132i	0.885822	+	0.464025i	$0.153595\pi$
$84$		0			0
$85$	−11.8869	+	6.14865i	−1.28932	+	0.666915i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	10.0215			1.06228			0.531141	−	0.847284i	$-0.321764\pi$
$89$	10.0215			1.06228			0.531141	+	0.847284i	$0.321764\pi$
$90$		0			0
$91$	−8.35782			−0.876137
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−7.37512	−	14.2580i	−0.756671	−	1.46284i
$96$		0			0
$97$	−12.4063	+	7.16276i	−1.25966	+	0.727268i	−0.973009	−	0.230766i	$-0.925877\pi$
$97$	−12.4063	+	7.16276i	−1.25966	+	0.727268i	−0.286655	+	0.958034i	$0.592543\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	0.340322	+	0.589454i	0.0338633	+	0.0586529i	0.882460	−	0.470387i	$-0.155886\pi$
$101$	0.340322	+	0.589454i	0.0338633	+	0.0586529i	−0.848597	+	0.529040i	$0.822552\pi$
$102$		0			0
$103$	2.21958	+	1.28148i	0.218702	+	0.126268i	0.605349	−	0.795960i	$-0.293034\pi$
$103$	2.21958	+	1.28148i	0.218702	+	0.126268i	−0.386647	+	0.922228i	$0.626367\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		0			0		1.00000			$0$
$107$		0			0		−1.00000			$\pi$
$108$		0			0
$109$	−7.00000			−0.670478			−0.335239	−	0.942133i	$-0.608817\pi$
$109$	−7.00000			−0.670478			−0.335239	+	0.942133i	$0.608817\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	7.86081	+	4.53844i	0.739483	+	0.426941i	0.821881	−	0.569659i	$-0.192925\pi$
$113$	7.86081	+	4.53844i	0.739483	+	0.426941i	−0.0823983	+	0.996599i	$0.526258\pi$
$114$		0			0
$115$	0.778363	−	16.8218i	0.0725827	−	1.56864i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	3.83487	+	6.64218i	0.351542	+	0.608888i
$120$		0			0
$121$	−3.08945	+	5.35109i	−0.280859	+	0.486463i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−11.0729	−	1.54591i	−0.990395	−	0.138270i
$126$		0			0
$127$			1.28148i			0.113713i	0.998382	+	0.0568563i	$0.0181077\pi$
$127$			1.28148i			0.113713i	−0.998382	+	0.0568563i	$0.981892\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−2.75302	+	4.76836i	−0.240532	+	0.416614i	−0.960866	−	0.277014i	$-0.910655\pi$
$131$	−2.75302	+	4.76836i	−0.240532	+	0.416614i	0.720334	+	0.693627i	$0.243989\pi$
$132$		0			0
$133$	−7.96709	+	4.59980i	−0.690835	+	0.398854i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−9.78303	+	5.64823i	−0.835820	+	0.482561i	−0.855841	−	0.517238i	$-0.826960\pi$
$137$	−9.78303	+	5.64823i	−0.835820	+	0.482561i	0.0200209	+	0.999800i	$0.493627\pi$
$138$		0			0
$139$	8.58945	−	14.8774i	0.728548	−	1.26188i	−0.228949	−	0.973438i	$-0.573529\pi$
$139$	8.58945	−	14.8774i	0.728548	−	1.26188i	0.957497	−	0.288444i	$-0.0931378\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$			27.0321i			2.26054i
$144$		0			0
$145$	−6.26836	+	9.78303i	−0.520559	+	0.812436i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−9.86660	+	17.0895i	−0.808303	+	1.40002i	0.105735	+	0.994394i	$0.466281\pi$
$149$	−9.86660	+	17.0895i	−0.808303	+	1.40002i	−0.914038	+	0.405628i	$0.867053\pi$
$150$		0			0
$151$	−2.58945	−	4.48507i	−0.210727	−	0.364990i	0.741215	−	0.671267i	$-0.234250\pi$
$151$	−2.58945	−	4.48507i	−0.210727	−	0.364990i	−0.951942	+	0.306278i	$0.900916\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−11.5680	−	0.535265i	−0.929165	−	0.0429935i
$156$		0			0
$157$	−4.53844	−	2.62027i	−0.362207	−	0.209120i	0.307841	−	0.951438i	$-0.400393\pi$
$157$	−4.53844	−	2.62027i	−0.362207	−	0.209120i	−0.670049	+	0.742317i	$0.733727\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−9.65078			−0.760588
$162$		0			0
$163$		−	11.7626i		−	0.921315i	−0.887578	−	0.460657i	$-0.847614\pi$
$163$		−	11.7626i		−	0.921315i	0.887578	−	0.460657i	$-0.152386\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−1.92222	−	1.10979i	−0.148746	−	0.0858783i	0.423780	−	0.905765i	$-0.360703\pi$
$167$	−1.92222	−	1.10979i	−0.148746	−	0.0858783i	−0.572526	+	0.819887i	$0.694036\pi$
$168$		0			0
$169$	14.7684	+	25.5796i	1.13603	+	1.96766i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−0.583422	+	0.336839i	−0.0443567	+	0.0256094i	−0.522014	−	0.852937i	$-0.674819\pi$
$173$	−0.583422	+	0.336839i	−0.0443567	+	0.0256094i	0.477658	+	0.878546i	$0.341486\pi$
$174$		0			0
$175$	−0.591687	+	6.38001i	−0.0447273	+	0.482283i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	14.5370			1.08655			0.543275	−	0.839555i	$-0.317184\pi$
$179$	14.5370			1.08655			0.543275	+	0.839555i	$0.317184\pi$
$180$		0			0
$181$	15.1789			1.12824			0.564120	−	0.825693i	$-0.309216\pi$
$181$	15.1789			1.12824			0.564120	+	0.825693i	$0.309216\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	10.4082	−	5.38377i	0.765229	−	0.395823i
$186$		0			0
$187$	21.4831	−	12.4033i	1.57100	−	0.907019i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−13.1453	−	22.7684i	−0.951162	−	1.64746i	−0.742916	−	0.669384i	$-0.766558\pi$
$191$	−13.1453	−	22.7684i	−0.951162	−	1.64746i	−0.208246	−	0.978077i	$-0.566775\pi$
$192$		0			0
$193$	−11.1972	−	6.46470i	−0.805992	−	0.465339i	0.0395704	−	0.999217i	$-0.487401\pi$
$193$	−11.1972	−	6.46470i	−0.805992	−	0.465339i	−0.845562	+	0.533877i	$0.820734\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		−	8.20466i		−	0.584558i	−0.956333	−	0.292279i	$-0.905586\pi$
$197$		−	8.20466i		−	0.584558i	0.956333	−	0.292279i	$-0.0944135\pi$
$198$		0			0
$199$	2.35782			0.167141			0.0835706	−	0.996502i	$-0.473368\pi$
$199$	2.35782			0.167141			0.0835706	+	0.996502i	$0.473368\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	5.76665	+	3.32937i	0.404739	+	0.233676i
$204$		0			0
$205$	−1.52034	−	0.0703477i	−0.106185	−	0.00491330i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	14.8774	+	25.7684i	1.02909	+	1.78243i
$210$		0			0
$211$	−2.41055	+	4.17519i	−0.165949	+	0.287432i	−0.936992	−	0.349351i	$-0.886402\pi$
$211$	−2.41055	+	4.17519i	−0.165949	+	0.287432i	0.771043	+	0.636783i	$0.219735\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−2.41269	−	1.54591i	−0.164544	−	0.105430i
$216$		0			0
$217$			6.63665i			0.450525i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	19.5174	−	33.8051i	1.31288	−	2.27398i
$222$		0			0
$223$	6.85730	−	3.95906i	0.459199	−	0.265119i	−0.252508	−	0.967595i	$-0.581256\pi$
$223$	6.85730	−	3.95906i	0.459199	−	0.265119i	0.711707	+	0.702476i	$0.247922\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	18.8107	−	10.8604i	1.24851	−	0.720827i	0.277697	−	0.960669i	$-0.410429\pi$
$227$	18.8107	−	10.8604i	1.24851	−	0.720827i	0.970812	+	0.239842i	$0.0770956\pi$
$228$		0			0
$229$	9.08945	−	15.7434i	0.600648	−	1.04035i	−0.392075	−	0.919933i	$-0.628243\pi$
$229$	9.08945	−	15.7434i	0.600648	−	1.04035i	0.992723	−	0.120420i	$-0.0384240\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$		−	21.0470i		−	1.37884i	−0.724363	−	0.689418i	$-0.757866\pi$
$233$		−	21.0470i		−	1.37884i	0.724363	−	0.689418i	$-0.242134\pi$
$234$		0			0
$235$	10.0000	+	6.40739i	0.652328	+	0.417972i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−11.0729	+	19.1789i	−0.716249	+	1.24058i	0.246226	+	0.969212i	$0.420809\pi$
$239$	−11.0729	+	19.1789i	−0.716249	+	1.24058i	−0.962476	+	0.271368i	$0.912524\pi$
$240$		0			0
$241$	−9.50000	−	16.4545i	−0.611949	−	1.05993i	−0.990912	−	0.134515i	$-0.957053\pi$
$241$	−9.50000	−	16.4545i	−0.611949	−	1.05993i	0.378963	−	0.925412i	$-0.376281\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−11.9676	−	0.553756i	−0.764584	−	0.0353782i
$246$		0			0
$247$	40.5482	+	23.4105i	2.58002	+	1.48957i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−17.3205			−1.09326			−0.546630	−	0.837374i	$-0.684090\pi$
$251$	−17.3205			−1.09326			−0.546630	+	0.837374i	$0.684090\pi$
$252$		0			0
$253$			31.2140i			1.96241i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	5.93860	+	3.42865i	0.370439	+	0.213873i	0.673650	−	0.739050i	$-0.264725\pi$
$257$	5.93860	+	3.42865i	0.370439	+	0.213873i	−0.303211	+	0.952923i	$0.598059\pi$
$258$		0			0
$259$	−3.35782	−	5.81591i	−0.208645	−	0.361383i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−13.0440	+	7.53098i	−0.804330	+	0.464380i	−0.844983	−	0.534793i	$-0.820389\pi$
$263$	−13.0440	+	7.53098i	−0.804330	+	0.464380i	0.0406531	+	0.999173i	$0.487056\pi$
$264$		0			0
$265$	4.40831	−	2.28025i	0.270801	−	0.140074i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−9.28001			−0.565812			−0.282906	−	0.959148i	$-0.591298\pi$
$269$	−9.28001			−0.565812			−0.282906	+	0.959148i	$0.591298\pi$
$270$		0			0
$271$	0.357817			0.0217358			0.0108679	−	0.999941i	$-0.496541\pi$
$271$	0.357817			0.0217358			0.0108679	+	0.999941i	$0.496541\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	20.6352	+	1.91372i	1.24435	+	0.115402i
$276$		0			0
$277$	−10.1867	+	5.88128i	−0.612058	+	0.353372i	−0.773770	−	0.633466i	$-0.781632\pi$
$277$	−10.1867	+	5.88128i	−0.612058	+	0.353372i	0.161712	+	0.986838i	$0.448298\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	3.61904	+	6.26836i	0.215894	+	0.373939i	0.953549	−	0.301239i	$-0.0974001\pi$
$281$	3.61904	+	6.26836i	0.215894	+	0.373939i	−0.737655	+	0.675178i	$0.764067\pi$
$282$		0			0
$283$	24.8125	+	14.3255i	1.47495	+	0.851563i	0.999601	−	0.0282335i	$-0.00898820\pi$
$283$	24.8125	+	14.3255i	1.47495	+	0.851563i	0.475350	+	0.879797i	$0.342322\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$			0.872228i			0.0514860i
$288$		0			0
$289$	−18.8211			−1.10712
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−15.5497	−	8.97761i	−0.908422	−	0.524477i	−0.0284987	−	0.999594i	$-0.509073\pi$
$293$	−15.5497	−	8.97761i	−0.908422	−	0.524477i	−0.879923	+	0.475116i	$0.842406\pi$
$294$		0			0
$295$	−16.9957	−	0.786411i	−0.989529	−	0.0457866i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	24.5586	+	42.5367i	1.42026	+	2.45996i
$300$		0			0
$301$	−0.821092	+	1.42217i	−0.0473269	+	0.0819727i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−2.62852	+	4.10233i	−0.150509	+	0.234899i
$306$		0			0
$307$		−	16.8885i		−	0.963876i	−0.876205	−	0.481938i	$-0.839933\pi$
$307$		−	16.8885i		−	0.963876i	0.876205	−	0.481938i	$-0.160067\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−4.48507	+	7.76836i	−0.254325	+	0.440503i	−0.964712	−	0.263308i	$-0.915187\pi$
$311$	−4.48507	+	7.76836i	−0.254325	+	0.440503i	0.710387	+	0.703811i	$0.248520\pi$
$312$		0			0
$313$	7.86782	−	4.54249i	0.444715	−	0.256757i	−0.260880	−	0.965371i	$-0.584013\pi$
$313$	7.86782	−	4.54249i	0.444715	−	0.256757i	0.705596	+	0.708615i	$0.250679\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−10.5384	+	6.08435i	−0.591895	+	0.341731i	−0.765847	−	0.643023i	$-0.777680\pi$
$317$	−10.5384	+	6.08435i	−0.591895	+	0.341731i	0.173951	+	0.984754i	$0.444347\pi$
$318$		0			0
$319$	10.7684	−	18.6514i	0.602913	−	1.04428i
$320$		0			0
$321$		0			0
$322$		0			0
$323$		−	42.9663i		−	2.39071i
$324$		0			0
$325$	29.6262	−	13.6275i	1.64336	−	0.755915i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	3.40322	−	5.89454i	0.187625	−	0.324977i
$330$		0			0
$331$	−0.768363	−	1.33084i	−0.0422330	−	0.0731497i	0.844136	−	0.536129i	$-0.180114\pi$
$331$	−0.768363	−	1.33084i	−0.0422330	−	0.0731497i	−0.886369	+	0.462979i	$0.846781\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	1.61306	−	34.8610i	0.0881307	−	1.90466i
$336$		0			0
$337$	2.21958	+	1.28148i	0.120908	+	0.0698065i	0.559234	−	0.829010i	$-0.311095\pi$
$337$	2.21958	+	1.28148i	0.120908	+	0.0698065i	−0.438326	+	0.898816i	$0.644428\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	21.4653			1.16241
$342$		0			0
$343$			15.8363i			0.855078i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−1.92222	−	1.10979i	−0.103190	−	0.0595767i	0.447517	−	0.894275i	$-0.352308\pi$
$347$	−1.92222	−	1.10979i	−0.103190	−	0.0595767i	−0.550707	+	0.834699i	$0.685642\pi$
$348$		0			0
$349$	4.41055	+	7.63929i	0.236091	+	0.408922i	0.959589	−	0.281405i	$-0.0908003\pi$
$349$	4.41055	+	7.63929i	0.236091	+	0.408922i	−0.723498	+	0.690326i	$0.757467\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−24.1659	+	13.9522i	−1.28622	+	0.742599i	−0.977978	−	0.208709i	$-0.933074\pi$
$353$	−24.1659	+	13.9522i	−1.28622	+	0.742599i	−0.308241	+	0.951308i	$0.599740\pi$
$354$		0			0
$355$	5.65652	+	10.9355i	0.300217	+	0.580397i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	19.3624			1.02191			0.510955	−	0.859607i	$-0.329292\pi$
$359$	19.3624			1.02191			0.510955	+	0.859607i	$0.329292\pi$
$360$		0			0
$361$	32.5367			1.71246
$362$		0			0
$363$		0			0
$364$		0			0
$365$	15.4985	−	8.01677i	0.811229	−	0.419617i
$366$		0			0
$367$	−2.21958	+	1.28148i	−0.115861	+	0.0668926i	−0.556811	−	0.830639i	$-0.687975\pi$
$367$	−2.21958	+	1.28148i	−0.115861	+	0.0668926i	0.440949	+	0.897532i	$0.354642\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−1.42217	−	2.46327i	−0.0738355	−	0.127887i
$372$		0			0
$373$	14.6258	+	8.44423i	0.757297	+	0.437226i	0.828325	−	0.560249i	$-0.189294\pi$
$373$	14.6258	+	8.44423i	0.757297	+	0.437226i	−0.0710272	+	0.997474i	$0.522628\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		−	33.8894i		−	1.74539i
$378$		0			0
$379$	−22.3578			−1.14844			−0.574222	−	0.818700i	$-0.694695\pi$
$379$	−22.3578			−1.14844			−0.574222	+	0.818700i	$0.694695\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	10.3664	+	5.98507i	0.529701	+	0.305823i	0.740895	−	0.671621i	$-0.234402\pi$
$383$	10.3664	+	5.98507i	0.529701	+	0.305823i	−0.211194	+	0.977444i	$0.567735\pi$
$384$		0			0
$385$	0.548958	−	11.8639i	0.0279775	−	0.604643i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	6.24756	+	10.8211i	0.316764	+	0.548651i	0.979811	−	0.199927i	$-0.0640704\pi$
$389$	6.24756	+	10.8211i	0.316764	+	0.548651i	−0.663047	+	0.748578i	$0.730737\pi$
$390$		0			0
$391$	22.5367	−	39.0348i	1.13973	−	1.97407i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−7.23808	+	11.2965i	−0.364187	+	0.568387i
$396$		0			0
$397$			24.6920i			1.23925i	0.784896	+	0.619627i	$0.212716\pi$
$397$			24.6920i			1.23925i	−0.784896	+	0.619627i	$0.787284\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−6.03173	+	10.4473i	−0.301210	+	0.521712i	−0.976410	−	0.215923i	$-0.930724\pi$
$401$	−6.03173	+	10.4473i	−0.301210	+	0.521712i	0.675200	+	0.737635i	$0.264057\pi$
$402$		0			0
$403$	29.2517	−	16.8885i	1.45713	−	0.841275i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−18.8107	+	10.8604i	−0.932411	+	0.538328i
$408$		0			0
$409$	9.08945	−	15.7434i	0.449445	−	0.778461i	−0.548905	−	0.835885i	$-0.684955\pi$
$409$	9.08945	−	15.7434i	0.449445	−	0.778461i	0.998350	+	0.0574237i	$0.0182886\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$			9.75056i			0.479794i
$414$		0			0
$415$	18.3578	+	11.7626i	0.901150	+	0.577401i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	4.82539	−	8.35782i	0.235736	−	0.408306i	−0.723751	−	0.690062i	$-0.757583\pi$
$419$	4.82539	−	8.35782i	0.235736	−	0.408306i	0.959486	+	0.281756i	$0.0909167\pi$
$420$		0			0
$421$	7.85782	+	13.6101i	0.382967	+	0.663318i	0.991485	−	0.130222i	$-0.0415691\pi$
$421$	7.85782	+	13.6101i	0.382967	+	0.663318i	−0.608518	+	0.793540i	$0.708236\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−24.4237	−	17.2920i	−1.18472	−	0.838783i
$426$		0			0
$427$	2.41813	+	1.39611i	0.117022	+	0.0675625i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−31.1160			−1.49881			−0.749403	−	0.662114i	$-0.769659\pi$
$431$	−31.1160			−1.49881			−0.749403	+	0.662114i	$0.769659\pi$
$432$		0			0
$433$			16.7738i			0.806099i	0.915178	+	0.403050i	$0.132050\pi$
$433$			16.7738i			0.806099i	−0.915178	+	0.403050i	$0.867950\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	46.8210	+	27.0321i	2.23975	+	1.29312i
$438$		0			0
$439$	−7.76836	−	13.4552i	−0.370764	−	0.642182i	0.618920	−	0.785454i	$-0.287571\pi$
$439$	−7.76836	−	13.4552i	−0.370764	−	0.642182i	−0.989683	+	0.143273i	$0.954237\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	17.6438	−	10.1867i	0.838284	−	0.483984i	−0.0183965	−	0.999831i	$-0.505856\pi$
$443$	17.6438	−	10.1867i	0.838284	−	0.483984i	0.856681	+	0.515847i	$0.172523\pi$
$444$		0			0
$445$	10.2954	+	19.9038i	0.488051	+	0.943529i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−33.8386			−1.59694			−0.798471	−	0.602033i	$-0.794358\pi$
$449$	−33.8386			−1.59694			−0.798471	+	0.602033i	$0.794358\pi$
$450$		0			0
$451$	2.82109			0.132840
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−8.58625	−	16.5995i	−0.402529	−	0.778194i
$456$		0			0
$457$	0.0992755	−	0.0573167i	0.00464391	−	0.00268116i	−0.497676	−	0.867363i	$-0.665813\pi$
$457$	0.0992755	−	0.0573167i	0.00464391	−	0.00268116i	0.502320	+	0.864682i	$0.332480\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	4.48507	+	7.76836i	0.208890	+	0.361809i	0.951365	−	0.308065i	$-0.0996815\pi$
$461$	4.48507	+	7.76836i	0.208890	+	0.361809i	−0.742475	+	0.669874i	$0.766348\pi$
$462$		0			0
$463$	−6.65875	−	3.84443i	−0.309458	−	0.178666i	0.337226	−	0.941424i	$-0.390511\pi$
$463$	−6.65875	−	3.84443i	−0.309458	−	0.178666i	−0.646684	+	0.762758i	$0.723845\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$			29.2517i			1.35361i	0.736164	+	0.676803i	$0.236635\pi$
$467$			29.2517i			1.35361i	−0.736164	+	0.676803i	$0.763365\pi$
$468$		0			0
$469$	−20.0000			−0.923514
$470$		0			0
$471$		0			0
$472$		0			0
$473$	4.59980	+	2.65570i	0.211499	+	0.122109i
$474$		0			0
$475$	20.7412	−	29.2954i	0.951670	−	1.34417i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	15.9288	+	27.5895i	0.727804	+	1.26059i	0.957809	+	0.287405i	$0.0927925\pi$
$479$	15.9288	+	27.5895i	0.727804	+	1.26059i	−0.230005	+	0.973190i	$0.573874\pi$
$480$		0			0
$481$	−17.0895	+	29.5998i	−0.779212	+	1.34963i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−26.9713	−	17.2815i	−1.22470	−	0.784714i
$486$		0			0
$487$			33.7769i			1.53058i	0.643686	+	0.765290i	$0.277404\pi$
$487$			33.7769i			1.53058i	−0.643686	+	0.765290i	$0.722596\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	11.7231	−	20.3051i	0.529058	−	0.916356i	−0.470367	−	0.882471i	$-0.655879\pi$
$491$	11.7231	−	20.3051i	0.529058	−	0.916356i	0.999426	−	0.0338851i	$-0.0107880\pi$
$492$		0			0
$493$	−26.9328	+	15.5497i	−1.21299	+	0.700322i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	6.11055	−	3.52793i	0.274095	−	0.158249i
$498$		0			0
$499$	−3.58945	+	6.21712i	−0.160686	+	0.278316i	−0.935115	−	0.354345i	$-0.884704\pi$
$499$	−3.58945	+	6.21712i	−0.160686	+	0.278316i	0.774429	+	0.632661i	$0.218037\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$			40.7467i			1.81681i	0.418096	+	0.908403i	$0.362698\pi$
$503$			40.7467i			1.81681i	−0.418096	+	0.908403i	$0.637302\pi$
$504$		0			0
$505$	−0.821092	+	1.28148i	−0.0365381	+	0.0570250i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−15.8983	+	27.5367i	−0.704681	+	1.22054i	0.262125	+	0.965034i	$0.415577\pi$
$509$	−15.8983	+	27.5367i	−0.704681	+	1.22054i	−0.966806	+	0.255510i	$0.917757\pi$
$510$		0			0
$511$	−5.00000	−	8.66025i	−0.221187	−	0.383107i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−0.264894	+	5.72481i	−0.0116726	+	0.252265i
$516$		0			0
$517$	−19.0650	−	11.0072i	−0.838478	−	0.484096i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	22.1459			0.970229			0.485115	−	0.874451i	$-0.338778\pi$
$521$	22.1459			0.970229			0.485115	+	0.874451i	$0.338778\pi$
$522$		0			0
$523$		−	41.6951i		−	1.82320i	−0.411081	−	0.911599i	$-0.634849\pi$
$523$		−	41.6951i		−	1.82320i	0.411081	−	0.911599i	$-0.365151\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−26.8434	−	15.4981i	−1.16932	−	0.675107i
$528$		0			0
$529$	16.8578	+	29.1986i	0.732949	+	1.26950i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	3.84443	−	2.21958i	0.166521	−	0.0961408i
$534$		0			0
$535$		0			0
$536$		0			0
$537$		0			0
$538$		0			0
$539$	22.2068			0.956514
$540$		0			0
$541$	−19.3578			−0.832258			−0.416129	−	0.909306i	$-0.636613\pi$
$541$	−19.3578			−0.832258			−0.416129	+	0.909306i	$0.636613\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−7.19132	−	13.9027i	−0.308042	−	0.595526i
$546$		0			0
$547$	4.43917	−	2.56295i	0.189805	−	0.109584i	−0.402086	−	0.915602i	$-0.631715\pi$
$547$	4.43917	−	2.56295i	0.189805	−	0.109584i	0.591891	+	0.806018i	$0.298381\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−18.6514	−	32.3051i	−0.794574	−	1.37624i
$552$		0			0
$553$	6.65875	+	3.84443i	0.283159	+	0.163482i
$554$		0			0
$555$		0			0
$556$		0			0
$557$		−	2.41813i		−	0.102460i	−0.998687	−	0.0512298i	$-0.983686\pi$
$557$		−	2.41813i		−	0.102460i	0.998687	−	0.0512298i	$-0.0163141\pi$
$558$		0			0
$559$	8.35782			0.353498
$560$		0			0
$561$		0			0
$562$		0			0
$563$	4.59980	+	2.65570i	0.193859	+	0.111924i	0.593788	−	0.804622i	$-0.297632\pi$
$563$	4.59980	+	2.65570i	0.193859	+	0.111924i	−0.399929	+	0.916546i	$0.630965\pi$
$564$		0			0
$565$	−0.938140	+	20.2748i	−0.0394678	+	0.852969i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	10.8876	+	18.8578i	0.456430	+	0.790561i	0.998769	−	0.0495991i	$-0.0157944\pi$
$569$	10.8876	+	18.8578i	0.456430	+	0.790561i	−0.542339	+	0.840160i	$0.682461\pi$
$570$		0			0
$571$	3.41055	−	5.90724i	0.142727	−	0.247210i	−0.785796	−	0.618486i	$-0.787746\pi$
$571$	3.41055	−	5.90724i	0.142727	−	0.247210i	0.928523	+	0.371276i	$0.121080\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	34.2094	−	15.7356i	1.42663	−	0.656221i
$576$		0			0
$577$		−	5.24054i		−	0.218167i	−0.994033	−	0.109083i	$-0.965208\pi$
$577$		−	5.24054i		−	0.218167i	0.994033	−	0.109083i	$-0.0347915\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	6.24756	−	10.8211i	0.259192	−	0.448935i
$582$		0			0
$583$	−7.96709	+	4.59980i	−0.329963	+	0.190504i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−41.0543	+	23.7027i	−1.69449	+	0.978316i	−0.743688	+	0.668527i	$0.766925\pi$
$587$	−41.0543	+	23.7027i	−1.69449	+	0.978316i	−0.950805	+	0.309790i	$0.899741\pi$
$588$		0			0
$589$	18.5895	−	32.1979i	0.765965	−	1.32669i
$590$		0			0
$591$		0			0
$592$		0			0
$593$			11.2965i			0.463890i	0.972729	+	0.231945i	$0.0745090\pi$
$593$			11.2965i			0.463890i	−0.972729	+	0.231945i	$0.925491\pi$
$594$		0			0
$595$	−9.25236	+	14.4401i	−0.379310	+	0.591988i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−18.3415	+	31.7684i	−0.749412	+	1.29802i	0.198692	+	0.980062i	$0.436331\pi$
$599$	−18.3415	+	31.7684i	−0.749412	+	1.29802i	−0.948105	+	0.317958i	$0.897003\pi$
$600$		0			0
$601$	−9.67891	−	16.7644i	−0.394811	−	0.683833i	0.598266	−	0.801297i	$-0.295857\pi$
$601$	−9.67891	−	16.7644i	−0.394811	−	0.683833i	−0.993077	+	0.117465i	$0.962523\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−13.8017	−	0.638620i	−0.561119	−	0.0259636i
$606$		0			0
$607$	1.10979	+	0.640739i	0.0450451	+	0.0260068i	0.522353	−	0.852729i	$-0.325054\pi$
$607$	1.10979	+	0.640739i	0.0450451	+	0.0260068i	−0.477308	+	0.878736i	$0.658388\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−34.6410			−1.40143
$612$		0			0
$613$		−	38.9028i		−	1.57127i	−0.618690	−	0.785636i	$-0.712336\pi$
$613$		−	38.9028i		−	1.57127i	0.618690	−	0.785636i	$-0.287664\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−26.6715	−	15.3988i	−1.07375	−	0.619932i	−0.144549	−	0.989498i	$-0.546173\pi$
$617$	−26.6715	−	15.3988i	−1.07375	−	0.619932i	−0.929205	+	0.369565i	$0.879507\pi$
$618$		0			0
$619$	17.1789	+	29.7547i	0.690479	+	1.19594i	0.971681	+	0.236296i	$0.0759334\pi$
$619$	17.1789	+	29.7547i	0.690479	+	1.19594i	−0.281203	+	0.959648i	$0.590733\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	11.1218	−	6.42119i	0.445586	−	0.257259i
$624$		0			0
$625$	−8.30526	−	23.5801i	−0.332210	−	0.943205i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	31.3650			1.25061
$630$		0			0
$631$	11.5367			0.459270			0.229635	−	0.973277i	$-0.426247\pi$
$631$	11.5367			0.459270			0.229635	+	0.973277i	$0.426247\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−2.54514	+	1.31650i	−0.101001	+	0.0522438i
$636$		0			0
$637$	30.2622	−	17.4719i	1.19903	−	0.692261i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−3.95936	−	6.85782i	−0.156385	−	0.270867i	0.777177	−	0.629282i	$-0.216651\pi$
$641$	−3.95936	−	6.85782i	−0.156385	−	0.270867i	−0.933563	+	0.358414i	$0.883318\pi$
$642$		0			0
$643$	−7.96709	−	4.59980i	−0.314191	−	0.181399i	0.334609	−	0.942357i	$-0.391396\pi$
$643$	−7.96709	−	4.59980i	−0.314191	−	0.181399i	−0.648801	+	0.760958i	$0.724729\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		−	13.7146i		−	0.539177i	−0.962976	−	0.269588i	$-0.913112\pi$
$647$		−	13.7146i		−	0.539177i	0.962976	−	0.269588i	$-0.0868876\pi$
$648$		0			0
$649$	31.5367			1.23792
$650$		0			0
$651$		0			0
$652$		0			0
$653$	36.4545	+	21.0470i	1.42658	+	0.823634i	0.996849	−	0.0793250i	$-0.0252765\pi$
$653$	36.4545	+	21.0470i	1.42658	+	0.823634i	0.429727	+	0.902959i	$0.358610\pi$
$654$		0			0
$655$	−12.2987	−	0.569075i	−0.480550	−	0.0222356i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−12.0635	−	20.8945i	−0.469926	−	0.813936i	0.529483	−	0.848321i	$-0.322386\pi$
$659$	−12.0635	−	20.8945i	−0.469926	−	0.813936i	−0.999409	+	0.0343850i	$0.989053\pi$
$660$		0			0
$661$	−22.2156	+	38.4786i	−0.864088	+	1.49664i	0.00386191	+	0.999993i	$0.498771\pi$
$661$	−22.2156	+	38.4786i	−0.864088	+	1.49664i	−0.867950	+	0.496652i	$0.834563\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−17.3205	−	11.0979i	−0.671660	−	0.430359i
$666$		0			0
$667$		−	39.1321i		−	1.51520i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	4.51551	−	7.82109i	0.174319	−	0.301930i
$672$		0			0
$673$	−28.2412	+	16.3050i	−1.08862	+	0.628513i	−0.933208	−	0.359337i	$-0.883003\pi$
$673$	−28.2412	+	16.3050i	−1.08862	+	0.628513i	−0.155409	+	0.987850i	$0.549670\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	44.1434	−	25.4862i	1.69657	−	0.979514i	0.747596	−	0.664154i	$-0.231208\pi$
$677$	44.1434	−	25.4862i	1.69657	−	0.979514i	0.948972	−	0.315360i	$-0.102125\pi$
$678$		0			0
$679$	−9.17891	+	15.8983i	−0.352254	+	0.610122i
$680$		0			0
$681$		0			0
$682$		0			0
$683$		−	28.3795i		−	1.08591i	−0.839762	−	0.542955i	$-0.817305\pi$
$683$		−	28.3795i		−	1.08591i	0.839762	−	0.542955i	$-0.182695\pi$
$684$		0			0
$685$	−21.2684	−	13.6275i	−0.812622	−	0.520678i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−7.23808	+	12.5367i	−0.275749	+	0.477611i
$690$		0			0
$691$	−7.35782	−	12.7441i	−0.279905	−	0.484809i	0.691456	−	0.722418i	$-0.256969\pi$
$691$	−7.35782	−	12.7441i	−0.279905	−	0.484809i	−0.971361	+	0.237609i	$0.923636\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	38.3722	+	1.77552i	1.45554	+	0.0673494i
$696$		0			0
$697$	−3.52793	−	2.03685i	−0.133630	−	0.0771512i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	14.2272			0.537353			0.268676	−	0.963230i	$-0.413414\pi$
$701$	14.2272			0.537353			0.268676	+	0.963230i	$0.413414\pi$
$702$		0			0
$703$			37.6214i			1.41892i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	0.755372	+	0.436114i	0.0284087	+	0.0164018i
$708$		0			0
$709$	−9.26836	−	16.0533i	−0.348081	−	0.602893i	0.637828	−	0.770179i	$-0.279833\pi$
$709$	−9.26836	−	16.0533i	−0.348081	−	0.602893i	−0.985908	+	0.167286i	$0.946500\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	33.7769	−	19.5011i	1.26496	−	0.730323i
$714$		0			0
$715$	−53.6884	+	27.7709i	−2.00783	+	1.03857i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	31.7358			1.18355			0.591773	−	0.806105i	$-0.298428\pi$
$719$	31.7358			1.18355			0.591773	+	0.806105i	$0.298428\pi$
$720$		0			0
$721$	3.28437			0.122316
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−25.8697	−	2.39918i	−0.960778	−	0.0891034i
$726$		0			0
$727$	−27.2307	+	15.7216i	−1.00993	+	0.583083i	−0.911171	−	0.412029i	$-0.864820\pi$
$727$	−27.2307	+	15.7216i	−1.00993	+	0.583083i	−0.0987581	+	0.995111i	$0.531487\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−3.83487	−	6.64218i	−0.141838	−	0.245670i
$732$		0			0
$733$	−4.43917	−	2.56295i	−0.163964	−	0.0946649i	0.415772	−	0.909469i	$-0.363511\pi$
$733$	−4.43917	−	2.56295i	−0.163964	−	0.0946649i	−0.579737	+	0.814804i	$0.696845\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$			64.6870i			2.38278i
$738$		0			0
$739$	−33.8945			−1.24683			−0.623415	−	0.781891i	$-0.714255\pi$
$739$	−33.8945			−1.24683			−0.623415	+	0.781891i	$0.714255\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−33.0216	−	19.0650i	−1.21144	−	0.699427i	−0.248370	−	0.968665i	$-0.579895\pi$
$743$	−33.0216	−	19.0650i	−1.21144	−	0.699427i	−0.963074	+	0.269238i	$0.913228\pi$
$744$		0			0
$745$	−44.0776	−	2.03952i	−1.61488	−	0.0747223i
$746$		0			0
$747$		0			0
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−8.17891	+	14.1663i	−0.298453	+	0.516935i	−0.975782	−	0.218745i	$-0.929804\pi$
$751$	−8.17891	+	14.1663i	−0.298453	+	0.516935i	0.677330	+	0.735680i	$0.263137\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	6.24756	−	9.75056i	0.227372	−	0.354859i
$756$		0			0
$757$		−	28.6510i		−	1.04134i	−0.853758	−	0.520670i	$-0.825682\pi$
$757$		−	28.6510i		−	1.04134i	0.853758	−	0.520670i	$-0.174318\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−0.866025	+	1.50000i	−0.0313934	+	0.0543750i	−0.881295	−	0.472566i	$-0.843328\pi$
$761$	−0.866025	+	1.50000i	−0.0313934	+	0.0543750i	0.849902	+	0.526941i	$0.176661\pi$
$762$		0			0
$763$	−7.76854	+	4.48517i	−0.281240	+	0.162374i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	42.9765	−	24.8125i	1.55179	−	0.895928i
$768$		0			0
$769$	−9.85782	+	17.0742i	−0.355482	+	0.615713i	−0.987200	−	0.159485i	$-0.949017\pi$
$769$	−9.85782	+	17.0742i	−0.355482	+	0.615713i	0.631718	+	0.775198i	$0.282350\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$		−	4.63772i		−	0.166807i	−0.996516	−	0.0834036i	$-0.973421\pi$
$773$		−	4.63772i		−	0.166807i	0.996516	−	0.0834036i	$-0.0265791\pi$
$774$		0			0
$775$	−10.8211	−	23.5251i	−0.388705	−	0.845047i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	2.44314	−	4.23164i	0.0875345	−	0.151614i
$780$		0			0
$781$	−11.4105	−	19.7636i	−0.408301	−	0.707199i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	0.541635	−	11.7057i	0.0193318	−	0.417794i
$786$		0			0
$787$	−39.6369	−	22.8844i	−1.41290	−	0.815740i	−0.417242	−	0.908795i	$-0.637003\pi$
$787$	−39.6369	−	22.8844i	−1.41290	−	0.815740i	−0.995661	+	0.0930552i	$0.970337\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	11.6318			0.413580
$792$		0			0
$793$		−	14.2109i		−	0.504643i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−22.8271	−	13.1792i	−0.808576	−	0.466832i	0.0378850	−	0.999282i	$-0.487938\pi$
$797$	−22.8271	−	13.1792i	−0.808576	−	0.466832i	−0.846461	+	0.532450i	$0.821271\pi$
$798$		0			0
$799$	15.8945	+	27.5302i	0.562308	+	0.973947i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−28.0103	+	16.1717i	−0.988462	+	0.570689i
$804$		0			0
$805$	−9.91454	−	19.1674i	−0.349442	−	0.675562i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−5.19615			−0.182687			−0.0913435	−	0.995819i	$-0.529116\pi$
$809$	−5.19615			−0.182687			−0.0913435	+	0.995819i	$0.529116\pi$
$810$		0			0
$811$	−49.8945			−1.75203			−0.876017	−	0.482280i	$-0.839809\pi$
$811$	−49.8945			−1.75203			−0.876017	+	0.482280i	$0.839809\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	23.3616	−	12.0840i	0.818322	−	0.423286i
$816$		0			0
$817$	7.96709	−	4.59980i	0.278733	−	0.160927i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−0.124496	−	0.215633i	−0.00434494	−	0.00752566i	0.863845	−	0.503758i	$-0.168050\pi$
$821$	−0.124496	−	0.215633i	−0.00434494	−	0.00752566i	−0.868190	+	0.496232i	$0.834716\pi$
$822$		0			0
$823$	−22.5929	−	13.0440i	−0.787540	−	0.454687i	0.0515557	−	0.998670i	$-0.483582\pi$
$823$	−22.5929	−	13.0440i	−0.787540	−	0.454687i	−0.839096	+	0.543984i	$0.816915\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	11.9701i		−	0.416243i	−0.978103	−	0.208121i	$-0.933265\pi$
$827$		−	11.9701i		−	0.416243i	0.978103	−	0.208121i	$-0.0667349\pi$
$828$		0			0
$829$	−7.17891			−0.249334			−0.124667	−	0.992199i	$-0.539786\pi$
$829$	−7.17891			−0.249334			−0.124667	+	0.992199i	$0.539786\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−27.7708	−	16.0335i	−0.962200	−	0.555526i
$834$		0			0
$835$	0.229405	−	4.95783i	0.00793887	−	0.171573i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−11.0425	−	19.1262i	−0.381230	−	0.660309i	0.610009	−	0.792395i	$-0.291166\pi$
$839$	−11.0425	−	19.1262i	−0.381230	−	0.660309i	−0.991238	+	0.132086i	$0.957833\pi$
$840$		0			0
$841$	1.00000	−	1.73205i	0.0344828	−	0.0597259i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−35.6315	+	55.6101i	−1.22576	+	1.91305i
$846$		0			0
$847$			7.91813i			0.272070i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−19.7332	+	34.1789i	−0.676445	+	1.17164i
$852$		0			0
$853$	34.9992	−	20.2068i	1.19835	−	0.691867i	0.238163	−	0.971225i	$-0.423455\pi$
$853$	34.9992	−	20.2068i	1.19835	−	0.691867i	0.960187	+	0.279358i	$0.0901216\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−1.75027	+	1.01052i	−0.0597879	+	0.0345186i	−0.529596	−	0.848250i	$-0.677656\pi$
$857$	−1.75027	+	1.01052i	−0.0597879	+	0.0345186i	0.469808	+	0.882769i	$0.344323\pi$
$858$		0			0
$859$	2.23164	−	3.86531i	0.0761425	−	0.131883i	−0.825440	−	0.564490i	$-0.809073\pi$
$859$	2.23164	−	3.86531i	0.0761425	−	0.131883i	0.901583	+	0.432607i	$0.142406\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$			2.21958i			0.0755555i	0.999286	+	0.0377777i	$0.0120279\pi$
$863$			2.21958i			0.0755555i	−0.999286	+	0.0377777i	$0.987972\pi$
$864$		0			0
$865$	−1.26836	−	0.812689i	−0.0431256	−	0.0276322i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	12.4342	−	21.5367i	0.421802	−	0.730583i
$870$		0			0
$871$	50.8945	+	88.1519i	1.72450	+	2.98691i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−13.2792	+	5.37923i	−0.448918	+	0.181851i
$876$		0			0
$877$	8.06637	+	4.65712i	0.272382	+	0.157260i	0.629970	−	0.776620i	$-0.283067\pi$
$877$	8.06637	+	4.65712i	0.272382	+	0.157260i	−0.357588	+	0.933880i	$0.616401\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	43.6111			1.46930			0.734648	−	0.678448i	$-0.237347\pi$
$881$	43.6111			1.46930			0.734648	+	0.678448i	$0.237347\pi$
$882$		0			0
$883$		−	1.51074i		−	0.0508406i	−0.999677	−	0.0254203i	$-0.991908\pi$
$883$		−	1.51074i		−	0.0508406i	0.999677	−	0.0254203i	$-0.00809240\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	5.76665	+	3.32937i	0.193625	+	0.111789i	0.593678	−	0.804702i	$-0.297675\pi$
$887$	5.76665	+	3.32937i	0.193625	+	0.111789i	−0.400053	+	0.916492i	$0.631008\pi$
$888$		0			0
$889$	0.821092	+	1.42217i	0.0275385	+	0.0476981i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−33.0216	+	19.0650i	−1.10502	+	0.637986i
$894$		0			0
$895$	14.9344	+	28.8720i	0.499201	+	0.965085i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−26.9104			−0.897512
$900$		0			0
$901$	13.2844			0.442566
$902$		0			0
$903$		0			0
$904$		0			0
$905$	15.5938	+	30.1468i	0.518354	+	1.00211i
$906$		0			0
$907$	−13.3175	+	7.68886i	−0.442200	+	0.255304i	−0.704531	−	0.709674i	$-0.748842\pi$
$907$	−13.3175	+	7.68886i	−0.442200	+	0.255304i	0.262330	+	0.964978i	$0.415509\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	11.7231	+	20.3051i	0.388405	+	0.672738i	0.992235	−	0.124376i	$-0.0396928\pi$
$911$	11.7231	+	20.3051i	0.388405	+	0.672738i	−0.603830	+	0.797113i	$0.706359\pi$
$912$		0			0
$913$	−34.9992	−	20.2068i	−1.15830	−	0.668747i
$914$		0			0
$915$		0			0
$916$		0			0
$917$			7.05585i			0.233005i
$918$		0			0
$919$	31.1789			1.02850			0.514249	−	0.857641i	$-0.328071\pi$
$919$	31.1789			1.02850			0.514249	+	0.857641i	$0.328071\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−31.0993	−	17.9552i	−1.02365	−	0.591003i
$924$		0			0
$925$	21.3854	+	15.1409i	0.703148	+	0.497829i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−13.3003	−	23.0367i	−0.436367	−	0.755810i	0.561039	−	0.827790i	$-0.310402\pi$
$929$	−13.3003	−	23.0367i	−0.436367	−	0.755810i	−0.997406	+	0.0719791i	$0.977069\pi$
$930$		0			0
$931$	19.2316	−	33.3102i	0.630291	−	1.09170i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	46.7045	+	29.9254i	1.52740	+	0.978664i
$936$		0			0
$937$		−	3.95906i		−	0.129337i	−0.997907	−	0.0646685i	$-0.979401\pi$
$937$		−	3.95906i		−	0.129337i	0.997907	−	0.0646685i	$-0.0205990\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−15.6825	+	27.1629i	−0.511235	+	0.885485i	0.488680	+	0.872463i	$0.337479\pi$
$941$	−15.6825	+	27.1629i	−0.511235	+	0.885485i	−0.999915	+	0.0130223i	$0.995855\pi$
$942$		0			0
$943$	4.43917	−	2.56295i	0.144559	−	0.0834613i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−23.4105	+	13.5161i	−0.760739	+	0.439213i	−0.829561	−	0.558416i	$-0.811409\pi$
$947$	−23.4105	+	13.5161i	−0.760739	+	0.439213i	0.0688223	+	0.997629i	$0.478076\pi$
$948$		0			0
$949$	−25.4473	+	44.0760i	−0.826053	+	1.43077i
$950$		0			0
$951$		0			0
$952$		0			0
$953$			26.3584i			0.853833i	0.904291	+	0.426917i	$0.140400\pi$
$953$			26.3584i			0.853833i	−0.904291	+	0.426917i	$0.859600\pi$
$954$		0			0
$955$	31.7156	−	49.4986i	1.02629	−	1.60174i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−7.23808	+	12.5367i	−0.233730	+	0.404832i
$960$		0			0
$961$	2.08945	+	3.61904i	0.0674017	+	0.116743i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	1.33632	−	28.8801i	0.0430175	−	0.929684i
$966$		0			0
$967$	−28.1419	−	16.2477i	−0.904982	−	0.522492i	−0.0261690	−	0.999658i	$-0.508331\pi$
$967$	−28.1419	−	16.2477i	−0.904982	−	0.522492i	−0.878813	+	0.477166i	$0.841664\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−37.3027			−1.19710			−0.598550	−	0.801085i	$-0.704256\pi$
$971$	−37.3027			−1.19710			−0.598550	+	0.801085i	$0.704256\pi$
$972$		0			0
$973$		−	22.0144i		−	0.705748i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	15.7216	+	9.07688i	0.502979	+	0.290395i	0.729943	−	0.683508i	$-0.239547\pi$
$977$	15.7216	+	9.07688i	0.502979	+	0.290395i	−0.226964	+	0.973903i	$0.572880\pi$
$978$		0			0
$979$	−20.7684	−	35.9719i	−0.663760	−	1.14967i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	42.2212	−	24.3764i	1.34665	−	0.777487i	0.358873	−	0.933386i	$-0.383161\pi$
$983$	42.2212	−	24.3764i	1.34665	−	0.777487i	0.987773	+	0.155900i	$0.0498277\pi$
$984$		0			0
$985$	16.2953	−	8.42890i	0.519210	−	0.268567i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	9.65078			0.306877
$990$		0			0
$991$	1.53673			0.0488157			0.0244078	−	0.999702i	$-0.492230\pi$
$991$	1.53673			0.0488157			0.0244078	+	0.999702i	$0.492230\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	2.42226	+	4.68286i	0.0767908	+	0.148457i
$996$		0			0
$997$	−38.2293	+	22.0717i	−1.21073	+	0.699018i	−0.962919	−	0.269790i	$-0.913046\pi$
$997$	−38.2293	+	22.0717i	−1.21073	+	0.699018i	−0.247815	+	0.968807i	$0.579712\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1620.2.r.h.109.6		16
3.2	odd	2	inner	1620.2.r.h.109.3		16
5.4	even	2	inner	1620.2.r.h.109.1		16
9.2	odd	6	inner	1620.2.r.h.1189.8		16
9.4	even	3		1620.2.d.e.649.5	yes	8
9.5	odd	6		1620.2.d.e.649.4	yes	8
9.7	even	3	inner	1620.2.r.h.1189.1		16
15.14	odd	2	inner	1620.2.r.h.109.8		16
45.4	even	6		1620.2.d.e.649.6	yes	8
45.13	odd	12		8100.2.a.be.1.6		8
45.14	odd	6		1620.2.d.e.649.3	✓	8
45.22	odd	12		8100.2.a.be.1.4		8
45.23	even	12		8100.2.a.be.1.5		8
45.29	odd	6	inner	1620.2.r.h.1189.3		16
45.32	even	12		8100.2.a.be.1.3		8
45.34	even	6	inner	1620.2.r.h.1189.6		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1620.2.d.e.649.3	✓	8	45.14	odd	6
1620.2.d.e.649.4	yes	8	9.5	odd	6
1620.2.d.e.649.5	yes	8	9.4	even	3
1620.2.d.e.649.6	yes	8	45.4	even	6
1620.2.r.h.109.1		16	5.4	even	2	inner
1620.2.r.h.109.3		16	3.2	odd	2	inner
1620.2.r.h.109.6		16	1.1	even	1	trivial
1620.2.r.h.109.8		16	15.14	odd	2	inner
1620.2.r.h.1189.1		16	9.7	even	3	inner
1620.2.r.h.1189.3		16	45.29	odd	6	inner
1620.2.r.h.1189.6		16	45.34	even	6	inner
1620.2.r.h.1189.8		16	9.2	odd	6	inner
8100.2.a.be.1.3		8	45.32	even	12
8100.2.a.be.1.4		8	45.22	odd	12
8100.2.a.be.1.5		8	45.23	even	12
8100.2.a.be.1.6		8	45.13	odd	12

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:	\( N \)	\(=\)	\( 1620 = 2^{2} \cdot 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1620.r (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.02733 + 1.98610i) q^{5} +(1.10979 - 0.640739i) q^{7} +O(q^{10})\)	\(q+(1.02733 + 1.98610i) q^{5} +(1.10979 - 0.640739i) q^{7} +(-2.07237 - 3.58945i) q^{11} +(-5.64823 - 3.26101i) q^{13} +5.98507i q^{17} -7.17891 q^{19} +(-6.52202 - 3.76549i) q^{23} +(-2.88918 + 4.08076i) q^{25} +(2.59808 + 4.50000i) q^{29} +(-2.58945 + 4.48507i) q^{31} +(2.41269 + 1.54591i) q^{35} -5.24054i q^{37} +(-0.340322 + 0.589454i) q^{41} +(-1.10979 + 0.640739i) q^{43} +(4.59980 - 2.65570i) q^{47} +(-2.67891 + 4.64001i) q^{49} -2.21958i q^{53} +(5.00000 - 7.80350i) q^{55} +(-3.80442 + 6.58945i) q^{59} +(1.08945 + 1.88699i) q^{61} +(0.674082 - 14.5681i) q^{65} +(-13.5161 - 7.80350i) q^{67} +5.50603 q^{71} -7.80350i q^{73} +(-4.59980 - 2.65570i) q^{77} +(3.00000 + 5.19615i) q^{79} +(8.44423 - 4.87528i) q^{83} +(-11.8869 + 6.14865i) q^{85} +10.0215 q^{89} -8.35782 q^{91} +(-7.37512 - 14.2580i) q^{95} +(-12.4063 + 7.16276i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q+O(q^{10}) \) 16 * q	\( 16 q - 24 q^{19} - 6 q^{25} + 4 q^{31} + 48 q^{49} + 80 q^{55} - 28 q^{61} + 48 q^{79} - 22 q^{85} + 48 q^{91}+O(q^{100}) \) 16 * q - 24 * q^19 - 6 * q^25 + 4 * q^31 + 48 * q^49 + 80 * q^55 - 28 * q^61 + 48 * q^79 - 22 * q^85 + 48 * q^91

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