LMFDB - Embedded newform 378.2.e.c.37.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [378,2,Mod(37,378)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(378, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("378.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 378 = 2 \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	378.e (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:	$3.01834519640$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.309123.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 $ x^6 - 3x^5 + 10x^4 - 15x^3 + 19x^2 - 12*x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			37.1
Root			$0.500000 + 2.05195i$ of defining polynomial
Character	$\chi$	$=$	378.37
Dual form			378.2.e.c.235.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{4} +(-0.230252 - 0.398809i) q^{5} +(0.0665372 + 2.64491i) q^{7} -1.00000 q^{8} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{4} +(-0.230252 - 0.398809i) q^{5} +(0.0665372 + 2.64491i) q^{7} -1.00000 q^{8} +(0.230252 + 0.398809i) q^{10} +(-1.82383 + 3.15897i) q^{11} +(0.730252 - 1.26483i) q^{13} +(-0.0665372 - 2.64491i) q^{14} +1.00000 q^{16} +(1.86693 + 3.23361i) q^{17} +(-2.02704 + 3.51094i) q^{19} +(-0.230252 - 0.398809i) q^{20} +(1.82383 - 3.15897i) q^{22} +(0.566537 + 0.981271i) q^{23} +(2.39397 - 4.14647i) q^{25} +(-0.730252 + 1.26483i) q^{26} +(0.0665372 + 2.64491i) q^{28} +(4.48755 + 7.77266i) q^{29} -0.514589 q^{31} -1.00000 q^{32} +(-1.86693 - 3.23361i) q^{34} +(1.03950 - 0.635534i) q^{35} +(-4.55408 + 7.88791i) q^{37} +(2.02704 - 3.51094i) q^{38} +(0.230252 + 0.398809i) q^{40} +(0.472958 - 0.819187i) q^{41} +(4.66372 + 8.07779i) q^{43} +(-1.82383 + 3.15897i) q^{44} +(-0.566537 - 0.981271i) q^{46} -2.32743 q^{47} +(-6.99115 + 0.351971i) q^{49} +(-2.39397 + 4.14647i) q^{50} +(0.730252 - 1.26483i) q^{52} +(-6.21780 - 10.7695i) q^{53} +1.67977 q^{55} +(-0.0665372 - 2.64491i) q^{56} +(-4.48755 - 7.77266i) q^{58} +12.8961 q^{59} +12.0833 q^{61} +0.514589 q^{62} +1.00000 q^{64} -0.672570 q^{65} -2.32023 q^{67} +(1.86693 + 3.23361i) q^{68} +(-1.03950 + 0.635534i) q^{70} -1.67977 q^{71} +(-6.62062 - 11.4673i) q^{73} +(4.55408 - 7.88791i) q^{74} +(-2.02704 + 3.51094i) q^{76} +(-8.47656 - 4.61369i) q^{77} -5.00720 q^{79} +(-0.230252 - 0.398809i) q^{80} +(-0.472958 + 0.819187i) q^{82} +(-3.32383 - 5.75705i) q^{83} +(0.859728 - 1.48909i) q^{85} +(-4.66372 - 8.07779i) q^{86} +(1.82383 - 3.15897i) q^{88} +(1.36333 - 2.36135i) q^{89} +(3.39397 + 1.84730i) q^{91} +(0.566537 + 0.981271i) q^{92} +2.32743 q^{94} +1.86693 q^{95} +(-5.59358 - 9.68836i) q^{97} +(6.99115 - 0.351971i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{2} + 6 q^{4} + 5 q^{5} + 4 q^{7} - 6 q^{8}+O(q^{10}) $ 6 * q - 6 * q^2 + 6 * q^4 + 5 * q^5 + 4 * q^7 - 6 * q^8	$ 6 q - 6 q^{2} + 6 q^{4} + 5 q^{5} + 4 q^{7} - 6 q^{8} - 5 q^{10} + q^{11} - 2 q^{13} - 4 q^{14} + 6 q^{16} + 4 q^{17} - 3 q^{19} + 5 q^{20} - q^{22} + 7 q^{23} - 2 q^{25} + 2 q^{26} + 4 q^{28} + 5 q^{29} + 28 q^{31} - 6 q^{32} - 4 q^{34} + 19 q^{35} - 9 q^{37} + 3 q^{38} - 5 q^{40} + 12 q^{41} + 18 q^{43} + q^{44} - 7 q^{46} + 6 q^{47} - 12 q^{49} + 2 q^{50} - 2 q^{52} - 9 q^{53} + 14 q^{55} - 4 q^{56} - 5 q^{58} + 8 q^{59} - 8 q^{61} - 28 q^{62} + 6 q^{64} - 24 q^{65} - 10 q^{67} + 4 q^{68} - 19 q^{70} - 14 q^{71} - 25 q^{73} + 9 q^{74} - 3 q^{76} - 52 q^{77} - 14 q^{79} + 5 q^{80} - 12 q^{82} - 8 q^{83} + 14 q^{85} - 18 q^{86} - q^{88} + 9 q^{89} + 4 q^{91} + 7 q^{92} - 6 q^{94} + 4 q^{95} - 28 q^{97} + 12 q^{98}+O(q^{100}) $ 6 * q - 6 * q^2 + 6 * q^4 + 5 * q^5 + 4 * q^7 - 6 * q^8 - 5 * q^10 + q^11 - 2 * q^13 - 4 * q^14 + 6 * q^16 + 4 * q^17 - 3 * q^19 + 5 * q^20 - q^22 + 7 * q^23 - 2 * q^25 + 2 * q^26 + 4 * q^28 + 5 * q^29 + 28 * q^31 - 6 * q^32 - 4 * q^34 + 19 * q^35 - 9 * q^37 + 3 * q^38 - 5 * q^40 + 12 * q^41 + 18 * q^43 + q^44 - 7 * q^46 + 6 * q^47 - 12 * q^49 + 2 * q^50 - 2 * q^52 - 9 * q^53 + 14 * q^55 - 4 * q^56 - 5 * q^58 + 8 * q^59 - 8 * q^61 - 28 * q^62 + 6 * q^64 - 24 * q^65 - 10 * q^67 + 4 * q^68 - 19 * q^70 - 14 * q^71 - 25 * q^73 + 9 * q^74 - 3 * q^76 - 52 * q^77 - 14 * q^79 + 5 * q^80 - 12 * q^82 - 8 * q^83 + 14 * q^85 - 18 * q^86 - q^88 + 9 * q^89 + 4 * q^91 + 7 * q^92 - 6 * q^94 + 4 * q^95 - 28 * q^97 + 12 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/378\mathbb{Z}\right)^\times$.

$n$	$29$	$325$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$		0			0
$3$		0			0
$4$	1.00000			0.500000
$5$	−0.230252	−	0.398809i	−0.102972	−	0.178353i	0.809936	−	0.586519i	$-0.199502\pi$
$5$	−0.230252	−	0.398809i	−0.102972	−	0.178353i	−0.912908	+	0.408166i	$0.866169\pi$
$6$		0			0
$7$	0.0665372	+	2.64491i	0.0251487	+	0.999684i
$7$	0.0665372	+	2.64491i	0.0251487	+	0.999684i
$8$	−1.00000			−0.353553
$9$		0			0
$10$	0.230252	+	0.398809i	0.0728122	+	0.126114i
$11$	−1.82383	+	3.15897i	−0.549906	+	0.952465i	0.448374	+	0.893846i	$0.352003\pi$
$11$	−1.82383	+	3.15897i	−0.549906	+	0.952465i	−0.998280	+	0.0586193i	$0.981330\pi$
$12$		0			0
$13$	0.730252	−	1.26483i	0.202536	−	0.350802i	−0.746809	−	0.665038i	$-0.768415\pi$
$13$	0.730252	−	1.26483i	0.202536	−	0.350802i	0.949345	+	0.314236i	$0.101748\pi$
$14$	−0.0665372	−	2.64491i	−0.0177828	−	0.706883i
$15$		0			0
$16$	1.00000			0.250000
$17$	1.86693	+	3.23361i	0.452796	+	0.784266i	0.998558	−	0.0536743i	$-0.0170933\pi$
$17$	1.86693	+	3.23361i	0.452796	+	0.784266i	−0.545763	+	0.837940i	$0.683760\pi$
$18$		0			0
$19$	−2.02704	+	3.51094i	−0.465035	+	0.805465i	−0.999203	−	0.0399136i	$-0.987292\pi$
$19$	−2.02704	+	3.51094i	−0.465035	+	0.805465i	0.534168	+	0.845378i	$0.320625\pi$
$20$	−0.230252	−	0.398809i	−0.0514860	−	0.0891764i
$21$		0			0
$22$	1.82383	−	3.15897i	0.388842	−	0.673495i
$23$	0.566537	+	0.981271i	0.118131	+	0.204609i	0.919027	−	0.394194i	$-0.128976\pi$
$23$	0.566537	+	0.981271i	0.118131	+	0.204609i	−0.800896	+	0.598804i	$0.795643\pi$
$24$		0			0
$25$	2.39397	−	4.14647i	0.478794	−	0.829295i
$26$	−0.730252	+	1.26483i	−0.143214	+	0.248054i
$27$		0			0
$28$	0.0665372	+	2.64491i	0.0125744	+	0.499842i
$29$	4.48755	+	7.77266i	0.833317	+	1.44335i	0.895394	+	0.445275i	$0.146894\pi$
$29$	4.48755	+	7.77266i	0.833317	+	1.44335i	−0.0620772	+	0.998071i	$0.519772\pi$
$30$		0			0
$31$	−0.514589			−0.0924229			−0.0462115	−	0.998932i	$-0.514715\pi$
$31$	−0.514589			−0.0924229			−0.0462115	+	0.998932i	$0.514715\pi$
$32$	−1.00000			−0.176777
$33$		0			0
$34$	−1.86693	−	3.23361i	−0.320175	−	0.554560i
$35$	1.03950	−	0.635534i	0.175707	−	0.107425i
$36$		0			0
$37$	−4.55408	+	7.88791i	−0.748687	+	1.29676i	0.199765	+	0.979844i	$0.435982\pi$
$37$	−4.55408	+	7.88791i	−0.748687	+	1.29676i	−0.948452	+	0.316920i	$0.897351\pi$
$38$	2.02704	−	3.51094i	0.328830	−	0.569550i
$39$		0			0
$40$	0.230252	+	0.398809i	0.0364061	+	0.0630572i
$41$	0.472958	−	0.819187i	0.0738636	−	0.127936i	−0.826728	−	0.562602i	$-0.809800\pi$
$41$	0.472958	−	0.819187i	0.0738636	−	0.127936i	0.900592	+	0.434666i	$0.143134\pi$
$42$		0			0
$43$	4.66372	+	8.07779i	0.711210	+	1.23185i	0.964403	+	0.264436i	$0.0851858\pi$
$43$	4.66372	+	8.07779i	0.711210	+	1.23185i	−0.253193	+	0.967416i	$0.581481\pi$
$44$	−1.82383	+	3.15897i	−0.274953	+	0.476233i
$45$		0			0
$46$	−0.566537	−	0.981271i	−0.0835314	−	0.144681i
$47$	−2.32743			−0.339491			−0.169745	−	0.985488i	$-0.554295\pi$
$47$	−2.32743			−0.339491			−0.169745	+	0.985488i	$0.554295\pi$
$48$		0			0
$49$	−6.99115	+	0.351971i	−0.998735	+	0.0502815i
$50$	−2.39397	+	4.14647i	−0.338558	+	0.586400i
$51$		0			0
$52$	0.730252	−	1.26483i	0.101268	−	0.175401i
$53$	−6.21780	−	10.7695i	−0.854080	−	1.47931i	−0.877495	−	0.479585i	$-0.840787\pi$
$53$	−6.21780	−	10.7695i	−0.854080	−	1.47931i	0.0234151	−	0.999726i	$-0.492546\pi$
$54$		0			0
$55$	1.67977			0.226500
$56$	−0.0665372	−	2.64491i	−0.00889141	−	0.353442i
$57$		0			0
$58$	−4.48755	−	7.77266i	−0.589244	−	1.02060i
$59$	12.8961			1.67893			0.839465	−	0.543414i	$-0.182869\pi$
$59$	12.8961			1.67893			0.839465	+	0.543414i	$0.182869\pi$
$60$		0			0
$61$	12.0833			1.54710			0.773552	−	0.633733i	$-0.218478\pi$
$61$	12.0833			1.54710			0.773552	+	0.633733i	$0.218478\pi$
$62$	0.514589			0.0653529
$63$		0			0
$64$	1.00000			0.125000
$65$	−0.672570			−0.0834220
$66$		0			0
$67$	−2.32023			−0.283462			−0.141731	−	0.989905i	$-0.545267\pi$
$67$	−2.32023			−0.283462			−0.141731	+	0.989905i	$0.545267\pi$
$68$	1.86693	+	3.23361i	0.226398	+	0.392133i
$69$		0			0
$70$	−1.03950	+	0.635534i	−0.124243	+	0.0759608i
$71$	−1.67977			−0.199352			−0.0996758	−	0.995020i	$-0.531781\pi$
$71$	−1.67977			−0.199352			−0.0996758	+	0.995020i	$0.531781\pi$
$72$		0			0
$73$	−6.62062	−	11.4673i	−0.774885	−	1.34214i	−0.934859	−	0.355019i	$-0.884474\pi$
$73$	−6.62062	−	11.4673i	−0.774885	−	1.34214i	0.159974	−	0.987121i	$-0.448859\pi$
$74$	4.55408	−	7.88791i	0.529402	−	0.916950i
$75$		0			0
$76$	−2.02704	+	3.51094i	−0.232518	+	0.402732i
$77$	−8.47656	−	4.61369i	−0.965993	−	0.525779i
$78$		0			0
$79$	−5.00720			−0.563354			−0.281677	−	0.959509i	$-0.590891\pi$
$79$	−5.00720			−0.563354			−0.281677	+	0.959509i	$0.590891\pi$
$80$	−0.230252	−	0.398809i	−0.0257430	−	0.0445882i
$81$		0			0
$82$	−0.472958	+	0.819187i	−0.0522295	+	0.0904641i
$83$	−3.32383	−	5.75705i	−0.364838	−	0.631918i	0.623912	−	0.781494i	$-0.285542\pi$
$83$	−3.32383	−	5.75705i	−0.364838	−	0.631918i	−0.988750	+	0.149577i	$0.952209\pi$
$84$		0			0
$85$	0.859728	−	1.48909i	0.0932506	−	0.161515i
$86$	−4.66372	−	8.07779i	−0.502901	−	0.871051i
$87$		0			0
$88$	1.82383	−	3.15897i	0.194421	−	0.336747i
$89$	1.36333	−	2.36135i	0.144512	−	0.250303i	−0.784679	−	0.619903i	$-0.787172\pi$
$89$	1.36333	−	2.36135i	0.144512	−	0.250303i	0.929191	+	0.369600i	$0.120505\pi$
$90$		0			0
$91$	3.39397	+	1.84730i	0.355784	+	0.193649i
$92$	0.566537	+	0.981271i	0.0590656	+	0.102305i
$93$		0			0
$94$	2.32743			0.240056
$95$	1.86693			0.191543
$96$		0			0
$97$	−5.59358	−	9.68836i	−0.567942	−	0.983704i	−0.996769	−	0.0803178i	$-0.974406\pi$
$97$	−5.59358	−	9.68836i	−0.567942	−	0.983704i	0.428827	−	0.903386i	$-0.358927\pi$
$98$	6.99115	−	0.351971i	0.706212	−	0.0355544i
$99$		0			0
$100$	2.39397	−	4.14647i	0.239397	−	0.414647i
$101$	6.87792	−	11.9129i	0.684378	−	1.18538i	−0.289254	−	0.957253i	$-0.593407\pi$
$101$	6.87792	−	11.9129i	0.684378	−	1.18538i	0.973632	−	0.228125i	$-0.0732596\pi$
$102$		0			0
$103$	−5.58113	−	9.66679i	−0.549925	−	0.952498i	−0.998279	−	0.0586417i	$-0.981323\pi$
$103$	−5.58113	−	9.66679i	−0.549925	−	0.952498i	0.448354	−	0.893856i	$-0.352010\pi$
$104$	−0.730252	+	1.26483i	−0.0716071	+	0.124027i
$105$		0			0
$106$	6.21780	+	10.7695i	0.603926	+	1.04603i
$107$	3.89037	−	6.73832i	0.376096	−	0.651418i	−0.614394	−	0.788999i	$-0.710600\pi$
$107$	3.89037	−	6.73832i	0.376096	−	0.651418i	0.990490	+	0.137581i	$0.0439329\pi$
$108$		0			0
$109$	−3.75729	−	6.50783i	−0.359884	−	0.623337i	0.628058	−	0.778167i	$-0.283850\pi$
$109$	−3.75729	−	6.50783i	−0.359884	−	0.623337i	−0.987941	+	0.154830i	$0.950517\pi$
$110$	−1.67977			−0.160159
$111$		0			0
$112$	0.0665372	+	2.64491i	0.00628718	+	0.249921i
$113$	−3.03064	+	5.24922i	−0.285099	+	0.493805i	−0.972633	−	0.232346i	$-0.925360\pi$
$113$	−3.03064	+	5.24922i	−0.285099	+	0.493805i	0.687534	+	0.726152i	$0.258693\pi$
$114$		0			0
$115$	0.260893	−	0.451880i	0.0243284	−	0.0421380i
$116$	4.48755	+	7.77266i	0.416658	+	0.721673i
$117$		0			0
$118$	−12.8961			−1.18718
$119$	−8.42840	+	5.15301i	−0.772630	+	0.472376i
$120$		0			0
$121$	−1.15272	−	1.99658i	−0.104793	−	0.181507i
$122$	−12.0833			−1.09397
$123$		0			0
$124$	−0.514589			−0.0462115
$125$	−4.50739			−0.403153
$126$		0			0
$127$	8.80992			0.781754			0.390877	−	0.920443i	$-0.372172\pi$
$127$	8.80992			0.781754			0.390877	+	0.920443i	$0.372172\pi$
$128$	−1.00000			−0.0883883
$129$		0			0
$130$	0.672570			0.0589883
$131$	10.5687	+	18.3055i	0.923389	+	1.59936i	0.794131	+	0.607746i	$0.207926\pi$
$131$	10.5687	+	18.3055i	0.923389	+	1.59936i	0.129258	+	0.991611i	$0.458740\pi$
$132$		0			0
$133$	−9.42101	−	5.12774i	−0.816905	−	0.444632i
$134$	2.32023			0.200438
$135$		0			0
$136$	−1.86693	−	3.23361i	−0.160088	−	0.277280i
$137$	−2.20321	+	3.81607i	−0.188233	+	0.326029i	−0.944661	−	0.328048i	$-0.893609\pi$
$137$	−2.20321	+	3.81607i	−0.188233	+	0.326029i	0.756428	+	0.654077i	$0.226943\pi$
$138$		0			0
$139$	−1.01245	+	1.75362i	−0.0858751	+	0.148740i	−0.905764	−	0.423783i	$-0.860702\pi$
$139$	−1.01245	+	1.75362i	−0.0858751	+	0.148740i	0.819889	+	0.572523i	$0.194035\pi$
$140$	1.03950	−	0.635534i	0.0878534	−	0.0537124i
$141$		0			0
$142$	1.67977			0.140963
$143$	2.66372	+	4.61369i	0.222751	+	0.385816i
$144$		0			0
$145$	2.06654	−	3.57935i	0.171617	−	0.297249i
$146$	6.62062	+	11.4673i	0.547927	+	0.949037i
$147$		0			0
$148$	−4.55408	+	7.88791i	−0.374343	+	0.648382i
$149$	−4.58113	−	7.93474i	−0.375300	−	0.650040i	0.615071	−	0.788471i	$-0.289127\pi$
$149$	−4.58113	−	7.93474i	−0.375300	−	0.650040i	−0.990372	+	0.138432i	$0.955794\pi$
$150$		0			0
$151$	0.0519482	−	0.0899768i	0.00422748	−	0.00732221i	−0.863904	−	0.503657i	$-0.831988\pi$
$151$	0.0519482	−	0.0899768i	0.00422748	−	0.00732221i	0.868131	+	0.496334i	$0.165321\pi$
$152$	2.02704	−	3.51094i	0.164415	−	0.284775i
$153$		0			0
$154$	8.47656	+	4.61369i	0.683060	+	0.371782i
$155$	0.118485	+	0.205223i	0.00951698	+	0.0164839i
$156$		0			0
$157$	20.9823			1.67457			0.837285	−	0.546767i	$-0.184142\pi$
$157$	20.9823			1.67457			0.837285	+	0.546767i	$0.184142\pi$
$158$	5.00720			0.398351
$159$		0			0
$160$	0.230252	+	0.398809i	0.0182031	+	0.0315286i
$161$	−2.55768	+	1.56373i	−0.201574	+	0.123239i
$162$		0			0
$163$	−11.5182	+	19.9501i	−0.902174	+	1.56261i	−0.0775078	+	0.996992i	$0.524696\pi$
$163$	−11.5182	+	19.9501i	−0.902174	+	1.56261i	−0.824666	+	0.565620i	$0.808637\pi$
$164$	0.472958	−	0.819187i	0.0369318	−	0.0639678i
$165$		0			0
$166$	3.32383	+	5.75705i	0.257979	+	0.446833i
$167$	5.31498	−	9.20581i	0.411285	−	0.712367i	−0.583745	−	0.811937i	$-0.698413\pi$
$167$	5.31498	−	9.20581i	0.411285	−	0.712367i	0.995031	+	0.0995698i	$0.0317467\pi$
$168$		0			0
$169$	5.43346	+	9.41103i	0.417959	+	0.723926i
$170$	−0.859728	+	1.48909i	−0.0659382	+	0.114208i
$171$		0			0
$172$	4.66372	+	8.07779i	0.355605	+	0.615926i
$173$	−2.93872			−0.223427			−0.111713	−	0.993740i	$-0.535634\pi$
$173$	−2.93872			−0.223427			−0.111713	+	0.993740i	$0.535634\pi$
$174$		0			0
$175$	11.1264	+	6.05594i	0.841073	+	0.457786i
$176$	−1.82383	+	3.15897i	−0.137476	+	0.238116i
$177$		0			0
$178$	−1.36333	+	2.36135i	−0.102186	+	0.176991i
$179$	4.58113	+	7.93474i	0.342409	+	0.593071i	0.984880	−	0.173240i	$-0.0554237\pi$
$179$	4.58113	+	7.93474i	0.342409	+	0.593071i	−0.642470	+	0.766311i	$0.722090\pi$
$180$		0			0
$181$	22.4284			1.66709			0.833545	−	0.552452i	$-0.186308\pi$
$181$	22.4284			1.66709			0.833545	+	0.552452i	$0.186308\pi$
$182$	−3.39397	−	1.84730i	−0.251578	−	0.136931i
$183$		0			0
$184$	−0.566537	−	0.981271i	−0.0417657	−	0.0723403i
$185$	4.19436			0.308375
$186$		0			0
$187$	−13.6198			−0.995981
$188$	−2.32743			−0.169745
$189$		0			0
$190$	−1.86693			−0.135441
$191$	−2.48968			−0.180147			−0.0900736	−	0.995935i	$-0.528710\pi$
$191$	−2.48968			−0.180147			−0.0900736	+	0.995935i	$0.528710\pi$
$192$		0			0
$193$	4.48968			0.323174			0.161587	−	0.986858i	$-0.448339\pi$
$193$	4.48968			0.323174			0.161587	+	0.986858i	$0.448339\pi$
$194$	5.59358	+	9.68836i	0.401596	+	0.695584i
$195$		0			0
$196$	−6.99115	+	0.351971i	−0.499368	+	0.0251408i
$197$	−12.7339			−0.907249			−0.453625	−	0.891193i	$-0.649869\pi$
$197$	−12.7339			−0.907249			−0.453625	+	0.891193i	$0.649869\pi$
$198$		0			0
$199$	−1.47296	−	2.55124i	−0.104415	−	0.180852i	0.809084	−	0.587693i	$-0.199964\pi$
$199$	−1.47296	−	2.55124i	−0.104415	−	0.180852i	−0.913499	+	0.406841i	$0.866630\pi$
$200$	−2.39397	+	4.14647i	−0.169279	+	0.293200i
$201$		0			0
$202$	−6.87792	+	11.9129i	−0.483928	+	0.838189i
$203$	−20.2594	+	12.3863i	−1.42193	+	0.869351i
$204$		0			0
$205$	−0.435599			−0.0304235
$206$	5.58113	+	9.66679i	0.388855	+	0.673517i
$207$		0			0
$208$	0.730252	−	1.26483i	0.0506339	−	0.0877005i
$209$	−7.39397	−	12.8067i	−0.511451	−	0.885860i
$210$		0			0
$211$	−0.608168	+	1.05338i	−0.0418680	+	0.0725176i	−0.886200	−	0.463303i	$-0.846664\pi$
$211$	−0.608168	+	1.05338i	−0.0418680	+	0.0725176i	0.844332	+	0.535820i	$0.179998\pi$
$212$	−6.21780	−	10.7695i	−0.427040	−	0.739655i
$213$		0			0
$214$	−3.89037	+	6.73832i	−0.265940	+	0.460622i
$215$	2.14766	−	3.71986i	0.146469	−	0.253693i
$216$		0			0
$217$	−0.0342393	−	1.36104i	−0.00232432	−	0.0923937i
$218$	3.75729	+	6.50783i	0.254476	+	0.440766i
$219$		0			0
$220$	1.67977			0.113250
$221$	5.45331			0.366829
$222$		0			0
$223$	−0.445916	−	0.772349i	−0.0298607	−	0.0517203i	0.850709	−	0.525637i	$-0.176173\pi$
$223$	−0.445916	−	0.772349i	−0.0298607	−	0.0517203i	−0.880570	+	0.473917i	$0.842840\pi$
$224$	−0.0665372	−	2.64491i	−0.00444571	−	0.176721i
$225$		0			0
$226$	3.03064	−	5.24922i	0.201595	−	0.349173i
$227$	−7.32597	+	12.6889i	−0.486242	+	0.842195i	−0.999875	−	0.0158147i	$-0.994966\pi$
$227$	−7.32597	+	12.6889i	−0.486242	+	0.842195i	0.513633	+	0.858010i	$0.328299\pi$
$228$		0			0
$229$	4.78794	+	8.29295i	0.316396	+	0.548013i	0.979733	−	0.200307i	$-0.0641939\pi$
$229$	4.78794	+	8.29295i	0.316396	+	0.548013i	−0.663338	+	0.748320i	$0.730861\pi$
$230$	−0.260893	+	0.451880i	−0.0172028	+	0.0297961i
$231$		0			0
$232$	−4.48755	−	7.77266i	−0.294622	−	0.510300i
$233$	−7.21420	+	12.4954i	−0.472618	+	0.818598i	−0.999509	−	0.0313345i	$-0.990024\pi$
$233$	−7.21420	+	12.4954i	−0.472618	+	0.818598i	0.526891	+	0.849933i	$0.323358\pi$
$234$		0			0
$235$	0.535897	+	0.928200i	0.0349580	+	0.0605491i
$236$	12.8961			0.839465
$237$		0			0
$238$	8.42840	−	5.15301i	0.546332	−	0.334020i
$239$	9.15486	−	15.8567i	0.592179	−	1.02568i	−0.401760	−	0.915745i	$-0.631601\pi$
$239$	9.15486	−	15.8567i	0.592179	−	1.02568i	0.993938	−	0.109938i	$-0.0350654\pi$
$240$		0			0
$241$	−0.0466924	+	0.0808735i	−0.00300772	+	0.00520952i	−0.867525	−	0.497393i	$-0.834291\pi$
$241$	−0.0466924	+	0.0808735i	−0.00300772	+	0.00520952i	0.864518	+	0.502602i	$0.167624\pi$
$242$	1.15272	+	1.99658i	0.0741000	+	0.128345i
$243$		0			0
$244$	12.0833			0.773552
$245$	1.75010	+	2.70709i	0.111810	+	0.172950i
$246$		0			0
$247$	2.96050	+	5.12774i	0.188372	+	0.326271i
$248$	0.514589			0.0326764
$249$		0			0
$250$	4.50739			0.285072
$251$	18.2733			1.15340			0.576702	−	0.816955i	$-0.304339\pi$
$251$	18.2733			1.15340			0.576702	+	0.816955i	$0.304339\pi$
$252$		0			0
$253$	−4.13307			−0.259844
$254$	−8.80992			−0.552783
$255$		0			0
$256$	1.00000			0.0625000
$257$	−10.5256	−	18.2308i	−0.656568	−	1.13721i	−0.981498	−	0.191471i	$-0.938674\pi$
$257$	−10.5256	−	18.2308i	−0.656568	−	1.13721i	0.324931	−	0.945738i	$-0.394659\pi$
$258$		0			0
$259$	−21.1659	−	11.5203i	−1.31518	−	0.715838i
$260$	−0.672570			−0.0417110
$261$		0			0
$262$	−10.5687	−	18.3055i	−0.652935	−	1.13092i
$263$	−2.58259	+	4.47318i	−0.159249	+	0.275828i	−0.934598	−	0.355705i	$-0.884241\pi$
$263$	−2.58259	+	4.47318i	−0.159249	+	0.275828i	0.775349	+	0.631533i	$0.217574\pi$
$264$		0			0
$265$	−2.86333	+	4.95943i	−0.175893	+	0.304655i
$266$	9.42101	+	5.12774i	0.577639	+	0.314402i
$267$		0			0
$268$	−2.32023			−0.141731
$269$	−8.42840	−	14.5984i	−0.513889	−	0.890081i	−0.999870	−	0.0161123i	$-0.994871\pi$
$269$	−8.42840	−	14.5984i	−0.513889	−	0.890081i	0.485981	−	0.873969i	$-0.338462\pi$
$270$		0			0
$271$	12.5562	−	21.7480i	0.762736	−	1.32110i	−0.178699	−	0.983904i	$-0.557189\pi$
$271$	12.5562	−	21.7480i	0.762736	−	1.32110i	0.941435	−	0.337194i	$-0.109478\pi$
$272$	1.86693	+	3.23361i	0.113199	+	0.196066i
$273$		0			0
$274$	2.20321	−	3.81607i	0.133101	−	0.230537i
$275$	8.73239	+	15.1249i	0.526583	+	0.912068i
$276$		0			0
$277$	−1.69076	+	2.92848i	−0.101588	+	0.175955i	−0.912339	−	0.409436i	$-0.865726\pi$
$277$	−1.69076	+	2.92848i	−0.101588	+	0.175955i	0.810751	+	0.585391i	$0.199059\pi$
$278$	1.01245	−	1.75362i	0.0607229	−	0.105175i
$279$		0			0
$280$	−1.03950	+	0.635534i	−0.0621217	+	0.0379804i
$281$	10.1388	+	17.5609i	0.604831	+	1.04760i	0.992078	+	0.125622i	$0.0400925\pi$
$281$	10.1388	+	17.5609i	0.604831	+	1.04760i	−0.387248	+	0.921976i	$0.626574\pi$
$282$		0			0
$283$	17.3494			1.03132			0.515658	−	0.856795i	$-0.327548\pi$
$283$	17.3494			1.03132			0.515658	+	0.856795i	$0.327548\pi$
$284$	−1.67977			−0.0996758
$285$		0			0
$286$	−2.66372	−	4.61369i	−0.157509	−	0.272813i
$287$	2.19815	+	1.19643i	0.129753	+	0.0706228i
$288$		0			0
$289$	1.52918	−	2.64861i	0.0899517	−	0.155801i
$290$	−2.06654	+	3.57935i	−0.121351	+	0.210187i
$291$		0			0
$292$	−6.62062	−	11.4673i	−0.387443	−	0.671070i
$293$	4.93560	−	8.54871i	0.288341	−	0.499421i	−0.685073	−	0.728474i	$-0.740230\pi$
$293$	4.93560	−	8.54871i	0.288341	−	0.499421i	0.973414	+	0.229054i	$0.0735631\pi$
$294$		0			0
$295$	−2.96936	−	5.14308i	−0.172883	−	0.299442i
$296$	4.55408	−	7.88791i	0.264701	−	0.458475i
$297$		0			0
$298$	4.58113	+	7.93474i	0.265378	+	0.459647i
$299$	1.65486			0.0957031
$300$		0			0
$301$	−21.0548	+	12.8726i	−1.21358	+	0.741964i
$302$	−0.0519482	+	0.0899768i	−0.00298928	+	0.00517759i
$303$		0			0
$304$	−2.02704	+	3.51094i	−0.116259	+	0.201366i
$305$	−2.78220	−	4.81891i	−0.159308	−	0.275930i
$306$		0			0
$307$	7.78794			0.444481			0.222240	−	0.974992i	$-0.428663\pi$
$307$	7.78794			0.444481			0.222240	+	0.974992i	$0.428663\pi$
$308$	−8.47656	−	4.61369i	−0.482997	−	0.262889i
$309$		0			0
$310$	−0.118485	−	0.205223i	−0.00672952	−	0.0116559i
$311$	−15.4107			−0.873860			−0.436930	−	0.899495i	$-0.643934\pi$
$311$	−15.4107			−0.873860			−0.436930	+	0.899495i	$0.643934\pi$
$312$		0			0
$313$	8.49688			0.480272			0.240136	−	0.970739i	$-0.422808\pi$
$313$	8.49688			0.480272			0.240136	+	0.970739i	$0.422808\pi$
$314$	−20.9823			−1.18410
$315$		0			0
$316$	−5.00720			−0.281677
$317$	14.1052			0.792229			0.396115	−	0.918201i	$-0.370358\pi$
$317$	14.1052			0.792229			0.396115	+	0.918201i	$0.370358\pi$
$318$		0			0
$319$	−32.7381			−1.83298
$320$	−0.230252	−	0.398809i	−0.0128715	−	0.0222941i
$321$		0			0
$322$	2.55768	−	1.56373i	0.142534	−	0.0871435i
$323$	−15.1373			−0.842264
$324$		0			0
$325$	−3.49640	−	6.05594i	−0.193945	−	0.335923i
$326$	11.5182	−	19.9501i	0.637933	−	1.10493i
$327$		0			0
$328$	−0.472958	+	0.819187i	−0.0261147	+	0.0452320i
$329$	−0.154861	−	6.15585i	−0.00853775	−	0.339383i
$330$		0			0
$331$	27.5438			1.51394			0.756971	−	0.653448i	$-0.226678\pi$
$331$	27.5438			1.51394			0.756971	+	0.653448i	$0.226678\pi$
$332$	−3.32383	−	5.75705i	−0.182419	−	0.315959i
$333$		0			0
$334$	−5.31498	+	9.20581i	−0.290823	+	0.503720i
$335$	0.534239	+	0.925330i	0.0291886	+	0.0505562i
$336$		0			0
$337$	0.748440	−	1.29634i	0.0407701	−	0.0706159i	−0.844920	−	0.534892i	$-0.820352\pi$
$337$	0.748440	−	1.29634i	0.0407701	−	0.0706159i	0.885690	+	0.464276i	$0.153686\pi$
$338$	−5.43346	−	9.41103i	−0.295541	−	0.511893i
$339$		0			0
$340$	0.859728	−	1.48909i	0.0466253	−	0.0807574i
$341$	0.938524	−	1.62557i	0.0508239	−	0.0880296i
$342$		0			0
$343$	−1.39610	−	18.4676i	−0.0753825	−	0.997155i
$344$	−4.66372	−	8.07779i	−0.251451	−	0.435525i
$345$		0			0
$346$	2.93872			0.157986
$347$	18.2881			0.981758			0.490879	−	0.871228i	$-0.336676\pi$
$347$	18.2881			0.981758			0.490879	+	0.871228i	$0.336676\pi$
$348$		0			0
$349$	−3.90136	−	6.75735i	−0.208835	−	0.361713i	0.742513	−	0.669832i	$-0.233634\pi$
$349$	−3.90136	−	6.75735i	−0.208835	−	0.361713i	−0.951348	+	0.308119i	$0.900300\pi$
$350$	−11.1264	−	6.05594i	−0.594729	−	0.323704i
$351$		0			0
$352$	1.82383	−	3.15897i	0.0972106	−	0.168374i
$353$	13.4626	−	23.3180i	0.716544	−	1.24109i	−0.245817	−	0.969316i	$-0.579056\pi$
$353$	13.4626	−	23.3180i	0.716544	−	1.24109i	0.962361	−	0.271774i	$-0.0876105\pi$
$354$		0			0
$355$	0.386770	+	0.669906i	0.0205276	+	0.0355549i
$356$	1.36333	−	2.36135i	0.0722562	−	0.125151i
$357$		0			0
$358$	−4.58113	−	7.93474i	−0.242120	−	0.419364i
$359$	3.13161	−	5.42411i	0.165280	−	0.286274i	−0.771475	−	0.636260i	$-0.780481\pi$
$359$	3.13161	−	5.42411i	0.165280	−	0.286274i	0.936755	+	0.349987i	$0.113814\pi$
$360$		0			0
$361$	1.28220	+	2.22084i	0.0674842	+	0.116886i
$362$	−22.4284			−1.17881
$363$		0			0
$364$	3.39397	+	1.84730i	0.177892	+	0.0968247i
$365$	−3.04883	+	5.28073i	−0.159583	+	0.276406i
$366$		0			0
$367$	−14.6367	+	25.3515i	−0.764028	+	1.32334i	0.176731	+	0.984259i	$0.443448\pi$
$367$	−14.6367	+	25.3515i	−0.764028	+	1.32334i	−0.940759	+	0.339076i	$0.889886\pi$
$368$	0.566537	+	0.981271i	0.0295328	+	0.0511523i
$369$		0			0
$370$	−4.19436			−0.218054
$371$	28.0708	−	17.1621i	1.45736	−	0.891013i
$372$		0			0
$373$	−8.92986	−	15.4670i	−0.462371	−	0.800850i	0.536708	−	0.843768i	$-0.319668\pi$
$373$	−8.92986	−	15.4670i	−0.462371	−	0.800850i	−0.999079	+	0.0429184i	$0.986334\pi$
$374$	13.6198			0.704265
$375$		0			0
$376$	2.32743			0.120028
$377$	13.1082			0.675105
$378$		0			0
$379$	−22.4255			−1.15192			−0.575960	−	0.817478i	$-0.695371\pi$
$379$	−22.4255			−1.15192			−0.575960	+	0.817478i	$0.695371\pi$
$380$	1.86693			0.0957713
$381$		0			0
$382$	2.48968			0.127383
$383$	−7.07014	−	12.2458i	−0.361267	−	0.625733i	0.626903	−	0.779098i	$-0.284322\pi$
$383$	−7.07014	−	12.2458i	−0.361267	−	0.625733i	−0.988170	+	0.153365i	$0.950989\pi$
$384$		0			0
$385$	0.111767	+	4.44284i	0.00569618	+	0.226428i
$386$	−4.48968			−0.228519
$387$		0			0
$388$	−5.59358	−	9.68836i	−0.283971	−	0.491852i
$389$	−11.5651	+	20.0313i	−0.586373	+	1.01563i	0.408330	+	0.912834i	$0.366111\pi$
$389$	−11.5651	+	20.0313i	−0.586373	+	1.01563i	−0.994703	+	0.102793i	$0.967222\pi$
$390$		0			0
$391$	−2.11537	+	3.66392i	−0.106979	+	0.185292i
$392$	6.99115	−	0.351971i	0.353106	−	0.0177772i
$393$		0			0
$394$	12.7339			0.641522
$395$	1.15292	+	1.99691i	0.0580097	+	0.100476i
$396$		0			0
$397$	−5.13307	+	8.89075i	−0.257622	+	0.446214i	−0.965604	−	0.260016i	$-0.916272\pi$
$397$	−5.13307	+	8.89075i	−0.257622	+	0.446214i	0.707983	+	0.706230i	$0.249605\pi$
$398$	1.47296	+	2.55124i	0.0738327	+	0.127882i
$399$		0			0
$400$	2.39397	−	4.14647i	0.119698	−	0.207324i
$401$	17.0167	+	29.4738i	0.849775	+	1.47185i	0.881409	+	0.472353i	$0.156595\pi$
$401$	17.0167	+	29.4738i	0.849775	+	1.47185i	−0.0316345	+	0.999500i	$0.510071\pi$
$402$		0			0
$403$	−0.375780	+	0.650870i	−0.0187189	+	0.0324221i
$404$	6.87792	−	11.9129i	0.342189	−	0.592689i
$405$		0			0
$406$	20.2594	−	12.3863i	1.00546	−	0.614724i
$407$	−16.6118	−	28.7724i	−0.823415	−	1.42620i
$408$		0			0
$409$	−3.48968			−0.172554			−0.0862769	−	0.996271i	$-0.527497\pi$
$409$	−3.48968			−0.172554			−0.0862769	+	0.996271i	$0.527497\pi$
$410$	0.435599			0.0215127
$411$		0			0
$412$	−5.58113	−	9.66679i	−0.274962	−	0.476249i
$413$	0.858071	+	34.1091i	0.0422229	+	1.67840i
$414$		0			0
$415$	−1.53064	+	2.65115i	−0.0751362	+	0.130140i
$416$	−0.730252	+	1.26483i	−0.0358036	+	0.0620136i
$417$		0			0
$418$	7.39397	+	12.8067i	0.361651	+	0.626398i
$419$	−14.4897	+	25.0969i	−0.707867	+	1.22606i	0.257779	+	0.966204i	$0.417009\pi$
$419$	−14.4897	+	25.0969i	−0.707867	+	1.22606i	−0.965647	+	0.259858i	$0.916324\pi$
$420$		0			0
$421$	−1.06128	−	1.83819i	−0.0517237	−	0.0895881i	0.839004	−	0.544125i	$-0.183138\pi$
$421$	−1.06128	−	1.83819i	−0.0517237	−	0.0895881i	−0.890728	+	0.454537i	$0.849805\pi$
$422$	0.608168	−	1.05338i	0.0296052	−	0.0512777i
$423$		0			0
$424$	6.21780	+	10.7695i	0.301963	+	0.523015i
$425$	17.8774			0.867183
$426$		0			0
$427$	0.803987	+	31.9592i	0.0389077	+	1.54661i
$428$	3.89037	−	6.73832i	0.188048	−	0.325709i
$429$		0			0
$430$	−2.14766	+	3.71986i	−0.103570	+	0.179388i
$431$	−10.9356	−	18.9410i	−0.526749	−	0.912356i	−0.999514	−	0.0311679i	$-0.990077\pi$
$431$	−10.9356	−	18.9410i	−0.526749	−	0.912356i	0.472765	−	0.881189i	$-0.343256\pi$
$432$		0			0
$433$	−13.0512			−0.627199			−0.313599	−	0.949555i	$-0.601535\pi$
$433$	−13.0512			−0.627199			−0.313599	+	0.949555i	$0.601535\pi$
$434$	0.0342393	+	1.36104i	0.00164354	+	0.0653322i
$435$		0			0
$436$	−3.75729	−	6.50783i	−0.179942	−	0.311668i
$437$	−4.59358			−0.219741
$438$		0			0
$439$	4.86400			0.232146			0.116073	−	0.993241i	$-0.462969\pi$
$439$	4.86400			0.232146			0.116073	+	0.993241i	$0.462969\pi$
$440$	−1.67977			−0.0800797
$441$		0			0
$442$	−5.45331			−0.259387
$443$	11.5395			0.548258			0.274129	−	0.961693i	$-0.411610\pi$
$443$	11.5395			0.548258			0.274129	+	0.961693i	$0.411610\pi$
$444$		0			0
$445$	−1.25564			−0.0595229
$446$	0.445916	+	0.772349i	0.0211147	+	0.0365718i
$447$		0			0
$448$	0.0665372	+	2.64491i	0.00314359	+	0.124960i
$449$	26.4251			1.24708			0.623538	−	0.781793i	$-0.285694\pi$
$449$	26.4251			1.24708			0.623538	+	0.781793i	$0.285694\pi$
$450$		0			0
$451$	1.72519	+	2.98812i	0.0812361	+	0.140705i
$452$	−3.03064	+	5.24922i	−0.142549	+	0.246903i
$453$		0			0
$454$	7.32597	−	12.6889i	0.343825	−	0.595522i
$455$	−0.0447509	−	1.77889i	−0.00209796	−	0.0833956i
$456$		0			0
$457$	−3.73812			−0.174862			−0.0874310	−	0.996171i	$-0.527866\pi$
$457$	−3.73812			−0.174862			−0.0874310	+	0.996171i	$0.527866\pi$
$458$	−4.78794	−	8.29295i	−0.223726	−	0.387504i
$459$		0			0
$460$	0.260893	−	0.451880i	0.0121642	−	0.0210690i
$461$	7.90496	+	13.6918i	0.368171	+	0.637690i	0.989280	−	0.146034i	$-0.0466509\pi$
$461$	7.90496	+	13.6918i	0.368171	+	0.637690i	−0.621109	+	0.783724i	$0.713318\pi$
$462$		0			0
$463$	19.1965	−	33.2493i	0.892137	−	1.54523i	0.0548278	−	0.998496i	$-0.482539\pi$
$463$	19.1965	−	33.2493i	0.892137	−	1.54523i	0.837309	−	0.546730i	$-0.184128\pi$
$464$	4.48755	+	7.77266i	0.208329	+	0.360837i
$465$		0			0
$466$	7.21420	−	12.4954i	0.334191	−	0.578836i
$467$	−3.15652	+	5.46725i	−0.146066	+	0.252994i	−0.929770	−	0.368140i	$-0.879995\pi$
$467$	−3.15652	+	5.46725i	−0.146066	+	0.252994i	0.783704	+	0.621134i	$0.213328\pi$
$468$		0			0
$469$	−0.154382	−	6.13682i	−0.00712869	−	0.283372i
$470$	−0.535897	−	0.928200i	−0.0247191	−	0.0428147i
$471$		0			0
$472$	−12.8961			−0.593591
$473$	−34.0233			−1.56439
$474$		0			0
$475$	9.70535	+	16.8102i	0.445312	+	0.771303i
$476$	−8.42840	+	5.15301i	−0.386315	+	0.236188i
$477$		0			0
$478$	−9.15486	+	15.8567i	−0.418734	+	0.725268i
$479$	−10.2068	+	17.6787i	−0.466361	+	0.807761i	−0.999262	−	0.0384168i	$-0.987769\pi$
$479$	−10.2068	+	17.6787i	−0.466361	+	0.807761i	0.532901	+	0.846178i	$0.321102\pi$
$480$		0			0
$481$	6.65126	+	11.5203i	0.303271	+	0.525282i
$482$	0.0466924	−	0.0808735i	0.00212678	−	0.00368369i
$483$		0			0
$484$	−1.15272	−	1.99658i	−0.0523966	−	0.0907535i
$485$	−2.57587	+	4.46154i	−0.116964	+	0.202588i
$486$		0			0
$487$	6.18190	+	10.7074i	0.280129	+	0.485197i	0.971416	−	0.237383i	$-0.0762895\pi$
$487$	6.18190	+	10.7074i	0.280129	+	0.485197i	−0.691287	+	0.722580i	$0.742956\pi$
$488$	−12.0833			−0.546984
$489$		0			0
$490$	−1.75010	−	2.70709i	−0.0790613	−	0.122294i
$491$	−0.207004	+	0.358541i	−0.00934194	+	0.0161807i	−0.870659	−	0.491888i	$-0.836307\pi$
$491$	−0.207004	+	0.358541i	−0.00934194	+	0.0161807i	0.861317	+	0.508069i	$0.169640\pi$
$492$		0			0
$493$	−16.7558	+	29.0220i	−0.754645	+	1.30708i
$494$	−2.96050	−	5.12774i	−0.133199	−	0.230708i
$495$		0			0
$496$	−0.514589			−0.0231057
$497$	−0.111767	−	4.44284i	−0.00501344	−	0.199289i
$498$		0			0
$499$	0.461967	+	0.800151i	0.0206805	+	0.0358197i	0.876180	−	0.481983i	$-0.160083\pi$
$499$	0.461967	+	0.800151i	0.0206805	+	0.0358197i	−0.855500	+	0.517803i	$0.826750\pi$
$500$	−4.50739			−0.201577
$501$		0			0
$502$	−18.2733			−0.815579
$503$	23.8142			1.06182			0.530911	−	0.847428i	$-0.321850\pi$
$503$	23.8142			1.06182			0.530911	+	0.847428i	$0.321850\pi$
$504$		0			0
$505$	−6.33463			−0.281887
$506$	4.13307			0.183738
$507$		0			0
$508$	8.80992			0.390877
$509$	−15.3171	−	26.5300i	−0.678919	−	1.17592i	−0.975307	−	0.220855i	$-0.929115\pi$
$509$	−15.3171	−	26.5300i	−0.678919	−	1.17592i	0.296388	−	0.955068i	$-0.404218\pi$
$510$		0			0
$511$	29.8894	−	18.2740i	1.32223	−	0.808393i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	10.5256	+	18.2308i	0.464263	+	0.804128i
$515$	−2.57014	+	4.45161i	−0.113254	+	0.196161i
$516$		0			0
$517$	4.24484	−	7.35228i	0.186688	−	0.323353i
$518$	21.1659	+	11.5203i	0.929974	+	0.506174i
$519$		0			0
$520$	0.672570			0.0294941
$521$	13.4518	+	23.2993i	0.589336	+	1.02076i	0.994320	+	0.106436i	$0.0339439\pi$
$521$	13.4518	+	23.2993i	0.589336	+	1.02076i	−0.404984	+	0.914324i	$0.632723\pi$
$522$		0			0
$523$	−7.85301	+	13.6018i	−0.343388	+	0.594766i	−0.985060	−	0.172214i	$-0.944908\pi$
$523$	−7.85301	+	13.6018i	−0.343388	+	0.594766i	0.641671	+	0.766980i	$0.278241\pi$
$524$	10.5687	+	18.3055i	0.461695	+	0.799679i
$525$		0			0
$526$	2.58259	−	4.47318i	0.112606	−	0.195040i
$527$	−0.960699	−	1.66398i	−0.0418487	−	0.0724841i
$528$		0			0
$529$	10.8581	−	18.8067i	0.472090	−	0.817684i
$530$	2.86333	−	4.95943i	0.124375	−	0.215424i
$531$		0			0
$532$	−9.42101	−	5.12774i	−0.408453	−	0.222316i
$533$	−0.690757	−	1.19643i	−0.0299200	−	0.0518230i
$534$		0			0
$535$	−3.58307			−0.154910
$536$	2.32023			0.100219
$537$		0			0
$538$	8.42840	+	14.5984i	0.363374	+	0.629383i
$539$	11.6388	−	22.7267i	0.501319	−	0.978910i
$540$		0			0
$541$	−2.05934	+	3.56688i	−0.0885379	+	0.153352i	−0.906893	−	0.421360i	$-0.861553\pi$
$541$	−2.05934	+	3.56688i	−0.0885379	+	0.153352i	0.818355	+	0.574713i	$0.194886\pi$
$542$	−12.5562	+	21.7480i	−0.539336	+	0.934157i
$543$		0			0
$544$	−1.86693	−	3.23361i	−0.0800438	−	0.138640i
$545$	−1.73025	+	2.99689i	−0.0741159	+	0.128372i
$546$		0			0
$547$	−11.8602	−	20.5425i	−0.507106	−	0.878333i	−0.999966	−	0.00822465i	$-0.997382\pi$
$547$	−11.8602	−	20.5425i	−0.507106	−	0.878333i	0.492860	−	0.870108i	$-0.335951\pi$
$548$	−2.20321	+	3.81607i	−0.0941165	+	0.163015i
$549$		0			0
$550$	−8.73239	−	15.1249i	−0.372350	−	0.644930i
$551$	−36.3858			−1.55009
$552$		0			0
$553$	−0.333165	−	13.2436i	−0.0141676	−	0.563176i
$554$	1.69076	−	2.92848i	0.0718334	−	0.124419i
$555$		0			0
$556$	−1.01245	+	1.75362i	−0.0429376	+	0.0743701i
$557$	21.0313	+	36.4273i	0.891125	+	1.54347i	0.838528	+	0.544859i	$0.183417\pi$
$557$	21.0313	+	36.4273i	0.891125	+	1.54347i	0.0525975	+	0.998616i	$0.483250\pi$
$558$		0			0
$559$	13.6228			0.576181
$560$	1.03950	−	0.635534i	0.0439267	−	0.0268562i
$561$		0			0
$562$	−10.1388	−	17.5609i	−0.427680	−	0.740763i
$563$	−11.8243			−0.498335			−0.249168	−	0.968460i	$-0.580157\pi$
$563$	−11.8243			−0.498335			−0.249168	+	0.968460i	$0.580157\pi$
$564$		0			0
$565$	2.79125			0.117429
$566$	−17.3494			−0.729250
$567$		0			0
$568$	1.67977			0.0704815
$569$	−14.2016			−0.595360			−0.297680	−	0.954666i	$-0.596213\pi$
$569$	−14.2016			−0.595360			−0.297680	+	0.954666i	$0.596213\pi$
$570$		0			0
$571$	11.9574			0.500401			0.250200	−	0.968194i	$-0.419503\pi$
$571$	11.9574			0.500401			0.250200	+	0.968194i	$0.419503\pi$
$572$	2.66372	+	4.61369i	0.111376	+	0.192908i
$573$		0			0
$574$	−2.19815	−	1.19643i	−0.0917490	−	0.0499379i
$575$	5.42509			0.226242
$576$		0			0
$577$	21.3135	+	36.9161i	0.887293	+	1.53684i	0.843062	+	0.537816i	$0.180750\pi$
$577$	21.3135	+	36.9161i	0.887293	+	1.53684i	0.0442307	+	0.999021i	$0.485916\pi$
$578$	−1.52918	+	2.64861i	−0.0636054	+	0.110168i
$579$		0			0
$580$	2.06654	−	3.57935i	0.0858083	−	0.148624i
$581$	15.0057	−	9.17431i	0.622543	−	0.380614i
$582$		0			0
$583$	45.3609			1.87866
$584$	6.62062	+	11.4673i	0.273963	+	0.474518i
$585$		0			0
$586$	−4.93560	+	8.54871i	−0.203888	+	0.353144i
$587$	−20.5328	−	35.5638i	−0.847478	−	1.46788i	−0.883451	−	0.468523i	$-0.844786\pi$
$587$	−20.5328	−	35.5638i	−0.847478	−	1.46788i	0.0359730	−	0.999353i	$-0.488547\pi$
$588$		0			0
$589$	1.04309	−	1.80669i	0.0429799	−	0.0744434i
$590$	2.96936	+	5.14308i	0.122247	+	0.211737i
$591$		0			0
$592$	−4.55408	+	7.88791i	−0.187172	+	0.324191i
$593$	−16.1008	+	27.8874i	−0.661180	+	1.14520i	0.319126	+	0.947712i	$0.396611\pi$
$593$	−16.1008	+	27.8874i	−0.661180	+	1.14520i	−0.980306	+	0.197485i	$0.936723\pi$
$594$		0			0
$595$	3.99573	+	2.17483i	0.163809	+	0.0891592i
$596$	−4.58113	−	7.93474i	−0.187650	−	0.325020i
$597$		0			0
$598$	−1.65486			−0.0676723
$599$	−19.0718			−0.779252			−0.389626	−	0.920973i	$-0.627396\pi$
$599$	−19.0718			−0.779252			−0.389626	+	0.920973i	$0.627396\pi$
$600$		0			0
$601$	4.27188	+	7.39912i	0.174254	+	0.301816i	0.939903	−	0.341442i	$-0.110915\pi$
$601$	4.27188	+	7.39912i	0.174254	+	0.301816i	−0.765649	+	0.643259i	$0.777582\pi$
$602$	21.0548	−	12.8726i	0.858128	−	0.524648i
$603$		0			0
$604$	0.0519482	−	0.0899768i	0.00211374	−	0.00366111i
$605$	−0.530835	+	0.919434i	−0.0215815	+	0.0373803i
$606$		0			0
$607$	−19.0057	−	32.9189i	−0.771419	−	1.33614i	−0.936785	−	0.349905i	$-0.886214\pi$
$607$	−19.0057	−	32.9189i	−0.771419	−	1.33614i	0.165366	−	0.986232i	$-0.447119\pi$
$608$	2.02704	−	3.51094i	0.0822074	−	0.142387i
$609$		0			0
$610$	2.78220	+	4.81891i	0.112648	+	0.195112i
$611$	−1.69961	+	2.94381i	−0.0687589	+	0.119094i
$612$		0			0
$613$	11.3296	+	19.6234i	0.457597	+	0.792581i	0.998833	−	0.0482894i	$-0.0153770\pi$
$613$	11.3296	+	19.6234i	0.457597	+	0.792581i	−0.541237	+	0.840870i	$0.682044\pi$
$614$	−7.78794			−0.314295
$615$		0			0
$616$	8.47656	+	4.61369i	0.341530	+	0.185891i
$617$	10.1388	−	17.5609i	0.408173	−	0.706977i	−0.586512	−	0.809941i	$-0.699499\pi$
$617$	10.1388	−	17.5609i	0.408173	−	0.706977i	0.994685	+	0.102964i	$0.0328327\pi$
$618$		0			0
$619$	−1.03064	+	1.78512i	−0.0414249	+	0.0717501i	−0.885994	−	0.463696i	$-0.846523\pi$
$619$	−1.03064	+	1.78512i	−0.0414249	+	0.0717501i	0.844570	+	0.535446i	$0.179856\pi$
$620$	0.118485	+	0.205223i	0.00475849	+	0.00824194i
$621$		0			0
$622$	15.4107			0.617912
$623$	6.33628	+	3.44877i	0.253858	+	0.138172i
$624$		0			0
$625$	−10.9320	−	18.9348i	−0.437280	−	0.757391i
$626$	−8.49688			−0.339604
$627$		0			0
$628$	20.9823			0.837285
$629$	−34.0085			−1.35601
$630$		0			0
$631$	1.63715			0.0651740			0.0325870	−	0.999469i	$-0.489625\pi$
$631$	1.63715			0.0651740			0.0325870	+	0.999469i	$0.489625\pi$
$632$	5.00720			0.199176
$633$		0			0
$634$	−14.1052			−0.560191
$635$	−2.02850	−	3.51347i	−0.0804988	−	0.139428i
$636$		0			0
$637$	−4.66012	+	9.09967i	−0.184641	+	0.360542i
$638$	32.7381			1.29611
$639$		0			0
$640$	0.230252	+	0.398809i	0.00910153	+	0.0157643i
$641$	10.9662	−	18.9941i	0.433140	−	0.750221i	−0.564001	−	0.825774i	$-0.690739\pi$
$641$	10.9662	−	18.9941i	0.433140	−	0.750221i	0.997142	+	0.0755526i	$0.0240721\pi$
$642$		0			0
$643$	−14.1819	+	24.5638i	−0.559280	+	0.968701i	0.438277	+	0.898840i	$0.355589\pi$
$643$	−14.1819	+	24.5638i	−0.559280	+	0.968701i	−0.997557	+	0.0698609i	$0.977744\pi$
$644$	−2.55768	+	1.56373i	−0.100787	+	0.0616197i
$645$		0			0
$646$	15.1373			0.595571
$647$	−17.3904	−	30.1210i	−0.683686	−	1.18418i	−0.973848	−	0.227201i	$-0.927042\pi$
$647$	−17.3904	−	30.1210i	−0.683686	−	1.18418i	0.290162	−	0.956978i	$-0.406291\pi$
$648$		0			0
$649$	−23.5203	+	40.7384i	−0.923253	+	1.59912i
$650$	3.49640	+	6.05594i	0.137140	+	0.237534i
$651$		0			0
$652$	−11.5182	+	19.9501i	−0.451087	+	0.781306i
$653$	−1.59931	−	2.77009i	−0.0625860	−	0.108402i	0.833035	−	0.553221i	$-0.186601\pi$
$653$	−1.59931	−	2.77009i	−0.0625860	−	0.108402i	−0.895621	+	0.444819i	$0.853268\pi$
$654$		0			0
$655$	4.86693	−	8.42976i	0.190167	−	0.329378i
$656$	0.472958	−	0.819187i	0.0184659	−	0.0319839i
$657$		0			0
$658$	0.154861	+	6.15585i	0.00603710	+	0.239980i
$659$	−5.30418	−	9.18711i	−0.206622	−	0.357879i	0.744027	−	0.668150i	$-0.232914\pi$
$659$	−5.30418	−	9.18711i	−0.206622	−	0.357879i	−0.950648	+	0.310271i	$0.899580\pi$
$660$		0			0
$661$	10.1301			0.394017			0.197009	−	0.980402i	$-0.436877\pi$
$661$	10.1301			0.394017			0.197009	+	0.980402i	$0.436877\pi$
$662$	−27.5438			−1.07052
$663$		0			0
$664$	3.32383	+	5.75705i	0.128990	+	0.223417i
$665$	0.124220	+	4.93786i	0.00481705	+	0.191482i
$666$		0			0
$667$	−5.08472	+	8.80700i	−0.196881	+	0.341008i
$668$	5.31498	−	9.20581i	0.205643	−	0.356184i
$669$		0			0
$670$	−0.534239	−	0.925330i	−0.0206395	−	0.0357486i
$671$	−22.0378	+	38.1707i	−0.850761	+	1.47356i
$672$		0			0
$673$	1.60817	+	2.78543i	0.0619903	+	0.107370i	0.895355	−	0.445353i	$-0.146922\pi$
$673$	1.60817	+	2.78543i	0.0619903	+	0.107370i	−0.833365	+	0.552724i	$0.813589\pi$
$674$	−0.748440	+	1.29634i	−0.0288288	+	0.0499330i
$675$		0			0
$676$	5.43346	+	9.41103i	0.208979	+	0.361963i
$677$	29.3638			1.12854			0.564271	−	0.825589i	$-0.309157\pi$
$677$	29.3638			1.12854			0.564271	+	0.825589i	$0.309157\pi$
$678$		0			0
$679$	25.2527	−	15.4392i	0.969110	−	0.592501i
$680$	−0.859728	+	1.48909i	−0.0329691	+	0.0571041i
$681$		0			0
$682$	−0.938524	+	1.62557i	−0.0359379	+	0.0622463i
$683$	−12.6278	−	21.8720i	−0.483190	−	0.836910i	0.516624	−	0.856213i	$-0.327189\pi$
$683$	−12.6278	−	21.8720i	−0.483190	−	0.836910i	−0.999814	+	0.0193029i	$0.993855\pi$
$684$		0			0
$685$	2.02918			0.0775309
$686$	1.39610	+	18.4676i	0.0533035	+	0.705095i
$687$		0			0
$688$	4.66372	+	8.07779i	0.177802	+	0.307963i
$689$	−18.1623			−0.691927
$690$		0			0
$691$	−15.3638			−0.584467			−0.292233	−	0.956347i	$-0.594398\pi$
$691$	−15.3638			−0.584467			−0.292233	+	0.956347i	$0.594398\pi$
$692$	−2.93872			−0.111713
$693$		0			0
$694$	−18.2881			−0.694208
$695$	0.932479			0.0353709
$696$		0			0
$697$	3.53191			0.133781
$698$	3.90136	+	6.75735i	0.147669	+	0.255770i
$699$		0			0
$700$	11.1264	+	6.05594i	0.420537	+	0.228893i
$701$	13.3700			0.504980			0.252490	−	0.967600i	$-0.418751\pi$
$701$	13.3700			0.504980			0.252490	+	0.967600i	$0.418751\pi$
$702$		0			0
$703$	−18.4626	−	31.9782i	−0.696332	−	1.20608i
$704$	−1.82383	+	3.15897i	−0.0687382	+	0.119058i
$705$		0			0
$706$	−13.4626	+	23.3180i	−0.506673	+	0.877584i
$707$	31.9662	+	17.3988i	1.20221	+	0.654351i
$708$		0			0
$709$	−1.12588			−0.0422832			−0.0211416	−	0.999776i	$-0.506730\pi$
$709$	−1.12588			−0.0422832			−0.0211416	+	0.999776i	$0.506730\pi$
$710$	−0.386770	−	0.669906i	−0.0145152	−	0.0251411i
$711$		0			0
$712$	−1.36333	+	2.36135i	−0.0510928	+	0.0884954i
$713$	−0.291534	−	0.504951i	−0.0109180	−	0.0189106i
$714$		0			0
$715$	1.22665	−	2.12463i	0.0458743	−	0.0794565i
$716$	4.58113	+	7.93474i	0.171205	+	0.296535i
$717$		0			0
$718$	−3.13161	+	5.42411i	−0.116871	+	0.202426i
$719$	−9.13667	+	15.8252i	−0.340740	+	0.590180i	−0.984570	−	0.174989i	$-0.944011\pi$
$719$	−9.13667	+	15.8252i	−0.340740	+	0.590180i	0.643830	+	0.765169i	$0.277344\pi$
$720$		0			0
$721$	25.1965	−	15.4048i	0.938366	−	0.573705i
$722$	−1.28220	−	2.22084i	−0.0477186	−	0.0826510i
$723$		0			0
$724$	22.4284			0.833545
$725$	42.9722			1.59595
$726$		0			0
$727$	−14.8478	−	25.7171i	−0.550673	−	0.953793i	−0.998226	−	0.0595359i	$-0.981038\pi$
$727$	−14.8478	−	25.7171i	−0.550673	−	0.953793i	0.447553	−	0.894257i	$-0.352295\pi$
$728$	−3.39397	−	1.84730i	−0.125789	−	0.0684654i
$729$		0			0
$730$	3.04883	−	5.28073i	0.112842	−	0.195448i
$731$	−17.4136	+	30.1613i	−0.644066	+	1.11555i
$732$		0			0
$733$	−9.61390	−	16.6518i	−0.355098	−	0.615047i	0.632037	−	0.774938i	$-0.282219\pi$
$733$	−9.61390	−	16.6518i	−0.355098	−	0.615047i	−0.987135	+	0.159891i	$0.948886\pi$
$734$	14.6367	−	25.3515i	0.540249	−	0.935740i
$735$		0			0
$736$	−0.566537	−	0.981271i	−0.0208828	−	0.0361701i
$737$	4.23171	−	7.32955i	0.155877	−	0.269987i
$738$		0			0
$739$	−15.1336	−	26.2121i	−0.556697	−	0.964227i	−0.997769	−	0.0667556i	$-0.978735\pi$
$739$	−15.1336	−	26.2121i	−0.556697	−	0.964227i	0.441073	−	0.897471i	$-0.354598\pi$
$740$	4.19436			0.154188
$741$		0			0
$742$	−28.0708	+	17.1621i	−1.03051	+	0.630041i
$743$	11.8815	−	20.5794i	0.435890	−	0.754984i	−0.561477	−	0.827492i	$-0.689767\pi$
$743$	11.8815	−	20.5794i	0.435890	−	0.754984i	0.997368	+	0.0725076i	$0.0231002\pi$
$744$		0			0
$745$	−2.10963	+	3.65399i	−0.0772909	+	0.133872i
$746$	8.92986	+	15.4670i	0.326946	+	0.566286i
$747$		0			0
$748$	−13.6198			−0.497990
$749$	18.0811	+	9.84134i	0.660670	+	0.359595i
$750$		0			0
$751$	−6.33415	−	10.9711i	−0.231136	−	0.400340i	0.727006	−	0.686631i	$-0.240911\pi$
$751$	−6.33415	−	10.9711i	−0.231136	−	0.400340i	−0.958143	+	0.286291i	$0.907578\pi$
$752$	−2.32743			−0.0848727
$753$		0			0
$754$	−13.1082			−0.477371
$755$	−0.0478448			−0.00174125
$756$		0			0
$757$	−29.0799			−1.05693			−0.528464	−	0.848955i	$-0.677232\pi$
$757$	−29.0799			−1.05693			−0.528464	+	0.848955i	$0.677232\pi$
$758$	22.4255			0.814530
$759$		0			0
$760$	−1.86693			−0.0677205
$761$	14.6015	+	25.2905i	0.529302	+	0.916778i	0.999416	+	0.0341724i	$0.0108795\pi$
$761$	14.6015	+	25.2905i	0.529302	+	0.916778i	−0.470114	+	0.882606i	$0.655787\pi$
$762$		0			0
$763$	16.9626	−	10.3707i	0.614089	−	0.375446i
$764$	−2.48968			−0.0900736
$765$		0			0
$766$	7.07014	+	12.2458i	0.255454	+	0.442460i
$767$	9.41741	−	16.3114i	0.340043	−	0.588972i
$768$		0			0
$769$	12.5869	−	21.8011i	0.453894	−	0.786167i	−0.544730	−	0.838611i	$-0.683368\pi$
$769$	12.5869	−	21.8011i	0.453894	−	0.786167i	0.998624	+	0.0524443i	$0.0167012\pi$
$770$	−0.111767	−	4.44284i	−0.00402780	−	0.160109i
$771$		0			0
$772$	4.48968			0.161587
$773$	0.752039	+	1.30257i	0.0270490	+	0.0468502i	0.879233	−	0.476392i	$-0.158056\pi$
$773$	0.752039	+	1.30257i	0.0270490	+	0.0468502i	−0.852184	+	0.523242i	$0.824722\pi$
$774$		0			0
$775$	−1.23191	+	2.13373i	−0.0442515	+	0.0766458i
$776$	5.59358	+	9.68836i	0.200798	+	0.347792i
$777$		0			0
$778$	11.5651	−	20.0313i	0.414628	−	0.718157i
$779$	1.91741	+	3.32105i	0.0686984	+	0.118989i
$780$		0			0
$781$	3.06361	−	5.30633i	0.109625	−	0.189875i
$782$	2.11537	−	3.66392i	0.0756453	−	0.131022i

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:	\( N \)	\(=\)	\( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	378.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{4} +(-0.230252 - 0.398809i) q^{5} +(0.0665372 + 2.64491i) q^{7} -1.00000 q^{8} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{4} +(-0.230252 - 0.398809i) q^{5} +(0.0665372 + 2.64491i) q^{7} -1.00000 q^{8} +(0.230252 + 0.398809i) q^{10} +(-1.82383 + 3.15897i) q^{11} +(0.730252 - 1.26483i) q^{13} +(-0.0665372 - 2.64491i) q^{14} +1.00000 q^{16} +(1.86693 + 3.23361i) q^{17} +(-2.02704 + 3.51094i) q^{19} +(-0.230252 - 0.398809i) q^{20} +(1.82383 - 3.15897i) q^{22} +(0.566537 + 0.981271i) q^{23} +(2.39397 - 4.14647i) q^{25} +(-0.730252 + 1.26483i) q^{26} +(0.0665372 + 2.64491i) q^{28} +(4.48755 + 7.77266i) q^{29} -0.514589 q^{31} -1.00000 q^{32} +(-1.86693 - 3.23361i) q^{34} +(1.03950 - 0.635534i) q^{35} +(-4.55408 + 7.88791i) q^{37} +(2.02704 - 3.51094i) q^{38} +(0.230252 + 0.398809i) q^{40} +(0.472958 - 0.819187i) q^{41} +(4.66372 + 8.07779i) q^{43} +(-1.82383 + 3.15897i) q^{44} +(-0.566537 - 0.981271i) q^{46} -2.32743 q^{47} +(-6.99115 + 0.351971i) q^{49} +(-2.39397 + 4.14647i) q^{50} +(0.730252 - 1.26483i) q^{52} +(-6.21780 - 10.7695i) q^{53} +1.67977 q^{55} +(-0.0665372 - 2.64491i) q^{56} +(-4.48755 - 7.77266i) q^{58} +12.8961 q^{59} +12.0833 q^{61} +0.514589 q^{62} +1.00000 q^{64} -0.672570 q^{65} -2.32023 q^{67} +(1.86693 + 3.23361i) q^{68} +(-1.03950 + 0.635534i) q^{70} -1.67977 q^{71} +(-6.62062 - 11.4673i) q^{73} +(4.55408 - 7.88791i) q^{74} +(-2.02704 + 3.51094i) q^{76} +(-8.47656 - 4.61369i) q^{77} -5.00720 q^{79} +(-0.230252 - 0.398809i) q^{80} +(-0.472958 + 0.819187i) q^{82} +(-3.32383 - 5.75705i) q^{83} +(0.859728 - 1.48909i) q^{85} +(-4.66372 - 8.07779i) q^{86} +(1.82383 - 3.15897i) q^{88} +(1.36333 - 2.36135i) q^{89} +(3.39397 + 1.84730i) q^{91} +(0.566537 + 0.981271i) q^{92} +2.32743 q^{94} +1.86693 q^{95} +(-5.59358 - 9.68836i) q^{97} +(6.99115 - 0.351971i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{2} + 6 q^{4} + 5 q^{5} + 4 q^{7} - 6 q^{8}+O(q^{10}) \) 6 * q - 6 * q^2 + 6 * q^4 + 5 * q^5 + 4 * q^7 - 6 * q^8	\( 6 q - 6 q^{2} + 6 q^{4} + 5 q^{5} + 4 q^{7} - 6 q^{8} - 5 q^{10} + q^{11} - 2 q^{13} - 4 q^{14} + 6 q^{16} + 4 q^{17} - 3 q^{19} + 5 q^{20} - q^{22} + 7 q^{23} - 2 q^{25} + 2 q^{26} + 4 q^{28} + 5 q^{29} + 28 q^{31} - 6 q^{32} - 4 q^{34} + 19 q^{35} - 9 q^{37} + 3 q^{38} - 5 q^{40} + 12 q^{41} + 18 q^{43} + q^{44} - 7 q^{46} + 6 q^{47} - 12 q^{49} + 2 q^{50} - 2 q^{52} - 9 q^{53} + 14 q^{55} - 4 q^{56} - 5 q^{58} + 8 q^{59} - 8 q^{61} - 28 q^{62} + 6 q^{64} - 24 q^{65} - 10 q^{67} + 4 q^{68} - 19 q^{70} - 14 q^{71} - 25 q^{73} + 9 q^{74} - 3 q^{76} - 52 q^{77} - 14 q^{79} + 5 q^{80} - 12 q^{82} - 8 q^{83} + 14 q^{85} - 18 q^{86} - q^{88} + 9 q^{89} + 4 q^{91} + 7 q^{92} - 6 q^{94} + 4 q^{95} - 28 q^{97} + 12 q^{98}+O(q^{100}) \) 6 * q - 6 * q^2 + 6 * q^4 + 5 * q^5 + 4 * q^7 - 6 * q^8 - 5 * q^10 + q^11 - 2 * q^13 - 4 * q^14 + 6 * q^16 + 4 * q^17 - 3 * q^19 + 5 * q^20 - q^22 + 7 * q^23 - 2 * q^25 + 2 * q^26 + 4 * q^28 + 5 * q^29 + 28 * q^31 - 6 * q^32 - 4 * q^34 + 19 * q^35 - 9 * q^37 + 3 * q^38 - 5 * q^40 + 12 * q^41 + 18 * q^43 + q^44 - 7 * q^46 + 6 * q^47 - 12 * q^49 + 2 * q^50 - 2 * q^52 - 9 * q^53 + 14 * q^55 - 4 * q^56 - 5 * q^58 + 8 * q^59 - 8 * q^61 - 28 * q^62 + 6 * q^64 - 24 * q^65 - 10 * q^67 + 4 * q^68 - 19 * q^70 - 14 * q^71 - 25 * q^73 + 9 * q^74 - 3 * q^76 - 52 * q^77 - 14 * q^79 + 5 * q^80 - 12 * q^82 - 8 * q^83 + 14 * q^85 - 18 * q^86 - q^88 + 9 * q^89 + 4 * q^91 + 7 * q^92 - 6 * q^94 + 4 * q^95 - 28 * q^97 + 12 * q^98

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