LMFDB - Embedded newform 1638.2.bj.g.127.3

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			127.3
Root			$0.500000 + 1.69027i$ of defining polynomial
Character	$\chi$	$=$	1638.127
Dual form			1638.2.bj.g.1135.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +3.48754i q^{5} +(0.866025 + 0.500000i) q^{7} +1.00000i q^{8} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +3.48754i q^{5} +(0.866025 + 0.500000i) q^{7} +1.00000i q^{8} +(-1.74377 - 3.02030i) q^{10} +(2.32244 - 1.34086i) q^{11} +(-3.15338 + 1.74819i) q^{13} -1.00000 q^{14} +(-0.500000 - 0.866025i) q^{16} +(2.95758 - 5.12268i) q^{17} +(4.50154 + 2.59896i) q^{19} +(3.02030 + 1.74377i) q^{20} +(-1.34086 + 2.32244i) q^{22} +(3.52634 + 6.10780i) q^{23} -7.16292 q^{25} +(1.85681 - 3.09067i) q^{26} +(0.866025 - 0.500000i) q^{28} +(3.56639 + 6.17717i) q^{29} +0.782383i q^{31} +(0.866025 + 0.500000i) q^{32} +5.91517i q^{34} +(-1.74377 + 3.02030i) q^{35} +(6.76756 - 3.90725i) q^{37} -5.19793 q^{38} -3.48754 q^{40} +(-0.136579 + 0.0788541i) q^{41} +(-0.165101 + 0.285963i) q^{43} -2.68172i q^{44} +(-6.10780 - 3.52634i) q^{46} +1.60161i q^{47} +(0.500000 + 0.866025i) q^{49} +(6.20327 - 3.58146i) q^{50} +(-0.0627130 + 3.60501i) q^{52} -3.92601 q^{53} +(4.67630 + 8.09958i) q^{55} +(-0.500000 + 0.866025i) q^{56} +(-6.17717 - 3.56639i) q^{58} +(-8.26207 - 4.77011i) q^{59} +(-7.70525 + 13.3459i) q^{61} +(-0.391192 - 0.677564i) q^{62} -1.00000 q^{64} +(-6.09688 - 10.9975i) q^{65} +(0.837243 - 0.483382i) q^{67} +(-2.95758 - 5.12268i) q^{68} -3.48754i q^{70} +(-3.62568 - 2.09329i) q^{71} -15.0361i q^{73} +(-3.90725 + 6.76756i) q^{74} +(4.50154 - 2.59896i) q^{76} +2.68172 q^{77} -0.293356 q^{79} +(3.02030 - 1.74377i) q^{80} +(0.0788541 - 0.136579i) q^{82} +2.87495i q^{83} +(17.8656 + 10.3147i) q^{85} -0.330202i q^{86} +(1.34086 + 2.32244i) q^{88} +(-4.51481 + 2.60662i) q^{89} +(-3.60501 - 0.0627130i) q^{91} +7.05268 q^{92} +(-0.800806 - 1.38704i) q^{94} +(-9.06398 + 15.6993i) q^{95} +(-2.73617 - 1.57973i) q^{97} +(-0.866025 - 0.500000i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$			3.48754i			1.55967i	0.625983	+	0.779837i	$0.284698\pi$
$5$			3.48754i			1.55967i	−0.625983	+	0.779837i	$0.715302\pi$
$6$		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
$10$	−1.74377	−	3.02030i	−0.551428	−	0.955101i
$11$	2.32244	−	1.34086i	0.700241	−	0.404284i	−0.107196	−	0.994238i	$-0.534187\pi$
$11$	2.32244	−	1.34086i	0.700241	−	0.404284i	0.807437	+	0.589954i	$0.200854\pi$
$12$		0			0
$13$	−3.15338	+	1.74819i	−0.874591	+	0.484861i
$13$	−3.15338	+	1.74819i	−0.874591	+	0.484861i
$14$	−1.00000			−0.267261
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	2.95758	−	5.12268i	0.717319	−	1.24243i	−0.244739	−	0.969589i	$-0.578702\pi$
$17$	2.95758	−	5.12268i	0.717319	−	1.24243i	0.962058	−	0.272844i	$-0.0879644\pi$
$18$		0			0
$19$	4.50154	+	2.59896i	1.03272	+	0.596243i	0.917764	−	0.397127i	$-0.129993\pi$
$19$	4.50154	+	2.59896i	1.03272	+	0.596243i	0.114960	+	0.993370i	$0.463326\pi$
$20$	3.02030	+	1.74377i	0.675359	+	0.389919i
$21$		0			0
$22$	−1.34086	+	2.32244i	−0.285872	+	0.495145i
$23$	3.52634	+	6.10780i	0.735292	+	1.27356i	0.954595	+	0.297907i	$0.0962885\pi$
$23$	3.52634	+	6.10780i	0.735292	+	1.27356i	−0.219303	+	0.975657i	$0.570378\pi$
$24$		0			0
$25$	−7.16292			−1.43258
$26$	1.85681	−	3.09067i	0.364151	−	0.606130i
$27$		0			0
$28$	0.866025	−	0.500000i	0.163663	−	0.0944911i
$29$	3.56639	+	6.17717i	0.662262	+	1.14707i	0.980020	+	0.198900i	$0.0637369\pi$
$29$	3.56639	+	6.17717i	0.662262	+	1.14707i	−0.317758	+	0.948172i	$0.602930\pi$
$30$		0			0
$31$			0.782383i			0.140520i	0.997529	+	0.0702601i	$0.0223829\pi$
$31$			0.782383i			0.140520i	−0.997529	+	0.0702601i	$0.977617\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$		0			0
$34$			5.91517i			1.01444i
$35$	−1.74377	+	3.02030i	−0.294751	+	0.510523i
$36$		0			0
$37$	6.76756	−	3.90725i	1.11258	−	0.642348i	0.173083	−	0.984907i	$-0.444627\pi$
$37$	6.76756	−	3.90725i	1.11258	−	0.642348i	0.939496	+	0.342559i	$0.111294\pi$
$38$	−5.19793			−0.843215
$39$		0			0
$40$	−3.48754			−0.551428
$41$	−0.136579	+	0.0788541i	−0.0213301	+	0.0123149i	−0.510627	−	0.859802i	$-0.670587\pi$
$41$	−0.136579	+	0.0788541i	−0.0213301	+	0.0123149i	0.489297	+	0.872117i	$0.337253\pi$
$42$		0			0
$43$	−0.165101	+	0.285963i	−0.0251777	+	0.0436090i	−0.878340	−	0.478037i	$-0.841348\pi$
$43$	−0.165101	+	0.285963i	−0.0251777	+	0.0436090i	0.853162	+	0.521646i	$0.174682\pi$
$44$		−	2.68172i		−	0.404284i
$45$		0			0
$46$	−6.10780	−	3.52634i	−0.900546	−	0.519930i
$47$			1.60161i			0.233619i	0.993154	+	0.116810i	$0.0372667\pi$
$47$			1.60161i			0.233619i	−0.993154	+	0.116810i	$0.962733\pi$
$48$		0			0
$49$	0.500000	+	0.866025i	0.0714286	+	0.123718i
$50$	6.20327	−	3.58146i	0.877275	−	0.506495i
$51$		0			0
$52$	−0.0627130	+	3.60501i	−0.00869673	+	0.499924i
$53$	−3.92601			−0.539279			−0.269639	−	0.962961i	$-0.586905\pi$
$53$	−3.92601			−0.539279			−0.269639	+	0.962961i	$0.586905\pi$
$54$		0			0
$55$	4.67630	+	8.09958i	0.630552	+	1.09215i
$56$	−0.500000	+	0.866025i	−0.0668153	+	0.115728i
$57$		0			0
$58$	−6.17717	−	3.56639i	−0.811102	−	0.468290i
$59$	−8.26207	−	4.77011i	−1.07563	−	0.621015i	−0.145915	−	0.989297i	$-0.546613\pi$
$59$	−8.26207	−	4.77011i	−1.07563	−	0.621015i	−0.929714	+	0.368282i	$0.879946\pi$
$60$		0			0
$61$	−7.70525	+	13.3459i	−0.986556	+	1.70877i	−0.351752	+	0.936093i	$0.614414\pi$
$61$	−7.70525	+	13.3459i	−0.986556	+	1.70877i	−0.634805	+	0.772673i	$0.718919\pi$
$62$	−0.391192	−	0.677564i	−0.0496814	−	0.0860507i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−6.09688	−	10.9975i	−0.756225	−	1.36408i
$66$		0			0
$67$	0.837243	−	0.483382i	0.102286	−	0.0590546i	−0.447985	−	0.894041i	$-0.647858\pi$
$67$	0.837243	−	0.483382i	0.102286	−	0.0590546i	0.550270	+	0.834987i	$0.314525\pi$
$68$	−2.95758	−	5.12268i	−0.358660	−	0.621217i
$69$		0			0
$70$		−	3.48754i		−	0.416840i
$71$	−3.62568	−	2.09329i	−0.430289	−	0.248428i	0.269181	−	0.963090i	$-0.413247\pi$
$71$	−3.62568	−	2.09329i	−0.430289	−	0.248428i	−0.699470	+	0.714662i	$0.746580\pi$
$72$		0			0
$73$		−	15.0361i		−	1.75984i	−0.475124	−	0.879919i	$-0.657597\pi$
$73$		−	15.0361i		−	1.75984i	0.475124	−	0.879919i	$-0.342403\pi$
$74$	−3.90725	+	6.76756i	−0.454209	+	0.786713i
$75$		0			0
$76$	4.50154	−	2.59896i	0.516362	−	0.298122i
$77$	2.68172			0.305610
$78$		0			0
$79$	−0.293356			−0.0330052			−0.0165026	−	0.999864i	$-0.505253\pi$
$79$	−0.293356			−0.0330052			−0.0165026	+	0.999864i	$0.505253\pi$
$80$	3.02030	−	1.74377i	0.337679	−	0.194959i
$81$		0			0
$82$	0.0788541	−	0.136579i	0.00870797	−	0.0150827i
$83$			2.87495i			0.315566i	0.987474	+	0.157783i	$0.0504347\pi$
$83$			2.87495i			0.315566i	−0.987474	+	0.157783i	$0.949565\pi$
$84$		0			0
$85$	17.8656	+	10.3147i	1.93779	+	1.11878i
$86$		−	0.330202i		−	0.0356066i
$87$		0			0
$88$	1.34086	+	2.32244i	0.142936	+	0.247573i
$89$	−4.51481	+	2.60662i	−0.478569	+	0.276302i	−0.719820	−	0.694161i	$-0.755776\pi$
$89$	−4.51481	+	2.60662i	−0.478569	+	0.276302i	0.241251	+	0.970463i	$0.422442\pi$
$90$		0			0
$91$	−3.60501	−	0.0627130i	−0.377907	−	0.00657411i
$92$	7.05268			0.735292
$93$		0			0
$94$	−0.800806	−	1.38704i	−0.0825968	−	0.143062i
$95$	−9.06398	+	15.6993i	−0.929945	+	1.61071i
$96$		0			0
$97$	−2.73617	−	1.57973i	−0.277816	−	0.160397i	0.354618	−	0.935011i	$-0.384611\pi$
$97$	−2.73617	−	1.57973i	−0.277816	−	0.160397i	−0.632434	+	0.774614i	$0.717944\pi$
$98$	−0.866025	−	0.500000i	−0.0874818	−	0.0505076i
$99$		0			0
$100$	−3.58146	+	6.20327i	−0.358146	+	0.620327i
$101$	−1.89325	−	3.27921i	−0.188386	−	0.326293i	0.756327	−	0.654194i	$-0.226992\pi$
$101$	−1.89325	−	3.27921i	−0.188386	−	0.326293i	−0.944712	+	0.327901i	$0.893659\pi$
$102$		0			0
$103$	−6.80839			−0.670850			−0.335425	−	0.942067i	$-0.608880\pi$
$103$	−6.80839			−0.670850			−0.335425	+	0.942067i	$0.608880\pi$
$104$	−1.74819	−	3.15338i	−0.171424	−	0.309215i
$105$		0			0
$106$	3.40002	−	1.96300i	0.330240	−	0.190664i
$107$	7.15083	+	12.3856i	0.691297	+	1.19736i	0.971413	+	0.237396i	$0.0762938\pi$
$107$	7.15083	+	12.3856i	0.691297	+	1.19736i	−0.280116	+	0.959966i	$0.590373\pi$
$108$		0			0
$109$			4.57669i			0.438367i	0.975684	+	0.219184i	$0.0703394\pi$
$109$			4.57669i			0.438367i	−0.975684	+	0.219184i	$0.929661\pi$
$110$	−8.09958	−	4.67630i	−0.772265	−	0.445867i
$111$		0			0
$112$		−	1.00000i		−	0.0944911i
$113$	−1.50648	+	2.60930i	−0.141718	+	0.245463i	−0.928144	−	0.372222i	$-0.878596\pi$
$113$	−1.50648	+	2.60930i	−0.141718	+	0.245463i	0.786426	+	0.617685i	$0.211929\pi$
$114$		0			0
$115$	−21.3012	+	12.2982i	−1.98634	+	1.14682i
$116$	7.13278			0.662262
$117$		0			0
$118$	9.54021			0.878248
$119$	5.12268	−	2.95758i	0.469596	−	0.271121i
$120$		0			0
$121$	−1.90419	+	3.29816i	−0.173108	+	0.299833i
$122$		−	15.4105i		−	1.39520i
$123$		0			0
$124$	0.677564	+	0.391192i	0.0608470	+	0.0351300i
$125$		−	7.54326i		−	0.674689i
$126$		0			0
$127$	5.56278	+	9.63501i	0.493616	+	0.854969i	0.999973	−	0.00735543i	$-0.00234133\pi$
$127$	5.56278	+	9.63501i	0.493616	+	0.854969i	−0.506356	+	0.862324i	$0.669008\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$		0			0
$130$	10.7788	+	6.47571i	0.945366	+	0.567957i
$131$	−14.9117			−1.30284			−0.651420	−	0.758718i	$-0.725826\pi$
$131$	−14.9117			−1.30284			−0.651420	+	0.758718i	$0.725826\pi$
$132$		0			0
$133$	2.59896	+	4.50154i	0.225359	+	0.390333i
$134$	−0.483382	+	0.837243i	−0.0417579	+	0.0723268i
$135$		0			0
$136$	5.12268	+	2.95758i	0.439267	+	0.253611i
$137$	13.3902	+	7.73086i	1.14401	+	0.660492i	0.947419	−	0.319995i	$-0.103681\pi$
$137$	13.3902	+	7.73086i	1.14401	+	0.660492i	0.196586	+	0.980487i	$0.437014\pi$
$138$		0			0
$139$	−7.15110	+	12.3861i	−0.606548	+	1.05057i	0.385256	+	0.922810i	$0.374113\pi$
$139$	−7.15110	+	12.3861i	−0.606548	+	1.05057i	−0.991805	+	0.127763i	$0.959220\pi$
$140$	1.74377	+	3.02030i	0.147375	+	0.255262i
$141$		0			0
$142$	4.18658			0.351330
$143$	−4.97945	+	8.28831i	−0.416403	+	0.693103i
$144$		0			0
$145$	−21.5431	+	12.4379i	−1.78906	+	1.03291i
$146$	7.51803	+	13.0216i	0.622197	+	1.07768i
$147$		0			0
$148$		−	7.81450i		−	0.642348i
$149$	3.08060	+	1.77859i	0.252373	+	0.145708i	0.620850	−	0.783929i	$-0.286787\pi$
$149$	3.08060	+	1.77859i	0.252373	+	0.145708i	−0.368477	+	0.929637i	$0.620121\pi$
$150$		0			0
$151$		−	9.52740i		−	0.775329i	−0.921801	−	0.387664i	$-0.873282\pi$
$151$		−	9.52740i		−	0.775329i	0.921801	−	0.387664i	$-0.126718\pi$
$152$	−2.59896	+	4.50154i	−0.210804	+	0.365123i
$153$		0			0
$154$	−2.32244	+	1.34086i	−0.187147	+	0.108050i
$155$	−2.72859			−0.219166
$156$		0			0
$157$	20.8345			1.66278			0.831388	−	0.555692i	$-0.187547\pi$
$157$	20.8345			1.66278			0.831388	+	0.555692i	$0.187547\pi$
$158$	0.254054	−	0.146678i	0.0202115	−	0.0116691i
$159$		0			0
$160$	−1.74377	+	3.02030i	−0.137857	+	0.238775i
$161$			7.05268i			0.555829i
$162$		0			0
$163$	5.46119	+	3.15302i	0.427753	+	0.246963i	0.698389	−	0.715718i	$-0.253901\pi$
$163$	5.46119	+	3.15302i	0.427753	+	0.246963i	−0.270636	+	0.962682i	$0.587234\pi$
$164$			0.157708i			0.0123149i
$165$		0			0
$166$	−1.43747	−	2.48978i	−0.111570	−	0.193244i
$167$	−5.77528	+	3.33436i	−0.446904	+	0.258020i	−0.706522	−	0.707691i	$-0.749737\pi$
$167$	−5.77528	+	3.33436i	−0.446904	+	0.258020i	0.259618	+	0.965711i	$0.416403\pi$
$168$		0			0
$169$	6.88765	−	11.0254i	0.529819	−	0.848111i
$170$	−20.6294			−1.58220
$171$		0			0
$172$	0.165101	+	0.285963i	0.0125888	+	0.0218045i
$173$	10.6596	−	18.4630i	0.810434	−	1.40371i	−0.102126	−	0.994771i	$-0.532565\pi$
$173$	10.6596	−	18.4630i	0.810434	−	1.40371i	0.912560	−	0.408942i	$-0.134102\pi$
$174$		0			0
$175$	−6.20327	−	3.58146i	−0.468923	−	0.270733i
$176$	−2.32244	−	1.34086i	−0.175060	−	0.101071i
$177$		0			0
$178$	2.60662	−	4.51481i	0.195375	−	0.338399i
$179$	−7.71921	−	13.3701i	−0.576961	−	0.999325i	−0.995826	−	0.0912768i	$-0.970905\pi$
$179$	−7.71921	−	13.3701i	−0.576961	−	0.999325i	0.418865	−	0.908049i	$-0.362428\pi$
$180$		0			0
$181$	−13.2818			−0.987231			−0.493616	−	0.869680i	$-0.664325\pi$
$181$	−13.2818			−0.987231			−0.493616	+	0.869680i	$0.664325\pi$
$182$	3.15338	−	1.74819i	0.233744	−	0.129585i
$183$		0			0
$184$	−6.10780	+	3.52634i	−0.450273	+	0.259965i
$185$	13.6267	+	23.6021i	1.00185	+	1.73526i
$186$		0			0
$187$		−	15.8628i		−	1.16000i
$188$	1.38704	+	0.800806i	0.101160	+	0.0584048i
$189$		0			0
$190$		−	18.1280i		−	1.31514i
$191$	−5.96230	+	10.3270i	−0.431417	+	0.747235i	−0.996996	−	0.0774587i	$-0.975319\pi$
$191$	−5.96230	+	10.3270i	−0.431417	+	0.747235i	0.565579	+	0.824694i	$0.308653\pi$
$192$		0			0
$193$	4.63268	−	2.67468i	0.333467	−	0.192528i	−0.323912	−	0.946087i	$-0.604998\pi$
$193$	4.63268	−	2.67468i	0.333467	−	0.192528i	0.657380	+	0.753560i	$0.271665\pi$
$194$	3.15946			0.226836
$195$		0			0
$196$	1.00000			0.0714286
$197$	11.4261	−	6.59688i	0.814079	−	0.470009i	−0.0342916	−	0.999412i	$-0.510917\pi$
$197$	11.4261	−	6.59688i	0.814079	−	0.470009i	0.848370	+	0.529403i	$0.177584\pi$
$198$		0			0
$199$	10.0258	−	17.3652i	0.710709	−	1.23098i	−0.253883	−	0.967235i	$-0.581708\pi$
$199$	10.0258	−	17.3652i	0.710709	−	1.23098i	0.964591	−	0.263749i	$-0.0849589\pi$
$200$		−	7.16292i		−	0.506495i
$201$		0			0
$202$	3.27921	+	1.89325i	0.230724	+	0.133209i
$203$			7.13278i			0.500623i
$204$		0			0
$205$	−0.275006	−	0.476325i	−0.0192073	−	0.0332680i
$206$	5.89623	−	3.40419i	0.410810	−	0.237181i
$207$		0			0
$208$	3.09067	+	1.85681i	0.214299	+	0.128747i
$209$	13.9394			0.964207
$210$		0			0
$211$	3.98072	+	6.89481i	0.274044	+	0.474658i	0.969893	−	0.243530i	$-0.0783053\pi$
$211$	3.98072	+	6.89481i	0.274044	+	0.474658i	−0.695849	+	0.718188i	$0.744972\pi$
$212$	−1.96300	+	3.40002i	−0.134820	+	0.233515i
$213$		0			0
$214$	−12.3856	−	7.15083i	−0.846663	−	0.488821i
$215$	−0.997308	−	0.575796i	−0.0680158	−	0.0392690i
$216$		0			0
$217$	−0.391192	+	0.677564i	−0.0265558	+	0.0459960i
$218$	−2.28834	−	3.96353i	−0.154986	−	0.268444i
$219$		0			0
$220$	9.35259			0.630552
$221$	−0.370958	+	21.3242i	−0.0249533	+	1.43442i
$222$		0			0
$223$	−18.6557	+	10.7709i	−1.24928	+	0.721271i	−0.970965	−	0.239220i	$-0.923108\pi$
$223$	−18.6557	+	10.7709i	−1.24928	+	0.721271i	−0.278312	+	0.960491i	$0.589775\pi$
$224$	0.500000	+	0.866025i	0.0334077	+	0.0578638i
$225$		0			0
$226$		−	3.01297i		−	0.200419i
$227$	−3.16767	−	1.82886i	−0.210246	−	0.121385i	0.391180	−	0.920314i	$-0.372067\pi$
$227$	−3.16767	−	1.82886i	−0.210246	−	0.121385i	−0.601426	+	0.798929i	$0.705400\pi$
$228$		0			0
$229$			9.74752i			0.644134i	0.946717	+	0.322067i	$0.104378\pi$
$229$			9.74752i			0.644134i	−0.946717	+	0.322067i	$0.895622\pi$
$230$	12.2982	−	21.3012i	0.810922	−	1.40456i
$231$		0			0
$232$	−6.17717	+	3.56639i	−0.405551	+	0.234145i
$233$	2.72895			0.178779			0.0893897	−	0.995997i	$-0.471508\pi$
$233$	2.72895			0.178779			0.0893897	+	0.995997i	$0.471508\pi$
$234$		0			0
$235$	−5.58568			−0.364370
$236$	−8.26207	+	4.77011i	−0.537815	+	0.310508i
$237$		0			0
$238$	−2.95758	+	5.12268i	−0.191712	+	0.332054i
$239$		−	12.2347i		−	0.791400i	−0.918380	−	0.395700i	$-0.870502\pi$
$239$		−	12.2347i		−	0.791400i	0.918380	−	0.395700i	$-0.129498\pi$
$240$		0			0
$241$	−20.9731	−	12.1088i	−1.35100	−	0.779998i	−0.362607	−	0.931942i	$-0.618113\pi$
$241$	−20.9731	−	12.1088i	−1.35100	−	0.779998i	−0.988389	+	0.151944i	$0.951447\pi$
$242$		−	3.80839i		−	0.244812i
$243$		0			0
$244$	7.70525	+	13.3459i	0.493278	+	0.854383i
$245$	−3.02030	+	1.74377i	−0.192960	+	0.111405i
$246$		0			0
$247$	−18.7386	−	0.325978i	−1.19231	−	0.0207415i
$248$	−0.782383			−0.0496814
$249$		0			0
$250$	3.77163	+	6.53265i	0.238539	+	0.413161i
$251$	−1.00685	+	1.74392i	−0.0635521	+	0.110075i	−0.896051	−	0.443952i	$-0.853576\pi$
$251$	−1.00685	+	1.74392i	−0.0635521	+	0.110075i	0.832499	+	0.554027i	$0.186910\pi$
$252$		0			0
$253$	16.3794	+	9.45665i	1.02976	+	0.594534i
$254$	−9.63501	−	5.56278i	−0.604554	−	0.349040i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	1.07109	+	1.85518i	0.0668127	+	0.115723i	0.897497	−	0.441021i	$-0.145384\pi$
$257$	1.07109	+	1.85518i	0.0668127	+	0.115723i	−0.830684	+	0.556744i	$0.812050\pi$
$258$		0			0
$259$	7.81450			0.485570
$260$	−12.5726	−	0.218714i	−0.779719	−	0.0135641i
$261$		0			0
$262$	12.9139	−	7.45584i	0.797823	−	0.460623i
$263$	−5.43131	−	9.40731i	−0.334909	−	0.580080i	0.648558	−	0.761165i	$-0.275372\pi$
$263$	−5.43131	−	9.40731i	−0.334909	−	0.580080i	−0.983467	+	0.181085i	$0.942039\pi$
$264$		0			0
$265$		−	13.6921i		−	0.841099i
$266$	−4.50154	−	2.59896i	−0.276007	−	0.159353i
$267$		0			0
$268$		−	0.966765i		−	0.0590546i
$269$	−7.40257	+	12.8216i	−0.451343	+	0.781749i	−0.998470	−	0.0553009i	$-0.982388\pi$
$269$	−7.40257	+	12.8216i	−0.451343	+	0.781749i	0.547127	+	0.837050i	$0.315722\pi$
$270$		0			0
$271$	0.0559765	−	0.0323180i	0.00340033	−	0.00196318i	−0.498299	−	0.867005i	$-0.666042\pi$
$271$	0.0559765	−	0.0323180i	0.00340033	−	0.00196318i	0.501699	+	0.865042i	$0.332708\pi$
$272$	−5.91517			−0.358660
$273$		0			0
$274$	−15.4617			−0.934077
$275$	−16.6354	+	9.60446i	−1.00315	+	0.579171i
$276$		0			0
$277$	2.12558	−	3.68160i	0.127713	−	0.221206i	−0.795077	−	0.606509i	$-0.792570\pi$
$277$	2.12558	−	3.68160i	0.127713	−	0.221206i	0.922790	+	0.385302i	$0.125903\pi$
$278$		−	14.3022i		−	0.857789i
$279$		0			0
$280$	−3.02030	−	1.74377i	−0.180497	−	0.104210i
$281$			11.0454i			0.658916i	0.944170	+	0.329458i	$0.106866\pi$
$281$			11.0454i			0.658916i	−0.944170	+	0.329458i	$0.893134\pi$
$282$		0			0
$283$	5.64271	+	9.77346i	0.335424	+	0.580972i	0.983566	−	0.180548i	$-0.0577870\pi$
$283$	5.64271	+	9.77346i	0.335424	+	0.580972i	−0.648142	+	0.761520i	$0.724454\pi$
$284$	−3.62568	+	2.09329i	−0.215145	+	0.124214i
$285$		0			0
$286$	0.168179	−	9.66761i	0.00994461	−	0.571658i
$287$	−0.157708			−0.00930922
$288$		0			0
$289$	−8.99459	−	15.5791i	−0.529094	−	0.916417i
$290$	12.4379	−	21.5431i	0.730380	−	1.26506i
$291$		0			0
$292$	−13.0216	−	7.51803i	−0.762032	−	0.439959i
$293$	22.5549	+	13.0221i	1.31767	+	0.760758i	0.983354	−	0.181703i	$-0.0581609\pi$
$293$	22.5549	+	13.0221i	1.31767	+	0.760758i	0.334318	+	0.942460i	$0.391494\pi$
$294$		0			0
$295$	16.6359	−	28.8143i	0.968581	−	1.67763i
$296$	3.90725	+	6.76756i	0.227104	+	0.393356i
$297$		0			0
$298$	−3.55717			−0.206062
$299$	−21.7975	−	13.0955i	−1.26058	−	0.757333i
$300$		0			0
$301$	−0.285963	+	0.165101i	−0.0164827	+	0.00951627i
$302$	4.76370	+	8.25097i	0.274120	+	0.474790i
$303$		0			0
$304$		−	5.19793i		−	0.298122i
$305$	−46.5443	−	26.8724i	−2.66512	−	1.53871i
$306$		0			0
$307$		−	25.0551i		−	1.42997i	−0.699139	−	0.714986i	$-0.746433\pi$
$307$		−	25.0551i		−	1.42997i	0.699139	−	0.714986i	$-0.253567\pi$
$308$	1.34086	−	2.32244i	0.0764025	−	0.132333i
$309$		0			0
$310$	2.36303	−	1.36430i	0.134211	−	0.0774868i
$311$	32.4330			1.83911			0.919554	−	0.392964i	$-0.128550\pi$
$311$	32.4330			1.83911			0.919554	+	0.392964i	$0.128550\pi$
$312$		0			0
$313$	2.22517			0.125774			0.0628870	−	0.998021i	$-0.479969\pi$
$313$	2.22517			0.125774			0.0628870	+	0.998021i	$0.479969\pi$
$314$	−18.0432	+	10.4173i	−1.01824	+	0.587880i
$315$		0			0
$316$	−0.146678	+	0.254054i	−0.00825129	+	0.0142917i
$317$		−	3.83753i		−	0.215537i	−0.994176	−	0.107769i	$-0.965629\pi$
$317$		−	3.83753i		−	0.215537i	0.994176	−	0.107769i	$-0.0343706\pi$
$318$		0			0
$319$	16.5654	+	9.56406i	0.927486	+	0.535484i
$320$		−	3.48754i		−	0.194959i
$321$		0			0
$322$	−3.52634	−	6.10780i	−0.196515	−	0.340374i
$323$	26.6273	−	15.3733i	1.48158	−	0.855393i
$324$		0			0
$325$	22.5874	−	12.5222i	1.25292	−	0.694604i
$326$	−6.30603			−0.349259
$327$		0			0
$328$	−0.0788541	−	0.136579i	−0.00435399	−	0.00754133i
$329$	−0.800806	+	1.38704i	−0.0441499	+	0.0764698i
$330$		0			0
$331$	5.26859	+	3.04182i	0.289588	+	0.167194i	0.637756	−	0.770238i	$-0.279863\pi$
$331$	5.26859	+	3.04182i	0.289588	+	0.167194i	−0.348168	+	0.937432i	$0.613196\pi$
$332$	2.48978	+	1.43747i	0.136644	+	0.0788916i
$333$		0			0
$334$	3.33436	−	5.77528i	0.182448	−	0.316009i
$335$	1.68581	+	2.91992i	0.0921059	+	0.159532i
$336$		0			0
$337$	−19.3746			−1.05540			−0.527700	−	0.849431i	$-0.676946\pi$
$337$	−19.3746			−1.05540			−0.527700	+	0.849431i	$0.676946\pi$
$338$	−0.452161	+	12.9921i	−0.0245943	+	0.706679i
$339$		0			0
$340$	17.8656	−	10.3147i	0.968896	−	0.559392i
$341$	1.04907	+	1.81703i	0.0568101	+	0.0983980i
$342$		0			0
$343$			1.00000i			0.0539949i
$344$	−0.285963	−	0.165101i	−0.0154181	−	0.00890165i
$345$		0			0
$346$			21.3192i			1.14613i
$347$	−4.51028	+	7.81203i	−0.242124	+	0.419372i	−0.961319	−	0.275437i	$-0.911178\pi$
$347$	−4.51028	+	7.81203i	−0.242124	+	0.419372i	0.719195	+	0.694809i	$0.244511\pi$
$348$		0			0
$349$	6.04213	−	3.48843i	0.323428	−	0.186731i	−0.329492	−	0.944159i	$-0.606877\pi$
$349$	6.04213	−	3.48843i	0.323428	−	0.186731i	0.652919	+	0.757427i	$0.273544\pi$
$350$	7.16292			0.382874
$351$		0			0
$352$	2.68172			0.142936
$353$	21.6841	−	12.5193i	1.15413	−	0.666335i	0.204237	−	0.978922i	$-0.434529\pi$
$353$	21.6841	−	12.5193i	1.15413	−	0.666335i	0.949889	+	0.312587i	$0.101195\pi$
$354$		0			0
$355$	7.30042	−	12.6447i	0.387466	−	0.671111i
$356$			5.21325i			0.276302i
$357$		0			0
$358$	13.3701	+	7.71921i	0.706630	+	0.407973i
$359$		−	37.6090i		−	1.98493i	−0.122545	−	0.992463i	$-0.539106\pi$
$359$		−	37.6090i		−	1.98493i	0.122545	−	0.992463i	$-0.460894\pi$
$360$		0			0
$361$	4.00922	+	6.94418i	0.211012	+	0.365483i
$362$	11.5024	−	6.64092i	0.604553	−	0.349039i
$363$		0			0
$364$	−1.85681	+	3.09067i	−0.0973235	+	0.161995i
$365$	52.4388			2.74477
$366$		0			0
$367$	−10.5455	−	18.2653i	−0.550470	−	0.953442i	−0.998241	−	0.0592934i	$-0.981115\pi$
$367$	−10.5455	−	18.2653i	−0.550470	−	0.953442i	0.447771	−	0.894148i	$-0.352218\pi$
$368$	3.52634	−	6.10780i	0.183823	−	0.318391i
$369$		0			0
$370$	−23.6021	−	13.6267i	−1.22702	−	0.708418i
$371$	−3.40002	−	1.96300i	−0.176520	−	0.101914i
$372$		0			0
$373$	−7.04708	+	12.2059i	−0.364884	+	0.631998i	−0.988758	−	0.149528i	$-0.952225\pi$
$373$	−7.04708	+	12.2059i	−0.364884	+	0.631998i	0.623874	+	0.781525i	$0.285558\pi$
$374$	7.93141	+	13.7376i	0.410123	+	0.710354i
$375$		0			0
$376$	−1.60161			−0.0825968
$377$	−22.0451	−	13.2443i	−1.13538	−	0.682114i
$378$		0			0
$379$	28.6773	−	16.5568i	1.47305	−	0.850467i	0.473512	−	0.880787i	$-0.342986\pi$
$379$	28.6773	−	16.5568i	1.47305	−	0.850467i	0.999540	+	0.0303204i	$0.00965277\pi$
$380$	9.06398	+	15.6993i	0.464973	+	0.805356i
$381$		0			0
$382$		−	11.9246i		−	0.610115i
$383$	22.4578	+	12.9660i	1.14754	+	0.662534i	0.948287	−	0.317414i	$-0.102814\pi$
$383$	22.4578	+	12.9660i	1.14754	+	0.662534i	0.199255	+	0.979948i	$0.436148\pi$
$384$		0			0
$385$			9.35259i			0.476652i
$386$	−2.67468	+	4.63268i	−0.136138	+	0.235797i
$387$		0			0
$388$	−2.73617	+	1.57973i	−0.138908	+	0.0801986i
$389$	30.5647			1.54969			0.774847	−	0.632149i	$-0.217827\pi$
$389$	30.5647			1.54969			0.774847	+	0.632149i	$0.217827\pi$
$390$		0			0
$391$	41.7178			2.10976
$392$	−0.866025	+	0.500000i	−0.0437409	+	0.0252538i
$393$		0			0
$394$	−6.59688	+	11.4261i	−0.332346	+	0.575641i
$395$		−	1.02309i		−	0.0514773i
$396$		0			0
$397$	19.4521	+	11.2307i	0.976275	+	0.563653i	0.901144	−	0.433521i	$-0.142729\pi$
$397$	19.4521	+	11.2307i	0.976275	+	0.563653i	0.0751317	+	0.997174i	$0.476062\pi$
$398$			20.0516i			1.00509i
$399$		0			0
$400$	3.58146	+	6.20327i	0.179073	+	0.310163i
$401$	14.7473	−	8.51438i	0.736447	−	0.425188i	−0.0843289	−	0.996438i	$-0.526875\pi$
$401$	14.7473	−	8.51438i	0.736447	−	0.425188i	0.820776	+	0.571250i	$0.193541\pi$
$402$		0			0
$403$	−1.36776	−	2.46715i	−0.0681328	−	0.122898i
$404$	−3.78650			−0.188386
$405$		0			0
$406$	−3.56639	−	6.17717i	−0.176997	−	0.306568i
$407$	10.4781	−	18.1487i	0.519382	−	0.899597i
$408$		0			0
$409$	4.44731	+	2.56766i	0.219906	+	0.126963i	0.605907	−	0.795536i	$-0.292811\pi$
$409$	4.44731	+	2.56766i	0.219906	+	0.126963i	−0.386001	+	0.922498i	$0.626144\pi$
$410$	0.476325	+	0.275006i	0.0235240	+	0.0135816i
$411$		0			0
$412$	−3.40419	+	5.89623i	−0.167713	+	0.290487i
$413$	−4.77011	−	8.26207i	−0.234722	−	0.406550i
$414$		0			0
$415$	−10.0265			−0.492181
$416$	−3.60501	−	0.0627130i	−0.176750	−	0.00307476i
$417$		0			0
$418$	−12.0719	+	6.96969i	−0.590454	+	0.340899i
$419$	−15.9418	−	27.6120i	−0.778808	−	1.34893i	−0.932629	−	0.360836i	$-0.882491\pi$
$419$	−15.9418	−	27.6120i	−0.778808	−	1.34893i	0.153822	−	0.988099i	$-0.450842\pi$
$420$		0			0
$421$		−	14.7648i		−	0.719594i	−0.933031	−	0.359797i	$-0.882846\pi$
$421$		−	14.7648i		−	0.719594i	0.933031	−	0.359797i	$-0.117154\pi$
$422$	−6.89481	−	3.98072i	−0.335634	−	0.193778i
$423$		0			0
$424$		−	3.92601i		−	0.190664i
$425$	−21.1849	+	36.6934i	−1.02762	+	1.77989i
$426$		0			0
$427$	−13.3459	+	7.70525i	−0.645853	+	0.372883i
$428$	14.3017			0.691297
$429$		0			0
$430$	1.15159			0.0555347
$431$	−30.4051	+	17.5544i	−1.46456	+	0.845565i	−0.999217	−	0.0395640i	$-0.987403\pi$
$431$	−30.4051	+	17.5544i	−1.46456	+	0.845565i	−0.465345	+	0.885129i	$0.654070\pi$
$432$		0			0
$433$	−1.98625	+	3.44029i	−0.0954533	+	0.165330i	−0.909798	−	0.415052i	$-0.863763\pi$
$433$	−1.98625	+	3.44029i	−0.0954533	+	0.165330i	0.814344	+	0.580382i	$0.197097\pi$
$434$		−	0.782383i		−	0.0375556i
$435$		0			0
$436$	3.96353	+	2.28834i	0.189819	+	0.109592i
$437$			36.6593i			1.75365i
$438$		0			0
$439$	2.87638	+	4.98204i	0.137282	+	0.237780i	0.926467	−	0.376376i	$-0.122830\pi$
$439$	2.87638	+	4.98204i	0.137282	+	0.237780i	−0.789185	+	0.614156i	$0.789497\pi$
$440$	−8.09958	+	4.67630i	−0.386133	+	0.222934i
$441$		0			0
$442$	−10.3408	−	18.6528i	−0.491864	−	0.887222i
$443$	27.0804			1.28663			0.643315	−	0.765602i	$-0.277559\pi$
$443$	27.0804			1.28663			0.643315	+	0.765602i	$0.277559\pi$
$444$		0			0
$445$	−9.09070	−	15.7456i	−0.430941	−	0.746411i
$446$	10.7709	−	18.6557i	0.510015	−	0.883373i
$447$		0			0
$448$	−0.866025	−	0.500000i	−0.0409159	−	0.0236228i
$449$	−7.14396	−	4.12457i	−0.337145	−	0.194650i	0.321864	−	0.946786i	$-0.395691\pi$
$449$	−7.14396	−	4.12457i	−0.337145	−	0.194650i	−0.659009	+	0.752135i	$0.729024\pi$
$450$		0			0
$451$	−0.211464	+	0.366267i	−0.00995747	+	0.0172468i
$452$	1.50648	+	2.60930i	0.0708590	+	0.122731i
$453$		0			0
$454$	3.65771			0.171665
$455$	0.218714	−	12.5726i	0.0102535	−	0.589412i
$456$		0			0
$457$	33.5123	−	19.3483i	1.56764	−	0.905077i	0.571197	−	0.820813i	$-0.306479\pi$
$457$	33.5123	−	19.3483i	1.56764	−	0.905077i	0.996443	−	0.0842643i	$-0.0268540\pi$
$458$	−4.87376	−	8.44160i	−0.227736	−	0.394450i
$459$		0			0
$460$			24.5965i			1.14682i
$461$	−11.3751	−	6.56742i	−0.529792	−	0.305875i	0.211140	−	0.977456i	$-0.432282\pi$
$461$	−11.3751	−	6.56742i	−0.529792	−	0.305875i	−0.740932	+	0.671581i	$0.765616\pi$
$462$		0			0
$463$		−	6.98417i		−	0.324582i	−0.986743	−	0.162291i	$-0.948112\pi$
$463$		−	6.98417i		−	0.324582i	0.986743	−	0.162291i	$-0.0518883\pi$
$464$	3.56639	−	6.17717i	0.165566	−	0.286768i
$465$		0			0
$466$	−2.36334	+	1.36448i	−0.109480	+	0.0632081i
$467$	−5.62691			−0.260382			−0.130191	−	0.991489i	$-0.541559\pi$
$467$	−5.62691			−0.260382			−0.130191	+	0.991489i	$0.541559\pi$
$468$		0			0
$469$	0.966765			0.0446411
$470$	4.83734	−	2.79284i	0.223130	−	0.128824i
$471$		0			0
$472$	4.77011	−	8.26207i	0.219562	−	0.380292i
$473$			0.885509i			0.0407158i
$474$		0			0
$475$	−32.2441	−	18.6162i	−1.47946	−	0.854168i
$476$		−	5.91517i		−	0.271121i
$477$		0			0
$478$	6.11737	+	10.5956i	0.279802	+	0.484632i
$479$	−21.7538	+	12.5596i	−0.993956	+	0.573861i	−0.906454	−	0.422304i	$-0.861222\pi$
$479$	−21.7538	+	12.5596i	−0.993956	+	0.573861i	−0.0875014	+	0.996164i	$0.527888\pi$
$480$		0			0
$481$	−14.5101	+	24.1520i	−0.661602	+	1.10124i
$482$	24.2176			1.10308
$483$		0			0
$484$	1.90419	+	3.29816i	0.0865542	+	0.149916i
$485$	5.50936	−	9.54249i	0.250167	−	0.433302i
$486$		0			0
$487$	−15.3077	−	8.83791i	−0.693659	−	0.400484i	0.111323	−	0.993784i	$-0.464491\pi$
$487$	−15.3077	−	8.83791i	−0.693659	−	0.400484i	−0.804981	+	0.593300i	$0.797825\pi$
$488$	−13.3459	−	7.70525i	−0.604140	−	0.348800i
$489$		0			0
$490$	1.74377	−	3.02030i	0.0787754	−	0.136443i
$491$	−15.9975	−	27.7084i	−0.721956	−	1.25046i	−0.960215	−	0.279262i	$-0.909910\pi$
$491$	−15.9975	−	27.7084i	−0.721956	−	1.25046i	0.238259	−	0.971202i	$-0.423423\pi$
$492$		0			0
$493$	42.1916			1.90021
$494$	16.3911	−	9.08697i	0.737468	−	0.408842i
$495$		0			0
$496$	0.677564	−	0.391192i	0.0304235	−	0.0175650i
$497$	−2.09329	−	3.62568i	−0.0938968	−	0.162634i
$498$		0			0
$499$		−	11.6416i		−	0.521149i	−0.965454	−	0.260574i	$-0.916088\pi$
$499$		−	11.6416i		−	0.521149i	0.965454	−	0.260574i	$-0.0839119\pi$
$500$	−6.53265	−	3.77163i	−0.292149	−	0.168672i
$501$		0			0
$502$		−	2.01371i		−	0.0898762i
$503$	7.51764	−	13.0209i	0.335195	−	0.580574i	−0.648327	−	0.761362i	$-0.724531\pi$
$503$	7.51764	−	13.0209i	0.335195	−	0.580574i	0.983522	+	0.180787i	$0.0578645\pi$
$504$		0			0
$505$	11.4364	−	6.60278i	0.508911	−	0.293820i
$506$	−18.9133			−0.840798
$507$		0			0
$508$	11.1256			0.493616
$509$	−2.21786	+	1.28048i	−0.0983047	+	0.0567563i	−0.548346	−	0.836251i	$-0.684742\pi$
$509$	−2.21786	+	1.28048i	−0.0983047	+	0.0567563i	0.450042	+	0.893008i	$0.351409\pi$
$510$		0			0
$511$	7.51803	−	13.0216i	0.332578	−	0.576042i
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	−1.85518	−	1.07109i	−0.0818285	−	0.0472437i
$515$		−	23.7445i		−	1.04631i
$516$		0			0
$517$	2.14754	+	3.71964i	0.0944485	+	0.163590i
$518$	−6.76756	+	3.90725i	−0.297349	+	0.171675i
$519$		0			0
$520$	10.9975	−	6.09688i	0.482274	−	0.267366i
$521$	31.0544			1.36052			0.680259	−	0.732972i	$-0.261867\pi$
$521$	31.0544			1.36052			0.680259	+	0.732972i	$0.261867\pi$
$522$		0			0
$523$	2.18180	+	3.77899i	0.0954035	+	0.165244i	0.909777	−	0.415098i	$-0.136253\pi$
$523$	2.18180	+	3.77899i	0.0954035	+	0.165244i	−0.814373	+	0.580341i	$0.802919\pi$
$524$	−7.45584	+	12.9139i	−0.325710	+	0.564146i
$525$		0			0
$526$	9.40731	+	5.43131i	0.410178	+	0.236817i
$527$	4.00790	+	2.31396i	0.174587	+	0.100798i
$528$		0			0
$529$	−13.3701	+	23.1577i	−0.581310	+	1.00686i
$530$	6.84605	+	11.8577i	0.297374	+	0.515066i
$531$		0			0
$532$	5.19793			0.225359
$533$	0.292835	−	0.487424i	0.0126841	−	0.0211127i
$534$		0			0
$535$	−43.1953	+	24.9388i	−1.86749	+	1.07820i
$536$	0.483382	+	0.837243i	0.0208789	+	0.0361634i
$537$		0			0
$538$		−	14.8051i		−	0.638295i
$539$	2.32244	+	1.34086i	0.100034	+	0.0577549i
$540$		0			0
$541$			17.2191i			0.740305i	0.928971	+	0.370152i	$0.120695\pi$
$541$			17.2191i			0.740305i	−0.928971	+	0.370152i	$0.879305\pi$
$542$	−0.0323180	+	0.0559765i	−0.00138818	+	0.00240440i
$543$		0			0
$544$	5.12268	−	2.95758i	0.219633	−	0.126805i
$545$	−15.9614			−0.683710
$546$		0			0
$547$	42.8331			1.83141			0.915706	−	0.401849i	$-0.131632\pi$
$547$	42.8331			1.83141			0.915706	+	0.401849i	$0.131632\pi$
$548$	13.3902	−	7.73086i	0.572003	−	0.330246i
$549$		0			0
$550$	9.60446	−	16.6354i	0.409536	−	0.709337i
$551$			37.0757i			1.57948i
$552$		0			0
$553$	−0.254054	−	0.146678i	−0.0108035	−	0.00623739i
$554$			4.25115i			0.180614i
$555$		0			0
$556$	7.15110	+	12.3861i	0.303274	+	0.525286i
$557$	20.9756	−	12.1103i	0.888765	−	0.513129i	0.0152269	−	0.999884i	$-0.495153\pi$
$557$	20.9756	−	12.1103i	0.888765	−	0.513129i	0.873538	+	0.486755i	$0.161820\pi$
$558$		0			0
$559$	0.0207080	−	1.19038i	0.000875853	−	0.0503477i
$560$	3.48754			0.147375
$561$		0			0
$562$	−5.52272	−	9.56563i	−0.232962	−	0.403502i
$563$	6.62405	−	11.4732i	0.279170	−	0.483537i	−0.692008	−	0.721889i	$-0.743274\pi$
$563$	6.62405	−	11.4732i	0.279170	−	0.483537i	0.971179	+	0.238352i	$0.0766072\pi$
$564$		0			0
$565$	−9.10005	−	5.25391i	−0.382842	−	0.221034i
$566$	−9.77346	−	5.64271i	−0.410809	−	0.237181i
$567$		0			0
$568$	2.09329	−	3.62568i	0.0878324	−	0.152130i
$569$	12.4960	+	21.6438i	0.523861	+	0.907354i	0.999614	+	0.0277752i	$0.00884224\pi$
$569$	12.4960	+	21.6438i	0.523861	+	0.907354i	−0.475753	+	0.879579i	$0.657824\pi$
$570$		0			0
$571$	22.5276			0.942750			0.471375	−	0.881933i	$-0.343758\pi$
$571$	22.5276			0.942750			0.471375	+	0.881933i	$0.343758\pi$
$572$	4.68816	+	8.45649i	0.196022	+	0.353583i
$573$		0			0
$574$	0.136579	−	0.0788541i	0.00570071	−	0.00329130i
$575$	−25.2589	−	43.7496i	−1.05337	−	1.82449i
$576$		0			0
$577$			12.9848i			0.540564i	0.962781	+	0.270282i	$0.0871170\pi$
$577$			12.9848i			0.540564i	−0.962781	+	0.270282i	$0.912883\pi$
$578$	15.5791	+	8.99459i	0.648005	+	0.374126i
$579$		0			0
$580$			24.8758i			1.03291i
$581$	−1.43747	+	2.48978i	−0.0596364	+	0.103293i
$582$		0			0
$583$	−9.11791	+	5.26423i	−0.377625	+	0.218022i
$584$	15.0361			0.622197
$585$		0			0
$586$	−26.0442			−1.07587
$587$	−3.02617	+	1.74716i	−0.124903	+	0.0721131i	−0.561150	−	0.827714i	$-0.689641\pi$
$587$	−3.02617	+	1.74716i	−0.124903	+	0.0721131i	0.436246	+	0.899827i	$0.356308\pi$
$588$		0			0
$589$	−2.03339	+	3.52193i	−0.0837842	+	0.145118i
$590$			33.2719i			1.36978i
$591$		0			0
$592$	−6.76756	−	3.90725i	−0.278145	−	0.160587i
$593$		−	23.2140i		−	0.953283i	−0.879098	−	0.476642i	$-0.841854\pi$
$593$		−	23.2140i		−	0.953283i	0.879098	−	0.476642i	$-0.158146\pi$
$594$		0			0
$595$	10.3147	+	17.8656i	0.422861	+	0.732416i
$596$	3.08060	−	1.77859i	0.126186	−	0.0728538i
$597$		0			0
$598$	25.4249	+	0.442294i	1.03970	+	0.0180868i
$599$	−18.3645			−0.750354			−0.375177	−	0.926953i	$-0.622418\pi$
$599$	−18.3645			−0.750354			−0.375177	+	0.926953i	$0.622418\pi$
$600$		0			0
$601$	2.37983	+	4.12198i	0.0970751	+	0.168139i	0.910473	−	0.413569i	$-0.135718\pi$
$601$	2.37983	+	4.12198i	0.0970751	+	0.168139i	−0.813398	+	0.581708i	$0.802385\pi$
$602$	0.165101	−	0.285963i	0.00672902	−	0.0116550i
$603$		0			0
$604$	−8.25097	−	4.76370i	−0.335727	−	0.193832i
$605$	−11.5025	−	6.64094i	−0.467641	−	0.269993i
$606$		0			0
$607$	−10.4828	+	18.1568i	−0.425484	+	0.736960i	−0.996466	−	0.0840029i	$-0.973230\pi$
$607$	−10.4828	+	18.1568i	−0.425484	+	0.736960i	0.570981	+	0.820963i	$0.306563\pi$
$608$	2.59896	+	4.50154i	0.105402	+	0.182561i
$609$		0			0
$610$	53.7447			2.17606
$611$	−2.79992	−	5.05050i	−0.113273	−	0.204321i
$612$		0			0
$613$	−25.3853	+	14.6562i	−1.02530	+	0.591959i	−0.915635	−	0.402010i	$-0.868312\pi$
$613$	−25.3853	+	14.6562i	−1.02530	+	0.591959i	−0.109667	+	0.993968i	$0.534978\pi$
$614$	12.5276	+	21.6984i	0.505571	+	0.875675i
$615$		0			0
$616$			2.68172i			0.108050i
$617$	4.55827	+	2.63172i	0.183509	+	0.105949i	0.588940	−	0.808177i	$-0.299545\pi$
$617$	4.55827	+	2.63172i	0.183509	+	0.105949i	−0.405431	+	0.914125i	$0.632879\pi$
$618$		0			0
$619$			10.9663i			0.440774i	0.975413	+	0.220387i	$0.0707320\pi$
$619$			10.9663i			0.440774i	−0.975413	+	0.220387i	$0.929268\pi$
$620$	−1.36430	+	2.36303i	−0.0547914	+	0.0949015i
$621$		0			0
$622$	−28.0878	+	16.2165i	−1.12622	+	0.650223i
$623$	−5.21325			−0.208864
$624$		0			0
$625$	−9.50720			−0.380288
$626$	−1.92705	+	1.11259i	−0.0770206	+	0.0444678i
$627$		0			0
$628$	10.4173	−	18.0432i	0.415694	−	0.720003i
$629$		−	46.2241i		−	1.84307i
$630$		0			0
$631$	−21.0642	−	12.1614i	−0.838553	−	0.484139i	0.0182188	−	0.999834i	$-0.494200\pi$
$631$	−21.0642	−	12.1614i	−0.838553	−	0.484139i	−0.856772	+	0.515695i	$0.827534\pi$
$632$		−	0.293356i		−	0.0116691i
$633$		0			0
$634$	1.91877	+	3.32340i	0.0762039	+	0.131989i
$635$	−33.6025	+	19.4004i	−1.33347	+	0.769881i
$636$		0			0
$637$	−3.09067	−	1.85681i	−0.122457	−	0.0735696i
$638$	−19.1281			−0.757289
$639$		0			0
$640$	1.74377	+	3.02030i	0.0689285	+	0.119388i
$641$	−0.650592	+	1.12686i	−0.0256968	+	0.0445082i	−0.878588	−	0.477581i	$-0.841514\pi$
$641$	−0.650592	+	1.12686i	−0.0256968	+	0.0445082i	0.852891	+	0.522089i	$0.174847\pi$
$642$		0			0
$643$	4.87547	+	2.81485i	0.192270	+	0.111007i	0.593045	−	0.805170i	$-0.297926\pi$
$643$	4.87547	+	2.81485i	0.192270	+	0.111007i	−0.400775	+	0.916177i	$0.631259\pi$
$644$	6.10780	+	3.52634i	0.240681	+	0.138957i
$645$		0			0
$646$	−15.3733	+	26.6273i	−0.604854	+	1.04764i
$647$	5.90635	+	10.2301i	0.232202	+	0.402186i	0.958456	−	0.285241i	$-0.0920735\pi$
$647$	5.90635	+	10.2301i	0.232202	+	0.402186i	−0.726254	+	0.687427i	$0.758740\pi$
$648$		0			0
$649$	−25.5842			−1.00427
$650$	−13.3002	+	22.1382i	−0.521677	+	0.868332i
$651$		0			0
$652$	5.46119	−	3.15302i	0.213877	−	0.123482i
$653$	−1.56006	−	2.70211i	−0.0610500	−	0.105742i	0.833885	−	0.551938i	$-0.186112\pi$
$653$	−1.56006	−	2.70211i	−0.0610500	−	0.105742i	−0.894935	+	0.446196i	$0.852778\pi$
$654$		0			0
$655$		−	52.0050i		−	2.03201i
$656$	0.136579	+	0.0788541i	0.00533252	+	0.00307873i
$657$		0			0
$658$		−	1.60161i		−	0.0624373i
$659$	18.7533	−	32.4817i	0.730526	−	1.26531i	−0.226133	−	0.974096i	$-0.572608\pi$
$659$	18.7533	−	32.4817i	0.730526	−	1.26531i	0.956659	−	0.291211i	$-0.0940583\pi$
$660$		0			0
$661$	30.9817	−	17.8873i	1.20505	−	0.695735i	0.243375	−	0.969932i	$-0.421746\pi$
$661$	30.9817	−	17.8873i	1.20505	−	0.695735i	0.961673	+	0.274198i	$0.0884122\pi$
$662$	−6.08365			−0.236448
$663$		0			0
$664$	−2.87495			−0.111570
$665$	−15.6993	+	9.06398i	−0.608792	+	0.351486i
$666$		0			0
$667$	−25.1526	+	43.5656i	−0.973913	+	1.68687i
$668$			6.66871i			0.258020i
$669$		0			0
$670$	−2.91992	−	1.68581i	−0.112806	−	0.0651287i
$671$			41.3266i			1.59540i
$672$		0			0
$673$	−4.31081	−	7.46655i	−0.166170	−	0.287814i	0.770900	−	0.636956i	$-0.219807\pi$
$673$	−4.31081	−	7.46655i	−0.166170	−	0.287814i	−0.937070	+	0.349141i	$0.886473\pi$
$674$	16.7789	−	9.68729i	0.646298	−	0.373140i
$675$		0			0
$676$	−6.10448	−	11.4776i	−0.234788	−	0.441446i
$677$	15.5551			0.597829			0.298915	−	0.954280i	$-0.403375\pi$
$677$	15.5551			0.597829			0.298915	+	0.954280i	$0.403375\pi$
$678$		0			0
$679$	−1.57973	−	2.73617i	−0.0606244	−	0.105005i
$680$	−10.3147	+	17.8656i	−0.395550	+	0.685113i
$681$		0			0
$682$	−1.81703	−	1.04907i	−0.0695779	−	0.0401708i
$683$	7.70585	+	4.44898i	0.294856	+	0.170235i	0.640130	−	0.768267i	$-0.278881\pi$
$683$	7.70585	+	4.44898i	0.294856	+	0.170235i	−0.345274	+	0.938502i	$0.612214\pi$
$684$		0			0
$685$	−26.9617	+	46.6990i	−1.03015	+	1.78428i
$686$	−0.500000	−	0.866025i	−0.0190901	−	0.0330650i
$687$		0			0
$688$	0.330202			0.0125888
$689$	12.3802	−	6.86342i	0.471648	−	0.261475i
$690$		0			0
$691$	−33.0646	+	19.0899i	−1.25784	+	0.726213i	−0.972654	−	0.232260i	$-0.925388\pi$
$691$	−33.0646	+	19.0899i	−1.25784	+	0.726213i	−0.285184	+	0.958473i	$0.592055\pi$
$692$	−10.6596	−	18.4630i	−0.405217	−	0.701857i
$693$		0			0
$694$		−	9.02056i		−	0.342416i
$695$	−43.1969	−	24.9397i	−1.63855	−	0.946018i
$696$		0			0
$697$			0.932870i			0.0353350i
$698$	−3.48843	+	6.04213i	−0.132039	+	0.228698i
$699$		0			0
$700$	−6.20327	+	3.58146i	−0.234462	+	0.135366i
$701$	−44.0952			−1.66545			−0.832727	−	0.553684i	$-0.813221\pi$
$701$	−44.0952			−1.66545			−0.832727	+	0.553684i	$0.813221\pi$
$702$		0			0
$703$	40.6192			1.53198
$704$	−2.32244	+	1.34086i	−0.0875301	+	0.0505355i
$705$		0			0
$706$	−12.5193	+	21.6841i	−0.471170	+	0.816090i
$707$		−	3.78650i		−	0.142406i
$708$		0			0
$709$	10.6207	+	6.13185i	0.398868	+	0.230287i	0.685995	−	0.727606i	$-0.259367\pi$
$709$	10.6207	+	6.13185i	0.398868	+	0.230287i	−0.287127	+	0.957892i	$0.592700\pi$
$710$			14.6008i			0.547960i
$711$		0			0
$712$	−2.60662	−	4.51481i	−0.0976874	−	0.169200i
$713$	−4.77864	+	2.75895i	−0.178961	+	0.103323i
$714$		0			0
$715$	−28.9058	−	17.3660i	−1.08101	−	0.649453i
$716$	−15.4384			−0.576961
$717$		0			0
$718$	18.8045	+	32.5703i	0.701777	+	1.21551i
$719$	−13.5967	+	23.5501i	−0.507070	+	0.878272i	0.492896	+	0.870088i	$0.335938\pi$
$719$	−13.5967	+	23.5501i	−0.507070	+	0.878272i	−0.999967	+	0.00818343i	$0.997395\pi$
$720$		0			0
$721$	−5.89623	−	3.40419i	−0.219587	−	0.126779i
$722$	−6.94418	−	4.00922i	−0.258436	−	0.149208i
$723$		0			0
$724$	−6.64092	+	11.5024i	−0.246808	+	0.427484i
$725$	−25.5458	−	44.2466i	−0.948746	−	1.64328i
$726$		0			0
$727$	−18.5289			−0.687200			−0.343600	−	0.939116i	$-0.611646\pi$
$727$	−18.5289			−0.687200			−0.343600	+	0.939116i	$0.611646\pi$
$728$	0.0627130	−	3.60501i	0.00232430	−	0.133610i
$729$		0			0
$730$	−45.4134	+	26.2194i	−1.68082	+	0.970424i
$731$	0.976600	+	1.69152i	0.0361209	+	0.0625632i
$732$		0			0
$733$		−	50.8986i		−	1.87998i	−0.341196	−	0.939992i	$-0.610832\pi$
$733$		−	50.8986i		−	1.87998i	0.341196	−	0.939992i	$-0.389168\pi$
$734$	18.2653	+	10.5455i	0.674185	+	0.389241i
$735$		0			0
$736$			7.05268i			0.259965i
$737$	1.29630	−	2.24525i	0.0477497	−	0.0827049i
$738$		0			0
$739$	−7.43889	+	4.29485i	−0.273644	+	0.157988i	−0.630542	−	0.776155i	$-0.717168\pi$
$739$	−7.43889	+	4.29485i	−0.273644	+	0.157988i	0.356898	+	0.934143i	$0.383834\pi$
$740$	27.2534			1.00185
$741$		0			0
$742$	3.92601			0.144128
$743$	−33.0711	+	19.0936i	−1.21326	+	0.700477i	−0.963468	−	0.267822i	$-0.913696\pi$
$743$	−33.0711	+	19.0936i	−1.21326	+	0.700477i	−0.249794	+	0.968299i	$0.580363\pi$
$744$		0			0
$745$	−6.20289	+	10.7437i	−0.227256	+	0.393619i
$746$		−	14.0942i		−	0.516024i
$747$		0			0
$748$	−13.7376	−	7.93141i	−0.502296	−	0.290001i
$749$			14.3017i			0.522572i
$750$		0			0
$751$	−1.42486	−	2.46792i	−0.0519937	−	0.0900558i	0.838857	−	0.544352i	$-0.183224\pi$
$751$	−1.42486	−	2.46792i	−0.0519937	−	0.0900558i	−0.890851	+	0.454296i	$0.849891\pi$
$752$	1.38704	−	0.800806i	0.0505800	−	0.0292024i
$753$		0			0
$754$	25.7137	+	0.447318i	0.936439	+	0.0162904i
$755$	33.2272			1.20926
$756$		0			0
$757$	−9.63950	−	16.6961i	−0.350354	−	0.606830i	0.635958	−	0.771724i	$-0.280605\pi$
$757$	−9.63950	−	16.6961i	−0.350354	−	0.606830i	−0.986311	+	0.164894i	$0.947272\pi$
$758$	−16.5568	+	28.6773i	−0.601371	+	1.04161i
$759$		0			0
$760$	−15.6993	−	9.06398i	−0.569473	−	0.328785i
$761$	10.0320	+	5.79199i	0.363660	+	0.209959i	0.670685	−	0.741742i	$-0.266000\pi$
$761$	10.0320	+	5.79199i	0.363660	+	0.209959i	−0.307025	+	0.951701i	$0.599334\pi$
$762$		0			0
$763$	−2.28834	+	3.96353i	−0.0828436	+	0.143489i
$764$	5.96230	+	10.3270i	0.215708	+	0.373618i
$765$		0			0
$766$	−25.9321			−0.936964
$767$	34.3925	+	0.598295i	1.24184	+	0.0216032i
$768$		0			0
$769$	21.1486	−	12.2102i	0.762639	−	0.440310i	−0.0676036	−	0.997712i	$-0.521535\pi$
$769$	21.1486	−	12.2102i	0.762639	−	0.440310i	0.830242	+	0.557403i	$0.188202\pi$
$770$	−4.67630	−	8.09958i	−0.168522	−	0.291889i
$771$		0			0
$772$		−	5.34936i		−	0.192528i
$773$	−6.05019	−	3.49308i	−0.217610	−	0.125637i	0.387233	−	0.921982i	$-0.373431\pi$
$773$	−6.05019	−	3.49308i	−0.217610	−	0.125637i	−0.604843	+	0.796345i	$0.706764\pi$
$774$		0			0
$775$		−	5.60415i		−	0.201307i
$776$	1.57973	−	2.73617i	0.0567089	−	0.0982228i
$777$		0			0
$778$	−26.4698	+	15.2824i	−0.948989	+	0.547899i
$779$	−0.819755			−0.0293708
$780$		0			0
$781$	−11.2272			−0.401741
$782$

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)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +3.48754i q^{5} +(0.866025 + 0.500000i) q^{7} +1.00000i q^{8} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +3.48754i q^{5} +(0.866025 + 0.500000i) q^{7} +1.00000i q^{8} +(-1.74377 - 3.02030i) q^{10} +(2.32244 - 1.34086i) q^{11} +(-3.15338 + 1.74819i) q^{13} -1.00000 q^{14} +(-0.500000 - 0.866025i) q^{16} +(2.95758 - 5.12268i) q^{17} +(4.50154 + 2.59896i) q^{19} +(3.02030 + 1.74377i) q^{20} +(-1.34086 + 2.32244i) q^{22} +(3.52634 + 6.10780i) q^{23} -7.16292 q^{25} +(1.85681 - 3.09067i) q^{26} +(0.866025 - 0.500000i) q^{28} +(3.56639 + 6.17717i) q^{29} +0.782383i q^{31} +(0.866025 + 0.500000i) q^{32} +5.91517i q^{34} +(-1.74377 + 3.02030i) q^{35} +(6.76756 - 3.90725i) q^{37} -5.19793 q^{38} -3.48754 q^{40} +(-0.136579 + 0.0788541i) q^{41} +(-0.165101 + 0.285963i) q^{43} -2.68172i q^{44} +(-6.10780 - 3.52634i) q^{46} +1.60161i q^{47} +(0.500000 + 0.866025i) q^{49} +(6.20327 - 3.58146i) q^{50} +(-0.0627130 + 3.60501i) q^{52} -3.92601 q^{53} +(4.67630 + 8.09958i) q^{55} +(-0.500000 + 0.866025i) q^{56} +(-6.17717 - 3.56639i) q^{58} +(-8.26207 - 4.77011i) q^{59} +(-7.70525 + 13.3459i) q^{61} +(-0.391192 - 0.677564i) q^{62} -1.00000 q^{64} +(-6.09688 - 10.9975i) q^{65} +(0.837243 - 0.483382i) q^{67} +(-2.95758 - 5.12268i) q^{68} -3.48754i q^{70} +(-3.62568 - 2.09329i) q^{71} -15.0361i q^{73} +(-3.90725 + 6.76756i) q^{74} +(4.50154 - 2.59896i) q^{76} +2.68172 q^{77} -0.293356 q^{79} +(3.02030 - 1.74377i) q^{80} +(0.0788541 - 0.136579i) q^{82} +2.87495i q^{83} +(17.8656 + 10.3147i) q^{85} -0.330202i q^{86} +(1.34086 + 2.32244i) q^{88} +(-4.51481 + 2.60662i) q^{89} +(-3.60501 - 0.0627130i) q^{91} +7.05268 q^{92} +(-0.800806 - 1.38704i) q^{94} +(-9.06398 + 15.6993i) q^{95} +(-2.73617 - 1.57973i) q^{97} +(-0.866025 - 0.500000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{4}+O(q^{10}) \) 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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