LMFDB - Embedded newform 1617.2.c.b.538.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1617,2,Mod(538,1617)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1617, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 1]))

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

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

chi := DirichletCharacter("1617.538");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1617 = 3 \cdot 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1617.c (of order $2$, degree $1$, 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:	$12.9118100068$
Analytic rank:	$0$
Dimension:	$48$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			538.10
Character	$\chi$	$=$	1617.538
Dual form			1617.2.c.b.538.39

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.06268i q^{2} +1.00000i q^{3} -2.25465 q^{4} -3.23777i q^{5} +2.06268 q^{6} +0.525252i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q-2.06268i q^{2} +1.00000i q^{3} -2.25465 q^{4} -3.23777i q^{5} +2.06268 q^{6} +0.525252i q^{8} -1.00000 q^{9} -6.67848 q^{10} +(-3.22162 + 0.788152i) q^{11} -2.25465i q^{12} -1.48363 q^{13} +3.23777 q^{15} -3.42586 q^{16} +3.63565 q^{17} +2.06268i q^{18} -7.29372 q^{19} +7.30003i q^{20} +(1.62570 + 6.64516i) q^{22} +2.21779 q^{23} -0.525252 q^{24} -5.48317 q^{25} +3.06025i q^{26} -1.00000i q^{27} +7.25254i q^{29} -6.67848i q^{30} -4.17015i q^{31} +8.11696i q^{32} +(-0.788152 - 3.22162i) q^{33} -7.49918i q^{34} +2.25465 q^{36} +7.60092 q^{37} +15.0446i q^{38} -1.48363i q^{39} +1.70065 q^{40} -11.7561 q^{41} +1.56172i q^{43} +(7.26360 - 1.77700i) q^{44} +3.23777i q^{45} -4.57460i q^{46} +2.39613i q^{47} -3.42586i q^{48} +11.3100i q^{50} +3.63565i q^{51} +3.34506 q^{52} +9.31456 q^{53} -2.06268 q^{54} +(2.55186 + 10.4309i) q^{55} -7.29372i q^{57} +14.9597 q^{58} -5.68806i q^{59} -7.30003 q^{60} -12.4587 q^{61} -8.60169 q^{62} +9.89096 q^{64} +4.80365i q^{65} +(-6.64516 + 1.62570i) q^{66} -10.8955 q^{67} -8.19711 q^{68} +2.21779i q^{69} -6.79823 q^{71} -0.525252i q^{72} -3.64146 q^{73} -15.6783i q^{74} -5.48317i q^{75} +16.4448 q^{76} -3.06025 q^{78} -6.69422i q^{79} +11.0922i q^{80} +1.00000 q^{81} +24.2491i q^{82} +3.19685 q^{83} -11.7714i q^{85} +3.22133 q^{86} -7.25254 q^{87} +(-0.413978 - 1.69216i) q^{88} -2.88049i q^{89} +6.67848 q^{90} -5.00034 q^{92} +4.17015 q^{93} +4.94244 q^{94} +23.6154i q^{95} -8.11696 q^{96} -7.77914i q^{97} +(3.22162 - 0.788152i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 64 q^{4} - 48 q^{9}+O(q^{10}) $ 48 * q - 64 * q^4 - 48 * q^9	$ 48 q - 64 q^{4} - 48 q^{9} - 16 q^{11} + 64 q^{16} + 16 q^{22} + 32 q^{23} - 80 q^{25} + 64 q^{36} - 96 q^{37} - 32 q^{44} + 64 q^{53} + 48 q^{58} - 48 q^{60} - 240 q^{64} + 96 q^{67} - 32 q^{71} + 48 q^{78} + 48 q^{81} - 96 q^{86} - 48 q^{88} - 32 q^{92} + 96 q^{93} + 16 q^{99}+O(q^{100}) $ 48 * q - 64 * q^4 - 48 * q^9 - 16 * q^11 + 64 * q^16 + 16 * q^22 + 32 * q^23 - 80 * q^25 + 64 * q^36 - 96 * q^37 - 32 * q^44 + 64 * q^53 + 48 * q^58 - 48 * q^60 - 240 * q^64 + 96 * q^67 - 32 * q^71 + 48 * q^78 + 48 * q^81 - 96 * q^86 - 48 * q^88 - 32 * q^92 + 96 * q^93 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1617\mathbb{Z}\right)^\times$.

$n$	$199$	$442$	$1079$
$\chi(n)$	$-1$	$-1$	$1$

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 $

$2$		−	2.06268i		−	1.45853i	−0.684229	−	0.729267i	$-0.739861\pi$
$2$		−	2.06268i		−	1.45853i	0.684229	−	0.729267i	$-0.260139\pi$
$3$			1.00000i			0.577350i
$3$			1.00000i			0.577350i
$4$	−2.25465			−1.12732
$5$		−	3.23777i		−	1.44798i	−0.689813	−	0.723988i	$-0.742307\pi$
$5$		−	3.23777i		−	1.44798i	0.689813	−	0.723988i	$-0.257693\pi$
$6$	2.06268			0.842085
$7$		0			0
$7$		0			0
$8$			0.525252i			0.185705i
$9$	−1.00000			−0.333333
$10$	−6.67848			−2.11192
$11$	−3.22162	+	0.788152i	−0.971354	+	0.237637i
$11$	−3.22162	+	0.788152i	−0.971354	+	0.237637i
$12$		−	2.25465i		−	0.650860i
$13$	−1.48363			−0.411484			−0.205742	−	0.978606i	$-0.565961\pi$
$13$	−1.48363			−0.411484			−0.205742	+	0.978606i	$0.565961\pi$
$14$		0			0
$15$	3.23777			0.835989
$16$	−3.42586			−0.856466
$17$	3.63565			0.881775			0.440888	−	0.897562i	$-0.354664\pi$
$17$	3.63565			0.881775			0.440888	+	0.897562i	$0.354664\pi$
$18$			2.06268i			0.486178i
$19$	−7.29372			−1.67329			−0.836647	−	0.547742i	$-0.815487\pi$
$19$	−7.29372			−1.67329			−0.836647	+	0.547742i	$0.815487\pi$
$20$			7.30003i			1.63234i
$21$		0			0
$22$	1.62570	+	6.64516i	0.346601	+	1.41675i
$23$	2.21779			0.462442			0.231221	−	0.972901i	$-0.425728\pi$
$23$	2.21779			0.462442			0.231221	+	0.972901i	$0.425728\pi$
$24$	−0.525252			−0.107217
$25$	−5.48317			−1.09663
$26$			3.06025i			0.600164i
$27$		−	1.00000i		−	0.192450i
$28$		0			0
$29$			7.25254i			1.34676i	0.739295	+	0.673382i	$0.235159\pi$
$29$			7.25254i			1.34676i	−0.739295	+	0.673382i	$0.764841\pi$
$30$		−	6.67848i		−	1.21932i
$31$		−	4.17015i		−	0.748982i	−0.927231	−	0.374491i	$-0.877817\pi$
$31$		−	4.17015i		−	0.748982i	0.927231	−	0.374491i	$-0.122183\pi$
$32$			8.11696i			1.43489i
$33$	−0.788152	−	3.22162i	−0.137200	−	0.560812i
$34$		−	7.49918i		−	1.28610i
$35$		0			0
$36$	2.25465			0.375774
$37$	7.60092			1.24958			0.624792	−	0.780791i	$-0.285184\pi$
$37$	7.60092			1.24958			0.624792	+	0.780791i	$0.285184\pi$
$38$			15.0446i			2.44056i
$39$		−	1.48363i		−	0.237571i
$40$	1.70065			0.268896
$41$	−11.7561			−1.83600			−0.917998	−	0.396585i	$-0.870195\pi$
$41$	−11.7561			−1.83600			−0.917998	+	0.396585i	$0.870195\pi$
$42$		0			0
$43$			1.56172i			0.238160i	0.992885	+	0.119080i	$0.0379945\pi$
$43$			1.56172i			0.238160i	−0.992885	+	0.119080i	$0.962005\pi$
$44$	7.26360	−	1.77700i	1.09503	−	0.267893i
$45$			3.23777i			0.482659i
$46$		−	4.57460i		−	0.674488i
$47$			2.39613i			0.349511i	0.984612	+	0.174755i	$0.0559135\pi$
$47$			2.39613i			0.349511i	−0.984612	+	0.174755i	$0.944087\pi$
$48$		−	3.42586i		−	0.494481i
$49$		0			0
$50$			11.3100i			1.59948i
$51$			3.63565i			0.509093i
$52$	3.34506			0.463876
$53$	9.31456			1.27945			0.639727	−	0.768602i	$-0.279048\pi$
$53$	9.31456			1.27945			0.639727	+	0.768602i	$0.279048\pi$
$54$	−2.06268			−0.280695
$55$	2.55186	+	10.4309i	0.344092	+	1.40650i
$56$		0			0
$57$		−	7.29372i		−	0.966077i
$58$	14.9597			1.96430
$59$		−	5.68806i		−	0.740523i	−0.928928	−	0.370261i	$-0.879268\pi$
$59$		−	5.68806i		−	0.740523i	0.928928	−	0.370261i	$-0.120732\pi$
$60$	−7.30003			−0.942430
$61$	−12.4587			−1.59517			−0.797586	−	0.603205i	$-0.793890\pi$
$61$	−12.4587			−1.59517			−0.797586	+	0.603205i	$0.793890\pi$
$62$	−8.60169			−1.09242
$63$		0			0
$64$	9.89096			1.23637
$65$			4.80365i			0.595819i
$66$	−6.64516	+	1.62570i	−0.817963	+	0.200110i
$67$	−10.8955			−1.33110			−0.665549	−	0.746354i	$-0.731803\pi$
$67$	−10.8955			−1.33110			−0.665549	+	0.746354i	$0.731803\pi$
$68$	−8.19711			−0.994045
$69$			2.21779i			0.266991i
$70$		0			0
$71$	−6.79823			−0.806802			−0.403401	−	0.915023i	$-0.632172\pi$
$71$	−6.79823			−0.806802			−0.403401	+	0.915023i	$0.632172\pi$
$72$		−	0.525252i		−	0.0619016i
$73$	−3.64146			−0.426201			−0.213100	−	0.977030i	$-0.568356\pi$
$73$	−3.64146			−0.426201			−0.213100	+	0.977030i	$0.568356\pi$
$74$		−	15.6783i		−	1.82256i
$75$		−	5.48317i		−	0.633142i
$76$	16.4448			1.88634
$77$		0			0
$78$	−3.06025			−0.346505
$79$		−	6.69422i		−	0.753158i	−0.926384	−	0.376579i	$-0.877100\pi$
$79$		−	6.69422i		−	0.753158i	0.926384	−	0.376579i	$-0.122900\pi$
$80$			11.0922i			1.24014i
$81$	1.00000			0.111111
$82$			24.2491i			2.67786i
$83$	3.19685			0.350899			0.175450	−	0.984488i	$-0.443862\pi$
$83$	3.19685			0.350899			0.175450	+	0.984488i	$0.443862\pi$
$84$		0			0
$85$		−	11.7714i		−	1.27679i
$86$	3.22133			0.347365
$87$	−7.25254			−0.777554
$88$	−0.413978	−	1.69216i	−0.0441302	−	0.180385i
$89$		−	2.88049i		−	0.305331i	−0.988278	−	0.152666i	$-0.951214\pi$
$89$		−	2.88049i		−	0.305331i	0.988278	−	0.152666i	$-0.0487857\pi$
$90$	6.67848			0.703974
$91$		0			0
$92$	−5.00034			−0.521321
$93$	4.17015			0.432425
$94$	4.94244			0.509774
$95$			23.6154i			2.42289i
$96$	−8.11696			−0.828434
$97$		−	7.77914i		−	0.789852i	−0.918713	−	0.394926i	$-0.870770\pi$
$97$		−	7.77914i		−	0.789852i	0.918713	−	0.394926i	$-0.129230\pi$
$98$		0			0
$99$	3.22162	−	0.788152i	0.323785	−	0.0792122i
$100$	12.3626			1.23626
$101$	−0.390995			−0.0389054			−0.0194527	−	0.999811i	$-0.506192\pi$
$101$	−0.390995			−0.0389054			−0.0194527	+	0.999811i	$0.506192\pi$
$102$	7.49918			0.742530
$103$			1.33166i			0.131213i	0.997846	+	0.0656064i	$0.0208982\pi$
$103$			1.33166i			0.131213i	−0.997846	+	0.0656064i	$0.979102\pi$
$104$		−	0.779279i		−	0.0764146i
$105$		0			0
$106$		−	19.2130i		−	1.86613i
$107$			15.8469i			1.53198i	0.642853	+	0.765989i	$0.277750\pi$
$107$			15.8469i			1.53198i	−0.642853	+	0.765989i	$0.722250\pi$
$108$			2.25465i			0.216953i
$109$			10.1613i			0.973280i	0.873603	+	0.486640i	$0.161778\pi$
$109$			10.1613i			0.973280i	−0.873603	+	0.486640i	$0.838222\pi$
$110$	21.5155	−	5.26366i	2.05142	−	0.501870i
$111$			7.60092i			0.721448i
$112$		0			0
$113$	9.43153			0.887244			0.443622	−	0.896214i	$-0.353693\pi$
$113$	9.43153			0.887244			0.443622	+	0.896214i	$0.353693\pi$
$114$	−15.0446			−1.40906
$115$		−	7.18071i		−	0.669605i
$116$		−	16.3519i		−	1.51824i
$117$	1.48363			0.137161
$118$	−11.7326			−1.08008
$119$		0			0
$120$			1.70065i			0.155247i
$121$	9.75763	−	5.07825i	0.887058	−	0.461659i
$122$			25.6983i			2.32661i
$123$		−	11.7561i		−	1.06001i
$124$			9.40222i			0.844344i
$125$			1.56438i			0.139923i
$126$		0			0
$127$		−	2.96409i		−	0.263020i	−0.991315	−	0.131510i	$-0.958017\pi$
$127$		−	2.96409i		−	0.263020i	0.991315	−	0.131510i	$-0.0419826\pi$
$128$		−	4.16796i		−	0.368399i
$129$	−1.56172			−0.137502
$130$	9.90839			0.869023
$131$	17.8335			1.55812			0.779060	−	0.626950i	$-0.215697\pi$
$131$	17.8335			1.55812			0.779060	+	0.626950i	$0.215697\pi$
$132$	1.77700	+	7.26360i	0.154668	+	0.632216i
$133$		0			0
$134$			22.4739i			1.94145i
$135$	−3.23777			−0.278663
$136$			1.90963i			0.163750i
$137$	−6.81143			−0.581940			−0.290970	−	0.956732i	$-0.593978\pi$
$137$	−6.81143			−0.581940			−0.290970	+	0.956732i	$0.593978\pi$
$138$	4.57460			0.389416
$139$	−12.8845			−1.09285			−0.546426	−	0.837508i	$-0.684012\pi$
$139$	−12.8845			−1.09285			−0.546426	+	0.837508i	$0.684012\pi$
$140$		0			0
$141$	−2.39613			−0.201790
$142$			14.0226i			1.17675i
$143$	4.77968	−	1.16932i	0.399697	−	0.0977838i
$144$	3.42586			0.285489
$145$	23.4821			1.95008
$146$			7.51116i			0.621628i
$147$		0			0
$148$	−17.1374			−1.40868
$149$			11.7176i			0.959946i	0.877283	+	0.479973i	$0.159354\pi$
$149$			11.7176i			0.959946i	−0.877283	+	0.479973i	$0.840646\pi$
$150$	−11.3100			−0.923459
$151$			7.44203i			0.605624i	0.953050	+	0.302812i	$0.0979254\pi$
$151$			7.44203i			0.605624i	−0.953050	+	0.302812i	$0.902075\pi$
$152$		−	3.83104i		−	0.310739i
$153$	−3.63565			−0.293925
$154$		0			0
$155$	−13.5020			−1.08451
$156$			3.34506i			0.267819i
$157$			15.8871i			1.26793i	0.773362	+	0.633964i	$0.218573\pi$
$157$			15.8871i			1.26793i	−0.773362	+	0.633964i	$0.781427\pi$
$158$	−13.8080			−1.09851
$159$			9.31456i			0.738693i
$160$	26.2809			2.07769
$161$		0			0
$162$		−	2.06268i		−	0.162059i
$163$	−7.97918			−0.624977			−0.312489	−	0.949921i	$-0.601163\pi$
$163$	−7.97918			−0.624977			−0.312489	+	0.949921i	$0.601163\pi$
$164$	26.5059			2.06976
$165$	−10.4309	+	2.55186i	−0.812041	+	0.198662i
$166$		−	6.59407i		−	0.511799i
$167$	−14.8341			−1.14789			−0.573947	−	0.818892i	$-0.694589\pi$
$167$	−14.8341			−1.14789			−0.573947	+	0.818892i	$0.694589\pi$
$168$		0			0
$169$	−10.7988			−0.830681
$170$	−24.2806			−1.86224
$171$	7.29372			0.557765
$172$		−	3.52113i		−	0.268483i
$173$	17.9668			1.36599			0.682995	−	0.730423i	$-0.260677\pi$
$173$	17.9668			1.36599			0.682995	+	0.730423i	$0.260677\pi$
$174$			14.9597i			1.13409i
$175$		0			0
$176$	11.0368	−	2.70010i	0.831932	−	0.203528i
$177$	5.68806			0.427541
$178$	−5.94152			−0.445336
$179$	−15.9619			−1.19305			−0.596524	−	0.802596i	$-0.703452\pi$
$179$	−15.9619			−1.19305			−0.596524	+	0.802596i	$0.703452\pi$
$180$		−	7.30003i		−	0.544112i
$181$		−	25.6807i		−	1.90883i	−0.298476	−	0.954417i	$-0.596478\pi$
$181$		−	25.6807i		−	1.90883i	0.298476	−	0.954417i	$-0.403522\pi$
$182$		0			0
$183$		−	12.4587i		−	0.920973i
$184$			1.16490i			0.0858777i
$185$		−	24.6100i		−	1.80937i
$186$		−	8.60169i		−	0.630707i
$187$	−11.7127	+	2.86545i	−0.856516	+	0.209542i
$188$		−	5.40241i		−	0.394012i
$189$		0			0
$190$	48.7110			3.53387
$191$	−25.0662			−1.81372			−0.906862	−	0.421427i	$-0.861529\pi$
$191$	−25.0662			−1.81372			−0.906862	+	0.421427i	$0.861529\pi$
$192$			9.89096i			0.713819i
$193$		−	25.1798i		−	1.81248i	−0.422761	−	0.906241i	$-0.638939\pi$
$193$		−	25.1798i		−	1.81248i	0.422761	−	0.906241i	$-0.361061\pi$
$194$	−16.0459			−1.15203
$195$	−4.80365			−0.343996
$196$		0			0
$197$		−	11.4963i		−	0.819075i	−0.912293	−	0.409537i	$-0.865690\pi$
$197$		−	11.4963i		−	0.819075i	0.912293	−	0.409537i	$-0.134310\pi$
$198$	−1.62570	−	6.64516i	−0.115534	−	0.472251i
$199$			9.79640i			0.694448i	0.937782	+	0.347224i	$0.112876\pi$
$199$			9.79640i			0.694448i	−0.937782	+	0.347224i	$0.887124\pi$
$200$		−	2.88005i		−	0.203650i
$201$		−	10.8955i		−	0.768510i
$202$			0.806497i			0.0567449i
$203$		0			0
$204$		−	8.19711i		−	0.573912i
$205$			38.0636i			2.65848i
$206$	2.74680			0.191378
$207$	−2.21779			−0.154147
$208$	5.08271			0.352422
$209$	23.4976	−	5.74856i	1.62536	−	0.397636i
$210$		0			0
$211$		−	1.43744i		−	0.0989572i	−0.998775	−	0.0494786i	$-0.984244\pi$
$211$		−	1.43744i		−	0.0989572i	0.998775	−	0.0494786i	$-0.0157560\pi$
$212$	−21.0010			−1.44236
$213$		−	6.79823i		−	0.465807i
$214$	32.6871			2.23444
$215$	5.05649			0.344850
$216$	0.525252			0.0357389
$217$		0			0
$218$	20.9596			1.41956
$219$		−	3.64146i		−	0.246067i
$220$	−5.75353	−	23.5179i	−0.387903	−	1.58558i
$221$	−5.39395			−0.362837
$222$	15.6783			1.05226
$223$			10.1483i			0.679581i	0.940501	+	0.339791i	$0.110356\pi$
$223$			10.1483i			0.679581i	−0.940501	+	0.339791i	$0.889644\pi$
$224$		0			0
$225$	5.48317			0.365544
$226$		−	19.4542i		−	1.29408i
$227$	−4.51913			−0.299945			−0.149972	−	0.988690i	$-0.547918\pi$
$227$	−4.51913			−0.299945			−0.149972	+	0.988690i	$0.547918\pi$
$228$			16.4448i			1.08908i
$229$		−	18.2738i		−	1.20757i	−0.797148	−	0.603784i	$-0.793659\pi$
$229$		−	18.2738i		−	1.20757i	0.797148	−	0.603784i	$-0.206341\pi$
$230$	−14.8115			−0.976642
$231$		0			0
$232$	−3.80941			−0.250100
$233$		−	27.1744i		−	1.78025i	−0.455713	−	0.890127i	$-0.650616\pi$
$233$		−	27.1744i		−	1.78025i	0.455713	−	0.890127i	$-0.349384\pi$
$234$		−	3.06025i		−	0.200055i
$235$	7.75811			0.506083
$236$			12.8246i			0.834808i
$237$	6.69422			0.434836
$238$		0			0
$239$		−	28.2719i		−	1.82876i	−0.404860	−	0.914379i	$-0.632680\pi$
$239$		−	28.2719i		−	1.82876i	0.404860	−	0.914379i	$-0.367320\pi$
$240$	−11.0922			−0.715996
$241$	−4.96050			−0.319534			−0.159767	−	0.987155i	$-0.551074\pi$
$241$	−4.96050			−0.319534			−0.159767	+	0.987155i	$0.551074\pi$
$242$	−10.4748	−	20.1269i	−0.673345	−	1.29380i
$243$			1.00000i			0.0641500i
$244$	28.0899			1.79827
$245$		0			0
$246$	−24.2491			−1.54606
$247$	10.8212			0.688534
$248$	2.19038			0.139089
$249$			3.19685i			0.202592i
$250$	3.22682			0.204082
$251$		−	19.6966i		−	1.24324i	−0.783320	−	0.621618i	$-0.786476\pi$
$251$		−	19.6966i		−	1.24324i	0.783320	−	0.621618i	$-0.213524\pi$
$252$		0			0
$253$	−7.14488	+	1.74796i	−0.449195	+	0.109893i
$254$	−6.11396			−0.383624
$255$	11.7714			0.737154
$256$	11.1848			0.699048
$257$		−	22.0941i		−	1.37819i	−0.724671	−	0.689095i	$-0.758008\pi$
$257$		−	22.0941i		−	1.37819i	0.724671	−	0.689095i	$-0.241992\pi$
$258$			3.22133i			0.200551i
$259$		0			0
$260$		−	10.8305i		−	0.671681i
$261$		−	7.25254i		−	0.448921i
$262$		−	36.7848i		−	2.27257i
$263$		−	23.0784i		−	1.42307i	−0.702649	−	0.711537i	$-0.747999\pi$
$263$		−	23.0784i		−	1.42307i	0.702649	−	0.711537i	$-0.252001\pi$
$264$	1.69216	−	0.413978i	0.104145	−	0.0254786i
$265$		−	30.1584i		−	1.85262i
$266$		0			0
$267$	2.88049			0.176283
$268$	24.5655			1.50058
$269$			17.9001i			1.09139i	0.837985	+	0.545693i	$0.183734\pi$
$269$			17.9001i			1.09139i	−0.837985	+	0.545693i	$0.816266\pi$
$270$			6.67848i			0.406440i
$271$	−16.7171			−1.01549			−0.507745	−	0.861507i	$-0.669521\pi$
$271$	−16.7171			−1.01549			−0.507745	+	0.861507i	$0.669521\pi$
$272$	−12.4553			−0.755211
$273$		0			0
$274$			14.0498i			0.848779i
$275$	17.6647	−	4.32157i	1.06522	−	0.260600i
$276$		−	5.00034i		−	0.300985i
$277$			6.63537i			0.398681i	0.979930	+	0.199340i	$0.0638799\pi$
$277$			6.63537i			0.398681i	−0.979930	+	0.199340i	$0.936120\pi$
$278$			26.5766i			1.59396i
$279$			4.17015i			0.249661i
$280$		0			0
$281$			25.9144i			1.54592i	0.634452	+	0.772962i	$0.281226\pi$
$281$			25.9144i			1.54592i	−0.634452	+	0.772962i	$0.718774\pi$
$282$			4.94244i			0.294318i
$283$	−10.8844			−0.647013			−0.323507	−	0.946226i	$-0.604862\pi$
$283$	−10.8844			−0.647013			−0.323507	+	0.946226i	$0.604862\pi$
$284$	15.3276			0.909526
$285$	−23.6154			−1.39886
$286$	−2.41194	−	9.85895i	−0.142621	−	0.582972i
$287$		0			0
$288$		−	8.11696i		−	0.478297i
$289$	−3.78203			−0.222473
$290$		−	48.4360i		−	2.84426i
$291$	7.77914			0.456021
$292$	8.21020			0.480466
$293$	−8.24726			−0.481810			−0.240905	−	0.970549i	$-0.577444\pi$
$293$	−8.24726			−0.481810			−0.240905	+	0.970549i	$0.577444\pi$
$294$		0			0
$295$	−18.4166			−1.07226
$296$			3.99240i			0.232054i
$297$	0.788152	+	3.22162i	0.0457332	+	0.186937i
$298$	24.1697			1.40011
$299$	−3.29038			−0.190288
$300$			12.3626i			0.713755i
$301$		0			0
$302$	15.3505			0.883323
$303$		−	0.390995i		−	0.0224621i
$304$	24.9873			1.43312
$305$			40.3384i			2.30977i
$306$			7.49918i			0.428700i
$307$	−32.1289			−1.83369			−0.916846	−	0.399241i	$-0.869274\pi$
$307$	−32.1289			−1.83369			−0.916846	+	0.399241i	$0.869274\pi$
$308$		0			0
$309$	−1.33166			−0.0757558
$310$			27.8503i			1.58179i
$311$		−	16.8669i		−	0.956436i	−0.878241	−	0.478218i	$-0.841283\pi$
$311$		−	16.8669i		−	0.956436i	0.878241	−	0.478218i	$-0.158717\pi$
$312$	0.779279			0.0441180
$313$		−	5.88598i		−	0.332695i	−0.986067	−	0.166348i	$-0.946803\pi$
$313$		−	5.88598i		−	0.332695i	0.986067	−	0.166348i	$-0.0531974\pi$
$314$	32.7700			1.84932
$315$		0			0
$316$			15.0931i			0.849052i
$317$	6.58797			0.370017			0.185009	−	0.982737i	$-0.440769\pi$
$317$	6.58797			0.370017			0.185009	+	0.982737i	$0.440769\pi$
$318$	19.2130			1.07741
$319$	−5.71610	−	23.3649i	−0.320040	−	1.30818i
$320$		−	32.0247i		−	1.79023i
$321$	−15.8469			−0.884488
$322$		0			0
$323$	−26.5174			−1.47547
$324$	−2.25465			−0.125258
$325$	8.13498			0.451247
$326$			16.4585i			0.911551i
$327$	−10.1613			−0.561924
$328$		−	6.17492i		−	0.340953i
$329$		0			0
$330$	5.26366	+	21.5155i	0.289755	+	1.18439i
$331$	22.2116			1.22086			0.610430	−	0.792070i	$-0.290997\pi$
$331$	22.2116			1.22086			0.610430	+	0.792070i	$0.290997\pi$
$332$	−7.20775			−0.395577
$333$	−7.60092			−0.416528
$334$			30.5979i			1.67424i
$335$			35.2772i			1.92740i
$336$		0			0
$337$		−	26.7238i		−	1.45574i	−0.685715	−	0.727870i	$-0.740510\pi$
$337$		−	26.7238i		−	1.45574i	0.685715	−	0.727870i	$-0.259490\pi$
$338$			22.2746i			1.21158i
$339$			9.43153i			0.512251i
$340$			26.5404i			1.43935i
$341$	3.28671	+	13.4346i	0.177986	+	0.727527i
$342$		−	15.0446i		−	0.813519i
$343$		0			0
$344$	−0.820297			−0.0442275
$345$	7.18071			0.386597
$346$		−	37.0597i		−	1.99234i
$347$			6.93052i			0.372050i	0.982545	+	0.186025i	$0.0595605\pi$
$347$			6.93052i			0.372050i	−0.982545	+	0.186025i	$0.940439\pi$
$348$	16.3519			0.876555
$349$	17.4632			0.934781			0.467391	−	0.884051i	$-0.345194\pi$
$349$	17.4632			0.934781			0.467391	+	0.884051i	$0.345194\pi$
$350$		0			0
$351$			1.48363i			0.0791902i
$352$	−6.39740	−	26.1497i	−0.340982	−	1.39379i
$353$		−	12.3351i		−	0.656529i	−0.944586	−	0.328264i	$-0.893536\pi$
$353$		−	12.3351i		−	0.656529i	0.944586	−	0.328264i	$-0.106464\pi$
$354$		−	11.7326i		−	0.623583i
$355$			22.0111i			1.16823i
$356$			6.49448i			0.344207i
$357$		0			0
$358$			32.9242i			1.74010i
$359$		−	0.203122i		−	0.0107204i	−0.999986	−	0.00536018i	$-0.998294\pi$
$359$		−	0.203122i		−	0.0107204i	0.999986	−	0.00536018i	$-0.00170621\pi$
$360$	−1.70065			−0.0896319
$361$	34.1984			1.79991
$362$	−52.9711			−2.78410
$363$	5.07825	+	9.75763i	0.266539	+	0.512143i
$364$		0			0
$365$			11.7902i			0.617128i
$366$	−25.6983			−1.34327
$367$			13.6790i			0.714036i	0.934097	+	0.357018i	$0.116207\pi$
$367$			13.6790i			0.714036i	−0.934097	+	0.357018i	$0.883793\pi$
$368$	−7.59786			−0.396066
$369$	11.7561			0.611999
$370$	−50.7626			−2.63902
$371$		0			0
$372$	−9.40222			−0.487482
$373$		−	11.7625i		−	0.609038i	−0.952506	−	0.304519i	$-0.901504\pi$
$373$		−	11.7625i		−	0.609038i	0.952506	−	0.304519i	$-0.0984956\pi$
$374$	5.91049	+	24.1595i	0.305624	+	1.24926i
$375$	−1.56438			−0.0807845
$376$	−1.25857			−0.0649058
$377$		−	10.7601i		−	0.554172i
$378$		0			0
$379$	−9.46898			−0.486389			−0.243194	−	0.969978i	$-0.578195\pi$
$379$	−9.46898			−0.486389			−0.243194	+	0.969978i	$0.578195\pi$
$380$		−	53.2444i		−	2.73138i
$381$	2.96409			0.151855
$382$			51.7035i			2.64538i
$383$		−	30.2365i		−	1.54501i	−0.635007	−	0.772506i	$-0.719003\pi$
$383$		−	30.2365i		−	1.54501i	0.635007	−	0.772506i	$-0.280997\pi$
$384$	4.16796			0.212695
$385$		0			0
$386$	−51.9379			−2.64357
$387$		−	1.56172i		−	0.0793867i
$388$			17.5392i			0.890418i
$389$	13.5302			0.686008			0.343004	−	0.939334i	$-0.388556\pi$
$389$	13.5302			0.686008			0.343004	+	0.939334i	$0.388556\pi$
$390$			9.90839i			0.501731i
$391$	8.06313			0.407770
$392$		0			0
$393$			17.8335i			0.899581i
$394$	−23.7131			−1.19465
$395$	−21.6743			−1.09055
$396$	−7.26360	+	1.77700i	−0.365010	+	0.0892977i
$397$		−	1.00066i		−	0.0502219i	−0.999685	−	0.0251109i	$-0.992006\pi$
$397$		−	1.00066i		−	0.0502219i	0.999685	−	0.0251109i	$-0.00799390\pi$
$398$	20.2068			1.01288
$399$		0			0
$400$	18.7846			0.939229
$401$	−26.9825			−1.34744			−0.673722	−	0.738985i	$-0.735305\pi$
$401$	−26.9825			−1.34744			−0.673722	+	0.738985i	$0.735305\pi$
$402$	−22.4739			−1.12090
$403$			6.18696i			0.308194i
$404$	0.881555			0.0438590
$405$		−	3.23777i		−	0.160886i
$406$		0			0
$407$	−24.4873	+	5.99068i	−1.21379	+	0.296947i
$408$	−1.90963			−0.0945410
$409$	−3.04242			−0.150438			−0.0752189	−	0.997167i	$-0.523966\pi$
$409$	−3.04242			−0.150438			−0.0752189	+	0.997167i	$0.523966\pi$
$410$	78.5130			3.87748
$411$		−	6.81143i		−	0.335983i
$412$		−	3.00243i		−	0.147919i
$413$		0			0
$414$			4.57460i			0.224829i
$415$		−	10.3507i		−	0.508094i
$416$		−	12.0426i		−	0.590435i
$417$		−	12.8845i		−	0.630958i
$418$	−11.8574	−	48.4680i	−0.579966	−	2.37065i
$419$			24.4315i			1.19356i	0.802406	+	0.596778i	$0.203553\pi$
$419$			24.4315i			1.19356i	−0.802406	+	0.596778i	$0.796447\pi$
$420$		0			0
$421$	4.67371			0.227783			0.113891	−	0.993493i	$-0.463668\pi$
$421$	4.67371			0.227783			0.113891	+	0.993493i	$0.463668\pi$
$422$	−2.96497			−0.144332
$423$		−	2.39613i		−	0.116504i
$424$			4.89249i			0.237601i
$425$	−19.9349			−0.966984
$426$	−14.0226			−0.679396
$427$		0			0
$428$		−	35.7292i		−	1.72703i
$429$	1.16932	+	4.77968i	0.0564555	+	0.230765i
$430$		−	10.4299i		−	0.502976i
$431$			5.99932i			0.288977i	0.989506	+	0.144489i	$0.0461537\pi$
$431$			5.99932i			0.288977i	−0.989506	+	0.144489i	$0.953846\pi$
$432$			3.42586i			0.164827i
$433$		−	18.5649i		−	0.892173i	−0.894990	−	0.446086i	$-0.852817\pi$
$433$		−	18.5649i		−	0.892173i	0.894990	−	0.446086i	$-0.147183\pi$
$434$		0			0
$435$			23.4821i			1.12588i
$436$		−	22.9102i		−	1.09720i
$437$	−16.1760			−0.773802
$438$	−7.51116			−0.358897
$439$	3.41070			0.162784			0.0813920	−	0.996682i	$-0.474063\pi$
$439$	3.41070			0.162784			0.0813920	+	0.996682i	$0.474063\pi$
$440$	−5.47883	+	1.34037i	−0.261193	+	0.0638995i
$441$		0			0
$442$			11.1260i			0.529210i
$443$	32.5265			1.54538			0.772689	−	0.634784i	$-0.218911\pi$
$443$	32.5265			1.54538			0.772689	+	0.634784i	$0.218911\pi$
$444$		−	17.1374i		−	0.813304i
$445$	−9.32636			−0.442112
$446$	20.9327			0.991193
$447$	−11.7176			−0.554225
$448$		0			0
$449$	24.7697			1.16895			0.584476	−	0.811411i	$-0.301300\pi$
$449$	24.7697			1.16895			0.584476	+	0.811411i	$0.301300\pi$
$450$		−	11.3100i		−	0.533159i
$451$	37.8737	−	9.26560i	1.78340	−	0.436300i
$452$	−21.2648			−1.00021
$453$	−7.44203			−0.349657
$454$			9.32151i			0.437480i
$455$		0			0
$456$	3.83104			0.179405
$457$			12.0575i			0.564028i	0.959410	+	0.282014i	$0.0910024\pi$
$457$			12.0575i			0.564028i	−0.959410	+	0.282014i	$0.908998\pi$
$458$	−37.6930			−1.76128
$459$		−	3.63565i		−	0.169698i
$460$			16.1900i			0.754861i
$461$	11.1289			0.518325			0.259162	−	0.965834i	$-0.416554\pi$
$461$	11.1289			0.518325			0.259162	+	0.965834i	$0.416554\pi$
$462$		0			0
$463$	−18.6637			−0.867375			−0.433688	−	0.901063i	$-0.642788\pi$
$463$	−18.6637			−0.867375			−0.433688	+	0.901063i	$0.642788\pi$
$464$		−	24.8462i		−	1.15346i
$465$		−	13.5020i		−	0.626141i
$466$	−56.0521			−2.59656
$467$			0.960379i			0.0444411i	0.999753	+	0.0222205i	$0.00707360\pi$
$467$			0.960379i			0.0444411i	−0.999753	+	0.0222205i	$0.992926\pi$
$468$	−3.34506			−0.154625
$469$		0			0
$470$		−	16.0025i		−	0.738140i
$471$	−15.8871			−0.732039
$472$	2.98767			0.137519
$473$	−1.23087	−	5.03127i	−0.0565956	−	0.231338i
$474$		−	13.8080i		−	0.634223i
$475$	39.9927			1.83499
$476$		0			0
$477$	−9.31456			−0.426485
$478$	−58.3159			−2.66731
$479$	−42.5555			−1.94441			−0.972205	−	0.234130i	$-0.924776\pi$
$479$	−42.5555			−1.94441			−0.972205	+	0.234130i	$0.924776\pi$
$480$			26.2809i			1.19955i
$481$	−11.2769			−0.514184
$482$			10.2319i			0.466051i
$483$		0			0
$484$	−22.0000	+	11.4496i	−1.00000	+	0.520438i
$485$	−25.1871			−1.14369
$486$	2.06268			0.0935650
$487$	−4.23397			−0.191860			−0.0959298	−	0.995388i	$-0.530582\pi$
$487$	−4.23397			−0.191860			−0.0959298	+	0.995388i	$0.530582\pi$
$488$		−	6.54396i		−	0.296231i
$489$		−	7.97918i		−	0.360831i
$490$		0			0
$491$			2.85225i			0.128720i	0.997927	+	0.0643601i	$0.0205006\pi$
$491$			2.85225i			0.128720i	−0.997927	+	0.0643601i	$0.979499\pi$
$492$			26.5059i			1.19498i
$493$			26.3677i			1.18754i
$494$		−	22.3206i		−	1.00425i
$495$	−2.55186	−	10.4309i	−0.114697	−	0.468832i
$496$			14.2864i			0.641478i
$497$		0			0
$498$	6.59407			0.295487
$499$	9.42969			0.422131			0.211065	−	0.977472i	$-0.432307\pi$
$499$	9.42969			0.422131			0.211065	+	0.977472i	$0.432307\pi$
$500$		−	3.52713i		−	0.157738i
$501$		−	14.8341i		−	0.662737i
$502$	−40.6277			−1.81330
$503$	8.39435			0.374286			0.187143	−	0.982333i	$-0.440077\pi$
$503$	8.39435			0.374286			0.187143	+	0.982333i	$0.440077\pi$
$504$		0			0
$505$			1.26595i			0.0563341i
$506$	3.60548	+	14.7376i	0.160283	+	0.655166i
$507$		−	10.7988i		−	0.479594i
$508$			6.68296i			0.296509i
$509$			28.4749i			1.26213i	0.775731	+	0.631064i	$0.217381\pi$
$509$			28.4749i			1.26213i	−0.775731	+	0.631064i	$0.782619\pi$
$510$		−	24.2806i		−	1.07517i
$511$		0			0
$512$		−	31.4065i		−	1.38798i
$513$			7.29372i			0.322026i
$514$	−45.5730			−2.01014
$515$	4.31163			0.189993
$516$	3.52113			0.155009
$517$	−1.88851	−	7.71940i	−0.0830566	−	0.339499i
$518$		0			0
$519$			17.9668i			0.788655i
$520$	−2.52313			−0.110646
$521$			12.4887i			0.547142i	0.961852	+	0.273571i	$0.0882048\pi$
$521$			12.4887i			0.547142i	−0.961852	+	0.273571i	$0.911795\pi$
$522$	−14.9597			−0.654767
$523$	31.7039			1.38631			0.693157	−	0.720786i	$-0.256219\pi$
$523$	31.7039			1.38631			0.693157	+	0.720786i	$0.256219\pi$
$524$	−40.2082			−1.75650
$525$		0			0
$526$	−47.6033			−2.07560
$527$		−	15.1612i		−	0.660434i
$528$	2.70010	+	11.0368i	0.117507	+	0.480316i
$529$	−18.0814			−0.786147
$530$	−62.2072			−2.70211
$531$			5.68806i			0.246841i
$532$		0			0
$533$	17.4417			0.755483
$534$		−	5.94152i		−	0.257115i
$535$	51.3087			2.21827
$536$		−	5.72289i		−	0.247191i
$537$		−	15.9619i		−	0.688806i
$538$	36.9221			1.59182
$539$		0			0
$540$	7.30003			0.314143
$541$		−	35.5526i		−	1.52853i	−0.644904	−	0.764263i	$-0.723103\pi$
$541$		−	35.5526i		−	1.52853i	0.644904	−	0.764263i	$-0.276897\pi$
$542$			34.4820i			1.48113i
$543$	25.6807			1.10207
$544$			29.5105i			1.26525i
$545$	32.9001			1.40929
$546$		0			0
$547$		−	10.1862i		−	0.435530i	−0.976001	−	0.217765i	$-0.930123\pi$
$547$		−	10.1862i		−	0.435530i	0.976001	−	0.217765i	$-0.0698766\pi$
$548$	15.3574			0.656034
$549$	12.4587			0.531724
$550$	−8.91401	−	36.4365i	−0.380095	−	1.55366i
$551$		−	52.8980i		−	2.25353i
$552$	−1.16490			−0.0495815
$553$		0			0
$554$	13.6866			0.581489
$555$	24.6100			1.04464
$556$	29.0500			1.23200
$557$			26.8902i			1.13938i	0.821861	+	0.569688i	$0.192936\pi$
$557$			26.8902i			1.13938i	−0.821861	+	0.569688i	$0.807064\pi$
$558$	8.60169			0.364139
$559$		−	2.31701i		−	0.0979992i
$560$		0			0
$561$	−2.86545	−	11.7127i	−0.120979	−	0.494510i
$562$	53.4531			2.25478
$563$	20.2933			0.855261			0.427631	−	0.903954i	$-0.359348\pi$
$563$	20.2933			0.855261			0.427631	+	0.903954i	$0.359348\pi$
$564$	5.40241			0.227483
$565$		−	30.5371i		−	1.28471i
$566$			22.4511i			0.943691i
$567$		0			0
$568$		−	3.57079i		−	0.149827i
$569$		−	4.30567i		−	0.180503i	−0.995919	−	0.0902516i	$-0.971233\pi$
$569$		−	4.30567i		−	0.180503i	0.995919	−	0.0902516i	$-0.0287671\pi$
$570$			48.7110i			2.04028i
$571$			20.0844i			0.840506i	0.907407	+	0.420253i	$0.138059\pi$
$571$			20.0844i			0.840506i	−0.907407	+	0.420253i	$0.861941\pi$
$572$	−10.7765	+	2.63641i	−0.450588	+	0.110234i
$573$		−	25.0662i		−	1.04715i
$574$		0			0
$575$	−12.1605			−0.507129
$576$	−9.89096			−0.412123
$577$		−	8.71221i		−	0.362694i	−0.983419	−	0.181347i	$-0.941954\pi$
$577$		−	8.71221i		−	0.362694i	0.983419	−	0.181347i	$-0.0580457\pi$
$578$			7.80112i			0.324484i
$579$	25.1798			1.04644
$580$	−52.9438			−2.19837
$581$		0			0
$582$		−	16.0459i		−	0.665123i
$583$	−30.0080	+	7.34129i	−1.24280	+	0.304045i
$584$		−	1.91268i		−	0.0791475i
$585$		−	4.80365i		−	0.198606i
$586$			17.0115i			0.702737i
$587$			26.8726i			1.10915i	0.832134	+	0.554575i	$0.187119\pi$
$587$			26.8726i			1.10915i	−0.832134	+	0.554575i	$0.812881\pi$
$588$		0			0
$589$			30.4159i			1.25327i
$590$			37.9876i			1.56393i
$591$	11.4963			0.472893
$592$	−26.0397			−1.07023
$593$	6.73925			0.276748			0.138374	−	0.990380i	$-0.455812\pi$
$593$	6.73925			0.276748			0.138374	+	0.990380i	$0.455812\pi$
$594$	6.64516	−	1.62570i	0.272654	−	0.0667034i
$595$		0			0
$596$		−	26.4191i		−	1.08217i
$597$	−9.79640			−0.400940
$598$			6.78700i			0.277541i
$599$	18.2733			0.746628			0.373314	−	0.927705i	$-0.378221\pi$
$599$	18.2733			0.746628			0.373314	+	0.927705i	$0.378221\pi$
$600$	2.88005			0.117577
$601$	−17.3928			−0.709468			−0.354734	−	0.934967i	$-0.615429\pi$
$601$	−17.3928			−0.709468			−0.354734	+	0.934967i	$0.615429\pi$
$602$		0			0
$603$	10.8955			0.443699
$604$		−	16.7791i		−	0.682734i
$605$	−16.4422	−	31.5930i	−0.668471	−	1.28444i
$606$	−0.806497			−0.0327617
$607$	21.3564			0.866831			0.433415	−	0.901194i	$-0.357308\pi$
$607$	21.3564			0.866831			0.433415	+	0.901194i	$0.357308\pi$
$608$		−	59.2029i		−	2.40099i
$609$		0			0
$610$	83.2052			3.36888
$611$		−	3.55496i		−	0.143818i
$612$	8.19711			0.331348
$613$		−	23.0564i		−	0.931238i	−0.884985	−	0.465619i	$-0.845832\pi$
$613$		−	23.0564i		−	0.931238i	0.884985	−	0.465619i	$-0.154168\pi$
$614$			66.2716i			2.67450i
$615$	−38.0636			−1.53487
$616$		0			0
$617$	44.2394			1.78101			0.890506	−	0.454972i	$-0.150351\pi$
$617$	44.2394			1.78101			0.890506	+	0.454972i	$0.150351\pi$
$618$			2.74680i			0.110492i
$619$		−	2.60928i		−	0.104876i	−0.998624	−	0.0524380i	$-0.983301\pi$
$619$		−	2.60928i		−	0.104876i	0.998624	−	0.0524380i	$-0.0166992\pi$
$620$	30.4422			1.22259
$621$		−	2.21779i		−	0.0889970i
$622$	−34.7911			−1.39499
$623$		0			0
$624$			5.08271i			0.203471i
$625$	−22.3507			−0.894029
$626$	−12.1409			−0.485247
$627$	5.74856	+	23.4976i	0.229575	+	0.938403i
$628$		−	35.8198i		−	1.42936i
$629$	27.6343			1.10185
$630$		0			0
$631$	−20.2358			−0.805574			−0.402787	−	0.915294i	$-0.631959\pi$
$631$	−20.2358			−0.805574			−0.402787	+	0.915294i	$0.631959\pi$
$632$	3.51615			0.139865
$633$	1.43744			0.0571329
$634$		−	13.5889i		−	0.539683i
$635$	−9.59703			−0.380847
$636$		−	21.0010i		−	0.832745i
$637$		0			0
$638$	−48.1943	+	11.7905i	−1.90803	+	0.466790i
$639$	6.79823			0.268934
$640$	−13.4949			−0.533433
$641$	−24.7965			−0.979405			−0.489702	−	0.871890i	$-0.662895\pi$
$641$	−24.7965			−0.979405			−0.489702	+	0.871890i	$0.662895\pi$
$642$			32.6871i			1.29006i
$643$		−	12.6787i		−	0.499998i	−0.968246	−	0.249999i	$-0.919570\pi$
$643$		−	12.6787i		−	0.499998i	0.968246	−	0.249999i	$-0.0804303\pi$
$644$		0			0
$645$			5.05649i			0.199099i
$646$			54.6970i			2.15202i
$647$			12.6318i			0.496606i	0.968682	+	0.248303i	$0.0798729\pi$
$647$			12.6318i			0.496606i	−0.968682	+	0.248303i	$0.920127\pi$
$648$			0.525252i			0.0206339i
$649$	4.48306	+	18.3248i	0.175975	+	0.719310i
$650$		−	16.7799i		−	0.658160i
$651$		0			0
$652$	17.9902			0.704551
$653$	38.8218			1.51921			0.759606	−	0.650383i	$-0.225392\pi$
$653$	38.8218			1.51921			0.759606	+	0.650383i	$0.225392\pi$
$654$			20.9596i			0.819585i
$655$		−	57.7408i		−	2.25612i
$656$	40.2748			1.57247
$657$	3.64146			0.142067
$658$		0			0
$659$			20.3177i			0.791466i	0.918366	+	0.395733i	$0.129509\pi$
$659$			20.3177i			0.791466i	−0.918366	+	0.395733i	$0.870491\pi$
$660$	23.5179	−	5.75353i	0.915433	−	0.223956i
$661$		−	32.3962i		−	1.26007i	−0.776568	−	0.630033i	$-0.783041\pi$
$661$		−	32.3962i		−	1.26007i	0.776568	−	0.630033i	$-0.216959\pi$
$662$		−	45.8154i		−	1.78067i
$663$		−	5.39395i		−	0.209484i
$664$			1.67915i			0.0651637i
$665$		0			0
$666$			15.6783i			0.607520i
$667$			16.0847i			0.622800i
$668$	33.4456			1.29405
$669$	−10.1483			−0.392356
$670$	72.7655			2.81118
$671$	40.1371	−	9.81934i	1.54948	−	0.379071i
$672$		0			0
$673$			26.5001i			1.02150i	0.859728	+	0.510752i	$0.170633\pi$
$673$			26.5001i			1.02150i	−0.859728	+	0.510752i	$0.829367\pi$
$674$	−55.1227			−2.12325
$675$			5.48317i			0.211047i
$676$	24.3476			0.936445
$677$	0.791657			0.0304258			0.0152129	−	0.999884i	$-0.495157\pi$
$677$	0.791657			0.0304258			0.0152129	+	0.999884i	$0.495157\pi$
$678$	19.4542			0.747135
$679$		0			0
$680$	6.18296			0.237106
$681$		−	4.51913i		−	0.173173i
$682$	27.7114	−	6.77944i	1.06112	−	0.259598i
$683$	−16.3625			−0.626094			−0.313047	−	0.949738i	$-0.601350\pi$
$683$	−16.3625			−0.626094			−0.313047	+	0.949738i	$0.601350\pi$
$684$	−16.4448			−0.628781
$685$			22.0539i			0.842634i
$686$		0			0
$687$	18.2738			0.697190
$688$		−	5.35024i		−	0.203976i
$689$	−13.8193			−0.526475
$690$		−	14.8115i		−	0.563864i
$691$			47.5490i			1.80885i	0.426632	+	0.904425i	$0.359700\pi$
$691$			47.5490i			1.80885i	−0.426632	+	0.904425i	$0.640300\pi$
$692$	−40.5088			−1.53991
$693$		0			0
$694$	14.2954			0.542647
$695$			41.7172i			1.58242i
$696$		−	3.80941i		−	0.144395i
$697$	−42.7411			−1.61894
$698$		−	36.0209i		−	1.36341i
$699$	27.1744			1.02783
$700$		0			0
$701$		−	35.3150i		−	1.33383i	−0.745135	−	0.666914i	$-0.767615\pi$
$701$		−	35.3150i		−	1.33383i	0.745135	−	0.666914i	$-0.232385\pi$
$702$	3.06025			0.115502
$703$	−55.4390			−2.09092
$704$	−31.8649	+	7.79558i	−1.20095	+	0.293807i
$705$			7.75811i			0.292187i
$706$	−25.4433			−0.957570
$707$		0			0
$708$	−12.8246			−0.481977
$709$	2.00856			0.0754329			0.0377164	−	0.999288i	$-0.487992\pi$
$709$	2.00856			0.0754329			0.0377164	+	0.999288i	$0.487992\pi$
$710$	45.4019			1.70390
$711$			6.69422i			0.251053i
$712$	1.51298			0.0567014
$713$		−	9.24854i		−	0.346361i
$714$		0			0
$715$	−3.78600	−	15.4755i	−0.141589	−	0.578752i
$716$	35.9884			1.34495
$717$	28.2719			1.05583
$718$	−0.418975			−0.0156360
$719$		−	17.1720i		−	0.640408i	−0.947349	−	0.320204i	$-0.896249\pi$
$719$		−	17.1720i		−	0.640408i	0.947349	−	0.320204i	$-0.103751\pi$
$720$		−	11.0922i		−	0.413381i
$721$		0			0
$722$		−	70.5403i		−	2.62524i
$723$		−	4.96050i		−	0.184483i
$724$			57.9010i			2.15187i
$725$		−	39.7669i		−	1.47691i
$726$	20.1269	−	10.4748i	0.746978	−	0.388756i
$727$			28.0896i			1.04179i	0.853622	+	0.520894i	$0.174401\pi$
$727$			28.0896i			1.04179i	−0.853622	+	0.520894i	$0.825599\pi$
$728$		0			0
$729$	−1.00000			−0.0370370
$730$	24.3194			0.900103
$731$			5.67787i			0.210004i
$732$			28.0899i			1.03823i
$733$	−23.2497			−0.858746			−0.429373	−	0.903127i	$-0.641265\pi$
$733$	−23.2497			−0.858746			−0.429373	+	0.903127i	$0.641265\pi$
$734$	28.2153			1.04145
$735$		0			0
$736$			18.0018i			0.663553i
$737$	35.1012	−	8.58731i	1.29297	−	0.316318i
$738$		−	24.2491i		−	0.892621i
$739$			22.5154i			0.828242i	0.910222	+	0.414121i	$0.135911\pi$
$739$			22.5154i			0.828242i	−0.910222	+	0.414121i	$0.864089\pi$
$740$			55.4869i			2.03974i
$741$			10.8212i			0.397526i
$742$		0			0
$743$			16.7336i			0.613897i	0.951726	+	0.306948i	$0.0993079\pi$
$743$			16.7336i			0.613897i	−0.951726	+	0.306948i	$0.900692\pi$
$744$			2.19038i			0.0803033i
$745$	37.9390			1.38998
$746$	−24.2622			−0.888302
$747$	−3.19685			−0.116966
$748$	26.4079	−	6.46056i	0.965570	−	0.236222i
$749$		0			0
$750$			3.22682i			0.117827i
$751$	−48.1064			−1.75543			−0.877714	−	0.479185i	$-0.840932\pi$
$751$	−48.1064			−1.75543			−0.877714	+	0.479185i	$0.840932\pi$
$752$		−	8.20880i		−	0.299344i
$753$	19.6966			0.717783
$754$	−22.1946			−0.808279
$755$	24.0956			0.876929
$756$		0			0
$757$	18.5939			0.675806			0.337903	−	0.941181i	$-0.390282\pi$
$757$	18.5939			0.675806			0.337903	+	0.941181i	$0.390282\pi$
$758$			19.5315i			0.709415i
$759$	−1.74796	−	7.14488i	−0.0634469	−	0.259343i
$760$	−12.4040			−0.449942
$761$	42.0419			1.52402			0.762008	−	0.647567i	$-0.224213\pi$
$761$	42.0419			1.52402			0.762008	+	0.647567i	$0.224213\pi$
$762$		−	6.11396i		−	0.221485i
$763$		0			0
$764$	56.5153			2.04465
$765$			11.7714i			0.425596i
$766$	−62.3682			−2.25345
$767$			8.43897i			0.304713i
$768$			11.1848i			0.403596i
$769$	26.0149			0.938120			0.469060	−	0.883166i	$-0.344593\pi$
$769$	26.0149			0.938120			0.469060	+	0.883166i	$0.344593\pi$
$770$		0			0
$771$	22.0941			0.795699
$772$			56.7716i			2.04325i
$773$		−	5.09360i		−	0.183204i	−0.995796	−	0.0916020i	$-0.970801\pi$
$773$		−	5.09360i		−	0.183204i	0.995796	−	0.0916020i	$-0.0291988\pi$
$774$	−3.22133			−0.115788
$775$			22.8657i			0.821358i
$776$	4.08601			0.146679
$777$		0			0
$778$		−	27.9084i		−	1.00057i
$779$	85.7458			3.07216
$780$	10.8305			0.387795
$781$	21.9013	−	5.35804i	0.783690	−	0.191726i
$782$		−	16.6316i		−	0.594746i
$783$	7.25254			0.259185
$784$		0			0
$785$	51.4388			1.83593
$786$	36.7848			1.31207
$787$	−42.4243			−1.51226			−0.756131	−	0.654421i	$-0.772913\pi$
$787$	−42.4243			−1.51226			−0.756131	+	0.654421i	$0.772913\pi$
$788$			25.9200i			0.923361i
$789$	23.0784			0.821612
$790$			44.7072i			1.59061i
$791$		0			0
$792$	0.413978	+	1.69216i	0.0147101	+	0.0601283i
$793$	18.4841			0.656388
$794$	−2.06405			−0.0732503
$795$	30.1584			1.06961
$796$		−	22.0874i		−	0.782867i
$797$			22.5922i			0.800258i	0.916459	+	0.400129i	$0.131035\pi$
$797$			22.5922i			0.800258i	−0.916459	+	0.400129i	$0.868965\pi$
$798$		0			0
$799$			8.71148i			0.308190i
$800$		−	44.5067i		−	1.57355i
$801$			2.88049i			0.101777i
$802$			55.6563i			1.96529i
$803$	11.7314	−	2.87002i	0.413992	−	0.101281i
$804$			24.5655i			0.866359i
$805$		0			0
$806$	12.7617			0.449512
$807$	−17.9001			−0.630112
$808$		−	0.205371i		−	0.00722492i
$809$		−	19.9505i		−	0.701422i	−0.936484	−	0.350711i	$-0.885940\pi$
$809$		−	19.9505i		−	0.701422i	0.936484	−	0.350711i	$-0.114060\pi$
$810$	−6.67848			−0.234658
$811$	−7.97419			−0.280012			−0.140006	−	0.990151i	$-0.544712\pi$
$811$	−7.97419			−0.280012			−0.140006	+	0.990151i	$0.544712\pi$
$812$		0			0
$813$		−	16.7171i		−	0.586293i
$814$	12.3568	+	50.5094i	0.433107	+	1.77035i
$815$			25.8348i			0.904952i
$816$		−	12.4553i		−	0.436021i
$817$		−	11.3908i		−	0.398512i
$818$			6.27553i			0.219419i
$819$		0			0
$820$		−	85.8199i		−	2.99696i
$821$			1.86259i			0.0650049i	0.999472	+	0.0325025i	$0.0103477\pi$
$821$			1.86259i			0.0650049i	−0.999472	+	0.0325025i	$0.989652\pi$
$822$	−14.0498			−0.490043
$823$	−6.22546			−0.217006			−0.108503	−	0.994096i	$-0.534606\pi$
$823$	−6.22546			−0.217006			−0.108503	+	0.994096i	$0.534606\pi$
$824$	−0.699460			−0.0243668
$825$	4.32157	+	17.6647i	0.150458	+	0.615005i
$826$		0			0
$827$		−	27.4469i		−	0.954423i	−0.878788	−	0.477212i	$-0.841648\pi$
$827$		−	27.4469i		−	0.954423i	0.878788	−	0.477212i	$-0.158352\pi$
$828$	5.00034			0.173774
$829$			40.6602i			1.41219i	0.708119	+	0.706093i	$0.249544\pi$
$829$			40.6602i			1.41219i	−0.708119	+	0.706093i	$0.750456\pi$
$830$	−21.3501			−0.741072
$831$	−6.63537			−0.230178
$832$	−14.6745			−0.508747
$833$		0			0
$834$	−26.5766			−0.920274
$835$			48.0293i			1.66212i
$836$	−52.9787	+	12.9610i	−1.83231	+	0.448264i
$837$	−4.17015			−0.144142
$838$	50.3943			1.74084
$839$			16.7250i			0.577412i	0.957418	+	0.288706i	$0.0932250\pi$
$839$			16.7250i			0.577412i	−0.957418	+	0.288706i	$0.906775\pi$
$840$		0			0
$841$	−23.5994			−0.813773
$842$		−	9.64036i		−	0.332229i
$843$	−25.9144			−0.892540
$844$			3.24091i			0.111557i
$845$			34.9642i			1.20281i
$846$	−4.94244			−0.169925
$847$		0			0
$848$	−31.9104			−1.09581
$849$		−	10.8844i		−	0.373553i
$850$			41.1193i			1.41038i
$851$	16.8573			0.577860
$852$			15.3276i			0.525115i
$853$	−3.92605			−0.134425			−0.0672127	−	0.997739i	$-0.521411\pi$
$853$	−3.92605			−0.134425			−0.0672127	+	0.997739i	$0.521411\pi$
$854$		0			0
$855$		−	23.6154i		−	0.807630i
$856$	−8.32362			−0.284496
$857$	1.48147			0.0506062			0.0253031	−	0.999680i	$-0.491945\pi$
$857$	1.48147			0.0506062			0.0253031	+	0.999680i	$0.491945\pi$
$858$	9.85895	−	2.41194i	0.336579	−	0.0823423i
$859$		−	17.2205i		−	0.587557i	−0.955874	−	0.293779i	$-0.905087\pi$
$859$		−	17.2205i		−	0.587557i	0.955874	−	0.293779i	$-0.0949128\pi$
$860$	−11.4006			−0.388757
$861$		0			0
$862$	12.3747			0.421483
$863$	21.4369			0.729722			0.364861	−	0.931062i	$-0.381117\pi$
$863$	21.4369			0.729722			0.364861	+	0.931062i	$0.381117\pi$
$864$	8.11696			0.276145
$865$		−	58.1724i		−	1.97792i
$866$	−38.2935			−1.30126
$867$		−	3.78203i		−	0.128445i
$868$		0			0
$869$	5.27606	+	21.5662i	0.178978	+	0.731583i
$870$	48.4360			1.64213
$871$	16.1649			0.547726
$872$	−5.33727			−0.180743
$873$			7.77914i			0.263284i
$874$			33.3658i			1.12862i
$875$		0			0
$876$			8.21020i			0.277397i
$877$		−	1.37476i		−	0.0464223i	−0.999731	−	0.0232112i	$-0.992611\pi$
$877$		−	1.37476i		−	0.0464223i	0.999731	−	0.0232112i	$-0.00738901\pi$
$878$		−	7.03519i		−	0.237426i
$879$		−	8.24726i		−	0.278173i
$880$	−8.74231	−	35.7347i	−0.294703	−	1.20462i
$881$		−	10.9845i		−	0.370077i	−0.982731	−	0.185039i	$-0.940759\pi$
$881$		−	10.9845i		−	0.370077i	0.982731	−	0.185039i	$-0.0592410\pi$
$882$		0			0
$883$	−14.7993			−0.498035			−0.249018	−	0.968499i	$-0.580108\pi$
$883$	−14.7993			−0.498035			−0.249018	+	0.968499i	$0.580108\pi$
$884$	12.1615			0.409034
$885$		−	18.4166i		−	0.619069i
$886$		−	67.0916i		−	2.25399i
$887$	53.4290			1.79397			0.896986	−	0.442060i	$-0.145752\pi$
$887$	53.4290			1.79397			0.896986	+	0.442060i	$0.145752\pi$
$888$	−3.99240			−0.133976
$889$		0			0
$890$			19.2373i			0.644835i
$891$	−3.22162	+	0.788152i	−0.107928	+	0.0264041i
$892$		−	22.8808i		−	0.766107i
$893$		−	17.4767i		−	0.584835i
$894$			24.1697i			0.808357i
$895$			51.6809i			1.72750i
$896$		0			0
$897$		−	3.29038i		−	0.109863i
$898$		−	51.0919i		−	1.70496i
$899$	30.2442			1.00870
$900$	−12.3626			−0.412087
$901$	33.8645			1.12819
$902$	−19.1120	−	78.1213i	−0.636358	−	2.60115i
$903$		0			0
$904$			4.95393i			0.164765i
$905$	−83.1484			−2.76395
$906$			15.3505i			0.509987i
$907$	49.4507			1.64198			0.820991	−	0.570941i	$-0.193421\pi$
$907$	49.4507			1.64198			0.820991	+	0.570941i	$0.193421\pi$
$908$	10.1890			0.338135
$909$	0.390995			0.0129685
$910$		0			0
$911$	35.4561			1.17471			0.587356	−	0.809329i	$-0.300169\pi$
$911$	35.4561			1.17471			0.587356	+	0.809329i	$0.300169\pi$
$912$			24.9873i			0.827412i
$913$	−10.2990	+	2.51960i	−0.340848	+	0.0833865i
$914$	24.8708			0.822654
$915$	−40.3384			−1.33355
$916$			41.2010i			1.36132i
$917$		0			0
$918$	−7.49918			−0.247510
$919$		−	51.5333i		−	1.69993i	−0.526841	−	0.849964i	$-0.676624\pi$
$919$		−	51.5333i		−	1.69993i	0.526841	−	0.849964i	$-0.323376\pi$
$920$	3.77168			0.124349
$921$		−	32.1289i		−	1.05868i
$922$		−	22.9554i		−	0.755995i
$923$	10.0860			0.331986
$924$		0			0
$925$	−41.6771			−1.37034
$926$			38.4972i			1.26510i
$927$		−	1.33166i		−	0.0437376i
$928$	−58.8686			−1.93246
$929$			39.6612i			1.30124i	0.759403	+	0.650621i	$0.225491\pi$
$929$			39.6612i			1.30124i	−0.759403	+	0.650621i	$0.774509\pi$
$930$	−27.8503			−0.913248
$931$		0			0
$932$			61.2686i			2.00692i
$933$	16.8669			0.552199
$934$	1.98095			0.0648188
$935$	9.27766	+	37.9230i	0.303412	+	1.24021i
$936$			0.779279i			0.0254715i
$937$	−0.874265			−0.0285610			−0.0142805	−	0.999898i	$-0.504546\pi$
$937$	−0.874265			−0.0285610			−0.0142805	+	0.999898i	$0.504546\pi$
$938$		0			0
$939$	5.88598			0.192082
$940$	−17.4918			−0.570519
$941$	−10.6006			−0.345569			−0.172784	−	0.984960i	$-0.555276\pi$
$941$	−10.6006			−0.345569			−0.172784	+	0.984960i	$0.555276\pi$
$942$			32.7700i			1.06770i
$943$	−26.0726			−0.849042
$944$			19.4865i			0.634232i
$945$		0			0
$946$	−10.3779	+	2.53890i	−0.337414	+	0.0825466i
$947$	−31.5170			−1.02416			−0.512082	−	0.858937i	$-0.671126\pi$
$947$	−31.5170			−1.02416			−0.512082	+	0.858937i	$0.671126\pi$
$948$	−15.0931			−0.490201
$949$	5.40257			0.175375
$950$		−	82.4921i		−	2.67640i
$951$			6.58797i			0.213630i
$952$		0			0
$953$			17.2801i			0.559758i	0.960035	+	0.279879i	$0.0902943\pi$
$953$			17.2801i			0.559758i	−0.960035	+	0.279879i	$0.909706\pi$
$954$			19.2130i			0.622042i
$955$			81.1585i			2.62623i
$956$			63.7431i			2.06160i
$957$	23.3649	−	5.71610i	0.755281	−	0.184775i
$958$			87.7784i			2.83599i
$959$		0			0
$960$	32.0247			1.03359
$961$	13.6098			0.439026
$962$			23.2607i			0.749955i
$963$		−	15.8469i		−	0.510659i
$964$	11.1842			0.360218
$965$	−81.5265			−2.62443
$966$		0			0
$967$			6.32224i			0.203309i	0.994820	+	0.101655i	$0.0324137\pi$
$967$			6.32224i			0.203309i	−0.994820	+	0.101655i	$0.967586\pi$
$968$	2.66736	+	5.12522i	0.0857322	+	0.164731i
$969$		−	26.5174i		−	0.851863i
$970$			51.9529i			1.66811i
$971$			32.6048i			1.04634i	0.852229	+	0.523169i	$0.175251\pi$
$971$			32.6048i			1.04634i	−0.852229	+	0.523169i	$0.824749\pi$
$972$		−	2.25465i		−	0.0723178i
$973$		0			0
$974$			8.73333i			0.279834i
$975$			8.13498i			0.260528i
$976$	42.6818			1.36621
$977$	−21.9427			−0.702011			−0.351005	−	0.936373i	$-0.614160\pi$
$977$	−21.9427			−0.702011			−0.351005	+	0.936373i	$0.614160\pi$
$978$	−16.4585			−0.526284
$979$	2.27026	+	9.27983i	0.0725578	+	0.296585i
$980$		0			0
$981$		−	10.1613i		−	0.324427i
$982$	5.88328			0.187743
$983$			10.4516i			0.333353i	0.986012	+	0.166677i	$0.0533036\pi$
$983$			10.4516i			0.333353i	−0.986012	+	0.166677i	$0.946696\pi$
$984$	6.17492			0.196849
$985$	−37.2223			−1.18600
$986$	54.3882			1.73207
$987$		0			0
$988$	−24.3979			−0.776201
$989$			3.46357i			0.110135i
$990$	−21.5155	+	5.26366i	−0.683808	+	0.167290i
$991$	−24.8680			−0.789959			−0.394979	−	0.918690i	$-0.629248\pi$
$991$	−24.8680			−0.789959			−0.394979	+	0.918690i	$0.629248\pi$
$992$	33.8490			1.07471
$993$			22.2116i			0.704864i
$994$		0			0
$995$	31.7185			1.00554
$996$		−	7.20775i		−	0.228386i
$997$	25.6264			0.811596			0.405798	−	0.913963i	$-0.366994\pi$
$997$	25.6264			0.811596			0.405798	+	0.913963i	$0.366994\pi$
$998$		−	19.4504i		−	0.615692i
$999$		−	7.60092i		−	0.240483i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1617.2.c.b.538.10	yes	48
7.6	odd	2	inner	1617.2.c.b.538.9	✓	48
11.10	odd	2	inner	1617.2.c.b.538.40	yes	48
77.76	even	2	inner	1617.2.c.b.538.39	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1617.2.c.b.538.9	✓	48	7.6	odd	2	inner
1617.2.c.b.538.10	yes	48	1.1	even	1	trivial
1617.2.c.b.538.39	yes	48	77.76	even	2	inner
1617.2.c.b.538.40	yes	48	11.10	odd	2	inner

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:	\( N \)	\(=\)	\( 1617 = 3 \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1617.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.06268i q^{2} +1.00000i q^{3} -2.25465 q^{4} -3.23777i q^{5} +2.06268 q^{6} +0.525252i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q-2.06268i q^{2} +1.00000i q^{3} -2.25465 q^{4} -3.23777i q^{5} +2.06268 q^{6} +0.525252i q^{8} -1.00000 q^{9} -6.67848 q^{10} +(-3.22162 + 0.788152i) q^{11} -2.25465i q^{12} -1.48363 q^{13} +3.23777 q^{15} -3.42586 q^{16} +3.63565 q^{17} +2.06268i q^{18} -7.29372 q^{19} +7.30003i q^{20} +(1.62570 + 6.64516i) q^{22} +2.21779 q^{23} -0.525252 q^{24} -5.48317 q^{25} +3.06025i q^{26} -1.00000i q^{27} +7.25254i q^{29} -6.67848i q^{30} -4.17015i q^{31} +8.11696i q^{32} +(-0.788152 - 3.22162i) q^{33} -7.49918i q^{34} +2.25465 q^{36} +7.60092 q^{37} +15.0446i q^{38} -1.48363i q^{39} +1.70065 q^{40} -11.7561 q^{41} +1.56172i q^{43} +(7.26360 - 1.77700i) q^{44} +3.23777i q^{45} -4.57460i q^{46} +2.39613i q^{47} -3.42586i q^{48} +11.3100i q^{50} +3.63565i q^{51} +3.34506 q^{52} +9.31456 q^{53} -2.06268 q^{54} +(2.55186 + 10.4309i) q^{55} -7.29372i q^{57} +14.9597 q^{58} -5.68806i q^{59} -7.30003 q^{60} -12.4587 q^{61} -8.60169 q^{62} +9.89096 q^{64} +4.80365i q^{65} +(-6.64516 + 1.62570i) q^{66} -10.8955 q^{67} -8.19711 q^{68} +2.21779i q^{69} -6.79823 q^{71} -0.525252i q^{72} -3.64146 q^{73} -15.6783i q^{74} -5.48317i q^{75} +16.4448 q^{76} -3.06025 q^{78} -6.69422i q^{79} +11.0922i q^{80} +1.00000 q^{81} +24.2491i q^{82} +3.19685 q^{83} -11.7714i q^{85} +3.22133 q^{86} -7.25254 q^{87} +(-0.413978 - 1.69216i) q^{88} -2.88049i q^{89} +6.67848 q^{90} -5.00034 q^{92} +4.17015 q^{93} +4.94244 q^{94} +23.6154i q^{95} -8.11696 q^{96} -7.77914i q^{97} +(3.22162 - 0.788152i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 64 q^{4} - 48 q^{9}+O(q^{10}) \) 48 * q - 64 * q^4 - 48 * q^9	\( 48 q - 64 q^{4} - 48 q^{9} - 16 q^{11} + 64 q^{16} + 16 q^{22} + 32 q^{23} - 80 q^{25} + 64 q^{36} - 96 q^{37} - 32 q^{44} + 64 q^{53} + 48 q^{58} - 48 q^{60} - 240 q^{64} + 96 q^{67} - 32 q^{71} + 48 q^{78} + 48 q^{81} - 96 q^{86} - 48 q^{88} - 32 q^{92} + 96 q^{93} + 16 q^{99}+O(q^{100}) \) 48 * q - 64 * q^4 - 48 * q^9 - 16 * q^11 + 64 * q^16 + 16 * q^22 + 32 * q^23 - 80 * q^25 + 64 * q^36 - 96 * q^37 - 32 * q^44 + 64 * q^53 + 48 * q^58 - 48 * q^60 - 240 * q^64 + 96 * q^67 - 32 * q^71 + 48 * q^78 + 48 * q^81 - 96 * q^86 - 48 * q^88 - 32 * q^92 + 96 * q^93 + 16 * q^99

Introduction

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