LMFDB - Embedded newform 441.2.u.d.127.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,2,Mod(64,441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(441, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([0, 10]))

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

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

chi := DirichletCharacter("441.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.u (of order $7$, degree $6$, 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:	$3.52140272914$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$6$ over $\Q(\zeta_{7})$
Twist minimal:	no (minimal twist has level 147)
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			127.1
Character	$\chi$	$=$	441.127
Dual form			441.2.u.d.316.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.24272 - 1.08004i) q^{2} +(2.61635 + 3.28080i) q^{4} +(0.222387 + 0.974342i) q^{5} +(-2.64454 + 0.0800852i) q^{7} +(-1.21655 - 5.33004i) q^{8} +O(q^{10})$	\(q+(-2.24272 - 1.08004i) q^{2} +(2.61635 + 3.28080i) q^{4} +(0.222387 + 0.974342i) q^{5} +(-2.64454 + 0.0800852i) q^{7} +(-1.21655 - 5.33004i) q^{8} +(0.553574 - 2.42537i) q^{10} +(-1.23480 - 0.594647i) q^{11} +(-3.37922 - 1.62735i) q^{13} +(6.01747 + 2.67660i) q^{14} +(-1.16074 + 5.08554i) q^{16} +(2.96789 - 3.72162i) q^{17} +4.98217 q^{19} +(-2.61478 + 3.27883i) q^{20} +(2.12707 + 2.66726i) q^{22} +(3.73204 + 4.67984i) q^{23} +(3.60496 - 1.73606i) q^{25} +(5.82107 + 7.29939i) q^{26} +(-7.18178 - 8.46667i) q^{28} +(4.13197 - 5.18133i) q^{29} +8.43703 q^{31} +(1.27844 - 1.60311i) q^{32} +(-10.6757 + 5.14113i) q^{34} +(-0.666142 - 2.55888i) q^{35} +(-3.36239 + 4.21631i) q^{37} +(-11.1736 - 5.38094i) q^{38} +(4.92273 - 2.37066i) q^{40} +(-0.231889 - 1.01597i) q^{41} +(2.13451 - 9.35192i) q^{43} +(-1.27974 - 5.60693i) q^{44} +(-3.31554 - 14.5263i) q^{46} +(3.97899 + 1.91618i) q^{47} +(6.98717 - 0.423577i) q^{49} -9.95994 q^{50} +(-3.50223 - 15.3443i) q^{52} +(-8.27143 - 10.3720i) q^{53} +(0.304787 - 1.33536i) q^{55} +(3.64406 + 13.9981i) q^{56} +(-14.8629 + 7.15760i) q^{58} +(1.11604 - 4.88969i) q^{59} +(-0.916644 + 1.14943i) q^{61} +(-18.9219 - 9.11233i) q^{62} +(4.80089 - 2.31199i) q^{64} +(0.834098 - 3.65442i) q^{65} +7.39128 q^{67} +19.9749 q^{68} +(-1.26971 + 6.45831i) q^{70} +(4.50428 + 5.64818i) q^{71} +(-13.6805 + 6.58819i) q^{73} +(12.0947 - 5.82450i) q^{74} +(13.0351 + 16.3455i) q^{76} +(3.31309 + 1.47368i) q^{77} -4.76890 q^{79} -5.21319 q^{80} +(-0.577227 + 2.52900i) q^{82} +(11.5050 - 5.54053i) q^{83} +(4.28615 + 2.06410i) q^{85} +(-14.8876 + 18.6684i) q^{86} +(-1.66730 + 7.30493i) q^{88} +(-8.28049 + 3.98768i) q^{89} +(9.06682 + 4.03296i) q^{91} +(-5.58927 + 24.4882i) q^{92} +(-6.85423 - 8.59494i) q^{94} +(1.10797 + 4.85434i) q^{95} +7.04354 q^{97} +(-16.1278 - 6.59645i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + q^{2} - 9 q^{4} + 4 q^{5} - 6 q^{7} + 15 q^{8}+O(q^{10}) $ 36 * q + q^2 - 9 * q^4 + 4 * q^5 - 6 * q^7 + 15 * q^8	$ 36 q + q^{2} - 9 q^{4} + 4 q^{5} - 6 q^{7} + 15 q^{8} + 10 q^{10} + 7 q^{11} - 12 q^{13} + q^{14} - 3 q^{16} + 3 q^{17} + 6 q^{19} - 25 q^{20} - 21 q^{22} + 20 q^{23} - 2 q^{25} - 6 q^{26} - q^{28} + 22 q^{29} + 16 q^{31} - 26 q^{32} + 6 q^{34} + 9 q^{35} + 32 q^{37} - 17 q^{38} - 21 q^{40} + 5 q^{41} - 34 q^{43} - 2 q^{44} - 32 q^{46} + 7 q^{47} + 20 q^{49} - 236 q^{50} + 20 q^{52} + 32 q^{53} - 17 q^{55} + 39 q^{56} - 53 q^{58} + q^{59} + 14 q^{61} + 60 q^{62} - 21 q^{64} + 39 q^{65} - 22 q^{67} + 110 q^{68} - 40 q^{70} - 36 q^{71} - 11 q^{73} + 46 q^{74} - 101 q^{76} + 17 q^{77} - 14 q^{79} + 112 q^{80} + 2 q^{82} - 12 q^{83} - 44 q^{85} - 184 q^{86} + 204 q^{88} - 12 q^{89} - 16 q^{91} + 105 q^{92} - 5 q^{94} - 18 q^{95} + 172 q^{97} - q^{98}+O(q^{100}) $ 36 * q + q^2 - 9 * q^4 + 4 * q^5 - 6 * q^7 + 15 * q^8 + 10 * q^10 + 7 * q^11 - 12 * q^13 + q^14 - 3 * q^16 + 3 * q^17 + 6 * q^19 - 25 * q^20 - 21 * q^22 + 20 * q^23 - 2 * q^25 - 6 * q^26 - q^28 + 22 * q^29 + 16 * q^31 - 26 * q^32 + 6 * q^34 + 9 * q^35 + 32 * q^37 - 17 * q^38 - 21 * q^40 + 5 * q^41 - 34 * q^43 - 2 * q^44 - 32 * q^46 + 7 * q^47 + 20 * q^49 - 236 * q^50 + 20 * q^52 + 32 * q^53 - 17 * q^55 + 39 * q^56 - 53 * q^58 + q^59 + 14 * q^61 + 60 * q^62 - 21 * q^64 + 39 * q^65 - 22 * q^67 + 110 * q^68 - 40 * q^70 - 36 * q^71 - 11 * q^73 + 46 * q^74 - 101 * q^76 + 17 * q^77 - 14 * q^79 + 112 * q^80 + 2 * q^82 - 12 * q^83 - 44 * q^85 - 184 * q^86 + 204 * q^88 - 12 * q^89 - 16 * q^91 + 105 * q^92 - 5 * q^94 - 18 * q^95 + 172 * q^97 - q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{3}{7}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−2.24272	−	1.08004i	−1.58585	−	0.763703i	−0.586902	−	0.809658i	$-0.699653\pi$
$2$	−2.24272	−	1.08004i	−1.58585	−	0.763703i	−0.998944	+	0.0459547i	$0.985367\pi$
$3$		0			0
$3$		0			0
$4$	2.61635	+	3.28080i	1.30817	+	1.64040i
$5$	0.222387	+	0.974342i	0.0994546	+	0.435739i	1.00000		0.000976097i	$0.000310701\pi$
$5$	0.222387	+	0.974342i	0.0994546	+	0.435739i	−0.900545	+	0.434763i	$0.856832\pi$
$6$		0			0
$7$	−2.64454	+	0.0800852i	−0.999542	+	0.0302694i
$7$	−2.64454	+	0.0800852i	−0.999542	+	0.0302694i
$8$	−1.21655	−	5.33004i	−0.430114	−	1.88445i
$9$		0			0
$10$	0.553574	−	2.42537i	0.175056	−	0.766969i
$11$	−1.23480	−	0.594647i	−0.372306	−	0.179293i	0.238369	−	0.971175i	$-0.423387\pi$
$11$	−1.23480	−	0.594647i	−0.372306	−	0.179293i	−0.610674	+	0.791882i	$0.709102\pi$
$12$		0			0
$13$	−3.37922	−	1.62735i	−0.937228	−	0.451345i	−0.0980376	−	0.995183i	$-0.531257\pi$
$13$	−3.37922	−	1.62735i	−0.937228	−	0.451345i	−0.839191	+	0.543837i	$0.816971\pi$
$14$	6.01747	+	2.67660i	1.60824	+	0.715351i
$15$		0			0
$16$	−1.16074	+	5.08554i	−0.290185	+	1.27139i
$17$	2.96789	−	3.72162i	0.719820	−	0.902626i	−0.278508	−	0.960434i	$-0.589840\pi$
$17$	2.96789	−	3.72162i	0.719820	−	0.902626i	0.998328	+	0.0578083i	$0.0184112\pi$
$18$		0			0
$19$	4.98217			1.14299			0.571494	−	0.820606i	$-0.306364\pi$
$19$	4.98217			1.14299			0.571494	+	0.820606i	$0.306364\pi$
$20$	−2.61478	+	3.27883i	−0.584682	+	0.733168i
$21$		0			0
$22$	2.12707	+	2.66726i	0.453493	+	0.568662i
$23$	3.73204	+	4.67984i	0.778185	+	0.975813i	1.00000		0.000724406i	$0.000230586\pi$
$23$	3.73204	+	4.67984i	0.778185	+	0.975813i	−0.221815	+	0.975089i	$0.571198\pi$
$24$		0			0
$25$	3.60496	−	1.73606i	0.720992	−	0.347211i
$26$	5.82107	+	7.29939i	1.14161	+	1.43153i
$27$		0			0
$28$	−7.18178	−	8.46667i	−1.35723	−	1.60005i
$29$	4.13197	−	5.18133i	0.767287	−	0.962148i	−0.232658	−	0.972559i	$-0.574742\pi$
$29$	4.13197	−	5.18133i	0.767287	−	0.962148i	0.999946	+	0.0104106i	$0.00331385\pi$
$30$		0			0
$31$	8.43703			1.51534			0.757668	−	0.652640i	$-0.226339\pi$
$31$	8.43703			1.51534			0.757668	+	0.652640i	$0.226339\pi$
$32$	1.27844	−	1.60311i	0.225998	−	0.283392i
$33$		0			0
$34$	−10.6757	+	5.14113i	−1.83086	+	0.881696i
$35$	−0.666142	−	2.55888i	−0.112599	−	0.432529i
$36$		0			0
$37$	−3.36239	+	4.21631i	−0.552774	+	0.693156i	−0.977204	−	0.212304i	$-0.931903\pi$
$37$	−3.36239	+	4.21631i	−0.552774	+	0.693156i	0.424430	+	0.905461i	$0.360475\pi$
$38$	−11.1736	−	5.38094i	−1.81260	−	0.872904i
$39$		0			0
$40$	4.92273	−	2.37066i	0.778353	−	0.374835i
$41$	−0.231889	−	1.01597i	−0.0362150	−	0.158668i	0.953587	−	0.301117i	$-0.0973595\pi$
$41$	−0.231889	−	1.01597i	−0.0362150	−	0.158668i	−0.989802	+	0.142449i	$0.954502\pi$
$42$		0			0
$43$	2.13451	−	9.35192i	0.325510	−	1.42615i	−0.502080	−	0.864821i	$-0.667432\pi$
$43$	2.13451	−	9.35192i	0.325510	−	1.42615i	0.827590	−	0.561333i	$-0.189711\pi$
$44$	−1.27974	−	5.60693i	−0.192929	−	0.845276i
$45$		0			0
$46$	−3.31554	−	14.5263i	−0.488850	−	2.14179i
$47$	3.97899	+	1.91618i	0.580396	+	0.279504i	0.700959	−	0.713202i	$-0.252756\pi$
$47$	3.97899	+	1.91618i	0.580396	+	0.279504i	−0.120563	+	0.992706i	$0.538470\pi$
$48$		0			0
$49$	6.98717	−	0.423577i	0.998168	−	0.0605110i
$50$	−9.95994			−1.40855
$51$		0			0
$52$	−3.50223	−	15.3443i	−0.485672	−	2.12787i
$53$	−8.27143	−	10.3720i	−1.13617	−	1.42471i	−0.890281	−	0.455411i	$-0.849492\pi$
$53$	−8.27143	−	10.3720i	−1.13617	−	1.42471i	−0.245887	−	0.969299i	$-0.579079\pi$
$54$		0			0
$55$	0.304787	−	1.33536i	0.0410974	−	0.180060i
$56$	3.64406	+	13.9981i	0.486958	+	1.87057i
$57$		0			0
$58$	−14.8629	+	7.15760i	−1.95159	+	0.939839i
$59$	1.11604	−	4.88969i	0.145296	−	0.636584i	−0.848859	−	0.528620i	$-0.822710\pi$
$59$	1.11604	−	4.88969i	0.145296	−	0.636584i	0.994155	−	0.107964i	$-0.0344332\pi$
$60$		0			0
$61$	−0.916644	+	1.14943i	−0.117364	+	0.147170i	−0.837043	−	0.547137i	$-0.815718\pi$
$61$	−0.916644	+	1.14943i	−0.117364	+	0.147170i	0.719679	+	0.694307i	$0.244289\pi$
$62$	−18.9219	−	9.11233i	−2.40309	−	1.15727i
$63$		0			0
$64$	4.80089	−	2.31199i	0.600111	−	0.288998i
$65$	0.834098	−	3.65442i	0.103457	−	0.453275i
$66$		0			0
$67$	7.39128			0.902988			0.451494	−	0.892274i	$-0.350891\pi$
$67$	7.39128			0.902988			0.451494	+	0.892274i	$0.350891\pi$
$68$	19.9749			2.42232
$69$		0			0
$70$	−1.26971	+	6.45831i	−0.151760	+	0.771916i
$71$	4.50428	+	5.64818i	0.534559	+	0.670316i	0.973629	−	0.228137i	$-0.0732634\pi$
$71$	4.50428	+	5.64818i	0.534559	+	0.670316i	−0.439070	+	0.898453i	$0.644692\pi$
$72$		0			0
$73$	−13.6805	+	6.58819i	−1.60118	+	0.771089i	−0.999615	−	0.0277323i	$-0.991171\pi$
$73$	−13.6805	+	6.58819i	−1.60118	+	0.771089i	−0.601568	+	0.798822i	$0.705457\pi$
$74$	12.0947	−	5.82450i	1.40598	−	0.677084i
$75$		0			0
$76$	13.0351	+	16.3455i	1.49523	+	1.87496i
$77$	3.31309	+	1.47368i	0.377562	+	0.167941i
$78$		0			0
$79$	−4.76890			−0.536543			−0.268272	−	0.963343i	$-0.586452\pi$
$79$	−4.76890			−0.536543			−0.268272	+	0.963343i	$0.586452\pi$
$80$	−5.21319			−0.582853
$81$		0			0
$82$	−0.577227	+	2.52900i	−0.0637441	+	0.279281i
$83$	11.5050	−	5.54053i	1.26284	−	0.608153i	0.321917	−	0.946768i	$-0.395673\pi$
$83$	11.5050	−	5.54053i	1.26284	−	0.608153i	0.940925	+	0.338615i	$0.109958\pi$
$84$		0			0
$85$	4.28615	+	2.06410i	0.464899	+	0.223883i
$86$	−14.8876	+	18.6684i	−1.60537	+	2.01307i
$87$		0			0
$88$	−1.66730	+	7.30493i	−0.177735	+	0.778708i
$89$	−8.28049	+	3.98768i	−0.877731	+	0.422693i	−0.817795	−	0.575510i	$-0.804804\pi$
$89$	−8.28049	+	3.98768i	−0.877731	+	0.422693i	−0.0599354	+	0.998202i	$0.519089\pi$
$90$		0			0
$91$	9.06682	+	4.03296i	0.950461	+	0.422769i
$92$	−5.58927	+	24.4882i	−0.582721	+	2.55307i
$93$		0			0
$94$	−6.85423	−	8.59494i	−0.706960	−	0.886500i
$95$	1.10797	+	4.85434i	0.113675	+	0.498045i
$96$		0			0
$97$	7.04354			0.715164			0.357582	−	0.933882i	$-0.383601\pi$
$97$	7.04354			0.715164			0.357582	+	0.933882i	$0.383601\pi$
$98$	−16.1278	−	6.59645i	−1.62915	−	0.666343i
$99$		0			0
$100$	15.1275	+	7.28501i	1.51275	+	0.728501i
$101$	1.22771	+	5.37895i	0.122162	+	0.535225i	0.998560	+	0.0536390i	$0.0170820\pi$
$101$	1.22771	+	5.37895i	0.122162	+	0.535225i	−0.876399	+	0.481586i	$0.840061\pi$
$102$		0			0
$103$	−0.319244	−	1.39870i	−0.0314560	−	0.137818i	0.956762	−	0.290873i	$-0.0939458\pi$
$103$	−0.319244	−	1.39870i	−0.0314560	−	0.137818i	−0.988218	+	0.153055i	$0.951089\pi$
$104$	−4.56284	+	19.9911i	−0.447424	+	1.96029i
$105$		0			0
$106$	7.34832	+	32.1951i	0.713732	+	3.12706i
$107$	1.70684	−	0.821969i	0.165006	−	0.0794627i	−0.349558	−	0.936915i	$-0.613668\pi$
$107$	1.70684	−	0.821969i	0.165006	−	0.0794627i	0.514564	+	0.857452i	$0.327954\pi$
$108$		0			0
$109$	−8.11854	−	3.90969i	−0.777616	−	0.374480i	0.00259522	−	0.999997i	$-0.499174\pi$
$109$	−8.11854	−	3.90969i	−0.777616	−	0.374480i	−0.780211	+	0.625517i	$0.784888\pi$
$110$	−2.12579	+	2.66566i	−0.202686	+	0.254160i
$111$		0			0
$112$	2.66235	−	13.5419i	0.251568	−	1.27959i
$113$	−3.65450	+	1.75991i	−0.343786	+	0.165559i	−0.597807	−	0.801640i	$-0.703961\pi$
$113$	−3.65450	+	1.75991i	−0.343786	+	0.165559i	0.254021	+	0.967199i	$0.418247\pi$
$114$		0			0
$115$	−3.72980	+	4.67702i	−0.347806	+	0.436135i
$116$	27.8096			2.58205
$117$		0			0
$118$	−7.78403	+	9.76087i	−0.716578	+	0.898561i
$119$	−7.55066	+	10.0797i	−0.692168	+	0.924001i
$120$		0			0
$121$	−5.68727	−	7.13161i	−0.517024	−	0.648328i
$122$	3.29721	−	1.58785i	0.298516	−	0.143758i
$123$		0			0
$124$	22.0742	+	27.6802i	1.98232	+	2.48576i
$125$	5.60879	+	7.03319i	0.501665	+	0.629068i
$126$		0			0
$127$	9.02478	−	11.3167i	0.800820	−	1.00420i	−0.198888	−	0.980022i	$-0.563733\pi$
$127$	9.02478	−	11.3167i	0.800820	−	1.00420i	0.999708	−	0.0241738i	$-0.00769552\pi$
$128$	−17.3650			−1.53487
$129$		0			0
$130$	−5.81757	+	7.29500i	−0.510235	+	0.639814i
$131$	−0.733579	+	3.21402i	−0.0640931	+	0.280810i	−0.996811	−	0.0797962i	$-0.974573\pi$
$131$	−0.733579	+	3.21402i	−0.0640931	+	0.280810i	0.932718	+	0.360606i	$0.117430\pi$
$132$		0			0
$133$	−13.1755	+	0.398998i	−1.14246	+	0.0345975i
$134$	−16.5766	−	7.98287i	−1.43200	−	0.689615i
$135$		0			0
$136$	−23.4470	−	11.2915i	−2.01056	−	0.968234i
$137$	3.83898	−	16.8197i	0.327987	−	1.43700i	−0.494976	−	0.868907i	$-0.664823\pi$
$137$	3.83898	−	16.8197i	0.327987	−	1.43700i	0.822962	−	0.568096i	$-0.192320\pi$
$138$		0			0
$139$	−2.78357	−	12.1956i	−0.236099	−	1.03442i	−0.944475	−	0.328582i	$-0.893429\pi$
$139$	−2.78357	−	12.1956i	−0.236099	−	1.03442i	0.708376	−	0.705835i	$-0.249428\pi$
$140$	6.65230	−	8.88039i	0.562222	−	0.750530i
$141$		0			0
$142$	−4.00159	−	17.5321i	−0.335806	−	1.47126i
$143$	3.20496	+	4.01889i	0.268012	+	0.336077i
$144$		0			0
$145$	5.96728	+	2.87369i	0.495556	+	0.238647i
$146$	37.7971			3.12811
$147$		0			0
$148$	−22.6300			−1.86018
$149$	19.0323	+	9.16545i	1.55918	+	0.750863i	0.997092	−	0.0762125i	$-0.0242827\pi$
$149$	19.0323	+	9.16545i	1.55918	+	0.750863i	0.562091	+	0.827075i	$0.309997\pi$
$150$		0			0
$151$	2.36319	+	2.96335i	0.192314	+	0.241154i	0.868634	−	0.495454i	$-0.164998\pi$
$151$	2.36319	+	2.96335i	0.192314	+	0.241154i	−0.676321	+	0.736607i	$0.736427\pi$
$152$	−6.06104	−	26.5551i	−0.491615	−	2.15391i
$153$		0			0
$154$	−5.83873	−	6.88333i	−0.470498	−	0.554674i
$155$	1.87629	+	8.22056i	0.150707	+	0.660291i
$156$		0			0
$157$	−0.626295	+	2.74398i	−0.0499838	+	0.218993i	−0.993751	−	0.111616i	$-0.964397\pi$
$157$	−0.626295	+	2.74398i	−0.0499838	+	0.218993i	0.943768	+	0.330610i	$0.107254\pi$
$158$	10.6953	+	5.15060i	0.850874	+	0.409760i
$159$		0			0
$160$	1.84629	+	0.889124i	0.145962	+	0.0702914i
$161$	−10.2443	−	12.0771i	−0.807366	−	0.951811i
$162$		0			0
$163$	−0.911373	+	3.99299i	−0.0713842	+	0.312755i	−0.997997	−	0.0632624i	$-0.979849\pi$
$163$	−0.911373	+	3.99299i	−0.0713842	+	0.312755i	0.926613	+	0.376017i	$0.122707\pi$
$164$	2.72650	−	3.41892i	0.212904	−	0.266973i
$165$		0			0
$166$	−31.7866			−2.46712
$167$	−12.2546	+	15.3668i	−0.948287	+	1.18911i	0.0335588	+	0.999437i	$0.489316\pi$
$167$	−12.2546	+	15.3668i	−0.948287	+	1.18911i	−0.981846	+	0.189678i	$0.939256\pi$
$168$		0			0
$169$	0.665526	+	0.834543i	0.0511943	+	0.0641956i
$170$	−7.38335	−	9.25843i	−0.566277	−	0.710089i
$171$		0			0
$172$	36.2664	−	17.4650i	2.76529	−	1.33169i
$173$	1.66327	+	2.08568i	0.126456	+	0.158571i	0.841029	−	0.540990i	$-0.181950\pi$
$173$	1.66327	+	2.08568i	0.126456	+	0.158571i	−0.714573	+	0.699561i	$0.753379\pi$
$174$		0			0
$175$	−9.39442	+	4.87977i	−0.710151	+	0.368876i
$176$	4.45738	−	5.58938i	0.335988	−	0.421316i
$177$		0			0
$178$	22.8777			1.71476
$179$	−2.25636	+	2.82939i	−0.168649	+	0.211479i	−0.858972	−	0.512022i	$-0.828897\pi$
$179$	−2.25636	+	2.82939i	−0.168649	+	0.211479i	0.690324	+	0.723501i	$0.257468\pi$
$180$		0			0
$181$	−3.21350	+	1.54754i	−0.238858	+	0.115028i	−0.549484	−	0.835504i	$-0.685176\pi$
$181$	−3.21350	+	1.54754i	−0.238858	+	0.115028i	0.310626	+	0.950532i	$0.399461\pi$
$182$	−15.9786	−	18.8373i	−1.18441	−	1.39632i
$183$		0			0
$184$	20.4035	−	25.5852i	1.50417	−	1.88616i
$185$	−4.85588	−	2.33847i	−0.357011	−	0.171928i
$186$		0			0
$187$	−5.87780	+	2.83060i	−0.429827	+	0.206994i
$188$	4.12383	+	18.0677i	0.300761	+	1.31772i
$189$		0			0
$190$	2.75800	−	12.0836i	0.200087	−	0.876636i
$191$	−3.49019	−	15.2915i	−0.252541	−	1.10646i	−0.929031	−	0.370003i	$-0.879357\pi$
$191$	−3.49019	−	15.2915i	−0.252541	−	1.10646i	0.676489	−	0.736452i	$-0.263500\pi$
$192$		0			0
$193$	−3.48501	−	15.2688i	−0.250856	−	1.09907i	−0.930719	−	0.365735i	$-0.880818\pi$
$193$	−3.48501	−	15.2688i	−0.250856	−	1.09907i	0.679863	−	0.733339i	$-0.262039\pi$
$194$	−15.7967	−	7.60730i	−1.13414	−	0.546173i
$195$		0			0
$196$	19.6706	+	21.8153i	1.40504	+	1.55823i
$197$	3.38611			0.241251			0.120625	−	0.992698i	$-0.461510\pi$
$197$	3.38611			0.241251			0.120625	+	0.992698i	$0.461510\pi$
$198$		0			0
$199$	1.46888	+	6.43557i	0.104126	+	0.456206i	0.999931	+	0.0117582i	$0.00374283\pi$
$199$	1.46888	+	6.43557i	0.104126	+	0.456206i	−0.895805	+	0.444448i	$0.853400\pi$
$200$	−13.6388	−	17.1026i	−0.964411	−	1.20933i
$201$		0			0
$202$	3.05606	−	13.3895i	0.215024	−	0.942080i
$203$	−10.5122	+	14.0331i	−0.737812	+	0.984932i
$204$		0			0
$205$	0.938337	−	0.451879i	0.0655363	−	0.0315606i
$206$	−0.794674	+	3.48169i	−0.0553676	+	0.242581i
$207$		0			0
$208$	12.1984	−	15.2963i	0.845804	−	1.06060i
$209$	−6.15197	−	2.96263i	−0.425541	−	0.204930i
$210$		0			0
$211$	−8.14197	+	3.92097i	−0.560517	+	0.269931i	−0.692617	−	0.721306i	$-0.743542\pi$
$211$	−8.14197	+	3.92097i	−0.560517	+	0.269931i	0.132100	+	0.991236i	$0.457828\pi$
$212$	12.3876	−	54.2738i	0.850786	−	3.72754i
$213$		0			0
$214$	−4.71572			−0.322360
$215$	9.58666			0.653805
$216$		0			0
$217$	−22.3121	+	0.675681i	−1.51464	+	0.0458682i
$218$	13.9850	+	17.5367i	0.947187	+	1.18773i
$219$		0			0
$220$	5.17847	−	2.49382i	0.349132	−	0.168133i
$221$	−16.0856	+	7.74639i	−1.08203	+	0.521079i
$222$		0			0
$223$	6.66688	+	8.36001i	0.446448	+	0.559827i	0.953230	−	0.302247i	$-0.0977366\pi$
$223$	6.66688	+	8.36001i	0.446448	+	0.559827i	−0.506782	+	0.862074i	$0.669165\pi$
$224$	−3.25249	+	4.34187i	−0.217316	+	0.290103i
$225$		0			0
$226$	10.0968			0.671630
$227$	0.136875			0.00908469			0.00454235	−	0.999990i	$-0.498554\pi$
$227$	0.136875			0.00908469			0.00454235	+	0.999990i	$0.498554\pi$
$228$		0			0
$229$	−0.113393	+	0.496807i	−0.00749322	+	0.0328300i	−0.978536	−	0.206074i	$-0.933931\pi$
$229$	−0.113393	+	0.496807i	−0.00749322	+	0.0328300i	0.971043	+	0.238904i	$0.0767882\pi$
$230$	13.4163	−	6.46094i	0.884644	−	0.426022i
$231$		0			0
$232$	−32.6434	−	15.7202i	−2.14314	−	1.03208i
$233$	5.70702	−	7.15638i	0.373880	−	0.468830i	−0.558922	−	0.829220i	$-0.688785\pi$
$233$	5.70702	−	7.15638i	0.373880	−	0.468830i	0.932802	+	0.360390i	$0.117356\pi$
$234$		0			0
$235$	−0.982140	+	4.30303i	−0.0640677	+	0.280699i
$236$	18.9621	−	9.13164i	1.23432	−	0.594419i
$237$		0			0
$238$	27.8205	−	14.4509i	1.80333	−	0.936711i
$239$	2.15312	−	9.43343i	0.139274	−	0.610198i	−0.856322	−	0.516443i	$-0.827256\pi$
$239$	2.15312	−	9.43343i	0.139274	−	0.610198i	0.995595	−	0.0937550i	$-0.0298870\pi$
$240$		0			0
$241$	17.9353	+	22.4902i	1.15532	+	1.44872i	0.871874	+	0.489731i	$0.162905\pi$
$241$	17.9353	+	22.4902i	1.15532	+	1.44872i	0.283442	+	0.958989i	$0.408524\pi$
$242$	5.05256	+	22.1367i	0.324791	+	1.42300i
$243$		0			0
$244$	−6.16932			−0.394950
$245$	1.96657	+	6.71370i	0.125639	+	0.428922i
$246$		0			0
$247$	−16.8359	−	8.10773i	−1.07124	−	0.515882i
$248$	−10.2640	−	44.9697i	−0.651767	−	2.85558i
$249$		0			0
$250$	−4.98284	−	21.8312i	−0.315142	−	1.38073i
$251$	4.44156	−	19.4597i	0.280349	−	1.22829i	−0.617000	−	0.786964i	$-0.711652\pi$
$251$	4.44156	−	19.4597i	0.280349	−	1.22829i	0.897348	−	0.441324i	$-0.145491\pi$
$252$		0			0
$253$	−1.82547	−	7.99790i	−0.114766	−	0.502824i
$254$	−32.4626	+	15.6332i	−2.03688	+	0.980912i
$255$		0			0
$256$	29.3432	+	14.1309i	1.83395	+	0.883183i
$257$	−6.67402	+	8.36895i	−0.416314	+	0.522041i	−0.945130	−	0.326696i	$-0.894065\pi$
$257$	−6.67402	+	8.36895i	−0.416314	+	0.522041i	0.528816	+	0.848737i	$0.322636\pi$
$258$		0			0
$259$	8.55431	−	11.4195i	0.531539	−	0.709571i
$260$	14.1717	−	6.82474i	0.878892	−	0.423252i
$261$		0			0
$262$	5.11648	−	6.41586i	0.316097	−	0.396373i
$263$	−2.15320			−0.132772			−0.0663859	−	0.997794i	$-0.521147\pi$
$263$	−2.15320			−0.132772			−0.0663859	+	0.997794i	$0.521147\pi$
$264$		0			0
$265$	8.26646	−	10.3658i	0.507805	−	0.636767i
$266$	29.9801	+	13.3353i	1.83820	+	0.817638i
$267$		0			0
$268$	19.3382	+	24.2493i	1.18127	+	1.48126i
$269$	8.29048	−	3.99248i	0.505479	−	0.243426i	−0.163723	−	0.986506i	$-0.552350\pi$
$269$	8.29048	−	3.99248i	0.505479	−	0.243426i	0.669202	+	0.743080i	$0.266636\pi$
$270$		0			0
$271$	16.7057	+	20.9483i	1.01480	+	1.27252i	0.961751	+	0.273925i	$0.0883220\pi$
$271$	16.7057	+	20.9483i	1.01480	+	1.27252i	0.0530475	+	0.998592i	$0.483107\pi$
$272$	15.4815	+	19.4132i	0.938704	+	1.17710i
$273$		0			0
$274$	−26.7757	+	33.5757i	−1.61758	+	2.02838i
$275$	−5.48374			−0.330682
$276$		0			0
$277$	−7.35366	+	9.22120i	−0.441839	+	0.554048i	−0.952027	−	0.306015i	$-0.901004\pi$
$277$	−7.35366	+	9.22120i	−0.441839	+	0.554048i	0.510188	+	0.860063i	$0.329576\pi$
$278$	−6.92895	+	30.3577i	−0.415571	+	1.82074i
$279$		0			0
$280$	−12.8285	+	6.66355i	−0.766650	+	0.398223i
$281$	−4.71604	−	2.27113i	−0.281336	−	0.135484i	0.287895	−	0.957662i	$-0.407045\pi$
$281$	−4.71604	−	2.27113i	−0.281336	−	0.135484i	−0.569231	+	0.822178i	$0.692759\pi$
$282$		0			0
$283$	22.1400	+	10.6620i	1.31608	+	0.633793i	0.954406	−	0.298511i	$-0.0964899\pi$
$283$	22.1400	+	10.6620i	1.31608	+	0.633793i	0.361677	+	0.932303i	$0.382204\pi$
$284$	−6.74579	+	29.5552i	−0.400289	+	1.75378i
$285$		0			0
$286$	−2.84728	−	12.4748i	−0.168363	−	0.737648i
$287$	0.694605	+	2.66821i	0.0410012	+	0.157499i
$288$		0			0
$289$	−1.25921	−	5.51698i	−0.0740714	−	0.324528i
$290$	−10.2793	−	12.8898i	−0.603619	−	0.756915i
$291$		0			0
$292$	−57.4075	−	27.6460i	−3.35952	−	1.61786i
$293$	5.69455			0.332679			0.166340	−	0.986069i	$-0.446805\pi$
$293$	5.69455			0.332679			0.166340	+	0.986069i	$0.446805\pi$
$294$		0			0
$295$	5.01243			0.291835
$296$	26.5636	+	12.7923i	1.54398	+	0.743539i
$297$		0			0
$298$	−32.7851	−	41.1112i	−1.89919	−	2.38151i
$299$	−4.99569	−	21.8876i	−0.288908	−	1.26579i
$300$		0			0
$301$	−4.89586	+	24.9025i	−0.282192	+	1.43535i
$302$	−2.09945	−	9.19831i	−0.120810	−	0.529303i
$303$		0			0
$304$	−5.78301	+	25.3370i	−0.331679	+	1.45318i
$305$	−1.32379	−	0.637505i	−0.0758001	−	0.0365034i
$306$		0			0
$307$	1.02326	+	0.492776i	0.0584005	+	0.0281242i	0.462856	−	0.886433i	$-0.346825\pi$
$307$	1.02326	+	0.492776i	0.0584005	+	0.0281242i	−0.404456	+	0.914558i	$0.632539\pi$
$308$	3.83337	+	14.7253i	0.218426	+	0.839049i
$309$		0			0
$310$	4.67053	−	20.4629i	0.265268	−	1.16222i
$311$	−7.86218	+	9.85886i	−0.445823	+	0.559045i	−0.953068	−	0.302758i	$-0.902093\pi$
$311$	−7.86218	+	9.85886i	−0.445823	+	0.559045i	0.507244	+	0.861802i	$0.330664\pi$
$312$		0			0
$313$	9.01903			0.509786			0.254893	−	0.966969i	$-0.417960\pi$
$313$	9.01903			0.509786			0.254893	+	0.966969i	$0.417960\pi$
$314$	4.36821	−	5.47756i	0.246512	−	0.309117i
$315$		0			0
$316$	−12.4771	−	15.6458i	−0.701892	−	0.880145i
$317$	−12.7649	−	16.0067i	−0.716947	−	0.899023i	0.281214	−	0.959645i	$-0.409263\pi$
$317$	−12.7649	−	16.0067i	−0.716947	−	0.899023i	−0.998161	+	0.0606221i	$0.980692\pi$
$318$		0			0
$319$	−8.18321	+	3.94082i	−0.458172	+	0.220644i
$320$	3.32032	+	4.16355i	0.185612	+	0.232750i
$321$		0			0
$322$	9.93142	+	38.1499i	0.553457	+	2.12601i
$323$	14.7866	−	18.5418i	0.822746	−	1.03169i
$324$		0			0
$325$	−15.0071			−0.832446
$326$	6.35654	−	7.97085i	0.352056	−	0.441464i
$327$		0			0
$328$	−5.13307	+	2.47196i	−0.283426	+	0.136491i
$329$	−10.6761	−	4.74876i	−0.588590	−	0.261808i
$330$		0			0
$331$	−17.6887	+	22.1810i	−0.972261	+	1.21918i	0.00342295	+	0.999994i	$0.498910\pi$
$331$	−17.6887	+	22.1810i	−0.972261	+	1.21918i	−0.975684	+	0.219183i	$0.929661\pi$
$332$	48.2786	+	23.2497i	2.64963	+	1.27600i
$333$		0			0
$334$	44.0803	−	21.2280i	2.41197	−	1.16154i
$335$	1.64373	+	7.20163i	0.0898063	+	0.393467i
$336$		0			0
$337$	−2.14084	+	9.37962i	−0.116619	+	0.510940i	0.882552	+	0.470216i	$0.155824\pi$
$337$	−2.14084	+	9.37962i	−0.116619	+	0.510940i	−0.999170	+	0.0407247i	$0.987033\pi$
$338$	−0.591252	−	2.59044i	−0.0321599	−	0.140902i
$339$		0			0
$340$	4.44217	+	19.4624i	0.240911	+	1.05550i
$341$	−10.4180	−	5.01706i	−0.564168	−	0.271689i
$342$		0			0
$343$	−18.4439	+	1.67973i	−0.995879	+	0.0906971i
$344$	−52.4428			−2.82753
$345$		0			0
$346$	−1.47765	−	6.47400i	−0.0794388	−	0.348044i
$347$	−7.16021	−	8.97862i	−0.384380	−	0.481997i	0.551571	−	0.834128i	$-0.314029\pi$
$347$	−7.16021	−	8.97862i	−0.384380	−	0.481997i	−0.935951	+	0.352131i	$0.885457\pi$
$348$		0			0
$349$	7.95444	−	34.8507i	0.425792	−	1.86551i	−0.0707382	−	0.997495i	$-0.522535\pi$
$349$	7.95444	−	34.8507i	0.425792	−	1.86551i	0.496530	−	0.868020i	$-0.334607\pi$
$350$	26.3394	−	0.797643i	1.40790	−	0.0426358i
$351$		0			0
$352$	−2.53190	+	1.21930i	−0.134951	+	0.0649887i
$353$	−4.84471	+	21.2261i	−0.257858	+	1.12975i	0.665679	+	0.746238i	$0.268142\pi$
$353$	−4.84471	+	21.2261i	−0.257858	+	1.12975i	−0.923537	+	0.383510i	$0.874715\pi$
$354$		0			0
$355$	−4.50157	+	5.64479i	−0.238918	+	0.299594i
$356$	−34.7474	−	16.7335i	−1.84161	−	0.886873i
$357$		0			0
$358$	8.11626	−	3.90858i	0.428958	−	0.206575i
$359$	−7.14631	+	31.3101i	−0.377168	+	1.65248i	0.328920	+	0.944358i	$0.393315\pi$
$359$	−7.14631	+	31.3101i	−0.377168	+	1.65248i	−0.706088	+	0.708124i	$0.749542\pi$
$360$		0			0
$361$	5.82203			0.306423
$362$	8.87840			0.466638
$363$		0			0
$364$	10.4906	+	40.2980i	0.549858	+	2.11219i
$365$	−9.46152	−	11.8644i	−0.495239	−	0.621010i
$366$		0			0
$367$	2.03444	−	0.979732i	0.106197	−	0.0511416i	−0.380031	−	0.924974i	$-0.624087\pi$
$367$	2.03444	−	0.979732i	0.106197	−	0.0511416i	0.486228	+	0.873832i	$0.338372\pi$
$368$	−28.1314	+	13.5474i	−1.46645	+	0.706206i
$369$		0			0
$370$	8.36476	+	10.4891i	0.434863	+	0.545301i
$371$	22.7048	+	26.7669i	1.17877	+	1.38967i
$372$		0			0
$373$	9.82385			0.508660			0.254330	−	0.967118i	$-0.418145\pi$
$373$	9.82385			0.508660			0.254330	+	0.967118i	$0.418145\pi$
$374$	16.2394			0.839722
$375$		0			0
$376$	5.37269	−	23.5393i	0.277075	−	1.21395i
$377$	−22.3947	+	10.7847i	−1.15338	+	0.555441i
$378$		0			0
$379$	−11.2883	−	5.43618i	−0.579843	−	0.279238i	0.120884	−	0.992667i	$-0.461427\pi$
$379$	−11.2883	−	5.43618i	−0.579843	−	0.279238i	−0.700728	+	0.713429i	$0.747141\pi$
$380$	−13.0273	+	16.3357i	−0.668285	+	0.838003i
$381$		0			0
$382$	−8.68791	+	38.0642i	−0.444512	+	1.94753i
$383$	25.2694	−	12.1691i	1.29121	−	0.621813i	0.342961	−	0.939349i	$-0.388570\pi$
$383$	25.2694	−	12.1691i	1.29121	−	0.621813i	0.948246	+	0.317537i	$0.102856\pi$
$384$		0			0
$385$	−0.699078	+	3.55581i	−0.0356283	+	0.181221i
$386$	−8.67501	+	38.0077i	−0.441547	+	1.93454i
$387$		0			0
$388$	18.4284	+	23.1084i	0.935559	+	1.17315i
$389$	−6.14250	−	26.9120i	−0.311437	−	1.36449i	−0.852154	−	0.523290i	$-0.824704\pi$
$389$	−6.14250	−	26.9120i	−0.311437	−	1.36449i	0.540718	−	0.841204i	$-0.318153\pi$
$390$		0			0
$391$	28.4929			1.44095
$392$	−10.7579	−	36.7266i	−0.543356	−	1.85497i
$393$		0			0
$394$	−7.59412	−	3.65714i	−0.382586	−	0.184244i
$395$	−1.06054	−	4.64654i	−0.0533617	−	0.233793i
$396$		0			0
$397$	−0.704828	−	3.08806i	−0.0353743	−	0.154985i	0.954156	−	0.299309i	$-0.0967563\pi$
$397$	−0.704828	−	3.08806i	−0.0353743	−	0.154985i	−0.989530	+	0.144324i	$0.953899\pi$
$398$	3.65638	−	16.0197i	0.183278	−	0.802993i
$399$		0			0
$400$	4.64436	+	20.3483i	0.232218	+	1.01741i
$401$	−28.4494	+	13.7005i	−1.42069	+	0.684171i	−0.977242	−	0.212127i	$-0.931961\pi$
$401$	−28.4494	+	13.7005i	−1.42069	+	0.684171i	−0.443453	+	0.896298i	$0.646247\pi$
$402$		0			0
$403$	−28.5106	−	13.7300i	−1.42022	−	0.683940i
$404$	−14.4351	+	18.1011i	−0.718174	+	0.900562i
$405$		0			0
$406$	38.7323	−	20.1188i	1.92225	−	0.998481i
$407$	6.65909	−	3.20685i	0.330079	−	0.158958i
$408$		0			0
$409$	18.6507	−	23.3873i	0.922220	−	1.15643i	−0.0651310	−	0.997877i	$-0.520747\pi$
$409$	18.6507	−	23.3873i	0.922220	−	1.15643i	0.987351	−	0.158550i	$-0.0506820\pi$
$410$	−2.59248			−0.128033
$411$		0			0
$412$	3.75360	−	4.70686i	0.184926	−	0.231890i
$413$	−2.55982	+	13.0204i	−0.125961	+	0.640690i
$414$		0			0
$415$	7.95695	+	9.97770i	0.390591	+	0.489786i
$416$	−6.92894	+	3.33680i	−0.339719	+	0.163600i
$417$		0			0
$418$	10.5974	+	13.2887i	0.518337	+	0.649974i
$419$	15.5301	+	19.4741i	0.758694	+	0.951372i	0.999817	−	0.0191223i	$-0.00608718\pi$
$419$	15.5301	+	19.4741i	0.758694	+	0.951372i	−0.241123	+	0.970495i	$0.577516\pi$
$420$		0			0
$421$	1.00205	−	1.25653i	0.0488370	−	0.0612396i	−0.756813	−	0.653631i	$-0.773245\pi$
$421$	1.00205	−	1.25653i	0.0488370	−	0.0612396i	0.805650	+	0.592392i	$0.201816\pi$
$422$	22.4950			1.09504
$423$		0			0
$424$	−45.2208	+	56.7051i	−2.19612	+	2.75384i
$425$	4.23819	−	18.5687i	0.205582	−	0.900715i
$426$		0			0
$427$	2.33205	−	3.11313i	0.112856	−	0.150655i
$428$	7.16239	+	3.44923i	0.346207	+	0.166725i
$429$		0			0
$430$	−21.5002	−	10.3540i	−1.03683	−	0.499313i
$431$	−3.53833	+	15.5024i	−0.170435	+	0.746725i	0.815385	+	0.578919i	$0.196525\pi$
$431$	−3.53833	+	15.5024i	−0.170435	+	0.746725i	−0.985820	+	0.167806i	$0.946332\pi$
$432$		0			0
$433$	2.88293	+	12.6310i	0.138545	+	0.607005i	0.995755	+	0.0920388i	$0.0293384\pi$
$433$	2.88293	+	12.6310i	0.138545	+	0.607005i	−0.857210	+	0.514966i	$0.827804\pi$
$434$	50.7696	+	22.5825i	2.43702	+	1.08400i
$435$		0			0
$436$	−8.41406	−	36.8644i	−0.402960	−	1.76549i
$437$	18.5937	+	23.3157i	0.889457	+	1.11534i
$438$		0			0
$439$	−11.1693	−	5.37887i	−0.533084	−	0.256720i	0.147920	−	0.988999i	$-0.452742\pi$
$439$	−11.1693	−	5.37887i	−0.533084	−	0.256720i	−0.681004	+	0.732280i	$0.738456\pi$
$440$	−7.48829			−0.356990
$441$		0			0
$442$	44.4419			2.11388
$443$	22.6375	+	10.9017i	1.07554	+	0.517953i	0.885888	−	0.463898i	$-0.153550\pi$
$443$	22.6375	+	10.9017i	1.07554	+	0.517953i	0.189652	+	0.981851i	$0.439264\pi$
$444$		0			0
$445$	−5.72684	−	7.18123i	−0.271478	−	0.340423i
$446$	−5.92285	−	25.9497i	−0.280455	−	1.22875i
$447$		0			0
$448$	−12.5110	+	6.49862i	−0.591088	+	0.307031i
$449$	−6.20012	−	27.1645i	−0.292602	−	1.28197i	−0.880890	−	0.473321i	$-0.843055\pi$
$449$	−6.20012	−	27.1645i	−0.292602	−	1.28197i	0.588288	−	0.808651i	$-0.299802\pi$
$450$		0			0
$451$	−0.317809	+	1.39241i	−0.0149651	+	0.0655662i
$452$	−15.3354	−	7.38512i	−0.721315	−	0.347367i
$453$		0			0
$454$	−0.306972	−	0.147830i	−0.0144069	−	0.00693801i
$455$	−1.91314	+	9.73106i	−0.0896894	+	0.456199i
$456$		0			0
$457$	3.47667	−	15.2323i	0.162632	−	0.712536i	−0.826185	−	0.563399i	$-0.809493\pi$
$457$	3.47667	−	15.2323i	0.162632	−	0.712536i	0.988817	−	0.149137i	$-0.0476496\pi$
$458$	0.790881	−	0.991733i	0.0369554	−	0.0463407i
$459$		0			0
$460$	−25.1028			−1.17043
$461$	9.36262	−	11.7404i	0.436061	−	0.546803i	−0.514439	−	0.857527i	$-0.672000\pi$
$461$	9.36262	−	11.7404i	0.436061	−	0.546803i	0.950500	+	0.310724i	$0.100571\pi$
$462$		0			0
$463$	−9.28649	−	11.6449i	−0.431580	−	0.541184i	0.517722	−	0.855549i	$-0.326780\pi$
$463$	−9.28649	−	11.6449i	−0.431580	−	0.541184i	−0.949302	+	0.314365i	$0.898209\pi$
$464$	21.5537	+	27.0275i	1.00061	+	1.25472i
$465$		0			0
$466$	−20.5285	+	9.88598i	−0.950962	+	0.457959i
$467$	9.42607	+	11.8199i	0.436186	+	0.546960i	0.950534	−	0.310622i	$-0.100537\pi$
$467$	9.42607	+	11.8199i	0.436186	+	0.546960i	−0.514347	+	0.857582i	$0.671966\pi$
$468$		0			0
$469$	−19.5465	+	0.591932i	−0.902574	+	0.0273329i
$470$	6.85011	−	8.58977i	0.315972	−	0.396217i
$471$		0			0
$472$	−27.4200			−1.26211
$473$	−8.19679	+	10.2784i	−0.376889	+	0.472603i
$474$		0			0
$475$	17.9605	−	8.64933i	0.824085	−	0.396858i
$476$	−52.8245	+	1.59970i	−2.42121	+	0.0733220i
$477$		0			0
$478$	−15.0173	+	18.8311i	−0.686877	+	0.861316i
$479$	−10.1123	−	4.86981i	−0.462041	−	0.222507i	0.188357	−	0.982101i	$-0.439684\pi$
$479$	−10.1123	−	4.86981i	−0.462041	−	0.222507i	−0.650398	+	0.759593i	$0.725398\pi$
$480$		0			0
$481$	18.2237	−	8.77606i	0.830928	−	0.400154i
$482$	−15.9337	−	69.8101i	−0.725761	−	3.17976i
$483$		0			0
$484$	8.51749	−	37.3176i	0.387159	−	1.69625i
$485$	1.56639	+	6.86282i	0.0711263	+	0.311625i
$486$		0			0
$487$	−6.39938	−	28.0375i	−0.289983	−	1.27050i	−0.884547	−	0.466452i	$-0.845532\pi$
$487$	−6.39938	−	28.0375i	−0.289983	−	1.27050i	0.594563	−	0.804049i	$-0.297325\pi$
$488$	7.24167	+	3.48740i	0.327815	+	0.157867i
$489$		0			0
$490$	2.84059	−	17.1809i	0.128325	−	0.776156i
$491$	3.62158			0.163440			0.0817198	−	0.996655i	$-0.473959\pi$
$491$	3.62158			0.163440			0.0817198	+	0.996655i	$0.473959\pi$
$492$		0			0
$493$	−7.01968	−	30.7552i	−0.316151	−	1.38515i
$494$	29.0016	+	36.3668i	1.30484	+	1.63622i
$495$		0			0
$496$	−9.79322	+	42.9069i	−0.439728	+	1.92658i
$497$	−12.3641	−	14.5761i	−0.554604	−	0.653828i
$498$		0			0
$499$	26.9200	−	12.9640i	1.20510	−	0.580348i	0.279978	−	0.960007i	$-0.409673\pi$
$499$	26.9200	−	12.9640i	1.20510	−	0.580348i	0.925127	+	0.379659i	$0.123959\pi$
$500$	−8.39995	+	36.8026i	−0.375657	+	1.64586i
$501$		0			0
$502$	−30.9785	+	38.8458i	−1.38264	+	1.73377i
$503$	−18.2566	−	8.79190i	−0.814020	−	0.392011i	−0.0199222	−	0.999802i	$-0.506342\pi$
$503$	−18.2566	−	8.79190i	−0.814020	−	0.392011i	−0.794098	+	0.607790i	$0.792056\pi$
$504$		0			0
$505$	−4.96791	+	2.39242i	−0.221069	+	0.106461i
$506$	−4.54402	+	19.9087i	−0.202006	+	0.885048i
$507$		0			0
$508$	60.7398			2.69489
$509$	−24.8948			−1.10344			−0.551722	−	0.834028i	$-0.686029\pi$
$509$	−24.8948			−1.10344			−0.551722	+	0.834028i	$0.686029\pi$
$510$		0			0
$511$	35.6510	−	18.5183i	1.57711	−	0.819203i
$512$	−28.8929	−	36.2305i	−1.27690	−	1.60118i
$513$		0			0
$514$	24.0068	−	11.5611i	1.05889	−	0.509936i
$515$	1.29182	−	0.622106i	0.0569242	−	0.0274133i
$516$		0			0
$517$	−3.77380	−	4.73219i	−0.165971	−	0.208122i
$518$	−31.5184	+	16.3717i	−1.38484	+	0.719332i
$519$		0			0
$520$	−20.4929			−0.898674
$521$	3.67256			0.160898			0.0804489	−	0.996759i	$-0.474365\pi$
$521$	3.67256			0.160898			0.0804489	+	0.996759i	$0.474365\pi$
$522$		0			0
$523$	−2.29902	+	10.0727i	−0.100529	+	0.440447i	0.899465	+	0.436993i	$0.143957\pi$
$523$	−2.29902	+	10.0727i	−0.100529	+	0.440447i	−0.999994	+	0.00345376i	$0.998901\pi$
$524$	−12.4638	+	6.00227i	−0.544486	+	0.262210i
$525$		0			0
$526$	4.82903	+	2.32554i	0.210556	+	0.101398i
$527$	25.0402	−	31.3994i	1.09077	−	1.36778i
$528$		0			0
$529$	−2.85473	+	12.5074i	−0.124119	+	0.543799i
$530$	−29.7349	+	14.3196i	−1.29160	+	0.622002i
$531$		0			0
$532$	−35.7809	−	42.1824i	−1.55130	−	1.82884i
$533$	−0.869737	+	3.81057i	−0.0376725	+	0.165054i
$534$		0			0
$535$	1.18046	+	1.48025i	0.0510356	+	0.0639966i
$536$	−8.99182	−	39.3958i	−0.388388	−	1.70164i
$537$		0			0
$538$	−22.9053			−0.987518
$539$	−8.87962	−	3.63187i	−0.382472	−	0.156436i
$540$		0			0
$541$	−14.8011	−	7.12783i	−0.636348	−	0.306449i	0.0877536	−	0.996142i	$-0.472031\pi$
$541$	−14.8011	−	7.12783i	−0.636348	−	0.306449i	−0.724102	+	0.689693i	$0.757745\pi$
$542$	−14.8413	−	65.0240i	−0.637489	−	2.79302i
$543$		0			0
$544$	−2.17190	−	9.51572i	−0.0931195	−	0.407983i
$545$	2.00391	−	8.77970i	0.0858381	−	0.376081i
$546$		0			0
$547$	−2.70025	−	11.8306i	−0.115454	−	0.505838i	−0.999277	−	0.0380165i	$-0.987896\pi$
$547$	−2.70025	−	11.8306i	−0.115454	−	0.505838i	0.883823	−	0.467822i	$-0.154961\pi$
$548$	65.2261	−	31.4112i	2.78632	−	1.34182i
$549$		0			0
$550$	12.2985	+	5.92265i	0.524410	+	0.252543i
$551$	20.5862	−	25.8142i	0.877001	−	1.09972i
$552$		0			0
$553$	12.6115	−	0.381918i	0.536297	−	0.0162408i
$554$	26.4515	−	12.7384i	1.12382	−	0.541201i
$555$		0			0
$556$	32.7285	−	41.0403i	1.38800	−	1.74049i
$557$	26.3084			1.11472			0.557362	−	0.830270i	$-0.311814\pi$
$557$	26.3084			1.11472			0.557362	+	0.830270i	$0.311814\pi$
$558$		0			0
$559$	−22.4318	+	28.1286i	−0.948765	+	1.18971i
$560$	13.7865	−	0.417499i	0.582585	−	0.0176426i
$561$		0			0
$562$	8.12388	+	10.1870i	0.342685	+	0.429714i
$563$	5.68502	−	2.73776i	0.239595	−	0.115383i	−0.310234	−	0.950660i	$-0.600407\pi$
$563$	5.68502	−	2.73776i	0.239595	−	0.115383i	0.549829	+	0.835277i	$0.314693\pi$
$564$		0			0
$565$	−2.52747	−	3.16935i	−0.106332	−	0.133336i
$566$	−38.1384	−	47.8240i	−1.60308	−	2.01019i
$567$		0			0
$568$	24.6254	−	30.8792i	1.03326	−	1.29566i
$569$	−0.265005			−0.0111096			−0.00555480	−	0.999985i	$-0.501768\pi$
$569$	−0.265005			−0.0111096			−0.00555480	+	0.999985i	$0.501768\pi$
$570$		0			0
$571$	−8.09472	+	10.1505i	−0.338753	+	0.424783i	−0.921806	−	0.387651i	$-0.873287\pi$
$571$	−8.09472	+	10.1505i	−0.338753	+	0.424783i	0.583053	+	0.812434i	$0.301858\pi$
$572$	−4.79988	+	21.0297i	−0.200693	+	0.879294i
$573$		0			0
$574$	1.32396	−	6.73426i	0.0552612	−	0.281083i
$575$	21.5783	+	10.3916i	0.899878	+	0.433359i
$576$		0			0
$577$	15.6724	+	7.54744i	0.652452	+	0.314204i	0.730669	−	0.682732i	$-0.239208\pi$
$577$	15.6724	+	7.54744i	0.652452	+	0.314204i	−0.0782171	+	0.996936i	$0.524923\pi$
$578$	−3.13448	+	13.7331i	−0.130377	+	0.571220i
$579$		0			0
$580$	6.18449	+	27.0960i	0.256797	+	1.12510i
$581$	−29.9818	+	15.5735i	−1.24385	+	0.646099i
$582$		0			0
$583$	4.04583	+	17.7260i	0.167561	+	0.734134i
$584$	51.7583	+	64.9028i	2.14177	+	2.68570i
$585$		0			0
$586$	−12.7713	−	6.15034i	−0.527578	−	0.254068i
$587$	−17.1168			−0.706484			−0.353242	−	0.935532i	$-0.614921\pi$
$587$	−17.1168			−0.706484			−0.353242	+	0.935532i	$0.614921\pi$
$588$		0			0
$589$	42.0347			1.73201
$590$	−11.2415	−	5.41362i	−0.462805	−	0.222875i
$591$		0			0
$592$	−17.5393	−	21.9936i	−0.720862	−	0.903932i
$593$	4.36350	+	19.1178i	0.179188	+	0.785072i	0.982006	+	0.188849i	$0.0604757\pi$
$593$	4.36350	+	19.1178i	0.179188	+	0.785072i	−0.802818	+	0.596224i	$0.796667\pi$
$594$		0			0
$595$	−11.5002	−	5.11534i	−0.471462	−	0.209709i
$596$	19.7250	+	86.4210i	0.807969	+	3.53994i
$597$		0			0
$598$	−12.4355	+	54.4833i	−0.508524	+	2.22799i
$599$	0.647643	+	0.311889i	0.0264620	+	0.0127434i	0.447068	−	0.894500i	$-0.352468\pi$
$599$	0.647643	+	0.311889i	0.0264620	+	0.0127434i	−0.420606	+	0.907243i	$0.638182\pi$
$600$		0			0
$601$	−25.4693	−	12.2654i	−1.03891	−	0.500314i	−0.164948	−	0.986302i	$-0.552746\pi$
$601$	−25.4693	−	12.2654i	−1.03891	−	0.500314i	−0.873966	+	0.485988i	$0.838460\pi$
$602$	37.8757	−	50.5616i	1.54370	−	2.06074i
$603$		0			0
$604$	−3.53921	+	15.5063i	−0.144008	+	0.630942i
$605$	5.68385	−	7.12732i	0.231081	−	0.289767i
$606$		0			0
$607$	−29.6604			−1.20388			−0.601940	−	0.798542i	$-0.705605\pi$
$607$	−29.6604			−1.20388			−0.601940	+	0.798542i	$0.705605\pi$
$608$	6.36939	−	7.98697i	0.258313	−	0.323914i
$609$		0			0
$610$	2.28037	+	2.85950i	0.0923296	+	0.115778i
$611$	−10.3276	−	12.9504i	−0.417810	−	0.523918i
$612$		0			0
$613$	7.58490	−	3.65270i	0.306351	−	0.147531i	−0.274392	−	0.961618i	$-0.588476\pi$
$613$	7.58490	−	3.65270i	0.306351	−	0.147531i	0.580743	+	0.814087i	$0.302762\pi$
$614$	−1.76267	−	2.21032i	−0.0711357	−	0.0892013i
$615$		0			0
$616$	3.82423	−	19.4517i	0.154083	−	0.783731i
$617$	−21.3895	+	26.8216i	−0.861110	+	1.07980i	0.134927	+	0.990856i	$0.456920\pi$
$617$	−21.3895	+	26.8216i	−0.861110	+	1.07980i	−0.996037	+	0.0889418i	$0.971651\pi$
$618$		0			0
$619$	28.3694			1.14026			0.570132	−	0.821553i	$-0.306892\pi$
$619$	28.3694			1.14026			0.570132	+	0.821553i	$0.306892\pi$
$620$	−22.0610	+	27.6636i	−0.885990	+	1.11100i
$621$		0			0
$622$	28.2807	−	13.6192i	1.13395	−	0.546082i
$623$	21.5787	−	11.2087i	0.864534	−	0.449067i
$624$		0			0
$625$	6.86813	−	8.61236i	0.274725	−	0.344494i
$626$	−20.2272	−	9.74091i	−0.808442	−	0.389325i
$627$		0			0
$628$	−10.6410	+	5.12446i	−0.424624	+	0.204488i
$629$	5.71227	+	25.0271i	0.227763	+	0.997896i
$630$		0			0
$631$	−4.02398	+	17.6302i	−0.160192	+	0.701848i	0.829484	+	0.558530i	$0.188634\pi$
$631$	−4.02398	+	17.6302i	−0.160192	+	0.701848i	−0.989677	+	0.143318i	$0.954223\pi$
$632$	5.80158	+	25.4184i	0.230775	+	1.01109i
$633$		0			0
$634$	11.3403	+	49.6851i	0.450381	+	1.97325i
$635$	13.0333	+	6.27653i	0.517213	+	0.249076i
$636$		0			0
$637$	−24.3005	−	9.93921i	−0.962822	−	0.393806i
$638$	22.6089			0.895096
$639$		0			0
$640$	−3.86176	−	16.9195i	−0.152649	−	0.668801i
$641$	−15.6365	−	19.6076i	−0.617605	−	0.774452i	0.370400	−	0.928872i	$-0.379220\pi$
$641$	−15.6365	−	19.6076i	−0.617605	−	0.774452i	−0.988005	+	0.154420i	$0.950649\pi$
$642$		0			0
$643$	−2.61665	+	11.4643i	−0.103191	+	0.452108i	0.896763	+	0.442510i	$0.145912\pi$
$643$	−2.61665	+	11.4643i	−0.103191	+	0.452108i	−0.999954	+	0.00959711i	$0.996945\pi$
$644$	12.8199	−	65.2075i	0.505174	−	2.56954i
$645$		0			0
$646$	−53.1880	+	25.6140i	−2.09265	+	1.00777i
$647$	−11.1073	+	48.6641i	−0.436672	+	1.91318i	−0.0301424	+	0.999546i	$0.509596\pi$
$647$	−11.1073	+	48.6641i	−0.436672	+	1.91318i	−0.406529	+	0.913638i	$0.633261\pi$
$648$		0			0
$649$	−4.28573	+	5.37413i	−0.168230	+	0.210953i
$650$	33.6569	+	16.2083i	1.32013	+	0.635741i
$651$		0			0
$652$	−15.4847	+	7.45702i	−0.606426	+	0.292039i
$653$	4.27318	−	18.7220i	0.167223	−	0.732650i	−0.819877	−	0.572540i	$-0.805958\pi$
$653$	4.27318	−	18.7220i	0.167223	−	0.732650i	0.987099	−	0.160110i	$-0.0511849\pi$
$654$		0			0
$655$	−3.29469			−0.128734
$656$	5.43594			0.212238
$657$		0			0
$658$	18.8146	+	22.1807i	0.733470	+	0.864695i
$659$	−21.3856	−	26.8167i	−0.833065	−	1.04463i	−0.998295	−	0.0583755i	$-0.981408\pi$
$659$	−21.3856	−	26.8167i	−0.833065	−	1.04463i	0.165230	−	0.986255i	$-0.447164\pi$
$660$		0			0
$661$	−35.5812	+	17.1350i	−1.38395	+	0.666475i	−0.969838	−	0.243751i	$-0.921622\pi$
$661$	−35.5812	+	17.1350i	−1.38395	+	0.666475i	−0.414112	+	0.910226i	$0.635908\pi$
$662$	63.6273	−	30.6413i	2.47294	−	1.19091i
$663$		0			0
$664$	−43.5276	−	54.5819i	−1.68920	−	2.11819i
$665$	−3.31883	−	12.7488i	−0.128699	−	0.494376i
$666$		0			0
$667$	39.6684			1.53597
$668$	−82.4775			−3.19115
$669$		0			0
$670$	4.09162	−	17.9266i	0.158073	−	0.692564i
$671$	1.81538	−	0.874240i	0.0700819	−	0.0337497i
$672$		0			0
$673$	11.1354	+	5.36254i	0.429239	+	0.206711i	0.636013	−	0.771678i	$-0.280582\pi$
$673$	11.1354	+	5.36254i	0.429239	+	0.206711i	−0.206774	+	0.978389i	$0.566297\pi$
$674$	14.9317	−	18.7237i	0.575146	−	0.721210i
$675$		0			0
$676$	−0.996719	+	4.36691i	−0.0383354	+	0.167958i
$677$	−7.12543	+	3.43143i	−0.273852	+	0.131880i	−0.565770	−	0.824563i	$-0.691421\pi$
$677$	−7.12543	+	3.43143i	−0.273852	+	0.131880i	0.291918	+	0.956443i	$0.405707\pi$
$678$		0			0
$679$	−18.6269	+	0.564084i	−0.714836	+	0.0216475i
$680$	5.78744	−	25.3564i	0.221938	−	0.972375i
$681$		0			0
$682$	17.9462	+	22.5038i	0.687194	+	0.861714i
$683$	2.88883	+	12.6568i	0.110538	+	0.484298i	0.999646	+	0.0266012i	$0.00846842\pi$
$683$	2.88883	+	12.6568i	0.110538	+	0.484298i	−0.889108	+	0.457697i	$0.848674\pi$
$684$		0			0
$685$	17.2419			0.658778
$686$	43.1788	+	16.1530i	1.64858	+	0.616724i
$687$		0			0
$688$	45.0819	+	21.7103i	1.71873	+	0.827698i
$689$	11.0721	+	48.5100i	0.421813	+	1.84808i
$690$		0			0
$691$	5.58212	+	24.4569i	0.212354	+	0.930384i	0.962962	+	0.269636i	$0.0869034\pi$
$691$	5.58212	+	24.4569i	0.212354	+	0.930384i	−0.750608	+	0.660748i	$0.770239\pi$
$692$	−2.49098	+	10.9137i	−0.0946930	+	0.414877i
$693$		0			0
$694$	6.36112	+	27.8699i	0.241465	+	1.05793i
$695$	11.2637	−	5.42429i	0.427255	−	0.205755i
$696$		0			0
$697$	−4.46929	−	2.15230i	−0.169286	−	0.0815241i
$698$	−55.4797	+	69.5694i	−2.09994	+	2.63324i
$699$		0			0
$700$	−40.5886	−	18.0540i	−1.53411	−	0.682377i
$701$	17.0282	−	8.20036i	0.643147	−	0.309723i	−0.0837324	−	0.996488i	$-0.526684\pi$
$701$	17.0282	−	8.20036i	0.643147	−	0.309723i	0.726880	+	0.686765i	$0.240970\pi$
$702$		0			0
$703$	−16.7520	+	21.0064i	−0.631814	+	0.792270i
$704$	−7.30295			−0.275240
$705$		0			0
$706$	33.7903	−	42.3717i	1.27172	−	1.59468i
$707$	−3.67750	−	14.1265i	−0.138307	−	0.531282i
$708$		0			0
$709$	−6.63693	−	8.32245i	−0.249255	−	0.312556i	0.641426	−	0.767185i	$-0.278343\pi$
$709$	−6.63693	−	8.32245i	−0.249255	−	0.312556i	−0.890681	+	0.454629i	$0.849772\pi$
$710$	16.1924	−	7.79784i	0.607689	−	0.292648i
$711$		0			0
$712$	31.3280	+	39.2841i	1.17407	+	1.47224i
$713$	31.4874	+	39.4839i	1.17921	+	1.47869i
$714$		0			0
$715$	−3.20303	+	4.01648i	−0.119787	+	0.150208i
$716$	−15.1861			−0.567531
$717$		0			0
$718$	49.8433	−	62.5015i	1.86014	−	2.33254i
$719$	−5.67428	+	24.8606i	−0.211615	+	0.927145i	0.751855	+	0.659328i	$0.229159\pi$
$719$	−5.67428	+	24.8606i	−0.211615	+	0.927145i	−0.963470	+	0.267817i	$0.913698\pi$
$720$		0			0
$721$	0.956268	+	3.67335i	0.0356133	+	0.136803i
$722$	−13.0572	−	6.28802i	−0.485939	−	0.234016i
$723$		0			0
$724$	−13.4848	−	6.49394i	−0.501159	−	0.241345i
$725$	5.90050	−	25.8518i	0.219139	−	0.960111i
$726$		0			0
$727$	10.0605	+	44.0781i	0.373125	+	1.63477i	0.717946	+	0.696099i	$0.245083\pi$
$727$	10.0605	+	44.0781i	0.373125	+	1.63477i	−0.344821	+	0.938669i	$0.612060\pi$
$728$	10.4656	−	53.2327i	0.387882	−	1.97294i
$729$		0			0
$730$	8.40560	+	36.8273i	0.311105	+	1.36304i
$731$	−28.4693	−	35.6993i	−1.05297	−	1.32039i
$732$		0			0
$733$	26.1096	+	12.5737i	0.964379	+	0.464420i	0.848705	−	0.528867i	$-0.177383\pi$
$733$	26.1096	+	12.5737i	0.964379	+	0.464420i	0.115674	+	0.993287i	$0.463097\pi$
$734$	−5.62083			−0.207469
$735$		0			0
$736$	12.2735			0.452406
$737$	−9.12673	−	4.39520i	−0.336187	−	0.161899i
$738$		0			0
$739$	−15.4301	−	19.3488i	−0.567607	−	0.711757i	0.412337	−	0.911032i	$-0.364713\pi$
$739$	−15.4301	−	19.3488i	−0.567607	−	0.711757i	−0.979944	+	0.199275i	$0.936141\pi$
$740$	−5.03263	−	22.0494i	−0.185003	−	0.810552i
$741$		0			0
$742$	−22.0113	−	84.5527i	−0.808059	−	3.10403i
$743$	2.15236	+	9.43010i	0.0789624	+	0.345957i	0.998941	−	0.0460121i	$-0.0146513\pi$
$743$	2.15236	+	9.43010i	0.0789624	+	0.345957i	−0.919979	+	0.391969i	$0.871794\pi$
$744$		0			0
$745$	−4.69775	+	20.5822i	−0.172112	+	0.754074i
$746$	−22.0322	−	10.6101i	−0.806656	−	0.388465i
$747$		0			0
$748$	−24.6650	−	11.8780i	−0.901842	−	0.434304i
$749$	−4.44797	+	2.31042i	−0.162525	+	0.0844209i
$750$		0			0
$751$	−7.40961	+	32.4636i	−0.270380	+	1.18461i	0.639185	+	0.769053i	$0.279272\pi$
$751$	−7.40961	+	32.4636i	−0.270380	+	1.18461i	−0.909565	+	0.415561i	$0.863585\pi$
$752$	−14.3634	+	18.0111i	−0.523779	+	0.656799i
$753$		0			0
$754$	61.8730			2.25328
$755$	−2.36177	+	2.96157i	−0.0859536	+	0.107782i
$756$		0			0
$757$	19.9120	+	24.9689i	0.723715	+	0.907509i	0.998542	−	0.0539842i	$-0.0171921\pi$
$757$	19.9120	+	24.9689i	0.723715	+	0.907509i	−0.274827	+	0.961494i	$0.588621\pi$
$758$	19.4454	+	24.3837i	0.706287	+	0.885656i
$759$		0			0
$760$	24.5259	−	11.8111i	0.889648	−	0.428432i
$761$	−28.4524	−	35.6782i	−1.03140	−	1.29334i	−0.955111	−	0.296249i	$-0.904264\pi$
$761$	−28.4524	−	35.6782i	−1.03140	−	1.29334i	−0.0762897	−	0.997086i	$-0.524307\pi$
$762$		0			0
$763$	21.7829	+	9.68914i	0.788594	+	0.350770i
$764$	41.0368	−	51.4586i	1.48466	−	1.86171i
$765$		0			0
$766$	−69.8155			−2.52254
$767$	−11.7286	+	14.7072i	−0.423495	+	0.531046i
$768$		0			0
$769$	−16.0320	+	7.72061i	−0.578129	+	0.278412i	−0.700011	−	0.714132i	$-0.746821\pi$
$769$	−16.0320	+	7.72061i	−0.578129	+	0.278412i	0.121882	+	0.992545i	$0.461107\pi$
$770$	5.40826	−	7.21968i	0.194900	−	0.260179i
$771$		0			0
$772$	40.9759	−	51.3822i	1.47476	−	1.84929i
$773$	−34.8965	−	16.8053i	−1.25514	−	0.604444i	−0.316255	−	0.948674i	$-0.602426\pi$
$773$	−34.8965	−	16.8053i	−1.25514	−	0.604444i	−0.938885	+	0.344230i	$0.888140\pi$
$774$		0			0
$775$	30.4152	−	14.6472i	1.09254	−	0.526142i
$776$	−8.56879	−	37.5423i	−0.307602	−	1.34769i
$777$		0			0
$778$	−15.2901	+	66.9904i	−0.548178	+	2.40172i
$779$	−1.15531	−	5.06175i	−0.0413934	−	0.181356i
$780$		0			0
$781$	−2.20319	−	9.65282i	−0.0788364	−	0.345405i
$782$	−63.9017	−	30.7734i	−2.28512	−	1.10046i
$783$		0			0
$784$	−5.95618	+	36.0252i	−0.212721	+	1.28661i
$785$	−2.81285			−0.100395
$786$		0			0
$787$	−9.34664	−	40.9503i	−0.333172	−	1.45972i	−0.812952	−	0.582331i	$-0.802141\pi$
$787$	−9.34664	−	40.9503i	−0.333172	−	1.45972i	0.479780	−	0.877389i	$-0.340717\pi$
$788$	8.85926	+	11.1092i	0.315598	+	0.395747i
$789$		0			0
$790$	−2.63994	+	11.5663i	−0.0939249	+	0.411512i
$791$	9.52352	−	4.94683i	0.338617	−	0.175889i
$792$		0			0
$793$	4.96808	−	2.39250i	0.176422	−	0.0849601i
$794$	−1.75448	+	7.68690i	−0.0622643	+	0.272798i
$795$		0			0
$796$	−17.2707	+	21.6568i	−0.612145	+	0.767605i
$797$	48.5633	+	23.3868i	1.72020	+	0.828404i	0.989296	+	0.145924i	$0.0466155\pi$
$797$	48.5633	+	23.3868i	1.72020	+	0.828404i	0.730904	+	0.682480i	$0.239099\pi$
$798$		0			0
$799$	18.9405	−	9.12128i	0.670068	−	0.322688i
$800$	1.82562	−	7.99858i	0.0645456	−	0.282793i
$801$		0			0
$802$	78.6012			2.77551
$803$	20.8103			0.734380
$804$		0			0
$805$	9.48905	−	12.6673i	0.334445	−	0.446463i
$806$	49.1126	+	61.5852i	1.72992	+	2.16925i
$807$		0			0
$808$	27.1764	−	13.0875i	0.956063	−	0.460416i
$809$	34.3226	−	16.5289i	1.20672	−	0.581124i	0.281134	−	0.959669i	$-0.409289\pi$
$809$	34.3226	−	16.5289i	1.20672	−	0.581124i	0.925583	+	0.378544i	$0.123575\pi$
$810$		0			0
$811$	−20.2874	−	25.4396i	−0.712387	−	0.893305i	0.285493	−	0.958381i	$-0.407843\pi$
$811$	−20.2874	−	25.4396i	−0.712387	−	0.893305i	−0.997880	+	0.0650758i	$0.979271\pi$
$812$	−73.5435	+	2.22713i	−2.58087	+	0.0781571i
$813$		0			0
$814$	−18.3980			−0.644850
$815$	−4.09321			−0.143379
$816$		0			0
$817$	10.6345	−	46.5929i	0.372055	−	1.63008i
$818$	−67.0877	+	32.3077i	−2.34567	+	1.12961i
$819$		0			0
$820$	3.93754	+	1.89622i	0.137505	+	0.0662189i
$821$	−26.0960	+	32.7233i	−0.910755	+	1.14205i	0.0786543	+	0.996902i	$0.474938\pi$
$821$	−26.0960	+	32.7233i	−0.910755	+	1.14205i	−0.989410	+	0.145149i	$0.953634\pi$
$822$		0			0
$823$	−1.54256	+	6.75838i	−0.0537702	+	0.235582i	−0.994671	−	0.103100i	$-0.967124\pi$
$823$	−1.54256	+	6.75838i	−0.0537702	+	0.235582i	0.940901	+	0.338682i	$0.109981\pi$
$824$	−7.06674	+	3.40316i	−0.246182	+	0.118555i
$825$		0			0
$826$	19.8035	−	26.4364i	0.689051	−	0.919840i
$827$	6.37988	−	27.9521i	0.221850	−	0.971989i	−0.734234	−	0.678897i	$-0.762458\pi$
$827$	6.37988	−	27.9521i	0.221850	−	0.971989i	0.956084	−	0.293092i	$-0.0946844\pi$
$828$		0			0
$829$	−9.71500	−	12.1822i	−0.337416	−	0.423106i	0.583958	−	0.811784i	$-0.301503\pi$
$829$	−9.71500	−	12.1822i	−0.337416	−	0.423106i	−0.921374	+	0.388678i	$0.872932\pi$
$830$	−7.06894	−	30.9711i	−0.245366	−	1.07502i
$831$		0			0
$832$	−19.9857			−0.692879
$833$	19.1608	−	27.2607i	0.663882	−	0.944529i
$834$		0			0
$835$	−17.6977	−	8.52278i	−0.612455	−	0.294943i
$836$	−6.37591	−	27.9347i	−0.220515	−	0.966141i
$837$		0			0
$838$	−13.7969	−	60.4482i	−0.476606	−	2.08815i
$839$	3.57261	−	15.6526i	0.123340	−	0.540389i	−0.875069	−	0.483999i	$-0.839184\pi$
$839$	3.57261	−	15.6526i	0.123340	−	0.540389i	0.998409	−	0.0563900i	$-0.0179590\pi$
$840$		0			0
$841$	−3.31986	−	14.5452i	−0.114478	−	0.501560i
$842$	−3.60443	+	1.73580i	−0.124217	+	0.0598196i
$843$		0			0
$844$	−34.1662	−	16.4536i	−1.17605	−	0.566355i
$845$	−0.665126	+	0.834042i	−0.0228810	+	0.0286919i
$846$		0			0
$847$	15.6113	+	18.4043i	0.536412	+	0.632381i
$848$	62.3484	−	30.0254i	2.14105	−	1.03108i
$849$		0			0
$850$	−29.5600	+	37.0671i	−1.01390	+	1.27139i
$851$	−32.2802			−1.10655
$852$		0			0
$853$	−28.4203	+	35.6379i	−0.973092	+	1.22022i	0.00235752	+	0.999997i	$0.499250\pi$
$853$	−28.4203	+	35.6379i	−0.973092	+	1.22022i	−0.975450	+	0.220222i	$0.929322\pi$
$854$	−8.59245	+	4.46320i	−0.294027	+	0.152728i
$855$		0			0
$856$	−6.45757	−	8.09753i	−0.220715	−	0.276768i
$857$	−13.0261	+	6.27305i	−0.444964	+	0.214283i	−0.642929	−	0.765926i	$-0.722281\pi$
$857$	−13.0261	+	6.27305i	−0.444964	+	0.214283i	0.197965	+	0.980209i	$0.436567\pi$
$858$		0			0
$859$	−23.2691	−	29.1785i	−0.793931	−	0.995558i	−0.999856	−	0.0169899i	$-0.994592\pi$
$859$	−23.2691	−	29.1785i	−0.793931	−	0.995558i	0.205925	−	0.978568i	$-0.433980\pi$
$860$	25.0820	+	31.4519i	0.855291	+	1.07250i
$861$		0			0
$862$	24.6787	−	30.9461i	0.840560	−	1.05403i
$863$	2.78269			0.0947239			0.0473620	−	0.998878i	$-0.484919\pi$
$863$	2.78269			0.0947239			0.0473620	+	0.998878i	$0.484919\pi$
$864$		0			0
$865$	−1.66227	+	2.08442i	−0.0565189	+	0.0708725i
$866$	7.17630	−	31.4414i	0.243861	−	1.06842i
$867$		0			0
$868$	−60.5929	−	71.4336i	−2.05666	−	2.42461i
$869$	5.88863	+	2.83581i	0.199758	+	0.0961984i
$870$		0			0
$871$	−24.9768	−	12.0282i	−0.846306	−	0.407559i
$872$	−10.9622	+	48.0284i	−0.371226	+	1.62645i
$873$		0			0
$874$	−16.5186	−	72.3727i	−0.558750	−	2.44804i
$875$	−15.3959	−	18.1504i	−0.520477	−	0.613595i
$876$		0			0
$877$	0.922298	+	4.04085i	0.0311438	+	0.136450i	0.988110	−	0.153750i	$-0.0491352\pi$
$877$	0.922298	+	4.04085i	0.0311438	+	0.136450i	−0.956966	+	0.290200i	$0.906278\pi$
$878$	19.2404	+	24.1267i	0.649331	+	0.814235i
$879$		0			0
$880$	6.43724	+	3.10001i	0.216999	+	0.104501i
$881$	−4.48889			−0.151235			−0.0756173	−	0.997137i	$-0.524093\pi$
$881$	−4.48889			−0.151235			−0.0756173	+	0.997137i	$0.524093\pi$
$882$		0			0
$883$	−38.3818			−1.29165			−0.645825	−	0.763486i	$-0.723486\pi$
$883$	−38.3818			−1.29165			−0.645825	+	0.763486i	$0.723486\pi$
$884$	−67.4998	−	32.5062i	−2.27026	−	1.09330i
$885$		0			0
$886$	−38.9955	−	48.8988i	−1.31008	−	1.64279i
$887$	8.84211	+	38.7398i	0.296889	+	1.30076i	0.874732	+	0.484607i	$0.161038\pi$
$887$	8.84211	+	38.7398i	0.296889	+	1.30076i	−0.577843	+	0.816148i	$0.696105\pi$
$888$		0			0
$889$	−22.9601	+	30.6502i	−0.770056	+	1.02798i
$890$	5.08771	+	22.2907i	0.170540	+	0.747187i
$891$		0			0
$892$	−9.98460	+	43.7454i	−0.334309	+	1.46470i
$893$	19.8240	+	9.54675i	0.663386	+	0.319470i
$894$		0			0
$895$	−3.25858	−	1.56925i	−0.108922	−	0.0524543i
$896$	45.9225	−	1.39068i	1.53416	−	0.0464594i
$897$		0			0
$898$	−15.4336	+	67.6189i	−0.515025	+	2.25647i
$899$	34.8616	−	43.7150i	1.16270	−	1.45798i
$900$		0			0
$901$	−63.1495			−2.10382
$902$	2.21662	−	2.77955i	0.0738054	−	0.0925491i
$903$		0			0
$904$	13.8263	+	17.3376i	0.459855	+	0.576640i
$905$	−2.22247	−	2.78690i	−0.0738776	−	0.0926395i
$906$		0			0
$907$	10.0959	−	4.86193i	0.335229	−	0.161438i	−0.258695	−	0.965959i	$-0.583292\pi$
$907$	10.0959	−	4.86193i	0.335229	−	0.161438i	0.593924	+	0.804521i	$0.297578\pi$
$908$	0.358112	+	0.449058i	0.0118844	+	0.0149025i
$909$		0			0
$910$	14.8006	−	19.7578i	0.490634	−	0.654966i
$911$	−10.4748	+	13.1349i	−0.347044	+	0.435180i	−0.924465	−	0.381267i	$-0.875488\pi$
$911$	−10.4748	+	13.1349i	−0.347044	+	0.435180i	0.577421	+	0.816447i	$0.304059\pi$
$912$		0			0
$913$	−17.5011			−0.579201
$914$	−24.2487	+	30.4069i	−0.802075	+	1.00577i
$915$		0			0
$916$	−1.92660	+	0.927802i	−0.0636567	+	0.0306554i
$917$	1.68258	−	8.55835i	0.0555638	−	0.282621i
$918$		0			0
$919$	−20.8486	+	26.1433i	−0.687732	+	0.862388i	−0.996041	−	0.0888979i	$-0.971666\pi$
$919$	−20.8486	+	26.1433i	−0.687732	+	0.862388i	0.308309	+	0.951286i	$0.400237\pi$
$920$	29.4662	+	14.1902i	0.971471	+	0.467836i
$921$		0			0
$922$	−33.6778	+	16.2184i	−1.10912	+	0.534124i
$923$	−6.02939	−	26.4165i	−0.198460	−	0.869510i
$924$		0			0
$925$	−4.80154	+	21.0369i	−0.157874	+	0.691689i
$926$	8.25010	+	36.1461i	0.271115	+	1.18783i
$927$		0			0
$928$	−3.02377	−	13.2480i	−0.0992601	−	0.434887i
$929$	41.2053	+	19.8434i	1.35190	+	0.651041i	0.962815	−	0.270161i	$-0.0870769\pi$
$929$	41.2053	+	19.8434i	1.35190	+	0.651041i	0.389085	+	0.921202i	$0.372791\pi$
$930$		0			0
$931$	34.8113	−	2.11033i	1.14089	−	0.0691633i
$932$	38.4102			1.25817
$933$		0			0
$934$	−8.37410	−	36.6893i	−0.274009	−	1.20051i
$935$	−4.06512	−	5.09750i	−0.132944	−	0.166706i
$936$		0			0
$937$	−6.04218	+	26.4725i	−0.197390	+	0.864820i	0.775093	+	0.631847i	$0.217703\pi$
$937$	−6.04218	+	26.4725i	−0.197390	+	0.864820i	−0.972483	+	0.232974i	$0.925154\pi$
$938$	44.4768	+	19.7835i	1.45222	+	0.645953i
$939$		0			0
$940$	−16.6870	+	8.03604i	−0.544270	+	0.262107i
$941$	−2.34434	+	10.2712i	−0.0764232	+	0.334832i	−0.998658	−	0.0517996i	$-0.983504\pi$
$941$	−2.34434	+	10.2712i	−0.0764232	+	0.334832i	0.922234	+	0.386631i	$0.126361\pi$
$942$		0			0
$943$	3.88917	−	4.87686i	0.126649	−	0.158812i
$944$	23.5713	+	11.3513i	0.767181	+	0.369455i
$945$		0			0
$946$	29.4843	−	14.1989i	0.958616	−	0.461645i
$947$	−5.43448	+	23.8100i	−0.176597	+	0.773721i	0.806589	+	0.591113i	$0.201311\pi$
$947$	−5.43448	+	23.8100i	−0.176597	+	0.773721i	−0.983186	+	0.182608i	$0.941546\pi$
$948$		0			0
$949$	56.9508			1.84870
$950$	−49.6221			−1.60995
$951$		0			0
$952$	62.9107	+	27.9829i	2.03895	+	0.906932i
$953$	17.7220	+	22.2227i	0.574071	+	0.719862i	0.981089	−	0.193558i	$-0.0620027\pi$
$953$	17.7220	+	22.2227i	0.574071	+	0.719862i	−0.407018	+	0.913420i	$0.633431\pi$
$954$		0			0
$955$	14.1230	−	6.80128i	0.457009	−	0.220084i
$956$	36.5825	−	17.6172i	1.18316	−	0.569781i
$957$		0			0
$958$	17.4194	+	21.8433i	0.562796	+	0.705724i
$959$	−8.80534	+	44.7878i	−0.284339	+	1.44627i
$960$		0			0
$961$	40.1835			1.29624
$962$	−50.3492			−1.62332
$963$		0			0
$964$	−26.8607	+	117.684i	−0.865124	+	3.79036i
$965$	14.1020	−	6.79118i	0.453961	−	0.218616i
$966$		0			0
$967$	−6.94680	−	3.34540i	−0.223394	−	0.107581i	0.318839	−	0.947809i	$-0.396707\pi$
$967$	−6.94680	−	3.34540i	−0.223394	−	0.107581i	−0.542234	+	0.840228i	$0.682421\pi$
$968$	−31.0929	+	38.9893i	−0.999364	+	1.25316i
$969$		0			0
$970$	3.89913	−	17.0832i	0.125193	−	0.548508i
$971$	35.7959	−	17.2384i	1.14874	−	0.553206i	0.240088	−	0.970751i	$-0.422824\pi$
$971$	35.7959	−	17.2384i	1.14874	−	0.553206i	0.908656	+	0.417545i	$0.137109\pi$
$972$		0			0
$973$	8.33793	+	32.0288i	0.267302	+	1.02680i
$974$	−15.9296	+	69.7920i	−0.510416	+	2.23628i
$975$		0			0
$976$	−4.78151	−	5.99583i	−0.153052	−	0.191922i
$977$	7.61120	+	33.3469i	0.243504	+	1.06686i	0.937801	+	0.347172i	$0.112858\pi$
$977$	7.61120	+	33.3469i	0.243504	+	1.06686i	−0.694297	+	0.719688i	$0.744285\pi$
$978$		0			0
$979$	12.5960			0.402570
$980$	−16.8811	+	24.0173i	−0.539246	+	0.767204i
$981$		0			0
$982$	−8.12221	−	3.91145i	−0.259190	−	0.124819i
$983$	2.37778	+	10.4177i	0.0758393	+	0.332274i	0.998588	−	0.0531293i	$-0.0169196\pi$
$983$	2.37778	+	10.4177i	0.0758393	+	0.332274i	−0.922748	+	0.385403i	$0.874062\pi$
$984$		0			0
$985$	0.753029	+	3.29923i	0.0239935	+	0.105122i
$986$	−17.4737	+	76.5571i	−0.556475	+	2.43807i
$987$		0			0
$988$	−17.4487	−	76.4478i	−0.555117	−	2.43213i
$989$	51.7315	−	24.9126i	1.64497	−	0.792174i
$990$		0			0
$991$	25.5220	+	12.2907i	0.810732	+	0.390428i	0.792853	−	0.609412i	$-0.208595\pi$
$991$	25.5220	+	12.2907i	0.810732	+	0.390428i	0.0178782	+	0.999840i	$0.494309\pi$
$992$	10.7862	−	13.5255i	0.342463	−	0.429435i
$993$		0			0
$994$	11.9864	+	46.0439i	0.380186	+	1.46042i
$995$	−5.94379	+	2.86238i	−0.188431	+	0.0907435i
$996$		0			0
$997$	−4.73626	+	5.93908i	−0.149999	+	0.188093i	−0.851154	−	0.524916i	$-0.824097\pi$
$997$	−4.73626	+	5.93908i	−0.149999	+	0.188093i	0.701155	+	0.713009i	$0.252668\pi$
$998$	−74.3757			−2.35432
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.u.d.127.1		36
3.2	odd	2		147.2.i.b.127.6	yes	36
49.22	even	7	inner	441.2.u.d.316.1		36
147.62	even	14		7203.2.a.g.1.3		18
147.71	odd	14		147.2.i.b.22.6	✓	36
147.134	odd	14		7203.2.a.h.1.3		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
147.2.i.b.22.6	✓	36	147.71	odd	14
147.2.i.b.127.6	yes	36	3.2	odd	2
441.2.u.d.127.1		36	1.1	even	1	trivial
441.2.u.d.316.1		36	49.22	even	7	inner
7203.2.a.g.1.3		18	147.62	even	14
7203.2.a.h.1.3		18	147.134	odd	14

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:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	441.u (of order \(7\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.24272 - 1.08004i) q^{2} +(2.61635 + 3.28080i) q^{4} +(0.222387 + 0.974342i) q^{5} +(-2.64454 + 0.0800852i) q^{7} +(-1.21655 - 5.33004i) q^{8} +O(q^{10})\)	\(q+(-2.24272 - 1.08004i) q^{2} +(2.61635 + 3.28080i) q^{4} +(0.222387 + 0.974342i) q^{5} +(-2.64454 + 0.0800852i) q^{7} +(-1.21655 - 5.33004i) q^{8} +(0.553574 - 2.42537i) q^{10} +(-1.23480 - 0.594647i) q^{11} +(-3.37922 - 1.62735i) q^{13} +(6.01747 + 2.67660i) q^{14} +(-1.16074 + 5.08554i) q^{16} +(2.96789 - 3.72162i) q^{17} +4.98217 q^{19} +(-2.61478 + 3.27883i) q^{20} +(2.12707 + 2.66726i) q^{22} +(3.73204 + 4.67984i) q^{23} +(3.60496 - 1.73606i) q^{25} +(5.82107 + 7.29939i) q^{26} +(-7.18178 - 8.46667i) q^{28} +(4.13197 - 5.18133i) q^{29} +8.43703 q^{31} +(1.27844 - 1.60311i) q^{32} +(-10.6757 + 5.14113i) q^{34} +(-0.666142 - 2.55888i) q^{35} +(-3.36239 + 4.21631i) q^{37} +(-11.1736 - 5.38094i) q^{38} +(4.92273 - 2.37066i) q^{40} +(-0.231889 - 1.01597i) q^{41} +(2.13451 - 9.35192i) q^{43} +(-1.27974 - 5.60693i) q^{44} +(-3.31554 - 14.5263i) q^{46} +(3.97899 + 1.91618i) q^{47} +(6.98717 - 0.423577i) q^{49} -9.95994 q^{50} +(-3.50223 - 15.3443i) q^{52} +(-8.27143 - 10.3720i) q^{53} +(0.304787 - 1.33536i) q^{55} +(3.64406 + 13.9981i) q^{56} +(-14.8629 + 7.15760i) q^{58} +(1.11604 - 4.88969i) q^{59} +(-0.916644 + 1.14943i) q^{61} +(-18.9219 - 9.11233i) q^{62} +(4.80089 - 2.31199i) q^{64} +(0.834098 - 3.65442i) q^{65} +7.39128 q^{67} +19.9749 q^{68} +(-1.26971 + 6.45831i) q^{70} +(4.50428 + 5.64818i) q^{71} +(-13.6805 + 6.58819i) q^{73} +(12.0947 - 5.82450i) q^{74} +(13.0351 + 16.3455i) q^{76} +(3.31309 + 1.47368i) q^{77} -4.76890 q^{79} -5.21319 q^{80} +(-0.577227 + 2.52900i) q^{82} +(11.5050 - 5.54053i) q^{83} +(4.28615 + 2.06410i) q^{85} +(-14.8876 + 18.6684i) q^{86} +(-1.66730 + 7.30493i) q^{88} +(-8.28049 + 3.98768i) q^{89} +(9.06682 + 4.03296i) q^{91} +(-5.58927 + 24.4882i) q^{92} +(-6.85423 - 8.59494i) q^{94} +(1.10797 + 4.85434i) q^{95} +7.04354 q^{97} +(-16.1278 - 6.59645i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + q^{2} - 9 q^{4} + 4 q^{5} - 6 q^{7} + 15 q^{8}+O(q^{10}) \) 36 * q + q^2 - 9 * q^4 + 4 * q^5 - 6 * q^7 + 15 * q^8	\( 36 q + q^{2} - 9 q^{4} + 4 q^{5} - 6 q^{7} + 15 q^{8} + 10 q^{10} + 7 q^{11} - 12 q^{13} + q^{14} - 3 q^{16} + 3 q^{17} + 6 q^{19} - 25 q^{20} - 21 q^{22} + 20 q^{23} - 2 q^{25} - 6 q^{26} - q^{28} + 22 q^{29} + 16 q^{31} - 26 q^{32} + 6 q^{34} + 9 q^{35} + 32 q^{37} - 17 q^{38} - 21 q^{40} + 5 q^{41} - 34 q^{43} - 2 q^{44} - 32 q^{46} + 7 q^{47} + 20 q^{49} - 236 q^{50} + 20 q^{52} + 32 q^{53} - 17 q^{55} + 39 q^{56} - 53 q^{58} + q^{59} + 14 q^{61} + 60 q^{62} - 21 q^{64} + 39 q^{65} - 22 q^{67} + 110 q^{68} - 40 q^{70} - 36 q^{71} - 11 q^{73} + 46 q^{74} - 101 q^{76} + 17 q^{77} - 14 q^{79} + 112 q^{80} + 2 q^{82} - 12 q^{83} - 44 q^{85} - 184 q^{86} + 204 q^{88} - 12 q^{89} - 16 q^{91} + 105 q^{92} - 5 q^{94} - 18 q^{95} + 172 q^{97} - q^{98}+O(q^{100}) \) 36 * q + q^2 - 9 * q^4 + 4 * q^5 - 6 * q^7 + 15 * q^8 + 10 * q^10 + 7 * q^11 - 12 * q^13 + q^14 - 3 * q^16 + 3 * q^17 + 6 * q^19 - 25 * q^20 - 21 * q^22 + 20 * q^23 - 2 * q^25 - 6 * q^26 - q^28 + 22 * q^29 + 16 * q^31 - 26 * q^32 + 6 * q^34 + 9 * q^35 + 32 * q^37 - 17 * q^38 - 21 * q^40 + 5 * q^41 - 34 * q^43 - 2 * q^44 - 32 * q^46 + 7 * q^47 + 20 * q^49 - 236 * q^50 + 20 * q^52 + 32 * q^53 - 17 * q^55 + 39 * q^56 - 53 * q^58 + q^59 + 14 * q^61 + 60 * q^62 - 21 * q^64 + 39 * q^65 - 22 * q^67 + 110 * q^68 - 40 * q^70 - 36 * q^71 - 11 * q^73 + 46 * q^74 - 101 * q^76 + 17 * q^77 - 14 * q^79 + 112 * q^80 + 2 * q^82 - 12 * q^83 - 44 * q^85 - 184 * q^86 + 204 * q^88 - 12 * q^89 - 16 * q^91 + 105 * q^92 - 5 * q^94 - 18 * q^95 + 172 * q^97 - q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more