LMFDB - Embedded newform 378.2.e.c.235.2

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			235.2
Root			$0.500000 + 1.41036i$ of defining polynomial
Character	$\chi$	$=$	378.235
Dual form			378.2.e.c.37.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{4} +(0.880438 - 1.52496i) q^{5} +(-0.710533 + 2.54856i) q^{7} -1.00000 q^{8} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{4} +(0.880438 - 1.52496i) q^{5} +(-0.710533 + 2.54856i) q^{7} -1.00000 q^{8} +(-0.880438 + 1.52496i) q^{10} +(3.06238 + 5.30420i) q^{11} +(-0.380438 - 0.658939i) q^{13} +(0.710533 - 2.54856i) q^{14} +1.00000 q^{16} +(3.42107 - 5.92546i) q^{17} +(0.971410 + 1.68253i) q^{19} +(0.880438 - 1.52496i) q^{20} +(-3.06238 - 5.30420i) q^{22} +(-0.210533 + 0.364654i) q^{23} +(0.949657 + 1.64485i) q^{25} +(0.380438 + 0.658939i) q^{26} +(-0.710533 + 2.54856i) q^{28} +(-0.732287 + 1.26836i) q^{29} +7.70370 q^{31} -1.00000 q^{32} +(-3.42107 + 5.92546i) q^{34} +(3.26088 + 3.32738i) q^{35} +(1.44282 + 2.49904i) q^{37} +(-0.971410 - 1.68253i) q^{38} +(-0.880438 + 1.52496i) q^{40} +(3.47141 + 6.01266i) q^{41} +(4.33009 - 7.49994i) q^{43} +(3.06238 + 5.30420i) q^{44} +(0.210533 - 0.364654i) q^{46} -1.66019 q^{47} +(-5.99028 - 3.62167i) q^{49} +(-0.949657 - 1.64485i) q^{50} +(-0.380438 - 0.658939i) q^{52} +(0.112725 - 0.195246i) q^{53} +10.7850 q^{55} +(0.710533 - 2.54856i) q^{56} +(0.732287 - 1.26836i) q^{58} -1.98633 q^{59} -10.3502 q^{61} -7.70370 q^{62} +1.00000 q^{64} -1.33981 q^{65} +6.78495 q^{67} +(3.42107 - 5.92546i) q^{68} +(-3.26088 - 3.32738i) q^{70} -10.7850 q^{71} +(0.153353 - 0.265616i) q^{73} +(-1.44282 - 2.49904i) q^{74} +(0.971410 + 1.68253i) q^{76} +(-15.6940 + 4.03584i) q^{77} -13.4451 q^{79} +(0.880438 - 1.52496i) q^{80} +(-3.47141 - 6.01266i) q^{82} +(1.56238 - 2.70612i) q^{83} +(-6.02408 - 10.4340i) q^{85} +(-4.33009 + 7.49994i) q^{86} +(-3.06238 - 5.30420i) q^{88} +(-1.30150 - 2.25427i) q^{89} +(1.94966 - 0.501371i) q^{91} +(-0.210533 + 0.364654i) q^{92} +1.66019 q^{94} +3.42107 q^{95} +(-1.81806 + 3.14897i) q^{97} +(5.99028 + 3.62167i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/378\mathbb{Z}\right)^\times$.

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

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 $

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$		0			0
$3$		0			0
$4$	1.00000			0.500000
$5$	0.880438	−	1.52496i	0.393744	−	0.681985i	−0.599196	−	0.800602i	$-0.704513\pi$
$5$	0.880438	−	1.52496i	0.393744	−	0.681985i	0.992940	+	0.118618i	$0.0378463\pi$
$6$		0			0
$7$	−0.710533	+	2.54856i	−0.268556	+	0.963264i
$7$	−0.710533	+	2.54856i	−0.268556	+	0.963264i
$8$	−1.00000			−0.353553
$9$		0			0
$10$	−0.880438	+	1.52496i	−0.278419	+	0.482236i
$11$	3.06238	+	5.30420i	0.923343	+	1.59928i	0.794205	+	0.607650i	$0.207888\pi$
$11$	3.06238	+	5.30420i	0.923343	+	1.59928i	0.129138	+	0.991627i	$0.458779\pi$
$12$		0			0
$13$	−0.380438	−	0.658939i	−0.105515	−	0.182757i	0.808434	−	0.588587i	$-0.200316\pi$
$13$	−0.380438	−	0.658939i	−0.105515	−	0.182757i	−0.913948	+	0.405831i	$0.866982\pi$
$14$	0.710533	−	2.54856i	0.189898	−	0.681130i
$15$		0			0
$16$	1.00000			0.250000
$17$	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
$23$	−0.210533	+	0.364654i	−0.0438992	+	0.0760357i	−0.887140	−	0.461500i	$-0.847311\pi$
$23$	−0.210533	+	0.364654i	−0.0438992	+	0.0760357i	0.843241	+	0.537536i	$0.180645\pi$
$24$		0			0
$25$	0.949657	+	1.64485i	0.189931	+	0.328971i
$26$	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	−0.925972	−	0.377592i	$-0.876752\pi$
$29$	−0.732287	+	1.26836i	−0.135982	+	0.235528i	0.789990	+	0.613120i	$0.210086\pi$
$30$		0			0
$31$	7.70370			1.38362			0.691812	−	0.722077i	$-0.256813\pi$
$31$	7.70370			1.38362			0.691812	+	0.722077i	$0.256813\pi$
$32$	−1.00000			−0.176777
$33$		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	$0.757104\pi$
$38$	−0.971410	−	1.68253i	−0.157584	−	0.272943i
$39$		0			0
$40$	−0.880438	+	1.52496i	−0.139210	+	0.241118i
$41$	3.47141	+	6.01266i	0.542143	+	0.939020i	0.998781	+	0.0493667i	$0.0157203\pi$
$41$	3.47141	+	6.01266i	0.542143	+	0.939020i	−0.456638	+	0.889653i	$0.650946\pi$
$42$		0			0
$43$	4.33009	−	7.49994i	0.660333	−	1.14373i	−0.320195	−	0.947352i	$-0.603748\pi$
$43$	4.33009	−	7.49994i	0.660333	−	1.14373i	0.980528	−	0.196379i	$-0.0629183\pi$
$44$	3.06238	+	5.30420i	0.461671	+	0.799638i
$45$		0			0
$46$	0.210533	−	0.364654i	0.0310414	−	0.0537654i
$47$	−1.66019			−0.242164			−0.121082	−	0.992643i	$-0.538636\pi$
$47$	−1.66019			−0.242164			−0.121082	+	0.992643i	$0.538636\pi$
$48$		0			0
$49$	−5.99028	−	3.62167i	−0.855755	−	0.517381i
$50$	−0.949657	−	1.64485i	−0.134302	−	0.232617i
$51$		0			0
$52$	−0.380438	−	0.658939i	−0.0527573	−	0.0913783i
$53$	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
$56$	0.710533	−	2.54856i	0.0949490	−	0.340565i
$57$		0			0
$58$	0.732287	−	1.26836i	0.0961540	−	0.166544i
$59$	−1.98633			−0.258598			−0.129299	−	0.991606i	$-0.541273\pi$
$59$	−1.98633			−0.258598			−0.129299	+	0.991606i	$0.541273\pi$
$60$		0			0
$61$	−10.3502			−1.32521			−0.662605	−	0.748969i	$-0.730549\pi$
$61$	−10.3502			−1.32521			−0.662605	+	0.748969i	$0.730549\pi$
$62$	−7.70370			−0.978370
$63$		0			0
$64$	1.00000			0.125000
$65$	−1.33981			−0.166183
$66$		0			0
$67$	6.78495			0.828914			0.414457	−	0.910069i	$-0.363972\pi$
$67$	6.78495			0.828914			0.414457	+	0.910069i	$0.363972\pi$
$68$	3.42107	−	5.92546i	0.414865	−	0.718568i
$69$		0			0
$70$	−3.26088	−	3.32738i	−0.389749	−	0.397699i
$71$	−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	$0.160953\pi$
$74$	−1.44282	−	2.49904i	−0.167724	−	0.290507i
$75$		0			0
$76$	0.971410	+	1.68253i	0.111428	+	0.193000i
$77$	−15.6940	+	4.03584i	−1.78850	+	0.459927i
$78$		0			0
$79$	−13.4451			−1.51270			−0.756348	−	0.654169i	$-0.773018\pi$
$79$	−13.4451			−1.51270			−0.756348	+	0.654169i	$0.773018\pi$
$80$	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	−0.767449	−	0.641110i	$-0.778474\pi$
$83$	1.56238	−	2.70612i	0.171494	−	0.297036i	0.938942	+	0.344075i	$0.111807\pi$
$84$		0			0
$85$	−6.02408	−	10.4340i	−0.653403	−	1.13173i
$86$	−4.33009	+	7.49994i	−0.466926	+	0.808740i
$87$		0			0
$88$	−3.06238	−	5.30420i	−0.326451	−	0.565430i
$89$	−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
$94$	1.66019			0.171236
$95$	3.42107			0.350994
$96$		0			0
$97$	−1.81806	+	3.14897i	−0.184596	+	0.319729i	−0.943440	−	0.331543i	$-0.892431\pi$
$97$	−1.81806	+	3.14897i	−0.184596	+	0.319729i	0.758845	+	0.651272i	$0.225764\pi$
$98$	5.99028	+	3.62167i	0.605110	+	0.365844i
$99$		0			0
$100$	0.949657	+	1.64485i	0.0949657	+	0.164485i
$101$	−4.00520	−	6.93721i	−0.398532	−	0.690278i	0.595013	−	0.803716i	$-0.297147\pi$
$101$	−4.00520	−	6.93721i	−0.398532	−	0.690278i	−0.993545	+	0.113438i	$0.963814\pi$
$102$		0			0
$103$	3.41423	−	5.91362i	0.336414	−	0.582686i	−0.647341	−	0.762200i	$-0.724119\pi$
$103$	3.41423	−	5.91362i	0.336414	−	0.582686i	0.983755	+	0.179514i	$0.0574525\pi$
$104$	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	$0.155937\pi$
$110$	−10.7850			−1.02830
$111$		0			0
$112$	−0.710533	+	2.54856i	−0.0671391	+	0.240816i
$113$	−4.25116	−	7.36323i	−0.399916	−	0.692674i	0.593799	−	0.804613i	$-0.297627\pi$
$113$	−4.25116	−	7.36323i	−0.399916	−	0.692674i	−0.993715	+	0.111939i	$0.964294\pi$
$114$		0			0
$115$	0.370723	+	0.642111i	0.0345701	+	0.0598772i
$116$	−0.732287	+	1.26836i	−0.0679911	+	0.117764i
$117$		0			0
$118$	1.98633			0.182856
$119$	12.6706	+	12.9290i	1.16151	+	1.18520i
$120$		0			0
$121$	−13.2564	+	22.9607i	−1.20512	+	2.08734i
$122$	10.3502			0.937064
$123$		0			0
$124$	7.70370			0.691812
$125$	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	$0.817982\pi$
$128$	−1.00000			−0.0883883
$129$		0			0
$130$	1.33981			0.117509
$131$	−3.64652	+	6.31595i	−0.318598	+	0.551827i	−0.980196	−	0.198031i	$-0.936545\pi$
$131$	−3.64652	+	6.31595i	−0.318598	+	0.551827i	0.661598	+	0.749859i	$0.269879\pi$
$132$		0			0
$133$	−4.97825	+	1.28020i	−0.431669	+	0.111007i
$134$	−6.78495			−0.586131
$135$		0			0
$136$	−3.42107	+	5.92546i	−0.293354	+	0.508104i
$137$	−4.09097	−	7.08577i	−0.349515	−	0.605378i	0.636648	−	0.771154i	$-0.280320\pi$
$137$	−4.09097	−	7.08577i	−0.349515	−	0.605378i	−0.986163	+	0.165776i	$0.946987\pi$
$138$		0			0
$139$	−6.23229	−	10.7946i	−0.528616	−	0.915589i	−0.999443	−	0.0333640i	$-0.989378\pi$
$139$	−6.23229	−	10.7946i	−0.528616	−	0.915589i	0.470828	−	0.882225i	$-0.343955\pi$
$140$	3.26088	+	3.32738i	0.275594	+	0.281215i
$141$		0			0
$142$	10.7850			0.905053
$143$	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
$149$	4.41423	−	7.64567i	0.361628	−	0.626358i	−0.626601	−	0.779340i	$-0.715554\pi$
$149$	4.41423	−	7.64567i	0.361628	−	0.626358i	0.988229	+	0.152982i	$0.0488878\pi$
$150$		0			0
$151$	7.49316	+	12.9785i	0.609785	+	1.05618i	0.991276	+	0.131806i	$0.0420775\pi$
$151$	7.49316	+	12.9785i	0.609785	+	1.05618i	−0.381491	+	0.924373i	$0.624589\pi$
$152$	−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
$157$	18.9806			1.51481			0.757407	−	0.652943i	$-0.226466\pi$
$157$	18.9806			1.51481			0.757407	+	0.652943i	$0.226466\pi$
$158$	13.4451			1.06964
$159$		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	$-0.367115\pi$
$164$	3.47141	+	6.01266i	0.271072	+	0.469510i
$165$		0			0
$166$	−1.56238	+	2.70612i	−0.121264	+	0.210036i
$167$	−0.572097	−	0.990901i	−0.0442702	−	0.0766782i	0.843041	−	0.537849i	$-0.180763\pi$
$167$	−0.572097	−	0.990901i	−0.0442702	−	0.0766782i	−0.887311	+	0.461171i	$0.847430\pi$
$168$		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
$173$	−0.497677			−0.0378377			−0.0189188	−	0.999821i	$-0.506022\pi$
$173$	−0.497677			−0.0378377			−0.0189188	+	0.999821i	$0.506022\pi$
$174$		0			0
$175$	−4.86677	+	1.25153i	−0.367893	+	0.0946068i
$176$	3.06238	+	5.30420i	0.230836	+	0.399819i
$177$		0			0
$178$	1.30150	+	2.25427i	0.0975519	+	0.168965i
$179$	−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	$0.484267\pi$
$182$	−1.94966	+	0.501371i	−0.144518	+	0.0371641i
$183$		0			0
$184$	0.210533	−	0.364654i	0.0155207	−	0.0268827i
$185$	5.08126			0.373581
$186$		0			0
$187$	41.9064			3.06450
$188$	−1.66019			−0.121082
$189$		0			0
$190$	−3.42107			−0.248190
$191$	16.1683			1.16989			0.584947	−	0.811071i	$-0.301115\pi$
$191$	16.1683			1.16989			0.584947	+	0.811071i	$0.301115\pi$
$192$		0			0
$193$	−14.1683			−1.01985			−0.509927	−	0.860218i	$-0.670328\pi$
$193$	−14.1683			−1.01985			−0.509927	+	0.860218i	$0.670328\pi$
$194$	1.81806	−	3.14897i	0.130529	−	0.226083i
$195$		0			0
$196$	−5.99028	−	3.62167i	−0.427877	−	0.258691i
$197$	−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	$0.269332\pi$
$200$	−0.949657	−	1.64485i	−0.0671509	−	0.116309i
$201$		0			0
$202$	4.00520	+	6.93721i	0.281805	+	0.488101i
$203$	−2.71217	−	2.76748i	−0.190357	−	0.194239i
$204$		0			0
$205$	12.2255			0.853862
$206$	−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	0.929702	+	0.368314i	$0.120065\pi$
$211$	11.3856	+	19.7205i	0.783820	+	1.35762i	−0.145882	+	0.989302i	$0.546602\pi$
$212$	0.112725	−	0.195246i	0.00774199	−	0.0134095i
$213$		0			0
$214$	1.77292	+	3.07078i	0.121194	+	0.209914i
$215$	−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
$220$	10.7850			0.727121
$221$	−5.20602			−0.350195
$222$		0			0
$223$	−6.44282	+	11.1593i	−0.431443	+	0.747281i	−0.996998	−	0.0774293i	$-0.975329\pi$
$223$	−6.44282	+	11.1593i	−0.431443	+	0.747281i	0.565555	+	0.824711i	$0.308662\pi$
$224$	0.710533	−	2.54856i	0.0474745	−	0.170283i
$225$		0			0
$226$	4.25116	+	7.36323i	0.282783	+	0.489795i
$227$	10.9984	+	19.0497i	0.729987	+	1.26437i	0.956888	+	0.290457i	$0.0938073\pi$
$227$	10.9984	+	19.0497i	0.729987	+	1.26437i	−0.226901	+	0.973918i	$0.572859\pi$
$228$		0			0
$229$	1.89931	−	3.28971i	0.125510	−	0.217390i	−0.796422	−	0.604741i	$-0.793277\pi$
$229$	1.89931	−	3.28971i	0.125510	−	0.217390i	0.921932	+	0.387351i	$0.126610\pi$
$230$	−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
$236$	−1.98633			−0.129299
$237$		0			0
$238$	−12.6706	−	12.9290i	−0.821313	−	0.838064i
$239$	7.82038	+	13.5453i	0.505858	+	0.876172i	0.999977	+	0.00677786i	$0.00215748\pi$
$239$	7.82038	+	13.5453i	0.505858	+	0.876172i	−0.494119	+	0.869394i	$0.664509\pi$
$240$		0			0
$241$	−10.7060	−	18.5434i	−0.689635	−	1.19448i	−0.971956	−	0.235163i	$-0.924437\pi$
$241$	−10.7060	−	18.5434i	−0.689635	−	1.19448i	0.282320	−	0.959320i	$-0.408896\pi$
$242$	13.2564	−	22.9607i	0.852151	−	1.47597i
$243$		0			0
$244$	−10.3502			−0.662605
$245$	−10.7970	+	5.94631i	−0.689794	+	0.379896i
$246$		0			0
$247$	0.739123	−	1.28020i	0.0470293	−	0.0814571i
$248$	−7.70370			−0.489185
$249$		0			0
$250$	−12.1488			−0.768360
$251$	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
$254$	18.9532			1.18923
$255$		0			0
$256$	1.00000			0.0625000
$257$	10.1300	−	17.5456i	0.631890	−	1.09447i	−0.355275	−	0.934762i	$-0.615613\pi$
$257$	10.1300	−	17.5456i	0.631890	−	1.09447i	0.987165	−	0.159704i	$-0.0510538\pi$
$258$		0			0
$259$	−7.39411	+	1.90146i	−0.459448	+	0.118151i
$260$	−1.33981			−0.0830915
$261$		0			0
$262$	3.64652	−	6.31595i	0.225283	−	0.390201i
$263$	−11.2443	−	19.4757i	−0.693355	−	1.20093i	−0.970732	−	0.240165i	$-0.922799\pi$
$263$	−11.2443	−	19.4757i	−0.693355	−	1.20093i	0.277377	−	0.960761i	$-0.410535\pi$
$264$		0			0
$265$	−0.198495	−	0.343803i	−0.0121935	−	0.0211197i
$266$	4.97825	−	1.28020i	0.305236	−	0.0784940i
$267$		0			0
$268$	6.78495			0.414457
$269$	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
$275$	−5.81642	+	10.0743i	−0.350743	+	0.607505i
$276$		0			0
$277$	1.64132	+	2.84284i	0.0986171	+	0.170810i	0.911112	−	0.412158i	$-0.135225\pi$
$277$	1.64132	+	2.84284i	0.0986171	+	0.170810i	−0.812495	+	0.582968i	$0.801891\pi$
$278$	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	−0.884330	−	0.466863i	$-0.845384\pi$
$281$	−0.634479	+	1.09895i	−0.0378498	+	0.0655578i	0.846480	+	0.532421i	$0.178718\pi$
$282$		0			0
$283$	−8.19235			−0.486984			−0.243492	−	0.969903i	$-0.578293\pi$
$283$	−8.19235			−0.486984			−0.243492	+	0.969903i	$0.578293\pi$
$284$	−10.7850			−0.639969
$285$		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
$290$	−1.28947	−	2.23342i	−0.0757201	−	0.131151i
$291$		0			0
$292$	0.153353	−	0.265616i	0.00897433	−	0.0155440i
$293$	−7.72545	−	13.3809i	−0.451326	−	0.781719i	0.547143	−	0.837039i	$-0.315715\pi$
$293$	−7.72545	−	13.3809i	−0.451326	−	0.781719i	−0.998469	+	0.0553202i	$0.982382\pi$
$294$		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
$299$	0.320380			0.0185280
$300$		0			0
$301$	16.0374	+	16.3645i	0.924378	+	0.943231i
$302$	−7.49316	−	12.9785i	−0.431183	−	0.746831i
$303$		0			0
$304$	0.971410	+	1.68253i	0.0557142	+	0.0964998i
$305$	−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	$0.455351\pi$
$308$	−15.6940	+	4.03584i	−0.894248	+	0.229963i
$309$		0			0
$310$	−6.78263	+	11.7479i	−0.385228	+	0.667234i
$311$	7.69002			0.436061			0.218031	−	0.975942i	$-0.430037\pi$
$311$	7.69002			0.436061			0.218031	+	0.975942i	$0.430037\pi$
$312$		0			0
$313$	−1.72313			−0.0973969			−0.0486985	−	0.998814i	$-0.515507\pi$
$313$	−1.72313			−0.0973969			−0.0486985	+	0.998814i	$0.515507\pi$
$314$	−18.9806			−1.07114
$315$		0			0
$316$	−13.4451			−0.756348
$317$	−33.2028			−1.86485			−0.932426	−	0.361361i	$-0.882312\pi$
$317$	−33.2028			−1.86485			−0.932426	+	0.361361i	$0.882312\pi$
$318$		0			0
$319$	−8.97017			−0.502233
$320$	0.880438	−	1.52496i	0.0492180	−	0.0852481i
$321$		0			0
$322$	0.779752	+	0.795655i	0.0434539	+	0.0443401i
$323$	13.2930			0.739644
$324$		0			0
$325$	0.722572	−	1.25153i	0.0400811	−	0.0694224i
$326$	7.51887	+	13.0231i	0.416432	+	0.721281i
$327$		0			0
$328$	−3.47141	−	6.01266i	−0.191677	−	0.331994i
$329$	1.17962	−	4.23109i	0.0650346	−	0.233267i
$330$		0			0
$331$	2.88891			0.158789			0.0793944	−	0.996843i	$-0.474701\pi$
$331$	2.88891			0.158789			0.0793944	+	0.996843i	$0.474701\pi$
$332$	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	0.722433	−	0.691441i	$-0.243024\pi$
$337$	−4.36156	−	7.55445i	−0.237590	−	0.411517i	−0.960022	+	0.279924i	$0.909691\pi$
$338$	−6.21053	+	10.7570i	−0.337808	+	0.585101i
$339$		0			0
$340$	−6.02408	−	10.4340i	−0.326701	−	0.565863i
$341$	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
$346$	0.497677			0.0267553
$347$	−9.69467			−0.520437			−0.260219	−	0.965550i	$-0.583795\pi$
$347$	−9.69467			−0.520437			−0.260219	+	0.965550i	$0.583795\pi$
$348$		0			0
$349$	14.1992	−	24.5937i	0.760065	−	1.31647i	−0.182752	−	0.983159i	$-0.558500\pi$
$349$	14.1992	−	24.5937i	0.760065	−	1.31647i	0.942817	−	0.333312i	$-0.108166\pi$
$350$	4.86677	−	1.25153i	0.260140	−	0.0668971i
$351$		0			0
$352$	−3.06238	−	5.30420i	−0.163225	−	0.282715i
$353$	−2.19686	−	3.80507i	−0.116927	−	0.202524i	0.801621	−	0.597832i	$-0.203971\pi$
$353$	−2.19686	−	3.80507i	−0.116927	−	0.202524i	−0.918548	+	0.395308i	$0.870638\pi$
$354$		0			0
$355$	−9.49549	+	16.4467i	−0.503968	+	0.872898i
$356$	−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
$362$	−1.32941			−0.0698721
$363$		0			0
$364$	1.94966	−	0.501371i	0.102190	−	0.0262790i
$365$	−0.270036	−	0.467717i	−0.0141343	−	0.0244814i
$366$		0			0
$367$	−17.3015	−	29.9671i	−0.903131	−	1.56427i	−0.823406	−	0.567452i	$-0.807929\pi$
$367$	−17.3015	−	29.9671i	−0.903131	−	1.56427i	−0.0797249	−	0.996817i	$-0.525404\pi$
$368$	−0.210533	+	0.364654i	−0.0109748	+	0.0190089i
$369$		0			0
$370$	−5.08126			−0.264162
$371$	0.417500	+	0.426015i	0.0216755	+	0.0221176i
$372$		0			0
$373$	−5.48796	+	9.50543i	−0.284156	+	0.492172i	−0.972404	−	0.233303i	$-0.925047\pi$
$373$	−5.48796	+	9.50543i	−0.284156	+	0.492172i	0.688248	+	0.725475i	$0.258380\pi$
$374$	−41.9064			−2.16693
$375$		0			0
$376$	1.66019			0.0856178
$377$	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	$0.162226\pi$
$380$	3.42107			0.175497
$381$		0			0
$382$	−16.1683			−0.827241
$383$	−10.5120	+	18.2074i	−0.537140	+	0.930354i	0.461916	+	0.886923i	$0.347162\pi$
$383$	−10.5120	+	18.2074i	−0.537140	+	0.930354i	−0.999056	+	0.0434304i	$0.986171\pi$
$384$		0			0
$385$	−7.66307	+	27.4861i	−0.390546	+	1.40082i
$386$	14.1683			0.721146
$387$		0			0
$388$	−1.81806	+	3.14897i	−0.0922978	+	0.159865i
$389$	6.86909	+	11.8976i	0.348277	+	0.603233i	0.985943	−	0.167080i	$-0.0534337\pi$
$389$	6.86909	+	11.8976i	0.348277	+	0.603233i	−0.637667	+	0.770312i	$0.720100\pi$
$390$		0			0
$391$	1.44050	+	2.49501i	0.0728491	+	0.126178i
$392$	5.99028	+	3.62167i	0.302555	+	0.182922i
$393$		0			0
$394$	15.8421			0.798115
$395$	−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
$401$	−4.63968	+	8.03616i	−0.231695	+	0.401307i	−0.958307	−	0.285741i	$-0.907760\pi$
$401$	−4.63968	+	8.03616i	−0.231695	+	0.401307i	0.726612	+	0.687048i	$0.241094\pi$
$402$		0			0
$403$	−2.93078	−	5.07626i	−0.145993	−	0.252867i
$404$	−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
$409$	15.1683			0.750023			0.375011	−	0.927020i	$-0.377639\pi$
$409$	15.1683			0.750023			0.375011	+	0.927020i	$0.377639\pi$
$410$	−12.2255			−0.603772
$411$		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
$416$	0.380438	+	0.658939i	0.0186525	+	0.0323071i
$417$		0			0
$418$	5.94966	−	10.3051i	0.291007	−	0.504039i
$419$	4.16827	+	7.21966i	0.203633	+	0.352703i	0.949696	−	0.313172i	$-0.101392\pi$
$419$	4.16827	+	7.21966i	0.203633	+	0.352703i	−0.746063	+	0.665875i	$0.768058\pi$
$420$		0			0
$421$	−3.50232	+	6.06620i	−0.170693	+	0.295649i	−0.938662	−	0.344838i	$-0.887934\pi$
$421$	−3.50232	+	6.06620i	−0.170693	+	0.295649i	0.767969	+	0.640486i	$0.221267\pi$
$422$	−11.3856	−	19.7205i	−0.554244	−	0.959979i
$423$		0			0
$424$	−0.112725	+	0.195246i	−0.00547442	+	0.00948197i
$425$	12.9954			0.630367
$426$		0			0
$427$	7.35417	−	26.3781i	0.355893	−	1.27653i
$428$	−1.77292	−	3.07078i	−0.0856971	−	0.148432i
$429$		0			0
$430$	7.62476	+	13.2065i	0.367699	+	0.636873i
$431$	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	$0.262395\pi$
$434$	5.47373	−	19.6333i	0.262748	−	0.942429i
$435$		0			0
$436$	0.351848	−	0.609419i	0.0168505	−	0.0291859i
$437$	−0.818057			−0.0391330
$438$		0			0
$439$	−28.8960			−1.37913			−0.689566	−	0.724222i	$-0.742199\pi$
$439$	−28.8960			−1.37913			−0.689566	+	0.724222i	$0.742199\pi$
$440$	−10.7850			−0.514152
$441$		0			0
$442$	5.20602			0.247625
$443$	13.7609			0.653799			0.326899	−	0.945059i	$-0.393996\pi$
$443$	13.7609			0.653799			0.326899	+	0.945059i	$0.393996\pi$
$444$		0			0
$445$	−4.58358			−0.217283
$446$	6.44282	−	11.1593i	0.305076	−	0.528408i
$447$		0			0
$448$	−0.710533	+	2.54856i	−0.0335695	+	0.120408i
$449$	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
$452$	−4.25116	−	7.36323i	−0.199958	−	0.346337i
$453$		0			0
$454$	−10.9984	−	19.0497i	−0.516179	−	0.894048i
$455$	0.951980	−	3.41458i	0.0446295	−	0.160078i
$456$		0			0
$457$	20.0298			0.936956			0.468478	−	0.883475i	$-0.344803\pi$
$457$	20.0298			0.936956			0.468478	+	0.883475i	$0.344803\pi$
$458$	−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	−0.970977	−	0.239173i	$-0.923124\pi$
$461$	−5.97661	+	10.3518i	−0.278359	+	0.482131i	0.692618	+	0.721304i	$0.256457\pi$
$462$		0			0
$463$	6.64527	+	11.5100i	0.308832	+	0.534913i	0.978107	−	0.208102i	$-0.0667286\pi$
$463$	6.64527	+	11.5100i	0.308832	+	0.534913i	−0.669275	+	0.743015i	$0.733395\pi$
$464$	−0.732287	+	1.26836i	−0.0339956	+	0.0588820i
$465$		0			0
$466$	−3.33530	−	5.77690i	−0.154505	−	0.267610i
$467$	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
$472$	1.98633			0.0914281
$473$	53.0416			2.43886
$474$		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
$479$	−16.3135	−	28.2559i	−0.745385	−	1.29104i	−0.950015	−	0.312205i	$-0.898932\pi$
$479$	−16.3135	−	28.2559i	−0.745385	−	1.29104i	0.204630	−	0.978839i	$-0.434401\pi$
$480$		0			0
$481$	1.09781	−	1.90146i	0.0500557	−	0.0866991i
$482$	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	$0.139966\pi$
$488$	10.3502			0.468532
$489$		0			0
$490$	10.7970	−	5.94631i	0.487758	−	0.268627i
$491$	18.7804	+	32.5287i	0.847549	+	1.46800i	0.883389	+	0.468641i	$0.155256\pi$
$491$	18.7804	+	32.5287i	0.847549	+	1.46800i	−0.0358393	+	0.999358i	$0.511410\pi$
$492$		0			0
$493$	5.01040	+	8.67827i	0.225657	+	0.390850i
$494$	−0.739123	+	1.28020i	−0.0332547	+	0.0575989i
$495$		0			0
$496$	7.70370			0.345906
$497$	7.66307	−	27.4861i	0.343736	−	1.23292i
$498$		0			0
$499$	15.8977	−	27.5356i	0.711678	−	1.23266i	−0.252549	−	0.967584i	$-0.581269\pi$
$499$	15.8977	−	27.5356i	0.711678	−	1.23266i	0.964227	−	0.265078i	$-0.0853977\pi$
$500$	12.1488			0.543313
$501$		0			0
$502$	−23.6030			−1.05345
$503$	−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
$506$	2.57893			0.114648
$507$		0			0
$508$	−18.9532			−0.840913
$509$	4.00808	−	6.94220i	0.177655	−	0.307708i	−0.763422	−	0.645900i	$-0.776482\pi$
$509$	4.00808	−	6.94220i	0.177655	−	0.307708i	0.941077	+	0.338193i	$0.109816\pi$
$510$		0			0
$511$	0.567974	+	0.579559i	0.0251257	+	0.0256382i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	−10.1300	+	17.5456i	−0.446814	+	0.773904i
$515$	−6.01204	−	10.4132i	−0.264922	−	0.458858i
$516$		0			0
$517$	−5.08414	−	8.80598i	−0.223600	−	0.387287i
$518$	7.39411	−	1.90146i	0.324879	−	0.0835453i
$519$		0			0
$520$	1.33981			0.0587546
$521$	−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
$527$	26.3549	−	45.6480i	1.14804	−	1.98846i
$528$		0			0
$529$	11.4114	+	19.7650i	0.496146	+	0.859350i
$530$	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
$535$	−6.24377			−0.269942
$536$	−6.78495			−0.293065
$537$		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	$0.733792\pi$
$542$	6.87880	+	11.9144i	0.295470	+	0.511769i
$543$		0			0
$544$	−3.42107	+	5.92546i	−0.146677	+	0.254052i
$545$	−0.619562	−	1.07311i	−0.0265391	−	0.0459671i
$546$		0			0
$547$	1.02463	−	1.77471i	0.0438101	−	0.0758813i	−0.843289	−	0.537461i	$-0.819384\pi$
$547$	1.02463	−	1.77471i	0.0438101	−	0.0758813i	0.887099	+	0.461579i	$0.152717\pi$
$548$	−4.09097	−	7.08577i	−0.174758	−	0.302689i
$549$		0			0
$550$	5.81642	−	10.0743i	0.248013	−	0.429571i
$551$	−2.84540			−0.121218
$552$		0			0
$553$	9.55322	−	34.2657i	0.406244	−	1.45713i
$554$	−1.64132	−	2.84284i	−0.0697328	−	0.120781i
$555$		0			0
$556$	−6.23229	−	10.7946i	−0.264308	−	0.457795i
$557$	−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
$560$	3.26088	+	3.32738i	0.137797	+	0.140608i
$561$		0			0
$562$	0.634479	−	1.09895i	0.0267639	−	0.0463564i
$563$	−0.937063			−0.0394925			−0.0197462	−	0.999805i	$-0.506286\pi$
$563$	−0.937063			−0.0394925			−0.0197462	+	0.999805i	$0.506286\pi$
$564$		0			0
$565$	−14.9715			−0.629858
$566$	8.19235			0.344350
$567$		0			0
$568$	10.7850			0.452527
$569$	−23.5264			−0.986278			−0.493139	−	0.869951i	$-0.664151\pi$
$569$	−23.5264			−0.986278			−0.493139	+	0.869951i	$0.664151\pi$
$570$		0			0
$571$	−0.484004			−0.0202549			−0.0101275	−	0.999949i	$-0.503224\pi$
$571$	−0.484004			−0.0202549			−0.0101275	+	0.999949i	$0.503224\pi$
$572$	2.33009	−	4.03584i	0.0974262	−	0.168747i
$573$		0			0
$574$	17.7902	−	4.57489i	0.742547	−	0.190952i
$575$	−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	$0.196269\pi$
$578$	14.9074	+	25.8204i	0.620066	+	1.07399i
$579$		0			0
$580$	1.28947	+	2.23342i	0.0535422	+	0.0927378i
$581$	5.78659	+	5.90461i	0.240068	+	0.244965i
$582$		0			0
$583$	1.38083			0.0571881
$584$	−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	−0.985026	−	0.172407i	$-0.944846\pi$
$587$	−8.31518	+	14.4023i	−0.343204	+	0.594447i	0.641822	+	0.766854i	$0.278179\pi$
$588$		0			0
$589$	7.48345	+	12.9617i	0.308350	+	0.534078i
$590$	1.74884	−	3.02908i	0.0719985	−	0.124705i
$591$		0			0
$592$	1.44282	+	2.49904i	0.0592995	+	0.102710i
$593$	−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
$598$	−0.320380			−0.0131013
$599$	−15.0766			−0.616014			−0.308007	−	0.951384i	$-0.599662\pi$
$599$	−15.0766			−0.616014			−0.308007	+	0.951384i	$0.599662\pi$
$600$		0			0
$601$	−8.05555	+	13.9526i	−0.328593	+	0.569139i	−0.982233	−	0.187666i	$-0.939908\pi$
$601$	−8.05555	+	13.9526i	−0.328593	+	0.569139i	0.653640	+	0.756805i	$0.273241\pi$
$602$	−16.0374	−	16.3645i	−0.653634	−	0.666965i
$603$		0			0
$604$	7.49316	+	12.9785i	0.304892	+	0.528089i
$605$	23.3428	+	40.4310i	0.949021	+	1.64375i
$606$		0			0
$607$	−9.78659	+	16.9509i	−0.397225	+	0.688014i	−0.993382	−	0.114853i	$-0.963360\pi$
$607$	−9.78659	+	16.9509i	−0.397225	+	0.688014i	0.596157	+	0.802868i	$0.296694\pi$
$608$	−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	$0.202429\pi$
$614$	−4.89931			−0.197720
$615$		0			0
$616$	15.6940	−	4.03584i	0.632329	−	0.162609i
$617$	−0.634479	−	1.09895i	−0.0255431	−	0.0442420i	0.852971	−	0.521958i	$-0.174798\pi$
$617$	−0.634479	−	1.09895i	−0.0255431	−	0.0442420i	−0.878514	+	0.477716i	$0.841465\pi$
$618$		0			0
$619$	−2.25116	−	3.89913i	−0.0904818	−	0.156719i	0.817232	−	0.576309i	$-0.195507\pi$
$619$	−2.25116	−	3.89913i	−0.0904818	−	0.156719i	−0.907714	+	0.419589i	$0.862174\pi$
$620$	6.78263	−	11.7479i	0.272397	−	0.471805i
$621$		0			0
$622$	−7.69002			−0.308342
$623$	6.66991	−	1.71522i	0.267224	−	0.0687190i
$624$		0			0
$625$	5.94802	−	10.3023i	0.237921	−	0.412091i
$626$	1.72313			0.0688700
$627$		0			0
$628$	18.9806			0.757407
$629$	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	$0.510767\pi$
$632$	13.4451			0.534819
$633$		0			0
$634$	33.2028			1.31865
$635$	−16.6871	+	28.9030i	−0.662209	+	1.14698i
$636$		0			0
$637$	−0.107523	+	5.32505i	−0.00426023	+	0.210986i
$638$	8.97017			0.355132
$639$		0			0
$640$	−0.880438	+	1.52496i	−0.0348024	+	0.0602795i
$641$	−0.474289	−	0.821492i	−0.0187333	−	0.0324470i	0.856507	−	0.516136i	$-0.172630\pi$
$641$	−0.474289	−	0.821492i	−0.0187333	−	0.0324470i	−0.875240	+	0.483689i	$0.839297\pi$
$642$		0			0
$643$	−9.84897	−	17.0589i	−0.388405	−	0.672738i	0.603830	−	0.797113i	$-0.293641\pi$
$643$	−9.84897	−	17.0589i	−0.388405	−	0.672738i	−0.992235	+	0.124375i	$0.960307\pi$
$644$	−0.779752	−	0.795655i	−0.0307265	−	0.0313532i
$645$		0			0
$646$	−13.2930			−0.523007
$647$	−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
$653$	11.3954	−	19.7373i	0.445935	−	0.772382i	−0.552182	−	0.833724i	$-0.686205\pi$
$653$	11.3954	−	19.7373i	0.445935	−	0.772382i	0.998117	+	0.0613420i	$0.0195380\pi$
$654$		0			0
$655$	6.42107	+	11.1216i	0.250892	+	0.434557i
$656$	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	−0.484083	−	0.875022i	$-0.660847\pi$
$659$	13.2398	−	22.9320i	0.515750	−	0.893305i	0.999833	−	0.0182828i	$-0.00581993\pi$
$660$		0			0
$661$	−26.7382			−1.03999			−0.519997	−	0.854168i	$-0.674067\pi$
$661$	−26.7382			−1.03999			−0.519997	+	0.854168i	$0.674067\pi$
$662$	−2.88891			−0.112281
$663$		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
$668$	−0.572097	−	0.990901i	−0.0221351	−	0.0383391i
$669$		0			0
$670$	−5.97373	+	10.3468i	−0.230785	+	0.399732i
$671$	−31.6963	−	54.8996i	−1.22362	−	2.11938i
$672$		0			0
$673$	−10.3856	+	17.9885i	−0.400337	+	0.693404i	−0.993766	−	0.111482i	$-0.964440\pi$
$673$	−10.3856	+	17.9885i	−0.400337	+	0.693404i	0.593429	+	0.804886i	$0.297774\pi$
$674$	4.36156	+	7.55445i	0.168001	+	0.290987i
$675$		0			0
$676$	6.21053	−	10.7570i	0.238867	−	0.413729i
$677$	20.6979			0.795486			0.397743	−	0.917497i	$-0.369793\pi$
$677$	20.6979			0.795486			0.397743	+	0.917497i	$0.369793\pi$
$678$		0			0
$679$	−6.73353	−	6.87087i	−0.258409	−	0.263680i
$680$	6.02408	+	10.4340i	0.231013	+	0.400126i
$681$		0			0
$682$	−23.5917	−	40.8620i	−0.903371	−	1.56469i
$683$	−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
$686$	−13.4863	+	12.6933i	−0.514910	+	0.484631i
$687$		0			0
$688$	4.33009	−	7.49994i	0.165083	−	0.285933i
$689$	−0.171540			−0.00653515
$690$		0			0
$691$	−6.69794			−0.254802			−0.127401	−	0.991851i	$-0.540663\pi$
$691$	−6.69794			−0.254802			−0.127401	+	0.991851i	$0.540663\pi$
$692$	−0.497677			−0.0189188
$693$		0			0
$694$	9.69467			0.368005
$695$	−21.9486			−0.832557
$696$		0			0
$697$	47.5037			1.79933
$698$	−14.1992	+	24.5937i	−0.537447	+	0.930886i
$699$		0			0
$700$	−4.86677	+	1.25153i	−0.183946	+	0.0473034i
$701$	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
$704$	3.06238	+	5.30420i	0.115418	+	0.199910i
$705$		0			0
$706$	2.19686	+	3.80507i	0.0826799	+	0.143206i
$707$	20.5257	−	5.27836i	0.771949	−	0.198513i
$708$		0			0
$709$	8.86621			0.332977			0.166489	−	0.986043i	$-0.446757\pi$
$709$	8.86621			0.332977			0.166489	+	0.986043i	$0.446757\pi$
$710$	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
$716$	−4.41423	+	7.64567i	−0.164968	+	0.285732i
$717$		0			0
$718$	16.0796	+	27.8507i	0.600086	+	1.03938i
$719$	−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
$724$	1.32941			0.0494070
$725$	−2.78168			−0.103309
$726$		0			0
$727$	3.25692	−	5.64115i	0.120792	−	0.209219i	−0.799288	−	0.600948i	$-0.794790\pi$
$727$	3.25692	−	5.64115i	0.120792	−	0.209219i	0.920080	+	0.391730i	$0.128123\pi$
$728$	−1.94966	+	0.501371i	−0.0722591	+	0.0185820i
$729$		0			0
$730$	0.270036	+	0.467717i	0.00999449	+	0.0173110i
$731$	−29.6271	−	51.3156i	−1.09580	−	1.89798i
$732$		0			0
$733$	11.5991	−	20.0901i	0.428421	−	0.742047i	−0.568312	−	0.822813i	$-0.692403\pi$
$733$	11.5991	−	20.0901i	0.428421	−	0.742047i	0.996733	+	0.0807664i	$0.0257368\pi$
$734$	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	$0.256595\pi$
$740$	5.08126			0.186791
$741$		0			0
$742$	−0.417500	−	0.426015i	−0.0153269	−	0.0156395i
$743$	5.21737	+	9.03675i	0.191407	+	0.331526i	0.945717	−	0.324992i	$-0.105362\pi$
$743$	5.21737	+	9.03675i	0.191407	+	0.331526i	−0.754310	+	0.656518i	$0.772028\pi$
$744$		0			0
$745$	−7.77292	−	13.4631i	−0.284778	−	0.493249i
$746$	5.48796	−	9.50543i	0.200929	−	0.348018i
$747$		0			0
$748$	41.9064			1.53225
$749$	9.08577	−	2.33648i	0.331987	−	0.0853733i
$750$		0			0
$751$	−20.1059	+	34.8244i	−0.733674	+	1.27076i	0.221628	+	0.975131i	$0.428863\pi$
$751$	−20.1059	+	34.8244i	−0.733674	+	1.27076i	−0.955303	+	0.295630i	$0.904470\pi$
$752$	−1.66019			−0.0605409
$753$		0			0
$754$	−1.11436			−0.0405826
$755$	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	$0.627902\pi$
$758$	−33.9877			−1.23449
$759$		0			0
$760$	−3.42107			−0.124095
$761$	−11.8313	+	20.4925i	−0.428886	+	0.742852i	−0.996774	−	0.0802535i	$-0.974427\pi$
$761$	−11.8313	+	20.4925i	−0.428886	+	0.742852i	0.567889	+	0.823105i	$0.307760\pi$
$762$		0			0
$763$	1.30314	+	1.32972i	0.0471768	+	0.0481390i
$764$	16.1683			0.584947
$765$		0			0
$766$	10.5120	−	18.2074i	0.379815	−	0.657860i
$767$	0.755675	+	1.30887i	0.0272858	+	0.0472605i
$768$		0			0
$769$	−5.62764	−	9.74736i	−0.202938	−	0.351499i	0.746536	−	0.665345i	$-0.231716\pi$
$769$	−5.62764	−	9.74736i	−0.202938	−	0.351499i	−0.949474	+	0.313846i	$0.898382\pi$
$770$	7.66307	−	27.4861i	0.276158	−	0.990529i
$771$		0			0
$772$	−14.1683			−0.509927
$773$	−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
$779$	−6.74433	+	11.6815i	−0.241641	+	0.418534i
$780$		0			0
$781$	−33.0276	−	57.2056i	−1.18182	−	2.04698i
$782$	−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.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{4} +(0.880438 - 1.52496i) q^{5} +(-0.710533 + 2.54856i) q^{7} -1.00000 q^{8} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{4} +(0.880438 - 1.52496i) q^{5} +(-0.710533 + 2.54856i) q^{7} -1.00000 q^{8} +(-0.880438 + 1.52496i) q^{10} +(3.06238 + 5.30420i) q^{11} +(-0.380438 - 0.658939i) q^{13} +(0.710533 - 2.54856i) q^{14} +1.00000 q^{16} +(3.42107 - 5.92546i) q^{17} +(0.971410 + 1.68253i) q^{19} +(0.880438 - 1.52496i) q^{20} +(-3.06238 - 5.30420i) q^{22} +(-0.210533 + 0.364654i) q^{23} +(0.949657 + 1.64485i) q^{25} +(0.380438 + 0.658939i) q^{26} +(-0.710533 + 2.54856i) q^{28} +(-0.732287 + 1.26836i) q^{29} +7.70370 q^{31} -1.00000 q^{32} +(-3.42107 + 5.92546i) q^{34} +(3.26088 + 3.32738i) q^{35} +(1.44282 + 2.49904i) q^{37} +(-0.971410 - 1.68253i) q^{38} +(-0.880438 + 1.52496i) q^{40} +(3.47141 + 6.01266i) q^{41} +(4.33009 - 7.49994i) q^{43} +(3.06238 + 5.30420i) q^{44} +(0.210533 - 0.364654i) q^{46} -1.66019 q^{47} +(-5.99028 - 3.62167i) q^{49} +(-0.949657 - 1.64485i) q^{50} +(-0.380438 - 0.658939i) q^{52} +(0.112725 - 0.195246i) q^{53} +10.7850 q^{55} +(0.710533 - 2.54856i) q^{56} +(0.732287 - 1.26836i) q^{58} -1.98633 q^{59} -10.3502 q^{61} -7.70370 q^{62} +1.00000 q^{64} -1.33981 q^{65} +6.78495 q^{67} +(3.42107 - 5.92546i) q^{68} +(-3.26088 - 3.32738i) q^{70} -10.7850 q^{71} +(0.153353 - 0.265616i) q^{73} +(-1.44282 - 2.49904i) q^{74} +(0.971410 + 1.68253i) q^{76} +(-15.6940 + 4.03584i) q^{77} -13.4451 q^{79} +(0.880438 - 1.52496i) q^{80} +(-3.47141 - 6.01266i) q^{82} +(1.56238 - 2.70612i) q^{83} +(-6.02408 - 10.4340i) q^{85} +(-4.33009 + 7.49994i) q^{86} +(-3.06238 - 5.30420i) q^{88} +(-1.30150 - 2.25427i) q^{89} +(1.94966 - 0.501371i) q^{91} +(-0.210533 + 0.364654i) q^{92} +1.66019 q^{94} +3.42107 q^{95} +(-1.81806 + 3.14897i) q^{97} +(5.99028 + 3.62167i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{2} + 6 q^{4} + 5 q^{5} + 4 q^{7} - 6 q^{8}+O(q^{10}) \) 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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