LMFDB - Embedded newform 1638.2.bj.g.127.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1638,2,Mod(127,1638)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1638, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 5]))

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

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

chi := DirichletCharacter("1638.127");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1638.bj (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$13.0794958511$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} + 39 x^{10} - 140 x^{9} + 460 x^{8} - 1066 x^{7} + 2127 x^{6} - 3172 x^{5} + \cdots + 169 $ x^12 - 6x^11 + 39x^10 - 140x^9 + 460x^8 - 1066x^7 + 2127x^6 - 3172x^5 + 3842x^4 - 3394x^3 + 2141x^2 - 832*x + 169
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 182)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			127.2
Root			$0.500000 - 3.15681i$ of defining polynomial
Character	$\chi$	$=$	1638.127
Dual form			1638.2.bj.g.1135.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +0.901839i q^{5} +(0.866025 + 0.500000i) q^{7} +1.00000i q^{8} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +0.901839i q^{5} +(0.866025 + 0.500000i) q^{7} +1.00000i q^{8} +(-0.450919 - 0.781015i) q^{10} +(3.75609 - 2.16858i) q^{11} +(-0.426876 - 3.58019i) q^{13} -1.00000 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-2.53296 + 4.38722i) q^{17} +(5.34544 + 3.08619i) q^{19} +(0.781015 + 0.450919i) q^{20} +(-2.16858 + 3.75609i) q^{22} +(-4.22559 - 7.31893i) q^{23} +4.18669 q^{25} +(2.15978 + 2.88710i) q^{26} +(0.866025 - 0.500000i) q^{28} +(-1.09643 - 1.89907i) q^{29} -0.873062i q^{31} +(0.866025 + 0.500000i) q^{32} -5.06592i q^{34} +(-0.450919 + 0.781015i) q^{35} +(0.124973 - 0.0721531i) q^{37} -6.17238 q^{38} -0.901839 q^{40} +(3.46110 - 1.99827i) q^{41} +(3.85426 - 6.67577i) q^{43} -4.33716i q^{44} +(7.31893 + 4.22559i) q^{46} -2.92115i q^{47} +(0.500000 + 0.866025i) q^{49} +(-3.62578 + 2.09334i) q^{50} +(-3.31398 - 1.42041i) q^{52} -1.69699 q^{53} +(1.95571 + 3.38739i) q^{55} +(-0.500000 + 0.866025i) q^{56} +(1.89907 + 1.09643i) q^{58} +(7.40394 + 4.27467i) q^{59} +(-4.16720 + 7.21780i) q^{61} +(0.436531 + 0.756094i) q^{62} -1.00000 q^{64} +(3.22876 - 0.384973i) q^{65} +(-8.99180 + 5.19142i) q^{67} +(2.53296 + 4.38722i) q^{68} -0.901839i q^{70} +(2.83932 + 1.63928i) q^{71} -0.539023i q^{73} +(-0.0721531 + 0.124973i) q^{74} +(5.34544 - 3.08619i) q^{76} +4.33716 q^{77} +6.53349 q^{79} +(0.781015 - 0.450919i) q^{80} +(-1.99827 + 3.46110i) q^{82} -13.2348i q^{83} +(-3.95656 - 2.28432i) q^{85} +7.70851i q^{86} +(2.16858 + 3.75609i) q^{88} +(6.74790 - 3.89590i) q^{89} +(1.42041 - 3.31398i) q^{91} -8.45117 q^{92} +(1.46057 + 2.52979i) q^{94} +(-2.78325 + 4.82072i) q^{95} +(10.1378 + 5.85305i) q^{97} +(-0.866025 - 0.500000i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{4}+O(q^{10}) $ 12 * q + 6 * q^4	$ 12 q + 6 q^{4} - 2 q^{10} + 18 q^{11} - 8 q^{13} - 12 q^{14} - 6 q^{16} - 4 q^{17} + 12 q^{19} - 2 q^{22} + 6 q^{23} - 24 q^{25} + 14 q^{26} + 10 q^{29} - 2 q^{35} - 6 q^{37} - 8 q^{38} - 4 q^{40} + 24 q^{41} + 26 q^{43} - 6 q^{46} + 6 q^{49} + 12 q^{50} - 4 q^{52} - 36 q^{53} - 6 q^{55} - 6 q^{56} + 24 q^{58} - 6 q^{59} - 28 q^{61} + 2 q^{62} - 12 q^{64} + 34 q^{65} - 42 q^{67} + 4 q^{68} - 48 q^{71} + 12 q^{76} + 4 q^{77} + 44 q^{79} + 6 q^{82} + 54 q^{85} + 2 q^{88} - 12 q^{89} - 16 q^{91} + 12 q^{92} + 8 q^{94} - 32 q^{95} + 60 q^{97}+O(q^{100}) $ 12 * q + 6 * q^4 - 2 * q^10 + 18 * q^11 - 8 * q^13 - 12 * q^14 - 6 * q^16 - 4 * q^17 + 12 * q^19 - 2 * q^22 + 6 * q^23 - 24 * q^25 + 14 * q^26 + 10 * q^29 - 2 * q^35 - 6 * q^37 - 8 * q^38 - 4 * q^40 + 24 * q^41 + 26 * q^43 - 6 * q^46 + 6 * q^49 + 12 * q^50 - 4 * q^52 - 36 * q^53 - 6 * q^55 - 6 * q^56 + 24 * q^58 - 6 * q^59 - 28 * q^61 + 2 * q^62 - 12 * q^64 + 34 * q^65 - 42 * q^67 + 4 * q^68 - 48 * q^71 + 12 * q^76 + 4 * q^77 + 44 * q^79 + 6 * q^82 + 54 * q^85 + 2 * q^88 - 12 * q^89 - 16 * q^91 + 12 * q^92 + 8 * q^94 - 32 * q^95 + 60 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1638\mathbb{Z}\right)^\times$.

$n$	$379$	$703$	$911$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$1$

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 $

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$			0.901839i			0.403315i	0.979456	+	0.201657i	$0.0646327\pi$
$5$			0.901839i			0.403315i	−0.979456	+	0.201657i	$0.935367\pi$
$6$		0			0
$7$	0.866025	+	0.500000i	0.327327	+	0.188982i
$7$	0.866025	+	0.500000i	0.327327	+	0.188982i
$8$			1.00000i			0.353553i
$9$		0			0
$10$	−0.450919	−	0.781015i	−0.142593	−	0.246979i
$11$	3.75609	−	2.16858i	1.13251	−	0.653852i	0.187941	−	0.982180i	$-0.439819\pi$
$11$	3.75609	−	2.16858i	1.13251	−	0.653852i	0.944564	+	0.328328i	$0.106485\pi$
$12$		0			0
$13$	−0.426876	−	3.58019i	−0.118394	−	0.992967i
$13$	−0.426876	−	3.58019i	−0.118394	−	0.992967i
$14$	−1.00000			−0.267261
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−2.53296	+	4.38722i	−0.614333	+	1.06406i	0.376168	+	0.926551i	$0.377242\pi$
$17$	−2.53296	+	4.38722i	−0.614333	+	1.06406i	−0.990501	+	0.137505i	$0.956092\pi$
$18$		0			0
$19$	5.34544	+	3.08619i	1.22633	+	0.708021i	0.966260	−	0.257570i	$-0.0829217\pi$
$19$	5.34544	+	3.08619i	1.22633	+	0.708021i	0.260068	+	0.965590i	$0.416255\pi$
$20$	0.781015	+	0.450919i	0.174640	+	0.100829i
$21$		0			0
$22$	−2.16858	+	3.75609i	−0.462343	+	0.800802i
$23$	−4.22559	−	7.31893i	−0.881096	−	1.52610i	−0.850124	−	0.526582i	$-0.823473\pi$
$23$	−4.22559	−	7.31893i	−0.881096	−	1.52610i	−0.0309711	−	0.999520i	$-0.509860\pi$
$24$		0			0
$25$	4.18669			0.837337
$26$	2.15978	+	2.88710i	0.423568	+	0.566207i
$27$		0			0
$28$	0.866025	−	0.500000i	0.163663	−	0.0944911i
$29$	−1.09643	−	1.89907i	−0.203602	−	0.352649i	0.746085	−	0.665851i	$-0.231931\pi$
$29$	−1.09643	−	1.89907i	−0.203602	−	0.352649i	−0.949686	+	0.313203i	$0.898598\pi$
$30$		0			0
$31$		−	0.873062i		−	0.156807i	−0.996922	−	0.0784033i	$-0.975018\pi$
$31$		−	0.873062i		−	0.156807i	0.996922	−	0.0784033i	$-0.0249822\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$		0			0
$34$		−	5.06592i		−	0.868798i
$35$	−0.450919	+	0.781015i	−0.0762193	+	0.132016i
$36$		0			0
$37$	0.124973	−	0.0721531i	0.0205454	−	0.0118619i	−0.489692	−	0.871895i	$-0.662891\pi$
$37$	0.124973	−	0.0721531i	0.0205454	−	0.0118619i	0.510238	+	0.860034i	$0.329557\pi$
$38$	−6.17238			−1.00129
$39$		0			0
$40$	−0.901839			−0.142593
$41$	3.46110	−	1.99827i	0.540533	−	0.312077i	−0.204762	−	0.978812i	$-0.565642\pi$
$41$	3.46110	−	1.99827i	0.540533	−	0.312077i	0.745295	+	0.666735i	$0.232309\pi$
$42$		0			0
$43$	3.85426	−	6.67577i	0.587768	−	1.01804i	−0.406756	−	0.913537i	$-0.633340\pi$
$43$	3.85426	−	6.67577i	0.587768	−	1.01804i	0.994524	−	0.104508i	$-0.0333267\pi$
$44$		−	4.33716i		−	0.653852i
$45$		0			0
$46$	7.31893	+	4.22559i	1.07912	+	0.623029i
$47$		−	2.92115i		−	0.426093i	−0.977042	−	0.213047i	$-0.931661\pi$
$47$		−	2.92115i		−	0.426093i	0.977042	−	0.213047i	$-0.0683387\pi$
$48$		0			0
$49$	0.500000	+	0.866025i	0.0714286	+	0.123718i
$50$	−3.62578	+	2.09334i	−0.512762	+	0.296043i
$51$		0			0
$52$	−3.31398	−	1.42041i	−0.459566	−	0.196976i
$53$	−1.69699			−0.233099			−0.116549	−	0.993185i	$-0.537183\pi$
$53$	−1.69699			−0.233099			−0.116549	+	0.993185i	$0.537183\pi$
$54$		0			0
$55$	1.95571	+	3.38739i	0.263708	+	0.456756i
$56$	−0.500000	+	0.866025i	−0.0668153	+	0.115728i
$57$		0			0
$58$	1.89907	+	1.09643i	0.249360	+	0.143968i
$59$	7.40394	+	4.27467i	0.963911	+	0.556514i	0.897374	−	0.441270i	$-0.145472\pi$
$59$	7.40394	+	4.27467i	0.963911	+	0.556514i	0.0665363	+	0.997784i	$0.478805\pi$
$60$		0			0
$61$	−4.16720	+	7.21780i	−0.533555	+	0.924145i	0.465676	+	0.884955i	$0.345811\pi$
$61$	−4.16720	+	7.21780i	−0.533555	+	0.924145i	−0.999232	+	0.0391900i	$0.987522\pi$
$62$	0.436531	+	0.756094i	0.0554395	+	0.0960241i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	3.22876	−	0.384973i	0.400478	−	0.0477501i
$66$		0			0
$67$	−8.99180	+	5.19142i	−1.09852	+	0.634233i	−0.935833	−	0.352444i	$-0.885351\pi$
$67$	−8.99180	+	5.19142i	−1.09852	+	0.634233i	−0.162691	+	0.986677i	$0.552017\pi$
$68$	2.53296	+	4.38722i	0.307167	+	0.532028i
$69$		0			0
$70$		−	0.901839i		−	0.107790i
$71$	2.83932	+	1.63928i	0.336965	+	0.194547i	0.658929	−	0.752205i	$-0.271010\pi$
$71$	2.83932	+	1.63928i	0.336965	+	0.194547i	−0.321964	+	0.946752i	$0.604343\pi$
$72$		0			0
$73$		−	0.539023i		−	0.0630879i	−0.999502	−	0.0315439i	$-0.989958\pi$
$73$		−	0.539023i		−	0.0630879i	0.999502	−	0.0315439i	$-0.0100424\pi$
$74$	−0.0721531	+	0.124973i	−0.00838763	+	0.0145278i
$75$		0			0
$76$	5.34544	−	3.08619i	0.613164	−	0.354010i
$77$	4.33716			0.494266
$78$		0			0
$79$	6.53349			0.735075			0.367537	−	0.930009i	$-0.380201\pi$
$79$	6.53349			0.735075			0.367537	+	0.930009i	$0.380201\pi$
$80$	0.781015	−	0.450919i	0.0873202	−	0.0504143i
$81$		0			0
$82$	−1.99827	+	3.46110i	−0.220672	+	0.382215i
$83$		−	13.2348i		−	1.45271i	−0.687319	−	0.726356i	$-0.741212\pi$
$83$		−	13.2348i		−	1.45271i	0.687319	−	0.726356i	$-0.258788\pi$
$84$		0			0
$85$	−3.95656	−	2.28432i	−0.429149	−	0.247769i
$86$			7.70851i			0.831230i
$87$		0			0
$88$	2.16858	+	3.75609i	0.231172	+	0.400401i
$89$	6.74790	−	3.89590i	0.715276	−	0.412965i	−0.0977357	−	0.995212i	$-0.531160\pi$
$89$	6.74790	−	3.89590i	0.715276	−	0.412965i	0.813011	+	0.582248i	$0.197827\pi$
$90$		0			0
$91$	1.42041	−	3.31398i	0.148900	−	0.347399i
$92$	−8.45117			−0.881096
$93$		0			0
$94$	1.46057	+	2.52979i	0.150647	+	0.260928i
$95$	−2.78325	+	4.82072i	−0.285555	+	0.494596i
$96$		0			0
$97$	10.1378	+	5.85305i	1.02934	+	0.594287i	0.916794	−	0.399360i	$-0.130768\pi$
$97$	10.1378	+	5.85305i	1.02934	+	0.594287i	0.112541	+	0.993647i	$0.464101\pi$
$98$	−0.866025	−	0.500000i	−0.0874818	−	0.0505076i
$99$		0			0
$100$	2.09334	−	3.62578i	0.209334	−	0.362578i
$101$	5.37145	+	9.30362i	0.534479	+	0.925745i	0.999188	+	0.0402814i	$0.0128254\pi$
$101$	5.37145	+	9.30362i	0.534479	+	0.925745i	−0.464709	+	0.885463i	$0.653841\pi$
$102$		0			0
$103$	4.81099			0.474041			0.237021	−	0.971505i	$-0.423829\pi$
$103$	4.81099			0.474041			0.237021	+	0.971505i	$0.423829\pi$
$104$	3.58019	−	0.426876i	0.351067	−	0.0418586i
$105$		0			0
$106$	1.46963	−	0.848493i	0.142743	−	0.0824129i
$107$	6.82652	+	11.8239i	0.659944	+	1.14306i	0.980630	+	0.195871i	$0.0627534\pi$
$107$	6.82652	+	11.8239i	0.659944	+	1.14306i	−0.320686	+	0.947186i	$0.603913\pi$
$108$		0			0
$109$		−	5.11747i		−	0.490165i	−0.969502	−	0.245082i	$-0.921185\pi$
$109$		−	5.11747i		−	0.490165i	0.969502	−	0.245082i	$-0.0788150\pi$
$110$	−3.38739	−	1.95571i	−0.322975	−	0.186470i
$111$		0			0
$112$		−	1.00000i		−	0.0944911i
$113$	8.96603	−	15.5296i	0.843453	−	1.46090i	−0.0435052	−	0.999053i	$-0.513853\pi$
$113$	8.96603	−	15.5296i	0.843453	−	1.46090i	0.886958	−	0.461850i	$-0.152814\pi$
$114$		0			0
$115$	6.60049	−	3.81080i	0.615499	−	0.355359i
$116$	−2.19286			−0.203602
$117$		0			0
$118$	−8.54933			−0.787030
$119$	−4.38722	+	2.53296i	−0.402175	+	0.232196i
$120$		0			0
$121$	3.90550	−	6.76452i	0.355045	−	0.614956i
$122$		−	8.33440i		−	0.754561i
$123$		0			0
$124$	−0.756094	−	0.436531i	−0.0678993	−	0.0392017i
$125$			8.28491i			0.741025i
$126$		0			0
$127$	−9.75681	−	16.8993i	−0.865777	−	1.49957i	−0.866273	−	0.499570i	$-0.833491\pi$
$127$	−9.75681	−	16.8993i	−0.865777	−	1.49957i	0.000496195	−	1.00000i	$-0.499842\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$		0			0
$130$	−2.60370	+	1.94777i	−0.228359	+	0.170831i
$131$	20.6496			1.80417			0.902083	−	0.431562i	$-0.142037\pi$
$131$	20.6496			1.80417			0.902083	+	0.431562i	$0.142037\pi$
$132$		0			0
$133$	3.08619	+	5.34544i	0.267607	+	0.463508i
$134$	5.19142	−	8.99180i	0.448470	−	0.776773i
$135$		0			0
$136$	−4.38722	−	2.53296i	−0.376201	−	0.217200i
$137$	−2.76224	−	1.59478i	−0.235994	−	0.136251i	0.377340	−	0.926075i	$-0.376839\pi$
$137$	−2.76224	−	1.59478i	−0.235994	−	0.136251i	−0.613334	+	0.789823i	$0.710172\pi$
$138$		0			0
$139$	0.297855	−	0.515900i	0.0252637	−	0.0437581i	−0.853117	−	0.521719i	$-0.825291\pi$
$139$	0.297855	−	0.515900i	0.0252637	−	0.0437581i	0.878381	+	0.477961i	$0.158624\pi$
$140$	0.450919	+	0.781015i	0.0381096	+	0.0660078i
$141$		0			0
$142$	−3.27856			−0.275131
$143$	−9.36733	−	12.5218i	−0.783335	−	1.04713i
$144$		0			0
$145$	1.71266	−	0.988802i	0.142228	−	0.0821155i
$146$	0.269511	+	0.466808i	0.0223049	+	0.0386333i
$147$		0			0
$148$		−	0.144306i		−	0.0118619i
$149$	−9.70783	−	5.60482i	−0.795297	−	0.459165i	0.0465273	−	0.998917i	$-0.485185\pi$
$149$	−9.70783	−	5.60482i	−0.795297	−	0.459165i	−0.841824	+	0.539752i	$0.818518\pi$
$150$		0			0
$151$			13.0731i			1.06387i	0.846785	+	0.531935i	$0.178535\pi$
$151$			13.0731i			1.06387i	−0.846785	+	0.531935i	$0.821465\pi$
$152$	−3.08619	+	5.34544i	−0.250323	+	0.433572i
$153$		0			0
$154$	−3.75609	+	2.16858i	−0.302675	+	0.174749i
$155$	0.787362			0.0632424
$156$		0			0
$157$	17.9245			1.43053			0.715266	−	0.698853i	$-0.246306\pi$
$157$	17.9245			1.43053			0.715266	+	0.698853i	$0.246306\pi$
$158$	−5.65817	+	3.26674i	−0.450139	+	0.259888i
$159$		0			0
$160$	−0.450919	+	0.781015i	−0.0356483	+	0.0617447i
$161$		−	8.45117i		−	0.666046i
$162$		0			0
$163$	17.5958	+	10.1589i	1.37821	+	0.795710i	0.991944	−	0.126677i	$-0.0404312\pi$
$163$	17.5958	+	10.1589i	1.37821	+	0.795710i	0.386266	+	0.922387i	$0.373765\pi$
$164$		−	3.99654i		−	0.312077i
$165$		0			0
$166$	6.61742	+	11.4617i	0.513611	+	0.889601i
$167$	2.79770	−	1.61525i	0.216493	−	0.124992i	−0.387833	−	0.921730i	$-0.626776\pi$
$167$	2.79770	−	1.61525i	0.216493	−	0.124992i	0.604325	+	0.796738i	$0.293443\pi$
$168$		0			0
$169$	−12.6356	+	3.05660i	−0.971966	+	0.235123i
$170$	4.56864			0.350399
$171$		0			0
$172$	−3.85426	−	6.67577i	−0.293884	−	0.509022i
$173$	4.58522	−	7.94183i	0.348608	−	0.603806i	−0.637395	−	0.770538i	$-0.719988\pi$
$173$	4.58522	−	7.94183i	0.348608	−	0.603806i	0.986002	+	0.166731i	$0.0533212\pi$
$174$		0			0
$175$	3.62578	+	2.09334i	0.274083	+	0.158242i
$176$	−3.75609	−	2.16858i	−0.283126	−	0.163463i
$177$		0			0
$178$	−3.89590	+	6.74790i	−0.292010	+	0.505776i
$179$	8.47747	+	14.6834i	0.633636	+	1.09749i	0.986802	+	0.161929i	$0.0517717\pi$
$179$	8.47747	+	14.6834i	0.633636	+	1.09749i	−0.353166	+	0.935561i	$0.614895\pi$
$180$		0			0
$181$	−2.65743			−0.197525			−0.0987626	−	0.995111i	$-0.531488\pi$
$181$	−2.65743			−0.197525			−0.0987626	+	0.995111i	$0.531488\pi$
$182$	0.426876	+	3.58019i	0.0316421	+	0.265382i
$183$		0			0
$184$	7.31893	−	4.22559i	0.539559	−	0.311514i
$185$	0.0650705	+	0.112705i	0.00478408	+	0.00828627i
$186$		0			0
$187$			21.9717i			1.60673i
$188$	−2.52979	−	1.46057i	−0.184504	−	0.106523i
$189$		0			0
$190$		−	5.56649i		−	0.403836i
$191$	−12.2430	+	21.2056i	−0.885875	+	1.53438i	−0.0411671	+	0.999152i	$0.513108\pi$
$191$	−12.2430	+	21.2056i	−0.885875	+	1.53438i	−0.844708	+	0.535228i	$0.820226\pi$
$192$		0			0
$193$	10.6009	−	6.12046i	0.763072	−	0.440560i	−0.0673254	−	0.997731i	$-0.521447\pi$
$193$	10.6009	−	6.12046i	0.763072	−	0.440560i	0.830398	+	0.557171i	$0.188113\pi$
$194$	−11.7061			−0.840449
$195$		0			0
$196$	1.00000			0.0714286
$197$	−4.72634	+	2.72876i	−0.336738	+	0.194416i	−0.658829	−	0.752293i	$-0.728948\pi$
$197$	−4.72634	+	2.72876i	−0.336738	+	0.194416i	0.322091	+	0.946709i	$0.395614\pi$
$198$		0			0
$199$	−6.40832	+	11.0995i	−0.454274	+	0.786825i	−0.998646	−	0.0520184i	$-0.983435\pi$
$199$	−6.40832	+	11.0995i	−0.454274	+	0.786825i	0.544372	+	0.838844i	$0.316768\pi$
$200$			4.18669i			0.296043i
$201$		0			0
$202$	−9.30362	−	5.37145i	−0.654600	−	0.377934i
$203$		−	2.19286i		−	0.153908i
$204$		0			0
$205$	1.80212	+	3.12136i	0.125865	+	0.218005i
$206$	−4.16644	+	2.40550i	−0.290290	+	0.167599i
$207$		0			0
$208$	−2.88710	+	2.15978i	−0.200184	+	0.149754i
$209$	26.7706			1.85176
$210$		0			0
$211$	9.65552	+	16.7239i	0.664713	+	1.15132i	0.979363	+	0.202110i	$0.0647797\pi$
$211$	9.65552	+	16.7239i	0.664713	+	1.15132i	−0.314649	+	0.949208i	$0.601887\pi$
$212$	−0.848493	+	1.46963i	−0.0582747	+	0.100935i
$213$		0			0
$214$	−11.8239	−	6.82652i	−0.808263	−	0.466651i
$215$	6.02046	+	3.47592i	0.410592	+	0.237056i
$216$		0			0
$217$	0.436531	−	0.756094i	0.0296337	−	0.0513270i
$218$	2.55874	+	4.43186i	0.173299	+	0.300163i
$219$		0			0
$220$	3.91142			0.263708
$221$	16.7883	+	7.19569i	1.12931	+	0.484034i
$222$		0			0
$223$	−9.21079	+	5.31785i	−0.616800	+	0.356110i	−0.775622	−	0.631197i	$-0.782564\pi$
$223$	−9.21079	+	5.31785i	−0.616800	+	0.356110i	0.158822	+	0.987307i	$0.449230\pi$
$224$	0.500000	+	0.866025i	0.0334077	+	0.0578638i
$225$		0			0
$226$			17.9321i			1.19282i
$227$	−19.6776	−	11.3609i	−1.30605	−	0.754047i	−0.324613	−	0.945847i	$-0.605234\pi$
$227$	−19.6776	−	11.3609i	−1.30605	−	0.754047i	−0.981434	+	0.191800i	$0.938567\pi$
$228$		0			0
$229$		−	20.3094i		−	1.34208i	−0.741420	−	0.671042i	$-0.765847\pi$
$229$		−	20.3094i		−	1.34208i	0.741420	−	0.671042i	$-0.234153\pi$
$230$	−3.81080	+	6.60049i	−0.251277	+	0.435224i
$231$		0			0
$232$	1.89907	−	1.09643i	0.124680	−	0.0719841i
$233$	−10.6446			−0.697352			−0.348676	−	0.937243i	$-0.613369\pi$
$233$	−10.6446			−0.697352			−0.348676	+	0.937243i	$0.613369\pi$
$234$		0			0
$235$	2.63441			0.171850
$236$	7.40394	−	4.27467i	0.481955	−	0.278257i
$237$		0			0
$238$	2.53296	−	4.38722i	0.164187	−	0.284381i
$239$		−	0.311564i		−	0.0201534i	−0.999949	−	0.0100767i	$-0.996792\pi$
$239$		−	0.311564i		−	0.0201534i	0.999949	−	0.0100767i	$-0.00320757\pi$
$240$		0			0
$241$	−21.9100	−	12.6498i	−1.41135	−	0.814843i	−0.415833	−	0.909441i	$-0.636510\pi$
$241$	−21.9100	−	12.6498i	−1.41135	−	0.814843i	−0.995516	+	0.0945983i	$0.969843\pi$
$242$			7.81099i			0.502110i
$243$		0			0
$244$	4.16720	+	7.21780i	0.266778	+	0.462073i
$245$	−0.781015	+	0.450919i	−0.0498972	+	0.0288082i
$246$		0			0
$247$	8.76732	−	20.4551i	0.557851	−	1.30153i
$248$	0.873062			0.0554395
$249$		0			0
$250$	−4.14246	−	7.17494i	−0.261992	−	0.453783i
$251$	−4.02015	+	6.96311i	−0.253750	+	0.439507i	−0.964555	−	0.263881i	$-0.914997\pi$
$251$	−4.02015	+	6.96311i	−0.253750	+	0.439507i	0.710805	+	0.703389i	$0.248331\pi$
$252$		0			0
$253$	−31.7434	−	18.3271i	−1.99569	−	1.15221i
$254$	16.8993	+	9.75681i	1.06036	+	0.612197i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	8.46634	+	14.6641i	0.528116	+	0.914723i	0.999463	+	0.0327753i	$0.0104346\pi$
$257$	8.46634	+	14.6641i	0.528116	+	0.914723i	−0.471347	+	0.881948i	$0.656232\pi$
$258$		0			0
$259$	0.144306			0.00896676
$260$	1.28098	−	2.98867i	0.0794431	−	0.185350i
$261$		0			0
$262$	−17.8831	+	10.3248i	−1.10482	+	0.637869i
$263$	5.16045	+	8.93817i	0.318207	+	0.551151i	0.980114	−	0.198435i	$-0.0635859\pi$
$263$	5.16045	+	8.93817i	0.318207	+	0.551151i	−0.661907	+	0.749586i	$0.730253\pi$
$264$		0			0
$265$		−	1.53041i		−	0.0940122i
$266$	−5.34544	−	3.08619i	−0.327750	−	0.189226i
$267$		0			0
$268$			10.3828i			0.634233i
$269$	−3.06999	+	5.31738i	−0.187181	+	0.324207i	−0.944309	−	0.329059i	$-0.893268\pi$
$269$	−3.06999	+	5.31738i	−0.187181	+	0.324207i	0.757128	+	0.653266i	$0.226602\pi$
$270$		0			0
$271$	9.24673	−	5.33860i	0.561699	−	0.324297i	−0.192128	−	0.981370i	$-0.561539\pi$
$271$	9.24673	−	5.33860i	0.561699	−	0.324297i	0.753827	+	0.657073i	$0.228206\pi$
$272$	5.06592			0.307167
$273$		0			0
$274$	3.18956			0.192689
$275$	15.7256	−	9.07917i	0.948289	−	0.547495i
$276$		0			0
$277$	10.9545	−	18.9737i	0.658191	−	1.14002i	−0.322892	−	0.946436i	$-0.604655\pi$
$277$	10.9545	−	18.9737i	0.658191	−	1.14002i	0.981084	−	0.193585i	$-0.0620114\pi$
$278$			0.595710i			0.0357283i
$279$		0			0
$280$	−0.781015	−	0.450919i	−0.0466746	−	0.0269476i
$281$		−	25.7719i		−	1.53743i	−0.639594	−	0.768713i	$-0.720898\pi$
$281$		−	25.7719i		−	1.53743i	0.639594	−	0.768713i	$-0.279102\pi$
$282$		0			0
$283$	−5.66344	−	9.80937i	−0.336657	−	0.583107i	0.647145	−	0.762367i	$-0.275963\pi$
$283$	−5.66344	−	9.80937i	−0.336657	−	0.583107i	−0.983802	+	0.179260i	$0.942630\pi$
$284$	2.83932	−	1.63928i	0.168482	−	0.0972733i
$285$		0			0
$286$	14.3733	+	6.16055i	0.849908	+	0.364281i
$287$	3.99654			0.235908
$288$		0			0
$289$	−4.33177	−	7.50285i	−0.254810	−	0.441344i
$290$	−0.988802	+	1.71266i	−0.0580645	+	0.100571i
$291$		0			0
$292$	−0.466808	−	0.269511i	−0.0273178	−	0.0157720i
$293$	−20.5646	−	11.8730i	−1.20140	−	0.693626i	−0.240530	−	0.970642i	$-0.577321\pi$
$293$	−20.5646	−	11.8730i	−1.20140	−	0.693626i	−0.960865	+	0.277016i	$0.910655\pi$
$294$		0			0
$295$	−3.85506	+	6.67716i	−0.224450	+	0.388759i
$296$	0.0721531	+	0.124973i	0.00419382	+	0.00726390i
$297$		0			0
$298$	11.2096			0.649357
$299$	−24.3994	+	18.2527i	−1.41105	+	1.05558i
$300$		0			0
$301$	6.67577	−	3.85426i	0.384785	−	0.222156i
$302$	−6.53653	−	11.3216i	−0.376135	−	0.651485i
$303$		0			0
$304$		−	6.17238i		−	0.354010i
$305$	−6.50930	−	3.75814i	−0.372721	−	0.215191i
$306$		0			0
$307$			6.68810i			0.381710i	0.981618	+	0.190855i	$0.0611261\pi$
$307$			6.68810i			0.381710i	−0.981618	+	0.190855i	$0.938874\pi$
$308$	2.16858	−	3.75609i	0.123566	−	0.214023i
$309$		0			0
$310$	−0.681875	+	0.393681i	−0.0387279	+	0.0223596i
$311$	−9.18724			−0.520961			−0.260480	−	0.965479i	$-0.583881\pi$
$311$	−9.18724			−0.520961			−0.260480	+	0.965479i	$0.583881\pi$
$312$		0			0
$313$	−17.1631			−0.970118			−0.485059	−	0.874481i	$-0.661202\pi$
$313$	−17.1631			−0.970118			−0.485059	+	0.874481i	$0.661202\pi$
$314$	−15.5231	+	8.96225i	−0.876018	+	0.505769i
$315$		0			0
$316$	3.26674	−	5.65817i	0.183769	−	0.318297i
$317$		−	3.76247i		−	0.211322i	−0.994402	−	0.105661i	$-0.966304\pi$
$317$		−	3.76247i		−	0.211322i	0.994402	−	0.105661i	$-0.0336958\pi$
$318$		0			0
$319$	−8.23658	−	4.75539i	−0.461160	−	0.266251i
$320$		−	0.901839i		−	0.0504143i
$321$		0			0
$322$	4.22559	+	7.31893i	0.235483	+	0.407868i
$323$	−27.0796	+	15.6344i	−1.50675	+	0.869921i
$324$		0			0
$325$	−1.78720	−	14.9891i	−0.0991358	−	0.831448i
$326$	−20.3179			−1.12530
$327$		0			0
$328$	1.99827	+	3.46110i	0.110336	+	0.191107i
$329$	1.46057	−	2.52979i	0.0805241	−	0.139472i
$330$		0			0
$331$	−27.9083	−	16.1129i	−1.53398	−	0.885643i	−0.999173	−	0.0406683i	$-0.987051\pi$
$331$	−27.9083	−	16.1129i	−1.53398	−	0.885643i	−0.534806	−	0.844975i	$-0.679615\pi$
$332$	−11.4617	−	6.61742i	−0.629043	−	0.363178i
$333$		0			0
$334$	−1.61525	+	2.79770i	−0.0883827	+	0.153083i
$335$	−4.68182	−	8.10916i	−0.255795	−	0.443051i
$336$		0			0
$337$	−3.01703			−0.164348			−0.0821740	−	0.996618i	$-0.526186\pi$
$337$	−3.01703			−0.164348			−0.0821740	+	0.996618i	$0.526186\pi$
$338$	9.41441	−	8.96487i	0.512077	−	0.487624i
$339$		0			0
$340$	−3.95656	+	2.28432i	−0.214575	+	0.123885i
$341$	−1.89331	−	3.27931i	−0.102528	−	0.177584i
$342$		0			0
$343$			1.00000i			0.0539949i
$344$	6.67577	+	3.85426i	0.359933	+	0.207808i
$345$		0			0
$346$			9.17044i			0.493006i
$347$	0.234270	−	0.405768i	0.0125763	−	0.0217828i	−0.859669	−	0.510852i	$-0.829330\pi$
$347$	0.234270	−	0.405768i	0.0125763	−	0.0217828i	0.872245	+	0.489069i	$0.162663\pi$
$348$		0			0
$349$	−27.9044	+	16.1106i	−1.49369	+	0.862380i	−0.999974	−	0.00724565i	$-0.997694\pi$
$349$	−27.9044	+	16.1106i	−1.49369	+	0.862380i	−0.493712	+	0.869625i	$0.664360\pi$
$350$	−4.18669			−0.223788
$351$		0			0
$352$	4.33716			0.231172
$353$	11.3583	−	6.55771i	0.604540	−	0.349031i	−0.166285	−	0.986078i	$-0.553177\pi$
$353$	11.3583	−	6.55771i	0.604540	−	0.349031i	0.770826	+	0.637046i	$0.219844\pi$
$354$		0			0
$355$	−1.47837	+	2.56060i	−0.0784635	+	0.135903i
$356$		−	7.79180i		−	0.412965i
$357$		0			0
$358$	−14.6834	−	8.47747i	−0.776043	−	0.448048i
$359$			4.37981i			0.231157i	0.993298	+	0.115579i	$0.0368722\pi$
$359$			4.37981i			0.231157i	−0.993298	+	0.115579i	$0.963128\pi$
$360$		0			0
$361$	9.54914	+	16.5396i	0.502586	+	0.870505i
$362$	2.30140	−	1.32871i	0.120959	−	0.0698357i
$363$		0			0
$364$	−2.15978	−	2.88710i	−0.113203	−	0.151325i
$365$	0.486112			0.0254443
$366$		0			0
$367$	−12.9094	−	22.3597i	−0.673865	−	1.16717i	−0.976799	−	0.214157i	$-0.931300\pi$
$367$	−12.9094	−	22.3597i	−0.673865	−	1.16717i	0.302934	−	0.953011i	$-0.402034\pi$
$368$	−4.22559	+	7.31893i	−0.220274	+	0.381526i
$369$		0			0
$370$	−0.112705	−	0.0650705i	−0.00585928	−	0.00338285i
$371$	−1.46963	−	0.848493i	−0.0762995	−	0.0440515i
$372$		0			0
$373$	−15.3143	+	26.5251i	−0.792942	+	1.37342i	0.131196	+	0.991356i	$0.458118\pi$
$373$	−15.3143	+	26.5251i	−0.792942	+	1.37342i	−0.924138	+	0.382059i	$0.875215\pi$
$374$	−10.9859	−	19.0281i	−0.568065	−	0.983918i
$375$		0			0
$376$	2.92115			0.150647
$377$	−6.33100	+	4.73609i	−0.326063	+	0.243921i
$378$		0			0
$379$	−33.0409	+	19.0762i	−1.69720	+	0.979877i	−0.748796	+	0.662801i	$0.769368\pi$
$379$	−33.0409	+	19.0762i	−1.69720	+	0.979877i	−0.948400	+	0.317076i	$0.897299\pi$
$380$	2.78325	+	4.82072i	0.142778	+	0.247298i
$381$		0			0
$382$		−	24.4861i		−	1.25282i
$383$	27.6783	+	15.9801i	1.41430	+	0.816544i	0.995790	−	0.0916693i	$-0.0292203\pi$
$383$	27.6783	+	15.9801i	1.41430	+	0.816544i	0.418507	+	0.908214i	$0.362554\pi$
$384$		0			0
$385$			3.91142i			0.199345i
$386$	−6.12046	+	10.6009i	−0.311523	+	0.539574i
$387$		0			0
$388$	10.1378	−	5.85305i	0.514668	−	0.297144i
$389$	−5.24585			−0.265975			−0.132988	−	0.991118i	$-0.542457\pi$
$389$	−5.24585			−0.265975			−0.132988	+	0.991118i	$0.542457\pi$
$390$		0			0
$391$	42.8130			2.16514
$392$	−0.866025	+	0.500000i	−0.0437409	+	0.0252538i
$393$		0			0
$394$	2.72876	−	4.72634i	0.137473	−	0.238110i
$395$			5.89215i			0.296466i
$396$		0			0
$397$	21.2432	+	12.2648i	1.06617	+	0.615552i	0.927132	−	0.374736i	$-0.122266\pi$
$397$	21.2432	+	12.2648i	1.06617	+	0.615552i	0.139035	+	0.990287i	$0.455600\pi$
$398$		−	12.8166i		−	0.642440i
$399$		0			0
$400$	−2.09334	−	3.62578i	−0.104667	−	0.181289i
$401$	−3.69916	+	2.13571i	−0.184727	+	0.106652i	−0.589512	−	0.807760i	$-0.700680\pi$
$401$	−3.69916	+	2.13571i	−0.184727	+	0.106652i	0.404784	+	0.914412i	$0.367347\pi$
$402$		0			0
$403$	−3.12573	+	0.372689i	−0.155704	+	0.0185650i
$404$	10.7429			0.534479
$405$		0			0
$406$	1.09643	+	1.89907i	0.0544149	+	0.0942493i
$407$	0.312940	−	0.542028i	0.0155119	−	0.0268673i
$408$		0			0
$409$	−1.39990	−	0.808235i	−0.0692208	−	0.0399646i	0.464990	−	0.885316i	$-0.346058\pi$
$409$	−1.39990	−	0.808235i	−0.0692208	−	0.0399646i	−0.534211	+	0.845351i	$0.679391\pi$
$410$	−3.12136	−	1.80212i	−0.154153	−	0.0890001i
$411$		0			0
$412$	2.40550	−	4.16644i	0.118510	−	0.205266i
$413$	4.27467	+	7.40394i	0.210343	+	0.364324i
$414$		0			0
$415$	11.9357			0.585900
$416$	1.42041	−	3.31398i	0.0696414	−	0.162481i
$417$		0			0
$418$	−23.1840	+	13.3853i	−1.13397	+	0.654697i
$419$	−13.0156	−	22.5437i	−0.635854	−	1.10133i	−0.986334	−	0.164761i	$-0.947315\pi$
$419$	−13.0156	−	22.5437i	−0.635854	−	1.10133i	0.350480	−	0.936570i	$-0.386018\pi$
$420$		0			0
$421$		−	37.5391i		−	1.82954i	−0.403971	−	0.914772i	$-0.632370\pi$
$421$		−	37.5391i		−	1.82954i	0.403971	−	0.914772i	$-0.367630\pi$
$422$	−16.7239	−	9.65552i	−0.814104	−	0.470023i
$423$		0			0
$424$		−	1.69699i		−	0.0824129i
$425$	−10.6047	+	18.3679i	−0.514404	+	0.890974i
$426$		0			0
$427$	−7.21780	+	4.16720i	−0.349294	+	0.201665i
$428$	13.6530			0.659944
$429$		0			0
$430$	−6.95183			−0.335247
$431$	−18.6662	+	10.7769i	−0.899118	+	0.519106i	−0.876914	−	0.480647i	$-0.840402\pi$
$431$	−18.6662	+	10.7769i	−0.899118	+	0.519106i	−0.0222041	+	0.999753i	$0.507068\pi$
$432$		0			0
$433$	1.59958	−	2.77056i	0.0768710	−	0.133145i	−0.825027	−	0.565093i	$-0.808840\pi$
$433$	1.59958	−	2.77056i	0.0768710	−	0.133145i	0.901898	+	0.431948i	$0.142174\pi$
$434$			0.873062i			0.0419083i
$435$		0			0
$436$	−4.43186	−	2.55874i	−0.212248	−	0.122541i
$437$		−	52.1638i		−	2.49534i
$438$		0			0
$439$	13.3114	+	23.0560i	0.635317	+	1.10040i	0.986448	+	0.164075i	$0.0524638\pi$
$439$	13.3114	+	23.0560i	0.635317	+	1.10040i	−0.351131	+	0.936326i	$0.614203\pi$
$440$	−3.38739	+	1.95571i	−0.161488	+	0.0932349i
$441$		0			0
$442$	−18.1370	+	2.16252i	−0.862688	+	0.102861i
$443$	−9.09867			−0.432291			−0.216145	−	0.976361i	$-0.569348\pi$
$443$	−9.09867			−0.432291			−0.216145	+	0.976361i	$0.569348\pi$
$444$		0			0
$445$	3.51347	+	6.08551i	0.166555	+	0.288481i
$446$	5.31785	−	9.21079i	0.251808	−	0.436144i
$447$		0			0
$448$	−0.866025	−	0.500000i	−0.0409159	−	0.0236228i
$449$	−6.08550	−	3.51346i	−0.287192	−	0.165811i	0.349483	−	0.936943i	$-0.386357\pi$
$449$	−6.08550	−	3.51346i	−0.287192	−	0.165811i	−0.636675	+	0.771132i	$0.719691\pi$
$450$		0			0
$451$	8.66681	−	15.0114i	0.408104	−	0.706858i
$452$	−8.96603	−	15.5296i	−0.421726	−	0.730452i
$453$		0			0
$454$	22.7217			1.06638
$455$	2.98867	+	1.28098i	0.140111	+	0.0600533i
$456$		0			0
$457$	−16.5853	+	9.57556i	−0.775830	+	0.447926i	−0.834950	−	0.550325i	$-0.814504\pi$
$457$	−16.5853	+	9.57556i	−0.775830	+	0.447926i	0.0591204	+	0.998251i	$0.481170\pi$
$458$	10.1547	+	17.5885i	0.474498	+	0.821855i
$459$		0			0
$460$		−	7.62159i		−	0.355359i
$461$	2.82026	+	1.62828i	0.131353	+	0.0758365i	0.564236	−	0.825613i	$-0.309171\pi$
$461$	2.82026	+	1.62828i	0.131353	+	0.0758365i	−0.432884	+	0.901450i	$0.642504\pi$
$462$		0			0
$463$		−	21.2761i		−	0.988786i	−0.869238	−	0.494393i	$-0.835390\pi$
$463$		−	21.2761i		−	0.988786i	0.869238	−	0.494393i	$-0.164610\pi$
$464$	−1.09643	+	1.89907i	−0.0509004	+	0.0881621i
$465$		0			0
$466$	9.21851	−	5.32231i	0.427039	−	0.246551i
$467$	3.33171			0.154173			0.0770866	−	0.997024i	$-0.475438\pi$
$467$	3.33171			0.154173			0.0770866	+	0.997024i	$0.475438\pi$
$468$		0			0
$469$	−10.3828			−0.479435
$470$	−2.28146	+	1.31720i	−0.105236	+	0.0607580i
$471$		0			0
$472$	−4.27467	+	7.40394i	−0.196757	+	0.340794i
$473$		−	33.4331i		−	1.53725i
$474$		0			0
$475$	22.3797	+	12.9209i	1.02685	+	0.592852i
$476$			5.06592i			0.232196i
$477$		0			0
$478$	0.155782	+	0.269822i	0.00712530	+	0.0123414i
$479$	0.160402	−	0.0926079i	0.00732894	−	0.00423136i	−0.496331	−	0.868133i	$-0.665320\pi$
$479$	0.160402	−	0.0926079i	0.00732894	−	0.00423136i	0.503660	+	0.863902i	$0.331986\pi$
$480$		0			0
$481$	−0.311670	−	0.416627i	−0.0142109	−	0.0189965i
$482$	25.2995			1.15236
$483$		0			0
$484$	−3.90550	−	6.76452i	−0.177523	−	0.307478i
$485$	−5.27851	+	9.14264i	−0.239685	+	0.415146i
$486$		0			0
$487$	−27.0466	−	15.6154i	−1.22560	−	0.707601i	−0.259494	−	0.965745i	$-0.583556\pi$
$487$	−27.0466	−	15.6154i	−1.22560	−	0.707601i	−0.966106	+	0.258144i	$0.916889\pi$
$488$	−7.21780	−	4.16720i	−0.326735	−	0.188640i
$489$		0			0
$490$	0.450919	−	0.781015i	0.0203705	−	0.0352827i
$491$	−13.4236	−	23.2504i	−0.605799	−	1.04927i	−0.991925	−	0.126829i	$-0.959520\pi$
$491$	−13.4236	−	23.2504i	−0.605799	−	1.04927i	0.386126	−	0.922446i	$-0.373813\pi$
$492$		0			0
$493$	11.1088			0.500317
$494$	2.63484	+	22.0983i	0.118547	+	0.994250i
$495$		0			0
$496$	−0.756094	+	0.436531i	−0.0339496	+	0.0196008i
$497$	1.63928	+	2.83932i	0.0735317	+	0.127361i
$498$		0			0
$499$			15.2869i			0.684337i	0.939639	+	0.342168i	$0.111161\pi$
$499$			15.2869i			0.684337i	−0.939639	+	0.342168i	$0.888839\pi$
$500$	7.17494	+	4.14246i	0.320873	+	0.185256i
$501$		0			0
$502$		−	8.04030i		−	0.358856i
$503$	−13.0551	+	22.6121i	−0.582097	+	1.00822i	0.413133	+	0.910671i	$0.364434\pi$
$503$	−13.0551	+	22.6121i	−0.582097	+	1.00822i	−0.995230	+	0.0975513i	$0.968899\pi$
$504$		0			0
$505$	−8.39036	+	4.84418i	−0.373366	+	0.215563i
$506$	36.6541			1.62947
$507$		0			0
$508$	−19.5136			−0.865777
$509$	−14.7459	+	8.51357i	−0.653602	+	0.377357i	−0.789835	−	0.613320i	$-0.789834\pi$
$509$	−14.7459	+	8.51357i	−0.653602	+	0.377357i	0.136233	+	0.990677i	$0.456500\pi$
$510$		0			0
$511$	0.269511	−	0.466808i	0.0119225	−	0.0206504i
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	−14.6641	−	8.46634i	−0.646807	−	0.373434i
$515$			4.33874i			0.191188i
$516$		0			0
$517$	−6.33475	−	10.9721i	−0.278602	−	0.482553i
$518$	−0.124973	+	0.0721531i	−0.00549099	+	0.00317023i
$519$		0			0
$520$	0.384973	+	3.22876i	0.0168822	+	0.141590i
$521$	18.7760			0.822593			0.411297	−	0.911502i	$-0.365076\pi$
$521$	18.7760			0.822593			0.411297	+	0.911502i	$0.365076\pi$
$522$		0			0
$523$	1.51624	+	2.62620i	0.0663004	+	0.114836i	0.897270	−	0.441482i	$-0.145547\pi$
$523$	1.51624	+	2.62620i	0.0663004	+	0.114836i	−0.830970	+	0.556318i	$0.812214\pi$
$524$	10.3248	−	17.8831i	0.451042	−	0.781227i
$525$		0			0
$526$	−8.93817	−	5.16045i	−0.389723	−	0.225006i
$527$	3.83031	+	2.21143i	0.166851	+	0.0963315i
$528$		0			0
$529$	−24.2111	+	41.9349i	−1.05266	+	1.82326i
$530$	0.765204	+	1.32537i	0.0332383	+	0.0575705i
$531$		0			0
$532$	6.17238			0.267607
$533$	−8.63164	−	11.5384i	−0.373878	−	0.499783i
$534$		0			0
$535$	−10.6632	+	6.15642i	−0.461011	+	0.266165i
$536$	−5.19142	−	8.99180i	−0.224235	−	0.388387i
$537$		0			0
$538$		−	6.13999i		−	0.264714i
$539$	3.75609	+	2.16858i	0.161786	+	0.0934074i
$540$		0			0
$541$		−	6.11845i		−	0.263053i	−0.991313	−	0.131526i	$-0.958012\pi$
$541$		−	6.11845i		−	0.263053i	0.991313	−	0.131526i	$-0.0419878\pi$
$542$	−5.33860	+	9.24673i	−0.229313	+	0.397181i
$543$		0			0
$544$	−4.38722	+	2.53296i	−0.188100	+	0.108600i
$545$	4.61513			0.197691
$546$		0			0
$547$	−37.4754			−1.60233			−0.801166	−	0.598442i	$-0.795786\pi$
$547$	−37.4754			−1.60233			−0.801166	+	0.598442i	$0.795786\pi$
$548$	−2.76224	+	1.59478i	−0.117997	+	0.0681257i
$549$		0			0
$550$	−9.07917	+	15.7256i	−0.387137	+	0.670541i
$551$		−	13.5352i		−	0.576617i
$552$		0			0
$553$	5.65817	+	3.26674i	0.240610	+	0.138916i
$554$			21.9090i			0.930823i
$555$		0			0
$556$	−0.297855	−	0.515900i	−0.0126319	−	0.0218790i
$557$	7.69941	−	4.44526i	0.326234	−	0.188352i	−0.327934	−	0.944701i	$-0.606352\pi$
$557$	7.69941	−	4.44526i	0.326234	−	0.188352i	0.654168	+	0.756349i	$0.273019\pi$
$558$		0			0
$559$	−25.5458	−	10.9493i	−1.08047	−	0.463104i
$560$	0.901839			0.0381096
$561$		0			0
$562$	12.8860	+	22.3192i	0.543562	+	0.941477i
$563$	−8.89598	+	15.4083i	−0.374921	+	0.649382i	−0.990315	−	0.138838i	$-0.955663\pi$
$563$	−8.89598	+	15.4083i	−0.374921	+	0.649382i	0.615394	+	0.788219i	$0.288997\pi$
$564$		0			0
$565$	14.0052	+	8.08591i	0.589204	+	0.340177i
$566$	9.80937	+	5.66344i	0.412319	+	0.238052i
$567$		0			0
$568$	−1.63928	+	2.83932i	−0.0687826	+	0.119135i
$569$	−5.58684	−	9.67669i	−0.234212	−	0.405668i	0.724831	−	0.688927i	$-0.241918\pi$
$569$	−5.58684	−	9.67669i	−0.234212	−	0.405668i	−0.959044	+	0.283259i	$0.908584\pi$
$570$		0			0
$571$	−16.7239			−0.699873			−0.349936	−	0.936773i	$-0.613797\pi$
$571$	−16.7239			−0.699873			−0.349936	+	0.936773i	$0.613797\pi$
$572$	−15.5279	+	1.85143i	−0.649253	+	0.0774122i
$573$		0			0
$574$	−3.46110	+	1.99827i	−0.144464	+	0.0834061i
$575$	−17.6912	−	30.6421i	−0.737774	−	1.27786i
$576$		0			0
$577$		−	0.798887i		−	0.0332581i	−0.999862	−	0.0166291i	$-0.994707\pi$
$577$		−	0.798887i		−	0.0332581i	0.999862	−	0.0166291i	$-0.00529344\pi$
$578$	7.50285	+	4.33177i	0.312078	+	0.180178i
$579$		0			0
$580$		−	1.97760i		−	0.0821155i
$581$	6.61742	−	11.4617i	0.274537	−	0.475512i
$582$		0			0
$583$	−6.37404	+	3.68005i	−0.263986	+	0.152412i
$584$	0.539023			0.0223049
$585$		0			0
$586$	23.7459			0.980935
$587$	−6.94921	+	4.01213i	−0.286825	+	0.165598i	−0.636509	−	0.771269i	$-0.719622\pi$
$587$	−6.94921	+	4.01213i	−0.286825	+	0.165598i	0.349684	+	0.936868i	$0.386289\pi$
$588$		0			0
$589$	2.69444	−	4.66690i	0.111022	−	0.192296i
$590$		−	7.71012i		−	0.317421i
$591$		0			0
$592$	−0.124973	−	0.0721531i	−0.00513635	−	0.00296548i
$593$		−	4.93120i		−	0.202500i	−0.994861	−	0.101250i	$-0.967716\pi$
$593$		−	4.93120i		−	0.202500i	0.994861	−	0.101250i	$-0.0322842\pi$
$594$		0			0
$595$	−2.28432	−	3.95656i	−0.0936481	−	0.162203i
$596$	−9.70783	+	5.60482i	−0.397648	+	0.229582i
$597$		0			0
$598$	12.0041	−	28.0070i	0.490886	−	1.14529i
$599$	17.8249			0.728306			0.364153	−	0.931339i	$-0.381358\pi$
$599$	17.8249			0.728306			0.364153	+	0.931339i	$0.381358\pi$
$600$		0			0
$601$	0.0809165	+	0.140152i	0.00330065	+	0.00571690i	0.867671	−	0.497139i	$-0.165616\pi$
$601$	0.0809165	+	0.140152i	0.00330065	+	0.00571690i	−0.864370	+	0.502856i	$0.832283\pi$
$602$	−3.85426	+	6.67577i	−0.157088	+	0.272084i
$603$		0			0
$604$	11.3216	+	6.53653i	0.460670	+	0.265968i
$605$	6.10050	+	3.52213i	0.248021	+	0.143195i
$606$		0			0
$607$	−3.09423	+	5.35937i	−0.125591	+	0.217530i	−0.921964	−	0.387276i	$-0.873416\pi$
$607$	−3.09423	+	5.35937i	−0.125591	+	0.217530i	0.796373	+	0.604806i	$0.206749\pi$
$608$	3.08619	+	5.34544i	0.125162	+	0.216786i
$609$		0			0
$610$	7.51629			0.304326
$611$	−10.4583	+	1.24697i	−0.423097	+	0.0504469i
$612$		0			0
$613$	32.2269	−	18.6062i	1.30163	−	0.751497i	0.320947	−	0.947097i	$-0.395999\pi$
$613$	32.2269	−	18.6062i	1.30163	−	0.751497i	0.980684	+	0.195600i	$0.0626654\pi$
$614$	−3.34405	−	5.79207i	−0.134955	−	0.233749i
$615$		0			0
$616$			4.33716i			0.174749i
$617$	5.78536	+	3.34018i	0.232910	+	0.134471i	0.611914	−	0.790924i	$-0.290400\pi$
$617$	5.78536	+	3.34018i	0.232910	+	0.134471i	−0.379004	+	0.925395i	$0.623733\pi$
$618$		0			0
$619$			23.7344i			0.953965i	0.878913	+	0.476982i	$0.158269\pi$
$619$			23.7344i			0.953965i	−0.878913	+	0.476982i	$0.841731\pi$
$620$	0.393681	−	0.681875i	0.0158106	−	0.0273848i
$621$		0			0
$622$	7.95639	−	4.59362i	0.319022	−	0.184187i
$623$	7.79180			0.312172
$624$		0			0
$625$	13.4618			0.538471
$626$	14.8637	−	8.58157i	0.594074	−	0.342989i
$627$		0			0
$628$	8.96225	−	15.5231i	0.357633	−	0.619438i
$629$			0.731044i			0.0291486i
$630$		0			0
$631$	19.9348	+	11.5093i	0.793590	+	0.458180i	0.841225	−	0.540685i	$-0.181835\pi$
$631$	19.9348	+	11.5093i	0.793590	+	0.458180i	−0.0476346	+	0.998865i	$0.515168\pi$
$632$			6.53349i			0.259888i
$633$		0			0
$634$	1.88124	+	3.25840i	0.0747135	+	0.129408i
$635$	15.2404	−	8.79907i	0.604798	−	0.349181i
$636$		0			0
$637$	2.88710	−	2.15978i	0.114391	−	0.0855737i
$638$	9.51078			0.376536
$639$		0			0
$640$	0.450919	+	0.781015i	0.0178242	+	0.0308723i
$641$	−6.32539	+	10.9559i	−0.249838	+	0.432732i	−0.963481	−	0.267778i	$-0.913711\pi$
$641$	−6.32539	+	10.9559i	−0.249838	+	0.432732i	0.713643	+	0.700510i	$0.247044\pi$
$642$		0			0
$643$	−13.1971	−	7.61938i	−0.520445	−	0.300479i	0.216672	−	0.976244i	$-0.430480\pi$
$643$	−13.1971	−	7.61938i	−0.520445	−	0.300479i	−0.737117	+	0.675766i	$0.763813\pi$
$644$	−7.31893	−	4.22559i	−0.288406	−	0.166511i
$645$		0			0
$646$	15.6344	−	27.0796i	0.615127	−	1.06543i
$647$	14.6821	+	25.4301i	0.577213	+	0.999762i	0.995797	+	0.0915840i	$0.0291930\pi$
$647$	14.6821	+	25.4301i	0.577213	+	0.999762i	−0.418585	+	0.908178i	$0.637474\pi$
$648$		0			0
$649$	37.0799			1.45551
$650$	9.04233	+	12.0874i	0.354669	+	0.474106i
$651$		0			0
$652$	17.5958	−	10.1589i	0.689105	−	0.397855i
$653$	−14.5106	−	25.1330i	−0.567842	−	0.983532i	−0.996779	−	0.0801974i	$-0.974445\pi$
$653$	−14.5106	−	25.1330i	−0.567842	−	0.983532i	0.428937	−	0.903335i	$-0.358888\pi$
$654$		0			0
$655$			18.6226i			0.727647i
$656$	−3.46110	−	1.99827i	−0.135133	−	0.0780192i
$657$		0			0
$658$			2.92115i			0.113878i
$659$	3.98651	−	6.90484i	0.155293	−	0.268975i	−0.777873	−	0.628422i	$-0.783701\pi$
$659$	3.98651	−	6.90484i	0.155293	−	0.268975i	0.933166	+	0.359447i	$0.117035\pi$
$660$		0			0
$661$	3.40668	−	1.96685i	0.132505	−	0.0765015i	−0.432282	−	0.901738i	$-0.642292\pi$
$661$	3.40668	−	1.96685i	0.132505	−	0.0765015i	0.564787	+	0.825237i	$0.308958\pi$
$662$	32.2257			1.25249
$663$		0			0
$664$	13.2348			0.513611
$665$	−4.82072	+	2.78325i	−0.186940	+	0.107930i
$666$		0			0
$667$	−9.26611	+	16.0494i	−0.358785	+	0.621434i
$668$		−	3.23051i		−	0.124992i
$669$		0			0
$670$	8.10916	+	4.68182i	0.313284	+	0.180875i
$671$			36.1477i			1.39547i
$672$		0			0
$673$	18.1599	+	31.4539i	0.700014	+	1.21246i	0.968461	+	0.249166i	$0.0801563\pi$
$673$	18.1599	+	31.4539i	0.700014	+	1.21246i	−0.268447	+	0.963295i	$0.586510\pi$
$674$	2.61282	−	1.50851i	0.100642	−	0.0581058i
$675$		0			0
$676$	−3.67069	+	12.4710i	−0.141180	+	0.479654i
$677$	21.1068			0.811201			0.405600	−	0.914051i	$-0.367062\pi$
$677$	21.1068			0.811201			0.405600	+	0.914051i	$0.367062\pi$
$678$		0			0
$679$	5.85305	+	10.1378i	0.224619	+	0.389052i
$680$	2.28432	−	3.95656i	0.0875997	−	0.151727i
$681$		0			0
$682$	3.27931	+	1.89331i	0.125571	+	0.0724985i
$683$	22.8854	+	13.2129i	0.875685	+	0.505577i	0.869233	−	0.494402i	$-0.164613\pi$
$683$	22.8854	+	13.2129i	0.875685	+	0.505577i	0.00645161	+	0.999979i	$0.497946\pi$
$684$		0			0
$685$	1.43824	−	2.49110i	0.0549522	−	0.0951799i
$686$	−0.500000	−	0.866025i	−0.0190901	−	0.0330650i
$687$		0			0
$688$	−7.70851			−0.293884
$689$	0.724402	+	6.07553i	0.0275975	+	0.231459i
$690$		0			0
$691$	0.675291	−	0.389880i	0.0256893	−	0.0148317i	−0.487100	−	0.873346i	$-0.661945\pi$
$691$	0.675291	−	0.389880i	0.0256893	−	0.0148317i	0.512790	+	0.858514i	$0.328612\pi$
$692$	−4.58522	−	7.94183i	−0.174304	−	0.301903i
$693$		0			0
$694$			0.468540i			0.0177855i
$695$	0.465259	+	0.268617i	0.0176483	+	0.0101892i
$696$		0			0
$697$			20.2461i			0.766877i
$698$	16.1106	−	27.9044i	0.609795	−	1.05620i
$699$		0			0
$700$	3.62578	−	2.09334i	0.137041	−	0.0791209i
$701$	−21.5491			−0.813899			−0.406950	−	0.913451i	$-0.633408\pi$
$701$	−21.5491			−0.813899			−0.406950	+	0.913451i	$0.633408\pi$
$702$		0			0
$703$	0.890713			0.0335939
$704$	−3.75609	+	2.16858i	−0.141563	+	0.0817315i
$705$		0			0
$706$	−6.55771	+	11.3583i	−0.246803	+	0.427474i
$707$			10.7429i			0.404028i
$708$		0			0
$709$	−3.92952	−	2.26871i	−0.147576	−	0.0852031i	0.424394	−	0.905478i	$-0.360487\pi$
$709$	−3.92952	−	2.26871i	−0.147576	−	0.0852031i	−0.571970	+	0.820275i	$0.693821\pi$
$710$		−	2.95673i		−	0.110964i
$711$		0			0
$712$	3.89590	+	6.74790i	0.146005	+	0.252888i
$713$	−6.38988	+	3.68920i	−0.239303	+	0.138162i
$714$		0			0
$715$	11.2927	−	8.44782i	0.422322	−	0.315931i
$716$	16.9549			0.633636
$717$		0			0
$718$	−2.18990	−	3.79302i	−0.0817265	−	0.141554i
$719$	7.30036	−	12.6446i	0.272258	−	0.471564i	−0.697182	−	0.716894i	$-0.745563\pi$
$719$	7.30036	−	12.6446i	0.272258	−	0.471564i	0.969440	+	0.245330i	$0.0788964\pi$
$720$		0			0
$721$	4.16644	+	2.40550i	0.155166	+	0.0895854i
$722$	−16.5396	−	9.54914i	−0.615540	−	0.355382i
$723$		0			0
$724$	−1.32871	+	2.30140i	−0.0493813	+	0.0855309i
$725$	−4.59040	−	7.95081i	−0.170483	−	0.295286i
$726$		0			0
$727$	30.6315			1.13606			0.568030	−	0.823008i	$-0.307706\pi$
$727$	30.6315			1.13606			0.568030	+	0.823008i	$0.307706\pi$
$728$	3.31398	+	1.42041i	0.122824	+	0.0526439i
$729$		0			0
$730$	−0.420985	+	0.243056i	−0.0155814	+	0.00899590i
$731$	19.5254	+	33.8189i	0.722171	+	1.25084i
$732$		0			0
$733$		−	17.7195i		−	0.654484i	−0.944941	−	0.327242i	$-0.893881\pi$
$733$		−	17.7195i		−	0.654484i	0.944941	−	0.327242i	$-0.106119\pi$
$734$	22.3597	+	12.9094i	0.825313	+	0.476495i
$735$		0			0
$736$		−	8.45117i		−	0.311514i
$737$	−22.5160	+	38.9989i	−0.829389	+	1.43654i
$738$		0			0
$739$	−9.05014	+	5.22510i	−0.332915	+	0.192208i	−0.657134	−	0.753773i	$-0.728232\pi$
$739$	−9.05014	+	5.22510i	−0.332915	+	0.192208i	0.324220	+	0.945982i	$0.394898\pi$
$740$	0.130141			0.00478408
$741$		0			0
$742$	1.69699			0.0622983
$743$	−42.0103	+	24.2547i	−1.54121	+	0.889818i	−0.542447	+	0.840090i	$0.682502\pi$
$743$	−42.0103	+	24.2547i	−1.54121	+	0.889818i	−0.998763	+	0.0497278i	$0.984165\pi$
$744$		0			0
$745$	5.05464	−	8.75490i	0.185188	−	0.320755i
$746$		−	30.6285i		−	1.12139i
$747$		0			0
$748$	19.0281	+	10.9859i	0.695735	+	0.401683i
$749$			13.6530i			0.498871i
$750$		0			0
$751$	15.7278	+	27.2413i	0.573914	+	0.994049i	0.996159	+	0.0875667i	$0.0279091\pi$
$751$	15.7278	+	27.2413i	0.573914	+	0.994049i	−0.422244	+	0.906482i	$0.638758\pi$
$752$	−2.52979	+	1.46057i	−0.0922519	+	0.0532617i
$753$		0			0
$754$	3.11476	−	7.26708i	0.113433	−	0.264651i
$755$	−11.7898			−0.429075
$756$		0			0
$757$	−24.3442	−	42.1654i	−0.884805	−	1.53253i	−0.845937	−	0.533283i	$-0.820958\pi$
$757$	−24.3442	−	42.1654i	−0.884805	−	1.53253i	−0.0388676	−	0.999244i	$-0.512375\pi$
$758$	19.0762	−	33.0409i	0.692877	−	1.20010i
$759$		0			0
$760$	−4.82072	−	2.78325i	−0.174866	−	0.100959i
$761$	40.3350	+	23.2874i	1.46214	+	0.844169i	0.999110	−	0.0421718i	$-0.0134277\pi$
$761$	40.3350	+	23.2874i	1.46214	+	0.844169i	0.463033	+	0.886341i	$0.346761\pi$
$762$		0			0
$763$	2.55874	−	4.43186i	0.0926325	−	0.160444i
$764$	12.2430	+	21.2056i	0.442937	+	0.767190i
$765$		0			0
$766$	−31.9602			−1.15477
$767$	12.1436	−	28.3323i	0.438479	−	1.02302i
$768$		0			0
$769$	−24.1069	+	13.9181i	−0.869315	+	0.501899i	−0.867121	−	0.498098i	$-0.834032\pi$
$769$	−24.1069	+	13.9181i	−0.869315	+	0.501899i	−0.00219468	+	0.999998i	$0.500699\pi$
$770$	−1.95571	−	3.38739i	−0.0704789	−	0.122073i
$771$		0			0
$772$		−	12.2409i		−	0.440560i
$773$	−24.6578	−	14.2362i	−0.886880	−	0.512040i	−0.0139594	−	0.999903i	$-0.504444\pi$
$773$	−24.6578	−	14.2362i	−0.886880	−	0.512040i	−0.872921	+	0.487862i	$0.837777\pi$
$774$		0			0
$775$		−	3.65524i		−	0.131300i
$776$	−5.85305	+	10.1378i	−0.210112	+	0.363925i
$777$		0			0
$778$	4.54304	−	2.62292i	0.162876	−	0.0940364i
$779$	24.6681			0.883828
$780$		0			0
$781$	14.2196			0.508819
$782$	−37.0771	+	21.4065i

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:	\( N \)	\(=\)	\( 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1638.bj (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +0.901839i q^{5} +(0.866025 + 0.500000i) q^{7} +1.00000i q^{8} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +0.901839i q^{5} +(0.866025 + 0.500000i) q^{7} +1.00000i q^{8} +(-0.450919 - 0.781015i) q^{10} +(3.75609 - 2.16858i) q^{11} +(-0.426876 - 3.58019i) q^{13} -1.00000 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-2.53296 + 4.38722i) q^{17} +(5.34544 + 3.08619i) q^{19} +(0.781015 + 0.450919i) q^{20} +(-2.16858 + 3.75609i) q^{22} +(-4.22559 - 7.31893i) q^{23} +4.18669 q^{25} +(2.15978 + 2.88710i) q^{26} +(0.866025 - 0.500000i) q^{28} +(-1.09643 - 1.89907i) q^{29} -0.873062i q^{31} +(0.866025 + 0.500000i) q^{32} -5.06592i q^{34} +(-0.450919 + 0.781015i) q^{35} +(0.124973 - 0.0721531i) q^{37} -6.17238 q^{38} -0.901839 q^{40} +(3.46110 - 1.99827i) q^{41} +(3.85426 - 6.67577i) q^{43} -4.33716i q^{44} +(7.31893 + 4.22559i) q^{46} -2.92115i q^{47} +(0.500000 + 0.866025i) q^{49} +(-3.62578 + 2.09334i) q^{50} +(-3.31398 - 1.42041i) q^{52} -1.69699 q^{53} +(1.95571 + 3.38739i) q^{55} +(-0.500000 + 0.866025i) q^{56} +(1.89907 + 1.09643i) q^{58} +(7.40394 + 4.27467i) q^{59} +(-4.16720 + 7.21780i) q^{61} +(0.436531 + 0.756094i) q^{62} -1.00000 q^{64} +(3.22876 - 0.384973i) q^{65} +(-8.99180 + 5.19142i) q^{67} +(2.53296 + 4.38722i) q^{68} -0.901839i q^{70} +(2.83932 + 1.63928i) q^{71} -0.539023i q^{73} +(-0.0721531 + 0.124973i) q^{74} +(5.34544 - 3.08619i) q^{76} +4.33716 q^{77} +6.53349 q^{79} +(0.781015 - 0.450919i) q^{80} +(-1.99827 + 3.46110i) q^{82} -13.2348i q^{83} +(-3.95656 - 2.28432i) q^{85} +7.70851i q^{86} +(2.16858 + 3.75609i) q^{88} +(6.74790 - 3.89590i) q^{89} +(1.42041 - 3.31398i) q^{91} -8.45117 q^{92} +(1.46057 + 2.52979i) q^{94} +(-2.78325 + 4.82072i) q^{95} +(10.1378 + 5.85305i) q^{97} +(-0.866025 - 0.500000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{4}+O(q^{10}) \) 12 * q + 6 * q^4	\( 12 q + 6 q^{4} - 2 q^{10} + 18 q^{11} - 8 q^{13} - 12 q^{14} - 6 q^{16} - 4 q^{17} + 12 q^{19} - 2 q^{22} + 6 q^{23} - 24 q^{25} + 14 q^{26} + 10 q^{29} - 2 q^{35} - 6 q^{37} - 8 q^{38} - 4 q^{40} + 24 q^{41} + 26 q^{43} - 6 q^{46} + 6 q^{49} + 12 q^{50} - 4 q^{52} - 36 q^{53} - 6 q^{55} - 6 q^{56} + 24 q^{58} - 6 q^{59} - 28 q^{61} + 2 q^{62} - 12 q^{64} + 34 q^{65} - 42 q^{67} + 4 q^{68} - 48 q^{71} + 12 q^{76} + 4 q^{77} + 44 q^{79} + 6 q^{82} + 54 q^{85} + 2 q^{88} - 12 q^{89} - 16 q^{91} + 12 q^{92} + 8 q^{94} - 32 q^{95} + 60 q^{97}+O(q^{100}) \) 12 * q + 6 * q^4 - 2 * q^10 + 18 * q^11 - 8 * q^13 - 12 * q^14 - 6 * q^16 - 4 * q^17 + 12 * q^19 - 2 * q^22 + 6 * q^23 - 24 * q^25 + 14 * q^26 + 10 * q^29 - 2 * q^35 - 6 * q^37 - 8 * q^38 - 4 * q^40 + 24 * q^41 + 26 * q^43 - 6 * q^46 + 6 * q^49 + 12 * q^50 - 4 * q^52 - 36 * q^53 - 6 * q^55 - 6 * q^56 + 24 * q^58 - 6 * q^59 - 28 * q^61 + 2 * q^62 - 12 * q^64 + 34 * q^65 - 42 * q^67 + 4 * q^68 - 48 * q^71 + 12 * q^76 + 4 * q^77 + 44 * q^79 + 6 * q^82 + 54 * q^85 + 2 * q^88 - 12 * q^89 - 16 * q^91 + 12 * q^92 + 8 * q^94 - 32 * q^95 + 60 * q^97

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