LMFDB - Embedded newform 3234.2.e.d.2155.18

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			2155.18
Character	$\chi$	$=$	3234.2155
Dual form			3234.2.e.d.2155.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} -0.500309i q^{5} +1.00000 q^{6} -1.00000i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} -0.500309i q^{5} +1.00000 q^{6} -1.00000i q^{8} -1.00000 q^{9} +0.500309 q^{10} +(0.278396 + 3.30492i) q^{11} +1.00000i q^{12} -0.920800 q^{13} -0.500309 q^{15} +1.00000 q^{16} +3.39195 q^{17} -1.00000i q^{18} -6.51893 q^{19} +0.500309i q^{20} +(-3.30492 + 0.278396i) q^{22} -0.975239 q^{23} -1.00000 q^{24} +4.74969 q^{25} -0.920800i q^{26} +1.00000i q^{27} +4.69715i q^{29} -0.500309i q^{30} -8.31055i q^{31} +1.00000i q^{32} +(3.30492 - 0.278396i) q^{33} +3.39195i q^{34} +1.00000 q^{36} -5.56701 q^{37} -6.51893i q^{38} +0.920800i q^{39} -0.500309 q^{40} -3.99913 q^{41} +0.666749i q^{43} +(-0.278396 - 3.30492i) q^{44} +0.500309i q^{45} -0.975239i q^{46} +5.52121i q^{47} -1.00000i q^{48} +4.74969i q^{50} -3.39195i q^{51} +0.920800 q^{52} -7.44375 q^{53} -1.00000 q^{54} +(1.65348 - 0.139284i) q^{55} +6.51893i q^{57} -4.69715 q^{58} -11.7273i q^{59} +0.500309 q^{60} -4.02998 q^{61} +8.31055 q^{62} -1.00000 q^{64} +0.460685i q^{65} +(0.278396 + 3.30492i) q^{66} -2.31123 q^{67} -3.39195 q^{68} +0.975239i q^{69} -9.35660 q^{71} +1.00000i q^{72} -1.70499 q^{73} -5.56701i q^{74} -4.74969i q^{75} +6.51893 q^{76} -0.920800 q^{78} +8.66533i q^{79} -0.500309i q^{80} +1.00000 q^{81} -3.99913i q^{82} +5.60082 q^{83} -1.69702i q^{85} -0.666749 q^{86} +4.69715 q^{87} +(3.30492 - 0.278396i) q^{88} +14.3564i q^{89} -0.500309 q^{90} +0.975239 q^{92} -8.31055 q^{93} -5.52121 q^{94} +3.26148i q^{95} +1.00000 q^{96} +10.5358i q^{97} +(-0.278396 - 3.30492i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$		−	0.500309i		−	0.223745i	−0.993723	−	0.111873i	$-0.964315\pi$
$5$		−	0.500309i		−	0.223745i	0.993723	−	0.111873i	$-0.0356848\pi$
$6$	1.00000			0.408248
$7$		0			0
$7$		0			0
$8$		−	1.00000i		−	0.353553i
$9$	−1.00000			−0.333333
$10$	0.500309			0.158212
$11$	0.278396	+	3.30492i	0.0839395	+	0.996471i
$11$	0.278396	+	3.30492i	0.0839395	+	0.996471i
$12$			1.00000i			0.288675i
$13$	−0.920800			−0.255384			−0.127692	−	0.991814i	$-0.540757\pi$
$13$	−0.920800			−0.255384			−0.127692	+	0.991814i	$0.540757\pi$
$14$		0			0
$15$	−0.500309			−0.129179
$16$	1.00000			0.250000
$17$	3.39195			0.822669			0.411335	−	0.911484i	$-0.365063\pi$
$17$	3.39195			0.822669			0.411335	+	0.911484i	$0.365063\pi$
$18$		−	1.00000i		−	0.235702i
$19$	−6.51893			−1.49555			−0.747773	−	0.663954i	$-0.768877\pi$
$19$	−6.51893			−1.49555			−0.747773	+	0.663954i	$0.768877\pi$
$20$			0.500309i			0.111873i
$21$		0			0
$22$	−3.30492	+	0.278396i	−0.704611	+	0.0593542i
$23$	−0.975239			−0.203351			−0.101676	−	0.994818i	$-0.532420\pi$
$23$	−0.975239			−0.203351			−0.101676	+	0.994818i	$0.532420\pi$
$24$	−1.00000			−0.204124
$25$	4.74969			0.949938
$26$		−	0.920800i		−	0.180584i
$27$			1.00000i			0.192450i
$28$		0			0
$29$			4.69715i			0.872239i	0.899889	+	0.436120i	$0.143648\pi$
$29$			4.69715i			0.872239i	−0.899889	+	0.436120i	$0.856352\pi$
$30$		−	0.500309i		−	0.0913435i
$31$		−	8.31055i		−	1.49262i	−0.665599	−	0.746310i	$-0.731824\pi$
$31$		−	8.31055i		−	1.49262i	0.665599	−	0.746310i	$-0.268176\pi$
$32$			1.00000i			0.176777i
$33$	3.30492	−	0.278396i	0.575313	−	0.0484625i
$34$			3.39195i			0.581715i
$35$		0			0
$36$	1.00000			0.166667
$37$	−5.56701			−0.915211			−0.457606	−	0.889155i	$-0.651293\pi$
$37$	−5.56701			−0.915211			−0.457606	+	0.889155i	$0.651293\pi$
$38$		−	6.51893i		−	1.05751i
$39$			0.920800i			0.147446i
$40$	−0.500309			−0.0791058
$41$	−3.99913			−0.624559			−0.312280	−	0.949990i	$-0.601093\pi$
$41$	−3.99913			−0.624559			−0.312280	+	0.949990i	$0.601093\pi$
$42$		0			0
$43$			0.666749i			0.101678i	0.998707	+	0.0508391i	$0.0161896\pi$
$43$			0.666749i			0.101678i	−0.998707	+	0.0508391i	$0.983810\pi$
$44$	−0.278396	−	3.30492i	−0.0419697	−	0.498235i
$45$			0.500309i			0.0745817i
$46$		−	0.975239i		−	0.143791i
$47$			5.52121i			0.805351i	0.915343	+	0.402675i	$0.131920\pi$
$47$			5.52121i			0.805351i	−0.915343	+	0.402675i	$0.868080\pi$
$48$		−	1.00000i		−	0.144338i
$49$		0			0
$50$			4.74969i			0.671708i
$51$		−	3.39195i		−	0.474968i
$52$	0.920800			0.127692
$53$	−7.44375			−1.02248			−0.511239	−	0.859439i	$-0.670813\pi$
$53$	−7.44375			−1.02248			−0.511239	+	0.859439i	$0.670813\pi$
$54$	−1.00000			−0.136083
$55$	1.65348	−	0.139284i	0.222955	−	0.0187810i
$56$		0			0
$57$			6.51893i			0.863454i
$58$	−4.69715			−0.616766
$59$		−	11.7273i		−	1.52676i	−0.645947	−	0.763382i	$-0.723537\pi$
$59$		−	11.7273i		−	1.52676i	0.645947	−	0.763382i	$-0.276463\pi$
$60$	0.500309			0.0645896
$61$	−4.02998			−0.515986			−0.257993	−	0.966147i	$-0.583061\pi$
$61$	−4.02998			−0.515986			−0.257993	+	0.966147i	$0.583061\pi$
$62$	8.31055			1.05544
$63$		0			0
$64$	−1.00000			−0.125000
$65$			0.460685i			0.0571409i
$66$	0.278396	+	3.30492i	0.0342681	+	0.406808i
$67$	−2.31123			−0.282361			−0.141181	−	0.989984i	$-0.545090\pi$
$67$	−2.31123			−0.282361			−0.141181	+	0.989984i	$0.545090\pi$
$68$	−3.39195			−0.411335
$69$			0.975239i			0.117405i
$70$		0			0
$71$	−9.35660			−1.11042			−0.555212	−	0.831709i	$-0.687363\pi$
$71$	−9.35660			−1.11042			−0.555212	+	0.831709i	$0.687363\pi$
$72$			1.00000i			0.117851i
$73$	−1.70499			−0.199554			−0.0997771	−	0.995010i	$-0.531813\pi$
$73$	−1.70499			−0.199554			−0.0997771	+	0.995010i	$0.531813\pi$
$74$		−	5.56701i		−	0.647152i
$75$		−	4.74969i		−	0.548447i
$76$	6.51893			0.747773
$77$		0			0
$78$	−0.920800			−0.104260
$79$			8.66533i			0.974926i	0.873144	+	0.487463i	$0.162078\pi$
$79$			8.66533i			0.974926i	−0.873144	+	0.487463i	$0.837922\pi$
$80$		−	0.500309i		−	0.0559363i
$81$	1.00000			0.111111
$82$		−	3.99913i		−	0.441630i
$83$	5.60082			0.614770			0.307385	−	0.951585i	$-0.400546\pi$
$83$	5.60082			0.614770			0.307385	+	0.951585i	$0.400546\pi$
$84$		0			0
$85$		−	1.69702i		−	0.184068i
$86$	−0.666749			−0.0718974
$87$	4.69715			0.503588
$88$	3.30492	−	0.278396i	0.352306	−	0.0296771i
$89$			14.3564i			1.52177i	0.648886	+	0.760886i	$0.275235\pi$
$89$			14.3564i			1.52177i	−0.648886	+	0.760886i	$0.724765\pi$
$90$	−0.500309			−0.0527372
$91$		0			0
$92$	0.975239			0.101676
$93$	−8.31055			−0.861764
$94$	−5.52121			−0.569469
$95$			3.26148i			0.334621i
$96$	1.00000			0.102062
$97$			10.5358i			1.06975i	0.844931	+	0.534875i	$0.179641\pi$
$97$			10.5358i			1.06975i	−0.844931	+	0.534875i	$0.820359\pi$
$98$		0			0
$99$	−0.278396	−	3.30492i	−0.0279798	−	0.332157i
$100$	−4.74969			−0.474969
$101$	1.82562			0.181656			0.0908281	−	0.995867i	$-0.471049\pi$
$101$	1.82562			0.181656			0.0908281	+	0.995867i	$0.471049\pi$
$102$	3.39195			0.335853
$103$		−	0.280707i		−	0.0276589i	−0.999904	−	0.0138295i	$-0.995598\pi$
$103$		−	0.280707i		−	0.0276589i	0.999904	−	0.0138295i	$-0.00440219\pi$
$104$			0.920800i			0.0902919i
$105$		0			0
$106$		−	7.44375i		−	0.723001i
$107$		−	10.8711i		−	1.05095i	−0.850808	−	0.525476i	$-0.823887\pi$
$107$		−	10.8711i		−	1.05095i	0.850808	−	0.525476i	$-0.176113\pi$
$108$		−	1.00000i		−	0.0962250i
$109$			16.6612i			1.59586i	0.602752	+	0.797929i	$0.294071\pi$
$109$			16.6612i			1.59586i	−0.602752	+	0.797929i	$0.705929\pi$
$110$	0.139284	+	1.65348i	0.0132802	+	0.157653i
$111$			5.56701i			0.528398i
$112$		0			0
$113$	−15.6890			−1.47590			−0.737949	−	0.674856i	$-0.764206\pi$
$113$	−15.6890			−1.47590			−0.737949	+	0.674856i	$0.764206\pi$
$114$	−6.51893			−0.610554
$115$			0.487921i			0.0454989i
$116$		−	4.69715i		−	0.436120i
$117$	0.920800			0.0851280
$118$	11.7273			1.07959
$119$		0			0
$120$			0.500309i			0.0456718i
$121$	−10.8450	+	1.84015i	−0.985908	+	0.167286i
$122$		−	4.02998i		−	0.364857i
$123$			3.99913i			0.360590i
$124$			8.31055i			0.746310i
$125$		−	4.87786i		−	0.436289i
$126$		0			0
$127$			13.7323i			1.21855i	0.792959	+	0.609274i	$0.208539\pi$
$127$			13.7323i			1.21855i	−0.792959	+	0.609274i	$0.791461\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	0.666749			0.0587040
$130$	−0.460685			−0.0404047
$131$	−2.57981			−0.225399			−0.112700	−	0.993629i	$-0.535950\pi$
$131$	−2.57981			−0.225399			−0.112700	+	0.993629i	$0.535950\pi$
$132$	−3.30492	+	0.278396i	−0.287656	+	0.0242312i
$133$		0			0
$134$		−	2.31123i		−	0.199660i
$135$	0.500309			0.0430597
$136$		−	3.39195i		−	0.290858i
$137$	−3.50632			−0.299565			−0.149783	−	0.988719i	$-0.547857\pi$
$137$	−3.50632			−0.299565			−0.149783	+	0.988719i	$0.547857\pi$
$138$	−0.975239			−0.0830179
$139$	−16.7304			−1.41905			−0.709525	−	0.704680i	$-0.751091\pi$
$139$	−16.7304			−1.41905			−0.709525	+	0.704680i	$0.751091\pi$
$140$		0			0
$141$	5.52121			0.464970
$142$		−	9.35660i		−	0.785189i
$143$	−0.256347	−	3.04317i	−0.0214368	−	0.254483i
$144$	−1.00000			−0.0833333
$145$	2.35003			0.195159
$146$		−	1.70499i		−	0.141106i
$147$		0			0
$148$	5.56701			0.457606
$149$			8.85337i			0.725296i	0.931926	+	0.362648i	$0.118127\pi$
$149$			8.85337i			0.725296i	−0.931926	+	0.362648i	$0.881873\pi$
$150$	4.74969			0.387811
$151$			14.8590i			1.20921i	0.796525	+	0.604606i	$0.206669\pi$
$151$			14.8590i			1.20921i	−0.796525	+	0.604606i	$0.793331\pi$
$152$			6.51893i			0.528755i
$153$	−3.39195			−0.274223
$154$		0			0
$155$	−4.15784			−0.333966
$156$		−	0.920800i		−	0.0737230i
$157$		−	9.38319i		−	0.748860i	−0.927255	−	0.374430i	$-0.877838\pi$
$157$		−	9.38319i		−	0.748860i	0.927255	−	0.374430i	$-0.122162\pi$
$158$	−8.66533			−0.689377
$159$			7.44375i			0.590328i
$160$	0.500309			0.0395529
$161$		0			0
$162$			1.00000i			0.0785674i
$163$	−22.3466			−1.75032			−0.875161	−	0.483832i	$-0.839244\pi$
$163$	−22.3466			−1.75032			−0.875161	+	0.483832i	$0.839244\pi$
$164$	3.99913			0.312280
$165$	−0.139284	−	1.65348i	−0.0108432	−	0.128723i
$166$			5.60082i			0.434708i
$167$	−8.40980			−0.650770			−0.325385	−	0.945582i	$-0.605494\pi$
$167$	−8.40980			−0.650770			−0.325385	+	0.945582i	$0.605494\pi$
$168$		0			0
$169$	−12.1521			−0.934779
$170$	1.69702			0.130156
$171$	6.51893			0.498515
$172$		−	0.666749i		−	0.0508391i
$173$	14.3931			1.09429			0.547143	−	0.837039i	$-0.315715\pi$
$173$	14.3931			1.09429			0.547143	+	0.837039i	$0.315715\pi$
$174$			4.69715i			0.356090i
$175$		0			0
$176$	0.278396	+	3.30492i	0.0209849	+	0.249118i
$177$	−11.7273			−0.881478
$178$	−14.3564			−1.07606
$179$	9.33241			0.697537			0.348769	−	0.937209i	$-0.386600\pi$
$179$	9.33241			0.697537			0.348769	+	0.937209i	$0.386600\pi$
$180$		−	0.500309i		−	0.0372908i
$181$			1.43553i			0.106702i	0.998576	+	0.0533512i	$0.0169903\pi$
$181$			1.43553i			0.106702i	−0.998576	+	0.0533512i	$0.983010\pi$
$182$		0			0
$183$			4.02998i			0.297905i
$184$			0.975239i			0.0718956i
$185$			2.78523i			0.204774i
$186$		−	8.31055i		−	0.609359i
$187$	0.944305	+	11.2101i	0.0690544	+	0.819766i
$188$		−	5.52121i		−	0.402675i
$189$		0			0
$190$	−3.26148			−0.236613
$191$	−6.28574			−0.454820			−0.227410	−	0.973799i	$-0.573026\pi$
$191$	−6.28574			−0.454820			−0.227410	+	0.973799i	$0.573026\pi$
$192$			1.00000i			0.0721688i
$193$			0.0824296i			0.00593341i	0.999996	+	0.00296671i	$0.000944333\pi$
$193$			0.0824296i			0.00593341i	−0.999996	+	0.00296671i	$0.999056\pi$
$194$	−10.5358			−0.756427
$195$	0.460685			0.0329903
$196$		0			0
$197$			7.93399i			0.565273i	0.959227	+	0.282637i	$0.0912091\pi$
$197$			7.93399i			0.565273i	−0.959227	+	0.282637i	$0.908791\pi$
$198$	3.30492	−	0.278396i	0.234870	−	0.0197847i
$199$			17.8628i			1.26626i	0.774045	+	0.633131i	$0.218230\pi$
$199$			17.8628i			1.26626i	−0.774045	+	0.633131i	$0.781770\pi$
$200$		−	4.74969i		−	0.335854i
$201$			2.31123i			0.163021i
$202$			1.82562i			0.128450i
$203$		0			0
$204$			3.39195i			0.237484i
$205$			2.00080i			0.139742i
$206$	0.280707			0.0195578
$207$	0.975239			0.0677838
$208$	−0.920800			−0.0638460
$209$	−1.81484	−	21.5446i	−0.125535	−	1.49027i
$210$		0			0
$211$		−	28.8538i		−	1.98638i	−0.116522	−	0.993188i	$-0.537175\pi$
$211$		−	28.8538i		−	1.98638i	0.116522	−	0.993188i	$-0.462825\pi$
$212$	7.44375			0.511239
$213$			9.35660i			0.641104i
$214$	10.8711			0.743135
$215$	0.333581			0.0227500
$216$	1.00000			0.0680414
$217$		0			0
$218$	−16.6612			−1.12844
$219$			1.70499i			0.115213i
$220$	−1.65348	+	0.139284i	−0.111478	+	0.00939052i
$221$	−3.12331			−0.210097
$222$	−5.56701			−0.373633
$223$			8.97060i			0.600716i	0.953827	+	0.300358i	$0.0971061\pi$
$223$			8.97060i			0.600716i	−0.953827	+	0.300358i	$0.902894\pi$
$224$		0			0
$225$	−4.74969			−0.316646
$226$		−	15.6890i		−	1.04362i
$227$	24.0104			1.59362			0.796812	−	0.604227i	$-0.206518\pi$
$227$	24.0104			1.59362			0.796812	+	0.604227i	$0.206518\pi$
$228$		−	6.51893i		−	0.431727i
$229$			3.71049i			0.245196i	0.992456	+	0.122598i	$0.0391226\pi$
$229$			3.71049i			0.245196i	−0.992456	+	0.122598i	$0.960877\pi$
$230$	−0.487921			−0.0321726
$231$		0			0
$232$	4.69715			0.308383
$233$			4.60105i			0.301425i	0.988578	+	0.150713i	$0.0481568\pi$
$233$			4.60105i			0.301425i	−0.988578	+	0.150713i	$0.951843\pi$
$234$			0.920800i			0.0601946i
$235$	2.76231			0.180193
$236$			11.7273i			0.763382i
$237$	8.66533			0.562874
$238$		0			0
$239$		−	20.6362i		−	1.33485i	−0.744679	−	0.667423i	$-0.767397\pi$
$239$		−	20.6362i		−	1.33485i	0.744679	−	0.667423i	$-0.232603\pi$
$240$	−0.500309			−0.0322948
$241$	−4.00574			−0.258032			−0.129016	−	0.991643i	$-0.541182\pi$
$241$	−4.00574			−0.258032			−0.129016	+	0.991643i	$0.541182\pi$
$242$	−1.84015	−	10.8450i	−0.118289	−	0.697142i
$243$		−	1.00000i		−	0.0641500i
$244$	4.02998			0.257993
$245$		0			0
$246$	−3.99913			−0.254975
$247$	6.00264			0.381939
$248$	−8.31055			−0.527721
$249$		−	5.60082i		−	0.354938i
$250$	4.87786			0.308503
$251$		−	6.13259i		−	0.387086i	−0.981092	−	0.193543i	$-0.938002\pi$
$251$		−	6.13259i		−	0.387086i	0.981092	−	0.193543i	$-0.0619979\pi$
$252$		0			0
$253$	−0.271502	−	3.22309i	−0.0170692	−	0.202634i
$254$	−13.7323			−0.861644
$255$	−1.69702			−0.106272
$256$	1.00000			0.0625000
$257$			15.5055i			0.967204i	0.875288	+	0.483602i	$0.160672\pi$
$257$			15.5055i			0.967204i	−0.875288	+	0.483602i	$0.839328\pi$
$258$			0.666749i			0.0415100i
$259$		0			0
$260$		−	0.460685i		−	0.0285705i
$261$		−	4.69715i		−	0.290746i
$262$		−	2.57981i		−	0.159381i
$263$			5.55512i			0.342543i	0.985224	+	0.171272i	$0.0547875\pi$
$263$			5.55512i			0.342543i	−0.985224	+	0.171272i	$0.945212\pi$
$264$	−0.278396	−	3.30492i	−0.0171341	−	0.203404i
$265$			3.72417i			0.228774i
$266$		0			0
$267$	14.3564			0.878596
$268$	2.31123			0.141181
$269$		−	29.4511i		−	1.79566i	−0.440338	−	0.897832i	$-0.645141\pi$
$269$		−	29.4511i		−	1.79566i	0.440338	−	0.897832i	$-0.354859\pi$
$270$			0.500309i			0.0304478i
$271$	−24.2318			−1.47198			−0.735988	−	0.676995i	$-0.763282\pi$
$271$	−24.2318			−1.47198			−0.735988	+	0.676995i	$0.763282\pi$
$272$	3.39195			0.205667
$273$		0			0
$274$		−	3.50632i		−	0.211825i
$275$	1.32229	+	15.6973i	0.0797373	+	0.946586i
$276$		−	0.975239i		−	0.0587025i
$277$		−	19.9326i		−	1.19763i	−0.800886	−	0.598816i	$-0.795638\pi$
$277$		−	19.9326i		−	1.19763i	0.800886	−	0.598816i	$-0.204362\pi$
$278$		−	16.7304i		−	1.00342i
$279$			8.31055i			0.497540i
$280$		0			0
$281$			5.03653i			0.300454i	0.988652	+	0.150227i	$0.0480005\pi$
$281$			5.03653i			0.300454i	−0.988652	+	0.150227i	$0.952000\pi$
$282$			5.52121i			0.328783i
$283$	−10.0242			−0.595875			−0.297938	−	0.954585i	$-0.596299\pi$
$283$	−10.0242			−0.595875			−0.297938	+	0.954585i	$0.596299\pi$
$284$	9.35660			0.555212
$285$	3.26148			0.193193
$286$	3.04317	−	0.256347i	0.179946	−	0.0151581i
$287$		0			0
$288$		−	1.00000i		−	0.0589256i
$289$	−5.49466			−0.323215
$290$			2.35003i			0.137998i
$291$	10.5358			0.617620
$292$	1.70499			0.0997771
$293$	−18.0732			−1.05585			−0.527924	−	0.849292i	$-0.677029\pi$
$293$	−18.0732			−1.05585			−0.527924	+	0.849292i	$0.677029\pi$
$294$		0			0
$295$	−5.86728			−0.341606
$296$			5.56701i			0.323576i
$297$	−3.30492	+	0.278396i	−0.191771	+	0.0161542i
$298$	−8.85337			−0.512862
$299$	0.898001			0.0519327
$300$			4.74969i			0.274224i
$301$		0			0
$302$	−14.8590			−0.855042
$303$		−	1.82562i		−	0.104879i
$304$	−6.51893			−0.373886
$305$			2.01624i			0.115449i
$306$		−	3.39195i		−	0.193905i
$307$	−6.52198			−0.372229			−0.186114	−	0.982528i	$-0.559590\pi$
$307$	−6.52198			−0.372229			−0.186114	+	0.982528i	$0.559590\pi$
$308$		0			0
$309$	−0.280707			−0.0159689
$310$		−	4.15784i		−	0.236150i
$311$		−	15.3276i		−	0.869147i	−0.900636	−	0.434574i	$-0.856899\pi$
$311$		−	15.3276i		−	0.869147i	0.900636	−	0.434574i	$-0.143101\pi$
$312$	0.920800			0.0521300
$313$			4.09732i			0.231594i	0.993273	+	0.115797i	$0.0369422\pi$
$313$			4.09732i			0.231594i	−0.993273	+	0.115797i	$0.963058\pi$
$314$	9.38319			0.529524
$315$		0			0
$316$		−	8.66533i		−	0.487463i
$317$	29.3301			1.64735			0.823673	−	0.567066i	$-0.191921\pi$
$317$	29.3301			1.64735			0.823673	+	0.567066i	$0.191921\pi$
$318$	−7.44375			−0.417425
$319$	−15.5237	+	1.30767i	−0.869161	+	0.0732153i
$320$			0.500309i			0.0279681i
$321$	−10.8711			−0.606768
$322$		0			0
$323$	−22.1119			−1.23034
$324$	−1.00000			−0.0555556
$325$	−4.37352			−0.242599
$326$		−	22.3466i		−	1.23766i
$327$	16.6612			0.921369
$328$			3.99913i			0.220815i
$329$		0			0
$330$	1.65348	−	0.139284i	0.0910212	−	0.00766733i
$331$	−4.45606			−0.244927			−0.122464	−	0.992473i	$-0.539079\pi$
$331$	−4.45606			−0.244927			−0.122464	+	0.992473i	$0.539079\pi$
$332$	−5.60082			−0.307385
$333$	5.56701			0.305070
$334$		−	8.40980i		−	0.460164i
$335$			1.15633i			0.0631770i
$336$		0			0
$337$		−	4.70543i		−	0.256321i	−0.991753	−	0.128160i	$-0.959093\pi$
$337$		−	4.70543i		−	0.256321i	0.991753	−	0.128160i	$-0.0409073\pi$
$338$		−	12.1521i		−	0.660989i
$339$			15.6890i			0.852110i
$340$			1.69702i			0.0920341i
$341$	27.4657	−	2.31362i	1.48735	−	0.125290i
$342$			6.51893i			0.352504i
$343$		0			0
$344$	0.666749			0.0359487
$345$	0.487921			0.0262688
$346$			14.3931i			0.773777i
$347$			18.6975i			1.00374i	0.864944	+	0.501868i	$0.167354\pi$
$347$			18.6975i			1.00374i	−0.864944	+	0.501868i	$0.832646\pi$
$348$	−4.69715			−0.251794
$349$	−13.2542			−0.709479			−0.354740	−	0.934965i	$-0.615430\pi$
$349$	−13.2542			−0.709479			−0.354740	+	0.934965i	$0.615430\pi$
$350$		0			0
$351$		−	0.920800i		−	0.0491487i
$352$	−3.30492	+	0.278396i	−0.176153	+	0.0148385i
$353$		−	6.55476i		−	0.348875i	−0.984668	−	0.174437i	$-0.944189\pi$
$353$		−	6.55476i		−	0.348875i	0.984668	−	0.174437i	$-0.0558106\pi$
$354$		−	11.7273i		−	0.623299i
$355$			4.68119i			0.248452i
$356$		−	14.3564i		−	0.760886i
$357$		0			0
$358$			9.33241i			0.493233i
$359$		−	2.85073i		−	0.150456i	−0.997166	−	0.0752278i	$-0.976032\pi$
$359$		−	2.85073i		−	0.150456i	0.997166	−	0.0752278i	$-0.0239684\pi$
$360$	0.500309			0.0263686
$361$	23.4965			1.23666
$362$	−1.43553			−0.0754499
$363$	1.84015	+	10.8450i	0.0965829	+	0.569214i
$364$		0			0
$365$			0.853023i			0.0446492i
$366$	−4.02998			−0.210651
$367$			20.8699i			1.08940i	0.838630	+	0.544701i	$0.183357\pi$
$367$			20.8699i			1.08940i	−0.838630	+	0.544701i	$0.816643\pi$
$368$	−0.975239			−0.0508379
$369$	3.99913			0.208186
$370$	−2.78523			−0.144797
$371$		0			0
$372$	8.31055			0.430882
$373$			20.3743i			1.05494i	0.849573	+	0.527471i	$0.176860\pi$
$373$			20.3743i			1.05494i	−0.849573	+	0.527471i	$0.823140\pi$
$374$	−11.2101	+	0.944305i	−0.579662	+	0.0488288i
$375$	−4.87786			−0.251892
$376$	5.52121			0.284735
$377$		−	4.32514i		−	0.222756i
$378$		0			0
$379$	12.3870			0.636279			0.318139	−	0.948044i	$-0.396942\pi$
$379$	12.3870			0.636279			0.318139	+	0.948044i	$0.396942\pi$
$380$		−	3.26148i		−	0.167310i
$381$	13.7323			0.703529
$382$		−	6.28574i		−	0.321606i
$383$			7.07537i			0.361535i	0.983526	+	0.180767i	$0.0578581\pi$
$383$			7.07537i			0.361535i	−0.983526	+	0.180767i	$0.942142\pi$
$384$	−1.00000			−0.0510310
$385$		0			0
$386$	−0.0824296			−0.00419555
$387$		−	0.666749i		−	0.0338928i
$388$		−	10.5358i		−	0.534875i
$389$	−16.6201			−0.842673			−0.421336	−	0.906904i	$-0.638439\pi$
$389$	−16.6201			−0.842673			−0.421336	+	0.906904i	$0.638439\pi$
$390$			0.460685i			0.0233277i
$391$	−3.30797			−0.167291
$392$		0			0
$393$			2.57981i			0.130134i
$394$	−7.93399			−0.399709
$395$	4.33534			0.218135
$396$	0.278396	+	3.30492i	0.0139899	+	0.166078i
$397$		−	25.1401i		−	1.26174i	−0.775887	−	0.630872i	$-0.782697\pi$
$397$		−	25.1401i		−	1.26174i	0.775887	−	0.630872i	$-0.217303\pi$
$398$	−17.8628			−0.895382
$399$		0			0
$400$	4.74969			0.237485
$401$	10.4062			0.519659			0.259829	−	0.965655i	$-0.416334\pi$
$401$	10.4062			0.519659			0.259829	+	0.965655i	$0.416334\pi$
$402$	−2.31123			−0.115274
$403$			7.65236i			0.381191i
$404$	−1.82562			−0.0908281
$405$		−	0.500309i		−	0.0248606i
$406$		0			0
$407$	−1.54983	−	18.3985i	−0.0768224	−	0.911982i
$408$	−3.39195			−0.167927
$409$	20.1535			0.996525			0.498263	−	0.867026i	$-0.333972\pi$
$409$	20.1535			0.996525			0.498263	+	0.867026i	$0.333972\pi$
$410$	−2.00080			−0.0988126
$411$			3.50632i			0.172954i
$412$			0.280707i			0.0138295i
$413$		0			0
$414$			0.975239i			0.0479304i
$415$		−	2.80214i		−	0.137552i
$416$		−	0.920800i		−	0.0451459i
$417$			16.7304i			0.819289i
$418$	21.5446	−	1.81484i	1.05378	−	0.0887669i
$419$		−	37.6211i		−	1.83791i	−0.394361	−	0.918956i	$-0.629034\pi$
$419$		−	37.6211i		−	1.83791i	0.394361	−	0.918956i	$-0.370966\pi$
$420$		0			0
$421$	16.9868			0.827886			0.413943	−	0.910303i	$-0.364151\pi$
$421$	16.9868			0.827886			0.413943	+	0.910303i	$0.364151\pi$
$422$	28.8538			1.40458
$423$		−	5.52121i		−	0.268450i
$424$			7.44375i			0.361500i
$425$	16.1107			0.781485
$426$	−9.35660			−0.453329
$427$		0			0
$428$			10.8711i			0.525476i
$429$	−3.04317	+	0.256347i	−0.146926	+	0.0123765i
$430$			0.333581i			0.0160867i
$431$		−	16.3150i		−	0.785866i	−0.919567	−	0.392933i	$-0.871460\pi$
$431$		−	16.3150i		−	0.785866i	0.919567	−	0.392933i	$-0.128540\pi$
$432$			1.00000i			0.0481125i
$433$			6.62647i			0.318448i	0.987243	+	0.159224i	$0.0508991\pi$
$433$			6.62647i			0.318448i	−0.987243	+	0.159224i	$0.949101\pi$
$434$		0			0
$435$		−	2.35003i		−	0.112675i
$436$		−	16.6612i		−	0.797929i
$437$	6.35752			0.304121
$438$	−1.70499			−0.0814676
$439$	−18.0440			−0.861191			−0.430596	−	0.902545i	$-0.641696\pi$
$439$	−18.0440			−0.861191			−0.430596	+	0.902545i	$0.641696\pi$
$440$	−0.139284	−	1.65348i	−0.00664010	−	0.0788266i
$441$		0			0
$442$		−	3.12331i		−	0.148561i
$443$	21.9305			1.04195			0.520975	−	0.853572i	$-0.325569\pi$
$443$	21.9305			1.04195			0.520975	+	0.853572i	$0.325569\pi$
$444$		−	5.56701i		−	0.264199i
$445$	7.18262			0.340489
$446$	−8.97060			−0.424770
$447$	8.85337			0.418750
$448$		0			0
$449$	−2.27658			−0.107439			−0.0537193	−	0.998556i	$-0.517108\pi$
$449$	−2.27658			−0.107439			−0.0537193	+	0.998556i	$0.517108\pi$
$450$		−	4.74969i		−	0.223903i
$451$	−1.11334	−	13.2168i	−0.0524252	−	0.622355i
$452$	15.6890			0.737949
$453$	14.8590			0.698139
$454$			24.0104i			1.12686i
$455$		0			0
$456$	6.51893			0.305277
$457$			38.5223i			1.80200i	0.433824	+	0.900998i	$0.357164\pi$
$457$			38.5223i			1.80200i	−0.433824	+	0.900998i	$0.642836\pi$
$458$	−3.71049			−0.173380
$459$			3.39195i			0.158323i
$460$		−	0.487921i		−	0.0227494i
$461$	30.0043			1.39744			0.698720	−	0.715395i	$-0.253753\pi$
$461$	30.0043			1.39744			0.698720	+	0.715395i	$0.253753\pi$
$462$		0			0
$463$	26.9051			1.25038			0.625192	−	0.780471i	$-0.285021\pi$
$463$	26.9051			1.25038			0.625192	+	0.780471i	$0.285021\pi$
$464$			4.69715i			0.218060i
$465$			4.15784i			0.192815i
$466$	−4.60105			−0.213140
$467$		−	26.8889i		−	1.24427i	−0.782911	−	0.622134i	$-0.786266\pi$
$467$		−	26.8889i		−	1.24427i	0.782911	−	0.622134i	$-0.213734\pi$
$468$	−0.920800			−0.0425640
$469$		0			0
$470$			2.76231i			0.127416i
$471$	−9.38319			−0.432355
$472$	−11.7273			−0.539793
$473$	−2.20355	+	0.185620i	−0.101319	+	0.00853482i
$474$			8.66533i			0.398012i
$475$	−30.9629			−1.42068
$476$		0			0
$477$	7.44375			0.340826
$478$	20.6362			0.943878
$479$	21.4319			0.979248			0.489624	−	0.871934i	$-0.337134\pi$
$479$	21.4319			0.979248			0.489624	+	0.871934i	$0.337134\pi$
$480$		−	0.500309i		−	0.0228359i
$481$	5.12611			0.233730
$482$		−	4.00574i		−	0.182456i
$483$		0			0
$484$	10.8450	−	1.84015i	0.492954	−	0.0836432i
$485$	5.27116			0.239351
$486$	1.00000			0.0453609
$487$	10.5307			0.477191			0.238595	−	0.971119i	$-0.423313\pi$
$487$	10.5307			0.477191			0.238595	+	0.971119i	$0.423313\pi$
$488$			4.02998i			0.182429i
$489$			22.3466i			1.01055i
$490$		0			0
$491$		−	13.9152i		−	0.627983i	−0.949426	−	0.313991i	$-0.898334\pi$
$491$		−	13.9152i		−	0.627983i	0.949426	−	0.313991i	$-0.101666\pi$
$492$		−	3.99913i		−	0.180295i
$493$			15.9325i			0.717565i
$494$			6.00264i			0.270071i
$495$	−1.65348	+	0.139284i	−0.0743185	+	0.00626034i
$496$		−	8.31055i		−	0.373155i
$497$		0			0
$498$	5.60082			0.250979
$499$	4.47121			0.200159			0.100079	−	0.994979i	$-0.468090\pi$
$499$	4.47121			0.200159			0.100079	+	0.994979i	$0.468090\pi$
$500$			4.87786i			0.218144i
$501$			8.40980i			0.375722i
$502$	6.13259			0.273711
$503$	15.0519			0.671131			0.335566	−	0.942017i	$-0.391073\pi$
$503$	15.0519			0.671131			0.335566	+	0.942017i	$0.391073\pi$
$504$		0			0
$505$		−	0.913375i		−	0.0406446i
$506$	3.22309	−	0.271502i	0.143284	−	0.0120698i
$507$			12.1521i			0.539695i
$508$		−	13.7323i		−	0.609274i
$509$		−	32.1804i		−	1.42637i	−0.700975	−	0.713186i	$-0.747251\pi$
$509$		−	32.1804i		−	1.42637i	0.700975	−	0.713186i	$-0.252749\pi$
$510$		−	1.69702i		−	0.0751455i
$511$		0			0
$512$			1.00000i			0.0441942i
$513$		−	6.51893i		−	0.287818i
$514$	−15.5055			−0.683917
$515$	−0.140440			−0.00618854
$516$	−0.666749			−0.0293520
$517$	−18.2471	+	1.53708i	−0.802509	+	0.0676007i
$518$		0			0
$519$		−	14.3931i		−	0.631786i
$520$	0.460685			0.0202024
$521$		−	1.03195i		−	0.0452106i	−0.999744	−	0.0226053i	$-0.992804\pi$
$521$		−	1.03195i		−	0.0452106i	0.999744	−	0.0226053i	$-0.00719611\pi$
$522$	4.69715			0.205589
$523$	−8.12522			−0.355291			−0.177646	−	0.984095i	$-0.556848\pi$
$523$	−8.12522			−0.355291			−0.177646	+	0.984095i	$0.556848\pi$
$524$	2.57981			0.112700
$525$		0			0
$526$	−5.55512			−0.242215
$527$		−	28.1890i		−	1.22793i
$528$	3.30492	−	0.278396i	0.143828	−	0.0121156i
$529$	−22.0489			−0.958648
$530$	−3.72417			−0.161768
$531$			11.7273i			0.508922i
$532$		0			0
$533$	3.68240			0.159503
$534$			14.3564i			0.621261i
$535$	−5.43893			−0.235145
$536$			2.31123i			0.0998299i
$537$		−	9.33241i		−	0.402723i
$538$	29.4511			1.26973
$539$		0			0
$540$	−0.500309			−0.0215299
$541$			40.9942i			1.76248i	0.472670	+	0.881240i	$0.343290\pi$
$541$			40.9942i			1.76248i	−0.472670	+	0.881240i	$0.656710\pi$
$542$		−	24.2318i		−	1.04084i
$543$	1.43553			0.0616046
$544$			3.39195i			0.145429i
$545$	8.33577			0.357065
$546$		0			0
$547$		−	33.5574i		−	1.43481i	−0.696656	−	0.717405i	$-0.745330\pi$
$547$		−	33.5574i		−	1.43481i	0.696656	−	0.717405i	$-0.254670\pi$
$548$	3.50632			0.149783
$549$	4.02998			0.171995
$550$	−15.6973	+	1.32229i	−0.669337	+	0.0563828i
$551$		−	30.6204i		−	1.30447i
$552$	0.975239			0.0415089
$553$		0			0
$554$	19.9326			0.846854
$555$	2.78523			0.118226
$556$	16.7304			0.709525
$557$			5.06960i			0.214806i	0.994216	+	0.107403i	$0.0342535\pi$
$557$			5.06960i			0.214806i	−0.994216	+	0.107403i	$0.965747\pi$
$558$	−8.31055			−0.351814
$559$		−	0.613943i		−	0.0259670i
$560$		0			0
$561$	11.2101	−	0.944305i	0.473292	−	0.0398686i
$562$	−5.03653			−0.212453
$563$	−36.0100			−1.51764			−0.758819	−	0.651301i	$-0.774223\pi$
$563$	−36.0100			−1.51764			−0.758819	+	0.651301i	$0.774223\pi$
$564$	−5.52121			−0.232485
$565$			7.84935i			0.330225i
$566$		−	10.0242i		−	0.421347i
$567$		0			0
$568$			9.35660i			0.392594i
$569$			6.72070i			0.281747i	0.990028	+	0.140873i	$0.0449910\pi$
$569$			6.72070i			0.281747i	−0.990028	+	0.140873i	$0.955009\pi$
$570$			3.26148i			0.136608i
$571$		−	2.13283i		−	0.0892561i	−0.999004	−	0.0446280i	$-0.985790\pi$
$571$		−	2.13283i		−	0.0892561i	0.999004	−	0.0446280i	$-0.0142103\pi$
$572$	0.256347	+	3.04317i	0.0107184	+	0.127241i
$573$			6.28574i			0.262590i
$574$		0			0
$575$	−4.63209			−0.193171
$576$	1.00000			0.0416667
$577$		−	8.16842i		−	0.340056i	−0.985439	−	0.170028i	$-0.945614\pi$
$577$		−	8.16842i		−	0.340056i	0.985439	−	0.170028i	$-0.0543858\pi$
$578$		−	5.49466i		−	0.228548i
$579$	0.0824296			0.00342566
$580$	−2.35003			−0.0975796
$581$		0			0
$582$			10.5358i			0.436723i
$583$	−2.07231	−	24.6010i	−0.0858262	−	1.01887i
$584$			1.70499i			0.0705530i
$585$		−	0.460685i		−	0.0190470i
$586$		−	18.0732i		−	0.746597i
$587$		−	38.1964i		−	1.57653i	−0.615334	−	0.788267i	$-0.710979\pi$
$587$		−	38.1964i		−	1.57653i	0.615334	−	0.788267i	$-0.289021\pi$
$588$		0			0
$589$			54.1759i			2.23228i
$590$		−	5.86728i		−	0.241552i
$591$	7.93399			0.326361
$592$	−5.56701			−0.228803
$593$	−0.610267			−0.0250607			−0.0125303	−	0.999921i	$-0.503989\pi$
$593$	−0.610267			−0.0250607			−0.0125303	+	0.999921i	$0.503989\pi$
$594$	−0.278396	−	3.30492i	−0.0114227	−	0.135603i
$595$		0			0
$596$		−	8.85337i		−	0.362648i
$597$	17.8628			0.731076
$598$			0.898001i			0.0367220i
$599$	−10.2968			−0.420717			−0.210358	−	0.977624i	$-0.567463\pi$
$599$	−10.2968			−0.420717			−0.210358	+	0.977624i	$0.567463\pi$
$600$	−4.74969			−0.193905
$601$	21.1849			0.864149			0.432075	−	0.901838i	$-0.357782\pi$
$601$	21.1849			0.864149			0.432075	+	0.901838i	$0.357782\pi$
$602$		0			0
$603$	2.31123			0.0941205
$604$		−	14.8590i		−	0.604606i
$605$	0.920644	+	5.42585i	0.0374295	+	0.220592i
$606$	1.82562			0.0741608
$607$	−20.5653			−0.834719			−0.417360	−	0.908741i	$-0.637044\pi$
$607$	−20.5653			−0.834719			−0.417360	+	0.908741i	$0.637044\pi$
$608$		−	6.51893i		−	0.264378i
$609$		0			0
$610$	−2.01624			−0.0816350
$611$		−	5.08393i		−	0.205674i
$612$	3.39195			0.137112
$613$		−	24.9090i		−	1.00607i	−0.864267	−	0.503033i	$-0.832217\pi$
$613$		−	24.9090i		−	1.00607i	0.864267	−	0.503033i	$-0.167783\pi$
$614$		−	6.52198i		−	0.263206i
$615$	2.00080			0.0806801
$616$		0			0
$617$	11.0119			0.443323			0.221661	−	0.975124i	$-0.428852\pi$
$617$	11.0119			0.443323			0.221661	+	0.975124i	$0.428852\pi$
$618$		−	0.280707i		−	0.0112917i
$619$			10.2729i			0.412902i	0.978457	+	0.206451i	$0.0661914\pi$
$619$			10.2729i			0.412902i	−0.978457	+	0.206451i	$0.933809\pi$
$620$	4.15784			0.166983
$621$		−	0.975239i		−	0.0391350i
$622$	15.3276			0.614580
$623$		0			0
$624$			0.920800i			0.0368615i
$625$	21.3080			0.852321
$626$	−4.09732			−0.163762
$627$	−21.5446	+	1.81484i	−0.860407	+	0.0724779i
$628$			9.38319i			0.374430i
$629$	−18.8830			−0.752916
$630$		0			0
$631$	23.9646			0.954016			0.477008	−	0.878899i	$-0.341721\pi$
$631$	23.9646			0.954016			0.477008	+	0.878899i	$0.341721\pi$
$632$	8.66533			0.344688
$633$	−28.8538			−1.14683
$634$			29.3301i			1.16485i
$635$	6.87042			0.272644
$636$		−	7.44375i		−	0.295164i
$637$		0			0
$638$	−1.30767	−	15.5237i	−0.0517710	−	0.614590i
$639$	9.35660			0.370141
$640$	−0.500309			−0.0197765
$641$	30.9163			1.22112			0.610561	−	0.791969i	$-0.290944\pi$
$641$	30.9163			1.22112			0.610561	+	0.791969i	$0.290944\pi$
$642$		−	10.8711i		−	0.429049i
$643$			22.8149i			0.899731i	0.893096	+	0.449866i	$0.148528\pi$
$643$			22.8149i			0.899731i	−0.893096	+	0.449866i	$0.851472\pi$
$644$		0			0
$645$		−	0.333581i		−	0.0131347i
$646$		−	22.1119i		−	0.869982i
$647$			4.54503i			0.178684i	0.996001	+	0.0893418i	$0.0284764\pi$
$647$			4.54503i			0.178684i	−0.996001	+	0.0893418i	$0.971524\pi$
$648$		−	1.00000i		−	0.0392837i
$649$	38.7578	−	3.26483i	1.52138	−	0.128156i
$650$		−	4.37352i		−	0.171543i
$651$		0			0
$652$	22.3466			0.875161
$653$	11.6209			0.454759			0.227380	−	0.973806i	$-0.426984\pi$
$653$	11.6209			0.454759			0.227380	+	0.973806i	$0.426984\pi$
$654$			16.6612i			0.651506i
$655$			1.29070i			0.0504320i
$656$	−3.99913			−0.156140
$657$	1.70499			0.0665180
$658$		0			0
$659$		−	0.213903i		−	0.00833246i	−0.999991	−	0.00416623i	$-0.998674\pi$
$659$		−	0.213903i		−	0.00833246i	0.999991	−	0.00416623i	$-0.00132616\pi$
$660$	0.139284	+	1.65348i	0.00542162	+	0.0643617i
$661$			39.2934i			1.52833i	0.645018	+	0.764167i	$0.276850\pi$
$661$			39.2934i			1.52833i	−0.645018	+	0.764167i	$0.723150\pi$
$662$		−	4.45606i		−	0.173190i
$663$			3.12331i			0.121299i
$664$		−	5.60082i		−	0.217354i
$665$		0			0
$666$			5.56701i			0.215717i
$667$		−	4.58085i		−	0.177371i
$668$	8.40980			0.325385
$669$	8.97060			0.346823
$670$	−1.15633			−0.0446729
$671$	−1.12193	−	13.3188i	−0.0433116	−	0.514165i
$672$		0			0
$673$			21.6147i			0.833187i	0.909093	+	0.416593i	$0.136776\pi$
$673$			21.6147i			0.833187i	−0.909093	+	0.416593i	$0.863224\pi$
$674$	4.70543			0.181246
$675$			4.74969i			0.182816i
$676$	12.1521			0.467389
$677$	−45.3241			−1.74195			−0.870973	−	0.491330i	$-0.836511\pi$
$677$	−45.3241			−1.74195			−0.870973	+	0.491330i	$0.836511\pi$
$678$	−15.6890			−0.602533
$679$		0			0
$680$	−1.69702			−0.0650779
$681$		−	24.0104i		−	0.920079i
$682$	2.31362	+	27.4657i	0.0885932	+	1.05172i
$683$	−44.0365			−1.68501			−0.842504	−	0.538690i	$-0.818919\pi$
$683$	−44.0365			−1.68501			−0.842504	+	0.538690i	$0.818919\pi$
$684$	−6.51893			−0.249258
$685$			1.75424i			0.0670262i
$686$		0			0
$687$	3.71049			0.141564
$688$			0.666749i			0.0254196i
$689$	6.85421			0.261124
$690$			0.487921i			0.0185748i
$691$		−	32.9815i		−	1.25468i	−0.778747	−	0.627338i	$-0.784145\pi$
$691$		−	32.9815i		−	1.25468i	0.778747	−	0.627338i	$-0.215855\pi$
$692$	−14.3931			−0.547143
$693$		0			0
$694$	−18.6975			−0.709748
$695$			8.37035i			0.317505i
$696$		−	4.69715i		−	0.178045i
$697$	−13.5649			−0.513806
$698$		−	13.2542i		−	0.501677i
$699$	4.60105			0.174028
$700$		0			0
$701$			18.3958i			0.694801i	0.937717	+	0.347400i	$0.112936\pi$
$701$			18.3958i			0.694801i	−0.937717	+	0.347400i	$0.887064\pi$
$702$	0.920800			0.0347534
$703$	36.2910			1.36874
$704$	−0.278396	−	3.30492i	−0.0104924	−	0.124559i
$705$		−	2.76231i		−	0.104035i
$706$	6.55476			0.246692
$707$		0			0
$708$	11.7273			0.440739
$709$	−0.742988			−0.0279035			−0.0139518	−	0.999903i	$-0.504441\pi$
$709$	−0.742988			−0.0279035			−0.0139518	+	0.999903i	$0.504441\pi$
$710$	−4.68119			−0.175682
$711$		−	8.66533i		−	0.324975i
$712$	14.3564			0.538028
$713$			8.10478i			0.303526i
$714$		0			0
$715$	−1.52253	+	0.128253i	−0.0569392	+	0.00479638i
$716$	−9.33241			−0.348769
$717$	−20.6362			−0.770673
$718$	2.85073			0.106388
$719$			19.2760i			0.718874i	0.933169	+	0.359437i	$0.117031\pi$
$719$			19.2760i			0.718874i	−0.933169	+	0.359437i	$0.882969\pi$
$720$			0.500309i			0.0186454i
$721$		0			0
$722$			23.4965i			0.874449i
$723$			4.00574i			0.148975i
$724$		−	1.43553i		−	0.0533512i
$725$			22.3100i			0.828574i
$726$	−10.8450	+	1.84015i	−0.402495	+	0.0682944i
$727$		−	15.6899i		−	0.581905i	−0.956737	−	0.290953i	$-0.906028\pi$
$727$		−	15.6899i		−	0.581905i	0.956737	−	0.290953i	$-0.0939722\pi$
$728$		0			0
$729$	−1.00000			−0.0370370
$730$	−0.853023			−0.0315718
$731$			2.26158i			0.0836476i
$732$		−	4.02998i		−	0.148952i
$733$	−39.4073			−1.45554			−0.727770	−	0.685821i	$-0.759443\pi$
$733$	−39.4073			−1.45554			−0.727770	+	0.685821i	$0.759443\pi$
$734$	−20.8699			−0.770324
$735$		0			0
$736$		−	0.975239i		−	0.0359478i
$737$	−0.643436	−	7.63842i	−0.0237013	−	0.281365i
$738$			3.99913i			0.147210i
$739$		−	17.2049i		−	0.632892i	−0.948611	−	0.316446i	$-0.897510\pi$
$739$		−	17.2049i		−	0.632892i	0.948611	−	0.316446i	$-0.102490\pi$
$740$		−	2.78523i		−	0.102387i
$741$		−	6.00264i		−	0.220512i
$742$		0			0
$743$			45.0824i			1.65391i	0.562266	+	0.826956i	$0.309930\pi$
$743$			45.0824i			1.65391i	−0.562266	+	0.826956i	$0.690070\pi$
$744$			8.31055i			0.304680i
$745$	4.42942			0.162281
$746$	−20.3743			−0.745957
$747$	−5.60082			−0.204923
$748$	−0.944305	−	11.2101i	−0.0345272	−	0.409883i
$749$		0			0
$750$		−	4.87786i		−	0.178114i
$751$	43.5808			1.59028			0.795142	−	0.606423i	$-0.207396\pi$
$751$	43.5808			1.59028			0.795142	+	0.606423i	$0.207396\pi$
$752$			5.52121i			0.201338i
$753$	−6.13259			−0.223484
$754$	4.32514			0.157512
$755$	7.43411			0.270555
$756$		0			0
$757$	48.8127			1.77413			0.887064	−	0.461646i	$-0.152741\pi$
$757$	48.8127			1.77413			0.887064	+	0.461646i	$0.152741\pi$
$758$			12.3870i			0.449917i
$759$	−3.22309	+	0.271502i	−0.116991	+	0.00985491i
$760$	3.26148			0.118306
$761$	39.2514			1.42286			0.711432	−	0.702755i	$-0.248047\pi$
$761$	39.2514			1.42286			0.711432	+	0.702755i	$0.248047\pi$
$762$			13.7323i			0.497470i
$763$		0			0
$764$	6.28574			0.227410
$765$			1.69702i			0.0613561i
$766$	−7.07537			−0.255644
$767$			10.7985i			0.389911i
$768$		−	1.00000i		−	0.0360844i
$769$	46.4630			1.67550			0.837749	−	0.546056i	$-0.183871\pi$
$769$	46.4630			1.67550			0.837749	+	0.546056i	$0.183871\pi$
$770$		0			0
$771$	15.5055			0.558416
$772$		−	0.0824296i		−	0.00296671i
$773$			21.0265i			0.756269i	0.925751	+	0.378134i	$0.123434\pi$
$773$			21.0265i			0.756269i	−0.925751	+	0.378134i	$0.876566\pi$
$774$	0.666749			0.0239658
$775$		−	39.4725i		−	1.41790i
$776$	10.5358			0.378214
$777$		0			0
$778$		−	16.6201i		−	0.595860i
$779$	26.0701			0.934057
$780$	−0.460685			−0.0164952
$781$	−2.60484	−	30.9228i	−0.0932084	−	1.10651i
$782$		−	3.30797i		−	0.118293i
$783$	−4.69715			−0.167863
$784$		0			0
$785$	−4.69450			−0.167554
$786$	−2.57981			−0.0920189
$787$	25.5908			0.912213			0.456107	−	0.889925i	$-0.349244\pi$
$787$	25.5908			0.912213			0.456107	+	0.889925i	$0.349244\pi$
$788$		−	7.93399i		−	0.282637i
$789$	5.55512			0.197767
$790$			4.33534i			0.154245i
$791$		0			0
$792$	−3.30492	+	0.278396i	−0.117435	+	0.00989236i
$793$	3.71081			0.131775
$794$	25.1401			0.892188
$795$	3.72417			0.132083
$796$		−	17.8628i		−	0.633131i
$797$		−	3.83185i		−	0.135731i	−0.997694	−	0.0678655i	$-0.978381\pi$
$797$		−	3.83185i		−	0.135731i	0.997694	−	0.0678655i	$-0.0216189\pi$
$798$		0			0
$799$			18.7277i			0.662537i
$800$			4.74969i			0.167927i
$801$		−	14.3564i		−	0.507257i
$802$			10.4062i			0.367454i
$803$	−0.474662	−	5.63486i	−0.0167505	−	0.198850i
$804$		−	2.31123i		−	0.0815107i
$805$		0			0
$806$	−7.65236			−0.269543
$807$	−29.4511			−1.03673
$808$		−	1.82562i		−	0.0642251i
$809$			54.6789i			1.92241i	0.275836	+	0.961205i	$0.411045\pi$
$809$			54.6789i			1.92241i	−0.275836	+	0.961205i	$0.588955\pi$
$810$	0.500309			0.0175791
$811$	−17.7011			−0.621570			−0.310785	−	0.950480i	$-0.600592\pi$
$811$	−17.7011			−0.621570			−0.310785	+	0.950480i	$0.600592\pi$
$812$		0			0
$813$			24.2318i			0.849845i
$814$	18.3985	−	1.54983i	0.644868	−	0.0543216i
$815$			11.1802i			0.391626i
$816$		−	3.39195i		−	0.118742i
$817$		−	4.34649i		−	0.152065i
$818$			20.1535i			0.704650i
$819$		0			0
$820$		−	2.00080i		−	0.0698710i
$821$			47.7253i			1.66562i	0.553557	+	0.832812i	$0.313270\pi$
$821$			47.7253i			1.66562i	−0.553557	+	0.832812i	$0.686730\pi$
$822$	−3.50632			−0.122297
$823$	−13.0797			−0.455929			−0.227965	−	0.973669i	$-0.573207\pi$
$823$	−13.0797			−0.455929			−0.227965	+	0.973669i	$0.573207\pi$
$824$	−0.280707			−0.00977890
$825$	15.6973	−	1.32229i	0.546512	−	0.0460363i
$826$		0			0
$827$		−	45.3610i		−	1.57736i	−0.614806	−	0.788678i	$-0.710766\pi$
$827$		−	45.3610i		−	1.57736i	0.614806	−	0.788678i	$-0.289234\pi$
$828$	−0.975239			−0.0338919
$829$			9.83154i			0.341463i	0.985318	+	0.170732i	$0.0546131\pi$
$829$			9.83154i			0.341463i	−0.985318	+	0.170732i	$0.945387\pi$
$830$	2.80214			0.0972638
$831$	−19.9326			−0.691454
$832$	0.920800			0.0319230
$833$		0			0
$834$	−16.7304			−0.579325
$835$			4.20750i			0.145607i
$836$	1.81484	+	21.5446i	0.0627677	+	0.745134i
$837$	8.31055			0.287255
$838$	37.6211			1.29960
$839$		−	3.59555i		−	0.124132i	−0.998072	−	0.0620660i	$-0.980231\pi$
$839$		−	3.59555i		−	0.124132i	0.998072	−	0.0620660i	$-0.0197689\pi$
$840$		0			0
$841$	6.93675			0.239198
$842$			16.9868i			0.585404i
$843$	5.03653			0.173467
$844$			28.8538i			0.993188i
$845$			6.07982i			0.209152i
$846$	5.52121			0.189823
$847$		0			0
$848$	−7.44375			−0.255619
$849$			10.0242i			0.344029i
$850$			16.1107i			0.552593i
$851$	5.42917			0.186110
$852$		−	9.35660i		−	0.320552i
$853$	25.2160			0.863378			0.431689	−	0.902023i	$-0.357918\pi$
$853$	25.2160			0.863378			0.431689	+	0.902023i	$0.357918\pi$
$854$		0			0
$855$		−	3.26148i		−	0.111540i
$856$	−10.8711			−0.371568
$857$	−37.3656			−1.27639			−0.638193	−	0.769877i	$-0.720318\pi$
$857$	−37.3656			−1.27639			−0.638193	+	0.769877i	$0.720318\pi$
$858$	−0.256347	−	3.04317i	−0.00875154	−	0.103892i
$859$			33.9787i			1.15934i	0.814852	+	0.579668i	$0.196818\pi$
$859$			33.9787i			1.15934i	−0.814852	+	0.579668i	$0.803182\pi$
$860$	−0.333581			−0.0113750
$861$		0			0
$862$	16.3150			0.555691
$863$	24.3433			0.828656			0.414328	−	0.910128i	$-0.364017\pi$
$863$	24.3433			0.828656			0.414328	+	0.910128i	$0.364017\pi$
$864$	−1.00000			−0.0340207
$865$		−	7.20099i		−	0.244841i
$866$	−6.62647			−0.225176
$867$			5.49466i			0.186608i
$868$		0			0
$869$	−28.6382	+	2.41239i	−0.971485	+	0.0818348i
$870$	2.35003			0.0796734
$871$	2.12818			0.0721106
$872$	16.6612			0.564221
$873$		−	10.5358i		−	0.356583i
$874$			6.35752i			0.215046i
$875$		0			0
$876$		−	1.70499i		−	0.0576063i
$877$			20.5584i			0.694207i	0.937827	+	0.347103i	$0.112835\pi$
$877$			20.5584i			0.694207i	−0.937827	+	0.347103i	$0.887165\pi$
$878$		−	18.0440i		−	0.608954i
$879$			18.0732i			0.609594i
$880$	1.65348	−	0.139284i	0.0557388	−	0.00469526i
$881$		−	40.5069i		−	1.36471i	−0.731020	−	0.682356i	$-0.760956\pi$
$881$		−	40.5069i		−	1.36471i	0.731020	−	0.682356i	$-0.239044\pi$
$882$		0			0
$883$	−32.6855			−1.09995			−0.549977	−	0.835179i	$-0.685364\pi$
$883$	−32.6855			−1.09995			−0.549977	+	0.835179i	$0.685364\pi$
$884$	3.12331			0.105048
$885$			5.86728i			0.197226i
$886$			21.9305i			0.736769i
$887$	−46.1540			−1.54970			−0.774849	−	0.632146i	$-0.782174\pi$
$887$	−46.1540			−1.54970			−0.774849	+	0.632146i	$0.782174\pi$
$888$	5.56701			0.186817
$889$		0			0
$890$			7.18262i			0.240762i
$891$	0.278396	+	3.30492i	0.00932661	+	0.110719i
$892$		−	8.97060i		−	0.300358i
$893$		−	35.9924i		−	1.20444i
$894$			8.85337i			0.296101i
$895$		−	4.66909i		−	0.156071i
$896$		0			0
$897$		−	0.898001i		−	0.0299834i
$898$		−	2.27658i		−	0.0759706i
$899$	39.0359			1.30192
$900$	4.74969			0.158323
$901$	−25.2488			−0.841161
$902$	13.2168	−	1.11334i	0.440072	−	0.0370702i
$903$		0			0
$904$			15.6890i			0.521809i
$905$	0.718210			0.0238741
$906$			14.8590i			0.493659i
$907$	24.9771			0.829351			0.414675	−	0.909969i	$-0.363895\pi$
$907$	24.9771			0.829351			0.414675	+	0.909969i	$0.363895\pi$
$908$	−24.0104			−0.796812
$909$	−1.82562			−0.0605520
$910$		0			0
$911$	44.0330			1.45888			0.729440	−	0.684045i	$-0.239781\pi$
$911$	44.0330			1.45888			0.729440	+	0.684045i	$0.239781\pi$
$912$			6.51893i			0.215863i
$913$	1.55924	+	18.5103i	0.0516035	+	0.612600i
$914$	−38.5223			−1.27420
$915$	2.01624			0.0666547
$916$		−	3.71049i		−	0.122598i
$917$		0			0
$918$	−3.39195			−0.111951
$919$		−	47.5003i		−	1.56689i	−0.621462	−	0.783444i	$-0.713461\pi$
$919$		−	47.5003i		−	1.56689i	0.621462	−	0.783444i	$-0.286539\pi$
$920$	0.487921			0.0160863
$921$			6.52198i			0.214906i
$922$			30.0043i			0.988139i
$923$	8.61556			0.283585
$924$		0			0
$925$	−26.4416			−0.869394
$926$			26.9051i			0.884156i
$927$			0.280707i			0.00921964i
$928$	−4.69715			−0.154192
$929$			17.1661i			0.563202i	0.959532	+	0.281601i	$0.0908655\pi$
$929$			17.1661i			0.563202i	−0.959532	+	0.281601i	$0.909135\pi$
$930$	−4.15784			−0.136341
$931$		0			0
$932$		−	4.60105i		−	0.150713i
$933$	−15.3276			−0.501803
$934$	26.8889			0.879830
$935$	5.60853	−	0.472444i	0.183419	−	0.0154506i
$936$		−	0.920800i		−	0.0300973i
$937$	−13.4834			−0.440485			−0.220243	−	0.975445i	$-0.570685\pi$
$937$	−13.4834			−0.440485			−0.220243	+	0.975445i	$0.570685\pi$
$938$		0			0
$939$	4.09732			0.133711
$940$	−2.76231			−0.0900966
$941$	−37.6975			−1.22890			−0.614452	−	0.788954i	$-0.710623\pi$
$941$	−37.6975			−1.22890			−0.614452	+	0.788954i	$0.710623\pi$
$942$		−	9.38319i		−	0.305721i
$943$	3.90011			0.127005
$944$		−	11.7273i		−	0.381691i
$945$		0			0
$946$	−0.185620	−	2.20355i	−0.00603503	−	0.0716437i
$947$	40.7407			1.32389			0.661947	−	0.749551i	$-0.269730\pi$
$947$	40.7407			1.32389			0.661947	+	0.749551i	$0.269730\pi$
$948$	−8.66533			−0.281437
$949$	1.56996			0.0509629
$950$		−	30.9629i		−	1.00457i
$951$		−	29.3301i		−	0.951095i
$952$		0			0
$953$			10.9510i			0.354739i	0.984144	+	0.177370i	$0.0567588\pi$
$953$			10.9510i			0.354739i	−0.984144	+	0.177370i	$0.943241\pi$
$954$			7.44375i			0.241000i
$955$			3.14481i			0.101764i
$956$			20.6362i			0.667423i
$957$	1.30767	+	15.5237i	0.0422709	+	0.501810i
$958$			21.4319i			0.692433i
$959$		0			0
$960$	0.500309			0.0161474
$961$	−38.0653			−1.22791
$962$			5.12611i			0.165272i
$963$			10.8711i			0.350317i
$964$	4.00574			0.129016
$965$	0.0412403			0.00132757
$966$		0			0
$967$			41.1072i			1.32192i	0.750421	+	0.660960i	$0.229851\pi$
$967$			41.1072i			1.32192i	−0.750421	+	0.660960i	$0.770149\pi$
$968$	1.84015	+	10.8450i	0.0591447	+	0.348571i
$969$			22.1119i			0.710337i
$970$			5.27116i			0.169247i
$971$			9.47642i			0.304113i	0.988372	+	0.152056i	$0.0485895\pi$
$971$			9.47642i			0.304113i	−0.988372	+	0.152056i	$0.951410\pi$
$972$			1.00000i			0.0320750i
$973$		0			0
$974$			10.5307i			0.337425i
$975$			4.37352i			0.140065i
$976$	−4.02998			−0.128997
$977$	−28.8034			−0.921501			−0.460751	−	0.887530i	$-0.652420\pi$
$977$	−28.8034			−0.921501			−0.460751	+	0.887530i	$0.652420\pi$
$978$	−22.3466			−0.714566
$979$	−47.4467	+	3.99675i	−1.51640	+	0.127737i
$980$		0			0
$981$		−	16.6612i		−	0.531952i
$982$	13.9152			0.444051
$983$			22.0346i			0.702794i	0.936226	+	0.351397i	$0.114293\pi$
$983$			22.0346i			0.702794i	−0.936226	+	0.351397i	$0.885707\pi$
$984$	3.99913			0.127488
$985$	3.96945			0.126477
$986$	−15.9325			−0.507395
$987$		0			0
$988$	−6.00264			−0.190969
$989$		−	0.650240i		−	0.0206764i
$990$	−0.139284	−	1.65348i	−0.00442673	−	0.0525511i
$991$	11.6088			0.368767			0.184384	−	0.982854i	$-0.440971\pi$
$991$	11.6088			0.368767			0.184384	+	0.982854i	$0.440971\pi$
$992$	8.31055			0.263860
$993$			4.45606i			0.141409i
$994$		0			0
$995$	8.93693			0.283320
$996$			5.60082i			0.177469i
$997$	−40.0010			−1.26684			−0.633422	−	0.773807i	$-0.718350\pi$
$997$	−40.0010			−1.26684			−0.633422	+	0.773807i	$0.718350\pi$
$998$			4.47121i			0.141534i
$999$		−	5.56701i		−	0.176133i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3234.2.e.d.2155.18	yes	24
7.6	odd	2		3234.2.e.c.2155.19	yes	24
11.10	odd	2		3234.2.e.c.2155.6	✓	24
77.76	even	2	inner	3234.2.e.d.2155.7	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3234.2.e.c.2155.6	✓	24	11.10	odd	2
3234.2.e.c.2155.19	yes	24	7.6	odd	2
3234.2.e.d.2155.7	yes	24	77.76	even	2	inner
3234.2.e.d.2155.18	yes	24	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} -0.500309i q^{5} +1.00000 q^{6} -1.00000i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} -0.500309i q^{5} +1.00000 q^{6} -1.00000i q^{8} -1.00000 q^{9} +0.500309 q^{10} +(0.278396 + 3.30492i) q^{11} +1.00000i q^{12} -0.920800 q^{13} -0.500309 q^{15} +1.00000 q^{16} +3.39195 q^{17} -1.00000i q^{18} -6.51893 q^{19} +0.500309i q^{20} +(-3.30492 + 0.278396i) q^{22} -0.975239 q^{23} -1.00000 q^{24} +4.74969 q^{25} -0.920800i q^{26} +1.00000i q^{27} +4.69715i q^{29} -0.500309i q^{30} -8.31055i q^{31} +1.00000i q^{32} +(3.30492 - 0.278396i) q^{33} +3.39195i q^{34} +1.00000 q^{36} -5.56701 q^{37} -6.51893i q^{38} +0.920800i q^{39} -0.500309 q^{40} -3.99913 q^{41} +0.666749i q^{43} +(-0.278396 - 3.30492i) q^{44} +0.500309i q^{45} -0.975239i q^{46} +5.52121i q^{47} -1.00000i q^{48} +4.74969i q^{50} -3.39195i q^{51} +0.920800 q^{52} -7.44375 q^{53} -1.00000 q^{54} +(1.65348 - 0.139284i) q^{55} +6.51893i q^{57} -4.69715 q^{58} -11.7273i q^{59} +0.500309 q^{60} -4.02998 q^{61} +8.31055 q^{62} -1.00000 q^{64} +0.460685i q^{65} +(0.278396 + 3.30492i) q^{66} -2.31123 q^{67} -3.39195 q^{68} +0.975239i q^{69} -9.35660 q^{71} +1.00000i q^{72} -1.70499 q^{73} -5.56701i q^{74} -4.74969i q^{75} +6.51893 q^{76} -0.920800 q^{78} +8.66533i q^{79} -0.500309i q^{80} +1.00000 q^{81} -3.99913i q^{82} +5.60082 q^{83} -1.69702i q^{85} -0.666749 q^{86} +4.69715 q^{87} +(3.30492 - 0.278396i) q^{88} +14.3564i q^{89} -0.500309 q^{90} +0.975239 q^{92} -8.31055 q^{93} -5.52121 q^{94} +3.26148i q^{95} +1.00000 q^{96} +10.5358i q^{97} +(-0.278396 - 3.30492i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 24 q^{4} + 24 q^{6} - 24 q^{9}+O(q^{10}) \) 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

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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