LMFDB - Embedded newform 729.2.c.d.244.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [729,2,Mod(244,729)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(729, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("729.244");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 729 = 3^{6} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	729.c (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.82109430735$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
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} + 18x^{10} + 105x^{8} + 266x^{6} + 306x^{4} + 132x^{2} + 1 $ x^12 + 18x^10 + 105x^8 + 266x^6 + 306x^4 + 132*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			244.6
Root			$-0.0878222i$ of defining polynomial
Character	$\chi$	$=$	729.244
Dual form			729.2.c.d.487.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.35253 + 2.34265i) q^{2} +(-2.65869 + 4.60498i) q^{4} +(-0.836192 + 1.44833i) q^{5} +(-0.250296 - 0.433525i) q^{7} -8.97372 q^{8} +O(q^{10})$	\(q+(1.35253 + 2.34265i) q^{2} +(-2.65869 + 4.60498i) q^{4} +(-0.836192 + 1.44833i) q^{5} +(-0.250296 - 0.433525i) q^{7} -8.97372 q^{8} -4.52391 q^{10} +(-0.958859 - 1.66079i) q^{11} +(-1.55622 + 2.69545i) q^{13} +(0.677066 - 1.17271i) q^{14} +(-6.81987 - 11.8124i) q^{16} -2.66467 q^{17} +5.79664 q^{19} +(-4.44635 - 7.70130i) q^{20} +(2.59378 - 4.49255i) q^{22} +(-2.32293 + 4.02344i) q^{23} +(1.10156 + 1.90797i) q^{25} -8.41934 q^{26} +2.66183 q^{28} +(-1.30754 - 2.26472i) q^{29} +(2.30730 - 3.99636i) q^{31} +(9.47446 - 16.4103i) q^{32} +(-3.60406 - 6.24241i) q^{34} +0.837181 q^{35} -4.85867 q^{37} +(7.84014 + 13.5795i) q^{38} +(7.50375 - 12.9969i) q^{40} +(-5.77408 + 10.0010i) q^{41} +(4.50217 + 7.79798i) q^{43} +10.1972 q^{44} -12.5674 q^{46} +(3.41612 + 5.91689i) q^{47} +(3.37470 - 5.84516i) q^{49} +(-2.97980 + 5.16117i) q^{50} +(-8.27499 - 14.3327i) q^{52} +5.43322 q^{53} +3.20716 q^{55} +(2.24608 + 3.89033i) q^{56} +(3.53697 - 6.12621i) q^{58} +(-1.09566 + 1.89773i) q^{59} +(-3.42017 - 5.92391i) q^{61} +12.4828 q^{62} +23.9786 q^{64} +(-2.60259 - 4.50783i) q^{65} +(-6.24180 + 10.8111i) q^{67} +(7.08453 - 12.2708i) q^{68} +(1.13231 + 1.96123i) q^{70} +2.83568 q^{71} +9.93497 q^{73} +(-6.57151 - 11.3822i) q^{74} +(-15.4114 + 26.6934i) q^{76} +(-0.479996 + 0.831378i) q^{77} +(-2.65561 - 4.59964i) q^{79} +22.8109 q^{80} -31.2385 q^{82} +(-1.36408 - 2.36265i) q^{83} +(2.22818 - 3.85932i) q^{85} +(-12.1787 + 21.0941i) q^{86} +(8.60453 + 14.9035i) q^{88} -11.2189 q^{89} +1.55806 q^{91} +(-12.3519 - 21.3941i) q^{92} +(-9.24082 + 16.0056i) q^{94} +(-4.84710 + 8.39543i) q^{95} +(3.44457 + 5.96617i) q^{97} +18.2576 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 3 q^{2} - 9 q^{4} - 3 q^{5} - 6 q^{7} - 12 q^{8}+O(q^{10}) $ 12 * q + 3 * q^2 - 9 * q^4 - 3 * q^5 - 6 * q^7 - 12 * q^8	$ 12 q + 3 q^{2} - 9 q^{4} - 3 q^{5} - 6 q^{7} - 12 q^{8} + 12 q^{10} - 6 q^{11} - 6 q^{13} + 24 q^{14} - 15 q^{16} + 18 q^{17} + 24 q^{19} - 21 q^{20} - 3 q^{22} - 12 q^{23} - 9 q^{25} - 48 q^{26} + 6 q^{28} + 21 q^{29} - 15 q^{31} - 60 q^{35} + 6 q^{37} + 15 q^{38} - 3 q^{40} - 12 q^{41} - 6 q^{43} + 66 q^{44} - 6 q^{46} - 15 q^{47} - 12 q^{49} - 24 q^{50} - 3 q^{52} + 18 q^{53} + 30 q^{55} + 12 q^{56} + 15 q^{58} + 6 q^{59} - 24 q^{61} + 60 q^{62} + 12 q^{64} - 15 q^{65} - 15 q^{67} + 36 q^{68} + 15 q^{70} + 24 q^{73} + 24 q^{74} - 9 q^{76} + 15 q^{77} - 24 q^{79} + 42 q^{80} - 42 q^{82} - 6 q^{83} + 18 q^{85} - 30 q^{86} + 21 q^{88} + 18 q^{89} + 36 q^{91} + 6 q^{92} + 6 q^{94} - 33 q^{95} + 21 q^{97} - 36 q^{98}+O(q^{100}) $ 12 * q + 3 * q^2 - 9 * q^4 - 3 * q^5 - 6 * q^7 - 12 * q^8 + 12 * q^10 - 6 * q^11 - 6 * q^13 + 24 * q^14 - 15 * q^16 + 18 * q^17 + 24 * q^19 - 21 * q^20 - 3 * q^22 - 12 * q^23 - 9 * q^25 - 48 * q^26 + 6 * q^28 + 21 * q^29 - 15 * q^31 - 60 * q^35 + 6 * q^37 + 15 * q^38 - 3 * q^40 - 12 * q^41 - 6 * q^43 + 66 * q^44 - 6 * q^46 - 15 * q^47 - 12 * q^49 - 24 * q^50 - 3 * q^52 + 18 * q^53 + 30 * q^55 + 12 * q^56 + 15 * q^58 + 6 * q^59 - 24 * q^61 + 60 * q^62 + 12 * q^64 - 15 * q^65 - 15 * q^67 + 36 * q^68 + 15 * q^70 + 24 * q^73 + 24 * q^74 - 9 * q^76 + 15 * q^77 - 24 * q^79 + 42 * q^80 - 42 * q^82 - 6 * q^83 + 18 * q^85 - 30 * q^86 + 21 * q^88 + 18 * q^89 + 36 * q^91 + 6 * q^92 + 6 * q^94 - 33 * q^95 + 21 * q^97 - 36 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/729\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	1.35253	+	2.34265i	0.956385	+	1.65651i	0.731167	+	0.682199i	$0.238976\pi$
$2$	1.35253	+	2.34265i	0.956385	+	1.65651i	0.225218	+	0.974308i	$0.427691\pi$
$3$		0			0
$3$		0			0
$4$	−2.65869	+	4.60498i	−1.32934	+	2.30249i
$5$	−0.836192	+	1.44833i	−0.373957	+	0.647712i	−0.990170	−	0.139867i	$-0.955332\pi$
$5$	−0.836192	+	1.44833i	−0.373957	+	0.647712i	0.616214	+	0.787579i	$0.288666\pi$
$6$		0			0
$7$	−0.250296	−	0.433525i	−0.0946028	−	0.163857i	0.814840	−	0.579686i	$-0.196825\pi$
$7$	−0.250296	−	0.433525i	−0.0946028	−	0.163857i	−0.909443	+	0.415829i	$0.863491\pi$
$8$	−8.97372			−3.17269
$9$		0			0
$10$	−4.52391			−1.43059
$11$	−0.958859	−	1.66079i	−0.289107	−	0.500748i	0.684490	−	0.729022i	$-0.260025\pi$
$11$	−0.958859	−	1.66079i	−0.289107	−	0.500748i	−0.973597	+	0.228275i	$0.926692\pi$
$12$		0			0
$13$	−1.55622	+	2.69545i	−0.431617	+	0.747583i	−0.997013	−	0.0772371i	$-0.975390\pi$
$13$	−1.55622	+	2.69545i	−0.431617	+	0.747583i	0.565396	+	0.824820i	$0.308723\pi$
$14$	0.677066	−	1.17271i	0.180953	−	0.313421i
$15$		0			0
$16$	−6.81987	−	11.8124i	−1.70497	−	2.95309i
$17$	−2.66467			−0.646278			−0.323139	−	0.946352i	$-0.604738\pi$
$17$	−2.66467			−0.646278			−0.323139	+	0.946352i	$0.604738\pi$
$18$		0			0
$19$	5.79664			1.32984			0.664920	−	0.746915i	$-0.268466\pi$
$19$	5.79664			1.32984			0.664920	+	0.746915i	$0.268466\pi$
$20$	−4.44635	−	7.70130i	−0.994234	−	1.72206i
$21$		0			0
$22$	2.59378	−	4.49255i	0.552995	−	0.957815i
$23$	−2.32293	+	4.02344i	−0.484365	+	0.838945i	−0.999839	−	0.0179603i	$-0.994283\pi$
$23$	−2.32293	+	4.02344i	−0.484365	+	0.838945i	0.515473	+	0.856906i	$0.327616\pi$
$24$		0			0
$25$	1.10156	+	1.90797i	0.220313	+	0.381593i
$26$	−8.41934			−1.65117
$27$		0			0
$28$	2.66183			0.503039
$29$	−1.30754	−	2.26472i	−0.242803	−	0.420547i	0.718709	−	0.695312i	$-0.244734\pi$
$29$	−1.30754	−	2.26472i	−0.242803	−	0.420547i	−0.961512	+	0.274764i	$0.911400\pi$
$30$		0			0
$31$	2.30730	−	3.99636i	0.414404	−	0.717768i	−0.580962	−	0.813931i	$-0.697324\pi$
$31$	2.30730	−	3.99636i	0.414404	−	0.717768i	0.995366	+	0.0961626i	$0.0306569\pi$
$32$	9.47446	−	16.4103i	1.67486	−	2.90095i
$33$		0			0
$34$	−3.60406	−	6.24241i	−0.618090	−	1.07056i
$35$	0.837181			0.141509
$36$		0			0
$37$	−4.85867			−0.798761			−0.399381	−	0.916785i	$-0.630775\pi$
$37$	−4.85867			−0.798761			−0.399381	+	0.916785i	$0.630775\pi$
$38$	7.84014	+	13.5795i	1.27184	+	2.20289i
$39$		0			0
$40$	7.50375	−	12.9969i	1.18645	−	2.05499i
$41$	−5.77408	+	10.0010i	−0.901760	+	1.56189i	−0.0765514	+	0.997066i	$0.524391\pi$
$41$	−5.77408	+	10.0010i	−0.901760	+	1.56189i	−0.825208	+	0.564828i	$0.808942\pi$
$42$		0			0
$43$	4.50217	+	7.79798i	0.686574	+	1.18918i	0.972939	+	0.231061i	$0.0742196\pi$
$43$	4.50217	+	7.79798i	0.686574	+	1.18918i	−0.286365	+	0.958121i	$0.592447\pi$
$44$	10.1972			1.53729
$45$		0			0
$46$	−12.5674			−1.85296
$47$	3.41612	+	5.91689i	0.498292	+	0.863067i	0.999998	−	0.00197091i	$-0.000627360\pi$
$47$	3.41612	+	5.91689i	0.498292	+	0.863067i	−0.501706	+	0.865038i	$0.667294\pi$
$48$		0			0
$49$	3.37470	−	5.84516i	0.482101	−	0.835023i
$50$	−2.97980	+	5.16117i	−0.421408	+	0.729900i
$51$		0			0
$52$	−8.27499	−	14.3327i	−1.14754	−	1.98759i
$53$	5.43322			0.746309			0.373155	−	0.927769i	$-0.378276\pi$
$53$	5.43322			0.746309			0.373155	+	0.927769i	$0.378276\pi$
$54$		0			0
$55$	3.20716			0.432454
$56$	2.24608	+	3.89033i	0.300145	+	0.519867i
$57$		0			0
$58$	3.53697	−	6.12621i	0.464427	−	0.804410i
$59$	−1.09566	+	1.89773i	−0.142642	+	0.247064i	−0.928491	−	0.371355i	$-0.878893\pi$
$59$	−1.09566	+	1.89773i	−0.142642	+	0.247064i	0.785849	+	0.618419i	$0.212227\pi$
$60$		0			0
$61$	−3.42017	−	5.92391i	−0.437908	−	0.758478i	0.559620	−	0.828749i	$-0.310947\pi$
$61$	−3.42017	−	5.92391i	−0.437908	−	0.758478i	−0.997528	+	0.0702708i	$0.977614\pi$
$62$	12.4828			1.58532
$63$		0			0
$64$	23.9786			2.99733
$65$	−2.60259	−	4.50783i	−0.322812	−	0.559127i
$66$		0			0
$67$	−6.24180	+	10.8111i	−0.762557	+	1.32079i	0.178971	+	0.983854i	$0.442723\pi$
$67$	−6.24180	+	10.8111i	−0.762557	+	1.32079i	−0.941529	+	0.336933i	$0.890610\pi$
$68$	7.08453	−	12.2708i	0.859126	−	1.48805i
$69$		0			0
$70$	1.13231	+	1.96123i	0.135337	+	0.234411i
$71$	2.83568			0.336534			0.168267	−	0.985741i	$-0.446183\pi$
$71$	2.83568			0.336534			0.168267	+	0.985741i	$0.446183\pi$
$72$		0			0
$73$	9.93497			1.16280			0.581400	−	0.813618i	$-0.302505\pi$
$73$	9.93497			1.16280			0.581400	+	0.813618i	$0.302505\pi$
$74$	−6.57151	−	11.3822i	−0.763923	−	1.32315i
$75$		0			0
$76$	−15.4114	+	26.6934i	−1.76781	+	3.06194i
$77$	−0.479996	+	0.831378i	−0.0547007	+	0.0947443i
$78$		0			0
$79$	−2.65561	−	4.59964i	−0.298779	−	0.517500i	0.677078	−	0.735911i	$-0.263246\pi$
$79$	−2.65561	−	4.59964i	−0.298779	−	0.517500i	−0.975857	+	0.218411i	$0.929913\pi$
$80$	22.8109			2.55033
$81$		0			0
$82$	−31.2385			−3.44972
$83$	−1.36408	−	2.36265i	−0.149727	−	0.259334i	0.781400	−	0.624031i	$-0.214506\pi$
$83$	−1.36408	−	2.36265i	−0.149727	−	0.259334i	−0.931126	+	0.364697i	$0.881173\pi$
$84$		0			0
$85$	2.22818	−	3.85932i	0.241680	−	0.418602i
$86$	−12.1787	+	21.0941i	−1.31326	+	2.27463i
$87$		0			0
$88$	8.60453	+	14.9035i	0.917246	+	1.58872i
$89$	−11.2189			−1.18920			−0.594600	−	0.804021i	$-0.702690\pi$
$89$	−11.2189			−1.18920			−0.594600	+	0.804021i	$0.702690\pi$
$90$		0			0
$91$	1.55806			0.163329
$92$	−12.3519	−	21.3941i	−1.28778	−	2.23049i
$93$		0			0
$94$	−9.24082	+	16.0056i	−0.953118	+	1.65085i
$95$	−4.84710	+	8.39543i	−0.497302	+	0.861353i
$96$		0			0
$97$	3.44457	+	5.96617i	0.349743	+	0.605773i	0.986204	−	0.165536i	$-0.0529355\pi$
$97$	3.44457	+	5.96617i	0.349743	+	0.605773i	−0.636461	+	0.771309i	$0.719602\pi$
$98$	18.2576			1.84429
$99$		0			0
$100$	−11.7149			−1.17149
$101$	1.86482	+	3.22997i	0.185557	+	0.321394i	0.943764	−	0.330620i	$-0.107258\pi$
$101$	1.86482	+	3.22997i	0.185557	+	0.321394i	−0.758207	+	0.652014i	$0.773924\pi$
$102$		0			0
$103$	−3.84040	+	6.65177i	−0.378406	+	0.655418i	−0.990830	−	0.135111i	$-0.956861\pi$
$103$	−3.84040	+	6.65177i	−0.378406	+	0.655418i	0.612425	+	0.790529i	$0.290194\pi$
$104$	13.9651	−	24.1882i	1.36939	−	2.37185i
$105$		0			0
$106$	7.34860	+	12.7281i	0.713759	+	1.23627i
$107$	10.7658			1.04077			0.520383	−	0.853933i	$-0.325789\pi$
$107$	10.7658			1.04077			0.520383	+	0.853933i	$0.325789\pi$
$108$		0			0
$109$	12.2298			1.17141			0.585703	−	0.810526i	$-0.300819\pi$
$109$	12.2298			1.17141			0.585703	+	0.810526i	$0.300819\pi$
$110$	4.33779	+	7.51328i	0.413592	+	0.716363i
$111$		0			0
$112$	−3.41396	+	5.91316i	−0.322589	+	0.558741i
$113$	−0.971975	+	1.68351i	−0.0914357	+	0.158371i	−0.908115	−	0.418720i	$-0.862479\pi$
$113$	−0.971975	+	1.68351i	−0.0914357	+	0.158371i	0.816680	+	0.577091i	$0.195812\pi$
$114$		0			0
$115$	−3.88484	−	6.72874i	−0.362263	−	0.627458i
$116$	13.9053			1.29108
$117$		0			0
$118$	−5.92764			−0.545684
$119$	0.666956	+	1.15520i	0.0611397	+	0.105897i
$120$		0			0
$121$	3.66118	−	6.34135i	0.332834	−	0.576486i
$122$	9.25178	−	16.0245i	0.837617	−	1.45079i
$123$		0			0
$124$	12.2688	+	21.2502i	1.10177	+	1.90832i
$125$	−12.0464			−1.07746
$126$		0			0
$127$	2.34433			0.208026			0.104013	−	0.994576i	$-0.466832\pi$
$127$	2.34433			0.208026			0.104013	+	0.994576i	$0.466832\pi$
$128$	13.4829	+	23.3531i	1.19173	+	2.06414i
$129$		0			0
$130$	7.04019	−	12.1940i	0.617465	−	1.06948i
$131$	−8.55119	+	14.8111i	−0.747121	+	1.29405i	0.202076	+	0.979370i	$0.435231\pi$
$131$	−8.55119	+	14.8111i	−0.747121	+	1.29405i	−0.949197	+	0.314682i	$0.898102\pi$
$132$		0			0
$133$	−1.45087	−	2.51298i	−0.125807	−	0.217903i
$134$	−33.7689			−2.91719
$135$		0			0
$136$	23.9120			2.05044
$137$	6.96358	+	12.0613i	0.594939	+	1.03046i	0.993556	+	0.113347i	$0.0361570\pi$
$137$	6.96358	+	12.0613i	0.594939	+	1.03046i	−0.398617	+	0.917118i	$0.630510\pi$
$138$		0			0
$139$	−3.95832	+	6.85601i	−0.335740	+	0.581519i	−0.983627	−	0.180218i	$-0.942320\pi$
$139$	−3.95832	+	6.85601i	−0.335740	+	0.581519i	0.647887	+	0.761737i	$0.275653\pi$
$140$	−2.22580	+	3.85520i	−0.188115	+	0.325824i
$141$		0			0
$142$	3.83536	+	6.64303i	0.321856	+	0.557471i
$143$	5.96877			0.499134
$144$		0			0
$145$	4.37340			0.363191
$146$	13.4374	+	23.2742i	1.11208	+	1.92619i
$147$		0			0
$148$	12.9177	−	22.3741i	1.06183	−	1.83914i
$149$	0.364067	−	0.630583i	0.0298255	−	0.0516594i	−0.850727	−	0.525607i	$-0.823838\pi$
$149$	0.364067	−	0.630583i	0.0298255	−	0.0516594i	0.880553	+	0.473948i	$0.157171\pi$
$150$		0			0
$151$	−2.17105	−	3.76036i	−0.176677	−	0.306014i	0.764063	−	0.645141i	$-0.223202\pi$
$151$	−2.17105	−	3.76036i	−0.176677	−	0.306014i	−0.940740	+	0.339128i	$0.889868\pi$
$152$	−52.0174			−4.21917
$153$		0			0
$154$	−2.59684			−0.209260
$155$	3.85870	+	6.68346i	0.309938	+	0.536828i
$156$		0			0
$157$	7.76163	−	13.4435i	0.619446	−	1.07291i	−0.370141	−	0.928975i	$-0.620691\pi$
$157$	7.76163	−	13.4435i	0.619446	−	1.07291i	0.989587	−	0.143936i	$-0.0459759\pi$
$158$	7.18359	−	12.4423i	0.571495	−	0.989859i
$159$		0			0
$160$	15.8449	+	27.4443i	1.25265	+	2.16966i
$161$	2.32568			0.183289
$162$		0			0
$163$	8.49738			0.665566			0.332783	−	0.943003i	$-0.392012\pi$
$163$	8.49738			0.665566			0.332783	+	0.943003i	$0.392012\pi$
$164$	−30.7030	−	53.1791i	−2.39750	−	4.15259i
$165$		0			0
$166$	3.68991	−	6.39111i	0.286393	−	0.496047i
$167$	11.5710	−	20.0415i	0.895389	−	1.55086i	0.0620658	−	0.998072i	$-0.480231\pi$
$167$	11.5710	−	20.0415i	0.895389	−	1.55086i	0.833323	−	0.552787i	$-0.186436\pi$
$168$		0			0
$169$	1.65637	+	2.86892i	0.127413	+	0.220686i
$170$	12.0547			0.924556
$171$		0			0
$172$	−47.8794			−3.65077
$173$	−1.28924	−	2.23303i	−0.0980190	−	0.169774i	0.812846	−	0.582479i	$-0.197917\pi$
$173$	−1.28924	−	2.23303i	−0.0980190	−	0.169774i	−0.910865	+	0.412705i	$0.864584\pi$
$174$		0			0
$175$	0.551433	−	0.955111i	0.0416845	−	0.0721996i
$176$	−13.0786	+	22.6528i	−0.985835	+	1.70752i
$177$		0			0
$178$	−15.1739	−	26.2820i	−1.13733	−	1.96992i
$179$	8.89613			0.664928			0.332464	−	0.943116i	$-0.392120\pi$
$179$	8.89613			0.664928			0.332464	+	0.943116i	$0.392120\pi$
$180$		0			0
$181$	7.91183			0.588082			0.294041	−	0.955793i	$-0.405000\pi$
$181$	7.91183			0.588082			0.294041	+	0.955793i	$0.405000\pi$
$182$	2.10732	+	3.64999i	0.156205	+	0.270555i
$183$		0			0
$184$	20.8454	−	36.1052i	1.53674	−	2.66171i
$185$	4.06279	−	7.03695i	0.298702	−	0.517367i
$186$		0			0
$187$	2.55504	+	4.42547i	0.186843	+	0.323622i
$188$	−36.3296			−2.64961
$189$		0			0
$190$	−26.2235			−1.90245
$191$	−7.94867	−	13.7675i	−0.575146	−	0.996182i	−0.996026	−	0.0890656i	$-0.971612\pi$
$191$	−7.94867	−	13.7675i	−0.575146	−	0.996182i	0.420880	−	0.907116i	$-0.361721\pi$
$192$		0			0
$193$	2.29239	−	3.97054i	0.165010	−	0.285805i	−0.771649	−	0.636049i	$-0.780568\pi$
$193$	2.29239	−	3.97054i	0.165010	−	0.285805i	0.936659	+	0.350243i	$0.113901\pi$
$194$	−9.31779	+	16.1389i	−0.668978	+	1.15870i
$195$		0			0
$196$	17.9446	+	31.0809i	1.28176	+	2.22006i
$197$	−2.99417			−0.213326			−0.106663	−	0.994295i	$-0.534017\pi$
$197$	−2.99417			−0.213326			−0.106663	+	0.994295i	$0.534017\pi$
$198$		0			0
$199$	14.8885			1.05542			0.527709	−	0.849425i	$-0.323051\pi$
$199$	14.8885			1.05542			0.527709	+	0.849425i	$0.323051\pi$
$200$	−9.88513	−	17.1215i	−0.698984	−	1.21068i
$201$		0			0
$202$	−5.04447	+	8.73727i	−0.354928	+	0.614753i
$203$	−0.654541	+	1.13370i	−0.0459397	+	0.0795700i
$204$		0			0
$205$	−9.65648	−	16.7255i	−0.674438	−	1.16816i
$206$	−20.7771			−1.44761
$207$		0			0
$208$	42.4528			2.94357
$209$	−5.55816	−	9.62701i	−0.384466	−	0.665914i
$210$		0			0
$211$	−6.93948	+	12.0195i	−0.477733	+	0.827459i	−0.999674	−	0.0255232i	$-0.991875\pi$
$211$	−6.93948	+	12.0195i	−0.477733	+	0.827459i	0.521941	+	0.852982i	$0.325208\pi$
$212$	−14.4452	+	25.0199i	−0.992102	+	1.71837i
$213$		0			0
$214$	14.5610	+	25.2205i	0.995372	+	1.72403i
$215$	−15.0587			−1.02700
$216$		0			0
$217$	−2.31003			−0.156815
$218$	16.5412	+	28.6503i	1.12031	+	1.94044i
$219$		0			0
$220$	−8.52684	+	14.7689i	−0.574880	+	0.995721i
$221$	4.14681	−	7.18248i	0.278945	−	0.483146i
$222$		0			0
$223$	3.40599	+	5.89935i	0.228082	+	0.395050i	0.957240	−	0.289296i	$-0.0934213\pi$
$223$	3.40599	+	5.89935i	0.228082	+	0.395050i	−0.729158	+	0.684346i	$0.760088\pi$
$224$	−9.48567			−0.633788
$225$		0			0
$226$	−5.25851			−0.349791
$227$	−4.87042	−	8.43582i	−0.323261	−	0.559905i	0.657898	−	0.753107i	$-0.271446\pi$
$227$	−4.87042	−	8.43582i	−0.323261	−	0.559905i	−0.981159	+	0.193202i	$0.938113\pi$
$228$		0			0
$229$	7.02242	−	12.1632i	0.464055	−	0.803766i	−0.535104	−	0.844786i	$-0.679727\pi$
$229$	7.02242	−	12.1632i	0.464055	−	0.803766i	0.999158	+	0.0410201i	$0.0130608\pi$
$230$	10.5087	−	18.2017i	0.692926	−	1.20018i
$231$		0			0
$232$	11.7334	+	20.3229i	0.770339	+	1.33427i
$233$	−5.32333			−0.348743			−0.174372	−	0.984680i	$-0.555789\pi$
$233$	−5.32333			−0.348743			−0.174372	+	0.984680i	$0.555789\pi$
$234$		0			0
$235$	−11.4261			−0.745359
$236$	−5.82602	−	10.0910i	−0.379241	−	0.656865i
$237$		0			0
$238$	−1.80416	+	3.12489i	−0.116946	+	0.202557i
$239$	8.88675	−	15.3923i	0.574836	−	0.995646i	−0.421223	−	0.906957i	$-0.638399\pi$
$239$	8.88675	−	15.3923i	0.574836	−	0.995646i	0.996059	−	0.0886886i	$-0.0282676\pi$
$240$		0			0
$241$	1.00340	+	1.73793i	0.0646344	+	0.111950i	0.896532	−	0.442979i	$-0.146079\pi$
$241$	1.00340	+	1.73793i	0.0646344	+	0.111950i	−0.831897	+	0.554930i	$0.812745\pi$
$242$	19.8075			1.27327
$243$		0			0
$244$	36.3726			2.32852
$245$	5.64380	+	9.77536i	0.360569	+	0.624525i
$246$		0			0
$247$	−9.02083	+	15.6245i	−0.573981	+	0.994165i
$248$	−20.7051	+	35.8622i	−1.31477	+	2.27725i
$249$		0			0
$250$	−16.2932	−	28.2206i	−1.03047	−	1.78483i
$251$	−23.5643			−1.48737			−0.743683	−	0.668533i	$-0.766923\pi$
$251$	−23.5643			−1.48737			−0.743683	+	0.668533i	$0.766923\pi$
$252$		0			0
$253$	8.90947			0.560133
$254$	3.17079	+	5.49196i	0.198953	+	0.344596i
$255$		0			0
$256$	−12.4936	+	21.6395i	−0.780848	+	1.35247i
$257$	2.93728	−	5.08752i	0.183223	−	0.317351i	−0.759754	−	0.650211i	$-0.774680\pi$
$257$	2.93728	−	5.08752i	0.183223	−	0.317351i	0.942976	+	0.332860i	$0.108014\pi$
$258$		0			0
$259$	1.21610	+	2.10635i	0.0755651	+	0.130883i
$260$	27.6779			1.71651
$261$		0			0
$262$	−46.2631			−2.85814
$263$	10.9891	+	19.0336i	0.677615	+	1.17366i	0.975697	+	0.219123i	$0.0703197\pi$
$263$	10.9891	+	19.0336i	0.677615	+	1.17366i	−0.298082	+	0.954540i	$0.596347\pi$
$264$		0			0
$265$	−4.54321	+	7.86908i	−0.279087	+	0.483393i
$266$	3.92470	−	6.79779i	0.240639	−	0.416799i
$267$		0			0
$268$	−33.1900	−	57.4867i	−2.02740	−	3.51156i
$269$	30.6026			1.86587			0.932937	−	0.360041i	$-0.117237\pi$
$269$	30.6026			1.86587			0.932937	+	0.360041i	$0.117237\pi$
$270$		0			0
$271$	−16.0823			−0.976928			−0.488464	−	0.872584i	$-0.662443\pi$
$271$	−16.0823			−0.976928			−0.488464	+	0.872584i	$0.662443\pi$
$272$	18.1727	+	31.4761i	1.10188	+	1.90852i
$273$		0			0
$274$	−18.8369	+	32.6265i	−1.13798	+	1.97104i
$275$	2.11249	−	3.65894i	0.127388	−	0.220642i
$276$		0			0
$277$	10.4068	+	18.0251i	0.625283	+	1.08302i	0.988486	+	0.151312i	$0.0483499\pi$
$277$	10.4068	+	18.0251i	0.625283	+	1.08302i	−0.363203	+	0.931710i	$0.618317\pi$
$278$	−21.4150			−1.28439
$279$		0			0
$280$	−7.51263			−0.448965
$281$	6.13014	+	10.6177i	0.365693	+	0.633400i	0.988887	−	0.148668i	$-0.0474985\pi$
$281$	6.13014	+	10.6177i	0.365693	+	0.633400i	−0.623194	+	0.782067i	$0.714165\pi$
$282$		0			0
$283$	−2.28629	+	3.95997i	−0.135906	+	0.235396i	−0.925943	−	0.377663i	$-0.876728\pi$
$283$	−2.28629	+	3.95997i	−0.135906	+	0.235396i	0.790037	+	0.613059i	$0.210061\pi$
$284$	−7.53920	+	13.0583i	−0.447369	+	0.774866i
$285$		0			0
$286$	8.07296	+	13.9828i	0.477364	+	0.826819i
$287$	5.78091			0.341236
$288$		0			0
$289$	−9.89952			−0.582325
$290$	5.91517	+	10.2454i	0.347351	+	0.601629i
$291$		0			0
$292$	−26.4140	+	45.7504i	−1.54576	+	2.67734i
$293$	13.0617	−	22.6235i	0.763073	−	1.32168i	−0.178186	−	0.983997i	$-0.557023\pi$
$293$	13.0617	−	22.6235i	0.763073	−	1.32168i	0.941259	−	0.337685i	$-0.109644\pi$
$294$		0			0
$295$	−1.83236	−	3.17374i	−0.106684	−	0.184782i
$296$	43.6004			2.53422
$297$		0			0
$298$	1.96965			0.114099
$299$	−7.22998	−	12.5227i	−0.418121	−	0.724206i
$300$		0			0
$301$	2.25375	−	3.90360i	0.129904	−	0.225000i
$302$	5.87282	−	10.1720i	0.337943	−	0.585334i
$303$		0			0
$304$	−39.5323	−	68.4719i	−2.26733	−	3.92713i
$305$	11.4397			0.655034
$306$		0			0
$307$	3.29277			0.187928			0.0939641	−	0.995576i	$-0.470046\pi$
$307$	3.29277			0.187928			0.0939641	+	0.995576i	$0.470046\pi$
$308$	−2.55232	−	4.42075i	−0.145432	−	0.251896i
$309$		0			0
$310$	−10.4380	+	18.0792i	−0.592840	+	1.02683i
$311$	17.3963	−	30.1313i	0.986455	−	1.70859i	0.351170	−	0.936312i	$-0.385784\pi$
$311$	17.3963	−	30.1313i	0.986455	−	1.70859i	0.635285	−	0.772278i	$-0.280883\pi$
$312$		0			0
$313$	−5.31392	−	9.20398i	−0.300360	−	0.520239i	0.675857	−	0.737033i	$-0.263774\pi$
$313$	−5.31392	−	9.20398i	−0.300360	−	0.520239i	−0.976218	+	0.216793i	$0.930440\pi$
$314$	41.9914			2.36971
$315$		0			0
$316$	28.2417			1.58872
$317$	−7.75011	−	13.4236i	−0.435290	−	0.753944i	0.562030	−	0.827117i	$-0.310021\pi$
$317$	−7.75011	−	13.4236i	−0.435290	−	0.753944i	−0.997319	+	0.0731733i	$0.976687\pi$
$318$		0			0
$319$	−2.50748	+	4.34309i	−0.140392	+	0.243166i
$320$	−20.0507	+	34.7289i	−1.12087	+	1.94140i
$321$		0			0
$322$	3.14556	+	5.44827i	0.175295	+	0.303620i
$323$	−15.4461			−0.859446
$324$		0			0
$325$	−6.85710			−0.380363
$326$	11.4930	+	19.9064i	0.636538	+	1.10252i
$327$		0			0
$328$	51.8150	−	89.7461i	2.86100	−	4.95540i
$329$	1.71008	−	2.96194i	0.0942797	−	0.163297i
$330$		0			0
$331$	7.28514	+	12.6182i	0.400427	+	0.693561i	0.993777	−	0.111384i	$-0.0355283\pi$
$331$	7.28514	+	12.6182i	0.400427	+	0.693561i	−0.593350	+	0.804945i	$0.702195\pi$
$332$	14.5066			0.796153
$333$		0			0
$334$	62.6005			3.42534
$335$	−10.4387	−	18.0803i	−0.570327	−	0.987834i
$336$		0			0
$337$	10.3074	−	17.8529i	0.561479	−	0.972511i	−0.435888	−	0.900001i	$-0.643566\pi$
$337$	10.3074	−	17.8529i	0.561479	−	0.972511i	0.997368	−	0.0725099i	$-0.0231009\pi$
$338$	−4.48060	+	7.76062i	−0.243712	+	0.422122i
$339$		0			0
$340$	11.8481	+	20.5214i	0.642551	+	1.11293i
$341$	−8.84951			−0.479228
$342$		0			0
$343$	−6.88283			−0.371638
$344$	−40.4012	−	69.9769i	−2.17829	−	3.77290i
$345$		0			0
$346$	3.48748	−	6.04048i	0.187488	−	0.324738i
$347$	−10.5918	+	18.3455i	−0.568596	+	0.984838i	0.428109	+	0.903727i	$0.359180\pi$
$347$	−10.5918	+	18.3455i	−0.568596	+	0.984838i	−0.996705	+	0.0811104i	$0.974153\pi$
$348$		0			0
$349$	2.31299	+	4.00621i	0.123811	+	0.214447i	0.921268	−	0.388929i	$-0.127155\pi$
$349$	2.31299	+	4.00621i	0.123811	+	0.214447i	−0.797456	+	0.603377i	$0.793822\pi$
$350$	2.98333			0.159466
$351$		0			0
$352$	−36.3387			−1.93686
$353$	−6.82171	−	11.8155i	−0.363083	−	0.628878i	0.625384	−	0.780317i	$-0.284942\pi$
$353$	−6.82171	−	11.8155i	−0.363083	−	0.628878i	−0.988467	+	0.151440i	$0.951609\pi$
$354$		0			0
$355$	−2.37118	+	4.10700i	−0.125849	+	0.217977i
$356$	29.8275	−	51.6628i	1.58086	−	2.73812i
$357$		0			0
$358$	12.0323	+	20.8406i	0.635927	+	1.10146i
$359$	28.2447			1.49070			0.745349	−	0.666675i	$-0.232283\pi$
$359$	28.2447			1.49070			0.745349	+	0.666675i	$0.232283\pi$
$360$		0			0
$361$	14.6010			0.768473
$362$	10.7010	+	18.5347i	0.562432	+	0.974162i
$363$		0			0
$364$	−4.14239	+	7.17483i	−0.217120	+	0.376063i
$365$	−8.30755	+	14.3891i	−0.434837	+	0.753160i
$366$		0			0
$367$	−17.4401	−	30.2071i	−0.910366	−	1.57680i	−0.813548	−	0.581498i	$-0.802467\pi$
$367$	−17.4401	−	30.2071i	−0.910366	−	1.57680i	−0.0968183	−	0.995302i	$-0.530867\pi$
$368$	63.3684			3.30331
$369$		0			0
$370$	21.9802			1.14270
$371$	−1.35991	−	2.35543i	−0.0706030	−	0.122288i
$372$		0			0
$373$	−1.52972	+	2.64955i	−0.0792059	+	0.137189i	−0.902908	−	0.429835i	$-0.858572\pi$
$373$	−1.52972	+	2.64955i	−0.0792059	+	0.137189i	0.823702	+	0.567023i	$0.191905\pi$
$374$	−6.91156	+	11.9712i	−0.357388	+	0.619015i
$375$		0			0
$376$	−30.6553	−	53.0965i	−1.58093	−	2.73824i
$377$	8.13924			0.419192
$378$		0			0
$379$	−7.67705			−0.394344			−0.197172	−	0.980369i	$-0.563176\pi$
$379$	−7.67705			−0.394344			−0.197172	+	0.980369i	$0.563176\pi$
$380$	−25.7739	−	44.6417i	−1.32217	−	2.29007i
$381$		0			0
$382$	21.5017	−	37.2420i	1.10012	−	1.90547i
$383$	5.18097	−	8.97370i	0.264735	−	0.458535i	−0.702759	−	0.711428i	$-0.748049\pi$
$383$	5.18097	−	8.97370i	0.264735	−	0.458535i	0.967494	+	0.252893i	$0.0813821\pi$
$384$		0			0
$385$	−0.802739	−	1.39038i	−0.0409113	−	0.0708605i
$386$	12.4021			0.631252
$387$		0			0
$388$	−36.6322			−1.85972
$389$	−0.213476	−	0.369751i	−0.0108236	−	0.0187471i	0.860563	−	0.509344i	$-0.170112\pi$
$389$	−0.213476	−	0.369751i	−0.0108236	−	0.0187471i	−0.871386	+	0.490597i	$0.836779\pi$
$390$		0			0
$391$	6.18986	−	10.7211i	0.313035	−	0.542192i
$392$	−30.2836	+	52.4528i	−1.52955	+	2.64927i
$393$		0			0
$394$	−4.04971	−	7.01430i	−0.204021	−	0.353376i
$395$	8.88239			0.446922
$396$		0			0
$397$	−27.0891			−1.35956			−0.679781	−	0.733416i	$-0.737925\pi$
$397$	−27.0891			−1.35956			−0.679781	+	0.733416i	$0.737925\pi$
$398$	20.1372	+	34.8786i	1.00939	+	1.74831i
$399$		0			0
$400$	15.0250	−	26.0241i	0.751252	−	1.30121i
$401$	14.6802	−	25.4269i	0.733096	−	1.26976i	−0.222458	−	0.974942i	$-0.571408\pi$
$401$	14.6802	−	25.4269i	0.733096	−	1.26976i	0.955554	−	0.294817i	$-0.0952588\pi$
$402$		0			0
$403$	7.18133	+	12.4384i	0.357727	+	0.619602i
$404$	−19.8319			−0.986675
$405$		0			0
$406$	−3.54115			−0.175744
$407$	4.65878	+	8.06925i	0.230927	+	0.399978i
$408$		0			0
$409$	10.0920	−	17.4798i	0.499015	−	0.864320i	−0.500984	−	0.865457i	$-0.667028\pi$
$409$	10.0920	−	17.4798i	0.499015	−	0.864320i	0.999999	+	0.00113651i	$0.000361762\pi$
$410$	26.1214	−	45.2436i	1.29004	−	2.23442i
$411$		0			0
$412$	−20.4208	−	35.3699i	−1.00606	−	1.74255i
$413$	1.09695			0.0539775
$414$		0			0
$415$	4.56252			0.223965
$416$	29.4887	+	51.0758i	1.44580	+	2.50420i
$417$		0			0
$418$	15.0352	−	26.0417i	0.735395	−	1.27374i
$419$	12.1852	−	21.1053i	0.595284	−	1.03106i	−0.398223	−	0.917289i	$-0.630373\pi$
$419$	12.1852	−	21.1053i	0.595284	−	1.03106i	0.993507	−	0.113774i	$-0.0362938\pi$
$420$		0			0
$421$	13.0873	+	22.6678i	0.637835	+	1.10476i	0.985907	+	0.167294i	$0.0535030\pi$
$421$	13.0873	+	22.6678i	0.637835	+	1.10476i	−0.348072	+	0.937468i	$0.613164\pi$
$422$	−37.5435			−1.82759
$423$		0			0
$424$	−48.7561			−2.36781
$425$	−2.93531	−	5.08410i	−0.142383	−	0.246615i
$426$		0			0
$427$	−1.71211	+	2.96545i	−0.0828546	+	0.143508i
$428$	−28.6228	+	49.5761i	−1.38353	+	2.39635i
$429$		0			0
$430$	−20.3674	−	35.2774i	−0.982203	−	1.70123i
$431$	−31.9185			−1.53746			−0.768731	−	0.639572i	$-0.779111\pi$
$431$	−31.9185			−1.53746			−0.768731	+	0.639572i	$0.779111\pi$
$432$		0			0
$433$	0.0123080			0.000591484			0.000295742	−	1.00000i	$-0.499906\pi$
$433$	0.0123080			0.000591484			0.000295742		1.00000i	$0.499906\pi$
$434$	−3.12439	−	5.41160i	−0.149976	−	0.259765i
$435$		0			0
$436$	−32.5153	+	56.3182i	−1.55720	+	2.69715i
$437$	−13.4652	+	23.3224i	−0.644128	+	1.11566i
$438$		0			0
$439$	−2.65240	−	4.59410i	−0.126592	−	0.219264i	0.795762	−	0.605610i	$-0.207071\pi$
$439$	−2.65240	−	4.59410i	−0.126592	−	0.219264i	−0.922354	+	0.386345i	$0.873737\pi$
$440$	−28.7802			−1.37204
$441$		0			0
$442$	22.4348			1.06711
$443$	20.3482	+	35.2441i	0.966771	+	1.67450i	0.704781	+	0.709425i	$0.251045\pi$
$443$	20.3482	+	35.2441i	0.966771	+	1.67450i	0.261990	+	0.965071i	$0.415621\pi$
$444$		0			0
$445$	9.38116	−	16.2486i	0.444709	−	0.770259i
$446$	−9.21342	+	15.9581i	−0.436268	+	0.755639i
$447$		0			0
$448$	−6.00174	−	10.3953i	−0.283556	−	0.491133i
$449$	−15.4280			−0.728093			−0.364047	−	0.931381i	$-0.618605\pi$
$449$	−15.4280			−0.728093			−0.364047	+	0.931381i	$0.618605\pi$
$450$		0			0
$451$	22.1461			1.04282
$452$	−5.16835	−	8.95185i	−0.243099	−	0.421060i
$453$		0			0
$454$	13.1748	−	22.8194i	0.618324	−	1.07097i
$455$	−1.30284	+	2.25658i	−0.0610779	+	0.105790i
$456$		0			0
$457$	−1.19437	−	2.06872i	−0.0558704	−	0.0967704i	0.836737	−	0.547604i	$-0.184460\pi$
$457$	−1.19437	−	2.06872i	−0.0558704	−	0.0967704i	−0.892608	+	0.450834i	$0.851127\pi$
$458$	37.9922			1.77526
$459$		0			0
$460$	41.3143			1.92629
$461$	16.2419	+	28.1319i	0.756462	+	1.31023i	0.944644	+	0.328097i	$0.106407\pi$
$461$	16.2419	+	28.1319i	0.756462	+	1.31023i	−0.188182	+	0.982134i	$0.560259\pi$
$462$		0			0
$463$	−16.9393	+	29.3397i	−0.787234	+	1.36353i	0.140421	+	0.990092i	$0.455155\pi$
$463$	−16.9393	+	29.3397i	−0.787234	+	1.36353i	−0.927655	+	0.373438i	$0.878179\pi$
$464$	−17.8344	+	30.8901i	−0.827943	+	1.43404i
$465$		0			0
$466$	−7.19998	−	12.4707i	−0.333533	−	0.577696i
$467$	13.8027			0.638711			0.319356	−	0.947635i	$-0.396534\pi$
$467$	13.8027			0.638711			0.319356	+	0.947635i	$0.396534\pi$
$468$		0			0
$469$	6.24918			0.288560
$470$	−15.4542	−	26.7675i	−0.712850	−	1.23469i
$471$		0			0
$472$	9.83211	−	17.0297i	0.452559	−	0.783856i
$473$	8.63389	−	14.9543i	0.396987	−	0.687601i
$474$		0			0
$475$	6.38537	+	11.0598i	0.292981	+	0.507458i
$476$	−7.09291			−0.325103
$477$		0			0
$478$	48.0785			2.19906
$479$	2.94556	+	5.10186i	0.134586	+	0.233110i	0.925439	−	0.378896i	$-0.123696\pi$
$479$	2.94556	+	5.10186i	0.134586	+	0.233110i	−0.790853	+	0.612006i	$0.790363\pi$
$480$		0			0
$481$	7.56115	−	13.0963i	0.344759	−	0.597140i
$482$	−2.71425	+	4.70122i	−0.123631	+	0.214135i
$483$		0			0
$484$	19.4679	+	33.7193i	0.884903	+	1.53270i
$485$	−11.5213			−0.523155
$486$		0			0
$487$	29.0299			1.31547			0.657736	−	0.753249i	$-0.271514\pi$
$487$	29.0299			1.31547			0.657736	+	0.753249i	$0.271514\pi$
$488$	30.6916	+	53.1594i	1.38934	+	2.40642i
$489$		0			0
$490$	−15.2669	+	26.4430i	−0.689686	+	1.19457i
$491$	2.19175	−	3.79623i	0.0989125	−	0.171321i	−0.812322	−	0.583209i	$-0.801797\pi$
$491$	2.19175	−	3.79623i	0.0989125	−	0.171321i	0.911235	+	0.411887i	$0.135130\pi$
$492$		0			0
$493$	3.48415	+	6.03473i	0.156918	+	0.271791i
$494$	−48.8038			−2.19579
$495$		0			0
$496$	−62.9420			−2.82618
$497$	−0.709759	−	1.22934i	−0.0318371	−	0.0551434i
$498$		0			0
$499$	−17.6718	+	30.6084i	−0.791096	+	1.37022i	0.134192	+	0.990955i	$0.457156\pi$
$499$	−17.6718	+	30.6084i	−0.791096	+	1.37022i	−0.925289	+	0.379264i	$0.876177\pi$
$500$	32.0276	−	55.4735i	1.43232	−	2.48085i
$501$		0			0
$502$	−31.8715	−	55.2030i	−1.42249	−	2.46383i
$503$	8.37659			0.373494			0.186747	−	0.982408i	$-0.440206\pi$
$503$	8.37659			0.373494			0.186747	+	0.982408i	$0.440206\pi$
$504$		0			0
$505$	−6.23740			−0.277561
$506$	12.0503	+	20.8718i	0.535703	+	0.927865i
$507$		0			0
$508$	−6.23285	+	10.7956i	−0.276538	+	0.478978i
$509$	−1.92148	+	3.32811i	−0.0851683	+	0.147516i	−0.905463	−	0.424425i	$-0.860476\pi$
$509$	−1.92148	+	3.32811i	−0.0851683	+	0.147516i	0.820295	+	0.571941i	$0.193809\pi$
$510$		0			0
$511$	−2.48668	−	4.30706i	−0.110004	−	0.190533i
$512$	−13.6601			−0.603699
$513$		0			0
$514$	15.8911			0.700925
$515$	−6.42262	−	11.1243i	−0.283015	−	0.490196i
$516$		0			0
$517$	6.55115	−	11.3469i	0.288119	−	0.499037i
$518$	−3.28964	+	5.69783i	−0.144539	+	0.250348i
$519$		0			0
$520$	23.3549	+	40.4520i	1.02418	+	1.77394i
$521$	−19.6523			−0.860983			−0.430491	−	0.902595i	$-0.641660\pi$
$521$	−19.6523			−0.860983			−0.430491	+	0.902595i	$0.641660\pi$
$522$		0			0
$523$	−39.6103			−1.73204			−0.866018	−	0.500012i	$-0.833329\pi$
$523$	−39.6103			−1.73204			−0.866018	+	0.500012i	$0.833329\pi$
$524$	−45.4699	−	78.7562i	−1.98636	−	3.44048i
$525$		0			0
$526$	−29.7261	+	51.4872i	−1.29612	+	2.24495i
$527$	−6.14820	+	10.6490i	−0.267820	+	0.463878i
$528$		0			0
$529$	0.707953	+	1.22621i	0.0307806	+	0.0533135i
$530$	−24.5794			−1.06766
$531$		0			0
$532$	15.4297			0.668961
$533$	−17.9715	−	31.1275i	−0.778430	−	1.34828i
$534$		0			0
$535$	−9.00224	+	15.5923i	−0.389201	+	0.674116i
$536$	56.0121	−	97.0159i	2.41936	−	4.19045i
$537$		0			0
$538$	41.3910	+	71.6913i	1.78449	+	3.09083i
$539$	−12.9435			−0.557514
$540$		0			0
$541$	−41.8257			−1.79823			−0.899115	−	0.437713i	$-0.855788\pi$
$541$	−41.8257			−1.79823			−0.899115	+	0.437713i	$0.855788\pi$
$542$	−21.7518	−	37.6752i	−0.934319	−	1.61829i
$543$		0			0
$544$	−25.2463	+	43.7279i	−1.08243	+	1.87482i
$545$	−10.2265	+	17.7128i	−0.438055	+	0.758733i
$546$		0			0
$547$	8.51716	+	14.7522i	0.364168	+	0.630757i	0.988642	−	0.150288i	$-0.0480202\pi$
$547$	8.51716	+	14.7522i	0.364168	+	0.630757i	−0.624475	+	0.781045i	$0.714687\pi$
$548$	−74.0559			−3.16351
$549$		0			0
$550$	11.4288			0.487328
$551$	−7.57931	−	13.1277i	−0.322889	−	0.559261i
$552$		0			0
$553$	−1.32937	+	2.30254i	−0.0565307	+	0.0979140i
$554$	−28.1510	+	48.7590i	−1.19602	+	2.07157i
$555$		0			0
$556$	−21.0479	−	36.4560i	−0.892628	−	1.54608i
$557$	33.7680			1.43080			0.715398	−	0.698717i	$-0.246245\pi$
$557$	33.7680			1.43080			0.715398	+	0.698717i	$0.246245\pi$
$558$		0			0
$559$	−28.0254			−1.18535
$560$	−5.70946	−	9.88908i	−0.241269	−	0.417890i
$561$		0			0
$562$	−16.5824	+	28.7216i	−0.699487	+	1.21155i
$563$	−11.3556	+	19.6685i	−0.478583	+	0.828930i	−0.999698	−	0.0245561i	$-0.992183\pi$
$563$	−11.3556	+	19.6685i	−0.478583	+	0.828930i	0.521115	+	0.853486i	$0.325516\pi$
$564$		0			0
$565$	−1.62552	−	2.81548i	−0.0683860	−	0.118448i
$566$	−12.3691			−0.519913
$567$		0			0
$568$	−25.4466			−1.06772
$569$	5.43572	+	9.41495i	0.227877	+	0.394695i	0.957179	−	0.289497i	$-0.0934881\pi$
$569$	5.43572	+	9.41495i	0.227877	+	0.394695i	−0.729301	+	0.684193i	$0.760155\pi$
$570$		0			0
$571$	−7.44185	+	12.8897i	−0.311432	+	0.539416i	−0.978673	−	0.205426i	$-0.934142\pi$
$571$	−7.44185	+	12.8897i	−0.311432	+	0.539416i	0.667241	+	0.744842i	$0.267475\pi$
$572$	−15.8691	+	27.4861i	−0.663521	+	1.14925i
$573$		0			0
$574$	7.81886	+	13.5427i	0.326353	+	0.565260i
$575$	−10.2354			−0.426848
$576$		0			0
$577$	−37.1163			−1.54517			−0.772586	−	0.634910i	$-0.781037\pi$
$577$	−37.1163			−1.54517			−0.772586	+	0.634910i	$0.781037\pi$
$578$	−13.3894	−	23.1912i	−0.556927	−	0.964625i
$579$		0			0
$580$	−11.6275	+	20.1394i	−0.482806	+	0.836245i
$581$	−0.682844	+	1.18272i	−0.0283291	+	0.0490675i
$582$		0			0
$583$	−5.20969	−	9.02344i	−0.215763	−	0.373713i
$584$	−89.1536			−3.68920
$585$		0			0
$586$	70.6655			2.91917
$587$	7.32161	+	12.6814i	0.302195	+	0.523417i	0.976633	−	0.214914i	$-0.0689472\pi$
$587$	7.32161	+	12.6814i	0.302195	+	0.523417i	−0.674438	+	0.738332i	$0.735614\pi$
$588$		0			0
$589$	13.3746	−	23.1655i	0.551090	−	0.954516i
$590$	4.95665	−	8.58517i	0.204062	−	0.353446i
$591$		0			0
$592$	33.1355	+	57.3924i	1.36186	+	2.35881i
$593$	36.4392			1.49638			0.748189	−	0.663485i	$-0.230924\pi$
$593$	36.4392			1.49638			0.748189	+	0.663485i	$0.230924\pi$
$594$		0			0
$595$	−2.23081			−0.0914544
$596$	1.93588	+	3.35305i	0.0792968	+	0.137346i
$597$		0			0
$598$	19.5576	−	33.8747i	0.799769	−	1.38524i
$599$	−13.7474	+	23.8113i	−0.561705	+	0.972902i	0.435642	+	0.900120i	$0.356521\pi$
$599$	−13.7474	+	23.8113i	−0.561705	+	0.972902i	−0.997348	+	0.0727826i	$0.976812\pi$
$600$		0			0
$601$	−22.5885	−	39.1244i	−0.921404	−	1.59592i	−0.797245	−	0.603656i	$-0.793710\pi$
$601$	−22.5885	−	39.1244i	−0.921404	−	1.59592i	−0.124159	−	0.992262i	$-0.539623\pi$
$602$	12.1931			0.496952
$603$		0			0
$604$	23.0885			0.939459
$605$	6.12290	+	10.6052i	0.248931	+	0.431162i
$606$		0			0
$607$	−8.56858	+	14.8412i	−0.347788	+	0.602387i	−0.985856	−	0.167593i	$-0.946400\pi$
$607$	−8.56858	+	14.8412i	−0.347788	+	0.602387i	0.638068	+	0.769980i	$0.279734\pi$
$608$	54.9200	−	95.1243i	2.22730	−	3.85780i
$609$		0			0
$610$	15.4725	+	26.7992i	0.626464	+	1.08507i
$611$	−21.2649			−0.860286
$612$		0			0
$613$	−0.468761			−0.0189331			−0.00946653	−	0.999955i	$-0.503013\pi$
$613$	−0.468761			−0.0189331			−0.00946653	+	0.999955i	$0.503013\pi$
$614$	4.45358	+	7.71382i	0.179732	+	0.311304i
$615$		0			0
$616$	4.30735	−	7.46055i	0.173548	−	0.300594i
$617$	1.06742	−	1.84883i	0.0429729	−	0.0744312i	−0.843739	−	0.536754i	$-0.819650\pi$
$617$	1.06742	−	1.84883i	0.0429729	−	0.0744312i	0.886712	+	0.462323i	$0.152984\pi$
$618$		0			0
$619$	−4.26880	−	7.39378i	−0.171578	−	0.297181i	0.767394	−	0.641176i	$-0.221553\pi$
$619$	−4.26880	−	7.39378i	−0.171578	−	0.297181i	−0.938972	+	0.343995i	$0.888220\pi$
$620$	−41.0363			−1.64806
$621$		0			0
$622$	94.1163			3.77372
$623$	2.80804	+	4.86367i	0.112502	+	0.194859i
$624$		0			0
$625$	4.56529	−	7.90731i	0.182612	−	0.316292i
$626$	14.3745	−	24.8974i	0.574520	−	0.995098i
$627$		0			0
$628$	41.2715	+	71.4844i	1.64691	+	2.85254i
$629$	12.9468			0.516222
$630$		0			0
$631$	−11.8708			−0.472569			−0.236284	−	0.971684i	$-0.575930\pi$
$631$	−11.8708			−0.472569			−0.236284	+	0.971684i	$0.575930\pi$
$632$	23.8307	+	41.2759i	0.947933	+	1.64187i
$633$		0			0
$634$	20.9646	−	36.3117i	0.832609	−	1.44212i
$635$	−1.96031	+	3.39536i	−0.0777926	+	0.134741i
$636$		0			0
$637$	10.5035	+	18.1927i	0.416166	+	0.720820i
$638$	−13.5658			−0.537076
$639$		0			0
$640$	−45.0973			−1.78263
$641$	−2.65183	−	4.59310i	−0.104741	−	0.181417i	0.808891	−	0.587958i	$-0.200068\pi$
$641$	−2.65183	−	4.59310i	−0.104741	−	0.181417i	−0.913632	+	0.406541i	$0.866735\pi$
$642$		0			0
$643$	0.411934	−	0.713491i	0.0162451	−	0.0281374i	−0.857789	−	0.514003i	$-0.828162\pi$
$643$	0.411934	−	0.713491i	0.0162451	−	0.0281374i	0.874034	+	0.485865i	$0.161495\pi$
$644$	−6.18326	+	10.7097i	−0.243655	+	0.422022i
$645$		0			0
$646$	−20.8914	−	36.1850i	−0.821961	−	1.42368i
$647$	−40.8373			−1.60548			−0.802740	−	0.596329i	$-0.796626\pi$
$647$	−40.8373			−1.60548			−0.802740	+	0.596329i	$0.796626\pi$
$648$		0			0
$649$	4.20232			0.164955
$650$	−9.27445	−	16.0638i	−0.363774	−	0.630074i
$651$		0			0
$652$	−22.5919	+	39.1303i	−0.884767	+	1.53246i
$653$	−0.534678	+	0.926090i	−0.0209236	+	0.0362407i	−0.876298	−	0.481770i	$-0.839994\pi$
$653$	−0.534678	+	0.926090i	−0.0209236	+	0.0362407i	0.855374	+	0.518011i	$0.173327\pi$
$654$		0			0
$655$	−14.3009	−	24.7699i	−0.558782	−	0.967838i
$656$	157.514			6.14988
$657$		0			0
$658$	9.25175			0.360671
$659$	14.3321	+	24.8240i	0.558301	+	0.967006i	0.997638	+	0.0686837i	$0.0218799\pi$
$659$	14.3321	+	24.8240i	0.558301	+	0.967006i	−0.439337	+	0.898322i	$0.644787\pi$
$660$		0			0
$661$	2.24786	−	3.89341i	0.0874316	−	0.151436i	−0.818993	−	0.573803i	$-0.805467\pi$
$661$	2.24786	−	3.89341i	0.0874316	−	0.151436i	0.906425	+	0.422367i	$0.138801\pi$
$662$	−19.7068	+	34.1331i	−0.765925	+	1.32662i
$663$		0			0
$664$	12.2408	+	21.2017i	0.475036	+	0.822787i
$665$	4.85283			0.188185
$666$		0			0
$667$	12.1493			0.470422
$668$	61.5272	+	106.568i	2.38056	+	4.12325i
$669$		0			0
$670$	28.2373	−	48.9085i	1.09090	−	1.88950i
$671$	−6.55892	+	11.3604i	−0.253204	+	0.438563i
$672$		0			0
$673$	−9.02929	−	15.6392i	−0.348054	−	0.602846i	0.637850	−	0.770161i	$-0.279824\pi$
$673$	−9.02929	−	15.6392i	−0.348054	−	0.602846i	−0.985904	+	0.167314i	$0.946491\pi$
$674$	55.7643			2.14796
$675$		0			0
$676$	−17.6151			−0.677505
$677$	−7.86959	−	13.6305i	−0.302453	−	0.523864i	0.674238	−	0.738514i	$-0.264472\pi$
$677$	−7.86959	−	13.6305i	−0.302453	−	0.523864i	−0.976691	+	0.214650i	$0.931139\pi$
$678$		0			0
$679$	1.72432	−	2.98661i	0.0661734	−	0.114616i
$680$	−19.9950	+	34.6324i	−0.766775	+	1.32809i
$681$		0			0
$682$	−11.9692	−	20.7313i	−0.458326	−	0.793844i
$683$	−2.76118			−0.105654			−0.0528268	−	0.998604i	$-0.516823\pi$
$683$	−2.76118			−0.105654			−0.0528268	+	0.998604i	$0.516823\pi$
$684$		0			0
$685$	−23.2916			−0.889925
$686$	−9.30925	−	16.1241i	−0.355429	−	0.615621i
$687$		0			0
$688$	61.4084	−	106.362i	2.34117	−	4.05503i
$689$	−8.45526	+	14.6449i	−0.322120	+	0.557928i
$690$		0			0
$691$	17.2628	+	29.9000i	0.656707	+	1.13745i	0.981463	+	0.191652i	$0.0613844\pi$
$691$	17.2628	+	29.9000i	0.656707	+	1.13745i	−0.324756	+	0.945798i	$0.605282\pi$
$692$	13.7107			0.521204
$693$		0			0
$694$	−57.3029			−2.17519
$695$	−6.61983	−	11.4659i	−0.251104	−	0.434926i
$696$		0			0
$697$	15.3860	−	26.6494i	0.582787	−	1.00942i
$698$	−6.25678	+	10.8371i	−0.236822	+	0.410189i
$699$		0			0
$700$	2.93218	+	5.07868i	0.110826	+	0.191956i
$701$	−20.7410			−0.783378			−0.391689	−	0.920098i	$-0.628109\pi$
$701$	−20.7410			−0.783378			−0.391689	+	0.920098i	$0.628109\pi$
$702$		0			0
$703$	−28.1640			−1.06222
$704$	−22.9921	−	39.8235i	−0.866548	−	1.50090i
$705$		0			0
$706$	18.4532	−	31.9618i	0.694494	−	1.20290i
$707$	0.933514	−	1.61689i	0.0351084	−	0.0608095i
$708$		0			0
$709$	−13.8536	−	23.9951i	−0.520281	−	0.901154i	−0.999722	−	0.0235795i	$-0.992494\pi$
$709$	−13.8536	−	23.9951i	−0.520281	−	0.901154i	0.479441	−	0.877574i	$-0.340840\pi$
$710$	−12.8284			−0.481441
$711$		0			0
$712$	100.675			3.77296
$713$	10.7194	+	18.5666i	0.401445	+	0.695324i
$714$		0			0
$715$	−4.99104	+	8.64474i	−0.186654	+	0.323295i
$716$	−23.6520	+	40.9665i	−0.883918	+	1.53099i
$717$		0			0
$718$	38.2018	+	66.1675i	1.42568	+	2.46935i
$719$	33.1314			1.23559			0.617797	−	0.786337i	$-0.288025\pi$
$719$	33.1314			1.23559			0.617797	+	0.786337i	$0.288025\pi$
$720$		0			0
$721$	3.84494			0.143193
$722$	19.7483	+	34.2051i	0.734956	+	1.27298i
$723$		0			0
$724$	−21.0351	+	36.4338i	−0.781763	+	1.35405i
$725$	2.88067	−	4.98946i	0.106985	−	0.185304i
$726$		0			0
$727$	0.0413027	+	0.0715384i	0.00153183	+	0.00265321i	0.866790	−	0.498673i	$-0.166179\pi$
$727$	0.0413027	+	0.0715384i	0.00153183	+	0.00265321i	−0.865258	+	0.501326i	$0.832846\pi$
$728$	−13.9816			−0.518191
$729$		0			0
$730$	−44.9449			−1.66349
$731$	−11.9968	−	20.7791i	−0.443718	−	0.768542i
$732$		0			0
$733$	15.9587	−	27.6414i	0.589450	−	1.02096i	−0.404855	−	0.914381i	$-0.632678\pi$
$733$	15.9587	−	27.6414i	0.589450	−	1.02096i	0.994305	−	0.106576i	$-0.0339887\pi$
$734$	47.1766	−	81.7123i	1.74132	−	3.01606i
$735$		0			0
$736$	44.0171	+	76.2399i	1.62249	+	2.81024i
$737$	23.9400			0.881842
$738$		0			0
$739$	−35.7919			−1.31663			−0.658314	−	0.752744i	$-0.728730\pi$
$739$	−35.7919			−1.31663			−0.658314	+	0.752744i	$0.728730\pi$
$740$	21.6034	+	37.4181i	0.794155	+	1.37552i
$741$		0			0
$742$	3.67864	−	6.37160i	0.135047	−	0.233909i
$743$	−9.88944	+	17.1290i	−0.362808	+	0.628402i	−0.988422	−	0.151731i	$-0.951515\pi$
$743$	−9.88944	+	17.1290i	−0.362808	+	0.628402i	0.625614	+	0.780133i	$0.284849\pi$
$744$		0			0
$745$	0.608860	+	1.05458i	0.0223069	+	0.0386367i
$746$	−8.27598			−0.303005
$747$		0			0
$748$	−27.1723			−0.993517
$749$	−2.69462	−	4.66722i	−0.0984593	−	0.170537i
$750$		0			0
$751$	−15.2903	+	26.4835i	−0.557950	+	0.966398i	0.439717	+	0.898136i	$0.355079\pi$
$751$	−15.2903	+	26.4835i	−0.557950	+	0.966398i	−0.997667	+	0.0682617i	$0.978255\pi$
$752$	46.5950	−	80.7048i	1.69914	−	2.94300i
$753$		0			0
$754$	11.0086	+	19.0674i	0.400909	+	0.694395i
$755$	7.26165			0.264278
$756$		0			0
$757$	25.4129			0.923647			0.461824	−	0.886972i	$-0.347195\pi$
$757$	25.4129			0.923647			0.461824	+	0.886972i	$0.347195\pi$
$758$	−10.3835	−	17.9847i	−0.377144	−	0.653233i
$759$		0			0
$760$	43.4965	−	75.3382i	1.57778	−	2.73280i
$761$	−23.4090	+	40.5456i	−0.848575	+	1.46978i	0.0339049	+	0.999425i	$0.489206\pi$
$761$	−23.4090	+	40.5456i	−0.848575	+	1.46978i	−0.882480	+	0.470350i	$0.844128\pi$
$762$		0			0
$763$	−3.06107	−	5.30194i	−0.110818	−	0.191943i
$764$	84.5322			3.05827
$765$		0			0
$766$	28.0297			1.01275
$767$	−3.41016	−	5.90657i	−0.123134	−	0.213274i
$768$		0			0
$769$	−7.28271	+	12.6140i	−0.262621	+	0.454873i	−0.966938	−	0.255013i	$-0.917920\pi$
$769$	−7.28271	+	12.6140i	−0.262621	+	0.454873i	0.704316	+	0.709886i	$0.251254\pi$
$770$	2.17146	−	3.76108i	0.0782540	−	0.135540i
$771$		0			0
$772$	12.1895	+	21.1128i	0.438710	+	0.759867i
$773$	−24.3533			−0.875929			−0.437964	−	0.898992i	$-0.644300\pi$
$773$	−24.3533			−0.875929			−0.437964	+	0.898992i	$0.644300\pi$
$774$		0			0
$775$	10.1666			0.365194
$776$	−30.9106	−	53.5387i	−1.10963	−	1.92193i
$777$		0			0
$778$	0.577465	−	1.00020i	0.0207031	−	0.0358589i
$779$	−33.4702	+	57.9722i	−1.19920	+	2.07707i
$780$		0			0
$781$	−2.71902	−	4.70948i	−0.0972943	−	0.168519i
$782$	33.4879			1.19753
$783$		0			0

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:	\( N \)	\(=\)	\( 729 = 3^{6} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	729.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.35253 + 2.34265i) q^{2} +(-2.65869 + 4.60498i) q^{4} +(-0.836192 + 1.44833i) q^{5} +(-0.250296 - 0.433525i) q^{7} -8.97372 q^{8} +O(q^{10})\)	\(q+(1.35253 + 2.34265i) q^{2} +(-2.65869 + 4.60498i) q^{4} +(-0.836192 + 1.44833i) q^{5} +(-0.250296 - 0.433525i) q^{7} -8.97372 q^{8} -4.52391 q^{10} +(-0.958859 - 1.66079i) q^{11} +(-1.55622 + 2.69545i) q^{13} +(0.677066 - 1.17271i) q^{14} +(-6.81987 - 11.8124i) q^{16} -2.66467 q^{17} +5.79664 q^{19} +(-4.44635 - 7.70130i) q^{20} +(2.59378 - 4.49255i) q^{22} +(-2.32293 + 4.02344i) q^{23} +(1.10156 + 1.90797i) q^{25} -8.41934 q^{26} +2.66183 q^{28} +(-1.30754 - 2.26472i) q^{29} +(2.30730 - 3.99636i) q^{31} +(9.47446 - 16.4103i) q^{32} +(-3.60406 - 6.24241i) q^{34} +0.837181 q^{35} -4.85867 q^{37} +(7.84014 + 13.5795i) q^{38} +(7.50375 - 12.9969i) q^{40} +(-5.77408 + 10.0010i) q^{41} +(4.50217 + 7.79798i) q^{43} +10.1972 q^{44} -12.5674 q^{46} +(3.41612 + 5.91689i) q^{47} +(3.37470 - 5.84516i) q^{49} +(-2.97980 + 5.16117i) q^{50} +(-8.27499 - 14.3327i) q^{52} +5.43322 q^{53} +3.20716 q^{55} +(2.24608 + 3.89033i) q^{56} +(3.53697 - 6.12621i) q^{58} +(-1.09566 + 1.89773i) q^{59} +(-3.42017 - 5.92391i) q^{61} +12.4828 q^{62} +23.9786 q^{64} +(-2.60259 - 4.50783i) q^{65} +(-6.24180 + 10.8111i) q^{67} +(7.08453 - 12.2708i) q^{68} +(1.13231 + 1.96123i) q^{70} +2.83568 q^{71} +9.93497 q^{73} +(-6.57151 - 11.3822i) q^{74} +(-15.4114 + 26.6934i) q^{76} +(-0.479996 + 0.831378i) q^{77} +(-2.65561 - 4.59964i) q^{79} +22.8109 q^{80} -31.2385 q^{82} +(-1.36408 - 2.36265i) q^{83} +(2.22818 - 3.85932i) q^{85} +(-12.1787 + 21.0941i) q^{86} +(8.60453 + 14.9035i) q^{88} -11.2189 q^{89} +1.55806 q^{91} +(-12.3519 - 21.3941i) q^{92} +(-9.24082 + 16.0056i) q^{94} +(-4.84710 + 8.39543i) q^{95} +(3.44457 + 5.96617i) q^{97} +18.2576 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 3 q^{2} - 9 q^{4} - 3 q^{5} - 6 q^{7} - 12 q^{8}+O(q^{10}) \) 12 * q + 3 * q^2 - 9 * q^4 - 3 * q^5 - 6 * q^7 - 12 * q^8	\( 12 q + 3 q^{2} - 9 q^{4} - 3 q^{5} - 6 q^{7} - 12 q^{8} + 12 q^{10} - 6 q^{11} - 6 q^{13} + 24 q^{14} - 15 q^{16} + 18 q^{17} + 24 q^{19} - 21 q^{20} - 3 q^{22} - 12 q^{23} - 9 q^{25} - 48 q^{26} + 6 q^{28} + 21 q^{29} - 15 q^{31} - 60 q^{35} + 6 q^{37} + 15 q^{38} - 3 q^{40} - 12 q^{41} - 6 q^{43} + 66 q^{44} - 6 q^{46} - 15 q^{47} - 12 q^{49} - 24 q^{50} - 3 q^{52} + 18 q^{53} + 30 q^{55} + 12 q^{56} + 15 q^{58} + 6 q^{59} - 24 q^{61} + 60 q^{62} + 12 q^{64} - 15 q^{65} - 15 q^{67} + 36 q^{68} + 15 q^{70} + 24 q^{73} + 24 q^{74} - 9 q^{76} + 15 q^{77} - 24 q^{79} + 42 q^{80} - 42 q^{82} - 6 q^{83} + 18 q^{85} - 30 q^{86} + 21 q^{88} + 18 q^{89} + 36 q^{91} + 6 q^{92} + 6 q^{94} - 33 q^{95} + 21 q^{97} - 36 q^{98}+O(q^{100}) \) 12 * q + 3 * q^2 - 9 * q^4 - 3 * q^5 - 6 * q^7 - 12 * q^8 + 12 * q^10 - 6 * q^11 - 6 * q^13 + 24 * q^14 - 15 * q^16 + 18 * q^17 + 24 * q^19 - 21 * q^20 - 3 * q^22 - 12 * q^23 - 9 * q^25 - 48 * q^26 + 6 * q^28 + 21 * q^29 - 15 * q^31 - 60 * q^35 + 6 * q^37 + 15 * q^38 - 3 * q^40 - 12 * q^41 - 6 * q^43 + 66 * q^44 - 6 * q^46 - 15 * q^47 - 12 * q^49 - 24 * q^50 - 3 * q^52 + 18 * q^53 + 30 * q^55 + 12 * q^56 + 15 * q^58 + 6 * q^59 - 24 * q^61 + 60 * q^62 + 12 * q^64 - 15 * q^65 - 15 * q^67 + 36 * q^68 + 15 * q^70 + 24 * q^73 + 24 * q^74 - 9 * q^76 + 15 * q^77 - 24 * q^79 + 42 * q^80 - 42 * q^82 - 6 * q^83 + 18 * q^85 - 30 * q^86 + 21 * q^88 + 18 * q^89 + 36 * q^91 + 6 * q^92 + 6 * q^94 - 33 * q^95 + 21 * q^97 - 36 * q^98

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