LMFDB - Embedded newform 819.2.bm.f.478.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(478,819)]

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, 2, 5]))

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

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

chi := DirichletCharacter("819.478");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.bm (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			478.1
Root			$1.32725 - 0.488273i$ of defining polynomial
Character	$\chi$	$=$	819.478
Dual form			819.2.bm.f.550.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.58860i q^{2} -4.70085 q^{4} +(1.39608 + 0.806027i) q^{5} +(1.06153 + 2.42346i) q^{7} +6.99143i q^{8} +O(q^{10})$	\(q-2.58860i q^{2} -4.70085 q^{4} +(1.39608 + 0.806027i) q^{5} +(1.06153 + 2.42346i) q^{7} +6.99143i q^{8} +(2.08648 - 3.61389i) q^{10} +(-2.34256 - 1.35248i) q^{11} +(2.36840 - 2.71858i) q^{13} +(6.27337 - 2.74787i) q^{14} +8.69632 q^{16} +3.12661 q^{17} +(3.18828 - 1.84075i) q^{19} +(-6.56276 - 3.78901i) q^{20} +(-3.50103 + 6.06396i) q^{22} +1.98604 q^{23} +(-1.20064 - 2.07957i) q^{25} +(-7.03732 - 6.13084i) q^{26} +(-4.99008 - 11.3923i) q^{28} +(-2.68636 - 4.65290i) q^{29} +(9.07425 - 5.23902i) q^{31} -8.52843i q^{32} -8.09354i q^{34} +(-0.471400 + 4.23896i) q^{35} -5.95346i q^{37} +(-4.76497 - 8.25317i) q^{38} +(-5.63528 + 9.76059i) q^{40} +(6.66970 - 3.85075i) q^{41} +(-1.67800 + 2.90638i) q^{43} +(11.0120 + 6.35780i) q^{44} -5.14106i q^{46} +(-0.913730 - 0.527542i) q^{47} +(-4.74633 + 5.14513i) q^{49} +(-5.38318 + 3.10798i) q^{50} +(-11.1335 + 12.7796i) q^{52} +(3.63284 + 6.29226i) q^{53} +(-2.18027 - 3.77633i) q^{55} +(-16.9435 + 7.42158i) q^{56} +(-12.0445 + 6.95390i) q^{58} +11.4241i q^{59} +(1.46254 + 2.53319i) q^{61} +(-13.5617 - 23.4896i) q^{62} -4.68406 q^{64} +(5.49772 - 1.88636i) q^{65} +(11.7622 + 6.79091i) q^{67} -14.6977 q^{68} +(10.9730 + 1.22027i) q^{70} +(-1.17009 - 0.675554i) q^{71} +(-7.88374 + 4.55168i) q^{73} -15.4111 q^{74} +(-14.9876 + 8.65311i) q^{76} +(0.790989 - 7.11280i) q^{77} +(3.10289 - 5.37436i) q^{79} +(12.1407 + 7.00946i) q^{80} +(-9.96806 - 17.2652i) q^{82} +2.69672i q^{83} +(4.36499 + 2.52013i) q^{85} +(7.52346 + 4.34367i) q^{86} +(9.45576 - 16.3779i) q^{88} +1.75988i q^{89} +(9.10249 + 2.85388i) q^{91} -9.33607 q^{92} +(-1.36560 + 2.36528i) q^{94} +5.93478 q^{95} +(-13.4078 - 7.74102i) q^{97} +(13.3187 + 12.2863i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 8 q^{4} + 3 q^{5} - 3 q^{7}+O(q^{10}) $ 12 * q - 8 * q^4 + 3 * q^5 - 3 * q^7	$ 12 q - 8 q^{4} + 3 q^{5} - 3 q^{7} + 12 q^{10} - 12 q^{11} - 2 q^{13} - 4 q^{14} + 16 q^{16} + 34 q^{17} + 9 q^{19} + 3 q^{20} - 15 q^{22} + 6 q^{23} - 5 q^{25} + 6 q^{26} - 9 q^{28} + q^{29} + 18 q^{31} + 6 q^{35} - 19 q^{38} - q^{40} + 6 q^{41} + 11 q^{43} + 33 q^{44} + 15 q^{47} - 3 q^{49} - 18 q^{50} - 7 q^{52} + 8 q^{53} - 15 q^{55} - 27 q^{56} - 24 q^{58} + 5 q^{61} - 41 q^{62} + 2 q^{64} - 21 q^{65} + 15 q^{67} - 22 q^{68} + 3 q^{70} - 30 q^{71} + 42 q^{73} - 66 q^{74} - 45 q^{76} + 19 q^{77} - 35 q^{79} + 63 q^{80} + 5 q^{82} - 21 q^{85} + 57 q^{86} - 14 q^{88} - 7 q^{91} + 66 q^{92} + q^{94} + 4 q^{95} - 3 q^{97} + 18 q^{98}+O(q^{100}) $ 12 * q - 8 * q^4 + 3 * q^5 - 3 * q^7 + 12 * q^10 - 12 * q^11 - 2 * q^13 - 4 * q^14 + 16 * q^16 + 34 * q^17 + 9 * q^19 + 3 * q^20 - 15 * q^22 + 6 * q^23 - 5 * q^25 + 6 * q^26 - 9 * q^28 + q^29 + 18 * q^31 + 6 * q^35 - 19 * q^38 - q^40 + 6 * q^41 + 11 * q^43 + 33 * q^44 + 15 * q^47 - 3 * q^49 - 18 * q^50 - 7 * q^52 + 8 * q^53 - 15 * q^55 - 27 * q^56 - 24 * q^58 + 5 * q^61 - 41 * q^62 + 2 * q^64 - 21 * q^65 + 15 * q^67 - 22 * q^68 + 3 * q^70 - 30 * q^71 + 42 * q^73 - 66 * q^74 - 45 * q^76 + 19 * q^77 - 35 * q^79 + 63 * q^80 + 5 * q^82 - 21 * q^85 + 57 * q^86 - 14 * q^88 - 7 * q^91 + 66 * q^92 + q^94 + 4 * q^95 - 3 * q^97 + 18 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$92$	$379$	$703$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$		−	2.58860i		−	1.83042i	−0.402981	−	0.915209i	$-0.632026\pi$
$2$		−	2.58860i		−	1.83042i	0.402981	−	0.915209i	$-0.367974\pi$
$3$		0			0
$3$		0			0
$4$	−4.70085			−2.35043
$5$	1.39608	+	0.806027i	0.624346	+	0.360466i	0.778559	−	0.627571i	$-0.215951\pi$
$5$	1.39608	+	0.806027i	0.624346	+	0.360466i	−0.154213	+	0.988038i	$0.549284\pi$
$6$		0			0
$7$	1.06153	+	2.42346i	0.401219	+	0.915982i
$7$	1.06153	+	2.42346i	0.401219	+	0.915982i
$8$			6.99143i			2.47184i
$9$		0			0
$10$	2.08648	−	3.61389i	0.659803	−	1.14281i
$11$	−2.34256	−	1.35248i	−0.706309	−	0.407788i	0.103384	−	0.994642i	$-0.467033\pi$
$11$	−2.34256	−	1.35248i	−0.706309	−	0.407788i	−0.809693	+	0.586854i	$0.800366\pi$
$12$		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
$16$	8.69632			2.17408
$17$	3.12661			0.758314			0.379157	−	0.925332i	$-0.376214\pi$
$17$	3.12661			0.758314			0.379157	+	0.925332i	$0.376214\pi$
$18$		0			0
$19$	3.18828	−	1.84075i	0.731441	−	0.422297i	−0.0875083	−	0.996164i	$-0.527890\pi$
$19$	3.18828	−	1.84075i	0.731441	−	0.422297i	0.818949	+	0.573866i	$0.194557\pi$
$20$	−6.56276	−	3.78901i	−1.46748	−	0.847249i
$21$		0			0
$22$	−3.50103	+	6.06396i	−0.746421	+	1.29284i
$23$	1.98604			0.414117			0.207059	−	0.978329i	$-0.433611\pi$
$23$	1.98604			0.414117			0.207059	+	0.978329i	$0.433611\pi$
$24$		0			0
$25$	−1.20064	−	2.07957i	−0.240128	−	0.415914i
$26$	−7.03732	−	6.13084i	−1.38013	−	1.20236i
$27$		0			0
$28$	−4.99008	−	11.3923i	−0.943036	−	2.15295i
$29$	−2.68636	−	4.65290i	−0.498844	−	0.864023i	0.501155	−	0.865357i	$-0.332908\pi$
$29$	−2.68636	−	4.65290i	−0.498844	−	0.864023i	−0.999999	+	0.00133469i	$0.999575\pi$
$30$		0			0
$31$	9.07425	−	5.23902i	1.62978	−	0.940956i	0.645627	−	0.763653i	$-0.276596\pi$
$31$	9.07425	−	5.23902i	1.62978	−	0.940956i	0.984156	−	0.177303i	$-0.0567372\pi$
$32$		−	8.52843i		−	1.50763i
$33$		0			0
$34$		−	8.09354i		−	1.38803i
$35$	−0.471400	+	4.23896i	−0.0796811	+	0.716515i
$36$		0			0
$37$		−	5.95346i		−	0.978743i	−0.872075	−	0.489371i	$-0.837226\pi$
$37$		−	5.95346i		−	0.978743i	0.872075	−	0.489371i	$-0.162774\pi$
$38$	−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	0.121337	−	0.992611i	$-0.461282\pi$
$41$	6.66970	−	3.85075i	1.04163	−	0.601386i	0.920295	+	0.391225i	$0.127949\pi$
$42$		0			0
$43$	−1.67800	+	2.90638i	−0.255892	+	0.443219i	−0.965138	−	0.261743i	$-0.915703\pi$
$43$	−1.67800	+	2.90638i	−0.255892	+	0.443219i	0.709245	+	0.704962i	$0.249036\pi$
$44$	11.0120	+	6.35780i	1.66013	+	0.958475i
$45$		0			0
$46$		−	5.14106i		−	0.758008i
$47$	−0.913730	−	0.527542i	−0.133281	−	0.0769500i	0.431877	−	0.901933i	$-0.357852\pi$
$47$	−0.913730	−	0.527542i	−0.133281	−	0.0769500i	−0.565158	+	0.824983i	$0.691185\pi$
$48$		0			0
$49$	−4.74633	+	5.14513i	−0.678046	+	0.735019i
$50$	−5.38318	+	3.10798i	−0.761297	+	0.439535i
$51$		0			0
$52$	−11.1335	+	12.7796i	−1.54394	+	1.77222i
$53$	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
$56$	−16.9435	+	7.42158i	−2.26416	+	0.991751i
$57$		0			0
$58$	−12.0445	+	6.95390i	−1.58152	+	0.913092i
$59$			11.4241i			1.48729i	0.668577	+	0.743643i	$0.266904\pi$
$59$			11.4241i			1.48729i	−0.668577	+	0.743643i	$0.733096\pi$
$60$		0			0
$61$	1.46254	+	2.53319i	0.187259	+	0.324341i	0.944335	−	0.328985i	$-0.106706\pi$
$61$	1.46254	+	2.53319i	0.187259	+	0.324341i	−0.757077	+	0.653326i	$0.773373\pi$
$62$	−13.5617	−	23.4896i	−1.72234	−	2.98318i
$63$		0			0
$64$	−4.68406			−0.585507
$65$	5.49772	−	1.88636i	0.681909	−	0.233974i
$66$		0			0
$67$	11.7622	+	6.79091i	1.43698	+	0.829642i	0.997639	−	0.0686778i	$-0.0218780\pi$
$67$	11.7622	+	6.79091i	1.43698	+	0.829642i	0.439343	+	0.898320i	$0.355211\pi$
$68$	−14.6977			−1.78236
$69$		0			0
$70$	10.9730	+	1.22027i	1.31152	+	0.145850i
$71$	−1.17009	−	0.675554i	−0.138865	−	0.0801736i	0.428958	−	0.903324i	$-0.358881\pi$
$71$	−1.17009	−	0.675554i	−0.138865	−	0.0801736i	−0.567823	+	0.823151i	$0.692214\pi$
$72$		0			0
$73$	−7.88374	+	4.55168i	−0.922721	+	0.532733i	−0.884502	−	0.466536i	$-0.845502\pi$
$73$	−7.88374	+	4.55168i	−0.922721	+	0.532733i	−0.0382192	+	0.999269i	$0.512169\pi$
$74$	−15.4111			−1.79151
$75$		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	$0.0531532\pi$
$80$	12.1407	+	7.00946i	1.35738	+	0.783682i
$81$		0			0
$82$	−9.96806	−	17.2652i	−1.10079	−	1.90662i
$83$			2.69672i			0.296003i	0.988987	+	0.148002i	$0.0472841\pi$
$83$			2.69672i			0.296003i	−0.988987	+	0.148002i	$0.952716\pi$
$84$		0			0
$85$	4.36499	+	2.52013i	0.473450	+	0.273346i
$86$	7.52346	+	4.34367i	0.811275	+	0.468390i
$87$		0			0
$88$	9.45576	−	16.3779i	1.00799	−	1.74589i
$89$			1.75988i			0.186546i	0.995641	+	0.0932732i	$0.0297330\pi$
$89$			1.75988i			0.186546i	−0.995641	+	0.0932732i	$0.970267\pi$
$90$		0			0
$91$	9.10249	+	2.85388i	0.954200	+	0.299168i
$92$	−9.33607			−0.973353
$93$		0			0
$94$	−1.36560	+	2.36528i	−0.140851	+	0.243960i
$95$	5.93478			0.608896
$96$		0			0
$97$	−13.4078	−	7.74102i	−1.36136	−	0.785981i	−0.371555	−	0.928411i	$-0.621175\pi$
$97$	−13.4078	−	7.74102i	−1.36136	−	0.785981i	−0.989805	+	0.142430i	$0.954509\pi$
$98$	13.3187	+	12.2863i	1.34539	+	1.24111i
$99$		0			0
$100$	5.64404	+	9.77576i	0.564404	+	0.977576i
$101$	0.639651	−	1.10791i	0.0636477	−	0.110241i	−0.832446	−	0.554107i	$-0.813060\pi$
$101$	0.639651	−	1.10791i	0.0636477	−	0.110241i	0.896093	+	0.443866i	$0.146393\pi$
$102$		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
$107$	5.13525			0.496444			0.248222	−	0.968703i	$-0.420154\pi$
$107$	5.13525			0.496444			0.248222	+	0.968703i	$0.420154\pi$
$108$		0			0
$109$	1.49635	−	0.863916i	0.143324	−	0.0827481i	−0.426623	−	0.904429i	$-0.640297\pi$
$109$	1.49635	−	0.863916i	0.143324	−	0.0827481i	0.569947	+	0.821681i	$0.306964\pi$
$110$	−9.77542	+	5.64384i	−0.932050	+	0.538119i
$111$		0			0
$112$	9.23136	+	21.0752i	0.872282	+	1.99142i
$113$	−4.29556	+	7.44014i	−0.404093	+	0.699909i	−0.994215	−	0.107404i	$-0.965746\pi$
$113$	−4.29556	+	7.44014i	−0.404093	+	0.699909i	0.590123	+	0.807314i	$0.299079\pi$
$114$		0			0
$115$	2.77267	+	1.60080i	0.258552	+	0.149275i
$116$	12.6282	+	21.8726i	1.17250	+	2.03082i
$117$		0			0
$118$	29.5723			2.72235
$119$	3.31897	+	7.57721i	0.304250	+	0.694602i
$120$		0			0
$121$	−1.84160	−	3.18975i	−0.167419	−	0.289977i
$122$	6.55741	−	3.78592i	0.593680	−	0.342761i
$123$		0			0
$124$	−42.6567	+	24.6279i	−3.83069	+	2.21165i
$125$		−	11.9313i		−	1.06716i
$126$		0			0
$127$	−1.56206	−	2.70556i	−0.138610	−	0.240080i	0.788361	−	0.615214i	$-0.210930\pi$
$127$	−1.56206	−	2.70556i	−0.138610	−	0.240080i	−0.926971	+	0.375133i	$0.877597\pi$
$128$		−	4.93170i		−	0.435904i
$129$		0			0
$130$	−4.88303	−	14.2314i	−0.428270	−	1.24818i
$131$	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
$133$	7.84543	+	5.77266i	0.680285	+	0.500553i
$134$	17.5790	−	30.4476i	1.51859	−	2.63028i
$135$		0			0
$136$			21.8595i			1.87443i
$137$		−	9.99261i		−	0.853726i	−0.904316	−	0.426863i	$-0.859619\pi$
$137$		−	9.99261i		−	0.853726i	0.904316	−	0.426863i	$-0.140381\pi$
$138$		0			0
$139$	0.832100	−	1.44124i	0.0705778	−	0.122244i	−0.828577	−	0.559875i	$-0.810849\pi$
$139$	0.832100	−	1.44124i	0.0705778	−	0.122244i	0.899155	+	0.437631i	$0.144182\pi$
$140$	2.21598	−	19.9267i	0.187285	−	1.68412i
$141$		0			0
$142$	−1.74874	+	3.02891i	−0.146751	+	0.254180i
$143$	−9.22495	+	3.16523i	−0.771429	+	0.264690i
$144$		0			0
$145$		−	8.66110i		−	0.719265i
$146$	11.7825	+	20.4078i	0.975124	+	1.68897i
$147$		0			0
$148$			27.9863i			2.30046i
$149$	−17.1456	+	9.89902i	−1.40462	+	0.810959i	−0.994863	−	0.101234i	$-0.967721\pi$
$149$	−17.1456	+	9.89902i	−1.40462	+	0.810959i	−0.409760	+	0.912193i	$0.634387\pi$
$150$		0			0
$151$	−6.52544	+	3.76746i	−0.531033	+	0.306592i	−0.741437	−	0.671023i	$-0.765855\pi$
$151$	−6.52544	+	3.76746i	−0.531033	+	0.306592i	0.210404	+	0.977614i	$0.432522\pi$
$152$	12.8695	+	22.2906i	1.04385	+	1.80801i
$153$		0			0
$154$	−18.4122	−	2.04755i	−1.48370	−	0.164997i
$155$	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	$-0.355420\pi$
$158$	−13.9121	−	8.03214i	−1.10679	−	0.639003i
$159$		0			0
$160$	6.87414	−	11.9064i	0.543448	−	0.941280i
$161$	2.10823	+	4.81308i	0.166152	+	0.379324i
$162$		0			0
$163$	6.20936	−	3.58498i	0.486355	−	0.280797i	−0.236706	−	0.971581i	$-0.576068\pi$
$163$	6.20936	−	3.58498i	0.486355	−	0.280797i	0.723061	+	0.690784i	$0.242735\pi$
$164$	−31.3533	+	18.1018i	−2.44828	+	1.41351i
$165$		0			0
$166$	6.98072			0.541809
$167$	−15.5716	+	8.99027i	−1.20497	+	0.695688i	−0.961656	−	0.274260i	$-0.911567\pi$
$167$	−15.5716	+	8.99027i	−1.20497	+	0.695688i	−0.243312	+	0.969948i	$0.578234\pi$
$168$		0			0
$169$	−1.78135	−	12.8774i	−0.137027	−	0.990567i
$170$	6.52361	−	11.2992i	0.500338	−	0.866611i
$171$		0			0
$172$	7.88803	−	13.6625i	0.601456	−	1.04175i
$173$	6.40579	+	11.0952i	0.487023	+	0.843549i	0.999889	−	0.0149198i	$-0.00474930\pi$
$173$	6.40579	+	11.0952i	0.487023	+	0.843549i	−0.512865	+	0.858469i	$0.671416\pi$
$174$		0			0
$175$	3.76525	−	5.11723i	0.284626	−	0.386826i
$176$	−20.3717	−	11.7616i	−1.53557	−	0.886562i
$177$		0			0
$178$	4.55561			0.341458
$179$	−0.920110	+	1.59368i	−0.0687723	+	0.119117i	−0.898361	−	0.439258i	$-0.855242\pi$
$179$	−0.920110	+	1.59368i	−0.0687723	+	0.119117i	0.829589	+	0.558375i	$0.188575\pi$
$180$		0			0
$181$	−3.29928			−0.245234			−0.122617	−	0.992454i	$-0.539129\pi$
$181$	−3.29928			−0.245234			−0.122617	+	0.992454i	$0.539129\pi$
$182$	7.38757	−	23.5627i	0.547603	−	1.74658i
$183$		0			0
$184$			13.8852i			1.02363i
$185$	4.79865	−	8.31150i	0.352804	−	0.611074i
$186$		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
$191$	2.44807	+	4.24018i	0.177136	+	0.306809i	0.940898	−	0.338689i	$-0.109983\pi$
$191$	2.44807	+	4.24018i	0.177136	+	0.306809i	−0.763762	+	0.645498i	$0.776650\pi$
$192$		0			0
$193$	2.61462	+	1.50955i	0.188204	+	0.108660i	0.591142	−	0.806568i	$-0.298677\pi$
$193$	2.61462	+	1.50955i	0.188204	+	0.108660i	−0.402937	+	0.915228i	$0.632011\pi$
$194$	−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	−0.636546	−	0.771238i	$-0.719638\pi$
$197$	−4.02694	+	2.32496i	−0.286908	+	0.165646i	0.349639	+	0.936885i	$0.386304\pi$
$198$		0			0
$199$	−0.410721			−0.0291152			−0.0145576	−	0.999894i	$-0.504634\pi$
$199$	−0.410721			−0.0291152			−0.0145576	+	0.999894i	$0.504634\pi$
$200$	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
$205$	12.4152			0.867118
$206$	25.7074	+	14.8422i	1.79112	+	1.03410i
$207$		0			0
$208$	20.5964	−	23.6416i	1.42810	−	1.63925i
$209$	−9.95831			−0.688831
$210$		0			0
$211$	3.75800	+	6.50905i	0.258711	+	0.448101i	0.965897	−	0.258927i	$-0.0833688\pi$
$211$	3.75800	+	6.50905i	0.258711	+	0.448101i	−0.707186	+	0.707028i	$0.750035\pi$
$212$	−17.0774	−	29.5790i	−1.17288	−	2.03149i
$213$		0			0
$214$		−	13.2931i		−	0.908699i
$215$	−4.68524	+	2.70502i	−0.319531	+	0.184481i
$216$		0			0
$217$	22.3291	+	16.4297i	1.51580	+	1.11532i
$218$	−2.23633	−	3.87344i	−0.151464	−	0.262343i
$219$		0			0
$220$	10.2491	+	17.7520i	0.690996	+	1.19684i
$221$	7.40506	−	8.49993i	0.498118	−	0.571767i
$222$		0			0
$223$	−19.5544	+	11.2897i	−1.30946	+	0.756016i	−0.982006	−	0.188852i	$-0.939523\pi$
$223$	−19.5544	+	11.2897i	−1.30946	+	0.756016i	−0.327452	+	0.944868i	$0.606190\pi$
$224$	20.6683	−	9.05315i	1.38096	−	0.604889i
$225$		0			0
$226$	19.2595	+	11.1195i	1.28113	+	0.739658i
$227$		−	13.6717i		−	0.907424i	−0.891148	−	0.453712i	$-0.850099\pi$
$227$		−	13.6717i		−	0.907424i	0.891148	−	0.453712i	$-0.149901\pi$
$228$		0			0
$229$	6.86832	+	3.96543i	0.453872	+	0.262043i	0.709464	−	0.704742i	$-0.248937\pi$
$229$	6.86832	+	3.96543i	0.453872	+	0.262043i	−0.255592	+	0.966785i	$0.582270\pi$
$230$	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
$236$		−	53.7028i		−	3.49576i
$237$		0			0
$238$	19.6144	−	8.59150i	1.27141	−	0.556904i
$239$			9.39284i			0.607572i	0.952740	+	0.303786i	$0.0982508\pi$
$239$			9.39284i			0.607572i	−0.952740	+	0.303786i	$0.901749\pi$
$240$		0			0
$241$			10.0858i			0.649686i	0.945768	+	0.324843i	$0.105311\pi$
$241$			10.0858i			0.649686i	−0.945768	+	0.324843i	$0.894689\pi$
$242$	−8.25699	+	4.76718i	−0.530780	+	0.306446i
$243$		0			0
$244$	−6.87517	−	11.9081i	−0.440137	−	0.762340i
$245$	−10.7734	+	3.35735i	−0.688285	+	0.214493i
$246$		0			0
$247$	2.54689	−	13.0272i	0.162054	−	0.828902i
$248$	36.6282	+	63.4420i	2.32590	+	4.02857i
$249$		0			0
$250$	−30.8853			−1.95336
$251$	5.17427	−	8.96209i	0.326597	−	0.565682i	−0.655237	−	0.755423i	$-0.727431\pi$
$251$	5.17427	−	8.96209i	0.326597	−	0.565682i	0.981834	+	0.189741i	$0.0607648\pi$
$252$		0			0
$253$	−4.65242	−	2.68607i	−0.292495	−	0.168872i
$254$	−7.00363	+	4.04355i	−0.439447	+	0.253715i
$255$		0			0
$256$	−22.1343			−1.38339
$257$	7.98658			0.498189			0.249095	−	0.968479i	$-0.419867\pi$
$257$	7.98658			0.498189			0.249095	+	0.968479i	$0.419867\pi$
$258$		0			0
$259$	14.4280	−	6.31975i	0.896511	−	0.392690i
$260$	−25.8440	+	8.86749i	−1.60278	+	0.549939i
$261$		0			0
$262$	−22.8869	−	13.2138i	−1.41396	−	0.816349i
$263$	2.52967	−	4.38152i	0.155986	−	0.270176i	−0.777431	−	0.628968i	$-0.783478\pi$
$263$	2.52967	−	4.38152i	0.155986	−	0.270176i	0.933418	+	0.358792i	$0.116811\pi$
$264$		0			0
$265$			11.7127i			0.719503i
$266$	14.9431	−	20.3087i	0.916220	−	1.24521i
$267$		0			0
$268$	−55.2924	−	31.9231i	−3.37752	−	1.95001i
$269$	−13.8902			−0.846902			−0.423451	−	0.905919i	$-0.639181\pi$
$269$	−13.8902			−0.846902			−0.423451	+	0.905919i	$0.639181\pi$
$270$		0			0
$271$			8.32721i			0.505842i	0.967487	+	0.252921i	$0.0813913\pi$
$271$			8.32721i			0.505842i	−0.967487	+	0.252921i	$0.918609\pi$
$272$	27.1900			1.64863
$273$		0			0
$274$	−25.8669			−1.56267
$275$			6.49537i			0.391685i
$276$		0			0
$277$	23.2116			1.39465			0.697325	−	0.716755i	$-0.254374\pi$
$277$	23.2116			1.39465			0.697325	+	0.716755i	$0.254374\pi$
$278$	−3.73080	−	2.15398i	−0.223758	−	0.129187i
$279$		0			0
$280$	−29.6364	−	3.29576i	−1.77111	−	0.196959i
$281$			27.1595i			1.62020i	0.586292	+	0.810100i	$0.300587\pi$
$281$			27.1595i			1.62020i	−0.586292	+	0.810100i	$0.699413\pi$
$282$		0			0
$283$	−8.07563	+	13.9874i	−0.480046	+	0.831464i	−0.999738	−	0.0228894i	$-0.992713\pi$
$283$	−8.07563	+	13.9874i	−0.480046	+	0.831464i	0.519692	+	0.854354i	$0.326047\pi$
$284$	5.50044	+	3.17568i	0.326391	+	0.188442i
$285$		0			0
$286$	8.19351	+	23.8797i	0.484493	+	1.41204i
$287$	16.4122	+	12.0761i	0.968782	+	0.712828i
$288$		0			0
$289$	−7.22433			−0.424960
$290$	−22.4201			−1.31656
$291$		0			0
$292$	37.0603	−	21.3968i	2.16879	−	1.25215i
$293$	12.6831	+	7.32260i	0.740956	+	0.427791i	0.822417	−	0.568885i	$-0.192625\pi$
$293$	12.6831	+	7.32260i	0.740956	+	0.427791i	−0.0814609	+	0.996677i	$0.525959\pi$
$294$		0			0
$295$	−9.20810	+	15.9489i	−0.536116	+	0.928580i
$296$	41.6232			2.41930
$297$		0			0
$298$	25.6246	+	44.3831i	1.48439	+	2.57104i
$299$	4.70373	−	5.39920i	0.272024	−	0.312244i
$300$		0			0
$301$	−8.82474	−	0.981368i	−0.508649	−	0.0565651i
$302$	9.75246	+	16.8918i	0.561191	+	0.972011i
$303$		0			0
$304$	27.7263	−	16.0078i	1.59021	−	0.918108i
$305$			4.71537i			0.270001i
$306$		0			0
$307$			8.97844i			0.512427i	0.966620	+	0.256213i	$0.0824750\pi$
$307$			8.97844i			0.512427i	−0.966620	+	0.256213i	$0.917525\pi$
$308$	−3.71832	+	33.4362i	−0.211871	+	1.90521i
$309$		0			0
$310$		−	43.7245i		−	2.48338i
$311$	−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	0.0349599	−	0.999389i	$-0.488870\pi$
$317$	−14.4761	−	8.35775i	−0.813056	−	0.469418i	−0.848016	+	0.529971i	$0.822203\pi$
$318$		0			0
$319$			14.5330i			0.813689i
$320$	−6.53932	−	3.77548i	−0.365559	−	0.211056i
$321$		0			0
$322$	12.4592	−	5.45737i	0.694321	−	0.304127i
$323$	9.96849	−	5.75531i	0.554661	−	0.320234i
$324$		0			0
$325$	−8.49708	−	1.66122i	−0.471333	−	0.0921480i
$326$	−9.28007	−	16.0736i	−0.513976	−	0.890232i
$327$		0			0
$328$	26.9223	+	46.6307i	1.48653	+	2.57475i
$329$	0.308530	−	2.77439i	0.0170098	−	0.152957i
$330$		0			0
$331$	−3.43522	+	1.98332i	−0.188817	+	0.109013i	−0.591428	−	0.806357i	$-0.701436\pi$
$331$	−3.43522	+	1.98332i	−0.188817	+	0.109013i	0.402612	+	0.915371i	$0.368102\pi$
$332$		−	12.6769i		−	0.695733i
$333$		0			0
$334$	23.2722	+	40.3087i	1.27340	+	2.20559i
$335$	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	$0.621750\pi$
$338$	−33.3344	+	4.61121i	−1.81315	+	0.250817i
$339$		0			0
$340$	−20.5192	−	11.8468i	−1.11281	−	0.642481i
$341$	−28.3426			−1.53484
$342$		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
$347$	26.3979			1.41711			0.708556	−	0.705655i	$-0.249347\pi$
$347$	26.3979			1.41711			0.708556	+	0.705655i	$0.249347\pi$
$348$		0			0
$349$	−4.23507	+	2.44512i	−0.226698	+	0.130884i	−0.609048	−	0.793133i	$-0.708448\pi$
$349$	−4.23507	+	2.44512i	−0.226698	+	0.130884i	0.382350	+	0.924018i	$0.375115\pi$
$350$	−13.2465	−	9.74673i	−0.708053	−	0.520984i
$351$		0			0
$352$	−11.5345	+	19.9784i	−0.614792	+	1.06485i
$353$	11.7413	+	6.77886i	0.624928	+	0.360802i	0.778785	−	0.627291i	$-0.215836\pi$
$353$	11.7413	+	6.77886i	0.624928	+	0.360802i	−0.153857	+	0.988093i	$0.549170\pi$
$354$		0			0
$355$	−1.08903	−	1.88626i	−0.0577997	−	0.100112i
$356$		−	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	0.290785	−	0.956789i	$-0.406084\pi$
$359$	−7.43541	−	4.29284i	−0.392426	−	0.226567i	−0.683211	+	0.730221i	$0.739417\pi$
$360$		0			0
$361$	−2.72326	+	4.71683i	−0.143330	+	0.248254i
$362$			8.54053i			0.448880i
$363$		0			0
$364$	−42.7895	−	13.4157i	−2.24278	−	0.703173i
$365$	−14.6751			−0.768130
$366$		0			0
$367$	0.831612	−	1.44039i	0.0434098	−	0.0751880i	−0.843504	−	0.537123i	$-0.819511\pi$
$367$	0.831612	−	1.44039i	0.0434098	−	0.0751880i	0.886914	+	0.461935i	$0.152845\pi$
$368$	17.2712			0.900324
$369$		0			0
$370$	−21.5152	−	12.4218i	−1.11852	−	0.645778i
$371$	−11.3927	+	15.4834i	−0.591479	+	0.803860i
$372$		0			0
$373$	−6.98174	−	12.0927i	−0.361501	−	0.626138i	0.626707	−	0.779255i	$-0.284402\pi$
$373$	−6.98174	−	12.0927i	−0.361501	−	0.626138i	−0.988208	+	0.153117i	$0.951069\pi$
$374$	−10.9463	+	18.9596i	−0.566022	+	0.980378i
$375$		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	−0.994864	−	0.101218i	$-0.967726\pi$
$379$	−27.3454	+	15.7879i	−1.40464	+	0.810969i	−0.409775	+	0.912187i	$0.634393\pi$
$380$	−27.8985			−1.43116
$381$		0			0
$382$	10.9761	−	6.33707i	0.561588	−	0.324233i
$383$	27.6333	−	15.9541i	1.41200	−	0.815217i	0.416420	−	0.909172i	$-0.363284\pi$
$383$	27.6333	−	15.9541i	1.41200	−	0.815217i	0.995576	+	0.0939554i	$0.0299511\pi$
$384$		0			0
$385$	6.83739	−	9.29247i	0.348466	−	0.473588i
$386$	3.90762	−	6.76820i	0.198893	−	0.344492i
$387$		0			0
$388$	63.0283	+	36.3894i	3.19978	+	1.84739i
$389$	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
$392$	−35.9718	−	33.1836i	−1.81685	−	1.67603i
$393$		0			0
$394$	6.01838	+	10.4241i	0.303202	+	0.525161i
$395$	8.66376	−	5.00203i	0.435921	−	0.251679i
$396$		0			0
$397$	−3.60178	+	2.07949i	−0.180768	+	0.104366i	−0.587653	−	0.809113i	$-0.699948\pi$
$397$	−3.60178	+	2.07949i	−0.180768	+	0.104366i	0.406885	+	0.913479i	$0.366615\pi$
$398$			1.06319i			0.0532930i
$399$		0			0
$400$	−10.4412	−	18.0846i	−0.522058	−	0.904231i
$401$		−	19.6013i		−	0.978844i	−0.872047	−	0.489422i	$-0.837208\pi$
$401$		−	19.6013i		−	0.978844i	0.872047	−	0.489422i	$-0.162792\pi$
$402$		0			0
$403$	7.24877	−	37.0772i	0.361087	−	1.84695i
$404$	−3.00691	+	5.20811i	−0.149599	+	0.259113i
$405$		0			0
$406$	−29.6381	−	21.8077i	−1.47091	−	1.08230i
$407$	−8.05193	+	13.9463i	−0.399119	+	0.691295i
$408$		0			0
$409$		−	17.6337i		−	0.871930i	−0.899964	−	0.435965i	$-0.856407\pi$
$409$		−	17.6337i		−	0.871930i	0.899964	−	0.435965i	$-0.143593\pi$
$410$		−	32.1381i		−	1.58719i
$411$		0			0
$412$	26.9532	−	46.6842i	1.32789	−	2.29997i
$413$	−27.6858	+	12.1269i	−1.36233	+	0.596727i
$414$		0			0
$415$	−2.17363	+	3.76483i	−0.106699	+	0.184808i
$416$	−23.1852	−	20.1987i	−1.13675	−	0.990324i
$417$		0			0
$418$			25.7781i			1.26085i
$419$	14.9455	+	25.8864i	0.730137	+	1.26463i	0.956824	+	0.290666i	$0.0938770\pi$
$419$	14.9455	+	25.8864i	0.730137	+	1.26463i	−0.226688	+	0.973968i	$0.572790\pi$
$420$		0			0
$421$		−	12.8528i		−	0.626407i	−0.949686	−	0.313203i	$-0.898598\pi$
$421$		−	12.8528i		−	0.626407i	0.949686	−	0.313203i	$-0.101402\pi$
$422$	16.8493	−	9.72796i	0.820212	−	0.473550i
$423$		0			0
$424$	−43.9919	+	25.3987i	−2.13644	+	1.23347i
$425$	−3.75393	−	6.50200i	−0.182093	−	0.315394i
$426$		0			0
$427$	−4.58656	+	6.23344i	−0.221959	+	0.301657i
$428$	−24.1401			−1.16685
$429$		0			0
$430$	7.00223	+	12.1282i	0.337677	+	0.584874i
$431$	−7.76876	−	4.48530i	−0.374208	−	0.216049i	0.301087	−	0.953597i	$-0.402650\pi$
$431$	−7.76876	−	4.48530i	−0.374208	−	0.216049i	−0.675295	+	0.737547i	$0.735984\pi$
$432$		0			0
$433$	−1.72531	+	2.98833i	−0.0829132	+	0.143610i	−0.904500	−	0.426473i	$-0.859756\pi$
$433$	−1.72531	+	2.98833i	−0.0829132	+	0.143610i	0.821587	+	0.570083i	$0.193089\pi$
$434$	42.5300	−	57.8012i	2.04151	−	2.77454i
$435$		0			0
$436$	−7.03410	+	4.06114i	−0.336872	+	0.194493i
$437$	6.33204	−	3.65580i	0.302902	−	0.174881i
$438$		0			0
$439$	38.5144			1.83819			0.919096	−	0.394034i	$-0.128921\pi$
$439$	38.5144			1.83819			0.919096	+	0.394034i	$0.128921\pi$
$440$	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
$445$	−1.41851	+	2.45693i	−0.0672437	+	0.116469i
$446$	29.2246	+	50.6185i	1.38382	+	2.39685i
$447$		0			0
$448$	−4.97225	−	11.3516i	−0.234917	−	0.536314i
$449$	−33.7087	−	19.4617i	−1.59081	−	0.918456i	−0.993168	−	0.116696i	$-0.962770\pi$
$449$	−33.7087	−	19.4617i	−1.59081	−	0.918456i	−0.597646	−	0.801760i	$-0.703897\pi$
$450$		0			0
$451$	−20.8322			−0.980952
$452$	20.1928	−	34.9750i	0.949790	−	1.64509i
$453$		0			0
$454$	−35.3906			−1.66097
$455$	10.4075	+	11.3211i	0.487911	+	0.530741i
$456$		0			0
$457$			13.9396i			0.652069i	0.945358	+	0.326034i	$0.105713\pi$
$457$			13.9396i			0.652069i	−0.945358	+	0.326034i	$0.894287\pi$
$458$	10.2649	−	17.7793i	0.479648	−	0.830774i
$459$		0			0
$460$	−13.0339	−	7.52512i	−0.607709	−	0.350861i
$461$	−32.4443	−	18.7317i	−1.51108	−	0.872424i	−0.999916	−	0.0129430i	$-0.995880\pi$
$461$	−32.4443	−	18.7317i	−1.51108	−	0.872424i	−0.511167	−	0.859481i	$-0.670787\pi$
$462$		0			0
$463$			6.75275i			0.313827i	0.987612	+	0.156913i	$0.0501544\pi$
$463$			6.75275i			0.313827i	−0.987612	+	0.156913i	$0.949846\pi$
$464$	−23.3614	−	40.4631i	−1.08453	−	1.87845i
$465$		0			0
$466$	−14.7324	−	8.50576i	−0.682466	−	0.394022i
$467$	−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
$472$	−79.8705			−3.67634
$473$	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
$478$	24.3143			1.11211
$479$	−8.18670	−	4.72659i	−0.374060	−	0.215964i	0.301171	−	0.953570i	$-0.402623\pi$
$479$	−8.18670	−	4.72659i	−0.374060	−	0.215964i	−0.675231	+	0.737607i	$0.735956\pi$
$480$		0			0
$481$	−16.1850	−	14.1002i	−0.737971	−	0.642913i
$482$	26.1082			1.18920
$483$		0			0
$484$	8.65711	+	14.9946i	0.393505	+	0.681571i
$485$	−12.4789	−	21.6142i	−0.566639	−	0.981448i
$486$		0			0
$487$			39.9996i			1.81255i	0.422684	+	0.906277i	$0.361088\pi$
$487$			39.9996i			1.81255i	−0.422684	+	0.906277i	$0.638912\pi$
$488$	−17.7106	+	10.2252i	−0.801721	+	0.462874i
$489$		0			0
$490$	8.69084	+	27.8879i	0.392612	+	1.25985i
$491$	3.38049	+	5.85517i	0.152559	+	0.264240i	0.932168	−	0.362027i	$-0.117915\pi$
$491$	3.38049	+	5.85517i	0.152559	+	0.264240i	−0.779608	+	0.626267i	$0.784582\pi$
$492$		0			0
$493$	−8.39918	−	14.5478i	−0.378280	−	0.655200i
$494$	−33.7223	−	6.59287i	−1.51724	−	0.296627i
$495$		0			0
$496$	78.9125	−	45.5602i	3.54328	−	2.04571i
$497$	0.395094	−	3.55280i	0.0177224	−	0.159365i
$498$		0			0
$499$	−9.83591	−	5.67877i	−0.440316	−	0.254217i	0.263416	−	0.964682i	$-0.415151\pi$
$499$	−9.83591	−	5.67877i	−0.440316	−	0.254217i	−0.703732	+	0.710466i	$0.748484\pi$
$500$			56.0871i			2.50829i
$501$		0			0
$502$	−23.1993	−	13.3941i	−1.03543	−	0.597808i
$503$	−6.96423	+	12.0624i	−0.310520	+	0.537836i	−0.978475	−	0.206365i	$-0.933836\pi$
$503$	−6.96423	+	12.0624i	−0.310520	+	0.537836i	0.667955	+	0.744202i	$0.267170\pi$
$504$		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
$509$			19.8149i			0.878281i	0.898418	+	0.439141i	$0.144717\pi$
$509$			19.8149i			0.878281i	−0.898418	+	0.439141i	$0.855283\pi$
$510$		0			0
$511$	−19.3996	−	14.2742i	−0.858188	−	0.631453i
$512$			47.4335i			2.09628i
$513$		0			0
$514$		−	20.6741i		−	0.911894i
$515$	−16.0093	+	9.24299i	−0.705455	+	0.407295i
$516$		0			0
$517$	1.42698	+	2.47160i	0.0627585	+	0.108701i
$518$	−16.3593	−	37.3483i	−0.718787	−	1.64099i
$519$		0			0
$520$	13.1883	+	38.4370i	0.578347	+	1.68557i
$521$	−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
$523$	22.7202			0.993485			0.496742	−	0.867898i	$-0.334529\pi$
$523$	22.7202			0.993485			0.496742	+	0.867898i	$0.334529\pi$
$524$	−23.9960	+	41.5622i	−1.04827	+	1.81565i
$525$		0			0
$526$	−11.3420	−	6.54831i	−0.494535	−	0.285520i
$527$	28.3716	−	16.3804i	1.23589	−	0.713540i
$528$		0			0
$529$	−19.0557			−0.828507
$530$	30.3194			1.31699
$531$		0			0
$532$	−36.8802	−	27.1364i	−1.59896	−	1.17651i
$533$	5.32794	−	27.2522i	0.230779	−	1.18043i
$534$		0			0
$535$	7.16922	+	4.13915i	0.309952	+	0.178951i
$536$	−47.4782	+	82.2346i	−2.05074	+	3.55199i
$537$		0			0
$538$			35.9563i			1.55018i
$539$	18.0772	−	5.63349i	0.778642	−	0.242651i
$540$		0			0
$541$	1.81754	+	1.04936i	0.0781423	+	0.0451155i	0.538562	−	0.842586i	$-0.318968\pi$
$541$	1.81754	+	1.04936i	0.0781423	+	0.0451155i	−0.460420	+	0.887701i	$0.652301\pi$
$542$	21.5558			0.925902
$543$		0			0
$544$		−	26.6650i		−	1.14325i
$545$	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	$0.317470\pi$
$548$			46.9738i			2.00662i
$549$		0			0
$550$	16.8139			0.716948
$551$	−17.1297	−	9.88983i	−0.729749	−	0.421321i
$552$		0			0
$553$	16.3184	+	1.81471i	0.693927	+	0.0771692i
$554$		−	60.0855i		−	2.55279i
$555$		0			0
$556$	−3.91158	+	6.77506i	−0.165888	+	0.287327i
$557$	38.3219	+	22.1252i	1.62375	+	0.937473i	0.985904	+	0.167309i	$0.0535078\pi$
$557$	38.3219	+	22.1252i	1.62375	+	0.937473i	0.637846	+	0.770164i	$0.279826\pi$
$558$		0			0
$559$	3.92705	+	11.4452i	0.166097	+	0.484082i
$560$	−4.09944	+	36.8634i	−0.173233	+	1.55776i
$561$		0			0
$562$	70.3051			2.96564
$563$	−38.8907			−1.63905			−0.819523	−	0.573046i	$-0.805762\pi$
$563$	−38.8907			−1.63905			−0.819523	+	0.573046i	$0.805762\pi$
$564$		0			0
$565$	−11.9939	+	6.92468i	−0.504587	+	0.291324i
$566$	36.2078	+	20.9046i	1.52193	+	0.878685i
$567$		0			0
$568$	4.72309	−	8.18063i	0.198177	−	0.343252i
$569$	46.1579			1.93504			0.967520	−	0.252796i	$-0.0813500\pi$
$569$	46.1579			1.93504			0.967520	+	0.252796i	$0.0813500\pi$
$570$		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	$0.687505\pi$
$572$	43.3651	−	14.8793i	1.81319	−	0.622134i
$573$		0			0
$574$	31.2601	−	42.4846i	1.30477	−	1.77327i
$575$	−2.38452	−	4.13011i	−0.0994413	−	0.172237i
$576$		0			0
$577$	21.9368	−	12.6652i	0.913239	−	0.527259i	0.0317671	−	0.999495i	$-0.489887\pi$
$577$	21.9368	−	12.6652i	0.913239	−	0.527259i	0.881472	+	0.472237i	$0.156553\pi$
$578$			18.7009i			0.777855i
$579$		0			0
$580$			40.7146i			1.69058i
$581$	−6.53539	+	2.86263i	−0.271133	+	0.118762i
$582$		0			0
$583$		−	19.6533i		−	0.813958i
$584$	−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	−0.562324	−	0.826917i	$-0.690092\pi$
$587$	−3.08554	+	1.78144i	−0.127354	+	0.0735278i	0.434970	+	0.900445i	$0.356759\pi$
$588$		0			0
$589$	19.2875	−	33.4069i	0.794727	−	1.37651i
$590$	41.2853	+	23.8361i	1.69969	+	0.981316i
$591$		0			0
$592$		−	51.7732i		−	2.12786i
$593$	−21.9568	−	12.6768i	−0.901659	−	0.520573i	−0.0239212	−	0.999714i	$-0.507615\pi$
$593$	−21.9568	−	12.6768i	−0.901659	−	0.520573i	−0.877738	+	0.479141i	$0.840948\pi$
$594$		0			0
$595$	−1.47388	+	13.2536i	−0.0604233	+	0.543343i
$596$	80.5990	−	46.5338i	3.30146	−	1.90610i
$597$		0			0
$598$	−13.9764	−	12.1761i	−0.571537	−	0.497917i
$599$	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	0.505262	−	0.862966i	$-0.331396\pi$
$601$	−12.1282	−	21.0067i	−0.494720	−	0.856880i	−0.999981	+	0.00608649i	$0.998063\pi$
$602$	−2.54037	+	22.8437i	−0.103538	+	0.931040i
$603$		0			0
$604$	30.6751	−	17.7103i	1.24815	−	0.720621i
$605$		−	5.93753i		−	0.241395i
$606$		0			0
$607$	4.92724	+	8.53422i	0.199990	+	0.346393i	0.948525	−	0.316702i	$-0.102576\pi$
$607$	4.92724	+	8.53422i	0.199990	+	0.346393i	−0.748535	+	0.663096i	$0.769242\pi$
$608$	−15.6987	−	27.1910i	−0.636667	−	1.10274i
$609$		0			0
$610$	12.2062			0.494215
$611$	−3.59825	+	1.23462i	−0.145569	+	0.0499472i
$612$		0			0
$613$	−3.18428	−	1.83844i	−0.128612	−	0.0742540i	0.434314	−	0.900762i	$-0.356991\pi$
$613$	−3.18428	−	1.83844i	−0.128612	−	0.0742540i	−0.562926	+	0.826508i	$0.690324\pi$
$614$	23.2416			0.937955
$615$		0			0
$616$	49.7286	+	5.53015i	2.00362	+	0.222816i
$617$	−16.2352	−	9.37341i	−0.653605	−	0.377359i	0.136231	−	0.990677i	$-0.456501\pi$
$617$	−16.2352	−	9.37341i	−0.653605	−	0.377359i	−0.789836	+	0.613318i	$0.789834\pi$
$618$		0			0
$619$	13.7650	−	7.94725i	0.553264	−	0.319427i	−0.197174	−	0.980369i	$-0.563176\pi$
$619$	13.7650	−	7.94725i	0.553264	−	0.319427i	0.750437	+	0.660942i	$0.229843\pi$
$620$	−79.4029			−3.18890
$621$		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
$626$	29.4212	+	16.9864i	1.17591	+	0.678911i
$627$		0			0
$628$	32.9165	+	57.0130i	1.31351	+	2.27507i
$629$		−	18.6141i		−	0.742194i
$630$		0			0
$631$	−17.0998	−	9.87255i	−0.680731	−	0.393020i	0.119400	−	0.992846i	$-0.461903\pi$
$631$	−17.0998	−	9.87255i	−0.680731	−	0.393020i	−0.800130	+	0.599826i	$0.795236\pi$
$632$	37.5745	+	21.6936i	1.49463	+	0.862927i
$633$		0			0
$634$	−21.6349	+	37.4727i	−0.859231	+	1.48823i
$635$		−	5.03624i		−	0.199857i
$636$		0			0
$637$	2.74625	+	25.0890i	0.108811	+	0.994063i
$638$	37.6200			1.48939
$639$		0			0
$640$	3.97508	−	6.88504i	0.157129	−	0.272155i
$641$	−29.7786			−1.17618			−0.588092	−	0.808794i	$-0.700121\pi$
$641$	−29.7786			−1.17618			−0.588092	+	0.808794i	$0.700121\pi$
$642$		0			0
$643$	10.0220	+	5.78623i	0.395231	+	0.228187i	0.684424	−	0.729084i	$-0.260054\pi$
$643$	10.0220	+	5.78623i	0.395231	+	0.228187i	−0.289193	+	0.957271i	$0.593387\pi$
$644$	−9.91048	−	22.6256i	−0.390528	−	0.891574i
$645$		0			0
$646$	−14.8982	−	25.8044i	−0.586162	−	1.01526i
$647$	−12.7533	+	22.0893i	−0.501382	+	0.868420i	0.498616	+	0.866823i	$0.333842\pi$
$647$	−12.7533	+	22.0893i	−0.501382	+	0.868420i	−0.999999	+	0.00159698i	$0.999492\pi$
$648$		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
$653$	44.8293			1.75430			0.877152	−	0.480212i	$-0.159440\pi$
$653$	44.8293			1.75430			0.877152	+	0.480212i	$0.159440\pi$
$654$		0			0
$655$	14.2529	−	8.22889i	0.556905	−	0.321529i
$656$	58.0018	−	33.4874i	2.26459	−	1.30746i
$657$		0			0
$658$	−7.18179	−	0.798661i	−0.279975	−	0.0311350i
$659$	20.5867	−	35.6572i	0.801944	−	1.38901i	−0.116390	−	0.993204i	$-0.537132\pi$
$659$	20.5867	−	35.6572i	0.801944	−	1.38901i	0.918335	−	0.395805i	$-0.129534\pi$
$660$		0			0
$661$	−18.9606	−	10.9469i	−0.737481	−	0.425785i	0.0836719	−	0.996493i	$-0.473335\pi$
$661$	−18.9606	−	10.9469i	−0.737481	−	0.425785i	−0.821153	+	0.570709i	$0.806669\pi$
$662$	5.13404	+	8.89241i	0.199540	+	0.345613i
$663$		0			0
$664$	−18.8539			−0.731673
$665$	6.29993	+	14.3827i	0.244301	+	0.557738i
$666$		0			0
$667$	−5.33520	−	9.24084i	−0.206580	−	0.357807i
$668$	73.1999	−	42.2620i	2.83219	−	1.63516i
$669$		0			0
$670$	49.0832	−	28.3382i	1.89625	−	1.09480i
$671$		−	7.91219i		−	0.305447i
$672$		0			0
$673$	17.8344	+	30.8901i	0.687466	+	1.19073i	0.972655	+	0.232254i	$0.0746102\pi$
$673$	17.8344	+	30.8901i	0.687466	+	1.19073i	−0.285189	+	0.958471i	$0.592056\pi$
$674$			35.4721i			1.36633i
$675$		0			0
$676$	8.37388	+	60.5347i	0.322072	+	2.32826i
$677$	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
$679$	4.52729	−	40.7107i	0.173741	−	1.56233i
$680$	−17.6193	+	30.5175i	−0.675670	+	1.17029i
$681$		0			0
$682$			73.3678i			2.80940i
$683$			35.7399i			1.36755i	0.729693	+	0.683775i	$0.239663\pi$
$683$			35.7399i			1.36755i	−0.729693	+	0.683775i	$0.760337\pi$
$684$		0			0
$685$	8.05431	−	13.9505i	0.307739	−	0.533020i
$686$	−15.6373	+	45.3196i	−0.597036	+	1.73031i
$687$		0			0
$688$	−14.5924	+	25.2748i	−0.556330	+	0.963592i
$689$	25.7100	+	5.02643i	0.979474	+	0.191492i
$690$		0			0
$691$		−	26.0292i		−	0.990197i	−0.868837	−	0.495099i	$-0.835132\pi$
$691$		−	26.0292i		−	0.990197i	0.868837	−	0.495099i	$-0.164868\pi$
$692$	−30.1127	−	52.1567i	−1.14471	−	1.98270i
$693$		0			0
$694$		−	68.3335i		−	2.59391i
$695$	2.32336	−	1.34139i	0.0881299	−	0.0508818i
$696$		0			0
$697$	20.8535	−	12.0398i	0.789884	−	0.456040i
$698$	6.32944	+	10.9629i	0.239573	+	0.414952i
$699$		0			0
$700$	−17.6999	+	24.0553i	−0.668993	+	0.909206i
$701$	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
$704$	10.9727	+	6.33509i	0.413549	+	0.238763i
$705$		0			0
$706$	17.5478	−	30.3936i	0.660419	−	1.14388i
$707$	3.36398	+	0.374096i	0.126515	+	0.0140693i
$708$		0			0
$709$	−5.23972	+	3.02515i	−0.196782	+	0.113612i	−0.595153	−	0.803612i	$-0.702909\pi$
$709$	−5.23972	+	3.02515i	−0.196782	+	0.113612i	0.398372	+	0.917224i	$0.369575\pi$
$710$	−4.88276	+	2.81906i	−0.183247	+	0.105798i
$711$		0			0
$712$	−12.3040			−0.461114
$713$	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
$718$	−11.1124	+	19.2473i	−0.414713	+	0.718304i
$719$	−23.5589	−	40.8052i	−0.878597	−	1.52178i	−0.852880	−	0.522106i	$-0.825146\pi$
$719$	−23.5589	−	40.8052i	−0.878597	−	1.52178i	−0.0257170	−	0.999669i	$-0.508187\pi$
$720$		0			0
$721$	−30.1539	−	3.35331i	−1.12299	−	0.124884i
$722$	12.2100	+	7.04944i	0.454409	+	0.262353i
$723$		0			0
$724$	15.5095			0.576404
$725$	−6.45070	+	11.1729i	−0.239573	+	0.414953i
$726$		0			0
$727$	17.9215			0.664671			0.332335	−	0.943161i	$-0.392163\pi$
$727$	17.9215			0.664671			0.332335	+	0.943161i	$0.392163\pi$
$728$	−19.9527	+	63.6394i	−0.739498	+	2.35863i
$729$		0			0
$730$			37.9880i			1.40600i
$731$	−5.24644	+	9.08711i	−0.194047	+	0.336099i
$732$		0			0
$733$	−39.2037	−	22.6343i	−1.44802	−	0.836016i	−0.449658	−	0.893201i	$-0.648454\pi$
$733$	−39.2037	−	22.6343i	−1.44802	−	0.836016i	−0.998364	+	0.0571848i	$0.981788\pi$
$734$	−3.72861	−	2.15271i	−0.137625	−	0.0794581i
$735$		0			0
$736$		−	16.9378i		−	0.624335i
$737$	−18.3691	−	31.8163i	−0.676635	−	1.17197i
$738$		0			0
$739$	16.6808	+	9.63066i	0.613613	+	0.354270i	0.774378	−	0.632723i	$-0.218063\pi$
$739$	16.6808	+	9.63066i	0.613613	+	0.354270i	−0.160765	+	0.986993i	$0.551396\pi$
$740$	−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	−0.938402	−	0.345545i	$-0.887694\pi$
$743$	−30.2115	+	17.4426i	−1.10835	+	0.639908i	−0.169951	+	0.985453i	$0.554361\pi$
$744$		0			0
$745$	−31.9155			−1.16929
$746$	−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
$751$	24.9668			0.911051			0.455526	−	0.890223i	$-0.349451\pi$
$751$	24.9668			0.911051			0.455526	+	0.890223i	$0.349451\pi$
$752$	−7.94609	−	4.58767i	−0.289764	−	0.167295i
$753$		0			0
$754$	−9.62150	+	49.2136i	−0.350394	+	1.79225i
$755$	−12.1467			−0.442064
$756$		0			0
$757$	5.30243	+	9.18408i	0.192720	+	0.333801i	0.946151	−	0.323726i	$-0.104936\pi$
$757$	5.30243	+	9.18408i	0.192720	+	0.333801i	−0.753431	+	0.657527i	$0.771602\pi$
$758$	40.8685	+	70.7863i	1.48441	+	2.57108i
$759$		0			0
$760$			41.4926i			1.50510i
$761$	−28.2660	+	16.3194i	−1.02464	+	0.591578i	−0.915446	−	0.402442i	$-0.868162\pi$
$761$	−28.2660	+	16.3194i	−1.02464	+	0.591578i	−0.109198	+	0.994020i	$0.534828\pi$
$762$		0			0
$763$	3.68208	+	2.70927i	0.133300	+	0.0980820i
$764$	−11.5080	−	19.9325i	−0.416345	−	0.721131i
$765$		0			0
$766$	−41.2988	−	71.5316i	−1.49219	−	2.58454i
$767$	31.0572	+	27.0568i	1.12141	+	0.976963i
$768$		0			0
$769$	−45.1851	+	26.0876i	−1.62942	+	0.940744i	−0.645148	+	0.764057i	$0.723204\pi$
$769$	−45.1851	+	26.0876i	−1.62942	+	0.940744i	−0.984267	+	0.176686i	$0.943462\pi$
$770$	−24.0545	−	17.6993i	−0.866864	−	0.637837i
$771$		0			0
$772$	−12.2909	−	7.09618i	−0.442360	−	0.255397i
$773$			35.7057i			1.28425i	0.766602	+	0.642123i	$0.221946\pi$
$773$			35.7057i			1.28425i	−0.766602	+	0.642123i	$0.778054\pi$
$774$		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
$782$		−	16.0741i		−	0.574808i
$783$		0			0
$784$	−41.2755	+	44.7437i	−1.47413	+	1.59799i
$785$		−	22.5760i		−	0.805770i
$786$		0			0
$787$			6.10621i			0.217663i	0.994060	+	0.108831i	$0.0347109\pi$
$787$			6.10621i			0.217663i	−0.994060	+	0.108831i	$0.965289\pi$
$788$	18.9301	−	10.9293i	0.674356	−	0.389339i
$789$		0			0
$790$	−12.9482	−	22.4270i	−0.460678	−	0.797918i
$791$	−22.5907	−	2.51224i	−0.803234	−	0.0893248i
$792$		0			0
$793$	10.3505	+	2.02358i	0.367559	+	0.0718595i
$794$	5.38296	+	9.32356i	0.191034	+	0.330881i
$795$		0			0
$796$	1.93074			0.0684332
$797$	23.1149	−	40.0363i	0.818773	−	1.41816i	−0.0878129	−	0.996137i	$-0.527988\pi$
$797$	23.1149	−	40.0363i	0.818773	−	1.41816i	0.906586	−	0.422020i	$-0.138679\pi$
$798$		0			0
$799$	−2.85688	−	1.64942i	−0.101069	−	0.0583522i
$800$	−17.7355	+	10.2396i	−0.627044	+	0.362024i
$801$		0			0
$802$	−50.7400			−1.79169
$803$	24.6242			0.868968
$804$		0			0
$805$	−0.936218	+	8.41874i	−0.0329974	+	0.296722i
$806$	−95.9780	−	18.7642i	−3.38068	−	0.660939i
$807$		0			0
$808$	7.74586	+	4.47208i	0.272498	+	0.157327i
$809$	19.6439	−	34.0243i	0.690644	−	1.19623i	−0.280983	−	0.959713i	$-0.590661\pi$
$809$	19.6439	−	34.0243i	0.690644	−	1.19623i	0.971627	−	0.236518i	$-0.0760061\pi$
$810$		0			0
$811$		−	6.90664i		−	0.242525i	−0.992620	−	0.121262i	$-0.961306\pi$
$811$		−	6.90664i		−	0.242525i	0.992620	−	0.121262i	$-0.0386943\pi$
$812$	−39.6023	+	53.8222i	−1.38977	+	1.88879i
$813$		0			0
$814$	36.1015	+	20.8432i	1.26536	+	0.730555i
$815$	11.5583			0.404871
$816$		0			0
$817$			12.3551i			0.432251i
$818$	−45.6466			−1.59600
$819$		0			0
$820$	−58.3622			−2.03810
$821$		−	1.91049i		−	0.0666765i	−0.999444	−	0.0333382i	$-0.989386\pi$
$821$		−	1.91049i		−	0.0666765i	0.999444	−	0.0333382i	$-0.0106139\pi$
$822$		0			0
$823$	−1.57969			−0.0550645			−0.0275322	−	0.999621i	$-0.508765\pi$
$823$	−1.57969			−0.0550645			−0.0275322	+	0.999621i	$0.508765\pi$
$824$	−69.4320	−	40.0866i	−2.41878	−	1.39648i
$825$		0			0
$826$	31.3918	+	71.6674i	1.09226	+	2.49363i
$827$			32.5050i			1.13031i	0.824985	+	0.565155i	$0.191184\pi$
$827$			32.5050i			1.13031i	−0.824985	+	0.565155i	$0.808816\pi$
$828$		0			0
$829$	−17.5269	+	30.3575i	−0.608735	+	1.05436i	0.382714	+	0.923867i	$0.374989\pi$
$829$	−17.5269	+	30.3575i	−0.608735	+	1.05436i	−0.991449	+	0.130493i	$0.958344\pi$
$830$	9.74564	+	5.62665i	0.338276	+	0.195304i
$831$		0			0
$832$	−11.0937	+	12.7340i	−0.384606	+	0.441472i
$833$	−14.8399	+	16.0868i	−0.514172	+	0.557375i
$834$		0			0
$835$	−28.9856			−1.00309
$836$	46.8126			1.61905
$837$		0			0
$838$	67.0096	−	38.6880i	2.31481	−	1.33645i
$839$	−4.63746	−	2.67744i	−0.160103	−	0.0924354i	0.417808	−	0.908535i	$-0.362798\pi$
$839$	−4.63746	−	2.67744i	−0.160103	−	0.0924354i	−0.577911	+	0.816100i	$0.696132\pi$
$840$		0			0
$841$	0.0669890	−	0.116028i	0.00230997	−	0.00400098i
$842$	−33.2708			−1.14659
$843$		0			0
$844$	−17.6658	−	30.5981i	−0.608082	−	1.05323i
$845$	7.89260	−	19.4137i	0.271514	−	0.667850i
$846$		0			0
$847$	5.77533	−	7.84906i	0.198443	−	0.269697i
$848$	31.5923	+	54.7195i	1.08488	+	1.87907i
$849$		0			0
$850$	−16.8311	+	9.71744i	−0.577302	+	0.333305i
$851$		−	11.8238i		−	0.405314i
$852$		0			0
$853$		−	49.6270i		−	1.69920i	−0.527431	−	0.849598i	$-0.676845\pi$
$853$		−	49.6270i		−	1.69920i	0.527431	−	0.849598i	$-0.323155\pi$
$854$	16.1359	+	11.8728i	0.552159	+	0.406278i
$855$		0			0
$856$			35.9028i			1.22713i
$857$	−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	−0.0347490	−	0.999396i	$-0.511063\pi$
$863$	−26.9570	−	15.5636i	−0.917626	−	0.529792i	−0.882877	+	0.469604i	$0.844397\pi$
$864$		0			0
$865$			20.6530i			0.702222i
$866$	7.73558	+	4.46614i	0.262866	+	0.151766i
$867$		0			0
$868$	−104.966	−	77.2338i	−3.56277	−	2.62148i
$869$	−14.5374	+	8.39318i	−0.493148	+	0.284719i
$870$		0			0
$871$	46.3192	−	15.8929i	1.56947	−	0.538510i
$872$	6.04001	+	10.4616i	0.204540	+	0.354274i
$873$		0			0
$874$	−9.46341	−	16.3911i	−0.320105	−	0.554438i
$875$	28.9150	−	12.6653i	0.977504	−	0.428167i
$876$		0			0
$877$	25.9033	−	14.9553i	0.874693	−	0.505004i	0.00578807	−	0.999983i	$-0.498158\pi$
$877$	25.9033	−	14.9553i	0.874693	−	0.505004i	0.868905	+	0.494979i	$0.164824\pi$
$878$		−	99.6984i		−	3.36466i
$879$		0			0
$880$	−18.9603	−	32.8402i	−0.639152	−	1.10704i
$881$	−7.28477	−	12.6176i	−0.245430	−	0.425097i	0.716822	−	0.697256i	$-0.245596\pi$
$881$	−7.28477	−	12.6176i	−0.245430	−	0.425097i	−0.962252	+	0.272159i	$0.912262\pi$
$882$		0			0
$883$	48.9296			1.64661			0.823307	−	0.567597i	$-0.192127\pi$
$883$	48.9296			1.64661			0.823307	+	0.567597i	$0.192127\pi$
$884$	−34.8101	+	39.9569i	−1.17079	+	1.34390i
$885$		0			0
$886$	33.7164	+	19.4662i	1.13273	+	0.653980i
$887$	−54.5902			−1.83296			−0.916480	−	0.400080i	$-0.868982\pi$
$887$	−54.5902			−1.83296			−0.916480	+	0.400080i	$0.868982\pi$
$888$		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
$893$	−3.88430			−0.129983
$894$		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
$899$	−48.7533	−	28.1477i	−1.62601	−	0.938780i
$900$		0			0
$901$	11.3585	+	19.6734i	0.378405	+	0.655417i
$902$			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
$907$	11.3628	−	19.6809i	0.377295	−	0.653494i	−0.613373	−	0.789793i	$-0.710188\pi$
$907$	11.3628	−	19.6809i	0.377295	−	0.653494i	0.990668	+	0.136300i	$0.0435211\pi$
$908$			64.2688i			2.13283i
$909$		0			0
$910$	29.3058	−	26.9408i	0.971478	−	0.893080i
$911$	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
$913$	3.64725	−	6.31722i	0.120706	−	0.209070i
$914$	36.0842			1.19356
$915$		0			0
$916$	−32.2870	−	18.6409i	−1.06679	−	0.615912i
$917$	26.8455	+	2.98539i	0.886517	+	0.0985864i
$918$		0			0
$919$	−15.3470	−	26.5818i	−0.506251	−	0.876853i	−0.999974	−	0.00723365i	$-0.997697\pi$
$919$	−15.3470	−	26.5818i	−0.506251	−	0.876853i	0.493722	−	0.869620i	$-0.335636\pi$
$920$	−11.1919	+	19.3849i	−0.368985	+	0.639101i
$921$		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
$926$	17.4802			0.574434
$927$		0			0
$928$	−39.6819	+	22.9104i	−1.30262	+	0.752070i
$929$	32.4110	−	18.7125i	1.06337	−	0.613936i	0.137007	−	0.990570i	$-0.456252\pi$
$929$	32.4110	−	18.7125i	1.06337	−	0.613936i	0.926362	+	0.376634i	$0.122918\pi$
$930$		0			0
$931$	−5.66168	+	25.1409i	−0.185554	+	0.823960i
$932$	−15.4463	+	26.7538i	−0.505961	+	0.876350i
$933$		0			0
$934$	11.3218	+	6.53663i	0.370460	+	0.213885i
$935$	−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	$0.242191\pi$
$938$	92.4492	+	10.2809i	3.01857	+	0.335685i
$939$		0			0
$940$	3.99773	+	6.92427i	0.130392	+	0.225845i
$941$	23.8202	−	13.7526i	0.776518	−	0.448323i	−0.0586770	−	0.998277i	$-0.518688\pi$
$941$	23.8202	−	13.7526i	0.776518	−	0.448323i	0.835195	+	0.549954i	$0.185355\pi$
$942$		0			0
$943$	13.2463	−	7.64774i	0.431358	−	0.249045i
$944$			99.3472i			3.23348i
$945$		0			0
$946$	−11.7494	−	20.3506i	−0.382007	−	0.661656i
$947$			5.08330i			0.165185i	0.996583	+	0.0825925i	$0.0263200\pi$
$947$			5.08330i			0.165185i	−0.996583	+	0.0825925i	$0.973680\pi$
$948$		0			0
$949$	−6.29775	+	32.2128i	−0.204434	+	1.04567i
$950$	−11.4420	+	19.8182i	−0.371229	+	0.642987i
$951$		0			0
$952$	−52.9755	+	23.2044i	−1.71695	+	0.752058i
$953$	−4.90718	+	8.49949i	−0.158959	+	0.275326i	−0.934494	−	0.355980i	$-0.884147\pi$
$953$	−4.90718	+	8.49949i	−0.158959	+	0.275326i	0.775534	+	0.631305i	$0.217481\pi$
$954$		0			0
$955$			7.89284i			0.255406i
$956$		−	44.1543i		−	1.42805i
$957$		0			0
$958$	−12.2353	+	21.1921i	−0.395303	+	0.684685i
$959$	24.2167	−	10.6074i	0.781998	−	0.342531i
$960$		0			0
$961$	39.3947	−	68.2336i	1.27080	−	2.20108i
$962$	−36.4997	+	41.8964i	−1.17680	+	1.35079i
$963$		0			0
$964$		−	47.4121i		−	1.52704i
$965$	2.43348	+	4.21490i	0.0783364	+	0.135683i
$966$		0			0
$967$		−	2.69619i		−	0.0867036i	−0.999060	−	0.0433518i	$-0.986196\pi$
$967$		−	2.69619i		−	0.0867036i	0.999060	−	0.0433518i	$-0.0138036\pi$
$968$	22.3009	−	12.8754i	0.716779	−	0.413832i
$969$		0			0
$970$	−55.9504	+	32.3030i	−1.79646	+	1.03719i
$971$	12.4620	+	21.5848i	0.399925	+	0.692691i	0.993716	−	0.111929i	$-0.0357028\pi$
$971$	12.4620	+	21.5848i	0.399925	+	0.692691i	−0.593791	+	0.804619i	$0.702369\pi$
$972$		0			0
$973$	4.37609	+	0.486649i	0.140291	+	0.0156013i
$974$	103.543			3.31773
$975$		0			0
$976$	12.7187	+	22.0294i	0.407115	+	0.705144i
$977$	−24.5197	−	14.1565i	−0.784456	−	0.452906i	0.0535514	−	0.998565i	$-0.482946\pi$
$977$	−24.5197	−	14.1565i	−0.784456	−	0.452906i	−0.838007	+	0.545659i	$0.816279\pi$
$978$		0			0
$979$	2.38019	−	4.12262i	0.0760713	−	0.131759i
$980$	50.6440	−	15.7824i	1.61776	−	0.504150i
$981$		0			0
$982$	15.1567	−	8.75073i	0.483670	−	0.279247i
$983$	32.7805	−	18.9258i	1.04554	−	0.603641i	0.124140	−	0.992265i	$-0.460383\pi$
$983$	32.7805	−	18.9258i	1.04554	−	0.603641i	0.921396	+	0.388624i	$0.127049\pi$
$984$		0			0
$985$	−7.49591			−0.238839
$986$	−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
$991$	−29.2079	+	50.5896i	−0.927820	+	1.60703i	−0.140858	+	0.990030i	$0.544986\pi$
$991$	−29.2079	+	50.5896i	−0.927820	+	1.60703i	−0.786962	+	0.617001i	$0.788347\pi$
$992$	−44.6806	−	77.3891i	−1.41861	−	2.45711i
$993$		0			0
$994$	−9.19677	−	1.02274i	−0.291704	−	0.0324394i
$995$	−0.573399	−	0.331052i	−0.0181780	−	0.0104950i
$996$		0			0
$997$	28.0588			0.888632			0.444316	−	0.895870i	$-0.353447\pi$
$997$	28.0588			0.888632			0.444316	+	0.895870i	$0.353447\pi$
$998$	−14.7001	+	25.4613i	−0.465322	+	0.805962i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.bm.f.478.1		12
3.2	odd	2		91.2.k.b.23.6	yes	12
7.4	even	3		819.2.do.e.361.6		12
13.4	even	6		819.2.do.e.667.6		12
21.2	odd	6		637.2.q.g.491.6		12
21.5	even	6		637.2.q.i.491.6		12
21.11	odd	6		91.2.u.b.88.1	yes	12
21.17	even	6		637.2.u.g.361.1		12
21.20	even	2		637.2.k.i.569.6		12
39.2	even	12		1183.2.e.j.170.1		24
39.11	even	12		1183.2.e.j.170.12		24
39.17	odd	6		91.2.u.b.30.1	yes	12
91.4	even	6	inner	819.2.bm.f.550.6		12
273.2	even	12		8281.2.a.cp.1.12		12
273.11	even	12		1183.2.e.j.508.12		24
273.17	even	6		637.2.k.i.459.1		12
273.89	odd	12		8281.2.a.co.1.1		12
273.95	odd	6		91.2.k.b.4.1	✓	12
273.128	even	12		8281.2.a.cp.1.1		12
273.158	even	12		1183.2.e.j.508.1		24
273.173	even	6		637.2.q.i.589.6		12
273.212	odd	6		637.2.q.g.589.6		12
273.236	odd	12		8281.2.a.co.1.12		12
273.251	even	6		637.2.u.g.30.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.k.b.4.1	✓	12	273.95	odd	6
91.2.k.b.23.6	yes	12	3.2	odd	2
91.2.u.b.30.1	yes	12	39.17	odd	6
91.2.u.b.88.1	yes	12	21.11	odd	6
637.2.k.i.459.1		12	273.17	even	6
637.2.k.i.569.6		12	21.20	even	2
637.2.q.g.491.6		12	21.2	odd	6
637.2.q.g.589.6		12	273.212	odd	6
637.2.q.i.491.6		12	21.5	even	6
637.2.q.i.589.6		12	273.173	even	6
637.2.u.g.30.1		12	273.251	even	6
637.2.u.g.361.1		12	21.17	even	6
819.2.bm.f.478.1		12	1.1	even	1	trivial
819.2.bm.f.550.6		12	91.4	even	6	inner
819.2.do.e.361.6		12	7.4	even	3
819.2.do.e.667.6		12	13.4	even	6
1183.2.e.j.170.1		24	39.2	even	12
1183.2.e.j.170.12		24	39.11	even	12
1183.2.e.j.508.1		24	273.158	even	12
1183.2.e.j.508.12		24	273.11	even	12
8281.2.a.co.1.1		12	273.89	odd	12
8281.2.a.co.1.12		12	273.236	odd	12
8281.2.a.cp.1.1		12	273.128	even	12
8281.2.a.cp.1.12		12	273.2	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.bm (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-2.58860i q^{2} -4.70085 q^{4} +(1.39608 + 0.806027i) q^{5} +(1.06153 + 2.42346i) q^{7} +6.99143i q^{8} +O(q^{10})\)	\(q-2.58860i q^{2} -4.70085 q^{4} +(1.39608 + 0.806027i) q^{5} +(1.06153 + 2.42346i) q^{7} +6.99143i q^{8} +(2.08648 - 3.61389i) q^{10} +(-2.34256 - 1.35248i) q^{11} +(2.36840 - 2.71858i) q^{13} +(6.27337 - 2.74787i) q^{14} +8.69632 q^{16} +3.12661 q^{17} +(3.18828 - 1.84075i) q^{19} +(-6.56276 - 3.78901i) q^{20} +(-3.50103 + 6.06396i) q^{22} +1.98604 q^{23} +(-1.20064 - 2.07957i) q^{25} +(-7.03732 - 6.13084i) q^{26} +(-4.99008 - 11.3923i) q^{28} +(-2.68636 - 4.65290i) q^{29} +(9.07425 - 5.23902i) q^{31} -8.52843i q^{32} -8.09354i q^{34} +(-0.471400 + 4.23896i) q^{35} -5.95346i q^{37} +(-4.76497 - 8.25317i) q^{38} +(-5.63528 + 9.76059i) q^{40} +(6.66970 - 3.85075i) q^{41} +(-1.67800 + 2.90638i) q^{43} +(11.0120 + 6.35780i) q^{44} -5.14106i q^{46} +(-0.913730 - 0.527542i) q^{47} +(-4.74633 + 5.14513i) q^{49} +(-5.38318 + 3.10798i) q^{50} +(-11.1335 + 12.7796i) q^{52} +(3.63284 + 6.29226i) q^{53} +(-2.18027 - 3.77633i) q^{55} +(-16.9435 + 7.42158i) q^{56} +(-12.0445 + 6.95390i) q^{58} +11.4241i q^{59} +(1.46254 + 2.53319i) q^{61} +(-13.5617 - 23.4896i) q^{62} -4.68406 q^{64} +(5.49772 - 1.88636i) q^{65} +(11.7622 + 6.79091i) q^{67} -14.6977 q^{68} +(10.9730 + 1.22027i) q^{70} +(-1.17009 - 0.675554i) q^{71} +(-7.88374 + 4.55168i) q^{73} -15.4111 q^{74} +(-14.9876 + 8.65311i) q^{76} +(0.790989 - 7.11280i) q^{77} +(3.10289 - 5.37436i) q^{79} +(12.1407 + 7.00946i) q^{80} +(-9.96806 - 17.2652i) q^{82} +2.69672i q^{83} +(4.36499 + 2.52013i) q^{85} +(7.52346 + 4.34367i) q^{86} +(9.45576 - 16.3779i) q^{88} +1.75988i q^{89} +(9.10249 + 2.85388i) q^{91} -9.33607 q^{92} +(-1.36560 + 2.36528i) q^{94} +5.93478 q^{95} +(-13.4078 - 7.74102i) q^{97} +(13.3187 + 12.2863i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 8 q^{4} + 3 q^{5} - 3 q^{7}+O(q^{10}) \) 12 * q - 8 * q^4 + 3 * q^5 - 3 * q^7	\( 12 q - 8 q^{4} + 3 q^{5} - 3 q^{7} + 12 q^{10} - 12 q^{11} - 2 q^{13} - 4 q^{14} + 16 q^{16} + 34 q^{17} + 9 q^{19} + 3 q^{20} - 15 q^{22} + 6 q^{23} - 5 q^{25} + 6 q^{26} - 9 q^{28} + q^{29} + 18 q^{31} + 6 q^{35} - 19 q^{38} - q^{40} + 6 q^{41} + 11 q^{43} + 33 q^{44} + 15 q^{47} - 3 q^{49} - 18 q^{50} - 7 q^{52} + 8 q^{53} - 15 q^{55} - 27 q^{56} - 24 q^{58} + 5 q^{61} - 41 q^{62} + 2 q^{64} - 21 q^{65} + 15 q^{67} - 22 q^{68} + 3 q^{70} - 30 q^{71} + 42 q^{73} - 66 q^{74} - 45 q^{76} + 19 q^{77} - 35 q^{79} + 63 q^{80} + 5 q^{82} - 21 q^{85} + 57 q^{86} - 14 q^{88} - 7 q^{91} + 66 q^{92} + q^{94} + 4 q^{95} - 3 q^{97} + 18 q^{98}+O(q^{100}) \) 12 * q - 8 * q^4 + 3 * q^5 - 3 * q^7 + 12 * q^10 - 12 * q^11 - 2 * q^13 - 4 * q^14 + 16 * q^16 + 34 * q^17 + 9 * q^19 + 3 * q^20 - 15 * q^22 + 6 * q^23 - 5 * q^25 + 6 * q^26 - 9 * q^28 + q^29 + 18 * q^31 + 6 * q^35 - 19 * q^38 - q^40 + 6 * q^41 + 11 * q^43 + 33 * q^44 + 15 * q^47 - 3 * q^49 - 18 * q^50 - 7 * q^52 + 8 * q^53 - 15 * q^55 - 27 * q^56 - 24 * q^58 + 5 * q^61 - 41 * q^62 + 2 * q^64 - 21 * q^65 + 15 * q^67 - 22 * q^68 + 3 * q^70 - 30 * q^71 + 42 * q^73 - 66 * q^74 - 45 * q^76 + 19 * q^77 - 35 * q^79 + 63 * q^80 + 5 * q^82 - 21 * q^85 + 57 * q^86 - 14 * q^88 - 7 * q^91 + 66 * q^92 + q^94 + 4 * q^95 - 3 * q^97 + 18 * q^98

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