LMFDB - Embedded newform 3234.2.e.c.2155.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3234,2,Mod(2155,3234)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3234, 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("3234.2155");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3234 = 2 \cdot 3 \cdot 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3234.e (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:	$25.8236200137$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			2155.15
Character	$\chi$	$=$	3234.2155
Dual form			3234.2.e.c.2155.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} -2.66749i q^{5} -1.00000 q^{6} -1.00000i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} -2.66749i q^{5} -1.00000 q^{6} -1.00000i q^{8} -1.00000 q^{9} +2.66749 q^{10} +(-2.85384 + 1.68986i) q^{11} -1.00000i q^{12} +2.50184 q^{13} +2.66749 q^{15} +1.00000 q^{16} +2.53541 q^{17} -1.00000i q^{18} -1.39472 q^{19} +2.66749i q^{20} +(-1.68986 - 2.85384i) q^{22} -3.15503 q^{23} +1.00000 q^{24} -2.11553 q^{25} +2.50184i q^{26} -1.00000i q^{27} -6.51317i q^{29} +2.66749i q^{30} +4.05080i q^{31} +1.00000i q^{32} +(-1.68986 - 2.85384i) q^{33} +2.53541i q^{34} +1.00000 q^{36} +2.54945 q^{37} -1.39472i q^{38} +2.50184i q^{39} -2.66749 q^{40} -2.65301 q^{41} -5.62214i q^{43} +(2.85384 - 1.68986i) q^{44} +2.66749i q^{45} -3.15503i q^{46} -2.76266i q^{47} +1.00000i q^{48} -2.11553i q^{50} +2.53541i q^{51} -2.50184 q^{52} -6.88010 q^{53} +1.00000 q^{54} +(4.50768 + 7.61259i) q^{55} -1.39472i q^{57} +6.51317 q^{58} +4.91595i q^{59} -2.66749 q^{60} -5.35288 q^{61} -4.05080 q^{62} -1.00000 q^{64} -6.67364i q^{65} +(2.85384 - 1.68986i) q^{66} +7.33059 q^{67} -2.53541 q^{68} -3.15503i q^{69} -6.05096 q^{71} +1.00000i q^{72} -9.63838 q^{73} +2.54945i q^{74} -2.11553i q^{75} +1.39472 q^{76} -2.50184 q^{78} -8.30093i q^{79} -2.66749i q^{80} +1.00000 q^{81} -2.65301i q^{82} -14.4528 q^{83} -6.76319i q^{85} +5.62214 q^{86} +6.51317 q^{87} +(1.68986 + 2.85384i) q^{88} -11.2019i q^{89} -2.66749 q^{90} +3.15503 q^{92} -4.05080 q^{93} +2.76266 q^{94} +3.72042i q^{95} -1.00000 q^{96} -4.03611i q^{97} +(2.85384 - 1.68986i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 24 q^{4} - 24 q^{6} - 24 q^{9}+O(q^{10}) $ 24 * q - 24 * q^4 - 24 * q^6 - 24 * q^9	$ 24 q - 24 q^{4} - 24 q^{6} - 24 q^{9} + 24 q^{16} + 16 q^{17} - 32 q^{19} - 8 q^{22} + 24 q^{24} - 8 q^{25} - 8 q^{33} + 24 q^{36} + 16 q^{37} - 16 q^{41} + 24 q^{54} + 16 q^{55} - 16 q^{62} - 24 q^{64} - 64 q^{67} - 16 q^{68} + 64 q^{71} + 32 q^{76} + 24 q^{81} - 16 q^{83} + 8 q^{88} - 16 q^{93} + 64 q^{94} - 24 q^{96}+O(q^{100}) $ 24 * q - 24 * q^4 - 24 * q^6 - 24 * q^9 + 24 * q^16 + 16 * q^17 - 32 * q^19 - 8 * q^22 + 24 * q^24 - 8 * q^25 - 8 * q^33 + 24 * q^36 + 16 * q^37 - 16 * q^41 + 24 * q^54 + 16 * q^55 - 16 * q^62 - 24 * q^64 - 64 * q^67 - 16 * q^68 + 64 * q^71 + 32 * q^76 + 24 * q^81 - 16 * q^83 + 8 * q^88 - 16 * q^93 + 64 * q^94 - 24 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3234\mathbb{Z}\right)^\times$.

$n$	$199$	$1079$	$2059$
$\chi(n)$	$-1$	$1$	$-1$

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 $

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$			1.00000i			0.577350i
$3$			1.00000i			0.577350i
$4$	−1.00000			−0.500000
$5$		−	2.66749i		−	1.19294i	−0.802635	−	0.596470i	$-0.796570\pi$
$5$		−	2.66749i		−	1.19294i	0.802635	−	0.596470i	$-0.203430\pi$
$6$	−1.00000			−0.408248
$7$		0			0
$7$		0			0
$8$		−	1.00000i		−	0.353553i
$9$	−1.00000			−0.333333
$10$	2.66749			0.843536
$11$	−2.85384	+	1.68986i	−0.860464	+	0.509511i
$11$	−2.85384	+	1.68986i	−0.860464	+	0.509511i
$12$		−	1.00000i		−	0.288675i
$13$	2.50184			0.693885			0.346943	−	0.937886i	$-0.387220\pi$
$13$	2.50184			0.693885			0.346943	+	0.937886i	$0.387220\pi$
$14$		0			0
$15$	2.66749			0.688744
$16$	1.00000			0.250000
$17$	2.53541			0.614927			0.307464	−	0.951560i	$-0.400520\pi$
$17$	2.53541			0.614927			0.307464	+	0.951560i	$0.400520\pi$
$18$		−	1.00000i		−	0.235702i
$19$	−1.39472			−0.319972			−0.159986	−	0.987119i	$-0.551145\pi$
$19$	−1.39472			−0.319972			−0.159986	+	0.987119i	$0.551145\pi$
$20$			2.66749i			0.596470i
$21$		0			0
$22$	−1.68986	−	2.85384i	−0.360279	−	0.608440i
$23$	−3.15503			−0.657869			−0.328935	−	0.944353i	$-0.606690\pi$
$23$	−3.15503			−0.657869			−0.328935	+	0.944353i	$0.606690\pi$
$24$	1.00000			0.204124
$25$	−2.11553			−0.423105
$26$			2.50184i			0.490651i
$27$		−	1.00000i		−	0.192450i
$28$		0			0
$29$		−	6.51317i		−	1.20947i	−0.796428	−	0.604733i	$-0.793280\pi$
$29$		−	6.51317i		−	1.20947i	0.796428	−	0.604733i	$-0.206720\pi$
$30$			2.66749i			0.487016i
$31$			4.05080i			0.727546i	0.931488	+	0.363773i	$0.118512\pi$
$31$			4.05080i			0.727546i	−0.931488	+	0.363773i	$0.881488\pi$
$32$			1.00000i			0.176777i
$33$	−1.68986	−	2.85384i	−0.294166	−	0.496789i
$34$			2.53541i			0.434819i
$35$		0			0
$36$	1.00000			0.166667
$37$	2.54945			0.419127			0.209564	−	0.977795i	$-0.432796\pi$
$37$	2.54945			0.419127			0.209564	+	0.977795i	$0.432796\pi$
$38$		−	1.39472i		−	0.226254i
$39$			2.50184i			0.400615i
$40$	−2.66749			−0.421768
$41$	−2.65301			−0.414331			−0.207166	−	0.978306i	$-0.566424\pi$
$41$	−2.65301			−0.414331			−0.207166	+	0.978306i	$0.566424\pi$
$42$		0			0
$43$		−	5.62214i		−	0.857368i	−0.903454	−	0.428684i	$-0.858977\pi$
$43$		−	5.62214i		−	0.857368i	0.903454	−	0.428684i	$-0.141023\pi$
$44$	2.85384	−	1.68986i	0.430232	−	0.254755i
$45$			2.66749i			0.397647i
$46$		−	3.15503i		−	0.465184i
$47$		−	2.76266i		−	0.402975i	−0.979491	−	0.201488i	$-0.935422\pi$
$47$		−	2.76266i		−	0.402975i	0.979491	−	0.201488i	$-0.0645776\pi$
$48$			1.00000i			0.144338i
$49$		0			0
$50$		−	2.11553i		−	0.299181i
$51$			2.53541i			0.355028i
$52$	−2.50184			−0.346943
$53$	−6.88010			−0.945054			−0.472527	−	0.881316i	$-0.656658\pi$
$53$	−6.88010			−0.945054			−0.472527	+	0.881316i	$0.656658\pi$
$54$	1.00000			0.136083
$55$	4.50768	+	7.61259i	0.607816	+	1.02648i
$56$		0			0
$57$		−	1.39472i		−	0.184736i
$58$	6.51317			0.855221
$59$			4.91595i			0.640002i	0.947417	+	0.320001i	$0.103683\pi$
$59$			4.91595i			0.640002i	−0.947417	+	0.320001i	$0.896317\pi$
$60$	−2.66749			−0.344372
$61$	−5.35288			−0.685366			−0.342683	−	0.939451i	$-0.611336\pi$
$61$	−5.35288			−0.685366			−0.342683	+	0.939451i	$0.611336\pi$
$62$	−4.05080			−0.514453
$63$		0			0
$64$	−1.00000			−0.125000
$65$		−	6.67364i		−	0.827763i
$66$	2.85384	−	1.68986i	0.351283	−	0.208007i
$67$	7.33059			0.895575			0.447787	−	0.894140i	$-0.352212\pi$
$67$	7.33059			0.895575			0.447787	+	0.894140i	$0.352212\pi$
$68$	−2.53541			−0.307464
$69$		−	3.15503i		−	0.379821i
$70$		0			0
$71$	−6.05096			−0.718116			−0.359058	−	0.933315i	$-0.616902\pi$
$71$	−6.05096			−0.718116			−0.359058	+	0.933315i	$0.616902\pi$
$72$			1.00000i			0.117851i
$73$	−9.63838			−1.12809			−0.564043	−	0.825745i	$-0.690755\pi$
$73$	−9.63838			−1.12809			−0.564043	+	0.825745i	$0.690755\pi$
$74$			2.54945i			0.296368i
$75$		−	2.11553i		−	0.244280i
$76$	1.39472			0.159986
$77$		0			0
$78$	−2.50184			−0.283277
$79$		−	8.30093i		−	0.933928i	−0.884276	−	0.466964i	$-0.845348\pi$
$79$		−	8.30093i		−	0.933928i	0.884276	−	0.466964i	$-0.154652\pi$
$80$		−	2.66749i		−	0.298235i
$81$	1.00000			0.111111
$82$		−	2.65301i		−	0.292976i
$83$	−14.4528			−1.58640			−0.793200	−	0.608961i	$-0.791587\pi$
$83$	−14.4528			−1.58640			−0.793200	+	0.608961i	$0.791587\pi$
$84$		0			0
$85$		−	6.76319i		−	0.733571i
$86$	5.62214			0.606251
$87$	6.51317			0.698285
$88$	1.68986	+	2.85384i	0.180139	+	0.304220i
$89$		−	11.2019i		−	1.18740i	−0.804686	−	0.593701i	$-0.797666\pi$
$89$		−	11.2019i		−	1.18740i	0.804686	−	0.593701i	$-0.202334\pi$
$90$	−2.66749			−0.281179
$91$		0			0
$92$	3.15503			0.328935
$93$	−4.05080			−0.420049
$94$	2.76266			0.284947
$95$			3.72042i			0.381707i
$96$	−1.00000			−0.102062
$97$		−	4.03611i		−	0.409805i	−0.978782	−	0.204903i	$-0.934312\pi$
$97$		−	4.03611i		−	0.409805i	0.978782	−	0.204903i	$-0.0656877\pi$
$98$		0			0
$99$	2.85384	−	1.68986i	0.286821	−	0.169837i
$100$	2.11553			0.211553
$101$	7.27104			0.723496			0.361748	−	0.932276i	$-0.382180\pi$
$101$	7.27104			0.723496			0.361748	+	0.932276i	$0.382180\pi$
$102$	−2.53541			−0.251043
$103$		−	4.71286i		−	0.464371i	−0.972671	−	0.232186i	$-0.925412\pi$
$103$		−	4.71286i		−	0.464371i	0.972671	−	0.232186i	$-0.0745877\pi$
$104$		−	2.50184i		−	0.245325i
$105$		0			0
$106$		−	6.88010i		−	0.668254i
$107$		−	19.6228i		−	1.89701i	−0.316761	−	0.948505i	$-0.602595\pi$
$107$		−	19.6228i		−	1.89701i	0.316761	−	0.948505i	$-0.397405\pi$
$108$			1.00000i			0.0962250i
$109$		−	15.1803i		−	1.45401i	−0.686633	−	0.727004i	$-0.740912\pi$
$109$		−	15.1803i		−	1.45401i	0.686633	−	0.727004i	$-0.259088\pi$
$110$	−7.61259	+	4.50768i	−0.725832	+	0.429791i
$111$			2.54945i			0.241983i
$112$		0			0
$113$	−4.06642			−0.382536			−0.191268	−	0.981538i	$-0.561260\pi$
$113$	−4.06642			−0.382536			−0.191268	+	0.981538i	$0.561260\pi$
$114$	1.39472			0.130628
$115$			8.41603i			0.784798i
$116$			6.51317i			0.604733i
$117$	−2.50184			−0.231295
$118$	−4.91595			−0.452550
$119$		0			0
$120$		−	2.66749i		−	0.243508i
$121$	5.28877	−	9.64515i	0.480797	−	0.876832i
$122$		−	5.35288i		−	0.484627i
$123$		−	2.65301i		−	0.239214i
$124$		−	4.05080i		−	0.363773i
$125$		−	7.69432i		−	0.688201i
$126$		0			0
$127$		−	8.01581i		−	0.711288i	−0.934621	−	0.355644i	$-0.884262\pi$
$127$		−	8.01581i		−	0.711288i	0.934621	−	0.355644i	$-0.115738\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	5.62214			0.495002
$130$	6.67364			0.585317
$131$	14.5316			1.26963			0.634815	−	0.772664i	$-0.281076\pi$
$131$	14.5316			1.26963			0.634815	+	0.772664i	$0.281076\pi$
$132$	1.68986	+	2.85384i	0.147083	+	0.248395i
$133$		0			0
$134$			7.33059i			0.633267i
$135$	−2.66749			−0.229581
$136$		−	2.53541i		−	0.217410i
$137$	−10.1601			−0.868040			−0.434020	−	0.900903i	$-0.642905\pi$
$137$	−10.1601			−0.868040			−0.434020	+	0.900903i	$0.642905\pi$
$138$	3.15503			0.268574
$139$	−2.15019			−0.182377			−0.0911885	−	0.995834i	$-0.529067\pi$
$139$	−2.15019			−0.182377			−0.0911885	+	0.995834i	$0.529067\pi$
$140$		0			0
$141$	2.76266			0.232658
$142$		−	6.05096i		−	0.507785i
$143$	−7.13984	+	4.22775i	−0.597063	+	0.353542i
$144$	−1.00000			−0.0833333
$145$	−17.3739			−1.44282
$146$		−	9.63838i		−	0.797678i
$147$		0			0
$148$	−2.54945			−0.209564
$149$		−	18.1396i		−	1.48606i	−0.669260	−	0.743028i	$-0.733389\pi$
$149$		−	18.1396i		−	1.48606i	0.669260	−	0.743028i	$-0.266611\pi$
$150$	2.11553			0.172732
$151$			1.69350i			0.137815i	0.997623	+	0.0689075i	$0.0219513\pi$
$151$			1.69350i			0.137815i	−0.997623	+	0.0689075i	$0.978049\pi$
$152$			1.39472i			0.113127i
$153$	−2.53541			−0.204976
$154$		0			0
$155$	10.8055			0.867918
$156$		−	2.50184i		−	0.200307i
$157$			6.48100i			0.517240i	0.965979	+	0.258620i	$0.0832677\pi$
$157$			6.48100i			0.517240i	−0.965979	+	0.258620i	$0.916732\pi$
$158$	8.30093			0.660387
$159$		−	6.88010i		−	0.545627i
$160$	2.66749			0.210884
$161$		0			0
$162$			1.00000i			0.0785674i
$163$	1.86138			0.145795			0.0728973	−	0.997339i	$-0.476775\pi$
$163$	1.86138			0.145795			0.0728973	+	0.997339i	$0.476775\pi$
$164$	2.65301			0.207166
$165$	−7.61259	+	4.50768i	−0.592640	+	0.350923i
$166$		−	14.4528i		−	1.12175i
$167$	−10.4965			−0.812240			−0.406120	−	0.913820i	$-0.633118\pi$
$167$	−10.4965			−0.812240			−0.406120	+	0.913820i	$0.633118\pi$
$168$		0			0
$169$	−6.74080			−0.518523
$170$	6.76319			0.518713
$171$	1.39472			0.106657
$172$			5.62214i			0.428684i
$173$	7.72136			0.587044			0.293522	−	0.955952i	$-0.405173\pi$
$173$	7.72136			0.587044			0.293522	+	0.955952i	$0.405173\pi$
$174$			6.51317i			0.493762i
$175$		0			0
$176$	−2.85384	+	1.68986i	−0.215116	+	0.127378i
$177$	−4.91595			−0.369505
$178$	11.2019			0.839620
$179$	−20.4836			−1.53102			−0.765509	−	0.643426i	$-0.777513\pi$
$179$	−20.4836			−1.53102			−0.765509	+	0.643426i	$0.777513\pi$
$180$		−	2.66749i		−	0.198823i
$181$		−	22.7331i		−	1.68974i	−0.534975	−	0.844868i	$-0.679679\pi$
$181$		−	22.7331i		−	1.68974i	0.534975	−	0.844868i	$-0.320321\pi$
$182$		0			0
$183$		−	5.35288i		−	0.395696i
$184$			3.15503i			0.232592i
$185$		−	6.80065i		−	0.499994i
$186$		−	4.05080i		−	0.297019i
$187$	−7.23565	+	4.28448i	−0.529123	+	0.313312i
$188$			2.76266i			0.201488i
$189$		0			0
$190$	−3.72042			−0.269908
$191$	21.7595			1.57446			0.787231	−	0.616659i	$-0.211514\pi$
$191$	21.7595			1.57446			0.787231	+	0.616659i	$0.211514\pi$
$192$		−	1.00000i		−	0.0721688i
$193$		−	7.69156i		−	0.553650i	−0.960920	−	0.276825i	$-0.910718\pi$
$193$		−	7.69156i		−	0.553650i	0.960920	−	0.276825i	$-0.0892823\pi$
$194$	4.03611			0.289776
$195$	6.67364			0.477909
$196$		0			0
$197$			21.1678i			1.50815i	0.656791	+	0.754073i	$0.271913\pi$
$197$			21.1678i			1.50815i	−0.656791	+	0.754073i	$0.728087\pi$
$198$	1.68986	+	2.85384i	0.120093	+	0.202813i
$199$			23.2150i			1.64566i	0.568284	+	0.822832i	$0.307607\pi$
$199$			23.2150i			1.64566i	−0.568284	+	0.822832i	$0.692393\pi$
$200$			2.11553i			0.149590i
$201$			7.33059i			0.517060i
$202$			7.27104i			0.511589i
$203$		0			0
$204$		−	2.53541i		−	0.177514i
$205$			7.07690i			0.494272i
$206$	4.71286			0.328360
$207$	3.15503			0.219290
$208$	2.50184			0.173471
$209$	3.98032	−	2.35688i	0.275324	−	0.163029i
$210$		0			0
$211$			14.1204i			0.972087i	0.873935	+	0.486044i	$0.161560\pi$
$211$			14.1204i			0.972087i	−0.873935	+	0.486044i	$0.838440\pi$
$212$	6.88010			0.472527
$213$		−	6.05096i		−	0.414605i
$214$	19.6228			1.34139
$215$	−14.9970			−1.02279
$216$	−1.00000			−0.0680414
$217$		0			0
$218$	15.1803			1.02814
$219$		−	9.63838i		−	0.651301i
$220$	−4.50768	−	7.61259i	−0.303908	−	0.513241i
$221$	6.34319			0.426689
$222$	−2.54945			−0.171108
$223$			12.4044i			0.830658i	0.909671	+	0.415329i	$0.136334\pi$
$223$			12.4044i			0.830658i	−0.909671	+	0.415329i	$0.863666\pi$
$224$		0			0
$225$	2.11553			0.141035
$226$		−	4.06642i		−	0.270494i
$227$	−15.2148			−1.00985			−0.504923	−	0.863165i	$-0.668479\pi$
$227$	−15.2148			−1.00985			−0.504923	+	0.863165i	$0.668479\pi$
$228$			1.39472i			0.0923679i
$229$			19.2052i			1.26911i	0.772876	+	0.634557i	$0.218817\pi$
$229$			19.2052i			1.26911i	−0.772876	+	0.634557i	$0.781183\pi$
$230$	−8.41603			−0.554936
$231$		0			0
$232$	−6.51317			−0.427611
$233$		−	11.5244i		−	0.754988i	−0.926012	−	0.377494i	$-0.876786\pi$
$233$		−	11.5244i		−	0.754988i	0.926012	−	0.377494i	$-0.123214\pi$
$234$		−	2.50184i		−	0.163550i
$235$	−7.36938			−0.480725
$236$		−	4.91595i		−	0.320001i
$237$	8.30093			0.539203
$238$		0			0
$239$			10.3520i			0.669613i	0.942287	+	0.334807i	$0.108671\pi$
$239$			10.3520i			0.669613i	−0.942287	+	0.334807i	$0.891329\pi$
$240$	2.66749			0.172186
$241$	25.1255			1.61848			0.809238	−	0.587481i	$-0.199880\pi$
$241$	25.1255			1.61848			0.809238	+	0.587481i	$0.199880\pi$
$242$	9.64515	+	5.28877i	0.620014	+	0.339975i
$243$			1.00000i			0.0641500i
$244$	5.35288			0.342683
$245$		0			0
$246$	2.65301			0.169150
$247$	−3.48938			−0.222024
$248$	4.05080			0.257226
$249$		−	14.4528i		−	0.915909i
$250$	7.69432			0.486631
$251$		−	7.97557i		−	0.503414i	−0.967804	−	0.251707i	$-0.919008\pi$
$251$		−	7.97557i		−	0.503414i	0.967804	−	0.251707i	$-0.0809918\pi$
$252$		0			0
$253$	9.00394	−	5.33155i	0.566073	−	0.335192i
$254$	8.01581			0.502957
$255$	6.76319			0.423528
$256$	1.00000			0.0625000
$257$			7.57023i			0.472218i	0.971727	+	0.236109i	$0.0758722\pi$
$257$			7.57023i			0.472218i	−0.971727	+	0.236109i	$0.924128\pi$
$258$			5.62214i			0.350019i
$259$		0			0
$260$			6.67364i			0.413882i
$261$			6.51317i			0.403155i
$262$			14.5316i			0.897764i
$263$		−	26.3900i		−	1.62728i	−0.581369	−	0.813640i	$-0.697483\pi$
$263$		−	26.3900i		−	1.62728i	0.581369	−	0.813640i	$-0.302517\pi$
$264$	−2.85384	+	1.68986i	−0.175642	+	0.104003i
$265$			18.3526i			1.12739i
$266$		0			0
$267$	11.2019			0.685547
$268$	−7.33059			−0.447787
$269$		−	5.00096i		−	0.304914i	−0.988310	−	0.152457i	$-0.951282\pi$
$269$		−	5.00096i		−	0.304914i	0.988310	−	0.152457i	$-0.0487185\pi$
$270$		−	2.66749i		−	0.162339i
$271$	−28.1218			−1.70828			−0.854140	−	0.520044i	$-0.825916\pi$
$271$	−28.1218			−1.70828			−0.854140	+	0.520044i	$0.825916\pi$
$272$	2.53541			0.153732
$273$		0			0
$274$		−	10.1601i		−	0.613797i
$275$	6.03737	−	3.57494i	0.364067	−	0.215577i
$276$			3.15503i			0.189910i
$277$		−	4.15631i		−	0.249728i	−0.992174	−	0.124864i	$-0.960150\pi$
$277$		−	4.15631i		−	0.249728i	0.992174	−	0.124864i	$-0.0398495\pi$
$278$		−	2.15019i		−	0.128960i
$279$		−	4.05080i		−	0.242515i
$280$		0			0
$281$		−	30.6193i		−	1.82660i	−0.407291	−	0.913299i	$-0.633526\pi$
$281$		−	30.6193i		−	1.82660i	0.407291	−	0.913299i	$-0.366474\pi$
$282$			2.76266i			0.164514i
$283$	5.38804			0.320286			0.160143	−	0.987094i	$-0.448805\pi$
$283$	5.38804			0.320286			0.160143	+	0.987094i	$0.448805\pi$
$284$	6.05096			0.359058
$285$	−3.72042			−0.220379
$286$	−4.22775	−	7.13984i	−0.249992	−	0.422188i
$287$		0			0
$288$		−	1.00000i		−	0.0589256i
$289$	−10.5717			−0.621864
$290$		−	17.3739i		−	1.02023i
$291$	4.03611			0.236601
$292$	9.63838			0.564043
$293$	−4.27517			−0.249758			−0.124879	−	0.992172i	$-0.539854\pi$
$293$	−4.27517			−0.249758			−0.124879	+	0.992172i	$0.539854\pi$
$294$		0			0
$295$	13.1133			0.763484
$296$		−	2.54945i		−	0.148184i
$297$	1.68986	+	2.85384i	0.0980554	+	0.165596i
$298$	18.1396			1.05080
$299$	−7.89338			−0.456486
$300$			2.11553i			0.122140i
$301$		0			0
$302$	−1.69350			−0.0974500
$303$			7.27104i			0.417710i
$304$	−1.39472			−0.0799929
$305$			14.2788i			0.817600i
$306$		−	2.53541i		−	0.144940i
$307$	4.80816			0.274416			0.137208	−	0.990542i	$-0.456187\pi$
$307$	4.80816			0.274416			0.137208	+	0.990542i	$0.456187\pi$
$308$		0			0
$309$	4.71286			0.268105
$310$			10.8055i			0.613711i
$311$			28.8146i			1.63393i	0.576690	+	0.816963i	$0.304344\pi$
$311$			28.8146i			1.63393i	−0.576690	+	0.816963i	$0.695656\pi$
$312$	2.50184			0.141639
$313$			21.6235i			1.22223i	0.791541	+	0.611117i	$0.209279\pi$
$313$			21.6235i			1.22223i	−0.791541	+	0.611117i	$0.790721\pi$
$314$	−6.48100			−0.365744
$315$		0			0
$316$			8.30093i			0.466964i
$317$	8.45799			0.475048			0.237524	−	0.971382i	$-0.423664\pi$
$317$	8.45799			0.475048			0.237524	+	0.971382i	$0.423664\pi$
$318$	6.88010			0.385817
$319$	11.0063	+	18.5875i	0.616236	+	1.04070i
$320$			2.66749i			0.149117i
$321$	19.6228			1.09524
$322$		0			0
$323$	−3.53620			−0.196759
$324$	−1.00000			−0.0555556
$325$	−5.29271			−0.293587
$326$			1.86138i			0.103092i
$327$	15.1803			0.839472
$328$			2.65301i			0.146488i
$329$		0			0
$330$	−4.50768	−	7.61259i	−0.248140	−	0.419060i
$331$	2.57208			0.141374			0.0706872	−	0.997499i	$-0.477481\pi$
$331$	2.57208			0.141374			0.0706872	+	0.997499i	$0.477481\pi$
$332$	14.4528			0.793200
$333$	−2.54945			−0.139709
$334$		−	10.4965i		−	0.574340i
$335$		−	19.5543i		−	1.06837i
$336$		0			0
$337$		−	15.2962i		−	0.833235i	−0.909082	−	0.416617i	$-0.863215\pi$
$337$		−	15.2962i		−	0.833235i	0.909082	−	0.416617i	$-0.136785\pi$
$338$		−	6.74080i		−	0.366651i
$339$		−	4.06642i		−	0.220857i
$340$			6.76319i			0.366786i
$341$	−6.84528	−	11.5603i	−0.370693	−	0.626027i
$342$			1.39472i			0.0754181i
$343$		0			0
$344$	−5.62214			−0.303125
$345$	−8.41603			−0.453104
$346$			7.72136i			0.415103i
$347$		−	10.6965i		−	0.574220i	−0.957898	−	0.287110i	$-0.907305\pi$
$347$		−	10.6965i		−	0.574220i	0.957898	−	0.287110i	$-0.0926945\pi$
$348$	−6.51317			−0.349143
$349$	25.2258			1.35030			0.675152	−	0.737679i	$-0.264078\pi$
$349$	25.2258			1.35030			0.675152	+	0.737679i	$0.264078\pi$
$350$		0			0
$351$		−	2.50184i		−	0.133538i
$352$	−1.68986	−	2.85384i	−0.0900696	−	0.152110i
$353$		−	28.3189i		−	1.50726i	−0.657297	−	0.753631i	$-0.728300\pi$
$353$		−	28.3189i		−	1.50726i	0.657297	−	0.753631i	$-0.271700\pi$
$354$		−	4.91595i		−	0.261280i
$355$			16.1409i			0.856670i
$356$			11.2019i			0.593701i
$357$		0			0
$358$		−	20.4836i		−	1.08259i
$359$			10.0681i			0.531374i	0.964059	+	0.265687i	$0.0855988\pi$
$359$			10.0681i			0.531374i	−0.964059	+	0.265687i	$0.914401\pi$
$360$	2.66749			0.140589
$361$	−17.0547			−0.897618
$362$	22.7331			1.19482
$363$	9.64515	+	5.28877i	0.506239	+	0.277589i
$364$		0			0
$365$			25.7103i			1.34574i
$366$	5.35288			0.279800
$367$			24.5516i			1.28158i	0.767716	+	0.640791i	$0.221393\pi$
$367$			24.5516i			1.28158i	−0.767716	+	0.640791i	$0.778607\pi$
$368$	−3.15503			−0.164467
$369$	2.65301			0.138110
$370$	6.80065			0.353549
$371$		0			0
$372$	4.05080			0.210024
$373$		−	1.27622i		−	0.0660802i	−0.999454	−	0.0330401i	$-0.989481\pi$
$373$		−	1.27622i		−	0.0660802i	0.999454	−	0.0330401i	$-0.0105189\pi$
$374$	−4.28448	−	7.23565i	−0.221545	−	0.374146i
$375$	7.69432			0.397333
$376$	−2.76266			−0.142473
$377$		−	16.2949i		−	0.839230i
$378$		0			0
$379$	38.0451			1.95425			0.977124	−	0.212672i	$-0.0682166\pi$
$379$	38.0451			1.95425			0.977124	+	0.212672i	$0.0682166\pi$
$380$		−	3.72042i		−	0.190854i
$381$	8.01581			0.410662
$382$			21.7595i			1.11331i
$383$			11.2055i			0.572574i	0.958144	+	0.286287i	$0.0924211\pi$
$383$			11.2055i			0.572574i	−0.958144	+	0.286287i	$0.907579\pi$
$384$	1.00000			0.0510310
$385$		0			0
$386$	7.69156			0.391490
$387$			5.62214i			0.285789i
$388$			4.03611i			0.204903i
$389$	7.21388			0.365758			0.182879	−	0.983135i	$-0.441458\pi$
$389$	7.21388			0.365758			0.182879	+	0.983135i	$0.441458\pi$
$390$			6.67364i			0.337933i
$391$	−7.99930			−0.404542
$392$		0			0
$393$			14.5316i			0.733021i
$394$	−21.1678			−1.06642
$395$	−22.1427			−1.11412
$396$	−2.85384	+	1.68986i	−0.143411	+	0.0849185i
$397$			19.4918i			0.978264i	0.872210	+	0.489132i	$0.162686\pi$
$397$			19.4918i			0.978264i	−0.872210	+	0.489132i	$0.837314\pi$
$398$	−23.2150			−1.16366
$399$		0			0
$400$	−2.11553			−0.105776
$401$	−13.0461			−0.651492			−0.325746	−	0.945457i	$-0.605615\pi$
$401$	−13.0461			−0.651492			−0.325746	+	0.945457i	$0.605615\pi$
$402$	−7.33059			−0.365617
$403$			10.1345i			0.504833i
$404$	−7.27104			−0.361748
$405$		−	2.66749i		−	0.132549i
$406$		0			0
$407$	−7.27572	+	4.30821i	−0.360644	+	0.213550i
$408$	2.53541			0.125522
$409$	33.8668			1.67461			0.837303	−	0.546739i	$-0.184131\pi$
$409$	33.8668			1.67461			0.837303	+	0.546739i	$0.184131\pi$
$410$	−7.07690			−0.349503
$411$		−	10.1601i		−	0.501163i
$412$			4.71286i			0.232186i
$413$		0			0
$414$			3.15503i			0.155061i
$415$			38.5528i			1.89248i
$416$			2.50184i			0.122663i
$417$		−	2.15019i		−	0.105295i
$418$	2.35688	+	3.98032i	0.115279	+	0.194684i
$419$		−	12.9005i		−	0.630233i	−0.949053	−	0.315116i	$-0.897956\pi$
$419$		−	12.9005i		−	0.630233i	0.949053	−	0.315116i	$-0.102044\pi$
$420$		0			0
$421$	−7.05921			−0.344045			−0.172022	−	0.985093i	$-0.555030\pi$
$421$	−7.05921			−0.344045			−0.172022	+	0.985093i	$0.555030\pi$
$422$	−14.1204			−0.687369
$423$			2.76266i			0.134325i
$424$			6.88010i			0.334127i
$425$	−5.36373			−0.260179
$426$	6.05096			0.293170
$427$		0			0
$428$			19.6228i			0.948505i
$429$	−4.22775	−	7.13984i	−0.204118	−	0.344715i
$430$		−	14.9970i		−	0.723221i
$431$			3.54328i			0.170674i	0.996352	+	0.0853368i	$0.0271966\pi$
$431$			3.54328i			0.170674i	−0.996352	+	0.0853368i	$0.972803\pi$
$432$		−	1.00000i		−	0.0481125i
$433$		−	16.2125i		−	0.779121i	−0.921001	−	0.389561i	$-0.872627\pi$
$433$		−	16.2125i		−	0.779121i	0.921001	−	0.389561i	$-0.127373\pi$
$434$		0			0
$435$		−	17.3739i		−	0.833012i
$436$			15.1803i			0.727004i
$437$	4.40040			0.210500
$438$	9.63838			0.460539
$439$	24.8095			1.18409			0.592047	−	0.805903i	$-0.298320\pi$
$439$	24.8095			1.18409			0.592047	+	0.805903i	$0.298320\pi$
$440$	7.61259	−	4.50768i	0.362916	−	0.214895i
$441$		0			0
$442$			6.34319i			0.301715i
$443$	−36.3380			−1.72647			−0.863235	−	0.504803i	$-0.831565\pi$
$443$	−36.3380			−1.72647			−0.863235	+	0.504803i	$0.831565\pi$
$444$		−	2.54945i		−	0.120992i
$445$	−29.8811			−1.41650
$446$	−12.4044			−0.587364
$447$	18.1396			0.857975
$448$		0			0
$449$	−27.6858			−1.30657			−0.653287	−	0.757110i	$-0.726611\pi$
$449$	−27.6858			−1.30657			−0.653287	+	0.757110i	$0.726611\pi$
$450$			2.11553i			0.0997269i
$451$	7.57127	−	4.48321i	0.356517	−	0.211106i
$452$	4.06642			0.191268
$453$	−1.69350			−0.0795676
$454$		−	15.2148i		−	0.714068i
$455$		0			0
$456$	−1.39472			−0.0653140
$457$			20.5828i			0.962821i	0.876495	+	0.481411i	$0.159875\pi$
$457$			20.5828i			0.962821i	−0.876495	+	0.481411i	$0.840125\pi$
$458$	−19.2052			−0.897399
$459$		−	2.53541i		−	0.118343i
$460$		−	8.41603i		−	0.392399i
$461$	−21.4634			−0.999648			−0.499824	−	0.866127i	$-0.666602\pi$
$461$	−21.4634			−0.999648			−0.499824	+	0.866127i	$0.666602\pi$
$462$		0			0
$463$	−5.62818			−0.261563			−0.130782	−	0.991411i	$-0.541749\pi$
$463$	−5.62818			−0.261563			−0.130782	+	0.991411i	$0.541749\pi$
$464$		−	6.51317i		−	0.302366i
$465$			10.8055i			0.501093i
$466$	11.5244			0.533857
$467$		−	14.8084i		−	0.685251i	−0.939472	−	0.342626i	$-0.888684\pi$
$467$		−	14.8084i		−	0.685251i	0.939472	−	0.342626i	$-0.111316\pi$
$468$	2.50184			0.115648
$469$		0			0
$470$		−	7.36938i		−	0.339924i
$471$	−6.48100			−0.298629
$472$	4.91595			0.226275
$473$	9.50061	+	16.0447i	0.436838	+	0.737735i
$474$			8.30093i			0.381274i
$475$	2.95058			0.135382
$476$		0			0
$477$	6.88010			0.315018
$478$	−10.3520			−0.473488
$479$	−27.8523			−1.27261			−0.636303	−	0.771439i	$-0.719537\pi$
$479$	−27.8523			−1.27261			−0.636303	+	0.771439i	$0.719537\pi$
$480$			2.66749i			0.121754i
$481$	6.37832			0.290826
$482$			25.1255i			1.14443i
$483$		0			0
$484$	−5.28877	+	9.64515i	−0.240399	+	0.438416i
$485$	−10.7663			−0.488873
$486$	−1.00000			−0.0453609
$487$	−19.4540			−0.881544			−0.440772	−	0.897619i	$-0.645295\pi$
$487$	−19.4540			−0.881544			−0.440772	+	0.897619i	$0.645295\pi$
$488$			5.35288i			0.242313i
$489$			1.86138i			0.0841745i
$490$		0			0
$491$			41.7607i			1.88463i	0.334724	+	0.942316i	$0.391357\pi$
$491$			41.7607i			1.88463i	−0.334724	+	0.942316i	$0.608643\pi$
$492$			2.65301i			0.119607i
$493$		−	16.5136i		−	0.743733i
$494$		−	3.48938i		−	0.156994i
$495$	−4.50768	−	7.61259i	−0.202605	−	0.342161i
$496$			4.05080i			0.181886i
$497$		0			0
$498$	14.4528			0.647645
$499$	13.9993			0.626694			0.313347	−	0.949639i	$-0.398550\pi$
$499$	13.9993			0.626694			0.313347	+	0.949639i	$0.398550\pi$
$500$			7.69432i			0.344100i
$501$		−	10.4965i		−	0.468947i
$502$	7.97557			0.355967
$503$	14.9827			0.668044			0.334022	−	0.942565i	$-0.391594\pi$
$503$	14.9827			0.668044			0.334022	+	0.942565i	$0.391594\pi$
$504$		0			0
$505$		−	19.3955i		−	0.863087i
$506$	5.33155	+	9.00394i	0.237016	+	0.400274i
$507$		−	6.74080i		−	0.299370i
$508$			8.01581i			0.355644i
$509$			1.76581i			0.0782680i	0.999234	+	0.0391340i	$0.0124599\pi$
$509$			1.76581i			0.0782680i	−0.999234	+	0.0391340i	$0.987540\pi$
$510$			6.76319i			0.299479i
$511$		0			0
$512$			1.00000i			0.0441942i
$513$			1.39472i			0.0615786i
$514$	−7.57023			−0.333908
$515$	−12.5715			−0.553967
$516$	−5.62214			−0.247501
$517$	4.66850	+	7.88418i	0.205320	+	0.346746i
$518$		0			0
$519$			7.72136i			0.338930i
$520$	−6.67364			−0.292659
$521$		−	37.9681i		−	1.66341i	−0.555217	−	0.831706i	$-0.687365\pi$
$521$		−	37.9681i		−	1.66341i	0.555217	−	0.831706i	$-0.312635\pi$
$522$	−6.51317			−0.285074
$523$	23.9395			1.04680			0.523400	−	0.852087i	$-0.324663\pi$
$523$	23.9395			1.04680			0.523400	+	0.852087i	$0.324663\pi$
$524$	−14.5316			−0.634815
$525$		0			0
$526$	26.3900			1.15066
$527$			10.2704i			0.447388i
$528$	−1.68986	−	2.85384i	−0.0735416	−	0.124197i
$529$	−13.0458			−0.567208
$530$	−18.3526			−0.797187
$531$		−	4.91595i		−	0.213334i
$532$		0			0
$533$	−6.63741			−0.287498
$534$			11.2019i			0.484755i
$535$	−52.3438			−2.26302
$536$		−	7.33059i		−	0.316633i
$537$		−	20.4836i		−	0.883933i
$538$	5.00096			0.215607
$539$		0			0
$540$	2.66749			0.114791
$541$			23.9757i			1.03079i	0.856951	+	0.515397i	$0.172356\pi$
$541$			23.9757i			1.03079i	−0.856951	+	0.515397i	$0.827644\pi$
$542$		−	28.1218i		−	1.20794i
$543$	22.7331			0.975569
$544$			2.53541i			0.108705i
$545$	−40.4933			−1.73454
$546$		0			0
$547$			21.5789i			0.922645i	0.887232	+	0.461323i	$0.152625\pi$
$547$			21.5789i			0.922645i	−0.887232	+	0.461323i	$0.847375\pi$
$548$	10.1601			0.434020
$549$	5.35288			0.228455
$550$	3.57494	+	6.03737i	0.152436	+	0.257434i
$551$			9.08408i			0.386995i
$552$	−3.15503			−0.134287
$553$		0			0
$554$	4.15631			0.176585
$555$	6.80065			0.288672
$556$	2.15019			0.0911885
$557$			3.24887i			0.137659i	0.997628	+	0.0688295i	$0.0219264\pi$
$557$			3.24887i			0.137659i	−0.997628	+	0.0688295i	$0.978074\pi$
$558$	4.05080			0.171484
$559$		−	14.0657i		−	0.594915i
$560$		0			0
$561$	−4.28448	−	7.23565i	−0.180891	−	0.305489i
$562$	30.6193			1.29160
$563$	−12.2902			−0.517969			−0.258984	−	0.965881i	$-0.583388\pi$
$563$	−12.2902			−0.517969			−0.258984	+	0.965881i	$0.583388\pi$
$564$	−2.76266			−0.116329
$565$			10.8471i			0.456343i
$566$			5.38804i			0.226476i
$567$		0			0
$568$			6.05096i			0.253892i
$569$		−	45.2479i		−	1.89689i	−0.316938	−	0.948446i	$-0.602655\pi$
$569$		−	45.2479i		−	1.89689i	0.316938	−	0.948446i	$-0.397345\pi$
$570$		−	3.72042i		−	0.155831i
$571$			2.89745i			0.121254i	0.998160	+	0.0606272i	$0.0193101\pi$
$571$			2.89745i			0.121254i	−0.998160	+	0.0606272i	$0.980690\pi$
$572$	7.13984	−	4.22775i	0.298532	−	0.176771i
$573$			21.7595i			0.909016i
$574$		0			0
$575$	6.67455			0.278348
$576$	1.00000			0.0416667
$577$			1.99114i			0.0828922i	0.999141	+	0.0414461i	$0.0131965\pi$
$577$			1.99114i			0.0828922i	−0.999141	+	0.0414461i	$0.986804\pi$
$578$		−	10.5717i		−	0.439725i
$579$	7.69156			0.319650
$580$	17.3739			0.721410
$581$		0			0
$582$			4.03611i			0.167302i
$583$	19.6347	−	11.6264i	0.813185	−	0.481515i
$584$			9.63838i			0.398839i
$585$			6.67364i			0.275921i
$586$		−	4.27517i		−	0.176606i
$587$		−	37.4423i		−	1.54541i	−0.634766	−	0.772705i	$-0.718903\pi$
$587$		−	37.4423i		−	1.54541i	0.634766	−	0.772705i	$-0.281097\pi$
$588$		0			0
$589$		−	5.64976i		−	0.232794i
$590$			13.1133i			0.539864i
$591$	−21.1678			−0.870728
$592$	2.54945			0.104782
$593$	42.0052			1.72495			0.862473	−	0.506103i	$-0.168914\pi$
$593$	42.0052			1.72495			0.862473	+	0.506103i	$0.168914\pi$
$594$	−2.85384	+	1.68986i	−0.117094	+	0.0693356i
$595$		0			0
$596$			18.1396i			0.743028i
$597$	−23.2150			−0.950125
$598$		−	7.89338i		−	0.322784i
$599$	−20.5239			−0.838585			−0.419292	−	0.907851i	$-0.637722\pi$
$599$	−20.5239			−0.838585			−0.419292	+	0.907851i	$0.637722\pi$
$600$	−2.11553			−0.0863660
$601$	−9.51509			−0.388128			−0.194064	−	0.980989i	$-0.562167\pi$
$601$	−9.51509			−0.388128			−0.194064	+	0.980989i	$0.562167\pi$
$602$		0			0
$603$	−7.33059			−0.298525
$604$		−	1.69350i		−	0.0689075i
$605$	−25.7284	−	14.1078i	−1.04601	−	0.573562i
$606$	−7.27104			−0.295366
$607$	1.47149			0.0597258			0.0298629	−	0.999554i	$-0.490493\pi$
$607$	1.47149			0.0597258			0.0298629	+	0.999554i	$0.490493\pi$
$608$		−	1.39472i		−	0.0565635i
$609$		0			0
$610$	−14.2788			−0.578131
$611$		−	6.91173i		−	0.279619i
$612$	2.53541			0.102488
$613$			11.0599i			0.446705i	0.974738	+	0.223353i	$0.0717002\pi$
$613$			11.0599i			0.446705i	−0.974738	+	0.223353i	$0.928300\pi$
$614$			4.80816i			0.194041i
$615$	−7.07690			−0.285368
$616$		0			0
$617$	−28.9204			−1.16429			−0.582146	−	0.813085i	$-0.697787\pi$
$617$	−28.9204			−1.16429			−0.582146	+	0.813085i	$0.697787\pi$
$618$			4.71286i			0.189579i
$619$			13.0186i			0.523261i	0.965168	+	0.261630i	$0.0842601\pi$
$619$			13.0186i			0.523261i	−0.965168	+	0.261630i	$0.915740\pi$
$620$	−10.8055			−0.433959
$621$			3.15503i			0.126607i
$622$	−28.8146			−1.15536
$623$		0			0
$624$			2.50184i			0.100154i
$625$	−31.1022			−1.24409
$626$	−21.6235			−0.864249
$627$	2.35688	+	3.98032i	0.0941249	+	0.158959i
$628$		−	6.48100i		−	0.258620i
$629$	6.46391			0.257733
$630$		0			0
$631$	−33.4603			−1.33204			−0.666018	−	0.745936i	$-0.732002\pi$
$631$	−33.4603			−1.33204			−0.666018	+	0.745936i	$0.732002\pi$
$632$	−8.30093			−0.330193
$633$	−14.1204			−0.561235
$634$			8.45799i			0.335910i
$635$	−21.3821			−0.848524
$636$			6.88010i			0.272814i
$637$		0			0
$638$	−18.5875	+	11.0063i	−0.735887	+	0.435745i
$639$	6.05096			0.239372
$640$	−2.66749			−0.105442
$641$	39.6896			1.56765			0.783823	−	0.620984i	$-0.213267\pi$
$641$	39.6896			1.56765			0.783823	+	0.620984i	$0.213267\pi$
$642$			19.6228i			0.774451i
$643$			1.46168i			0.0576432i	0.999585	+	0.0288216i	$0.00917547\pi$
$643$			1.46168i			0.0576432i	−0.999585	+	0.0288216i	$0.990825\pi$
$644$		0			0
$645$		−	14.9970i		−	0.590507i
$646$		−	3.53620i		−	0.139130i
$647$			0.0217615i			0.000855533i	1.00000		0.000427766i	$0.000136162\pi$
$647$			0.0217615i			0.000855533i	−1.00000		0.000427766i	$0.999864\pi$
$648$		−	1.00000i		−	0.0392837i
$649$	−8.30724	−	14.0293i	−0.326088	−	0.550699i
$650$		−	5.29271i		−	0.207597i
$651$		0			0
$652$	−1.86138			−0.0728973
$653$	22.9725			0.898985			0.449493	−	0.893284i	$-0.351605\pi$
$653$	22.9725			0.898985			0.449493	+	0.893284i	$0.351605\pi$
$654$			15.1803i			0.593596i
$655$		−	38.7629i		−	1.51459i
$656$	−2.65301			−0.103583
$657$	9.63838			0.376029
$658$		0			0
$659$		−	2.84925i		−	0.110991i	−0.998459	−	0.0554956i	$-0.982326\pi$
$659$		−	2.84925i		−	0.110991i	0.998459	−	0.0554956i	$-0.0176739\pi$
$660$	7.61259	−	4.50768i	0.296320	−	0.175461i
$661$		−	44.2307i		−	1.72038i	−0.509977	−	0.860188i	$-0.670346\pi$
$661$		−	44.2307i		−	1.72038i	0.509977	−	0.860188i	$-0.329654\pi$
$662$			2.57208i			0.0999668i
$663$			6.34319i			0.246349i
$664$			14.4528i			0.560877i
$665$		0			0
$666$		−	2.54945i		−	0.0987893i
$667$			20.5493i			0.795670i
$668$	10.4965			0.406120
$669$	−12.4044			−0.479581
$670$	19.5543			0.755449
$671$	15.2762	−	9.04560i	0.589733	−	0.349201i
$672$		0			0
$673$			21.2881i			0.820597i	0.911951	+	0.410299i	$0.134576\pi$
$673$			21.2881i			0.820597i	−0.911951	+	0.410299i	$0.865424\pi$
$674$	15.2962			0.589186
$675$			2.11553i			0.0814267i
$676$	6.74080			0.259262
$677$	27.2776			1.04836			0.524182	−	0.851606i	$-0.324371\pi$
$677$	27.2776			1.04836			0.524182	+	0.851606i	$0.324371\pi$
$678$	4.06642			0.156170
$679$		0			0
$680$	−6.76319			−0.259357
$681$		−	15.2148i		−	0.583034i
$682$	11.5603	−	6.84528i	0.442668	−	0.262119i
$683$	25.2966			0.967947			0.483973	−	0.875083i	$-0.339193\pi$
$683$	25.2966			0.967947			0.483973	+	0.875083i	$0.339193\pi$
$684$	−1.39472			−0.0533286
$685$			27.1021i			1.03552i
$686$		0			0
$687$	−19.2052			−0.732723
$688$		−	5.62214i		−	0.214342i
$689$	−17.2129			−0.655759
$690$		−	8.41603i		−	0.320393i
$691$		−	18.3503i		−	0.698077i	−0.937108	−	0.349039i	$-0.886508\pi$
$691$		−	18.3503i		−	0.698077i	0.937108	−	0.349039i	$-0.113492\pi$
$692$	−7.72136			−0.293522
$693$		0			0
$694$	10.6965			0.406035
$695$			5.73563i			0.217565i
$696$		−	6.51317i		−	0.246881i
$697$	−6.72648			−0.254783
$698$			25.2258i			0.954809i
$699$	11.5244			0.435892
$700$		0			0
$701$			26.1203i			0.986550i	0.869873	+	0.493275i	$0.164200\pi$
$701$			26.1203i			0.986550i	−0.869873	+	0.493275i	$0.835800\pi$
$702$	2.50184			0.0944258
$703$	−3.55578			−0.134109
$704$	2.85384	−	1.68986i	0.107558	−	0.0636889i
$705$		−	7.36938i		−	0.277547i
$706$	28.3189			1.06580
$707$		0			0
$708$	4.91595			0.184753
$709$	−16.9144			−0.635232			−0.317616	−	0.948219i	$-0.602882\pi$
$709$	−16.9144			−0.635232			−0.317616	+	0.948219i	$0.602882\pi$
$710$	−16.1409			−0.605757
$711$			8.30093i			0.311309i
$712$	−11.2019			−0.419810
$713$		−	12.7804i		−	0.478630i
$714$		0			0
$715$	11.2775	+	19.0455i	0.421754	+	0.712261i
$716$	20.4836			0.765509
$717$	−10.3520			−0.386602
$718$	−10.0681			−0.375738
$719$			2.96473i			0.110566i	0.998471	+	0.0552829i	$0.0176061\pi$
$719$			2.96473i			0.110566i	−0.998471	+	0.0552829i	$0.982394\pi$
$720$			2.66749i			0.0994116i
$721$		0			0
$722$		−	17.0547i		−	0.634712i
$723$			25.1255i			0.934427i
$724$			22.7331i			0.844868i
$725$			13.7788i			0.511731i
$726$	−5.28877	+	9.64515i	−0.196285	+	0.357965i
$727$			35.7180i			1.32471i	0.749191	+	0.662354i	$0.230443\pi$
$727$			35.7180i			1.32471i	−0.749191	+	0.662354i	$0.769557\pi$
$728$		0			0
$729$	−1.00000			−0.0370370
$730$	−25.7103			−0.951582
$731$		−	14.2544i		−	0.527219i
$732$			5.35288i			0.197848i
$733$	−3.01235			−0.111264			−0.0556318	−	0.998451i	$-0.517717\pi$
$733$	−3.01235			−0.111264			−0.0556318	+	0.998451i	$0.517717\pi$
$734$	−24.5516			−0.906215
$735$		0			0
$736$		−	3.15503i		−	0.116296i
$737$	−20.9203	+	12.3876i	−0.770610	+	0.456305i
$738$			2.65301i			0.0976588i
$739$		−	32.7689i		−	1.20542i	−0.797959	−	0.602711i	$-0.794087\pi$
$739$		−	32.7689i		−	1.20542i	0.797959	−	0.602711i	$-0.205913\pi$
$740$			6.80065i			0.249997i
$741$		−	3.48938i		−	0.128185i
$742$		0			0
$743$		−	48.6910i		−	1.78630i	−0.449759	−	0.893150i	$-0.648490\pi$
$743$		−	48.6910i		−	1.78630i	0.449759	−	0.893150i	$-0.351510\pi$
$744$			4.05080i			0.148510i
$745$	−48.3874			−1.77278
$746$	1.27622			0.0467257
$747$	14.4528			0.528800
$748$	7.23565	−	4.28448i	0.264561	−	0.156656i
$749$		0			0
$750$			7.69432i			0.280957i
$751$	−1.97476			−0.0720600			−0.0360300	−	0.999351i	$-0.511471\pi$
$751$	−1.97476			−0.0720600			−0.0360300	+	0.999351i	$0.511471\pi$
$752$		−	2.76266i		−	0.100744i
$753$	7.97557			0.290646
$754$	16.2949			0.593425
$755$	4.51740			0.164405
$756$		0			0
$757$	−44.7224			−1.62546			−0.812731	−	0.582639i	$-0.802020\pi$
$757$	−44.7224			−1.62546			−0.812731	+	0.582639i	$0.802020\pi$
$758$			38.0451i			1.38186i
$759$	5.33155	+	9.00394i	0.193523	+	0.326822i
$760$	3.72042			0.134954
$761$	−35.3144			−1.28014			−0.640072	−	0.768315i	$-0.721096\pi$
$761$	−35.3144			−1.28014			−0.640072	+	0.768315i	$0.721096\pi$
$762$			8.01581i			0.290382i
$763$		0			0
$764$	−21.7595			−0.787231
$765$			6.76319i			0.244524i
$766$	−11.2055			−0.404871
$767$			12.2989i			0.444088i
$768$			1.00000i			0.0360844i
$769$	9.12167			0.328936			0.164468	−	0.986382i	$-0.447409\pi$
$769$	9.12167			0.328936			0.164468	+	0.986382i	$0.447409\pi$
$770$		0			0
$771$	−7.57023			−0.272635
$772$			7.69156i			0.276825i
$773$			29.4632i			1.05972i	0.848086	+	0.529859i	$0.177755\pi$
$773$			29.4632i			1.05972i	−0.848086	+	0.529859i	$0.822245\pi$
$774$	−5.62214			−0.202084
$775$		−	8.56958i		−	0.307829i
$776$	−4.03611			−0.144888
$777$		0			0
$778$			7.21388i			0.258630i
$779$	3.70022			0.132574
$780$	−6.67364			−0.238955
$781$	17.2684	−	10.2252i	0.617913	−	0.365888i
$782$		−	7.99930i		−	0.286054i
$783$	−6.51317			−0.232762
$784$		0			0
$785$	17.2880			0.617036
$786$	−14.5316			−0.518324
$787$	−4.31295			−0.153740			−0.0768700	−	0.997041i	$-0.524493\pi$
$787$	−4.31295			−0.153740			−0.0768700	+	0.997041i	$0.524493\pi$
$788$		−	21.1678i		−	0.754073i
$789$	26.3900			0.939511
$790$		−	22.1427i		−	0.787801i
$791$		0			0
$792$	−1.68986	−	2.85384i	−0.0600464	−	0.101407i
$793$	−13.3920			−0.475565
$794$	−19.4918			−0.691737
$795$	−18.3526			−0.650900
$796$		−	23.2150i		−	0.822832i
$797$			37.1341i			1.31536i	0.753299	+	0.657679i	$0.228462\pi$
$797$			37.1341i			1.31536i	−0.753299	+	0.657679i	$0.771538\pi$
$798$		0			0
$799$		−	7.00448i		−	0.247801i
$800$		−	2.11553i		−	0.0747952i
$801$			11.2019i			0.395801i
$802$		−	13.0461i		−	0.460674i
$803$	27.5064	−	16.2875i	0.970678	−	0.574772i
$804$		−	7.33059i		−	0.258530i
$805$		0			0
$806$	−10.1345			−0.356971
$807$	5.00096			0.176042
$808$		−	7.27104i		−	0.255794i
$809$			2.82043i			0.0991610i	0.998770	+	0.0495805i	$0.0157884\pi$
$809$			2.82043i			0.0991610i	−0.998770	+	0.0495805i	$0.984212\pi$
$810$	2.66749			0.0937262
$811$	26.7441			0.939114			0.469557	−	0.882902i	$-0.344414\pi$
$811$	26.7441			0.939114			0.469557	+	0.882902i	$0.344414\pi$
$812$		0			0
$813$		−	28.1218i		−	0.986275i
$814$	−4.30821	−	7.27572i	−0.151003	−	0.255014i
$815$		−	4.96522i		−	0.173924i
$816$			2.53541i			0.0887571i
$817$			7.84134i			0.274334i
$818$			33.8668i			1.18413i
$819$		0			0
$820$		−	7.07690i		−	0.247136i
$821$			47.3792i			1.65355i	0.562535	+	0.826773i	$0.309826\pi$
$821$			47.3792i			1.65355i	−0.562535	+	0.826773i	$0.690174\pi$
$822$	10.1601			0.354376
$823$	17.9168			0.624542			0.312271	−	0.949993i	$-0.398910\pi$
$823$	17.9168			0.624542			0.312271	+	0.949993i	$0.398910\pi$
$824$	−4.71286			−0.164180
$825$	3.57494	+	6.03737i	0.124463	+	0.210194i
$826$		0			0
$827$			54.3119i			1.88861i	0.329072	+	0.944305i	$0.393264\pi$
$827$			54.3119i			1.88861i	−0.329072	+	0.944305i	$0.606736\pi$
$828$	−3.15503			−0.109645
$829$		−	5.77320i		−	0.200512i	−0.994962	−	0.100256i	$-0.968034\pi$
$829$		−	5.77320i		−	0.200512i	0.994962	−	0.100256i	$-0.0319661\pi$
$830$	−38.5528			−1.33819
$831$	4.15631			0.144181
$832$	−2.50184			−0.0867356
$833$		0			0
$834$	2.15019			0.0744551
$835$			27.9992i			0.968953i
$836$	−3.98032	+	2.35688i	−0.137662	+	0.0815145i
$837$	4.05080			0.140016
$838$	12.9005			0.445642
$839$		−	36.9556i		−	1.27585i	−0.770099	−	0.637925i	$-0.779793\pi$
$839$		−	36.9556i		−	1.27585i	0.770099	−	0.637925i	$-0.220207\pi$
$840$		0			0
$841$	−13.4214			−0.462807
$842$		−	7.05921i		−	0.243276i
$843$	30.6193			1.05459
$844$		−	14.1204i		−	0.486044i
$845$			17.9811i			0.618567i
$846$	−2.76266			−0.0949822
$847$		0			0
$848$	−6.88010			−0.236263
$849$			5.38804i			0.184917i
$850$		−	5.36373i		−	0.183974i
$851$	−8.04360			−0.275731
$852$			6.05096i			0.207302i
$853$	−30.9159			−1.05854			−0.529269	−	0.848454i	$-0.677534\pi$
$853$	−30.9159			−1.05854			−0.529269	+	0.848454i	$0.677534\pi$
$854$		0			0
$855$		−	3.72042i		−	0.127236i
$856$	−19.6228			−0.670695
$857$	−19.5344			−0.667284			−0.333642	−	0.942700i	$-0.608278\pi$
$857$	−19.5344			−0.667284			−0.333642	+	0.942700i	$0.608278\pi$
$858$	7.13984	−	4.22775i	0.243750	−	0.144333i
$859$			23.0367i			0.786002i	0.919538	+	0.393001i	$0.128563\pi$
$859$			23.0367i			0.786002i	−0.919538	+	0.393001i	$0.871437\pi$
$860$	14.9970			0.511394
$861$		0			0
$862$	−3.54328			−0.120685
$863$	17.4076			0.592562			0.296281	−	0.955101i	$-0.404253\pi$
$863$	17.4076			0.592562			0.296281	+	0.955101i	$0.404253\pi$
$864$	1.00000			0.0340207
$865$		−	20.5967i		−	0.700308i
$866$	16.2125			0.550922
$867$		−	10.5717i		−	0.359034i
$868$		0			0
$869$	14.0274	+	23.6895i	0.475846	+	0.803611i
$870$	17.3739			0.589029
$871$	18.3400			0.621426
$872$	−15.1803			−0.514070
$873$			4.03611i			0.136602i
$874$			4.40040i			0.148846i
$875$		0			0
$876$			9.63838i			0.325651i
$877$		−	7.81136i		−	0.263771i	−0.991265	−	0.131885i	$-0.957897\pi$
$877$		−	7.81136i		−	0.263771i	0.991265	−	0.131885i	$-0.0421031\pi$
$878$			24.8095i			0.837281i
$879$		−	4.27517i		−	0.144198i
$880$	4.50768	+	7.61259i	0.151954	+	0.256621i
$881$			27.9273i			0.940895i	0.882428	+	0.470448i	$0.155908\pi$
$881$			27.9273i			0.940895i	−0.882428	+	0.470448i	$0.844092\pi$
$882$		0			0
$883$	31.2909			1.05302			0.526511	−	0.850168i	$-0.323500\pi$
$883$	31.2909			1.05302			0.526511	+	0.850168i	$0.323500\pi$
$884$	−6.34319			−0.213344
$885$			13.1133i			0.440797i
$886$		−	36.3380i		−	1.22080i
$887$	44.7264			1.50177			0.750883	−	0.660435i	$-0.229628\pi$
$887$	44.7264			1.50177			0.750883	+	0.660435i	$0.229628\pi$
$888$	2.54945			0.0855540
$889$		0			0
$890$		−	29.8811i		−	1.00162i
$891$	−2.85384	+	1.68986i	−0.0956071	+	0.0566123i
$892$		−	12.4044i		−	0.415329i
$893$			3.85315i			0.128941i
$894$			18.1396i			0.606680i
$895$			54.6399i			1.82641i
$896$		0			0
$897$		−	7.89338i		−	0.263552i
$898$		−	27.6858i		−	0.923887i
$899$	26.3836			0.879942
$900$	−2.11553			−0.0705176
$901$	−17.4439			−0.581139
$902$	4.48321	+	7.57127i	0.149275	+	0.252096i
$903$		0			0
$904$			4.06642i			0.135247i
$905$	−60.6403			−2.01575
$906$		−	1.69350i		−	0.0562628i
$907$	−30.2825			−1.00552			−0.502758	−	0.864427i	$-0.667681\pi$
$907$	−30.2825			−1.00552			−0.502758	+	0.864427i	$0.667681\pi$
$908$	15.2148			0.504923
$909$	−7.27104			−0.241165
$910$		0			0
$911$	−26.7787			−0.887217			−0.443609	−	0.896221i	$-0.646302\pi$
$911$	−26.7787			−0.887217			−0.443609	+	0.896221i	$0.646302\pi$
$912$		−	1.39472i		−	0.0461839i
$913$	41.2459	−	24.4232i	1.36504	−	0.808288i
$914$	−20.5828			−0.680818
$915$	−14.2788			−0.472042
$916$		−	19.2052i		−	0.634557i
$917$		0			0
$918$	2.53541			0.0836810
$919$			18.0347i			0.594909i	0.954736	+	0.297455i	$0.0961377\pi$
$919$			18.0347i			0.594909i	−0.954736	+	0.297455i	$0.903862\pi$
$920$	8.41603			0.277468
$921$			4.80816i			0.158434i
$922$		−	21.4634i		−	0.706858i
$923$	−15.1385			−0.498290
$924$		0			0
$925$	−5.39344			−0.177335
$926$		−	5.62818i		−	0.184953i
$927$			4.71286i			0.154790i
$928$	6.51317			0.213805
$929$			19.9369i			0.654108i	0.945006	+	0.327054i	$0.106056\pi$
$929$			19.9369i			0.654108i	−0.945006	+	0.327054i	$0.893944\pi$
$930$	−10.8055			−0.354326
$931$		0			0
$932$			11.5244i			0.377494i
$933$	−28.8146			−0.943348
$934$	14.8084			0.484546
$935$	11.4288	+	19.3010i	0.373762	+	0.631212i
$936$			2.50184i			0.0817752i
$937$	34.1520			1.11570			0.557849	−	0.829943i	$-0.311627\pi$
$937$	34.1520			1.11570			0.557849	+	0.829943i	$0.311627\pi$
$938$		0			0
$939$	−21.6235			−0.705657
$940$	7.36938			0.240363
$941$	16.9067			0.551142			0.275571	−	0.961281i	$-0.411133\pi$
$941$	16.9067			0.551142			0.275571	+	0.961281i	$0.411133\pi$
$942$		−	6.48100i		−	0.211162i
$943$	8.37034			0.272576
$944$			4.91595i			0.160000i
$945$		0			0
$946$	−16.0447	+	9.50061i	−0.521657	+	0.308891i
$947$	27.4767			0.892872			0.446436	−	0.894815i	$-0.352693\pi$
$947$	27.4767			0.892872			0.446436	+	0.894815i	$0.352693\pi$
$948$	−8.30093			−0.269602
$949$	−24.1137			−0.782763
$950$			2.95058i			0.0957293i
$951$			8.45799i			0.274269i
$952$		0			0
$953$			21.4315i			0.694234i	0.937822	+	0.347117i	$0.112839\pi$
$953$			21.4315i			0.694234i	−0.937822	+	0.347117i	$0.887161\pi$
$954$			6.88010i			0.222751i
$955$		−	58.0433i		−	1.87824i
$956$		−	10.3520i		−	0.334807i
$957$	−18.5875	+	11.0063i	−0.600850	+	0.355784i
$958$		−	27.8523i		−	0.899868i
$959$		0			0
$960$	−2.66749			−0.0860930
$961$	14.5910			0.470677
$962$			6.37832i			0.205645i
$963$			19.6228i			0.632337i
$964$	−25.1255			−0.809238
$965$	−20.5172			−0.660472
$966$		0			0
$967$		−	52.7348i		−	1.69584i	−0.530126	−	0.847919i	$-0.677855\pi$
$967$		−	52.7348i		−	1.69584i	0.530126	−	0.847919i	$-0.322145\pi$
$968$	−9.64515	−	5.28877i	−0.310007	−	0.169988i
$969$		−	3.53620i		−	0.113599i
$970$		−	10.7663i		−	0.345685i
$971$		−	33.9902i		−	1.09080i	−0.838177	−	0.545398i	$-0.816378\pi$
$971$		−	33.9902i		−	1.09080i	0.838177	−	0.545398i	$-0.183622\pi$
$972$		−	1.00000i		−	0.0320750i
$973$		0			0
$974$		−	19.4540i		−	0.623346i
$975$		−	5.29271i		−	0.169502i
$976$	−5.35288			−0.171342
$977$	8.79178			0.281274			0.140637	−	0.990061i	$-0.455085\pi$
$977$	8.79178			0.281274			0.140637	+	0.990061i	$0.455085\pi$
$978$	−1.86138			−0.0595204
$979$	18.9296	+	31.9685i	0.604994	+	1.02172i
$980$		0			0
$981$			15.1803i			0.484669i
$982$	−41.7607			−1.33264
$983$			25.6832i			0.819167i	0.912273	+	0.409583i	$0.134326\pi$
$983$			25.6832i			0.819167i	−0.912273	+	0.409583i	$0.865674\pi$
$984$	−2.65301			−0.0845750
$985$	56.4651			1.79913
$986$	16.5136			0.525899
$987$		0			0
$988$	3.48938			0.111012
$989$			17.7380i			0.564036i
$990$	7.61259	−	4.50768i	0.241944	−	0.143264i
$991$	22.4094			0.711858			0.355929	−	0.934513i	$-0.384165\pi$
$991$	22.4094			0.711858			0.355929	+	0.934513i	$0.384165\pi$
$992$	−4.05080			−0.128613
$993$			2.57208i			0.0816226i
$994$		0			0
$995$	61.9258			1.96318
$996$			14.4528i			0.457954i
$997$	19.6542			0.622454			0.311227	−	0.950336i	$-0.399260\pi$
$997$	19.6542			0.622454			0.311227	+	0.950336i	$0.399260\pi$
$998$			13.9993i			0.443140i
$999$		−	2.54945i		−	0.0806611i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3234.2.e.c.2155.15	yes	24
7.6	odd	2		3234.2.e.d.2155.22	yes	24
11.10	odd	2		3234.2.e.d.2155.3	yes	24
77.76	even	2	inner	3234.2.e.c.2155.10	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3234.2.e.c.2155.10	✓	24	77.76	even	2	inner
3234.2.e.c.2155.15	yes	24	1.1	even	1	trivial
3234.2.e.d.2155.3	yes	24	11.10	odd	2
3234.2.e.d.2155.22	yes	24	7.6	odd	2

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:	\( N \)	\(=\)	\( 3234 = 2 \cdot 3 \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3234.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} -2.66749i q^{5} -1.00000 q^{6} -1.00000i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} -2.66749i q^{5} -1.00000 q^{6} -1.00000i q^{8} -1.00000 q^{9} +2.66749 q^{10} +(-2.85384 + 1.68986i) q^{11} -1.00000i q^{12} +2.50184 q^{13} +2.66749 q^{15} +1.00000 q^{16} +2.53541 q^{17} -1.00000i q^{18} -1.39472 q^{19} +2.66749i q^{20} +(-1.68986 - 2.85384i) q^{22} -3.15503 q^{23} +1.00000 q^{24} -2.11553 q^{25} +2.50184i q^{26} -1.00000i q^{27} -6.51317i q^{29} +2.66749i q^{30} +4.05080i q^{31} +1.00000i q^{32} +(-1.68986 - 2.85384i) q^{33} +2.53541i q^{34} +1.00000 q^{36} +2.54945 q^{37} -1.39472i q^{38} +2.50184i q^{39} -2.66749 q^{40} -2.65301 q^{41} -5.62214i q^{43} +(2.85384 - 1.68986i) q^{44} +2.66749i q^{45} -3.15503i q^{46} -2.76266i q^{47} +1.00000i q^{48} -2.11553i q^{50} +2.53541i q^{51} -2.50184 q^{52} -6.88010 q^{53} +1.00000 q^{54} +(4.50768 + 7.61259i) q^{55} -1.39472i q^{57} +6.51317 q^{58} +4.91595i q^{59} -2.66749 q^{60} -5.35288 q^{61} -4.05080 q^{62} -1.00000 q^{64} -6.67364i q^{65} +(2.85384 - 1.68986i) q^{66} +7.33059 q^{67} -2.53541 q^{68} -3.15503i q^{69} -6.05096 q^{71} +1.00000i q^{72} -9.63838 q^{73} +2.54945i q^{74} -2.11553i q^{75} +1.39472 q^{76} -2.50184 q^{78} -8.30093i q^{79} -2.66749i q^{80} +1.00000 q^{81} -2.65301i q^{82} -14.4528 q^{83} -6.76319i q^{85} +5.62214 q^{86} +6.51317 q^{87} +(1.68986 + 2.85384i) q^{88} -11.2019i q^{89} -2.66749 q^{90} +3.15503 q^{92} -4.05080 q^{93} +2.76266 q^{94} +3.72042i q^{95} -1.00000 q^{96} -4.03611i q^{97} +(2.85384 - 1.68986i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 24 q^{4} - 24 q^{6} - 24 q^{9}+O(q^{10}) \) 24 * q - 24 * q^4 - 24 * q^6 - 24 * q^9	\( 24 q - 24 q^{4} - 24 q^{6} - 24 q^{9} + 24 q^{16} + 16 q^{17} - 32 q^{19} - 8 q^{22} + 24 q^{24} - 8 q^{25} - 8 q^{33} + 24 q^{36} + 16 q^{37} - 16 q^{41} + 24 q^{54} + 16 q^{55} - 16 q^{62} - 24 q^{64} - 64 q^{67} - 16 q^{68} + 64 q^{71} + 32 q^{76} + 24 q^{81} - 16 q^{83} + 8 q^{88} - 16 q^{93} + 64 q^{94} - 24 q^{96}+O(q^{100}) \) 24 * q - 24 * q^4 - 24 * q^6 - 24 * q^9 + 24 * q^16 + 16 * q^17 - 32 * q^19 - 8 * q^22 + 24 * q^24 - 8 * q^25 - 8 * q^33 + 24 * q^36 + 16 * q^37 - 16 * q^41 + 24 * q^54 + 16 * q^55 - 16 * q^62 - 24 * q^64 - 64 * q^67 - 16 * q^68 + 64 * q^71 + 32 * q^76 + 24 * q^81 - 16 * q^83 + 8 * q^88 - 16 * q^93 + 64 * q^94 - 24 * q^96

Introduction

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