LMFDB - Embedded newform 441.2.f.g.148.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,2,Mod(148,441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(441, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0]))

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

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

chi := DirichletCharacter("441.148");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.f (of order $3$, 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:	$3.52140272914$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 7x^{10} + 37x^{8} - 78x^{6} + 123x^{4} - 36x^{2} + 9 $ x^12 - 7x^10 + 37x^8 - 78x^6 + 123x^4 - 36*x^2 + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			148.5
Root			$0.474636 - 0.274031i$ of defining polynomial
Character	$\chi$	$=$	441.148
Dual form			441.2.f.g.295.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.849814 + 1.47192i) q^{2} +(-1.40434 - 1.01381i) q^{3} +(-0.444368 + 0.769668i) q^{4} +(-0.474636 + 0.822093i) q^{5} +(0.298820 - 2.92864i) q^{6} +1.88874 q^{8} +(0.944368 + 2.84748i) q^{9} +O(q^{10})$	\(q+(0.849814 + 1.47192i) q^{2} +(-1.40434 - 1.01381i) q^{3} +(-0.444368 + 0.769668i) q^{4} +(-0.474636 + 0.822093i) q^{5} +(0.298820 - 2.92864i) q^{6} +1.88874 q^{8} +(0.944368 + 2.84748i) q^{9} -1.61341 q^{10} +(0.294182 + 0.509538i) q^{11} +(1.40434 - 0.630373i) q^{12} +(-2.50987 + 4.34722i) q^{13} +(1.50000 - 0.673310i) q^{15} +(2.49381 + 4.31941i) q^{16} +7.58242 q^{17} +(-3.38874 + 3.80987i) q^{18} +4.46122 q^{19} +(-0.421826 - 0.730623i) q^{20} +(-0.500000 + 0.866025i) q^{22} +(-1.23855 + 2.14523i) q^{23} +(-2.65244 - 1.91482i) q^{24} +(2.04944 + 3.54974i) q^{25} -8.53169 q^{26} +(1.56060 - 4.95626i) q^{27} +(-2.73855 - 4.74331i) q^{29} +(2.26578 + 1.63569i) q^{30} +(-3.03731 + 5.26078i) q^{31} +(-2.34981 + 4.07000i) q^{32} +(0.103443 - 1.01381i) q^{33} +(6.44364 + 11.1607i) q^{34} +(-2.61126 - 0.538481i) q^{36} -6.98762 q^{37} +(3.79121 + 6.56657i) q^{38} +(7.93199 - 3.56046i) q^{39} +(-0.896461 + 1.55272i) q^{40} +(-0.527445 + 0.913562i) q^{41} +(-3.49381 - 6.05146i) q^{43} -0.522900 q^{44} +(-2.78913 - 0.575159i) q^{45} -4.21015 q^{46} +(-3.73840 - 6.47510i) q^{47} +(0.876899 - 8.59419i) q^{48} +(-3.48329 + 6.03323i) q^{50} +(-10.6483 - 7.68715i) q^{51} +(-2.23061 - 3.86353i) q^{52} +6.92216 q^{53} +(8.62145 - 1.91482i) q^{54} -0.558517 q^{55} +(-6.26509 - 4.52284i) q^{57} +(4.65452 - 8.06186i) q^{58} +(5.21512 - 9.03284i) q^{59} +(-0.148327 + 1.45370i) q^{60} +(5.82644 + 10.0917i) q^{61} -10.3246 q^{62} +1.98762 q^{64} +(-2.38255 - 4.12669i) q^{65} +(1.58016 - 0.709292i) q^{66} +(5.93199 - 10.2745i) q^{67} +(-3.36938 + 5.83594i) q^{68} +(3.91421 - 1.75699i) q^{69} +4.30037 q^{71} +(1.78366 + 5.37815i) q^{72} -4.46122 q^{73} +(-5.93818 - 10.2852i) q^{74} +(0.720646 - 7.06281i) q^{75} +(-1.98242 + 3.43366i) q^{76} +(11.9814 + 8.64953i) q^{78} +(0.666896 + 1.15510i) q^{79} -4.73460 q^{80} +(-7.21634 + 5.37815i) q^{81} -1.79292 q^{82} +(-2.84194 - 4.92238i) q^{83} +(-3.59888 + 6.23345i) q^{85} +(5.93818 - 10.2852i) q^{86} +(-0.962957 + 9.43762i) q^{87} +(0.555632 + 0.962383i) q^{88} -0.843651 q^{89} +(-1.52365 - 4.59415i) q^{90} +(-1.10074 - 1.90654i) q^{92} +(9.59888 - 4.30868i) q^{93} +(6.35389 - 11.0053i) q^{94} +(-2.11745 + 3.66754i) q^{95} +(7.42616 - 3.33341i) q^{96} +(-1.70317 - 2.94997i) q^{97} +(-1.17309 + 1.31887i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 2 q^{2} - 6 q^{4} + 24 q^{8} + 12 q^{9}+O(q^{10}) $ 12 * q - 2 * q^2 - 6 * q^4 + 24 * q^8 + 12 * q^9	$ 12 q - 2 q^{2} - 6 q^{4} + 24 q^{8} + 12 q^{9} - 8 q^{11} + 18 q^{15} - 6 q^{16} - 42 q^{18} - 6 q^{22} - 4 q^{23} - 12 q^{25} - 22 q^{29} - 48 q^{30} - 16 q^{32} - 30 q^{36} - 12 q^{37} + 24 q^{39} - 6 q^{43} - 28 q^{44} + 24 q^{46} - 56 q^{50} - 18 q^{51} + 56 q^{53} - 6 q^{57} - 18 q^{58} + 108 q^{60} - 48 q^{64} + 6 q^{65} + 76 q^{71} + 60 q^{72} - 36 q^{74} + 36 q^{78} + 6 q^{79} - 48 q^{81} + 30 q^{85} + 36 q^{86} + 6 q^{88} - 62 q^{92} + 42 q^{93} - 60 q^{95} - 48 q^{99}+O(q^{100}) $ 12 * q - 2 * q^2 - 6 * q^4 + 24 * q^8 + 12 * q^9 - 8 * q^11 + 18 * q^15 - 6 * q^16 - 42 * q^18 - 6 * q^22 - 4 * q^23 - 12 * q^25 - 22 * q^29 - 48 * q^30 - 16 * q^32 - 30 * q^36 - 12 * q^37 + 24 * q^39 - 6 * q^43 - 28 * q^44 + 24 * q^46 - 56 * q^50 - 18 * q^51 + 56 * q^53 - 6 * q^57 - 18 * q^58 + 108 * q^60 - 48 * q^64 + 6 * q^65 + 76 * q^71 + 60 * q^72 - 36 * q^74 + 36 * q^78 + 6 * q^79 - 48 * q^81 + 30 * q^85 + 36 * q^86 + 6 * q^88 - 62 * q^92 + 42 * q^93 - 60 * q^95 - 48 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	0.849814	+	1.47192i	0.600909	+	1.04081i	0.992684	+	0.120744i	$0.0385280\pi$
$2$	0.849814	+	1.47192i	0.600909	+	1.04081i	−0.391774	+	0.920061i	$0.628139\pi$
$3$	−1.40434	−	1.01381i	−0.810799	−	0.585325i
$3$	−1.40434	−	1.01381i	−0.810799	−	0.585325i
$4$	−0.444368	+	0.769668i	−0.222184	+	0.384834i
$5$	−0.474636	+	0.822093i	−0.212263	+	0.367651i	−0.952423	−	0.304781i	$-0.901417\pi$
$5$	−0.474636	+	0.822093i	−0.212263	+	0.367651i	0.740159	+	0.672432i	$0.234750\pi$
$6$	0.298820	−	2.92864i	0.121993	−	1.19561i
$7$		0			0
$7$		0			0
$8$	1.88874			0.667769
$9$	0.944368	+	2.84748i	0.314789	+	0.949162i
$10$	−1.61341			−0.510204
$11$	0.294182	+	0.509538i	0.0886992	+	0.153632i	0.906962	−	0.421213i	$-0.138396\pi$
$11$	0.294182	+	0.509538i	0.0886992	+	0.153632i	−0.818262	+	0.574845i	$0.805062\pi$
$12$	1.40434	−	0.630373i	0.405399	−	0.181973i
$13$	−2.50987	+	4.34722i	−0.696112	+	1.20570i	0.273692	+	0.961817i	$0.411755\pi$
$13$	−2.50987	+	4.34722i	−0.696112	+	1.20570i	−0.969804	+	0.243885i	$0.921578\pi$
$14$		0			0
$15$	1.50000	−	0.673310i	0.387298	−	0.173848i
$16$	2.49381	+	4.31941i	0.623453	+	1.07985i
$17$	7.58242			1.83901			0.919503	−	0.393083i	$-0.128591\pi$
$17$	7.58242			1.83901			0.919503	+	0.393083i	$0.128591\pi$
$18$	−3.38874	+	3.80987i	−0.798733	+	0.897994i
$19$	4.46122			1.02347			0.511737	−	0.859142i	$-0.329002\pi$
$19$	4.46122			1.02347			0.511737	+	0.859142i	$0.329002\pi$
$20$	−0.421826	−	0.730623i	−0.0943231	−	0.163372i
$21$		0			0
$22$	−0.500000	+	0.866025i	−0.106600	+	0.184637i
$23$	−1.23855	+	2.14523i	−0.258256	+	0.447312i	−0.965775	−	0.259382i	$-0.916481\pi$
$23$	−1.23855	+	2.14523i	−0.258256	+	0.447312i	0.707519	+	0.706694i	$0.249814\pi$
$24$	−2.65244	−	1.91482i	−0.541426	−	0.390862i
$25$	2.04944	+	3.54974i	0.409888	+	0.709948i
$26$	−8.53169			−1.67320
$27$	1.56060	−	4.95626i	0.300337	−	0.953833i
$28$		0			0
$29$	−2.73855	−	4.74331i	−0.508536	−	0.880810i	−0.999951	−	0.00988468i	$-0.996854\pi$
$29$	−2.73855	−	4.74331i	−0.508536	−	0.880810i	0.491415	−	0.870925i	$-0.336480\pi$
$30$	2.26578	+	1.63569i	0.413673	+	0.298635i
$31$	−3.03731	+	5.26078i	−0.545518	+	0.944865i	0.453056	+	0.891482i	$0.350334\pi$
$31$	−3.03731	+	5.26078i	−0.545518	+	0.944865i	−0.998574	+	0.0533826i	$0.983000\pi$
$32$	−2.34981	+	4.07000i	−0.415392	+	0.719481i
$33$	0.103443	−	1.01381i	0.0180072	−	0.176482i
$34$	6.44364	+	11.1607i	1.10508	+	1.91405i
$35$		0			0
$36$	−2.61126	−	0.538481i	−0.435211	−	0.0897469i
$37$	−6.98762			−1.14876			−0.574379	−	0.818590i	$-0.694756\pi$
$37$	−6.98762			−1.14876			−0.574379	+	0.818590i	$0.694756\pi$
$38$	3.79121	+	6.56657i	0.615015	+	1.06524i
$39$	7.93199	−	3.56046i	1.27013	−	0.570130i
$40$	−0.896461	+	1.55272i	−0.141743	+	0.245506i
$41$	−0.527445	+	0.913562i	−0.0823731	+	0.142674i	−0.904269	−	0.426964i	$-0.859583\pi$
$41$	−0.527445	+	0.913562i	−0.0823731	+	0.142674i	0.821896	+	0.569638i	$0.192917\pi$
$42$		0			0
$43$	−3.49381	−	6.05146i	−0.532801	−	0.922838i	−0.999266	−	0.0382990i	$-0.987806\pi$
$43$	−3.49381	−	6.05146i	−0.532801	−	0.922838i	0.466465	−	0.884540i	$-0.345527\pi$
$44$	−0.522900			−0.0788302
$45$	−2.78913	−	0.575159i	−0.415779	−	0.0857397i
$46$	−4.21015			−0.620753
$47$	−3.73840	−	6.47510i	−0.545301	−	0.944490i	−0.998588	−	0.0531249i	$-0.983082\pi$
$47$	−3.73840	−	6.47510i	−0.545301	−	0.944490i	0.453286	−	0.891365i	$-0.350251\pi$
$48$	0.876899	−	8.59419i	0.126569	−	1.24046i
$49$		0			0
$50$	−3.48329	+	6.03323i	−0.492612	+	0.853228i
$51$	−10.6483	−	7.68715i	−1.49106	−	1.07642i
$52$	−2.23061	−	3.86353i	−0.309330	−	0.535775i
$53$	6.92216			0.950831			0.475416	−	0.879761i	$-0.342298\pi$
$53$	6.92216			0.950831			0.475416	+	0.879761i	$0.342298\pi$
$54$	8.62145	−	1.91482i	1.17323	−	0.260575i
$55$	−0.558517			−0.0753104
$56$		0			0
$57$	−6.26509	−	4.52284i	−0.829832	−	0.599065i
$58$	4.65452	−	8.06186i	0.611168	−	1.05857i
$59$	5.21512	−	9.03284i	0.678950	−	1.17598i	−0.296347	−	0.955080i	$-0.595769\pi$
$59$	5.21512	−	9.03284i	0.678950	−	1.17598i	0.975297	−	0.220896i	$-0.0708981\pi$
$60$	−0.148327	+	1.45370i	−0.0191489	+	0.187672i
$61$	5.82644	+	10.0917i	0.745999	+	1.29211i	0.949726	+	0.313081i	$0.101361\pi$
$61$	5.82644	+	10.0917i	0.745999	+	1.29211i	−0.203727	+	0.979028i	$0.565305\pi$
$62$	−10.3246			−1.31123
$63$		0			0
$64$	1.98762			0.248453
$65$	−2.38255	−	4.12669i	−0.295518	−	0.511853i
$66$	1.58016	−	0.709292i	0.194504	−	0.0873078i
$67$	5.93199	−	10.2745i	0.724708	−	1.25523i	−0.234387	−	0.972143i	$-0.575308\pi$
$67$	5.93199	−	10.2745i	0.724708	−	1.25523i	0.959094	−	0.283087i	$-0.0913585\pi$
$68$	−3.36938	+	5.83594i	−0.408598	+	0.707712i
$69$	3.91421	−	1.75699i	0.471216	−	0.211516i
$70$		0			0
$71$	4.30037			0.510360			0.255180	−	0.966894i	$-0.417865\pi$
$71$	4.30037			0.510360			0.255180	+	0.966894i	$0.417865\pi$
$72$	1.78366	+	5.37815i	0.210207	+	0.633821i
$73$	−4.46122			−0.522146			−0.261073	−	0.965319i	$-0.584076\pi$
$73$	−4.46122			−0.522146			−0.261073	+	0.965319i	$0.584076\pi$
$74$	−5.93818	−	10.2852i	−0.690299	−	1.19563i
$75$	0.720646	−	7.06281i	0.0832130	−	0.815543i
$76$	−1.98242	+	3.43366i	−0.227400	+	0.393868i
$77$		0			0
$78$	11.9814	+	8.64953i	1.35663	+	0.979367i
$79$	0.666896	+	1.15510i	0.0750317	+	0.129959i	0.901100	−	0.433611i	$-0.142761\pi$
$79$	0.666896	+	1.15510i	0.0750317	+	0.129959i	−0.826068	+	0.563570i	$0.809428\pi$
$80$	−4.73460			−0.529345
$81$	−7.21634	+	5.37815i	−0.801815	+	0.597572i
$82$	−1.79292			−0.197995
$83$	−2.84194	−	4.92238i	−0.311943	−	0.540301i	0.666840	−	0.745201i	$-0.267647\pi$
$83$	−2.84194	−	4.92238i	−0.311943	−	0.540301i	−0.978783	+	0.204900i	$0.934313\pi$
$84$		0			0
$85$	−3.59888	+	6.23345i	−0.390354	+	0.676113i
$86$	5.93818	−	10.2852i	0.640330	−	1.10908i
$87$	−0.962957	+	9.43762i	−0.103240	+	1.01182i
$88$	0.555632	+	0.962383i	0.0592306	+	0.102590i
$89$	−0.843651			−0.0894269			−0.0447134	−	0.999000i	$-0.514237\pi$
$89$	−0.843651			−0.0894269			−0.0447134	+	0.999000i	$0.514237\pi$
$90$	−1.52365	−	4.59415i	−0.160607	−	0.484266i
$91$		0			0
$92$	−1.10074	−	1.90654i	−0.114760	−	0.198771i
$93$	9.59888	−	4.30868i	0.995358	−	0.446790i
$94$	6.35389	−	11.0053i	0.655353	−	1.13511i
$95$	−2.11745	+	3.66754i	−0.217246	+	0.376281i
$96$	7.42616	−	3.33341i	0.757930	−	0.340215i
$97$	−1.70317	−	2.94997i	−0.172930	−	0.299524i	0.766513	−	0.642229i	$-0.221990\pi$
$97$	−1.70317	−	2.94997i	−0.172930	−	0.299524i	−0.939443	+	0.342705i	$0.888657\pi$
$98$		0			0
$99$	−1.17309	+	1.31887i	−0.117900	+	0.132551i
$100$	−3.64283			−0.364283
$101$	−4.79329	−	8.30222i	−0.476950	−	0.826102i	0.522701	−	0.852516i	$-0.324924\pi$
$101$	−4.79329	−	8.30222i	−0.476950	−	0.826102i	−0.999651	+	0.0264143i	$0.991591\pi$
$102$	2.26578	−	22.2061i	0.224346	−	2.19874i
$103$	−5.82644	+	10.0917i	−0.574096	+	0.994364i	0.422043	+	0.906576i	$0.361313\pi$
$103$	−5.82644	+	10.0917i	−0.574096	+	0.994364i	−0.996139	+	0.0877882i	$0.972020\pi$
$104$	−4.74048	+	8.21075i	−0.464842	+	0.805130i
$105$		0			0
$106$	5.88255	+	10.1889i	0.571363	+	0.989630i
$107$	−3.79851			−0.367216			−0.183608	−	0.983000i	$-0.558778\pi$
$107$	−3.79851			−0.367216			−0.183608	+	0.983000i	$0.558778\pi$
$108$	3.12120	+	3.40355i	0.300337	+	0.327506i
$109$	−12.8640			−1.23215			−0.616073	−	0.787689i	$-0.711277\pi$
$109$	−12.8640			−1.23215			−0.616073	+	0.787689i	$0.711277\pi$
$110$	−0.474636	−	0.822093i	−0.0452547	−	0.0783835i
$111$	9.81303	+	7.08414i	0.931411	+	0.672397i
$112$		0			0
$113$	−4.51052	+	7.81245i	−0.424314	+	0.734934i	−0.996356	−	0.0852908i	$-0.972818\pi$
$113$	−4.51052	+	7.81245i	−0.424314	+	0.734934i	0.572042	+	0.820224i	$0.306151\pi$
$114$	1.33310	−	13.0653i	0.124857	−	1.22368i
$115$	−1.17572	−	2.03641i	−0.109636	−	0.189896i
$116$	4.86769			0.451954
$117$	−14.7489	−	3.04144i	−1.36353	−	0.281181i
$118$	17.7275			1.63195
$119$		0			0
$120$	2.83310	−	1.27171i	0.258626	−	0.116090i
$121$	5.32691	−	9.22649i	0.484265	−	0.838771i
$122$	−9.90278	+	17.1521i	−0.896556	+	1.55288i
$123$	1.66690	−	0.748226i	0.150299	−	0.0674652i
$124$	−2.69937	−	4.67545i	−0.242411	−	0.419867i
$125$	−8.63731			−0.772544
$126$		0			0
$127$	6.43268			0.570808			0.285404	−	0.958407i	$-0.407872\pi$
$127$	6.43268			0.570808			0.285404	+	0.958407i	$0.407872\pi$
$128$	6.38874	+	11.0656i	0.564690	+	0.978071i
$129$	−1.22853	+	12.0404i	−0.108166	+	1.06010i
$130$	4.04944	−	7.01384i	0.355160	−	0.615154i
$131$	3.31657	−	5.74447i	0.289770	−	0.501897i	−0.683984	−	0.729497i	$-0.739754\pi$
$131$	3.31657	−	5.74447i	0.289770	−	0.501897i	0.973755	+	0.227600i	$0.0730877\pi$
$132$	0.734332	+	0.530123i	0.0639154	+	0.0461413i
$133$		0			0
$134$	20.1643			1.74193
$135$	3.33379	+	3.63537i	0.286927	+	0.312883i
$136$	14.3212			1.22803
$137$	−7.01671	−	12.1533i	−0.599478	−	1.03833i	−0.992898	−	0.118968i	$-0.962042\pi$
$137$	−7.01671	−	12.1533i	−0.599478	−	1.03833i	0.393420	−	0.919359i	$-0.371292\pi$
$138$	5.91250	+	4.26830i	0.503305	+	0.363342i
$139$	4.40254	−	7.62541i	0.373418	−	0.646779i	−0.616671	−	0.787221i	$-0.711519\pi$
$139$	4.40254	−	7.62541i	0.373418	−	0.646779i	0.990089	+	0.140442i	$0.0448523\pi$
$140$		0			0
$141$	−1.31453	+	12.8833i	−0.110704	+	1.08497i
$142$	3.65452	+	6.32981i	0.306680	+	0.531186i
$143$	−2.95343			−0.246978
$144$	−9.94437	+	11.1802i	−0.828697	+	0.931683i
$145$	5.19925			0.431774
$146$	−3.79121	−	6.56657i	−0.313763	−	0.543453i
$147$		0			0
$148$	3.10507	−	5.37815i	0.255236	−	0.442081i
$149$	2.18292	−	3.78092i	0.178832	−	0.309745i	−0.762649	−	0.646813i	$-0.776102\pi$
$149$	2.18292	−	3.78092i	0.178832	−	0.309745i	0.941481	+	0.337067i	$0.109435\pi$
$150$	11.0083	−	4.94134i	0.898825	−	0.403459i
$151$	6.32691	+	10.9585i	0.514877	+	0.891793i	0.999851	+	0.0172645i	$0.00549573\pi$
$151$	6.32691	+	10.9585i	0.514877	+	0.891793i	−0.484974	+	0.874529i	$0.661171\pi$
$152$	8.42607			0.683444
$153$	7.16059	+	21.5908i	0.578899	+	1.74551i
$154$		0			0
$155$	−2.88323	−	4.99391i	−0.231587	−	0.401120i
$156$	−0.784350	+	7.68715i	−0.0627983	+	0.615465i
$157$	5.63694	−	9.76347i	0.449877	−	0.779210i	−0.548501	−	0.836150i	$-0.684801\pi$
$157$	5.63694	−	9.76347i	0.449877	−	0.779210i	0.998378	+	0.0569405i	$0.0181345\pi$
$158$	−1.13348	+	1.96324i	−0.0901745	+	0.156187i
$159$	−9.72109	−	7.01777i	−0.770933	−	0.556545i
$160$	−2.23061	−	3.86353i	−0.176345	−	0.305439i
$161$		0			0
$162$	−14.0488	−	6.05146i	−1.10377	−	0.475447i
$163$	−1.66621			−0.130507			−0.0652537	−	0.997869i	$-0.520786\pi$
$163$	−1.66621			−0.130507			−0.0652537	+	0.997869i	$0.520786\pi$
$164$	−0.468760	−	0.811916i	−0.0366040	−	0.0634000i
$165$	0.784350	+	0.566231i	0.0610616	+	0.0440811i
$166$	4.83024	−	8.36622i	0.374899	−	0.649344i
$167$	1.95135	−	3.37984i	0.151000	−	0.261540i	−0.780595	−	0.625037i	$-0.785084\pi$
$167$	1.95135	−	3.37984i	0.151000	−	0.261540i	0.931595	+	0.363497i	$0.118417\pi$
$168$		0			0
$169$	−6.09888	−	10.5636i	−0.469145	−	0.812583i
$170$	−12.2335			−0.938269
$171$	4.21303	+	12.7033i	0.322179	+	0.971442i
$172$	6.21015			0.473519
$173$	8.05705	+	13.9552i	0.612566	+	1.06100i	0.990806	+	0.135288i	$0.0431961\pi$
$173$	8.05705	+	13.9552i	0.612566	+	1.06100i	−0.378240	+	0.925708i	$0.623471\pi$
$174$	−14.7098	+	6.60282i	−1.11514	+	0.500559i
$175$		0			0
$176$	−1.46727	+	2.54138i	−0.110599	+	0.191564i
$177$	−16.4814	+	7.39808i	−1.23882	+	0.556074i
$178$	−0.716947	−	1.24179i	−0.0537374	−	0.0930760i
$179$	14.2880			1.06793			0.533967	−	0.845505i	$-0.320701\pi$
$179$	14.2880			1.06793			0.533967	+	0.845505i	$0.320701\pi$
$180$	1.68208	−	1.89112i	0.125375	−	0.140956i
$181$	−12.8873			−0.957905			−0.478952	−	0.877841i	$-0.658983\pi$
$181$	−12.8873			−0.957905			−0.478952	+	0.877841i	$0.658983\pi$
$182$		0			0
$183$	2.04875	−	20.0791i	0.151448	−	1.48429i
$184$	−2.33929	+	4.05178i	−0.172455	+	0.298701i
$185$	3.31657	−	5.74447i	0.243839	−	0.422342i
$186$	14.4993	+	10.4672i	1.06314	+	0.767494i
$187$	2.23061	+	3.86353i	0.163118	+	0.282529i
$188$	6.64490			0.484629
$189$		0			0
$190$	−7.19777			−0.522181
$191$	1.08217	+	1.87438i	0.0783034	+	0.135625i	0.902518	−	0.430652i	$-0.141716\pi$
$191$	1.08217	+	1.87438i	0.0783034	+	0.135625i	−0.824215	+	0.566277i	$0.808383\pi$
$192$	−2.79130	−	2.01507i	−0.201445	−	0.145425i
$193$	−5.21565	+	9.03377i	−0.375431	+	0.650265i	−0.990391	−	0.138293i	$-0.955839\pi$
$193$	−5.21565	+	9.03377i	−0.375431	+	0.650265i	0.614961	+	0.788558i	$0.289172\pi$
$194$	2.89475	−	5.01385i	0.207831	−	0.359973i
$195$	−0.837775	+	8.21075i	−0.0599943	+	0.587984i
$196$		0			0
$197$	−18.7848			−1.33836			−0.669179	−	0.743101i	$-0.733354\pi$
$197$	−18.7848			−1.33836			−0.669179	+	0.743101i	$0.733354\pi$
$198$	−2.93818	−	0.605896i	−0.208807	−	0.0430591i
$199$	−8.42607			−0.597308			−0.298654	−	0.954361i	$-0.596538\pi$
$199$	−8.42607			−0.597308			−0.298654	+	0.954361i	$0.596538\pi$
$200$	3.87085	+	6.70452i	0.273711	+	0.474081i
$201$	−18.7470	+	8.41502i	−1.32231	+	0.593550i
$202$	8.14681	−	14.1107i	0.573208	−	0.992825i
$203$		0			0
$204$	10.6483	−	4.77975i	0.745532	−	0.334650i
$205$	−0.500689	−	0.867218i	−0.0349696	−	0.0605692i
$206$	−19.8056			−1.37992
$207$	−7.27816	−	1.50086i	−0.505867	−	0.104317i
$208$	−25.0365			−1.73597
$209$	1.31241	+	2.27316i	0.0907814	+	0.157238i
$210$		0			0
$211$	−5.61126	+	9.71899i	−0.386295	+	0.669083i	−0.991948	−	0.126646i	$-0.959579\pi$
$211$	−5.61126	+	9.71899i	−0.386295	+	0.669083i	0.605653	+	0.795729i	$0.292912\pi$
$212$	−3.07598	+	5.32776i	−0.211259	+	0.365912i
$213$	−6.03920	−	4.35977i	−0.413799	−	0.298727i
$214$	−3.22803	−	5.59111i	−0.220664	−	0.382200i
$215$	6.63315			0.452377
$216$	2.94756	−	9.36107i	0.200556	−	0.636940i
$217$		0			0
$218$	−10.9320	−	18.9348i	−0.740408	−	1.28242i
$219$	6.26509	+	4.52284i	0.423356	+	0.305625i
$220$	0.248187	−	0.429872i	0.0167328	−	0.0289820i
$221$	−19.0309	+	32.9624i	−1.28016	+	2.21729i
$222$	−2.08804	+	20.4642i	−0.140140	+	1.37347i
$223$	−10.3774	−	17.9742i	−0.694923	−	1.20364i	−0.970206	−	0.242279i	$-0.922105\pi$
$223$	−10.3774	−	17.9742i	−0.694923	−	1.20364i	0.275283	−	0.961363i	$-0.411228\pi$
$224$		0			0
$225$	−8.17240	+	9.18801i	−0.544826	+	0.612534i
$226$	−15.3324			−1.01990
$227$	−5.21512	−	9.03284i	−0.346139	−	0.599531i	0.639421	−	0.768857i	$-0.279174\pi$
$227$	−5.21512	−	9.03284i	−0.346139	−	0.599531i	−0.985560	+	0.169326i	$0.945841\pi$
$228$	6.26509	−	2.81223i	0.414916	−	0.186245i
$229$	7.52961	−	13.0417i	0.497570	−	0.861817i	−0.502426	−	0.864620i	$-0.667559\pi$
$229$	7.52961	−	13.0417i	0.497570	−	0.861817i	0.999996	+	0.00280316i	$0.000892274\pi$
$230$	1.99829	−	3.46113i	0.131763	−	0.228220i
$231$		0			0
$232$	−5.17240	−	8.95886i	−0.339585	−	0.588178i
$233$	4.38688			0.287394			0.143697	−	0.989622i	$-0.454101\pi$
$233$	4.38688			0.287394			0.143697	+	0.989622i	$0.454101\pi$
$234$	−8.05705	−	24.2939i	−0.526706	−	1.58814i
$235$	7.09751			0.462990
$236$	4.63486	+	8.02781i	0.301704	+	0.522566i
$237$	0.234501	−	2.29826i	0.0152325	−	0.149288i
$238$		0			0
$239$	4.77561	−	8.27160i	0.308909	−	0.535046i	−0.669215	−	0.743069i	$-0.733370\pi$
$239$	4.77561	−	8.27160i	0.308909	−	0.535046i	0.978124	+	0.208023i	$0.0667029\pi$
$240$	6.64902	+	4.80000i	0.429192	+	0.309839i
$241$	5.26792	+	9.12431i	0.339337	+	0.587749i	0.984308	−	0.176458i	$-0.0564640\pi$
$241$	5.26792	+	9.12431i	0.339337	+	0.587749i	−0.644971	+	0.764207i	$0.723131\pi$
$242$	18.1075			1.16400
$243$	15.5867	−	0.236756i	0.999885	−	0.0151879i
$244$	−10.3563			−0.662996
$245$		0			0
$246$	2.51788	+	1.81769i	0.160534	+	0.115892i
$247$	−11.1971	+	19.3939i	−0.712453	+	1.23401i
$248$	−5.73668	+	9.93623i	−0.364280	+	0.630951i
$249$	−0.999311	+	9.79391i	−0.0633288	+	0.620664i
$250$	−7.34011	−	12.7134i	−0.464229	−	0.804068i
$251$	24.4346			1.54230			0.771148	−	0.636656i	$-0.219683\pi$
$251$	24.4346			1.54230			0.771148	+	0.636656i	$0.219683\pi$
$252$		0			0
$253$	−1.45744			−0.0916282
$254$	5.46658	+	9.46839i	0.343004	+	0.594100i
$255$	11.3736	−	5.10532i	0.712244	−	0.319707i
$256$	−8.87085	+	15.3648i	−0.554428	+	0.960298i
$257$	2.00416	−	3.47131i	0.125016	−	0.216534i	−0.796723	−	0.604345i	$-0.793435\pi$
$257$	2.00416	−	3.47131i	0.125016	−	0.216534i	0.921739	+	0.387810i	$0.126768\pi$
$258$	−18.7665	+	8.42380i	−1.16835	+	0.524443i
$259$		0			0
$260$	4.23491			0.262638
$261$	10.9203	−	12.2774i	0.675949	−	0.759952i
$262$	11.2739			0.696503
$263$	−8.84362	−	15.3176i	−0.545321	−	0.944524i	−0.998587	−	0.0531485i	$-0.983074\pi$
$263$	−8.84362	−	15.3176i	−0.545321	−	0.944524i	0.453265	−	0.891376i	$-0.350259\pi$
$264$	0.195377	−	1.91482i	0.0120246	−	0.117849i
$265$	−3.28550	+	5.69066i	−0.201827	+	0.349574i
$266$		0			0
$267$	1.18478	+	0.855304i	0.0725072	+	0.0523438i
$268$	5.27197	+	9.13132i	0.322037	+	0.557784i
$269$	14.2273			0.867455			0.433727	−	0.901044i	$-0.357198\pi$
$269$	14.2273			0.867455			0.433727	+	0.901044i	$0.357198\pi$
$270$	−2.51788	+	7.99647i	−0.153233	+	0.486650i
$271$	5.39874			0.327950			0.163975	−	0.986464i	$-0.447568\pi$
$271$	5.39874			0.327950			0.163975	+	0.986464i	$0.447568\pi$
$272$	18.9091	+	32.7515i	1.14653	+	1.98585i
$273$		0			0
$274$	11.9258	−	20.6561i	0.720464	−	1.24788i
$275$	−1.20582	+	2.08854i	−0.0727136	+	0.125944i
$276$	−0.387055	+	3.79339i	−0.0232980	+	0.228335i
$277$	−3.83310	−	6.63913i	−0.230309	−	0.398907i	0.727590	−	0.686012i	$-0.240640\pi$
$277$	−3.83310	−	6.63913i	−0.230309	−	0.398907i	−0.957899	+	0.287105i	$0.907307\pi$
$278$	14.9653			0.897562
$279$	−17.8483	−	3.68059i	−1.06855	−	0.220351i
$280$		0			0
$281$	11.3312	+	19.6263i	0.675965	+	1.17081i	0.976186	+	0.216936i	$0.0696065\pi$
$281$	11.3312	+	19.6263i	0.675965	+	1.17081i	−0.300220	+	0.953870i	$0.597060\pi$
$282$	−20.0803	+	9.01352i	−1.19577	+	0.536747i
$283$	−15.9246	+	27.5822i	−0.946619	+	1.63959i	−0.194144	+	0.980973i	$0.562193\pi$
$283$	−15.9246	+	27.5822i	−0.946619	+	1.63959i	−0.752476	+	0.658620i	$0.771141\pi$
$284$	−1.91095	+	3.30986i	−0.113394	+	0.196404i
$285$	6.69183	−	3.00379i	0.396390	−	0.177929i
$286$	−2.50987	−	4.34722i	−0.148412	−	0.257057i
$287$		0			0
$288$	−13.8083	−	2.84748i	−0.813664	−	0.167790i
$289$	40.4930			2.38194
$290$	4.41840	+	7.65289i	0.259457	+	0.449393i
$291$	−0.598884	+	5.86946i	−0.0351072	+	0.344074i
$292$	1.98242	−	3.43366i	0.116013	−	0.200940i
$293$	13.7468	−	23.8102i	0.803097	−	1.39100i	−0.114472	−	0.993427i	$-0.536517\pi$
$293$	13.7468	−	23.8102i	0.803097	−	1.39100i	0.917568	−	0.397578i	$-0.130149\pi$
$294$		0			0
$295$	4.95056	+	8.57462i	0.288233	+	0.499234i
$296$	−13.1978			−0.767105
$297$	2.98450	−	0.662859i	0.173179	−	0.0384630i
$298$	7.42030			0.429846
$299$	−6.21720	−	10.7685i	−0.359550	−	0.622758i
$300$	5.11578	+	3.69314i	0.295360	+	0.213224i
$301$		0			0
$302$	−10.7534	+	18.6254i	−0.618789	+	1.07177i
$303$	−1.68547	+	16.5187i	−0.0968275	+	0.948973i
$304$	11.1254	+	19.2698i	0.638088	+	1.10520i
$305$	−11.0617			−0.633394
$306$	−25.6948	+	28.8880i	−1.46887	+	1.65142i
$307$	−14.8176			−0.845683			−0.422841	−	0.906204i	$-0.638967\pi$
$307$	−14.8176			−0.845683			−0.422841	+	0.906204i	$0.638967\pi$
$308$		0			0
$309$	18.4134	−	8.26530i	1.04750	−	0.470196i
$310$	4.90043	−	8.48779i	0.278326	−	0.482074i
$311$	14.5318	−	25.1698i	0.824021	−	1.42725i	−0.0786442	−	0.996903i	$-0.525059\pi$
$311$	14.5318	−	25.1698i	0.824021	−	1.42725i	0.902665	−	0.430343i	$-0.141608\pi$
$312$	14.9814	−	6.72477i	0.848156	−	0.380715i
$313$	−12.2390	−	21.1986i	−0.691790	−	1.19822i	−0.971251	−	0.238058i	$-0.923489\pi$
$313$	−12.2390	−	21.1986i	−0.691790	−	1.19822i	0.279461	−	0.960157i	$-0.409844\pi$
$314$	19.1614			1.08134
$315$		0			0
$316$	−1.18539			−0.0666834
$317$	3.69344	+	6.39722i	0.207444	+	0.359304i	0.950909	−	0.309472i	$-0.100152\pi$
$317$	3.69344	+	6.39722i	0.207444	+	0.359304i	−0.743465	+	0.668775i	$0.766819\pi$
$318$	2.06848	−	20.2725i	0.115995	−	1.13682i
$319$	1.61126	−	2.79079i	0.0902135	−	0.156254i
$320$	−0.943395	+	1.63401i	−0.0527374	+	0.0913438i
$321$	5.33442	+	3.85098i	0.297738	+	0.214941i
$322$		0			0
$323$	33.8268			1.88218
$324$	−0.932677	−	7.94406i	−0.0518154	−	0.441337i
$325$	−20.5753			−1.14131
$326$	−1.41597	−	2.45253i	−0.0784231	−	0.135833i
$327$	18.0655	+	13.0417i	0.999022	+	0.721206i
$328$	−0.996205	+	1.72548i	−0.0550062	+	0.0952736i
$329$		0			0
$330$	−0.166896	+	1.63569i	−0.00918734	+	0.0900419i
$331$	−10.0309	−	17.3740i	−0.551347	−	0.954960i	−0.998178	−	0.0603420i	$-0.980781\pi$
$331$	−10.0309	−	17.3740i	−0.551347	−	0.954960i	0.446831	−	0.894618i	$-0.352552\pi$
$332$	5.05146			0.277235
$333$	−6.59888	−	19.8971i	−0.361617	−	1.09036i
$334$	6.63315			0.362950
$335$	5.63106	+	9.75329i	0.307658	+	0.532879i
$336$		0			0
$337$	−3.20327	+	5.54823i	−0.174493	+	0.302231i	−0.939986	−	0.341214i	$-0.889162\pi$
$337$	−3.20327	+	5.54823i	−0.174493	+	0.302231i	0.765493	+	0.643445i	$0.222495\pi$
$338$	10.3658	−	17.9542i	0.563827	−	0.976577i
$339$	14.2547	−	6.39855i	0.774208	−	0.347522i
$340$	−3.19846	−	5.53989i	−0.173461	−	0.300443i
$341$	−3.57409			−0.193548
$342$	−15.1179	+	16.9967i	−0.817482	+	0.919074i
$343$		0			0
$344$	−6.59888	−	11.4296i	−0.355788	−	0.616243i
$345$	−0.413419	+	4.05178i	−0.0222577	+	0.218140i
$346$	−13.6940	+	23.7187i	−0.736194	+	1.27512i
$347$	14.5963	−	25.2816i	0.783572	−	1.35719i	−0.146276	−	0.989244i	$-0.546729\pi$
$347$	14.5963	−	25.2816i	0.783572	−	1.35719i	0.929848	−	0.367943i	$-0.119938\pi$
$348$	−6.83592	−	4.93493i	−0.366444	−	0.264540i
$349$	−2.17192	−	3.76188i	−0.116260	−	0.201369i	0.802022	−	0.597294i	$-0.203757\pi$
$349$	−2.17192	−	3.76188i	−0.116260	−	0.201369i	−0.918283	+	0.395925i	$0.870424\pi$
$350$		0			0
$351$	17.6291	+	19.2238i	0.940970	+	1.02609i
$352$	−2.76509			−0.147380
$353$	12.8503	+	22.2574i	0.683955	+	1.18464i	0.973764	+	0.227560i	$0.0730747\pi$
$353$	12.8503	+	22.2574i	0.683955	+	1.18464i	−0.289809	+	0.957084i	$0.593592\pi$
$354$	−24.8955	−	17.9724i	−1.32318	−	0.955221i
$355$	−2.04111	+	3.53530i	−0.108331	+	0.187635i
$356$	0.374892	−	0.649331i	0.0198692	−	0.0344145i
$357$		0			0
$358$	12.1421	+	21.0308i	0.641732	+	1.11151i
$359$	20.6872			1.09183			0.545916	−	0.837840i	$-0.316182\pi$
$359$	20.6872			1.09183			0.545916	+	0.837840i	$0.316182\pi$
$360$	−5.26792	−	1.08632i	−0.277644	−	0.0572543i
$361$	0.902493			0.0474996
$362$	−10.9518	−	18.9691i	−0.575614	−	0.996992i
$363$	−16.8348	+	7.55667i	−0.883595	+	0.396622i
$364$		0			0
$365$	2.11745	−	3.66754i	0.110833	−	0.191968i
$366$	31.2960	−	14.0479i	1.63587	−	0.734297i
$367$	−1.42391	−	2.46628i	−0.0743273	−	0.128739i	0.826466	−	0.562986i	$-0.190348\pi$
$367$	−1.42391	−	2.46628i	−0.0743273	−	0.128739i	−0.900794	+	0.434248i	$0.857014\pi$
$368$	−12.3548			−0.644040
$369$	−3.09946	−	0.639154i	−0.161351	−	0.0332730i
$370$	11.2739			0.586101
$371$		0			0
$372$	−0.949180	+	9.30259i	−0.0492127	+	0.482317i
$373$	−10.7163	+	18.5612i	−0.554871	+	0.961065i	0.443043	+	0.896501i	$0.353899\pi$
$373$	−10.7163	+	18.5612i	−0.554871	+	0.961065i	−0.997914	+	0.0645641i	$0.979434\pi$
$374$	−3.79121	+	6.56657i	−0.196039	+	0.339549i
$375$	12.1298	+	8.75661i	0.626378	+	0.452189i
$376$	−7.06085	−	12.2297i	−0.364135	−	0.630701i
$377$	27.4936			1.41599
$378$		0			0
$379$	27.0494			1.38943			0.694716	−	0.719284i	$-0.255530\pi$
$379$	27.0494			1.38943			0.694716	+	0.719284i	$0.255530\pi$
$380$	−1.88186	−	3.25947i	−0.0965372	−	0.167207i
$381$	−9.03370	−	6.52153i	−0.462810	−	0.334108i
$382$	−1.83929	+	3.18575i	−0.0941064	+	0.162997i
$383$	−7.21340	+	12.4940i	−0.368588	+	0.638412i	−0.989345	−	0.145590i	$-0.953492\pi$
$383$	−7.21340	+	12.4940i	−0.368588	+	0.638412i	0.620757	+	0.784003i	$0.286825\pi$
$384$	2.24647	−	22.0169i	0.114640	−	1.12355i
$385$		0			0
$386$	−17.7293			−0.902399
$387$	13.9320	−	15.6634i	0.708203	−	0.796214i
$388$	3.02733			0.153689
$389$	3.05377	+	5.28929i	0.154832	+	0.268178i	0.932998	−	0.359882i	$-0.117183\pi$
$389$	3.05377	+	5.28929i	0.154832	+	0.268178i	−0.778166	+	0.628059i	$0.783850\pi$
$390$	−12.7975	+	5.74447i	−0.648028	+	0.290883i
$391$	−9.39120	+	16.2660i	−0.474933	+	0.822609i
$392$		0			0
$393$	−10.4814	+	4.70484i	−0.528718	+	0.237328i
$394$	−15.9635	−	27.6497i	−0.804232	−	1.39297i
$395$	−1.26613			−0.0637059
$396$	−0.493810	−	1.48895i	−0.0248149	−	0.0748226i
$397$	12.8873			0.646794			0.323397	−	0.946263i	$-0.395175\pi$
$397$	12.8873			0.646794			0.323397	+	0.946263i	$0.395175\pi$
$398$	−7.16059	−	12.4025i	−0.358928	−	0.621682i
$399$		0			0
$400$	−10.2218	+	17.7047i	−0.511092	+	0.885237i
$401$	−4.19530	+	7.26647i	−0.209503	+	0.362870i	−0.951558	−	0.307469i	$-0.900518\pi$
$401$	−4.19530	+	7.26647i	−0.209503	+	0.362870i	0.742055	+	0.670339i	$0.233851\pi$
$402$	−28.3177	−	20.4429i	−1.41236	−	1.01960i
$403$	−15.2465	−	26.4078i	−0.759483	−	1.31546i
$404$	8.51994			0.423883
$405$	−0.996205	−	8.48516i	−0.0495018	−	0.421631i
$406$		0			0
$407$	−2.05563	−	3.56046i	−0.101894	−	0.176485i
$408$	−20.1119	−	14.5190i	−0.995686	−	0.718797i
$409$	3.40633	−	5.89994i	0.168432	−	0.291733i	−0.769437	−	0.638723i	$-0.779463\pi$
$409$	3.40633	−	5.89994i	0.168432	−	0.291733i	0.937869	+	0.346990i	$0.112796\pi$
$410$	0.850985	−	1.47395i	0.0420271	−	0.0727931i
$411$	−2.46729	+	24.1810i	−0.121702	+	1.19276i
$412$	−5.17817	−	8.96885i	−0.255110	−	0.441864i
$413$		0			0
$414$	−3.97593	−	11.9883i	−0.195406	−	0.589194i
$415$	5.39554			0.264857
$416$	−11.7955	−	20.4303i	−0.578320	−	1.00168i
$417$	−13.9134	+	6.24536i	−0.681343	+	0.305837i
$418$	−2.23061	+	3.86353i	−0.109103	+	0.188971i
$419$	−5.16231	+	8.94137i	−0.252195	+	0.436815i	−0.964130	−	0.265431i	$-0.914486\pi$
$419$	−5.16231	+	8.94137i	−0.252195	+	0.436815i	0.711935	+	0.702246i	$0.247819\pi$
$420$		0			0
$421$	−1.56801	−	2.71588i	−0.0764202	−	0.132364i	0.825283	−	0.564720i	$-0.191016\pi$
$421$	−1.56801	−	2.71588i	−0.0764202	−	0.132364i	−0.901703	+	0.432356i	$0.857682\pi$
$422$	−19.0741			−0.928514
$423$	14.9073	−	16.7599i	0.724818	−	0.814894i
$424$	13.0741			0.634936
$425$	15.5397	+	26.9156i	0.753787	+	1.30560i
$426$	1.28504	−	12.5942i	0.0622603	−	0.610192i
$427$		0			0
$428$	1.68794	−	2.92359i	0.0815895	−	0.141317i
$429$	4.14764	+	2.99423i	0.200250	+	0.144563i
$430$	5.63694	+	9.76347i	0.271837	+	0.470836i
$431$	31.8726			1.53525			0.767625	−	0.640899i	$-0.221438\pi$
$431$	31.8726			1.53525			0.767625	+	0.640899i	$0.221438\pi$
$432$	25.2999	−	5.61912i	1.21724	−	0.270350i
$433$	−7.48855			−0.359877			−0.179938	−	0.983678i	$-0.557590\pi$
$433$	−7.48855			−0.359877			−0.179938	+	0.983678i	$0.557590\pi$
$434$		0			0
$435$	−7.30154	−	5.27107i	−0.350082	−	0.252728i
$436$	5.71634	−	9.90099i	0.273763	−	0.474171i
$437$	−5.52544	+	9.57035i	−0.264318	+	0.457812i
$438$	−1.33310	+	13.0653i	−0.0636982	+	0.624284i
$439$	1.14465	+	1.98259i	0.0546311	+	0.0946238i	0.892048	−	0.451941i	$-0.149268\pi$
$439$	1.14465	+	1.98259i	0.0546311	+	0.0946238i	−0.837417	+	0.546565i	$0.815935\pi$
$440$	−1.05489			−0.0502900
$441$		0			0
$442$	−64.6908			−3.07703
$443$	−18.6749	−	32.3458i	−0.887270	−	1.53680i	−0.843090	−	0.537773i	$-0.819266\pi$
$443$	−18.6749	−	32.3458i	−0.887270	−	1.53680i	−0.0441800	−	0.999024i	$-0.514067\pi$
$444$	−9.81303	+	4.40481i	−0.465706	+	0.209043i
$445$	0.400427	−	0.693560i	0.0189821	−	0.0328779i
$446$	17.6378	−	30.5495i	0.835172	−	1.44656i
$447$	−6.89872	+	3.09665i	−0.326298	+	0.146467i
$448$		0			0
$449$	−6.20286			−0.292731			−0.146366	−	0.989231i	$-0.546758\pi$
$449$	−6.20286			−0.292731			−0.146366	+	0.989231i	$0.546758\pi$
$450$	−20.4691	−	4.22102i	−0.964920	−	0.198981i
$451$	−0.620660			−0.0292257
$452$	−4.00866	−	6.94320i	−0.188552	−	0.326581i
$453$	2.22473	−	21.8039i	0.104527	−	1.02444i
$454$	8.86376	−	15.3525i	0.415997	−	0.720527i
$455$		0			0
$456$	−11.8331	−	8.54245i	−0.554136	−	0.400037i
$457$	−10.0858	−	17.4691i	−0.471795	−	0.817172i	0.527685	−	0.849440i	$-0.323060\pi$
$457$	−10.0858	−	17.4691i	−0.471795	−	0.817172i	−0.999479	+	0.0322682i	$0.989727\pi$
$458$	25.5951			1.19598
$459$	11.8331	−	37.5804i	0.552322	−	1.75410i
$460$	2.08981			0.0974378
$461$	−11.2680	−	19.5168i	−0.524803	−	0.908986i	−0.999583	−	0.0288813i	$-0.990806\pi$
$461$	−11.2680	−	19.5168i	−0.524803	−	0.908986i	0.474780	−	0.880105i	$-0.342528\pi$
$462$		0			0
$463$	13.8145	−	23.9275i	0.642016	−	1.11200i	−0.342966	−	0.939348i	$-0.611432\pi$
$463$	13.8145	−	23.9275i	0.642016	−	1.11200i	0.984982	−	0.172656i	$-0.0552350\pi$
$464$	13.6588	−	23.6578i	0.634096	−	1.09829i
$465$	−1.01383	+	9.93623i	−0.0470154	+	0.460782i
$466$	3.72803	+	6.45714i	0.172698	+	0.299121i
$467$	−20.1224			−0.931155			−0.465577	−	0.885007i	$-0.654153\pi$
$467$	−20.1224			−0.931155			−0.465577	+	0.885007i	$0.654153\pi$
$468$	8.89483	−	10.0002i	0.411164	−	0.462261i
$469$		0			0
$470$	6.03156	+	10.4470i	0.278215	+	0.481883i
$471$	−17.8145	+	7.99647i	−0.820850	+	0.368458i
$472$	9.84997	−	17.0607i	0.453382	−	0.785280i
$473$	2.05563	−	3.56046i	0.0945181	−	0.163710i
$474$	3.58215	−	1.60793i	0.164533	−	0.0738547i
$475$	9.14301	+	15.8362i	0.419510	+	0.726613i
$476$		0			0
$477$	6.53706	+	19.7107i	0.299312	+	0.902493i
$478$	16.2335			0.742504
$479$	−4.79329	−	8.30222i	−0.219011	−	0.379338i	0.735495	−	0.677530i	$-0.236950\pi$
$479$	−4.79329	−	8.30222i	−0.219011	−	0.379338i	−0.954506	+	0.298192i	$0.903616\pi$
$480$	−0.784350	+	7.68715i	−0.0358005	+	0.350869i
$481$	17.5380	−	30.3767i	0.799664	−	1.38506i
$482$	−8.95351	+	15.5079i	−0.407821	+	0.706367i
$483$		0			0
$484$	4.73422	+	8.19991i	0.215192	+	0.372723i
$485$	3.23353			0.146827
$486$	13.5942	+	22.7411i	0.616648	+	1.03156i
$487$	13.0741			0.592445			0.296223	−	0.955119i	$-0.404273\pi$
$487$	13.0741			0.592445			0.296223	+	0.955119i	$0.404273\pi$
$488$	11.0046	+	19.0605i	0.498155	+	0.862830i
$489$	2.33993	+	1.68922i	0.105815	+	0.0763893i
$490$		0			0
$491$	−7.67054	+	13.2858i	−0.346167	+	0.599578i	−0.985565	−	0.169298i	$-0.945850\pi$
$491$	−7.67054	+	13.2858i	−0.346167	+	0.599578i	0.639398	+	0.768876i	$0.279183\pi$
$492$	−0.164830	+	1.61544i	−0.00743112	+	0.0728298i
$493$	−20.7648	−	35.9657i	−0.935201	−	1.61982i
$494$	−38.0617			−1.71248
$495$	−0.527445	−	1.59037i	−0.0237069	−	0.0714817i
$496$	−30.2979			−1.36042
$497$		0			0
$498$	−15.2651	+	6.85210i	−0.684045	+	0.307050i
$499$	−2.43268	+	4.21352i	−0.108902	+	0.188623i	−0.915326	−	0.402715i	$-0.868067\pi$
$499$	−2.43268	+	4.21352i	−0.108902	+	0.188623i	0.806424	+	0.591338i	$0.201400\pi$
$500$	3.83814	−	6.64786i	0.171647	−	0.297301i
$501$	−6.16690	+	2.76816i	−0.275517	+	0.123672i
$502$	20.7648	+	35.9657i	0.926780	+	1.60523i
$503$	−16.0085			−0.713783			−0.356892	−	0.934146i	$-0.616163\pi$
$503$	−16.0085			−0.713783			−0.356892	+	0.934146i	$0.616163\pi$
$504$		0			0
$505$	9.10026			0.404956
$506$	−1.23855	−	2.14523i	−0.0550603	−	0.0953672i
$507$	−2.14455	+	21.0180i	−0.0952429	+	0.933443i
$508$	−2.85848	+	4.95102i	−0.126824	+	0.219666i
$509$	−15.5925	+	27.0071i	−0.691127	+	1.19707i	0.280342	+	0.959900i	$0.409552\pi$
$509$	−15.5925	+	27.0071i	−0.691127	+	1.19707i	−0.971469	+	0.237167i	$0.923781\pi$
$510$	17.1801	+	12.4025i	0.760747	+	0.549192i
$511$		0			0
$512$	−4.59937			−0.203265
$513$	6.96217	−	22.1110i	0.307387	−	0.976224i
$514$	6.81266			0.300494
$515$	−5.53087	−	9.57975i	−0.243719	−	0.422134i
$516$	−8.72119	−	6.29593i	−0.383929	−	0.277163i
$517$	2.19954	−	3.80971i	0.0967356	−	0.167551i
$518$		0			0
$519$	2.83310	−	27.7663i	0.124359	−	1.21880i
$520$	−4.50000	−	7.79423i	−0.197338	−	0.341800i
$521$	−20.9661			−0.918541			−0.459270	−	0.888297i	$-0.651889\pi$
$521$	−20.9661			−0.918541			−0.459270	+	0.888297i	$0.651889\pi$
$522$	27.3516	+	5.64030i	1.19715	+	0.246869i
$523$	−43.5642			−1.90493			−0.952465	−	0.304647i	$-0.901462\pi$
$523$	−43.5642			−1.90493			−0.952465	+	0.304647i	$0.901462\pi$
$524$	2.94756	+	5.10532i	0.128765	+	0.223027i
$525$		0			0
$526$	15.0309	−	26.0342i	0.655377	−	1.13515i
$527$	−23.0302	+	39.8894i	−1.00321	+	1.73761i
$528$	4.63704	−	2.08144i	0.201801	−	0.0905832i
$529$	8.43199	+	14.6046i	0.366608	+	0.634984i
$530$	−11.1683			−0.485118
$531$	30.6459	+	6.31963i	1.32992	+	0.274249i
$532$		0			0
$533$	−2.64764	−	4.58584i	−0.114682	−	0.198635i
$534$	−0.252100	+	2.47075i	−0.0109094	+	0.106920i
$535$	1.80291	−	3.12273i	0.0779466	−	0.135007i
$536$	11.2040	−	19.4058i	0.483937	−	0.838204i
$537$	−20.0653	−	14.4853i	−0.865880	−	0.625089i
$538$	12.0906	+	20.9415i	0.521262	+	0.902852i
$539$		0			0
$540$	−4.27946	+	0.950469i	−0.184159	+	0.0409017i
$541$	9.86535			0.424145			0.212072	−	0.977254i	$-0.431979\pi$
$541$	9.86535			0.424145			0.212072	+	0.977254i	$0.431979\pi$
$542$	4.58793	+	7.94652i	0.197068	+	0.341332i
$543$	18.0982	+	13.0653i	0.776668	+	0.560686i
$544$	−17.8173	+	30.8604i	−0.763909	+	1.32313i
$545$	6.10570	−	10.5754i	0.261539	−	0.453000i
$546$		0			0
$547$	−0.284350	−	0.492509i	−0.0121579	−	0.0210582i	0.859882	−	0.510492i	$-0.170537\pi$
$547$	−0.284350	−	0.492509i	−0.0121579	−	0.0210582i	−0.872040	+	0.489434i	$0.837203\pi$
$548$	12.4720			0.532778
$549$	−23.2336	+	26.1210i	−0.991587	+	1.11482i
$550$	−4.09888			−0.174777
$551$	−12.2173	−	21.1609i	−0.520473	−	0.901487i
$552$	7.39292	−	3.31848i	0.314663	−	0.141244i
$553$		0			0
$554$	6.51485	−	11.2841i	0.276789	−	0.479413i
$555$	−10.4814	+	4.70484i	−0.444912	+	0.199709i
$556$	3.91269	+	6.77698i	0.165935	+	0.287408i
$557$	−2.58699			−0.109614			−0.0548071	−	0.998497i	$-0.517454\pi$
$557$	−2.58699			−0.109614			−0.0548071	+	0.998497i	$0.517454\pi$
$558$	−9.75023	−	29.3992i	−0.412760	−	1.24457i
$559$	35.0760			1.48356
$560$		0			0
$561$	0.784350	−	7.68715i	0.0331153	−	0.324552i
$562$	−19.2589	+	33.3574i	−0.812388	+	1.40710i
$563$	−16.6416	+	28.8240i	−0.701358	+	1.21479i	0.266632	+	0.963798i	$0.414089\pi$
$563$	−16.6416	+	28.8240i	−0.701358	+	1.21479i	−0.967990	+	0.250989i	$0.919244\pi$
$564$	−9.33173	−	6.73668i	−0.392937	−	0.283665i
$565$	−4.28171	−	7.41613i	−0.180133	−	0.311999i
$566$	−54.1318			−2.27533
$567$		0			0
$568$	8.12227			0.340803
$569$	2.67673	+	4.63623i	0.112214	+	0.194361i	0.916663	−	0.399662i	$-0.130872\pi$
$569$	2.67673	+	4.63623i	0.112214	+	0.194361i	−0.804448	+	0.594022i	$0.797539\pi$
$570$	10.1081	+	7.29719i	0.423384	+	0.305646i
$571$	−2.45056	+	4.24449i	−0.102553	+	0.177626i	−0.912736	−	0.408551i	$-0.866034\pi$
$571$	−2.45056	+	4.24449i	−0.102553	+	0.177626i	0.810183	+	0.586177i	$0.199368\pi$
$572$	1.31241	−	2.27316i	0.0548747	−	0.0950457i
$573$	0.380525	−	3.72940i	0.0158967	−	0.155798i
$574$		0			0
$575$	−10.1533			−0.423424
$576$	1.87704	+	5.65972i	0.0782102	+	0.235822i
$577$	36.0757			1.50185			0.750925	−	0.660387i	$-0.229608\pi$
$577$	36.0757			1.50185			0.750925	+	0.660387i	$0.229608\pi$
$578$	34.4116	+	59.6026i	1.43133	+	2.47914i
$579$	16.4831	−	7.39884i	0.685015	−	0.307485i
$580$	−2.31038	+	4.00170i	−0.0959333	+	0.166161i
$581$		0			0
$582$	−9.14833	+	4.10644i	−0.379210	+	0.170217i
$583$	2.03637	+	3.52710i	0.0843380	+	0.146078i
$584$	−8.42607			−0.348673
$585$	9.50069	−	10.6814i	0.392805	−	0.441621i
$586$	46.7289			1.93035
$587$	0.527445	+	0.913562i	0.0217700	+	0.0377068i	0.876705	−	0.481028i	$-0.159737\pi$
$587$	0.527445	+	0.913562i	0.0217700	+	0.0377068i	−0.854935	+	0.518735i	$0.826403\pi$
$588$		0			0
$589$	−13.5501	+	23.4695i	−0.558323	+	0.967045i
$590$	−8.41411	+	14.5737i	−0.346403	+	0.599988i
$591$	26.3803	+	19.0442i	1.08514	+	0.783375i
$592$	−17.4258	−	30.1824i	−0.716196	−	1.24049i
$593$	15.0710			0.618890			0.309445	−	0.950917i	$-0.399857\pi$
$593$	15.0710			0.618890			0.309445	+	0.950917i	$0.399857\pi$
$594$	3.51195	+	3.82965i	0.144097	+	0.157132i
$595$		0			0
$596$	1.94004	+	3.36024i	0.0794670	+	0.137641i
$597$	11.8331	+	8.54245i	0.484297	+	0.349619i
$598$	10.5669	−	18.3024i	0.432114	−	0.748443i
$599$	−21.0283	+	36.4221i	−0.859194	+	1.48817i	0.0135047	+	0.999909i	$0.495701\pi$
$599$	−21.0283	+	36.4221i	−0.859194	+	1.48817i	−0.872699	+	0.488259i	$0.837632\pi$
$600$	1.36111	−	13.3398i	0.0555671	−	0.544594i
$601$	9.44989	+	16.3677i	0.385469	+	0.667652i	0.991834	−	0.127534i	$-0.0407064\pi$
$601$	9.44989	+	16.3677i	0.385469	+	0.667652i	−0.606365	+	0.795186i	$0.707373\pi$
$602$		0			0
$603$	34.8585	+	7.18833i	1.41955	+	0.292732i
$604$	−11.2459			−0.457590
$605$	5.05669	+	8.75844i	0.205583	+	0.356081i
$606$	−25.7465	+	11.5569i	−1.04588	+	0.469468i
$607$	−14.7213	+	25.4980i	−0.597518	+	1.03493i	0.395668	+	0.918393i	$0.370513\pi$
$607$	−14.7213	+	25.4980i	−0.597518	+	1.03493i	−0.993186	+	0.116538i	$0.962820\pi$
$608$	−10.4830	+	18.1572i	−0.425143	+	0.736370i
$609$		0			0
$610$	−9.40043	−	16.2820i	−0.380612	−	0.659240i
$611$	37.5316			1.51836
$612$	−19.7997	−	4.08299i	−0.800355	−	0.165045i
$613$	−11.6676			−0.471249			−0.235625	−	0.971844i	$-0.575714\pi$
$613$	−11.6676			−0.471249			−0.235625	+	0.971844i	$0.575714\pi$
$614$	−12.5922	−	21.8103i	−0.508179	−	0.880191i
$615$	−0.176057	+	1.72548i	−0.00709932	+	0.0695780i
$616$		0			0
$617$	16.4054	−	28.4151i	0.660458	−	1.14395i	−0.320037	−	0.947405i	$-0.603695\pi$
$617$	16.4054	−	28.4151i	0.660458	−	1.14395i	0.980495	−	0.196542i	$-0.0629713\pi$
$618$	27.8138	+	20.0791i	1.11884	+	0.807701i
$619$	−12.0806	−	20.9242i	−0.485560	−	0.841014i	0.514303	−	0.857609i	$-0.328051\pi$
$619$	−12.0806	−	20.9242i	−0.485560	−	0.841014i	−0.999862	+	0.0165947i	$0.994717\pi$
$620$	5.12487			0.205820
$621$	8.69945	+	9.48642i	0.349097	+	0.380677i
$622$	49.3972			1.98065
$623$		0			0
$624$	35.1599	+	25.3824i	1.40752	+	1.01611i
$625$	−6.14764	+	10.6480i	−0.245906	+	0.425921i
$626$	20.8018	−	36.0297i	0.831406	−	1.44004i
$627$	0.461483	−	4.52284i	0.0184299	−	0.180625i
$628$	5.00975	+	8.67714i	0.199911	+	0.346256i
$629$	−52.9830			−2.11257
$630$		0			0
$631$	−11.1003			−0.441894			−0.220947	−	0.975286i	$-0.570915\pi$
$631$	−11.1003			−0.441894			−0.220947	+	0.975286i	$0.570915\pi$
$632$	1.25959	+	2.18168i	0.0501038	+	0.0867824i
$633$	17.7334	−	7.96005i	0.704839	−	0.316383i
$634$	−6.27747	+	10.8729i	−0.249310	+	0.431818i
$635$	−3.05318	+	5.28826i	−0.121162	+	0.209858i
$636$	9.72109	−	4.36354i	0.385466	−	0.173026i
$637$		0			0
$638$	5.47710			0.216840
$639$	4.06113	+	12.2452i	0.160656	+	0.484414i
$640$	−12.1293			−0.479452
$641$	−3.65019	−	6.32231i	−0.144174	−	0.249716i	0.784891	−	0.619634i	$-0.212719\pi$
$641$	−3.65019	−	6.32231i	−0.144174	−	0.249716i	−0.929064	+	0.369918i	$0.879386\pi$
$642$	−1.13507	+	11.1245i	−0.0447978	+	0.439048i
$643$	10.6256	−	18.4041i	0.419033	−	0.725787i	−0.576809	−	0.816879i	$-0.695702\pi$
$643$	10.6256	−	18.4041i	0.419033	−	0.725787i	0.995842	+	0.0910922i	$0.0290358\pi$
$644$		0			0
$645$	−9.31522	−	6.72477i	−0.366787	−	0.264787i
$646$	28.7465	+	49.7904i	1.13102	+	1.95898i
$647$	−16.9460			−0.666216			−0.333108	−	0.942889i	$-0.608097\pi$
$647$	−16.9460			−0.666216			−0.333108	+	0.942889i	$0.608097\pi$
$648$	−13.6298	+	10.1579i	−0.535427	+	0.399040i
$649$	6.13677			0.240889
$650$	−17.4852	−	30.2853i	−0.685826	−	1.18789i
$651$		0			0
$652$	0.740409	−	1.28243i	0.0289967	−	0.0502237i
$653$	1.86652	−	3.23292i	0.0730427	−	0.126514i	−0.827191	−	0.561921i	$-0.810062\pi$
$653$	1.86652	−	3.23292i	0.0730427	−	0.126514i	0.900233	+	0.435408i	$0.143396\pi$
$654$	−3.84402	+	37.6739i	−0.150313	+	1.47317i
$655$	3.14833	+	5.45306i	0.123015	+	0.213069i
$656$	−5.26140			−0.205423
$657$	−4.21303	−	12.7033i	−0.164366	−	0.495601i
$658$		0			0
$659$	11.7992	+	20.4368i	0.459632	+	0.796105i	0.998941	−	0.0460022i	$-0.0146481\pi$
$659$	11.7992	+	20.4368i	0.459632	+	0.796105i	−0.539310	+	0.842107i	$0.681315\pi$
$660$	−0.784350	+	0.352074i	−0.0305308	+	0.0137045i
$661$	17.2588	−	29.8930i	0.671288	−	1.16270i	−0.306252	−	0.951951i	$-0.599075\pi$
$661$	17.2588	−	29.8930i	0.671288	−	1.16270i	0.977539	−	0.210754i	$-0.0675918\pi$
$662$	17.0488	−	29.5293i	0.662619	−	1.14769i
$663$	60.1436	−	26.9969i	2.33579	−	1.04847i
$664$	−5.36767	−	9.29708i	−0.208306	−	0.360796i
$665$		0			0
$666$	23.6792	−	26.6219i	0.917550	−	1.03158i
$667$	13.5673			0.525329
$668$	1.73424	+	3.00379i	0.0670996	+	0.116220i
$669$	−3.64902	+	35.7628i	−0.141079	+	1.38267i
$670$	−9.57072	+	16.5770i	−0.369749	+	0.640424i
$671$	−3.42807	+	5.93759i	−0.132339	+	0.229218i
$672$		0			0
$673$	12.2287	+	21.1808i	0.471382	+	0.816458i	0.999464	−	0.0327353i	$-0.0104218\pi$
$673$	12.2287	+	21.1808i	0.471382	+	0.816458i	−0.528082	+	0.849194i	$0.677088\pi$
$674$	−10.8887			−0.419418
$675$	20.7918	−	4.61786i	0.800276	−	0.177741i
$676$	10.8406			0.416946
$677$	−4.16022	−	7.20572i	−0.159890	−	0.276938i	0.774939	−	0.632037i	$-0.217781\pi$
$677$	−4.16022	−	7.20572i	−0.159890	−	0.276938i	−0.934829	+	0.355098i	$0.884447\pi$
$678$	21.5320	+	15.5442i	0.826931	+	0.596971i
$679$		0			0
$680$	−6.79734	+	11.7733i	−0.260666	+	0.451487i
$681$	−1.83379	+	17.9724i	−0.0702711	+	0.688703i
$682$	−3.03731	−	5.26078i	−0.116305	−	0.201446i
$683$	−42.4624			−1.62478			−0.812389	−	0.583116i	$-0.801833\pi$
$683$	−42.4624			−1.62478			−0.812389	+	0.583116i	$0.801833\pi$
$684$	−11.6494	−	2.40228i	−0.445427	−	0.0918536i
$685$	13.3215			0.508989
$686$		0			0
$687$	−23.7960	+	10.6814i	−0.907873	+	0.407520i
$688$	17.4258	−	30.1824i	0.664352	−	1.15069i
$689$	−17.3737	+	30.0921i	−0.661885	+	1.14642i
$690$	−6.31522	+	2.83474i	−0.240416	+	0.107917i
$691$	17.6964	+	30.6511i	0.673204	+	1.16602i	0.976990	+	0.213284i	$0.0684159\pi$
$691$	17.6964	+	30.6511i	0.673204	+	1.16602i	−0.303786	+	0.952740i	$0.598251\pi$
$692$	−14.3212			−0.544410
$693$		0			0
$694$	49.6167			1.88342
$695$	4.17920	+	7.23859i	0.158526	+	0.274575i
$696$	−1.81877	+	17.8252i	−0.0689404	+	0.675661i
$697$	−3.99931	+	6.92701i	−0.151485	+	0.262379i
$698$	3.69146	−	6.39380i	0.139724	−	0.242009i
$699$	−6.16069	−	4.44747i	−0.233019	−	0.168219i
$700$		0			0
$701$	−7.00372			−0.264527			−0.132263	−	0.991215i	$-0.542224\pi$
$701$	−7.00372			−0.264527			−0.132263	+	0.991215i	$0.542224\pi$
$702$	−13.3145	+	42.2853i	−0.502525	+	1.59596i
$703$	−31.1733			−1.17572
$704$	0.584722	+	1.01277i	0.0220375	+	0.0381701i
$705$	−9.96735	−	7.19554i	−0.375392	−	0.271000i
$706$	−21.8408	+	37.8294i	−0.821989	+	1.42373i
$707$		0			0
$708$	1.62976	−	15.9727i	0.0612500	−	0.600291i
$709$	1.11126	+	1.92477i	0.0417344	+	0.0722861i	0.886138	−	0.463421i	$-0.153378\pi$
$709$	1.11126	+	1.92477i	0.0417344	+	0.0722861i	−0.844404	+	0.535707i	$0.820045\pi$
$710$	−6.93825			−0.260388
$711$	−2.65933	+	2.98981i	−0.0997326	+	0.112127i
$712$	−1.59343			−0.0597165
$713$	−7.52373	−	13.0315i	−0.281766	−	0.488033i
$714$		0			0
$715$	1.40180	−	2.42800i	0.0524245	−	0.0908019i
$716$	−6.34913	+	10.9970i	−0.237278	+	0.410977i
$717$	−15.0925	+	6.77461i	−0.563638	+	0.253002i
$718$	17.5803	+	30.4500i	0.656092	+	1.13638i
$719$	−26.0175			−0.970291			−0.485145	−	0.874434i	$-0.661233\pi$
$719$	−26.0175			−0.970291			−0.485145	+	0.874434i	$0.661233\pi$
$720$	−4.47121	−	13.4817i	−0.166632	−	0.502434i
$721$		0			0
$722$	0.766951	+	1.32840i	0.0285430	+	0.0494379i
$723$	1.85236	−	18.1544i	0.0688901	−	0.675168i
$724$	5.72670	−	9.91893i	0.212831	−	0.368634i
$725$	11.2250	−	19.4423i	0.416886	−	0.722068i
$726$	−25.4292	−	18.3577i	−0.943767	−	0.681317i
$727$	−0.685875	−	1.18797i	−0.0254377	−	0.0440594i	0.853026	−	0.521868i	$-0.174765\pi$
$727$	−0.685875	−	1.18797i	−0.0254377	−	0.0440594i	−0.878464	+	0.477809i	$0.841431\pi$
$728$		0			0
$729$	−22.1291	−	15.4695i	−0.819595	−	0.572943i
$730$	7.19777			0.266401
$731$	−26.4915	−	45.8847i	−0.979824	−	1.69711i
$732$	14.5439	+	10.4994i	0.537557	+	0.388068i
$733$	−0.400087	+	0.692971i	−0.0147776	+	0.0255955i	−0.873320	−	0.487148i	$-0.838037\pi$
$733$	−0.400087	+	0.692971i	−0.0147776	+	0.0255955i	0.858542	+	0.512743i	$0.171371\pi$
$734$	2.42011	−	4.19176i	0.0893280	−	0.154721i
$735$		0			0
$736$	−5.82072	−	10.0818i	−0.214555	−	0.371620i
$737$	6.98034			0.257124
$738$	−1.69318	−	5.10532i	−0.0623268	−	0.187929i
$739$	5.37093			0.197573			0.0987865	−	0.995109i	$-0.468504\pi$
$739$	5.37093			0.197573			0.0987865	+	0.995109i	$0.468504\pi$
$740$	2.94756	+	5.10532i	0.108354	+	0.187675i
$741$	35.3864	−	15.8840i	1.29995	−	0.583513i
$742$		0			0
$743$	6.63162	−	11.4863i	0.243290	−	0.421391i	−0.718359	−	0.695672i	$-0.755107\pi$
$743$	6.63162	−	11.4863i	0.243290	−	0.421391i	0.961650	+	0.274281i	$0.0884399\pi$
$744$	18.1298	−	8.13797i	0.664669	−	0.298352i
$745$	2.07218	+	3.58912i	0.0759188	+	0.131495i
$746$	−36.4276			−1.33371
$747$	11.3326	−	12.7409i	0.414637	−	0.466166i
$748$	−3.96485			−0.144969
$749$		0			0
$750$	−2.58100	+	25.2955i	−0.0942449	+	0.923662i
$751$	−2.77816	+	4.81191i	−0.101377	+	0.175589i	−0.912252	−	0.409629i	$-0.865658\pi$
$751$	−2.77816	+	4.81191i	−0.101377	+	0.175589i	0.810875	+	0.585219i	$0.198991\pi$
$752$	18.6457	−	32.2953i	0.679939	−	1.17769i
$753$	−34.3145	−	24.7721i	−1.25049	−	0.902744i
$754$	23.3645	+	40.4684i	0.850883	+	1.47377i
$755$	−12.0119			−0.437158
$756$		0			0
$757$	−13.3942			−0.486819			−0.243410	−	0.969924i	$-0.578266\pi$
$757$	−13.3942			−0.486819			−0.243410	+	0.969924i	$0.578266\pi$
$758$	22.9869	+	39.8145i	0.834923	+	1.44613i
$759$	2.04674	+	1.47757i	0.0742921	+	0.0536323i
$760$	−3.99931	+	6.92701i	−0.145070	+	0.251269i
$761$	−6.42191	+	11.1231i	−0.232794	+	0.403211i	−0.958629	−	0.284658i	$-0.908120\pi$
$761$	−6.42191	+	11.1231i	−0.232794	+	0.403211i	0.725835	+	0.687868i	$0.241453\pi$
$762$	1.92221	−	18.8390i	0.0696345	−	0.682464i
$763$		0			0
$764$	−1.92353			−0.0695910
$765$	−21.1483	−	4.36110i	−0.764619	−	0.157676i
$766$	−24.5202			−0.885951
$767$	26.1785	+	45.3425i	0.945251	+	1.63722i
$768$	28.0347	−	12.5841i	1.01162	−	0.454088i
$769$	1.48259	−	2.56793i	0.0534636	−	0.0926018i	−0.838055	−	0.545586i	$-0.816307\pi$
$769$	1.48259	−	2.56793i	0.0534636	−	0.0926018i	0.891519	+	0.452984i	$0.149641\pi$
$770$		0			0
$771$	−6.33379	+	2.84307i	−0.228106	+	0.102391i
$772$	−4.63533	−	8.02864i	−0.166829	−	0.288957i
$773$	19.2788			0.693409			0.346705	−	0.937974i	$-0.387301\pi$
$773$	19.2788			0.693409			0.346705	+	0.937974i	$0.387301\pi$
$774$	34.8948	+	7.19583i	1.25427	+	0.258649i
$775$	−24.8992			−0.894406
$776$	−3.21683	−	5.57171i	−0.115477	−	0.200013i
$777$		0			0
$778$	−5.19028	+	8.98983i	−0.186080	+	0.322301i
$779$	−2.35305	+	4.07560i	−0.0843068	+	0.146024i
$780$	−5.94727	−	4.29340i	−0.212946	−	0.153728i
$781$	1.26509	+	2.19120i	0.0452685	+	0.0784074i
$782$	−31.9231			−1.14157
$783$	−27.7829	+	6.17058i	−0.992878	+	0.220518i
$784$		0			0
$785$	5.35098	+	9.26818i	0.190985	+	0.330795i
$786$	−15.8324	−	11.4296i	−0.564724	−	0.407680i
$787$	6.82265	−	11.8172i	0.243201	−	0.421237i	−0.718423	−	0.695606i	$-0.755136\pi$
$787$	6.82265	−	11.8172i	0.243201	−	0.421237i	0.961624	+	0.274370i	$0.0884692\pi$
$788$	8.34734	−	14.4580i	0.297362	−	0.515046i
$789$	−3.10969	+	30.4770i	−0.110708	+	1.08501i
$790$	−1.07598	−	1.86364i	−0.0382815	−	0.0663055i
$791$		0			0
$792$	−2.21565	+	2.49100i	−0.0787297	+	0.0885137i
$793$	−58.4944			−2.07720
$794$	10.9518	+	18.9691i	0.388665	+	0.673187i
$795$	10.3832	−	4.66076i	0.368255	−	0.165300i
$796$	3.74427	−	6.48527i	0.132712	−	0.229864i
$797$	−11.4792	+	19.8826i	−0.406616	+	0.704279i	−0.994508	−	0.104660i	$-0.966625\pi$
$797$	−11.4792	+	19.8826i	−0.406616	+	0.704279i	0.587892	+	0.808939i	$0.299958\pi$
$798$		0			0
$799$	−28.3461	−	49.0969i	−1.00281	−	1.73692i
$800$	−19.2632			−0.681058
$801$	−0.796717	−	2.40228i	−0.0281506	−	0.0848805i
$802$	−14.2609			−0.503570
$803$	−1.31241	−	2.27316i	−0.0463140	−	0.0802182i
$804$	1.85378	−	18.1683i	0.0653779	−	0.640747i
$805$		0			0
$806$	25.9134	−	44.8834i	0.912761	−	1.58095i
$807$	−19.9801	−	14.4238i	−0.703331	−	0.507743i
$808$	−9.05326	−	15.6807i	−0.318492	−	0.551645i
$809$	39.4582			1.38728			0.693639	−	0.720323i	$-0.256006\pi$
$809$	39.4582			1.38728			0.693639	+	0.720323i	$0.256006\pi$
$810$	11.6429	−	8.67714i	0.409090	−	0.304884i
$811$	0.496374			0.0174300			0.00871502	−	0.999962i	$-0.497226\pi$
$811$	0.496374			0.0174300			0.00871502	+	0.999962i	$0.497226\pi$
$812$		0			0
$813$	−7.58169	−	5.47331i	−0.265902	−	0.191957i
$814$	3.49381	−	6.05146i	0.122458	−	0.212103i
$815$	0.790841	−	1.36978i	0.0277020	−	0.0479812i
$816$	6.64902	−	65.1647i	0.232762	−	2.28122i
$817$	−15.5867	−	26.9969i	−0.545308	−	0.944501i
$818$	11.5790			0.404850
$819$		0			0
$820$	0.889960			0.0310788
$821$	−23.5519	−	40.7931i	−0.821967	−	1.42369i	−0.904215	−	0.427077i	$-0.859543\pi$
$821$	−23.5519	−	40.7931i	−0.821967	−	1.42369i	0.0822476	−	0.996612i	$-0.473790\pi$
$822$	−37.6893	+	16.9177i	−1.31457	+	0.590074i
$823$	1.09888	−	1.90332i	0.0383047	−	0.0663457i	−0.846237	−	0.532806i	$-0.821138\pi$
$823$	1.09888	−	1.90332i	0.0383047	−	0.0663457i	0.884542	+	0.466460i	$0.154471\pi$
$824$	−11.0046	+	19.0605i	−0.383364	+	0.664005i
$825$	3.81077	−	1.71055i	0.132674	−	0.0595538i
$826$		0			0
$827$	−55.3360			−1.92422			−0.962110	−	0.272661i	$-0.912096\pi$
$827$	−55.3360			−1.92422			−0.962110	+	0.272661i	$0.912096\pi$
$828$	4.38935	−	4.93483i	0.152540	−	0.171497i
$829$	20.3206			0.705764			0.352882	−	0.935668i	$-0.385202\pi$
$829$	20.3206			0.705764			0.352882	+	0.935668i	$0.385202\pi$
$830$	4.58520	+	7.94181i	0.159155	+	0.275664i
$831$	−1.34784	+	13.2097i	−0.0467559	+	0.458239i
$832$	−4.98867	+	8.64062i	−0.172951	+	0.299560i
$833$		0			0
$834$	−21.0165	−	15.1721i	−0.727742	−	0.525365i
$835$	1.85236	+	3.20839i	0.0641036	+	0.111031i
$836$	−2.33277			−0.0806806
$837$	21.3338	+	23.2637i	0.737404	+	0.804111i
$838$	−17.5480			−0.606186
$839$	12.2760	+	21.2626i	0.423813	+	0.734066i	0.996309	−	0.0858417i	$-0.0273579\pi$
$839$	12.2760	+	21.2626i	0.423813	+	0.734066i	−0.572496	+	0.819908i	$0.694025\pi$
$840$		0			0
$841$	−0.499311	+	0.864833i	−0.0172176	+	0.0298218i
$842$	2.66504	−	4.61598i	0.0918432	−	0.159077i
$843$	3.98441	−	39.0498i	0.137230	−	1.34495i
$844$	−4.98693	−	8.63762i	−0.171657	−	0.297319i
$845$	11.5790			0.398329
$846$	37.3377	+	7.69959i	1.28370	+	0.264717i
$847$		0			0
$848$	17.2625	+	29.8996i	0.592798	+	1.02676i
$849$	50.3268	−	22.5904i	1.72721	−	0.775300i
$850$	−26.4118	+	45.7465i	−0.905916	+	1.56909i
$851$	8.65452	−	14.9901i	0.296673	−	0.513853i
$852$	6.03920	−	2.71084i	0.206900	−	0.0928718i
$853$	26.7708	+	46.3684i	0.916614	+	1.58762i	0.804521	+	0.593925i	$0.202422\pi$
$853$	26.7708	+	46.3684i	0.916614	+	1.58762i	0.112093	+	0.993698i	$0.464244\pi$
$854$		0			0
$855$	−12.4429	−	2.56591i	−0.425539	−	0.0877524i
$856$	−7.17439			−0.245215
$857$	27.0777	+	46.8999i	0.924955	+	1.60207i	0.791633	+	0.610996i	$0.209231\pi$
$857$	27.0777	+	46.8999i	0.924955	+	1.60207i	0.133322	+	0.991073i	$0.457436\pi$
$858$	−0.882546	+	8.64953i	−0.0301296	+	0.295290i
$859$	−0.896461	+	1.55272i	−0.0305869	+	0.0529780i	−0.880914	−	0.473277i	$-0.843071\pi$
$859$	−0.896461	+	1.55272i	−0.0305869	+	0.0529780i	0.850327	+	0.526255i	$0.176404\pi$
$860$	−2.94756	+	5.10532i	−0.100511	+	0.174090i
$861$		0			0
$862$	27.0858	+	46.9140i	0.922547	+	1.59790i
$863$	−32.5709			−1.10873			−0.554363	−	0.832275i	$-0.687038\pi$
$863$	−32.5709			−1.10873			−0.554363	+	0.832275i	$0.687038\pi$
$864$	16.5049	+	17.9979i	0.561507	+	0.612302i
$865$	−15.2967			−0.520102
$866$	−6.36387	−	11.0226i	−0.216253	−	0.374562i
$867$	−56.8662	−	41.0524i	−1.93128	−	1.39421i
$868$		0			0
$869$	−0.392378	+	0.679618i	−0.0133105	+	0.0230545i
$870$	1.55364	−	15.2267i	0.0526734	−	0.516234i
$871$	29.7770	+	51.5753i	1.00896	+	1.74756i
$872$	−24.2967			−0.822789
$873$	6.79158	−	7.63559i	0.229860	−	0.258426i
$874$	−18.7824			−0.635324
$875$		0			0
$876$	−6.26509	+	2.81223i	−0.211678	+	0.0950166i
$877$	18.3647	−	31.8085i	0.620131	−	1.07410i	−0.369330	−	0.929298i	$-0.620413\pi$
$877$	18.3647	−	31.8085i	0.620131	−	1.07410i	0.989461	−	0.144800i	$-0.0462538\pi$
$878$	−1.94548	+	3.36966i	−0.0656566	+	0.113721i
$879$	−43.4443	+	19.5010i	−1.46534	+	0.657752i
$880$	−1.39284	−	2.41246i	−0.0469525	−	0.0813241i
$881$	25.3721			0.854807			0.427403	−	0.904061i	$-0.359428\pi$
$881$	25.3721			0.854807			0.427403	+	0.904061i	$0.359428\pi$
$882$		0			0
$883$	−16.9381			−0.570012			−0.285006	−	0.958526i	$-0.591996\pi$
$883$	−16.9381			−0.570012			−0.285006	+	0.958526i	$0.591996\pi$
$884$	−16.9134	−	29.2949i	−0.568860	−	0.985294i
$885$	1.74077	−	17.0607i	0.0585152	−	0.573488i
$886$	31.7403	−	54.9759i	1.06634	−	1.84695i
$887$	24.0069	−	41.5811i	0.806071	−	1.39616i	−0.109494	−	0.993987i	$-0.534923\pi$
$887$	24.0069	−	41.5811i	0.806071	−	1.39616i	0.915566	−	0.402169i	$-0.131744\pi$
$888$	18.5342	+	13.3801i	0.621968	+	0.449006i
$889$		0			0
$890$	1.36115			0.0456260
$891$	−4.86329	−	2.09485i	−0.162926	−	0.0701800i
$892$	18.4456			0.617603
$893$	−16.6778	−	28.8868i	−0.558102	−	0.966661i
$894$	−10.4207	−	7.52279i	−0.348519	−	0.251600i
$895$	−6.78159	+	11.7461i	−0.226684	+	0.392627i
$896$		0			0
$897$	−2.18615	+	21.4258i	−0.0729936	+	0.715385i
$898$	−5.27128	−	9.13013i	−0.175905	−	0.304676i
$899$	33.2713			1.10966
$900$	−3.44017	−	10.3729i	−0.114672	−	0.345763i
$901$	52.4867			1.74858
$902$	−0.527445	−	0.913562i	−0.0175620	−	0.0304183i
$903$		0			0
$904$	−8.51918	+	14.7557i	−0.283344	+	0.490766i
$905$	6.11677	−	10.5945i	0.203328	−	0.352175i
$906$	33.9842	−	15.2546i	1.12905	−	0.506800i
$907$	12.3887	+	21.4579i	0.411361	+	0.712499i	0.995039	−	0.0994869i	$-0.0317201\pi$
$907$	12.3887	+	21.4579i	0.411361	+	0.712499i	−0.583678	+	0.811985i	$0.698387\pi$
$908$	9.26972			0.307626
$909$	19.1138	−	21.4892i	0.633965	−	0.712751i
$910$		0			0
$911$	−15.7916	−	27.3519i	−0.523200	−	0.906209i	−0.999635	−	0.0269997i	$-0.991405\pi$
$911$	−15.7916	−	27.3519i	−0.523200	−	0.906209i	0.476435	−	0.879210i	$-0.341929\pi$
$912$	3.91204	−	38.3406i	0.129541	−	1.26958i
$913$	1.67209	−	2.89615i	0.0553382	−	0.0958486i
$914$	17.1421	−	29.6911i	0.567011	−	0.982093i
$915$	15.5345	+	11.2145i	0.513555	+	0.370741i
$916$	6.69183	+	11.5906i	0.221104	+	0.382964i
$917$		0			0
$918$	65.3714	−	14.5190i	2.15758	−	0.479198i
$919$	1.59208			0.0525180			0.0262590	−	0.999655i	$-0.491641\pi$
$919$	1.59208			0.0525180			0.0262590	+	0.999655i	$0.491641\pi$
$920$	−2.22062	−	3.84623i	−0.0732118	−	0.126807i
$921$	20.8090	+	15.0222i	0.685678	+	0.494999i
$922$	19.1514	−	33.1712i	0.630718	−	1.09244i
$923$	−10.7934	+	18.6947i	−0.355268	+	0.615342i
$924$		0			0
$925$	−14.3207	−	24.8042i	−0.470863	−	0.815558i
$926$	46.9591			1.54317
$927$	−34.2382	−	7.06043i	−1.12453	−	0.231895i
$928$	25.7403			0.844968
$929$	13.5356	+	23.4443i	0.444087	+	0.769182i	0.997988	−	0.0634007i	$-0.0201946\pi$
$929$	13.5356	+	23.4443i	0.444087	+	0.769182i	−0.553901	+	0.832583i	$0.686861\pi$
$930$	−15.4869	+	6.95167i	−0.507836	+	0.227954i
$931$		0			0
$932$	−1.94939	+	3.37644i	−0.0638543	+	0.110599i
$933$	−45.9250	+	20.6145i	−1.50352	+	0.674889i
$934$	−17.1003	−	29.6186i	−0.559540	−	0.969151i
$935$	−4.23491			−0.138496
$936$	−27.8567	−	5.74447i	−0.910526	−	0.187764i
$937$	−32.6624			−1.06704			−0.533518	−	0.845789i	$-0.679130\pi$
$937$	−32.6624			−1.06704			−0.533518	+	0.845789i	$0.679130\pi$
$938$		0			0
$939$	−4.30361	+	42.1782i	−0.140443	+	1.37643i
$940$	−3.15390	+	5.46272i	−0.102869	+	0.178174i
$941$	2.36143	−	4.09011i	0.0769803	−	0.133334i	−0.824965	−	0.565183i	$-0.808805\pi$
$941$	2.36143	−	4.09011i	0.0769803	−	0.133334i	0.901946	+	0.431849i	$0.142139\pi$
$942$	−26.9092	−	19.4261i	−0.876750	−	0.632936i
$943$	−1.30654	−	2.26299i	−0.0425466	−	0.0736929i
$944$	52.0220			1.69317
$945$		0			0
$946$	6.98762			0.227187
$947$	−28.3905	−	49.1738i	−0.922568	−	1.59793i	−0.795427	−	0.606050i	$-0.792753\pi$
$947$	−28.3905	−	49.1738i	−0.922568	−	1.59793i	−0.127141	−	0.991885i	$-0.540580\pi$
$948$	1.66469	+	1.20176i	0.0540668	+	0.0390314i
$949$	11.1971	−	19.3939i	0.363473	−	0.629553i
$950$	−15.5397	+	26.9156i	−0.504175	+	0.873257i
$951$	1.29872	−	12.7284i	0.0421140	−	0.412745i
$952$		0			0
$953$	−47.1693			−1.52796			−0.763982	−	0.645238i	$-0.776758\pi$
$953$	−47.1693			−1.52796			−0.763982	+	0.645238i	$0.776758\pi$
$954$	−23.4574	+	26.3725i	−0.759460	+	0.853841i
$955$	−2.05455			−0.0664838
$956$	4.24426	+	7.35127i	0.137269	+	0.237757i
$957$	−5.09211	+	2.28571i	−0.164605	+	0.0738866i
$958$	8.14681	−	14.1107i	0.263211	−	0.455896i
$959$		0			0
$960$	2.98143	−	1.33829i	0.0962253	−	0.0431930i
$961$	−2.95056	−	5.11052i	−0.0951793	−	0.164855i
$962$	59.6162			1.92210
$963$	−3.58719	−	10.8162i	−0.115596	−	0.348547i
$964$	−9.36359			−0.301581
$965$	−4.95107	−	8.57550i	−0.159380	−	0.276055i
$966$		0			0
$967$	−23.6985	+	41.0469i	−0.762091	+	1.31998i	0.179680	+	0.983725i	$0.442494\pi$
$967$	−23.6985	+	41.0469i	−0.762091	+	1.31998i	−0.941771	+	0.336255i	$0.890840\pi$
$968$	10.0611	−	17.4264i	0.323377	−	0.560106i
$969$	−47.5045	−	34.2941i	−1.52607	−	1.10168i
$970$	2.74790	+	4.75950i	0.0882297	+	0.152818i
$971$	−22.7473			−0.729994			−0.364997	−	0.931009i	$-0.618930\pi$
$971$	−22.7473			−0.729994			−0.364997	+	0.931009i	$0.618930\pi$
$972$	−6.74399	+	12.1018i	−0.216314	+	0.388164i
$973$		0			0
$974$	11.1106	+	19.2441i	0.356006	+	0.616620i
$975$	28.8948	+	20.8595i	0.925376	+	0.668039i
$976$	−29.0601	+	50.3335i	−0.930190	+	1.61114i
$977$	−17.8425	+	30.9040i	−0.570831	+	0.988708i	0.425650	+	0.904888i	$0.360045\pi$
$977$	−17.8425	+	30.9040i	−0.570831	+	0.988708i	−0.996481	+	0.0838200i	$0.973288\pi$
$978$	−0.497897	+	4.87972i	−0.0159210	+	0.156036i
$979$	−0.248187	−	0.429872i	−0.00793209	−	0.0137388i
$980$		0			0
$981$	−12.1483	−	36.6300i	−0.387866	−	1.16951i
$982$	−26.0741			−0.832059
$983$	12.0067	+	20.7962i	0.382954	+	0.663296i	0.991483	−	0.130236i	$-0.0415735\pi$
$983$	12.0067	+	20.7962i	0.382954	+	0.663296i	−0.608529	+	0.793532i	$0.708240\pi$
$984$	3.14833	−	1.41320i	0.100365	−	0.0450512i
$985$	8.91591	−	15.4428i	0.284085	−	0.492049i
$986$	35.2925	−	61.1284i	1.12394	−	1.94672i
$987$		0			0
$988$	−9.95125	−	17.2361i	−0.316591	−	0.548352i
$989$	17.3090			0.550395
$990$	1.89267	−	2.12788i	0.0601529	−	0.0676283i
$991$	−44.4189			−1.41101			−0.705507	−	0.708703i	$-0.749281\pi$
$991$	−44.4189			−1.41101			−0.705507	+	0.708703i	$0.749281\pi$
$992$	−14.2742	−	24.7237i	−0.453208	−	0.784979i
$993$	−3.52716	+	34.5685i	−0.111931	+	1.09700i
$994$		0			0
$995$	3.99931	−	6.92701i	0.126787	−	0.219601i
$996$	−7.09400	−	5.12124i	−0.224782	−	0.162273i
$997$	4.52336	+	7.83470i	0.143256	+	0.248127i	0.928721	−	0.370779i	$-0.120909\pi$
$997$	4.52336	+	7.83470i	0.143256	+	0.248127i	−0.785465	+	0.618906i	$0.787576\pi$
$998$	−8.26929			−0.261760
$999$	−10.9049	+	34.6325i	−0.345015	+	1.09572i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.f.g.148.5	✓	12
3.2	odd	2		1323.2.f.g.442.2		12
7.2	even	3		441.2.g.g.67.6		12
7.3	odd	6		441.2.h.g.373.2		12
7.4	even	3		441.2.h.g.373.1		12
7.5	odd	6		441.2.g.g.67.5		12
7.6	odd	2	inner	441.2.f.g.148.6	yes	12
9.2	odd	6		1323.2.f.g.883.2		12
9.4	even	3		3969.2.a.be.1.2		6
9.5	odd	6		3969.2.a.bd.1.5		6
9.7	even	3	inner	441.2.f.g.295.5	yes	12
21.2	odd	6		1323.2.g.g.361.1		12
21.5	even	6		1323.2.g.g.361.2		12
21.11	odd	6		1323.2.h.g.226.6		12
21.17	even	6		1323.2.h.g.226.5		12
21.20	even	2		1323.2.f.g.442.1		12
63.2	odd	6		1323.2.h.g.802.6		12
63.11	odd	6		1323.2.g.g.667.1		12
63.13	odd	6		3969.2.a.be.1.1		6
63.16	even	3		441.2.h.g.214.1		12
63.20	even	6		1323.2.f.g.883.1		12
63.25	even	3		441.2.g.g.79.6		12
63.34	odd	6	inner	441.2.f.g.295.6	yes	12
63.38	even	6		1323.2.g.g.667.2		12
63.41	even	6		3969.2.a.bd.1.6		6
63.47	even	6		1323.2.h.g.802.5		12
63.52	odd	6		441.2.g.g.79.5		12
63.61	odd	6		441.2.h.g.214.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.f.g.148.5	✓	12	1.1	even	1	trivial
441.2.f.g.148.6	yes	12	7.6	odd	2	inner
441.2.f.g.295.5	yes	12	9.7	even	3	inner
441.2.f.g.295.6	yes	12	63.34	odd	6	inner
441.2.g.g.67.5		12	7.5	odd	6
441.2.g.g.67.6		12	7.2	even	3
441.2.g.g.79.5		12	63.52	odd	6
441.2.g.g.79.6		12	63.25	even	3
441.2.h.g.214.1		12	63.16	even	3
441.2.h.g.214.2		12	63.61	odd	6
441.2.h.g.373.1		12	7.4	even	3
441.2.h.g.373.2		12	7.3	odd	6
1323.2.f.g.442.1		12	21.20	even	2
1323.2.f.g.442.2		12	3.2	odd	2
1323.2.f.g.883.1		12	63.20	even	6
1323.2.f.g.883.2		12	9.2	odd	6
1323.2.g.g.361.1		12	21.2	odd	6
1323.2.g.g.361.2		12	21.5	even	6
1323.2.g.g.667.1		12	63.11	odd	6
1323.2.g.g.667.2		12	63.38	even	6
1323.2.h.g.226.5		12	21.17	even	6
1323.2.h.g.226.6		12	21.11	odd	6
1323.2.h.g.802.5		12	63.47	even	6
1323.2.h.g.802.6		12	63.2	odd	6
3969.2.a.bd.1.5		6	9.5	odd	6
3969.2.a.bd.1.6		6	63.41	even	6
3969.2.a.be.1.1		6	63.13	odd	6
3969.2.a.be.1.2		6	9.4	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.849814 + 1.47192i) q^{2} +(-1.40434 - 1.01381i) q^{3} +(-0.444368 + 0.769668i) q^{4} +(-0.474636 + 0.822093i) q^{5} +(0.298820 - 2.92864i) q^{6} +1.88874 q^{8} +(0.944368 + 2.84748i) q^{9} +O(q^{10})\)	\(q+(0.849814 + 1.47192i) q^{2} +(-1.40434 - 1.01381i) q^{3} +(-0.444368 + 0.769668i) q^{4} +(-0.474636 + 0.822093i) q^{5} +(0.298820 - 2.92864i) q^{6} +1.88874 q^{8} +(0.944368 + 2.84748i) q^{9} -1.61341 q^{10} +(0.294182 + 0.509538i) q^{11} +(1.40434 - 0.630373i) q^{12} +(-2.50987 + 4.34722i) q^{13} +(1.50000 - 0.673310i) q^{15} +(2.49381 + 4.31941i) q^{16} +7.58242 q^{17} +(-3.38874 + 3.80987i) q^{18} +4.46122 q^{19} +(-0.421826 - 0.730623i) q^{20} +(-0.500000 + 0.866025i) q^{22} +(-1.23855 + 2.14523i) q^{23} +(-2.65244 - 1.91482i) q^{24} +(2.04944 + 3.54974i) q^{25} -8.53169 q^{26} +(1.56060 - 4.95626i) q^{27} +(-2.73855 - 4.74331i) q^{29} +(2.26578 + 1.63569i) q^{30} +(-3.03731 + 5.26078i) q^{31} +(-2.34981 + 4.07000i) q^{32} +(0.103443 - 1.01381i) q^{33} +(6.44364 + 11.1607i) q^{34} +(-2.61126 - 0.538481i) q^{36} -6.98762 q^{37} +(3.79121 + 6.56657i) q^{38} +(7.93199 - 3.56046i) q^{39} +(-0.896461 + 1.55272i) q^{40} +(-0.527445 + 0.913562i) q^{41} +(-3.49381 - 6.05146i) q^{43} -0.522900 q^{44} +(-2.78913 - 0.575159i) q^{45} -4.21015 q^{46} +(-3.73840 - 6.47510i) q^{47} +(0.876899 - 8.59419i) q^{48} +(-3.48329 + 6.03323i) q^{50} +(-10.6483 - 7.68715i) q^{51} +(-2.23061 - 3.86353i) q^{52} +6.92216 q^{53} +(8.62145 - 1.91482i) q^{54} -0.558517 q^{55} +(-6.26509 - 4.52284i) q^{57} +(4.65452 - 8.06186i) q^{58} +(5.21512 - 9.03284i) q^{59} +(-0.148327 + 1.45370i) q^{60} +(5.82644 + 10.0917i) q^{61} -10.3246 q^{62} +1.98762 q^{64} +(-2.38255 - 4.12669i) q^{65} +(1.58016 - 0.709292i) q^{66} +(5.93199 - 10.2745i) q^{67} +(-3.36938 + 5.83594i) q^{68} +(3.91421 - 1.75699i) q^{69} +4.30037 q^{71} +(1.78366 + 5.37815i) q^{72} -4.46122 q^{73} +(-5.93818 - 10.2852i) q^{74} +(0.720646 - 7.06281i) q^{75} +(-1.98242 + 3.43366i) q^{76} +(11.9814 + 8.64953i) q^{78} +(0.666896 + 1.15510i) q^{79} -4.73460 q^{80} +(-7.21634 + 5.37815i) q^{81} -1.79292 q^{82} +(-2.84194 - 4.92238i) q^{83} +(-3.59888 + 6.23345i) q^{85} +(5.93818 - 10.2852i) q^{86} +(-0.962957 + 9.43762i) q^{87} +(0.555632 + 0.962383i) q^{88} -0.843651 q^{89} +(-1.52365 - 4.59415i) q^{90} +(-1.10074 - 1.90654i) q^{92} +(9.59888 - 4.30868i) q^{93} +(6.35389 - 11.0053i) q^{94} +(-2.11745 + 3.66754i) q^{95} +(7.42616 - 3.33341i) q^{96} +(-1.70317 - 2.94997i) q^{97} +(-1.17309 + 1.31887i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 2 q^{2} - 6 q^{4} + 24 q^{8} + 12 q^{9}+O(q^{10}) \) 12 * q - 2 * q^2 - 6 * q^4 + 24 * q^8 + 12 * q^9	\( 12 q - 2 q^{2} - 6 q^{4} + 24 q^{8} + 12 q^{9} - 8 q^{11} + 18 q^{15} - 6 q^{16} - 42 q^{18} - 6 q^{22} - 4 q^{23} - 12 q^{25} - 22 q^{29} - 48 q^{30} - 16 q^{32} - 30 q^{36} - 12 q^{37} + 24 q^{39} - 6 q^{43} - 28 q^{44} + 24 q^{46} - 56 q^{50} - 18 q^{51} + 56 q^{53} - 6 q^{57} - 18 q^{58} + 108 q^{60} - 48 q^{64} + 6 q^{65} + 76 q^{71} + 60 q^{72} - 36 q^{74} + 36 q^{78} + 6 q^{79} - 48 q^{81} + 30 q^{85} + 36 q^{86} + 6 q^{88} - 62 q^{92} + 42 q^{93} - 60 q^{95} - 48 q^{99}+O(q^{100}) \) 12 * q - 2 * q^2 - 6 * q^4 + 24 * q^8 + 12 * q^9 - 8 * q^11 + 18 * q^15 - 6 * q^16 - 42 * q^18 - 6 * q^22 - 4 * q^23 - 12 * q^25 - 22 * q^29 - 48 * q^30 - 16 * q^32 - 30 * q^36 - 12 * q^37 + 24 * q^39 - 6 * q^43 - 28 * q^44 + 24 * q^46 - 56 * q^50 - 18 * q^51 + 56 * q^53 - 6 * q^57 - 18 * q^58 + 108 * q^60 - 48 * q^64 + 6 * q^65 + 76 * q^71 + 60 * q^72 - 36 * q^74 + 36 * q^78 + 6 * q^79 - 48 * q^81 + 30 * q^85 + 36 * q^86 + 6 * q^88 - 62 * q^92 + 42 * q^93 - 60 * q^95 - 48 * q^99

Introduction

L-functions

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