LMFDB - Embedded newform 1617.2.c.b.538.4

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			538.4
Character	$\chi$	$=$	1617.538
Dual form			1617.2.c.b.538.45

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.69641i q^{2} +1.00000i q^{3} -5.27065 q^{4} +3.60829i q^{5} +2.69641 q^{6} +8.81904i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q-2.69641i q^{2} +1.00000i q^{3} -5.27065 q^{4} +3.60829i q^{5} +2.69641 q^{6} +8.81904i q^{8} -1.00000 q^{9} +9.72943 q^{10} +(-2.32133 + 2.36885i) q^{11} -5.27065i q^{12} +4.29996 q^{13} -3.60829 q^{15} +13.2385 q^{16} -6.77627 q^{17} +2.69641i q^{18} +2.03085 q^{19} -19.0180i q^{20} +(6.38740 + 6.25926i) q^{22} +1.20664 q^{23} -8.81904 q^{24} -8.01972 q^{25} -11.5945i q^{26} -1.00000i q^{27} -0.635849i q^{29} +9.72943i q^{30} -5.92651i q^{31} -18.0583i q^{32} +(-2.36885 - 2.32133i) q^{33} +18.2716i q^{34} +5.27065 q^{36} -9.93807 q^{37} -5.47602i q^{38} +4.29996i q^{39} -31.8216 q^{40} -1.61156 q^{41} -6.25967i q^{43} +(12.2349 - 12.4854i) q^{44} -3.60829i q^{45} -3.25361i q^{46} -0.262840i q^{47} +13.2385i q^{48} +21.6245i q^{50} -6.77627i q^{51} -22.6636 q^{52} -7.12675 q^{53} -2.69641 q^{54} +(-8.54748 - 8.37601i) q^{55} +2.03085i q^{57} -1.71451 q^{58} +3.79946i q^{59} +19.0180 q^{60} -6.15699 q^{61} -15.9803 q^{62} -22.2158 q^{64} +15.5155i q^{65} +(-6.25926 + 6.38740i) q^{66} +6.29206 q^{67} +35.7154 q^{68} +1.20664i q^{69} -13.9977 q^{71} -8.81904i q^{72} +5.55556 q^{73} +26.7972i q^{74} -8.01972i q^{75} -10.7039 q^{76} +11.5945 q^{78} +12.5001i q^{79} +47.7682i q^{80} +1.00000 q^{81} +4.34544i q^{82} +1.67071 q^{83} -24.4507i q^{85} -16.8787 q^{86} +0.635849 q^{87} +(-20.8910 - 20.4719i) q^{88} -8.75251i q^{89} -9.72943 q^{90} -6.35979 q^{92} +5.92651 q^{93} -0.708725 q^{94} +7.32790i q^{95} +18.0583 q^{96} +2.61309i q^{97} +(2.32133 - 2.36885i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$		−	2.69641i		−	1.90665i	−0.301941	−	0.953327i	$-0.597635\pi$
$2$		−	2.69641i		−	1.90665i	0.301941	−	0.953327i	$-0.402365\pi$
$3$			1.00000i			0.577350i
$3$			1.00000i			0.577350i
$4$	−5.27065			−2.63533
$5$			3.60829i			1.61367i	0.590774	+	0.806837i	$0.298823\pi$
$5$			3.60829i			1.61367i	−0.590774	+	0.806837i	$0.701177\pi$
$6$	2.69641			1.10081
$7$		0			0
$7$		0			0
$8$			8.81904i			3.11800i
$9$	−1.00000			−0.333333
$10$	9.72943			3.07672
$11$	−2.32133	+	2.36885i	−0.699906	+	0.714235i
$11$	−2.32133	+	2.36885i	−0.699906	+	0.714235i
$12$		−	5.27065i		−	1.52151i
$13$	4.29996			1.19259			0.596297	−	0.802764i	$-0.296638\pi$
$13$	4.29996			1.19259			0.596297	+	0.802764i	$0.296638\pi$
$14$		0			0
$15$	−3.60829			−0.931655
$16$	13.2385			3.30962
$17$	−6.77627			−1.64349			−0.821743	−	0.569858i	$-0.806998\pi$
$17$	−6.77627			−1.64349			−0.821743	+	0.569858i	$0.806998\pi$
$18$			2.69641i			0.635551i
$19$	2.03085			0.465910			0.232955	−	0.972488i	$-0.425161\pi$
$19$	2.03085			0.465910			0.232955	+	0.972488i	$0.425161\pi$
$20$		−	19.0180i		−	4.25256i
$21$		0			0
$22$	6.38740	+	6.25926i	1.36180	+	1.33448i
$23$	1.20664			0.251602			0.125801	−	0.992055i	$-0.459850\pi$
$23$	1.20664			0.251602			0.125801	+	0.992055i	$0.459850\pi$
$24$	−8.81904			−1.80018
$25$	−8.01972			−1.60394
$26$		−	11.5945i		−	2.27386i
$27$		−	1.00000i		−	0.192450i
$28$		0			0
$29$		−	0.635849i		−	0.118074i	−0.998256	−	0.0590371i	$-0.981197\pi$
$29$		−	0.635849i		−	0.118074i	0.998256	−	0.0590371i	$-0.0188030\pi$
$30$			9.72943i			1.77634i
$31$		−	5.92651i		−	1.06443i	−0.846608	−	0.532217i	$-0.821359\pi$
$31$		−	5.92651i		−	1.06443i	0.846608	−	0.532217i	$-0.178641\pi$
$32$		−	18.0583i		−	3.19229i
$33$	−2.36885	−	2.32133i	−0.412364	−	0.404091i
$34$			18.2716i			3.13356i
$35$		0			0
$36$	5.27065			0.878442
$37$	−9.93807			−1.63381			−0.816905	−	0.576773i	$-0.804312\pi$
$37$	−9.93807			−1.63381			−0.816905	+	0.576773i	$0.804312\pi$
$38$		−	5.47602i		−	0.888328i
$39$			4.29996i			0.688544i
$40$	−31.8216			−5.03144
$41$	−1.61156			−0.251684			−0.125842	−	0.992050i	$-0.540163\pi$
$41$	−1.61156			−0.251684			−0.125842	+	0.992050i	$0.540163\pi$
$42$		0			0
$43$		−	6.25967i		−	0.954590i	−0.878743	−	0.477295i	$-0.841617\pi$
$43$		−	6.25967i		−	0.954590i	0.878743	−	0.477295i	$-0.158383\pi$
$44$	12.2349	−	12.4854i	1.84448	−	1.88224i
$45$		−	3.60829i		−	0.537891i
$46$		−	3.25361i		−	0.479718i
$47$		−	0.262840i		−	0.0383391i	−0.999816	−	0.0191696i	$-0.993898\pi$
$47$		−	0.262840i		−	0.0383391i	0.999816	−	0.0191696i	$-0.00610224\pi$
$48$			13.2385i			1.91081i
$49$		0			0
$50$			21.6245i			3.05817i
$51$		−	6.77627i		−	0.948867i
$52$	−22.6636			−3.14287
$53$	−7.12675			−0.978934			−0.489467	−	0.872022i	$-0.662809\pi$
$53$	−7.12675			−0.978934			−0.489467	+	0.872022i	$0.662809\pi$
$54$	−2.69641			−0.366936
$55$	−8.54748	−	8.37601i	−1.15254	−	1.12942i
$56$		0			0
$57$			2.03085i			0.268993i
$58$	−1.71451			−0.225126
$59$			3.79946i			0.494647i	0.968933	+	0.247324i	$0.0795510\pi$
$59$			3.79946i			0.494647i	−0.968933	+	0.247324i	$0.920449\pi$
$60$	19.0180			2.45522
$61$	−6.15699			−0.788322			−0.394161	−	0.919041i	$-0.628965\pi$
$61$	−6.15699			−0.788322			−0.394161	+	0.919041i	$0.628965\pi$
$62$	−15.9803			−2.02951
$63$		0			0
$64$	−22.2158			−2.77698
$65$			15.5155i			1.92446i
$66$	−6.25926	+	6.38740i	−0.770461	+	0.786234i
$67$	6.29206			0.768698			0.384349	−	0.923188i	$-0.374426\pi$
$67$	6.29206			0.768698			0.384349	+	0.923188i	$0.374426\pi$
$68$	35.7154			4.33112
$69$			1.20664i			0.145263i
$70$		0			0
$71$	−13.9977			−1.66123			−0.830613	−	0.556850i	$-0.812010\pi$
$71$	−13.9977			−1.66123			−0.830613	+	0.556850i	$0.812010\pi$
$72$		−	8.81904i		−	1.03933i
$73$	5.55556			0.650229			0.325114	−	0.945675i	$-0.394597\pi$
$73$	5.55556			0.650229			0.325114	+	0.945675i	$0.394597\pi$
$74$			26.7972i			3.11511i
$75$		−	8.01972i		−	0.926038i
$76$	−10.7039			−1.22782
$77$		0			0
$78$	11.5945			1.31282
$79$			12.5001i			1.40637i	0.711009	+	0.703183i	$0.248239\pi$
$79$			12.5001i			1.40637i	−0.711009	+	0.703183i	$0.751761\pi$
$80$			47.7682i			5.34065i
$81$	1.00000			0.111111
$82$			4.34544i			0.479874i
$83$	1.67071			0.183384			0.0916922	−	0.995787i	$-0.470772\pi$
$83$	1.67071			0.183384			0.0916922	+	0.995787i	$0.470772\pi$
$84$		0			0
$85$		−	24.4507i		−	2.65205i
$86$	−16.8787			−1.82007
$87$	0.635849			0.0681702
$88$	−20.8910	−	20.4719i	−2.22698	−	2.18231i
$89$		−	8.75251i		−	0.927765i	−0.885897	−	0.463882i	$-0.846456\pi$
$89$		−	8.75251i		−	0.927765i	0.885897	−	0.463882i	$-0.153544\pi$
$90$	−9.72943			−1.02557
$91$		0			0
$92$	−6.35979			−0.663054
$93$	5.92651			0.614551
$94$	−0.708725			−0.0730994
$95$			7.32790i			0.751827i
$96$	18.0583			1.84307
$97$			2.61309i			0.265319i	0.991162	+	0.132659i	$0.0423517\pi$
$97$			2.61309i			0.265319i	−0.991162	+	0.132659i	$0.957648\pi$
$98$		0			0
$99$	2.32133	−	2.36885i	0.233302	−	0.238078i
$100$	42.2692			4.22692
$101$	16.7431			1.66601			0.833003	−	0.553269i	$-0.186620\pi$
$101$	16.7431			1.66601			0.833003	+	0.553269i	$0.186620\pi$
$102$	−18.2716			−1.80916
$103$			3.27821i			0.323012i	0.986872	+	0.161506i	$0.0516351\pi$
$103$			3.27821i			0.323012i	−0.986872	+	0.161506i	$0.948365\pi$
$104$			37.9215i			3.71851i
$105$		0			0
$106$			19.2167i			1.86649i
$107$		−	0.957874i		−	0.0926012i	−0.998928	−	0.0463006i	$-0.985257\pi$
$107$		−	0.957874i		−	0.0926012i	0.998928	−	0.0463006i	$-0.0147432\pi$
$108$			5.27065i			0.507169i
$109$		−	9.45840i		−	0.905950i	−0.891523	−	0.452975i	$-0.850363\pi$
$109$		−	9.45840i		−	0.905950i	0.891523	−	0.452975i	$-0.149637\pi$
$110$	−22.5852	+	23.0476i	−2.15341	+	2.19750i
$111$		−	9.93807i		−	0.943280i
$112$		0			0
$113$	2.41711			0.227383			0.113691	−	0.993516i	$-0.463733\pi$
$113$	2.41711			0.227383			0.113691	+	0.993516i	$0.463733\pi$
$114$	5.47602			0.512877
$115$			4.35391i			0.406004i
$116$			3.35134i			0.311164i
$117$	−4.29996			−0.397531
$118$	10.2449			0.943120
$119$		0			0
$120$		−	31.8216i		−	2.90490i
$121$	−0.222889	−	10.9977i	−0.0202626	−	0.999795i
$122$			16.6018i			1.50306i
$123$		−	1.61156i		−	0.145310i
$124$			31.2366i			2.80513i
$125$		−	10.8960i		−	0.974571i
$126$		0			0
$127$		−	6.35512i		−	0.563926i	−0.959425	−	0.281963i	$-0.909015\pi$
$127$		−	6.35512i		−	0.563926i	0.959425	−	0.281963i	$-0.0909855\pi$
$128$			23.7864i			2.10244i
$129$	6.25967			0.551133
$130$	41.8362			3.66927
$131$	−9.66621			−0.844541			−0.422270	−	0.906470i	$-0.638767\pi$
$131$	−9.66621			−0.844541			−0.422270	+	0.906470i	$0.638767\pi$
$132$	12.4854	+	12.2349i	1.08671	+	1.06491i
$133$		0			0
$134$		−	16.9660i		−	1.46564i
$135$	3.60829			0.310552
$136$		−	59.7602i		−	5.12439i
$137$	−19.1945			−1.63990			−0.819950	−	0.572435i	$-0.805999\pi$
$137$	−19.1945			−1.63990			−0.819950	+	0.572435i	$0.805999\pi$
$138$	3.25361			0.276966
$139$	−19.5976			−1.66225			−0.831124	−	0.556087i	$-0.812302\pi$
$139$	−19.5976			−1.66225			−0.831124	+	0.556087i	$0.812302\pi$
$140$		0			0
$141$	0.262840			0.0221351
$142$			37.7437i			3.16738i
$143$	−9.98161	+	10.1860i	−0.834704	+	0.851792i
$144$	−13.2385			−1.10321
$145$	2.29432			0.190533
$146$		−	14.9801i		−	1.23976i
$147$		0			0
$148$	52.3801			4.30562
$149$			4.25350i			0.348461i	0.984705	+	0.174230i	$0.0557437\pi$
$149$			4.25350i			0.348461i	−0.984705	+	0.174230i	$0.944256\pi$
$150$	−21.6245			−1.76563
$151$			12.3281i			1.00325i	0.865086	+	0.501623i	$0.167264\pi$
$151$			12.3281i			1.00325i	−0.865086	+	0.501623i	$0.832736\pi$
$152$			17.9102i			1.45271i
$153$	6.77627			0.547829
$154$		0			0
$155$	21.3846			1.71765
$156$		−	22.6636i		−	1.81454i
$157$			9.99917i			0.798021i	0.916946	+	0.399010i	$0.130646\pi$
$157$			9.99917i			0.798021i	−0.916946	+	0.399010i	$0.869354\pi$
$158$	33.7053			2.68145
$159$		−	7.12675i		−	0.565188i
$160$	65.1596			5.15132
$161$		0			0
$162$		−	2.69641i		−	0.211850i
$163$	−18.8081			−1.47317			−0.736583	−	0.676347i	$-0.763562\pi$
$163$	−18.8081			−1.47317			−0.736583	+	0.676347i	$0.763562\pi$
$164$	8.49399			0.663269
$165$	8.37601	−	8.54748i	0.652071	−	0.665421i
$166$		−	4.50493i		−	0.349651i
$167$	2.50122			0.193550			0.0967751	−	0.995306i	$-0.469147\pi$
$167$	2.50122			0.193550			0.0967751	+	0.995306i	$0.469147\pi$
$168$		0			0
$169$	5.48964			0.422280
$170$	−65.9293			−5.05654
$171$	−2.03085			−0.155303
$172$			32.9925i			2.51566i
$173$	7.34165			0.558175			0.279088	−	0.960266i	$-0.409968\pi$
$173$	7.34165			0.558175			0.279088	+	0.960266i	$0.409968\pi$
$174$		−	1.71451i		−	0.129977i
$175$		0			0
$176$	−30.7308	+	31.3599i	−2.31642	+	2.36384i
$177$	−3.79946			−0.285585
$178$	−23.6004			−1.76893
$179$	2.29833			0.171785			0.0858925	−	0.996304i	$-0.472626\pi$
$179$	2.29833			0.171785			0.0858925	+	0.996304i	$0.472626\pi$
$180$			19.0180i			1.41752i
$181$		−	15.2428i		−	1.13299i	−0.824065	−	0.566496i	$-0.808299\pi$
$181$		−	15.2428i		−	1.13299i	0.824065	−	0.566496i	$-0.191701\pi$
$182$		0			0
$183$		−	6.15699i		−	0.455138i
$184$			10.6414i			0.784496i
$185$		−	35.8594i		−	2.63644i
$186$		−	15.9803i		−	1.17174i
$187$	15.7299	−	16.0520i	1.15029	−	1.17384i
$188$			1.38534i			0.101036i
$189$		0			0
$190$	19.7591			1.43347
$191$	0.499692			0.0361565			0.0180782	−	0.999837i	$-0.494245\pi$
$191$	0.499692			0.0361565			0.0180782	+	0.999837i	$0.494245\pi$
$192$		−	22.2158i		−	1.60329i
$193$		−	26.4909i		−	1.90686i	−0.301620	−	0.953428i	$-0.597527\pi$
$193$		−	26.4909i		−	1.90686i	0.301620	−	0.953428i	$-0.402473\pi$
$194$	7.04597			0.505871
$195$	−15.5155			−1.11109
$196$		0			0
$197$		−	10.1854i		−	0.725678i	−0.931852	−	0.362839i	$-0.881808\pi$
$197$		−	10.1854i		−	0.725678i	0.931852	−	0.362839i	$-0.118192\pi$
$198$	−6.38740	−	6.25926i	−0.453933	−	0.444826i
$199$			5.34398i			0.378825i	0.981898	+	0.189412i	$0.0606583\pi$
$199$			5.34398i			0.378825i	−0.981898	+	0.189412i	$0.939342\pi$
$200$		−	70.7262i		−	5.00110i
$201$			6.29206i			0.443808i
$202$		−	45.1465i		−	3.17649i
$203$		0			0
$204$			35.7154i			2.50058i
$205$		−	5.81498i		−	0.406136i
$206$	8.83943			0.615872
$207$	−1.20664			−0.0838675
$208$	56.9249			3.94703
$209$	−4.71427	+	4.81079i	−0.326093	+	0.332769i
$210$		0			0
$211$		−	3.85818i		−	0.265608i	−0.991142	−	0.132804i	$-0.957602\pi$
$211$		−	3.85818i		−	0.265608i	0.991142	−	0.132804i	$-0.0423981\pi$
$212$	37.5626			2.57981
$213$		−	13.9977i		−	0.959110i
$214$	−2.58283			−0.176558
$215$	22.5867			1.54040
$216$	8.81904			0.600059
$217$		0			0
$218$	−25.5038			−1.72733
$219$			5.55556i			0.375410i
$220$	45.0508	+	44.1470i	3.03733	+	2.97639i
$221$	−29.1377			−1.96001
$222$	−26.7972			−1.79851
$223$			6.01737i			0.402953i	0.979493	+	0.201476i	$0.0645739\pi$
$223$			6.01737i			0.402953i	−0.979493	+	0.201476i	$0.935426\pi$
$224$		0			0
$225$	8.01972			0.534648
$226$		−	6.51753i		−	0.433540i
$227$	−18.2991			−1.21455			−0.607277	−	0.794490i	$-0.707738\pi$
$227$	−18.2991			−1.21455			−0.607277	+	0.794490i	$0.707738\pi$
$228$		−	10.7039i		−	0.708885i
$229$		−	2.09509i		−	0.138448i	−0.997601	−	0.0692238i	$-0.977948\pi$
$229$		−	2.09509i		−	0.138448i	0.997601	−	0.0692238i	$-0.0220523\pi$
$230$	11.7400			0.774109
$231$		0			0
$232$	5.60757			0.368155
$233$			23.5872i			1.54525i	0.634863	+	0.772624i	$0.281056\pi$
$233$			23.5872i			1.54525i	−0.634863	+	0.772624i	$0.718944\pi$
$234$			11.5945i			0.757954i
$235$	0.948401			0.0618669
$236$		−	20.0256i		−	1.30356i
$237$	−12.5001			−0.811966
$238$		0			0
$239$			20.3272i			1.31486i	0.753517	+	0.657429i	$0.228356\pi$
$239$			20.3272i			1.31486i	−0.753517	+	0.657429i	$0.771644\pi$
$240$	−47.7682			−3.08342
$241$	12.1121			0.780212			0.390106	−	0.920770i	$-0.372438\pi$
$241$	12.1121			0.780212			0.390106	+	0.920770i	$0.372438\pi$
$242$	−29.6545	+	0.601001i	−1.90626	+	0.0386338i
$243$			1.00000i			0.0641500i
$244$	32.4514			2.07749
$245$		0			0
$246$	−4.34544			−0.277055
$247$	8.73259			0.555641
$248$	52.2661			3.31890
$249$			1.67071i			0.105877i
$250$	−29.3802			−1.85817
$251$		−	2.48699i		−	0.156977i	−0.996915	−	0.0784887i	$-0.974991\pi$
$251$		−	2.48699i		−	0.156977i	0.996915	−	0.0784887i	$-0.0250095\pi$
$252$		0			0
$253$	−2.80101	+	2.85835i	−0.176098	+	0.179703i
$254$	−17.1360			−1.07521
$255$	24.4507			1.53116
$256$	19.7064			1.23165
$257$			1.67467i			0.104463i	0.998635	+	0.0522314i	$0.0166333\pi$
$257$			1.67467i			0.104463i	−0.998635	+	0.0522314i	$0.983367\pi$
$258$		−	16.8787i		−	1.05082i
$259$		0			0
$260$		−	81.7767i		−	5.07158i
$261$			0.635849i			0.0393581i
$262$			26.0641i			1.61025i
$263$			28.2449i			1.74165i	0.491590	+	0.870827i	$0.336416\pi$
$263$			28.2449i			1.74165i	−0.491590	+	0.870827i	$0.663584\pi$
$264$	20.4719	−	20.8910i	1.25996	−	1.28575i
$265$		−	25.7153i		−	1.57968i
$266$		0			0
$267$	8.75251			0.535645
$268$	−33.1633			−2.02577
$269$		−	19.7827i		−	1.20617i	−0.797675	−	0.603087i	$-0.793937\pi$
$269$		−	19.7827i		−	1.20617i	0.797675	−	0.603087i	$-0.206063\pi$
$270$		−	9.72943i		−	0.592115i
$271$	2.89104			0.175618			0.0878092	−	0.996137i	$-0.472013\pi$
$271$	2.89104			0.175618			0.0878092	+	0.996137i	$0.472013\pi$
$272$	−89.7074			−5.43931
$273$		0			0
$274$			51.7565i			3.12672i
$275$	18.6164	−	18.9975i	1.12261	−	1.14559i
$276$		−	6.35979i		−	0.382815i
$277$			29.0861i			1.74762i	0.486271	+	0.873808i	$0.338357\pi$
$277$			29.0861i			1.74762i	−0.486271	+	0.873808i	$0.661643\pi$
$278$			52.8433i			3.16933i
$279$			5.92651i			0.354811i
$280$		0			0
$281$			6.12577i			0.365433i	0.983166	+	0.182716i	$0.0584890\pi$
$281$			6.12577i			0.365433i	−0.983166	+	0.182716i	$0.941511\pi$
$282$		−	0.708725i		−	0.0422040i
$283$	−6.54038			−0.388785			−0.194393	−	0.980924i	$-0.562274\pi$
$283$	−6.54038			−0.388785			−0.194393	+	0.980924i	$0.562274\pi$
$284$	73.7772			4.37787
$285$	−7.32790			−0.434067
$286$	27.4656	+	26.9146i	1.62407	+	1.59149i
$287$		0			0
$288$			18.0583i			1.06410i
$289$	28.9178			1.70105
$290$		−	6.18645i		−	0.363281i
$291$	−2.61309			−0.153182
$292$	−29.2814			−1.71357
$293$	−25.2990			−1.47798			−0.738991	−	0.673715i	$-0.764697\pi$
$293$	−25.2990			−1.47798			−0.738991	+	0.673715i	$0.764697\pi$
$294$		0			0
$295$	−13.7095			−0.798199
$296$		−	87.6442i		−	5.09422i
$297$	2.36885	+	2.32133i	0.137455	+	0.134697i
$298$	11.4692			0.664394
$299$	5.18851			0.300059
$300$			42.2692i			2.44041i
$301$		0			0
$302$	33.2417			1.91284
$303$			16.7431i			0.961869i
$304$	26.8854			1.54198
$305$		−	22.2162i		−	1.27210i
$306$		−	18.2716i		−	1.04452i
$307$	26.3097			1.50157			0.750787	−	0.660545i	$-0.229675\pi$
$307$	26.3097			1.50157			0.750787	+	0.660545i	$0.229675\pi$
$308$		0			0
$309$	−3.27821			−0.186491
$310$		−	57.6616i		−	3.27496i
$311$		−	10.8220i		−	0.613657i	−0.951765	−	0.306828i	$-0.900732\pi$
$311$		−	10.8220i		−	0.613657i	0.951765	−	0.306828i	$-0.0992677\pi$
$312$	−37.9215			−2.14688
$313$			3.55998i			0.201222i	0.994926	+	0.100611i	$0.0320798\pi$
$313$			3.55998i			0.201222i	−0.994926	+	0.100611i	$0.967920\pi$
$314$	26.9619			1.52155
$315$		0			0
$316$		−	65.8835i		−	3.70623i
$317$	23.1694			1.30132			0.650661	−	0.759368i	$-0.274492\pi$
$317$	23.1694			1.30132			0.650661	+	0.759368i	$0.274492\pi$
$318$	−19.2167			−1.07762
$319$	1.50623	+	1.47601i	0.0843327	+	0.0826408i
$320$		−	80.1611i		−	4.48114i
$321$	0.957874			0.0534633
$322$		0			0
$323$	−13.7616			−0.765717
$324$	−5.27065			−0.292814
$325$	−34.4845			−1.91286
$326$			50.7145i			2.80882i
$327$	9.45840			0.523051
$328$		−	14.2124i		−	0.784750i
$329$		0			0
$330$	−23.0476	−	22.5852i	−1.26873	−	1.24327i
$331$	−1.99367			−0.109582			−0.0547909	−	0.998498i	$-0.517449\pi$
$331$	−1.99367			−0.109582			−0.0547909	+	0.998498i	$0.517449\pi$
$332$	−8.80574			−0.483278
$333$	9.93807			0.544603
$334$		−	6.74433i		−	0.369033i
$335$			22.7036i			1.24043i
$336$		0			0
$337$		−	0.126135i		−	0.00687099i	−0.999994	−	0.00343550i	$-0.998906\pi$
$337$		−	0.126135i		−	0.00687099i	0.999994	−	0.00343550i	$-0.00109355\pi$
$338$		−	14.8024i		−	0.805142i
$339$			2.41711i			0.131279i
$340$			128.871i			6.98902i
$341$	14.0390	+	13.7574i	0.760255	+	0.745004i
$342$			5.47602i			0.296109i
$343$		0			0
$344$	55.2042			2.97641
$345$	−4.35391			−0.234407
$346$		−	19.7961i		−	1.06425i
$347$		−	10.3411i		−	0.555140i	−0.960705	−	0.277570i	$-0.910471\pi$
$347$		−	10.3411i		−	0.555140i	0.960705	−	0.277570i	$-0.0895290\pi$
$348$	−3.35134			−0.179651
$349$	15.0350			0.804807			0.402403	−	0.915462i	$-0.368175\pi$
$349$	15.0350			0.804807			0.402403	+	0.915462i	$0.368175\pi$
$350$		0			0
$351$		−	4.29996i		−	0.229515i
$352$	42.7775	+	41.9193i	2.28005	+	2.23431i
$353$			26.6483i			1.41835i	0.705034	+	0.709173i	$0.250932\pi$
$353$			26.6483i			1.41835i	−0.705034	+	0.709173i	$0.749068\pi$
$354$			10.2449i			0.544511i
$355$		−	50.5079i		−	2.68068i
$356$			46.1315i			2.44496i
$357$		0			0
$358$		−	6.19724i		−	0.327534i
$359$			20.8044i			1.09801i	0.835818	+	0.549006i	$0.184994\pi$
$359$			20.8044i			1.09801i	−0.835818	+	0.549006i	$0.815006\pi$
$360$	31.8216			1.67715
$361$	−14.8756			−0.782928
$362$	−41.1010			−2.16022
$363$	10.9977	−	0.222889i	0.577232	−	0.0116986i
$364$		0			0
$365$			20.0460i			1.04926i
$366$	−16.6018			−0.867791
$367$		−	2.49789i		−	0.130389i	−0.997873	−	0.0651944i	$-0.979233\pi$
$367$		−	2.49789i		−	0.130389i	0.997873	−	0.0651944i	$-0.0207667\pi$
$368$	15.9741			0.832708
$369$	1.61156			0.0838946
$370$	−96.6918			−5.02677
$371$		0			0
$372$	−31.2366			−1.61954
$373$			19.1864i			0.993435i	0.867912	+	0.496717i	$0.165461\pi$
$373$			19.1864i			0.993435i	−0.867912	+	0.496717i	$0.834539\pi$
$374$	−43.2827	−	42.4144i	−2.23810	−	2.19320i
$375$	10.8960			0.562669
$376$	2.31799			0.119541
$377$		−	2.73412i		−	0.140815i
$378$		0			0
$379$	−9.05705			−0.465229			−0.232615	−	0.972569i	$-0.574728\pi$
$379$	−9.05705			−0.465229			−0.232615	+	0.972569i	$0.574728\pi$
$380$		−	38.6228i		−	1.98131i
$381$	6.35512			0.325583
$382$		−	1.34738i		−	0.0689378i
$383$			35.2243i			1.79988i	0.436015	+	0.899939i	$0.356389\pi$
$383$			35.2243i			1.79988i	−0.436015	+	0.899939i	$0.643611\pi$
$384$	−23.7864			−1.21385
$385$		0			0
$386$	−71.4304			−3.63571
$387$			6.25967i			0.318197i
$388$		−	13.7727i		−	0.699202i
$389$	−29.7762			−1.50971			−0.754856	−	0.655891i	$-0.772293\pi$
$389$	−29.7762			−1.50971			−0.754856	+	0.655891i	$0.772293\pi$
$390$			41.8362i			2.11846i
$391$	−8.17654			−0.413505
$392$		0			0
$393$		−	9.66621i		−	0.487596i
$394$	−27.4640			−1.38362
$395$	−45.1038			−2.26942
$396$	−12.2349	+	12.4854i	−0.614827	+	0.627414i
$397$		−	0.924891i		−	0.0464190i	−0.999731	−	0.0232095i	$-0.992612\pi$
$397$		−	0.924891i		−	0.0464190i	0.999731	−	0.0232095i	$-0.00738847\pi$
$398$	14.4096			0.722287
$399$		0			0
$400$	−106.169			−5.30844
$401$	0.0759980			0.00379516			0.00189758	−	0.999998i	$-0.499396\pi$
$401$	0.0759980			0.00379516			0.00189758	+	0.999998i	$0.499396\pi$
$402$	16.9660			0.846188
$403$		−	25.4838i		−	1.26944i
$404$	−88.2473			−4.39047
$405$			3.60829i			0.179297i
$406$		0			0
$407$	23.0695	−	23.5418i	1.14351	−	1.16692i
$408$	59.7602			2.95857
$409$	24.2455			1.19886			0.599431	−	0.800426i	$-0.295394\pi$
$409$	24.2455			1.19886			0.599431	+	0.800426i	$0.295394\pi$
$410$	−15.6796			−0.774360
$411$		−	19.1945i		−	0.946797i
$412$		−	17.2783i		−	0.851242i
$413$		0			0
$414$			3.25361i			0.159906i
$415$			6.02841i			0.295923i
$416$		−	77.6501i		−	3.80711i
$417$		−	19.5976i		−	0.959699i
$418$	12.9719	+	12.7116i	0.634475	+	0.621747i
$419$			24.2981i			1.18704i	0.804819	+	0.593520i	$0.202262\pi$
$419$			24.2981i			1.18704i	−0.804819	+	0.593520i	$0.797738\pi$
$420$		0			0
$421$	−20.7872			−1.01311			−0.506554	−	0.862208i	$-0.669081\pi$
$421$	−20.7872			−1.01311			−0.506554	+	0.862208i	$0.669081\pi$
$422$	−10.4033			−0.506423
$423$			0.262840i			0.0127797i
$424$		−	62.8510i		−	3.05232i
$425$	54.3438			2.63606
$426$	−37.7437			−1.82869
$427$		0			0
$428$			5.04862i			0.244034i
$429$	−10.1860	−	9.98161i	−0.491782	−	0.481917i
$430$		−	60.9030i		−	2.93700i
$431$			27.5588i			1.32746i	0.747973	+	0.663729i	$0.231027\pi$
$431$			27.5588i			1.32746i	−0.747973	+	0.663729i	$0.768973\pi$
$432$		−	13.2385i		−	0.636936i
$433$			31.2563i			1.50208i	0.660256	+	0.751041i	$0.270448\pi$
$433$			31.2563i			1.50208i	−0.660256	+	0.751041i	$0.729552\pi$
$434$		0			0
$435$			2.29432i			0.110004i
$436$			49.8519i			2.38747i
$437$	2.45051			0.117224
$438$	14.9801			0.715776
$439$	−19.7687			−0.943507			−0.471754	−	0.881730i	$-0.656379\pi$
$439$	−19.7687			−0.943507			−0.471754	+	0.881730i	$0.656379\pi$
$440$	73.8683	−	75.3806i	3.52153	−	3.59363i
$441$		0			0
$442$			78.5673i			3.73706i
$443$	−23.9940			−1.13999			−0.569996	−	0.821648i	$-0.693055\pi$
$443$	−23.9940			−1.13999			−0.569996	+	0.821648i	$0.693055\pi$
$444$			52.3801i			2.48585i
$445$	31.5816			1.49711
$446$	16.2253			0.768291
$447$	−4.25350			−0.201184
$448$		0			0
$449$	−10.8976			−0.514288			−0.257144	−	0.966373i	$-0.582781\pi$
$449$	−10.8976			−0.514288			−0.257144	+	0.966373i	$0.582781\pi$
$450$		−	21.6245i		−	1.01939i
$451$	3.74096	−	3.81755i	0.176155	−	0.179761i
$452$	−12.7397			−0.599227
$453$	−12.3281			−0.579225
$454$			49.3420i			2.31573i
$455$		0			0
$456$	−17.9102			−0.838721
$457$		−	21.7813i		−	1.01889i	−0.860505	−	0.509443i	$-0.829852\pi$
$457$		−	21.7813i		−	1.01889i	0.860505	−	0.509443i	$-0.170148\pi$
$458$	−5.64924			−0.263972
$459$			6.77627i			0.316289i
$460$		−	22.9480i		−	1.06995i
$461$	−3.20717			−0.149373			−0.0746863	−	0.997207i	$-0.523796\pi$
$461$	−3.20717			−0.149373			−0.0746863	+	0.997207i	$0.523796\pi$
$462$		0			0
$463$	−20.9702			−0.974567			−0.487283	−	0.873244i	$-0.662012\pi$
$463$	−20.9702			−0.974567			−0.487283	+	0.873244i	$0.662012\pi$
$464$		−	8.41767i		−	0.390780i
$465$			21.3846i			0.991685i
$466$	63.6009			2.94625
$467$		−	21.5700i		−	0.998139i	−0.866562	−	0.499070i	$-0.833675\pi$
$467$		−	21.5700i		−	0.998139i	0.866562	−	0.499070i	$-0.166325\pi$
$468$	22.6636			1.04762
$469$		0			0
$470$		−	2.55728i		−	0.117959i
$471$	−9.99917			−0.460738
$472$	−33.5075			−1.54231
$473$	14.8282	+	14.5307i	0.681802	+	0.668124i
$474$			33.7053i			1.54814i
$475$	−16.2869			−0.747294
$476$		0			0
$477$	7.12675			0.326311
$478$	54.8106			2.50698
$479$	2.47449			0.113062			0.0565311	−	0.998401i	$-0.481996\pi$
$479$	2.47449			0.113062			0.0565311	+	0.998401i	$0.481996\pi$
$480$			65.1596i			2.97412i
$481$	−42.7333			−1.94847
$482$		−	32.6594i		−	1.48759i
$483$		0			0
$484$	1.17477	+	57.9653i	0.0533987	+	2.63479i
$485$	−9.42877			−0.428138
$486$	2.69641			0.122312
$487$	7.30210			0.330890			0.165445	−	0.986219i	$-0.447094\pi$
$487$	7.30210			0.330890			0.165445	+	0.986219i	$0.447094\pi$
$488$		−	54.2987i		−	2.45799i
$489$		−	18.8081i		−	0.850532i
$490$		0			0
$491$		−	15.4129i		−	0.695573i	−0.937574	−	0.347787i	$-0.886933\pi$
$491$		−	15.4129i		−	0.695573i	0.937574	−	0.347787i	$-0.113067\pi$
$492$			8.49399i			0.382939i
$493$			4.30868i			0.194053i
$494$		−	23.5467i		−	1.05942i
$495$	8.54748	+	8.37601i	0.384181	+	0.376474i
$496$		−	78.4580i		−	3.52287i
$497$		0			0
$498$	4.50493			0.201871
$499$	18.6916			0.836751			0.418375	−	0.908274i	$-0.362600\pi$
$499$	18.6916			0.836751			0.418375	+	0.908274i	$0.362600\pi$
$500$			57.4292i			2.56831i
$501$			2.50122i			0.111746i
$502$	−6.70596			−0.299301
$503$	31.5255			1.40565			0.702827	−	0.711361i	$-0.251921\pi$
$503$	31.5255			1.40565			0.702827	+	0.711361i	$0.251921\pi$
$504$		0			0
$505$			60.4141i			2.68839i
$506$	7.70731	+	7.55269i	0.342632	+	0.335758i
$507$			5.48964i			0.243804i
$508$			33.4956i			1.48613i
$509$		−	22.5707i		−	1.00043i	−0.865902	−	0.500213i	$-0.833255\pi$
$509$		−	22.5707i		−	1.00043i	0.865902	−	0.500213i	$-0.166745\pi$
$510$		−	65.9293i		−	2.91940i
$511$		0			0
$512$		−	5.56372i		−	0.245884i
$513$		−	2.03085i		−	0.0896644i
$514$	4.51559			0.199174
$515$	−11.8287			−0.521236
$516$	−32.9925			−1.45242
$517$	0.622628	+	0.610137i	0.0273831	+	0.0268338i
$518$		0			0
$519$			7.34165i			0.322263i
$520$	−136.832			−6.00046
$521$		−	16.6758i		−	0.730582i	−0.930893	−	0.365291i	$-0.880970\pi$
$521$		−	16.6758i		−	0.730582i	0.930893	−	0.365291i	$-0.119030\pi$
$522$	1.71451			0.0750422
$523$	4.22170			0.184602			0.0923010	−	0.995731i	$-0.470578\pi$
$523$	4.22170			0.184602			0.0923010	+	0.995731i	$0.470578\pi$
$524$	50.9472			2.22564
$525$		0			0
$526$	76.1599			3.32073
$527$			40.1597i			1.74938i
$528$	−31.3599	−	30.7308i	−1.36477	−	1.33739i
$529$	−21.5440			−0.936696
$530$	−69.3392			−3.01190
$531$		−	3.79946i		−	0.164882i
$532$		0			0
$533$	−6.92965			−0.300157
$534$		−	23.6004i		−	1.02129i
$535$	3.45628			0.149428
$536$			55.4899i			2.39680i
$537$			2.29833i			0.0991801i
$538$	−53.3425			−2.29976
$539$		0			0
$540$	−19.0180			−0.818405
$541$		−	21.3290i		−	0.917006i	−0.888693	−	0.458503i	$-0.848386\pi$
$541$		−	21.3290i		−	0.917006i	0.888693	−	0.458503i	$-0.151614\pi$
$542$		−	7.79545i		−	0.334843i
$543$	15.2428			0.654133
$544$			122.368i			5.24649i
$545$	34.1286			1.46191
$546$		0			0
$547$		−	38.4068i		−	1.64215i	−0.570817	−	0.821077i	$-0.693374\pi$
$547$		−	38.4068i		−	1.64215i	0.570817	−	0.821077i	$-0.306626\pi$
$548$	101.168			4.32167
$549$	6.15699			0.262774
$550$	−51.2252	−	50.1975i	−2.18425	−	2.14043i
$551$		−	1.29132i		−	0.0550119i
$552$	−10.6414			−0.452929
$553$		0			0
$554$	78.4283			3.33210
$555$	35.8594			1.52215
$556$	103.292			4.38057
$557$		−	12.6297i		−	0.535139i	−0.963539	−	0.267570i	$-0.913779\pi$
$557$		−	12.6297i		−	0.535139i	0.963539	−	0.267570i	$-0.0862206\pi$
$558$	15.9803			0.676502
$559$		−	26.9163i		−	1.13844i
$560$		0			0
$561$	16.0520	+	15.7299i	0.677714	+	0.664118i
$562$	16.5176			0.696754
$563$	39.4336			1.66193			0.830964	−	0.556327i	$-0.187790\pi$
$563$	39.4336			1.66193			0.830964	+	0.556327i	$0.187790\pi$
$564$	−1.38534			−0.0583332
$565$			8.72162i			0.366921i
$566$			17.6356i			0.741279i
$567$		0			0
$568$		−	123.447i		−	5.17970i
$569$		−	25.3311i		−	1.06193i	−0.847393	−	0.530967i	$-0.821829\pi$
$569$		−	25.3311i		−	1.06193i	0.847393	−	0.530967i	$-0.178171\pi$
$570$			19.7591i			0.827616i
$571$		−	18.4152i		−	0.770651i	−0.922781	−	0.385326i	$-0.874089\pi$
$571$		−	18.4152i		−	0.770651i	0.922781	−	0.385326i	$-0.125911\pi$
$572$	52.6096	−	53.6866i	2.19972	−	2.24475i
$573$			0.499692i			0.0208749i
$574$		0			0
$575$	−9.67694			−0.403556
$576$	22.2158			0.925660
$577$			0.127232i			0.00529674i	0.999996	+	0.00264837i	$0.000843003\pi$
$577$			0.127232i			0.00529674i	−0.999996	+	0.00264837i	$0.999157\pi$
$578$		−	77.9744i		−	3.24331i
$579$	26.4909			1.10092
$580$	−12.0926			−0.502117
$581$		0			0
$582$			7.04597i			0.292065i
$583$	16.5435	−	16.8822i	0.685162	−	0.699189i
$584$			48.9947i			2.02741i
$585$		−	15.5155i		−	0.641486i
$586$			68.2165i			2.81800i
$587$			44.5734i			1.83974i	0.392222	+	0.919871i	$0.371706\pi$
$587$			44.5734i			1.83974i	−0.392222	+	0.919871i	$0.628294\pi$
$588$		0			0
$589$		−	12.0359i		−	0.495930i
$590$			36.9666i			1.52189i
$591$	10.1854			0.418970
$592$	−131.565			−5.40728
$593$	−27.1730			−1.11586			−0.557931	−	0.829888i	$-0.688404\pi$
$593$	−27.1730			−1.11586			−0.557931	+	0.829888i	$0.688404\pi$
$594$	6.25926	−	6.38740i	0.256820	−	0.262078i
$595$		0			0
$596$		−	22.4187i		−	0.918308i
$597$	−5.34398			−0.218715
$598$		−	13.9904i		−	0.572109i
$599$	29.4785			1.20446			0.602229	−	0.798323i	$-0.294279\pi$
$599$	29.4785			1.20446			0.602229	+	0.798323i	$0.294279\pi$
$600$	70.7262			2.88739
$601$	38.2524			1.56035			0.780174	−	0.625563i	$-0.215131\pi$
$601$	38.2524			1.56035			0.780174	+	0.625563i	$0.215131\pi$
$602$		0			0
$603$	−6.29206			−0.256233
$604$		−	64.9772i		−	2.64388i
$605$	39.6830	−	0.804247i	1.61334	−	0.0326973i
$606$	45.1465			1.83395
$607$	−14.2774			−0.579503			−0.289751	−	0.957102i	$-0.593573\pi$
$607$	−14.2774			−0.579503			−0.289751	+	0.957102i	$0.593573\pi$
$608$		−	36.6738i		−	1.48732i
$609$		0			0
$610$	−59.9041			−2.42544
$611$		−	1.13020i		−	0.0457230i
$612$	−35.7154			−1.44371
$613$			8.21585i			0.331835i	0.986140	+	0.165917i	$0.0530585\pi$
$613$			8.21585i			0.331835i	−0.986140	+	0.165917i	$0.946941\pi$
$614$		−	70.9418i		−	2.86298i
$615$	5.81498			0.234483
$616$		0			0
$617$	2.00680			0.0807906			0.0403953	−	0.999184i	$-0.487138\pi$
$617$	2.00680			0.0807906			0.0403953	+	0.999184i	$0.487138\pi$
$618$			8.83943i			0.355574i
$619$			47.7929i			1.92096i	0.278352	+	0.960479i	$0.410212\pi$
$619$			47.7929i			1.92096i	−0.278352	+	0.960479i	$0.589788\pi$
$620$	−112.711			−4.52657
$621$		−	1.20664i		−	0.0484209i
$622$	−29.1805			−1.17003
$623$		0			0
$624$			56.9249i			2.27882i
$625$	−0.782638			−0.0313055
$626$	9.59918			0.383661
$627$	−4.81079	−	4.71427i	−0.192124	−	0.188270i
$628$		−	52.7022i		−	2.10305i
$629$	67.3431			2.68514
$630$		0			0
$631$	−15.0345			−0.598515			−0.299258	−	0.954172i	$-0.596739\pi$
$631$	−15.0345			−0.598515			−0.299258	+	0.954172i	$0.596739\pi$
$632$	−110.238			−4.38505
$633$	3.85818			0.153349
$634$		−	62.4743i		−	2.48117i
$635$	22.9311			0.909992
$636$			37.5626i			1.48945i
$637$		0			0
$638$	3.97994	−	4.06142i	0.157567	−	0.160793i
$639$	13.9977			0.553742
$640$	−85.8282			−3.39266
$641$	21.9277			0.866094			0.433047	−	0.901371i	$-0.357438\pi$
$641$	21.9277			0.866094			0.433047	+	0.901371i	$0.357438\pi$
$642$		−	2.58283i		−	0.101936i
$643$			46.0769i			1.81710i	0.417780	+	0.908548i	$0.362808\pi$
$643$			46.0769i			1.81710i	−0.417780	+	0.908548i	$0.637192\pi$
$644$		0			0
$645$			22.5867i			0.889349i
$646$			37.1070i			1.45996i
$647$		−	3.21028i		−	0.126209i	−0.998007	−	0.0631045i	$-0.979900\pi$
$647$		−	3.21028i		−	0.126209i	0.998007	−	0.0631045i	$-0.0201001\pi$
$648$			8.81904i			0.346444i
$649$	−9.00034	−	8.81978i	−0.353294	−	0.346207i
$650$			92.9845i			3.64715i
$651$		0			0
$652$	99.1310			3.88227
$653$	−11.9803			−0.468827			−0.234414	−	0.972137i	$-0.575317\pi$
$653$	−11.9803			−0.468827			−0.234414	+	0.972137i	$0.575317\pi$
$654$		−	25.5038i		−	0.997276i
$655$		−	34.8784i		−	1.36281i
$656$	−21.3346			−0.832977
$657$	−5.55556			−0.216743
$658$		0			0
$659$		−	10.5905i		−	0.412549i	−0.978494	−	0.206275i	$-0.933866\pi$
$659$		−	10.5905i		−	0.412549i	0.978494	−	0.206275i	$-0.0661340\pi$
$660$	−44.1470	+	45.0508i	−1.71842	+	1.75360i
$661$			21.3048i			0.828661i	0.910126	+	0.414331i	$0.135984\pi$
$661$			21.3048i			0.828661i	−0.910126	+	0.414331i	$0.864016\pi$
$662$			5.37575i			0.208934i
$663$		−	29.1377i		−	1.13161i
$664$			14.7341i			0.571793i
$665$		0			0
$666$		−	26.7972i		−	1.03837i
$667$		−	0.767242i		−	0.0297077i
$668$	−13.1831			−0.510068
$669$	−6.01737			−0.232645
$670$	61.2182			2.36507
$671$	14.2924	−	14.5850i	0.551752	−	0.563047i
$672$		0			0
$673$		−	12.3537i		−	0.476201i	−0.971240	−	0.238101i	$-0.923475\pi$
$673$		−	12.3537i		−	0.476201i	0.971240	−	0.238101i	$-0.0765248\pi$
$674$	−0.340111			−0.0131006
$675$			8.01972i			0.308679i
$676$	−28.9340			−1.11285
$677$	1.16828			0.0449008			0.0224504	−	0.999748i	$-0.492853\pi$
$677$	1.16828			0.0449008			0.0224504	+	0.999748i	$0.492853\pi$
$678$	6.51753			0.250304
$679$		0			0
$680$	215.632			8.26910
$681$		−	18.2991i		−	0.701224i
$682$	37.0956	−	37.8550i	1.42046	−	1.44954i
$683$	31.9827			1.22379			0.611893	−	0.790941i	$-0.290408\pi$
$683$	31.9827			1.22379			0.611893	+	0.790941i	$0.290408\pi$
$684$	10.7039			0.409275
$685$		−	69.2594i		−	2.64627i
$686$		0			0
$687$	2.09509			0.0799328
$688$		−	82.8684i		−	3.15933i
$689$	−30.6447			−1.16747
$690$			11.7400i			0.446932i
$691$			13.1040i			0.498501i	0.968439	+	0.249251i	$0.0801843\pi$
$691$			13.1040i			0.498501i	−0.968439	+	0.249251i	$0.919816\pi$
$692$	−38.6953			−1.47097
$693$		0			0
$694$	−27.8839			−1.05846
$695$		−	70.7138i		−	2.68233i
$696$			5.60757i			0.212555i
$697$	10.9204			0.413639
$698$		−	40.5407i		−	1.53449i
$699$	−23.5872			−0.892150
$700$		0			0
$701$		−	0.796393i		−	0.0300794i	−0.999887	−	0.0150397i	$-0.995213\pi$
$701$		−	0.796393i		−	0.0300794i	0.999887	−	0.0150397i	$-0.00478746\pi$
$702$	−11.5945			−0.437605
$703$	−20.1828			−0.761208
$704$	51.5702	−	52.6259i	1.94362	−	1.98341i
$705$			0.948401i			0.0357189i
$706$	71.8549			2.70430
$707$		0			0
$708$	20.0256			0.752609
$709$	−14.2697			−0.535909			−0.267954	−	0.963432i	$-0.586348\pi$
$709$	−14.2697			−0.535909			−0.267954	+	0.963432i	$0.586348\pi$
$710$	−136.190			−5.11112
$711$		−	12.5001i		−	0.468789i
$712$	77.1887			2.89277
$713$		−	7.15119i		−	0.267814i
$714$		0			0
$715$	−36.7538	−	36.0165i	−1.37452	−	1.34694i
$716$	−12.1137			−0.452709
$717$	−20.3272			−0.759133
$718$	56.0972			2.09353
$719$			32.2139i			1.20138i	0.799484	+	0.600688i	$0.205106\pi$
$719$			32.2139i			1.20138i	−0.799484	+	0.600688i	$0.794894\pi$
$720$		−	47.7682i		−	1.78022i
$721$		0			0
$722$			40.1109i			1.49277i
$723$			12.1121i			0.450455i
$724$			80.3397i			2.98580i
$725$			5.09933i			0.189384i
$726$	−0.601001	−	29.6545i	−0.0223053	−	1.10058i
$727$		−	7.26942i		−	0.269608i	−0.990872	−	0.134804i	$-0.956960\pi$
$727$		−	7.26942i		−	0.269608i	0.990872	−	0.134804i	$-0.0430405\pi$
$728$		0			0
$729$	−1.00000			−0.0370370
$730$	54.0524			2.00057
$731$			42.4172i			1.56886i
$732$			32.4514i			1.19944i
$733$	−12.3554			−0.456358			−0.228179	−	0.973619i	$-0.573277\pi$
$733$	−12.3554			−0.456358			−0.228179	+	0.973619i	$0.573277\pi$
$734$	−6.73534			−0.248606
$735$		0			0
$736$		−	21.7900i		−	0.803189i
$737$	−14.6059	+	14.9049i	−0.538016	+	0.549031i
$738$		−	4.34544i		−	0.159958i
$739$		−	21.4336i		−	0.788449i	−0.919014	−	0.394225i	$-0.871013\pi$
$739$		−	21.4336i		−	0.788449i	0.919014	−	0.394225i	$-0.128987\pi$
$740$			189.002i			6.94787i
$741$			8.73259i			0.320800i
$742$		0			0
$743$			52.0680i			1.91019i	0.296303	+	0.955094i	$0.404246\pi$
$743$			52.0680i			1.91019i	−0.296303	+	0.955094i	$0.595754\pi$
$744$			52.2661i			1.91617i
$745$	−15.3479			−0.562302
$746$	51.7345			1.89414
$747$	−1.67071			−0.0611281
$748$	−82.9070	+	84.6043i	−3.03138	+	3.09344i
$749$		0			0
$750$		−	29.3802i		−	1.07281i
$751$	−5.61997			−0.205076			−0.102538	−	0.994729i	$-0.532696\pi$
$751$	−5.61997			−0.205076			−0.102538	+	0.994729i	$0.532696\pi$
$752$		−	3.47960i		−	0.126888i
$753$	2.48699			0.0906309
$754$	−7.37233			−0.268484
$755$	−44.4833			−1.61891
$756$		0			0
$757$	−1.45924			−0.0530371			−0.0265186	−	0.999648i	$-0.508442\pi$
$757$	−1.45924			−0.0530371			−0.0265186	+	0.999648i	$0.508442\pi$
$758$			24.4216i			0.887031i
$759$	−2.85835	−	2.80101i	−0.103752	−	0.101670i
$760$	−64.6250			−2.34420
$761$	44.3261			1.60682			0.803409	−	0.595427i	$-0.203017\pi$
$761$	44.3261			1.60682			0.803409	+	0.595427i	$0.203017\pi$
$762$		−	17.1360i		−	0.620773i
$763$		0			0
$764$	−2.63370			−0.0952841
$765$			24.4507i			0.884017i
$766$	94.9794			3.43174
$767$			16.3375i			0.589913i
$768$			19.7064i			0.711092i
$769$	29.9861			1.08132			0.540662	−	0.841240i	$-0.318174\pi$
$769$	29.9861			1.08132			0.540662	+	0.841240i	$0.318174\pi$
$770$		0			0
$771$	−1.67467			−0.0603116
$772$			139.624i			5.02519i
$773$		−	46.4454i		−	1.67053i	−0.549851	−	0.835263i	$-0.685316\pi$
$773$		−	46.4454i		−	1.67053i	0.549851	−	0.835263i	$-0.314684\pi$
$774$	16.8787			0.606691
$775$			47.5290i			1.70729i
$776$	−23.0449			−0.827264
$777$		0			0
$778$			80.2889i			2.87850i
$779$	−3.27285			−0.117262
$780$	81.7767			2.92808
$781$	32.4933	−	33.1585i	1.16270	−	1.18651i
$782$			22.0473i			0.788411i
$783$	−0.635849			−0.0227234
$784$		0			0
$785$	−36.0799			−1.28775
$786$	−26.0641			−0.929676
$787$	−34.6562			−1.23536			−0.617679	−	0.786430i	$-0.711927\pi$
$787$	−34.6562			−1.23536			−0.617679	+	0.786430i	$0.711927\pi$
$788$			53.6836i			1.91240i
$789$	−28.2449			−1.00554
$790$			121.619i			4.32699i
$791$		0			0
$792$	20.8910	+	20.4719i	0.742328	+	0.727436i
$793$	−26.4748			−0.940148
$794$	−2.49389			−0.0885048
$795$	25.7153			0.912029
$796$		−	28.1663i		−	0.998327i
$797$		−	2.94331i		−	0.104257i	−0.998640	−	0.0521287i	$-0.983399\pi$
$797$		−	2.94331i		−	0.104257i	0.998640	−	0.0521287i	$-0.0166006\pi$
$798$		0			0
$799$			1.78107i			0.0630099i
$800$			144.823i			5.12026i
$801$			8.75251i			0.309255i
$802$		−	0.204922i		−	0.00723606i
$803$	−12.8963	+	13.1603i	−0.455099	+	0.464416i
$804$		−	33.1633i		−	1.16958i
$805$		0			0
$806$	−68.7148			−2.42038
$807$	19.7827			0.696385
$808$			147.658i			5.19460i
$809$		−	27.4222i		−	0.964115i	−0.876140	−	0.482057i	$-0.839890\pi$
$809$		−	27.4222i		−	0.964115i	0.876140	−	0.482057i	$-0.160110\pi$
$810$	9.72943			0.341857
$811$	−25.1938			−0.884673			−0.442337	−	0.896849i	$-0.645850\pi$
$811$	−25.1938			−0.884673			−0.442337	+	0.896849i	$0.645850\pi$
$812$		0			0
$813$			2.89104i			0.101393i
$814$	−63.4784	−	62.2050i	−2.22492	−	2.18028i
$815$		−	67.8651i		−	2.37721i
$816$		−	89.7074i		−	3.14039i
$817$		−	12.7125i		−	0.444753i
$818$		−	65.3759i		−	2.28581i
$819$		0			0
$820$			30.6487i			1.07030i
$821$		−	15.4635i		−	0.539680i	−0.962905	−	0.269840i	$-0.913029\pi$
$821$		−	15.4635i		−	0.539680i	0.962905	−	0.269840i	$-0.0869709\pi$
$822$	−51.7565			−1.80521
$823$	−36.4901			−1.27197			−0.635983	−	0.771703i	$-0.719405\pi$
$823$	−36.4901			−1.27197			−0.635983	+	0.771703i	$0.719405\pi$
$824$	−28.9107			−1.00715
$825$	18.9975	+	18.6164i	0.661409	+	0.648140i
$826$		0			0
$827$			5.67576i			0.197365i	0.995119	+	0.0986827i	$0.0314629\pi$
$827$			5.67576i			0.197365i	−0.995119	+	0.0986827i	$0.968537\pi$
$828$	6.35979			0.221018
$829$			38.9012i			1.35109i	0.737317	+	0.675547i	$0.236093\pi$
$829$			38.9012i			1.35109i	−0.737317	+	0.675547i	$0.763907\pi$
$830$	16.2551			0.564222
$831$	−29.0861			−1.00899
$832$	−95.5271			−3.31181
$833$		0			0
$834$	−52.8433			−1.82981
$835$			9.02512i			0.312327i
$836$	24.8473	−	25.3560i	0.859362	−	0.876955i
$837$	−5.92651			−0.204850
$838$	65.5177			2.26327
$839$			19.1147i			0.659911i	0.943996	+	0.329956i	$0.107034\pi$
$839$			19.1147i			0.659911i	−0.943996	+	0.329956i	$0.892966\pi$
$840$		0			0
$841$	28.5957			0.986058
$842$			56.0510i			1.93165i
$843$	−6.12577			−0.210983
$844$			20.3351i			0.699964i
$845$			19.8082i			0.681423i
$846$	0.708725			0.0243665
$847$		0			0
$848$	−94.3472			−3.23990
$849$		−	6.54038i		−	0.224465i
$850$		−	146.533i		−	5.02606i
$851$	−11.9917			−0.411070
$852$			73.7772i			2.52757i
$853$	3.75770			0.128661			0.0643306	−	0.997929i	$-0.479509\pi$
$853$	3.75770			0.128661			0.0643306	+	0.997929i	$0.479509\pi$
$854$		0			0
$855$		−	7.32790i		−	0.250609i
$856$	8.44752			0.288730
$857$	17.9972			0.614772			0.307386	−	0.951585i	$-0.400546\pi$
$857$	17.9972			0.614772			0.307386	+	0.951585i	$0.400546\pi$
$858$	−26.9146	+	27.4656i	−0.918848	+	0.937658i
$859$			49.8030i			1.69926i	0.527383	+	0.849628i	$0.323173\pi$
$859$			49.8030i			1.69926i	−0.527383	+	0.849628i	$0.676827\pi$
$860$	−119.046			−4.05945
$861$		0			0
$862$	74.3099			2.53100
$863$	−0.522080			−0.0177718			−0.00888590	−	0.999961i	$-0.502829\pi$
$863$	−0.522080			−0.0177718			−0.00888590	+	0.999961i	$0.502829\pi$
$864$	−18.0583			−0.614357
$865$			26.4908i			0.900713i
$866$	84.2799			2.86395
$867$			28.9178i			0.982101i
$868$		0			0
$869$	−29.6107	−	29.0167i	−1.00448	−	0.984325i
$870$	6.18645			0.209740
$871$	27.0556			0.916744
$872$	83.4139			2.82475
$873$		−	2.61309i		−	0.0884396i
$874$		−	6.60760i		−	0.223506i
$875$		0			0
$876$		−	29.2814i		−	0.989327i
$877$			10.8998i			0.368059i	0.982921	+	0.184029i	$0.0589142\pi$
$877$			10.8998i			0.368059i	−0.982921	+	0.184029i	$0.941086\pi$
$878$			53.3045i			1.79894i
$879$		−	25.2990i		−	0.853313i
$880$	−113.156	−	110.886i	−3.81447	−	3.73795i
$881$			2.83670i			0.0955710i	0.998858	+	0.0477855i	$0.0152164\pi$
$881$			2.83670i			0.0955710i	−0.998858	+	0.0477855i	$0.984784\pi$
$882$		0			0
$883$	−47.0454			−1.58320			−0.791601	−	0.611038i	$-0.790752\pi$
$883$	−47.0454			−1.58320			−0.791601	+	0.611038i	$0.790752\pi$
$884$	153.575			5.16527
$885$		−	13.7095i		−	0.460841i
$886$			64.6979i			2.17357i
$887$	−36.9139			−1.23945			−0.619724	−	0.784820i	$-0.712756\pi$
$887$	−36.9139			−1.23945			−0.619724	+	0.784820i	$0.712756\pi$
$888$	87.6442			2.94115
$889$		0			0
$890$		−	85.1570i		−	2.85447i
$891$	−2.32133	+	2.36885i	−0.0777674	+	0.0793594i
$892$		−	31.7155i		−	1.06191i
$893$		−	0.533789i		−	0.0178626i
$894$			11.4692i			0.383588i
$895$			8.29302i			0.277205i
$896$		0			0
$897$			5.18851i			0.173239i
$898$			29.3844i			0.980569i
$899$	−3.76837			−0.125682
$900$	−42.2692			−1.40897
$901$	48.2928			1.60886
$902$	−10.2937	−	10.0872i	−0.342743	−	0.335867i
$903$		0			0
$904$			21.3166i			0.708979i
$905$	55.0005			1.82828
$906$			33.2417i			1.10438i
$907$	−19.9787			−0.663383			−0.331692	−	0.943388i	$-0.607619\pi$
$907$	−19.9787			−0.663383			−0.331692	+	0.943388i	$0.607619\pi$
$908$	96.4483			3.20075
$909$	−16.7431			−0.555335
$910$		0			0
$911$	9.58172			0.317456			0.158728	−	0.987322i	$-0.449261\pi$
$911$	9.58172			0.317456			0.158728	+	0.987322i	$0.449261\pi$
$912$			26.8854i			0.890265i
$913$	−3.87827	+	3.95766i	−0.128352	+	0.130980i
$914$	−58.7314			−1.94266
$915$	22.2162			0.734445
$916$			11.0425i			0.364855i
$917$		0			0
$918$	18.2716			0.603054
$919$			30.6515i			1.01110i	0.862797	+	0.505550i	$0.168710\pi$
$919$			30.6515i			1.01110i	−0.862797	+	0.505550i	$0.831290\pi$
$920$	−38.3973			−1.26592
$921$			26.3097i			0.866934i
$922$			8.64785i			0.284802i
$923$	−60.1897			−1.98117
$924$		0			0
$925$	79.7006			2.62054
$926$			56.5443i			1.85816i
$927$		−	3.27821i		−	0.107671i
$928$	−11.4824			−0.376927
$929$		−	4.24691i		−	0.139336i	−0.997570	−	0.0696682i	$-0.977806\pi$
$929$		−	4.24691i		−	0.139336i	0.997570	−	0.0696682i	$-0.0221941\pi$
$930$	57.6616			1.89080
$931$		0			0
$932$		−	124.320i		−	4.07223i
$933$	10.8220			0.354295
$934$	−58.1616			−1.90311
$935$	57.9200	+	56.7581i	1.89419	+	1.85619i
$936$		−	37.9215i		−	1.23950i
$937$	2.54355			0.0830942			0.0415471	−	0.999137i	$-0.486771\pi$
$937$	2.54355			0.0830942			0.0415471	+	0.999137i	$0.486771\pi$
$938$		0			0
$939$	−3.55998			−0.116176
$940$	−4.99869			−0.163039
$941$	−4.16005			−0.135614			−0.0678069	−	0.997698i	$-0.521600\pi$
$941$	−4.16005			−0.135614			−0.0678069	+	0.997698i	$0.521600\pi$
$942$			26.9619i			0.878467i
$943$	−1.94458			−0.0633243
$944$			50.2990i			1.63709i
$945$		0			0
$946$	39.1809	−	39.9830i	1.27388	−	1.29996i
$947$	−14.5564			−0.473020			−0.236510	−	0.971629i	$-0.576004\pi$
$947$	−14.5564			−0.473020			−0.236510	+	0.971629i	$0.576004\pi$
$948$	65.8835			2.13980
$949$	23.8887			0.775459
$950$			43.9162i			1.42483i
$951$			23.1694i			0.751319i
$952$		0			0
$953$			50.5968i			1.63899i	0.573085	+	0.819496i	$0.305746\pi$
$953$			50.5968i			1.63899i	−0.573085	+	0.819496i	$0.694254\pi$
$954$		−	19.2167i		−	0.622163i
$955$			1.80303i			0.0583447i
$956$		−	107.138i		−	3.46508i
$957$	−1.47601	+	1.50623i	−0.0477127	+	0.0486895i
$958$		−	6.67225i		−	0.215571i
$959$		0			0
$960$	80.1611			2.58719
$961$	−4.12357			−0.133018
$962$			115.227i			3.71506i
$963$			0.957874i			0.0308671i
$964$	−63.8389			−2.05611
$965$	95.5867			3.07705
$966$		0			0
$967$		−	35.8657i		−	1.15336i	−0.816969	−	0.576682i	$-0.804347\pi$
$967$		−	35.8657i		−	1.15336i	0.816969	−	0.576682i	$-0.195653\pi$
$968$	96.9895	−	1.96567i	3.11736	−	0.0631789i
$969$		−	13.7616i		−	0.442087i
$970$			25.4239i			0.816311i
$971$			18.6260i			0.597735i	0.954295	+	0.298868i	$0.0966089\pi$
$971$			18.6260i			0.597735i	−0.954295	+	0.298868i	$0.903391\pi$
$972$		−	5.27065i		−	0.169056i
$973$		0			0
$974$		−	19.6895i		−	0.630892i
$975$		−	34.4845i		−	1.10439i
$976$	−81.5092			−2.60905
$977$	−29.3802			−0.939954			−0.469977	−	0.882679i	$-0.655738\pi$
$977$	−29.3802			−0.939954			−0.469977	+	0.882679i	$0.655738\pi$
$978$	−50.7145			−1.62167
$979$	20.7334	+	20.3174i	0.662642	+	0.649348i
$980$		0			0
$981$			9.45840i			0.301983i
$982$	−41.5595			−1.32622
$983$		−	17.3837i		−	0.554454i	−0.960804	−	0.277227i	$-0.910585\pi$
$983$		−	17.3837i		−	0.554454i	0.960804	−	0.277227i	$-0.0894155\pi$
$984$	14.2124			0.453076
$985$	36.7517			1.17101
$986$	11.6180			0.369992
$987$		0			0
$988$	−46.0264			−1.46430
$989$		−	7.55318i		−	0.240177i
$990$	22.5852	−	23.0476i	0.717804	−	0.732500i
$991$	47.4579			1.50755			0.753774	−	0.657133i	$-0.228231\pi$
$991$	47.4579			1.50755			0.753774	+	0.657133i	$0.228231\pi$
$992$	−107.023			−3.39798
$993$		−	1.99367i		−	0.0632671i
$994$		0			0
$995$	−19.2826			−0.611300
$996$		−	8.80574i		−	0.279021i
$997$	22.9579			0.727082			0.363541	−	0.931578i	$-0.381568\pi$
$997$	22.9579			0.727082			0.363541	+	0.931578i	$0.381568\pi$
$998$		−	50.4003i		−	1.59539i
$999$			9.93807i			0.314427i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1617.2.c.b.538.4	yes	48
7.6	odd	2	inner	1617.2.c.b.538.3	✓	48
11.10	odd	2	inner	1617.2.c.b.538.46	yes	48
77.76	even	2	inner	1617.2.c.b.538.45	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1617.2.c.b.538.3	✓	48	7.6	odd	2	inner
1617.2.c.b.538.4	yes	48	1.1	even	1	trivial
1617.2.c.b.538.45	yes	48	77.76	even	2	inner
1617.2.c.b.538.46	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)

\(f(q)\)	\(=\)	\(q-2.69641i q^{2} +1.00000i q^{3} -5.27065 q^{4} +3.60829i q^{5} +2.69641 q^{6} +8.81904i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q-2.69641i q^{2} +1.00000i q^{3} -5.27065 q^{4} +3.60829i q^{5} +2.69641 q^{6} +8.81904i q^{8} -1.00000 q^{9} +9.72943 q^{10} +(-2.32133 + 2.36885i) q^{11} -5.27065i q^{12} +4.29996 q^{13} -3.60829 q^{15} +13.2385 q^{16} -6.77627 q^{17} +2.69641i q^{18} +2.03085 q^{19} -19.0180i q^{20} +(6.38740 + 6.25926i) q^{22} +1.20664 q^{23} -8.81904 q^{24} -8.01972 q^{25} -11.5945i q^{26} -1.00000i q^{27} -0.635849i q^{29} +9.72943i q^{30} -5.92651i q^{31} -18.0583i q^{32} +(-2.36885 - 2.32133i) q^{33} +18.2716i q^{34} +5.27065 q^{36} -9.93807 q^{37} -5.47602i q^{38} +4.29996i q^{39} -31.8216 q^{40} -1.61156 q^{41} -6.25967i q^{43} +(12.2349 - 12.4854i) q^{44} -3.60829i q^{45} -3.25361i q^{46} -0.262840i q^{47} +13.2385i q^{48} +21.6245i q^{50} -6.77627i q^{51} -22.6636 q^{52} -7.12675 q^{53} -2.69641 q^{54} +(-8.54748 - 8.37601i) q^{55} +2.03085i q^{57} -1.71451 q^{58} +3.79946i q^{59} +19.0180 q^{60} -6.15699 q^{61} -15.9803 q^{62} -22.2158 q^{64} +15.5155i q^{65} +(-6.25926 + 6.38740i) q^{66} +6.29206 q^{67} +35.7154 q^{68} +1.20664i q^{69} -13.9977 q^{71} -8.81904i q^{72} +5.55556 q^{73} +26.7972i q^{74} -8.01972i q^{75} -10.7039 q^{76} +11.5945 q^{78} +12.5001i q^{79} +47.7682i q^{80} +1.00000 q^{81} +4.34544i q^{82} +1.67071 q^{83} -24.4507i q^{85} -16.8787 q^{86} +0.635849 q^{87} +(-20.8910 - 20.4719i) q^{88} -8.75251i q^{89} -9.72943 q^{90} -6.35979 q^{92} +5.92651 q^{93} -0.708725 q^{94} +7.32790i q^{95} +18.0583 q^{96} +2.61309i q^{97} +(2.32133 - 2.36885i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 64 q^{4} - 48 q^{9}+O(q^{10}) \) 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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