LMFDB - Embedded newform 1620.2.r.h.1189.8

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			1189.8
Root			$-2.23368 + 0.103355i$ of defining polynomial
Character	$\chi$	$=$	1620.1189
Dual form			1620.2.r.h.109.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.23368 + 0.103355i) q^{5} +(-1.10979 - 0.640739i) q^{7} +O(q^{10})$	$q+(2.23368 + 0.103355i) q^{5} +(-1.10979 - 0.640739i) q^{7} +(2.07237 - 3.58945i) q^{11} +(5.64823 - 3.26101i) q^{13} -5.98507i q^{17} -7.17891 q^{19} +(-6.52202 + 3.76549i) q^{23} +(4.97864 + 0.461723i) q^{25} +(-2.59808 + 4.50000i) q^{29} +(-2.58945 - 4.48507i) q^{31} +(-2.41269 - 1.54591i) q^{35} -5.24054i q^{37} +(0.340322 + 0.589454i) q^{41} +(1.10979 + 0.640739i) q^{43} +(4.59980 + 2.65570i) q^{47} +(-2.67891 - 4.64001i) q^{49} +2.21958i q^{53} +(5.00000 - 7.80350i) q^{55} +(3.80442 + 6.58945i) q^{59} +(1.08945 - 1.88699i) q^{61} +(12.9534 - 6.70027i) q^{65} +(13.5161 - 7.80350i) q^{67} -5.50603 q^{71} -7.80350i q^{73} +(-4.59980 + 2.65570i) q^{77} +(3.00000 - 5.19615i) q^{79} +(8.44423 + 4.87528i) q^{83} +(0.618586 - 13.3687i) q^{85} -10.0215 q^{89} -8.35782 q^{91} +(-16.0354 - 0.741975i) q^{95} +(12.4063 + 7.16276i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/1620\mathbb{Z}\right)^\times$.

$n$	$811$	$1297$	$1541$
$\chi(n)$	$1$	$-1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	2.23368	+	0.103355i	0.998931	+	0.0462217i
$5$	2.23368	+	0.103355i	0.998931	+	0.0462217i
$6$		0			0
$7$	−1.10979	−	0.640739i	−0.419462	−	0.242176i	0.275385	−	0.961334i	$-0.411195\pi$
$7$	−1.10979	−	0.640739i	−0.419462	−	0.242176i	−0.694847	+	0.719158i	$0.744528\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	2.07237	−	3.58945i	0.624844	−	1.08226i	−0.363727	−	0.931505i	$-0.618496\pi$
$11$	2.07237	−	3.58945i	0.624844	−	1.08226i	0.988571	−	0.150756i	$-0.0481707\pi$
$12$		0			0
$13$	5.64823	−	3.26101i	1.56654	−	0.904441i	0.569970	−	0.821666i	$-0.306955\pi$
$13$	5.64823	−	3.26101i	1.56654	−	0.904441i	0.996568	−	0.0827757i	$-0.0263785\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$		−	5.98507i		−	1.45159i	−0.687909	−	0.725797i	$-0.741471\pi$
$17$		−	5.98507i		−	1.45159i	0.687909	−	0.725797i	$-0.258529\pi$
$18$		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	−0.989615	−	0.143745i	$-0.954085\pi$
$23$	−6.52202	+	3.76549i	−1.35993	+	0.785159i	−0.370320	+	0.928904i	$0.620752\pi$
$24$		0			0
$25$	4.97864	+	0.461723i	0.995727	+	0.0923445i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−2.59808	+	4.50000i	−0.482451	+	0.835629i	−0.999797	−	0.0201471i	$-0.993587\pi$
$29$	−2.59808	+	4.50000i	−0.482451	+	0.835629i	0.517346	+	0.855776i	$0.326920\pi$
$30$		0			0
$31$	−2.58945	−	4.48507i	−0.465080	−	0.805542i	0.534125	−	0.845405i	$-0.320641\pi$
$31$	−2.58945	−	4.48507i	−0.465080	−	0.805542i	−0.999205	+	0.0398636i	$0.987308\pi$
$32$		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	$-0.149741\pi$
$41$	0.340322	+	0.589454i	0.0531493	+	0.0920573i	−0.838227	+	0.545322i	$0.816407\pi$
$42$		0			0
$43$	1.10979	+	0.640739i	0.169242	+	0.0977117i	0.582228	−	0.813025i	$-0.302181\pi$
$43$	1.10979	+	0.640739i	0.169242	+	0.0977117i	−0.412987	+	0.910737i	$0.635514\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	4.59980	+	2.65570i	0.670950	+	0.387373i	0.796437	−	0.604722i	$-0.206716\pi$
$47$	4.59980	+	2.65570i	0.670950	+	0.387373i	−0.125486	+	0.992095i	$0.540049\pi$
$48$		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	$0.0487136\pi$
$53$			2.21958i			0.304883i	−0.988312	+	0.152442i	$0.951286\pi$
$54$		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	$-0.00172711\pi$
$59$	3.80442	+	6.58945i	0.495294	+	0.857874i	−0.504692	+	0.863300i	$0.668394\pi$
$60$		0			0
$61$	1.08945	−	1.88699i	0.139490	−	0.241604i	−0.787813	−	0.615914i	$-0.788787\pi$
$61$	1.08945	−	1.88699i	0.139490	−	0.241604i	0.927304	+	0.374310i	$0.122120\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	12.9534	−	6.70027i	1.60667	−	0.831067i
$66$		0			0
$67$	13.5161	−	7.80350i	1.65125	−	0.953349i	0.674689	−	0.738103i	$-0.264278\pi$
$67$	13.5161	−	7.80350i	1.65125	−	0.953349i	0.976560	−	0.215246i	$-0.0690554\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−5.50603			−0.653446			−0.326723	−	0.945120i	$-0.605944\pi$
$71$	−5.50603			−0.653446			−0.326723	+	0.945120i	$0.605944\pi$
$72$		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	−0.646440	−	0.762964i	$-0.723743\pi$
$79$	3.00000	−	5.19615i	0.337526	−	0.584613i	0.983967	+	0.178352i	$0.0570765\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	8.44423	+	4.87528i	0.926875	+	0.535132i	0.885822	−	0.464025i	$-0.153595\pi$
$83$	8.44423	+	4.87528i	0.926875	+	0.535132i	0.0410532	+	0.999157i	$0.486929\pi$
$84$		0			0
$85$	0.618586	−	13.3687i	0.0670951	−	1.45004i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−10.0215			−1.06228			−0.531141	−	0.847284i	$-0.678236\pi$
$89$	−10.0215			−1.06228			−0.531141	+	0.847284i	$0.678236\pi$
$90$		0			0
$91$	−8.35782			−0.876137
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−16.0354	−	0.741975i	−1.64519	−	0.0761250i
$96$		0			0
$97$	12.4063	+	7.16276i	1.25966	+	0.727268i	0.973009	−	0.230766i	$-0.0741232\pi$
$97$	12.4063	+	7.16276i	1.25966	+	0.727268i	0.286655	+	0.958034i	$0.407457\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−0.340322	+	0.589454i	−0.0338633	+	0.0586529i	−0.882460	−	0.470387i	$-0.844114\pi$
$101$	−0.340322	+	0.589454i	−0.0338633	+	0.0586529i	0.848597	+	0.529040i	$0.177448\pi$
$102$		0			0
$103$	−2.21958	+	1.28148i	−0.218702	+	0.126268i	−0.605349	−	0.795960i	$-0.706966\pi$
$103$	−2.21958	+	1.28148i	−0.218702	+	0.126268i	0.386647	+	0.922228i	$0.373633\pi$
$104$		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	−0.0823983	−	0.996599i	$-0.526258\pi$
$113$	7.86081	−	4.53844i	0.739483	−	0.426941i	0.821881	+	0.569659i	$0.192925\pi$
$114$		0			0
$115$	−14.9573	+	7.73681i	−1.39477	+	0.721461i
$116$		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	$-0.0893447\pi$
$131$	2.75302	+	4.76836i	0.240532	+	0.416614i	−0.720334	+	0.693627i	$0.756011\pi$
$132$		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	0.0200209	−	0.999800i	$-0.493627\pi$
$137$	−9.78303	−	5.64823i	−0.835820	−	0.482561i	−0.855841	+	0.517238i	$0.826960\pi$
$138$		0			0
$139$	8.58945	+	14.8774i	0.728548	+	1.26188i	0.957497	+	0.288444i	$0.0931378\pi$
$139$	8.58945	+	14.8774i	0.728548	+	1.26188i	−0.228949	+	0.973438i	$0.573529\pi$
$140$		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	0.914038	+	0.405628i	$0.132947\pi$
$149$	9.86660	+	17.0895i	0.808303	+	1.40002i	−0.105735	+	0.994394i	$0.533719\pi$
$150$		0			0
$151$	−2.58945	+	4.48507i	−0.210727	+	0.364990i	−0.951942	−	0.306278i	$-0.900916\pi$
$151$	−2.58945	+	4.48507i	−0.210727	+	0.364990i	0.741215	+	0.671267i	$0.234250\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−5.32045	−	10.2858i	−0.427349	−	0.826177i
$156$		0			0
$157$	4.53844	−	2.62027i	0.362207	−	0.209120i	−0.307841	−	0.951438i	$-0.599607\pi$
$157$	4.53844	−	2.62027i	0.362207	−	0.209120i	0.670049	+	0.742317i	$0.266273\pi$
$158$		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	−0.572526	−	0.819887i	$-0.694036\pi$
$167$	−1.92222	+	1.10979i	−0.148746	+	0.0858783i	0.423780	+	0.905765i	$0.360703\pi$
$168$		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	0.477658	−	0.878546i	$-0.341486\pi$
$173$	−0.583422	−	0.336839i	−0.0443567	−	0.0256094i	−0.522014	+	0.852937i	$0.674819\pi$
$174$		0			0
$175$	−5.22940	−	3.70242i	−0.395306	−	0.279877i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−14.5370			−1.08655			−0.543275	−	0.839555i	$-0.682816\pi$
$179$	−14.5370			−1.08655			−0.543275	+	0.839555i	$0.682816\pi$
$180$		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
$185$	0.541635	−	11.7057i	0.0398218	−	0.860619i
$186$		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	0.208246	−	0.978077i	$-0.433225\pi$
$191$	13.1453	−	22.7684i	0.951162	−	1.64746i	0.742916	−	0.669384i	$-0.233442\pi$
$192$		0			0
$193$	11.1972	−	6.46470i	0.805992	−	0.465339i	−0.0395704	−	0.999217i	$-0.512599\pi$
$193$	11.1972	−	6.46470i	0.805992	−	0.465339i	0.845562	+	0.533877i	$0.179266\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$			8.20466i			0.584558i	0.956333	+	0.292279i	$0.0944135\pi$
$197$			8.20466i			0.584558i	−0.956333	+	0.292279i	$0.905586\pi$
$198$		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
$205$	0.699246	+	1.35182i	0.0488374	+	0.0944155i
$206$		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	0.771043	−	0.636783i	$-0.219735\pi$
$211$	−2.41055	−	4.17519i	−0.165949	−	0.287432i	−0.936992	+	0.349351i	$0.886402\pi$
$212$		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	$-0.418744\pi$
$223$	−6.85730	−	3.95906i	−0.459199	−	0.265119i	−0.711707	+	0.702476i	$0.752078\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	18.8107	+	10.8604i	1.24851	+	0.720827i	0.970812	−	0.239842i	$-0.0770956\pi$
$227$	18.8107	+	10.8604i	1.24851	+	0.720827i	0.277697	+	0.960669i	$0.410429\pi$
$228$		0			0
$229$	9.08945	+	15.7434i	0.600648	+	1.04035i	0.992723	+	0.120420i	$0.0384240\pi$
$229$	9.08945	+	15.7434i	0.600648	+	1.04035i	−0.392075	+	0.919933i	$0.628243\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$			21.0470i			1.37884i	0.724363	+	0.689418i	$0.242134\pi$
$233$			21.0470i			1.37884i	−0.724363	+	0.689418i	$0.757866\pi$
$234$		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	0.962476	+	0.271368i	$0.0874761\pi$
$239$	11.0729	+	19.1789i	0.716249	+	1.24058i	−0.246226	+	0.969212i	$0.579191\pi$
$240$		0			0
$241$	−9.50000	+	16.4545i	−0.611949	+	1.05993i	0.378963	+	0.925412i	$0.376281\pi$
$241$	−9.50000	+	16.4545i	−0.611949	+	1.05993i	−0.990912	+	0.134515i	$0.957053\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−5.50425	−	10.6412i	−0.351654	−	0.679839i
$246$		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	$-0.315910\pi$
$251$	17.3205			1.09326			0.546630	+	0.837374i	$0.315910\pi$
$252$		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	−0.303211	−	0.952923i	$-0.598059\pi$
$257$	5.93860	−	3.42865i	0.370439	−	0.213873i	0.673650	+	0.739050i	$0.264725\pi$
$258$		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	0.0406531	−	0.999173i	$-0.487056\pi$
$263$	−13.0440	−	7.53098i	−0.804330	−	0.464380i	−0.844983	+	0.534793i	$0.820389\pi$
$264$		0			0
$265$	−0.229405	+	4.95783i	−0.0140922	+	0.304557i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	9.28001			0.565812			0.282906	−	0.959148i	$-0.408702\pi$
$269$	9.28001			0.565812			0.282906	+	0.959148i	$0.408702\pi$
$270$		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
$275$	11.9749	−	16.9137i	0.722115	−	1.01994i
$276$		0			0
$277$	10.1867	+	5.88128i	0.612058	+	0.353372i	0.773770	−	0.633466i	$-0.218368\pi$
$277$	10.1867	+	5.88128i	0.612058	+	0.353372i	−0.161712	+	0.986838i	$0.551702\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−3.61904	+	6.26836i	−0.215894	+	0.373939i	−0.953549	−	0.301239i	$-0.902600\pi$
$281$	−3.61904	+	6.26836i	−0.215894	+	0.373939i	0.737655	+	0.675178i	$0.235933\pi$
$282$		0			0
$283$	−24.8125	+	14.3255i	−1.47495	+	0.851563i	−0.999601	−	0.0282335i	$-0.991012\pi$
$283$	−24.8125	+	14.3255i	−1.47495	+	0.851563i	−0.475350	+	0.879797i	$0.657678\pi$
$284$		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	−0.879923	−	0.475116i	$-0.842406\pi$
$293$	−15.5497	+	8.97761i	−0.908422	+	0.524477i	−0.0284987	+	0.999594i	$0.509073\pi$
$294$		0			0
$295$	7.81680	+	15.1119i	0.455112	+	0.879850i
$296$		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	$-0.0848135\pi$
$311$	4.48507	+	7.76836i	0.254325	+	0.440503i	−0.710387	+	0.703811i	$0.751480\pi$
$312$		0			0
$313$	−7.86782	−	4.54249i	−0.444715	−	0.256757i	0.260880	−	0.965371i	$-0.415987\pi$
$313$	−7.86782	−	4.54249i	−0.444715	−	0.256757i	−0.705596	+	0.708615i	$0.749321\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−10.5384	−	6.08435i	−0.591895	−	0.341731i	0.173951	−	0.984754i	$-0.444347\pi$
$317$	−10.5384	−	6.08435i	−0.591895	−	0.341731i	−0.765847	+	0.643023i	$0.777680\pi$
$318$		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	−0.886369	−	0.462979i	$-0.846781\pi$
$331$	−0.768363	+	1.33084i	−0.0422330	+	0.0731497i	0.844136	+	0.536129i	$0.180114\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	30.9970	−	16.0335i	1.69355	−	0.876006i
$336$		0			0
$337$	−2.21958	+	1.28148i	−0.120908	+	0.0698065i	−0.559234	−	0.829010i	$-0.688905\pi$
$337$	−2.21958	+	1.28148i	−0.120908	+	0.0698065i	0.438326	+	0.898816i	$0.355572\pi$
$338$		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	−0.550707	−	0.834699i	$-0.685642\pi$
$347$	−1.92222	+	1.10979i	−0.103190	+	0.0595767i	0.447517	+	0.894275i	$0.352308\pi$
$348$		0			0
$349$	4.41055	−	7.63929i	0.236091	−	0.408922i	−0.723498	−	0.690326i	$-0.757467\pi$
$349$	4.41055	−	7.63929i	0.236091	−	0.408922i	0.959589	+	0.281405i	$0.0908003\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−24.1659	−	13.9522i	−1.28622	−	0.742599i	−0.308241	−	0.951308i	$-0.599740\pi$
$353$	−24.1659	−	13.9522i	−1.28622	−	0.742599i	−0.977978	+	0.208709i	$0.933074\pi$
$354$		0			0
$355$	−12.2987	−	0.569075i	−0.652747	−	0.0302034i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−19.3624			−1.02191			−0.510955	−	0.859607i	$-0.670708\pi$
$359$	−19.3624			−1.02191			−0.510955	+	0.859607i	$0.670708\pi$
$360$		0			0
$361$	32.5367			1.71246
$362$		0			0
$363$		0			0
$364$		0			0
$365$	0.806529	−	17.4305i	0.0422156	−	0.912354i
$366$		0			0
$367$	2.21958	+	1.28148i	0.115861	+	0.0668926i	0.556811	−	0.830639i	$-0.312025\pi$
$367$	2.21958	+	1.28148i	0.115861	+	0.0668926i	−0.440949	+	0.897532i	$0.645358\pi$
$368$		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	$-0.810706\pi$
$373$	−14.6258	+	8.44423i	−0.757297	+	0.437226i	0.0710272	+	0.997474i	$0.477372\pi$
$374$		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	−0.211194	−	0.977444i	$-0.567735\pi$
$383$	10.3664	−	5.98507i	0.529701	−	0.305823i	0.740895	+	0.671621i	$0.234402\pi$
$384$		0			0
$385$	−10.5490	+	5.45656i	−0.537625	+	0.278092i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−6.24756	+	10.8211i	−0.316764	+	0.548651i	−0.979811	−	0.199927i	$-0.935930\pi$
$389$	−6.24756	+	10.8211i	−0.316764	+	0.548651i	0.663047	+	0.748578i	$0.269263\pi$
$390$		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	$-0.0692760\pi$
$401$	6.03173	+	10.4473i	0.301210	+	0.521712i	−0.675200	+	0.737635i	$0.735943\pi$
$402$		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	0.998350	−	0.0574237i	$-0.0182886\pi$
$409$	9.08945	+	15.7434i	0.449445	+	0.778461i	−0.548905	+	0.835885i	$0.684955\pi$
$410$		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	$-0.242417\pi$
$419$	−4.82539	−	8.35782i	−0.235736	−	0.408306i	−0.959486	+	0.281756i	$0.909083\pi$
$420$		0			0
$421$	7.85782	−	13.6101i	0.382967	−	0.663318i	−0.608518	−	0.793540i	$-0.708236\pi$
$421$	7.85782	−	13.6101i	0.382967	−	0.663318i	0.991485	+	0.130222i	$0.0415691\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	2.76344	−	29.7975i	0.134047	−	1.44539i
$426$		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	$-0.230341\pi$
$431$	31.1160			1.49881			0.749403	+	0.662114i	$0.230341\pi$
$432$		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	−0.989683	−	0.143273i	$-0.954237\pi$
$439$	−7.76836	+	13.4552i	−0.370764	+	0.642182i	0.618920	+	0.785454i	$0.287571\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	17.6438	+	10.1867i	0.838284	+	0.483984i	0.856681	−	0.515847i	$-0.172523\pi$
$443$	17.6438	+	10.1867i	0.838284	+	0.483984i	−0.0183965	+	0.999831i	$0.505856\pi$
$444$		0			0
$445$	−22.3849	−	1.03577i	−1.06115	−	0.0491004i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	33.8386			1.59694			0.798471	−	0.602033i	$-0.205642\pi$
$449$	33.8386			1.59694			0.798471	+	0.602033i	$0.205642\pi$
$450$		0			0
$451$	2.82109			0.132840
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−18.6687	−	0.863821i	−0.875201	−	0.0404965i
$456$		0			0
$457$	−0.0992755	−	0.0573167i	−0.00464391	−	0.00268116i	0.497676	−	0.867363i	$-0.334187\pi$
$457$	−0.0992755	−	0.0573167i	−0.00464391	−	0.00268116i	−0.502320	+	0.864682i	$0.667520\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−4.48507	+	7.76836i	−0.208890	+	0.361809i	−0.951365	−	0.308065i	$-0.900319\pi$
$461$	−4.48507	+	7.76836i	−0.208890	+	0.361809i	0.742475	+	0.669874i	$0.233652\pi$
$462$		0			0
$463$	6.65875	−	3.84443i	0.309458	−	0.178666i	−0.337226	−	0.941424i	$-0.609489\pi$
$463$	6.65875	−	3.84443i	0.309458	−	0.178666i	0.646684	+	0.762758i	$0.276155\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$		−	29.2517i		−	1.35361i	−0.736164	−	0.676803i	$-0.763365\pi$
$467$		−	29.2517i		−	1.35361i	0.736164	−	0.676803i	$-0.236635\pi$
$468$		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
$475$	−35.7412	−	3.31467i	−1.63992	−	0.152087i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−15.9288	+	27.5895i	−0.727804	+	1.26059i	0.230005	+	0.973190i	$0.426126\pi$
$479$	−15.9288	+	27.5895i	−0.727804	+	1.26059i	−0.957809	+	0.287405i	$0.907207\pi$
$480$		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	−0.999426	−	0.0338851i	$-0.989212\pi$
$491$	−11.7231	−	20.3051i	−0.529058	−	0.916356i	0.470367	−	0.882471i	$-0.344121\pi$
$492$		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	0.774429	−	0.632661i	$-0.218037\pi$
$499$	−3.58945	−	6.21712i	−0.160686	−	0.278316i	−0.935115	+	0.354345i	$0.884704\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$		−	40.7467i		−	1.81681i	−0.418096	−	0.908403i	$-0.637302\pi$
$503$		−	40.7467i		−	1.81681i	0.418096	−	0.908403i	$-0.362698\pi$
$504$		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	0.966806	+	0.255510i	$0.0822434\pi$
$509$	15.8983	+	27.5367i	0.704681	+	1.22054i	−0.262125	+	0.965034i	$0.584423\pi$
$510$		0			0
$511$	−5.00000	+	8.66025i	−0.221187	+	0.383107i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−5.09028	+	2.63300i	−0.224305	+	0.116024i
$516$		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	$-0.661222\pi$
$521$	−22.1459			−0.970229			−0.485115	+	0.874451i	$0.661222\pi$
$522$		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
$545$	−15.6357	−	0.723484i	−0.669762	−	0.0309906i
$546$		0			0
$547$	−4.43917	−	2.56295i	−0.189805	−	0.109584i	0.402086	−	0.915602i	$-0.368285\pi$
$547$	−4.43917	−	2.56295i	−0.189805	−	0.109584i	−0.591891	+	0.806018i	$0.701619\pi$
$548$		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	$0.0163141\pi$
$557$			2.41813i			0.102460i	−0.998687	+	0.0512298i	$0.983686\pi$
$558$		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	−0.399929	−	0.916546i	$-0.630965\pi$
$563$	4.59980	−	2.65570i	0.193859	−	0.111924i	0.593788	+	0.804622i	$0.297632\pi$
$564$		0			0
$565$	18.0276	−	9.32497i	0.758427	−	0.392304i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−10.8876	+	18.8578i	−0.456430	+	0.790561i	−0.998769	−	0.0495991i	$-0.984206\pi$
$569$	−10.8876	+	18.8578i	−0.456430	+	0.790561i	0.542339	+	0.840160i	$0.317539\pi$
$570$		0			0
$571$	3.41055	+	5.90724i	0.142727	+	0.247210i	0.928523	−	0.371276i	$-0.121080\pi$
$571$	3.41055	+	5.90724i	0.142727	+	0.247210i	−0.785796	+	0.618486i	$0.787746\pi$
$572$		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	−0.950805	−	0.309790i	$-0.899741\pi$
$587$	−41.0543	−	23.7027i	−1.69449	−	0.978316i	−0.743688	−	0.668527i	$-0.766925\pi$
$588$		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	$-0.925491\pi$
$593$		−	11.2965i		−	0.463890i	0.972729	−	0.231945i	$-0.0745090\pi$
$594$		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	0.948105	+	0.317958i	$0.102997\pi$
$599$	18.3415	+	31.7684i	0.749412	+	1.29802i	−0.198692	+	0.980062i	$0.563669\pi$
$600$		0			0
$601$	−9.67891	+	16.7644i	−0.394811	+	0.683833i	−0.993077	−	0.117465i	$-0.962523\pi$
$601$	−9.67891	+	16.7644i	−0.394811	+	0.683833i	0.598266	+	0.801297i	$0.295857\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−6.34779	−	12.2719i	−0.258074	−	0.498925i
$606$		0			0
$607$	−1.10979	+	0.640739i	−0.0450451	+	0.0260068i	−0.522353	−	0.852729i	$-0.674946\pi$
$607$	−1.10979	+	0.640739i	−0.0450451	+	0.0260068i	0.477308	+	0.878736i	$0.341612\pi$
$608$		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	−0.929205	−	0.369565i	$-0.879507\pi$
$617$	−26.6715	+	15.3988i	−1.07375	+	0.619932i	−0.144549	+	0.989498i	$0.546173\pi$
$618$		0			0
$619$	17.1789	−	29.7547i	0.690479	−	1.19594i	−0.281203	−	0.959648i	$-0.590733\pi$
$619$	17.1789	−	29.7547i	0.690479	−	1.19594i	0.971681	−	0.236296i	$-0.0759334\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	11.1218	+	6.42119i	0.445586	+	0.257259i
$624$		0			0
$625$	24.5736	+	4.59750i	0.982945	+	0.183900i
$626$		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
$635$	−0.132447	+	2.86241i	−0.00525599	+	0.113591i
$636$		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	$-0.783349\pi$
$641$	3.95936	−	6.85782i	0.156385	−	0.270867i	0.933563	+	0.358414i	$0.116682\pi$
$642$		0			0
$643$	7.96709	−	4.59980i	0.314191	−	0.181399i	−0.334609	−	0.942357i	$-0.608604\pi$
$643$	7.96709	−	4.59980i	0.314191	−	0.181399i	0.648801	+	0.760958i	$0.275271\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$			13.7146i			0.539177i	0.962976	+	0.269588i	$0.0868876\pi$
$647$			13.7146i			0.539177i	−0.962976	+	0.269588i	$0.913112\pi$
$648$		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	0.429727	−	0.902959i	$-0.358610\pi$
$653$	36.4545	−	21.0470i	1.42658	−	0.823634i	0.996849	+	0.0793250i	$0.0252765\pi$
$654$		0			0
$655$	5.65652	+	10.9355i	0.221018	+	0.427286i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	12.0635	−	20.8945i	0.469926	−	0.813936i	−0.529483	−	0.848321i	$-0.677614\pi$
$659$	12.0635	−	20.8945i	0.469926	−	0.813936i	0.999409	+	0.0343850i	$0.0109472\pi$
$660$		0			0
$661$	−22.2156	−	38.4786i	−0.864088	−	1.49664i	−0.867950	−	0.496652i	$-0.834563\pi$
$661$	−22.2156	−	38.4786i	−0.864088	−	1.49664i	0.00386191	−	0.999993i	$-0.498771\pi$
$662$		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	$-0.116997\pi$
$673$	28.2412	+	16.3050i	1.08862	+	0.628513i	0.155409	+	0.987850i	$0.450330\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	44.1434	+	25.4862i	1.69657	+	0.979514i	0.948972	+	0.315360i	$0.102125\pi$
$677$	44.1434	+	25.4862i	1.69657	+	0.979514i	0.747596	+	0.664154i	$0.231208\pi$
$678$		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	$0.182695\pi$
$683$			28.3795i			1.08591i	−0.839762	+	0.542955i	$0.817305\pi$
$684$		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	−0.971361	−	0.237609i	$-0.923636\pi$
$691$	−7.35782	+	12.7441i	−0.279905	+	0.484809i	0.691456	+	0.722418i	$0.256969\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	17.6484	+	34.1190i	0.669443	+	1.29421i
$696$		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	$-0.586586\pi$
$701$	−14.2272			−0.537353			−0.268676	+	0.963230i	$0.586586\pi$
$702$		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	−0.985908	−	0.167286i	$-0.946500\pi$
$709$	−9.26836	+	16.0533i	−0.348081	+	0.602893i	0.637828	+	0.770179i	$0.279833\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	33.7769	+	19.5011i	1.26496	+	0.730323i
$714$		0			0
$715$	2.79390	−	60.3810i	0.104486	−	2.25812i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−31.7358			−1.18355			−0.591773	−	0.806105i	$-0.701572\pi$
$719$	−31.7358			−1.18355			−0.591773	+	0.806105i	$0.701572\pi$
$720$		0			0
$721$	3.28437			0.122316
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−15.0126	+	21.2043i	−0.557555	+	0.787507i
$726$		0			0
$727$	27.2307	+	15.7216i	1.00993	+	0.583083i	0.911171	−	0.412029i	$-0.135180\pi$
$727$	27.2307	+	15.7216i	1.00993	+	0.583083i	0.0987581	+	0.995111i	$0.468513\pi$
$728$		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	$-0.636489\pi$
$733$	4.43917	−	2.56295i	0.163964	−	0.0946649i	0.579737	+	0.814804i	$0.303155\pi$
$734$		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	−0.963074	−	0.269238i	$-0.913228\pi$
$743$	−33.0216	+	19.0650i	−1.21144	+	0.699427i	−0.248370	+	0.968665i	$0.579895\pi$
$744$		0			0
$745$	20.2725	+	39.1921i	0.742728	+	1.43589i
$746$		0			0
$747$		0			0
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−8.17891	−	14.1663i	−0.298453	−	0.516935i	0.677330	−	0.735680i	$-0.263137\pi$
$751$	−8.17891	−	14.1663i	−0.298453	−	0.516935i	−0.975782	+	0.218745i	$0.929804\pi$
$752$		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	$-0.156672\pi$
$761$	0.866025	+	1.50000i	0.0313934	+	0.0543750i	−0.849902	+	0.526941i	$0.823339\pi$
$762$		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	0.631718	−	0.775198i	$-0.282350\pi$
$769$	−9.85782	−	17.0742i	−0.355482	−	0.615713i	−0.987200	+	0.159485i	$0.949017\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$			4.63772i			0.166807i	0.996516	+	0.0834036i	$0.0265791\pi$
$773$			4.63772i			0.166807i	−0.996516	+	0.0834036i	$0.973421\pi$
$774$		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
$785$	10.4082	−	5.38377i	0.371486	−	0.192155i
$786$		0			0
$787$	39.6369	−	22.8844i	1.41290	−	0.815740i	0.417242	−	0.908795i	$-0.362997\pi$
$787$	39.6369	−	22.8844i	1.41290	−	0.815740i	0.995661	+	0.0930552i	$0.0296633\pi$
$788$		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	−0.846461	−	0.532450i	$-0.821271\pi$
$797$	−22.8271	+	13.1792i	−0.808576	+	0.466832i	0.0378850	+	0.999282i	$0.487938\pi$
$798$		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
$805$	21.5567	+	0.997454i	0.759775	+	0.0351556i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	5.19615			0.182687			0.0913435	−	0.995819i	$-0.470884\pi$
$809$	5.19615			0.182687			0.0913435	+	0.995819i	$0.470884\pi$
$810$		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
$815$	1.21572	−	26.2738i	0.0425847	−	0.920330i
$816$		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	$-0.831950\pi$
$821$	0.124496	−	0.215633i	0.00434494	−	0.00752566i	0.868190	+	0.496232i	$0.165284\pi$
$822$		0			0
$823$	22.5929	−	13.0440i	0.787540	−	0.454687i	−0.0515557	−	0.998670i	$-0.516418\pi$
$823$	22.5929	−	13.0440i	0.787540	−	0.454687i	0.839096	+	0.543984i	$0.183085\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$			11.9701i			0.416243i	0.978103	+	0.208121i	$0.0667349\pi$
$827$			11.9701i			0.416243i	−0.978103	+	0.208121i	$0.933265\pi$
$828$		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
$835$	−4.40831	+	2.28025i	−0.152556	+	0.0789112i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	11.0425	−	19.1262i	0.381230	−	0.660309i	−0.610009	−	0.792395i	$-0.708834\pi$
$839$	11.0425	−	19.1262i	0.381230	−	0.660309i	0.991238	+	0.132086i	$0.0421674\pi$
$840$		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	$-0.576545\pi$
$853$	−34.9992	−	20.2068i	−1.19835	−	0.691867i	−0.960187	+	0.279358i	$0.909878\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−1.75027	−	1.01052i	−0.0597879	−	0.0345186i	0.469808	−	0.882769i	$-0.344323\pi$
$857$	−1.75027	−	1.01052i	−0.0597879	−	0.0345186i	−0.529596	+	0.848250i	$0.677656\pi$
$858$		0			0
$859$	2.23164	+	3.86531i	0.0761425	+	0.131883i	0.901583	−	0.432607i	$-0.142406\pi$
$859$	2.23164	+	3.86531i	0.0761425	+	0.131883i	−0.825440	+	0.564490i	$0.809073\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		−	2.21958i		−	0.0755555i	−0.999286	−	0.0377777i	$-0.987972\pi$
$863$		−	2.21958i		−	0.0755555i	0.999286	−	0.0377777i	$-0.0120279\pi$
$864$		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
$875$	−11.2981	−	8.81050i	−0.381947	−	0.297849i
$876$		0			0
$877$	−8.06637	+	4.65712i	−0.272382	+	0.157260i	−0.629970	−	0.776620i	$-0.716933\pi$
$877$	−8.06637	+	4.65712i	−0.272382	+	0.157260i	0.357588	+	0.933880i	$0.383599\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−43.6111			−1.46930			−0.734648	−	0.678448i	$-0.762653\pi$
$881$	−43.6111			−1.46930			−0.734648	+	0.678448i	$0.762653\pi$
$882$		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	−0.400053	−	0.916492i	$-0.631008\pi$
$887$	5.76665	−	3.32937i	0.193625	−	0.111789i	0.593678	+	0.804702i	$0.297675\pi$
$888$		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
$895$	−32.4711	−	1.50247i	−1.08539	−	0.0502222i
$896$		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
$905$	33.9048	+	1.56881i	1.12703	+	0.0521491i
$906$		0			0
$907$	13.3175	+	7.68886i	0.442200	+	0.255304i	0.704531	−	0.709674i	$-0.251158\pi$
$907$	13.3175	+	7.68886i	0.442200	+	0.255304i	−0.262330	+	0.964978i	$0.584491\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−11.7231	+	20.3051i	−0.388405	+	0.672738i	−0.992235	−	0.124376i	$-0.960307\pi$
$911$	−11.7231	+	20.3051i	−0.388405	+	0.672738i	0.603830	+	0.797113i	$0.293641\pi$
$912$		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
$925$	2.41968	−	26.0907i	0.0795585	−	0.857858i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	13.3003	−	23.0367i	0.436367	−	0.755810i	−0.561039	−	0.827790i	$-0.689598\pi$
$929$	13.3003	−	23.0367i	0.436367	−	0.755810i	0.997406	+	0.0719791i	$0.0229315\pi$
$930$		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	0.999915	+	0.0130223i	$0.00414523\pi$
$941$	15.6825	+	27.1629i	0.511235	+	0.885485i	−0.488680	+	0.872463i	$0.662521\pi$
$942$		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	0.0688223	−	0.997629i	$-0.478076\pi$
$947$	−23.4105	−	13.5161i	−0.760739	−	0.439213i	−0.829561	+	0.558416i	$0.811409\pi$
$948$		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	$-0.859600\pi$
$953$		−	26.3584i		−	0.853833i	0.904291	−	0.426917i	$-0.140400\pi$
$954$		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
$965$	25.6791	−	13.2828i	0.826639	−	0.427588i
$966$		0			0
$967$	28.1419	−	16.2477i	0.904982	−	0.522492i	0.0261690	−	0.999658i	$-0.491669\pi$
$967$	28.1419	−	16.2477i	0.904982	−	0.522492i	0.878813	+	0.477166i	$0.158336\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	37.3027			1.19710			0.598550	−	0.801085i	$-0.295744\pi$
$971$	37.3027			1.19710			0.598550	+	0.801085i	$0.295744\pi$
$972$		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	−0.226964	−	0.973903i	$-0.572880\pi$
$977$	15.7216	−	9.07688i	0.502979	−	0.290395i	0.729943	+	0.683508i	$0.239547\pi$
$978$		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	0.987773	−	0.155900i	$-0.0498277\pi$
$983$	42.2212	+	24.3764i	1.34665	+	0.777487i	0.358873	+	0.933386i	$0.383161\pi$
$984$		0			0
$985$	−0.847991	+	18.3266i	−0.0270192	+	0.583933i
$986$		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
$995$	5.26660	+	0.243692i	0.166963	+	0.00772555i
$996$		0			0
$997$	38.2293	+	22.0717i	1.21073	+	0.699018i	0.962919	−	0.269790i	$-0.0869543\pi$
$997$	38.2293	+	22.0717i	1.21073	+	0.699018i	0.247815	+	0.968807i	$0.420288\pi$
$998$		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.1189.8		16
3.2	odd	2	inner	1620.2.r.h.1189.1		16
5.4	even	2	inner	1620.2.r.h.1189.3		16
9.2	odd	6		1620.2.d.e.649.5	yes	8
9.4	even	3	inner	1620.2.r.h.109.3		16
9.5	odd	6	inner	1620.2.r.h.109.6		16
9.7	even	3		1620.2.d.e.649.4	yes	8
15.14	odd	2	inner	1620.2.r.h.1189.6		16
45.2	even	12		8100.2.a.be.1.4		8
45.4	even	6	inner	1620.2.r.h.109.8		16
45.7	odd	12		8100.2.a.be.1.3		8
45.14	odd	6	inner	1620.2.r.h.109.1		16
45.29	odd	6		1620.2.d.e.649.6	yes	8
45.34	even	6		1620.2.d.e.649.3	✓	8
45.38	even	12		8100.2.a.be.1.6		8
45.43	odd	12		8100.2.a.be.1.5		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1620.2.d.e.649.3	✓	8	45.34	even	6
1620.2.d.e.649.4	yes	8	9.7	even	3
1620.2.d.e.649.5	yes	8	9.2	odd	6
1620.2.d.e.649.6	yes	8	45.29	odd	6
1620.2.r.h.109.1		16	45.14	odd	6	inner
1620.2.r.h.109.3		16	9.4	even	3	inner
1620.2.r.h.109.6		16	9.5	odd	6	inner
1620.2.r.h.109.8		16	45.4	even	6	inner
1620.2.r.h.1189.1		16	3.2	odd	2	inner
1620.2.r.h.1189.3		16	5.4	even	2	inner
1620.2.r.h.1189.6		16	15.14	odd	2	inner
1620.2.r.h.1189.8		16	1.1	even	1	trivial
8100.2.a.be.1.3		8	45.7	odd	12
8100.2.a.be.1.4		8	45.2	even	12
8100.2.a.be.1.5		8	45.43	odd	12
8100.2.a.be.1.6		8	45.38	even	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)

\(f(q)\)	\(=\)	\(q+(2.23368 + 0.103355i) q^{5} +(-1.10979 - 0.640739i) q^{7} +O(q^{10})\)	\(q+(2.23368 + 0.103355i) q^{5} +(-1.10979 - 0.640739i) q^{7} +(2.07237 - 3.58945i) q^{11} +(5.64823 - 3.26101i) q^{13} -5.98507i q^{17} -7.17891 q^{19} +(-6.52202 + 3.76549i) q^{23} +(4.97864 + 0.461723i) q^{25} +(-2.59808 + 4.50000i) q^{29} +(-2.58945 - 4.48507i) q^{31} +(-2.41269 - 1.54591i) q^{35} -5.24054i q^{37} +(0.340322 + 0.589454i) q^{41} +(1.10979 + 0.640739i) q^{43} +(4.59980 + 2.65570i) q^{47} +(-2.67891 - 4.64001i) q^{49} +2.21958i q^{53} +(5.00000 - 7.80350i) q^{55} +(3.80442 + 6.58945i) q^{59} +(1.08945 - 1.88699i) q^{61} +(12.9534 - 6.70027i) q^{65} +(13.5161 - 7.80350i) q^{67} -5.50603 q^{71} -7.80350i q^{73} +(-4.59980 + 2.65570i) q^{77} +(3.00000 - 5.19615i) q^{79} +(8.44423 + 4.87528i) q^{83} +(0.618586 - 13.3687i) q^{85} -10.0215 q^{89} -8.35782 q^{91} +(-16.0354 - 0.741975i) q^{95} +(12.4063 + 7.16276i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q+O(q^{10}) \) 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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