LMFDB - Embedded newform 378.2.h.d.361.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [378,2,Mod(289,378)]

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([4, 2]))

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

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

chi := DirichletCharacter("378.289");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 378 = 2 \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	378.h (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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			361.2
Root			$0.500000 - 1.41036i$ of defining polynomial
Character	$\chi$	$=$	378.361
Dual form			378.2.h.d.289.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} -1.76088 q^{5} +(-1.85185 - 1.88962i) q^{7} -1.00000 q^{8} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} -1.76088 q^{5} +(-1.85185 - 1.88962i) q^{7} -1.00000 q^{8} +(-0.880438 + 1.52496i) q^{10} -6.12476 q^{11} +(-0.380438 + 0.658939i) q^{13} +(-2.56238 + 0.658939i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(3.42107 - 5.92546i) q^{17} +(0.971410 + 1.68253i) q^{19} +(0.880438 + 1.52496i) q^{20} +(-3.06238 + 5.30420i) q^{22} +0.421067 q^{23} -1.89931 q^{25} +(0.380438 + 0.658939i) q^{26} +(-0.710533 + 2.54856i) q^{28} +(-0.732287 - 1.26836i) q^{29} +(-3.85185 - 6.67160i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-3.42107 - 5.92546i) q^{34} +(3.26088 + 3.32738i) q^{35} +(1.44282 + 2.49904i) q^{37} +1.94282 q^{38} +1.76088 q^{40} +(3.47141 - 6.01266i) q^{41} +(4.33009 + 7.49994i) q^{43} +(3.06238 + 5.30420i) q^{44} +(0.210533 - 0.364654i) q^{46} +(0.830095 - 1.43777i) q^{47} +(-0.141315 + 6.99857i) q^{49} +(-0.949657 + 1.64485i) q^{50} +0.760877 q^{52} +(0.112725 - 0.195246i) q^{53} +10.7850 q^{55} +(1.85185 + 1.88962i) q^{56} -1.46457 q^{58} +(0.993163 + 1.72021i) q^{59} +(5.17511 - 8.96355i) q^{61} -7.70370 q^{62} +1.00000 q^{64} +(0.669905 - 1.16031i) q^{65} +(-3.39248 - 5.87594i) q^{67} -6.84213 q^{68} +(4.51204 - 1.16031i) q^{70} -10.7850 q^{71} +(0.153353 - 0.265616i) q^{73} +2.88564 q^{74} +(0.971410 - 1.68253i) q^{76} +(11.3421 + 11.5735i) q^{77} +(6.72257 - 11.6438i) q^{79} +(0.880438 - 1.52496i) q^{80} +(-3.47141 - 6.01266i) q^{82} +(1.56238 + 2.70612i) q^{83} +(-6.02408 + 10.4340i) q^{85} +8.66019 q^{86} +6.12476 q^{88} +(-1.30150 - 2.25427i) q^{89} +(1.94966 - 0.501371i) q^{91} +(-0.210533 - 0.364654i) q^{92} +(-0.830095 - 1.43777i) q^{94} +(-1.71053 - 2.96273i) q^{95} +(-1.81806 - 3.14897i) q^{97} +(5.99028 + 3.62167i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{2} - 3 q^{4} - 10 q^{5} - 2 q^{7} - 6 q^{8}+O(q^{10}) $ 6 * q + 3 * q^2 - 3 * q^4 - 10 * q^5 - 2 * q^7 - 6 * q^8	$ 6 q + 3 q^{2} - 3 q^{4} - 10 q^{5} - 2 q^{7} - 6 q^{8} - 5 q^{10} - 2 q^{11} - 2 q^{13} + 2 q^{14} - 3 q^{16} + 4 q^{17} - 3 q^{19} + 5 q^{20} - q^{22} - 14 q^{23} + 4 q^{25} + 2 q^{26} + 4 q^{28} + 5 q^{29} - 14 q^{31} + 3 q^{32} - 4 q^{34} + 19 q^{35} - 9 q^{37} - 6 q^{38} + 10 q^{40} + 12 q^{41} + 18 q^{43} + q^{44} - 7 q^{46} - 3 q^{47} + 2 q^{50} + 4 q^{52} - 9 q^{53} + 14 q^{55} + 2 q^{56} + 10 q^{58} - 4 q^{59} + 4 q^{61} - 28 q^{62} + 6 q^{64} + 12 q^{65} + 5 q^{67} - 8 q^{68} + 2 q^{70} - 14 q^{71} - 25 q^{73} - 18 q^{74} - 3 q^{76} + 35 q^{77} + 7 q^{79} + 5 q^{80} - 12 q^{82} - 8 q^{83} + 14 q^{85} + 36 q^{86} + 2 q^{88} + 9 q^{89} + 4 q^{91} + 7 q^{92} + 3 q^{94} - 2 q^{95} - 28 q^{97} + 12 q^{98}+O(q^{100}) $ 6 * q + 3 * q^2 - 3 * q^4 - 10 * q^5 - 2 * q^7 - 6 * q^8 - 5 * q^10 - 2 * q^11 - 2 * q^13 + 2 * q^14 - 3 * q^16 + 4 * q^17 - 3 * q^19 + 5 * q^20 - q^22 - 14 * q^23 + 4 * q^25 + 2 * q^26 + 4 * q^28 + 5 * q^29 - 14 * q^31 + 3 * q^32 - 4 * q^34 + 19 * q^35 - 9 * q^37 - 6 * q^38 + 10 * q^40 + 12 * q^41 + 18 * q^43 + q^44 - 7 * q^46 - 3 * q^47 + 2 * q^50 + 4 * q^52 - 9 * q^53 + 14 * q^55 + 2 * q^56 + 10 * q^58 - 4 * q^59 + 4 * q^61 - 28 * q^62 + 6 * q^64 + 12 * q^65 + 5 * q^67 - 8 * q^68 + 2 * q^70 - 14 * q^71 - 25 * q^73 - 18 * q^74 - 3 * q^76 + 35 * q^77 + 7 * q^79 + 5 * q^80 - 12 * q^82 - 8 * q^83 + 14 * q^85 + 36 * q^86 + 2 * q^88 + 9 * q^89 + 4 * q^91 + 7 * q^92 + 3 * q^94 - 2 * q^95 - 28 * q^97 + 12 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$29$	$325$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−1.76088			−0.787488			−0.393744	−	0.919220i	$-0.628820\pi$
$5$	−1.76088			−0.787488			−0.393744	+	0.919220i	$0.628820\pi$
$6$		0			0
$7$	−1.85185	−	1.88962i	−0.699933	−	0.714209i
$7$	−1.85185	−	1.88962i	−0.699933	−	0.714209i
$8$	−1.00000			−0.353553
$9$		0			0
$10$	−0.880438	+	1.52496i	−0.278419	+	0.482236i
$11$	−6.12476			−1.84669			−0.923343	−	0.383977i	$-0.874554\pi$
$11$	−6.12476			−1.84669			−0.923343	+	0.383977i	$0.874554\pi$
$12$		0			0
$13$	−0.380438	+	0.658939i	−0.105515	+	0.182757i	−0.913948	−	0.405831i	$-0.866982\pi$
$13$	−0.380438	+	0.658939i	−0.105515	+	0.182757i	0.808434	+	0.588587i	$0.200316\pi$
$14$	−2.56238	+	0.658939i	−0.684825	+	0.176109i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	3.42107	−	5.92546i	0.829731	−	1.43714i	−0.0685191	−	0.997650i	$-0.521827\pi$
$17$	3.42107	−	5.92546i	0.829731	−	1.43714i	0.898250	−	0.439486i	$-0.144839\pi$
$18$		0			0
$19$	0.971410	+	1.68253i	0.222857	+	0.385999i	0.955674	−	0.294426i	$-0.0951285\pi$
$19$	0.971410	+	1.68253i	0.222857	+	0.385999i	−0.732818	+	0.680425i	$0.761795\pi$
$20$	0.880438	+	1.52496i	0.196872	+	0.340992i
$21$		0			0
$22$	−3.06238	+	5.30420i	−0.652902	+	1.13086i
$23$	0.421067			0.0877985			0.0438992	−	0.999036i	$-0.486022\pi$
$23$	0.421067			0.0877985			0.0438992	+	0.999036i	$0.486022\pi$
$24$		0			0
$25$	−1.89931			−0.379863
$26$	0.380438	+	0.658939i	0.0746101	+	0.129228i
$27$		0			0
$28$	−0.710533	+	2.54856i	−0.134278	+	0.481632i
$29$	−0.732287	−	1.26836i	−0.135982	−	0.235528i	0.789990	−	0.613120i	$-0.210086\pi$
$29$	−0.732287	−	1.26836i	−0.135982	−	0.235528i	−0.925972	+	0.377592i	$0.876752\pi$
$30$		0			0
$31$	−3.85185	−	6.67160i	−0.691812	−	1.19825i	−0.971243	−	0.238088i	$-0.923479\pi$
$31$	−3.85185	−	6.67160i	−0.691812	−	1.19825i	0.279431	−	0.960166i	$-0.409854\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$		0			0
$34$	−3.42107	−	5.92546i	−0.586708	−	1.01621i
$35$	3.26088	+	3.32738i	0.551189	+	0.562431i
$36$		0			0
$37$	1.44282	+	2.49904i	0.237198	+	0.410839i	0.959909	−	0.280311i	$-0.0904376\pi$
$37$	1.44282	+	2.49904i	0.237198	+	0.410839i	−0.722711	+	0.691150i	$0.757104\pi$
$38$	1.94282			0.315167
$39$		0			0
$40$	1.76088			0.278419
$41$	3.47141	−	6.01266i	0.542143	−	0.939020i	−0.456638	−	0.889653i	$-0.650946\pi$
$41$	3.47141	−	6.01266i	0.542143	−	0.939020i	0.998781	−	0.0493667i	$-0.0157203\pi$
$42$		0			0
$43$	4.33009	+	7.49994i	0.660333	+	1.14373i	0.980528	+	0.196379i	$0.0629183\pi$
$43$	4.33009	+	7.49994i	0.660333	+	1.14373i	−0.320195	+	0.947352i	$0.603748\pi$
$44$	3.06238	+	5.30420i	0.461671	+	0.799638i
$45$		0			0
$46$	0.210533	−	0.364654i	0.0310414	−	0.0537654i
$47$	0.830095	−	1.43777i	0.121082	−	0.209720i	−0.799113	−	0.601181i	$-0.794697\pi$
$47$	0.830095	−	1.43777i	0.121082	−	0.209720i	0.920195	+	0.391461i	$0.128030\pi$
$48$		0			0
$49$	−0.141315	+	6.99857i	−0.0201879	+	0.999796i
$50$	−0.949657	+	1.64485i	−0.134302	+	0.232617i
$51$		0			0
$52$	0.760877			0.105515
$53$	0.112725	−	0.195246i	0.0154840	−	0.0268190i	−0.858180	−	0.513350i	$-0.828404\pi$
$53$	0.112725	−	0.195246i	0.0154840	−	0.0268190i	0.873664	+	0.486531i	$0.161738\pi$
$54$		0			0
$55$	10.7850			1.45424
$56$	1.85185	+	1.88962i	0.247464	+	0.252511i
$57$		0			0
$58$	−1.46457			−0.192308
$59$	0.993163	+	1.72021i	0.129299	+	0.223952i	0.923405	−	0.383827i	$-0.125394\pi$
$59$	0.993163	+	1.72021i	0.129299	+	0.223952i	−0.794106	+	0.607779i	$0.792061\pi$
$60$		0			0
$61$	5.17511	−	8.96355i	0.662605	−	1.14766i	−0.317324	−	0.948317i	$-0.602784\pi$
$61$	5.17511	−	8.96355i	0.662605	−	1.14766i	0.979929	−	0.199348i	$-0.0638823\pi$
$62$	−7.70370			−0.978370
$63$		0			0
$64$	1.00000			0.125000
$65$	0.669905	−	1.16031i	0.0830915	−	0.143919i
$66$		0			0
$67$	−3.39248	−	5.87594i	−0.414457	−	0.717861i	0.580914	−	0.813965i	$-0.302695\pi$
$67$	−3.39248	−	5.87594i	−0.414457	−	0.717861i	−0.995371	+	0.0961042i	$0.969362\pi$
$68$	−6.84213			−0.829731
$69$		0			0
$70$	4.51204	−	1.16031i	0.539292	−	0.138684i
$71$	−10.7850			−1.27994			−0.639969	−	0.768401i	$-0.721053\pi$
$71$	−10.7850			−1.27994			−0.639969	+	0.768401i	$0.721053\pi$
$72$		0			0
$73$	0.153353	−	0.265616i	0.0179487	−	0.0310880i	−0.856912	−	0.515463i	$-0.827620\pi$
$73$	0.153353	−	0.265616i	0.0179487	−	0.0310880i	0.874860	+	0.484375i	$0.160953\pi$
$74$	2.88564			0.335449
$75$		0			0
$76$	0.971410	−	1.68253i	0.111428	−	0.193000i
$77$	11.3421	+	11.5735i	1.29256	+	1.31892i
$78$		0			0
$79$	6.72257	−	11.6438i	0.756348	−	1.31003i	−0.188353	−	0.982101i	$-0.560315\pi$
$79$	6.72257	−	11.6438i	0.756348	−	1.31003i	0.944701	−	0.327932i	$-0.106352\pi$
$80$	0.880438	−	1.52496i	0.0984360	−	0.170496i
$81$		0			0
$82$	−3.47141	−	6.01266i	−0.383353	−	0.663987i
$83$	1.56238	+	2.70612i	0.171494	+	0.297036i	0.938942	−	0.344075i	$-0.111807\pi$
$83$	1.56238	+	2.70612i	0.171494	+	0.297036i	−0.767449	+	0.641110i	$0.778474\pi$
$84$		0			0
$85$	−6.02408	+	10.4340i	−0.653403	+	1.13173i
$86$	8.66019			0.933852
$87$		0			0
$88$	6.12476			0.652902
$89$	−1.30150	−	2.25427i	−0.137959	−	0.238952i	0.788765	−	0.614695i	$-0.210721\pi$
$89$	−1.30150	−	2.25427i	−0.137959	−	0.238952i	−0.926724	+	0.375743i	$0.877388\pi$
$90$		0			0
$91$	1.94966	−	0.501371i	0.204380	−	0.0525580i
$92$	−0.210533	−	0.364654i	−0.0219496	−	0.0380178i
$93$		0			0
$94$	−0.830095	−	1.43777i	−0.0856178	−	0.148294i
$95$	−1.71053	−	2.96273i	−0.175497	−	0.303970i
$96$		0			0
$97$	−1.81806	−	3.14897i	−0.184596	−	0.319729i	0.758845	−	0.651272i	$-0.225764\pi$
$97$	−1.81806	−	3.14897i	−0.184596	−	0.319729i	−0.943440	+	0.331543i	$0.892431\pi$
$98$	5.99028	+	3.62167i	0.605110	+	0.365844i
$99$		0			0
$100$	0.949657	+	1.64485i	0.0949657	+	0.164485i
$101$	8.01040			0.797065			0.398532	−	0.917154i	$-0.369520\pi$
$101$	8.01040			0.797065			0.398532	+	0.917154i	$0.369520\pi$
$102$		0			0
$103$	−6.82846			−0.672828			−0.336414	−	0.941714i	$-0.609214\pi$
$103$	−6.82846			−0.672828			−0.336414	+	0.941714i	$0.609214\pi$
$104$	0.380438	−	0.658939i	0.0373051	−	0.0646142i
$105$		0			0
$106$	−0.112725	−	0.195246i	−0.0109488	−	0.0189639i
$107$	−1.77292	−	3.07078i	−0.171394	−	0.296863i	0.767513	−	0.641033i	$-0.221494\pi$
$107$	−1.77292	−	3.07078i	−0.171394	−	0.296863i	−0.938908	+	0.344170i	$0.888160\pi$
$108$		0			0
$109$	0.351848	−	0.609419i	0.0337010	−	0.0583718i	−0.848683	−	0.528902i	$-0.822604\pi$
$109$	0.351848	−	0.609419i	0.0337010	−	0.0583718i	0.882384	+	0.470530i	$0.155937\pi$
$110$	5.39248	−	9.34004i	0.514152	−	0.890538i
$111$		0			0
$112$	2.56238	−	0.658939i	0.242122	−	0.0622638i
$113$	−4.25116	+	7.36323i	−0.399916	+	0.692674i	−0.993715	−	0.111939i	$-0.964294\pi$
$113$	−4.25116	+	7.36323i	−0.399916	+	0.692674i	0.593799	+	0.804613i	$0.297627\pi$
$114$		0			0
$115$	−0.741446			−0.0691402
$116$	−0.732287	+	1.26836i	−0.0679911	+	0.117764i
$117$		0			0
$118$	1.98633			0.182856
$119$	−17.5322	+	4.50855i	−1.60717	+	0.413298i
$120$		0			0
$121$	26.5127			2.41025
$122$	−5.17511	−	8.96355i	−0.468532	−	0.811521i
$123$		0			0
$124$	−3.85185	+	6.67160i	−0.345906	+	0.599127i
$125$	12.1488			1.08663
$126$		0			0
$127$	−18.9532			−1.68183			−0.840913	−	0.541170i	$-0.817982\pi$
$127$	−18.9532			−1.68183			−0.840913	+	0.541170i	$0.817982\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$		0			0
$130$	−0.669905	−	1.16031i	−0.0587546	−	0.101766i
$131$	7.29303			0.637195			0.318598	−	0.947890i	$-0.396788\pi$
$131$	7.29303			0.637195			0.318598	+	0.947890i	$0.396788\pi$
$132$		0			0
$133$	1.38044	−	4.95139i	0.119699	−	0.429340i
$134$	−6.78495			−0.586131
$135$		0			0
$136$	−3.42107	+	5.92546i	−0.293354	+	0.508104i
$137$	8.18194			0.699031			0.349515	−	0.936931i	$-0.386346\pi$
$137$	8.18194			0.699031			0.349515	+	0.936931i	$0.386346\pi$
$138$		0			0
$139$	−6.23229	+	10.7946i	−0.528616	+	0.915589i	0.470828	+	0.882225i	$0.343955\pi$
$139$	−6.23229	+	10.7946i	−0.528616	+	0.915589i	−0.999443	+	0.0333640i	$0.989378\pi$
$140$	1.25116	−	4.48769i	0.105742	−	0.379279i
$141$		0			0
$142$	−5.39248	+	9.34004i	−0.452527	+	0.783799i
$143$	2.33009	−	4.03584i	0.194852	−	0.337494i
$144$		0			0
$145$	1.28947	+	2.23342i	0.107084	+	0.185476i
$146$	−0.153353	−	0.265616i	−0.0126916	−	0.0219825i
$147$		0			0
$148$	1.44282	−	2.49904i	0.118599	−	0.205420i
$149$	−8.82846			−0.723256			−0.361628	−	0.932323i	$-0.617779\pi$
$149$	−8.82846			−0.723256			−0.361628	+	0.932323i	$0.617779\pi$
$150$		0			0
$151$	−14.9863			−1.21957			−0.609785	−	0.792567i	$-0.708744\pi$
$151$	−14.9863			−1.21957			−0.609785	+	0.792567i	$0.708744\pi$
$152$	−0.971410	−	1.68253i	−0.0787918	−	0.136471i
$153$		0			0
$154$	15.6940	−	4.03584i	1.26466	−	0.325217i
$155$	6.78263	+	11.7479i	0.544794	+	0.943611i
$156$		0			0
$157$	−9.49028	−	16.4377i	−0.757407	−	1.31187i	−0.944169	−	0.329462i	$-0.893132\pi$
$157$	−9.49028	−	16.4377i	−0.757407	−	1.31187i	0.186761	−	0.982405i	$-0.440201\pi$
$158$	−6.72257	−	11.6438i	−0.534819	−	0.926334i
$159$		0			0
$160$	−0.880438	−	1.52496i	−0.0696048	−	0.120559i
$161$	−0.779752	−	0.795655i	−0.0614530	−	0.0627064i
$162$		0			0
$163$	−7.51887	−	13.0231i	−0.588924	−	1.02005i	−0.994374	−	0.105929i	$-0.966219\pi$
$163$	−7.51887	−	13.0231i	−0.588924	−	1.02005i	0.405450	−	0.914117i	$-0.367115\pi$
$164$	−6.94282			−0.542143
$165$		0			0
$166$	3.12476			0.242529
$167$	−0.572097	+	0.990901i	−0.0442702	+	0.0766782i	−0.887311	−	0.461171i	$-0.847430\pi$
$167$	−0.572097	+	0.990901i	−0.0442702	+	0.0766782i	0.843041	+	0.537849i	$0.180763\pi$
$168$		0			0
$169$	6.21053	+	10.7570i	0.477733	+	0.827458i
$170$	6.02408	+	10.4340i	0.462026	+	0.800252i
$171$		0			0
$172$	4.33009	−	7.49994i	0.330167	−	0.571865i
$173$	0.248838	−	0.431001i	0.0189188	−	0.0327684i	−0.856411	−	0.516295i	$-0.827311\pi$
$173$	0.248838	−	0.431001i	0.0189188	−	0.0327684i	0.875330	+	0.483526i	$0.160644\pi$
$174$		0			0
$175$	3.51724	+	3.58898i	0.265878	+	0.271301i
$176$	3.06238	−	5.30420i	0.230836	−	0.399819i
$177$		0			0
$178$	−2.60301			−0.195104
$179$	−4.41423	+	7.64567i	−0.329935	+	0.571464i	−0.982499	−	0.186270i	$-0.940360\pi$
$179$	−4.41423	+	7.64567i	−0.329935	+	0.571464i	0.652564	+	0.757734i	$0.273694\pi$
$180$		0			0
$181$	1.32941			0.0988140			0.0494070	−	0.998779i	$-0.484267\pi$
$181$	1.32941			0.0988140			0.0494070	+	0.998779i	$0.484267\pi$
$182$	0.540628	−	1.93914i	0.0400740	−	0.143738i
$183$		0			0
$184$	−0.421067			−0.0310414
$185$	−2.54063	−	4.40050i	−0.186791	−	0.323531i
$186$		0			0
$187$	−20.9532	+	36.2920i	−1.53225	+	2.65394i
$188$	−1.66019			−0.121082
$189$		0			0
$190$	−3.42107			−0.248190
$191$	−8.08414	+	14.0021i	−0.584947	+	1.01316i	0.409934	+	0.912115i	$0.365552\pi$
$191$	−8.08414	+	14.0021i	−0.584947	+	1.01316i	−0.994882	+	0.101044i	$0.967782\pi$
$192$		0			0
$193$	7.08414	+	12.2701i	0.509927	+	0.883220i	0.999934	+	0.0115011i	$0.00366101\pi$
$193$	7.08414	+	12.2701i	0.509927	+	0.883220i	−0.490007	+	0.871719i	$0.663006\pi$
$194$	−3.63611			−0.261058
$195$		0			0
$196$	6.13160	−	3.37690i	0.437971	−	0.241207i
$197$	−15.8421			−1.12871			−0.564353	−	0.825534i	$-0.690874\pi$
$197$	−15.8421			−1.12871			−0.564353	+	0.825534i	$0.690874\pi$
$198$		0			0
$199$	−4.47141	+	7.74471i	−0.316970	+	0.549008i	−0.979854	−	0.199714i	$-0.935999\pi$
$199$	−4.47141	+	7.74471i	−0.316970	+	0.549008i	0.662884	+	0.748722i	$0.269332\pi$
$200$	1.89931			0.134302
$201$		0			0
$202$	4.00520	−	6.93721i	0.281805	−	0.488101i
$203$	−1.04063	+	3.73255i	−0.0730378	+	0.261974i
$204$		0			0
$205$	−6.11273	+	10.5876i	−0.426931	+	0.739467i
$206$	−3.41423	+	5.91362i	−0.237881	+	0.412021i
$207$		0			0
$208$	−0.380438	−	0.658939i	−0.0263787	−	0.0456892i
$209$	−5.94966	−	10.3051i	−0.411546	−	0.712819i
$210$		0			0
$211$	11.3856	−	19.7205i	0.783820	−	1.35762i	−0.145882	−	0.989302i	$-0.546602\pi$
$211$	11.3856	−	19.7205i	0.783820	−	1.35762i	0.929702	−	0.368314i	$-0.120065\pi$
$212$	−0.225450			−0.0154840
$213$		0			0
$214$	−3.54583			−0.242388
$215$	−7.62476	−	13.2065i	−0.520005	−	0.900674i
$216$		0			0
$217$	−5.47373	+	19.6333i	−0.371581	+	1.33280i
$218$	−0.351848	−	0.609419i	−0.0238302	−	0.0412751i
$219$		0			0
$220$	−5.39248	−	9.34004i	−0.363561	−	0.629706i
$221$	2.60301	+	4.50855i	0.175097	+	0.303278i
$222$		0			0
$223$	−6.44282	−	11.1593i	−0.431443	−	0.747281i	0.565555	−	0.824711i	$-0.308662\pi$
$223$	−6.44282	−	11.1593i	−0.431443	−	0.747281i	−0.996998	+	0.0774293i	$0.975329\pi$
$224$	0.710533	−	2.54856i	0.0474745	−	0.170283i
$225$		0			0
$226$	4.25116	+	7.36323i	0.282783	+	0.489795i
$227$	−21.9967			−1.45997			−0.729987	−	0.683461i	$-0.760474\pi$
$227$	−21.9967			−1.45997			−0.729987	+	0.683461i	$0.760474\pi$
$228$		0			0
$229$	−3.79863			−0.251020			−0.125510	−	0.992092i	$-0.540057\pi$
$229$	−3.79863			−0.251020			−0.125510	+	0.992092i	$0.540057\pi$
$230$	−0.370723	+	0.642111i	−0.0244448	+	0.0423396i
$231$		0			0
$232$	0.732287	+	1.26836i	0.0480770	+	0.0832718i
$233$	3.33530	+	5.77690i	0.218503	+	0.378458i	0.954350	−	0.298689i	$-0.0965495\pi$
$233$	3.33530	+	5.77690i	0.218503	+	0.378458i	−0.735848	+	0.677147i	$0.763216\pi$
$234$		0			0
$235$	−1.46169	+	2.53173i	−0.0953505	+	0.165152i
$236$	0.993163	−	1.72021i	0.0646494	−	0.111976i
$237$		0			0
$238$	−4.86156	+	17.4376i	−0.315128	+	1.13031i
$239$	7.82038	−	13.5453i	0.505858	−	0.876172i	−0.494119	−	0.869394i	$-0.664509\pi$
$239$	7.82038	−	13.5453i	0.505858	−	0.876172i	0.999977	−	0.00677786i	$-0.00215748\pi$
$240$		0			0
$241$	21.4120			1.37927			0.689635	−	0.724157i	$-0.257771\pi$
$241$	21.4120			1.37927			0.689635	+	0.724157i	$0.257771\pi$
$242$	13.2564	−	22.9607i	0.852151	−	1.47597i
$243$		0			0
$244$	−10.3502			−0.662605
$245$	0.248838	−	12.3236i	0.0158977	−	0.787328i
$246$		0			0
$247$	−1.47825			−0.0940586
$248$	3.85185	+	6.67160i	0.244593	+	0.423647i
$249$		0			0
$250$	6.07442	−	10.5212i	0.384180	−	0.665419i
$251$	23.6030			1.48981			0.744904	−	0.667171i	$-0.232495\pi$
$251$	23.6030			1.48981			0.744904	+	0.667171i	$0.232495\pi$
$252$		0			0
$253$	−2.57893			−0.162136
$254$	−9.47661	+	16.4140i	−0.594616	+	1.02990i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−20.2599			−1.26378			−0.631890	−	0.775058i	$-0.717721\pi$
$257$	−20.2599			−1.26378			−0.631890	+	0.775058i	$0.717721\pi$
$258$		0			0
$259$	2.05034	−	7.35422i	0.127402	−	0.456969i
$260$	−1.33981			−0.0830915
$261$		0			0
$262$	3.64652	−	6.31595i	0.225283	−	0.390201i
$263$	22.4887			1.38671			0.693355	−	0.720596i	$-0.256132\pi$
$263$	22.4887			1.38671			0.693355	+	0.720596i	$0.256132\pi$
$264$		0			0
$265$	−0.198495	+	0.343803i	−0.0121935	+	0.0211197i
$266$	−3.59781	−	3.67119i	−0.220596	−	0.225095i
$267$		0			0
$268$	−3.39248	+	5.87594i	−0.207228	+	0.358930i
$269$	12.6706	−	21.9461i	0.772540	−	1.33808i	−0.163627	−	0.986522i	$-0.552319\pi$
$269$	12.6706	−	21.9461i	0.772540	−	1.33808i	0.936167	−	0.351556i	$-0.114347\pi$
$270$		0			0
$271$	−6.87880	−	11.9144i	−0.417858	−	0.723751i	0.577866	−	0.816132i	$-0.303886\pi$
$271$	−6.87880	−	11.9144i	−0.417858	−	0.723751i	−0.995724	+	0.0923810i	$0.970552\pi$
$272$	3.42107	+	5.92546i	0.207433	+	0.359284i
$273$		0			0
$274$	4.09097	−	7.08577i	0.247145	−	0.428067i
$275$	11.6328			0.701487
$276$		0			0
$277$	−3.28263			−0.197234			−0.0986171	−	0.995125i	$-0.531442\pi$
$277$	−3.28263			−0.197234			−0.0986171	+	0.995125i	$0.531442\pi$
$278$	6.23229	+	10.7946i	0.373788	+	0.647419i
$279$		0			0
$280$	−3.26088	−	3.32738i	−0.194875	−	0.198849i
$281$	−0.634479	−	1.09895i	−0.0378498	−	0.0655578i	0.846480	−	0.532421i	$-0.178718\pi$
$281$	−0.634479	−	1.09895i	−0.0378498	−	0.0655578i	−0.884330	+	0.466863i	$0.845384\pi$
$282$		0			0
$283$	4.09617	+	7.09478i	0.243492	+	0.421741i	0.961707	−	0.274081i	$-0.0883736\pi$
$283$	4.09617	+	7.09478i	0.243492	+	0.421741i	−0.718214	+	0.695822i	$0.755040\pi$
$284$	5.39248	+	9.34004i	0.319985	+	0.554230i
$285$		0			0
$286$	−2.33009	−	4.03584i	−0.137781	−	0.238644i
$287$	−17.7902	+	4.57489i	−1.05012	+	0.270047i
$288$		0			0
$289$	−14.9074	−	25.8204i	−0.876906	−	1.51884i
$290$	2.57893			0.151440
$291$		0			0
$292$	−0.306707			−0.0179487
$293$	−7.72545	+	13.3809i	−0.451326	+	0.781719i	−0.998469	−	0.0553202i	$-0.982382\pi$
$293$	−7.72545	+	13.3809i	−0.451326	+	0.781719i	0.547143	+	0.837039i	$0.315715\pi$
$294$		0			0
$295$	−1.74884	−	3.02908i	−0.101821	−	0.176360i
$296$	−1.44282	−	2.49904i	−0.0838622	−	0.145254i
$297$		0			0
$298$	−4.41423	+	7.64567i	−0.255709	+	0.442902i
$299$	−0.160190	+	0.277457i	−0.00926402	+	0.0160458i
$300$		0			0
$301$	6.15335	−	22.0710i	0.354673	−	1.27215i
$302$	−7.49316	+	12.9785i	−0.431183	+	0.746831i
$303$		0			0
$304$	−1.94282			−0.111428
$305$	−9.11273	+	15.7837i	−0.521793	+	0.903772i
$306$		0			0
$307$	4.89931			0.279619			0.139809	−	0.990178i	$-0.455351\pi$
$307$	4.89931			0.279619			0.139809	+	0.990178i	$0.455351\pi$
$308$	4.35185	−	15.6093i	0.247970	−	0.889423i
$309$		0			0
$310$	13.5653			0.770455
$311$	−3.84501	−	6.65976i	−0.218031	−	0.377640i	0.736175	−	0.676791i	$-0.236630\pi$
$311$	−3.84501	−	6.65976i	−0.218031	−	0.377640i	−0.954206	+	0.299151i	$0.903297\pi$
$312$		0			0
$313$	0.861564	−	1.49227i	0.0486985	−	0.0843482i	−0.840649	−	0.541581i	$-0.817826\pi$
$313$	0.861564	−	1.49227i	0.0486985	−	0.0843482i	0.889347	+	0.457233i	$0.151159\pi$
$314$	−18.9806			−1.07114
$315$		0			0
$316$	−13.4451			−0.756348
$317$	16.6014	−	28.7544i	0.932426	−	1.61501i	0.153266	−	0.988185i	$-0.451021\pi$
$317$	16.6014	−	28.7544i	0.932426	−	1.61501i	0.779161	−	0.626824i	$-0.215646\pi$
$318$		0			0
$319$	4.48508	+	7.76839i	0.251116	+	0.434946i
$320$	−1.76088			−0.0984360
$321$		0			0
$322$	−1.07893	+	0.277457i	−0.0601266	+	0.0154621i
$323$	13.2930			0.739644
$324$		0			0
$325$	0.722572	−	1.25153i	0.0400811	−	0.0694224i
$326$	−15.0377			−0.832864
$327$		0			0
$328$	−3.47141	+	6.01266i	−0.191677	+	0.331994i
$329$	−4.25404	+	1.09396i	−0.234533	+	0.0603121i
$330$		0			0
$331$	−1.44445	+	2.50187i	−0.0793944	+	0.137515i	−0.902989	−	0.429664i	$-0.858632\pi$
$331$	−1.44445	+	2.50187i	−0.0793944	+	0.137515i	0.823594	+	0.567179i	$0.191965\pi$
$332$	1.56238	−	2.70612i	0.0857468	−	0.148518i
$333$		0			0
$334$	0.572097	+	0.990901i	0.0313037	+	0.0542197i
$335$	5.97373	+	10.3468i	0.326380	+	0.565307i
$336$		0			0
$337$	−4.36156	+	7.55445i	−0.237590	+	0.411517i	−0.960022	−	0.279924i	$-0.909691\pi$
$337$	−4.36156	+	7.55445i	−0.237590	+	0.411517i	0.722433	+	0.691441i	$0.243024\pi$
$338$	12.4211			0.675617
$339$		0			0
$340$	12.0482			0.653403
$341$	23.5917	+	40.8620i	1.27756	+	2.21280i
$342$		0			0
$343$	13.4863	−	12.6933i	0.728193	−	0.685372i
$344$	−4.33009	−	7.49994i	−0.233463	−	0.404370i
$345$		0			0
$346$	−0.248838	−	0.431001i	−0.0133776	−	0.0231707i
$347$	4.84733	+	8.39583i	0.260219	+	0.450712i	0.966300	−	0.257419i	$-0.0828720\pi$
$347$	4.84733	+	8.39583i	0.260219	+	0.450712i	−0.706081	+	0.708131i	$0.749539\pi$
$348$		0			0
$349$	14.1992	+	24.5937i	0.760065	+	1.31647i	0.942817	+	0.333312i	$0.108166\pi$
$349$	14.1992	+	24.5937i	0.760065	+	1.31647i	−0.182752	+	0.983159i	$0.558500\pi$
$350$	4.86677	−	1.25153i	0.260140	−	0.0668971i
$351$		0			0
$352$	−3.06238	−	5.30420i	−0.163225	−	0.282715i
$353$	4.39372			0.233854			0.116927	−	0.993141i	$-0.462696\pi$
$353$	4.39372			0.233854			0.116927	+	0.993141i	$0.462696\pi$
$354$		0			0
$355$	18.9910			1.00794
$356$	−1.30150	+	2.25427i	−0.0689796	+	0.119476i
$357$		0			0
$358$	4.41423	+	7.64567i	0.233299	+	0.404086i
$359$	−16.0796	−	27.8507i	−0.848650	−	1.46990i	−0.882413	−	0.470475i	$-0.844083\pi$
$359$	−16.0796	−	27.8507i	−0.848650	−	1.46990i	0.0337633	−	0.999430i	$-0.489251\pi$
$360$		0			0
$361$	7.61273	−	13.1856i	0.400670	−	0.693980i
$362$	0.664703	−	1.15130i	0.0349360	−	0.0605110i
$363$		0			0
$364$	−1.40903	−	1.43777i	−0.0738532	−	0.0753594i
$365$	−0.270036	+	0.467717i	−0.0141343	+	0.0244814i
$366$		0			0
$367$	34.6030			1.80626			0.903131	−	0.429365i	$-0.141262\pi$
$367$	34.6030			1.80626			0.903131	+	0.429365i	$0.141262\pi$
$368$	−0.210533	+	0.364654i	−0.0109748	+	0.0190089i
$369$		0			0
$370$	−5.08126			−0.264162
$371$	−0.577690	+	0.148558i	−0.0299921	+	0.00771274i
$372$		0			0
$373$	10.9759			0.568312			0.284156	−	0.958778i	$-0.408287\pi$
$373$	10.9759			0.568312			0.284156	+	0.958778i	$0.408287\pi$
$374$	20.9532	+	36.2920i	1.08347	+	1.87662i
$375$		0			0
$376$	−0.830095	+	1.43777i	−0.0428089	+	0.0741472i
$377$	1.11436			0.0573925
$378$		0			0
$379$	33.9877			1.74583			0.872916	−	0.487871i	$-0.162226\pi$
$379$	33.9877			1.74583			0.872916	+	0.487871i	$0.162226\pi$
$380$	−1.71053	+	2.96273i	−0.0877485	+	0.151985i
$381$		0			0
$382$	8.08414	+	14.0021i	0.413620	+	0.716411i
$383$	21.0241			1.07428			0.537140	−	0.843493i	$-0.319505\pi$
$383$	21.0241			1.07428			0.537140	+	0.843493i	$0.319505\pi$
$384$		0			0
$385$	−19.9721	−	20.3794i	−1.01787	−	1.03863i
$386$	14.1683			0.721146
$387$		0			0
$388$	−1.81806	+	3.14897i	−0.0922978	+	0.159865i
$389$	−13.7382			−0.696553			−0.348277	−	0.937392i	$-0.613233\pi$
$389$	−13.7382			−0.696553			−0.348277	+	0.937392i	$0.613233\pi$
$390$		0			0
$391$	1.44050	−	2.49501i	0.0728491	−	0.126178i
$392$	0.141315	−	6.99857i	0.00713749	−	0.353481i
$393$		0			0
$394$	−7.92107	+	13.7197i	−0.399058	+	0.691188i
$395$	−11.8376	+	20.5034i	−0.595615	+	1.03164i
$396$		0			0
$397$	−3.57893	−	6.19889i	−0.179622	−	0.311114i	0.762129	−	0.647425i	$-0.224154\pi$
$397$	−3.57893	−	6.19889i	−0.179622	−	0.311114i	−0.941751	+	0.336311i	$0.890821\pi$
$398$	4.47141	+	7.74471i	0.224132	+	0.388207i
$399$		0			0
$400$	0.949657	−	1.64485i	0.0474828	−	0.0822427i
$401$	9.27936			0.463389			0.231695	−	0.972789i	$-0.425573\pi$
$401$	9.27936			0.463389			0.231695	+	0.972789i	$0.425573\pi$
$402$		0			0
$403$	5.86156			0.291985
$404$	−4.00520	−	6.93721i	−0.199266	−	0.345139i
$405$		0			0
$406$	2.71217	+	2.76748i	0.134603	+	0.137348i
$407$	−8.83693	−	15.3060i	−0.438030	−	0.758691i
$408$		0			0
$409$	−7.58414	−	13.1361i	−0.375011	−	0.649539i	0.615317	−	0.788279i	$-0.289028\pi$
$409$	−7.58414	−	13.1361i	−0.375011	−	0.649539i	−0.990329	+	0.138741i	$0.955695\pi$
$410$	6.11273	+	10.5876i	0.301886	+	0.522882i
$411$		0			0
$412$	3.41423	+	5.91362i	0.168207	+	0.291343i
$413$	1.41135	−	5.06227i	0.0694481	−	0.249098i
$414$		0			0
$415$	−2.75116	−	4.76515i	−0.135049	−	0.233912i
$416$	−0.760877			−0.0373051
$417$		0			0
$418$	−11.8993			−0.582014
$419$	4.16827	−	7.21966i	0.203633	−	0.352703i	−0.746063	−	0.665875i	$-0.768058\pi$
$419$	4.16827	−	7.21966i	0.203633	−	0.352703i	0.949696	+	0.313172i	$0.101392\pi$
$420$		0			0
$421$	−3.50232	−	6.06620i	−0.170693	−	0.295649i	0.767969	−	0.640486i	$-0.221267\pi$
$421$	−3.50232	−	6.06620i	−0.170693	−	0.295649i	−0.938662	+	0.344838i	$0.887934\pi$
$422$	−11.3856	−	19.7205i	−0.554244	−	0.959979i
$423$		0			0
$424$	−0.112725	+	0.195246i	−0.00547442	+	0.00948197i
$425$	−6.49768	+	11.2543i	−0.315184	+	0.545914i
$426$		0			0
$427$	−26.5212	+	6.82015i	−1.28345	+	0.330050i
$428$	−1.77292	+	3.07078i	−0.0856971	+	0.148432i
$429$		0			0
$430$	−15.2495			−0.735397
$431$	1.72545	−	2.98857i	0.0831120	−	0.143954i	−0.821473	−	0.570247i	$-0.806847\pi$
$431$	1.72545	−	2.98857i	0.0831120	−	0.143954i	0.904585	+	0.426293i	$0.140181\pi$
$432$		0			0
$433$	28.2599			1.35809			0.679043	−	0.734099i	$-0.262395\pi$
$433$	28.2599			1.35809			0.679043	+	0.734099i	$0.262395\pi$
$434$	14.2661	+	14.5570i	0.684794	+	0.698761i
$435$		0			0
$436$	−0.703697			−0.0337010
$437$	0.409028	+	0.708458i	0.0195665	+	0.0338901i
$438$		0			0
$439$	14.4480	−	25.0247i	0.689566	−	1.19436i	−0.282412	−	0.959293i	$-0.591134\pi$
$439$	14.4480	−	25.0247i	0.689566	−	1.19436i	0.971978	−	0.235071i	$-0.0755322\pi$
$440$	−10.7850			−0.514152
$441$		0			0
$442$	5.20602			0.247625
$443$	−6.88044	+	11.9173i	−0.326899	+	0.566207i	−0.981895	−	0.189426i	$-0.939337\pi$
$443$	−6.88044	+	11.9173i	−0.326899	+	0.566207i	0.654995	+	0.755633i	$0.272671\pi$
$444$		0			0
$445$	2.29179	+	3.96950i	0.108641	+	0.188172i
$446$	−12.8856			−0.610153
$447$		0			0
$448$	−1.85185	−	1.88962i	−0.0874916	−	0.0892761i
$449$	20.2003			0.953309			0.476655	−	0.879091i	$-0.341849\pi$
$449$	20.2003			0.953309			0.476655	+	0.879091i	$0.341849\pi$
$450$		0			0
$451$	−21.2616	+	36.8261i	−1.00117	+	1.73407i
$452$	8.50232			0.399916
$453$		0			0
$454$	−10.9984	+	19.0497i	−0.516179	+	0.894048i
$455$	−3.43310	+	0.882853i	−0.160946	+	0.0413888i
$456$		0			0
$457$	−10.0149	+	17.3463i	−0.468478	+	0.811428i	−0.999351	−	0.0360237i	$-0.988531\pi$
$457$	−10.0149	+	17.3463i	−0.468478	+	0.811428i	0.530873	+	0.847451i	$0.321864\pi$
$458$	−1.89931	+	3.28971i	−0.0887491	+	0.153718i
$459$		0			0
$460$	0.370723	+	0.642111i	0.0172851	+	0.0299386i
$461$	−5.97661	−	10.3518i	−0.278359	−	0.482131i	0.692618	−	0.721304i	$-0.256457\pi$
$461$	−5.97661	−	10.3518i	−0.278359	−	0.482131i	−0.970977	+	0.239173i	$0.923124\pi$
$462$		0			0
$463$	6.64527	−	11.5100i	0.308832	−	0.534913i	−0.669275	−	0.743015i	$-0.733395\pi$
$463$	6.64527	−	11.5100i	0.308832	−	0.534913i	0.978107	+	0.208102i	$0.0667286\pi$
$464$	1.46457			0.0679911
$465$		0			0
$466$	6.67059			0.309009
$467$	5.61505	+	9.72555i	0.259833	+	0.450045i	0.966197	−	0.257804i	$-0.0829990\pi$
$467$	5.61505	+	9.72555i	0.259833	+	0.450045i	−0.706364	+	0.707849i	$0.749666\pi$
$468$		0			0
$469$	−4.82094	+	17.2918i	−0.222610	+	0.798463i
$470$	1.46169	+	2.53173i	0.0674230	+	0.116780i
$471$		0			0
$472$	−0.993163	−	1.72021i	−0.0457141	−	0.0791791i
$473$	−26.5208	−	45.9354i	−1.21943	−	2.11211i
$474$		0			0
$475$	−1.84501	−	3.19565i	−0.0846550	−	0.146627i
$476$	12.6706	+	12.9290i	0.580756	+	0.592601i
$477$		0			0
$478$	−7.82038	−	13.5453i	−0.357696	−	0.619547i
$479$	32.6271			1.49077			0.745385	−	0.666634i	$-0.232266\pi$
$479$	32.6271			1.49077			0.745385	+	0.666634i	$0.232266\pi$
$480$		0			0
$481$	−2.19562			−0.100111
$482$	10.7060	−	18.5434i	0.487646	−	0.844627i
$483$		0			0
$484$	−13.2564	−	22.9607i	−0.602562	−	1.04367i
$485$	3.20137	+	5.54494i	0.145367	+	0.251783i
$486$		0			0
$487$	1.84897	−	3.20251i	0.0837848	−	0.145120i	−0.821088	−	0.570802i	$-0.806632\pi$
$487$	1.84897	−	3.20251i	0.0837848	−	0.145120i	0.904873	+	0.425682i	$0.139966\pi$
$488$	−5.17511	+	8.96355i	−0.234266	+	0.405761i
$489$		0			0
$490$	−10.5482	−	6.37731i	−0.476517	−	0.288098i
$491$	18.7804	−	32.5287i	0.847549	−	1.46800i	−0.0358393	−	0.999358i	$-0.511410\pi$
$491$	18.7804	−	32.5287i	0.847549	−	1.46800i	0.883389	−	0.468641i	$-0.155256\pi$
$492$		0			0
$493$	−10.0208			−0.451314
$494$	−0.739123	+	1.28020i	−0.0332547	+	0.0575989i
$495$		0			0
$496$	7.70370			0.345906
$497$	19.9721	+	20.3794i	0.895871	+	0.914143i
$498$		0			0
$499$	−31.7954			−1.42336			−0.711678	−	0.702506i	$-0.752064\pi$
$499$	−31.7954			−1.42336			−0.711678	+	0.702506i	$0.752064\pi$
$500$	−6.07442	−	10.5212i	−0.271656	−	0.470523i
$501$		0			0
$502$	11.8015	−	20.4408i	0.526727	−	0.912318i
$503$	−30.8252			−1.37443			−0.687214	−	0.726455i	$-0.741166\pi$
$503$	−30.8252			−1.37443			−0.687214	+	0.726455i	$0.741166\pi$
$504$		0			0
$505$	−14.1053			−0.627679
$506$	−1.28947	+	2.23342i	−0.0573238	+	0.0992877i
$507$		0			0
$508$	9.47661	+	16.4140i	0.420457	+	0.728252i
$509$	−8.01616			−0.355310			−0.177655	−	0.984093i	$-0.556851\pi$
$509$	−8.01616			−0.355310			−0.177655	+	0.984093i	$0.556851\pi$
$510$		0			0
$511$	−0.785900	+	0.202101i	−0.0347662	+	0.00894042i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	−10.1300	+	17.5456i	−0.446814	+	0.773904i
$515$	12.0241			0.529844
$516$		0			0
$517$	−5.08414	+	8.80598i	−0.223600	+	0.387287i
$518$	−5.34377	−	5.45276i	−0.234792	−	0.239580i
$519$		0			0
$520$	−0.669905	+	1.16031i	−0.0293773	+	0.0508829i
$521$	−14.8646	+	25.7462i	−0.651229	+	1.12796i	0.331596	+	0.943421i	$0.392413\pi$
$521$	−14.8646	+	25.7462i	−0.651229	+	1.12796i	−0.982825	+	0.184540i	$0.940920\pi$
$522$		0			0
$523$	13.4698	+	23.3303i	0.588992	+	1.02016i	0.994365	+	0.106013i	$0.0338084\pi$
$523$	13.4698	+	23.3303i	0.588992	+	1.02016i	−0.405373	+	0.914152i	$0.632858\pi$
$524$	−3.64652	−	6.31595i	−0.159299	−	0.275914i
$525$		0			0
$526$	11.2443	−	19.4757i	0.490276	−	0.849183i
$527$	−52.7097			−2.29607
$528$		0			0
$529$	−22.8227			−0.992291
$530$	0.198495	+	0.343803i	0.00862207	+	0.0149339i
$531$		0			0
$532$	−4.97825	+	1.28020i	−0.215834	+	0.0555037i
$533$	2.64132	+	4.57489i	0.114408	+	0.198161i
$534$		0			0
$535$	3.12188	+	5.40726i	0.134971	+	0.233776i
$536$	3.39248	+	5.87594i	0.146533	+	0.253802i
$537$		0			0
$538$	−12.6706	−	21.9461i	−0.546268	−	0.946164i
$539$	0.865521	−	42.8646i	0.0372806	−	1.84631i
$540$		0			0
$541$	7.15568	+	12.3940i	0.307647	+	0.532859i	0.977847	−	0.209321i	$-0.0671252\pi$
$541$	7.15568	+	12.3940i	0.307647	+	0.532859i	−0.670201	+	0.742180i	$0.733792\pi$
$542$	−13.7576			−0.590940
$543$		0			0
$544$	6.84213			0.293354
$545$	−0.619562	+	1.07311i	−0.0265391	+	0.0459671i
$546$		0			0
$547$	1.02463	+	1.77471i	0.0438101	+	0.0758813i	0.887099	−	0.461579i	$-0.152717\pi$
$547$	1.02463	+	1.77471i	0.0438101	+	0.0758813i	−0.843289	+	0.537461i	$0.819384\pi$
$548$	−4.09097	−	7.08577i	−0.174758	−	0.302689i
$549$		0			0
$550$	5.81642	−	10.0743i	0.248013	−	0.429571i
$551$	1.42270	−	2.46419i	0.0606091	−	0.104978i
$552$		0			0
$553$	−34.4516	+	8.85952i	−1.46503	+	0.376745i
$554$	−1.64132	+	2.84284i	−0.0697328	+	0.120781i
$555$		0			0
$556$	12.4646			0.528616
$557$	−8.84338	+	15.3172i	−0.374706	+	0.649010i	−0.990283	−	0.139067i	$-0.955590\pi$
$557$	−8.84338	+	15.3172i	−0.374706	+	0.649010i	0.615577	+	0.788077i	$0.288923\pi$
$558$		0			0
$559$	−6.58934			−0.278699
$560$	−4.51204	+	1.16031i	−0.190668	+	0.0490320i
$561$		0			0
$562$	−1.26896			−0.0535277
$563$	0.468531	+	0.811520i	0.0197462	+	0.0342015i	0.875730	−	0.482802i	$-0.160381\pi$
$563$	0.468531	+	0.811520i	0.0197462	+	0.0342015i	−0.855983	+	0.517003i	$0.827048\pi$
$564$		0			0
$565$	7.48577	−	12.9657i	0.314929	−	0.545473i
$566$	8.19235			0.344350
$567$		0			0
$568$	10.7850			0.452527
$569$	11.7632	−	20.3745i	0.493139	−	0.854142i	−0.506830	−	0.862046i	$-0.669183\pi$
$569$	11.7632	−	20.3745i	0.493139	−	0.854142i	0.999969	+	0.00790437i	$0.00251607\pi$
$570$		0			0
$571$	0.242002	+	0.419160i	0.0101275	+	0.0175413i	0.871045	−	0.491204i	$-0.163443\pi$
$571$	0.242002	+	0.419160i	0.0101275	+	0.0175413i	−0.860917	+	0.508745i	$0.830110\pi$
$572$	−4.66019			−0.194852
$573$		0			0
$574$	−4.93310	+	17.6942i	−0.205904	+	0.738540i
$575$	−0.799737			−0.0333514
$576$		0			0
$577$	−2.23065	+	3.86360i	−0.0928633	+	0.160844i	−0.908715	−	0.417417i	$-0.862935\pi$
$577$	−2.23065	+	3.86360i	−0.0928633	+	0.160844i	0.815852	+	0.578261i	$0.196269\pi$
$578$	−29.8148			−1.24013
$579$		0			0
$580$	1.28947	−	2.23342i	0.0535422	−	0.0927378i
$581$	2.22025	−	7.96364i	0.0921114	−	0.330387i
$582$		0			0
$583$	−0.690415	+	1.19583i	−0.0285941	+	0.0495264i
$584$	−0.153353	+	0.265616i	−0.00634581	+	0.0109913i
$585$		0			0
$586$	7.72545	+	13.3809i	0.319135	+	0.552759i
$587$	−8.31518	−	14.4023i	−0.343204	−	0.594447i	0.641822	−	0.766854i	$-0.278179\pi$
$587$	−8.31518	−	14.4023i	−0.343204	−	0.594447i	−0.985026	+	0.172407i	$0.944846\pi$
$588$		0			0
$589$	7.48345	−	12.9617i	0.308350	−	0.534078i
$590$	−3.49768			−0.143997
$591$		0			0
$592$	−2.88564			−0.118599
$593$	−20.7632	−	35.9629i	−0.852642	−	1.47682i	−0.878815	−	0.477163i	$-0.841665\pi$
$593$	−20.7632	−	35.9629i	−0.852642	−	1.47682i	0.0261726	−	0.999657i	$-0.491668\pi$
$594$		0			0
$595$	30.8720	−	7.93899i	1.26563	−	0.325467i
$596$	4.41423	+	7.64567i	0.180814	+	0.313179i
$597$		0			0
$598$	0.160190	+	0.277457i	0.00655065	+	0.0113461i
$599$	7.53831	+	13.0567i	0.308007	+	0.533483i	0.977926	−	0.208950i	$-0.0670047\pi$
$599$	7.53831	+	13.0567i	0.308007	+	0.533483i	−0.669919	+	0.742434i	$0.733671\pi$
$600$		0			0
$601$	−8.05555	−	13.9526i	−0.328593	−	0.569139i	0.653640	−	0.756805i	$-0.273241\pi$
$601$	−8.05555	−	13.9526i	−0.328593	−	0.569139i	−0.982233	+	0.187666i	$0.939908\pi$
$602$	−16.0374	−	16.3645i	−0.653634	−	0.666965i
$603$		0			0
$604$	7.49316	+	12.9785i	0.304892	+	0.528089i
$605$	−46.6856			−1.89804
$606$		0			0
$607$	19.5732			0.794451			0.397225	−	0.917721i	$-0.369973\pi$
$607$	19.5732			0.794451			0.397225	+	0.917721i	$0.369973\pi$
$608$	−0.971410	+	1.68253i	−0.0393959	+	0.0682357i
$609$		0			0
$610$	9.11273	+	15.7837i	0.368963	+	0.639063i
$611$	0.631600	+	1.09396i	0.0255518	+	0.0442570i
$612$		0			0
$613$	−2.77579	+	4.80782i	−0.112113	+	0.194186i	−0.916622	−	0.399755i	$-0.869095\pi$
$613$	−2.77579	+	4.80782i	−0.112113	+	0.194186i	0.804509	+	0.593941i	$0.202429\pi$
$614$	2.44966	−	4.24293i	0.0988601	−	0.171231i
$615$		0			0
$616$	−11.3421	−	11.5735i	−0.456988	−	0.466308i
$617$	−0.634479	+	1.09895i	−0.0255431	+	0.0442420i	−0.878514	−	0.477716i	$-0.841465\pi$
$617$	−0.634479	+	1.09895i	−0.0255431	+	0.0442420i	0.852971	+	0.521958i	$0.174798\pi$
$618$		0			0
$619$	4.50232			0.180964			0.0904818	−	0.995898i	$-0.471159\pi$
$619$	4.50232			0.180964			0.0904818	+	0.995898i	$0.471159\pi$
$620$	6.78263	−	11.7479i	0.272397	−	0.471805i
$621$		0			0
$622$	−7.69002			−0.308342
$623$	−1.84953	+	6.63392i	−0.0740997	+	0.265782i
$624$		0			0
$625$	−11.8960			−0.475842
$626$	−0.861564	−	1.49227i	−0.0344350	−	0.0596432i
$627$		0			0
$628$	−9.49028	+	16.4377i	−0.378704	+	0.655934i
$629$	19.7439			0.787242
$630$		0			0
$631$	−1.69905			−0.0676381			−0.0338191	−	0.999428i	$-0.510767\pi$
$631$	−1.69905			−0.0676381			−0.0338191	+	0.999428i	$0.510767\pi$
$632$	−6.72257	+	11.6438i	−0.267410	+	0.463167i
$633$		0			0
$634$	−16.6014	−	28.7544i	−0.659325	−	1.14198i
$635$	33.3743			1.32442
$636$		0			0
$637$	−4.55787	−	2.75564i	−0.180589	−	0.109183i
$638$	8.97017			0.355132
$639$		0			0
$640$	−0.880438	+	1.52496i	−0.0348024	+	0.0602795i
$641$	0.948577			0.0374666			0.0187333	−	0.999825i	$-0.494037\pi$
$641$	0.948577			0.0374666			0.0187333	+	0.999825i	$0.494037\pi$
$642$		0			0
$643$	−9.84897	+	17.0589i	−0.388405	+	0.672738i	−0.992235	−	0.124375i	$-0.960307\pi$
$643$	−9.84897	+	17.0589i	−0.388405	+	0.672738i	0.603830	+	0.797113i	$0.293641\pi$
$644$	−0.299182	+	1.07311i	−0.0117894	+	0.0422865i
$645$		0			0
$646$	6.64652	−	11.5121i	0.261504	−	0.452938i
$647$	−11.7271	+	20.3119i	−0.461039	+	0.798543i	−0.999013	−	0.0444181i	$-0.985857\pi$
$647$	−11.7271	+	20.3119i	−0.461039	+	0.798543i	0.537974	+	0.842962i	$0.319190\pi$
$648$		0			0
$649$	−6.08289	−	10.5359i	−0.238774	−	0.413569i
$650$	−0.722572	−	1.25153i	−0.0283416	−	0.0490891i
$651$		0			0
$652$	−7.51887	+	13.0231i	−0.294462	+	0.510023i
$653$	−22.7907			−0.891869			−0.445935	−	0.895065i	$-0.647129\pi$
$653$	−22.7907			−0.891869			−0.445935	+	0.895065i	$0.647129\pi$
$654$		0			0
$655$	−12.8421			−0.501784
$656$	3.47141	+	6.01266i	0.135536	+	0.234755i
$657$		0			0
$658$	−1.17962	+	4.23109i	−0.0459864	+	0.164945i
$659$	13.2398	+	22.9320i	0.515750	+	0.893305i	0.999833	+	0.0182828i	$0.00581993\pi$
$659$	13.2398	+	22.9320i	0.515750	+	0.893305i	−0.484083	+	0.875022i	$0.660847\pi$
$660$		0			0
$661$	13.3691	+	23.1559i	0.519997	+	0.900662i	0.999730	+	0.0232469i	$0.00740038\pi$
$661$	13.3691	+	23.1559i	0.519997	+	0.900662i	−0.479732	+	0.877415i	$0.659266\pi$
$662$	1.44445	+	2.50187i	0.0561403	+	0.0972379i
$663$		0			0
$664$	−1.56238	−	2.70612i	−0.0606322	−	0.105018i
$665$	−2.43078	+	8.71878i	−0.0942617	+	0.338100i
$666$		0			0
$667$	−0.308342	−	0.534063i	−0.0119390	−	0.0206790i
$668$	1.14419			0.0442702
$669$		0			0
$670$	11.9475			0.461571
$671$	−31.6963	+	54.8996i	−1.22362	+	2.11938i
$672$		0			0
$673$	−10.3856	−	17.9885i	−0.400337	−	0.693404i	0.593429	−	0.804886i	$-0.297774\pi$
$673$	−10.3856	−	17.9885i	−0.400337	−	0.693404i	−0.993766	+	0.111482i	$0.964440\pi$
$674$	4.36156	+	7.55445i	0.168001	+	0.290987i
$675$		0			0
$676$	6.21053	−	10.7570i	0.238867	−	0.413729i
$677$	−10.3490	+	17.9249i	−0.397743	+	0.688911i	−0.993447	−	0.114293i	$-0.963540\pi$
$677$	−10.3490	+	17.9249i	−0.397743	+	0.688911i	0.595704	+	0.803204i	$0.296873\pi$
$678$		0			0
$679$	−2.58358	+	9.26684i	−0.0991487	+	0.355629i
$680$	6.02408	−	10.4340i	0.231013	−	0.400126i
$681$		0			0
$682$	47.1833			1.80674
$683$	−14.2918	+	24.7541i	−0.546860	+	0.947190i	0.451627	+	0.892207i	$0.350844\pi$
$683$	−14.2918	+	24.7541i	−0.546860	+	0.947190i	−0.998487	+	0.0549828i	$0.982490\pi$
$684$		0			0
$685$	−14.4074			−0.550478
$686$	−4.24953	−	18.0261i	−0.162248	−	0.688241i
$687$		0			0
$688$	−8.66019			−0.330167
$689$	0.0857699	+	0.148558i	0.00326757	+	0.00565960i
$690$		0			0
$691$	3.34897	−	5.80059i	0.127401	−	0.220665i	−0.795268	−	0.606258i	$-0.792670\pi$
$691$	3.34897	−	5.80059i	0.127401	−	0.220665i	0.922669	+	0.385593i	$0.126003\pi$
$692$	−0.497677			−0.0189188
$693$		0			0
$694$	9.69467			0.368005
$695$	10.9743	−	19.0080i	0.416278	−	0.721016i
$696$		0			0
$697$	−23.7518	−	41.1394i	−0.899665	−	1.55827i
$698$	28.3984			1.07489
$699$		0			0
$700$	1.34953	−	4.84051i	0.0510073	−	0.182954i
$701$	25.1442			0.949683			0.474842	−	0.880071i	$-0.342505\pi$
$701$	25.1442			0.949683			0.474842	+	0.880071i	$0.342505\pi$
$702$		0			0
$703$	−2.80314	+	4.85518i	−0.105722	+	0.183117i
$704$	−6.12476			−0.230836
$705$		0			0
$706$	2.19686	−	3.80507i	0.0826799	−	0.143206i
$707$	−14.8341	−	15.1366i	−0.557892	−	0.569271i
$708$		0			0
$709$	−4.43310	+	7.67836i	−0.166489	+	0.288367i	−0.937183	−	0.348838i	$-0.886576\pi$
$709$	−4.43310	+	7.67836i	−0.166489	+	0.288367i	0.770694	+	0.637205i	$0.219910\pi$
$710$	9.49549	−	16.4467i	0.356359	−	0.617232i
$711$		0			0
$712$	1.30150	+	2.25427i	0.0487760	+	0.0844824i
$713$	−1.62188	−	2.80919i	−0.0607401	−	0.105205i
$714$		0			0
$715$	−4.10301	+	7.10662i	−0.153444	+	0.265773i
$716$	8.82846			0.329935
$717$		0			0
$718$	−32.1592			−1.20017
$719$	−11.8015	−	20.4408i	−0.440122	−	0.762313i	0.557576	−	0.830126i	$-0.311731\pi$
$719$	−11.8015	−	20.4408i	−0.440122	−	0.762313i	−0.997698	+	0.0678123i	$0.978398\pi$
$720$		0			0
$721$	12.6453	+	12.9032i	0.470935	+	0.480540i
$722$	−7.61273	−	13.1856i	−0.283316	−	0.490718i
$723$		0			0
$724$	−0.664703	−	1.15130i	−0.0247035	−	0.0427877i
$725$	1.39084	+	2.40901i	0.0516546	+	0.0894683i
$726$		0			0
$727$	3.25692	+	5.64115i	0.120792	+	0.209219i	0.920080	−	0.391730i	$-0.128123\pi$
$727$	3.25692	+	5.64115i	0.120792	+	0.209219i	−0.799288	+	0.600948i	$0.794790\pi$
$728$	−1.94966	+	0.501371i	−0.0722591	+	0.0185820i
$729$		0			0
$730$	0.270036	+	0.467717i	0.00999449	+	0.0173110i
$731$	59.2542			2.19159
$732$		0			0
$733$	−23.1981			−0.856842			−0.428421	−	0.903579i	$-0.640930\pi$
$733$	−23.1981			−0.856842			−0.428421	+	0.903579i	$0.640930\pi$
$734$	17.3015	−	29.9671i	0.638610	−	1.10611i
$735$		0			0
$736$	0.210533	+	0.364654i	0.00776036	+	0.0134413i
$737$	20.7781	+	35.9888i	0.765372	+	1.32566i
$738$		0			0
$739$	−7.57838	+	13.1261i	−0.278775	+	0.482853i	−0.971081	−	0.238752i	$-0.923262\pi$
$739$	−7.57838	+	13.1261i	−0.278775	+	0.482853i	0.692305	+	0.721605i	$0.256595\pi$
$740$	−2.54063	+	4.40050i	−0.0933954	+	0.161765i
$741$		0			0
$742$	−0.160190	+	0.574573i	−0.00588076	+	0.0210932i
$743$	5.21737	−	9.03675i	0.191407	−	0.331526i	−0.754310	−	0.656518i	$-0.772028\pi$
$743$	5.21737	−	9.03675i	0.191407	−	0.331526i	0.945717	+	0.324992i	$0.105362\pi$
$744$		0			0
$745$	15.5458			0.569555
$746$	5.48796	−	9.50543i	0.200929	−	0.348018i
$747$		0			0
$748$	41.9064			1.53225
$749$	−2.51943	+	9.03675i	−0.0920580	+	0.330196i
$750$		0			0
$751$	40.2118			1.46735			0.733674	−	0.679501i	$-0.237804\pi$
$751$	40.2118			1.46735			0.733674	+	0.679501i	$0.237804\pi$
$752$	0.830095	+	1.43777i	0.0302704	+	0.0524300i
$753$		0			0
$754$	0.557180	−	0.965064i	0.0202913	−	0.0351456i
$755$	26.3891			0.960397
$756$		0			0
$757$	−21.5206			−0.782181			−0.391091	−	0.920352i	$-0.627902\pi$
$757$	−21.5206			−0.782181			−0.391091	+	0.920352i	$0.627902\pi$
$758$	16.9939	−	29.4342i	0.617244	−	1.06910i
$759$		0			0
$760$	1.71053	+	2.96273i	0.0620476	+	0.107470i
$761$	23.6627			0.857771			0.428886	−	0.903359i	$-0.358906\pi$
$761$	23.6627			0.857771			0.428886	+	0.903359i	$0.358906\pi$
$762$		0			0
$763$	−1.80314	+	0.463693i	−0.0652780	+	0.0167868i
$764$	16.1683			0.584947
$765$		0			0
$766$	10.5120	−	18.2074i	0.379815	−	0.657860i
$767$	−1.51135			−0.0545717
$768$		0			0
$769$	−5.62764	+	9.74736i	−0.202938	+	0.351499i	−0.949474	−	0.313846i	$-0.898382\pi$
$769$	−5.62764	+	9.74736i	−0.202938	+	0.351499i	0.746536	+	0.665345i	$0.231716\pi$
$770$	−27.6352	+	7.10662i	−0.995902	+	0.256105i
$771$		0			0
$772$	7.08414	−	12.2701i	0.254964	−	0.441610i
$773$	−0.138992	+	0.240741i	−0.00499919	+	0.00865886i	−0.868514	−	0.495664i	$-0.834925\pi$
$773$	−0.138992	+	0.240741i	−0.00499919	+	0.00865886i	0.863515	+	0.504323i	$0.168258\pi$
$774$		0			0
$775$	7.31587	+	12.6715i	0.262794	+	0.455172i
$776$	1.81806	+	3.14897i	0.0652644	+	0.113041i
$777$		0			0
$778$	−6.86909	+	11.8976i	−0.246269	+	0.426550i
$779$	13.4887			0.483281
$780$		0			0
$781$	66.0553			2.36364
$782$	−1.44050	−	2.49501i	−0.0515121	−	0.0892215i

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.h (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} -1.76088 q^{5} +(-1.85185 - 1.88962i) q^{7} -1.00000 q^{8} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} -1.76088 q^{5} +(-1.85185 - 1.88962i) q^{7} -1.00000 q^{8} +(-0.880438 + 1.52496i) q^{10} -6.12476 q^{11} +(-0.380438 + 0.658939i) q^{13} +(-2.56238 + 0.658939i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(3.42107 - 5.92546i) q^{17} +(0.971410 + 1.68253i) q^{19} +(0.880438 + 1.52496i) q^{20} +(-3.06238 + 5.30420i) q^{22} +0.421067 q^{23} -1.89931 q^{25} +(0.380438 + 0.658939i) q^{26} +(-0.710533 + 2.54856i) q^{28} +(-0.732287 - 1.26836i) q^{29} +(-3.85185 - 6.67160i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-3.42107 - 5.92546i) q^{34} +(3.26088 + 3.32738i) q^{35} +(1.44282 + 2.49904i) q^{37} +1.94282 q^{38} +1.76088 q^{40} +(3.47141 - 6.01266i) q^{41} +(4.33009 + 7.49994i) q^{43} +(3.06238 + 5.30420i) q^{44} +(0.210533 - 0.364654i) q^{46} +(0.830095 - 1.43777i) q^{47} +(-0.141315 + 6.99857i) q^{49} +(-0.949657 + 1.64485i) q^{50} +0.760877 q^{52} +(0.112725 - 0.195246i) q^{53} +10.7850 q^{55} +(1.85185 + 1.88962i) q^{56} -1.46457 q^{58} +(0.993163 + 1.72021i) q^{59} +(5.17511 - 8.96355i) q^{61} -7.70370 q^{62} +1.00000 q^{64} +(0.669905 - 1.16031i) q^{65} +(-3.39248 - 5.87594i) q^{67} -6.84213 q^{68} +(4.51204 - 1.16031i) q^{70} -10.7850 q^{71} +(0.153353 - 0.265616i) q^{73} +2.88564 q^{74} +(0.971410 - 1.68253i) q^{76} +(11.3421 + 11.5735i) q^{77} +(6.72257 - 11.6438i) q^{79} +(0.880438 - 1.52496i) q^{80} +(-3.47141 - 6.01266i) q^{82} +(1.56238 + 2.70612i) q^{83} +(-6.02408 + 10.4340i) q^{85} +8.66019 q^{86} +6.12476 q^{88} +(-1.30150 - 2.25427i) q^{89} +(1.94966 - 0.501371i) q^{91} +(-0.210533 - 0.364654i) q^{92} +(-0.830095 - 1.43777i) q^{94} +(-1.71053 - 2.96273i) q^{95} +(-1.81806 - 3.14897i) q^{97} +(5.99028 + 3.62167i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{2} - 3 q^{4} - 10 q^{5} - 2 q^{7} - 6 q^{8}+O(q^{10}) \) 6 * q + 3 * q^2 - 3 * q^4 - 10 * q^5 - 2 * q^7 - 6 * q^8	\( 6 q + 3 q^{2} - 3 q^{4} - 10 q^{5} - 2 q^{7} - 6 q^{8} - 5 q^{10} - 2 q^{11} - 2 q^{13} + 2 q^{14} - 3 q^{16} + 4 q^{17} - 3 q^{19} + 5 q^{20} - q^{22} - 14 q^{23} + 4 q^{25} + 2 q^{26} + 4 q^{28} + 5 q^{29} - 14 q^{31} + 3 q^{32} - 4 q^{34} + 19 q^{35} - 9 q^{37} - 6 q^{38} + 10 q^{40} + 12 q^{41} + 18 q^{43} + q^{44} - 7 q^{46} - 3 q^{47} + 2 q^{50} + 4 q^{52} - 9 q^{53} + 14 q^{55} + 2 q^{56} + 10 q^{58} - 4 q^{59} + 4 q^{61} - 28 q^{62} + 6 q^{64} + 12 q^{65} + 5 q^{67} - 8 q^{68} + 2 q^{70} - 14 q^{71} - 25 q^{73} - 18 q^{74} - 3 q^{76} + 35 q^{77} + 7 q^{79} + 5 q^{80} - 12 q^{82} - 8 q^{83} + 14 q^{85} + 36 q^{86} + 2 q^{88} + 9 q^{89} + 4 q^{91} + 7 q^{92} + 3 q^{94} - 2 q^{95} - 28 q^{97} + 12 q^{98}+O(q^{100}) \) 6 * q + 3 * q^2 - 3 * q^4 - 10 * q^5 - 2 * q^7 - 6 * q^8 - 5 * q^10 - 2 * q^11 - 2 * q^13 + 2 * q^14 - 3 * q^16 + 4 * q^17 - 3 * q^19 + 5 * q^20 - q^22 - 14 * q^23 + 4 * q^25 + 2 * q^26 + 4 * q^28 + 5 * q^29 - 14 * q^31 + 3 * q^32 - 4 * q^34 + 19 * q^35 - 9 * q^37 - 6 * q^38 + 10 * q^40 + 12 * q^41 + 18 * q^43 + q^44 - 7 * q^46 - 3 * q^47 + 2 * q^50 + 4 * q^52 - 9 * q^53 + 14 * q^55 + 2 * q^56 + 10 * q^58 - 4 * q^59 + 4 * q^61 - 28 * q^62 + 6 * q^64 + 12 * q^65 + 5 * q^67 - 8 * q^68 + 2 * q^70 - 14 * q^71 - 25 * q^73 - 18 * q^74 - 3 * q^76 + 35 * q^77 + 7 * q^79 + 5 * q^80 - 12 * q^82 - 8 * q^83 + 14 * q^85 + 36 * q^86 + 2 * q^88 + 9 * q^89 + 4 * q^91 + 7 * q^92 + 3 * q^94 - 2 * q^95 - 28 * q^97 + 12 * q^98

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