LMFDB - Embedded newform 1734.2.f.n.1483.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1734,2,Mod(829,1734)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1734, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("1734.829");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1734 = 2 \cdot 3 \cdot 17^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1734.f (of order $4$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$13.8460597105$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	12.0.722204136308736.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 18x^{8} + 69x^{4} + 1 $ x^12 + 18x^8 + 69x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			1483.2
Root			$1.08335 + 1.08335i$ of defining polynomial
Character	$\chi$	$=$	1734.1483
Dual form			1734.2.f.n.829.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +(-0.707107 + 0.707107i) q^{3} -1.00000 q^{4} +(1.65979 - 1.65979i) q^{5} +(0.707107 + 0.707107i) q^{6} +(2.87381 + 2.87381i) q^{7} +1.00000i q^{8} -1.00000i q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(-0.707107 + 0.707107i) q^{3} -1.00000 q^{4} +(1.65979 - 1.65979i) q^{5} +(0.707107 + 0.707107i) q^{6} +(2.87381 + 2.87381i) q^{7} +1.00000i q^{8} -1.00000i q^{9} +(-1.65979 - 1.65979i) q^{10} +(-2.00641 - 2.00641i) q^{11} +(0.707107 - 0.707107i) q^{12} -2.69459 q^{13} +(2.87381 - 2.87381i) q^{14} +2.34730i q^{15} +1.00000 q^{16} -1.00000 q^{18} -6.45336i q^{19} +(-1.65979 + 1.65979i) q^{20} -4.06418 q^{21} +(-2.00641 + 2.00641i) q^{22} +(-4.24264 - 4.24264i) q^{23} +(-0.707107 - 0.707107i) q^{24} -0.509800i q^{25} +2.69459i q^{26} +(0.707107 + 0.707107i) q^{27} +(-2.87381 - 2.87381i) q^{28} +(6.15348 - 6.15348i) q^{29} +2.34730 q^{30} +(-0.405864 + 0.405864i) q^{31} -1.00000i q^{32} +2.83750 q^{33} +9.53983 q^{35} +1.00000i q^{36} +(5.57704 - 5.57704i) q^{37} -6.45336 q^{38} +(1.90536 - 1.90536i) q^{39} +(1.65979 + 1.65979i) q^{40} +(-2.42804 - 2.42804i) q^{41} +4.06418i q^{42} +11.6459i q^{43} +(2.00641 + 2.00641i) q^{44} +(-1.65979 - 1.65979i) q^{45} +(-4.24264 + 4.24264i) q^{46} +10.5817 q^{47} +(-0.707107 + 0.707107i) q^{48} +9.51754i q^{49} -0.509800 q^{50} +2.69459 q^{52} -3.29086i q^{53} +(0.707107 - 0.707107i) q^{54} -6.66044 q^{55} +(-2.87381 + 2.87381i) q^{56} +(4.56322 + 4.56322i) q^{57} +(-6.15348 - 6.15348i) q^{58} -4.34730i q^{59} -2.34730i q^{60} +(-9.23777 - 9.23777i) q^{61} +(0.405864 + 0.405864i) q^{62} +(2.87381 - 2.87381i) q^{63} -1.00000 q^{64} +(-4.47246 + 4.47246i) q^{65} -2.83750i q^{66} +12.2121 q^{67} +6.00000 q^{69} -9.53983i q^{70} +(8.20337 - 8.20337i) q^{71} +1.00000 q^{72} +(-1.67008 + 1.67008i) q^{73} +(-5.57704 - 5.57704i) q^{74} +(0.360483 + 0.360483i) q^{75} +6.45336i q^{76} -11.5321i q^{77} +(-1.90536 - 1.90536i) q^{78} +(5.21466 + 5.21466i) q^{79} +(1.65979 - 1.65979i) q^{80} -1.00000 q^{81} +(-2.42804 + 2.42804i) q^{82} +3.21213i q^{83} +4.06418 q^{84} +11.6459 q^{86} +8.70233i q^{87} +(2.00641 - 2.00641i) q^{88} +6.34049 q^{89} +(-1.65979 + 1.65979i) q^{90} +(-7.74374 - 7.74374i) q^{91} +(4.24264 + 4.24264i) q^{92} -0.573978i q^{93} -10.5817i q^{94} +(-10.7112 - 10.7112i) q^{95} +(0.707107 + 0.707107i) q^{96} +(5.73733 - 5.73733i) q^{97} +9.51754 q^{98} +(-2.00641 + 2.00641i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 12 q^{4}+O(q^{10}) $ 12 * q - 12 * q^4	$ 12 q - 12 q^{4} - 24 q^{13} + 12 q^{16} - 12 q^{18} - 12 q^{21} + 24 q^{30} + 24 q^{33} - 24 q^{38} - 12 q^{50} + 24 q^{52} + 12 q^{55} - 12 q^{64} + 48 q^{67} + 72 q^{69} + 12 q^{72} - 12 q^{81} + 12 q^{84} - 24 q^{86} - 96 q^{89} + 24 q^{98}+O(q^{100}) $ 12 * q - 12 * q^4 - 24 * q^13 + 12 * q^16 - 12 * q^18 - 12 * q^21 + 24 * q^30 + 24 * q^33 - 24 * q^38 - 12 * q^50 + 24 * q^52 + 12 * q^55 - 12 * q^64 + 48 * q^67 + 72 * q^69 + 12 * q^72 - 12 * q^81 + 12 * q^84 - 24 * q^86 - 96 * q^89 + 24 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1734\mathbb{Z}\right)^\times$.

$n$	$1157$	$1159$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$

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
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$4$	−1.00000			−0.500000
$5$	1.65979	−	1.65979i	0.742280	−	0.742280i	−0.230736	−	0.973016i	$-0.574113\pi$
$5$	1.65979	−	1.65979i	0.742280	−	0.742280i	0.973016	+	0.230736i	$0.0741134\pi$
$6$	0.707107	+	0.707107i	0.288675	+	0.288675i
$7$	2.87381	+	2.87381i	1.08620	+	1.08620i	0.995916	+	0.0902809i	$0.0287765\pi$
$7$	2.87381	+	2.87381i	1.08620	+	1.08620i	0.0902809	+	0.995916i	$0.471224\pi$
$8$			1.00000i			0.353553i
$9$		−	1.00000i		−	0.333333i
$10$	−1.65979	−	1.65979i	−0.524871	−	0.524871i
$11$	−2.00641	−	2.00641i	−0.604956	−	0.604956i	0.336667	−	0.941624i	$-0.390700\pi$
$11$	−2.00641	−	2.00641i	−0.604956	−	0.604956i	−0.941624	+	0.336667i	$0.890700\pi$
$12$	0.707107	−	0.707107i	0.204124	−	0.204124i
$13$	−2.69459			−0.747346			−0.373673	−	0.927561i	$-0.621902\pi$
$13$	−2.69459			−0.747346			−0.373673	+	0.927561i	$0.621902\pi$
$14$	2.87381	−	2.87381i	0.768057	−	0.768057i
$15$			2.34730i			0.606069i
$16$	1.00000			0.250000
$17$		0			0
$17$		0			0
$18$	−1.00000			−0.235702
$19$		−	6.45336i		−	1.48050i	−0.672330	−	0.740252i	$-0.734706\pi$
$19$		−	6.45336i		−	1.48050i	0.672330	−	0.740252i	$-0.265294\pi$
$20$	−1.65979	+	1.65979i	−0.371140	+	0.371140i
$21$	−4.06418			−0.886876
$22$	−2.00641	+	2.00641i	−0.427769	+	0.427769i
$23$	−4.24264	−	4.24264i	−0.884652	−	0.884652i	0.109351	−	0.994003i	$-0.465123\pi$
$23$	−4.24264	−	4.24264i	−0.884652	−	0.884652i	−0.994003	+	0.109351i	$0.965123\pi$
$24$	−0.707107	−	0.707107i	−0.144338	−	0.144338i
$25$		−	0.509800i		−	0.101960i
$26$			2.69459i			0.528453i
$27$	0.707107	+	0.707107i	0.136083	+	0.136083i
$28$	−2.87381	−	2.87381i	−0.543099	−	0.543099i
$29$	6.15348	−	6.15348i	1.14267	−	1.14267i	0.154713	−	0.987959i	$-0.450555\pi$
$29$	6.15348	−	6.15348i	1.14267	−	1.14267i	0.987959	−	0.154713i	$-0.0494453\pi$
$30$	2.34730			0.428556
$31$	−0.405864	+	0.405864i	−0.0728953	+	0.0728953i	−0.742614	−	0.669719i	$-0.766414\pi$
$31$	−0.405864	+	0.405864i	−0.0728953	+	0.0728953i	0.669719	+	0.742614i	$0.266414\pi$
$32$		−	1.00000i		−	0.176777i
$33$	2.83750			0.493945
$34$		0			0
$35$	9.53983			1.61253
$36$			1.00000i			0.166667i
$37$	5.57704	−	5.57704i	0.916860	−	0.916860i	−0.0799399	−	0.996800i	$-0.525473\pi$
$37$	5.57704	−	5.57704i	0.916860	−	0.916860i	0.996800	+	0.0799399i	$0.0254728\pi$
$38$	−6.45336			−1.04687
$39$	1.90536	−	1.90536i	0.305103	−	0.305103i
$40$	1.65979	+	1.65979i	0.262436	+	0.262436i
$41$	−2.42804	−	2.42804i	−0.379196	−	0.379196i	0.491616	−	0.870812i	$-0.336406\pi$
$41$	−2.42804	−	2.42804i	−0.379196	−	0.379196i	−0.870812	+	0.491616i	$0.836406\pi$
$42$			4.06418i			0.627116i
$43$			11.6459i			1.77598i	0.459860	+	0.887991i	$0.347899\pi$
$43$			11.6459i			1.77598i	−0.459860	+	0.887991i	$0.652101\pi$
$44$	2.00641	+	2.00641i	0.302478	+	0.302478i
$45$	−1.65979	−	1.65979i	−0.247427	−	0.247427i
$46$	−4.24264	+	4.24264i	−0.625543	+	0.625543i
$47$	10.5817			1.54350			0.771751	−	0.635925i	$-0.219381\pi$
$47$	10.5817			1.54350			0.771751	+	0.635925i	$0.219381\pi$
$48$	−0.707107	+	0.707107i	−0.102062	+	0.102062i
$49$			9.51754i			1.35965i
$50$	−0.509800			−0.0720966
$51$		0			0
$52$	2.69459			0.373673
$53$		−	3.29086i		−	0.452034i	−0.974123	−	0.226017i	$-0.927429\pi$
$53$		−	3.29086i		−	0.452034i	0.974123	−	0.226017i	$-0.0725705\pi$
$54$	0.707107	−	0.707107i	0.0962250	−	0.0962250i
$55$	−6.66044			−0.898094
$56$	−2.87381	+	2.87381i	−0.384029	+	0.384029i
$57$	4.56322	+	4.56322i	0.604413	+	0.604413i
$58$	−6.15348	−	6.15348i	−0.807991	−	0.807991i
$59$		−	4.34730i		−	0.565970i	−0.959124	−	0.282985i	$-0.908675\pi$
$59$		−	4.34730i		−	0.565970i	0.959124	−	0.282985i	$-0.0913246\pi$
$60$		−	2.34730i		−	0.303035i
$61$	−9.23777	−	9.23777i	−1.18278	−	1.18278i	−0.979022	−	0.203753i	$-0.934686\pi$
$61$	−9.23777	−	9.23777i	−1.18278	−	1.18278i	−0.203753	−	0.979022i	$-0.565314\pi$
$62$	0.405864	+	0.405864i	0.0515447	+	0.0515447i
$63$	2.87381	−	2.87381i	0.362066	−	0.362066i
$64$	−1.00000			−0.125000
$65$	−4.47246	+	4.47246i	−0.554740	+	0.554740i
$66$		−	2.83750i		−	0.349272i
$67$	12.2121			1.49195			0.745975	−	0.665974i	$-0.231984\pi$
$67$	12.2121			1.49195			0.745975	+	0.665974i	$0.231984\pi$
$68$		0			0
$69$	6.00000			0.722315
$70$		−	9.53983i		−	1.14023i
$71$	8.20337	−	8.20337i	0.973561	−	0.973561i	−0.0260983	−	0.999659i	$-0.508308\pi$
$71$	8.20337	−	8.20337i	0.973561	−	0.973561i	0.999659	+	0.0260983i	$0.00830829\pi$
$72$	1.00000			0.117851
$73$	−1.67008	+	1.67008i	−0.195468	+	0.195468i	−0.798054	−	0.602586i	$-0.794137\pi$
$73$	−1.67008	+	1.67008i	−0.195468	+	0.195468i	0.602586	+	0.798054i	$0.294137\pi$
$74$	−5.57704	−	5.57704i	−0.648318	−	0.648318i
$75$	0.360483	+	0.360483i	0.0416250	+	0.0416250i
$76$			6.45336i			0.740252i
$77$		−	11.5321i		−	1.31420i
$78$	−1.90536	−	1.90536i	−0.215740	−	0.215740i
$79$	5.21466	+	5.21466i	0.586695	+	0.586695i	0.936735	−	0.350040i	$-0.113832\pi$
$79$	5.21466	+	5.21466i	0.586695	+	0.586695i	−0.350040	+	0.936735i	$0.613832\pi$
$80$	1.65979	−	1.65979i	0.185570	−	0.185570i
$81$	−1.00000			−0.111111
$82$	−2.42804	+	2.42804i	−0.268132	+	0.268132i
$83$			3.21213i			0.352577i	0.984338	+	0.176289i	$0.0564092\pi$
$83$			3.21213i			0.352577i	−0.984338	+	0.176289i	$0.943591\pi$
$84$	4.06418			0.443438
$85$		0			0
$86$	11.6459			1.25581
$87$			8.70233i			0.932988i
$88$	2.00641	−	2.00641i	0.213884	−	0.213884i
$89$	6.34049			0.672091			0.336045	−	0.941846i	$-0.390910\pi$
$89$	6.34049			0.672091			0.336045	+	0.941846i	$0.390910\pi$
$90$	−1.65979	+	1.65979i	−0.174957	+	0.174957i
$91$	−7.74374	−	7.74374i	−0.811765	−	0.811765i
$92$	4.24264	+	4.24264i	0.442326	+	0.442326i
$93$		−	0.573978i		−	0.0595187i
$94$		−	10.5817i		−	1.09142i
$95$	−10.7112	−	10.7112i	−1.09895	−	1.09895i
$96$	0.707107	+	0.707107i	0.0721688	+	0.0721688i
$97$	5.73733	−	5.73733i	0.582537	−	0.582537i	−0.353062	−	0.935600i	$-0.614860\pi$
$97$	5.73733	−	5.73733i	0.582537	−	0.582537i	0.935600	+	0.353062i	$0.114860\pi$
$98$	9.51754			0.961417
$99$	−2.00641	+	2.00641i	−0.201652	+	0.201652i
$100$			0.509800i			0.0509800i
$101$	−9.17024			−0.912473			−0.456237	−	0.889858i	$-0.650803\pi$
$101$	−9.17024			−0.912473			−0.456237	+	0.889858i	$0.650803\pi$
$102$		0			0
$103$	−7.35235			−0.724448			−0.362224	−	0.932091i	$-0.617983\pi$
$103$	−7.35235			−0.724448			−0.362224	+	0.932091i	$0.617983\pi$
$104$		−	2.69459i		−	0.264227i
$105$	−6.74568	+	6.74568i	−0.658311	+	0.658311i
$106$	−3.29086			−0.319637
$107$	−3.55487	+	3.55487i	−0.343662	+	0.343662i	−0.857742	−	0.514080i	$-0.828133\pi$
$107$	−3.55487	+	3.55487i	−0.343662	+	0.343662i	0.514080	+	0.857742i	$0.328133\pi$
$108$	−0.707107	−	0.707107i	−0.0680414	−	0.0680414i
$109$	−6.40934	−	6.40934i	−0.613904	−	0.613904i	0.330057	−	0.943961i	$-0.392932\pi$
$109$	−6.40934	−	6.40934i	−0.613904	−	0.613904i	−0.943961	+	0.330057i	$0.892932\pi$
$110$			6.66044i			0.635048i
$111$			7.88713i			0.748613i
$112$	2.87381	+	2.87381i	0.271549	+	0.271549i
$113$	−7.88280	−	7.88280i	−0.741551	−	0.741551i	0.231325	−	0.972876i	$-0.425694\pi$
$113$	−7.88280	−	7.88280i	−0.741551	−	0.741551i	−0.972876	+	0.231325i	$0.925694\pi$
$114$	4.56322	−	4.56322i	0.427384	−	0.427384i
$115$	−14.0838			−1.31332
$116$	−6.15348	+	6.15348i	−0.571336	+	0.571336i
$117$			2.69459i			0.249115i
$118$	−4.34730			−0.400201
$119$		0			0
$120$	−2.34730			−0.214278
$121$		−	2.94862i		−	0.268056i
$122$	−9.23777	+	9.23777i	−0.836348	+	0.836348i
$123$	3.43376			0.309612
$124$	0.405864	−	0.405864i	0.0364476	−	0.0364476i
$125$	7.45279	+	7.45279i	0.666597	+	0.666597i
$126$	−2.87381	−	2.87381i	−0.256019	−	0.256019i
$127$			1.93582i			0.171776i	0.996305	+	0.0858882i	$0.0273728\pi$
$127$			1.93582i			0.171776i	−0.996305	+	0.0858882i	$0.972627\pi$
$128$			1.00000i			0.0883883i
$129$	−8.23489	−	8.23489i	−0.725042	−	0.725042i
$130$	4.47246	+	4.47246i	0.392260	+	0.392260i
$131$	11.8297	−	11.8297i	1.03356	−	1.03356i	0.0341459	−	0.999417i	$-0.489129\pi$
$131$	11.8297	−	11.8297i	1.03356	−	1.03356i	0.999417	−	0.0341459i	$-0.0108711\pi$
$132$	−2.83750			−0.246972
$133$	18.5457	−	18.5457i	1.60812	−	1.60812i
$134$		−	12.2121i		−	1.05497i
$135$	2.34730			0.202023
$136$		0			0
$137$	4.45336			0.380476			0.190238	−	0.981738i	$-0.439074\pi$
$137$	4.45336			0.380476			0.190238	+	0.981738i	$0.439074\pi$
$138$		−	6.00000i		−	0.510754i
$139$	9.00795	−	9.00795i	0.764045	−	0.764045i	−0.213006	−	0.977051i	$-0.568325\pi$
$139$	9.00795	−	9.00795i	0.764045	−	0.764045i	0.977051	+	0.213006i	$0.0683255\pi$
$140$	−9.53983			−0.806263
$141$	−7.48241	+	7.48241i	−0.630132	+	0.630132i
$142$	−8.20337	−	8.20337i	−0.688412	−	0.688412i
$143$	5.40647	+	5.40647i	0.452111	+	0.452111i
$144$		−	1.00000i		−	0.0833333i
$145$		−	20.4270i		−	1.69637i
$146$	1.67008	+	1.67008i	0.138216	+	0.138216i
$147$	−6.72992	−	6.72992i	−0.555074	−	0.555074i
$148$	−5.57704	+	5.57704i	−0.458430	+	0.458430i
$149$	−19.2909			−1.58037			−0.790184	−	0.612869i	$-0.790015\pi$
$149$	−19.2909			−1.58037			−0.790184	+	0.612869i	$0.790015\pi$
$150$	0.360483	−	0.360483i	0.0294333	−	0.0294333i
$151$			13.0787i			1.06433i	0.846640	+	0.532166i	$0.178622\pi$
$151$			13.0787i			1.06433i	−0.846640	+	0.532166i	$0.821378\pi$
$152$	6.45336			0.523437
$153$		0			0
$154$	−11.5321			−0.929282
$155$			1.34730i			0.108217i
$156$	−1.90536	+	1.90536i	−0.152551	+	0.152551i
$157$	−10.1284			−0.808331			−0.404165	−	0.914686i	$-0.632438\pi$
$157$	−10.1284			−0.808331			−0.404165	+	0.914686i	$0.632438\pi$
$158$	5.21466	−	5.21466i	0.414856	−	0.414856i
$159$	2.32699	+	2.32699i	0.184542	+	0.184542i
$160$	−1.65979	−	1.65979i	−0.131218	−	0.131218i
$161$		−	24.3851i		−	1.92181i
$162$			1.00000i			0.0785674i
$163$	0.150001	+	0.150001i	0.0117490	+	0.0117490i	0.712957	−	0.701208i	$-0.247356\pi$
$163$	0.150001	+	0.150001i	0.0117490	+	0.0117490i	−0.701208	+	0.712957i	$0.747356\pi$
$164$	2.42804	+	2.42804i	0.189598	+	0.189598i
$165$	4.70965	−	4.70965i	0.366645	−	0.366645i
$166$	3.21213			0.249310
$167$	−6.00895	+	6.00895i	−0.464987	+	0.464987i	−0.900286	−	0.435299i	$-0.856643\pi$
$167$	−6.00895	+	6.00895i	−0.464987	+	0.464987i	0.435299	+	0.900286i	$0.356643\pi$
$168$		−	4.06418i		−	0.313558i
$169$	−5.73917			−0.441475
$170$		0			0
$171$	−6.45336			−0.493501
$172$		−	11.6459i		−	0.887991i
$173$	−0.160288	+	0.160288i	−0.0121865	+	0.0121865i	−0.713174	−	0.700987i	$-0.752743\pi$
$173$	−0.160288	+	0.160288i	−0.0121865	+	0.0121865i	0.700987	+	0.713174i	$0.252743\pi$
$174$	8.70233			0.659722
$175$	1.46507	−	1.46507i	0.110749	−	0.110749i
$176$	−2.00641	−	2.00641i	−0.151239	−	0.151239i
$177$	3.07400	+	3.07400i	0.231056	+	0.231056i
$178$		−	6.34049i		−	0.475240i
$179$		−	11.6946i		−	0.874095i	−0.899438	−	0.437047i	$-0.856024\pi$
$179$		−	11.6946i		−	0.874095i	0.899438	−	0.437047i	$-0.143976\pi$
$180$	1.65979	+	1.65979i	0.123713	+	0.123713i
$181$	−1.76631	−	1.76631i	−0.131289	−	0.131289i	0.638409	−	0.769698i	$-0.279593\pi$
$181$	−1.76631	−	1.76631i	−0.131289	−	0.131289i	−0.769698	+	0.638409i	$0.779593\pi$
$182$	−7.74374	+	7.74374i	−0.574004	+	0.574004i
$183$	13.0642			0.965732
$184$	4.24264	−	4.24264i	0.312772	−	0.312772i
$185$		−	18.5134i		−	1.36113i
$186$	−0.573978			−0.0420861
$187$		0			0
$188$	−10.5817			−0.771751
$189$			4.06418i			0.295625i
$190$	−10.7112	+	10.7112i	−0.777074	+	0.777074i
$191$	2.73917			0.198199			0.0990997	−	0.995078i	$-0.468404\pi$
$191$	2.73917			0.198199			0.0990997	+	0.995078i	$0.468404\pi$
$192$	0.707107	−	0.707107i	0.0510310	−	0.0510310i
$193$	−9.37201	−	9.37201i	−0.674612	−	0.674612i	0.284164	−	0.958776i	$-0.408284\pi$
$193$	−9.37201	−	9.37201i	−0.674612	−	0.674612i	−0.958776	+	0.284164i	$0.908284\pi$
$194$	−5.73733	−	5.73733i	−0.411916	−	0.411916i
$195$		−	6.32501i		−	0.452943i
$196$		−	9.51754i		−	0.679824i
$197$	16.2744	+	16.2744i	1.15950	+	1.15950i	0.984583	+	0.174921i	$0.0559669\pi$
$197$	16.2744	+	16.2744i	1.15950	+	1.15950i	0.174921	+	0.984583i	$0.444033\pi$
$198$	2.00641	+	2.00641i	0.142590	+	0.142590i
$199$	−12.8139	+	12.8139i	−0.908351	+	0.908351i	−0.996139	−	0.0877880i	$-0.972020\pi$
$199$	−12.8139	+	12.8139i	−0.908351	+	0.908351i	0.0877880	+	0.996139i	$0.472020\pi$
$200$	0.509800			0.0360483
$201$	−8.63528	+	8.63528i	−0.609086	+	0.609086i
$202$			9.17024i			0.645216i
$203$	35.3678			2.48234
$204$		0			0
$205$	−8.06006			−0.562939
$206$			7.35235i			0.512262i
$207$	−4.24264	+	4.24264i	−0.294884	+	0.294884i
$208$	−2.69459			−0.186836
$209$	−12.9481	+	12.9481i	−0.895640	+	0.895640i
$210$	6.74568	+	6.74568i	0.465496	+	0.465496i
$211$	11.0041	+	11.0041i	0.757552	+	0.757552i	0.975876	−	0.218324i	$-0.0700590\pi$
$211$	11.0041	+	11.0041i	0.757552	+	0.757552i	−0.218324	+	0.975876i	$0.570059\pi$
$212$			3.29086i			0.226017i
$213$			11.6013i			0.794909i
$214$	3.55487	+	3.55487i	0.243006	+	0.243006i
$215$	19.3297	+	19.3297i	1.31828	+	1.31828i
$216$	−0.707107	+	0.707107i	−0.0481125	+	0.0481125i
$217$	−2.33275			−0.158357
$218$	−6.40934	+	6.40934i	−0.434095	+	0.434095i
$219$		−	2.36184i		−	0.159599i
$220$	6.66044			0.449047
$221$		0			0
$222$	7.88713			0.529349
$223$			13.3063i			0.891058i	0.895267	+	0.445529i	$0.146984\pi$
$223$			13.3063i			0.891058i	−0.895267	+	0.445529i	$0.853016\pi$
$224$	2.87381	−	2.87381i	0.192014	−	0.192014i
$225$	−0.509800			−0.0339867
$226$	−7.88280	+	7.88280i	−0.524356	+	0.524356i
$227$	2.61247	+	2.61247i	0.173396	+	0.173396i	0.788470	−	0.615074i	$-0.210874\pi$
$227$	2.61247	+	2.61247i	0.173396	+	0.173396i	−0.615074	+	0.788470i	$0.710874\pi$
$228$	−4.56322	−	4.56322i	−0.302206	−	0.302206i
$229$		−	8.85204i		−	0.584960i	−0.956272	−	0.292480i	$-0.905520\pi$
$229$		−	8.85204i		−	0.584960i	0.956272	−	0.292480i	$-0.0944804\pi$
$230$			14.0838i			0.928657i
$231$	8.15442	+	8.15442i	0.536521	+	0.536521i
$232$	6.15348	+	6.15348i	0.403996	+	0.403996i
$233$	−4.16283	+	4.16283i	−0.272716	+	0.272716i	−0.830193	−	0.557477i	$-0.811770\pi$
$233$	−4.16283	+	4.16283i	−0.272716	+	0.272716i	0.557477	+	0.830193i	$0.311770\pi$
$234$	2.69459			0.176151
$235$	17.5634	−	17.5634i	1.14571	−	1.14571i
$236$			4.34730i			0.282985i
$237$	−7.37464			−0.479034
$238$		0			0
$239$	16.6108			1.07446			0.537232	−	0.843434i	$-0.319470\pi$
$239$	16.6108			1.07446			0.537232	+	0.843434i	$0.319470\pi$
$240$			2.34730i			0.151517i
$241$	6.02091	−	6.02091i	0.387841	−	0.387841i	−0.486076	−	0.873917i	$-0.661572\pi$
$241$	6.02091	−	6.02091i	0.387841	−	0.387841i	0.873917	+	0.486076i	$0.161572\pi$
$242$	−2.94862			−0.189544
$243$	0.707107	−	0.707107i	0.0453609	−	0.0453609i
$244$	9.23777	+	9.23777i	0.591388	+	0.591388i
$245$	15.7971	+	15.7971i	1.00924	+	1.00924i
$246$		−	3.43376i		−	0.218929i
$247$			17.3892i			1.10645i
$248$	−0.405864	−	0.405864i	−0.0257724	−	0.0257724i
$249$	−2.27132	−	2.27132i	−0.143939	−	0.143939i
$250$	7.45279	−	7.45279i	0.471356	−	0.471356i
$251$	6.89899			0.435460			0.217730	−	0.976009i	$-0.430135\pi$
$251$	6.89899			0.435460			0.217730	+	0.976009i	$0.430135\pi$
$252$	−2.87381	+	2.87381i	−0.181033	+	0.181033i
$253$			17.0250i			1.07035i
$254$	1.93582			0.121464
$255$		0			0
$256$	1.00000			0.0625000
$257$			22.5526i			1.40679i	0.710797	+	0.703397i	$0.248334\pi$
$257$			22.5526i			1.40679i	−0.710797	+	0.703397i	$0.751666\pi$
$258$	−8.23489	+	8.23489i	−0.512682	+	0.512682i
$259$	32.0547			1.99178
$260$	4.47246	−	4.47246i	0.277370	−	0.277370i
$261$	−6.15348	−	6.15348i	−0.380891	−	0.380891i
$262$	−11.8297	−	11.8297i	−0.730839	−	0.730839i
$263$			16.9513i			1.04526i	0.852559	+	0.522631i	$0.175049\pi$
$263$			16.9513i			1.04526i	−0.852559	+	0.522631i	$0.824951\pi$
$264$			2.83750i			0.174636i
$265$	−5.46213	−	5.46213i	−0.335536	−	0.335536i
$266$	−18.5457	−	18.5457i	−1.13711	−	1.13711i
$267$	−4.48340	+	4.48340i	−0.274380	+	0.274380i
$268$	−12.2121			−0.745975
$269$	−7.64269	+	7.64269i	−0.465983	+	0.465983i	−0.900610	−	0.434627i	$-0.856880\pi$
$269$	−7.64269	+	7.64269i	−0.465983	+	0.465983i	0.434627	+	0.900610i	$0.356880\pi$
$270$		−	2.34730i		−	0.142852i
$271$	−21.3131			−1.29468			−0.647341	−	0.762201i	$-0.724119\pi$
$271$	−21.3131			−1.29468			−0.647341	+	0.762201i	$0.724119\pi$
$272$		0			0
$273$	10.9513			0.662803
$274$		−	4.45336i		−	0.269038i
$275$	−1.02287	+	1.02287i	−0.0616814	+	0.0616814i
$276$	−6.00000			−0.361158
$277$	15.6581	−	15.6581i	0.940801	−	0.940801i	−0.0575416	−	0.998343i	$-0.518326\pi$
$277$	15.6581	−	15.6581i	0.940801	−	0.940801i	0.998343	+	0.0575416i	$0.0183262\pi$
$278$	−9.00795	−	9.00795i	−0.540261	−	0.540261i
$279$	0.405864	+	0.405864i	0.0242984	+	0.0242984i
$280$			9.53983i			0.570114i
$281$			10.0155i			0.597474i	0.954336	+	0.298737i	$0.0965653\pi$
$281$			10.0155i			0.597474i	−0.954336	+	0.298737i	$0.903435\pi$
$282$	7.48241	+	7.48241i	0.445571	+	0.445571i
$283$	7.13031	+	7.13031i	0.423853	+	0.423853i	0.886528	−	0.462675i	$-0.153110\pi$
$283$	7.13031	+	7.13031i	0.423853	+	0.423853i	−0.462675	+	0.886528i	$0.653110\pi$
$284$	−8.20337	+	8.20337i	−0.486781	+	0.486781i
$285$	15.1480			0.897287
$286$	5.40647	−	5.40647i	0.319691	−	0.319691i
$287$		−	13.9554i		−	0.823763i
$288$	−1.00000			−0.0589256
$289$		0			0
$290$	−20.4270			−1.19951
$291$			8.11381i			0.475640i
$292$	1.67008	−	1.67008i	0.0977338	−	0.0977338i
$293$	14.5594			0.850571			0.425285	−	0.905059i	$-0.360174\pi$
$293$	14.5594			0.850571			0.425285	+	0.905059i	$0.360174\pi$
$294$	−6.72992	+	6.72992i	−0.392497	+	0.392497i
$295$	−7.21560	−	7.21560i	−0.420108	−	0.420108i
$296$	5.57704	+	5.57704i	0.324159	+	0.324159i
$297$		−	2.83750i		−	0.164648i
$298$			19.2909i			1.11749i
$299$	11.4322	+	11.4322i	0.661141	+	0.661141i
$300$	−0.360483	−	0.360483i	−0.0208125	−	0.0208125i
$301$	−33.4681	+	33.4681i	−1.92907	+	1.92907i
$302$	13.0787			0.752596
$303$	6.48434	−	6.48434i	0.372516	−	0.372516i
$304$		−	6.45336i		−	0.370126i
$305$	−30.6655			−1.75590
$306$		0			0
$307$	−19.6459			−1.12125			−0.560625	−	0.828070i	$-0.689439\pi$
$307$	−19.6459			−1.12125			−0.560625	+	0.828070i	$0.689439\pi$
$308$			11.5321i			0.657102i
$309$	5.19890	−	5.19890i	0.295755	−	0.295755i
$310$	1.34730			0.0765213
$311$	10.0810	−	10.0810i	0.571642	−	0.571642i	−0.360945	−	0.932587i	$-0.617546\pi$
$311$	10.0810	−	10.0810i	0.571642	−	0.571642i	0.932587	+	0.360945i	$0.117546\pi$
$312$	1.90536	+	1.90536i	0.107870	+	0.107870i
$313$	14.8740	+	14.8740i	0.840731	+	0.840731i	0.988954	−	0.148223i	$-0.0473553\pi$
$313$	14.8740	+	14.8740i	0.840731	+	0.840731i	−0.148223	+	0.988954i	$0.547355\pi$
$314$			10.1284i			0.571576i
$315$		−	9.53983i		−	0.537509i
$316$	−5.21466	−	5.21466i	−0.293347	−	0.293347i
$317$	4.04726	+	4.04726i	0.227317	+	0.227317i	0.811571	−	0.584254i	$-0.198613\pi$
$317$	4.04726	+	4.04726i	0.227317	+	0.227317i	−0.584254	+	0.811571i	$0.698613\pi$
$318$	2.32699	−	2.32699i	0.130491	−	0.130491i
$319$	−24.6928			−1.38253
$320$	−1.65979	+	1.65979i	−0.0927850	+	0.0927850i
$321$		−	5.02734i		−	0.280599i
$322$	−24.3851			−1.35893
$323$		0			0
$324$	1.00000			0.0555556
$325$			1.37370i			0.0761994i
$326$	0.150001	−	0.150001i	0.00830780	−	0.00830780i
$327$	9.06418			0.501250
$328$	2.42804	−	2.42804i	0.134066	−	0.134066i
$329$	30.4098	+	30.4098i	1.67655	+	1.67655i
$330$	−4.70965	−	4.70965i	−0.259257	−	0.259257i
$331$		−	3.14796i		−	0.173027i	−0.996251	−	0.0865137i	$-0.972427\pi$
$331$		−	3.14796i		−	0.173027i	0.996251	−	0.0865137i	$-0.0275726\pi$
$332$		−	3.21213i		−	0.176289i
$333$	−5.57704	−	5.57704i	−0.305620	−	0.305620i
$334$	6.00895	+	6.00895i	0.328795	+	0.328795i
$335$	20.2696	−	20.2696i	1.10744	−	1.10744i
$336$	−4.06418			−0.221719
$337$	−22.5834	+	22.5834i	−1.23019	+	1.23019i	−0.266305	+	0.963889i	$0.585803\pi$
$337$	−22.5834	+	22.5834i	−1.23019	+	1.23019i	−0.963889	+	0.266305i	$0.914197\pi$
$338$			5.73917i			0.312170i
$339$	11.1480			0.605474
$340$		0			0
$341$	1.62866			0.0881969
$342$			6.45336i			0.348958i
$343$	−7.23493	+	7.23493i	−0.390649	+	0.390649i
$344$	−11.6459			−0.627905
$345$	9.95874	−	9.95874i	0.536160	−	0.536160i
$346$	0.160288	+	0.160288i	0.00861714	+	0.00861714i
$347$	−25.5418	−	25.5418i	−1.37116	−	1.37116i	−0.858735	−	0.512421i	$-0.828749\pi$
$347$	−25.5418	−	25.5418i	−1.37116	−	1.37116i	−0.512421	−	0.858735i	$-0.671251\pi$
$348$		−	8.70233i		−	0.466494i
$349$		−	12.7493i		−	0.682453i	−0.939981	−	0.341227i	$-0.889158\pi$
$349$		−	12.7493i		−	0.682453i	0.939981	−	0.341227i	$-0.110842\pi$
$350$	−1.46507	−	1.46507i	−0.0783112	−	0.0783112i
$351$	−1.90536	−	1.90536i	−0.101701	−	0.101701i
$352$	−2.00641	+	2.00641i	−0.106942	+	0.106942i
$353$	7.09327			0.377537			0.188768	−	0.982022i	$-0.439550\pi$
$353$	7.09327			0.377537			0.188768	+	0.982022i	$0.439550\pi$
$354$	3.07400	−	3.07400i	0.163381	−	0.163381i
$355$		−	27.2317i		−	1.44531i
$356$	−6.34049			−0.336045
$357$		0			0
$358$	−11.6946			−0.618078
$359$			10.6655i			0.562903i	0.959575	+	0.281452i	$0.0908159\pi$
$359$			10.6655i			0.562903i	−0.959575	+	0.281452i	$0.909184\pi$
$360$	1.65979	−	1.65979i	0.0874786	−	0.0874786i
$361$	−22.6459			−1.19189
$362$	−1.76631	+	1.76631i	−0.0928352	+	0.0928352i
$363$	2.08499	+	2.08499i	0.109433	+	0.109433i
$364$	7.74374	+	7.74374i	0.405882	+	0.405882i
$365$			5.54395i			0.290184i
$366$		−	13.0642i		−	0.682876i
$367$	−17.1473	−	17.1473i	−0.895080	−	0.895080i	0.0999156	−	0.994996i	$-0.468143\pi$
$367$	−17.1473	−	17.1473i	−0.895080	−	0.895080i	−0.994996	+	0.0999156i	$0.968143\pi$
$368$	−4.24264	−	4.24264i	−0.221163	−	0.221163i
$369$	−2.42804	+	2.42804i	−0.126399	+	0.126399i
$370$	−18.5134			−0.962467
$371$	9.45730	−	9.45730i	0.490998	−	0.490998i
$372$			0.573978i			0.0297594i
$373$	−22.7547			−1.17819			−0.589096	−	0.808063i	$-0.700516\pi$
$373$	−22.7547			−1.17819			−0.589096	+	0.808063i	$0.700516\pi$
$374$		0			0
$375$	−10.5398			−0.544274
$376$			10.5817i			0.545710i
$377$	−16.5811	+	16.5811i	−0.853971	+	0.853971i
$378$	4.06418			0.209039
$379$	14.0308	−	14.0308i	0.720714	−	0.720714i	−0.248037	−	0.968751i	$-0.579785\pi$
$379$	14.0308	−	14.0308i	0.720714	−	0.720714i	0.968751	+	0.248037i	$0.0797854\pi$
$380$	10.7112	+	10.7112i	0.549474	+	0.549474i
$381$	−1.36883	−	1.36883i	−0.0701274	−	0.0701274i
$382$		−	2.73917i		−	0.140148i
$383$			15.7196i			0.803232i	0.915808	+	0.401616i	$0.131551\pi$
$383$			15.7196i			0.803232i	−0.915808	+	0.401616i	$0.868449\pi$
$384$	−0.707107	−	0.707107i	−0.0360844	−	0.0360844i
$385$	−19.1408	−	19.1408i	−0.975507	−	0.975507i
$386$	−9.37201	+	9.37201i	−0.477023	+	0.477023i
$387$	11.6459			0.591994
$388$	−5.73733	+	5.73733i	−0.291269	+	0.291269i
$389$			32.4766i			1.64663i	0.567586	+	0.823314i	$0.307877\pi$
$389$			32.4766i			1.64663i	−0.567586	+	0.823314i	$0.692123\pi$
$390$	−6.32501			−0.320279
$391$		0			0
$392$	−9.51754			−0.480708
$393$			16.7297i			0.843900i
$394$	16.2744	−	16.2744i	0.819893	−	0.819893i
$395$	17.3105			0.870984
$396$	2.00641	−	2.00641i	0.100826	−	0.100826i
$397$	−1.30288	−	1.30288i	−0.0653896	−	0.0653896i	0.673656	−	0.739045i	$-0.264723\pi$
$397$	−1.30288	−	1.30288i	−0.0653896	−	0.0653896i	−0.739045	+	0.673656i	$0.764723\pi$
$398$	12.8139	+	12.8139i	0.642301	+	0.642301i
$399$			26.2276i			1.31302i
$400$		−	0.509800i		−	0.0254900i
$401$	7.54165	+	7.54165i	0.376612	+	0.376612i	0.869878	−	0.493266i	$-0.164197\pi$
$401$	7.54165	+	7.54165i	0.376612	+	0.376612i	−0.493266	+	0.869878i	$0.664197\pi$
$402$	8.63528	+	8.63528i	0.430689	+	0.430689i
$403$	1.09364	−	1.09364i	0.0544780	−	0.0544780i
$404$	9.17024			0.456237
$405$	−1.65979	+	1.65979i	−0.0824756	+	0.0824756i
$406$		−	35.3678i		−	1.75528i
$407$	−22.3797			−1.10932
$408$		0			0
$409$	−5.33544			−0.263820			−0.131910	−	0.991262i	$-0.542111\pi$
$409$	−5.33544			−0.263820			−0.131910	+	0.991262i	$0.542111\pi$
$410$			8.06006i			0.398058i
$411$	−3.14900	+	3.14900i	−0.155329	+	0.155329i
$412$	7.35235			0.362224
$413$	12.4933	−	12.4933i	0.614755	−	0.614755i
$414$	4.24264	+	4.24264i	0.208514	+	0.208514i
$415$	5.33146	+	5.33146i	0.261711	+	0.261711i
$416$			2.69459i			0.132113i
$417$			12.7392i			0.623840i
$418$	12.9481	+	12.9481i	0.633313	+	0.633313i
$419$	17.3977	+	17.3977i	0.849931	+	0.849931i	0.990124	−	0.140193i	$-0.0447723\pi$
$419$	17.3977	+	17.3977i	0.849931	+	0.849931i	−0.140193	+	0.990124i	$0.544772\pi$
$420$	6.74568	−	6.74568i	0.329155	−	0.329155i
$421$	2.89662			0.141173			0.0705863	−	0.997506i	$-0.477513\pi$
$421$	2.89662			0.141173			0.0705863	+	0.997506i	$0.477513\pi$
$422$	11.0041	−	11.0041i	0.535670	−	0.535670i
$423$		−	10.5817i		−	0.514501i
$424$	3.29086			0.159818
$425$		0			0
$426$	11.6013			0.562086
$427$		−	53.0951i		−	2.56945i
$428$	3.55487	−	3.55487i	0.171831	−	0.171831i
$429$	−7.64590			−0.369147
$430$	19.3297	−	19.3297i	0.932162	−	0.932162i
$431$	5.77914	+	5.77914i	0.278371	+	0.278371i	0.832459	−	0.554087i	$-0.186933\pi$
$431$	5.77914	+	5.77914i	0.278371	+	0.278371i	−0.554087	+	0.832459i	$0.686933\pi$
$432$	0.707107	+	0.707107i	0.0340207	+	0.0340207i
$433$			21.7365i			1.04459i	0.852765	+	0.522294i	$0.174924\pi$
$433$			21.7365i			1.04459i	−0.852765	+	0.522294i	$0.825076\pi$
$434$			2.33275i			0.111976i
$435$	14.4440	+	14.4440i	0.692539	+	0.692539i
$436$	6.40934	+	6.40934i	0.306952	+	0.306952i
$437$	−27.3793	+	27.3793i	−1.30973	+	1.30973i
$438$	−2.36184			−0.112853
$439$	−7.96261	+	7.96261i	−0.380035	+	0.380035i	−0.871115	−	0.491080i	$-0.836602\pi$
$439$	−7.96261	+	7.96261i	−0.380035	+	0.380035i	0.491080	+	0.871115i	$0.336602\pi$
$440$		−	6.66044i		−	0.317524i
$441$	9.51754			0.453216
$442$		0			0
$443$	−22.4730			−1.06772			−0.533861	−	0.845572i	$-0.679260\pi$
$443$	−22.4730			−1.06772			−0.533861	+	0.845572i	$0.679260\pi$
$444$		−	7.88713i		−	0.374306i
$445$	10.5239	−	10.5239i	0.498880	−	0.498880i
$446$	13.3063			0.630074
$447$	13.6407	−	13.6407i	0.645183	−	0.645183i
$448$	−2.87381	−	2.87381i	−0.135775	−	0.135775i
$449$	−6.58706	−	6.58706i	−0.310863	−	0.310863i	0.534381	−	0.845244i	$-0.320545\pi$
$449$	−6.58706	−	6.58706i	−0.310863	−	0.310863i	−0.845244	+	0.534381i	$0.820545\pi$
$450$			0.509800i			0.0240322i
$451$			9.74329i			0.458794i
$452$	7.88280	+	7.88280i	0.370775	+	0.370775i
$453$	−9.24806	−	9.24806i	−0.434512	−	0.434512i
$454$	2.61247	−	2.61247i	0.122609	−	0.122609i
$455$	−25.7060			−1.20511
$456$	−4.56322	+	4.56322i	−0.213692	+	0.213692i
$457$			21.4124i			1.00163i	0.865554	+	0.500815i	$0.166966\pi$
$457$			21.4124i			1.00163i	−0.865554	+	0.500815i	$0.833034\pi$
$458$	−8.85204			−0.413629
$459$		0			0
$460$	14.0838			0.656660
$461$		−	20.6287i		−	0.960772i	−0.877057	−	0.480386i	$-0.840496\pi$
$461$		−	20.6287i		−	0.960772i	0.877057	−	0.480386i	$-0.159504\pi$
$462$	8.15442	−	8.15442i	0.379378	−	0.379378i
$463$	25.6973			1.19425			0.597127	−	0.802147i	$-0.296309\pi$
$463$	25.6973			1.19425			0.597127	+	0.802147i	$0.296309\pi$
$464$	6.15348	−	6.15348i	0.285668	−	0.285668i
$465$	−0.952682	−	0.952682i	−0.0441796	−	0.0441796i
$466$	4.16283	+	4.16283i	0.192839	+	0.192839i
$467$			3.15570i			0.146028i	0.997331	+	0.0730141i	$0.0232618\pi$
$467$			3.15570i			0.146028i	−0.997331	+	0.0730141i	$0.976738\pi$
$468$		−	2.69459i		−	0.124558i
$469$	35.0953	+	35.0953i	1.62055	+	1.62055i
$470$	−17.5634	−	17.5634i	−0.810140	−	0.810140i
$471$	7.16183	−	7.16183i	0.330000	−	0.330000i
$472$	4.34730			0.200101
$473$	23.3665	−	23.3665i	1.07439	−	1.07439i
$474$			7.37464i			0.338728i
$475$	−3.28993			−0.150952
$476$		0			0
$477$	−3.29086			−0.150678
$478$		−	16.6108i		−	0.759761i
$479$	−1.36212	+	1.36212i	−0.0622368	+	0.0622368i	−0.737540	−	0.675303i	$-0.764013\pi$
$479$	−1.36212	+	1.36212i	−0.0622368	+	0.0622368i	0.675303	+	0.737540i	$0.264013\pi$
$480$	2.34730			0.107139
$481$	−15.0279	+	15.0279i	−0.685211	+	0.685211i
$482$	−6.02091	−	6.02091i	−0.274245	−	0.274245i
$483$	17.2428	+	17.2428i	0.784577	+	0.784577i
$484$			2.94862i			0.134028i
$485$		−	19.0455i		−	0.864812i
$486$	−0.707107	−	0.707107i	−0.0320750	−	0.0320750i
$487$	5.62052	+	5.62052i	0.254690	+	0.254690i	0.822890	−	0.568200i	$-0.192360\pi$
$487$	5.62052	+	5.62052i	0.254690	+	0.254690i	−0.568200	+	0.822890i	$0.692360\pi$
$488$	9.23777	−	9.23777i	0.418174	−	0.418174i
$489$	−0.212134			−0.00959302
$490$	15.7971	−	15.7971i	0.713641	−	0.713641i
$491$			5.25402i			0.237111i	0.992947	+	0.118555i	$0.0378263\pi$
$491$			5.25402i			0.237111i	−0.992947	+	0.118555i	$0.962174\pi$
$492$	−3.43376			−0.154806
$493$		0			0
$494$	17.3892			0.782376
$495$			6.66044i			0.299365i
$496$	−0.405864	+	0.405864i	−0.0182238	+	0.0182238i
$497$	47.1498			2.11496
$498$	−2.27132	+	2.27132i	−0.101780	+	0.101780i
$499$	17.5911	+	17.5911i	0.787488	+	0.787488i	0.981082	−	0.193594i	$-0.0620145\pi$
$499$	17.5911	+	17.5911i	0.787488	+	0.787488i	−0.193594	+	0.981082i	$0.562014\pi$
$500$	−7.45279	−	7.45279i	−0.333299	−	0.333299i
$501$		−	8.49794i		−	0.379660i
$502$		−	6.89899i		−	0.307917i
$503$	−7.73279	−	7.73279i	−0.344788	−	0.344788i	0.513376	−	0.858164i	$-0.328395\pi$
$503$	−7.73279	−	7.73279i	−0.344788	−	0.344788i	−0.858164	+	0.513376i	$0.828395\pi$
$504$	2.87381	+	2.87381i	0.128010	+	0.128010i
$505$	−15.2207	+	15.2207i	−0.677311	+	0.677311i
$506$	17.0250			0.756853
$507$	4.05821	−	4.05821i	0.180231	−	0.180231i
$508$		−	1.93582i		−	0.0858882i
$509$	38.4219			1.70302			0.851510	−	0.524338i	$-0.175687\pi$
$509$	38.4219			1.70302			0.851510	+	0.524338i	$0.175687\pi$
$510$		0			0
$511$	−9.59896			−0.424633
$512$		−	1.00000i		−	0.0441942i
$513$	4.56322	−	4.56322i	0.201471	−	0.201471i
$514$	22.5526			0.994754
$515$	−12.2033	+	12.2033i	−0.537744	+	0.537744i
$516$	8.23489	+	8.23489i	0.362521	+	0.362521i
$517$	−21.2313	−	21.2313i	−0.933751	−	0.933751i
$518$		−	32.0547i		−	1.40840i
$519$		−	0.226682i		−	0.00995022i
$520$	−4.47246	−	4.47246i	−0.196130	−	0.196130i
$521$	−22.0745	−	22.0745i	−0.967103	−	0.967103i	0.0323725	−	0.999476i	$-0.489694\pi$
$521$	−22.0745	−	22.0745i	−0.967103	−	0.967103i	−0.999476	+	0.0323725i	$0.989694\pi$
$522$	−6.15348	+	6.15348i	−0.269330	+	0.269330i
$523$	17.5567			0.767703			0.383851	−	0.923395i	$-0.374598\pi$
$523$	17.5567			0.767703			0.383851	+	0.923395i	$0.374598\pi$
$524$	−11.8297	+	11.8297i	−0.516781	+	0.516781i
$525$			2.07192i			0.0904259i
$526$	16.9513			0.739112
$527$		0			0
$528$	2.83750			0.123486
$529$			13.0000i			0.565217i
$530$	−5.46213	+	5.46213i	−0.237260	+	0.237260i
$531$	−4.34730			−0.188657
$532$	−18.5457	+	18.5457i	−0.804059	+	0.804059i
$533$	6.54257	+	6.54257i	0.283390	+	0.283390i
$534$	4.48340	+	4.48340i	0.194016	+	0.194016i
$535$			11.8007i			0.510187i
$536$			12.2121i			0.527484i
$537$	8.26933	+	8.26933i	0.356848	+	0.356848i
$538$	7.64269	+	7.64269i	0.329500	+	0.329500i
$539$	19.0961	−	19.0961i	0.822528	−	0.822528i
$540$	−2.34730			−0.101012
$541$	7.55127	−	7.55127i	0.324655	−	0.324655i	−0.525895	−	0.850550i	$-0.676270\pi$
$541$	7.55127	−	7.55127i	0.324655	−	0.324655i	0.850550	+	0.525895i	$0.176270\pi$
$542$			21.3131i			0.915478i
$543$	2.49794			0.107197
$544$		0			0
$545$	−21.2763			−0.911377
$546$		−	10.9513i		−	0.468673i
$547$	−5.34723	+	5.34723i	−0.228631	+	0.228631i	−0.812121	−	0.583490i	$-0.801687\pi$
$547$	−5.34723	+	5.34723i	−0.228631	+	0.228631i	0.583490	+	0.812121i	$0.301687\pi$
$548$	−4.45336			−0.190238
$549$	−9.23777	+	9.23777i	−0.394258	+	0.394258i
$550$	1.02287	+	1.02287i	0.0436153	+	0.0436153i
$551$	−39.7106	−	39.7106i	−1.69173	−	1.69173i
$552$			6.00000i			0.255377i
$553$			29.9718i			1.27453i
$554$	−15.6581	−	15.6581i	−0.665247	−	0.665247i
$555$	13.0910	+	13.0910i	0.555681	+	0.555681i
$556$	−9.00795	+	9.00795i	−0.382022	+	0.382022i
$557$	13.9222			0.589903			0.294951	−	0.955512i	$-0.404697\pi$
$557$	13.9222			0.589903			0.294951	+	0.955512i	$0.404697\pi$
$558$	0.405864	−	0.405864i	0.0171816	−	0.0171816i
$559$		−	31.3809i		−	1.32727i
$560$	9.53983			0.403131
$561$		0			0
$562$	10.0155			0.422478
$563$		−	2.71595i		−	0.114464i	−0.998361	−	0.0572318i	$-0.981773\pi$
$563$		−	2.71595i		−	0.114464i	0.998361	−	0.0572318i	$-0.0182274\pi$
$564$	7.48241	−	7.48241i	0.315066	−	0.315066i
$565$	−26.1676			−1.10088
$566$	7.13031	−	7.13031i	0.299709	−	0.299709i
$567$	−2.87381	−	2.87381i	−0.120689	−	0.120689i
$568$	8.20337	+	8.20337i	0.344206	+	0.344206i
$569$		−	29.8735i		−	1.25236i	−0.779677	−	0.626181i	$-0.784617\pi$
$569$		−	29.8735i		−	1.25236i	0.779677	−	0.626181i	$-0.215383\pi$
$570$		−	15.1480i		−	0.634478i
$571$	23.3703	+	23.3703i	0.978016	+	0.978016i	0.999763	−	0.0217478i	$-0.00692309\pi$
$571$	23.3703	+	23.3703i	0.978016	+	0.978016i	−0.0217478	+	0.999763i	$0.506923\pi$
$572$	−5.40647	−	5.40647i	−0.226056	−	0.226056i
$573$	−1.93689	+	1.93689i	−0.0809146	+	0.0809146i
$574$	−13.9554			−0.582488
$575$	−2.16290	+	2.16290i	−0.0901991	+	0.0901991i
$576$			1.00000i			0.0416667i
$577$	8.96080			0.373043			0.186521	−	0.982451i	$-0.440279\pi$
$577$	8.96080			0.373043			0.186521	+	0.982451i	$0.440279\pi$
$578$		0			0
$579$	13.2540			0.550818
$580$			20.4270i			0.848183i
$581$	−9.23105	+	9.23105i	−0.382969	+	0.382969i
$582$	8.11381			0.336328
$583$	−6.60282	+	6.60282i	−0.273461	+	0.273461i
$584$	−1.67008	−	1.67008i	−0.0691082	−	0.0691082i
$585$	4.47246	+	4.47246i	0.184913	+	0.184913i
$586$		−	14.5594i		−	0.601445i
$587$			12.3919i			0.511467i	0.966747	+	0.255734i	$0.0823170\pi$
$587$			12.3919i			0.511467i	−0.966747	+	0.255734i	$0.917683\pi$
$588$	6.72992	+	6.72992i	0.277537	+	0.277537i
$589$	2.61919	+	2.61919i	0.107922	+	0.107922i
$590$	−7.21560	+	7.21560i	−0.297061	+	0.297061i
$591$	−23.0155			−0.946730
$592$	5.57704	−	5.57704i	0.229215	−	0.229215i
$593$		−	46.4005i		−	1.90544i	−0.303846	−	0.952721i	$-0.598271\pi$
$593$		−	46.4005i		−	1.90544i	0.303846	−	0.952721i	$-0.401729\pi$
$594$	−2.83750			−0.116424
$595$		0			0
$596$	19.2909			0.790184
$597$		−	18.1215i		−	0.741666i
$598$	11.4322	−	11.4322i	0.467497	−	0.467497i
$599$	−19.4492			−0.794675			−0.397337	−	0.917673i	$-0.630066\pi$
$599$	−19.4492			−0.794675			−0.397337	+	0.917673i	$0.630066\pi$
$600$	−0.360483	+	0.360483i	−0.0147167	+	0.0147167i
$601$	22.4623	+	22.4623i	0.916257	+	0.916257i	0.996755	−	0.0804978i	$-0.0256510\pi$
$601$	22.4623	+	22.4623i	0.916257	+	0.916257i	−0.0804978	+	0.996755i	$0.525651\pi$
$602$	33.4681	+	33.4681i	1.36406	+	1.36406i
$603$		−	12.2121i		−	0.497317i
$604$		−	13.0787i		−	0.532166i
$605$	−4.89408	−	4.89408i	−0.198973	−	0.198973i
$606$	−6.48434	−	6.48434i	−0.263408	−	0.263408i
$607$	6.52235	−	6.52235i	0.264734	−	0.264734i	−0.562240	−	0.826974i	$-0.690060\pi$
$607$	6.52235	−	6.52235i	0.264734	−	0.264734i	0.826974	+	0.562240i	$0.190060\pi$
$608$	−6.45336			−0.261718
$609$	−25.0088	+	25.0088i	−1.01341	+	1.01341i
$610$			30.6655i			1.24161i
$611$	−28.5134			−1.15353
$612$		0			0
$613$	17.1634			0.693225			0.346612	−	0.938008i	$-0.387332\pi$
$613$	17.1634			0.693225			0.346612	+	0.938008i	$0.387332\pi$
$614$			19.6459i			0.792844i
$615$	5.69932	−	5.69932i	0.229819	−	0.229819i
$616$	11.5321			0.464641
$617$	−11.5788	+	11.5788i	−0.466147	+	0.466147i	−0.900664	−	0.434517i	$-0.856919\pi$
$617$	−11.5788	+	11.5788i	−0.466147	+	0.466147i	0.434517	+	0.900664i	$0.356919\pi$
$618$	−5.19890	−	5.19890i	−0.209130	−	0.209130i
$619$	21.3742	+	21.3742i	0.859100	+	0.859100i	0.991232	−	0.132132i	$-0.0421824\pi$
$619$	21.3742	+	21.3742i	0.859100	+	0.859100i	−0.132132	+	0.991232i	$0.542182\pi$
$620$		−	1.34730i		−	0.0541087i
$621$		−	6.00000i		−	0.240772i
$622$	−10.0810	−	10.0810i	−0.404212	−	0.404212i
$623$	18.2213	+	18.2213i	0.730023	+	0.730023i
$624$	1.90536	−	1.90536i	0.0762756	−	0.0762756i
$625$	27.2891			1.09156
$626$	14.8740	−	14.8740i	0.594487	−	0.594487i
$627$		−	18.3114i		−	0.731287i
$628$	10.1284			0.404165
$629$		0			0
$630$	−9.53983			−0.380076
$631$			15.1848i			0.604497i	0.953229	+	0.302249i	$0.0977372\pi$
$631$			15.1848i			0.604497i	−0.953229	+	0.302249i	$0.902263\pi$
$632$	−5.21466	+	5.21466i	−0.207428	+	0.207428i
$633$	−15.5621			−0.618539
$634$	4.04726	−	4.04726i	0.160737	−	0.160737i
$635$	3.21306	+	3.21306i	0.127506	+	0.127506i
$636$	−2.32699	−	2.32699i	−0.0922711	−	0.0922711i
$637$		−	25.6459i		−	1.01613i
$638$			24.6928i			0.977599i
$639$	−8.20337	−	8.20337i	−0.324520	−	0.324520i
$640$	1.65979	+	1.65979i	0.0656089	+	0.0656089i
$641$	5.92914	−	5.92914i	0.234187	−	0.234187i	−0.580251	−	0.814438i	$-0.697046\pi$
$641$	5.92914	−	5.92914i	0.234187	−	0.234187i	0.814438	+	0.580251i	$0.197046\pi$
$642$	−5.02734			−0.198413
$643$	3.84225	−	3.84225i	0.151524	−	0.151524i	−0.627275	−	0.778798i	$-0.715830\pi$
$643$	3.84225	−	3.84225i	0.151524	−	0.151524i	0.778798	+	0.627275i	$0.215830\pi$
$644$			24.3851i			0.960906i
$645$	−27.3364			−1.07637
$646$		0			0
$647$	13.0797			0.514214			0.257107	−	0.966383i	$-0.417231\pi$
$647$	13.0797			0.514214			0.257107	+	0.966383i	$0.417231\pi$
$648$		−	1.00000i		−	0.0392837i
$649$	−8.72247	+	8.72247i	−0.342387	+	0.342387i
$650$	1.37370			0.0538811
$651$	1.64950	−	1.64950i	0.0646491	−	0.0646491i
$652$	−0.150001	−	0.150001i	−0.00587450	−	0.00587450i
$653$	−20.8721	−	20.8721i	−0.816787	−	0.816787i	0.168854	−	0.985641i	$-0.445993\pi$
$653$	−20.8721	−	20.8721i	−0.816787	−	0.816787i	−0.985641	+	0.168854i	$0.945993\pi$
$654$		−	9.06418i		−	0.354437i
$655$		−	39.2695i		−	1.53439i
$656$	−2.42804	−	2.42804i	−0.0947989	−	0.0947989i
$657$	1.67008	+	1.67008i	0.0651559	+	0.0651559i
$658$	30.4098	−	30.4098i	1.18550	−	1.18550i
$659$	−21.5084			−0.837847			−0.418924	−	0.908022i	$-0.637592\pi$
$659$	−21.5084			−0.837847			−0.418924	+	0.908022i	$0.637592\pi$
$660$	−4.70965	+	4.70965i	−0.183323	+	0.183323i
$661$			35.2080i			1.36943i	0.728809	+	0.684717i	$0.240074\pi$
$661$			35.2080i			1.36943i	−0.728809	+	0.684717i	$0.759926\pi$
$662$	−3.14796			−0.122349
$663$		0			0
$664$	−3.21213			−0.124655
$665$		−	61.5640i		−	2.38735i
$666$	−5.57704	+	5.57704i	−0.216106	+	0.216106i
$667$	−52.2140			−2.02173
$668$	6.00895	−	6.00895i	0.232493	−	0.232493i
$669$	−9.40900	−	9.40900i	−0.363773	−	0.363773i
$670$	−20.2696	−	20.2696i	−0.783082	−	0.783082i
$671$			37.0696i			1.43105i
$672$			4.06418i			0.156779i
$673$	−1.37307	−	1.37307i	−0.0529278	−	0.0529278i	0.680147	−	0.733075i	$-0.261916\pi$
$673$	−1.37307	−	1.37307i	−0.0529278	−	0.0529278i	−0.733075	+	0.680147i	$0.761916\pi$
$674$	22.5834	+	22.5834i	0.869878	+	0.869878i
$675$	0.360483	−	0.360483i	0.0138750	−	0.0138750i
$676$	5.73917			0.220737
$677$	1.02388	−	1.02388i	0.0393509	−	0.0393509i	−0.687158	−	0.726508i	$-0.741142\pi$
$677$	1.02388	−	1.02388i	0.0393509	−	0.0393509i	0.726508	+	0.687158i	$0.241142\pi$
$678$		−	11.1480i		−	0.428135i
$679$	32.9760			1.26550
$680$		0			0
$681$	−3.69459			−0.141577
$682$		−	1.62866i		−	0.0623646i
$683$	12.4135	−	12.4135i	0.474989	−	0.474989i	−0.428536	−	0.903525i	$-0.640971\pi$
$683$	12.4135	−	12.4135i	0.474989	−	0.474989i	0.903525	+	0.428536i	$0.140971\pi$
$684$	6.45336			0.246751
$685$	7.39164	−	7.39164i	0.282420	−	0.282420i
$686$	7.23493	+	7.23493i	0.276231	+	0.276231i
$687$	6.25934	+	6.25934i	0.238809	+	0.238809i
$688$			11.6459i			0.443996i
$689$			8.86753i			0.337826i
$690$	−9.95874	−	9.95874i	−0.379123	−	0.379123i
$691$	−12.6166	−	12.6166i	−0.479958	−	0.479958i	0.425160	−	0.905118i	$-0.360218\pi$
$691$	−12.6166	−	12.6166i	−0.479958	−	0.479958i	−0.905118	+	0.425160i	$0.860218\pi$
$692$	0.160288	−	0.160288i	0.00609324	−	0.00609324i
$693$	−11.5321			−0.438068
$694$	−25.5418	+	25.5418i	−0.969553	+	0.969553i
$695$		−	29.9026i		−	1.13427i
$696$	−8.70233			−0.329861
$697$		0			0
$698$	−12.7493			−0.482567
$699$		−	5.88713i		−	0.222672i
$700$	−1.46507	+	1.46507i	−0.0553744	+	0.0553744i
$701$	−43.0051			−1.62428			−0.812139	−	0.583464i	$-0.801697\pi$
$701$	−43.0051			−1.62428			−0.812139	+	0.583464i	$0.801697\pi$
$702$	−1.90536	+	1.90536i	−0.0719134	+	0.0719134i
$703$	−35.9907	−	35.9907i	−1.35741	−	1.35741i
$704$	2.00641	+	2.00641i	0.0756195	+	0.0756195i
$705$			24.8384i			0.935469i
$706$		−	7.09327i		−	0.266959i
$707$	−26.3535	−	26.3535i	−0.991126	−	0.991126i
$708$	−3.07400	−	3.07400i	−0.115528	−	0.115528i
$709$	7.70507	−	7.70507i	0.289370	−	0.289370i	−0.547461	−	0.836831i	$-0.684406\pi$
$709$	7.70507	−	7.70507i	0.289370	−	0.289370i	0.836831	+	0.547461i	$0.184406\pi$
$710$	−27.2317			−1.02199
$711$	5.21466	−	5.21466i	0.195565	−	0.195565i
$712$			6.34049i			0.237620i
$713$	3.44387			0.128974
$714$		0			0
$715$	17.9472			0.671187
$716$			11.6946i			0.437047i
$717$	−11.7456	+	11.7456i	−0.438648	+	0.438648i
$718$	10.6655			0.398033
$719$	6.93201	−	6.93201i	0.258520	−	0.258520i	−0.565932	−	0.824452i	$-0.691483\pi$
$719$	6.93201	−	6.93201i	0.258520	−	0.258520i	0.824452	+	0.565932i	$0.191483\pi$
$720$	−1.65979	−	1.65979i	−0.0618567	−	0.0618567i
$721$	−21.1292	−	21.1292i	−0.786894	−	0.786894i
$722$			22.6459i			0.842793i
$723$			8.51485i			0.316671i
$724$	1.76631	+	1.76631i	0.0656444	+	0.0656444i
$725$	−3.13704	−	3.13704i	−0.116507	−	0.116507i
$726$	2.08499	−	2.08499i	0.0773811	−	0.0773811i
$727$	0.598631			0.0222020			0.0111010	−	0.999938i	$-0.496466\pi$
$727$	0.598631			0.0222020			0.0111010	+	0.999938i	$0.496466\pi$
$728$	7.74374	−	7.74374i	0.287002	−	0.287002i
$729$			1.00000i			0.0370370i
$730$	5.54395			0.205191
$731$		0			0
$732$	−13.0642			−0.482866
$733$			44.4944i			1.64344i	0.569892	+	0.821720i	$0.306985\pi$
$733$			44.4944i			1.64344i	−0.569892	+	0.821720i	$0.693015\pi$
$734$	−17.1473	+	17.1473i	−0.632917	+	0.632917i
$735$	−22.3405			−0.824041
$736$	−4.24264	+	4.24264i	−0.156386	+	0.156386i
$737$	−24.5026	−	24.5026i	−0.902564	−	0.902564i
$738$	2.42804	+	2.42804i	0.0893773	+	0.0893773i
$739$			21.0060i			0.772718i	0.922349	+	0.386359i	$0.126267\pi$
$739$			21.0060i			0.772718i	−0.922349	+	0.386359i	$0.873733\pi$
$740$			18.5134i			0.680567i
$741$	−12.2960	−	12.2960i	−0.451705	−	0.451705i
$742$	−9.45730	−	9.45730i	−0.347188	−	0.347188i
$743$	17.0202	−	17.0202i	0.624410	−	0.624410i	−0.322246	−	0.946656i	$-0.604438\pi$
$743$	17.0202	−	17.0202i	0.624410	−	0.624410i	0.946656	+	0.322246i	$0.104438\pi$
$744$	0.573978			0.0210431
$745$	−32.0188	+	32.0188i	−1.17308	+	1.17308i
$746$			22.7547i			0.833107i
$747$	3.21213			0.117526
$748$		0			0
$749$	−20.4320			−0.746569
$750$			10.5398i			0.384860i
$751$	−1.05016	+	1.05016i	−0.0383208	+	0.0383208i	−0.726008	−	0.687687i	$-0.758626\pi$
$751$	−1.05016	+	1.05016i	−0.0383208	+	0.0383208i	0.687687	+	0.726008i	$0.258626\pi$
$752$	10.5817			0.385876
$753$	−4.87832	+	4.87832i	−0.177776	+	0.177776i
$754$	16.5811	+	16.5811i	0.603849	+	0.603849i
$755$	21.7079	+	21.7079i	0.790032	+	0.790032i
$756$		−	4.06418i		−	0.147813i
$757$		−	36.5134i		−	1.32710i	−0.748131	−	0.663551i	$-0.769048\pi$
$757$		−	36.5134i		−	1.32710i	0.748131	−	0.663551i	$-0.230952\pi$
$758$	−14.0308	−	14.0308i	−0.509622	−	0.509622i
$759$	−12.0385	−	12.0385i	−0.436969	−	0.436969i
$760$	10.7112	−	10.7112i	0.388537	−	0.388537i
$761$	7.06418			0.256076			0.128038	−	0.991769i	$-0.459132\pi$
$761$	7.06418			0.256076			0.128038	+	0.991769i	$0.459132\pi$
$762$	−1.36883	+	1.36883i	−0.0495876	+	0.0495876i
$763$		−	36.8384i		−	1.33364i
$764$	−2.73917			−0.0990997
$765$		0			0
$766$	15.7196			0.567971
$767$			11.7142i			0.422975i
$768$	−0.707107	+	0.707107i	−0.0255155	+	0.0255155i
$769$	−9.04189			−0.326059			−0.163029	−	0.986621i	$-0.552127\pi$
$769$	−9.04189			−0.326059			−0.163029	+	0.986621i	$0.552127\pi$
$770$	−19.1408	+	19.1408i	−0.689788	+	0.689788i
$771$	−15.9471	−	15.9471i	−0.574321	−	0.574321i
$772$	9.37201	+	9.37201i	0.337306	+	0.337306i
$773$		−	3.06324i		−	0.110177i	−0.998481	−	0.0550886i	$-0.982456\pi$
$773$		−	3.06324i		−	0.110177i	0.998481	−	0.0550886i	$-0.0175441\pi$
$774$		−	11.6459i		−	0.418603i
$775$	0.206909	+	0.206909i	0.00743240	+	0.00743240i
$776$	5.73733	+	5.73733i	0.205958	+	0.205958i
$777$	−22.6661	+	22.6661i	−0.813141	+	0.813141i
$778$	32.4766			1.16434
$779$	−15.6690	+	15.6690i	−0.561400	+	0.561400i
$780$			6.32501i			0.226472i
$781$	−32.9187			−1.17792
$782$		0			0
$783$	8.70233			0.310996
$784$			9.51754i			0.339912i
$785$	−16.8109	+	16.8109i	−0.600008	+	0.600008i
$786$	16.7297			0.596728
$787$	−12.9023	+	12.9023i	−0.459917	+	0.459917i	−0.898628	−	0.438711i	$-0.855435\pi$
$787$	−12.9023	+	12.9023i	−0.459917	+	0.459917i	0.438711	+	0.898628i	$0.355435\pi$
$788$	−16.2744	−	16.2744i	−0.579752	−	0.579752i
$789$	−11.9864	−	11.9864i	−0.426726	−	0.426726i
$790$		−	17.3105i		−	0.615879i
$791$		−	45.3073i		−	1.61094i
$792$	−2.00641	−	2.00641i	−0.0712948	−	0.0712948i
$793$	24.8920	+	24.8920i	0.883942	+	0.883942i
$794$	−1.30288	+	1.30288i	−0.0462374	+	0.0462374i
$795$	7.72462			0.273964
$796$	12.8139	−	12.8139i	0.454176	−	0.454176i
$797$			45.2222i			1.60185i	0.598762	+	0.800927i	$0.295659\pi$
$797$			45.2222i			1.60185i	−0.598762	+	0.800927i	$0.704341\pi$
$798$	26.2276			0.928448
$799$		0			0
$800$	−0.509800			−0.0180242
$801$		−	6.34049i		−	0.224030i
$802$	7.54165	−	7.54165i	0.266305	−	0.266305i
$803$	6.70172			0.236499
$804$	8.63528	−	8.63528i	0.304543	−	0.304543i
$805$	−40.4741	−	40.4741i	−1.42652	−	1.42652i
$806$	−1.09364	−	1.09364i	−0.0385217	−	0.0385217i
$807$		−	10.8084i		−	0.380474i
$808$		−	9.17024i		−	0.322608i
$809$	−10.5999	−	10.5999i	−0.372672	−	0.372672i	0.495777	−	0.868450i	$-0.334883\pi$
$809$	−10.5999	−	10.5999i	−0.372672	−	0.372672i	−0.868450	+	0.495777i	$0.834883\pi$
$810$	1.65979	+	1.65979i	0.0583190	+	0.0583190i
$811$	14.2438	−	14.2438i	0.500169	−	0.500169i	−0.411321	−	0.911490i	$-0.634933\pi$
$811$	14.2438	−	14.2438i	0.500169	−	0.500169i	0.911490	+	0.411321i	$0.134933\pi$
$812$	−35.3678			−1.24117
$813$	15.0707	−	15.0707i	0.528552	−	0.528552i
$814$			22.3797i			0.784408i
$815$	0.497941			0.0174421
$816$		0			0
$817$	75.1552			2.62935
$818$			5.33544i			0.186549i
$819$	−7.74374	+	7.74374i	−0.270588	+	0.270588i
$820$	8.06006			0.281469
$821$	−30.4027	+	30.4027i	−1.06106	+	1.06106i	−0.0630505	+	0.998010i	$0.520083\pi$
$821$	−30.4027	+	30.4027i	−1.06106	+	1.06106i	−0.998010	+	0.0630505i	$0.979917\pi$
$822$	3.14900	+	3.14900i	0.109834	+	0.109834i
$823$	−10.6140	−	10.6140i	−0.369980	−	0.369980i	0.497490	−	0.867470i	$-0.334255\pi$
$823$	−10.6140	−	10.6140i	−0.369980	−	0.369980i	−0.867470	+	0.497490i	$0.834255\pi$
$824$		−	7.35235i		−	0.256131i
$825$		−	1.44656i		−	0.0503626i
$826$	−12.4933	−	12.4933i	−0.434697	−	0.434697i
$827$	5.18861	+	5.18861i	0.180426	+	0.180426i	0.791541	−	0.611116i	$-0.209279\pi$
$827$	5.18861	+	5.18861i	0.180426	+	0.180426i	−0.611116	+	0.791541i	$0.709279\pi$
$828$	4.24264	−	4.24264i	0.147442	−	0.147442i
$829$	14.0310			0.487315			0.243658	−	0.969861i	$-0.421653\pi$
$829$	14.0310			0.487315			0.243658	+	0.969861i	$0.421653\pi$
$830$	5.33146	−	5.33146i	0.185058	−	0.185058i
$831$			22.1438i			0.768161i
$832$	2.69459			0.0934182
$833$		0			0
$834$	12.7392			0.441121
$835$			19.9472i			0.690301i
$836$	12.9481	−	12.9481i	0.447820	−	0.447820i
$837$	−0.573978			−0.0198396
$838$	17.3977	−	17.3977i	0.600992	−	0.600992i
$839$	−22.3674	−	22.3674i	−0.772208	−	0.772208i	0.206284	−	0.978492i	$-0.433863\pi$
$839$	−22.3674	−	22.3674i	−0.772208	−	0.772208i	−0.978492	+	0.206284i	$0.933863\pi$
$840$	−6.74568	−	6.74568i	−0.232748	−	0.232748i
$841$		−	46.7306i		−	1.61140i
$842$		−	2.89662i		−	0.0998242i
$843$	−7.08201	−	7.08201i	−0.243918	−	0.243918i
$844$	−11.0041	−	11.0041i	−0.378776	−	0.378776i
$845$	−9.52581	+	9.52581i	−0.327698	+	0.327698i
$846$	−10.5817			−0.363807
$847$	8.47375	−	8.47375i	0.291162	−	0.291162i
$848$		−	3.29086i		−	0.113009i
$849$	−10.0838			−0.346074
$850$		0			0
$851$	−47.3228			−1.62220
$852$		−	11.6013i		−	0.397455i
$853$	−23.8820	+	23.8820i	−0.817704	+	0.817704i	−0.985775	−	0.168071i	$-0.946246\pi$
$853$	−23.8820	+	23.8820i	−0.817704	+	0.817704i	0.168071	+	0.985775i	$0.446246\pi$
$854$	−53.0951			−1.81688
$855$	−10.7112	+	10.7112i	−0.366316	+	0.366316i
$856$	−3.55487	−	3.55487i	−0.121503	−	0.121503i
$857$	−6.76858	−	6.76858i	−0.231210	−	0.231210i	0.581987	−	0.813198i	$-0.302275\pi$
$857$	−6.76858	−	6.76858i	−0.231210	−	0.231210i	−0.813198	+	0.581987i	$0.802275\pi$
$858$			7.64590i			0.261027i
$859$			45.6870i			1.55882i	0.626515	+	0.779410i	$0.284481\pi$
$859$			45.6870i			1.55882i	−0.626515	+	0.779410i	$0.715519\pi$
$860$	−19.3297	−	19.3297i	−0.659138	−	0.659138i
$861$	9.86797	+	9.86797i	0.336300	+	0.336300i
$862$	5.77914	−	5.77914i	0.196838	−	0.196838i
$863$	38.6674			1.31625			0.658126	−	0.752908i	$-0.271349\pi$
$863$	38.6674			1.31625			0.658126	+	0.752908i	$0.271349\pi$
$864$	0.707107	−	0.707107i	0.0240563	−	0.0240563i
$865$			0.532089i			0.0180916i
$866$	21.7365			0.738636
$867$		0			0
$868$	2.33275			0.0791786
$869$		−	20.9255i		−	0.709849i
$870$	14.4440	−	14.4440i	0.489699	−	0.489699i
$871$	−32.9067			−1.11500
$872$	6.40934	−	6.40934i	0.217048	−	0.217048i
$873$	−5.73733	−	5.73733i	−0.194179	−	0.194179i
$874$	27.3793	+	27.3793i	0.926119	+	0.926119i
$875$			42.8357i			1.44811i
$876$			2.36184i			0.0797993i
$877$	−6.78201	−	6.78201i	−0.229012	−	0.229012i	0.583268	−	0.812280i	$-0.301774\pi$
$877$	−6.78201	−	6.78201i	−0.229012	−	0.229012i	−0.812280	+	0.583268i	$0.801774\pi$
$878$	7.96261	+	7.96261i	0.268725	+	0.268725i
$879$	−10.2951	+	10.2951i	−0.347244	+	0.347244i
$880$	−6.66044			−0.224524
$881$	−32.1652	+	32.1652i	−1.08367	+	1.08367i	−0.0875090	+	0.996164i	$0.527891\pi$
$881$	−32.1652	+	32.1652i	−1.08367	+	1.08367i	−0.996164	+	0.0875090i	$0.972109\pi$
$882$		−	9.51754i		−	0.320472i
$883$	47.3911			1.59484			0.797418	−	0.603427i	$-0.206199\pi$
$883$	47.3911			1.59484			0.797418	+	0.603427i	$0.206199\pi$
$884$		0			0
$885$	10.2044			0.343017
$886$			22.4730i			0.754994i
$887$	0.784008	−	0.784008i	0.0263244	−	0.0263244i	−0.693822	−	0.720146i	$-0.744075\pi$
$887$	0.784008	−	0.784008i	0.0263244	−	0.0263244i	0.720146	+	0.693822i	$0.244075\pi$
$888$	−7.88713			−0.264675
$889$	−5.56318	+	5.56318i	−0.186583	+	0.186583i
$890$	−10.5239	−	10.5239i	−0.352761	−	0.352761i
$891$	2.00641	+	2.00641i	0.0672174	+	0.0672174i
$892$		−	13.3063i		−	0.445529i
$893$		−	68.2877i		−	2.28516i
$894$	−13.6407	−	13.6407i	−0.456213	−	0.456213i
$895$	−19.4106	−	19.4106i	−0.648823	−	0.648823i
$896$	−2.87381	+	2.87381i	−0.0960072	+	0.0960072i
$897$	−16.1676			−0.539819
$898$	−6.58706	+	6.58706i	−0.219813	+	0.219813i
$899$			4.99495i			0.166591i
$900$	0.509800			0.0169933
$901$		0			0
$902$	9.74329			0.324416
$903$		−	47.3310i		−	1.57508i
$904$	7.88280	−	7.88280i	0.262178	−	0.262178i
$905$	−5.86341			−0.194906
$906$	−9.24806	+	9.24806i	−0.307246	+	0.307246i
$907$	−2.57672	−	2.57672i	−0.0855585	−	0.0855585i	0.663032	−	0.748591i	$-0.269269\pi$
$907$	−2.57672	−	2.57672i	−0.0855585	−	0.0855585i	−0.748591	+	0.663032i	$0.769269\pi$
$908$	−2.61247	−	2.61247i	−0.0866979	−	0.0866979i
$909$			9.17024i			0.304158i
$910$			25.7060i			0.852144i
$911$	−3.85902	−	3.85902i	−0.127855	−	0.127855i	0.640284	−	0.768139i	$-0.278817\pi$
$911$	−3.85902	−	3.85902i	−0.127855	−	0.127855i	−0.768139	+	0.640284i	$0.778817\pi$
$912$	4.56322	+	4.56322i	0.151103	+	0.151103i
$913$	6.44487	−	6.44487i	0.213294	−	0.213294i
$914$	21.4124			0.708259
$915$	21.6838	−	21.6838i	0.716844	−	0.716844i
$916$			8.85204i			0.292480i
$917$	67.9924			2.24531
$918$		0			0
$919$	−44.0060			−1.45162			−0.725812	−	0.687893i	$-0.758536\pi$
$919$	−44.0060			−1.45162			−0.725812	+	0.687893i	$0.758536\pi$
$920$		−	14.0838i		−	0.464328i
$921$	13.8917	−	13.8917i	0.457749	−	0.457749i
$922$	−20.6287			−0.679369
$923$	−22.1047	+	22.1047i	−0.727587	+	0.727587i
$924$	−8.15442	−	8.15442i	−0.268261	−	0.268261i
$925$	−2.84318	−	2.84318i	−0.0934831	−	0.0934831i
$926$		−	25.6973i		−	0.844465i
$927$			7.35235i			0.241483i
$928$	−6.15348	−	6.15348i	−0.201998	−	0.201998i
$929$	−33.4088	−	33.4088i	−1.09611	−	1.09611i	−0.994861	−	0.101247i	$-0.967717\pi$
$929$	−33.4088	−	33.4088i	−1.09611	−	1.09611i	−0.101247	−	0.994861i	$-0.532283\pi$
$930$	−0.952682	+	0.952682i	−0.0312397	+	0.0312397i
$931$	61.4201			2.01296
$932$	4.16283	−	4.16283i	0.136358	−	0.136358i
$933$			14.2567i			0.466744i
$934$	3.15570			0.103258
$935$		0			0
$936$	−2.69459			−0.0880755
$937$		−	42.9445i		−	1.40294i	−0.712701	−	0.701468i	$-0.752528\pi$
$937$		−	42.9445i		−	1.40294i	0.712701	−	0.701468i	$-0.247472\pi$
$938$	35.0953	−	35.0953i	1.14590	−	1.14590i
$939$	−21.0351			−0.686454
$940$	−17.5634	+	17.5634i	−0.572856	+	0.572856i
$941$	40.0518	+	40.0518i	1.30565	+	1.30565i	0.924522	+	0.381129i	$0.124465\pi$
$941$	40.0518	+	40.0518i	1.30565	+	1.30565i	0.381129	+	0.924522i	$0.375535\pi$
$942$	−7.16183	−	7.16183i	−0.233345	−	0.233345i
$943$			20.6026i			0.670912i
$944$		−	4.34730i		−	0.141492i
$945$	6.74568	+	6.74568i	0.219437	+	0.219437i
$946$	−23.3665	−	23.3665i	−0.759710	−	0.759710i
$947$	−39.6411	+	39.6411i	−1.28816	+	1.28816i	−0.352261	+	0.935902i	$0.614587\pi$
$947$	−39.6411	+	39.6411i	−1.28816	+	1.28816i	−0.935902	+	0.352261i	$0.885413\pi$
$948$	7.37464			0.239517
$949$	4.50017	−	4.50017i	0.146082	−	0.146082i
$950$			3.28993i			0.106739i
$951$	−5.72369			−0.185603
$952$		0			0
$953$	41.5586			1.34622			0.673108	−	0.739544i	$-0.264959\pi$
$953$	41.5586			1.34622			0.673108	+	0.739544i	$0.264959\pi$
$954$			3.29086i			0.106546i
$955$	4.54644	−	4.54644i	0.147120	−	0.147120i
$956$	−16.6108			−0.537232
$957$	17.4605	−	17.4605i	0.564417	−	0.564417i
$958$	1.36212	+	1.36212i	0.0440081	+	0.0440081i
$959$	12.7981	+	12.7981i	0.413273	+	0.413273i
$960$		−	2.34730i		−	0.0757587i
$961$			30.6705i			0.989373i
$962$	15.0279	+	15.0279i	0.484517	+	0.484517i
$963$	3.55487	+	3.55487i	0.114554	+	0.114554i
$964$	−6.02091	+	6.02091i	−0.193920	+	0.193920i
$965$	−31.1111			−1.00150
$966$	17.2428	−	17.2428i	0.554779	−	0.554779i
$967$		−	25.3040i		−	0.813721i	−0.913490	−	0.406861i	$-0.866624\pi$
$967$		−	25.3040i		−	0.813721i	0.913490	−	0.406861i	$-0.133376\pi$
$968$	2.94862			0.0947721
$969$		0			0
$970$	−19.0455			−0.611515
$971$			20.2558i			0.650039i	0.945707	+	0.325019i	$0.105371\pi$
$971$			20.2558i			0.650039i	−0.945707	+	0.325019i	$0.894629\pi$
$972$	−0.707107	+	0.707107i	−0.0226805	+	0.0226805i
$973$	51.7743			1.65981
$974$	5.62052	−	5.62052i	0.180093	−	0.180093i
$975$	−0.971355	−	0.971355i	−0.0311083	−	0.0311083i
$976$	−9.23777	−	9.23777i	−0.295694	−	0.295694i
$977$		−	1.17705i		−	0.0376572i	−0.999823	−	0.0188286i	$-0.994006\pi$
$977$		−	1.17705i		−	0.0376572i	0.999823	−	0.0188286i	$-0.00599369\pi$
$978$			0.212134i			0.00678329i
$979$	−12.7216	−	12.7216i	−0.406585	−	0.406585i
$980$	−15.7971	−	15.7971i	−0.504620	−	0.504620i
$981$	−6.40934	+	6.40934i	−0.204635	+	0.204635i
$982$	5.25402			0.167663
$983$	24.1543	−	24.1543i	0.770402	−	0.770402i	−0.207775	−	0.978177i	$-0.566622\pi$
$983$	24.1543	−	24.1543i	0.770402	−	0.770402i	0.978177	+	0.207775i	$0.0666221\pi$
$984$			3.43376i			0.109464i
$985$	54.0242			1.72135
$986$		0			0
$987$	−43.0060			−1.36890
$988$		−	17.3892i		−	0.553224i
$989$	49.4094	−	49.4094i	1.57113	−	1.57113i
$990$	6.66044			0.211683
$991$	−11.3591	+	11.3591i	−0.360833	+	0.360833i	−0.864120	−	0.503286i	$-0.832124\pi$
$991$	−11.3591	+	11.3591i	−0.360833	+	0.360833i	0.503286	+	0.864120i	$0.332124\pi$
$992$	0.405864	+	0.405864i	0.0128862	+	0.0128862i
$993$	2.22594	+	2.22594i	0.0706381	+	0.0706381i
$994$		−	47.1498i		−	1.49550i
$995$			42.5366i			1.34850i
$996$	2.27132	+	2.27132i	0.0719696	+	0.0719696i
$997$	−13.2783	−	13.2783i	−0.420528	−	0.420528i	0.464857	−	0.885386i	$-0.346106\pi$
$997$	−13.2783	−	13.2783i	−0.420528	−	0.420528i	−0.885386	+	0.464857i	$0.846106\pi$
$998$	17.5911	−	17.5911i	0.556838	−	0.556838i
$999$	7.88713			0.249538

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1734.2.f.n.1483.2		12
17.2	even	8		1734.2.b.j.577.5		6
17.4	even	4	inner	1734.2.f.n.829.5		12
17.8	even	8		1734.2.a.q.1.2	yes	3
17.9	even	8		1734.2.a.p.1.2	✓	3
17.13	even	4	inner	1734.2.f.n.829.2		12
17.15	even	8		1734.2.b.j.577.2		6
17.16	even	2	inner	1734.2.f.n.1483.5		12
51.8	odd	8		5202.2.a.bm.1.2		3
51.26	odd	8		5202.2.a.bp.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1734.2.a.p.1.2	✓	3	17.9	even	8
1734.2.a.q.1.2	yes	3	17.8	even	8
1734.2.b.j.577.2		6	17.15	even	8
1734.2.b.j.577.5		6	17.2	even	8
1734.2.f.n.829.2		12	17.13	even	4	inner
1734.2.f.n.829.5		12	17.4	even	4	inner
1734.2.f.n.1483.2		12	1.1	even	1	trivial
1734.2.f.n.1483.5		12	17.16	even	2	inner
5202.2.a.bm.1.2		3	51.8	odd	8
5202.2.a.bp.1.2		3	51.26	odd	8

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:	\( N \)	\(=\)	\( 1734 = 2 \cdot 3 \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1734.f (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(-0.707107 + 0.707107i) q^{3} -1.00000 q^{4} +(1.65979 - 1.65979i) q^{5} +(0.707107 + 0.707107i) q^{6} +(2.87381 + 2.87381i) q^{7} +1.00000i q^{8} -1.00000i q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +(-0.707107 + 0.707107i) q^{3} -1.00000 q^{4} +(1.65979 - 1.65979i) q^{5} +(0.707107 + 0.707107i) q^{6} +(2.87381 + 2.87381i) q^{7} +1.00000i q^{8} -1.00000i q^{9} +(-1.65979 - 1.65979i) q^{10} +(-2.00641 - 2.00641i) q^{11} +(0.707107 - 0.707107i) q^{12} -2.69459 q^{13} +(2.87381 - 2.87381i) q^{14} +2.34730i q^{15} +1.00000 q^{16} -1.00000 q^{18} -6.45336i q^{19} +(-1.65979 + 1.65979i) q^{20} -4.06418 q^{21} +(-2.00641 + 2.00641i) q^{22} +(-4.24264 - 4.24264i) q^{23} +(-0.707107 - 0.707107i) q^{24} -0.509800i q^{25} +2.69459i q^{26} +(0.707107 + 0.707107i) q^{27} +(-2.87381 - 2.87381i) q^{28} +(6.15348 - 6.15348i) q^{29} +2.34730 q^{30} +(-0.405864 + 0.405864i) q^{31} -1.00000i q^{32} +2.83750 q^{33} +9.53983 q^{35} +1.00000i q^{36} +(5.57704 - 5.57704i) q^{37} -6.45336 q^{38} +(1.90536 - 1.90536i) q^{39} +(1.65979 + 1.65979i) q^{40} +(-2.42804 - 2.42804i) q^{41} +4.06418i q^{42} +11.6459i q^{43} +(2.00641 + 2.00641i) q^{44} +(-1.65979 - 1.65979i) q^{45} +(-4.24264 + 4.24264i) q^{46} +10.5817 q^{47} +(-0.707107 + 0.707107i) q^{48} +9.51754i q^{49} -0.509800 q^{50} +2.69459 q^{52} -3.29086i q^{53} +(0.707107 - 0.707107i) q^{54} -6.66044 q^{55} +(-2.87381 + 2.87381i) q^{56} +(4.56322 + 4.56322i) q^{57} +(-6.15348 - 6.15348i) q^{58} -4.34730i q^{59} -2.34730i q^{60} +(-9.23777 - 9.23777i) q^{61} +(0.405864 + 0.405864i) q^{62} +(2.87381 - 2.87381i) q^{63} -1.00000 q^{64} +(-4.47246 + 4.47246i) q^{65} -2.83750i q^{66} +12.2121 q^{67} +6.00000 q^{69} -9.53983i q^{70} +(8.20337 - 8.20337i) q^{71} +1.00000 q^{72} +(-1.67008 + 1.67008i) q^{73} +(-5.57704 - 5.57704i) q^{74} +(0.360483 + 0.360483i) q^{75} +6.45336i q^{76} -11.5321i q^{77} +(-1.90536 - 1.90536i) q^{78} +(5.21466 + 5.21466i) q^{79} +(1.65979 - 1.65979i) q^{80} -1.00000 q^{81} +(-2.42804 + 2.42804i) q^{82} +3.21213i q^{83} +4.06418 q^{84} +11.6459 q^{86} +8.70233i q^{87} +(2.00641 - 2.00641i) q^{88} +6.34049 q^{89} +(-1.65979 + 1.65979i) q^{90} +(-7.74374 - 7.74374i) q^{91} +(4.24264 + 4.24264i) q^{92} -0.573978i q^{93} -10.5817i q^{94} +(-10.7112 - 10.7112i) q^{95} +(0.707107 + 0.707107i) q^{96} +(5.73733 - 5.73733i) q^{97} +9.51754 q^{98} +(-2.00641 + 2.00641i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 12 q^{4}+O(q^{10}) \) 12 * q - 12 * q^4	\( 12 q - 12 q^{4} - 24 q^{13} + 12 q^{16} - 12 q^{18} - 12 q^{21} + 24 q^{30} + 24 q^{33} - 24 q^{38} - 12 q^{50} + 24 q^{52} + 12 q^{55} - 12 q^{64} + 48 q^{67} + 72 q^{69} + 12 q^{72} - 12 q^{81} + 12 q^{84} - 24 q^{86} - 96 q^{89} + 24 q^{98}+O(q^{100}) \) 12 * q - 12 * q^4 - 24 * q^13 + 12 * q^16 - 12 * q^18 - 12 * q^21 + 24 * q^30 + 24 * q^33 - 24 * q^38 - 12 * q^50 + 24 * q^52 + 12 * q^55 - 12 * q^64 + 48 * q^67 + 72 * q^69 + 12 * q^72 - 12 * q^81 + 12 * q^84 - 24 * q^86 - 96 * q^89 + 24 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more