LMFDB - Embedded newform 147.2.g.b.68.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [147,2,Mod(68,147)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(147, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 5]))

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

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

chi := DirichletCharacter("147.68");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 147 = 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	147.g (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.17380090971$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{14} - 16 x^{13} + 50 x^{12} + 56 x^{11} - 80 x^{10} + 240 x^{9} + 381 x^{8} + 144 x^{7} + \cdots + 49 $ x^16 - 8x^14 - 16x^13 + 50x^12 + 56x^11 - 80x^10 + 240x^9 + 381x^8 + 144x^7 + 400x^6 + 184x^5 + 158x^4 + 112x^3 + 112*x^2 + 49
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			68.3
Root			$-0.0510945 + 0.786997i$ of defining polynomial
Character	$\chi$	$=$	147.68
Dual form			147.2.g.b.80.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.09057 - 0.629640i) q^{2} +(-0.353975 - 1.69549i) q^{3} +(-0.207107 - 0.358719i) q^{4} +(1.16342 - 2.01511i) q^{5} +(-0.681517 + 2.07193i) q^{6} +3.04017i q^{8} +(-2.74940 + 1.20032i) q^{9} +O(q^{10})$	\(q+(-1.09057 - 0.629640i) q^{2} +(-0.353975 - 1.69549i) q^{3} +(-0.207107 - 0.358719i) q^{4} +(1.16342 - 2.01511i) q^{5} +(-0.681517 + 2.07193i) q^{6} +3.04017i q^{8} +(-2.74940 + 1.20032i) q^{9} +(-2.53759 + 1.46508i) q^{10} +(-1.54230 + 0.890446i) q^{11} +(-0.534896 + 0.478126i) q^{12} -4.46088i q^{13} +(-3.82843 - 1.25928i) q^{15} +(1.50000 - 2.59808i) q^{16} +(0.481906 + 0.834685i) q^{17} +(3.75419 + 0.422098i) q^{18} +(-1.87476 - 1.08239i) q^{19} -0.963811 q^{20} +2.24264 q^{22} +(3.72343 + 2.14973i) q^{23} +(5.15459 - 1.07614i) q^{24} +(-0.207107 - 0.358719i) q^{25} +(-2.80875 + 4.86490i) q^{26} +(3.00836 + 4.23671i) q^{27} -7.86123i q^{29} +(3.38227 + 3.78386i) q^{30} +(0.937379 - 0.541196i) q^{31} +(1.99403 - 1.15125i) q^{32} +(2.05568 + 2.29976i) q^{33} -1.21371i q^{34} +(1.00000 + 0.737669i) q^{36} +(2.53553 - 4.39167i) q^{37} +(1.36303 + 2.36085i) q^{38} +(-7.56341 + 1.57904i) q^{39} +(6.12627 + 3.53701i) q^{40} +4.25447 q^{41} +2.00000 q^{43} +(0.638840 + 0.368835i) q^{44} +(-0.779936 + 6.93683i) q^{45} +(-2.70711 - 4.68885i) q^{46} +(0.282294 - 0.488947i) q^{47} +(-4.93599 - 1.62359i) q^{48} +0.521611i q^{50} +(1.24462 - 1.11253i) q^{51} +(-1.60021 + 0.923880i) q^{52} +(5.26573 - 3.04017i) q^{53} +(-0.613222 - 6.51461i) q^{54} +4.14386i q^{55} +(-1.17157 + 3.56178i) q^{57} +(-4.94975 + 8.57321i) q^{58} +(-4.65369 - 8.06043i) q^{59} +(0.341165 + 1.63414i) q^{60} +(-6.51455 - 3.76118i) q^{61} -1.36303 q^{62} -8.89949 q^{64} +(-8.98916 - 5.18990i) q^{65} +(-0.793838 - 3.80239i) q^{66} +(7.24264 + 12.5446i) q^{67} +(0.199612 - 0.345738i) q^{68} +(2.32685 - 7.07401i) q^{69} +7.86123i q^{71} +(-3.64919 - 8.35866i) q^{72} +(5.57717 - 3.21998i) q^{73} +(-5.53035 + 3.19295i) q^{74} +(-0.534896 + 0.478126i) q^{75} +0.896683i q^{76} +(9.24264 + 3.04017i) q^{78} +(-2.41421 + 4.18154i) q^{79} +(-3.49027 - 6.04532i) q^{80} +(6.11844 - 6.60035i) q^{81} +(-4.63979 - 2.67878i) q^{82} -14.5257 q^{83} +2.24264 q^{85} +(-2.18114 - 1.25928i) q^{86} +(-13.3287 + 2.78268i) q^{87} +(-2.70711 - 4.68885i) q^{88} +(4.17179 - 7.22575i) q^{89} +(5.21828 - 7.07401i) q^{90} -1.78089i q^{92} +(-1.24940 - 1.39775i) q^{93} +(-0.615721 + 0.355487i) q^{94} +(-4.36227 + 2.51856i) q^{95} +(-2.65777 - 2.97334i) q^{96} +13.8310i q^{97} +(3.17157 - 4.29945i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{4} - 8 q^{9}+O(q^{10}) $ 16 * q + 8 * q^4 - 8 * q^9	$ 16 q + 8 q^{4} - 8 q^{9} - 16 q^{15} + 24 q^{16} - 16 q^{18} - 32 q^{22} + 8 q^{25} - 24 q^{30} + 16 q^{36} - 16 q^{37} - 8 q^{39} + 32 q^{43} - 32 q^{46} + 24 q^{51} - 64 q^{57} + 24 q^{60} + 16 q^{64} + 48 q^{67} + 32 q^{72} + 80 q^{78} - 16 q^{79} + 24 q^{81} - 32 q^{85} - 32 q^{88} + 16 q^{93} + 96 q^{99}+O(q^{100}) $ 16 * q + 8 * q^4 - 8 * q^9 - 16 * q^15 + 24 * q^16 - 16 * q^18 - 32 * q^22 + 8 * q^25 - 24 * q^30 + 16 * q^36 - 16 * q^37 - 8 * q^39 + 32 * q^43 - 32 * q^46 + 24 * q^51 - 64 * q^57 + 24 * q^60 + 16 * q^64 + 48 * q^67 + 32 * q^72 + 80 * q^78 - 16 * q^79 + 24 * q^81 - 32 * q^85 - 32 * q^88 + 16 * q^93 + 96 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/147\mathbb{Z}\right)^\times$.

$n$	$50$	$52$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	−1.09057	−	0.629640i	−0.771148	−	0.445223i	0.0621357	−	0.998068i	$-0.480209\pi$
$2$	−1.09057	−	0.629640i	−0.771148	−	0.445223i	−0.833284	+	0.552845i	$0.813542\pi$
$3$	−0.353975	−	1.69549i	−0.204367	−	0.978894i
$3$	−0.353975	−	1.69549i	−0.204367	−	0.978894i
$4$	−0.207107	−	0.358719i	−0.103553	−	0.179360i
$5$	1.16342	−	2.01511i	0.520299	−	0.901184i	−0.479423	−	0.877584i	$-0.659154\pi$
$5$	1.16342	−	2.01511i	0.520299	−	0.901184i	0.999721	−	0.0235997i	$-0.00751270\pi$
$6$	−0.681517	+	2.07193i	−0.278228	+	0.845862i
$7$		0			0
$7$		0			0
$8$			3.04017i			1.07486i
$9$	−2.74940	+	1.20032i	−0.916468	+	0.400108i
$10$	−2.53759	+	1.46508i	−0.802455	+	0.463298i
$11$	−1.54230	+	0.890446i	−0.465020	+	0.268479i	−0.714153	−	0.699990i	$-0.753188\pi$
$11$	−1.54230	+	0.890446i	−0.465020	+	0.268479i	0.249133	+	0.968469i	$0.419854\pi$
$12$	−0.534896	+	0.478126i	−0.154411	+	0.138023i
$13$		−	4.46088i		−	1.23723i	−0.785695	−	0.618613i	$-0.787695\pi$
$13$		−	4.46088i		−	1.23723i	0.785695	−	0.618613i	$-0.212305\pi$
$14$		0			0
$15$	−3.82843	−	1.25928i	−0.988496	−	0.325145i
$16$	1.50000	−	2.59808i	0.375000	−	0.649519i
$17$	0.481906	+	0.834685i	0.116879	+	0.202441i	0.918529	−	0.395353i	$-0.129378\pi$
$17$	0.481906	+	0.834685i	0.116879	+	0.202441i	−0.801650	+	0.597793i	$0.796044\pi$
$18$	3.75419	+	0.422098i	0.884870	+	0.0994895i
$19$	−1.87476	−	1.08239i	−0.430099	−	0.248318i	0.269290	−	0.963059i	$-0.413211\pi$
$19$	−1.87476	−	1.08239i	−0.430099	−	0.248318i	−0.699389	+	0.714741i	$0.746544\pi$
$20$	−0.963811			−0.215515
$21$		0			0
$22$	2.24264			0.478133
$23$	3.72343	+	2.14973i	0.776390	+	0.448249i	0.835149	−	0.550023i	$-0.185381\pi$
$23$	3.72343	+	2.14973i	0.776390	+	0.448249i	−0.0587596	+	0.998272i	$0.518715\pi$
$24$	5.15459	−	1.07614i	1.05218	−	0.219667i
$25$	−0.207107	−	0.358719i	−0.0414214	−	0.0717439i
$26$	−2.80875	+	4.86490i	−0.550842	+	0.954086i
$27$	3.00836	+	4.23671i	0.578960	+	0.815356i
$28$		0			0
$29$		−	7.86123i		−	1.45979i	−0.683557	−	0.729897i	$-0.739568\pi$
$29$		−	7.86123i		−	1.45979i	0.683557	−	0.729897i	$-0.260432\pi$
$30$	3.38227	+	3.78386i	0.617515	+	0.690836i
$31$	0.937379	−	0.541196i	0.168358	−	0.0972017i	−0.413453	−	0.910525i	$-0.635677\pi$
$31$	0.937379	−	0.541196i	0.168358	−	0.0972017i	0.581811	+	0.813324i	$0.302344\pi$
$32$	1.99403	−	1.15125i	0.352497	−	0.203514i
$33$	2.05568	+	2.29976i	0.357848	+	0.400337i
$34$		−	1.21371i		−	0.208149i
$35$		0			0
$36$	1.00000	+	0.737669i	0.166667	+	0.122945i
$37$	2.53553	−	4.39167i	0.416839	−	0.721987i	−0.578780	−	0.815483i	$-0.696471\pi$
$37$	2.53553	−	4.39167i	0.416839	−	0.721987i	0.995620	+	0.0934968i	$0.0298045\pi$
$38$	1.36303	+	2.36085i	0.221113	+	0.382980i
$39$	−7.56341	+	1.57904i	−1.21111	+	0.252849i
$40$	6.12627	+	3.53701i	0.968649	+	0.559250i
$41$	4.25447			0.664436			0.332218	−	0.943203i	$-0.392203\pi$
$41$	4.25447			0.664436			0.332218	+	0.943203i	$0.392203\pi$
$42$		0			0
$43$	2.00000			0.304997			0.152499	−	0.988304i	$-0.451268\pi$
$43$	2.00000			0.304997			0.152499	+	0.988304i	$0.451268\pi$
$44$	0.638840	+	0.368835i	0.0963088	+	0.0556039i
$45$	−0.779936	+	6.93683i	−0.116266	+	1.03408i
$46$	−2.70711	−	4.68885i	−0.399141	−	0.691333i
$47$	0.282294	−	0.488947i	0.0411768	−	0.0713203i	−0.844703	−	0.535236i	$-0.820223\pi$
$47$	0.282294	−	0.488947i	0.0411768	−	0.0713203i	0.885879	+	0.463916i	$0.153556\pi$
$48$	−4.93599	−	1.62359i	−0.712448	−	0.234345i
$49$		0			0
$50$			0.521611i			0.0737669i
$51$	1.24462	−	1.11253i	0.174282	−	0.155785i
$52$	−1.60021	+	0.923880i	−0.221909	+	0.128119i
$53$	5.26573	−	3.04017i	0.723304	−	0.417600i	−0.0926637	−	0.995697i	$-0.529538\pi$
$53$	5.26573	−	3.04017i	0.723304	−	0.417600i	0.815967	+	0.578098i	$0.196205\pi$
$54$	−0.613222	−	6.51461i	−0.0834489	−	0.886527i
$55$			4.14386i			0.558758i
$56$		0			0
$57$	−1.17157	+	3.56178i	−0.155179	+	0.471770i
$58$	−4.94975	+	8.57321i	−0.649934	+	1.12572i
$59$	−4.65369	−	8.06043i	−0.605859	−	1.04938i	−0.991915	−	0.126903i	$-0.959496\pi$
$59$	−4.65369	−	8.06043i	−0.605859	−	1.04938i	0.386056	−	0.922475i	$-0.373837\pi$
$60$	0.341165	+	1.63414i	0.0440442	+	0.210966i
$61$	−6.51455	−	3.76118i	−0.834102	−	0.481569i	0.0211528	−	0.999776i	$-0.493266\pi$
$61$	−6.51455	−	3.76118i	−0.834102	−	0.481569i	−0.855255	+	0.518207i	$0.826600\pi$
$62$	−1.36303			−0.173106
$63$		0			0
$64$	−8.89949			−1.11244
$65$	−8.98916	−	5.18990i	−1.11497	−	0.643727i
$66$	−0.793838	−	3.80239i	−0.0977147	−	0.468041i
$67$	7.24264	+	12.5446i	0.884829	+	1.53257i	0.845909	+	0.533327i	$0.179059\pi$
$67$	7.24264	+	12.5446i	0.884829	+	1.53257i	0.0389203	+	0.999242i	$0.487608\pi$
$68$	0.199612	−	0.345738i	0.0242065	−	0.0419269i
$69$	2.32685	−	7.07401i	0.280119	−	0.851611i
$70$		0			0
$71$			7.86123i			0.932957i	0.884533	+	0.466478i	$0.154477\pi$
$71$			7.86123i			0.932957i	−0.884533	+	0.466478i	$0.845523\pi$
$72$	−3.64919	−	8.35866i	−0.430061	−	0.985077i
$73$	5.57717	−	3.21998i	0.652758	−	0.376870i	−0.136754	−	0.990605i	$-0.543667\pi$
$73$	5.57717	−	3.21998i	0.652758	−	0.376870i	0.789512	+	0.613735i	$0.210334\pi$
$74$	−5.53035	+	3.19295i	−0.642890	+	0.371173i
$75$	−0.534896	+	0.478126i	−0.0617645	+	0.0552092i
$76$			0.896683i			0.102857i
$77$		0			0
$78$	9.24264	+	3.04017i	1.04652	+	0.344232i
$79$	−2.41421	+	4.18154i	−0.271620	+	0.470460i	−0.969277	−	0.245972i	$-0.920893\pi$
$79$	−2.41421	+	4.18154i	−0.271620	+	0.470460i	0.697657	+	0.716432i	$0.254226\pi$
$80$	−3.49027	−	6.04532i	−0.390224	−	0.675888i
$81$	6.11844	−	6.60035i	0.679827	−	0.733373i
$82$	−4.63979	−	2.67878i	−0.512379	−	0.295822i
$83$	−14.5257			−1.59440			−0.797199	−	0.603716i	$-0.793686\pi$
$83$	−14.5257			−1.59440			−0.797199	+	0.603716i	$0.793686\pi$
$84$		0			0
$85$	2.24264			0.243249
$86$	−2.18114	−	1.25928i	−0.235198	−	0.135792i
$87$	−13.3287	+	2.78268i	−1.42898	+	0.298334i
$88$	−2.70711	−	4.68885i	−0.288579	−	0.499833i
$89$	4.17179	−	7.22575i	0.442209	−	0.765928i	−0.555645	−	0.831420i	$-0.687528\pi$
$89$	4.17179	−	7.22575i	0.442209	−	0.765928i	0.997853	+	0.0654923i	$0.0208618\pi$
$90$	5.21828	−	7.07401i	0.550055	−	0.745666i
$91$		0			0
$92$		−	1.78089i		−	0.185671i
$93$	−1.24940	−	1.39775i	−0.129557	−	0.144940i
$94$	−0.615721	+	0.355487i	−0.0635068	+	0.0366657i
$95$	−4.36227	+	2.51856i	−0.447560	+	0.258399i
$96$	−2.65777	−	2.97334i	−0.271258	−	0.303466i
$97$			13.8310i			1.40432i	0.712017	+	0.702162i	$0.247782\pi$
$97$			13.8310i			1.40432i	−0.712017	+	0.702162i	$0.752218\pi$
$98$		0			0
$99$	3.17157	−	4.29945i	0.318755	−	0.432111i
$100$	−0.0857864	+	0.148586i	−0.00857864	+	0.0148586i
$101$	6.49863	+	11.2560i	0.646638	+	1.12001i	0.983921	+	0.178607i	$0.0571590\pi$
$101$	6.49863	+	11.2560i	0.646638	+	1.12001i	−0.337282	+	0.941404i	$0.609508\pi$
$102$	−2.05784	+	0.429622i	−0.203756	+	0.0425389i
$103$	13.9665	+	8.06355i	1.37616	+	0.794525i	0.991695	−	0.128615i	$-0.0410532\pi$
$103$	13.9665	+	8.06355i	1.37616	+	0.794525i	0.384463	+	0.923140i	$0.374387\pi$
$104$	13.5619			1.32985
$105$		0			0
$106$	−7.65685			−0.743699
$107$	7.71148	+	4.45223i	0.745497	+	0.430413i	0.824065	−	0.566496i	$-0.191701\pi$
$107$	7.71148	+	4.45223i	0.745497	+	0.430413i	−0.0785673	+	0.996909i	$0.525035\pi$
$108$	0.896739	−	1.95661i	0.0862888	−	0.188275i
$109$	−4.70711	−	8.15295i	−0.450859	−	0.780911i	0.547581	−	0.836753i	$-0.315549\pi$
$109$	−4.70711	−	8.15295i	−0.450859	−	0.780911i	−0.998440	+	0.0558422i	$0.982216\pi$
$110$	2.60914	−	4.51916i	0.248772	−	0.430885i
$111$	−8.34357	−	2.74444i	−0.791937	−	0.260491i
$112$		0			0
$113$			11.1175i			1.04584i	0.852381	+	0.522921i	$0.175158\pi$
$113$			11.1175i			1.04584i	−0.852381	+	0.522921i	$0.824842\pi$
$114$	3.52032	−	3.14670i	0.329708	−	0.294715i
$115$	8.66386	−	5.00208i	0.807909	−	0.466446i
$116$	−2.81998	+	1.62811i	−0.261828	+	0.151167i
$117$	5.35451	+	12.2648i	0.495025	+	1.13388i
$118$			11.7206i			1.07897i
$119$		0			0
$120$	3.82843	−	11.6391i	0.349486	−	1.06250i
$121$	−3.91421	+	6.77962i	−0.355838	+	0.616329i
$122$	4.73637	+	8.20364i	0.428811	+	0.742723i
$123$	−1.50597	−	7.21343i	−0.135789	−	0.650413i
$124$	−0.388275	−	0.224171i	−0.0348681	−	0.0201311i
$125$	10.6704			0.954391
$126$		0			0
$127$	2.00000			0.177471			0.0887357	−	0.996055i	$-0.471717\pi$
$127$	2.00000			0.177471			0.0887357	+	0.996055i	$0.471717\pi$
$128$	5.71746	+	3.30098i	0.505357	+	0.291768i
$129$	−0.707950	−	3.39099i	−0.0623315	−	0.298560i
$130$	6.53553	+	11.3199i	0.573204	+	0.992819i
$131$	−8.22664	+	14.2490i	−0.718765	+	1.24494i	0.242724	+	0.970095i	$0.421959\pi$
$131$	−8.22664	+	14.2490i	−0.718765	+	1.24494i	−0.961489	+	0.274842i	$0.911374\pi$
$132$	0.399224	−	1.21371i	0.0347480	−	0.105640i
$133$		0			0
$134$		−	18.2410i		−	1.57578i
$135$	12.0374	−	1.13309i	1.03602	−	0.0975206i
$136$	−2.53759	+	1.46508i	−0.217596	+	0.125629i
$137$	8.08571	−	4.66829i	0.690809	−	0.398839i	−0.113106	−	0.993583i	$-0.536080\pi$
$137$	8.08571	−	4.66829i	0.690809	−	0.398839i	0.803915	+	0.594744i	$0.202747\pi$
$138$	−6.99167	+	6.24962i	−0.595170	+	0.532003i
$139$		−	17.3952i		−	1.47544i	−0.675106	−	0.737721i	$-0.735902\pi$
$139$		−	17.3952i		−	1.47544i	0.675106	−	0.737721i	$-0.264098\pi$
$140$		0			0
$141$	−0.928932	−	0.305553i	−0.0782302	−	0.0257322i
$142$	4.94975	−	8.57321i	0.415374	−	0.719448i
$143$	3.97218	+	6.88001i	0.332170	+	0.575335i
$144$	−1.00557	+	8.94365i	−0.0837975	+	0.745304i
$145$	−15.8412	−	9.14594i	−1.31554	−	0.759529i
$146$	−8.10971			−0.671165
$147$		0			0
$148$	−2.10051			−0.172660
$149$	6.54341	+	3.77784i	0.536057	+	0.309493i	0.743479	−	0.668759i	$-0.233174\pi$
$149$	6.54341	+	3.77784i	0.536057	+	0.309493i	−0.207422	+	0.978251i	$0.566507\pi$
$150$	0.884388	−	0.184637i	0.0722100	−	0.0150756i
$151$	0.242641	+	0.420266i	0.0197458	+	0.0342008i	0.875729	−	0.482802i	$-0.160381\pi$
$151$	0.242641	+	0.420266i	0.0197458	+	0.0342008i	−0.855984	+	0.517003i	$0.827048\pi$
$152$	3.29066	−	5.69959i	0.266908	−	0.462297i
$153$	−2.32685	−	1.71644i	−0.188114	−	0.138766i
$154$		0			0
$155$		−	2.51856i		−	0.202296i
$156$	2.13287	+	2.38611i	0.170766	+	0.191042i
$157$	5.57717	−	3.21998i	0.445107	−	0.256982i	−0.260655	−	0.965432i	$-0.583938\pi$
$157$	5.57717	−	3.21998i	0.445107	−	0.256982i	0.705761	+	0.708450i	$0.250605\pi$
$158$	5.26573	−	3.04017i	0.418919	−	0.241863i
$159$	−7.01853	−	7.85187i	−0.556606	−	0.622694i
$160$		−	5.35757i		−	0.423553i
$161$		0			0
$162$	−10.8284	+	3.34572i	−0.850762	+	0.262865i
$163$	4.58579	−	7.94282i	0.359187	−	0.622129i	−0.628639	−	0.777698i	$-0.716388\pi$
$163$	4.58579	−	7.94282i	0.359187	−	0.622129i	0.987825	+	0.155568i	$0.0497209\pi$
$164$	−0.881129	−	1.52616i	−0.0688046	−	0.119173i
$165$	7.02589	−	1.46682i	0.546965	−	0.114192i
$166$	15.8412	+	9.14594i	1.22952	+	0.709863i
$167$	−6.01673			−0.465588			−0.232794	−	0.972526i	$-0.574787\pi$
$167$	−6.01673			−0.465588			−0.232794	+	0.972526i	$0.574787\pi$
$168$		0			0
$169$	−6.89949			−0.530730
$170$	−2.44575	−	1.41206i	−0.187581	−	0.108300i
$171$	6.45369	+	0.725614i	0.493526	+	0.0554891i
$172$	−0.414214	−	0.717439i	−0.0315835	−	0.0547042i
$173$	−9.10777	+	15.7751i	−0.692451	+	1.19936i	0.278581	+	0.960413i	$0.410136\pi$
$173$	−9.10777	+	15.7751i	−0.692451	+	1.19936i	−0.971032	+	0.238948i	$0.923197\pi$
$174$	16.2879	+	5.35757i	1.23478	+	0.406156i
$175$		0			0
$176$			5.34267i			0.402719i
$177$	−12.0191	+	10.7435i	−0.903413	+	0.807531i
$178$	−9.09924	+	5.25345i	−0.682017	+	0.393763i
$179$	−11.1703	+	6.44918i	−0.834908	+	0.482034i	−0.855530	−	0.517753i	$-0.826769\pi$
$179$	−11.1703	+	6.44918i	−0.834908	+	0.482034i	0.0206224	+	0.999787i	$0.493435\pi$
$180$	2.64991	−	1.15689i	0.197512	−	0.0862292i
$181$			3.11586i			0.231600i	0.993273	+	0.115800i	$0.0369432\pi$
$181$			3.11586i			0.231600i	−0.993273	+	0.115800i	$0.963057\pi$
$182$		0			0
$183$	−4.07107	+	12.3767i	−0.300942	+	0.914915i
$184$	−6.53553	+	11.3199i	−0.481806	+	0.834512i
$185$	−5.89980	−	10.2187i	−0.433762	−	0.751297i
$186$	0.482480	+	2.31102i	0.0353772	+	0.169452i
$187$	−1.48648	−	0.858221i	−0.108702	−	0.0627594i
$188$	−0.233860			−0.0170560
$189$		0			0
$190$	6.34315			0.460180
$191$	−9.89262	−	5.71151i	−0.715805	−	0.413270i	0.0974017	−	0.995245i	$-0.468947\pi$
$191$	−9.89262	−	5.71151i	−0.715805	−	0.413270i	−0.813207	+	0.581975i	$0.802280\pi$
$192$	3.15020	+	15.0890i	0.227346	+	1.08896i
$193$	−2.65685	−	4.60181i	−0.191245	−	0.331245i	0.754418	−	0.656394i	$-0.227919\pi$
$193$	−2.65685	−	4.60181i	−0.191245	−	0.331245i	−0.945663	+	0.325149i	$0.894586\pi$
$194$	8.70855	−	15.0837i	0.625237	−	1.08294i
$195$	−5.61750	+	17.0782i	−0.402278	+	1.22299i
$196$		0			0
$197$		0			0		1.00000			$0$
$197$		0			0		−1.00000			$\pi$
$198$	−6.16592	+	2.69190i	−0.438193	+	0.191305i
$199$	−14.9039	+	8.60474i	−1.05651	+	0.609974i	−0.924464	−	0.381270i	$-0.875487\pi$
$199$	−14.9039	+	8.60474i	−1.05651	+	0.609974i	−0.132042	+	0.991244i	$0.542154\pi$
$200$	1.09057	−	0.629640i	0.0771148	−	0.0445223i
$201$	18.7056	−	16.7203i	1.31939	−	1.17936i
$202$		−	16.3672i		−	1.15159i
$203$		0			0
$204$	−0.656854	−	0.216058i	−0.0459890	−	0.0151271i
$205$	4.94975	−	8.57321i	0.345705	−	0.598779i
$206$	−10.1543	−	17.5877i	−0.707481	−	1.22539i
$207$	−12.8176	−	1.44113i	−0.890884	−	0.100166i
$208$	−11.5897	−	6.69133i	−0.803602	−	0.463960i
$209$	3.85525			0.266673
$210$		0			0
$211$	21.7990			1.50070			0.750352	−	0.661038i	$-0.229884\pi$
$211$	21.7990			1.50070			0.750352	+	0.661038i	$0.229884\pi$
$212$	−2.18114	−	1.25928i	−0.149801	−	0.0864877i
$213$	13.3287	−	2.78268i	0.913266	−	0.190666i
$214$	−5.60660	−	9.71092i	−0.383259	−	0.663825i
$215$	2.32685	−	4.03022i	0.158690	−	0.274858i
$216$	−12.8803	+	9.14594i	−0.876396	+	0.622302i
$217$		0			0
$218$			11.8551i			0.802931i
$219$	−7.43364	−	8.31627i	−0.502319	−	0.561961i
$220$	1.48648	−	0.858221i	0.100219	−	0.0578613i
$221$	3.72343	−	2.14973i	0.250465	−	0.144606i
$222$	7.37123	+	8.24645i	0.494724	+	0.553466i
$223$			0.896683i			0.0600463i	0.999549	+	0.0300232i	$0.00955811\pi$
$223$			0.896683i			0.0600463i	−0.999549	+	0.0300232i	$0.990442\pi$
$224$		0			0
$225$	1.00000	+	0.737669i	0.0666667	+	0.0491779i
$226$	7.00000	−	12.1244i	0.465633	−	0.806500i
$227$	−8.90816	−	15.4294i	−0.591255	−	1.02408i	−0.994064	−	0.108800i	$-0.965299\pi$
$227$	−8.90816	−	15.4294i	−0.591255	−	1.02408i	0.402808	−	0.915284i	$-0.368034\pi$
$228$	1.52032	−	0.317403i	0.100686	−	0.0210205i
$229$	9.32669	+	5.38476i	0.616325	+	0.355835i	0.775437	−	0.631425i	$-0.217530\pi$
$229$	9.32669	+	5.38476i	0.616325	+	0.355835i	−0.159112	+	0.987261i	$0.550863\pi$
$230$	−12.5980			−0.830690
$231$		0			0
$232$	23.8995			1.56908
$233$	−15.5326	−	8.96774i	−1.01757	−	0.587496i	−0.104173	−	0.994559i	$-0.533220\pi$
$233$	−15.5326	−	8.96774i	−1.01757	−	0.587496i	−0.913400	+	0.407063i	$0.866553\pi$
$234$	1.88293	−	16.7470i	0.123091	−	1.09479i
$235$	−0.656854	−	1.13770i	−0.0428484	−	0.0742157i
$236$	−1.92762	+	3.33874i	−0.125478	+	0.217333i
$237$	7.94435	+	2.61313i	0.516041	+	0.169741i
$238$		0			0
$239$		−	14.3737i		−	0.929757i	−0.885375	−	0.464878i	$-0.846098\pi$
$239$		−	14.3737i		−	0.929757i	0.885375	−	0.464878i	$-0.153902\pi$
$240$	−9.01435	+	8.05763i	−0.581874	+	0.520117i
$241$	−10.2641	+	5.92596i	−0.661167	+	0.381725i	−0.792721	−	0.609584i	$-0.791336\pi$
$241$	−10.2641	+	5.92596i	−0.661167	+	0.381725i	0.131555	+	0.991309i	$0.458003\pi$
$242$	8.53744	−	4.92909i	0.548807	−	0.316854i
$243$	−13.3566	−	8.03742i	−0.856829	−	0.515601i
$244$			3.11586i			0.199473i
$245$		0			0
$246$	−2.89949	+	8.81496i	−0.184865	+	0.562021i
$247$	−4.82843	+	8.36308i	−0.307225	+	0.532130i
$248$	1.64533	+	2.84979i	0.104478	+	0.180962i
$249$	5.14172	+	24.6282i	0.325843	+	1.56075i
$250$	−11.6368	−	6.71852i	−0.735977	−	0.424917i
$251$	12.0335			0.759545			0.379772	−	0.925080i	$-0.376002\pi$
$251$	12.0335			0.759545			0.379772	+	0.925080i	$0.376002\pi$
$252$		0			0
$253$	−7.65685			−0.481382
$254$	−2.18114	−	1.25928i	−0.136857	−	0.0790143i
$255$	−0.793838	−	3.80239i	−0.0497121	−	0.238115i
$256$	4.74264	+	8.21449i	0.296415	+	0.513406i
$257$	5.41789	−	9.38406i	0.337959	−	0.585362i	−0.646090	−	0.763261i	$-0.723597\pi$
$257$	5.41789	−	9.38406i	0.337959	−	0.585362i	0.984049	+	0.177900i	$0.0569302\pi$
$258$	−1.36303	+	4.14386i	−0.0848589	+	0.257985i
$259$		0			0
$260$			4.29945i			0.266641i
$261$	9.43603	+	21.6137i	0.584076	+	1.33785i
$262$	17.9434	−	10.3596i	1.10855	−	0.640021i
$263$	2.44575	−	1.41206i	0.150812	−	0.0870711i	−0.422695	−	0.906272i	$-0.638916\pi$
$263$	2.44575	−	1.41206i	0.150812	−	0.0870711i	0.573507	+	0.819201i	$0.305583\pi$
$264$	−6.99167	+	6.24962i	−0.430307	+	0.384637i
$265$		−	14.1480i		−	0.869106i
$266$		0			0
$267$	−13.7279	−	4.51551i	−0.840135	−	0.276345i
$268$	3.00000	−	5.19615i	0.183254	−	0.317406i
$269$	8.99084	+	15.5726i	0.548181	+	0.949478i	0.998399	+	0.0565593i	$0.0180130\pi$
$269$	8.99084	+	15.5726i	0.548181	+	0.949478i	−0.450218	+	0.892919i	$0.648654\pi$
$270$	−13.8411	−	6.34354i	−0.842342	−	0.386056i
$271$	4.68690	+	2.70598i	0.284709	+	0.164377i	0.635553	−	0.772057i	$-0.280772\pi$
$271$	4.68690	+	2.70598i	0.284709	+	0.164377i	−0.350845	+	0.936434i	$0.614105\pi$
$272$	2.89143			0.175319
$273$		0			0
$274$	−11.7574			−0.710288
$275$	0.638840	+	0.368835i	0.0385235	+	0.0222416i
$276$	−3.01949	+	0.630391i	−0.181752	+	0.0379451i
$277$	0.242641	+	0.420266i	0.0145789	+	0.0252513i	0.873223	−	0.487321i	$-0.162026\pi$
$277$	0.242641	+	0.420266i	0.0145789	+	0.0252513i	−0.858644	+	0.512573i	$0.828693\pi$
$278$	−10.9527	+	18.9707i	−0.656900	+	1.13778i
$279$	−1.92762	+	2.61313i	−0.115404	+	0.156444i
$280$		0			0
$281$			1.34877i			0.0804611i	0.999190	+	0.0402306i	$0.0128092\pi$
$281$			1.34877i			0.0804611i	−0.999190	+	0.0402306i	$0.987191\pi$
$282$	0.820676	+	0.918119i	0.0488706	+	0.0546732i
$283$	−14.9039	+	8.60474i	−0.885942	+	0.511499i	−0.872613	−	0.488412i	$-0.837576\pi$
$283$	−14.9039	+	8.60474i	−0.885942	+	0.511499i	−0.0133292	+	0.999911i	$0.504243\pi$
$284$	2.81998	−	1.62811i	0.167335	−	0.0966108i
$285$	5.81434	+	6.50471i	0.344412	+	0.385306i
$286$		−	10.0042i		−	0.591559i
$287$		0			0
$288$	−4.10051	+	5.55873i	−0.241625	+	0.327551i
$289$	8.03553	−	13.9180i	0.472678	−	0.818703i
$290$	11.5173	+	19.9486i	0.676319	+	1.17142i
$291$	23.4504	−	4.89582i	1.37469	−	0.286998i
$292$	−2.31014	−	1.33376i	−0.135191	−	0.0780524i
$293$	−6.74668			−0.394145			−0.197073	−	0.980389i	$-0.563143\pi$
$293$	−6.74668			−0.394145			−0.197073	+	0.980389i	$0.563143\pi$
$294$		0			0
$295$	−21.6569			−1.26091
$296$	13.3514	+	7.70846i	0.776037	+	0.448045i
$297$	−8.41235	−	3.85549i	−0.488134	−	0.223718i
$298$	−4.75736	−	8.23999i	−0.275586	−	0.477330i
$299$	9.58968	−	16.6098i	0.554585	−	0.960570i
$300$	0.282294	+	0.0928546i	0.0162982	+	0.00536096i
$301$		0			0
$302$		−	0.611105i		−	0.0351652i
$303$	16.7841	−	15.0027i	0.964220	−	0.861884i
$304$	−5.62427	+	3.24718i	−0.322574	+	0.186238i
$305$	−15.1584	+	8.75168i	−0.867965	+	0.501120i
$306$	1.45684	+	3.33697i	0.0832822	+	0.190762i
$307$		−	9.81845i		−	0.560369i	−0.959946	−	0.280184i	$-0.909604\pi$
$307$		−	9.81845i		−	0.560369i	0.959946	−	0.280184i	$-0.0903956\pi$
$308$		0			0
$309$	8.72792	−	26.5344i	0.496514	−	1.50949i
$310$	−1.58579	+	2.74666i	−0.0900666	+	0.156000i
$311$	8.62587	+	14.9404i	0.489128	+	0.847195i	0.999922	−	0.0125086i	$-0.00398173\pi$
$311$	8.62587	+	14.9404i	0.489128	+	0.847195i	−0.510794	+	0.859703i	$0.670648\pi$
$312$	−4.80055	−	22.9940i	−0.271778	−	1.30178i
$313$	0.0471057	+	0.0271965i	0.00266257	+	0.00153724i	0.501331	−	0.865256i	$-0.332844\pi$
$313$	0.0471057	+	0.0271965i	0.00266257	+	0.00153724i	−0.498668	+	0.866793i	$0.666177\pi$
$314$	−8.10971			−0.457658
$315$		0			0
$316$	2.00000			0.112509
$317$	29.7875	+	17.1978i	1.67303	+	0.965925i	0.965927	+	0.258816i	$0.0833323\pi$
$317$	29.7875	+	17.1978i	1.67303	+	0.965925i	0.707104	+	0.707109i	$0.250001\pi$
$318$	2.71033	+	12.9822i	0.151988	+	0.728003i
$319$	7.00000	+	12.1244i	0.391925	+	0.678834i
$320$	−10.3539	+	17.9334i	−0.578799	+	1.00251i
$321$	4.81906	−	14.6508i	0.268973	−	0.817725i
$322$		0			0
$323$		−	2.08644i		−	0.116093i
$324$	−3.63485	−	0.827826i	−0.201936	−	0.0459903i
$325$	−1.60021	+	0.923880i	−0.0887635	+	0.0512476i
$326$	−10.0022	+	5.77479i	−0.553972	+	0.319836i
$327$	−12.1571	+	10.8668i	−0.672288	+	0.600936i
$328$			12.9343i			0.714178i
$329$		0			0
$330$	−8.58579	−	2.82411i	−0.472632	−	0.155462i
$331$	−9.41421	+	16.3059i	−0.517452	+	0.896253i	0.482343	+	0.875983i	$0.339786\pi$
$331$	−9.41421	+	16.3059i	−0.517452	+	0.896253i	−0.999795	+	0.0202704i	$0.993547\pi$
$332$	3.00836	+	5.21064i	0.165105	+	0.285971i
$333$	−1.69977	+	15.1179i	−0.0931469	+	0.828458i
$334$	6.56165	+	3.78837i	0.359038	+	0.207291i
$335$	33.7050			1.84150
$336$		0			0
$337$	6.10051			0.332316			0.166158	−	0.986099i	$-0.446864\pi$
$337$	6.10051			0.332316			0.166158	+	0.986099i	$0.446864\pi$
$338$	7.52437	+	4.34420i	0.409272	+	0.236293i
$339$	18.8496	−	3.93530i	1.02377	−	0.213736i
$340$	−0.464466	−	0.804479i	−0.0251892	−	0.0436290i
$341$	−0.963811	+	1.66937i	−0.0521933	+	0.0904015i
$342$	−6.58132	−	4.85483i	−0.355877	−	0.262519i
$343$		0			0
$344$			6.08034i			0.327830i
$345$	−11.5478	−	12.9189i	−0.621712	−	0.695531i
$346$	19.8653	−	11.4692i	1.06797	−	0.616590i
$347$	−5.53035	+	3.19295i	−0.296885	+	0.171406i	−0.641043	−	0.767505i	$-0.721498\pi$
$347$	−5.53035	+	3.19295i	−0.296885	+	0.171406i	0.344158	+	0.938912i	$0.388164\pi$
$348$	3.75866	+	4.20494i	0.201485	+	0.225409i
$349$			28.9845i			1.55150i	0.631038	+	0.775752i	$0.282629\pi$
$349$			28.9845i			1.55150i	−0.631038	+	0.775752i	$0.717371\pi$
$350$		0			0
$351$	18.8995	−	13.4200i	1.00878	−	0.716305i
$352$	−2.05025	+	3.55114i	−0.109279	+	0.189276i
$353$	−12.7977	−	22.1662i	−0.681150	−	1.17979i	−0.974630	−	0.223822i	$-0.928147\pi$
$353$	−12.7977	−	22.1662i	−0.681150	−	1.17979i	0.293480	−	0.955965i	$-0.405187\pi$
$354$	19.8722	−	4.14880i	1.05620	−	0.220506i
$355$	15.8412	+	9.14594i	0.840765	+	0.485416i
$356$	−3.45602			−0.183169
$357$		0			0
$358$	16.2426			0.858450
$359$	−1.91652	−	1.10650i	−0.101150	−	0.0583990i	0.448572	−	0.893747i	$-0.351933\pi$
$359$	−1.91652	−	1.10650i	−0.101150	−	0.0583990i	−0.549722	+	0.835348i	$0.685266\pi$
$360$	−21.0892	−	2.37114i	−1.11150	−	0.124970i
$361$	−7.15685	−	12.3960i	−0.376677	−	0.652423i
$362$	1.96187	−	3.39806i	0.103114	−	0.178598i
$363$	12.8803	+	4.23671i	0.676042	+	0.222370i
$364$		0			0
$365$		−	14.9848i		−	0.784340i
$366$	12.2327	−	10.9344i	0.639412	−	0.571549i
$367$	29.9019	−	17.2639i	1.56087	−	0.901167i	0.563698	−	0.825981i	$-0.309378\pi$
$367$	29.9019	−	17.2639i	1.56087	−	0.901167i	0.997169	−	0.0751864i	$-0.0239552\pi$
$368$	11.1703	−	6.44918i	0.582292	−	0.336187i
$369$	−11.6973	+	5.10674i	−0.608935	+	0.265846i
$370$			14.8590i			0.772482i
$371$		0			0
$372$	−0.242641	+	0.737669i	−0.0125803	+	0.0382464i
$373$	4.58579	−	7.94282i	0.237443	−	0.411263i	−0.722537	−	0.691332i	$-0.757024\pi$
$373$	4.58579	−	7.94282i	0.237443	−	0.411263i	0.959980	+	0.280069i	$0.0903574\pi$
$374$	1.08074	+	1.87190i	0.0558838	+	0.0967936i
$375$	−3.77706	−	18.0916i	−0.195047	−	0.934248i
$376$	1.48648	+	0.858221i	0.0766595	+	0.0442594i
$377$	−35.0681			−1.80610
$378$		0			0
$379$	−12.0000			−0.616399			−0.308199	−	0.951322i	$-0.599726\pi$
$379$	−12.0000			−0.616399			−0.308199	+	0.951322i	$0.599726\pi$
$380$	1.80691	+	1.04322i	0.0926927	+	0.0535161i
$381$	−0.707950	−	3.39099i	−0.0362694	−	0.173726i
$382$	7.19239	+	12.4576i	0.367995	+	0.637385i
$383$	7.54513	−	13.0685i	0.385538	−	0.667771i	−0.606306	−	0.795232i	$-0.707349\pi$
$383$	7.54513	−	13.0685i	0.385538	−	0.667771i	0.991844	+	0.127460i	$0.0406826\pi$
$384$	3.57295	−	10.8624i	0.182331	−	0.554319i
$385$		0			0
$386$			6.69145i			0.340586i
$387$	−5.49881	+	2.40065i	−0.279520	+	0.122032i
$388$	4.96145	−	2.86449i	0.251879	−	0.145423i
$389$	−3.19420	+	1.84417i	−0.161952	+	0.0935033i	−0.578786	−	0.815480i	$-0.696473\pi$
$389$	−3.19420	+	1.84417i	−0.161952	+	0.0935033i	0.416833	+	0.908983i	$0.363140\pi$
$390$	16.8794	−	15.0879i	0.854720	−	0.764006i
$391$			4.14386i			0.209564i
$392$		0			0
$393$	27.0711	+	8.90446i	1.36555	+	0.449170i
$394$		0			0
$395$	5.61750	+	9.72980i	0.282647	+	0.489559i
$396$	−2.19915	−	0.247259i	−0.110512	−	0.0124253i
$397$	−19.6379	−	11.3379i	−0.985596	−	0.569034i	−0.0816409	−	0.996662i	$-0.526016\pi$
$397$	−19.6379	−	11.3379i	−0.985596	−	0.569034i	−0.903955	+	0.427628i	$0.859349\pi$
$398$	21.6716			1.08630
$399$		0			0
$400$	−1.24264			−0.0621320
$401$	−29.1486	−	16.8290i	−1.45561	−	0.840399i	−0.456822	−	0.889558i	$-0.651012\pi$
$401$	−29.1486	−	16.8290i	−1.45561	−	0.840399i	−0.998791	+	0.0491593i	$0.984346\pi$
$402$	−30.9276	+	6.45686i	−1.54253	+	0.322039i
$403$	−2.41421	−	4.18154i	−0.120261	−	0.208297i
$404$	2.69182	−	4.66237i	0.133923	−	0.231962i
$405$	−6.18209	−	20.0083i	−0.307191	−	0.994222i
$406$		0			0
$407$			9.03102i			0.447651i
$408$	3.38227	+	3.78386i	0.167447	+	0.187329i
$409$	−26.1053	+	15.0719i	−1.29082	+	0.745258i	−0.978800	−	0.204817i	$-0.934340\pi$
$409$	−26.1053	+	15.0719i	−1.29082	+	0.745258i	−0.312024	+	0.950074i	$0.601007\pi$
$410$	−10.7961	+	6.23312i	−0.533180	+	0.307832i
$411$	−10.7772	−	12.0568i	−0.531600	−	0.594719i
$412$		−	6.68006i		−	0.329103i
$413$		0			0
$414$	13.0711	+	9.64212i	0.642408	+	0.473885i
$415$	−16.8995	+	29.2708i	−0.829564	+	1.43685i
$416$	−5.13560	−	8.89512i	−0.251793	−	0.436119i
$417$	−29.4935	+	6.15746i	−1.44430	+	0.301532i
$418$	−4.20441	−	2.42742i	−0.205644	−	0.118729i
$419$	−3.52452			−0.172184			−0.0860920	−	0.996287i	$-0.527438\pi$
$419$	−3.52452			−0.172184			−0.0860920	+	0.996287i	$0.527438\pi$
$420$		0			0
$421$	−31.7990			−1.54979			−0.774894	−	0.632091i	$-0.782197\pi$
$421$	−31.7990			−1.54979			−0.774894	+	0.632091i	$0.782197\pi$
$422$	−23.7733	−	13.7255i	−1.15727	−	0.668148i
$423$	−0.189244	+	1.68316i	−0.00920137	+	0.0818379i
$424$	9.24264	+	16.0087i	0.448862	+	0.777452i
$425$	0.199612	−	0.345738i	0.00968260	−	0.0167708i
$426$	−16.2879	−	5.35757i	−0.789152	−	0.259575i
$427$		0			0
$428$		−	3.68835i		−	0.178283i
$429$	10.2590	−	9.17015i	0.495308	−	0.442739i
$430$	−5.07517	+	2.93015i	−0.244746	+	0.141304i
$431$	23.3537	−	13.4832i	1.12491	−	0.649465i	0.182258	−	0.983251i	$-0.441660\pi$
$431$	23.3537	−	13.4832i	1.12491	−	0.649465i	0.942649	+	0.333786i	$0.108326\pi$
$432$	15.5199	−	1.46089i	0.746699	−	0.0702870i
$433$			6.25425i			0.300560i	0.988643	+	0.150280i	$0.0480175\pi$
$433$			6.25425i			0.300560i	−0.988643	+	0.150280i	$0.951982\pi$
$434$		0			0
$435$	−9.89949	+	30.0962i	−0.474644	+	1.44300i
$436$	−1.94975	+	3.37706i	−0.0933760	+	0.161732i
$437$	−4.65369	−	8.06043i	−0.222616	−	0.385583i
$438$	2.87063	+	13.7500i	0.137164	+	0.656999i
$439$	11.2485	+	6.49435i	0.536864	+	0.309959i	0.743807	−	0.668394i	$-0.233018\pi$
$439$	11.2485	+	6.49435i	0.536864	+	0.309959i	−0.206943	+	0.978353i	$0.566351\pi$
$440$	−12.5980			−0.600588
$441$		0			0
$442$	−5.41421			−0.257528
$443$	−4.25267	−	2.45528i	−0.202050	−	0.116654i	0.395561	−	0.918440i	$-0.370550\pi$
$443$	−4.25267	−	2.45528i	−0.202050	−	0.116654i	−0.597611	+	0.801786i	$0.703883\pi$
$444$	0.743526	+	3.56139i	0.0352862	+	0.169016i
$445$	−9.70711	−	16.8132i	−0.460161	−	0.797022i
$446$	0.564588	−	0.977894i	0.0267340	−	0.0463046i
$447$	4.08910	−	12.4316i	0.193408	−	0.587994i
$448$		0			0
$449$			26.8399i			1.26665i	0.773884	+	0.633327i	$0.218311\pi$
$449$			26.8399i			1.26665i	−0.773884	+	0.633327i	$0.781689\pi$
$450$	−0.626102	−	1.43412i	−0.0295148	−	0.0676050i
$451$	−6.56165	+	3.78837i	−0.308976	+	0.178388i
$452$	3.98805	−	2.30250i	0.187582	−	0.108301i
$453$	0.626670	−	0.560160i	0.0294435	−	0.0263186i
$454$			22.4357i			1.05296i
$455$		0			0
$456$	−10.8284	−	3.56178i	−0.507088	−	0.166796i
$457$	−5.31371	+	9.20361i	−0.248565	+	0.430527i	−0.963128	−	0.269044i	$-0.913292\pi$
$457$	−5.31371	+	9.20361i	−0.248565	+	0.430527i	0.714563	+	0.699571i	$0.246626\pi$
$458$	−6.78093	−	11.7449i	−0.316852	−	0.548804i
$459$	−2.08657	+	4.55273i	−0.0973930	+	0.212503i
$460$	−3.58869	−	2.07193i	−0.167323	−	0.0966042i
$461$	0.729951			0.0339972			0.0169986	−	0.999856i	$-0.494589\pi$
$461$	0.729951			0.0339972			0.0169986	+	0.999856i	$0.494589\pi$
$462$		0			0
$463$	−12.0000			−0.557687			−0.278844	−	0.960337i	$-0.589951\pi$
$463$	−12.0000			−0.557687			−0.278844	+	0.960337i	$0.589951\pi$
$464$	−20.4241	−	11.7919i	−0.948164	−	0.547423i
$465$	−4.27021	+	0.891507i	−0.198026	+	0.0413426i
$466$	11.2929	+	19.5599i	0.523133	+	0.906093i
$467$	−0.963811	+	1.66937i	−0.0445999	+	0.0772492i	−0.887464	−	0.460878i	$-0.847535\pi$
$467$	−0.963811	+	1.66937i	−0.0445999	+	0.0772492i	0.842864	+	0.538127i	$0.180868\pi$
$468$	3.29066	−	4.46088i	0.152111	−	0.206204i
$469$		0			0
$470$			1.65433i			0.0763084i
$471$	−7.43364	−	8.31627i	−0.342524	−	0.383193i
$472$	24.5051	−	14.1480i	1.12794	−	0.651215i
$473$	−3.08459	+	1.78089i	−0.141830	+	0.0818855i
$474$	−7.01853	−	7.85187i	−0.322372	−	0.360649i
$475$			0.896683i			0.0411426i
$476$		0			0
$477$	−10.8284	+	14.6792i	−0.495800	+	0.672116i
$478$	−9.05025	+	15.6755i	−0.413949	+	0.716981i
$479$	−11.9165	−	20.6400i	−0.544480	−	0.943067i	−0.998639	−	0.0521465i	$-0.983394\pi$
$479$	−11.9165	−	20.6400i	−0.544480	−	0.943067i	0.454160	−	0.890920i	$-0.349940\pi$
$480$	−9.08373	+	1.89644i	−0.414614	+	0.0865604i
$481$	−19.5908	−	11.3107i	−0.893261	−	0.515725i
$482$	14.9249			0.679810
$483$		0			0
$484$	3.24264			0.147393
$485$	27.8710	+	16.0913i	1.26555	+	0.730668i
$486$	9.50565	+	17.1752i	0.431185	+	0.779085i
$487$	0.242641	+	0.420266i	0.0109951	+	0.0190441i	0.871471	−	0.490448i	$-0.163167\pi$
$487$	0.242641	+	0.420266i	0.0109951	+	0.0190441i	−0.860476	+	0.509492i	$0.829833\pi$
$488$	11.4346	−	19.8053i	0.517621	−	0.896546i
$489$	−15.0903	−	4.96362i	−0.682405	−	0.224463i
$490$		0			0
$491$		−	12.4662i		−	0.562593i	−0.959621	−	0.281297i	$-0.909235\pi$
$491$		−	12.4662i		−	0.562593i	0.959621	−	0.281297i	$-0.0907645\pi$
$492$	−2.27570	+	2.03417i	−0.102596	+	0.0917076i
$493$	6.56165	−	3.78837i	0.295522	−	0.170620i
$494$	10.5315	−	6.08034i	0.473833	−	0.273568i
$495$	−4.97398	−	11.3931i	−0.223564	−	0.512084i
$496$		−	3.24718i		−	0.145803i
$497$		0			0
$498$	9.89949	−	30.0962i	0.443607	−	1.34864i
$499$	4.58579	−	7.94282i	0.205288	−	0.355569i	−0.744936	−	0.667135i	$-0.767520\pi$
$499$	4.58579	−	7.94282i	0.205288	−	0.355569i	0.950224	+	0.311566i	$0.100854\pi$
$500$	−2.20992	−	3.82769i	−0.0988305	−	0.171179i
$501$	2.12977	+	10.2013i	0.0951511	+	0.455762i
$502$	−13.1233	−	7.57675i	−0.585722	−	0.338167i
$503$	−8.50894			−0.379395			−0.189697	−	0.981843i	$-0.560751\pi$
$503$	−8.50894			−0.379395			−0.189697	+	0.981843i	$0.560751\pi$
$504$		0			0
$505$	30.2426			1.34578
$506$	8.35032	+	4.82106i	0.371217	+	0.214322i
$507$	2.44225	+	11.6981i	0.108464	+	0.519529i
$508$	−0.414214	−	0.717439i	−0.0183778	−	0.0318312i
$509$	−18.1329	+	31.4070i	−0.803725	+	1.39209i	0.113423	+	0.993547i	$0.463818\pi$
$509$	−18.1329	+	31.4070i	−0.803725	+	1.39209i	−0.917148	+	0.398546i	$0.869515\pi$
$510$	−1.52840	+	4.64659i	−0.0676786	+	0.205755i
$511$		0			0
$512$		−	25.1485i		−	1.11142i
$513$	−1.05417	−	11.1990i	−0.0465427	−	0.494450i
$514$	−11.8172	+	6.82264i	−0.521233	+	0.300934i
$515$	32.4978	−	18.7626i	1.43203	−	0.826781i
$516$	−1.06979	+	0.956252i	−0.0470950	+	0.0420967i
$517$			1.00547i			0.0442205i
$518$		0			0
$519$	29.9706	+	9.85818i	1.31556	+	0.432726i
$520$	15.7782	−	27.3286i	0.691919	−	1.19844i
$521$	−0.764199	−	1.32363i	−0.0334802	−	0.0579894i	0.848800	−	0.528714i	$-0.177326\pi$
$521$	−0.764199	−	1.32363i	−0.0334802	−	0.0579894i	−0.882280	+	0.470725i	$0.843992\pi$
$522$	3.31821	−	29.5125i	0.145234	−	1.29173i
$523$	36.3694	+	20.9979i	1.59032	+	0.918172i	0.993251	+	0.115983i	$0.0370019\pi$
$523$	36.3694	+	20.9979i	1.59032	+	0.918172i	0.597070	+	0.802189i	$0.296331\pi$
$524$	6.81517			0.297722
$525$		0			0
$526$	−3.55635			−0.155064
$527$	0.903457	+	0.521611i	0.0393552	+	0.0227217i
$528$	9.05847	−	1.89117i	0.394219	−	0.0823027i
$529$	−2.25736	−	3.90986i	−0.0981461	−	0.169994i
$530$	−8.90816	+	15.4294i	−0.386946	+	0.670210i
$531$	22.4700	+	16.5754i	0.975116	+	0.719313i
$532$		0			0
$533$		−	18.9787i		−	0.822059i
$534$	12.1281	+	13.5681i	0.524834	+	0.587150i
$535$	17.9434	−	10.3596i	0.775763	−	0.447887i
$536$	−38.1378	+	22.0189i	−1.64730	+	0.951070i
$537$	14.8886	+	16.6563i	0.642488	+	0.718774i
$538$		−	22.6440i		−	0.976251i
$539$		0			0
$540$	−2.89949	−	4.08339i	−0.124774	−	0.175721i
$541$	7.48528	−	12.9649i	0.321817	−	0.557404i	−0.659046	−	0.752103i	$-0.729040\pi$
$541$	7.48528	−	12.9649i	0.321817	−	0.557404i	0.980863	+	0.194699i	$0.0623730\pi$
$542$	−3.40759	−	5.90211i	−0.146368	−	0.253518i
$543$	5.28292	−	1.10294i	0.226712	−	0.0473315i
$544$	1.92186	+	1.10959i	0.0823992	+	0.0475732i
$545$	−21.9054			−0.938325
$546$		0			0
$547$	21.7990			0.932058			0.466029	−	0.884770i	$-0.345684\pi$
$547$	21.7990			0.932058			0.466029	+	0.884770i	$0.345684\pi$
$548$	−3.34921	−	1.93367i	−0.143071	−	0.0826022i
$549$	22.4258	+	2.52142i	0.957108	+	0.107611i
$550$	−0.464466	−	0.804479i	−0.0198049	−	0.0343031i
$551$	−8.50894	+	14.7379i	−0.362493	+	0.627856i
$552$	21.5062	+	7.07401i	0.915365	+	0.301090i
$553$		0			0
$554$		−	0.611105i		−	0.0259634i
$555$	−15.2375	+	13.6203i	−0.646794	+	0.578148i
$556$	−6.24000	+	3.60266i	−0.264635	+	0.152787i
$557$	−23.6183	+	13.6360i	−1.00074	+	0.577777i	−0.908467	−	0.417957i	$-0.862746\pi$
$557$	−23.6183	+	13.6360i	−1.00074	+	0.577777i	−0.0922720	+	0.995734i	$0.529413\pi$
$558$	3.74753	−	1.63608i	0.158646	−	0.0692610i
$559$		−	8.92177i		−	0.377351i
$560$		0			0
$561$	−0.928932	+	2.82411i	−0.0392195	+	0.119234i
$562$	0.849242	−	1.47093i	0.0358231	−	0.0620475i
$563$	21.9054	+	37.9413i	0.923204	+	1.59904i	0.794425	+	0.607362i	$0.207772\pi$
$563$	21.9054	+	37.9413i	0.923204	+	1.59904i	0.128779	+	0.991673i	$0.458894\pi$
$564$	0.0827805	+	0.396508i	0.00348569	+	0.0166960i
$565$	22.4029	+	12.9343i	0.942497	+	0.544151i
$566$	21.6716			0.910924
$567$		0			0
$568$	−23.8995			−1.00280
$569$	30.9555	+	17.8722i	1.29772	+	0.749241i	0.980011	−	0.198946i	$-0.0637517\pi$
$569$	30.9555	+	17.8722i	1.29772	+	0.749241i	0.317713	+	0.948187i	$0.397085\pi$
$570$	−2.24531	−	10.7548i	−0.0940458	−	0.450468i
$571$	−12.5563	−	21.7482i	−0.525467	−	0.910135i	−0.999560	−	0.0296606i	$-0.990557\pi$
$571$	−12.5563	−	21.7482i	−0.525467	−	0.910135i	0.474093	−	0.880475i	$-0.342776\pi$
$572$	1.64533	−	2.84979i	0.0687947	−	0.119156i
$573$	−6.18209	+	18.7946i	−0.258261	+	0.785156i
$574$		0			0
$575$		−	1.78089i		−	0.0742683i
$576$	24.4683	−	10.6823i	1.01951	−	0.445095i
$577$	−0.984485	+	0.568393i	−0.0409846	+	0.0236625i	−0.520352	−	0.853952i	$-0.674199\pi$
$577$	−0.984485	+	0.568393i	−0.0409846	+	0.0236625i	0.479368	+	0.877614i	$0.340866\pi$
$578$	−17.5266	+	10.1190i	−0.729011	+	0.420894i
$579$	−6.86188	+	6.13361i	−0.285170	+	0.254904i
$580$			7.57675i			0.314607i
$581$		0			0
$582$	−28.6569	−	9.42607i	−1.18786	−	0.390723i
$583$	−5.41421	+	9.37769i	−0.224234	+	0.388384i
$584$	9.78929	+	16.9555i	0.405084	+	0.701626i
$585$	30.9444	+	3.47920i	1.27939	+	0.143847i
$586$	7.35772	+	4.24798i	0.303944	+	0.175482i
$587$		0			0			−	1.00000i	$-0.5\pi$
$587$		0			0				1.00000i	$0.5\pi$
$588$		0			0
$589$	−2.34315			−0.0965476
$590$	23.6183	+	13.6360i	0.972349	+	0.561386i
$591$		0			0
$592$	−7.60660	−	13.1750i	−0.312629	−	0.541490i
$593$	12.6807	−	21.9637i	0.520735	−	0.901939i	−0.478974	−	0.877829i	$-0.658991\pi$
$593$	12.6807	−	21.9637i	0.520735	−	0.901939i	0.999709	−	0.0241105i	$-0.00767535\pi$
$594$	6.74668	+	9.50143i	0.276820	+	0.389848i
$595$		0			0
$596$		−	3.12967i		−	0.128196i
$597$	19.8649	+	22.2235i	0.813016	+	0.909549i
$598$	−20.9164	+	12.0761i	−0.855335	+	0.493828i
$599$	35.3178	−	20.3908i	1.44305	−	0.833144i	0.444995	−	0.895533i	$-0.353205\pi$
$599$	35.3178	−	20.3908i	1.44305	−	0.833144i	0.998052	+	0.0623894i	$0.0198721\pi$
$600$	−1.45359	−	1.62618i	−0.0593424	−	0.0663884i
$601$			13.8310i			0.564178i	0.959388	+	0.282089i	$0.0910274\pi$
$601$			13.8310i			0.564178i	−0.959388	+	0.282089i	$0.908973\pi$
$602$		0			0
$603$	−34.9706	−	25.7967i	−1.42411	−	1.05052i
$604$	0.100505	−	0.174080i	0.00408949	−	0.00708321i
$605$	9.10777	+	15.7751i	0.370284	+	0.641350i
$606$	−27.7505	+	5.79358i	−1.12729	+	0.235348i
$607$	−33.5572	−	19.3743i	−1.36205	−	0.786378i	−0.372150	−	0.928173i	$-0.621379\pi$
$607$	−33.5572	−	19.3743i	−1.36205	−	0.786378i	−0.989896	+	0.141795i	$0.954713\pi$
$608$	−4.98442			−0.202145
$609$		0			0
$610$	22.0416			0.892440
$611$	−2.18114	−	1.25928i	−0.0882394	−	0.0509450i
$612$	−0.133816	+	1.19017i	−0.00540918	+	0.0481099i
$613$	19.1924	+	33.2422i	0.775173	+	1.34264i	0.934697	+	0.355445i	$0.115671\pi$
$613$	19.1924	+	33.2422i	0.775173	+	1.34264i	−0.159524	+	0.987194i	$0.550996\pi$
$614$	−6.18209	+	10.7077i	−0.249489	+	0.432127i
$615$	−16.2879	−	5.35757i	−0.656792	−	0.216038i
$616$		0			0
$617$			17.0712i			0.687262i	0.939105	+	0.343631i	$0.111657\pi$
$617$			17.0712i			0.687262i	−0.939105	+	0.343631i	$0.888343\pi$
$618$	−26.2255	+	23.4421i	−1.05494	+	0.942980i
$619$	−21.4655	+	12.3931i	−0.862772	+	0.498121i	−0.864939	−	0.501876i	$-0.832643\pi$
$619$	−21.4655	+	12.3931i	−0.862772	+	0.498121i	0.00216781	+	0.999998i	$0.499310\pi$
$620$	−0.903457	+	0.521611i	−0.0362837	+	0.0209484i
$621$	2.09367	+	22.2423i	0.0840161	+	0.892552i
$622$		−	21.7248i		−	0.871084i
$623$		0			0
$624$	−7.24264	+	22.0189i	−0.289938	+	0.881460i
$625$	13.4497	−	23.2956i	0.537990	−	0.931826i
$626$	−0.0342480	−	0.0593192i	−0.00136882	−	0.00237087i
$627$	−1.36466	−	6.53655i	−0.0544993	−	0.261045i
$628$	−2.31014	−	1.33376i	−0.0921846	−	0.0532228i
$629$	4.88755			0.194879
$630$		0			0
$631$	7.79899			0.310473			0.155236	−	0.987877i	$-0.450386\pi$
$631$	7.79899			0.310473			0.155236	+	0.987877i	$0.450386\pi$
$632$	−12.7126	−	7.33962i	−0.505680	−	0.291955i
$633$	−7.71629	−	36.9601i	−0.306695	−	1.46903i
$634$	−21.6569	−	37.5108i	−0.860104	−	1.48974i
$635$	2.32685	−	4.03022i	0.0923381	−	0.159934i
$636$	−1.36303	+	4.14386i	−0.0540479	+	0.164315i
$637$		0			0
$638$		−	17.6299i		−	0.697975i
$639$	−9.43603	−	21.6137i	−0.373284	−	0.855025i
$640$	13.3036	−	7.68087i	0.525873	−	0.303613i
$641$	−5.53035	+	3.19295i	−0.218436	+	0.126114i	−0.605226	−	0.796054i	$-0.706917\pi$
$641$	−5.53035	+	3.19295i	−0.218436	+	0.126114i	0.386790	+	0.922168i	$0.373584\pi$
$642$	−14.4802	+	12.9434i	−0.571488	+	0.510835i
$643$		−	35.6871i		−	1.40736i	−0.710517	−	0.703681i	$-0.751539\pi$
$643$		−	35.6871i		−	1.40736i	0.710517	−	0.703681i	$-0.248461\pi$
$644$		0			0
$645$	−7.65685	−	2.51856i	−0.301488	−	0.0991682i
$646$	−1.31371	+	2.27541i	−0.0516872	+	0.0895248i
$647$	6.86361	+	11.8881i	0.269836	+	0.467370i	0.968819	−	0.247768i	$-0.0796971\pi$
$647$	6.86361	+	11.8881i	0.269836	+	0.467370i	−0.698983	+	0.715138i	$0.746364\pi$
$648$	20.0662	+	18.6011i	0.788275	+	0.730721i
$649$	14.3548	+	8.28772i	0.563473	+	0.325321i
$650$	2.32685			0.0912664
$651$		0			0
$652$	−3.79899			−0.148780
$653$	−1.91652	−	1.10650i	−0.0749993	−	0.0433008i	0.462031	−	0.886864i	$-0.347121\pi$
$653$	−1.91652	−	1.10650i	−0.0749993	−	0.0433008i	−0.537031	+	0.843563i	$0.680454\pi$
$654$	20.1003	−	4.19642i	0.785984	−	0.164093i
$655$	19.1421	+	33.1552i	0.747945	+	1.29548i
$656$	6.38170	−	11.0534i	0.249164	−	0.431564i
$657$	−11.4689	+	15.5474i	−0.447443	+	0.606563i
$658$		0			0
$659$			50.4236i			1.96423i	0.188293	+	0.982113i	$0.439704\pi$
$659$			50.4236i			1.96423i	−0.188293	+	0.982113i	$0.560296\pi$
$660$	−1.98129	−	2.21654i	−0.0771215	−	0.0862785i
$661$	−16.8257	+	9.71433i	−0.654445	+	0.377844i	−0.790157	−	0.612905i	$-0.790001\pi$
$661$	−16.8257	+	9.71433i	−0.654445	+	0.377844i	0.135712	+	0.990748i	$0.456668\pi$
$662$	20.5337	−	11.8551i	0.798065	−	0.460763i
$663$	−4.96285	−	5.55211i	−0.192741	−	0.215626i
$664$		−	44.1605i		−	1.71376i
$665$		0			0
$666$	11.3726	−	15.4169i	0.440679	−	0.597393i
$667$	16.8995	−	29.2708i	0.654351	−	1.13337i
$668$	1.24611	+	2.15832i	0.0482133	+	0.0835078i
$669$	1.52032	−	0.317403i	0.0587790	−	0.0122715i
$670$	−36.7576	−	21.2220i	−1.42007	−	0.819879i
$671$	13.3965			0.517166
$672$		0			0
$673$	−7.89949			−0.304503			−0.152252	−	0.988342i	$-0.548652\pi$
$673$	−7.89949			−0.304503			−0.152252	+	0.988342i	$0.548652\pi$
$674$	−6.65302	−	3.84112i	−0.256265	−	0.147955i
$675$	0.896739	−	1.95661i	0.0345155	−	0.0753100i
$676$	1.42893	+	2.47498i	0.0549589	+	0.0951917i
$677$	−0.598836	+	1.03721i	−0.0230151	+	0.0398634i	−0.877304	−	0.479936i	$-0.840660\pi$
$677$	−0.598836	+	1.03721i	−0.0230151	+	0.0398634i	0.854288	+	0.519799i	$0.173993\pi$
$678$	−23.0346	−	7.57675i	−0.884639	−	0.290983i
$679$		0			0
$680$			6.81801i			0.261459i
$681$	−23.0072	+	20.5654i	−0.881637	+	0.788066i
$682$	2.10220	−	1.21371i	0.0804976	−	0.0464753i
$683$	−24.7864	+	14.3104i	−0.948424	+	0.547573i	−0.892591	−	0.450868i	$-0.851115\pi$
$683$	−24.7864	+	14.3104i	−0.948424	+	0.547573i	−0.0558327	+	0.998440i	$0.517781\pi$
$684$	−1.07631	−	2.46534i	−0.0411538	−	0.0942648i
$685$		−	21.7248i		−	0.830061i
$686$		0			0
$687$	5.82843	−	17.7194i	0.222368	−	0.676038i
$688$	3.00000	−	5.19615i	0.114374	−	0.198101i
$689$	−13.5619	−	23.4898i	−0.516665	−	0.894891i
$690$	4.45939	+	21.3599i	0.169766	+	0.813158i
$691$	−17.7160	−	10.2283i	−0.673948	−	0.389104i	0.123623	−	0.992329i	$-0.460549\pi$
$691$	−17.7160	−	10.2283i	−0.673948	−	0.389104i	−0.797571	+	0.603225i	$0.793882\pi$
$692$	7.54513			0.286823
$693$		0			0
$694$	8.04163			0.305256
$695$	−35.0532	−	20.2380i	−1.32964	−	0.767670i
$696$	−8.45982	−	40.5215i	−0.320669	−	1.53596i
$697$	2.05025	+	3.55114i	0.0776589	+	0.134509i
$698$	18.2498	−	31.6096i	0.690765	−	1.19644i
$699$	−9.70661	+	29.5098i	−0.367138	+	1.11616i
$700$		0			0
$701$		−	1.34877i		−	0.0509425i	−0.999676	−	0.0254713i	$-0.991891\pi$
$701$		−	1.34877i		−	0.0509425i	0.999676	−	0.0254713i	$-0.00810863\pi$
$702$	−29.0609	+	2.73551i	−1.09683	+	0.103245i
$703$	−9.50703	+	5.48888i	−0.358564	+	0.207017i
$704$	13.7257	−	7.92452i	0.517305	−	0.298666i
$705$	−1.69646	+	1.51641i	−0.0638925	+	0.0571114i
$706$			32.2317i			1.21305i
$707$		0			0
$708$	6.34315	+	2.08644i	0.238390	+	0.0784134i
$709$	−14.3640	+	24.8791i	−0.539450	+	0.934355i	0.459484	+	0.888186i	$0.348034\pi$
$709$	−14.3640	+	24.8791i	−0.539450	+	0.934355i	−0.998934	+	0.0461684i	$0.985299\pi$
$710$	−11.5173	−	19.9486i	−0.432237	−	0.748656i
$711$	1.61844	−	14.3946i	0.0606963	−	0.539839i
$712$	21.9675	+	12.6829i	0.823267	+	0.475314i
$713$	4.65369			0.174282
$714$		0			0
$715$	18.4853			0.691310
$716$	4.62689	+	2.67134i	0.172915	+	0.0998325i
$717$	−24.3705	+	5.08793i	−0.910134	+	0.190012i
$718$	1.39340	+	2.41344i	0.0520012	+	0.0900687i
$719$	−3.45602	+	5.98600i	−0.128888	+	0.223240i	−0.923246	−	0.384209i	$-0.874474\pi$
$719$	−3.45602	+	5.98600i	−0.128888	+	0.223240i	0.794358	+	0.607450i	$0.207807\pi$
$720$	16.8525	+	12.4316i	0.628056	+	0.463298i
$721$		0			0
$722$			18.0250i			0.670820i
$723$	13.6807	+	15.3050i	0.508789	+	0.569200i
$724$	1.11772	−	0.645316i	0.0415397	−	0.0239830i
$725$	−2.81998	+	1.62811i	−0.104731	+	0.0604667i
$726$	−11.3793	−	12.7304i	−0.422325	−	0.472470i
$727$			29.9037i			1.10907i	0.832161	+	0.554533i	$0.187103\pi$
$727$			29.9037i			1.10907i	−0.832161	+	0.554533i	$0.812897\pi$
$728$		0			0
$729$	−8.89949	+	25.4912i	−0.329611	+	0.944117i
$730$	−9.43503	+	16.3419i	−0.349206	+	0.604843i
$731$	0.963811	+	1.66937i	0.0356478	+	0.0617439i
$732$	5.28292	−	1.10294i	0.195263	−	0.0407657i
$733$	−13.0762	−	7.54955i	−0.482981	−	0.278849i	0.238677	−	0.971099i	$-0.423286\pi$
$733$	−13.0762	−	7.54955i	−0.482981	−	0.278849i	−0.721658	+	0.692250i	$0.756620\pi$
$734$	−43.4801			−1.60488
$735$		0			0
$736$	9.89949			0.364900
$737$	−22.3406	−	12.8984i	−0.822927	−	0.475117i
$738$	15.9721	+	1.79580i	0.587940	+	0.0661044i
$739$	−19.5563	−	33.8726i	−0.719392	−	1.24602i	−0.961241	−	0.275709i	$-0.911087\pi$
$739$	−19.5563	−	33.8726i	−0.719392	−	1.24602i	0.241849	−	0.970314i	$-0.422246\pi$
$740$	−2.44378	+	4.23274i	−0.0898350	+	0.155599i
$741$	15.8887	+	5.22625i	0.583686	+	0.191991i
$742$		0			0
$743$		−	3.25623i		−	0.119459i	−0.998215	−	0.0597297i	$-0.980976\pi$
$743$		−	3.25623i		−	0.119459i	0.998215	−	0.0597297i	$-0.0190239\pi$
$744$	4.24940	−	3.79840i	0.155791	−	0.139256i
$745$	15.2255	−	8.79045i	0.557820	−	0.322057i
$746$	−10.0022	+	5.77479i	−0.366208	+	0.211430i
$747$	39.9369	−	17.4355i	1.46122	−	0.637932i
$748$			0.710974i			0.0259958i
$749$		0			0
$750$	−7.27208	+	22.1084i	−0.265539	+	0.807283i
$751$	17.3848	−	30.1113i	0.634379	−	1.09878i	−0.352267	−	0.935900i	$-0.614589\pi$
$751$	17.3848	−	30.1113i	0.634379	−	1.09878i	0.986646	−	0.162878i	$-0.0520777\pi$
$752$	−0.846881	−	1.46684i	−0.0308826	−	0.0534902i
$753$	−4.25954	−	20.4027i	−0.155226	−	0.743514i
$754$	38.2441	+	22.0803i	1.39277	+	0.804115i
$755$	1.12918			0.0410949
$756$		0			0
$757$	25.8995			0.941333			0.470667	−	0.882311i	$-0.344013\pi$
$757$	25.8995			0.941333			0.470667	+	0.882311i	$0.344013\pi$
$758$	13.0868	+	7.55568i	0.475335	+	0.274435i
$759$	2.71033	+	12.9822i	0.0983789	+	0.471222i
$760$	−7.65685	−	13.2621i	−0.277743	−	0.481065i
$761$	18.6975	−	32.3849i	0.677782	−	1.17395i	−0.297865	−	0.954608i	$-0.596275\pi$
$761$	18.6975	−	32.3849i	0.677782	−	1.17395i	0.975647	−	0.219345i	$-0.0703921\pi$
$762$	−1.36303	+	4.14386i	−0.0493775	+	0.150116i
$763$		0			0
$764$			4.73157i			0.171182i
$765$	−6.16592	+	2.69190i	−0.222929	+	0.0973257i
$766$	−16.4570	+	9.50143i	−0.594614	+	0.343301i
$767$	−35.9567	+	20.7596i	−1.29832	+	0.749585i
$768$	12.2489	−	10.9488i	0.441993	−	0.395082i
$769$			21.4077i			0.771983i	0.922502	+	0.385991i	$0.126141\pi$
$769$			21.4077i			0.771983i	−0.922502	+	0.385991i	$0.873859\pi$
$770$		0			0
$771$	−17.8284	−	5.86428i	−0.642075	−	0.211197i
$772$	−1.10051	+	1.90613i	−0.0396080	+	0.0686031i
$773$	−15.2899	−	26.4828i	−0.549938	−	0.952521i	−0.998278	−	0.0586578i	$-0.981318\pi$
$773$	−15.2899	−	26.4828i	−0.549938	−	0.952521i	0.448340	−	0.893863i	$-0.352015\pi$
$774$	7.50837	+	0.844196i	0.269883	+	0.0303440i
$775$	−0.388275	−	0.224171i	−0.0139473	−	0.00805245i
$776$	−42.0486			−1.50946
$777$		0			0
$778$	4.64466			0.166519
$779$	−7.97610	−	4.60500i	−0.285773	−	0.164991i
$780$	7.28970	−	1.52190i	0.261013	−	0.0544927i
$781$	−7.00000	−	12.1244i	−0.250480	−	0.433844i
$782$	2.60914	−	4.51916i	0.0933027	−	0.161605i
$783$	33.3058	−	23.6494i	1.19025	−	0.845162i
$784$		0			0
$785$		−	14.9848i		−	0.534830i
$786$	−23.9163	−	26.7559i	−0.853065	−	0.954353i
$787$	−12.1859	+	7.03555i	−0.434381	+	0.250790i	−0.701211	−	0.712953i	$-0.747357\pi$
$787$	−12.1859	+	7.03555i	−0.434381	+	0.250790i	0.266830	+	0.963744i	$0.414024\pi$
$788$		0			0
$789$	−3.25987	−	3.64693i	−0.116054	−	0.129834i
$790$		−	14.1480i		−	0.503364i
$791$		0			0
$792$	13.0711	+	9.64212i	0.464460	+	0.342618i
$793$	−16.7782	+	29.0607i	−0.595810	+	1.03197i
$794$	14.2776	+	24.7296i	0.506694	+	0.877619i
$795$	−23.9879	+	5.00804i	−0.850763	+	0.177617i
$796$	6.17338	+	3.56420i	0.218810	+	0.126330i
$797$	30.8136			1.09147			0.545737	−	0.837957i	$-0.316250\pi$
$797$	30.8136			1.09147			0.545737	+	0.837957i	$0.316250\pi$
$798$		0			0
$799$	0.544156			0.0192509
$800$	−0.825952	−	0.476864i	−0.0292018	−	0.0168597i
$801$	−2.79668	+	24.8740i	−0.0988159	+	0.878879i
$802$	21.1924	+	36.7063i	0.748329	+	1.29614i
$803$	−5.73443	+	9.93233i	−0.202364	+	0.350504i
$804$	−9.87197	−	3.24718i	−0.348158	−	0.114519i
$805$		0			0
$806$			6.08034i			0.214171i
$807$	23.2207	−	20.7562i	0.817408	−	0.730654i
$808$	−34.2201	+	19.7570i	−1.20386	+	0.695047i
$809$	−4.36227	+	2.51856i	−0.153369	+	0.0885479i	−0.574721	−	0.818350i	$-0.694889\pi$
$809$	−4.36227	+	2.51856i	−0.153369	+	0.0885479i	0.421351	+	0.906898i	$0.361556\pi$
$810$	−5.85605	+	25.7129i	−0.205761	+	0.903461i
$811$		−	38.8255i		−	1.36335i	−0.731657	−	0.681673i	$-0.761253\pi$
$811$		−	38.8255i		−	1.36335i	0.731657	−	0.681673i	$-0.238747\pi$
$812$		0			0
$813$	2.92893	−	8.90446i	0.102722	−	0.312293i
$814$	5.68629	−	9.84895i	0.199304	−	0.345205i
$815$	−10.6704	−	18.4817i	−0.373769	−	0.647386i
$816$	−1.02349	−	4.90241i	−0.0358295	−	0.171619i
$817$	−3.74952	−	2.16478i	−0.131179	−	0.0757362i
$818$	37.9595			1.32722
$819$		0			0
$820$	−4.10051			−0.143196
$821$	−11.0607	−	6.38589i	−0.386021	−	0.222869i	0.294414	−	0.955678i	$-0.404876\pi$
$821$	−11.0607	−	6.38589i	−0.386021	−	0.222869i	−0.680435	+	0.732809i	$0.738209\pi$
$822$	4.16181	+	19.9345i	0.145160	+	0.695297i
$823$	−6.75736	−	11.7041i	−0.235547	−	0.407979i	0.723885	−	0.689921i	$-0.242355\pi$
$823$	−6.75736	−	11.7041i	−0.235547	−	0.407979i	−0.959431	+	0.281942i	$0.909021\pi$
$824$	−24.5146	+	42.4605i	−0.854005	+	1.47918i
$825$	0.399224	−	1.21371i	0.0138992	−	0.0422559i
$826$		0			0
$827$		−	32.0036i		−	1.11287i	−0.830890	−	0.556437i	$-0.812168\pi$
$827$		−	32.0036i		−	1.11287i	0.830890	−	0.556437i	$-0.187832\pi$
$828$	2.13765	+	4.89639i	0.0742884	+	0.170161i
$829$	43.8213	−	25.3002i	1.52198	−	0.878713i	0.522313	−	0.852754i	$-0.325069\pi$
$829$	43.8213	−	25.3002i	1.52198	−	0.878713i	0.999663	−	0.0259598i	$-0.00826420\pi$
$830$	36.8601	−	21.2812i	1.27943	−	0.738681i
$831$	0.626670	−	0.560160i	0.0217389	−	0.0194317i
$832$			39.6996i			1.37634i
$833$		0			0
$834$	36.0416	+	11.8551i	1.24802	+	0.410510i
$835$	−7.00000	+	12.1244i	−0.242245	+	0.419581i
$836$	−0.798447	−	1.38295i	−0.0276149	−	0.0478304i
$837$	5.11287	+	2.34329i	0.176727	+	0.0809960i
$838$	3.84373	+	2.21918i	0.132779	+	0.0766602i
$839$	−43.5770			−1.50444			−0.752222	−	0.658909i	$-0.771018\pi$
$839$	−43.5770			−1.50444			−0.752222	+	0.658909i	$0.771018\pi$
$840$		0			0
$841$	−32.7990			−1.13100
$842$	34.6790	+	20.0219i	1.19512	+	0.690001i
$843$	2.28684	−	0.477432i	0.0787629	−	0.0164436i
$844$	−4.51472	−	7.81972i	−0.155403	−	0.269166i
$845$	−8.02703	+	13.9032i	−0.276138	+	0.478286i
$846$	1.26617	−	1.71644i	0.0435317	−	0.0590125i
$847$		0			0
$848$		−	18.2410i		−	0.626399i
$849$	19.8649	+	22.2235i	0.681761	+	0.762710i
$850$	−0.435381	+	0.251367i	−0.0149334	+	0.00862183i
$851$	18.8818	−	10.9014i	0.647259	−	0.373695i
$852$	−3.75866	−	4.20494i	−0.128770	−	0.144059i
$853$		−	12.0376i		−	0.412161i	−0.978535	−	0.206080i	$-0.933929\pi$
$853$		−	12.0376i		−	0.412161i	0.978535	−	0.206080i	$-0.0660708\pi$
$854$		0			0
$855$	8.97056	−	12.1607i	0.306787	−	0.415887i
$856$	−13.5355	+	23.4442i	−0.462635	+	0.801307i
$857$	2.24416	+	3.88701i	0.0766592	+	0.132778i	0.901807	−	0.432140i	$-0.142241\pi$
$857$	2.24416	+	3.88701i	0.0766592	+	0.132778i	−0.825147	+	0.564917i	$0.808908\pi$
$858$	−16.9620	+	3.54122i	−0.579073	+	0.120895i
$859$	−37.4010	−	21.5935i	−1.27610	−	0.736759i	−0.299974	−	0.953947i	$-0.596978\pi$
$859$	−37.4010	−	21.5935i	−1.27610	−	0.736759i	−0.976130	+	0.217188i	$0.930311\pi$
$860$	−1.92762			−0.0657314
$861$		0			0
$862$	−33.9584			−1.15663
$863$	24.6313	+	14.2209i	0.838461	+	0.484086i	0.856741	−	0.515747i	$-0.172486\pi$
$863$	24.6313	+	14.2209i	0.838461	+	0.484086i	−0.0182799	+	0.999833i	$0.505819\pi$
$864$	10.8763	+	4.98473i	0.370018	+	0.169584i
$865$	21.1924	+	36.7063i	0.720563	+	1.24805i
$866$	3.93793	−	6.82069i	0.133816	−	0.231776i
$867$	−26.4422	−	8.69760i	−0.898024	−	0.295386i
$868$		0			0
$869$		−	8.59890i		−	0.291698i
$870$	29.7458	−	26.5888i	1.00848	−	0.901445i
$871$	55.9601	−	32.3086i	1.89614	−	1.09473i
$872$	24.7864	−	14.3104i	0.839372	−	0.484612i
$873$	−16.6017	−	38.0270i	−0.561882	−	1.28702i
$874$			11.7206i			0.396455i
$875$		0			0
$876$	−1.44365	+	4.38895i	−0.0487764	+	0.148289i
$877$	19.4350	−	33.6625i	0.656274	−	1.13670i	−0.325298	−	0.945611i	$-0.605465\pi$
$877$	19.4350	−	33.6625i	0.656274	−	1.13670i	0.981573	−	0.191089i	$-0.0612019\pi$
$878$	−8.17821	−	14.1651i	−0.276001	−	0.478048i
$879$	2.38815	+	11.4390i	0.0805505	+	0.385826i
$880$	10.7661	+	6.21579i	0.362924	+	0.209534i
$881$	39.3225			1.32481			0.662405	−	0.749146i	$-0.269536\pi$
$881$	39.3225			1.32481			0.662405	+	0.749146i	$0.269536\pi$
$882$		0			0
$883$	−12.0000			−0.403832			−0.201916	−	0.979403i	$-0.564717\pi$
$883$	−12.0000			−0.403832			−0.201916	+	0.979403i	$0.564717\pi$
$884$	−1.54230	−	0.890446i	−0.0518731	−	0.0299489i
$885$	7.66598	+	36.7191i	0.257689	+	1.23430i
$886$	3.09188	+	5.35530i	0.103874	+	0.179915i
$887$	−18.4978	+	32.0392i	−0.621097	+	1.07577i	0.368185	+	0.929752i	$0.379979\pi$
$887$	−18.4978	+	32.0392i	−0.621097	+	1.07577i	−0.989282	+	0.146019i	$0.953354\pi$
$888$	8.34357	−	25.3659i	0.279992	−	0.851224i
$889$		0			0
$890$			24.4479i			0.819497i
$891$	−3.55920	+	15.6278i	−0.119238	+	0.523552i
$892$	0.321658	−	0.185709i	0.0107699	−	0.00621800i
$893$	−1.05847	+	0.611105i	−0.0354202	+	0.0204499i
$894$	−12.2869	+	10.9828i	−0.410934	+	0.367321i
$895$			30.0125i			1.00321i
$896$		0			0
$897$	−31.5563	−	10.3798i	−1.05364	−	0.346571i
$898$	16.8995	−	29.2708i	0.563943	−	0.976779i
$899$	−4.25447	−	7.36896i	−0.141894	−	0.245768i
$900$	0.0575095	−	0.511496i	0.00191698	−	0.0170499i
$901$	5.07517	+	2.93015i	0.169078	+	0.0976175i
$902$	9.54124			0.317689
$903$		0			0
$904$	−33.7990			−1.12414
$905$	6.27880	+	3.62506i	0.208714	+	0.120501i
$906$	−1.03613	+	0.216316i	−0.0344230	+	0.00718661i
$907$	24.1421	+	41.8154i	0.801626	+	1.38846i	0.918545	+	0.395316i	$0.129365\pi$
$907$	24.1421	+	41.8154i	0.801626	+	1.38846i	−0.116919	+	0.993141i	$0.537302\pi$
$908$	−3.68988	+	6.39106i	−0.122453	+	0.212095i
$909$	−31.3782	−	23.1467i	−1.04075	−	0.767728i
$910$		0			0
$911$		−	50.4236i		−	1.67061i	−0.549787	−	0.835305i	$-0.685291\pi$
$911$		−	50.4236i		−	1.67061i	0.549787	−	0.835305i	$-0.314709\pi$
$912$	7.49642	+	8.38651i	0.248231	+	0.277705i
$913$	22.4029	−	12.9343i	0.741427	−	0.428063i
$914$	11.5899	−	6.69145i	0.383361	−	0.221333i
$915$	20.2041	+	22.6030i	0.667927	+	0.747233i
$916$		−	4.46088i		−	0.147392i
$917$		0			0
$918$	5.14214	−	3.65128i	0.169716	−	0.120510i
$919$	−22.2132	+	38.4744i	−0.732746	+	1.26915i	0.222959	+	0.974828i	$0.428428\pi$
$919$	−22.2132	+	38.4744i	−0.732746	+	1.26915i	−0.955705	+	0.294325i	$0.904905\pi$
$920$	15.2072	+	26.3396i	0.501366	+	0.868391i
$921$	−16.6471	+	3.47549i	−0.548542	+	0.114521i
$922$	−0.796062	−	0.459607i	−0.0262169	−	0.0151363i
$923$	35.0681			1.15428
$924$		0			0
$925$	−2.10051			−0.0690642
$926$	13.0868	+	7.55568i	0.430060	+	0.248295i
$927$	−48.0784	−	5.40564i	−1.57910	−	0.177545i
$928$	−9.05025	−	15.6755i	−0.297089	−	0.514573i
$929$	−14.6083	+	25.3024i	−0.479284	+	0.830145i	−0.999718	−	0.0237574i	$-0.992437\pi$
$929$	−14.6083	+	25.3024i	−0.479284	+	0.830145i	0.520433	+	0.853902i	$0.325770\pi$
$930$	5.21828	+	1.71644i	0.171114	+	0.0562844i
$931$		0			0
$932$			7.42912i			0.243349i
$933$	22.2781	−	19.9137i	0.729352	−	0.651944i
$934$	2.10220	−	1.21371i	0.0687862	−	0.0397138i
$935$	−3.45882	+	1.99695i	−0.113115	+	0.0653072i
$936$	−37.2870	+	16.2786i	−1.21876	+	0.532084i
$937$		−	12.0376i		−	0.393252i	−0.980479	−	0.196626i	$-0.937001\pi$
$937$		−	12.0376i		−	0.393252i	0.980479	−	0.196626i	$-0.0629985\pi$
$938$		0			0
$939$	0.0294373	−	0.0894943i	0.000960648	−	0.00292054i
$940$	−0.272078	+	0.471253i	−0.00887420	+	0.0153706i
$941$	15.0076	+	25.9939i	0.489233	+	0.847376i	0.999923	−	0.0123886i	$-0.00394350\pi$
$941$	15.0076	+	25.9939i	0.489233	+	0.847376i	−0.510690	+	0.859765i	$0.670610\pi$
$942$	2.87063	+	13.7500i	0.0935303	+	0.447998i
$943$	15.8412	+	9.14594i	0.515862	+	0.297833i
$944$	−27.9222			−0.908789
$945$		0			0
$946$	4.48528			0.145829
$947$	−1.91652	−	1.10650i	−0.0622786	−	0.0359565i	0.468537	−	0.883444i	$-0.344781\pi$
$947$	−1.91652	−	1.10650i	−0.0622786	−	0.0359565i	−0.530816	+	0.847487i	$0.678114\pi$
$948$	−0.707950	−	3.39099i	−0.0229931	−	0.110134i
$949$	−14.3640	−	24.8791i	−0.466274	−	0.807610i
$950$	0.564588	−	0.977894i	0.0183176	−	0.0317271i
$951$	18.6148	−	56.5921i	0.603625	−	1.83512i
$952$		0			0
$953$		−	22.2349i		−	0.720260i	−0.932902	−	0.360130i	$-0.882732\pi$
$953$		−	22.2349i		−	0.720260i	0.932902	−	0.360130i	$-0.117268\pi$
$954$	21.0518	−	9.19071i	0.681577	−	0.297560i
$955$	−23.0186	+	13.2898i	−0.744865	+	0.430048i
$956$	−5.15612	+	2.97689i	−0.166761	+	0.0962795i
$957$	18.0790	−	16.1602i	0.584410	−	0.522384i
$958$			30.0125i			0.969659i
$959$		0			0
$960$	34.0711	+	11.2070i	1.09964	+	0.361703i
$961$	−14.9142	+	25.8322i	−0.481104	+	0.833296i
$962$	14.2434	+	24.6702i	0.459225	+	0.795401i
$963$	−26.5461	−	2.98469i	−0.855436	−	0.0961801i
$964$	4.25151	+	2.45461i	0.136932	+	0.0790578i
$965$	−12.3642			−0.398017
$966$		0			0
$967$	10.2010			0.328042			0.164021	−	0.986457i	$-0.447553\pi$
$967$	10.2010			0.328042			0.164021	+	0.986457i	$0.447553\pi$
$968$	−20.6112	−	11.8999i	−0.662469	−	0.382477i
$969$	−3.53755	+	0.738549i	−0.113643	+	0.0237256i
$970$	−20.2635	−	35.0973i	−0.650620	−	1.12691i
$971$	19.0624	−	33.0171i	0.611742	−	1.05957i	−0.379204	−	0.925313i	$-0.623802\pi$
$971$	19.0624	−	33.0171i	0.611742	−	1.05957i	0.990947	−	0.134256i	$-0.0428644\pi$
$972$	−0.116930	+	6.45589i	−0.00375053	+	0.207073i
$973$		0			0
$974$		−	0.611105i		−	0.0195811i
$975$	2.13287	+	2.38611i	0.0683064	+	0.0764167i
$976$	−19.5436	+	11.2835i	−0.625577	+	0.361177i
$977$	−3.19420	+	1.84417i	−0.102192	+	0.0590003i	−0.550225	−	0.835017i	$-0.685458\pi$
$977$	−3.19420	+	1.84417i	−0.102192	+	0.0590003i	0.448033	+	0.894017i	$0.352125\pi$
$978$	13.3317	+	14.9146i	0.426300	+	0.476916i
$979$			14.8590i			0.474896i
$980$		0			0
$981$	22.7279	+	16.7657i	0.725647	+	0.535287i
$982$	−7.84924	+	13.5953i	−0.250479	+	0.433843i
$983$	3.12529	+	5.41317i	0.0996814	+	0.172653i	0.911553	−	0.411183i	$-0.134884\pi$
$983$	3.12529	+	5.41317i	0.0996814	+	0.172653i	−0.811871	+	0.583836i	$0.801551\pi$
$984$	21.9301	−	4.57842i	0.699105	−	0.145955i
$985$		0			0
$986$	−9.54124			−0.303855
$987$		0			0
$988$	4.00000			0.127257
$989$	7.44687	+	4.29945i	0.236797	+	0.136715i
$990$	−1.74912	+	15.5568i	−0.0555905	+	0.494428i
$991$	7.24264	+	12.5446i	0.230070	+	0.398493i	0.957828	−	0.287341i	$-0.0927711\pi$
$991$	7.24264	+	12.5446i	0.230070	+	0.398493i	−0.727758	+	0.685834i	$0.759438\pi$
$992$	1.24611	−	2.15832i	0.0395639	−	0.0685266i
$993$	30.9790	+	10.1899i	0.983087	+	0.323366i
$994$		0			0
$995$			40.0438i			1.26947i
$996$	7.76972	−	6.94510i	0.246193	−	0.220064i
$997$	−12.9820	+	7.49516i	−0.411144	+	0.237374i	−0.691281	−	0.722586i	$-0.742953\pi$
$997$	−12.9820	+	7.49516i	−0.411144	+	0.237374i	0.280137	+	0.959960i	$0.409620\pi$
$998$	−10.0022	+	5.77479i	−0.316615	+	0.182798i
$999$	26.2341	−	2.46942i	0.830009	−	0.0781290i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	147.2.g.b.68.3		16
3.2	odd	2	inner	147.2.g.b.68.6		16
7.2	even	3		147.2.c.b.146.6	yes	8
7.3	odd	6	inner	147.2.g.b.80.6		16
7.4	even	3	inner	147.2.g.b.80.5		16
7.5	odd	6		147.2.c.b.146.5	yes	8
7.6	odd	2	inner	147.2.g.b.68.4		16
21.2	odd	6		147.2.c.b.146.3	✓	8
21.5	even	6		147.2.c.b.146.4	yes	8
21.11	odd	6	inner	147.2.g.b.80.4		16
21.17	even	6	inner	147.2.g.b.80.3		16
21.20	even	2	inner	147.2.g.b.68.5		16
28.19	even	6		2352.2.k.h.881.8		8
28.23	odd	6		2352.2.k.h.881.1		8
84.23	even	6		2352.2.k.h.881.7		8
84.47	odd	6		2352.2.k.h.881.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
147.2.c.b.146.3	✓	8	21.2	odd	6
147.2.c.b.146.4	yes	8	21.5	even	6
147.2.c.b.146.5	yes	8	7.5	odd	6
147.2.c.b.146.6	yes	8	7.2	even	3
147.2.g.b.68.3		16	1.1	even	1	trivial
147.2.g.b.68.4		16	7.6	odd	2	inner
147.2.g.b.68.5		16	21.20	even	2	inner
147.2.g.b.68.6		16	3.2	odd	2	inner
147.2.g.b.80.3		16	21.17	even	6	inner
147.2.g.b.80.4		16	21.11	odd	6	inner
147.2.g.b.80.5		16	7.4	even	3	inner
147.2.g.b.80.6		16	7.3	odd	6	inner
2352.2.k.h.881.1		8	28.23	odd	6
2352.2.k.h.881.2		8	84.47	odd	6
2352.2.k.h.881.7		8	84.23	even	6
2352.2.k.h.881.8		8	28.19	even	6

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:	\( N \)	\(=\)	\( 147 = 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	147.g (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.09057 - 0.629640i) q^{2} +(-0.353975 - 1.69549i) q^{3} +(-0.207107 - 0.358719i) q^{4} +(1.16342 - 2.01511i) q^{5} +(-0.681517 + 2.07193i) q^{6} +3.04017i q^{8} +(-2.74940 + 1.20032i) q^{9} +O(q^{10})\)	\(q+(-1.09057 - 0.629640i) q^{2} +(-0.353975 - 1.69549i) q^{3} +(-0.207107 - 0.358719i) q^{4} +(1.16342 - 2.01511i) q^{5} +(-0.681517 + 2.07193i) q^{6} +3.04017i q^{8} +(-2.74940 + 1.20032i) q^{9} +(-2.53759 + 1.46508i) q^{10} +(-1.54230 + 0.890446i) q^{11} +(-0.534896 + 0.478126i) q^{12} -4.46088i q^{13} +(-3.82843 - 1.25928i) q^{15} +(1.50000 - 2.59808i) q^{16} +(0.481906 + 0.834685i) q^{17} +(3.75419 + 0.422098i) q^{18} +(-1.87476 - 1.08239i) q^{19} -0.963811 q^{20} +2.24264 q^{22} +(3.72343 + 2.14973i) q^{23} +(5.15459 - 1.07614i) q^{24} +(-0.207107 - 0.358719i) q^{25} +(-2.80875 + 4.86490i) q^{26} +(3.00836 + 4.23671i) q^{27} -7.86123i q^{29} +(3.38227 + 3.78386i) q^{30} +(0.937379 - 0.541196i) q^{31} +(1.99403 - 1.15125i) q^{32} +(2.05568 + 2.29976i) q^{33} -1.21371i q^{34} +(1.00000 + 0.737669i) q^{36} +(2.53553 - 4.39167i) q^{37} +(1.36303 + 2.36085i) q^{38} +(-7.56341 + 1.57904i) q^{39} +(6.12627 + 3.53701i) q^{40} +4.25447 q^{41} +2.00000 q^{43} +(0.638840 + 0.368835i) q^{44} +(-0.779936 + 6.93683i) q^{45} +(-2.70711 - 4.68885i) q^{46} +(0.282294 - 0.488947i) q^{47} +(-4.93599 - 1.62359i) q^{48} +0.521611i q^{50} +(1.24462 - 1.11253i) q^{51} +(-1.60021 + 0.923880i) q^{52} +(5.26573 - 3.04017i) q^{53} +(-0.613222 - 6.51461i) q^{54} +4.14386i q^{55} +(-1.17157 + 3.56178i) q^{57} +(-4.94975 + 8.57321i) q^{58} +(-4.65369 - 8.06043i) q^{59} +(0.341165 + 1.63414i) q^{60} +(-6.51455 - 3.76118i) q^{61} -1.36303 q^{62} -8.89949 q^{64} +(-8.98916 - 5.18990i) q^{65} +(-0.793838 - 3.80239i) q^{66} +(7.24264 + 12.5446i) q^{67} +(0.199612 - 0.345738i) q^{68} +(2.32685 - 7.07401i) q^{69} +7.86123i q^{71} +(-3.64919 - 8.35866i) q^{72} +(5.57717 - 3.21998i) q^{73} +(-5.53035 + 3.19295i) q^{74} +(-0.534896 + 0.478126i) q^{75} +0.896683i q^{76} +(9.24264 + 3.04017i) q^{78} +(-2.41421 + 4.18154i) q^{79} +(-3.49027 - 6.04532i) q^{80} +(6.11844 - 6.60035i) q^{81} +(-4.63979 - 2.67878i) q^{82} -14.5257 q^{83} +2.24264 q^{85} +(-2.18114 - 1.25928i) q^{86} +(-13.3287 + 2.78268i) q^{87} +(-2.70711 - 4.68885i) q^{88} +(4.17179 - 7.22575i) q^{89} +(5.21828 - 7.07401i) q^{90} -1.78089i q^{92} +(-1.24940 - 1.39775i) q^{93} +(-0.615721 + 0.355487i) q^{94} +(-4.36227 + 2.51856i) q^{95} +(-2.65777 - 2.97334i) q^{96} +13.8310i q^{97} +(3.17157 - 4.29945i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4} - 8 q^{9}+O(q^{10}) \) 16 * q + 8 * q^4 - 8 * q^9	\( 16 q + 8 q^{4} - 8 q^{9} - 16 q^{15} + 24 q^{16} - 16 q^{18} - 32 q^{22} + 8 q^{25} - 24 q^{30} + 16 q^{36} - 16 q^{37} - 8 q^{39} + 32 q^{43} - 32 q^{46} + 24 q^{51} - 64 q^{57} + 24 q^{60} + 16 q^{64} + 48 q^{67} + 32 q^{72} + 80 q^{78} - 16 q^{79} + 24 q^{81} - 32 q^{85} - 32 q^{88} + 16 q^{93} + 96 q^{99}+O(q^{100}) \) 16 * q + 8 * q^4 - 8 * q^9 - 16 * q^15 + 24 * q^16 - 16 * q^18 - 32 * q^22 + 8 * q^25 - 24 * q^30 + 16 * q^36 - 16 * q^37 - 8 * q^39 + 32 * q^43 - 32 * q^46 + 24 * q^51 - 64 * q^57 + 24 * q^60 + 16 * q^64 + 48 * q^67 + 32 * q^72 + 80 * q^78 - 16 * q^79 + 24 * q^81 - 32 * q^85 - 32 * q^88 + 16 * q^93 + 96 * q^99

Introduction

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