LMFDB - Embedded newform 882.2.z.f.37.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [882,2,Mod(37,882)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(882, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([0, 32]))

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

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

chi := DirichletCharacter("882.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 882 = 2 \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	882.z (of order $21$, degree $12$, 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:	$7.04280545828$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$3$ over $\Q(\zeta_{21})$
Twist minimal:	no (minimal twist has level 294)
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			37.1
Character	$\chi$	$=$	882.37
Dual form			882.2.z.f.739.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.826239 - 0.563320i) q^{2} +(0.365341 - 0.930874i) q^{4} +(-3.05947 - 0.943720i) q^{5} +(-1.76838 + 1.96795i) q^{7} +(-0.222521 - 0.974928i) q^{8} +O(q^{10})$	\(q+(0.826239 - 0.563320i) q^{2} +(0.365341 - 0.930874i) q^{4} +(-3.05947 - 0.943720i) q^{5} +(-1.76838 + 1.96795i) q^{7} +(-0.222521 - 0.974928i) q^{8} +(-3.05947 + 0.943720i) q^{10} +(0.192183 + 2.56450i) q^{11} +(6.17821 + 2.97527i) q^{13} +(-0.352517 + 2.62216i) q^{14} +(-0.733052 - 0.680173i) q^{16} +(1.47228 + 0.221910i) q^{17} +(-3.35121 + 5.80446i) q^{19} +(-1.99623 + 2.50320i) q^{20} +(1.60342 + 2.01063i) q^{22} +(-1.36686 + 0.206021i) q^{23} +(4.33853 + 2.95796i) q^{25} +(6.78071 - 1.02203i) q^{26} +(1.18585 + 2.36511i) q^{28} +(5.60865 - 7.03303i) q^{29} +(0.922116 + 1.59715i) q^{31} +(-0.988831 - 0.149042i) q^{32} +(1.34146 - 0.646013i) q^{34} +(7.26749 - 4.35203i) q^{35} +(3.18718 + 8.12080i) q^{37} +(0.500872 + 6.68367i) q^{38} +(-0.239264 + 3.19276i) q^{40} +(2.09113 + 9.16184i) q^{41} +(1.06195 - 4.65269i) q^{43} +(2.45744 + 0.758019i) q^{44} +(-1.01330 + 0.940204i) q^{46} +(-7.96008 + 5.42709i) q^{47} +(-0.745670 - 6.96017i) q^{49} +5.25094 q^{50} +(5.02675 - 4.66415i) q^{52} +(-3.44377 + 8.77459i) q^{53} +(1.83219 - 8.02736i) q^{55} +(2.31211 + 1.28613i) q^{56} +(0.672241 - 8.97043i) q^{58} +(-1.85613 + 0.572540i) q^{59} +(1.83106 + 4.66546i) q^{61} +(1.66160 + 0.800183i) q^{62} +(-0.900969 + 0.433884i) q^{64} +(-16.0942 - 14.9332i) q^{65} +(-3.77414 - 6.53700i) q^{67} +(0.744454 - 1.28943i) q^{68} +(3.55310 - 7.68974i) q^{70} +(-0.630544 - 0.790678i) q^{71} +(-7.37497 - 5.02817i) q^{73} +(7.20798 + 4.91432i) q^{74} +(4.17888 + 5.24016i) q^{76} +(-5.38666 - 4.15680i) q^{77} +(0.795922 - 1.37858i) q^{79} +(1.60085 + 2.77276i) q^{80} +(6.88882 + 6.39190i) q^{82} +(-8.83741 + 4.25587i) q^{83} +(-4.29496 - 2.06835i) q^{85} +(-1.74353 - 4.44245i) q^{86} +(2.45744 - 0.758019i) q^{88} +(-1.05713 + 14.1064i) q^{89} +(-16.7806 + 6.89702i) q^{91} +(-0.307591 + 1.34765i) q^{92} +(-3.51974 + 8.96815i) q^{94} +(15.7307 - 14.5959i) q^{95} -3.99911 q^{97} +(-4.53691 - 5.33071i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 3 q^{2} + 3 q^{4} - 2 q^{5} - 5 q^{7} - 6 q^{8}+O(q^{10}) $ 36 * q + 3 * q^2 + 3 * q^4 - 2 * q^5 - 5 * q^7 - 6 * q^8	$ 36 q + 3 q^{2} + 3 q^{4} - 2 q^{5} - 5 q^{7} - 6 q^{8} - 2 q^{10} - 9 q^{11} + 10 q^{13} + 4 q^{14} + 3 q^{16} - 7 q^{17} + 16 q^{19} - 3 q^{20} + 4 q^{22} - 42 q^{23} - 23 q^{25} + 16 q^{26} + 15 q^{28} + 12 q^{29} - 3 q^{31} + 3 q^{32} - 21 q^{34} - 26 q^{35} - 25 q^{37} + 2 q^{38} - 2 q^{40} + 28 q^{41} + 4 q^{43} + 19 q^{44} - 7 q^{46} + 4 q^{47} - 25 q^{49} + 74 q^{50} + 9 q^{52} + 37 q^{53} - 54 q^{55} + 9 q^{56} + 8 q^{58} - 23 q^{59} - 79 q^{61} + 34 q^{62} - 6 q^{64} - 55 q^{65} + 19 q^{67} + 7 q^{68} + 18 q^{70} + 34 q^{71} - 15 q^{73} + 24 q^{74} + 3 q^{76} - 129 q^{77} + 11 q^{79} + 5 q^{80} + 49 q^{82} + 44 q^{83} - 77 q^{85} - 72 q^{86} + 19 q^{88} - 39 q^{89} - 43 q^{91} - 7 q^{92} + 25 q^{94} + 36 q^{95} - 8 q^{97} + 48 q^{98}+O(q^{100}) $ 36 * q + 3 * q^2 + 3 * q^4 - 2 * q^5 - 5 * q^7 - 6 * q^8 - 2 * q^10 - 9 * q^11 + 10 * q^13 + 4 * q^14 + 3 * q^16 - 7 * q^17 + 16 * q^19 - 3 * q^20 + 4 * q^22 - 42 * q^23 - 23 * q^25 + 16 * q^26 + 15 * q^28 + 12 * q^29 - 3 * q^31 + 3 * q^32 - 21 * q^34 - 26 * q^35 - 25 * q^37 + 2 * q^38 - 2 * q^40 + 28 * q^41 + 4 * q^43 + 19 * q^44 - 7 * q^46 + 4 * q^47 - 25 * q^49 + 74 * q^50 + 9 * q^52 + 37 * q^53 - 54 * q^55 + 9 * q^56 + 8 * q^58 - 23 * q^59 - 79 * q^61 + 34 * q^62 - 6 * q^64 - 55 * q^65 + 19 * q^67 + 7 * q^68 + 18 * q^70 + 34 * q^71 - 15 * q^73 + 24 * q^74 + 3 * q^76 - 129 * q^77 + 11 * q^79 + 5 * q^80 + 49 * q^82 + 44 * q^83 - 77 * q^85 - 72 * q^86 + 19 * q^88 - 39 * q^89 - 43 * q^91 - 7 * q^92 + 25 * q^94 + 36 * q^95 - 8 * q^97 + 48 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/882\mathbb{Z}\right)^\times$.

$n$	$199$	$785$
$\chi(n)$	$e\left(\frac{16}{21}\right)$	$1$

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 $

$2$	0.826239	−	0.563320i	0.584239	−	0.398327i
$2$	0.826239	−	0.563320i	0.584239	−	0.398327i
$3$		0			0
$3$		0			0
$4$	0.365341	−	0.930874i	0.182671	−	0.465437i
$5$	−3.05947	−	0.943720i	−1.36823	−	0.422044i	−0.478326	−	0.878183i	$-0.658756\pi$
$5$	−3.05947	−	0.943720i	−1.36823	−	0.422044i	−0.889909	+	0.456138i	$0.849232\pi$
$6$		0			0
$7$	−1.76838	+	1.96795i	−0.668385	+	0.743816i
$7$	−1.76838	+	1.96795i	−0.668385	+	0.743816i
$8$	−0.222521	−	0.974928i	−0.0786730	−	0.344689i
$9$		0			0
$10$	−3.05947	+	0.943720i	−0.967488	+	0.298431i
$11$	0.192183	+	2.56450i	0.0579452	+	0.773225i	0.948182	+	0.317727i	$0.102920\pi$
$11$	0.192183	+	2.56450i	0.0579452	+	0.773225i	−0.890237	+	0.455498i	$0.849461\pi$
$12$		0			0
$13$	6.17821	+	2.97527i	1.71353	+	0.825191i	0.991002	+	0.133847i	$0.0427331\pi$
$13$	6.17821	+	2.97527i	1.71353	+	0.825191i	0.722526	+	0.691344i	$0.242981\pi$
$14$	−0.352517	+	2.62216i	−0.0942140	+	0.700802i
$15$		0			0
$16$	−0.733052	−	0.680173i	−0.183263	−	0.170043i
$17$	1.47228	+	0.221910i	0.357080	+	0.0538211i	0.325133	−	0.945668i	$-0.394591\pi$
$17$	1.47228	+	0.221910i	0.357080	+	0.0538211i	0.0319473	+	0.999490i	$0.489829\pi$
$18$		0			0
$19$	−3.35121	+	5.80446i	−0.768819	+	1.33163i	0.169384	+	0.985550i	$0.445822\pi$
$19$	−3.35121	+	5.80446i	−0.768819	+	1.33163i	−0.938204	+	0.346084i	$0.887511\pi$
$20$	−1.99623	+	2.50320i	−0.446371	+	0.559732i
$21$		0			0
$22$	1.60342	+	2.01063i	0.341851	+	0.428667i
$23$	−1.36686	+	0.206021i	−0.285011	+	0.0429585i	−0.289992	−	0.957029i	$-0.593653\pi$
$23$	−1.36686	+	0.206021i	−0.285011	+	0.0429585i	0.00498105	+	0.999988i	$0.498414\pi$
$24$		0			0
$25$	4.33853	+	2.95796i	0.867705	+	0.591592i
$26$	6.78071	−	1.02203i	1.32981	−	0.200436i
$27$		0			0
$28$	1.18585	+	2.36511i	0.224105	+	0.446964i
$29$	5.60865	−	7.03303i	1.04150	−	1.30600i	0.0908078	−	0.995868i	$-0.471055\pi$
$29$	5.60865	−	7.03303i	1.04150	−	1.30600i	0.950693	−	0.310133i	$-0.100373\pi$
$30$		0			0
$31$	0.922116	+	1.59715i	0.165617	+	0.286857i	0.936874	−	0.349667i	$-0.113705\pi$
$31$	0.922116	+	1.59715i	0.165617	+	0.286857i	−0.771257	+	0.636524i	$0.780372\pi$
$32$	−0.988831	−	0.149042i	−0.174802	−	0.0263472i
$33$		0			0
$34$	1.34146	−	0.646013i	0.230059	−	0.110790i
$35$	7.26749	−	4.35203i	1.22843	−	0.735627i
$36$		0			0
$37$	3.18718	+	8.12080i	0.523969	+	1.33505i	0.910780	+	0.412892i	$0.135481\pi$
$37$	3.18718	+	8.12080i	0.523969	+	1.33505i	−0.386811	+	0.922159i	$0.626423\pi$
$38$	0.500872	+	6.68367i	0.0812521	+	1.08423i
$39$		0			0
$40$	−0.239264	+	3.19276i	−0.0378310	+	0.504819i
$41$	2.09113	+	9.16184i	0.326580	+	1.43084i	0.825603	+	0.564251i	$0.190835\pi$
$41$	2.09113	+	9.16184i	0.326580	+	1.43084i	−0.499023	+	0.866589i	$0.666308\pi$
$42$		0			0
$43$	1.06195	−	4.65269i	0.161945	−	0.709529i	−0.827117	−	0.562030i	$-0.810021\pi$
$43$	1.06195	−	4.65269i	0.161945	−	0.709529i	0.989062	−	0.147499i	$-0.0471223\pi$
$44$	2.45744	+	0.758019i	0.370472	+	0.114276i
$45$		0			0
$46$	−1.01330	+	0.940204i	−0.149403	+	0.138626i
$47$	−7.96008	+	5.42709i	−1.16110	+	0.791623i	−0.981376	−	0.192095i	$-0.938472\pi$
$47$	−7.96008	+	5.42709i	−1.16110	+	0.791623i	−0.179721	+	0.983718i	$0.557520\pi$
$48$		0			0
$49$	−0.745670	−	6.96017i	−0.106524	−	0.994310i
$50$	5.25094			0.742595
$51$		0			0
$52$	5.02675	−	4.66415i	0.697085	−	0.646801i
$53$	−3.44377	+	8.77459i	−0.473039	+	1.20528i	0.472952	+	0.881088i	$0.343188\pi$
$53$	−3.44377	+	8.77459i	−0.473039	+	1.20528i	−0.945990	+	0.324194i	$0.894907\pi$
$54$		0			0
$55$	1.83219	−	8.02736i	0.247053	−	1.08241i
$56$	2.31211	+	1.28613i	0.308969	+	0.171867i
$57$		0			0
$58$	0.672241	−	8.97043i	0.0882695	−	1.17788i
$59$	−1.85613	+	0.572540i	−0.241647	+	0.0745383i	−0.413213	−	0.910634i	$-0.635594\pi$
$59$	−1.85613	+	0.572540i	−0.241647	+	0.0745383i	0.171566	+	0.985173i	$0.445117\pi$
$60$		0			0
$61$	1.83106	+	4.66546i	0.234443	+	0.597350i	0.998878	−	0.0473497i	$-0.0150775\pi$
$61$	1.83106	+	4.66546i	0.234443	+	0.597350i	−0.764436	+	0.644700i	$0.776982\pi$
$62$	1.66160	+	0.800183i	0.211023	+	0.101623i
$63$		0			0
$64$	−0.900969	+	0.433884i	−0.112621	+	0.0542355i
$65$	−16.0942	−	14.9332i	−1.99624	−	1.85224i
$66$		0			0
$67$	−3.77414	−	6.53700i	−0.461084	−	0.798621i	0.537931	−	0.842989i	$-0.319206\pi$
$67$	−3.77414	−	6.53700i	−0.461084	−	0.798621i	−0.999015	+	0.0443676i	$0.985873\pi$
$68$	0.744454	−	1.28943i	0.0902783	−	0.156367i
$69$		0			0
$70$	3.55310	−	7.68974i	0.424677	−	0.919099i
$71$	−0.630544	−	0.790678i	−0.0748319	−	0.0938362i	0.743006	−	0.669284i	$-0.233399\pi$
$71$	−0.630544	−	0.790678i	−0.0748319	−	0.0938362i	−0.817838	+	0.575448i	$0.804828\pi$
$72$		0			0
$73$	−7.37497	−	5.02817i	−0.863175	−	0.588503i	0.0487721	−	0.998810i	$-0.484469\pi$
$73$	−7.37497	−	5.02817i	−0.863175	−	0.588503i	−0.911947	+	0.410307i	$0.865422\pi$
$74$	7.20798	+	4.91432i	0.837911	+	0.571278i
$75$		0			0
$76$	4.17888	+	5.24016i	0.479351	+	0.601087i
$77$	−5.38666	−	4.15680i	−0.613867	−	0.473711i
$78$		0			0
$79$	0.795922	−	1.37858i	0.0895482	−	0.155102i	−0.817772	−	0.575542i	$-0.804791\pi$
$79$	0.795922	−	1.37858i	0.0895482	−	0.155102i	0.907320	+	0.420440i	$0.138124\pi$
$80$	1.60085	+	2.77276i	0.178981	+	0.310004i
$81$		0			0
$82$	6.88882	+	6.39190i	0.760743	+	0.705867i
$83$	−8.83741	+	4.25587i	−0.970032	+	0.467143i	−0.850665	−	0.525707i	$-0.823801\pi$
$83$	−8.83741	+	4.25587i	−0.970032	+	0.467143i	−0.119367	+	0.992850i	$0.538086\pi$
$84$		0			0
$85$	−4.29496	−	2.06835i	−0.465854	−	0.224344i
$86$	−1.74353	−	4.44245i	−0.188010	−	0.479042i
$87$		0			0
$88$	2.45744	−	0.758019i	0.261964	−	0.0808051i
$89$	−1.05713	+	14.1064i	−0.112055	+	1.49527i	0.603864	+	0.797087i	$0.293627\pi$
$89$	−1.05713	+	14.1064i	−0.112055	+	1.49527i	−0.715919	+	0.698183i	$0.753992\pi$
$90$		0			0
$91$	−16.7806	+	6.89702i	−1.75909	+	0.723004i
$92$	−0.307591	+	1.34765i	−0.0320686	+	0.140502i
$93$		0			0
$94$	−3.51974	+	8.96815i	−0.363033	+	0.924994i
$95$	15.7307	−	14.5959i	1.61393	−	1.49751i
$96$		0			0
$97$	−3.99911			−0.406048			−0.203024	−	0.979174i	$-0.565077\pi$
$97$	−3.99911			−0.406048			−0.203024	+	0.979174i	$0.565077\pi$
$98$	−4.53691	−	5.33071i	−0.458297	−	0.538483i
$99$		0			0
$100$	4.33853	−	2.95796i	0.433853	−	0.295796i
$101$	−4.34613	+	4.03262i	−0.432456	+	0.401261i	−0.866138	−	0.499805i	$-0.833405\pi$
$101$	−4.34613	+	4.03262i	−0.432456	+	0.401261i	0.433681	+	0.901066i	$0.357214\pi$
$102$		0			0
$103$	10.4665	+	3.22848i	1.03129	+	0.318112i	0.763804	−	0.645449i	$-0.223330\pi$
$103$	10.4665	+	3.22848i	1.03129	+	0.318112i	0.267490	+	0.963561i	$0.413806\pi$
$104$	1.52589	−	6.68537i	0.149626	−	0.655555i
$105$		0			0
$106$	2.09752	+	9.18985i	0.203730	+	0.892597i
$107$	0.168050	−	2.24247i	0.0162460	−	0.216788i	−0.983172	−	0.182681i	$-0.941522\pi$
$107$	0.168050	−	2.24247i	0.0162460	−	0.216788i	0.999418	−	0.0341068i	$-0.0108586\pi$
$108$		0			0
$109$	−0.351040	−	4.68430i	−0.0336235	−	0.448675i	−0.988454	−	0.151523i	$-0.951582\pi$
$109$	−0.351040	−	4.68430i	−0.0336235	−	0.448675i	0.954830	−	0.297152i	$-0.0960368\pi$
$110$	−3.00814	−	7.66463i	−0.286815	−	0.730794i
$111$		0			0
$112$	2.63486	−	0.239808i	0.248971	−	0.0226597i
$113$	11.8942	−	5.72794i	1.11891	−	0.538839i	0.219356	−	0.975645i	$-0.429605\pi$
$113$	11.8942	−	5.72794i	1.11891	−	0.538839i	0.899556	+	0.436806i	$0.143890\pi$
$114$		0			0
$115$	4.37630	+	0.659621i	0.408092	+	0.0615100i
$116$	−4.49779	−	7.79040i	−0.417610	−	0.723321i
$117$		0			0
$118$	−1.21108	+	1.51865i	−0.111489	+	0.139803i
$119$	−3.04026	+	2.50495i	−0.278700	+	0.229629i
$120$		0			0
$121$	4.33742	−	0.653761i	0.394311	−	0.0594328i
$122$	4.14103	+	2.82331i	0.374912	+	0.255610i
$123$		0			0
$124$	1.82363	−	0.274869i	0.163767	−	0.0246839i
$125$	−0.500928	−	0.628144i	−0.0448044	−	0.0561829i
$126$		0			0
$127$	−5.89497	+	7.39206i	−0.523094	+	0.655939i	−0.971263	−	0.238010i	$-0.923505\pi$
$127$	−5.89497	+	7.39206i	−0.523094	+	0.655939i	0.448169	+	0.893949i	$0.352076\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$		0			0
$130$	−21.7098	−	3.27223i	−1.90408	−	0.286994i
$131$	−1.76766	−	1.64015i	−0.154441	−	0.143300i	0.599168	−	0.800623i	$-0.295498\pi$
$131$	−1.76766	−	1.64015i	−0.154441	−	0.143300i	−0.753609	+	0.657323i	$0.771689\pi$
$132$		0			0
$133$	−5.49669	−	16.8595i	−0.476624	−	1.46190i
$134$	−6.80076	−	3.27507i	−0.587496	−	0.282923i
$135$		0			0
$136$	−0.111266	−	1.48475i	−0.00954100	−	0.127316i
$137$	3.74393	−	1.15485i	0.319865	−	0.0986654i	−0.130665	−	0.991427i	$-0.541711\pi$
$137$	3.74393	−	1.15485i	0.319865	−	0.0986654i	0.450530	+	0.892761i	$0.351235\pi$
$138$		0			0
$139$	−5.22353	−	22.8858i	−0.443054	−	1.94115i	−0.313566	−	0.949566i	$-0.601524\pi$
$139$	−5.22353	−	22.8858i	−0.443054	−	1.94115i	−0.129488	−	0.991581i	$-0.541333\pi$
$140$	−1.39607	−	8.35509i	−0.117990	−	0.706134i
$141$		0			0
$142$	−0.966385	−	0.298090i	−0.0810972	−	0.0250152i
$143$	−6.44273	+	16.4158i	−0.538768	+	1.37276i
$144$		0			0
$145$	−23.7967	+	16.2243i	−1.97621	+	1.34736i
$146$	−8.92596			−0.738718
$147$		0			0
$148$	8.72385			0.717096
$149$	3.99350	−	2.72272i	0.327160	−	0.223054i	−0.388590	−	0.921411i	$-0.627038\pi$
$149$	3.99350	−	2.72272i	0.327160	−	0.223054i	0.715750	+	0.698357i	$0.246085\pi$
$150$		0			0
$151$	−2.17641	+	5.54541i	−0.177114	+	0.451279i	−0.991670	−	0.128806i	$-0.958885\pi$
$151$	−2.17641	+	5.54541i	−0.177114	+	0.451279i	0.814556	+	0.580085i	$0.196981\pi$
$152$	6.40464	+	1.97557i	0.519485	+	0.160240i
$153$		0			0
$154$	−6.79228	−	0.400095i	−0.547337	−	0.0322405i
$155$	−1.31392	−	5.75665i	−0.105536	−	0.462385i
$156$		0			0
$157$	16.6214	−	5.12702i	1.32653	−	0.409180i	0.451078	−	0.892485i	$-0.351040\pi$
$157$	16.6214	−	5.12702i	1.32653	−	0.409180i	0.875453	+	0.483304i	$0.160563\pi$
$158$	−0.118959	−	1.58739i	−0.00946384	−	0.126286i
$159$		0			0
$160$	2.88464	+	1.38917i	0.228051	+	0.109823i
$161$	2.01169	−	3.05425i	0.158544	−	0.240708i
$162$		0			0
$163$	−1.12438	−	1.04327i	−0.0880684	−	0.0817155i	0.634910	−	0.772586i	$-0.281037\pi$
$163$	−1.12438	−	1.04327i	−0.0880684	−	0.0817155i	−0.722979	+	0.690870i	$0.757228\pi$
$164$	9.29250	+	1.40062i	0.725622	+	0.109370i
$165$		0			0
$166$	−4.90439	+	8.49466i	−0.380655	+	0.659314i
$167$	9.60150	−	12.0399i	0.742986	−	0.931675i	−0.256405	−	0.966569i	$-0.582538\pi$
$167$	9.60150	−	12.0399i	0.742986	−	0.931675i	0.999391	+	0.0348944i	$0.0111095\pi$
$168$		0			0
$169$	21.2127	+	26.5999i	1.63175	+	2.04614i
$170$	−4.71381	+	0.710492i	−0.361532	+	0.0544922i
$171$		0			0
$172$	−3.94310	−	2.68836i	−0.300658	−	0.204985i
$173$	2.50825	−	0.378058i	0.190699	−	0.0287432i	−0.0529983	−	0.998595i	$-0.516878\pi$
$173$	2.50825	−	0.378058i	0.190699	−	0.0287432i	0.243697	+	0.969851i	$0.421640\pi$
$174$		0			0
$175$	−13.4933	+	3.30722i	−1.02000	+	0.250002i
$176$	1.60342	−	2.01063i	0.120862	−	0.151557i
$177$		0			0
$178$	7.07296	+	12.2507i	0.530140	+	0.918230i
$179$	−11.0628	−	1.66745i	−0.826872	−	0.124631i	−0.278046	−	0.960568i	$-0.589687\pi$
$179$	−11.0628	−	1.66745i	−0.826872	−	0.124631i	−0.548826	+	0.835937i	$0.684925\pi$
$180$		0			0
$181$	6.36821	−	3.06677i	0.473345	−	0.227951i	−0.181974	−	0.983303i	$-0.558249\pi$
$181$	6.36821	−	3.06677i	0.473345	−	0.227951i	0.655319	+	0.755352i	$0.272534\pi$
$182$	−9.97956	+	15.1514i	−0.739734	+	1.12310i
$183$		0			0
$184$	0.505012	+	1.28675i	0.0372300	+	0.0948604i
$185$	−2.08730	−	27.8531i	−0.153462	−	2.04780i
$186$		0			0
$187$	−0.286142	+	3.81830i	−0.0209248	+	0.279222i
$188$	2.14379	+	9.39257i	0.156352	+	0.685024i
$189$		0			0
$190$	4.77511	−	20.9211i	0.346423	−	1.51778i
$191$	10.1282	+	3.12415i	0.732854	+	0.226055i	0.638650	−	0.769497i	$-0.279493\pi$
$191$	10.1282	+	3.12415i	0.732854	+	0.226055i	0.0942040	+	0.995553i	$0.469969\pi$
$192$		0			0
$193$	8.12412	−	7.53808i	0.584787	−	0.542603i	−0.331330	−	0.943515i	$-0.607497\pi$
$193$	8.12412	−	7.53808i	0.584787	−	0.542603i	0.916116	+	0.400912i	$0.131307\pi$
$194$	−3.30422	+	2.25278i	−0.237229	+	0.161740i
$195$		0			0
$196$	−6.75146	−	1.84871i	−0.482247	−	0.132051i
$197$	−0.526319			−0.0374987			−0.0187494	−	0.999824i	$-0.505968\pi$
$197$	−0.526319			−0.0374987			−0.0187494	+	0.999824i	$0.505968\pi$
$198$		0			0
$199$	−4.93064	+	4.57497i	−0.349524	+	0.324311i	−0.835323	−	0.549760i	$-0.814719\pi$
$199$	−4.93064	+	4.57497i	−0.349524	+	0.324311i	0.485799	+	0.874071i	$0.338529\pi$
$200$	1.91838	−	4.88796i	0.135650	−	0.345631i
$201$		0			0
$202$	−1.31929	+	5.78017i	−0.0928247	+	0.406691i
$203$	3.92244	+	23.4746i	0.275301	+	1.64760i
$204$		0			0
$205$	2.24847	−	30.0038i	0.157040	−	2.09556i
$206$	10.4665	−	3.22848i	0.729235	−	0.224939i
$207$		0			0
$208$	−2.50525	−	6.38328i	−0.173708	−	0.442601i
$209$	−15.5296	−	7.47864i	−1.07420	−	0.517309i
$210$		0			0
$211$	5.49638	−	2.64692i	0.378386	−	0.182221i	−0.235017	−	0.971991i	$-0.575514\pi$
$211$	5.49638	−	2.64692i	0.378386	−	0.182221i	0.613403	+	0.789770i	$0.289800\pi$
$212$	6.90988	+	6.41144i	0.474573	+	0.440339i
$213$		0			0
$214$	−1.12438	−	1.94749i	−0.0768611	−	0.133127i
$215$	−7.63983	+	13.2326i	−0.521032	+	0.902454i
$216$		0			0
$217$	−4.77377	−	1.00969i	−0.324065	−	0.0685422i
$218$	−2.92880	−	3.67260i	−0.198364	−	0.248740i
$219$		0			0
$220$	−6.80308	−	4.63826i	−0.458664	−	0.312712i
$221$	8.43580	+	5.75143i	0.567454	+	0.386883i
$222$		0			0
$223$	6.06624	+	7.60683i	0.406226	+	0.509391i	0.942295	−	0.334783i	$-0.108663\pi$
$223$	6.06624	+	7.60683i	0.406226	+	0.509391i	−0.536070	+	0.844174i	$0.680092\pi$
$224$	2.04194	−	1.68241i	0.136433	−	0.112411i
$225$		0			0
$226$	6.60078	−	11.4329i	0.439077	−	0.760504i
$227$	−3.58355	−	6.20689i	−0.237849	−	0.411966i	0.722248	−	0.691634i	$-0.243109\pi$
$227$	−3.58355	−	6.20689i	−0.237849	−	0.411966i	−0.960097	+	0.279668i	$0.909776\pi$
$228$		0			0
$229$	−21.6432	−	20.0820i	−1.43023	−	1.32706i	−0.864666	−	0.502348i	$-0.832470\pi$
$229$	−21.6432	−	20.0820i	−1.43023	−	1.32706i	−0.565560	−	0.824707i	$-0.691340\pi$
$230$	3.98744	−	1.92025i	0.262924	−	0.126618i
$231$		0			0
$232$	−8.10474	−	3.90304i	−0.532102	−	0.256247i
$233$	−2.93497	−	7.47818i	−0.192276	−	0.489912i	0.801928	−	0.597421i	$-0.203808\pi$
$233$	−2.93497	−	7.47818i	−0.192276	−	0.489912i	−0.994204	+	0.107509i	$0.965713\pi$
$234$		0			0
$235$	29.4753	−	9.09191i	1.92275	−	0.593091i
$236$	−0.145158	+	1.93699i	−0.00944896	+	0.126088i
$237$		0			0
$238$	−1.10089	+	3.78233i	−0.0713599	+	0.245172i
$239$	−0.444253	+	1.94640i	−0.0287363	+	0.125902i	−0.987262	−	0.159106i	$-0.949139\pi$
$239$	−0.444253	+	1.94640i	−0.0287363	+	0.125902i	0.958525	+	0.285008i	$0.0919961\pi$
$240$		0			0
$241$	3.40652	−	8.67968i	0.219433	−	0.559107i	−0.778188	−	0.628031i	$-0.783861\pi$
$241$	3.40652	−	8.67968i	0.219433	−	0.559107i	0.997622	+	0.0689235i	$0.0219564\pi$
$242$	3.21547	−	2.98352i	0.206698	−	0.191788i
$243$		0			0
$244$	5.01191			0.320855
$245$	−4.28710	+	21.9981i	−0.273893	+	1.40541i
$246$		0			0
$247$	−37.9743	+	25.8904i	−2.41625	+	1.64737i
$248$	1.35192	−	1.25440i	0.0858469	−	0.0796543i
$249$		0			0
$250$	−0.767732	−	0.236814i	−0.0485556	−	0.0149774i
$251$	2.88157	−	12.6250i	0.181883	−	0.796881i	−0.798850	−	0.601530i	$-0.794558\pi$
$251$	2.88157	−	12.6250i	0.181883	−	0.796881i	0.980733	−	0.195351i	$-0.0625847\pi$
$252$		0			0
$253$	−0.791029	−	3.46572i	−0.0497316	−	0.217888i
$254$	−0.706558	+	9.42836i	−0.0443334	+	0.591588i
$255$		0			0
$256$	0.0747301	+	0.997204i	0.00467063	+	0.0623252i
$257$	−4.10553	−	10.4607i	−0.256096	−	0.652522i	0.743777	−	0.668427i	$-0.233032\pi$
$257$	−4.10553	−	10.4607i	−0.256096	−	0.652522i	−0.999874	+	0.0159051i	$0.994937\pi$
$258$		0			0
$259$	−21.6175	−	8.08844i	−1.34325	−	0.502591i
$260$	−19.7808	+	9.52595i	−1.22676	+	0.590774i
$261$		0			0
$262$	−2.38443	−	0.359396i	−0.147311	−	0.0222035i
$263$	11.8301	+	20.4904i	0.729478	+	1.26349i	0.957104	+	0.289744i	$0.0935703\pi$
$263$	11.8301	+	20.4904i	0.729478	+	1.26349i	−0.227626	+	0.973749i	$0.573096\pi$
$264$		0			0
$265$	18.8169	−	23.5956i	1.15591	−	1.44947i
$266$	−14.0389	−	10.8336i	−0.860778	−	0.664249i
$267$		0			0
$268$	−7.46396	+	1.12501i	−0.455934	+	0.0687210i
$269$	11.0231	+	7.51540i	0.672088	+	0.458222i	0.850668	−	0.525703i	$-0.176198\pi$
$269$	11.0231	+	7.51540i	0.672088	+	0.458222i	−0.178580	+	0.983925i	$0.557150\pi$
$270$		0			0
$271$	0.125606	−	0.0189320i	0.00763001	−	0.00115004i	−0.145226	−	0.989398i	$-0.546391\pi$
$271$	0.125606	−	0.0189320i	0.00763001	−	0.00115004i	0.152856	+	0.988248i	$0.451153\pi$
$272$	−0.928319	−	1.16408i	−0.0562876	−	0.0705824i
$273$		0			0
$274$	2.44283	−	3.06321i	0.147577	−	0.185055i
$275$	−6.75189	+	11.6946i	−0.407154	+	0.705212i
$276$		0			0
$277$	−6.68520	−	1.00763i	−0.401675	−	0.0605427i	−0.0549016	−	0.998492i	$-0.517485\pi$
$277$	−6.68520	−	1.00763i	−0.401675	−	0.0605427i	−0.346773	+	0.937949i	$0.612723\pi$
$278$	−17.2079	−	15.9666i	−1.03206	−	0.957613i
$279$		0			0
$280$	−5.86008	−	6.11686i	−0.350207	−	0.365552i
$281$	15.9631	+	7.68743i	0.952280	+	0.458594i	0.844485	−	0.535579i	$-0.179907\pi$
$281$	15.9631	+	7.68743i	0.952280	+	0.458594i	0.107795	+	0.994173i	$0.465621\pi$
$282$		0			0
$283$	2.12849	+	28.4028i	0.126526	+	1.68837i	0.594080	+	0.804406i	$0.297516\pi$
$283$	2.12849	+	28.4028i	0.126526	+	1.68837i	−0.467554	+	0.883965i	$0.654865\pi$
$284$	−0.966385	+	0.298090i	−0.0573444	+	0.0176884i
$285$		0			0
$286$	3.92412	+	17.1927i	0.232038	+	1.01663i
$287$	−21.7280	−	12.0864i	−1.28256	−	0.713436i
$288$		0			0
$289$	−14.1264	−	4.35741i	−0.830963	−	0.256318i
$290$	−10.5223	+	26.8103i	−0.617889	+	1.57436i
$291$		0			0
$292$	−7.37497	+	5.02817i	−0.431588	+	0.294252i
$293$	−25.2456			−1.47486			−0.737431	−	0.675423i	$-0.763961\pi$
$293$	−25.2456			−1.47486			−0.737431	+	0.675423i	$0.763961\pi$
$294$		0			0
$295$	6.21908			0.362089
$296$	7.20798	−	4.91432i	0.418955	−	0.285639i
$297$		0			0
$298$	1.76582	−	4.49923i	0.102291	−	0.260634i
$299$	−9.05774	−	2.79394i	−0.523823	−	0.161578i
$300$		0			0
$301$	7.27835	+	10.3176i	0.419517	+	0.594696i
$302$	1.32560	+	5.80785i	0.0762799	+	0.334204i
$303$		0			0
$304$	6.40464	−	1.97557i	0.367331	−	0.113307i
$305$	−1.19917	−	16.0018i	−0.0686643	−	0.916261i
$306$		0			0
$307$	−3.49090	−	1.68113i	−0.199236	−	0.0959472i	0.331605	−	0.943418i	$-0.392410\pi$
$307$	−3.49090	−	1.68113i	−0.199236	−	0.0959472i	−0.530842	+	0.847471i	$0.678124\pi$
$308$	−5.83742	+	3.49565i	−0.332618	+	0.199183i
$309$		0			0
$310$	−4.32845	−	4.01621i	−0.245839	−	0.228106i
$311$	27.9620	+	4.21460i	1.58558	+	0.238988i	0.881868	−	0.471496i	$-0.156286\pi$
$311$	27.9620	+	4.21460i	1.58558	+	0.238988i	0.703714	+	0.710484i	$0.251524\pi$
$312$		0			0
$313$	13.0735	−	22.6439i	0.738957	−	1.27991i	−0.214008	−	0.976832i	$-0.568652\pi$
$313$	13.0735	−	22.6439i	0.738957	−	1.27991i	0.952965	−	0.303080i	$-0.0980148\pi$
$314$	10.8451	−	13.5993i	0.612023	−	0.767453i
$315$		0			0
$316$	−0.992498	−	1.24455i	−0.0558324	−	0.0700116i
$317$	−1.07714	+	0.162353i	−0.0604984	+	0.00911866i	−0.179222	−	0.983809i	$-0.557358\pi$
$317$	−1.07714	+	0.162353i	−0.0604984	+	0.00911866i	0.118723	+	0.992927i	$0.462120\pi$
$318$		0			0
$319$	19.1141	+	13.0318i	1.07018	+	0.729638i
$320$	3.16595	−	0.477190i	0.176982	−	0.0266757i
$321$		0			0
$322$	−0.0583796	−	3.65676i	−0.00325337	−	0.203783i
$323$	−6.22198	+	7.80211i	−0.346200	+	0.434121i
$324$		0			0
$325$	18.0036	+	31.1832i	0.998661	+	1.72973i
$326$	−1.51671	−	0.228607i	−0.0840025	−	0.0126613i
$327$		0			0
$328$	8.46682	−	4.07740i	0.467502	−	0.225137i
$329$	3.39619	−	25.2622i	0.187238	−	1.39275i
$330$		0			0
$331$	−7.08510	−	18.0525i	−0.389432	−	0.992257i	−0.982360	−	0.187001i	$-0.940123\pi$
$331$	−7.08510	−	18.0525i	−0.389432	−	0.992257i	0.592927	−	0.805256i	$-0.297972\pi$
$332$	0.733012	+	9.78136i	0.0402292	+	0.536822i
$333$		0			0
$334$	1.15081	−	15.3565i	0.0629697	−	0.840273i
$335$	5.37775	+	23.5614i	0.293818	+	1.28730i
$336$		0			0
$337$	−4.31052	+	18.8856i	−0.234809	+	1.02876i	0.710784	+	0.703411i	$0.248341\pi$
$337$	−4.31052	+	18.8856i	−0.234809	+	1.02876i	−0.945592	+	0.325354i	$0.894517\pi$
$338$	32.5110	+	10.0283i	1.76837	+	0.545468i
$339$		0			0
$340$	−3.49450	+	3.24242i	−0.189516	+	0.175845i
$341$	−3.91868	+	2.67171i	−0.212208	+	0.144681i
$342$		0			0
$343$	15.0159	+	10.8408i	0.810783	+	0.585347i
$344$	−4.77234			−0.257308
$345$		0			0
$346$	1.85945	−	1.72532i	0.0999645	−	0.0927535i
$347$	2.04184	−	5.20253i	0.109612	−	0.279286i	−0.865534	−	0.500850i	$-0.833021\pi$
$347$	2.04184	−	5.20253i	0.109612	−	0.279286i	0.975146	+	0.221564i	$0.0711161\pi$
$348$		0			0
$349$	−4.37683	+	19.1761i	−0.234286	+	1.02647i	0.711755	+	0.702428i	$0.247901\pi$
$349$	−4.37683	+	19.1761i	−0.234286	+	1.02647i	−0.946041	+	0.324047i	$0.894956\pi$
$350$	−9.28565	+	10.3336i	−0.496339	+	0.552354i
$351$		0			0
$352$	0.192183	−	2.56450i	0.0102434	−	0.136688i
$353$	10.5343	−	3.24940i	0.560685	−	0.172948i	−0.00144266	−	0.999999i	$-0.500459\pi$
$353$	10.5343	−	3.24940i	0.560685	−	0.172948i	0.562127	+	0.827051i	$0.309983\pi$
$354$		0			0
$355$	1.18295	+	3.01411i	0.0627845	+	0.159972i
$356$	12.7450	+	6.13768i	0.675485	+	0.325296i
$357$		0			0
$358$	−10.0798	+	4.85419i	−0.532735	+	0.256552i
$359$	4.98280	+	4.62336i	0.262982	+	0.244012i	0.800632	−	0.599156i	$-0.204497\pi$
$359$	4.98280	+	4.62336i	0.262982	+	0.244012i	−0.537650	+	0.843168i	$0.680688\pi$
$360$		0			0
$361$	−12.9612	−	22.4494i	−0.682166	−	1.18155i
$362$	3.53409	−	6.12122i	0.185748	−	0.321724i
$363$		0			0
$364$	0.289608	+	18.1404i	0.0151796	+	0.950815i
$365$	17.8183	+	22.3434i	0.932652	+	1.16951i
$366$		0			0
$367$	16.7790	+	11.4397i	0.875856	+	0.597148i	0.915613	−	0.402061i	$-0.131706\pi$
$367$	16.7790	+	11.4397i	0.875856	+	0.597148i	−0.0397570	+	0.999209i	$0.512658\pi$
$368$	1.14211	+	0.778679i	0.0595367	+	0.0405914i
$369$		0			0
$370$	−17.4148	−	21.8375i	−0.905354	−	1.13528i
$371$	−11.1781	−	22.2940i	−0.580337	−	1.15745i
$372$		0			0
$373$	−6.38522	+	11.0595i	−0.330614	+	0.572641i	−0.982632	−	0.185563i	$-0.940589\pi$
$373$	−6.38522	+	11.0595i	−0.330614	+	0.572641i	0.652018	+	0.758203i	$0.273923\pi$
$374$	1.91450	+	3.31602i	0.0989967	+	0.171467i
$375$		0			0
$376$	7.06231	+	6.55287i	0.364211	+	0.337938i
$377$	55.5766	−	26.7643i	2.86234	−	1.37843i
$378$		0			0
$379$	−11.6460	−	5.60844i	−0.598217	−	0.288086i	0.110167	−	0.993913i	$-0.464861\pi$
$379$	−11.6460	−	5.60844i	−0.598217	−	0.288086i	−0.708384	+	0.705827i	$0.750576\pi$
$380$	−7.83991	−	19.9758i	−0.402179	−	1.02474i
$381$		0			0
$382$	10.1282	−	3.12415i	0.518206	−	0.159845i
$383$	−2.23309	+	29.7985i	−0.114105	+	1.52263i	0.587007	+	0.809582i	$0.300306\pi$
$383$	−2.23309	+	29.7985i	−0.114105	+	1.52263i	−0.701113	+	0.713050i	$0.747313\pi$
$384$		0			0
$385$	12.5574	+	17.8011i	0.639987	+	0.907227i
$386$	2.46611	−	10.8047i	0.125522	−	0.549946i
$387$		0			0
$388$	−1.46104	+	3.72267i	−0.0741731	+	0.188990i
$389$	14.5259	−	13.4780i	0.736491	−	0.683364i	−0.219878	−	0.975527i	$-0.570566\pi$
$389$	14.5259	−	13.4780i	0.736491	−	0.683364i	0.956368	+	0.292164i	$0.0943753\pi$
$390$		0			0
$391$	−2.05812			−0.104084
$392$	−6.61974	+	2.27576i	−0.334347	+	0.114943i
$393$		0			0
$394$	−0.434866	+	0.296486i	−0.0219082	+	0.0149368i
$395$	−3.73609	+	3.46658i	−0.187983	+	0.174423i
$396$		0			0
$397$	−8.06327	−	2.48719i	−0.404684	−	0.124828i	0.0857293	−	0.996318i	$-0.472678\pi$
$397$	−8.06327	−	2.48719i	−0.404684	−	0.124828i	−0.490413	+	0.871490i	$0.663154\pi$
$398$	−1.49672	+	6.55754i	−0.0750236	+	0.328700i
$399$		0			0
$400$	−1.16844	−	5.11928i	−0.0584222	−	0.255964i
$401$	2.00816	−	26.7970i	0.100283	−	1.33818i	−0.689274	−	0.724501i	$-0.742070\pi$
$401$	2.00816	−	26.7970i	0.100283	−	1.33818i	0.789556	−	0.613678i	$-0.210311\pi$
$402$		0			0
$403$	0.945071	+	12.6111i	0.0470773	+	0.628203i
$404$	2.16604	+	5.51898i	0.107765	+	0.274580i
$405$		0			0
$406$	16.4646	+	17.1861i	0.817124	+	0.852930i
$407$	−20.2133	+	9.73419i	−1.00193	+	0.482506i
$408$		0			0
$409$	−8.26903	−	1.24636i	−0.408877	−	0.0616284i	−0.0586166	−	0.998281i	$-0.518669\pi$
$409$	−8.26903	−	1.24636i	−0.408877	−	0.0616284i	−0.350261	+	0.936652i	$0.613907\pi$
$410$	−15.0440	−	26.0569i	−0.742968	−	1.28686i
$411$		0			0
$412$	6.82915	−	8.56348i	0.336448	−	0.421892i
$413$	2.15561	−	4.66524i	0.106071	−	0.229561i
$414$		0			0
$415$	31.0541	−	4.68065i	1.52439	−	0.229764i
$416$	−5.66577	−	3.86285i	−0.277787	−	0.189392i
$417$		0			0
$418$	−17.0440	+	2.56897i	−0.833649	+	0.125652i
$419$	−8.48212	−	10.6362i	−0.414379	−	0.519615i	0.530212	−	0.847865i	$-0.322112\pi$
$419$	−8.48212	−	10.6362i	−0.414379	−	0.519615i	−0.944591	+	0.328251i	$0.893541\pi$
$420$		0			0
$421$	12.7027	−	15.9286i	0.619090	−	0.776314i	−0.369126	−	0.929379i	$-0.620343\pi$
$421$	12.7027	−	15.9286i	0.619090	−	0.776314i	0.988216	+	0.153065i	$0.0489145\pi$
$422$	3.05026	−	5.28321i	0.148484	−	0.257182i
$423$		0			0
$424$	9.32090	+	1.40490i	0.452663	+	0.0682280i
$425$	5.73112	+	5.31770i	0.278000	+	0.257946i
$426$		0			0
$427$	−12.4194	−	4.64686i	−0.601017	−	0.224878i
$428$	−2.02606	−	0.975701i	−0.0979335	−	0.0471623i
$429$		0			0
$430$	1.14185	+	15.2369i	0.0550649	+	0.734790i
$431$	−32.1950	+	9.93085i	−1.55078	+	0.478352i	−0.947656	−	0.319295i	$-0.896554\pi$
$431$	−32.1950	+	9.93085i	−1.55078	+	0.478352i	−0.603125	+	0.797647i	$0.706078\pi$
$432$		0			0
$433$	8.73417	+	38.2669i	0.419737	+	1.83899i	0.533926	+	0.845531i	$0.320716\pi$
$433$	8.73417	+	38.2669i	0.419737	+	1.83899i	−0.114189	+	0.993459i	$0.536427\pi$
$434$	−4.51305	+	1.85492i	−0.216633	+	0.0890388i
$435$		0			0
$436$	−4.48874	−	1.38459i	−0.214972	−	0.0663100i
$437$	3.38480	−	8.62432i	0.161917	−	0.412557i
$438$		0			0
$439$	17.8426	−	12.1649i	0.851582	−	0.580599i	−0.0569674	−	0.998376i	$-0.518143\pi$
$439$	17.8426	−	12.1649i	0.851582	−	0.580599i	0.908550	+	0.417777i	$0.137191\pi$
$440$	−8.23380			−0.392531
$441$		0			0
$442$	10.2099			0.485635
$443$	−27.5572	+	18.7882i	−1.30928	+	0.892655i	−0.998330	−	0.0577699i	$-0.981601\pi$
$443$	−27.5572	+	18.7882i	−1.30928	+	0.892655i	−0.310954	+	0.950425i	$0.600649\pi$
$444$		0			0
$445$	16.5467	−	42.1603i	0.784388	−	1.99859i
$446$	9.29724	+	2.86782i	0.440237	+	0.135795i
$447$		0			0
$448$	0.739392	−	2.54033i	0.0349330	−	0.120020i
$449$	3.76094	+	16.4778i	0.177490	+	0.777634i	0.982784	+	0.184758i	$0.0591502\pi$
$449$	3.76094	+	16.4778i	0.177490	+	0.777634i	−0.805294	+	0.592875i	$0.797993\pi$
$450$		0			0
$451$	−23.0937	+	7.12345i	−1.08744	+	0.335430i
$452$	−0.986554	−	13.1646i	−0.0464036	−	0.619213i
$453$		0			0
$454$	−6.45733	−	3.10969i	−0.303058	−	0.145945i
$455$	57.8485	−	5.26499i	2.71198	−	0.246827i
$456$		0			0
$457$	5.08684	+	4.71990i	0.237953	+	0.220788i	0.790131	−	0.612938i	$-0.210013\pi$
$457$	5.08684	+	4.71990i	0.237953	+	0.220788i	−0.552178	+	0.833726i	$0.686203\pi$
$458$	−29.1951	−	4.40045i	−1.36420	−	0.205619i
$459$		0			0
$460$	2.21286	−	3.83279i	0.103175	−	0.178705i
$461$	6.79901	−	8.52569i	0.316662	−	0.397081i	−0.597872	−	0.801592i	$-0.703987\pi$
$461$	6.79901	−	8.52569i	0.316662	−	0.397081i	0.914533	+	0.404511i	$0.132558\pi$
$462$		0			0
$463$	14.5758	+	18.2775i	0.677396	+	0.849428i	0.995111	−	0.0987582i	$-0.0314870\pi$
$463$	14.5758	+	18.2775i	0.677396	+	0.849428i	−0.317715	+	0.948186i	$0.602916\pi$
$464$	−8.89511	+	1.34072i	−0.412945	+	0.0622415i
$465$		0			0
$466$	−6.63760	−	4.52544i	−0.307481	−	0.209637i
$467$	2.78017	−	0.419043i	0.128651	−	0.0193910i	−0.0844012	−	0.996432i	$-0.526898\pi$
$467$	2.78017	−	0.419043i	0.128651	−	0.0193910i	0.213052	+	0.977041i	$0.431660\pi$
$468$		0			0
$469$	19.5386	+	4.13257i	0.902209	+	0.190824i
$470$	19.2319	−	24.1161i	0.887103	−	1.11239i
$471$		0			0
$472$	0.971213	+	1.68219i	0.0447037	+	0.0774290i
$473$	12.1359	+	1.82919i	0.558010	+	0.0841064i
$474$		0			0
$475$	−31.7086	+	15.2701i	−1.45489	+	0.700639i
$476$	1.22106	+	3.74526i	0.0559674	+	0.171664i
$477$		0			0
$478$	0.729386	+	1.85845i	0.0333613	+	0.0850033i
$479$	−1.51196	−	20.1757i	−0.0690832	−	0.921851i	−0.918828	−	0.394658i	$-0.870863\pi$
$479$	−1.51196	−	20.1757i	−0.0690832	−	0.921851i	0.849745	−	0.527194i	$-0.176756\pi$
$480$		0			0
$481$	−4.47051	+	59.6548i	−0.203838	+	2.72002i
$482$	−2.07484	−	9.09045i	−0.0945062	−	0.414059i
$483$		0			0
$484$	0.976069	−	4.27644i	0.0443668	−	0.194384i
$485$	12.2351	+	3.77404i	0.555569	+	0.171370i
$486$		0			0
$487$	9.19516	−	8.53186i	0.416673	−	0.386616i	−0.443789	−	0.896131i	$-0.646366\pi$
$487$	9.19516	−	8.53186i	0.416673	−	0.386616i	0.860461	+	0.509516i	$0.170175\pi$
$488$	4.14103	−	2.82331i	0.187456	−	0.127805i
$489$		0			0
$490$	8.84980	+	20.5907i	0.399793	+	0.930193i
$491$	5.78677			0.261153			0.130577	−	0.991438i	$-0.458317\pi$
$491$	5.78677			0.261153			0.130577	+	0.991438i	$0.458317\pi$
$492$		0			0
$493$	9.81820	−	9.10996i	0.442190	−	0.410292i
$494$	−16.7912	+	42.7834i	−0.755473	+	1.92491i
$495$		0			0
$496$	0.410380	−	1.79799i	0.0184266	−	0.0807323i
$497$	2.67106	+	0.157337i	0.119813	+	0.00705752i
$498$		0			0
$499$	2.91173	−	38.8544i	0.130347	−	1.73936i	−0.422752	−	0.906245i	$-0.638936\pi$
$499$	2.91173	−	38.8544i	0.130347	−	1.73936i	0.553099	−	0.833115i	$-0.313445\pi$
$500$	−0.767732	+	0.236814i	−0.0343340	+	0.0105906i
$501$		0			0
$502$	−4.73104	−	12.0545i	−0.211156	−	0.538018i
$503$	4.24458	+	2.04408i	0.189257	+	0.0911412i	0.526112	−	0.850415i	$-0.323649\pi$
$503$	4.24458	+	2.04408i	0.189257	+	0.0911412i	−0.336856	+	0.941556i	$0.609363\pi$
$504$		0			0
$505$	17.1025	−	8.23613i	0.761052	−	0.366503i
$506$	−2.60589	−	2.41791i	−0.115846	−	0.107489i
$507$		0			0
$508$	4.72740	+	8.18809i	0.209744	+	0.363288i
$509$	3.25763	−	5.64238i	0.144392	−	0.250094i	−0.784754	−	0.619807i	$-0.787211\pi$
$509$	3.25763	−	5.64238i	0.144392	−	0.250094i	0.929146	+	0.369713i	$0.120544\pi$
$510$		0			0
$511$	22.9370	−	5.62188i	1.01467	−	0.248697i
$512$	0.623490	+	0.781831i	0.0275546	+	0.0345524i
$513$		0			0
$514$	−9.28489	−	6.33033i	−0.409539	−	0.279219i
$515$	−28.9751	−	19.7549i	−1.27679	−	0.870503i
$516$		0			0
$517$	−15.4476	−	19.3706i	−0.679383	−	0.851919i
$518$	−22.4176	+	5.49458i	−0.984972	+	0.241418i
$519$		0			0
$520$	−10.9775	+	19.0136i	−0.481397	+	0.833804i
$521$	−10.2183	−	17.6987i	−0.447674	−	0.775393i	0.550561	−	0.834795i	$-0.314414\pi$
$521$	−10.2183	−	17.6987i	−0.447674	−	0.775393i	−0.998234	+	0.0594019i	$0.981081\pi$
$522$		0			0
$523$	24.2435	+	22.4947i	1.06010	+	0.983625i	0.999894	−	0.0145615i	$-0.00463524\pi$
$523$	24.2435	+	22.4947i	1.06010	+	0.983625i	0.0602014	+	0.998186i	$0.480826\pi$
$524$	−2.17257	+	1.04625i	−0.0949090	+	0.0457058i
$525$		0			0
$526$	21.3172	+	10.2658i	0.929473	+	0.447611i
$527$	1.00319	+	2.55608i	0.0436995	+	0.111345i
$528$		0			0
$529$	−20.1523	+	6.21616i	−0.876187	+	0.270268i
$530$	2.25535	−	30.0955i	0.0979660	−	1.30727i
$531$		0			0
$532$	−17.7022	−	1.04274i	−0.767489	−	0.0452084i
$533$	−14.3395	+	62.8255i	−0.621113	+	2.72127i
$534$		0			0
$535$	−2.63041	+	6.70218i	−0.113723	+	0.289761i
$536$	−5.53328	+	5.13413i	−0.239001	+	0.221761i
$537$		0			0
$538$	13.3413			0.575183
$539$	17.7060	−	3.24989i	0.762653	−	0.139983i
$540$		0			0
$541$	−15.0829	+	10.2834i	−0.648466	+	0.442117i	−0.842367	−	0.538905i	$-0.818838\pi$
$541$	−15.0829	+	10.2834i	−0.648466	+	0.442117i	0.193901	+	0.981021i	$0.437886\pi$
$542$	0.0931156	−	0.0863986i	0.00399966	−	0.00371114i
$543$		0			0
$544$	−1.42276	−	0.438863i	−0.0610003	−	0.0188161i
$545$	−3.34667	+	14.6627i	−0.143356	+	0.628083i
$546$		0			0
$547$	3.06033	+	13.4082i	0.130850	+	0.573292i	0.997261	+	0.0739607i	$0.0235639\pi$
$547$	3.06033	+	13.4082i	0.130850	+	0.573292i	−0.866411	+	0.499332i	$0.833579\pi$
$548$	0.292792	−	3.90704i	0.0125075	−	0.166900i
$549$		0			0
$550$	1.00914	+	13.4660i	0.0430298	+	0.574193i
$551$	22.0272	+	56.1243i	0.938389	+	2.39098i
$552$		0			0
$553$	1.30548	+	4.00418i	0.0555147	+	0.170275i
$554$	−6.09119	+	2.93336i	−0.258790	+	0.124627i
$555$		0			0
$556$	−23.2122	−	3.49867i	−0.984414	−	0.148377i
$557$	8.39561	+	14.5416i	0.355734	+	0.616149i	0.987243	−	0.159219i	$-0.0508977\pi$
$557$	8.39561	+	14.5416i	0.355734	+	0.616149i	−0.631510	+	0.775368i	$0.717564\pi$
$558$		0			0
$559$	20.4039	−	25.5857i	0.862995	−	1.08216i
$560$	−8.28758	−	1.75289i	−0.350214	−	0.0740731i
$561$		0			0
$562$	17.5198	−	2.64069i	0.739030	−	0.111391i
$563$	−2.62496	−	1.78967i	−0.110629	−	0.0754255i	0.506742	−	0.862098i	$-0.330850\pi$
$563$	−2.62496	−	1.78967i	−0.110629	−	0.0754255i	−0.617371	+	0.786672i	$0.711802\pi$
$564$		0			0
$565$	−41.7954	+	6.29965i	−1.75835	+	0.265028i
$566$	17.7585	+	22.2685i	0.746446	+	0.936013i
$567$		0			0
$568$	−0.630544	+	0.790678i	−0.0264571	+	0.0331761i
$569$	20.6465	−	35.7607i	0.865544	−	1.49917i	−0.000961187	−	1.00000i	$-0.500306\pi$
$569$	20.6465	−	35.7607i	0.865544	−	1.49917i	0.866506	−	0.499167i	$-0.166361\pi$
$570$		0			0
$571$	−4.72022	−	0.711459i	−0.197535	−	0.0297736i	0.0495293	−	0.998773i	$-0.484228\pi$
$571$	−4.72022	−	0.711459i	−0.197535	−	0.0297736i	−0.247065	+	0.968999i	$0.579466\pi$
$572$	12.9273	+	11.9947i	0.540515	+	0.501525i
$573$		0			0
$574$	−24.7610	+	2.25358i	−1.03350	+	0.0940627i
$575$	−6.53958	−	3.14929i	−0.272719	−	0.131335i
$576$		0			0
$577$	−0.631405	−	8.42551i	−0.0262857	−	0.350759i	−0.994803	−	0.101814i	$-0.967535\pi$
$577$	−0.631405	−	8.42551i	−0.0262857	−	0.350759i	0.968518	−	0.248945i	$-0.0800837\pi$
$578$	−14.1264	+	4.35741i	−0.587580	+	0.181244i
$579$		0			0
$580$	6.40888	+	28.0791i	0.266114	+	1.16592i
$581$	7.25254	−	24.9176i	0.300886	−	1.03376i
$582$		0			0
$583$	−23.1643	−	7.14523i	−0.959365	−	0.295925i
$584$	−3.26102	+	8.30894i	−0.134942	+	0.343826i
$585$		0			0
$586$	−20.8589	+	14.2213i	−0.861672	+	0.587478i
$587$	8.51385			0.351404			0.175702	−	0.984443i	$-0.443780\pi$
$587$	8.51385			0.351404			0.175702	+	0.984443i	$0.443780\pi$
$588$		0			0
$589$	−12.3608			−0.509318
$590$	5.13844	−	3.50333i	0.211546	−	0.144230i
$591$		0			0
$592$	3.18718	−	8.12080i	0.130992	−	0.333763i
$593$	−0.0814692	−	0.0251299i	−0.00334554	−	0.00103196i	0.293082	−	0.956087i	$-0.405319\pi$
$593$	−0.0814692	−	0.0251299i	−0.00334554	−	0.00103196i	−0.296427	+	0.955055i	$0.595795\pi$
$594$		0			0
$595$	11.6655	−	4.79466i	0.478240	−	0.196562i
$596$	−1.07552	−	4.71216i	−0.0440550	−	0.193018i
$597$		0			0
$598$	−9.05774	+	2.79394i	−0.370399	+	0.114253i
$599$	−0.766036	−	10.2220i	−0.0312994	−	0.417661i	−0.990742	−	0.135758i	$-0.956653\pi$
$599$	−0.766036	−	10.2220i	−0.0312994	−	0.417661i	0.959443	−	0.281904i	$-0.0909659\pi$
$600$		0			0
$601$	14.0807	+	6.78090i	0.574363	+	0.276599i	0.698434	−	0.715675i	$-0.253881\pi$
$601$	14.0807	+	6.78090i	0.574363	+	0.276599i	−0.124070	+	0.992273i	$0.539595\pi$
$602$	11.8258	+	4.42475i	0.481982	+	0.180339i
$603$		0			0
$604$	4.36694	+	4.05193i	0.177688	+	0.164871i
$605$	−13.8872	−	2.09315i	−0.564593	−	0.0850988i
$606$		0			0
$607$	13.5303	−	23.4352i	0.549178	−	0.951205i	−0.449153	−	0.893455i	$-0.648274\pi$
$607$	13.5303	−	23.4352i	0.549178	−	0.951205i	0.998331	−	0.0577497i	$-0.0183925\pi$
$608$	4.17888	−	5.24016i	0.169476	−	0.212516i
$609$		0			0
$610$	−10.0049	−	12.5458i	−0.405088	−	0.507964i
$611$	−65.3261	+	9.84633i	−2.64281	+	0.398340i
$612$		0			0
$613$	3.33862	+	2.27623i	0.134846	+	0.0919362i	0.628864	−	0.777515i	$-0.283520\pi$
$613$	3.33862	+	2.27623i	0.134846	+	0.0919362i	−0.494019	+	0.869451i	$0.664473\pi$
$614$	−3.83133	+	0.577481i	−0.154620	+	0.0233052i
$615$		0			0
$616$	−2.85393	+	6.17658i	−0.114988	+	0.248862i
$617$	27.3631	−	34.3122i	1.10160	−	1.38136i	0.184435	−	0.982845i	$-0.440955\pi$
$617$	27.3631	−	34.3122i	1.10160	−	1.38136i	0.917162	−	0.398514i	$-0.130474\pi$
$618$		0			0
$619$	8.16982	+	14.1506i	0.328373	+	0.568759i	0.982189	−	0.187895i	$-0.0601664\pi$
$619$	8.16982	+	14.1506i	0.328373	+	0.568759i	−0.653816	+	0.756653i	$0.726833\pi$
$620$	−5.83874	−	0.880049i	−0.234490	−	0.0353436i
$621$		0			0
$622$	25.4775	−	12.2693i	1.02155	−	0.491955i
$623$	−25.8912	−	27.0258i	−1.03731	−	1.08276i
$624$		0			0
$625$	−8.65213	−	22.0453i	−0.346085	−	0.881811i
$626$	−1.95397	−	26.0739i	−0.0780962	−	1.04212i
$627$		0			0
$628$	1.29987	−	17.3455i	0.0518703	−	0.692161i
$629$	2.89033	+	12.6633i	0.115245	+	0.504921i
$630$		0			0
$631$	−3.54996	+	15.5534i	−0.141322	+	0.619171i	0.853807	+	0.520589i	$0.174288\pi$
$631$	−3.54996	+	15.5534i	−0.141322	+	0.619171i	−0.995129	+	0.0985818i	$0.968569\pi$
$632$	−1.52112	−	0.469204i	−0.0605070	−	0.0186639i
$633$		0			0
$634$	−0.798521	+	0.740919i	−0.0317133	+	0.0294256i
$635$	25.0115	−	17.0525i	0.992550	−	0.676709i
$636$		0			0
$637$	16.1015	−	45.2200i	0.637964	−	1.79168i
$638$	23.1338			0.915878
$639$		0			0
$640$	2.34702	−	2.17771i	0.0927740	−	0.0860817i
$641$	−14.3656	+	36.6029i	−0.567406	+	1.44573i	0.302807	+	0.953052i	$0.402076\pi$
$641$	−14.3656	+	36.6029i	−0.567406	+	1.44573i	−0.870213	+	0.492676i	$0.836019\pi$
$642$		0			0
$643$	9.71641	−	42.5704i	0.383178	−	1.67881i	−0.304277	−	0.952584i	$-0.598415\pi$
$643$	9.71641	−	42.5704i	0.383178	−	1.67881i	0.687455	−	0.726227i	$-0.258728\pi$
$644$	−2.10816	−	2.98847i	−0.0830733	−	0.117762i
$645$		0			0
$646$	−0.745752	+	9.95137i	−0.0293412	+	0.391531i
$647$	25.7943	−	7.95649i	1.01408	−	0.312802i	0.257201	−	0.966358i	$-0.417200\pi$
$647$	25.7943	−	7.95649i	1.01408	−	0.312802i	0.756878	+	0.653556i	$0.226724\pi$
$648$		0			0
$649$	−1.82499	−	4.65001i	−0.0716372	−	0.182529i
$650$	32.4414	+	15.6230i	1.27246	+	0.612783i
$651$		0			0
$652$	−1.38194	+	0.665507i	−0.0541209	+	0.0260633i
$653$	21.6224	+	20.0627i	0.846151	+	0.785113i	0.978534	−	0.206085i	$-0.0660724\pi$
$653$	21.6224	+	20.0627i	0.846151	+	0.785113i	−0.132383	+	0.991199i	$0.542263\pi$
$654$		0			0
$655$	3.86025	+	6.68614i	0.150832	+	0.261249i
$656$	4.69873	−	8.13844i	0.183455	−	0.317753i
$657$		0			0
$658$	−11.4247	−	22.7858i	−0.445379	−	0.888282i
$659$	7.48983	+	9.39195i	0.291762	+	0.365858i	0.906011	−	0.423254i	$-0.139112\pi$
$659$	7.48983	+	9.39195i	0.291762	+	0.365858i	−0.614249	+	0.789113i	$0.710541\pi$
$660$		0			0
$661$	−3.65481	−	2.49181i	−0.142156	−	0.0969202i	0.490154	−	0.871636i	$-0.336941\pi$
$661$	−3.65481	−	2.49181i	−0.142156	−	0.0969202i	−0.632310	+	0.774716i	$0.717893\pi$
$662$	−16.0233	−	10.9245i	−0.622765	−	0.424594i
$663$		0			0
$664$	6.11568	+	7.66882i	0.237334	+	0.297608i
$665$	0.906297	+	56.7684i	0.0351447	+	2.20138i
$666$		0			0
$667$	−6.21731	+	10.7687i	−0.240735	+	0.416966i
$668$	−7.69980	−	13.3364i	−0.297914	−	0.516003i
$669$		0			0
$670$	17.7159	+	16.4380i	0.684426	+	0.635055i
$671$	−11.6127	+	5.59236i	−0.448302	+	0.215891i
$672$		0			0
$673$	3.54671	+	1.70801i	0.136716	+	0.0658388i	0.500991	−	0.865453i	$-0.332969\pi$
$673$	3.54671	+	1.70801i	0.136716	+	0.0658388i	−0.364275	+	0.931291i	$0.618683\pi$
$674$	7.07713	+	18.0322i	0.272601	+	0.694575i
$675$		0			0
$676$	32.5110	−	10.0283i	1.25042	−	0.385704i
$677$	−1.75973	+	23.4819i	−0.0676318	+	0.902484i	0.855451	+	0.517883i	$0.173280\pi$
$677$	−1.75973	+	23.4819i	−0.0676318	+	0.902484i	−0.923083	+	0.384601i	$0.874339\pi$
$678$		0			0
$679$	7.07195	−	7.87006i	0.271396	−	0.302025i
$680$	−1.06077	+	4.64753i	−0.0406786	+	0.178225i
$681$		0			0
$682$	−1.73274	+	4.41494i	−0.0663499	+	0.169057i
$683$	1.00287	−	0.930524i	0.0383736	−	0.0356055i	−0.660753	−	0.750603i	$-0.729763\pi$
$683$	1.00287	−	0.930524i	0.0383736	−	0.0356055i	0.699127	+	0.714998i	$0.253572\pi$
$684$		0			0
$685$	−12.5443			−0.479292
$686$	18.5136	+	0.498310i	0.706851	+	0.0190255i
$687$		0			0
$688$	−3.94310	+	2.68836i	−0.150329	+	0.102493i
$689$	−47.3831	+	43.9651i	−1.80515	+	1.67494i
$690$		0			0
$691$	−37.5253	−	11.5750i	−1.42753	−	0.440335i	−0.517788	−	0.855509i	$-0.673244\pi$
$691$	−37.5253	−	11.5750i	−1.42753	−	0.440335i	−0.909742	+	0.415174i	$0.863721\pi$
$692$	0.564443	−	2.47299i	0.0214569	−	0.0940089i
$693$		0			0
$694$	−1.24364	−	5.44874i	−0.0472079	−	0.206831i
$695$	−5.61656	+	74.9478i	−0.213048	+	2.84293i
$696$		0			0
$697$	1.04562	+	13.9528i	0.0396057	+	0.528501i
$698$	7.18600	+	18.3096i	0.271994	+	0.693029i
$699$		0			0
$700$	−1.85104	+	13.7688i	−0.0699628	+	0.520412i
$701$	−1.92927	+	0.929089i	−0.0728676	+	0.0350912i	−0.469963	−	0.882686i	$-0.655733\pi$
$701$	−1.92927	+	0.929089i	−0.0728676	+	0.0350912i	0.397095	+	0.917778i	$0.370018\pi$
$702$		0			0
$703$	−57.8177	−	8.71462i	−2.18064	−	0.328678i
$704$	−1.28584	−	2.22715i	−0.0484621	−	0.0839388i
$705$		0			0
$706$	6.87340	−	8.61897i	0.258684	−	0.324379i
$707$	−0.250395	−	15.6842i	−0.00941708	−	0.589864i
$708$		0			0
$709$	12.7938	−	1.92836i	0.480482	−	0.0724211i	0.0956646	−	0.995414i	$-0.469502\pi$
$709$	12.7938	−	1.92836i	0.480482	−	0.0724211i	0.384818	+	0.922993i	$0.374264\pi$
$710$	2.67531	+	1.82399i	0.100402	+	0.0684533i
$711$		0			0
$712$	13.9879	−	2.10834i	0.524219	−	0.0790133i
$713$	−1.58945	−	1.99311i	−0.0595255	−	0.0746427i
$714$		0			0
$715$	35.2032	−	44.1435i	1.31653	−	1.65087i
$716$	−5.59388	+	9.68888i	−0.209053	+	0.362091i
$717$		0			0
$718$	6.72142	+	1.01309i	0.250841	+	0.0378082i
$719$	−17.6740	−	16.3991i	−0.659129	−	0.611582i	0.277994	−	0.960583i	$-0.410331\pi$
$719$	−17.6740	−	16.3991i	−0.659129	−	0.611582i	−0.937122	+	0.349001i	$0.886521\pi$
$720$		0			0
$721$	−24.8622	+	14.8884i	−0.925917	+	0.554471i
$722$	−23.3552	−	11.2473i	−0.869190	−	0.418580i
$723$		0			0
$724$	−0.528206	−	7.04842i	−0.0196306	−	0.261952i
$725$	45.1367	−	13.9228i	1.67634	−	0.517081i
$726$		0			0
$727$	5.75853	+	25.2298i	0.213572	+	0.935720i	0.962117	+	0.272636i	$0.0878955\pi$
$727$	5.75853	+	25.2298i	0.213572	+	0.935720i	−0.748545	+	0.663084i	$0.769247\pi$
$728$	10.4581	+	14.8252i	0.387604	+	0.549457i
$729$		0			0
$730$	27.3087	+	8.42361i	1.01074	+	0.311772i
$731$	2.59596	−	6.61440i	0.0960151	−	0.244642i
$732$		0			0
$733$	−4.68723	+	3.19570i	−0.173127	+	0.118036i	−0.646783	−	0.762674i	$-0.723886\pi$
$733$	−4.68723	+	3.19570i	−0.173127	+	0.118036i	0.473657	+	0.880710i	$0.342934\pi$
$734$	20.3077			0.749570
$735$		0			0
$736$	1.38230			0.0509523
$737$	16.0388	−	10.9351i	0.590796	−	0.402798i
$738$		0			0
$739$	−14.6178	+	37.2455i	−0.537724	+	1.37010i	0.361403	+	0.932410i	$0.382298\pi$
$739$	−14.6178	+	37.2455i	−0.537724	+	1.37010i	−0.899127	+	0.437688i	$0.855797\pi$
$740$	−26.6903	−	8.23287i	−0.981155	−	0.302646i
$741$		0			0
$742$	−21.7944	−	12.1233i	−0.800098	−	0.445061i
$743$	4.81486	+	21.0953i	0.176640	+	0.773911i	0.983166	+	0.182713i	$0.0584878\pi$
$743$	4.81486	+	21.0953i	0.176640	+	0.773911i	−0.806526	+	0.591198i	$0.798655\pi$
$744$		0			0
$745$	−14.7874	+	4.56132i	−0.541770	+	0.167114i
$746$	0.954337	+	12.7347i	0.0349408	+	0.466252i
$747$		0			0
$748$	3.44982	+	1.66134i	0.126138	+	0.0607448i
$749$	4.11591	+	4.29626i	0.150392	+	0.156982i
$750$		0			0
$751$	11.8686	+	11.0124i	0.433090	+	0.401848i	0.866364	−	0.499414i	$-0.166451\pi$
$751$	11.8686	+	11.0124i	0.433090	+	0.401848i	−0.433274	+	0.901262i	$0.642642\pi$
$752$	9.52652	+	1.43589i	0.347396	+	0.0523616i
$753$		0			0
$754$	30.8427	−	53.4211i	1.12322	−	1.94548i
$755$	11.8920	−	14.9121i	0.432793	−	0.542705i
$756$		0			0
$757$	−1.29255	−	1.62081i	−0.0469786	−	0.0589093i	0.757787	−	0.652502i	$-0.226281\pi$
$757$	−1.29255	−	1.62081i	−0.0469786	−	0.0589093i	−0.804766	+	0.593593i	$0.797709\pi$
$758$	−12.7818	+	1.92654i	−0.464255	+	0.0699751i
$759$		0			0
$760$	−17.7304	−	12.0884i	−0.643149	−	0.438492i
$761$	3.09242	−	0.466107i	0.112100	−	0.0168964i	−0.0927526	−	0.995689i	$-0.529567\pi$
$761$	3.09242	−	0.466107i	0.112100	−	0.0168964i	0.204853	+	0.978793i	$0.434328\pi$
$762$		0			0
$763$	9.83925	+	7.59279i	0.356205	+	0.274878i
$764$	6.60845	−	8.28673i	0.239085	−	0.299804i
$765$		0			0
$766$	14.9410	+	25.8786i	0.539841	+	0.935032i
$767$	−13.1710	−	1.98521i	−0.475578	−	0.0716818i
$768$		0			0
$769$	−24.1138	+	11.6126i	−0.869566	+	0.418761i	−0.814803	−	0.579738i	$-0.803155\pi$
$769$	−24.1138	+	11.6126i	−0.869566	+	0.418761i	−0.0547633	+	0.998499i	$0.517440\pi$
$770$	20.4032	+	7.63408i	0.735279	+	0.275113i
$771$		0			0
$772$	−4.04893	−	10.3165i	−0.145724	−	0.371299i
$773$	−1.37228	−	18.3118i	−0.0493575	−	0.658629i	−0.965937	−	0.258777i	$-0.916680\pi$
$773$	−1.37228	−	18.3118i	−0.0493575	−	0.658629i	0.916580	−	0.399852i	$-0.130939\pi$
$774$		0			0
$775$	−0.723682	+	9.65687i	−0.0259954	+	0.346885i
$776$	0.889886	+	3.89885i	0.0319451	+	0.139960i
$777$		0			0
$778$	4.40939	−	19.3188i	0.158084	−	0.692612i
$779$	−60.1874	−	18.5653i	−2.15644	−	0.665172i
$780$		0			0
$781$	1.90651	−	1.76898i	0.0682204	−	0.0632992i
$782$	−1.70050	+	1.15938i	−0.0608098	+	0.0414594i
$783$		0			0
$784$	−4.18750	+	5.60935i	−0.149554	+	0.200334i
$785$	−55.6910			−1.98770
$786$		0			0
$787$	29.9203	−	27.7620i	1.06654	−	0.989608i	0.0665774	−	0.997781i	$-0.478792\pi$
$787$	29.9203	−	27.7620i	1.06654	−	0.989608i	0.999967	+	0.00817302i	$0.00260158\pi$
$788$	−0.192286	+	0.489937i	−0.00684991	+	0.0174533i
$789$		0			0
$790$	−1.13410	+	4.96883i	−0.0403496	+	0.176783i
$791$	−9.76113	+	33.5364i	−0.347066	+	1.19242i
$792$		0			0
$793$	−2.56834	+	34.2721i	−0.0912043	+	1.21704i
$794$	−8.06327	+	2.48719i	−0.286155	+	0.0882671i
$795$		0			0
$796$	2.45735	+	6.26123i	0.0870985	+	0.221923i
$797$	−30.8114	−	14.8380i	−1.09140	−	0.525588i	−0.200452	−	0.979703i	$-0.564241\pi$
$797$	−30.8114	−	14.8380i	−1.09140	−	0.525588i	−0.890943	+	0.454115i	$0.849956\pi$
$798$		0			0
$799$	−12.9238	+	6.22377i	−0.457211	+	0.220181i
$800$	−3.84921	−	3.57154i	−0.136090	−	0.126273i
$801$		0			0
$802$	−13.4361	−	23.2720i	−0.474444	−	0.821762i
$803$	11.4774	−	19.8794i	0.405029	−	0.701530i
$804$		0			0
$805$	−9.03706	+	7.44588i	−0.318514	+	0.262433i
$806$	7.88493	+	9.88739i	0.277735	+	0.348269i
$807$		0			0
$808$	4.89862	+	3.33982i	0.172333	+	0.117495i
$809$	4.53792	+	3.09390i	0.159545	+	0.108776i	0.640461	−	0.767991i	$-0.278743\pi$
$809$	4.53792	+	3.09390i	0.159545	+	0.108776i	−0.480916	+	0.876767i	$0.659696\pi$
$810$		0			0
$811$	−14.4659	−	18.1397i	−0.507967	−	0.636971i	0.460038	−	0.887899i	$-0.347836\pi$
$811$	−14.4659	−	18.1397i	−0.507967	−	0.636971i	−0.968006	+	0.250928i	$0.919264\pi$
$812$	23.2849	+	4.92495i	0.817141	+	0.172832i
$813$		0			0
$814$	−11.2175	+	19.4293i	−0.393174	+	0.680997i
$815$	2.45545	+	4.25296i	0.0860106	+	0.148975i
$816$		0			0
$817$	23.4476	+	21.7561i	0.820326	+	0.761151i
$818$	−7.53429	+	3.62832i	−0.263430	+	0.126861i
$819$		0			0
$820$	−27.1083	−	13.0547i	−0.946662	−	0.455889i
$821$	−15.2904	−	38.9593i	−0.533639	−	1.35969i	−0.902694	−	0.430282i	$-0.858414\pi$
$821$	−15.2904	−	38.9593i	−0.533639	−	1.35969i	0.369055	−	0.929407i	$-0.379681\pi$
$822$		0			0
$823$	−47.3660	+	14.6105i	−1.65108	+	0.509289i	−0.973985	−	0.226611i	$-0.927235\pi$
$823$	−47.3660	+	14.6105i	−1.65108	+	0.509289i	−0.677090	+	0.735900i	$0.736759\pi$
$824$	0.818526	−	10.9225i	0.0285147	−	0.380502i
$825$		0			0
$826$	−0.846976	−	5.06890i	−0.0294701	−	0.176370i
$827$	10.2592	−	44.9485i	0.356748	−	1.56301i	−0.404491	−	0.914542i	$-0.632551\pi$
$827$	10.2592	−	44.9485i	0.356748	−	1.56301i	0.761239	−	0.648471i	$-0.224591\pi$
$828$		0			0
$829$	9.48473	−	24.1667i	0.329418	−	0.839344i	−0.666195	−	0.745778i	$-0.732078\pi$
$829$	9.48473	−	24.1667i	0.329418	−	0.839344i	0.995613	−	0.0935662i	$-0.0298267\pi$
$830$	23.0214	−	21.3607i	0.799085	−	0.741442i
$831$		0			0
$832$	−6.85730			−0.237734
$833$	0.446700	−	10.4128i	0.0154772	−	0.360781i
$834$		0			0
$835$	−40.7377	+	27.7745i	−1.40979	+	0.961177i
$836$	−12.6353	+	11.7238i	−0.437000	+	0.405476i
$837$		0			0
$838$	−12.9999	−	4.00993i	−0.449073	−	0.138521i
$839$	6.76234	−	29.6278i	0.233462	−	1.02286i	−0.713282	−	0.700877i	$-0.752792\pi$
$839$	6.76234	−	29.6278i	0.233462	−	1.02286i	0.946744	−	0.321987i	$-0.104351\pi$
$840$		0			0
$841$	−11.5534	−	50.6188i	−0.398393	−	1.74548i
$842$	1.52251	−	20.3165i	0.0524692	−	0.700153i
$843$		0			0
$844$	−0.455892	−	6.08346i	−0.0156925	−	0.209401i
$845$	−39.7967	−	101.400i	−1.36905	−	3.48828i
$846$		0			0
$847$	−6.38364	+	9.69194i	−0.219344	+	0.333019i
$848$	8.49270	−	4.08987i	0.291641	−	0.140447i
$849$		0			0
$850$	7.73084	+	1.16524i	0.265166	+	0.0399673i
$851$	−6.02950	−	10.4434i	−0.206689	−	0.357995i
$852$		0			0
$853$	−5.99355	+	7.51568i	−0.205215	+	0.257332i	−0.873779	−	0.486323i	$-0.838338\pi$
$853$	−5.99355	+	7.51568i	−0.205215	+	0.257332i	0.668564	+	0.743655i	$0.266909\pi$
$854$	−12.8791	+	3.15668i	−0.440712	+	0.108019i
$855$		0			0
$856$	−2.22365	+	0.335161i	−0.0760026	+	0.0114556i
$857$	−19.5309	−	13.3160i	−0.667164	−	0.454865i	0.181786	−	0.983338i	$-0.441812\pi$
$857$	−19.5309	−	13.3160i	−0.667164	−	0.454865i	−0.848950	+	0.528473i	$0.822765\pi$
$858$		0			0
$859$	54.6754	−	8.24098i	1.86550	−	0.281179i	0.883270	−	0.468865i	$-0.155337\pi$
$859$	54.6754	−	8.24098i	1.86550	−	0.281179i	0.982229	+	0.187686i	$0.0600987\pi$
$860$	9.52671	+	11.9461i	0.324858	+	0.407359i
$861$		0			0
$862$	−21.0065	+	26.3414i	−0.715485	+	0.897190i
$863$	17.7501	−	30.7441i	0.604220	−	1.04654i	−0.387954	−	0.921679i	$-0.626818\pi$
$863$	17.7501	−	30.7441i	0.604220	−	1.04654i	0.992174	−	0.124861i	$-0.0398486\pi$
$864$		0			0
$865$	−8.03069	−	1.21043i	−0.273052	−	0.0411559i
$866$	28.7730	+	26.6975i	0.977747	+	0.907217i
$867$		0			0
$868$	−2.68395	+	4.07490i	−0.0910991	+	0.138311i
$869$	3.68832	+	1.77620i	0.125118	+	0.0602535i
$870$		0			0
$871$	−3.86809	−	51.6160i	−0.131065	−	1.74894i
$872$	−4.48874	+	1.38459i	−0.152008	+	0.0468883i
$873$		0			0
$874$	−2.06160	−	9.03247i	−0.0697348	−	0.305528i
$875$	2.12199	+	0.124994i	0.0717363	+	0.00422558i
$876$		0			0
$877$	−5.16672	−	1.59372i	−0.174468	−	0.0538162i	0.206290	−	0.978491i	$-0.433861\pi$
$877$	−5.16672	−	1.59372i	−0.174468	−	0.0538162i	−0.380758	+	0.924675i	$0.624337\pi$
$878$	7.88954	−	20.1022i	0.266259	−	0.678417i
$879$		0			0
$880$	−6.80308	+	4.63826i	−0.229332	+	0.156356i
$881$	−14.1504			−0.476739			−0.238369	−	0.971175i	$-0.576613\pi$
$881$	−14.1504			−0.476739			−0.238369	+	0.971175i	$0.576613\pi$
$882$		0			0
$883$	−35.4651			−1.19350			−0.596748	−	0.802429i	$-0.703541\pi$
$883$	−35.4651			−1.19350			−0.596748	+	0.802429i	$0.703541\pi$
$884$	8.43580	−	5.75143i	0.283727	−	0.193442i
$885$		0			0
$886$	−12.1851	+	31.0471i	−0.409366	+	1.04305i
$887$	8.38312	+	2.58585i	0.281477	+	0.0868243i	0.432279	−	0.901740i	$-0.357709\pi$
$887$	8.38312	+	2.58585i	0.281477	+	0.0868243i	−0.150802	+	0.988564i	$0.548186\pi$
$888$		0			0
$889$	−4.12267	−	24.6730i	−0.138270	−	0.827505i
$890$	−10.0782	−	44.1555i	−0.337822	−	1.48010i
$891$		0			0
$892$	9.29724	−	2.86782i	0.311295	−	0.0960217i
$893$	−4.82546	−	64.3913i	−0.161478	−	2.15477i
$894$		0			0
$895$	32.2726	+	15.5417i	1.07876	+	0.519501i
$896$	−0.820107	−	2.51544i	−0.0273978	−	0.0840349i
$897$		0			0
$898$	12.3897	+	11.4959i	0.413449	+	0.383625i
$899$	16.4047	+	2.47260i	0.547126	+	0.0824659i
$900$		0			0
$901$	−7.01736	+	12.1544i	−0.233782	+	0.404923i
$902$	−15.0681	+	18.8948i	−0.501713	+	0.629128i
$903$		0			0
$904$	−8.23104	−	10.3214i	−0.273760	−	0.343284i
$905$	−22.3775	+	3.37286i	−0.743853	+	0.112118i
$906$		0			0
$907$	0.957243	+	0.652637i	0.0317847	+	0.0216705i	0.579108	−	0.815251i	$-0.303401\pi$
$907$	0.957243	+	0.652637i	0.0317847	+	0.0216705i	−0.547323	+	0.836921i	$0.684353\pi$
$908$	−7.08705	+	1.06820i	−0.235192	+	0.0354495i
$909$		0			0
$910$	44.8308	−	36.9374i	1.48613	−	1.22446i
$911$	13.0460	−	16.3591i	0.432232	−	0.542002i	−0.517245	−	0.855837i	$-0.673042\pi$
$911$	13.0460	−	16.3591i	0.432232	−	0.542002i	0.949478	+	0.313835i	$0.101614\pi$
$912$		0			0
$913$	−12.6126	−	21.8456i	−0.417415	−	0.722985i
$914$	6.86176	+	1.03424i	0.226967	+	0.0342098i
$915$		0			0
$916$	−26.6010	+	12.8103i	−0.878920	+	0.423266i
$917$	6.35362	−	0.578264i	0.209815	−	0.0190960i
$918$		0			0
$919$	−13.8957	−	35.4057i	−0.458378	−	1.16793i	−0.954111	−	0.299452i	$-0.903196\pi$
$919$	−13.8957	−	35.4057i	−0.458378	−	1.16793i	0.495734	−	0.868475i	$-0.334899\pi$
$920$	−0.330735	−	4.41335i	−0.0109040	−	0.145504i
$921$		0			0
$922$	0.814915	−	10.8743i	0.0268378	−	0.358125i
$923$	−1.54316	−	6.76101i	−0.0507936	−	0.222541i
$924$		0			0
$925$	−10.1933	+	44.6599i	−0.335154	+	1.46841i
$926$	22.3392	+	6.89073i	0.734112	+	0.226443i
$927$		0			0
$928$	−6.59423	+	6.11855i	−0.216466	+	0.200851i
$929$	−21.9375	+	14.9567i	−0.719745	+	0.490714i	−0.866952	−	0.498392i	$-0.833924\pi$
$929$	−21.9375	+	14.9567i	−0.719745	+	0.490714i	0.147207	+	0.989106i	$0.452972\pi$
$930$		0			0
$931$	42.8989	+	18.9968i	1.40596	+	0.622593i
$932$	−8.03351			−0.263146
$933$		0			0
$934$	2.06103	−	1.91235i	0.0674388	−	0.0625741i
$935$	4.47885	−	11.4119i	0.146474	−	0.373210i
$936$		0			0
$937$	−4.16129	+	18.2318i	−0.135943	+	0.595607i	0.860359	+	0.509689i	$0.170239\pi$
$937$	−4.16129	+	18.2318i	−0.135943	+	0.595607i	−0.996302	+	0.0859180i	$0.972618\pi$
$938$	18.4715	−	7.59200i	0.603116	−	0.247887i
$939$		0			0
$940$	2.30510	−	30.7594i	0.0751840	−	1.00326i
$941$	−47.9037	+	14.7763i	−1.56162	+	0.481695i	−0.950729	−	0.310023i	$-0.899663\pi$
$941$	−47.9037	+	14.7763i	−1.56162	+	0.481695i	−0.610887	+	0.791718i	$0.709187\pi$
$942$		0			0
$943$	−4.74583	−	12.0922i	−0.154545	−	0.393775i
$944$	1.75006	+	0.842787i	0.0569597	+	0.0274304i
$945$		0			0
$946$	11.0576	−	5.32505i	0.359513	−	0.173132i
$947$	24.1849	+	22.4403i	0.785904	+	0.729213i	0.967145	−	0.254226i	$-0.0818207\pi$
$947$	24.1849	+	22.4403i	0.785904	+	0.729213i	−0.181240	+	0.983439i	$0.558011\pi$
$948$		0			0
$949$	−30.6040	−	53.0076i	−0.993447	−	1.72070i
$950$	−17.5970	+	30.4788i	−0.570921	+	0.988864i
$951$		0			0
$952$	3.11867	+	2.40663i	0.101077	+	0.0779992i
$953$	18.8931	+	23.6913i	0.612009	+	0.767435i	0.987196	−	0.159514i	$-0.0509928\pi$
$953$	18.8931	+	23.6913i	0.612009	+	0.767435i	−0.375187	+	0.926949i	$0.622421\pi$
$954$		0			0
$955$	−28.0387	−	19.1165i	−0.907311	−	0.618594i
$956$	1.64955	+	1.12464i	0.0533502	+	0.0363735i
$957$		0			0
$958$	−12.6146	−	15.8182i	−0.407560	−	0.511064i
$959$	−4.34800	+	9.41008i	−0.140404	+	0.303867i
$960$		0			0
$961$	13.7994	−	23.9013i	0.445142	−	0.771009i
$962$	29.9110	+	51.8074i	0.964370	+	1.67034i
$963$		0			0
$964$	−6.83514	−	6.34209i	−0.220145	−	0.204265i
$965$	−31.9693	+	15.3956i	−1.02913	+	0.495602i
$966$		0			0
$967$	53.3077	+	25.6717i	1.71426	+	0.825545i	0.990825	+	0.135154i	$0.0431529\pi$
$967$	53.3077	+	25.6717i	1.71426	+	0.825545i	0.723437	+	0.690391i	$0.242561\pi$
$968$	−1.60254	−	4.08320i	−0.0515075	−	0.131239i
$969$		0			0
$970$	12.2351	−	3.77404i	0.392847	−	0.121177i
$971$	0.913578	−	12.1909i	0.0293181	−	0.391223i	−0.963171	−	0.268890i	$-0.913343\pi$
$971$	0.913578	−	12.1909i	0.0293181	−	0.391223i	0.992489	−	0.122333i	$-0.0390377\pi$
$972$		0			0
$973$	54.2753	+	30.1911i	1.73999	+	0.967882i
$974$	2.79123	−	12.2292i	0.0894368	−	0.391848i
$975$		0			0
$976$	1.83106	−	4.66546i	0.0586107	−	0.149338i
$977$	−10.5365	+	9.77641i	−0.337091	+	0.312775i	−0.830496	−	0.557025i	$-0.811943\pi$
$977$	−10.5365	+	9.77641i	−0.337091	+	0.312775i	0.493404	+	0.869800i	$0.335752\pi$
$978$		0			0
$979$	−36.3789			−1.16267
$980$	18.9112	+	12.0276i	0.604096	+	0.384206i
$981$		0			0
$982$	4.78125	−	3.25980i	0.152576	−	0.104025i
$983$	15.0525	−	13.9667i	0.480100	−	0.445468i	−0.402620	−	0.915367i	$-0.631900\pi$
$983$	15.0525	−	13.9667i	0.480100	−	0.445468i	0.882720	+	0.469900i	$0.155710\pi$
$984$		0			0
$985$	1.61026	+	0.496698i	0.0513070	+	0.0158261i
$986$	2.98036	−	13.0578i	0.0949139	−	0.415845i
$987$		0			0
$988$	10.2272	+	44.8081i	0.325369	+	1.42554i
$989$	−0.492981	+	6.57838i	−0.0156759	+	0.209180i
$990$		0			0
$991$	1.50400	+	20.0695i	0.0477762	+	0.637528i	0.968772	+	0.247955i	$0.0797585\pi$
$991$	1.50400	+	20.0695i	0.0477762	+	0.637528i	−0.920995	+	0.389573i	$0.872622\pi$
$992$	−0.673774	−	1.71675i	−0.0213923	−	0.0545068i
$993$		0			0
$994$	2.29556	−	1.37466i	0.0728108	−	0.0436016i
$995$	19.4026	−	9.34380i	0.615104	−	0.296218i
$996$		0			0
$997$	−20.1792	−	3.04152i	−0.639081	−	0.0963260i	−0.178495	−	0.983941i	$-0.557123\pi$
$997$	−20.1792	−	3.04152i	−0.639081	−	0.0963260i	−0.460586	+	0.887615i	$0.652361\pi$
$998$	−19.4817	−	33.7432i	−0.616681	−	1.06812i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	882.2.z.f.37.1		36
3.2	odd	2		294.2.m.c.37.3	✓	36
49.4	even	21	inner	882.2.z.f.739.1		36
147.53	odd	42		294.2.m.c.151.3	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
294.2.m.c.37.3	✓	36	3.2	odd	2
294.2.m.c.151.3	yes	36	147.53	odd	42
882.2.z.f.37.1		36	1.1	even	1	trivial
882.2.z.f.739.1		36	49.4	even	21	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	882.z (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.826239 - 0.563320i) q^{2} +(0.365341 - 0.930874i) q^{4} +(-3.05947 - 0.943720i) q^{5} +(-1.76838 + 1.96795i) q^{7} +(-0.222521 - 0.974928i) q^{8} +O(q^{10})\)	\(q+(0.826239 - 0.563320i) q^{2} +(0.365341 - 0.930874i) q^{4} +(-3.05947 - 0.943720i) q^{5} +(-1.76838 + 1.96795i) q^{7} +(-0.222521 - 0.974928i) q^{8} +(-3.05947 + 0.943720i) q^{10} +(0.192183 + 2.56450i) q^{11} +(6.17821 + 2.97527i) q^{13} +(-0.352517 + 2.62216i) q^{14} +(-0.733052 - 0.680173i) q^{16} +(1.47228 + 0.221910i) q^{17} +(-3.35121 + 5.80446i) q^{19} +(-1.99623 + 2.50320i) q^{20} +(1.60342 + 2.01063i) q^{22} +(-1.36686 + 0.206021i) q^{23} +(4.33853 + 2.95796i) q^{25} +(6.78071 - 1.02203i) q^{26} +(1.18585 + 2.36511i) q^{28} +(5.60865 - 7.03303i) q^{29} +(0.922116 + 1.59715i) q^{31} +(-0.988831 - 0.149042i) q^{32} +(1.34146 - 0.646013i) q^{34} +(7.26749 - 4.35203i) q^{35} +(3.18718 + 8.12080i) q^{37} +(0.500872 + 6.68367i) q^{38} +(-0.239264 + 3.19276i) q^{40} +(2.09113 + 9.16184i) q^{41} +(1.06195 - 4.65269i) q^{43} +(2.45744 + 0.758019i) q^{44} +(-1.01330 + 0.940204i) q^{46} +(-7.96008 + 5.42709i) q^{47} +(-0.745670 - 6.96017i) q^{49} +5.25094 q^{50} +(5.02675 - 4.66415i) q^{52} +(-3.44377 + 8.77459i) q^{53} +(1.83219 - 8.02736i) q^{55} +(2.31211 + 1.28613i) q^{56} +(0.672241 - 8.97043i) q^{58} +(-1.85613 + 0.572540i) q^{59} +(1.83106 + 4.66546i) q^{61} +(1.66160 + 0.800183i) q^{62} +(-0.900969 + 0.433884i) q^{64} +(-16.0942 - 14.9332i) q^{65} +(-3.77414 - 6.53700i) q^{67} +(0.744454 - 1.28943i) q^{68} +(3.55310 - 7.68974i) q^{70} +(-0.630544 - 0.790678i) q^{71} +(-7.37497 - 5.02817i) q^{73} +(7.20798 + 4.91432i) q^{74} +(4.17888 + 5.24016i) q^{76} +(-5.38666 - 4.15680i) q^{77} +(0.795922 - 1.37858i) q^{79} +(1.60085 + 2.77276i) q^{80} +(6.88882 + 6.39190i) q^{82} +(-8.83741 + 4.25587i) q^{83} +(-4.29496 - 2.06835i) q^{85} +(-1.74353 - 4.44245i) q^{86} +(2.45744 - 0.758019i) q^{88} +(-1.05713 + 14.1064i) q^{89} +(-16.7806 + 6.89702i) q^{91} +(-0.307591 + 1.34765i) q^{92} +(-3.51974 + 8.96815i) q^{94} +(15.7307 - 14.5959i) q^{95} -3.99911 q^{97} +(-4.53691 - 5.33071i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 3 q^{2} + 3 q^{4} - 2 q^{5} - 5 q^{7} - 6 q^{8}+O(q^{10}) \) 36 * q + 3 * q^2 + 3 * q^4 - 2 * q^5 - 5 * q^7 - 6 * q^8	\( 36 q + 3 q^{2} + 3 q^{4} - 2 q^{5} - 5 q^{7} - 6 q^{8} - 2 q^{10} - 9 q^{11} + 10 q^{13} + 4 q^{14} + 3 q^{16} - 7 q^{17} + 16 q^{19} - 3 q^{20} + 4 q^{22} - 42 q^{23} - 23 q^{25} + 16 q^{26} + 15 q^{28} + 12 q^{29} - 3 q^{31} + 3 q^{32} - 21 q^{34} - 26 q^{35} - 25 q^{37} + 2 q^{38} - 2 q^{40} + 28 q^{41} + 4 q^{43} + 19 q^{44} - 7 q^{46} + 4 q^{47} - 25 q^{49} + 74 q^{50} + 9 q^{52} + 37 q^{53} - 54 q^{55} + 9 q^{56} + 8 q^{58} - 23 q^{59} - 79 q^{61} + 34 q^{62} - 6 q^{64} - 55 q^{65} + 19 q^{67} + 7 q^{68} + 18 q^{70} + 34 q^{71} - 15 q^{73} + 24 q^{74} + 3 q^{76} - 129 q^{77} + 11 q^{79} + 5 q^{80} + 49 q^{82} + 44 q^{83} - 77 q^{85} - 72 q^{86} + 19 q^{88} - 39 q^{89} - 43 q^{91} - 7 q^{92} + 25 q^{94} + 36 q^{95} - 8 q^{97} + 48 q^{98}+O(q^{100}) \) 36 * q + 3 * q^2 + 3 * q^4 - 2 * q^5 - 5 * q^7 - 6 * q^8 - 2 * q^10 - 9 * q^11 + 10 * q^13 + 4 * q^14 + 3 * q^16 - 7 * q^17 + 16 * q^19 - 3 * q^20 + 4 * q^22 - 42 * q^23 - 23 * q^25 + 16 * q^26 + 15 * q^28 + 12 * q^29 - 3 * q^31 + 3 * q^32 - 21 * q^34 - 26 * q^35 - 25 * q^37 + 2 * q^38 - 2 * q^40 + 28 * q^41 + 4 * q^43 + 19 * q^44 - 7 * q^46 + 4 * q^47 - 25 * q^49 + 74 * q^50 + 9 * q^52 + 37 * q^53 - 54 * q^55 + 9 * q^56 + 8 * q^58 - 23 * q^59 - 79 * q^61 + 34 * q^62 - 6 * q^64 - 55 * q^65 + 19 * q^67 + 7 * q^68 + 18 * q^70 + 34 * q^71 - 15 * q^73 + 24 * q^74 + 3 * q^76 - 129 * q^77 + 11 * q^79 + 5 * q^80 + 49 * q^82 + 44 * q^83 - 77 * q^85 - 72 * q^86 + 19 * q^88 - 39 * q^89 - 43 * q^91 - 7 * q^92 + 25 * q^94 + 36 * q^95 - 8 * q^97 + 48 * q^98

Introduction

L-functions

Modular forms

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Database

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