LMFDB - Embedded newform 1638.2.bj.c.127.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1638,2,Mod(127,1638)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1638, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 5]))

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

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

chi := DirichletCharacter("1638.127");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1638.bj (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$13.0794958511$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 182)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			127.1
Root			$0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1638.127
Dual form			1638.2.bj.c.1135.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +1.00000i q^{5} +(-0.866025 - 0.500000i) q^{7} +1.00000i q^{8} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +1.00000i q^{5} +(-0.866025 - 0.500000i) q^{7} +1.00000i q^{8} +(-0.500000 - 0.866025i) q^{10} +(-0.633975 + 0.366025i) q^{11} +(2.59808 + 2.50000i) q^{13} +1.00000 q^{14} +(-0.500000 - 0.866025i) q^{16} +(2.86603 - 4.96410i) q^{17} +(-1.26795 - 0.732051i) q^{19} +(0.866025 + 0.500000i) q^{20} +(0.366025 - 0.633975i) q^{22} +(-0.633975 - 1.09808i) q^{23} +4.00000 q^{25} +(-3.50000 - 0.866025i) q^{26} +(-0.866025 + 0.500000i) q^{28} +(-1.50000 - 2.59808i) q^{29} +5.26795i q^{31} +(0.866025 + 0.500000i) q^{32} +5.73205i q^{34} +(0.500000 - 0.866025i) q^{35} +(4.50000 - 2.59808i) q^{37} +1.46410 q^{38} -1.00000 q^{40} +(2.13397 - 1.23205i) q^{41} +(-6.09808 + 10.5622i) q^{43} +0.732051i q^{44} +(1.09808 + 0.633975i) q^{46} +2.92820i q^{47} +(0.500000 + 0.866025i) q^{49} +(-3.46410 + 2.00000i) q^{50} +(3.46410 - 1.00000i) q^{52} -1.53590 q^{53} +(-0.366025 - 0.633975i) q^{55} +(0.500000 - 0.866025i) q^{56} +(2.59808 + 1.50000i) q^{58} +(9.29423 + 5.36603i) q^{59} +(5.86603 - 10.1603i) q^{61} +(-2.63397 - 4.56218i) q^{62} -1.00000 q^{64} +(-2.50000 + 2.59808i) q^{65} +(10.0981 - 5.83013i) q^{67} +(-2.86603 - 4.96410i) q^{68} +1.00000i q^{70} +(12.0000 + 6.92820i) q^{71} +11.3923i q^{73} +(-2.59808 + 4.50000i) q^{74} +(-1.26795 + 0.732051i) q^{76} +0.732051 q^{77} -3.80385 q^{79} +(0.866025 - 0.500000i) q^{80} +(-1.23205 + 2.13397i) q^{82} +3.80385i q^{83} +(4.96410 + 2.86603i) q^{85} -12.1962i q^{86} +(-0.366025 - 0.633975i) q^{88} +(-2.19615 + 1.26795i) q^{89} +(-1.00000 - 3.46410i) q^{91} -1.26795 q^{92} +(-1.46410 - 2.53590i) q^{94} +(0.732051 - 1.26795i) q^{95} +(-4.73205 - 2.73205i) q^{97} +(-0.866025 - 0.500000i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{4}+O(q^{10}) $ 4 * q + 2 * q^4	$ 4 q + 2 q^{4} - 2 q^{10} - 6 q^{11} + 4 q^{14} - 2 q^{16} + 8 q^{17} - 12 q^{19} - 2 q^{22} - 6 q^{23} + 16 q^{25} - 14 q^{26} - 6 q^{29} + 2 q^{35} + 18 q^{37} - 8 q^{38} - 4 q^{40} + 12 q^{41} - 14 q^{43} - 6 q^{46} + 2 q^{49} - 20 q^{53} + 2 q^{55} + 2 q^{56} + 6 q^{59} + 20 q^{61} - 14 q^{62} - 4 q^{64} - 10 q^{65} + 30 q^{67} - 8 q^{68} + 48 q^{71} - 12 q^{76} - 4 q^{77} - 36 q^{79} + 2 q^{82} + 6 q^{85} + 2 q^{88} + 12 q^{89} - 4 q^{91} - 12 q^{92} + 8 q^{94} - 4 q^{95} - 12 q^{97}+O(q^{100}) $ 4 * q + 2 * q^4 - 2 * q^10 - 6 * q^11 + 4 * q^14 - 2 * q^16 + 8 * q^17 - 12 * q^19 - 2 * q^22 - 6 * q^23 + 16 * q^25 - 14 * q^26 - 6 * q^29 + 2 * q^35 + 18 * q^37 - 8 * q^38 - 4 * q^40 + 12 * q^41 - 14 * q^43 - 6 * q^46 + 2 * q^49 - 20 * q^53 + 2 * q^55 + 2 * q^56 + 6 * q^59 + 20 * q^61 - 14 * q^62 - 4 * q^64 - 10 * q^65 + 30 * q^67 - 8 * q^68 + 48 * q^71 - 12 * q^76 - 4 * q^77 - 36 * q^79 + 2 * q^82 + 6 * q^85 + 2 * q^88 + 12 * q^89 - 4 * q^91 - 12 * q^92 + 8 * q^94 - 4 * q^95 - 12 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1638\mathbb{Z}\right)^\times$.

$n$	$379$	$703$	$911$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$			1.00000i			0.447214i	0.974679	+	0.223607i	$0.0717831\pi$
$5$			1.00000i			0.447214i	−0.974679	+	0.223607i	$0.928217\pi$
$6$		0			0
$7$	−0.866025	−	0.500000i	−0.327327	−	0.188982i
$7$	−0.866025	−	0.500000i	−0.327327	−	0.188982i
$8$			1.00000i			0.353553i
$9$		0			0
$10$	−0.500000	−	0.866025i	−0.158114	−	0.273861i
$11$	−0.633975	+	0.366025i	−0.191151	+	0.110361i	−0.592521	−	0.805555i	$-0.701867\pi$
$11$	−0.633975	+	0.366025i	−0.191151	+	0.110361i	0.401371	+	0.915916i	$0.368534\pi$
$12$		0			0
$13$	2.59808	+	2.50000i	0.720577	+	0.693375i
$13$	2.59808	+	2.50000i	0.720577	+	0.693375i
$14$	1.00000			0.267261
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	2.86603	−	4.96410i	0.695113	−	1.20397i	−0.275029	−	0.961436i	$-0.588688\pi$
$17$	2.86603	−	4.96410i	0.695113	−	1.20397i	0.970143	−	0.242536i	$-0.0779791\pi$
$18$		0			0
$19$	−1.26795	−	0.732051i	−0.290887	−	0.167944i	0.347455	−	0.937697i	$-0.387046\pi$
$19$	−1.26795	−	0.732051i	−0.290887	−	0.167944i	−0.638342	+	0.769753i	$0.720379\pi$
$20$	0.866025	+	0.500000i	0.193649	+	0.111803i
$21$		0			0
$22$	0.366025	−	0.633975i	0.0780369	−	0.135164i
$23$	−0.633975	−	1.09808i	−0.132193	−	0.228965i	0.792329	−	0.610094i	$-0.208868\pi$
$23$	−0.633975	−	1.09808i	−0.132193	−	0.228965i	−0.924522	+	0.381130i	$0.875535\pi$
$24$		0			0
$25$	4.00000			0.800000
$26$	−3.50000	−	0.866025i	−0.686406	−	0.169842i
$27$		0			0
$28$	−0.866025	+	0.500000i	−0.163663	+	0.0944911i
$29$	−1.50000	−	2.59808i	−0.278543	−	0.482451i	0.692480	−	0.721437i	$-0.256518\pi$
$29$	−1.50000	−	2.59808i	−0.278543	−	0.482451i	−0.971023	+	0.238987i	$0.923185\pi$
$30$		0			0
$31$			5.26795i			0.946152i	0.881022	+	0.473076i	$0.156856\pi$
$31$			5.26795i			0.946152i	−0.881022	+	0.473076i	$0.843144\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$		0			0
$34$			5.73205i			0.983039i
$35$	0.500000	−	0.866025i	0.0845154	−	0.146385i
$36$		0			0
$37$	4.50000	−	2.59808i	0.739795	−	0.427121i	−0.0821995	−	0.996616i	$-0.526194\pi$
$37$	4.50000	−	2.59808i	0.739795	−	0.427121i	0.821995	+	0.569495i	$0.192861\pi$
$38$	1.46410			0.237509
$39$		0			0
$40$	−1.00000			−0.158114
$41$	2.13397	−	1.23205i	0.333271	−	0.192414i	−0.324021	−	0.946050i	$-0.605035\pi$
$41$	2.13397	−	1.23205i	0.333271	−	0.192414i	0.657292	+	0.753636i	$0.271702\pi$
$42$		0			0
$43$	−6.09808	+	10.5622i	−0.929948	+	1.61072i	−0.146544	+	0.989204i	$0.546815\pi$
$43$	−6.09808	+	10.5622i	−0.929948	+	1.61072i	−0.783404	+	0.621513i	$0.786518\pi$
$44$			0.732051i			0.110361i
$45$		0			0
$46$	1.09808	+	0.633975i	0.161903	+	0.0934745i
$47$			2.92820i			0.427122i	0.976930	+	0.213561i	$0.0685063\pi$
$47$			2.92820i			0.427122i	−0.976930	+	0.213561i	$0.931494\pi$
$48$		0			0
$49$	0.500000	+	0.866025i	0.0714286	+	0.123718i
$50$	−3.46410	+	2.00000i	−0.489898	+	0.282843i
$51$		0			0
$52$	3.46410	−	1.00000i	0.480384	−	0.138675i
$53$	−1.53590			−0.210972			−0.105486	−	0.994421i	$-0.533640\pi$
$53$	−1.53590			−0.210972			−0.105486	+	0.994421i	$0.533640\pi$
$54$		0			0
$55$	−0.366025	−	0.633975i	−0.0493549	−	0.0854851i
$56$	0.500000	−	0.866025i	0.0668153	−	0.115728i
$57$		0			0
$58$	2.59808	+	1.50000i	0.341144	+	0.196960i
$59$	9.29423	+	5.36603i	1.21001	+	0.698597i	0.962760	−	0.270356i	$-0.0871414\pi$
$59$	9.29423	+	5.36603i	1.21001	+	0.698597i	0.247245	+	0.968953i	$0.420475\pi$
$60$		0			0
$61$	5.86603	−	10.1603i	0.751068	−	1.30089i	−0.196238	−	0.980556i	$-0.562873\pi$
$61$	5.86603	−	10.1603i	0.751068	−	1.30089i	0.947306	−	0.320331i	$-0.103794\pi$
$62$	−2.63397	−	4.56218i	−0.334515	−	0.579397i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−2.50000	+	2.59808i	−0.310087	+	0.322252i
$66$		0			0
$67$	10.0981	−	5.83013i	1.23368	−	0.712263i	0.265882	−	0.964006i	$-0.414337\pi$
$67$	10.0981	−	5.83013i	1.23368	−	0.712263i	0.967794	+	0.251742i	$0.0810035\pi$
$68$	−2.86603	−	4.96410i	−0.347557	−	0.601986i
$69$		0			0
$70$			1.00000i			0.119523i
$71$	12.0000	+	6.92820i	1.42414	+	0.822226i	0.996649	−	0.0817942i	$-0.0260650\pi$
$71$	12.0000	+	6.92820i	1.42414	+	0.822226i	0.427489	+	0.904021i	$0.359398\pi$
$72$		0			0
$73$			11.3923i			1.33337i	0.745340	+	0.666684i	$0.232287\pi$
$73$			11.3923i			1.33337i	−0.745340	+	0.666684i	$0.767713\pi$
$74$	−2.59808	+	4.50000i	−0.302020	+	0.523114i
$75$		0			0
$76$	−1.26795	+	0.732051i	−0.145444	+	0.0839720i
$77$	0.732051			0.0834249
$78$		0			0
$79$	−3.80385			−0.427966			−0.213983	−	0.976837i	$-0.568644\pi$
$79$	−3.80385			−0.427966			−0.213983	+	0.976837i	$0.568644\pi$
$80$	0.866025	−	0.500000i	0.0968246	−	0.0559017i
$81$		0			0
$82$	−1.23205	+	2.13397i	−0.136057	+	0.235658i
$83$			3.80385i			0.417527i	0.977966	+	0.208763i	$0.0669438\pi$
$83$			3.80385i			0.417527i	−0.977966	+	0.208763i	$0.933056\pi$
$84$		0			0
$85$	4.96410	+	2.86603i	0.538432	+	0.310864i
$86$		−	12.1962i		−	1.31514i
$87$		0			0
$88$	−0.366025	−	0.633975i	−0.0390184	−	0.0675819i
$89$	−2.19615	+	1.26795i	−0.232792	+	0.134402i	−0.611859	−	0.790967i	$-0.709578\pi$
$89$	−2.19615	+	1.26795i	−0.232792	+	0.134402i	0.379068	+	0.925369i	$0.376245\pi$
$90$		0			0
$91$	−1.00000	−	3.46410i	−0.104828	−	0.363137i
$92$	−1.26795			−0.132193
$93$		0			0
$94$	−1.46410	−	2.53590i	−0.151011	−	0.261558i
$95$	0.732051	−	1.26795i	0.0751068	−	0.130089i
$96$		0			0
$97$	−4.73205	−	2.73205i	−0.480467	−	0.277398i	0.240144	−	0.970737i	$-0.422805\pi$
$97$	−4.73205	−	2.73205i	−0.480467	−	0.277398i	−0.720611	+	0.693340i	$0.756139\pi$
$98$	−0.866025	−	0.500000i	−0.0874818	−	0.0505076i
$99$		0			0
$100$	2.00000	−	3.46410i	0.200000	−	0.346410i
$101$	−0.598076	−	1.03590i	−0.0595108	−	0.103076i	0.834735	−	0.550652i	$-0.185621\pi$
$101$	−0.598076	−	1.03590i	−0.0595108	−	0.103076i	−0.894246	+	0.447576i	$0.852287\pi$
$102$		0			0
$103$	8.39230			0.826918			0.413459	−	0.910523i	$-0.364320\pi$
$103$	8.39230			0.826918			0.413459	+	0.910523i	$0.364320\pi$
$104$	−2.50000	+	2.59808i	−0.245145	+	0.254762i
$105$		0			0
$106$	1.33013	−	0.767949i	0.129193	−	0.0745898i
$107$	5.46410	+	9.46410i	0.528235	+	0.914929i	0.999458	+	0.0329154i	$0.0104792\pi$
$107$	5.46410	+	9.46410i	0.528235	+	0.914929i	−0.471224	+	0.882014i	$0.656187\pi$
$108$		0			0
$109$		−	10.0000i		−	0.957826i	−0.877862	−	0.478913i	$-0.841031\pi$
$109$		−	10.0000i		−	0.957826i	0.877862	−	0.478913i	$-0.158969\pi$
$110$	0.633975	+	0.366025i	0.0604471	+	0.0348992i
$111$		0			0
$112$			1.00000i			0.0944911i
$113$	5.69615	−	9.86603i	0.535849	−	0.928118i	−0.463273	−	0.886216i	$-0.653325\pi$
$113$	5.69615	−	9.86603i	0.535849	−	0.928118i	0.999122	−	0.0419019i	$-0.0133417\pi$
$114$		0			0
$115$	1.09808	−	0.633975i	0.102396	−	0.0591184i
$116$	−3.00000			−0.278543
$117$		0			0
$118$	−10.7321			−0.987965
$119$	−4.96410	+	2.86603i	−0.455058	+	0.262728i
$120$		0			0
$121$	−5.23205	+	9.06218i	−0.475641	+	0.823834i
$122$			11.7321i			1.06217i
$123$		0			0
$124$	4.56218	+	2.63397i	0.409696	+	0.236538i
$125$			9.00000i			0.804984i
$126$		0			0
$127$	4.92820	+	8.53590i	0.437307	+	0.757438i	0.997481	−	0.0709368i	$-0.0225989\pi$
$127$	4.92820	+	8.53590i	0.437307	+	0.757438i	−0.560173	+	0.828375i	$0.689266\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$		0			0
$130$	0.866025	−	3.50000i	0.0759555	−	0.306970i
$131$	5.07180			0.443125			0.221562	−	0.975146i	$-0.428884\pi$
$131$	5.07180			0.443125			0.221562	+	0.975146i	$0.428884\pi$
$132$		0			0
$133$	0.732051	+	1.26795i	0.0634769	+	0.109945i
$134$	−5.83013	+	10.0981i	−0.503646	+	0.872341i
$135$		0			0
$136$	4.96410	+	2.86603i	0.425668	+	0.245760i
$137$	5.30385	+	3.06218i	0.453138	+	0.261620i	0.709155	−	0.705053i	$-0.249077\pi$
$137$	5.30385	+	3.06218i	0.453138	+	0.261620i	−0.256016	+	0.966672i	$0.582410\pi$
$138$		0			0
$139$	0.169873	−	0.294229i	0.0144084	−	0.0249561i	−0.858731	−	0.512426i	$-0.828747\pi$
$139$	0.169873	−	0.294229i	0.0144084	−	0.0249561i	0.873140	+	0.487470i	$0.162080\pi$
$140$	−0.500000	−	0.866025i	−0.0422577	−	0.0731925i
$141$		0			0
$142$	−13.8564			−1.16280
$143$	−2.56218	−	0.633975i	−0.214260	−	0.0530156i
$144$		0			0
$145$	2.59808	−	1.50000i	0.215758	−	0.124568i
$146$	−5.69615	−	9.86603i	−0.471417	−	0.816518i
$147$		0			0
$148$		−	5.19615i		−	0.427121i
$149$	14.8923	+	8.59808i	1.22003	+	0.704382i	0.964923	−	0.262532i	$-0.0845576\pi$
$149$	14.8923	+	8.59808i	1.22003	+	0.704382i	0.255102	+	0.966914i	$0.417891\pi$
$150$		0			0
$151$			12.3923i			1.00847i	0.863566	+	0.504236i	$0.168226\pi$
$151$			12.3923i			1.00847i	−0.863566	+	0.504236i	$0.831774\pi$
$152$	0.732051	−	1.26795i	0.0593772	−	0.102844i
$153$		0			0
$154$	−0.633975	+	0.366025i	−0.0510871	+	0.0294952i
$155$	−5.26795			−0.423132
$156$		0			0
$157$	13.7321			1.09594			0.547968	−	0.836499i	$-0.315401\pi$
$157$	13.7321			1.09594			0.547968	+	0.836499i	$0.315401\pi$
$158$	3.29423	−	1.90192i	0.262075	−	0.151309i
$159$		0			0
$160$	−0.500000	+	0.866025i	−0.0395285	+	0.0684653i
$161$			1.26795i			0.0999284i
$162$		0			0
$163$	−0.633975	−	0.366025i	−0.0496567	−	0.0286693i	0.474966	−	0.880004i	$-0.342460\pi$
$163$	−0.633975	−	0.366025i	−0.0496567	−	0.0286693i	−0.524623	+	0.851335i	$0.675794\pi$
$164$		−	2.46410i		−	0.192414i
$165$		0			0
$166$	−1.90192	−	3.29423i	−0.147618	−	0.255682i
$167$	4.56218	−	2.63397i	0.353032	−	0.203823i	−0.312988	−	0.949757i	$-0.601330\pi$
$167$	4.56218	−	2.63397i	0.353032	−	0.203823i	0.666020	+	0.745934i	$0.267997\pi$
$168$		0			0
$169$	0.500000	+	12.9904i	0.0384615	+	0.999260i
$170$	−5.73205			−0.439628
$171$		0			0
$172$	6.09808	+	10.5622i	0.464974	+	0.805359i
$173$	10.4641	−	18.1244i	0.795571	−	1.37797i	−0.126905	−	0.991915i	$-0.540504\pi$
$173$	10.4641	−	18.1244i	0.795571	−	1.37797i	0.922476	−	0.386054i	$-0.126162\pi$
$174$		0			0
$175$	−3.46410	−	2.00000i	−0.261861	−	0.151186i
$176$	0.633975	+	0.366025i	0.0477876	+	0.0275902i
$177$		0			0
$178$	1.26795	−	2.19615i	0.0950368	−	0.164609i
$179$	−8.19615	−	14.1962i	−0.612609	−	1.06107i	−0.990799	−	0.135342i	$-0.956787\pi$
$179$	−8.19615	−	14.1962i	−0.612609	−	1.06107i	0.378190	−	0.925728i	$-0.376547\pi$
$180$		0			0
$181$	3.19615			0.237568			0.118784	−	0.992920i	$-0.462100\pi$
$181$	3.19615			0.237568			0.118784	+	0.992920i	$0.462100\pi$
$182$	2.59808	+	2.50000i	0.192582	+	0.185312i
$183$		0			0
$184$	1.09808	−	0.633975i	0.0809513	−	0.0467372i
$185$	2.59808	+	4.50000i	0.191014	+	0.330847i
$186$		0			0
$187$			4.19615i			0.306853i
$188$	2.53590	+	1.46410i	0.184949	+	0.106781i
$189$		0			0
$190$			1.46410i			0.106217i
$191$	3.56218	−	6.16987i	0.257750	−	0.446436i	−0.707889	−	0.706324i	$-0.750352\pi$
$191$	3.56218	−	6.16987i	0.257750	−	0.446436i	0.965639	+	0.259888i	$0.0836855\pi$
$192$		0			0
$193$	−20.0885	+	11.5981i	−1.44600	+	0.834848i	−0.998240	−	0.0593065i	$-0.981111\pi$
$193$	−20.0885	+	11.5981i	−1.44600	+	0.834848i	−0.447759	+	0.894154i	$0.647778\pi$
$194$	5.46410			0.392300
$195$		0			0
$196$	1.00000			0.0714286
$197$	−6.12436	+	3.53590i	−0.436342	+	0.251922i	−0.702045	−	0.712133i	$-0.747729\pi$
$197$	−6.12436	+	3.53590i	−0.436342	+	0.251922i	0.265703	+	0.964055i	$0.414396\pi$
$198$		0			0
$199$	−2.73205	+	4.73205i	−0.193670	+	0.335446i	−0.946464	−	0.322810i	$-0.895372\pi$
$199$	−2.73205	+	4.73205i	−0.193670	+	0.335446i	0.752794	+	0.658256i	$0.228706\pi$
$200$			4.00000i			0.282843i
$201$		0			0
$202$	1.03590	+	0.598076i	0.0728856	+	0.0420805i
$203$			3.00000i			0.210559i
$204$		0			0
$205$	1.23205	+	2.13397i	0.0860502	+	0.149043i
$206$	−7.26795	+	4.19615i	−0.506382	+	0.292360i
$207$		0			0
$208$	0.866025	−	3.50000i	0.0600481	−	0.242681i
$209$	1.07180			0.0741377
$210$		0			0
$211$	10.6340	+	18.4186i	0.732073	+	1.26799i	0.955996	+	0.293381i	$0.0947804\pi$
$211$	10.6340	+	18.4186i	0.732073	+	1.26799i	−0.223923	+	0.974607i	$0.571886\pi$
$212$	−0.767949	+	1.33013i	−0.0527430	+	0.0913535i
$213$		0			0
$214$	−9.46410	−	5.46410i	−0.646953	−	0.373518i
$215$	−10.5622	−	6.09808i	−0.720335	−	0.415885i
$216$		0			0
$217$	2.63397	−	4.56218i	0.178806	−	0.309701i
$218$	5.00000	+	8.66025i	0.338643	+	0.586546i
$219$		0			0
$220$	−0.732051			−0.0493549
$221$	19.8564	−	5.73205i	1.33569	−	0.385579i
$222$		0			0
$223$	10.7321	−	6.19615i	0.718671	−	0.414925i	−0.0955922	−	0.995421i	$-0.530474\pi$
$223$	10.7321	−	6.19615i	0.718671	−	0.414925i	0.814263	+	0.580496i	$0.197141\pi$
$224$	−0.500000	−	0.866025i	−0.0334077	−	0.0578638i
$225$		0			0
$226$			11.3923i			0.757805i
$227$	−1.09808	−	0.633975i	−0.0728819	−	0.0420784i	0.463116	−	0.886298i	$-0.346731\pi$
$227$	−1.09808	−	0.633975i	−0.0728819	−	0.0420784i	−0.535998	+	0.844219i	$0.680065\pi$
$228$		0			0
$229$		−	24.3923i		−	1.61189i	−0.591991	−	0.805944i	$-0.701658\pi$
$229$		−	24.3923i		−	1.61189i	0.591991	−	0.805944i	$-0.298342\pi$
$230$	−0.633975	+	1.09808i	−0.0418030	+	0.0724050i
$231$		0			0
$232$	2.59808	−	1.50000i	0.170572	−	0.0984798i
$233$	−4.39230			−0.287749			−0.143875	−	0.989596i	$-0.545956\pi$
$233$	−4.39230			−0.287749			−0.143875	+	0.989596i	$0.545956\pi$
$234$		0			0
$235$	−2.92820			−0.191015
$236$	9.29423	−	5.36603i	0.605003	−	0.349299i
$237$		0			0
$238$	2.86603	−	4.96410i	0.185777	−	0.321775i
$239$			29.5167i			1.90927i	0.297772	+	0.954637i	$0.403756\pi$
$239$			29.5167i			1.90927i	−0.297772	+	0.954637i	$0.596244\pi$
$240$		0			0
$241$	−13.3301	−	7.69615i	−0.858669	−	0.495753i	0.00489737	−	0.999988i	$-0.498441\pi$
$241$	−13.3301	−	7.69615i	−0.858669	−	0.495753i	−0.863566	+	0.504235i	$0.831774\pi$
$242$		−	10.4641i		−	0.672658i
$243$		0			0
$244$	−5.86603	−	10.1603i	−0.375534	−	0.650444i
$245$	−0.866025	+	0.500000i	−0.0553283	+	0.0319438i
$246$		0			0
$247$	−1.46410	−	5.07180i	−0.0931586	−	0.322711i
$248$	−5.26795			−0.334515
$249$		0			0
$250$	−4.50000	−	7.79423i	−0.284605	−	0.492950i
$251$	−11.4641	+	19.8564i	−0.723608	+	1.25333i	0.235937	+	0.971768i	$0.424184\pi$
$251$	−11.4641	+	19.8564i	−0.723608	+	1.25333i	−0.959545	+	0.281557i	$0.909149\pi$
$252$		0			0
$253$	0.803848	+	0.464102i	0.0505375	+	0.0291778i
$254$	−8.53590	−	4.92820i	−0.535590	−	0.309223i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−0.669873	−	1.16025i	−0.0417855	−	0.0723747i	0.844376	−	0.535751i	$-0.179971\pi$
$257$	−0.669873	−	1.16025i	−0.0417855	−	0.0723747i	−0.886162	+	0.463376i	$0.846638\pi$
$258$		0			0
$259$	−5.19615			−0.322873
$260$	1.00000	+	3.46410i	0.0620174	+	0.214834i
$261$		0			0
$262$	−4.39230	+	2.53590i	−0.271357	+	0.156668i
$263$	−10.2942	−	17.8301i	−0.634769	−	1.09945i	−0.986564	−	0.163376i	$-0.947762\pi$
$263$	−10.2942	−	17.8301i	−0.634769	−	1.09945i	0.351795	−	0.936077i	$-0.385572\pi$
$264$		0			0
$265$		−	1.53590i		−	0.0943495i
$266$	−1.26795	−	0.732051i	−0.0777430	−	0.0448849i
$267$		0			0
$268$		−	11.6603i		−	0.712263i
$269$	−14.3923	+	24.9282i	−0.877514	+	1.51990i	−0.0234543	+	0.999725i	$0.507466\pi$
$269$	−14.3923	+	24.9282i	−0.877514	+	1.51990i	−0.854060	+	0.520174i	$0.825867\pi$
$270$		0			0
$271$	6.16987	−	3.56218i	0.374793	−	0.216387i	−0.300757	−	0.953701i	$-0.597239\pi$
$271$	6.16987	−	3.56218i	0.374793	−	0.216387i	0.675550	+	0.737314i	$0.263906\pi$
$272$	−5.73205			−0.347557
$273$		0			0
$274$	−6.12436			−0.369986
$275$	−2.53590	+	1.46410i	−0.152920	+	0.0882886i
$276$		0			0
$277$	4.69615	−	8.13397i	0.282164	−	0.488723i	−0.689753	−	0.724045i	$-0.742281\pi$
$277$	4.69615	−	8.13397i	0.282164	−	0.488723i	0.971918	+	0.235321i	$0.0756143\pi$
$278$			0.339746i			0.0203766i
$279$		0			0
$280$	0.866025	+	0.500000i	0.0517549	+	0.0298807i
$281$			16.6603i			0.993867i	0.867789	+	0.496934i	$0.165541\pi$
$281$			16.6603i			0.993867i	−0.867789	+	0.496934i	$0.834459\pi$
$282$		0			0
$283$	−5.29423	−	9.16987i	−0.314709	−	0.545092i	0.664666	−	0.747140i	$-0.268574\pi$
$283$	−5.29423	−	9.16987i	−0.314709	−	0.545092i	−0.979376	+	0.202048i	$0.935240\pi$
$284$	12.0000	−	6.92820i	0.712069	−	0.411113i
$285$		0			0
$286$	2.53590	−	0.732051i	0.149951	−	0.0432871i
$287$	−2.46410			−0.145451
$288$		0			0
$289$	−7.92820	−	13.7321i	−0.466365	−	0.807768i
$290$	−1.50000	+	2.59808i	−0.0880830	+	0.152564i
$291$		0			0
$292$	9.86603	+	5.69615i	0.577365	+	0.333342i
$293$	−15.0622	−	8.69615i	−0.879942	−	0.508035i	−0.00930260	−	0.999957i	$-0.502961\pi$
$293$	−15.0622	−	8.69615i	−0.879942	−	0.508035i	−0.870639	+	0.491922i	$0.836294\pi$
$294$		0			0
$295$	−5.36603	+	9.29423i	−0.312422	+	0.541131i
$296$	2.59808	+	4.50000i	0.151010	+	0.261557i
$297$		0			0
$298$	−17.1962			−0.996146
$299$	1.09808	−	4.43782i	0.0635034	−	0.256646i
$300$		0			0
$301$	10.5622	−	6.09808i	0.608794	−	0.351487i
$302$	−6.19615	−	10.7321i	−0.356549	−	0.617560i
$303$		0			0
$304$			1.46410i			0.0839720i
$305$	10.1603	+	5.86603i	0.581774	+	0.335888i
$306$		0			0
$307$		−	23.5167i		−	1.34217i	−0.741382	−	0.671083i	$-0.765829\pi$
$307$		−	23.5167i		−	1.34217i	0.741382	−	0.671083i	$-0.234171\pi$
$308$	0.366025	−	0.633975i	0.0208562	−	0.0361241i
$309$		0			0
$310$	4.56218	−	2.63397i	0.259114	−	0.149600i
$311$	−10.1962			−0.578171			−0.289085	−	0.957303i	$-0.593351\pi$
$311$	−10.1962			−0.578171			−0.289085	+	0.957303i	$0.593351\pi$
$312$		0			0
$313$	−32.0000			−1.80875			−0.904373	−	0.426742i	$-0.859661\pi$
$313$	−32.0000			−1.80875			−0.904373	+	0.426742i	$0.859661\pi$
$314$	−11.8923	+	6.86603i	−0.671122	+	0.387472i
$315$		0			0
$316$	−1.90192	+	3.29423i	−0.106992	+	0.185315i
$317$		−	7.05256i		−	0.396111i	−0.980191	−	0.198056i	$-0.936537\pi$
$317$		−	7.05256i		−	0.396111i	0.980191	−	0.198056i	$-0.0634627\pi$
$318$		0			0
$319$	1.90192	+	1.09808i	0.106487	+	0.0614805i
$320$		−	1.00000i		−	0.0559017i
$321$		0			0
$322$	−0.633975	−	1.09808i	−0.0353300	−	0.0611934i
$323$	−7.26795	+	4.19615i	−0.404400	+	0.233480i
$324$		0			0
$325$	10.3923	+	10.0000i	0.576461	+	0.554700i
$326$	0.732051			0.0405445
$327$		0			0
$328$	1.23205	+	2.13397i	0.0680286	+	0.117829i
$329$	1.46410	−	2.53590i	0.0807185	−	0.139809i
$330$		0			0
$331$	3.75833	+	2.16987i	0.206577	+	0.119267i	0.599719	−	0.800210i	$-0.295279\pi$
$331$	3.75833	+	2.16987i	0.206577	+	0.119267i	−0.393143	+	0.919477i	$0.628612\pi$
$332$	3.29423	+	1.90192i	0.180794	+	0.104382i
$333$		0			0
$334$	−2.63397	+	4.56218i	−0.144125	+	0.249631i
$335$	5.83013	+	10.0981i	0.318534	+	0.551717i
$336$		0			0
$337$	−6.32051			−0.344300			−0.172150	−	0.985071i	$-0.555071\pi$
$337$	−6.32051			−0.344300			−0.172150	+	0.985071i	$0.555071\pi$
$338$	−6.92820	−	11.0000i	−0.376845	−	0.598321i
$339$		0			0
$340$	4.96410	−	2.86603i	0.269216	−	0.155432i
$341$	−1.92820	−	3.33975i	−0.104418	−	0.180857i
$342$		0			0
$343$		−	1.00000i		−	0.0539949i
$344$	−10.5622	−	6.09808i	−0.569474	−	0.328786i
$345$		0			0
$346$			20.9282i			1.12511i
$347$	14.4904	−	25.0981i	0.777884	−	1.34734i	−0.155275	−	0.987871i	$-0.549626\pi$
$347$	14.4904	−	25.0981i	0.777884	−	1.34734i	0.933159	−	0.359464i	$-0.117040\pi$
$348$		0			0
$349$	−1.73205	+	1.00000i	−0.0927146	+	0.0535288i	−0.545640	−	0.838019i	$-0.683714\pi$
$349$	−1.73205	+	1.00000i	−0.0927146	+	0.0535288i	0.452926	+	0.891548i	$0.350380\pi$
$350$	4.00000			0.213809
$351$		0			0
$352$	−0.732051			−0.0390184
$353$	31.3301	−	18.0885i	1.66753	−	0.962751i	0.698573	−	0.715539i	$-0.253819\pi$
$353$	31.3301	−	18.0885i	1.66753	−	0.962751i	0.968961	−	0.247213i	$-0.0795147\pi$
$354$		0			0
$355$	−6.92820	+	12.0000i	−0.367711	+	0.636894i
$356$			2.53590i			0.134402i
$357$		0			0
$358$	14.1962	+	8.19615i	0.750290	+	0.433180i
$359$		−	16.3923i		−	0.865153i	−0.901597	−	0.432576i	$-0.857605\pi$
$359$		−	16.3923i		−	0.865153i	0.901597	−	0.432576i	$-0.142395\pi$
$360$		0			0
$361$	−8.42820	−	14.5981i	−0.443590	−	0.768320i
$362$	−2.76795	+	1.59808i	−0.145480	+	0.0839930i
$363$		0			0
$364$	−3.50000	−	0.866025i	−0.183450	−	0.0453921i
$365$	−11.3923			−0.596300
$366$		0			0
$367$	−16.9545	−	29.3660i	−0.885017	−	1.53289i	−0.845694	−	0.533667i	$-0.820813\pi$
$367$	−16.9545	−	29.3660i	−0.885017	−	1.53289i	−0.0393224	−	0.999227i	$-0.512520\pi$
$368$	−0.633975	+	1.09808i	−0.0330482	+	0.0572412i
$369$		0			0
$370$	−4.50000	−	2.59808i	−0.233944	−	0.135068i
$371$	1.33013	+	0.767949i	0.0690568	+	0.0398699i
$372$		0			0
$373$	16.2321	−	28.1147i	0.840464	−	1.45573i	−0.0490394	−	0.998797i	$-0.515616\pi$
$373$	16.2321	−	28.1147i	0.840464	−	1.45573i	0.889503	−	0.456929i	$-0.151051\pi$
$374$	−2.09808	−	3.63397i	−0.108489	−	0.187908i
$375$		0			0
$376$	−2.92820			−0.151011
$377$	2.59808	−	10.5000i	0.133808	−	0.540778i
$378$		0			0
$379$	19.2224	−	11.0981i	0.987390	−	0.570070i	0.0828969	−	0.996558i	$-0.473583\pi$
$379$	19.2224	−	11.0981i	0.987390	−	0.570070i	0.904493	+	0.426488i	$0.140249\pi$
$380$	−0.732051	−	1.26795i	−0.0375534	−	0.0650444i
$381$		0			0
$382$			7.12436i			0.364514i
$383$	−28.2224	−	16.2942i	−1.44210	−	0.832596i	−0.444109	−	0.895973i	$-0.646480\pi$
$383$	−28.2224	−	16.2942i	−1.44210	−	0.832596i	−0.997990	+	0.0633765i	$0.979813\pi$
$384$		0			0
$385$			0.732051i			0.0373088i
$386$	11.5981	−	20.0885i	0.590327	−	1.02248i
$387$		0			0
$388$	−4.73205	+	2.73205i	−0.240233	+	0.138699i
$389$	24.3205			1.23310			0.616549	−	0.787316i	$-0.288530\pi$
$389$	24.3205			1.23310			0.616549	+	0.787316i	$0.288530\pi$
$390$		0			0
$391$	−7.26795			−0.367556
$392$	−0.866025	+	0.500000i	−0.0437409	+	0.0252538i
$393$		0			0
$394$	3.53590	−	6.12436i	0.178136	−	0.308541i
$395$		−	3.80385i		−	0.191392i
$396$		0			0
$397$	−25.5167	−	14.7321i	−1.28064	−	0.739380i	−0.303678	−	0.952775i	$-0.598215\pi$
$397$	−25.5167	−	14.7321i	−1.28064	−	0.739380i	−0.976966	+	0.213394i	$0.931548\pi$
$398$		−	5.46410i		−	0.273891i
$399$		0			0
$400$	−2.00000	−	3.46410i	−0.100000	−	0.173205i
$401$	28.6244	−	16.5263i	1.42943	−	0.825283i	0.432356	−	0.901703i	$-0.357682\pi$
$401$	28.6244	−	16.5263i	1.42943	−	0.825283i	0.997076	+	0.0764198i	$0.0243489\pi$
$402$		0			0
$403$	−13.1699	+	13.6865i	−0.656038	+	0.681775i
$404$	−1.19615			−0.0595108
$405$		0			0
$406$	−1.50000	−	2.59808i	−0.0744438	−	0.128940i
$407$	−1.90192	+	3.29423i	−0.0942749	+	0.163289i
$408$		0			0
$409$	22.7942	+	13.1603i	1.12710	+	0.650733i	0.943204	−	0.332213i	$-0.107795\pi$
$409$	22.7942	+	13.1603i	1.12710	+	0.650733i	0.183898	+	0.982945i	$0.441129\pi$
$410$	−2.13397	−	1.23205i	−0.105389	−	0.0608467i
$411$		0			0
$412$	4.19615	−	7.26795i	0.206730	−	0.358066i
$413$	−5.36603	−	9.29423i	−0.264045	−	0.457339i
$414$		0			0
$415$	−3.80385			−0.186724
$416$	1.00000	+	3.46410i	0.0490290	+	0.169842i
$417$		0			0
$418$	−0.928203	+	0.535898i	−0.0453999	+	0.0262116i
$419$	2.56218	+	4.43782i	0.125171	+	0.216802i	0.921800	−	0.387667i	$-0.126719\pi$
$419$	2.56218	+	4.43782i	0.125171	+	0.216802i	−0.796629	+	0.604469i	$0.793386\pi$
$420$		0			0
$421$			14.1244i			0.688379i	0.938900	+	0.344189i	$0.111846\pi$
$421$			14.1244i			0.688379i	−0.938900	+	0.344189i	$0.888154\pi$
$422$	−18.4186	−	10.6340i	−0.896603	−	0.517654i
$423$		0			0
$424$		−	1.53590i		−	0.0745898i
$425$	11.4641	−	19.8564i	0.556091	−	0.963177i
$426$		0			0
$427$	−10.1603	+	5.86603i	−0.491689	+	0.283877i
$428$	10.9282			0.528235
$429$		0			0
$430$	12.1962			0.588151
$431$	−22.9808	+	13.2679i	−1.10694	+	0.639095i	−0.938036	−	0.346537i	$-0.887357\pi$
$431$	−22.9808	+	13.2679i	−1.10694	+	0.639095i	−0.168908	+	0.985632i	$0.554024\pi$
$432$		0			0
$433$	10.8660	−	18.8205i	0.522188	−	0.904456i	−0.477479	−	0.878643i	$-0.658449\pi$
$433$	10.8660	−	18.8205i	0.522188	−	0.904456i	0.999667	−	0.0258127i	$-0.00821735\pi$
$434$			5.26795i			0.252870i
$435$		0			0
$436$	−8.66025	−	5.00000i	−0.414751	−	0.239457i
$437$			1.85641i			0.0888040i
$438$		0			0
$439$	−9.63397	−	16.6865i	−0.459805	−	0.796405i	0.539146	−	0.842212i	$-0.318747\pi$
$439$	−9.63397	−	16.6865i	−0.459805	−	0.796405i	−0.998950	+	0.0458077i	$0.985414\pi$
$440$	0.633975	−	0.366025i	0.0302236	−	0.0174496i
$441$		0			0
$442$	−14.3301	+	14.8923i	−0.681615	+	0.708355i
$443$	−35.3205			−1.67813			−0.839064	−	0.544033i	$-0.816897\pi$
$443$	−35.3205			−1.67813			−0.839064	+	0.544033i	$0.816897\pi$
$444$		0			0
$445$	−1.26795	−	2.19615i	−0.0601066	−	0.104108i
$446$	−6.19615	+	10.7321i	−0.293396	+	0.508177i
$447$		0			0
$448$	0.866025	+	0.500000i	0.0409159	+	0.0236228i
$449$	−15.5885	−	9.00000i	−0.735665	−	0.424736i	0.0848262	−	0.996396i	$-0.472967\pi$
$449$	−15.5885	−	9.00000i	−0.735665	−	0.424736i	−0.820491	+	0.571660i	$0.806300\pi$
$450$		0			0
$451$	−0.901924	+	1.56218i	−0.0424699	+	0.0735601i
$452$	−5.69615	−	9.86603i	−0.267924	−	0.464059i
$453$		0			0
$454$	1.26795			0.0595078
$455$	3.46410	−	1.00000i	0.162400	−	0.0468807i
$456$		0			0
$457$	−12.3564	+	7.13397i	−0.578008	+	0.333713i	−0.760341	−	0.649524i	$-0.774968\pi$
$457$	−12.3564	+	7.13397i	−0.578008	+	0.333713i	0.182333	+	0.983237i	$0.441635\pi$
$458$	12.1962	+	21.1244i	0.569889	+	0.987076i
$459$		0			0
$460$		−	1.26795i		−	0.0591184i
$461$	−7.20577	−	4.16025i	−0.335606	−	0.193762i	0.322721	−	0.946494i	$-0.395402\pi$
$461$	−7.20577	−	4.16025i	−0.335606	−	0.193762i	−0.658327	+	0.752732i	$0.728736\pi$
$462$		0			0
$463$		−	3.94744i		−	0.183453i	−0.995784	−	0.0917266i	$-0.970761\pi$
$463$		−	3.94744i		−	0.183453i	0.995784	−	0.0917266i	$-0.0292386\pi$
$464$	−1.50000	+	2.59808i	−0.0696358	+	0.120613i
$465$		0			0
$466$	3.80385	−	2.19615i	0.176210	−	0.101735i
$467$	−24.7321			−1.14446			−0.572231	−	0.820092i	$-0.693922\pi$
$467$	−24.7321			−1.14446			−0.572231	+	0.820092i	$0.693922\pi$
$468$		0			0
$469$	−11.6603			−0.538421
$470$	2.53590	−	1.46410i	0.116972	−	0.0675340i
$471$		0			0
$472$	−5.36603	+	9.29423i	−0.246991	+	0.427802i
$473$		−	8.92820i		−	0.410519i
$474$		0			0
$475$	−5.07180	−	2.92820i	−0.232710	−	0.134355i
$476$			5.73205i			0.262728i
$477$		0			0
$478$	−14.7583	−	25.5622i	−0.675030	−	1.16919i
$479$	−27.8827	+	16.0981i	−1.27399	+	0.735540i	−0.975737	−	0.218946i	$-0.929738\pi$
$479$	−27.8827	+	16.0981i	−1.27399	+	0.735540i	−0.298256	+	0.954486i	$0.596405\pi$
$480$		0			0
$481$	18.1865	+	4.50000i	0.829235	+	0.205182i
$482$	15.3923			0.701100
$483$		0			0
$484$	5.23205	+	9.06218i	0.237820	+	0.411917i
$485$	2.73205	−	4.73205i	0.124056	−	0.214871i
$486$		0			0
$487$	27.1244	+	15.6603i	1.22912	+	0.709634i	0.966846	−	0.255359i	$-0.0821937\pi$
$487$	27.1244	+	15.6603i	1.22912	+	0.709634i	0.262276	+	0.964993i	$0.415527\pi$
$488$	10.1603	+	5.86603i	0.459933	+	0.265542i
$489$		0			0
$490$	0.500000	−	0.866025i	0.0225877	−	0.0391230i
$491$	13.8564	+	24.0000i	0.625331	+	1.08310i	0.988477	+	0.151373i	$0.0483693\pi$
$491$	13.8564	+	24.0000i	0.625331	+	1.08310i	−0.363146	+	0.931732i	$0.618297\pi$
$492$		0			0
$493$	−17.1962			−0.774476
$494$	3.80385	+	3.66025i	0.171143	+	0.164683i
$495$		0			0
$496$	4.56218	−	2.63397i	0.204848	−	0.118269i
$497$	−6.92820	−	12.0000i	−0.310772	−	0.538274i
$498$		0			0
$499$			11.2679i			0.504423i	0.967672	+	0.252211i	$0.0811578\pi$
$499$			11.2679i			0.504423i	−0.967672	+	0.252211i	$0.918842\pi$
$500$	7.79423	+	4.50000i	0.348569	+	0.201246i
$501$		0			0
$502$		−	22.9282i		−	1.02334i
$503$	10.3660	−	17.9545i	0.462198	−	0.800551i	−0.536872	−	0.843664i	$-0.680394\pi$
$503$	10.3660	−	17.9545i	0.462198	−	0.800551i	0.999070	+	0.0431129i	$0.0137275\pi$
$504$		0			0
$505$	1.03590	−	0.598076i	0.0460969	−	0.0266140i
$506$	−0.928203			−0.0412637
$507$		0			0
$508$	9.85641			0.437307
$509$	23.7224	−	13.6962i	1.05148	−	0.607071i	0.128415	−	0.991720i	$-0.459011\pi$
$509$	23.7224	−	13.6962i	1.05148	−	0.607071i	0.923063	+	0.384649i	$0.125678\pi$
$510$		0			0
$511$	5.69615	−	9.86603i	0.251983	−	0.436447i
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	1.16025	+	0.669873i	0.0511766	+	0.0295468i
$515$			8.39230i			0.369809i
$516$		0			0
$517$	−1.07180	−	1.85641i	−0.0471376	−	0.0816447i
$518$	4.50000	−	2.59808i	0.197719	−	0.114153i
$519$		0			0
$520$	−2.59808	−	2.50000i	−0.113933	−	0.109632i
$521$	−44.3731			−1.94402			−0.972010	−	0.234941i	$-0.924510\pi$
$521$	−44.3731			−1.94402			−0.972010	+	0.234941i	$0.924510\pi$
$522$		0			0
$523$	−10.7321	−	18.5885i	−0.469280	−	0.812816i	0.530103	−	0.847933i	$-0.322153\pi$
$523$	−10.7321	−	18.5885i	−0.469280	−	0.812816i	−0.999383	+	0.0351165i	$0.988820\pi$
$524$	2.53590	−	4.39230i	0.110781	−	0.191879i
$525$		0			0
$526$	17.8301	+	10.2942i	0.777430	+	0.448850i
$527$	26.1506	+	15.0981i	1.13914	+	0.657683i
$528$		0			0
$529$	10.6962	−	18.5263i	0.465050	−	0.805490i
$530$	0.767949	+	1.33013i	0.0333576	+	0.0577770i
$531$		0			0
$532$	1.46410			0.0634769
$533$	8.62436	+	2.13397i	0.373562	+	0.0924327i
$534$		0			0
$535$	−9.46410	+	5.46410i	−0.409169	+	0.236234i
$536$	5.83013	+	10.0981i	0.251823	+	0.436170i
$537$		0			0
$538$		−	28.7846i		−	1.24099i
$539$	−0.633975	−	0.366025i	−0.0273072	−	0.0157658i
$540$		0			0
$541$			8.26795i			0.355467i	0.984079	+	0.177733i	$0.0568765\pi$
$541$			8.26795i			0.355467i	−0.984079	+	0.177733i	$0.943124\pi$
$542$	−3.56218	+	6.16987i	−0.153009	+	0.265019i
$543$		0			0
$544$	4.96410	−	2.86603i	0.212834	−	0.122880i
$545$	10.0000			0.428353
$546$		0			0
$547$	−30.4449			−1.30173			−0.650864	−	0.759194i	$-0.725593\pi$
$547$	−30.4449			−1.30173			−0.650864	+	0.759194i	$0.725593\pi$
$548$	5.30385	−	3.06218i	0.226569	−	0.130810i
$549$		0			0
$550$	1.46410	−	2.53590i	0.0624295	−	0.108131i
$551$			4.39230i			0.187118i
$552$		0			0
$553$	3.29423	+	1.90192i	0.140085	+	0.0808780i
$554$			9.39230i			0.399041i
$555$		0			0
$556$	−0.169873	−	0.294229i	−0.00720422	−	0.0124781i
$557$	−22.6244	+	13.0622i	−0.958625	+	0.553462i	−0.895749	−	0.444559i	$-0.853360\pi$
$557$	−22.6244	+	13.0622i	−0.958625	+	0.553462i	−0.0628752	+	0.998021i	$0.520027\pi$
$558$		0			0
$559$	−42.2487	+	12.1962i	−1.78693	+	0.515842i
$560$	−1.00000			−0.0422577
$561$		0			0
$562$	−8.33013	−	14.4282i	−0.351385	−	0.608617i
$563$	14.2224	−	24.6340i	0.599404	−	1.03820i	−0.393505	−	0.919322i	$-0.628738\pi$
$563$	14.2224	−	24.6340i	0.599404	−	1.03820i	0.992909	−	0.118876i	$-0.0379290\pi$
$564$		0			0
$565$	9.86603	+	5.69615i	0.415067	+	0.239639i
$566$	9.16987	+	5.29423i	0.385439	+	0.222533i
$567$		0			0
$568$	−6.92820	+	12.0000i	−0.290701	+	0.503509i
$569$	5.66025	+	9.80385i	0.237290	+	0.410999i	0.959936	−	0.280220i	$-0.0904074\pi$
$569$	5.66025	+	9.80385i	0.237290	+	0.410999i	−0.722646	+	0.691219i	$0.757074\pi$
$570$		0			0
$571$	5.46410			0.228666			0.114333	−	0.993443i	$-0.463527\pi$
$571$	5.46410			0.228666			0.114333	+	0.993443i	$0.463527\pi$
$572$	−1.83013	+	1.90192i	−0.0765215	+	0.0795234i
$573$		0			0
$574$	2.13397	−	1.23205i	0.0890704	−	0.0514248i
$575$	−2.53590	−	4.39230i	−0.105754	−	0.183172i
$576$		0			0
$577$			34.1769i			1.42280i	0.702786	+	0.711402i	$0.251939\pi$
$577$			34.1769i			1.42280i	−0.702786	+	0.711402i	$0.748061\pi$
$578$	13.7321	+	7.92820i	0.571178	+	0.329770i
$579$		0			0
$580$		−	3.00000i		−	0.124568i
$581$	1.90192	−	3.29423i	0.0789051	−	0.136668i
$582$		0			0
$583$	0.973721	−	0.562178i	0.0403274	−	0.0232830i
$584$	−11.3923			−0.471417
$585$		0			0
$586$	17.3923			0.718469
$587$	24.9282	−	14.3923i	1.02890	−	0.594034i	0.112229	−	0.993682i	$-0.464201\pi$
$587$	24.9282	−	14.3923i	1.02890	−	0.594034i	0.916668	+	0.399648i	$0.130868\pi$
$588$		0			0
$589$	3.85641	−	6.67949i	0.158900	−	0.275224i
$590$		−	10.7321i		−	0.441832i
$591$		0			0
$592$	−4.50000	−	2.59808i	−0.184949	−	0.106780i
$593$			3.14359i			0.129092i	0.997915	+	0.0645460i	$0.0205599\pi$
$593$			3.14359i			0.129092i	−0.997915	+	0.0645460i	$0.979440\pi$
$594$		0			0
$595$	−2.86603	−	4.96410i	−0.117496	−	0.203508i
$596$	14.8923	−	8.59808i	0.610013	−	0.352191i
$597$		0			0
$598$	1.26795	+	4.39230i	0.0518503	+	0.179615i
$599$	−30.9282			−1.26369			−0.631846	−	0.775094i	$-0.717703\pi$
$599$	−30.9282			−1.26369			−0.631846	+	0.775094i	$0.717703\pi$
$600$		0			0
$601$	11.5263	+	19.9641i	0.470167	+	0.814353i	0.999418	−	0.0341125i	$-0.0108604\pi$
$601$	11.5263	+	19.9641i	0.470167	+	0.814353i	−0.529251	+	0.848465i	$0.677527\pi$
$602$	−6.09808	+	10.5622i	−0.248539	+	0.430482i
$603$		0			0
$604$	10.7321	+	6.19615i	0.436681	+	0.252118i
$605$	−9.06218	−	5.23205i	−0.368430	−	0.212713i
$606$		0			0
$607$	4.92820	−	8.53590i	0.200030	−	0.346461i	−0.748508	−	0.663126i	$-0.769230\pi$
$607$	4.92820	−	8.53590i	0.200030	−	0.346461i	0.948538	+	0.316664i	$0.102563\pi$
$608$	−0.732051	−	1.26795i	−0.0296886	−	0.0514221i
$609$		0			0
$610$	−11.7321			−0.475017
$611$	−7.32051	+	7.60770i	−0.296156	+	0.307774i
$612$		0			0
$613$	13.8397	−	7.99038i	0.558982	−	0.322728i	−0.193755	−	0.981050i	$-0.562067\pi$
$613$	13.8397	−	7.99038i	0.558982	−	0.322728i	0.752737	+	0.658322i	$0.228733\pi$
$614$	11.7583	+	20.3660i	0.474528	+	0.821906i
$615$		0			0
$616$			0.732051i			0.0294952i
$617$	28.7487	+	16.5981i	1.15738	+	0.668213i	0.950675	−	0.310190i	$-0.100393\pi$
$617$	28.7487	+	16.5981i	1.15738	+	0.668213i	0.206705	+	0.978403i	$0.433726\pi$
$618$		0			0
$619$			34.0526i			1.36869i	0.729159	+	0.684344i	$0.239911\pi$
$619$			34.0526i			1.36869i	−0.729159	+	0.684344i	$0.760089\pi$
$620$	−2.63397	+	4.56218i	−0.105783	+	0.183221i
$621$		0			0
$622$	8.83013	−	5.09808i	0.354056	−	0.204414i
$623$	2.53590			0.101599
$624$		0			0
$625$	11.0000			0.440000
$626$	27.7128	−	16.0000i	1.10763	−	0.639489i
$627$		0			0
$628$	6.86603	−	11.8923i	0.273984	−	0.474555i
$629$		−	29.7846i		−	1.18759i
$630$		0			0
$631$	9.12436	+	5.26795i	0.363235	+	0.209714i	0.670499	−	0.741911i	$-0.266080\pi$
$631$	9.12436	+	5.26795i	0.363235	+	0.209714i	−0.307264	+	0.951624i	$0.599413\pi$
$632$		−	3.80385i		−	0.151309i
$633$		0			0
$634$	3.52628	+	6.10770i	0.140046	+	0.242568i
$635$	−8.53590	+	4.92820i	−0.338737	+	0.195570i
$636$		0			0
$637$	−0.866025	+	3.50000i	−0.0343132	+	0.138675i
$638$	−2.19615			−0.0869465
$639$		0			0
$640$	0.500000	+	0.866025i	0.0197642	+	0.0342327i
$641$	−22.2321	+	38.5070i	−0.878113	+	1.52094i	−0.0247042	+	0.999695i	$0.507864\pi$
$641$	−22.2321	+	38.5070i	−0.878113	+	1.52094i	−0.853409	+	0.521242i	$0.825469\pi$
$642$		0			0
$643$	30.9282	+	17.8564i	1.21969	+	0.704188i	0.964851	−	0.262796i	$-0.0846446\pi$
$643$	30.9282	+	17.8564i	1.21969	+	0.704188i	0.254838	+	0.966984i	$0.417978\pi$
$644$	1.09808	+	0.633975i	0.0432703	+	0.0249821i
$645$		0			0
$646$	4.19615	−	7.26795i	0.165095	−	0.285954i
$647$	6.92820	+	12.0000i	0.272376	+	0.471769i	0.969470	−	0.245211i	$-0.0788573\pi$
$647$	6.92820	+	12.0000i	0.272376	+	0.471769i	−0.697094	+	0.716980i	$0.745524\pi$
$648$		0			0
$649$	−7.85641			−0.308391
$650$	−14.0000	−	3.46410i	−0.549125	−	0.135873i
$651$		0			0
$652$	−0.633975	+	0.366025i	−0.0248284	+	0.0143347i
$653$	6.19615	+	10.7321i	0.242474	+	0.419978i	0.961418	−	0.275090i	$-0.0887077\pi$
$653$	6.19615	+	10.7321i	0.242474	+	0.419978i	−0.718944	+	0.695068i	$0.755374\pi$
$654$		0			0
$655$			5.07180i			0.198171i
$656$	−2.13397	−	1.23205i	−0.0833177	−	0.0481035i
$657$		0			0
$658$			2.92820i			0.114153i
$659$	4.39230	−	7.60770i	0.171100	−	0.296354i	−0.767705	−	0.640804i	$-0.778601\pi$
$659$	4.39230	−	7.60770i	0.171100	−	0.296354i	0.938805	+	0.344450i	$0.111935\pi$
$660$		0			0
$661$	1.66987	−	0.964102i	0.0649505	−	0.0374992i	−0.467173	−	0.884166i	$-0.654727\pi$
$661$	1.66987	−	0.964102i	0.0649505	−	0.0374992i	0.532124	+	0.846667i	$0.321394\pi$
$662$	−4.33975			−0.168669
$663$		0			0
$664$	−3.80385			−0.147618
$665$	−1.26795	+	0.732051i	−0.0491690	+	0.0283877i
$666$		0			0
$667$	−1.90192	+	3.29423i	−0.0736428	+	0.127553i
$668$		−	5.26795i		−	0.203823i
$669$		0			0
$670$	−10.0981	−	5.83013i	−0.390123	−	0.225237i
$671$			8.58846i			0.331554i
$672$		0			0
$673$	10.8923	+	18.8660i	0.419867	+	0.727232i	0.995926	−	0.0901768i	$-0.0287432\pi$
$673$	10.8923	+	18.8660i	0.419867	+	0.727232i	−0.576058	+	0.817409i	$0.695410\pi$
$674$	5.47372	−	3.16025i	0.210840	−	0.121728i
$675$		0			0
$676$	11.5000	+	6.06218i	0.442308	+	0.233161i
$677$	−27.8564			−1.07061			−0.535304	−	0.844659i	$-0.679803\pi$
$677$	−27.8564			−1.07061			−0.535304	+	0.844659i	$0.679803\pi$
$678$		0			0
$679$	2.73205	+	4.73205i	0.104846	+	0.181599i
$680$	−2.86603	+	4.96410i	−0.109907	+	0.190365i
$681$		0			0
$682$	3.33975	+	1.92820i	0.127885	+	0.0738347i
$683$	−5.66025	−	3.26795i	−0.216584	−	0.125045i	0.387784	−	0.921750i	$-0.373241\pi$
$683$	−5.66025	−	3.26795i	−0.216584	−	0.125045i	−0.604367	+	0.796706i	$0.706574\pi$
$684$		0			0
$685$	−3.06218	+	5.30385i	−0.117000	+	0.202650i
$686$	0.500000	+	0.866025i	0.0190901	+	0.0330650i
$687$		0			0
$688$	12.1962			0.464974
$689$	−3.99038	−	3.83975i	−0.152021	−	0.146283i
$690$		0			0
$691$	5.07180	−	2.92820i	0.192940	−	0.111394i	−0.400418	−	0.916333i	$-0.631135\pi$
$691$	5.07180	−	2.92820i	0.192940	−	0.111394i	0.593358	+	0.804938i	$0.297802\pi$
$692$	−10.4641	−	18.1244i	−0.397785	−	0.688985i
$693$		0			0
$694$			28.9808i			1.10009i
$695$	0.294229	+	0.169873i	0.0111607	+	0.00644365i
$696$		0			0
$697$		−	14.1244i		−	0.534998i
$698$	1.00000	−	1.73205i	0.0378506	−	0.0655591i
$699$		0			0
$700$	−3.46410	+	2.00000i	−0.130931	+	0.0755929i
$701$	14.5359			0.549013			0.274507	−	0.961585i	$-0.411485\pi$
$701$	14.5359			0.549013			0.274507	+	0.961585i	$0.411485\pi$
$702$		0			0
$703$	−7.60770			−0.286930
$704$	0.633975	−	0.366025i	0.0238938	−	0.0137951i
$705$		0			0
$706$	−18.0885	+	31.3301i	−0.680768	+	1.17912i
$707$			1.19615i			0.0449859i
$708$		0			0
$709$	−5.64359	−	3.25833i	−0.211950	−	0.122369i	0.390268	−	0.920702i	$-0.372383\pi$
$709$	−5.64359	−	3.25833i	−0.211950	−	0.122369i	−0.602217	+	0.798332i	$0.705716\pi$
$710$		−	13.8564i		−	0.520022i
$711$		0			0
$712$	−1.26795	−	2.19615i	−0.0475184	−	0.0823043i
$713$	5.78461	−	3.33975i	0.216635	−	0.125074i
$714$		0			0
$715$	0.633975	−	2.56218i	0.0237093	−	0.0958200i
$716$	−16.3923			−0.612609
$717$		0			0
$718$	8.19615	+	14.1962i	0.305878	+	0.529796i
$719$	3.09808	−	5.36603i	0.115539	−	0.200119i	−0.802456	−	0.596711i	$-0.796474\pi$
$719$	3.09808	−	5.36603i	0.115539	−	0.200119i	0.917995	+	0.396592i	$0.129807\pi$
$720$		0			0
$721$	−7.26795	−	4.19615i	−0.270673	−	0.156273i
$722$	14.5981	+	8.42820i	0.543284	+	0.313665i
$723$		0			0
$724$	1.59808	−	2.76795i	0.0593920	−	0.102870i
$725$	−6.00000	−	10.3923i	−0.222834	−	0.385961i
$726$		0			0
$727$	−53.8564			−1.99742			−0.998712	−	0.0507424i	$-0.983841\pi$
$727$	−53.8564			−1.99742			−0.998712	+	0.0507424i	$0.983841\pi$
$728$	3.46410	−	1.00000i	0.128388	−	0.0370625i
$729$		0			0
$730$	9.86603	−	5.69615i	0.365158	−	0.210824i
$731$	34.9545	+	60.5429i	1.29284	+	2.23926i
$732$		0			0
$733$		−	2.46410i		−	0.0910137i	−0.998964	−	0.0455068i	$-0.985510\pi$
$733$		−	2.46410i		−	0.0910137i	0.998964	−	0.0455068i	$-0.0144903\pi$
$734$	29.3660	+	16.9545i	1.08392	+	0.625801i
$735$		0			0
$736$		−	1.26795i		−	0.0467372i
$737$	−4.26795	+	7.39230i	−0.157212	+	0.272299i
$738$		0			0
$739$	5.66025	−	3.26795i	0.208216	−	0.120213i	−0.392266	−	0.919852i	$-0.628309\pi$
$739$	5.66025	−	3.26795i	0.208216	−	0.120213i	0.600482	+	0.799638i	$0.294975\pi$
$740$	5.19615			0.191014
$741$		0			0
$742$	−1.53590			−0.0563846
$743$	4.39230	−	2.53590i	0.161138	−	0.0930331i	−0.417262	−	0.908786i	$-0.637010\pi$
$743$	4.39230	−	2.53590i	0.161138	−	0.0930331i	0.578401	+	0.815753i	$0.303677\pi$
$744$		0			0
$745$	−8.59808	+	14.8923i	−0.315009	+	0.545612i
$746$			32.4641i			1.18860i
$747$		0			0
$748$	3.63397	+	2.09808i	0.132871	+	0.0767133i
$749$		−	10.9282i		−	0.399308i
$750$		0			0
$751$	3.22243	+	5.58142i	0.117588	+	0.203669i	0.918811	−	0.394697i	$-0.129150\pi$
$751$	3.22243	+	5.58142i	0.117588	+	0.203669i	−0.801223	+	0.598366i	$0.795817\pi$
$752$	2.53590	−	1.46410i	0.0924747	−	0.0533903i
$753$		0			0
$754$	3.00000	+	10.3923i	0.109254	+	0.378465i
$755$	−12.3923			−0.451002
$756$		0			0
$757$	22.1962	+	38.4449i	0.806733	+	1.39730i	0.915115	+	0.403193i	$0.132100\pi$
$757$	22.1962	+	38.4449i	0.806733	+	1.39730i	−0.108382	+	0.994109i	$0.534567\pi$
$758$	−11.0981	+	19.2224i	−0.403100	+	0.698190i
$759$		0			0
$760$	1.26795	+	0.732051i	0.0459934	+	0.0265543i
$761$	−15.8038	−	9.12436i	−0.572889	−	0.330758i	0.185413	−	0.982661i	$-0.440638\pi$
$761$	−15.8038	−	9.12436i	−0.572889	−	0.330758i	−0.758302	+	0.651903i	$0.773971\pi$
$762$		0			0
$763$	−5.00000	+	8.66025i	−0.181012	+	0.313522i
$764$	−3.56218	−	6.16987i	−0.128875	−	0.223218i
$765$		0			0
$766$	32.5885			1.17747
$767$	10.7321	+	37.1769i	0.387512	+	1.34238i
$768$		0			0
$769$	0.339746	−	0.196152i	0.0122516	−	0.00707344i	−0.493862	−	0.869540i	$-0.664415\pi$
$769$	0.339746	−	0.196152i	0.0122516	−	0.00707344i	0.506113	+	0.862467i	$0.331082\pi$
$770$	−0.366025	−	0.633975i	−0.0131906	−	0.0228469i
$771$		0			0
$772$			23.1962i			0.834848i
$773$	−40.0526	−	23.1244i	−1.44059	−	0.831725i	−0.442701	−	0.896669i	$-0.645980\pi$
$773$	−40.0526	−	23.1244i	−1.44059	−	0.831725i	−0.997889	+	0.0649438i	$0.979313\pi$
$774$		0			0
$775$			21.0718i			0.756921i
$776$	2.73205	−	4.73205i	0.0980749	−	0.169871i
$777$		0			0
$778$	−21.0622	+	12.1603i	−0.755116	+	0.435966i
$779$	−3.60770			−0.129259
$780$		0			0
$781$	−10.1436			−0.362966
$782$	6.29423	−	3.63397i	0.225081	−	0.129951i

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1638.bj (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +1.00000i q^{5} +(-0.866025 - 0.500000i) q^{7} +1.00000i q^{8} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +1.00000i q^{5} +(-0.866025 - 0.500000i) q^{7} +1.00000i q^{8} +(-0.500000 - 0.866025i) q^{10} +(-0.633975 + 0.366025i) q^{11} +(2.59808 + 2.50000i) q^{13} +1.00000 q^{14} +(-0.500000 - 0.866025i) q^{16} +(2.86603 - 4.96410i) q^{17} +(-1.26795 - 0.732051i) q^{19} +(0.866025 + 0.500000i) q^{20} +(0.366025 - 0.633975i) q^{22} +(-0.633975 - 1.09808i) q^{23} +4.00000 q^{25} +(-3.50000 - 0.866025i) q^{26} +(-0.866025 + 0.500000i) q^{28} +(-1.50000 - 2.59808i) q^{29} +5.26795i q^{31} +(0.866025 + 0.500000i) q^{32} +5.73205i q^{34} +(0.500000 - 0.866025i) q^{35} +(4.50000 - 2.59808i) q^{37} +1.46410 q^{38} -1.00000 q^{40} +(2.13397 - 1.23205i) q^{41} +(-6.09808 + 10.5622i) q^{43} +0.732051i q^{44} +(1.09808 + 0.633975i) q^{46} +2.92820i q^{47} +(0.500000 + 0.866025i) q^{49} +(-3.46410 + 2.00000i) q^{50} +(3.46410 - 1.00000i) q^{52} -1.53590 q^{53} +(-0.366025 - 0.633975i) q^{55} +(0.500000 - 0.866025i) q^{56} +(2.59808 + 1.50000i) q^{58} +(9.29423 + 5.36603i) q^{59} +(5.86603 - 10.1603i) q^{61} +(-2.63397 - 4.56218i) q^{62} -1.00000 q^{64} +(-2.50000 + 2.59808i) q^{65} +(10.0981 - 5.83013i) q^{67} +(-2.86603 - 4.96410i) q^{68} +1.00000i q^{70} +(12.0000 + 6.92820i) q^{71} +11.3923i q^{73} +(-2.59808 + 4.50000i) q^{74} +(-1.26795 + 0.732051i) q^{76} +0.732051 q^{77} -3.80385 q^{79} +(0.866025 - 0.500000i) q^{80} +(-1.23205 + 2.13397i) q^{82} +3.80385i q^{83} +(4.96410 + 2.86603i) q^{85} -12.1962i q^{86} +(-0.366025 - 0.633975i) q^{88} +(-2.19615 + 1.26795i) q^{89} +(-1.00000 - 3.46410i) q^{91} -1.26795 q^{92} +(-1.46410 - 2.53590i) q^{94} +(0.732051 - 1.26795i) q^{95} +(-4.73205 - 2.73205i) q^{97} +(-0.866025 - 0.500000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{4}+O(q^{10}) \) 4 * q + 2 * q^4	\( 4 q + 2 q^{4} - 2 q^{10} - 6 q^{11} + 4 q^{14} - 2 q^{16} + 8 q^{17} - 12 q^{19} - 2 q^{22} - 6 q^{23} + 16 q^{25} - 14 q^{26} - 6 q^{29} + 2 q^{35} + 18 q^{37} - 8 q^{38} - 4 q^{40} + 12 q^{41} - 14 q^{43} - 6 q^{46} + 2 q^{49} - 20 q^{53} + 2 q^{55} + 2 q^{56} + 6 q^{59} + 20 q^{61} - 14 q^{62} - 4 q^{64} - 10 q^{65} + 30 q^{67} - 8 q^{68} + 48 q^{71} - 12 q^{76} - 4 q^{77} - 36 q^{79} + 2 q^{82} + 6 q^{85} + 2 q^{88} + 12 q^{89} - 4 q^{91} - 12 q^{92} + 8 q^{94} - 4 q^{95} - 12 q^{97}+O(q^{100}) \) 4 * q + 2 * q^4 - 2 * q^10 - 6 * q^11 + 4 * q^14 - 2 * q^16 + 8 * q^17 - 12 * q^19 - 2 * q^22 - 6 * q^23 + 16 * q^25 - 14 * q^26 - 6 * q^29 + 2 * q^35 + 18 * q^37 - 8 * q^38 - 4 * q^40 + 12 * q^41 - 14 * q^43 - 6 * q^46 + 2 * q^49 - 20 * q^53 + 2 * q^55 + 2 * q^56 + 6 * q^59 + 20 * q^61 - 14 * q^62 - 4 * q^64 - 10 * q^65 + 30 * q^67 - 8 * q^68 + 48 * q^71 - 12 * q^76 - 4 * q^77 - 36 * q^79 + 2 * q^82 + 6 * q^85 + 2 * q^88 + 12 * q^89 - 4 * q^91 - 12 * q^92 + 8 * q^94 - 4 * q^95 - 12 * q^97

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