LMFDB - Embedded newform 864.2.p.b.719.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [864,2,Mod(143,864)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(864, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 1]))

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

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

chi := DirichletCharacter("864.143");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 864 = 2^{5} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	864.p (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:	$6.89907473464$
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} - 3 x^{15} + 7 x^{14} - 12 x^{13} + 16 x^{12} - 12 x^{11} - 8 x^{10} + 36 x^{9} - 68 x^{8} + \cdots + 256 $ x^16 - 3x^15 + 7x^14 - 12x^13 + 16x^12 - 12x^11 - 8x^10 + 36x^9 - 68x^8 + 72x^7 - 32x^6 - 96x^5 + 256x^4 - 384x^3 + 448x^2 - 384*x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{10} $
Twist minimal:	no (minimal twist has level 72)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			719.6
Root			$-0.533474 + 1.30973i$ of defining polynomial
Character	$\chi$	$=$	864.719
Dual form			864.2.p.b.143.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.895377 - 1.55084i) q^{5} +(-2.08793 + 1.20546i) q^{7} +O(q^{10})$	$q+(0.895377 - 1.55084i) q^{5} +(-2.08793 + 1.20546i) q^{7} +(-1.36975 + 0.790826i) q^{11} +(-5.35491 - 3.09166i) q^{13} -3.69943i q^{17} -3.12941 q^{19} +(1.36036 - 2.35622i) q^{23} +(0.896599 + 1.55296i) q^{25} +(-2.55291 - 4.42177i) q^{29} +(-5.95312 - 3.43703i) q^{31} +4.31738i q^{35} +5.24328i q^{37} +(5.32220 + 3.07278i) q^{41} +(0.452455 + 0.783675i) q^{43} +(-4.88993 - 8.46960i) q^{47} +(-0.593711 + 1.02834i) q^{49} -7.05913 q^{53} +2.83235i q^{55} +(-6.10118 - 3.52252i) q^{59} +(3.05109 - 1.76155i) q^{61} +(-9.58933 + 5.53640i) q^{65} +(-1.03786 + 1.79762i) q^{67} -3.31507 q^{71} +0.631029 q^{73} +(1.90662 - 3.30237i) q^{77} +(7.82515 - 4.51785i) q^{79} +(13.5542 - 7.82551i) q^{83} +(-5.73722 - 3.31239i) q^{85} +1.16402i q^{89} +14.9075 q^{91} +(-2.80200 + 4.85321i) q^{95} +(-6.72981 - 11.6564i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q+O(q^{10}) $ 16 * q	$ 16 q + 12 q^{11} + 4 q^{19} - 14 q^{25} + 36 q^{41} - 8 q^{43} + 10 q^{49} + 12 q^{59} + 6 q^{65} + 16 q^{67} - 4 q^{73} + 54 q^{83} + 36 q^{91} + 8 q^{97}+O(q^{100}) $ 16 * q + 12 * q^11 + 4 * q^19 - 14 * q^25 + 36 * q^41 - 8 * q^43 + 10 * q^49 + 12 * q^59 + 6 * q^65 + 16 * q^67 - 4 * q^73 + 54 * q^83 + 36 * q^91 + 8 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/864\mathbb{Z}\right)^\times$.

$n$	$325$	$353$	$703$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	0.895377	−	1.55084i	0.400425	−	0.693556i	−0.593352	−	0.804943i	$-0.702196\pi$
$5$	0.895377	−	1.55084i	0.400425	−	0.693556i	0.993777	+	0.111387i	$0.0355292\pi$
$6$		0			0
$7$	−2.08793	+	1.20546i	−0.789162	+	0.455623i	−0.839667	−	0.543101i	$-0.817250\pi$
$7$	−2.08793	+	1.20546i	−0.789162	+	0.455623i	0.0505056	+	0.998724i	$0.483917\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−1.36975	+	0.790826i	−0.412995	+	0.238443i	−0.692076	−	0.721825i	$-0.743304\pi$
$11$	−1.36975	+	0.790826i	−0.412995	+	0.238443i	0.279081	+	0.960268i	$0.409970\pi$
$12$		0			0
$13$	−5.35491	−	3.09166i	−1.48519	−	0.857472i	−0.485327	−	0.874332i	$-0.661300\pi$
$13$	−5.35491	−	3.09166i	−1.48519	−	0.857472i	−0.999858	+	0.0168604i	$0.994633\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$		−	3.69943i		−	0.897244i	−0.893722	−	0.448622i	$-0.851915\pi$
$17$		−	3.69943i		−	0.897244i	0.893722	−	0.448622i	$-0.148085\pi$
$18$		0			0
$19$	−3.12941			−0.717936			−0.358968	−	0.933350i	$-0.616871\pi$
$19$	−3.12941			−0.717936			−0.358968	+	0.933350i	$0.616871\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	1.36036	−	2.35622i	0.283655	−	0.491305i	−0.688627	−	0.725116i	$-0.741786\pi$
$23$	1.36036	−	2.35622i	0.283655	−	0.491305i	0.972282	+	0.233811i	$0.0751196\pi$
$24$		0			0
$25$	0.896599	+	1.55296i	0.179320	+	0.310591i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−2.55291	−	4.42177i	−0.474064	−	0.821102i	0.525495	−	0.850796i	$-0.323880\pi$
$29$	−2.55291	−	4.42177i	−0.474064	−	0.821102i	−0.999559	+	0.0296942i	$0.990547\pi$
$30$		0			0
$31$	−5.95312	−	3.43703i	−1.06921	−	0.617310i	−0.141246	−	0.989975i	$-0.545111\pi$
$31$	−5.95312	−	3.43703i	−1.06921	−	0.617310i	−0.927966	+	0.372665i	$0.878444\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$			4.31738i			0.729771i
$36$		0			0
$37$			5.24328i			0.861990i	0.902354	+	0.430995i	$0.141837\pi$
$37$			5.24328i			0.861990i	−0.902354	+	0.430995i	$0.858163\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	5.32220	+	3.07278i	0.831189	+	0.479887i	0.854260	−	0.519847i	$-0.174011\pi$
$41$	5.32220	+	3.07278i	0.831189	+	0.479887i	−0.0230708	+	0.999734i	$0.507344\pi$
$42$		0			0
$43$	0.452455	+	0.783675i	0.0689987	+	0.119509i	0.898461	−	0.439054i	$-0.144686\pi$
$43$	0.452455	+	0.783675i	0.0689987	+	0.119509i	−0.829462	+	0.558563i	$0.811353\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−4.88993	−	8.46960i	−0.713269	−	1.23542i	−0.963623	−	0.267264i	$-0.913880\pi$
$47$	−4.88993	−	8.46960i	−0.713269	−	1.23542i	0.250354	−	0.968154i	$-0.419453\pi$
$48$		0			0
$49$	−0.593711	+	1.02834i	−0.0848159	+	0.146905i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−7.05913			−0.969646			−0.484823	−	0.874612i	$-0.661116\pi$
$53$	−7.05913			−0.969646			−0.484823	+	0.874612i	$0.661116\pi$
$54$		0			0
$55$			2.83235i			0.381914i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−6.10118	−	3.52252i	−0.794306	−	0.458593i	0.0471702	−	0.998887i	$-0.484980\pi$
$59$	−6.10118	−	3.52252i	−0.794306	−	0.458593i	−0.841476	+	0.540294i	$0.818313\pi$
$60$		0			0
$61$	3.05109	−	1.76155i	0.390652	−	0.225543i	−0.291790	−	0.956482i	$-0.594251\pi$
$61$	3.05109	−	1.76155i	0.390652	−	0.225543i	0.682443	+	0.730939i	$0.260918\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−9.58933	+	5.53640i	−1.18941	+	0.686706i
$66$		0			0
$67$	−1.03786	+	1.79762i	−0.126794	+	0.219614i	−0.922433	−	0.386158i	$-0.873802\pi$
$67$	−1.03786	+	1.79762i	−0.126794	+	0.219614i	0.795639	+	0.605772i	$0.207135\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−3.31507			−0.393426			−0.196713	−	0.980461i	$-0.563027\pi$
$71$	−3.31507			−0.393426			−0.196713	+	0.980461i	$0.563027\pi$
$72$		0			0
$73$	0.631029			0.0738563			0.0369282	−	0.999318i	$-0.488243\pi$
$73$	0.631029			0.0738563			0.0369282	+	0.999318i	$0.488243\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	1.90662	−	3.30237i	0.217280	−	0.376340i
$78$		0			0
$79$	7.82515	−	4.51785i	0.880398	−	0.508298i	0.00960849	−	0.999954i	$-0.496941\pi$
$79$	7.82515	−	4.51785i	0.880398	−	0.508298i	0.870790	+	0.491656i	$0.163608\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	13.5542	−	7.82551i	1.48776	−	0.858961i	0.487861	−	0.872921i	$-0.337777\pi$
$83$	13.5542	−	7.82551i	1.48776	−	0.858961i	0.999903	+	0.0139604i	$0.00444387\pi$
$84$		0			0
$85$	−5.73722	−	3.31239i	−0.622289	−	0.359279i
$86$		0			0
$87$		0			0
$88$		0			0
$89$			1.16402i			0.123386i	0.998095	+	0.0616929i	$0.0196499\pi$
$89$			1.16402i			0.123386i	−0.998095	+	0.0616929i	$0.980350\pi$
$90$		0			0
$91$	14.9075			1.56274
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−2.80200	+	4.85321i	−0.287479	+	0.497929i
$96$		0			0
$97$	−6.72981	−	11.6564i	−0.683309	−	1.18353i	−0.973965	−	0.226698i	$-0.927207\pi$
$97$	−6.72981	−	11.6564i	−0.683309	−	1.18353i	0.290656	−	0.956827i	$-0.406126\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	3.28047	+	5.68195i	0.326419	+	0.565375i	0.981799	−	0.189925i	$-0.0608245\pi$
$101$	3.28047	+	5.68195i	0.326419	+	0.565375i	−0.655379	+	0.755300i	$0.727491\pi$
$102$		0			0
$103$	−5.12167	−	2.95700i	−0.504653	−	0.291361i	0.225980	−	0.974132i	$-0.427442\pi$
$103$	−5.12167	−	2.95700i	−0.504653	−	0.291361i	−0.730633	+	0.682771i	$0.760775\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		−	1.01487i		−	0.0981111i	−0.998796	−	0.0490555i	$-0.984379\pi$
$107$		−	1.01487i		−	0.0981111i	0.998796	−	0.0490555i	$-0.0156211\pi$
$108$		0			0
$109$			4.46314i			0.427491i	0.976889	+	0.213746i	$0.0685664\pi$
$109$			4.46314i			0.427491i	−0.976889	+	0.213746i	$0.931434\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−7.35628	−	4.24715i	−0.692021	−	0.399538i	0.112348	−	0.993669i	$-0.464163\pi$
$113$	−7.35628	−	4.24715i	−0.692021	−	0.399538i	−0.804369	+	0.594131i	$0.797496\pi$
$114$		0			0
$115$	−2.43607	−	4.21940i	−0.227165	−	0.393462i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	4.45953	+	7.72414i	0.408805	+	0.708071i
$120$		0			0
$121$	−4.24919	+	7.35981i	−0.386290	+	0.669074i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	12.1650			1.08807
$126$		0			0
$127$			15.9098i			1.41176i	0.708329	+	0.705882i	$0.249449\pi$
$127$			15.9098i			1.41176i	−0.708329	+	0.705882i	$0.750551\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	1.38769	+	0.801182i	0.121243	+	0.0699996i	0.559395	−	0.828901i	$-0.311034\pi$
$131$	1.38769	+	0.801182i	0.121243	+	0.0699996i	−0.438152	+	0.898901i	$0.644367\pi$
$132$		0			0
$133$	6.53397	−	3.77239i	0.566567	−	0.327108i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	10.6153	−	6.12877i	0.906930	−	0.523616i	0.0274877	−	0.999622i	$-0.491249\pi$
$137$	10.6153	−	6.12877i	0.906930	−	0.523616i	0.879442	+	0.476006i	$0.157916\pi$
$138$		0			0
$139$	0.618940	−	1.07204i	0.0524978	−	0.0909289i	−0.838582	−	0.544775i	$-0.816615\pi$
$139$	0.618940	−	1.07204i	0.0524978	−	0.0909289i	0.891080	+	0.453846i	$0.149948\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	9.77985			0.817832
$144$		0			0
$145$	−9.14327			−0.759307
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−2.96982	+	5.14387i	−0.243297	+	0.421402i	−0.961651	−	0.274275i	$-0.911562\pi$
$149$	−2.96982	+	5.14387i	−0.243297	+	0.421402i	0.718355	+	0.695677i	$0.244896\pi$
$150$		0			0
$151$	11.9663	−	6.90874i	0.973803	−	0.562226i	0.0734098	−	0.997302i	$-0.476612\pi$
$151$	11.9663	−	6.90874i	0.973803	−	0.562226i	0.900394	+	0.435076i	$0.143279\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−10.6606	+	6.15488i	−0.856278	+	0.494372i
$156$		0			0
$157$	4.98995	+	2.88095i	0.398241	+	0.229925i	0.685725	−	0.727861i	$-0.259485\pi$
$157$	4.98995	+	2.88095i	0.398241	+	0.229925i	−0.287483	+	0.957786i	$0.592819\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$			6.55947i			0.516959i
$162$		0			0
$163$	−11.2888			−0.884209			−0.442104	−	0.896964i	$-0.645768\pi$
$163$	−11.2888			−0.884209			−0.442104	+	0.896964i	$0.645768\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	0.378448	−	0.655492i	0.0292852	−	0.0507235i	−0.851011	−	0.525147i	$-0.824010\pi$
$167$	0.378448	−	0.655492i	0.0292852	−	0.0507235i	0.880297	+	0.474424i	$0.157344\pi$
$168$		0			0
$169$	12.6167	+	21.8528i	0.970517	+	1.68098i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	4.62735	+	8.01480i	0.351811	+	0.609354i	0.986567	−	0.163359i	$-0.0522327\pi$
$173$	4.62735	+	8.01480i	0.351811	+	0.609354i	−0.634756	+	0.772713i	$0.718899\pi$
$174$		0			0
$175$	−3.74406	−	2.16164i	−0.283025	−	0.163404i
$176$		0			0
$177$		0			0
$178$		0			0
$179$			1.56530i			0.116996i	0.998288	+	0.0584980i	$0.0186311\pi$
$179$			1.56530i			0.116996i	−0.998288	+	0.0584980i	$0.981369\pi$
$180$		0			0
$181$			3.68300i			0.273755i	0.990588	+	0.136878i	$0.0437067\pi$
$181$			3.68300i			0.273755i	−0.990588	+	0.136878i	$0.956293\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	8.13148	+	4.69471i	0.597838	+	0.345162i
$186$		0			0
$187$	2.92561	+	5.06730i	0.213941	+	0.370558i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	11.8678	+	20.5556i	0.858722	+	1.48735i	0.873148	+	0.487455i	$0.162075\pi$
$191$	11.8678	+	20.5556i	0.858722	+	1.48735i	−0.0144258	+	0.999896i	$0.504592\pi$
$192$		0			0
$193$	12.8012	−	22.1723i	0.921451	−	1.59600i	0.124279	−	0.992247i	$-0.460338\pi$
$193$	12.8012	−	22.1723i	0.921451	−	1.59600i	0.797172	−	0.603752i	$-0.206328\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	5.76656			0.410850			0.205425	−	0.978673i	$-0.434142\pi$
$197$	5.76656			0.410850			0.205425	+	0.978673i	$0.434142\pi$
$198$		0			0
$199$		−	1.24163i		−	0.0880169i	−0.999031	−	0.0440085i	$-0.985987\pi$
$199$		−	1.24163i		−	0.0880169i	0.999031	−	0.0440085i	$-0.0140129\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	10.6606	+	6.15488i	0.748226	+	0.431988i
$204$		0			0
$205$	9.53076	−	5.50259i	0.665657	−	0.384317i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	4.28651	−	2.47482i	0.296504	−	0.171187i
$210$		0			0
$211$	−1.62194	+	2.80928i	−0.111659	+	0.193399i	−0.916439	−	0.400174i	$-0.868950\pi$
$211$	−1.62194	+	2.80928i	−0.111659	+	0.193399i	0.804780	+	0.593573i	$0.202283\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	1.62047			0.110515
$216$		0			0
$217$	16.5729			1.12504
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−11.4374	+	19.8101i	−0.769362	+	1.33257i
$222$		0			0
$223$	12.1221	−	6.99871i	0.811758	−	0.468669i	−0.0358081	−	0.999359i	$-0.511401\pi$
$223$	12.1221	−	6.99871i	0.811758	−	0.468669i	0.847566	+	0.530690i	$0.178067\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−8.75366	+	5.05393i	−0.581001	+	0.335441i	−0.761531	−	0.648128i	$-0.775552\pi$
$227$	−8.75366	+	5.05393i	−0.581001	+	0.335441i	0.180530	+	0.983569i	$0.442219\pi$
$228$		0			0
$229$	9.93043	+	5.73334i	0.656221	+	0.378869i	0.790836	−	0.612029i	$-0.209646\pi$
$229$	9.93043	+	5.73334i	0.656221	+	0.378869i	−0.134615	+	0.990898i	$0.542980\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$		−	6.74860i		−	0.442115i	−0.975261	−	0.221058i	$-0.929049\pi$
$233$		−	6.74860i		−	0.442115i	0.975261	−	0.221058i	$-0.0709509\pi$
$234$		0			0
$235$	−17.5133			−1.14244
$236$		0			0
$237$		0			0
$238$		0			0
$239$	0.0677896	−	0.117415i	0.00438494	−	0.00759495i	−0.863825	−	0.503793i	$-0.831938\pi$
$239$	0.0677896	−	0.117415i	0.00438494	−	0.00759495i	0.868210	+	0.496198i	$0.165271\pi$
$240$		0			0
$241$	−9.71742	−	16.8311i	−0.625954	−	1.08418i	−0.988355	−	0.152163i	$-0.951376\pi$
$241$	−9.71742	−	16.8311i	−0.625954	−	1.08418i	0.362401	−	0.932022i	$-0.381957\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	1.06319	+	1.84150i	0.0679248	+	0.117649i
$246$		0			0
$247$	16.7577	+	9.67507i	1.06627	+	0.615610i
$248$		0			0
$249$		0			0
$250$		0			0
$251$		−	18.7837i		−	1.18561i	−0.805344	−	0.592807i	$-0.798020\pi$
$251$		−	18.7837i		−	1.18561i	0.805344	−	0.592807i	$-0.201980\pi$
$252$		0			0
$253$			4.30324i			0.270542i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−18.6937	−	10.7928i	−1.16608	−	0.673238i	−0.213329	−	0.976981i	$-0.568430\pi$
$257$	−18.6937	−	10.7928i	−1.16608	−	0.673238i	−0.952754	+	0.303742i	$0.901764\pi$
$258$		0			0
$259$	−6.32058	−	10.9476i	−0.392742	−	0.680249i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−8.56995	−	14.8436i	−0.528446	−	0.915295i	−0.999450	−	0.0331642i	$-0.989442\pi$
$263$	−8.56995	−	14.8436i	−0.528446	−	0.915295i	0.471004	−	0.882131i	$-0.343892\pi$
$264$		0			0
$265$	−6.32058	+	10.9476i	−0.388270	+	0.672504i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−20.1271			−1.22717			−0.613585	−	0.789629i	$-0.710273\pi$
$269$	−20.1271			−1.22717			−0.613585	+	0.789629i	$0.710273\pi$
$270$		0			0
$271$			6.20336i			0.376827i	0.982090	+	0.188414i	$0.0603345\pi$
$271$			6.20336i			0.376827i	−0.982090	+	0.188414i	$0.939665\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−2.45623	−	1.41811i	−0.148116	−	0.0855151i
$276$		0			0
$277$	10.6060	−	6.12340i	0.637256	−	0.367920i	−0.146301	−	0.989240i	$-0.546737\pi$
$277$	10.6060	−	6.12340i	0.637256	−	0.367920i	0.783557	+	0.621320i	$0.213403\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	15.1623	−	8.75399i	0.904510	−	0.522219i	0.0258492	−	0.999666i	$-0.491771\pi$
$281$	15.1623	−	8.75399i	0.904510	−	0.522219i	0.878661	+	0.477447i	$0.158438\pi$
$282$		0			0
$283$	3.79698	−	6.57656i	0.225707	−	0.390936i	−0.730824	−	0.682565i	$-0.760864\pi$
$283$	3.79698	−	6.57656i	0.225707	−	0.390936i	0.956531	+	0.291630i	$0.0941975\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−14.8165			−0.874590
$288$		0			0
$289$	3.31420			0.194953
$290$		0			0
$291$		0			0
$292$		0			0
$293$	12.6164	−	21.8523i	0.737061	−	1.27663i	−0.216753	−	0.976227i	$-0.569546\pi$
$293$	12.6164	−	21.8523i	0.737061	−	1.27663i	0.953813	−	0.300400i	$-0.0971202\pi$
$294$		0			0
$295$	−10.9257	+	6.30797i	−0.636120	+	0.367264i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−14.5692	+	8.41155i	−0.842561	+	0.486453i
$300$		0			0
$301$	−1.88938	−	1.09084i	−0.108902	−	0.0628748i
$302$		0			0
$303$		0			0
$304$		0			0
$305$		−	6.30900i		−	0.361253i
$306$		0			0
$307$	29.5997			1.68934			0.844671	−	0.535286i	$-0.179796\pi$
$307$	29.5997			1.68934			0.844671	+	0.535286i	$0.179796\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−10.3607	+	17.9453i	−0.587502	+	1.01758i	0.407057	+	0.913403i	$0.366555\pi$
$311$	−10.3607	+	17.9453i	−0.587502	+	1.01758i	−0.994558	+	0.104180i	$0.966778\pi$
$312$		0			0
$313$	1.73680	+	3.00823i	0.0981700	+	0.170035i	0.910927	−	0.412567i	$-0.135368\pi$
$313$	1.73680	+	3.00823i	0.0981700	+	0.170035i	−0.812757	+	0.582603i	$0.802034\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−7.64385	−	13.2395i	−0.429321	−	0.743606i	0.567492	−	0.823379i	$-0.307914\pi$
$317$	−7.64385	−	13.2395i	−0.429321	−	0.743606i	−0.996813	+	0.0797728i	$0.974581\pi$
$318$		0			0
$319$	6.99370	+	4.03781i	0.391572	+	0.226074i
$320$		0			0
$321$		0			0
$322$		0			0
$323$			11.5770i			0.644164i
$324$		0			0
$325$		−	11.0879i		−	0.615047i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	20.4196	+	11.7893i	1.12577	+	0.649963i
$330$		0			0
$331$	−3.09986	−	5.36912i	−0.170384	−	0.295114i	0.768170	−	0.640246i	$-0.221167\pi$
$331$	−3.09986	−	5.36912i	−0.170384	−	0.295114i	−0.938554	+	0.345132i	$0.887834\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	1.85854	+	3.21909i	0.101543	+	0.175878i
$336$		0			0
$337$	−9.63097	+	16.6813i	−0.524632	+	0.908690i	0.474956	+	0.880009i	$0.342464\pi$
$337$	−9.63097	+	16.6813i	−0.524632	+	0.908690i	−0.999589	+	0.0286803i	$0.990870\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	10.8724			0.588772
$342$		0			0
$343$		−	19.7393i		−	1.06582i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	22.9191	+	13.2323i	1.23036	+	0.710349i	0.967105	−	0.254378i	$-0.0818706\pi$
$347$	22.9191	+	13.2323i	1.23036	+	0.710349i	0.263255	+	0.964726i	$0.415204\pi$
$348$		0			0
$349$	−14.8362	+	8.56568i	−0.794164	+	0.458511i	−0.841426	−	0.540372i	$-0.818284\pi$
$349$	−14.8362	+	8.56568i	−0.794164	+	0.458511i	0.0472627	+	0.998882i	$0.484950\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−26.8134	+	15.4807i	−1.42713	+	0.823955i	−0.996894	−	0.0787597i	$-0.974904\pi$
$353$	−26.8134	+	15.4807i	−1.42713	+	0.823955i	−0.430239	+	0.902715i	$0.641571\pi$
$354$		0			0
$355$	−2.96823	+	5.14113i	−0.157538	+	0.272863i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	6.43781			0.339775			0.169887	−	0.985463i	$-0.445660\pi$
$359$	6.43781			0.339775			0.169887	+	0.985463i	$0.445660\pi$
$360$		0			0
$361$	−9.20680			−0.484569
$362$		0			0
$363$		0			0
$364$		0			0
$365$	0.565009	−	0.978624i	0.0295739	−	0.0512235i
$366$		0			0
$367$	−23.8725	+	13.7828i	−1.24614	+	0.719457i	−0.970337	−	0.241758i	$-0.922276\pi$
$367$	−23.8725	+	13.7828i	−1.24614	+	0.719457i	−0.275800	+	0.961215i	$0.588943\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	14.7389	−	8.50953i	0.765208	−	0.441793i
$372$		0			0
$373$	−23.2547	−	13.4261i	−1.20408	−	0.695178i	−0.242623	−	0.970121i	$-0.578008\pi$
$373$	−23.2547	−	13.4261i	−1.20408	−	0.695178i	−0.961461	+	0.274942i	$0.911341\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$			31.5709i			1.62599i
$378$		0			0
$379$	−4.63966			−0.238323			−0.119162	−	0.992875i	$-0.538021\pi$
$379$	−4.63966			−0.238323			−0.119162	+	0.992875i	$0.538021\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	17.7531	−	30.7493i	0.907141	−	1.57122i	0.0891248	−	0.996020i	$-0.471593\pi$
$383$	17.7531	−	30.7493i	0.907141	−	1.57122i	0.818017	−	0.575195i	$-0.195074\pi$
$384$		0			0
$385$	−3.41430	−	5.91373i	−0.174009	−	0.301392i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−3.19920	−	5.54117i	−0.162206	−	0.280949i	0.773454	−	0.633853i	$-0.218527\pi$
$389$	−3.19920	−	5.54117i	−0.162206	−	0.280949i	−0.935659	+	0.352904i	$0.885194\pi$
$390$		0			0
$391$	−8.71666	−	5.03257i	−0.440821	−	0.254508i
$392$		0			0
$393$		0			0
$394$		0			0
$395$		−	16.1807i		−	0.814141i
$396$		0			0
$397$			3.01894i			0.151516i	0.997126	+	0.0757581i	$0.0241377\pi$
$397$			3.01894i			0.151516i	−0.997126	+	0.0757581i	$0.975862\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−25.1191	−	14.5025i	−1.25439	−	0.724222i	−0.282411	−	0.959294i	$-0.591134\pi$
$401$	−25.1191	−	14.5025i	−1.25439	−	0.724222i	−0.971978	+	0.235072i	$0.924467\pi$
$402$		0			0
$403$	21.2523	+	36.8100i	1.05865	+	1.83364i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−4.14652	−	7.18198i	−0.205535	−	0.355998i
$408$		0			0
$409$	−0.662169	+	1.14691i	−0.0327422	+	0.0567111i	−0.881932	−	0.471376i	$-0.843757\pi$
$409$	−0.662169	+	1.14691i	−0.0327422	+	0.0567111i	0.849190	+	0.528087i	$0.177091\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	16.9851			0.835781
$414$		0			0
$415$		−	28.0271i		−	1.37580i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−27.2974	−	15.7602i	−1.33357	−	0.769935i	−0.347722	−	0.937598i	$-0.613045\pi$
$419$	−27.2974	−	15.7602i	−1.33357	−	0.769935i	−0.985844	+	0.167663i	$0.946378\pi$
$420$		0			0
$421$	−30.9851	+	17.8893i	−1.51012	+	0.871869i	−0.510192	+	0.860061i	$0.670426\pi$
$421$	−30.9851	+	17.8893i	−1.51012	+	0.871869i	−0.999930	+	0.0118087i	$0.996241\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	5.74505	−	3.31691i	0.278676	−	0.160894i
$426$		0			0
$427$	−4.24697	+	7.35597i	−0.205525	+	0.355980i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−17.1129			−0.824301			−0.412150	−	0.911116i	$-0.635222\pi$
$431$	−17.1129			−0.824301			−0.412150	+	0.911116i	$0.635222\pi$
$432$		0			0
$433$	−19.1099			−0.918363			−0.459182	−	0.888342i	$-0.651857\pi$
$433$	−19.1099			−0.918363			−0.459182	+	0.888342i	$0.651857\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−4.25713	+	7.37356i	−0.203646	+	0.352725i
$438$		0			0
$439$	−29.4886	+	17.0253i	−1.40742	+	0.812572i	−0.995138	−	0.0984868i	$-0.968600\pi$
$439$	−29.4886	+	17.0253i	−1.40742	+	0.812572i	−0.412277	+	0.911058i	$0.635266\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	17.1586	−	9.90651i	0.815229	−	0.470673i	−0.0335394	−	0.999437i	$-0.510678\pi$
$443$	17.1586	−	9.90651i	0.815229	−	0.470673i	0.848768	+	0.528765i	$0.177345\pi$
$444$		0			0
$445$	1.80521	+	1.04224i	0.0855749	+	0.0494067i
$446$		0			0
$447$		0			0
$448$		0			0
$449$			8.73916i			0.412426i	0.978507	+	0.206213i	$0.0661140\pi$
$449$			8.73916i			0.412426i	−0.978507	+	0.206213i	$0.933886\pi$
$450$		0			0
$451$	−9.72012			−0.457703
$452$		0			0
$453$		0			0
$454$		0			0
$455$	13.3479	−	23.1192i	0.625758	−	1.08384i
$456$		0			0
$457$	−1.25081	−	2.16647i	−0.0585104	−	0.101343i	0.835287	−	0.549815i	$-0.185302\pi$
$457$	−1.25081	−	2.16647i	−0.0585104	−	0.101343i	−0.893797	+	0.448472i	$0.851968\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	2.63419	+	4.56255i	0.122686	+	0.212499i	0.920826	−	0.389973i	$-0.127516\pi$
$461$	2.63419	+	4.56255i	0.122686	+	0.212499i	−0.798140	+	0.602472i	$0.794182\pi$
$462$		0			0
$463$	−15.2227	−	8.78883i	−0.707459	−	0.408451i	0.102661	−	0.994716i	$-0.467264\pi$
$463$	−15.2227	−	8.78883i	−0.707459	−	0.408451i	−0.810119	+	0.586265i	$0.800598\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$		−	2.29842i		−	0.106358i	−0.998585	−	0.0531791i	$-0.983065\pi$
$467$		−	2.29842i		−	0.106358i	0.998585	−	0.0531791i	$-0.0169354\pi$
$468$		0			0
$469$		−	5.00439i		−	0.231081i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−1.23950	−	0.715626i	−0.0569923	−	0.0329045i
$474$		0			0
$475$	−2.80582	−	4.85983i	−0.128740	−	0.222984i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−18.0219	−	31.2149i	−0.823442	−	1.42624i	−0.903104	−	0.429422i	$-0.858717\pi$
$479$	−18.0219	−	31.2149i	−0.823442	−	1.42624i	0.0796622	−	0.996822i	$-0.474616\pi$
$480$		0			0
$481$	16.2104	−	28.0773i	0.739132	−	1.28021i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−24.1029			−1.09446
$486$		0			0
$487$		−	2.72292i		−	0.123387i	−0.998095	−	0.0616937i	$-0.980350\pi$
$487$		−	2.72292i		−	0.123387i	0.998095	−	0.0616937i	$-0.0196502\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	13.1715	+	7.60457i	0.594421	+	0.343189i	0.766844	−	0.641834i	$-0.221826\pi$
$491$	13.1715	+	7.60457i	0.594421	+	0.343189i	−0.172422	+	0.985023i	$0.555159\pi$
$492$		0			0
$493$	−16.3580	+	9.44432i	−0.736729	+	0.425351i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	6.92161	−	3.99619i	0.310477	−	0.179254i
$498$		0			0
$499$	19.7305	−	34.1743i	0.883260	−	1.52985i	0.0355642	−	0.999367i	$-0.488677\pi$
$499$	19.7305	−	34.1743i	0.883260	−	1.52985i	0.847695	−	0.530483i	$-0.177990\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	18.4749			0.823756			0.411878	−	0.911239i	$-0.364873\pi$
$503$	18.4749			0.823756			0.411878	+	0.911239i	$0.364873\pi$
$504$		0			0
$505$	11.7490			0.522826
$506$		0			0
$507$		0			0
$508$		0			0
$509$	17.0068	−	29.4566i	0.753813	−	1.30564i	−0.192149	−	0.981366i	$-0.561546\pi$
$509$	17.0068	−	29.4566i	0.753813	−	1.30564i	0.945962	−	0.324277i	$-0.105121\pi$
$510$		0			0
$511$	−1.31754	+	0.760683i	−0.0582846	+	0.0336506i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−9.17165	+	5.29525i	−0.404151	+	0.233337i
$516$		0			0
$517$	13.3960	+	7.73416i	0.589153	+	0.340148i
$518$		0			0
$519$		0			0
$520$		0			0
$521$		−	12.0788i		−	0.529182i	−0.964361	−	0.264591i	$-0.914763\pi$
$521$		−	12.0788i		−	0.529182i	0.964361	−	0.264591i	$-0.0852369\pi$
$522$		0			0
$523$	−5.27483			−0.230652			−0.115326	−	0.993328i	$-0.536791\pi$
$523$	−5.27483			−0.230652			−0.115326	+	0.993328i	$0.536791\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−12.7151	+	22.0232i	−0.553877	+	0.959344i
$528$		0			0
$529$	7.79883	+	13.5080i	0.339080	+	0.587303i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−19.0000	−	32.9089i	−0.822980	−	1.42544i
$534$		0			0
$535$	−1.57390	−	0.908690i	−0.0680455	−	0.0392861i
$536$		0			0
$537$		0			0
$538$		0			0
$539$		−	1.87809i		−	0.0808950i
$540$		0			0
$541$		−	23.6734i		−	1.01780i	−0.860826	−	0.508900i	$-0.830052\pi$
$541$		−	23.6734i		−	1.01780i	0.860826	−	0.508900i	$-0.169948\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	6.92161	+	3.99619i	0.296489	+	0.171178i
$546$		0			0
$547$	−10.5319	−	18.2418i	−0.450312	−	0.779964i	0.548093	−	0.836417i	$-0.315354\pi$
$547$	−10.5319	−	18.2418i	−0.450312	−	0.779964i	−0.998405	+	0.0564536i	$0.982021\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	7.98910	+	13.8375i	0.340347	+	0.589498i
$552$		0			0
$553$	−10.8922	+	18.8659i	−0.463184	+	0.802259i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−9.64427			−0.408641			−0.204321	−	0.978904i	$-0.565498\pi$
$557$	−9.64427			−0.408641			−0.204321	+	0.978904i	$0.565498\pi$
$558$		0			0
$559$		−	5.59535i		−	0.236658i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−36.8534	−	21.2773i	−1.55319	−	0.896733i	−0.997880	−	0.0650873i	$-0.979267\pi$
$563$	−36.8534	−	21.2773i	−1.55319	−	0.896733i	−0.555307	−	0.831645i	$-0.687399\pi$
$564$		0			0
$565$	−13.1733	+	7.60561i	−0.554205	+	0.319970i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	8.25996	−	4.76889i	0.346275	−	0.199922i	−0.316768	−	0.948503i	$-0.602598\pi$
$569$	8.25996	−	4.76889i	0.346275	−	0.199922i	0.663044	+	0.748581i	$0.269264\pi$
$570$		0			0
$571$	−13.4455	+	23.2882i	−0.562675	+	0.974582i	0.434587	+	0.900630i	$0.356894\pi$
$571$	−13.4455	+	23.2882i	−0.562675	+	0.974582i	−0.997262	+	0.0739518i	$0.976439\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	4.87880			0.203460
$576$		0			0
$577$	−8.52363			−0.354843			−0.177422	−	0.984135i	$-0.556776\pi$
$577$	−8.52363			−0.354843			−0.177422	+	0.984135i	$0.556776\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−18.8667	+	32.6781i	−0.782724	+	1.35572i
$582$		0			0
$583$	9.66924	−	5.58254i	0.400459	−	0.231205i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−19.4568	+	11.2334i	−0.803067	+	0.463651i	−0.844542	−	0.535489i	$-0.820127\pi$
$587$	−19.4568	+	11.2334i	−0.803067	+	0.463651i	0.0414756	+	0.999140i	$0.486794\pi$
$588$		0			0
$589$	18.6297	+	10.7559i	0.767625	+	0.443189i
$590$		0			0
$591$		0			0
$592$		0			0
$593$		−	28.8424i		−	1.18442i	−0.805785	−	0.592208i	$-0.798257\pi$
$593$		−	28.8424i		−	1.18442i	0.805785	−	0.592208i	$-0.201743\pi$
$594$		0			0
$595$	15.9719			0.654783
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−8.40225	+	14.5531i	−0.343307	+	0.594625i	−0.985045	−	0.172299i	$-0.944880\pi$
$599$	−8.40225	+	14.5531i	−0.343307	+	0.594625i	0.641738	+	0.766924i	$0.278214\pi$
$600$		0			0
$601$	14.8802	+	25.7732i	0.606974	+	1.05131i	0.991736	+	0.128294i	$0.0409502\pi$
$601$	14.8802	+	25.7732i	0.606974	+	1.05131i	−0.384762	+	0.923016i	$0.625716\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	7.60926	+	13.1796i	0.309360	+	0.535828i
$606$		0			0
$607$	20.9599	+	12.1012i	0.850737	+	0.491173i	0.860899	−	0.508775i	$-0.169902\pi$
$607$	20.9599	+	12.1012i	0.850737	+	0.491173i	−0.0101625	+	0.999948i	$0.503235\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$			60.4720i			2.44643i
$612$		0			0
$613$		−	38.3189i		−	1.54769i	−0.633377	−	0.773843i	$-0.718332\pi$
$613$		−	38.3189i		−	1.54769i	0.633377	−	0.773843i	$-0.281668\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	7.31357	+	4.22249i	0.294433	+	0.169991i	0.639939	−	0.768425i	$-0.278959\pi$
$617$	7.31357	+	4.22249i	0.294433	+	0.169991i	−0.345506	+	0.938417i	$0.612293\pi$
$618$		0			0
$619$	−4.12431	−	7.14352i	−0.165770	−	0.287122i	0.771158	−	0.636643i	$-0.219678\pi$
$619$	−4.12431	−	7.14352i	−0.165770	−	0.287122i	−0.936929	+	0.349521i	$0.886344\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−1.40318	−	2.43038i	−0.0562173	−	0.0973713i
$624$		0			0
$625$	6.40923	−	11.1011i	0.256369	−	0.444044i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	19.3972			0.773415
$630$		0			0
$631$			34.0954i			1.35732i	0.734454	+	0.678659i	$0.237439\pi$
$631$			34.0954i			1.35732i	−0.734454	+	0.678659i	$0.762561\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	24.6735	+	14.2452i	0.979138	+	0.565305i
$636$		0			0
$637$	6.35854	−	3.67111i	0.251935	−	0.145455i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−20.9715	+	12.1079i	−0.828324	+	0.478233i	−0.853279	−	0.521455i	$-0.825389\pi$
$641$	−20.9715	+	12.1079i	−0.828324	+	0.478233i	0.0249544	+	0.999689i	$0.492056\pi$
$642$		0			0
$643$	−11.3299	+	19.6240i	−0.446808	+	0.773895i	−0.998176	−	0.0603676i	$-0.980773\pi$
$643$	−11.3299	+	19.6240i	−0.446808	+	0.773895i	0.551368	+	0.834262i	$0.314106\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−38.6020			−1.51760			−0.758800	−	0.651323i	$-0.774214\pi$
$647$	−38.6020			−1.51760			−0.758800	+	0.651323i	$0.774214\pi$
$648$		0			0
$649$	11.1428			0.437393
$650$		0			0
$651$		0			0
$652$		0			0
$653$	13.1416	−	22.7619i	0.514271	−	0.890743i	−0.485592	−	0.874185i	$-0.661396\pi$
$653$	13.1416	−	22.7619i	0.514271	−	0.890743i	0.999863	−	0.0165576i	$-0.00527069\pi$
$654$		0			0
$655$	2.48501	−	1.43472i	0.0970973	−	0.0560592i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	33.1862	−	19.1601i	1.29275	−	0.746370i	0.313610	−	0.949552i	$-0.398462\pi$
$659$	33.1862	−	19.1601i	1.29275	−	0.746370i	0.979141	+	0.203182i	$0.0651283\pi$
$660$		0			0
$661$	38.7145	+	22.3518i	1.50582	+	0.869385i	0.999977	+	0.00675901i	$0.00215148\pi$
$661$	38.7145	+	22.3518i	1.50582	+	0.869385i	0.505842	+	0.862626i	$0.331182\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$		−	13.5109i		−	0.523928i
$666$		0			0
$667$	−13.8915			−0.537882
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−2.78616	+	4.82576i	−0.107558	+	0.186297i
$672$		0			0
$673$	−12.8138	−	22.1942i	−0.493937	−	0.855524i	0.506039	−	0.862511i	$-0.331109\pi$
$673$	−12.8138	−	22.1942i	−0.493937	−	0.855524i	−0.999976	+	0.00698696i	$0.997776\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	11.1613	+	19.3320i	0.428964	+	0.742988i	0.996781	−	0.0801666i	$-0.0255452\pi$
$677$	11.1613	+	19.3320i	0.428964	+	0.742988i	−0.567817	+	0.823155i	$0.692212\pi$
$678$		0			0
$679$	28.1027	+	16.2251i	1.07848	+	0.622662i
$680$		0			0
$681$		0			0
$682$		0			0
$683$			20.5229i			0.785288i	0.919691	+	0.392644i	$0.128440\pi$
$683$			20.5229i			0.785288i	−0.919691	+	0.392644i	$0.871560\pi$
$684$		0			0
$685$		−	21.9502i		−	0.838676i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	37.8010	+	21.8244i	1.44010	+	0.831444i
$690$		0			0
$691$	5.97960	+	10.3570i	0.227475	+	0.393998i	0.957059	−	0.289893i	$-0.0936198\pi$
$691$	5.97960	+	10.3570i	0.227475	+	0.393998i	−0.729584	+	0.683891i	$0.760286\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−1.10837	−	1.91975i	−0.0420429	−	0.0728204i
$696$		0			0
$697$	11.3675	−	19.6891i	0.430576	−	0.745779i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−41.9171			−1.58319			−0.791593	−	0.611049i	$-0.790748\pi$
$701$	−41.9171			−1.58319			−0.791593	+	0.611049i	$0.790748\pi$
$702$		0			0
$703$		−	16.4084i		−	0.618853i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−13.6988	−	7.90899i	−0.515195	−	0.297448i
$708$		0			0
$709$	4.41486	−	2.54892i	0.165803	−	0.0957266i	−0.414802	−	0.909912i	$-0.636149\pi$
$709$	4.41486	−	2.54892i	0.165803	−	0.0957266i	0.580606	+	0.814185i	$0.302816\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−16.1968	+	9.35122i	−0.606575	+	0.350206i
$714$		0			0
$715$	8.75666	−	15.1670i	0.327480	−	0.567213i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	35.1676			1.31153			0.655765	−	0.754965i	$-0.272346\pi$
$719$	35.1676			1.31153			0.655765	+	0.754965i	$0.272346\pi$
$720$		0			0
$721$	14.2582			0.531003
$722$		0			0
$723$		0			0
$724$		0			0
$725$	4.57787	−	7.92911i	0.170018	−	0.294480i
$726$		0			0
$727$	19.9209	−	11.5013i	0.738826	−	0.426561i	−0.0828164	−	0.996565i	$-0.526391\pi$
$727$	19.9209	−	11.5013i	0.738826	−	0.426561i	0.821642	+	0.570003i	$0.193058\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	2.89915	−	1.67383i	0.107229	−	0.0619087i
$732$		0			0
$733$	−7.38177	−	4.26187i	−0.272652	−	0.157416i	0.357440	−	0.933936i	$-0.383650\pi$
$733$	−7.38177	−	4.26187i	−0.272652	−	0.157416i	−0.630092	+	0.776520i	$0.716983\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		−	3.28305i		−	0.120933i
$738$		0			0
$739$	−32.3956			−1.19169			−0.595846	−	0.803099i	$-0.703183\pi$
$739$	−32.3956			−1.19169			−0.595846	+	0.803099i	$0.703183\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−2.22350	+	3.85122i	−0.0815725	+	0.141288i	−0.903926	−	0.427690i	$-0.859328\pi$
$743$	−2.22350	+	3.85122i	−0.0815725	+	0.141288i	0.822353	+	0.568978i	$0.192661\pi$
$744$		0			0
$745$	5.31821	+	9.21141i	0.194844	+	0.337480i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	1.22339	+	2.11897i	0.0447016	+	0.0774255i
$750$		0			0
$751$	32.3801	+	18.6946i	1.18157	+	0.682177i	0.956376	−	0.292138i	$-0.0943666\pi$
$751$	32.3801	+	18.6946i	1.18157	+	0.682177i	0.225189	+	0.974315i	$0.427700\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$		−	24.7437i		−	0.900517i
$756$		0			0
$757$			46.7837i			1.70038i	0.526474	+	0.850191i	$0.323514\pi$
$757$			46.7837i			1.70038i	−0.526474	+	0.850191i	$0.676486\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−5.83226	−	3.36726i	−0.211419	−	0.122063i	0.390552	−	0.920581i	$-0.372284\pi$
$761$	−5.83226	−	3.36726i	−0.211419	−	0.122063i	−0.601971	+	0.798518i	$0.705618\pi$
$762$		0			0
$763$	−5.38016	−	9.31870i	−0.194775	−	0.337360i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	21.7809	+	37.7255i	0.786461	+	1.36219i
$768$		0			0
$769$	−8.91160	+	15.4353i	−0.321361	+	0.556613i	−0.980769	−	0.195172i	$-0.937473\pi$
$769$	−8.91160	+	15.4353i	−0.321361	+	0.556613i	0.659408	+	0.751785i	$0.270807\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	18.9682			0.682237			0.341119	−	0.940020i	$-0.389194\pi$
$773$	18.9682			0.682237			0.341119	+	0.940020i	$0.389194\pi$
$774$		0			0
$775$		−	12.3266i		−	0.442783i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−16.6554	−	9.61597i	−0.596740	−	0.344528i
$780$		0			0
$781$	4.54081	−	2.62164i	0.162483	−	0.0938096i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	8.93578	−	5.15907i	0.318932	−	0.184135i
$786$		0			0
$787$	1.03810	−	1.79804i	0.0370041	−	0.0640931i	−0.846930	−	0.531704i	$-0.821552\pi$
$787$	1.03810	−	1.79804i	0.0370041	−	0.0640931i	0.883934	+	0.467611i	$0.154885\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	20.4792			0.728155
$792$		0			0
$793$	−21.7844			−0.773588
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−17.7593	+	30.7601i	−0.629068	+	1.08958i	0.358671	+	0.933464i	$0.383230\pi$
$797$	−17.7593	+	30.7601i	−0.629068	+	1.08958i	−0.987739	+	0.156113i	$0.950103\pi$
$798$		0			0
$799$	−31.3327	+	18.0900i	−1.10847	+	0.639977i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−0.864352	+	0.499034i	−0.0305023	+	0.0176105i
$804$		0			0
$805$	10.1727	+	5.87320i	0.358540	+	0.207003i
$806$		0			0
$807$		0			0
$808$		0			0
$809$		−	41.7225i		−	1.46688i	−0.679752	−	0.733442i	$-0.737913\pi$
$809$		−	41.7225i		−	1.46688i	0.679752	−	0.733442i	$-0.262087\pi$
$810$		0			0
$811$	3.03064			0.106420			0.0532102	−	0.998583i	$-0.483055\pi$
$811$	3.03064			0.106420			0.0532102	+	0.998583i	$0.483055\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−10.1078	+	17.5071i	−0.354059	+	0.613248i
$816$		0			0
$817$	−1.41592	−	2.45244i	−0.0495366	−	0.0858000i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	25.9259	+	44.9049i	0.904819	+	1.56719i	0.821160	+	0.570698i	$0.193327\pi$
$821$	25.9259	+	44.9049i	0.904819	+	1.56719i	0.0836589	+	0.996494i	$0.473339\pi$
$822$		0			0
$823$	−28.3812	−	16.3859i	−0.989307	−	0.571177i	−0.0842401	−	0.996445i	$-0.526846\pi$
$823$	−28.3812	−	16.3859i	−0.989307	−	0.571177i	−0.905067	+	0.425269i	$0.860180\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	52.8295i		−	1.83706i	−0.395350	−	0.918531i	$-0.629377\pi$
$827$		−	52.8295i		−	1.83706i	0.395350	−	0.918531i	$-0.370623\pi$
$828$		0			0
$829$			0.0144624i			0.000502300i	1.00000		0.000251150i	$7.99435e-5\pi$
$829$			0.0144624i			0.000502300i	−1.00000		0.000251150i	$0.999920\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	3.80427	+	2.19639i	0.131810	+	0.0761006i
$834$		0			0
$835$	−0.677708	−	1.17382i	−0.0234531	−	0.0406219i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	16.6802	+	28.8909i	0.575864	+	0.997425i	0.995947	+	0.0899399i	$0.0286675\pi$
$839$	16.6802	+	28.8909i	0.575864	+	0.997425i	−0.420083	+	0.907486i	$0.637999\pi$
$840$		0			0
$841$	1.46530	−	2.53797i	0.0505275	−	0.0875162i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	45.1869			1.55448
$846$		0			0
$847$		−	20.4890i		−	0.704010i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	12.3543	+	7.13276i	0.423500	+	0.244508i
$852$		0			0
$853$	32.7219	−	18.8920i	1.12038	−	0.646850i	0.178880	−	0.983871i	$-0.442753\pi$
$853$	32.7219	−	18.8920i	1.12038	−	0.646850i	0.941497	+	0.337021i	$0.109419\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−9.00665	+	5.19999i	−0.307661	+	0.177628i	−0.645879	−	0.763439i	$-0.723509\pi$
$857$	−9.00665	+	5.19999i	−0.307661	+	0.177628i	0.338218	+	0.941068i	$0.390176\pi$
$858$		0			0
$859$	10.3547	−	17.9348i	0.353297	−	0.611929i	−0.633528	−	0.773720i	$-0.718394\pi$
$859$	10.3547	−	17.9348i	0.353297	−	0.611929i	0.986825	+	0.161791i	$0.0517271\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	4.67705			0.159209			0.0796043	−	0.996827i	$-0.474634\pi$
$863$	4.67705			0.159209			0.0796043	+	0.996827i	$0.474634\pi$
$864$		0			0
$865$	16.5729			0.563495
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−7.14567	+	12.3767i	−0.242400	+	0.419849i
$870$		0			0
$871$	11.1152	−	6.41739i	0.376626	−	0.217445i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−25.3995	+	14.6644i	−0.858660	+	0.495748i
$876$		0			0
$877$	−9.04467	−	5.22194i	−0.305417	−	0.176333i	0.339457	−	0.940622i	$-0.389757\pi$
$877$	−9.04467	−	5.22194i	−0.305417	−	0.176333i	−0.644874	+	0.764289i	$0.723090\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$			29.7734i			1.00309i	0.865131	+	0.501546i	$0.167235\pi$
$881$			29.7734i			1.00309i	−0.865131	+	0.501546i	$0.832765\pi$
$882$		0			0
$883$	52.9294			1.78122			0.890608	−	0.454772i	$-0.150279\pi$
$883$	52.9294			1.78122			0.890608	+	0.454772i	$0.150279\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	22.4416	−	38.8700i	0.753515	−	1.30513i	−0.192594	−	0.981278i	$-0.561690\pi$
$887$	22.4416	−	38.8700i	0.753515	−	1.30513i	0.946109	−	0.323848i	$-0.104977\pi$
$888$		0			0
$889$	−19.1787	−	33.2184i	−0.643232	−	1.11411i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	15.3026	+	26.5048i	0.512081	+	0.886951i
$894$		0			0
$895$	2.42753	+	1.40153i	0.0811434	+	0.0468481i
$896$		0			0
$897$		0			0
$898$		0			0
$899$			35.0978i			1.17058i
$900$		0			0
$901$			26.1148i			0.870009i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	5.71174	+	3.29768i	0.189865	+	0.109618i
$906$		0			0
$907$	8.19627	+	14.1964i	0.272153	+	0.471382i	0.969413	−	0.245436i	$-0.0789311\pi$
$907$	8.19627	+	14.1964i	0.272153	+	0.471382i	−0.697260	+	0.716818i	$0.745598\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−13.4518	−	23.2991i	−0.445677	−	0.771935i	0.552422	−	0.833564i	$-0.313704\pi$
$911$	−13.4518	−	23.2991i	−0.445677	−	0.771935i	−0.998099	+	0.0616295i	$0.980370\pi$
$912$		0			0
$913$	−12.3772	+	21.4380i	−0.409626	+	0.709493i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−3.86319			−0.127574
$918$		0			0
$919$		−	22.2518i		−	0.734020i	−0.930217	−	0.367010i	$-0.880381\pi$
$919$		−	22.2518i		−	0.734020i	0.930217	−	0.367010i	$-0.119619\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	17.7519	+	10.2491i	0.584310	+	0.337352i
$924$		0			0
$925$	−8.14257	+	4.70112i	−0.267726	+	0.154572i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	8.55489	−	4.93917i	0.280677	−	0.162049i	−0.353053	−	0.935603i	$-0.614856\pi$
$929$	8.55489	−	4.93917i	0.280677	−	0.162049i	0.633730	+	0.773555i	$0.281523\pi$
$930$		0			0
$931$	1.85796	−	3.21809i	0.0608923	−	0.105469i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	10.4781			0.342670
$936$		0			0
$937$	−2.11802			−0.0691926			−0.0345963	−	0.999401i	$-0.511015\pi$
$937$	−2.11802			−0.0691926			−0.0345963	+	0.999401i	$0.511015\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−3.56180	+	6.16922i	−0.116111	+	0.201111i	−0.918223	−	0.396063i	$-0.870376\pi$
$941$	−3.56180	+	6.16922i	−0.116111	+	0.201111i	0.802112	+	0.597173i	$0.203710\pi$
$942$		0			0
$943$	14.4803	−	8.36018i	0.471542	−	0.272245i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	44.5581	−	25.7256i	1.44794	−	0.835970i	0.449584	−	0.893238i	$-0.351572\pi$
$947$	44.5581	−	25.7256i	1.44794	−	0.835970i	0.998359	+	0.0572679i	$0.0182389\pi$
$948$		0			0
$949$	−3.37910	−	1.95093i	−0.109690	−	0.0633297i
$950$		0			0
$951$		0			0
$952$		0			0
$953$			45.3652i			1.46952i	0.678326	+	0.734761i	$0.262706\pi$
$953$			45.3652i			1.46952i	−0.678326	+	0.734761i	$0.737294\pi$
$954$		0			0
$955$	42.5046			1.37542
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−14.7760	+	25.5928i	−0.477143	+	0.826436i
$960$		0			0
$961$	8.12641	+	14.0754i	0.262142	+	0.454044i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−22.9238	−	39.7052i	−0.737944	−	1.27816i
$966$		0			0
$967$	2.55341	+	1.47421i	0.0821121	+	0.0474075i	0.540494	−	0.841348i	$-0.318237\pi$
$967$	2.55341	+	1.47421i	0.0821121	+	0.0474075i	−0.458382	+	0.888755i	$0.651571\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$		−	21.8052i		−	0.699763i	−0.936794	−	0.349882i	$-0.886222\pi$
$971$		−	21.8052i		−	0.699763i	0.936794	−	0.349882i	$-0.113778\pi$
$972$		0			0
$973$			2.98444i			0.0956768i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−26.7110	−	15.4216i	−0.854560	−	0.493381i	0.00762657	−	0.999971i	$-0.497572\pi$
$977$	−26.7110	−	15.4216i	−0.854560	−	0.493381i	−0.862187	+	0.506590i	$0.830906\pi$
$978$		0			0
$979$	−0.920536	−	1.59441i	−0.0294204	−	0.0509577i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−6.49316	−	11.2465i	−0.207100	−	0.358707i	0.743700	−	0.668513i	$-0.233069\pi$
$983$	−6.49316	−	11.2465i	−0.207100	−	0.358707i	−0.950800	+	0.309806i	$0.899736\pi$
$984$		0			0
$985$	5.16324	−	8.94300i	0.164515	−	0.284948i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	2.46201			0.0782873
$990$		0			0
$991$			47.5865i			1.51163i	0.654783	+	0.755817i	$0.272760\pi$
$991$			47.5865i			1.51163i	−0.654783	+	0.755817i	$0.727240\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−1.92557	−	1.11173i	−0.0610447	−	0.0352442i
$996$		0			0
$997$	−7.41748	+	4.28248i	−0.234914	+	0.135628i	−0.612837	−	0.790209i	$-0.709972\pi$
$997$	−7.41748	+	4.28248i	−0.234914	+	0.135628i	0.377923	+	0.925837i	$0.376638\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	864.2.p.b.719.6		16
3.2	odd	2		288.2.p.b.239.1		16
4.3	odd	2		216.2.l.b.179.2		16
8.3	odd	2	inner	864.2.p.b.719.3		16
8.5	even	2		216.2.l.b.179.6		16
9.2	odd	6	inner	864.2.p.b.143.3		16
9.4	even	3		2592.2.f.b.1295.5		16
9.5	odd	6		2592.2.f.b.1295.11		16
9.7	even	3		288.2.p.b.47.2		16
12.11	even	2		72.2.l.b.59.7	yes	16
24.5	odd	2		72.2.l.b.59.3	yes	16
24.11	even	2		288.2.p.b.239.2		16
36.7	odd	6		72.2.l.b.11.3	✓	16
36.11	even	6		216.2.l.b.35.6		16
36.23	even	6		648.2.f.b.323.1		16
36.31	odd	6		648.2.f.b.323.16		16
72.5	odd	6		648.2.f.b.323.15		16
72.11	even	6	inner	864.2.p.b.143.6		16
72.13	even	6		648.2.f.b.323.2		16
72.29	odd	6		216.2.l.b.35.2		16
72.43	odd	6		288.2.p.b.47.1		16
72.59	even	6		2592.2.f.b.1295.6		16
72.61	even	6		72.2.l.b.11.7	yes	16
72.67	odd	6		2592.2.f.b.1295.12		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
72.2.l.b.11.3	✓	16	36.7	odd	6
72.2.l.b.11.7	yes	16	72.61	even	6
72.2.l.b.59.3	yes	16	24.5	odd	2
72.2.l.b.59.7	yes	16	12.11	even	2
216.2.l.b.35.2		16	72.29	odd	6
216.2.l.b.35.6		16	36.11	even	6
216.2.l.b.179.2		16	4.3	odd	2
216.2.l.b.179.6		16	8.5	even	2
288.2.p.b.47.1		16	72.43	odd	6
288.2.p.b.47.2		16	9.7	even	3
288.2.p.b.239.1		16	3.2	odd	2
288.2.p.b.239.2		16	24.11	even	2
648.2.f.b.323.1		16	36.23	even	6
648.2.f.b.323.2		16	72.13	even	6
648.2.f.b.323.15		16	72.5	odd	6
648.2.f.b.323.16		16	36.31	odd	6
864.2.p.b.143.3		16	9.2	odd	6	inner
864.2.p.b.143.6		16	72.11	even	6	inner
864.2.p.b.719.3		16	8.3	odd	2	inner
864.2.p.b.719.6		16	1.1	even	1	trivial
2592.2.f.b.1295.5		16	9.4	even	3
2592.2.f.b.1295.6		16	72.59	even	6
2592.2.f.b.1295.11		16	9.5	odd	6
2592.2.f.b.1295.12		16	72.67	odd	6

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:	\( N \)	\(=\)	\( 864 = 2^{5} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	864.p (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.895377 - 1.55084i) q^{5} +(-2.08793 + 1.20546i) q^{7} +O(q^{10})\)	\(q+(0.895377 - 1.55084i) q^{5} +(-2.08793 + 1.20546i) q^{7} +(-1.36975 + 0.790826i) q^{11} +(-5.35491 - 3.09166i) q^{13} -3.69943i q^{17} -3.12941 q^{19} +(1.36036 - 2.35622i) q^{23} +(0.896599 + 1.55296i) q^{25} +(-2.55291 - 4.42177i) q^{29} +(-5.95312 - 3.43703i) q^{31} +4.31738i q^{35} +5.24328i q^{37} +(5.32220 + 3.07278i) q^{41} +(0.452455 + 0.783675i) q^{43} +(-4.88993 - 8.46960i) q^{47} +(-0.593711 + 1.02834i) q^{49} -7.05913 q^{53} +2.83235i q^{55} +(-6.10118 - 3.52252i) q^{59} +(3.05109 - 1.76155i) q^{61} +(-9.58933 + 5.53640i) q^{65} +(-1.03786 + 1.79762i) q^{67} -3.31507 q^{71} +0.631029 q^{73} +(1.90662 - 3.30237i) q^{77} +(7.82515 - 4.51785i) q^{79} +(13.5542 - 7.82551i) q^{83} +(-5.73722 - 3.31239i) q^{85} +1.16402i q^{89} +14.9075 q^{91} +(-2.80200 + 4.85321i) q^{95} +(-6.72981 - 11.6564i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q+O(q^{10}) \) 16 * q	\( 16 q + 12 q^{11} + 4 q^{19} - 14 q^{25} + 36 q^{41} - 8 q^{43} + 10 q^{49} + 12 q^{59} + 6 q^{65} + 16 q^{67} - 4 q^{73} + 54 q^{83} + 36 q^{91} + 8 q^{97}+O(q^{100}) \) 16 * q + 12 * q^11 + 4 * q^19 - 14 * q^25 + 36 * q^41 - 8 * q^43 + 10 * q^49 + 12 * q^59 + 6 * q^65 + 16 * q^67 - 4 * q^73 + 54 * q^83 + 36 * q^91 + 8 * q^97

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