LMFDB - Embedded newform 819.2.do.e.667.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(361,819)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(819, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4, 5]))

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

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

chi := DirichletCharacter("819.361");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.do (of order $6$, degree $2$, 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:	$6.53974792554$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.2346760387617129.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} + x^{10} + 10 x^{9} - 15 x^{8} - 10 x^{7} + 45 x^{6} - 20 x^{5} - 60 x^{4} + 80 x^{3} + \cdots + 64 $ x^12 - 3x^11 + x^10 + 10x^9 - 15x^8 - 10x^7 + 45x^6 - 20x^5 - 60x^4 + 80x^3 + 16x^2 - 96x + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			667.6
Root			$1.32725 - 0.488273i$ of defining polynomial
Character	$\chi$	$=$	819.667
Dual form			819.2.do.e.361.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.24179 - 1.29430i) q^{2} +(2.35043 - 4.07106i) q^{4} +(-1.39608 - 0.806027i) q^{5} +(2.62954 + 0.292422i) q^{7} -6.99143i q^{8} +O(q^{10})$	\(q+(2.24179 - 1.29430i) q^{2} +(2.35043 - 4.07106i) q^{4} +(-1.39608 - 0.806027i) q^{5} +(2.62954 + 0.292422i) q^{7} -6.99143i q^{8} -4.17296 q^{10} -2.70496i q^{11} +(2.36840 + 2.71858i) q^{13} +(6.27337 - 2.74787i) q^{14} +(-4.34816 - 7.53123i) q^{16} +(-1.56330 + 2.70772i) q^{17} -3.68150i q^{19} +(-6.56276 + 3.78901i) q^{20} +(-3.50103 - 6.06396i) q^{22} +(-0.993019 - 1.71996i) q^{23} +(-1.20064 - 2.07957i) q^{25} +(8.82813 + 3.02907i) q^{26} +(7.37101 - 10.0177i) q^{28} +(-2.68636 + 4.65290i) q^{29} +(-9.07425 + 5.23902i) q^{31} +(-7.38583 - 4.26421i) q^{32} +8.09354i q^{34} +(-3.43535 - 2.52773i) q^{35} +(5.15585 - 2.97673i) q^{37} +(-4.76497 - 8.25317i) q^{38} +(-5.63528 + 9.76059i) q^{40} +(6.66970 + 3.85075i) q^{41} +(-1.67800 - 2.90638i) q^{43} +(-11.0120 - 6.35780i) q^{44} +(-4.45229 - 2.57053i) q^{46} +(0.913730 + 0.527542i) q^{47} +(6.82898 + 1.53787i) q^{49} +(-5.38318 - 3.10798i) q^{50} +(16.6343 - 3.25208i) q^{52} +(3.63284 + 6.29226i) q^{53} +(-2.18027 + 3.77633i) q^{55} +(2.04445 - 18.3843i) q^{56} +13.9078i q^{58} +(9.89352 + 5.71203i) q^{59} -2.92507 q^{61} +(-13.5617 + 23.4896i) q^{62} -4.68406 q^{64} +(-1.11523 - 5.70435i) q^{65} +13.5818i q^{67} +(7.34886 + 12.7286i) q^{68} +(-10.9730 - 1.22027i) q^{70} +(-1.17009 + 0.675554i) q^{71} +(7.88374 - 4.55168i) q^{73} +(7.70557 - 13.3464i) q^{74} +(-14.9876 - 8.65311i) q^{76} +(0.790989 - 7.11280i) q^{77} +(3.10289 - 5.37436i) q^{79} +14.0189i q^{80} +19.9361 q^{82} -2.69672i q^{83} +(4.36499 - 2.52013i) q^{85} +(-7.52346 - 4.34367i) q^{86} -18.9115 q^{88} +(-1.52410 + 0.879938i) q^{89} +(5.43284 + 7.84119i) q^{91} -9.33607 q^{92} +2.73119 q^{94} +(-2.96739 + 5.13967i) q^{95} +(-13.4078 + 7.74102i) q^{97} +(17.2996 - 5.39116i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 4 q^{4} - 3 q^{5} + 3 q^{7}+O(q^{10}) $ 12 * q + 4 * q^4 - 3 * q^5 + 3 * q^7	$ 12 q + 4 q^{4} - 3 q^{5} + 3 q^{7} - 24 q^{10} - 2 q^{13} - 4 q^{14} - 8 q^{16} - 17 q^{17} + 3 q^{20} - 15 q^{22} - 3 q^{23} - 5 q^{25} + 9 q^{26} + 27 q^{28} + q^{29} - 18 q^{31} - 18 q^{32} - 18 q^{35} + 15 q^{37} - 19 q^{38} - q^{40} + 6 q^{41} + 11 q^{43} - 33 q^{44} - 30 q^{46} - 15 q^{47} + 9 q^{49} - 18 q^{50} + 47 q^{52} + 8 q^{53} - 15 q^{55} - 27 q^{59} - 10 q^{61} - 41 q^{62} + 2 q^{64} + 3 q^{65} + 11 q^{68} - 3 q^{70} - 30 q^{71} - 42 q^{73} + 33 q^{74} - 45 q^{76} + 19 q^{77} - 35 q^{79} - 10 q^{82} - 21 q^{85} - 57 q^{86} + 28 q^{88} - 48 q^{89} - 16 q^{91} + 66 q^{92} - 2 q^{94} - 2 q^{95} - 3 q^{97} + 36 q^{98}+O(q^{100}) $ 12 * q + 4 * q^4 - 3 * q^5 + 3 * q^7 - 24 * q^10 - 2 * q^13 - 4 * q^14 - 8 * q^16 - 17 * q^17 + 3 * q^20 - 15 * q^22 - 3 * q^23 - 5 * q^25 + 9 * q^26 + 27 * q^28 + q^29 - 18 * q^31 - 18 * q^32 - 18 * q^35 + 15 * q^37 - 19 * q^38 - q^40 + 6 * q^41 + 11 * q^43 - 33 * q^44 - 30 * q^46 - 15 * q^47 + 9 * q^49 - 18 * q^50 + 47 * q^52 + 8 * q^53 - 15 * q^55 - 27 * q^59 - 10 * q^61 - 41 * q^62 + 2 * q^64 + 3 * q^65 + 11 * q^68 - 3 * q^70 - 30 * q^71 - 42 * q^73 + 33 * q^74 - 45 * q^76 + 19 * q^77 - 35 * q^79 - 10 * q^82 - 21 * q^85 - 57 * q^86 + 28 * q^88 - 48 * q^89 - 16 * q^91 + 66 * q^92 - 2 * q^94 - 2 * q^95 - 3 * q^97 + 36 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/819\mathbb{Z}\right)^\times$.

$n$	$92$	$379$	$703$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	2.24179	−	1.29430i	1.58519	−	0.915209i	0.591104	−	0.806596i	$-0.298692\pi$
$2$	2.24179	−	1.29430i	1.58519	−	0.915209i	0.994084	−	0.108613i	$-0.0346409\pi$
$3$		0			0
$3$		0			0
$4$	2.35043	−	4.07106i	1.17521	−	2.03553i
$5$	−1.39608	−	0.806027i	−0.624346	−	0.360466i	0.154213	−	0.988038i	$-0.450716\pi$
$5$	−1.39608	−	0.806027i	−0.624346	−	0.360466i	−0.778559	+	0.627571i	$0.784049\pi$
$6$		0			0
$7$	2.62954	+	0.292422i	0.993873	+	0.110525i
$7$	2.62954	+	0.292422i	0.993873	+	0.110525i
$8$		−	6.99143i		−	2.47184i
$9$		0			0
$10$	−4.17296			−1.31961
$11$		−	2.70496i		−	0.815575i	−0.913077	−	0.407788i	$-0.866300\pi$
$11$		−	2.70496i		−	0.815575i	0.913077	−	0.407788i	$-0.133700\pi$
$12$		0			0
$13$	2.36840	+	2.71858i	0.656876	+	0.753998i
$13$	2.36840	+	2.71858i	0.656876	+	0.753998i
$14$	6.27337	−	2.74787i	1.67663	−	0.734398i
$15$		0			0
$16$	−4.34816	−	7.53123i	−1.08704	−	1.88281i
$17$	−1.56330	+	2.70772i	−0.379157	+	0.656719i	−0.990940	−	0.134307i	$-0.957119\pi$
$17$	−1.56330	+	2.70772i	−0.379157	+	0.656719i	0.611783	+	0.791026i	$0.290453\pi$
$18$		0			0
$19$		−	3.68150i		−	0.844595i	−0.906457	−	0.422297i	$-0.861224\pi$
$19$		−	3.68150i		−	0.844595i	0.906457	−	0.422297i	$-0.138776\pi$
$20$	−6.56276	+	3.78901i	−1.46748	+	0.847249i
$21$		0			0
$22$	−3.50103	−	6.06396i	−0.746421	−	1.29284i
$23$	−0.993019	−	1.71996i	−0.207059	−	0.358636i	0.743728	−	0.668482i	$-0.233056\pi$
$23$	−0.993019	−	1.71996i	−0.207059	−	0.358636i	−0.950787	+	0.309846i	$0.899722\pi$
$24$		0			0
$25$	−1.20064	−	2.07957i	−0.240128	−	0.415914i
$26$	8.82813	+	3.02907i	1.73134	+	0.594050i
$27$		0			0
$28$	7.37101	−	10.0177i	1.39299	−	1.89317i
$29$	−2.68636	+	4.65290i	−0.498844	+	0.864023i	−0.999999	−	0.00133469i	$-0.999575\pi$
$29$	−2.68636	+	4.65290i	−0.498844	+	0.864023i	0.501155	+	0.865357i	$0.332908\pi$
$30$		0			0
$31$	−9.07425	+	5.23902i	−1.62978	+	0.940956i	−0.645627	+	0.763653i	$0.723404\pi$
$31$	−9.07425	+	5.23902i	−1.62978	+	0.940956i	−0.984156	+	0.177303i	$0.943263\pi$
$32$	−7.38583	−	4.26421i	−1.30564	−	0.753813i
$33$		0			0
$34$			8.09354i			1.38803i
$35$	−3.43535	−	2.52773i	−0.580680	−	0.427264i
$36$		0			0
$37$	5.15585	−	2.97673i	0.847616	−	0.489371i	−0.0122297	−	0.999925i	$-0.503893\pi$
$37$	5.15585	−	2.97673i	0.847616	−	0.489371i	0.859846	+	0.510554i	$0.170560\pi$
$38$	−4.76497	−	8.25317i	−0.772981	−	1.33884i
$39$		0			0
$40$	−5.63528	+	9.76059i	−0.891016	+	1.54329i
$41$	6.66970	+	3.85075i	1.04163	+	0.601386i	0.920295	−	0.391225i	$-0.127949\pi$
$41$	6.66970	+	3.85075i	1.04163	+	0.601386i	0.121337	+	0.992611i	$0.461282\pi$
$42$		0			0
$43$	−1.67800	−	2.90638i	−0.255892	−	0.443219i	0.709245	−	0.704962i	$-0.249036\pi$
$43$	−1.67800	−	2.90638i	−0.255892	−	0.443219i	−0.965138	+	0.261743i	$0.915703\pi$
$44$	−11.0120	−	6.35780i	−1.66013	−	0.958475i
$45$		0			0
$46$	−4.45229	−	2.57053i	−0.656454	−	0.379004i
$47$	0.913730	+	0.527542i	0.133281	+	0.0769500i	0.565158	−	0.824983i	$-0.308815\pi$
$47$	0.913730	+	0.527542i	0.133281	+	0.0769500i	−0.431877	+	0.901933i	$0.642148\pi$
$48$		0			0
$49$	6.82898	+	1.53787i	0.975568	+	0.219696i
$50$	−5.38318	−	3.10798i	−0.761297	−	0.439535i
$51$		0			0
$52$	16.6343	−	3.25208i	2.30676	−	0.450982i
$53$	3.63284	+	6.29226i	0.499009	+	0.864308i	0.999999	−	0.00114437i	$-0.000364265\pi$
$53$	3.63284	+	6.29226i	0.499009	+	0.864308i	−0.500991	+	0.865453i	$0.667031\pi$
$54$		0			0
$55$	−2.18027	+	3.77633i	−0.293987	+	0.509201i
$56$	2.04445	−	18.3843i	0.273201	−	2.45670i
$57$		0			0
$58$			13.9078i			1.82618i
$59$	9.89352	+	5.71203i	1.28803	+	0.743643i	0.978302	−	0.207183i	$-0.0664297\pi$
$59$	9.89352	+	5.71203i	1.28803	+	0.743643i	0.309725	+	0.950826i	$0.399763\pi$
$60$		0			0
$61$	−2.92507			−0.374517			−0.187259	−	0.982311i	$-0.559960\pi$
$61$	−2.92507			−0.374517			−0.187259	+	0.982311i	$0.559960\pi$
$62$	−13.5617	+	23.4896i	−1.72234	+	2.98318i
$63$		0			0
$64$	−4.68406			−0.585507
$65$	−1.11523	−	5.70435i	−0.138327	−	0.707537i
$66$		0			0
$67$			13.5818i			1.65928i	0.558296	+	0.829642i	$0.311455\pi$
$67$			13.5818i			1.65928i	−0.558296	+	0.829642i	$0.688545\pi$
$68$	7.34886	+	12.7286i	0.891180	+	1.54357i
$69$		0			0
$70$	−10.9730	−	1.22027i	−1.31152	−	0.145850i
$71$	−1.17009	+	0.675554i	−0.138865	+	0.0801736i	−0.567823	−	0.823151i	$-0.692214\pi$
$71$	−1.17009	+	0.675554i	−0.138865	+	0.0801736i	0.428958	+	0.903324i	$0.358881\pi$
$72$		0			0
$73$	7.88374	−	4.55168i	0.922721	−	0.532733i	0.0382192	−	0.999269i	$-0.487831\pi$
$73$	7.88374	−	4.55168i	0.922721	−	0.532733i	0.884502	+	0.466536i	$0.154498\pi$
$74$	7.70557	−	13.3464i	0.895754	−	1.55149i
$75$		0			0
$76$	−14.9876	−	8.65311i	−1.71920	−	0.992579i
$77$	0.790989	−	7.11280i	0.0901416	−	0.810578i
$78$		0			0
$79$	3.10289	−	5.37436i	0.349102	−	0.604663i	−0.636988	−	0.770874i	$-0.719820\pi$
$79$	3.10289	−	5.37436i	0.349102	−	0.604663i	0.986090	+	0.166211i	$0.0531532\pi$
$80$			14.0189i			1.56736i
$81$		0			0
$82$	19.9361			2.20158
$83$		−	2.69672i		−	0.296003i	−0.988987	−	0.148002i	$-0.952716\pi$
$83$		−	2.69672i		−	0.296003i	0.988987	−	0.148002i	$-0.0472841\pi$
$84$		0			0
$85$	4.36499	−	2.52013i	0.473450	−	0.273346i
$86$	−7.52346	−	4.34367i	−0.811275	−	0.468390i
$87$		0			0
$88$	−18.9115			−2.01597
$89$	−1.52410	+	0.879938i	−0.161554	+	0.0932732i	−0.578597	−	0.815613i	$-0.696400\pi$
$89$	−1.52410	+	0.879938i	−0.161554	+	0.0932732i	0.417043	+	0.908887i	$0.363066\pi$
$90$		0			0
$91$	5.43284	+	7.84119i	0.569516	+	0.821980i
$92$	−9.33607			−0.973353
$93$		0			0
$94$	2.73119			0.281701
$95$	−2.96739	+	5.13967i	−0.304448	+	0.527319i
$96$		0			0
$97$	−13.4078	+	7.74102i	−1.36136	+	0.785981i	−0.989805	−	0.142430i	$-0.954509\pi$
$97$	−13.4078	+	7.74102i	−1.36136	+	0.785981i	−0.371555	+	0.928411i	$0.621175\pi$
$98$	17.2996	−	5.39116i	1.74753	−	0.544589i
$99$		0			0
$100$	−11.2881			−1.12881
$101$	−1.27930			−0.127295			−0.0636477	−	0.997972i	$-0.520273\pi$
$101$	−1.27930			−0.127295			−0.0636477	+	0.997972i	$0.520273\pi$
$102$		0			0
$103$	−5.73367	+	9.93101i	−0.564956	+	0.978532i	0.432098	+	0.901827i	$0.357773\pi$
$103$	−5.73367	+	9.93101i	−0.564956	+	0.978532i	−0.997054	+	0.0767054i	$0.975560\pi$
$104$	19.0068	−	16.5585i	1.86377	−	1.62370i
$105$		0			0
$106$	16.2881	+	9.40397i	1.58204	+	0.913394i
$107$	−2.56763	−	4.44726i	−0.248222	−	0.429933i	0.714811	−	0.699318i	$-0.246513\pi$
$107$	−2.56763	−	4.44726i	−0.248222	−	0.429933i	−0.963033	+	0.269385i	$0.913180\pi$
$108$		0			0
$109$	−1.49635	+	0.863916i	−0.143324	+	0.0827481i	−0.569947	−	0.821681i	$-0.693036\pi$
$109$	−1.49635	+	0.863916i	−0.143324	+	0.0827481i	0.426623	+	0.904429i	$0.359703\pi$
$110$			11.2877i			1.07624i
$111$		0			0
$112$	−9.23136	−	21.0752i	−0.872282	−	1.99142i
$113$	−4.29556	−	7.44014i	−0.404093	−	0.699909i	0.590123	−	0.807314i	$-0.299079\pi$
$113$	−4.29556	−	7.44014i	−0.404093	−	0.699909i	−0.994215	+	0.107404i	$0.965746\pi$
$114$		0			0
$115$			3.20160i			0.298551i
$116$	12.6282	+	21.8726i	1.17250	+	2.03082i
$117$		0			0
$118$	29.5723			2.72235
$119$	−4.90257	+	6.66292i	−0.449418	+	0.610789i
$120$		0			0
$121$	3.68321			0.334837
$122$	−6.55741	+	3.78592i	−0.593680	+	0.342761i
$123$		0			0
$124$			49.2557i			4.42330i
$125$			11.9313i			1.06716i
$126$		0			0
$127$	−1.56206	+	2.70556i	−0.138610	+	0.240080i	−0.926971	−	0.375133i	$-0.877597\pi$
$127$	−1.56206	+	2.70556i	−0.138610	+	0.240080i	0.788361	+	0.615214i	$0.210930\pi$
$128$	4.27097	−	2.46585i	0.377504	−	0.217952i
$129$		0			0
$130$	−9.88325	−	11.3445i	−0.866818	−	0.994981i
$131$	5.10460	−	8.84142i	0.445991	−	0.772479i	−0.552130	−	0.833758i	$-0.686185\pi$
$131$	5.10460	−	8.84142i	0.445991	−	0.772479i	0.998121	+	0.0612793i	$0.0195180\pi$
$132$		0			0
$133$	1.07655	−	9.68067i	0.0933490	−	0.839420i
$134$	17.5790	+	30.4476i	1.51859	+	2.63028i
$135$		0			0
$136$	18.9308	+	10.9297i	1.62331	+	0.937216i
$137$	−8.65385	−	4.99630i	−0.739348	−	0.426863i	0.0824839	−	0.996592i	$-0.473715\pi$
$137$	−8.65385	−	4.99630i	−0.739348	−	0.426863i	−0.821832	+	0.569729i	$0.807048\pi$
$138$		0			0
$139$	0.832100	+	1.44124i	0.0705778	+	0.122244i	0.899155	−	0.437631i	$-0.144182\pi$
$139$	0.832100	+	1.44124i	0.0705778	+	0.122244i	−0.828577	+	0.559875i	$0.810849\pi$
$140$	−18.3651	+	8.04427i	−1.55213	+	0.679865i
$141$		0			0
$142$	−1.74874	+	3.02891i	−0.146751	+	0.254180i
$143$	7.35364	−	6.40642i	0.614942	−	0.535732i
$144$		0			0
$145$	7.50073	−	4.33055i	0.622902	−	0.359633i
$146$	11.7825	−	20.4078i	0.975124	−	1.68897i
$147$		0			0
$148$		−	27.9863i		−	2.30046i
$149$			19.7980i			1.62192i	0.585103	+	0.810959i	$0.301054\pi$
$149$			19.7980i			1.62192i	−0.585103	+	0.810959i	$0.698946\pi$
$150$		0			0
$151$	6.52544	−	3.76746i	0.531033	−	0.306592i	−0.210404	−	0.977614i	$-0.567478\pi$
$151$	6.52544	−	3.76746i	0.531033	−	0.306592i	0.741437	+	0.671023i	$0.234145\pi$
$152$	−25.7390			−2.08771
$153$		0			0
$154$	−7.43286	−	16.9692i	−0.598957	−	1.36742i
$155$	16.8912			1.35673
$156$		0			0
$157$	−7.00223	−	12.1282i	−0.558839	−	0.967938i	−0.997594	−	0.0693309i	$-0.977914\pi$
$157$	−7.00223	−	12.1282i	−0.558839	−	0.967938i	0.438755	−	0.898607i	$-0.355420\pi$
$158$		−	16.0643i		−	1.27801i
$159$		0			0
$160$	6.87414	+	11.9064i	0.543448	+	0.941280i
$161$	−2.10823	−	4.81308i	−0.166152	−	0.379324i
$162$		0			0
$163$		−	7.16995i		−	0.561594i	−0.959767	−	0.280797i	$-0.909401\pi$
$163$		−	7.16995i		−	0.561594i	0.959767	−	0.280797i	$-0.0905987\pi$
$164$	31.3533	−	18.1018i	2.44828	−	1.41351i
$165$		0			0
$166$	−3.49036	−	6.04548i	−0.270904	−	0.469220i
$167$	−15.5716	−	8.99027i	−1.20497	−	0.695688i	−0.243312	−	0.969948i	$-0.578234\pi$
$167$	−15.5716	−	8.99027i	−1.20497	−	0.695688i	−0.961656	+	0.274260i	$0.911567\pi$
$168$		0			0
$169$	−1.78135	+	12.8774i	−0.137027	+	0.990567i
$170$	6.52361	−	11.2992i	0.500338	−	0.866611i
$171$		0			0
$172$	−15.7761			−1.20291
$173$	−12.8116			−0.974047			−0.487023	−	0.873389i	$-0.661917\pi$
$173$	−12.8116			−0.974047			−0.487023	+	0.873389i	$0.661917\pi$
$174$		0			0
$175$	−2.54902	−	5.81942i	−0.192688	−	0.439906i
$176$	−20.3717	+	11.7616i	−1.53557	+	0.886562i
$177$		0			0
$178$	−2.27781	+	3.94528i	−0.170729	+	0.295711i
$179$	1.84022			0.137545			0.0687723	−	0.997632i	$-0.478092\pi$
$179$	1.84022			0.137545			0.0687723	+	0.997632i	$0.478092\pi$
$180$		0			0
$181$	−3.29928			−0.245234			−0.122617	−	0.992454i	$-0.539129\pi$
$181$	−3.29928			−0.245234			−0.122617	+	0.992454i	$0.539129\pi$
$182$	22.3282	+	10.5466i	1.65507	+	0.781767i
$183$		0			0
$184$	−12.0250	+	6.94262i	−0.886493	+	0.511817i
$185$	−9.59730			−0.705607
$186$		0			0
$187$	7.32427	+	4.22867i	0.535604	+	0.309231i
$188$	4.29531	−	2.47990i	0.313268	−	0.180865i
$189$		0			0
$190$			15.3628i			1.11453i
$191$	−4.89614			−0.354272			−0.177136	−	0.984186i	$-0.556683\pi$
$191$	−4.89614			−0.354272			−0.177136	+	0.984186i	$0.556683\pi$
$192$		0			0
$193$			3.01910i			0.217320i	0.994079	+	0.108660i	$0.0346559\pi$
$193$			3.01910i			0.217320i	−0.994079	+	0.108660i	$0.965344\pi$
$194$	−20.0384	+	34.7075i	−1.43867	+	2.49186i
$195$		0			0
$196$	22.3118	−	24.1865i	1.59370	−	1.72761i
$197$	−4.02694	−	2.32496i	−0.286908	−	0.165646i	0.349639	−	0.936885i	$-0.386304\pi$
$197$	−4.02694	−	2.32496i	−0.286908	−	0.165646i	−0.636546	+	0.771238i	$0.719638\pi$
$198$		0			0
$199$	0.205360	−	0.355694i	0.0145576	−	0.0252145i	−0.858655	−	0.512554i	$-0.828699\pi$
$199$	0.205360	−	0.355694i	0.0145576	−	0.0252145i	0.873212	+	0.487340i	$0.162033\pi$
$200$	−14.5392	+	8.39420i	−1.02808	+	0.593560i
$201$		0			0
$202$	−2.86793	+	1.65580i	−0.201787	+	0.116502i
$203$	−8.42450	+	11.4495i	−0.591284	+	0.803594i
$204$		0			0
$205$	−6.20762	−	10.7519i	−0.433559	−	0.750946i
$206$			29.6844i			2.06821i
$207$		0			0
$208$	10.1761	−	29.6578i	0.705583	−	2.05640i
$209$	−9.95831			−0.688831
$210$		0			0
$211$	3.75800	−	6.50905i	0.258711	−	0.448101i	−0.707186	−	0.707028i	$-0.750035\pi$
$211$	3.75800	−	6.50905i	0.258711	−	0.448101i	0.965897	+	0.258927i	$0.0833688\pi$
$212$	34.1549			2.34577
$213$		0			0
$214$	−11.5122	−	6.64656i	−0.786956	−	0.454349i
$215$			5.41005i			0.368962i
$216$		0			0
$217$	−25.3931	+	11.1227i	−1.72380	+	0.755059i
$218$	−2.23633	+	3.87344i	−0.151464	+	0.262343i
$219$		0			0
$220$	10.2491	+	17.7520i	0.690996	+	1.19684i
$221$	−11.0637	+	2.16300i	−0.744224	+	0.145499i
$222$		0			0
$223$	−19.5544	−	11.2897i	−1.30946	−	0.756016i	−0.327452	−	0.944868i	$-0.606190\pi$
$223$	−19.5544	−	11.2897i	−1.30946	−	0.756016i	−0.982006	+	0.188852i	$0.939523\pi$
$224$	−18.1744	−	13.3727i	−1.21433	−	0.893502i
$225$		0			0
$226$	−19.2595	−	11.1195i	−1.28113	−	0.739658i
$227$	−11.8401	−	6.83586i	−0.785853	−	0.453712i	0.0526478	−	0.998613i	$-0.483234\pi$
$227$	−11.8401	−	6.83586i	−0.785853	−	0.453712i	−0.838500	+	0.544901i	$0.816567\pi$
$228$		0			0
$229$	−6.86832	−	3.96543i	−0.453872	−	0.262043i	0.255592	−	0.966785i	$-0.417730\pi$
$229$	−6.86832	−	3.96543i	−0.453872	−	0.262043i	−0.709464	+	0.704742i	$0.751063\pi$
$230$	4.14383	+	7.17733i	0.273236	+	0.473259i
$231$		0			0
$232$	32.5305	+	18.7815i	2.13573	+	1.23306i
$233$	3.28585	−	5.69127i	0.215263	−	0.372847i	−0.738091	−	0.674702i	$-0.764272\pi$
$233$	3.28585	−	5.69127i	0.215263	−	0.372847i	0.953354	+	0.301854i	$0.0976056\pi$
$234$		0			0
$235$	−0.850427	−	1.47298i	−0.0554757	−	0.0960868i
$236$	46.5080	−	26.8514i	3.02741	−	1.74788i
$237$		0			0
$238$	−2.36673	+	21.2823i	−0.153412	+	1.37953i
$239$		−	9.39284i		−	0.607572i	−0.952740	−	0.303786i	$-0.901749\pi$
$239$		−	9.39284i		−	0.607572i	0.952740	−	0.303786i	$-0.0982508\pi$
$240$		0			0
$241$	8.73460	+	5.04292i	0.562645	+	0.324843i	0.754206	−	0.656637i	$-0.228022\pi$
$241$	8.73460	+	5.04292i	0.562645	+	0.324843i	−0.191562	+	0.981481i	$0.561355\pi$
$242$	8.25699	−	4.76718i	0.530780	−	0.306446i
$243$		0			0
$244$	−6.87517	+	11.9081i	−0.440137	+	0.762340i
$245$	−8.29423	−	7.65133i	−0.529899	−	0.488826i
$246$		0			0
$247$	10.0085	−	8.71928i	0.636823	−	0.554794i
$248$	36.6282	+	63.4420i	2.32590	+	4.02857i
$249$		0			0
$250$	15.4426	+	26.7474i	0.976678	+	1.69166i
$251$	5.17427	+	8.96209i	0.326597	+	0.565682i	0.981834	−	0.189741i	$-0.0607648\pi$
$251$	5.17427	+	8.96209i	0.326597	+	0.565682i	−0.655237	+	0.755423i	$0.727431\pi$
$252$		0			0
$253$	−4.65242	+	2.68607i	−0.292495	+	0.168872i
$254$			8.08709i			0.507429i
$255$		0			0
$256$	11.0672	−	19.1689i	0.691697	−	1.19805i
$257$	−3.99329	−	6.91658i	−0.249095	−	0.431445i	0.714180	−	0.699962i	$-0.246800\pi$
$257$	−3.99329	−	6.91658i	−0.249095	−	0.431445i	−0.963275	+	0.268517i	$0.913466\pi$
$258$		0			0
$259$	14.4280	−	6.31975i	0.896511	−	0.392690i
$260$	−25.8440	−	8.86749i	−1.60278	−	0.549939i
$261$		0			0
$262$		−	26.4275i		−	1.63270i
$263$	−5.05934			−0.311972			−0.155986	−	0.987759i	$-0.549856\pi$
$263$	−5.05934			−0.311972			−0.155986	+	0.987759i	$0.549856\pi$
$264$		0			0
$265$		−	11.7127i		−	0.719503i
$266$	−10.1163	−	23.0954i	−0.620269	−	1.41607i
$267$		0			0
$268$	55.2924	+	31.9231i	3.37752	+	1.95001i
$269$	6.94512	−	12.0293i	0.423451	−	0.733439i	−0.572823	−	0.819679i	$-0.694152\pi$
$269$	6.94512	−	12.0293i	0.423451	−	0.733439i	0.996274	+	0.0862400i	$0.0274852\pi$
$270$		0			0
$271$	−7.21158	+	4.16361i	−0.438072	+	0.252921i	−0.702780	−	0.711408i	$-0.748058\pi$
$271$	−7.21158	+	4.16361i	−0.438072	+	0.252921i	0.264707	+	0.964329i	$0.414725\pi$
$272$	27.1900			1.64863
$273$		0			0
$274$	−25.8669			−1.56267
$275$	−5.62515	+	3.24768i	−0.339210	+	0.195843i
$276$		0			0
$277$	−11.6058	+	20.1018i	−0.697325	+	1.20780i	0.272066	+	0.962279i	$0.412293\pi$
$277$	−11.6058	+	20.1018i	−0.697325	+	1.20780i	−0.969391	+	0.245523i	$0.921040\pi$
$278$	3.73080	+	2.15398i	0.223758	+	0.129187i
$279$		0			0
$280$	−17.6724	+	24.0180i	−1.05613	+	1.43535i
$281$		−	27.1595i		−	1.62020i	−0.586292	−	0.810100i	$-0.699413\pi$
$281$		−	27.1595i		−	1.62020i	0.586292	−	0.810100i	$-0.300587\pi$
$282$		0			0
$283$	16.1513			0.960092			0.480046	−	0.877243i	$-0.340620\pi$
$283$	16.1513			0.960092			0.480046	+	0.877243i	$0.340620\pi$
$284$			6.35136i			0.376884i
$285$		0			0
$286$	8.19351	−	23.8797i	0.484493	−	1.41204i
$287$	16.4122	+	12.0761i	0.968782	+	0.712828i
$288$		0			0
$289$	3.61216	+	6.25645i	0.212480	+	0.368027i
$290$	11.2101	−	19.4164i	0.658278	−	1.14017i
$291$		0			0
$292$		−	42.7935i		−	2.50430i
$293$	12.6831	−	7.32260i	0.740956	−	0.427791i	−0.0814609	−	0.996677i	$-0.525959\pi$
$293$	12.6831	−	7.32260i	0.740956	−	0.427791i	0.822417	+	0.568885i	$0.192625\pi$
$294$		0			0
$295$	−9.20810	−	15.9489i	−0.536116	−	0.928580i
$296$	−20.8116	−	36.0468i	−1.20965	−	2.09517i
$297$		0			0
$298$	25.6246	+	44.3831i	1.48439	+	2.57104i
$299$	2.32398	−	6.77315i	0.134399	−	0.391702i
$300$		0			0
$301$	−3.56248	−	8.13313i	−0.205338	−	0.468786i
$302$	9.75246	−	16.8918i	0.561191	−	0.972011i
$303$		0			0
$304$	−27.7263	+	16.0078i	−1.59021	+	0.918108i
$305$	4.08363	+	2.35769i	0.233828	+	0.135001i
$306$		0			0
$307$		−	8.97844i		−	0.512427i	−0.966620	−	0.256213i	$-0.917525\pi$
$307$		−	8.97844i		−	0.512427i	0.966620	−	0.256213i	$-0.0824750\pi$
$308$	−27.0975	−	19.9383i	−1.54402	−	1.13609i
$309$		0			0
$310$	37.8665	−	21.8622i	2.15067	−	1.24169i
$311$	−6.09080	−	10.5496i	−0.345378	−	0.598212i	0.640045	−	0.768338i	$-0.278916\pi$
$311$	−6.09080	−	10.5496i	−0.345378	−	0.598212i	−0.985422	+	0.170126i	$0.945583\pi$
$312$		0			0
$313$	−6.56198	+	11.3657i	−0.370905	+	0.642427i	−0.989705	−	0.143122i	$-0.954286\pi$
$313$	−6.56198	+	11.3657i	−0.370905	+	0.642427i	0.618800	+	0.785549i	$0.287619\pi$
$314$	−31.3951	−	18.1260i	−1.77173	−	1.02291i
$315$		0			0
$316$	−14.5862	−	25.2641i	−0.820540	−	1.42122i
$317$	14.4761	+	8.35775i	0.813056	+	0.469418i	0.848016	−	0.529971i	$-0.177797\pi$
$317$	14.4761	+	8.35775i	0.813056	+	0.469418i	−0.0349599	+	0.999389i	$0.511130\pi$
$318$		0			0
$319$	12.5859	+	7.26648i	0.704675	+	0.406845i
$320$	6.53932	+	3.77548i	0.365559	+	0.211056i
$321$		0			0
$322$	−10.9558	−	8.06126i	−0.610543	−	0.449236i
$323$	9.96849	+	5.75531i	0.554661	+	0.320234i
$324$		0			0
$325$	2.80988	−	8.18930i	0.155864	−	0.454261i
$326$	−9.28007	−	16.0736i	−0.513976	−	0.890232i
$327$		0			0
$328$	26.9223	−	46.6307i	1.48653	−	2.57475i
$329$	2.24843	+	1.65439i	0.123960	+	0.0912094i
$330$		0			0
$331$			3.96665i			0.218027i	0.994040	+	0.109013i	$0.0347691\pi$
$331$			3.96665i			0.218027i	−0.994040	+	0.109013i	$0.965231\pi$
$332$	−10.9785	−	6.33843i	−0.602523	−	0.347867i
$333$		0			0
$334$	−46.5445			−2.54680
$335$	10.9473	−	18.9613i	0.598116	−	1.03597i
$336$		0			0
$337$	−13.7032			−0.746461			−0.373230	−	0.927739i	$-0.621750\pi$
$337$	−13.7032			−0.746461			−0.373230	+	0.927739i	$0.621750\pi$
$338$	12.6738	+	31.1740i	0.689362	+	1.69564i
$339$		0			0
$340$		−	23.6935i		−	1.28496i
$341$	14.1713	+	24.5455i	0.767420	+	1.32921i
$342$		0			0
$343$	17.5074	+	6.04084i	0.945309	+	0.326175i
$344$	−20.3197	+	11.7316i	−1.09557	+	0.632526i
$345$		0			0
$346$	−28.7209	+	16.5820i	−1.54405	+	0.891456i
$347$	−13.1989	+	22.8612i	−0.708556	+	1.22725i	0.256837	+	0.966455i	$0.417320\pi$
$347$	−13.1989	+	22.8612i	−0.708556	+	1.22725i	−0.965393	+	0.260800i	$0.916014\pi$
$348$		0			0
$349$	−4.23507	−	2.44512i	−0.226698	−	0.130884i	0.382350	−	0.924018i	$-0.375115\pi$
$349$	−4.23507	−	2.44512i	−0.226698	−	0.130884i	−0.609048	+	0.793133i	$0.708448\pi$
$350$	−13.2465	−	9.74673i	−0.708053	−	0.520984i
$351$		0			0
$352$	−11.5345	+	19.9784i	−0.614792	+	1.06485i
$353$			13.5577i			0.721605i	0.932642	+	0.360802i	$0.117497\pi$
$353$			13.5577i			0.721605i	−0.932642	+	0.360802i	$0.882503\pi$
$354$		0			0
$355$	2.17806			0.115599
$356$			8.27291i			0.438464i
$357$		0			0
$358$	4.12540	−	2.38180i	0.218034	−	0.125882i
$359$	7.43541	+	4.29284i	0.392426	+	0.226567i	0.683211	−	0.730221i	$-0.260583\pi$
$359$	7.43541	+	4.29284i	0.392426	+	0.226567i	−0.290785	+	0.956789i	$0.593916\pi$
$360$		0			0
$361$	5.44653			0.286659
$362$	−7.39632	+	4.27026i	−0.388742	+	0.224440i
$363$		0			0
$364$	44.6914	−	3.68725i	2.34247	−	0.193264i
$365$	−14.6751			−0.768130
$366$		0			0
$367$	−1.66322			−0.0868196			−0.0434098	−	0.999057i	$-0.513822\pi$
$367$	−1.66322			−0.0868196			−0.0434098	+	0.999057i	$0.513822\pi$
$368$	−8.63560	+	14.9573i	−0.450162	+	0.779703i
$369$		0			0
$370$	−21.5152	+	12.4218i	−1.11852	+	0.645778i
$371$	7.71270	+	17.6081i	0.400424	+	0.914166i
$372$		0			0
$373$	13.9635			0.723002			0.361501	−	0.932372i	$-0.382264\pi$
$373$	13.9635			0.723002			0.361501	+	0.932372i	$0.382264\pi$
$374$	21.8927			1.13204
$375$		0			0
$376$	3.68828	−	6.38828i	0.190208	−	0.329450i
$377$	−19.0117	+	3.71687i	−0.979150	+	0.191429i
$378$		0			0
$379$	−27.3454	−	15.7879i	−1.40464	−	0.810969i	−0.409775	−	0.912187i	$-0.634393\pi$
$379$	−27.3454	−	15.7879i	−1.40464	−	0.810969i	−0.994864	+	0.101218i	$0.967726\pi$
$380$	13.9493	+	24.1608i	0.715582	+	1.23943i
$381$		0			0
$382$	−10.9761	+	6.33707i	−0.561588	+	0.324233i
$383$		−	31.9082i		−	1.63043i	−0.579156	−	0.815217i	$-0.696618\pi$
$383$		−	31.9082i		−	1.63043i	0.579156	−	0.815217i	$-0.303382\pi$
$384$		0			0
$385$	−6.83739	+	9.29247i	−0.348466	+	0.473588i
$386$	3.90762	+	6.76820i	0.198893	+	0.344492i
$387$		0			0
$388$			72.7788i			3.69478i
$389$	12.7075	+	22.0100i	0.644296	+	1.11595i	0.984464	+	0.175589i	$0.0561829\pi$
$389$	12.7075	+	22.0100i	0.644296	+	1.11595i	−0.340168	+	0.940365i	$0.610484\pi$
$390$		0			0
$391$	6.20956			0.314031
$392$	10.7519	−	47.7443i	0.543054	−	2.41145i
$393$		0			0
$394$	−12.0368			−0.606403
$395$	−8.66376	+	5.00203i	−0.435921	+	0.251679i
$396$		0			0
$397$			4.15897i			0.208733i	0.994539	+	0.104366i	$0.0332815\pi$
$397$			4.15897i			0.208733i	−0.994539	+	0.104366i	$0.966719\pi$
$398$		−	1.06319i		−	0.0532930i
$399$		0			0
$400$	−10.4412	+	18.0846i	−0.522058	+	0.904231i
$401$	16.9753	−	9.80067i	0.847704	−	0.489422i	−0.0121716	−	0.999926i	$-0.503874\pi$
$401$	16.9753	−	9.80067i	0.847704	−	0.489422i	0.859875	+	0.510504i	$0.170541\pi$
$402$		0			0
$403$	−35.7342	−	12.2610i	−1.78005	−	0.610762i
$404$	−3.00691	+	5.20811i	−0.149599	+	0.259113i
$405$		0			0
$406$	−4.06695	+	36.5711i	−0.201839	+	1.81500i
$407$	−8.05193	−	13.9463i	−0.399119	−	0.691295i
$408$		0			0
$409$	−15.2712	−	8.81685i	−0.755114	−	0.435965i	0.0724249	−	0.997374i	$-0.476926\pi$
$409$	−15.2712	−	8.81685i	−0.755114	−	0.435965i	−0.827539	+	0.561409i	$0.810260\pi$
$410$	−27.8324	−	16.0690i	−1.37454	−	0.793594i
$411$		0			0
$412$	26.9532	+	46.6842i	1.32789	+	2.29997i
$413$	24.3451	+	17.9131i	1.19794	+	0.881446i
$414$		0			0
$415$	−2.17363	+	3.76483i	−0.106699	+	0.184808i
$416$	−5.90001	−	30.1783i	−0.289272	−	1.47962i
$417$		0			0
$418$	−22.3245	+	12.8890i	−1.09193	+	0.630424i
$419$	14.9455	−	25.8864i	0.730137	−	1.26463i	−0.226688	−	0.973968i	$-0.572790\pi$
$419$	14.9455	−	25.8864i	0.730137	−	1.26463i	0.956824	−	0.290666i	$-0.0938770\pi$
$420$		0			0
$421$			12.8528i			0.626407i	0.949686	+	0.313203i	$0.101402\pi$
$421$			12.8528i			0.626407i	−0.949686	+	0.313203i	$0.898598\pi$
$422$		−	19.4559i		−	0.947100i
$423$		0			0
$424$	43.9919	−	25.3987i	2.13644	−	1.23347i
$425$	7.50787			0.364185
$426$		0			0
$427$	−7.69160	−	0.855355i	−0.372223	−	0.0413936i
$428$	−24.1401			−1.16685
$429$		0			0
$430$	7.00223	+	12.1282i	0.337677	+	0.584874i
$431$		−	8.97060i		−	0.432098i	−0.976382	−	0.216049i	$-0.930683\pi$
$431$		−	8.97060i		−	0.432098i	0.976382	−	0.216049i	$-0.0693172\pi$
$432$		0			0
$433$	−1.72531	−	2.98833i	−0.0829132	−	0.143610i	0.821587	−	0.570083i	$-0.193089\pi$
$433$	−1.72531	−	2.98833i	−0.0829132	−	0.143610i	−0.904500	+	0.426473i	$0.859756\pi$
$434$	−42.5300	+	57.8012i	−2.04151	+	2.77454i
$435$		0			0
$436$			8.12228i			0.388987i
$437$	−6.33204	+	3.65580i	−0.302902	+	0.174881i
$438$		0			0
$439$	−19.2572	−	33.3544i	−0.919096	−	1.59192i	−0.800792	−	0.598943i	$-0.795588\pi$
$439$	−19.2572	−	33.3544i	−0.919096	−	1.59192i	−0.118304	−	0.992977i	$-0.537746\pi$
$440$	26.4020	+	15.2432i	1.25867	+	0.726691i
$441$		0			0
$442$	−22.0029	+	19.1687i	−1.04657	+	0.911764i
$443$	−7.51997	+	13.0250i	−0.357284	+	0.618835i	−0.987506	−	0.157580i	$-0.949631\pi$
$443$	−7.51997	+	13.0250i	−0.357284	+	0.618835i	0.630222	+	0.776415i	$0.282964\pi$
$444$		0			0
$445$	2.83701			0.134487
$446$	−58.4492			−2.76765
$447$		0			0
$448$	−12.3169	−	1.36972i	−0.581920	−	0.0647133i
$449$	−33.7087	+	19.4617i	−1.59081	+	0.918456i	−0.597646	+	0.801760i	$0.703897\pi$
$449$	−33.7087	+	19.4617i	−1.59081	+	0.918456i	−0.993168	+	0.116696i	$0.962770\pi$
$450$		0			0
$451$	10.4161	−	18.0412i	0.490476	−	0.849529i
$452$	−40.3856			−1.89958
$453$		0			0
$454$	−35.3906			−1.66097
$455$	−1.26446	−	15.3259i	−0.0592788	−	0.718491i
$456$		0			0
$457$	−12.0721	+	6.96982i	−0.564708	+	0.326034i	−0.755033	−	0.655687i	$-0.772379\pi$
$457$	−12.0721	+	6.96982i	−0.564708	+	0.326034i	0.190325	+	0.981721i	$0.439046\pi$
$458$	−20.5298			−0.959295
$459$		0			0
$460$	13.0339	+	7.52512i	0.607709	+	0.350861i
$461$	−32.4443	+	18.7317i	−1.51108	+	0.872424i	−0.511167	+	0.859481i	$0.670787\pi$
$461$	−32.4443	+	18.7317i	−1.51108	+	0.872424i	−0.999916	+	0.0129430i	$0.995880\pi$
$462$		0			0
$463$		−	6.75275i		−	0.313827i	−0.987612	−	0.156913i	$-0.949846\pi$
$463$		−	6.75275i		−	0.313827i	0.987612	−	0.156913i	$-0.0501544\pi$
$464$	46.7228			2.16905
$465$		0			0
$466$		−	17.0115i		−	0.788044i
$467$	−2.52516	+	4.37371i	−0.116851	+	0.202391i	−0.918518	−	0.395379i	$-0.870613\pi$
$467$	−2.52516	+	4.37371i	−0.116851	+	0.202391i	0.801667	+	0.597770i	$0.203947\pi$
$468$		0			0
$469$	−3.97162	+	35.7140i	−0.183393	+	1.64912i
$470$	−3.81296	−	2.20141i	−0.175879	−	0.101544i
$471$		0			0
$472$	39.9353	−	69.1699i	1.83817	−	3.18380i
$473$	−7.86163	+	4.53892i	−0.361478	+	0.208700i
$474$		0			0
$475$	−7.65595	+	4.42017i	−0.351279	+	0.202811i
$476$	15.6020	+	35.6194i	0.715117	+	1.63261i
$477$		0			0
$478$	−12.1572	−	21.0568i	−0.556055	−	0.963116i
$479$		−	9.45319i		−	0.431927i	−0.976401	−	0.215964i	$-0.930711\pi$
$479$		−	9.45319i		−	0.431927i	0.976401	−	0.215964i	$-0.0692892\pi$
$480$		0			0
$481$	20.3036	+	6.96649i	0.925764	+	0.317645i
$482$	26.1082			1.18920
$483$		0			0
$484$	8.65711	−	14.9946i	0.393505	−	0.681571i
$485$	24.9579			1.13328
$486$		0			0
$487$	34.6407	+	19.9998i	1.56972	+	0.906277i	0.996201	+	0.0870831i	$0.0277546\pi$
$487$	34.6407	+	19.9998i	1.56972	+	0.906277i	0.573517	+	0.819194i	$0.305579\pi$
$488$			20.4504i			0.925748i
$489$		0			0
$490$	−28.4971	−	6.41748i	−1.28737	−	0.289912i
$491$	3.38049	−	5.85517i	0.152559	−	0.264240i	−0.779608	−	0.626267i	$-0.784582\pi$
$491$	3.38049	−	5.85517i	0.152559	−	0.264240i	0.932168	+	0.362027i	$0.117915\pi$
$492$		0			0
$493$	−8.39918	−	14.5478i	−0.378280	−	0.655200i
$494$	11.1515	−	32.5008i	0.501732	−	1.46228i
$495$		0			0
$496$	78.9125	+	45.5602i	3.54328	+	2.04571i
$497$	−3.27436	+	1.43424i	−0.146875	+	0.0643343i
$498$		0			0
$499$	9.83591	+	5.67877i	0.440316	+	0.254217i	0.703732	−	0.710466i	$-0.251516\pi$
$499$	9.83591	+	5.67877i	0.440316	+	0.254217i	−0.263416	+	0.964682i	$0.584849\pi$
$500$	48.5729	+	28.0436i	2.17225	+	1.25415i
$501$		0			0
$502$	23.1993	+	13.3941i	1.03543	+	0.597808i
$503$	−6.96423	−	12.0624i	−0.310520	−	0.537836i	0.667955	−	0.744202i	$-0.267170\pi$
$503$	−6.96423	−	12.0624i	−0.310520	−	0.537836i	−0.978475	+	0.206365i	$0.933836\pi$
$504$		0			0
$505$	1.78601	+	1.03115i	0.0794763	+	0.0458857i
$506$	−6.95317	+	12.0432i	−0.309106	+	0.535388i
$507$		0			0
$508$	7.34301	+	12.7185i	0.325793	+	0.564290i
$509$	−17.1602	+	9.90746i	−0.760614	+	0.439141i	−0.829516	−	0.558483i	$-0.811384\pi$
$509$	−17.1602	+	9.90746i	−0.760614	+	0.439141i	0.0689022	+	0.997623i	$0.478050\pi$
$510$		0			0
$511$	22.0616	−	9.66345i	0.975949	−	0.427486i
$512$		−	47.4335i		−	2.09628i
$513$		0			0
$514$	−17.9043	−	10.3370i	−0.789724	−	0.455947i
$515$	16.0093	−	9.24299i	0.705455	−	0.407295i
$516$		0			0
$517$	1.42698	−	2.47160i	0.0627585	−	0.108701i
$518$	24.1649	−	32.8417i	1.06174	−	1.44298i
$519$		0			0
$520$	−39.8816	+	7.79704i	−1.74892	+	0.341923i
$521$	−15.5476	−	26.9292i	−0.681151	−	1.17979i	−0.974630	−	0.223823i	$-0.928146\pi$
$521$	−15.5476	−	26.9292i	−0.681151	−	1.17979i	0.293479	−	0.955966i	$-0.405187\pi$
$522$		0			0
$523$	−11.3601	−	19.6763i	−0.496742	−	0.860383i	0.503251	−	0.864140i	$-0.332137\pi$
$523$	−11.3601	−	19.6763i	−0.496742	−	0.860383i	−0.999993	+	0.00375758i	$0.998804\pi$
$524$	−23.9960	−	41.5622i	−1.04827	−	1.81565i
$525$		0			0
$526$	−11.3420	+	6.54831i	−0.494535	+	0.285520i
$527$		−	32.7607i		−	1.42708i
$528$		0			0
$529$	9.52783	−	16.5027i	0.414253	−	0.717508i
$530$	−15.1597	−	26.2574i	−0.658495	−	1.14055i
$531$		0			0
$532$	−36.8802	−	27.1364i	−1.59896	−	1.17651i
$533$	5.32794	+	27.2522i	0.230779	+	1.18043i
$534$		0			0
$535$			8.27830i			0.357902i
$536$	94.9564			4.10149
$537$		0			0
$538$		−	35.9563i		−	1.55018i
$539$	4.15988	−	18.4721i	0.179179	−	0.795649i
$540$		0			0
$541$	−1.81754	−	1.04936i	−0.0781423	−	0.0451155i	0.460420	−	0.887701i	$-0.347699\pi$
$541$	−1.81754	−	1.04936i	−0.0781423	−	0.0451155i	−0.538562	+	0.842586i	$0.681032\pi$
$542$	−10.7779	+	18.6679i	−0.462951	+	0.801855i
$543$		0			0
$544$	23.0926	−	13.3325i	0.990087	−	0.571627i
$545$	2.78536			0.119312
$546$		0			0
$547$	25.3770			1.08504			0.542521	−	0.840042i	$-0.317470\pi$
$547$	25.3770			1.08504			0.542521	+	0.840042i	$0.317470\pi$
$548$	−40.6805	+	23.4869i	−1.73778	+	1.00331i
$549$		0			0
$550$	−8.40696	+	14.5613i	−0.358474	+	0.620895i
$551$	17.1297	+	9.88983i	0.729749	+	0.421321i
$552$		0			0
$553$	9.73076	−	13.2248i	0.413794	−	0.562374i
$554$			60.0855i			2.55279i
$555$		0			0
$556$	7.82316			0.331776
$557$			44.2503i			1.87495i	0.348058	+	0.937473i	$0.386841\pi$
$557$			44.2503i			1.87495i	−0.348058	+	0.937473i	$0.613159\pi$
$558$		0			0
$559$	3.92705	−	11.4452i	0.166097	−	0.484082i
$560$	−4.09944	+	36.8634i	−0.173233	+	1.55776i
$561$		0			0
$562$	−35.1526	−	60.8860i	−1.48282	−	2.56832i
$563$	19.4453	−	33.6803i	0.819523	−	1.41946i	−0.0865108	−	0.996251i	$-0.527572\pi$
$563$	19.4453	−	33.6803i	0.819523	−	1.41946i	0.906034	−	0.423205i	$-0.139095\pi$
$564$		0			0
$565$			13.8494i			0.582647i
$566$	36.2078	−	20.9046i	1.52193	−	0.878685i
$567$		0			0
$568$	4.72309	+	8.18063i	0.198177	+	0.343252i
$569$	−23.0789	−	39.9739i	−0.967520	−	1.67579i	−0.702687	−	0.711499i	$-0.748017\pi$
$569$	−23.0789	−	39.9739i	−0.967520	−	1.67579i	−0.264832	−	0.964294i	$-0.585317\pi$
$570$		0			0
$571$	10.5684	+	18.3050i	0.442274	+	0.766041i	0.997858	−	0.0654194i	$-0.0208385\pi$
$571$	10.5684	+	18.3050i	0.442274	+	0.766041i	−0.555584	+	0.831461i	$0.687505\pi$
$572$	−8.79673	−	44.9949i	−0.367810	−	1.88133i
$573$		0			0
$574$	52.4229	+	5.82976i	2.18809	+	0.243329i
$575$	−2.38452	+	4.13011i	−0.0994413	+	0.172237i
$576$		0			0
$577$	−21.9368	+	12.6652i	−0.913239	+	0.527259i	−0.881472	−	0.472237i	$-0.843447\pi$
$577$	−21.9368	+	12.6652i	−0.913239	+	0.527259i	−0.0317671	+	0.999495i	$0.510113\pi$
$578$	16.1955	+	9.35045i	0.673642	+	0.388927i
$579$		0			0
$580$		−	40.7146i		−	1.69058i
$581$	0.788579	−	7.09113i	0.0327158	−	0.294190i
$582$		0			0
$583$	17.0203	−	9.82667i	0.704908	−	0.406979i
$584$	−31.8227	−	55.1186i	−1.31683	−	2.28082i
$585$		0			0
$586$	18.9553	−	32.8315i	0.783036	−	1.35626i
$587$	−3.08554	−	1.78144i	−0.127354	−	0.0735278i	0.434970	−	0.900445i	$-0.356759\pi$
$587$	−3.08554	−	1.78144i	−0.127354	−	0.0735278i	−0.562324	+	0.826917i	$0.690092\pi$
$588$		0			0
$589$	19.2875	+	33.4069i	0.794727	+	1.37651i
$590$	−41.2853	−	23.8361i	−1.69969	−	0.981316i
$591$		0			0
$592$	−44.8369	−	25.8866i	−1.84278	−	1.06393i
$593$	21.9568	+	12.6768i	0.901659	+	0.520573i	0.877738	−	0.479141i	$-0.159052\pi$
$593$	21.9568	+	12.6768i	0.901659	+	0.520573i	0.0239212	+	0.999714i	$0.492385\pi$
$594$		0			0
$595$	12.2149	−	5.35037i	0.500761	−	0.219344i
$596$	80.5990	+	46.5338i	3.30146	+	1.90610i
$597$		0			0
$598$	−3.55661	−	18.1919i	−0.145441	−	0.743924i
$599$	5.46078	+	9.45835i	0.223122	+	0.386458i	0.955754	−	0.294166i	$-0.0950420\pi$
$599$	5.46078	+	9.45835i	0.223122	+	0.386458i	−0.732633	+	0.680624i	$0.761709\pi$
$600$		0			0
$601$	−12.1282	+	21.0067i	−0.494720	+	0.856880i	−0.999981	−	0.00608649i	$-0.998063\pi$
$601$	−12.1282	+	21.0067i	−0.494720	+	0.856880i	0.505262	+	0.862966i	$0.331396\pi$
$602$	−18.5131	−	13.6219i	−0.754536	−	0.555187i
$603$		0			0
$604$		−	35.4206i		−	1.44124i
$605$	−5.14205	−	2.96876i	−0.209054	−	0.120697i
$606$		0			0
$607$	−9.85447			−0.399981			−0.199990	−	0.979798i	$-0.564091\pi$
$607$	−9.85447			−0.399981			−0.199990	+	0.979798i	$0.564091\pi$
$608$	−15.6987	+	27.1910i	−0.636667	+	1.10274i
$609$		0			0
$610$	12.2062			0.494215
$611$	0.729914	+	3.73348i	0.0295291	+	0.151040i
$612$		0			0
$613$		−	3.67688i		−	0.148508i	−0.997239	−	0.0742540i	$-0.976342\pi$
$613$		−	3.67688i		−	0.148508i	0.997239	−	0.0742540i	$-0.0236575\pi$
$614$	−11.6208	−	20.1278i	−0.468977	−	0.812293i
$615$		0			0
$616$	−49.7286	−	5.53015i	−2.00362	−	0.222816i
$617$	−16.2352	+	9.37341i	−0.653605	+	0.377359i	−0.789836	−	0.613318i	$-0.789834\pi$
$617$	−16.2352	+	9.37341i	−0.653605	+	0.377359i	0.136231	+	0.990677i	$0.456501\pi$
$618$		0			0
$619$	−13.7650	+	7.94725i	−0.553264	+	0.319427i	−0.750437	−	0.660942i	$-0.770157\pi$
$619$	−13.7650	+	7.94725i	−0.553264	+	0.319427i	0.197174	+	0.980369i	$0.436824\pi$
$620$	39.7014	−	68.7649i	1.59445	−	2.76167i
$621$		0			0
$622$	−27.3086	−	15.7667i	−1.09498	−	0.632185i
$623$	−4.26499	+	1.86815i	−0.170873	+	0.0748460i
$624$		0			0
$625$	3.61371	−	6.25913i	0.144549	−	0.250365i
$626$			33.9727i			1.35782i
$627$		0			0
$628$	−65.8330			−2.62702
$629$			18.6141i			0.742194i
$630$		0			0
$631$	−17.0998	+	9.87255i	−0.680731	+	0.393020i	−0.800130	−	0.599826i	$-0.795236\pi$
$631$	−17.0998	+	9.87255i	−0.680731	+	0.393020i	0.119400	+	0.992846i	$0.461903\pi$
$632$	−37.5745	−	21.6936i	−1.49463	−	0.862927i
$633$		0			0
$634$	43.2698			1.71846
$635$	4.36151	−	2.51812i	0.173081	−	0.0999286i
$636$		0			0
$637$	11.9929	+	22.2074i	0.475177	+	0.879890i
$638$	37.6200			1.48939
$639$		0			0
$640$	−7.95016			−0.314258
$641$	14.8893	−	25.7890i	0.588092	−	1.01860i	−0.406390	−	0.913699i	$-0.633213\pi$
$641$	14.8893	−	25.7890i	0.588092	−	1.01860i	0.994482	−	0.104905i	$-0.0334539\pi$
$642$		0			0
$643$	10.0220	−	5.78623i	0.395231	−	0.228187i	−0.289193	−	0.957271i	$-0.593387\pi$
$643$	10.0220	−	5.78623i	0.395231	−	0.228187i	0.684424	+	0.729084i	$0.260054\pi$
$644$	−24.5496	−	2.73007i	−0.967389	−	0.107580i
$645$		0			0
$646$	29.7964			1.17232
$647$	25.5065			1.00276			0.501382	−	0.865226i	$-0.332825\pi$
$647$	25.5065			1.00276			0.501382	+	0.865226i	$0.332825\pi$
$648$		0			0
$649$	15.4508	−	26.7616i	0.606497	−	1.05048i
$650$	−4.30024	−	21.9956i	−0.168669	−	0.862737i
$651$		0			0
$652$	−29.1893	−	16.8524i	−1.14314	−	0.659993i
$653$	−22.4146	−	38.8233i	−0.877152	−	1.51927i	−0.854452	−	0.519530i	$-0.826107\pi$
$653$	−22.4146	−	38.8233i	−0.877152	−	1.51927i	−0.0227004	−	0.999742i	$-0.507226\pi$
$654$		0			0
$655$	−14.2529	+	8.22889i	−0.556905	+	0.321529i
$656$		−	66.9747i		−	2.61492i
$657$		0			0
$658$	7.18179	+	0.798661i	0.279975	+	0.0311350i
$659$	20.5867	+	35.6572i	0.801944	+	1.38901i	0.918335	+	0.395805i	$0.129534\pi$
$659$	20.5867	+	35.6572i	0.801944	+	1.38901i	−0.116390	+	0.993204i	$0.537132\pi$
$660$		0			0
$661$		−	21.8938i		−	0.851569i	−0.904825	−	0.425785i	$-0.859998\pi$
$661$		−	21.8938i		−	0.851569i	0.904825	−	0.425785i	$-0.140002\pi$
$662$	5.13404	+	8.89241i	0.199540	+	0.345613i
$663$		0			0
$664$	−18.8539			−0.731673
$665$	−9.30583	+	12.6473i	−0.360865	+	0.490439i
$666$		0			0
$667$	10.6704			0.413160
$668$	−73.1999	+	42.2620i	−2.83219	+	1.63516i
$669$		0			0
$670$		−	56.6764i		−	2.18960i
$671$			7.91219i			0.305447i
$672$		0			0
$673$	17.8344	−	30.8901i	0.687466	−	1.19073i	−0.285189	−	0.958471i	$-0.592056\pi$
$673$	17.8344	−	30.8901i	0.687466	−	1.19073i	0.972655	−	0.232254i	$-0.0746102\pi$
$674$	−30.7197	+	17.7361i	−1.18328	+	0.683167i
$675$		0			0
$676$	48.2376	+	37.5193i	1.85529	+	1.44305i
$677$	1.27766	−	2.21297i	0.0491044	−	0.0850514i	−0.840428	−	0.541923i	$-0.817697\pi$
$677$	1.27766	−	2.21297i	0.0491044	−	0.0850514i	0.889533	+	0.456871i	$0.151030\pi$
$678$		0			0
$679$	−37.5201	+	16.4346i	−1.43989	+	0.630701i
$680$	−17.6193	−	30.5175i	−0.675670	−	1.17029i
$681$		0			0
$682$	63.5384	+	36.6839i	2.43301	+	1.40470i
$683$	30.9517	+	17.8700i	1.18433	+	0.683775i	0.957013	−	0.290045i	$-0.0936704\pi$
$683$	30.9517	+	17.8700i	1.18433	+	0.683775i	0.227320	+	0.973820i	$0.427004\pi$
$684$		0			0
$685$	8.05431	+	13.9505i	0.307739	+	0.533020i
$686$	47.0666	−	9.11748i	1.79701	−	0.348107i
$687$		0			0
$688$	−14.5924	+	25.2748i	−0.556330	+	0.963592i
$689$	−8.50199	+	24.7788i	−0.323900	+	0.943995i
$690$		0			0
$691$	22.5419	−	13.0146i	0.857536	−	0.495099i	−0.00565028	−	0.999984i	$-0.501799\pi$
$691$	22.5419	−	13.0146i	0.857536	−	0.495099i	0.863186	+	0.504885i	$0.168465\pi$
$692$	−30.1127	+	52.1567i	−1.14471	+	1.98270i
$693$		0			0
$694$			68.3335i			2.59391i
$695$		−	2.68278i		−	0.101764i
$696$		0			0
$697$	−20.8535	+	12.0398i	−0.789884	+	0.456040i
$698$	−12.6589			−0.479146
$699$		0			0
$700$	−29.6825	−	3.30088i	−1.12189	−	0.124762i
$701$	1.12731			0.0425779			0.0212890	−	0.999773i	$-0.493223\pi$
$701$	1.12731			0.0425779			0.0212890	+	0.999773i	$0.493223\pi$
$702$		0			0
$703$	−10.9588	−	18.9813i	−0.413321	−	0.715892i
$704$			12.6702i			0.477525i
$705$		0			0
$706$	17.5478	+	30.3936i	0.660419	+	1.14388i
$707$	−3.36398	−	0.374096i	−0.126515	−	0.0140693i
$708$		0			0
$709$			6.05031i			0.227224i	0.993525	+	0.113612i	$0.0362421\pi$
$709$			6.05031i			0.227224i	−0.993525	+	0.113612i	$0.963758\pi$
$710$	4.88276	−	2.81906i	0.183247	−	0.105798i
$711$		0			0
$712$	6.15202	+	10.6556i	0.230557	+	0.399336i
$713$	18.0218	+	10.4049i	0.674922	+	0.389666i
$714$		0			0
$715$	−15.4300	+	3.01664i	−0.577050	+	0.112816i
$716$	4.32530	−	7.49164i	0.161644	−	0.279976i
$717$		0			0
$718$	22.2249			0.829425
$719$	47.1177			1.75719			0.878597	−	0.477563i	$-0.158480\pi$
$719$	47.1177			1.75719			0.878597	+	0.477563i	$0.158480\pi$
$720$		0			0
$721$	−17.9810	+	24.4374i	−0.669647	+	0.910095i
$722$	12.2100	−	7.04944i	0.454409	−	0.262353i
$723$		0			0
$724$	−7.75473	+	13.4316i	−0.288202	+	0.499181i
$725$	12.9014			0.479146
$726$		0			0
$727$	17.9215			0.664671			0.332335	−	0.943161i	$-0.392163\pi$
$727$	17.9215			0.664671			0.332335	+	0.943161i	$0.392163\pi$
$728$	54.8211	−	37.9833i	2.03181	−	1.40775i
$729$		0			0
$730$	−32.8985	+	18.9940i	−1.21763	+	0.702999i
$731$	10.4929			0.388093
$732$		0			0
$733$	39.2037	+	22.6343i	1.44802	+	0.836016i	0.998364	−	0.0571848i	$-0.0182124\pi$
$733$	39.2037	+	22.6343i	1.44802	+	0.836016i	0.449658	+	0.893201i	$0.351546\pi$
$734$	−3.72861	+	2.15271i	−0.137625	+	0.0794581i
$735$		0			0
$736$			16.9378i			0.624335i
$737$	36.7382			1.35327
$738$		0			0
$739$			19.2613i			0.708539i	0.935143	+	0.354270i	$0.115270\pi$
$739$			19.2613i			0.708539i	−0.935143	+	0.354270i	$0.884730\pi$
$740$	−22.5577	+	39.0712i	−0.829239	+	1.43628i
$741$		0			0
$742$	40.0804	+	29.4911i	1.47140	+	1.08265i
$743$	−30.2115	−	17.4426i	−1.10835	−	0.639908i	−0.169951	−	0.985453i	$-0.554361\pi$
$743$	−30.2115	−	17.4426i	−1.10835	−	0.639908i	−0.938402	+	0.345545i	$0.887694\pi$
$744$		0			0
$745$	15.9577	−	27.6396i	0.584647	−	1.01264i
$746$	31.3032	−	18.0729i	1.14609	−	0.661697i
$747$		0			0
$748$	34.4303	−	19.8784i	1.25890	−	0.726825i
$749$	−5.45120	−	12.4451i	−0.199183	−	0.454733i
$750$		0			0
$751$	−12.4834	−	21.6219i	−0.455526	−	0.788993i	0.543193	−	0.839608i	$-0.317215\pi$
$751$	−12.4834	−	21.6219i	−0.455526	−	0.788993i	−0.998718	+	0.0506146i	$0.983882\pi$
$752$		−	9.17535i		−	0.334591i
$753$		0			0
$754$	−37.8095	+	32.9393i	−1.37694	+	1.19958i
$755$	−12.1467			−0.442064
$756$		0			0
$757$	5.30243	−	9.18408i	0.192720	−	0.333801i	−0.753431	−	0.657527i	$-0.771602\pi$
$757$	5.30243	−	9.18408i	0.192720	−	0.333801i	0.946151	+	0.323726i	$0.104936\pi$
$758$	−81.7370			−2.96882
$759$		0			0
$760$	35.9337	+	20.7463i	1.30345	+	0.752548i
$761$			32.6388i			1.18316i	0.806248	+	0.591578i	$0.201495\pi$
$761$			32.6388i			1.18316i	−0.806248	+	0.591578i	$0.798505\pi$
$762$		0			0
$763$	−4.18733	+	1.83414i	−0.151592	+	0.0664002i
$764$	−11.5080	+	19.9325i	−0.416345	+	0.721131i
$765$		0			0
$766$	−41.2988	−	71.5316i	−1.49219	−	2.58454i
$767$	7.90323	+	40.4247i	0.285369	+	1.45965i
$768$		0			0
$769$	−45.1851	−	26.0876i	−1.62942	−	0.940744i	−0.984267	−	0.176686i	$-0.943462\pi$
$769$	−45.1851	−	26.0876i	−1.62942	−	0.940744i	−0.645148	−	0.764057i	$-0.723204\pi$
$770$	−3.30077	+	29.6814i	−0.118951	+	1.06964i
$771$		0			0
$772$	12.2909	+	7.09618i	0.442360	+	0.255397i
$773$	30.9221	+	17.8529i	1.11219	+	0.642123i	0.939396	−	0.342835i	$-0.111387\pi$
$773$	30.9221	+	17.8529i	1.11219	+	0.642123i	0.172794	+	0.984958i	$0.444721\pi$
$774$		0			0
$775$	21.7898	+	12.5804i	0.782714	+	0.451900i
$776$	54.1208	+	93.7400i	1.94282	+	3.36507i
$777$		0			0
$778$	56.9752	+	32.8947i	2.04266	+	1.17933i
$779$	14.1766	−	24.5545i	0.507928	−	0.879757i
$780$		0			0
$781$	1.82735	+	3.16506i	0.0653876	+	0.113255i
$782$	13.9206	−	8.03703i	0.497798	−	0.287404i
$783$		0			0
$784$	−18.1114	−	58.1175i	−0.646836	−	2.07563i
$785$			22.5760i			0.805770i
$786$		0			0
$787$	5.28813	+	3.05310i	0.188501	+	0.108831i	0.591281	−	0.806466i	$-0.298622\pi$
$787$	5.28813	+	3.05310i	0.188501	+	0.108831i	−0.402779	+	0.915297i	$0.631956\pi$
$788$	−18.9301	+	10.9293i	−0.674356	+	0.389339i
$789$		0			0
$790$	−12.9482	+	22.4270i	−0.460678	+	0.797918i
$791$	−9.11971	−	20.8203i	−0.324259	−	0.740283i
$792$		0			0
$793$	−6.92774	−	7.95204i	−0.246011	−	0.282385i
$794$	5.38296	+	9.32356i	0.191034	+	0.330881i
$795$		0			0
$796$	−0.965369	−	1.67207i	−0.0342166	−	0.0592649i
$797$	23.1149	+	40.0363i	0.818773	+	1.41816i	0.906586	+	0.422020i	$0.138679\pi$
$797$	23.1149	+	40.0363i	0.818773	+	1.41816i	−0.0878129	+	0.996137i	$0.527988\pi$
$798$		0			0
$799$	−2.85688	+	1.64942i	−0.101069	+	0.0583522i
$800$			20.4792i			0.724048i
$801$		0			0
$802$	25.3700	−	43.9422i	0.895847	−	1.55165i
$803$	−12.3121	−	21.3252i	−0.434484	−	0.752549i
$804$		0			0
$805$	−0.936218	+	8.41874i	−0.0329974	+	0.296722i
$806$	−95.9780	+	18.7642i	−3.38068	+	0.660939i
$807$		0			0
$808$			8.94415i			0.314654i
$809$	−39.2879			−1.38129			−0.690644	−	0.723195i	$-0.742673\pi$
$809$	−39.2879			−1.38129			−0.690644	+	0.723195i	$0.742673\pi$
$810$		0			0
$811$			6.90664i			0.242525i	0.992620	+	0.121262i	$0.0386943\pi$
$811$			6.90664i			0.242525i	−0.992620	+	0.121262i	$0.961306\pi$
$812$	26.8102	+	61.2077i	0.940855	+	2.14797i
$813$		0			0
$814$	−36.1015	−	20.8432i	−1.26536	−	0.730555i
$815$	−5.77917	+	10.0098i	−0.202436	+	0.350629i
$816$		0			0
$817$	−10.6998	+	6.17756i	−0.374340	+	0.216125i
$818$	−45.6466			−1.59600
$819$		0			0
$820$	−58.3622			−2.03810
$821$	1.65453	−	0.955244i	0.0577435	−	0.0333382i	−0.470850	−	0.882213i	$-0.656053\pi$
$821$	1.65453	−	0.955244i	0.0577435	−	0.0333382i	0.528594	+	0.848875i	$0.322719\pi$
$822$		0			0
$823$	0.789844	−	1.36805i	0.0275322	−	0.0476872i	−0.851931	−	0.523654i	$-0.824568\pi$
$823$	0.789844	−	1.36805i	0.0275322	−	0.0476872i	0.879463	+	0.475967i	$0.157902\pi$
$824$	69.4320	+	40.0866i	2.41878	+	1.39648i
$825$		0			0
$826$	77.7617	+	8.64760i	2.70567	+	0.300888i
$827$		−	32.5050i		−	1.13031i	−0.824985	−	0.565155i	$-0.808816\pi$
$827$		−	32.5050i		−	1.13031i	0.824985	−	0.565155i	$-0.191184\pi$
$828$		0			0
$829$	35.0538			1.21747			0.608735	−	0.793373i	$-0.291677\pi$
$829$	35.0538			1.21747			0.608735	+	0.793373i	$0.291677\pi$
$830$			11.2533i			0.390608i
$831$		0			0
$832$	−11.0937	−	12.7340i	−0.384606	−	0.441472i
$833$	−14.8399	+	16.0868i	−0.514172	+	0.557375i
$834$		0			0
$835$	14.4928	+	25.1023i	0.501544	+	0.868700i
$836$	−23.4063	+	40.5409i	−0.809523	+	1.40214i
$837$		0			0
$838$		−	77.3760i		−	2.67291i
$839$	−4.63746	+	2.67744i	−0.160103	+	0.0924354i	−0.577911	−	0.816100i	$-0.696132\pi$
$839$	−4.63746	+	2.67744i	−0.160103	+	0.0924354i	0.417808	+	0.908535i	$0.362798\pi$
$840$		0			0
$841$	0.0669890	+	0.116028i	0.00230997	+	0.00400098i
$842$	16.6354	+	28.8133i	0.573293	+	0.992973i
$843$		0			0
$844$	−17.6658	−	30.5981i	−0.608082	−	1.05323i
$845$	12.8664	−	16.5420i	0.442618	−	0.569063i
$846$		0			0
$847$	9.68515	+	1.07705i	0.332786	+	0.0370079i
$848$	31.5923	−	54.7195i	1.08488	−	1.87907i
$849$		0			0
$850$	16.8311	−	9.71744i	0.577302	−	0.333305i
$851$	−10.2397	−	5.91190i	−0.351013	−	0.202657i
$852$		0			0
$853$			49.6270i			1.69920i	0.527431	+	0.849598i	$0.323155\pi$
$853$			49.6270i			1.69920i	−0.527431	+	0.849598i	$0.676845\pi$
$854$	−18.3501	+	8.03771i	−0.627926	+	0.275045i
$855$		0			0
$856$	−31.0927	+	17.9514i	−1.06273	+	0.613566i
$857$	−2.94196	−	5.09563i	−0.100496	−	0.174063i	0.811393	−	0.584500i	$-0.198709\pi$
$857$	−2.94196	−	5.09563i	−0.100496	−	0.174063i	−0.911889	+	0.410437i	$0.865376\pi$
$858$		0			0
$859$	−21.6931	+	37.5735i	−0.740159	+	1.28199i	0.212264	+	0.977212i	$0.431916\pi$
$859$	−21.6931	+	37.5735i	−0.740159	+	1.28199i	−0.952423	+	0.304780i	$0.901417\pi$
$860$	22.0246	+	12.7159i	0.751033	+	0.433609i
$861$		0			0
$862$	−11.6106	−	20.1102i	−0.395460	−	0.684957i
$863$	26.9570	+	15.5636i	0.917626	+	0.529792i	0.882877	−	0.469604i	$-0.155603\pi$
$863$	26.9570	+	15.5636i	0.917626	+	0.529792i	0.0347490	+	0.999396i	$0.488937\pi$
$864$		0			0
$865$	17.8860	+	10.3265i	0.608142	+	0.351111i
$866$	−7.73558	−	4.46614i	−0.262866	−	0.151766i
$867$		0			0
$868$	−14.4035	+	129.520i	−0.488885	+	4.39620i
$869$	−14.5374	−	8.39318i	−0.493148	−	0.284719i
$870$		0			0
$871$	−36.9233	+	32.1672i	−1.25110	+	1.08994i
$872$	6.04001	+	10.4616i	0.204540	+	0.354274i
$873$		0			0
$874$	−9.46341	+	16.3911i	−0.320105	+	0.554438i
$875$	−3.48896	+	31.3738i	−0.117949	+	1.06063i
$876$		0			0
$877$		−	29.9106i		−	1.01001i	−0.863117	−	0.505004i	$-0.831491\pi$
$877$		−	29.9106i		−	1.01001i	0.863117	−	0.505004i	$-0.168509\pi$
$878$	−86.3413	−	49.8492i	−2.91388	−	1.68233i
$879$		0			0
$880$	37.9206			1.27830
$881$	−7.28477	+	12.6176i	−0.245430	+	0.425097i	−0.962252	−	0.272159i	$-0.912262\pi$
$881$	−7.28477	+	12.6176i	−0.245430	+	0.425097i	0.716822	+	0.697256i	$0.245596\pi$
$882$		0			0
$883$	48.9296			1.64661			0.823307	−	0.567597i	$-0.192127\pi$
$883$	48.9296			1.64661			0.823307	+	0.567597i	$0.192127\pi$
$884$	−17.1987	+	50.1249i	−0.578454	+	1.68588i
$885$		0			0
$886$			38.9324i			1.30796i
$887$	27.2951	+	47.2765i	0.916480	+	1.58739i	0.804719	+	0.593655i	$0.202316\pi$
$887$	27.2951	+	47.2765i	0.916480	+	1.58739i	0.111761	+	0.993735i	$0.464351\pi$
$888$		0			0
$889$	−4.89866	+	6.65761i	−0.164296	+	0.223289i
$890$	6.36000	−	3.67195i	0.213188	−	0.123084i
$891$		0			0
$892$	−91.9222	+	53.0713i	−3.07778	+	1.77696i
$893$	1.94215	−	3.36390i	0.0649916	−	0.112569i
$894$		0			0
$895$	−2.56909	−	1.48327i	−0.0858753	−	0.0495801i
$896$	11.9518	−	5.23512i	0.399281	−	0.174893i
$897$		0			0
$898$	−50.3787	+	87.2584i	−1.68116	+	2.91185i
$899$		−	56.2955i		−	1.87756i
$900$		0			0
$901$	−22.7169			−0.756810
$902$		−	53.9263i		−	1.79555i
$903$		0			0
$904$	−52.0172	+	30.0321i	−1.73007	+	0.998854i
$905$	4.60606	+	2.65931i	0.153111	+	0.0883985i
$906$		0			0
$907$	−22.7255			−0.754589			−0.377295	−	0.926093i	$-0.623146\pi$
$907$	−22.7255			−0.754589			−0.377295	+	0.926093i	$0.623146\pi$
$908$	−55.6584	+	32.1344i	−1.84709	+	1.06642i
$909$		0			0
$910$	−22.6710	−	32.7210i	−0.751537	−	1.08469i
$911$	42.2359			1.39934			0.699669	−	0.714467i	$-0.253331\pi$
$911$	42.2359			1.39934			0.699669	+	0.714467i	$0.253331\pi$
$912$		0			0
$913$	−7.29450			−0.241413
$914$	−18.0421	+	31.2498i	−0.596779	+	1.03365i
$915$		0			0
$916$	−32.2870	+	18.6409i	−1.06679	+	0.615912i
$917$	16.0082	−	21.7562i	0.528637	−	0.718453i
$918$		0			0
$919$	30.6940			1.01250			0.506251	−	0.862386i	$-0.331031\pi$
$919$	30.6940			1.01250			0.506251	+	0.862386i	$0.331031\pi$
$920$	22.3838			0.737971
$921$		0			0
$922$	−48.4890	+	83.9854i	−1.59690	+	2.76591i
$923$	−4.60780	−	1.58101i	−0.151668	−	0.0520396i
$924$		0			0
$925$	−12.3806	−	7.14797i	−0.407073	−	0.235024i
$926$	−8.74009	−	15.1383i	−0.287217	−	0.497474i
$927$		0			0
$928$	39.6819	−	22.9104i	1.30262	−	0.752070i
$929$		−	37.4250i		−	1.22787i	−0.789355	−	0.613936i	$-0.789585\pi$
$929$		−	37.4250i		−	1.22787i	0.789355	−	0.613936i	$-0.210415\pi$
$930$		0			0
$931$	5.66168	−	25.1409i	0.185554	−	0.823960i
$932$	−15.4463	−	26.7538i	−0.505961	−	0.876350i
$933$		0			0
$934$			13.0733i			0.427770i
$935$	−6.81684	−	11.8071i	−0.222935	−	0.386134i
$936$		0			0
$937$	44.3386			1.44848			0.724239	−	0.689549i	$-0.242191\pi$
$937$	44.3386			1.44848			0.724239	+	0.689549i	$0.242191\pi$
$938$	37.3210	+	85.2038i	1.21857	+	2.78200i
$939$		0			0
$940$	−7.99546			−0.260783
$941$	−23.8202	+	13.7526i	−0.776518	+	0.448323i	−0.835195	−	0.549954i	$-0.814645\pi$
$941$	−23.8202	+	13.7526i	−0.776518	+	0.448323i	0.0586770	+	0.998277i	$0.481312\pi$
$942$		0			0
$943$		−	15.2955i		−	0.498089i
$944$		−	99.3472i		−	3.23348i
$945$		0			0
$946$	−11.7494	+	20.3506i	−0.382007	+	0.661656i
$947$	−4.40226	+	2.54165i	−0.143054	+	0.0825925i	−0.569819	−	0.821770i	$-0.692987\pi$
$947$	−4.40226	+	2.54165i	−0.143054	+	0.0825925i	0.426765	+	0.904363i	$0.359653\pi$
$948$		0			0
$949$	31.0459	+	10.6524i	1.00779	+	0.345790i
$950$	−11.4420	+	19.8182i	−0.371229	+	0.642987i
$951$		0			0
$952$	46.5834	+	34.2760i	1.50978	+	1.11089i
$953$	−4.90718	−	8.49949i	−0.158959	−	0.275326i	0.775534	−	0.631305i	$-0.217481\pi$
$953$	−4.90718	−	8.49949i	−0.158959	−	0.275326i	−0.934494	+	0.355980i	$0.884147\pi$
$954$		0			0
$955$	6.83540	+	3.94642i	0.221188	+	0.127703i
$956$	−38.2388	−	22.0772i	−1.23673	−	0.714027i
$957$		0			0
$958$	−12.2353	−	21.1921i	−0.395303	−	0.684685i
$959$	−21.2946	−	15.6686i	−0.687640	−	0.505964i
$960$		0			0
$961$	39.3947	−	68.2336i	1.27080	−	2.20108i
$962$	54.5332	−	10.6615i	1.75822	−	0.343741i
$963$		0			0
$964$	41.0601	−	23.7060i	1.32246	−	0.763520i
$965$	2.43348	−	4.21490i	0.0783364	−	0.135683i
$966$		0			0
$967$			2.69619i			0.0867036i	0.999060	+	0.0433518i	$0.0138036\pi$
$967$			2.69619i			0.0867036i	−0.999060	+	0.0433518i	$0.986196\pi$
$968$		−	25.7509i		−	0.827665i
$969$		0			0
$970$	55.9504	−	32.3030i	1.79646	−	1.03719i
$971$	−24.9240			−0.799850			−0.399925	−	0.916548i	$-0.630964\pi$
$971$	−24.9240			−0.799850			−0.399925	+	0.916548i	$0.630964\pi$
$972$		0			0
$973$	1.76659	+	4.03313i	0.0566344	+	0.129296i
$974$	103.543			3.31773
$975$		0			0
$976$	12.7187	+	22.0294i	0.407115	+	0.705144i
$977$		−	28.3129i		−	0.905811i	−0.891558	−	0.452906i	$-0.850387\pi$
$977$		−	28.3129i		−	0.905811i	0.891558	−	0.452906i	$-0.149613\pi$
$978$		0			0
$979$	2.38019	+	4.12262i	0.0760713	+	0.131759i
$980$	−50.6440	+	15.7824i	−1.61776	+	0.504150i
$981$		0			0
$982$		−	17.5015i		−	0.558494i
$983$	−32.7805	+	18.9258i	−1.04554	+	0.603641i	−0.921396	−	0.388624i	$-0.872951\pi$
$983$	−32.7805	+	18.9258i	−1.04554	+	0.603641i	−0.124140	+	0.992265i	$0.539617\pi$
$984$		0			0
$985$	3.74795	+	6.49165i	0.119420	+	0.206841i
$986$	−37.6585	−	21.7421i	−1.19929	−	0.692410i
$987$		0			0
$988$	−11.9725	−	61.2391i	−0.380897	−	1.94827i
$989$	−3.33257	+	5.77218i	−0.105970	+	0.183545i
$990$		0			0
$991$	58.4158			1.85564			0.927820	−	0.373028i	$-0.121681\pi$
$991$	58.4158			1.85564			0.927820	+	0.373028i	$0.121681\pi$
$992$	89.3612			2.83722
$993$		0			0
$994$	−5.48410	+	7.45327i	−0.173945	+	0.236403i
$995$	−0.573399	+	0.331052i	−0.0181780	+	0.0104950i
$996$		0			0
$997$	−14.0294	+	24.2997i	−0.444316	+	0.769578i	−0.998004	−	0.0631462i	$-0.979887\pi$
$997$	−14.0294	+	24.2997i	−0.444316	+	0.769578i	0.553688	+	0.832724i	$0.313220\pi$
$998$	29.4001			0.930645
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.do.e.667.6		12
3.2	odd	2		91.2.u.b.30.1	yes	12
7.4	even	3		819.2.bm.f.550.6		12
13.10	even	6		819.2.bm.f.478.1		12
21.2	odd	6		637.2.q.g.589.6		12
21.5	even	6		637.2.q.i.589.6		12
21.11	odd	6		91.2.k.b.4.1	✓	12
21.17	even	6		637.2.k.i.459.1		12
21.20	even	2		637.2.u.g.30.1		12
39.20	even	12		1183.2.e.j.170.1		24
39.23	odd	6		91.2.k.b.23.6	yes	12
39.32	even	12		1183.2.e.j.170.12		24
91.88	even	6	inner	819.2.do.e.361.6		12
273.23	odd	6		637.2.q.g.491.6		12
273.32	even	12		1183.2.e.j.508.12		24
273.62	even	6		637.2.k.i.569.6		12
273.101	even	6		637.2.u.g.361.1		12
273.110	odd	12		8281.2.a.co.1.1		12
273.137	even	12		1183.2.e.j.508.1		24
273.149	even	12		8281.2.a.cp.1.1		12
273.179	odd	6		91.2.u.b.88.1	yes	12
273.215	odd	12		8281.2.a.co.1.12		12
273.254	even	12		8281.2.a.cp.1.12		12
273.257	even	6		637.2.q.i.491.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.k.b.4.1	✓	12	21.11	odd	6
91.2.k.b.23.6	yes	12	39.23	odd	6
91.2.u.b.30.1	yes	12	3.2	odd	2
91.2.u.b.88.1	yes	12	273.179	odd	6
637.2.k.i.459.1		12	21.17	even	6
637.2.k.i.569.6		12	273.62	even	6
637.2.q.g.491.6		12	273.23	odd	6
637.2.q.g.589.6		12	21.2	odd	6
637.2.q.i.491.6		12	273.257	even	6
637.2.q.i.589.6		12	21.5	even	6
637.2.u.g.30.1		12	21.20	even	2
637.2.u.g.361.1		12	273.101	even	6
819.2.bm.f.478.1		12	13.10	even	6
819.2.bm.f.550.6		12	7.4	even	3
819.2.do.e.361.6		12	91.88	even	6	inner
819.2.do.e.667.6		12	1.1	even	1	trivial
1183.2.e.j.170.1		24	39.20	even	12
1183.2.e.j.170.12		24	39.32	even	12
1183.2.e.j.508.1		24	273.137	even	12
1183.2.e.j.508.12		24	273.32	even	12
8281.2.a.co.1.1		12	273.110	odd	12
8281.2.a.co.1.12		12	273.215	odd	12
8281.2.a.cp.1.1		12	273.149	even	12
8281.2.a.cp.1.12		12	273.254	even	12

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:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.do (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.24179 - 1.29430i) q^{2} +(2.35043 - 4.07106i) q^{4} +(-1.39608 - 0.806027i) q^{5} +(2.62954 + 0.292422i) q^{7} -6.99143i q^{8} +O(q^{10})\)	\(q+(2.24179 - 1.29430i) q^{2} +(2.35043 - 4.07106i) q^{4} +(-1.39608 - 0.806027i) q^{5} +(2.62954 + 0.292422i) q^{7} -6.99143i q^{8} -4.17296 q^{10} -2.70496i q^{11} +(2.36840 + 2.71858i) q^{13} +(6.27337 - 2.74787i) q^{14} +(-4.34816 - 7.53123i) q^{16} +(-1.56330 + 2.70772i) q^{17} -3.68150i q^{19} +(-6.56276 + 3.78901i) q^{20} +(-3.50103 - 6.06396i) q^{22} +(-0.993019 - 1.71996i) q^{23} +(-1.20064 - 2.07957i) q^{25} +(8.82813 + 3.02907i) q^{26} +(7.37101 - 10.0177i) q^{28} +(-2.68636 + 4.65290i) q^{29} +(-9.07425 + 5.23902i) q^{31} +(-7.38583 - 4.26421i) q^{32} +8.09354i q^{34} +(-3.43535 - 2.52773i) q^{35} +(5.15585 - 2.97673i) q^{37} +(-4.76497 - 8.25317i) q^{38} +(-5.63528 + 9.76059i) q^{40} +(6.66970 + 3.85075i) q^{41} +(-1.67800 - 2.90638i) q^{43} +(-11.0120 - 6.35780i) q^{44} +(-4.45229 - 2.57053i) q^{46} +(0.913730 + 0.527542i) q^{47} +(6.82898 + 1.53787i) q^{49} +(-5.38318 - 3.10798i) q^{50} +(16.6343 - 3.25208i) q^{52} +(3.63284 + 6.29226i) q^{53} +(-2.18027 + 3.77633i) q^{55} +(2.04445 - 18.3843i) q^{56} +13.9078i q^{58} +(9.89352 + 5.71203i) q^{59} -2.92507 q^{61} +(-13.5617 + 23.4896i) q^{62} -4.68406 q^{64} +(-1.11523 - 5.70435i) q^{65} +13.5818i q^{67} +(7.34886 + 12.7286i) q^{68} +(-10.9730 - 1.22027i) q^{70} +(-1.17009 + 0.675554i) q^{71} +(7.88374 - 4.55168i) q^{73} +(7.70557 - 13.3464i) q^{74} +(-14.9876 - 8.65311i) q^{76} +(0.790989 - 7.11280i) q^{77} +(3.10289 - 5.37436i) q^{79} +14.0189i q^{80} +19.9361 q^{82} -2.69672i q^{83} +(4.36499 - 2.52013i) q^{85} +(-7.52346 - 4.34367i) q^{86} -18.9115 q^{88} +(-1.52410 + 0.879938i) q^{89} +(5.43284 + 7.84119i) q^{91} -9.33607 q^{92} +2.73119 q^{94} +(-2.96739 + 5.13967i) q^{95} +(-13.4078 + 7.74102i) q^{97} +(17.2996 - 5.39116i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{4} - 3 q^{5} + 3 q^{7}+O(q^{10}) \) 12 * q + 4 * q^4 - 3 * q^5 + 3 * q^7	\( 12 q + 4 q^{4} - 3 q^{5} + 3 q^{7} - 24 q^{10} - 2 q^{13} - 4 q^{14} - 8 q^{16} - 17 q^{17} + 3 q^{20} - 15 q^{22} - 3 q^{23} - 5 q^{25} + 9 q^{26} + 27 q^{28} + q^{29} - 18 q^{31} - 18 q^{32} - 18 q^{35} + 15 q^{37} - 19 q^{38} - q^{40} + 6 q^{41} + 11 q^{43} - 33 q^{44} - 30 q^{46} - 15 q^{47} + 9 q^{49} - 18 q^{50} + 47 q^{52} + 8 q^{53} - 15 q^{55} - 27 q^{59} - 10 q^{61} - 41 q^{62} + 2 q^{64} + 3 q^{65} + 11 q^{68} - 3 q^{70} - 30 q^{71} - 42 q^{73} + 33 q^{74} - 45 q^{76} + 19 q^{77} - 35 q^{79} - 10 q^{82} - 21 q^{85} - 57 q^{86} + 28 q^{88} - 48 q^{89} - 16 q^{91} + 66 q^{92} - 2 q^{94} - 2 q^{95} - 3 q^{97} + 36 q^{98}+O(q^{100}) \) 12 * q + 4 * q^4 - 3 * q^5 + 3 * q^7 - 24 * q^10 - 2 * q^13 - 4 * q^14 - 8 * q^16 - 17 * q^17 + 3 * q^20 - 15 * q^22 - 3 * q^23 - 5 * q^25 + 9 * q^26 + 27 * q^28 + q^29 - 18 * q^31 - 18 * q^32 - 18 * q^35 + 15 * q^37 - 19 * q^38 - q^40 + 6 * q^41 + 11 * q^43 - 33 * q^44 - 30 * q^46 - 15 * q^47 + 9 * q^49 - 18 * q^50 + 47 * q^52 + 8 * q^53 - 15 * q^55 - 27 * q^59 - 10 * q^61 - 41 * q^62 + 2 * q^64 + 3 * q^65 + 11 * q^68 - 3 * q^70 - 30 * q^71 - 42 * q^73 + 33 * q^74 - 45 * q^76 + 19 * q^77 - 35 * q^79 - 10 * q^82 - 21 * q^85 - 57 * q^86 + 28 * q^88 - 48 * q^89 - 16 * q^91 + 66 * q^92 - 2 * q^94 - 2 * q^95 - 3 * q^97 + 36 * q^98

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