LMFDB - Embedded newform 441.2.f.e.148.4

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:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	10.0.991381711347.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} + 9x^{8} - 8x^{7} + 40x^{6} - 36x^{5} + 90x^{4} - 3x^{3} + 36x^{2} - 9x + 9 $ x^10 - 2x^9 + 9x^8 - 8x^7 + 40x^6 - 36x^5 + 90x^4 - 3x^3 + 36x^2 - 9*x + 9
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			148.4
Root			$0.920620 + 1.59456i$ of defining polynomial
Character	$\chi$	$=$	441.148
Dual form			441.2.f.e.295.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.920620 + 1.59456i) q^{2} +(0.195084 + 1.72103i) q^{3} +(-0.695084 + 1.20392i) q^{4} +(-0.667377 + 1.15593i) q^{5} +(-2.56469 + 1.89549i) q^{6} +1.12285 q^{8} +(-2.92388 + 0.671489i) q^{9} +O(q^{10})$	\(q+(0.920620 + 1.59456i) q^{2} +(0.195084 + 1.72103i) q^{3} +(-0.695084 + 1.20392i) q^{4} +(-0.667377 + 1.15593i) q^{5} +(-2.56469 + 1.89549i) q^{6} +1.12285 q^{8} +(-2.92388 + 0.671489i) q^{9} -2.45760 q^{10} +(-0.756508 - 1.31031i) q^{11} +(-2.20758 - 0.961394i) q^{12} +(-2.58800 + 4.48254i) q^{13} +(-2.11958 - 0.923072i) q^{15} +(2.42388 + 4.19829i) q^{16} -1.54893 q^{17} +(-3.76252 - 4.04413i) q^{18} +2.50422 q^{19} +(-0.927765 - 1.60694i) q^{20} +(1.39291 - 2.41260i) q^{22} +(3.68039 - 6.37463i) q^{23} +(0.219049 + 1.93246i) q^{24} +(1.60922 + 2.78725i) q^{25} -9.53025 q^{26} +(-1.72605 - 4.90110i) q^{27} +(-0.0309713 - 0.0536439i) q^{29} +(-0.479438 - 4.22961i) q^{30} +(1.92388 - 3.33227i) q^{31} +(-3.34011 + 5.78523i) q^{32} +(2.10750 - 1.55759i) q^{33} +(-1.42597 - 2.46986i) q^{34} +(1.22392 - 3.98687i) q^{36} +0.563216 q^{37} +(2.30543 + 3.99313i) q^{38} +(-8.21946 - 3.57955i) q^{39} +(-0.749363 + 1.29794i) q^{40} +(4.51188 - 7.81481i) q^{41} +(5.09988 + 8.83325i) q^{43} +2.10335 q^{44} +(1.17514 - 3.82794i) q^{45} +13.5530 q^{46} +(4.75925 + 8.24327i) q^{47} +(-6.75252 + 4.99060i) q^{48} +(-2.96296 + 5.13199i) q^{50} +(-0.302170 - 2.66575i) q^{51} +(-3.59775 - 6.23148i) q^{52} -1.51075 q^{53} +(6.22605 - 7.26435i) q^{54} +2.01950 q^{55} +(0.488532 + 4.30983i) q^{57} +(0.0570257 - 0.0987714i) q^{58} +(4.22166 - 7.31212i) q^{59} +(2.58459 - 1.91020i) q^{60} +(-1.61958 - 2.80520i) q^{61} +7.08467 q^{62} -2.60434 q^{64} +(-3.45434 - 5.98309i) q^{65} +(4.42388 + 1.92659i) q^{66} +(-3.46670 + 6.00449i) q^{67} +(1.07663 - 1.86478i) q^{68} +(11.6889 + 5.09048i) q^{69} -12.3304 q^{71} +(-3.28308 + 0.753981i) q^{72} +2.75871 q^{73} +(0.518508 + 0.898083i) q^{74} +(-4.48300 + 3.31326i) q^{75} +(-1.74064 + 3.01488i) q^{76} +(-1.85920 - 16.4018i) q^{78} +(2.95969 + 5.12633i) q^{79} -6.47058 q^{80} +(8.09820 - 3.92671i) q^{81} +16.6149 q^{82} +(2.80111 + 4.85167i) q^{83} +(1.03372 - 1.79045i) q^{85} +(-9.39010 + 16.2641i) q^{86} +(0.0862808 - 0.0637676i) q^{87} +(-0.849444 - 1.47128i) q^{88} -1.40657 q^{89} +(7.18575 - 1.65025i) q^{90} +(5.11636 + 8.86180i) q^{92} +(6.11025 + 2.66099i) q^{93} +(-8.76293 + 15.1778i) q^{94} +(-1.67126 + 2.89470i) q^{95} +(-10.6082 - 4.61982i) q^{96} +(-6.09713 - 10.5605i) q^{97} +(3.09180 + 3.32321i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 2 q^{2} - q^{3} - 4 q^{4} + 4 q^{5} - 2 q^{6} - 6 q^{8} - 7 q^{9}+O(q^{10}) $ 10 * q + 2 * q^2 - q^3 - 4 * q^4 + 4 * q^5 - 2 * q^6 - 6 * q^8 - 7 * q^9	$ 10 q + 2 q^{2} - q^{3} - 4 q^{4} + 4 q^{5} - 2 q^{6} - 6 q^{8} - 7 q^{9} + 14 q^{10} + 4 q^{11} - 2 q^{12} - 8 q^{13} - 19 q^{15} + 2 q^{16} - 24 q^{17} - 2 q^{18} - 2 q^{19} + 5 q^{20} - q^{22} + 3 q^{23} - 9 q^{24} - q^{25} - 22 q^{26} - 7 q^{27} + 7 q^{29} + 10 q^{30} - 3 q^{31} - 2 q^{32} - 13 q^{33} + 3 q^{34} + 34 q^{36} + 20 q^{38} - 22 q^{39} - 3 q^{40} + 5 q^{41} - 7 q^{43} + 20 q^{44} + 17 q^{45} - 6 q^{46} + 27 q^{47} - 5 q^{48} + 19 q^{50} - 15 q^{51} - 10 q^{52} + 42 q^{53} + 52 q^{54} + 4 q^{55} - 4 q^{57} - 10 q^{58} + 30 q^{59} + 31 q^{60} - 14 q^{61} - 12 q^{62} - 50 q^{64} - 11 q^{65} + 22 q^{66} - 2 q^{67} + 27 q^{68} + 15 q^{69} - 6 q^{71} - 12 q^{72} - 30 q^{73} - 36 q^{74} - 17 q^{75} + 5 q^{76} - 20 q^{78} - 4 q^{79} - 40 q^{80} - 31 q^{81} + 10 q^{82} + 9 q^{83} - 6 q^{85} - 8 q^{86} - 34 q^{87} - 18 q^{88} - 56 q^{89} + 28 q^{90} + 27 q^{92} + 18 q^{93} - 3 q^{94} - 14 q^{95} - 58 q^{96} - 12 q^{97} + 35 q^{99}+O(q^{100}) $ 10 * q + 2 * q^2 - q^3 - 4 * q^4 + 4 * q^5 - 2 * q^6 - 6 * q^8 - 7 * q^9 + 14 * q^10 + 4 * q^11 - 2 * q^12 - 8 * q^13 - 19 * q^15 + 2 * q^16 - 24 * q^17 - 2 * q^18 - 2 * q^19 + 5 * q^20 - q^22 + 3 * q^23 - 9 * q^24 - q^25 - 22 * q^26 - 7 * q^27 + 7 * q^29 + 10 * q^30 - 3 * q^31 - 2 * q^32 - 13 * q^33 + 3 * q^34 + 34 * q^36 + 20 * q^38 - 22 * q^39 - 3 * q^40 + 5 * q^41 - 7 * q^43 + 20 * q^44 + 17 * q^45 - 6 * q^46 + 27 * q^47 - 5 * q^48 + 19 * q^50 - 15 * q^51 - 10 * q^52 + 42 * q^53 + 52 * q^54 + 4 * q^55 - 4 * q^57 - 10 * q^58 + 30 * q^59 + 31 * q^60 - 14 * q^61 - 12 * q^62 - 50 * q^64 - 11 * q^65 + 22 * q^66 - 2 * q^67 + 27 * q^68 + 15 * q^69 - 6 * q^71 - 12 * q^72 - 30 * q^73 - 36 * q^74 - 17 * q^75 + 5 * q^76 - 20 * q^78 - 4 * q^79 - 40 * q^80 - 31 * q^81 + 10 * q^82 + 9 * q^83 - 6 * q^85 - 8 * q^86 - 34 * q^87 - 18 * q^88 - 56 * q^89 + 28 * q^90 + 27 * q^92 + 18 * q^93 - 3 * q^94 - 14 * q^95 - 58 * q^96 - 12 * q^97 + 35 * 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 $

$2$	0.920620	+	1.59456i	0.650977	+	1.12753i	0.982886	+	0.184214i	$0.0589739\pi$
$2$	0.920620	+	1.59456i	0.650977	+	1.12753i	−0.331909	+	0.943311i	$0.607693\pi$
$3$	0.195084	+	1.72103i	0.112632	+	0.993637i
$3$	0.195084	+	1.72103i	0.112632	+	0.993637i
$4$	−0.695084	+	1.20392i	−0.347542	+	0.601960i
$5$	−0.667377	+	1.15593i	−0.298460	+	0.516948i	−0.975784	−	0.218737i	$-0.929806\pi$
$5$	−0.667377	+	1.15593i	−0.298460	+	0.516948i	0.677324	+	0.735685i	$0.263140\pi$
$6$	−2.56469	+	1.89549i	−1.04703	+	0.773830i
$7$		0			0
$7$		0			0
$8$	1.12285			0.396987
$9$	−2.92388	+	0.671489i	−0.974628	+	0.223830i
$10$	−2.45760			−0.777162
$11$	−0.756508	−	1.31031i	−0.228096	−	0.395073i	0.729148	−	0.684356i	$-0.239917\pi$
$11$	−0.756508	−	1.31031i	−0.228096	−	0.395073i	−0.957244	+	0.289283i	$0.906583\pi$
$12$	−2.20758	−	0.961394i	−0.637274	−	0.277531i
$13$	−2.58800	+	4.48254i	−0.717781	+	1.24323i	0.244096	+	0.969751i	$0.421509\pi$
$13$	−2.58800	+	4.48254i	−0.717781	+	1.24323i	−0.961877	+	0.273482i	$0.911824\pi$
$14$		0			0
$15$	−2.11958	−	0.923072i	−0.547274	−	0.238336i
$16$	2.42388	+	4.19829i	0.605971	+	1.04957i
$17$	−1.54893			−0.375670			−0.187835	−	0.982201i	$-0.560147\pi$
$17$	−1.54893			−0.375670			−0.187835	+	0.982201i	$0.560147\pi$
$18$	−3.76252	−	4.04413i	−0.886834	−	0.953210i
$19$	2.50422			0.574507			0.287254	−	0.957855i	$-0.407258\pi$
$19$	2.50422			0.574507			0.287254	+	0.957855i	$0.407258\pi$
$20$	−0.927765	−	1.60694i	−0.207455	−	0.359322i
$21$		0			0
$22$	1.39291	−	2.41260i	0.296970	−	0.514367i
$23$	3.68039	−	6.37463i	0.767415	−	1.32920i	−0.171545	−	0.985176i	$-0.554876\pi$
$23$	3.68039	−	6.37463i	0.767415	−	1.32920i	0.938960	−	0.344025i	$-0.111791\pi$
$24$	0.219049	+	1.93246i	0.0447133	+	0.394461i
$25$	1.60922	+	2.78725i	0.321843	+	0.557449i
$26$	−9.53025			−1.86904
$27$	−1.72605	−	4.90110i	−0.332179	−	0.943216i
$28$		0			0
$29$	−0.0309713	−	0.0536439i	−0.00575123	−	0.00996143i	0.863135	−	0.504972i	$-0.168497\pi$
$29$	−0.0309713	−	0.0536439i	−0.00575123	−	0.00996143i	−0.868887	+	0.495011i	$0.835164\pi$
$30$	−0.479438	−	4.22961i	−0.0875330	−	0.772217i
$31$	1.92388	−	3.33227i	0.345540	−	0.598493i	−0.639912	−	0.768448i	$-0.721029\pi$
$31$	1.92388	−	3.33227i	0.345540	−	0.598493i	0.985452	+	0.169956i	$0.0543625\pi$
$32$	−3.34011	+	5.78523i	−0.590453	+	1.02269i
$33$	2.10750	−	1.55759i	0.366869	−	0.271142i
$34$	−1.42597	−	2.46986i	−0.244552	−	0.423577i
$35$		0			0
$36$	1.22392	−	3.98687i	0.203987	−	0.664478i
$37$	0.563216			0.0925922			0.0462961	−	0.998928i	$-0.485258\pi$
$37$	0.563216			0.0925922			0.0462961	+	0.998928i	$0.485258\pi$
$38$	2.30543	+	3.99313i	0.373991	+	0.647771i
$39$	−8.21946	−	3.57955i	−1.31617	−	0.573186i
$40$	−0.749363	+	1.29794i	−0.118485	+	0.205222i
$41$	4.51188	−	7.81481i	0.704638	−	1.22047i	−0.262185	−	0.965018i	$-0.584443\pi$
$41$	4.51188	−	7.81481i	0.704638	−	1.22047i	0.966822	−	0.255450i	$-0.0822237\pi$
$42$		0			0
$43$	5.09988	+	8.83325i	0.777724	+	1.34706i	0.933251	+	0.359226i	$0.116959\pi$
$43$	5.09988	+	8.83325i	0.777724	+	1.34706i	−0.155526	+	0.987832i	$0.549707\pi$
$44$	2.10335			0.317091
$45$	1.17514	−	3.82794i	0.175179	−	0.570636i
$46$	13.5530			1.99828
$47$	4.75925	+	8.24327i	0.694209	+	1.20240i	0.970447	+	0.241315i	$0.0775788\pi$
$47$	4.75925	+	8.24327i	0.694209	+	1.20240i	−0.276238	+	0.961089i	$0.589088\pi$
$48$	−6.75252	+	4.99060i	−0.974643	+	0.720330i
$49$		0			0
$50$	−2.96296	+	5.13199i	−0.419025	+	0.725773i
$51$	−0.302170	−	2.66575i	−0.0423123	−	0.373279i
$52$	−3.59775	−	6.23148i	−0.498918	−	0.864151i
$53$	−1.51075			−0.207517			−0.103759	−	0.994603i	$-0.533087\pi$
$53$	−1.51075			−0.207517			−0.103759	+	0.994603i	$0.533087\pi$
$54$	6.22605	−	7.26435i	0.847259	−	0.988553i
$55$	2.01950			0.272310
$56$		0			0
$57$	0.488532	+	4.30983i	0.0647077	+	0.570851i
$58$	0.0570257	−	0.0987714i	0.00748784	−	0.0129693i
$59$	4.22166	−	7.31212i	0.549613	−	0.951957i	−0.448688	−	0.893688i	$-0.648109\pi$
$59$	4.22166	−	7.31212i	0.549613	−	0.951957i	0.998301	−	0.0582689i	$-0.0185581\pi$
$60$	2.58459	−	1.91020i	0.333670	−	0.246606i
$61$	−1.61958	−	2.80520i	−0.207367	−	0.359169i	0.743518	−	0.668716i	$-0.233156\pi$
$61$	−1.61958	−	2.80520i	−0.207367	−	0.359169i	−0.950884	+	0.309547i	$0.899823\pi$
$62$	7.08467			0.899754
$63$		0			0
$64$	−2.60434			−0.325543
$65$	−3.45434	−	5.98309i	−0.428458	−	0.742111i
$66$	4.42388	+	1.92659i	0.544543	+	0.237146i
$67$	−3.46670	+	6.00449i	−0.423524	+	0.733566i	−0.996281	−	0.0861595i	$-0.972541\pi$
$67$	−3.46670	+	6.00449i	−0.423524	+	0.733566i	0.572757	+	0.819725i	$0.305874\pi$
$68$	1.07663	−	1.86478i	0.130561	−	0.226138i
$69$	11.6889	+	5.09048i	1.40718	+	0.612822i
$70$		0			0
$71$	−12.3304			−1.46335			−0.731673	−	0.681656i	$-0.761260\pi$
$71$	−12.3304			−1.46335			−0.731673	+	0.681656i	$0.761260\pi$
$72$	−3.28308	+	0.753981i	−0.386915	+	0.0888575i
$73$	2.75871			0.322883			0.161442	−	0.986882i	$-0.448386\pi$
$73$	2.75871			0.322883			0.161442	+	0.986882i	$0.448386\pi$
$74$	0.518508	+	0.898083i	0.0602754	+	0.104400i
$75$	−4.48300	+	3.31326i	−0.517652	+	0.382582i
$76$	−1.74064	+	3.01488i	−0.199665	+	0.345830i
$77$		0			0
$78$	−1.85920	−	16.4018i	−0.210512	−	1.85714i
$79$	2.95969	+	5.12633i	0.332991	+	0.576758i	0.983097	−	0.183086i	$-0.0586087\pi$
$79$	2.95969	+	5.12633i	0.332991	+	0.576758i	−0.650106	+	0.759844i	$0.725275\pi$
$80$	−6.47058			−0.723432
$81$	8.09820	−	3.92671i	0.899800	−	0.436302i
$82$	16.6149			1.83481
$83$	2.80111	+	4.85167i	0.307462	+	0.532540i	0.977806	−	0.209510i	$-0.0671870\pi$
$83$	2.80111	+	4.85167i	0.307462	+	0.532540i	−0.670344	+	0.742050i	$0.733854\pi$
$84$		0			0
$85$	1.03372	−	1.79045i	0.112122	−	0.194202i
$86$	−9.39010	+	16.2641i	−1.01256	+	1.75381i
$87$	0.0862808	−	0.0637676i	0.00925027	−	0.00683661i
$88$	−0.849444	−	1.47128i	−0.0905511	−	0.156839i
$89$	−1.40657			−0.149097			−0.0745483	−	0.997217i	$-0.523751\pi$
$89$	−1.40657			−0.149097			−0.0745483	+	0.997217i	$0.523751\pi$
$90$	7.18575	−	1.65025i	0.757444	−	0.173952i
$91$		0			0
$92$	5.11636	+	8.86180i	0.533418	+	0.923906i
$93$	6.11025	+	2.66099i	0.633603	+	0.275932i
$94$	−8.76293	+	15.1778i	−0.903827	+	1.56548i
$95$	−1.67126	+	2.89470i	−0.171467	+	0.296990i
$96$	−10.6082	−	4.61982i	−1.08269	−	0.471508i
$97$	−6.09713	−	10.5605i	−0.619070	−	1.07226i	−0.989656	−	0.143462i	$-0.954176\pi$
$97$	−6.09713	−	10.5605i	−0.619070	−	1.07226i	0.370586	−	0.928798i	$-0.379157\pi$
$98$		0			0
$99$	3.09180	+	3.32321i	0.310738	+	0.333995i
$100$	−4.47416			−0.447416
$101$	−0.559336	−	0.968798i	−0.0556560	−	0.0963990i	0.836855	−	0.547425i	$-0.184392\pi$
$101$	−0.559336	−	0.968798i	−0.0556560	−	0.0963990i	−0.892511	+	0.451025i	$0.851058\pi$
$102$	3.97251	−	2.93597i	0.393338	−	0.290704i
$103$	−0.965224	+	1.67182i	−0.0951063	+	0.164729i	−0.909653	−	0.415369i	$-0.863652\pi$
$103$	−0.965224	+	1.67182i	−0.0951063	+	0.164729i	0.814547	+	0.580098i	$0.196986\pi$
$104$	−2.90593	+	5.03322i	−0.284950	+	0.493548i
$105$		0			0
$106$	−1.39082	−	2.40898i	−0.135089	−	0.233981i
$107$	−5.77938			−0.558714			−0.279357	−	0.960187i	$-0.590121\pi$
$107$	−5.77938			−0.558714			−0.279357	+	0.960187i	$0.590121\pi$
$108$	7.10028	+	1.32864i	0.683225	+	0.127848i
$109$	8.24211			0.789451			0.394726	−	0.918799i	$-0.370840\pi$
$109$	8.24211			0.789451			0.394726	+	0.918799i	$0.370840\pi$
$110$	1.85920	+	3.22022i	0.177267	+	0.307036i
$111$	0.109874	+	0.969312i	0.0104288	+	0.0920030i
$112$		0			0
$113$	7.25105	−	12.5592i	0.682121	−	1.18147i	−0.292211	−	0.956354i	$-0.594391\pi$
$113$	7.25105	−	12.5592i	0.682121	−	1.18147i	0.974332	−	0.225115i	$-0.0722758\pi$
$114$	−6.42254	+	4.74672i	−0.601526	+	0.444571i
$115$	4.91242	+	8.50856i	0.458085	+	0.793427i
$116$	0.0861107			0.00799518
$117$	4.55703	−	14.8442i	0.421297	−	1.37235i
$118$	15.5462			1.43114
$119$		0			0
$120$	−2.37997	−	1.03647i	−0.217261	−	0.0946164i
$121$	4.35539	−	7.54376i	0.395945	−	0.685796i
$122$	2.98204	−	5.16505i	0.269982	−	0.467622i
$123$	14.3297	+	6.24054i	1.29207	+	0.562691i
$124$	2.67452	+	4.63241i	0.240179	+	0.416002i
$125$	−10.9696			−0.981149
$126$		0			0
$127$	8.50004			0.754257			0.377128	−	0.926161i	$-0.376912\pi$
$127$	8.50004			0.754257			0.377128	+	0.926161i	$0.376912\pi$
$128$	4.28260	+	7.41769i	0.378532	+	0.655637i
$129$	−14.2074	+	10.5003i	−1.25089	+	0.924497i
$130$	6.36027	−	11.0163i	0.557832	−	0.966194i
$131$	1.00673	−	1.74371i	0.0879585	−	0.152349i	−0.818690	−	0.574236i	$-0.805299\pi$
$131$	1.00673	−	1.74371i	0.0879585	−	0.152349i	0.906648	+	0.421888i	$0.138632\pi$
$132$	0.410328	+	3.61992i	0.0357145	+	0.315074i
$133$		0			0
$134$	−12.7660			−1.10282
$135$	6.81725	+	1.27568i	0.586736	+	0.109793i
$136$	−1.73921			−0.149136
$137$	−1.10870	−	1.92032i	−0.0947225	−	0.164064i	0.814770	−	0.579784i	$-0.196863\pi$
$137$	−1.10870	−	1.92032i	−0.0947225	−	0.164064i	−0.909493	+	0.415720i	$0.863530\pi$
$138$	2.64396	+	23.3251i	0.225069	+	1.98556i
$139$	0.377669	−	0.654143i	0.0320335	−	0.0554836i	−0.849564	−	0.527485i	$-0.823135\pi$
$139$	0.377669	−	0.654143i	0.0320335	−	0.0554836i	0.881598	+	0.472002i	$0.156468\pi$
$140$		0			0
$141$	−13.2585	+	9.79894i	−1.11656	+	0.825220i
$142$	−11.3516	−	19.6615i	−0.952604	−	1.64996i
$143$	7.83136			0.654891
$144$	−9.90627	−	10.6477i	−0.825522	−	0.887309i
$145$	0.0826782			0.00686605
$146$	2.53973	+	4.39894i	0.210189	+	0.364059i
$147$		0			0
$148$	−0.391482	+	0.678068i	−0.0321797	+	0.0557368i
$149$	−3.29249	+	5.70277i	−0.269732	+	0.467189i	−0.968792	−	0.247873i	$-0.920268\pi$
$149$	−3.29249	+	5.70277i	−0.269732	+	0.467189i	0.699061	+	0.715062i	$0.253602\pi$
$150$	−9.41033	−	4.09817i	−0.768350	−	0.334614i
$151$	−6.33356	−	10.9700i	−0.515417	−	0.892729i	−0.999840	−	0.0178950i	$-0.994304\pi$
$151$	−6.33356	−	10.9700i	−0.515417	−	0.892729i	0.484422	−	0.874834i	$-0.339030\pi$
$152$	2.81186			0.228072
$153$	4.52888	−	1.04009i	0.366138	−	0.0840861i
$154$		0			0
$155$	2.56791	+	4.44775i	0.206260	+	0.357252i
$156$	10.0227	−	7.40749i	0.802459	−	0.593074i
$157$	8.65372	−	14.9887i	0.690642	−	1.19623i	−0.280986	−	0.959712i	$-0.590662\pi$
$157$	8.65372	−	14.9887i	0.690642	−	1.19623i	0.971628	−	0.236515i	$-0.0760052\pi$
$158$	−5.44950	+	9.43882i	−0.433539	+	0.750912i
$159$	−0.294722	−	2.60004i	−0.0233730	−	0.206197i
$160$	−4.45822	−	7.72186i	−0.352453	−	0.610467i
$161$		0			0
$162$	13.7168	+	9.29807i	1.07769	+	0.730525i
$163$	−12.2193			−0.957086			−0.478543	−	0.878064i	$-0.658835\pi$
$163$	−12.2193			−0.957086			−0.478543	+	0.878064i	$0.658835\pi$
$164$	6.27227	+	10.8639i	0.489782	+	0.848327i
$165$	0.393972	+	3.47562i	0.0306707	+	0.270577i
$166$	−5.15752	+	8.93309i	−0.400301	+	0.693342i
$167$	1.76248	−	3.05270i	0.136385	−	0.236225i	−0.789741	−	0.613440i	$-0.789785\pi$
$167$	1.76248	−	3.05270i	0.136385	−	0.236225i	0.926126	+	0.377215i	$0.123118\pi$
$168$		0			0
$169$	−6.89546	−	11.9433i	−0.530420	−	0.918714i
$170$	3.80665			0.291956
$171$	−7.32205	+	1.68156i	−0.559931	+	0.128592i
$172$	−14.1794			−1.08117
$173$	−5.07046	−	8.78229i	−0.385500	−	0.667705i	0.606339	−	0.795206i	$-0.292638\pi$
$173$	−5.07046	−	8.78229i	−0.385500	−	0.667705i	−0.991838	+	0.127502i	$0.959304\pi$
$174$	0.181113	+	0.0788742i	0.0137302	+	0.00597944i
$175$		0			0
$176$	3.66738	−	6.35208i	0.276439	−	0.478806i
$177$	13.4080	+	5.83912i	1.00780	+	0.438895i
$178$	−1.29492	−	2.24287i	−0.0970584	−	0.168110i
$179$	−1.70116			−0.127150			−0.0635752	−	0.997977i	$-0.520250\pi$
$179$	−1.70116			−0.127150			−0.0635752	+	0.997977i	$0.520250\pi$
$180$	3.79172	+	4.07551i	0.282618	+	0.303771i
$181$	−16.9941			−1.26316			−0.631581	−	0.775310i	$-0.717594\pi$
$181$	−16.9941			−1.26316			−0.631581	+	0.775310i	$0.717594\pi$
$182$		0			0
$183$	4.51188	−	3.33460i	0.333528	−	0.246501i
$184$	4.13252	−	7.15774i	0.304654	−	0.527676i
$185$	−0.375877	+	0.651039i	−0.0276351	+	0.0478653i
$186$	1.38210	+	12.1929i	0.101341	+	0.894029i
$187$	1.17178	+	2.02957i	0.0856887	+	0.148417i
$188$	−13.2323			−0.965066
$189$		0			0
$190$	−6.15437			−0.446485
$191$	−11.3470	−	19.6535i	−0.821038	−	1.42208i	−0.904910	−	0.425603i	$-0.860062\pi$
$191$	−11.3470	−	19.6535i	−0.821038	−	1.42208i	0.0838717	−	0.996477i	$-0.473271\pi$
$192$	−0.508064	−	4.48215i	−0.0366664	−	0.323471i
$193$	−3.09349	+	5.35808i	−0.222674	+	0.385683i	−0.955619	−	0.294605i	$-0.904812\pi$
$193$	−3.09349	+	5.35808i	−0.222674	+	0.385683i	0.732945	+	0.680288i	$0.238145\pi$
$194$	11.2263	−	19.4445i	0.806001	−	1.39603i
$195$	9.62319	−	7.11222i	0.689131	−	0.509317i
$196$		0			0
$197$	9.77010			0.696091			0.348045	−	0.937478i	$-0.386846\pi$
$197$	9.77010			0.696091			0.348045	+	0.937478i	$0.386846\pi$
$198$	−2.45269	+	7.98948i	−0.174305	+	0.567788i
$199$	8.67947			0.615271			0.307636	−	0.951504i	$-0.400462\pi$
$199$	8.67947			0.615271			0.307636	+	0.951504i	$0.400462\pi$
$200$	1.80691	+	3.12965i	0.127768	+	0.221300i
$201$	−11.0102	−	4.79491i	−0.776600	−	0.338207i
$202$	1.02987	−	1.78379i	0.0724615	−	0.125507i
$203$		0			0
$204$	3.41938	+	1.48913i	0.239405	+	0.104260i
$205$	6.02225	+	10.4308i	0.420612	+	0.728522i
$206$	−3.55442			−0.247648
$207$	−6.48055	+	21.1100i	−0.450429	+	1.46725i
$208$	−25.0920			−1.73982
$209$	−1.89446	−	3.28130i	−0.131043	−	0.226973i
$210$		0			0
$211$	−2.84219	+	4.92283i	−0.195665	+	0.338901i	−0.947118	−	0.320885i	$-0.896020\pi$
$211$	−2.84219	+	4.92283i	−0.195665	+	0.338901i	0.751453	+	0.659786i	$0.229353\pi$
$212$	1.05010	−	1.81882i	0.0721209	−	0.124917i
$213$	−2.40545	−	21.2209i	−0.164819	−	1.45403i
$214$	−5.32062	−	9.21558i	−0.363710	−	0.629964i
$215$	−13.6142			−0.928478
$216$	−1.93810	−	5.50319i	−0.131871	−	0.374445i
$217$		0			0
$218$	7.58786	+	13.1426i	0.513915	+	0.890126i
$219$	0.538180	+	4.74783i	0.0363668	+	0.320828i
$220$	−1.40372	+	2.43132i	−0.0946390	+	0.163920i
$221$	4.00862	−	6.94313i	0.269649	−	0.467045i
$222$	−1.44447	+	1.06757i	−0.0969468	+	0.0716506i
$223$	5.86133	+	10.1521i	0.392503	+	0.679836i	0.992779	−	0.119957i	$-0.0382758\pi$
$223$	5.86133	+	10.1521i	0.392503	+	0.679836i	−0.600276	+	0.799793i	$0.704942\pi$
$224$		0			0
$225$	−6.57677	−	7.06901i	−0.438451	−	0.471267i
$226$	26.7019			1.77618
$227$	−5.59154	−	9.68482i	−0.371123	−	0.642804i	0.618615	−	0.785694i	$-0.287694\pi$
$227$	−5.59154	−	9.68482i	−0.371123	−	0.642804i	−0.989739	+	0.142890i	$0.954361\pi$
$228$	−5.52827	−	2.40754i	−0.366118	−	0.159443i
$229$	4.82824	−	8.36275i	0.319059	−	0.552626i	−0.661233	−	0.750181i	$-0.729967\pi$
$229$	4.82824	−	8.36275i	0.319059	−	0.552626i	0.980292	+	0.197554i	$0.0632999\pi$
$230$	−9.04494	+	15.6663i	−0.596406	+	1.03301i
$231$		0			0
$232$	−0.0347761	−	0.0602340i	−0.00228317	−	0.00395456i
$233$	19.2898			1.26372			0.631860	−	0.775083i	$-0.282292\pi$
$233$	19.2898			1.26372			0.631860	+	0.775083i	$0.282292\pi$
$234$	27.8654	−	6.39946i	1.82162	−	0.418346i
$235$	−12.7049			−0.828774
$236$	5.86881	+	10.1651i	0.382027	+	0.661690i
$237$	−8.24519	+	6.09378i	−0.535582	+	0.395833i
$238$		0			0
$239$	−0.194641	+	0.337128i	−0.0125903	+	0.0218070i	−0.872252	−	0.489057i	$-0.837341\pi$
$239$	−0.194641	+	0.337128i	−0.0125903	+	0.0218070i	0.859662	+	0.510864i	$0.170674\pi$
$240$	−1.26230	−	11.1361i	−0.0814813	−	0.718829i
$241$	−5.31807	−	9.21117i	−0.342567	−	0.593344i	0.642342	−	0.766419i	$-0.277963\pi$
$241$	−5.31807	−	9.21117i	−0.342567	−	0.593344i	−0.984909	+	0.173075i	$0.944630\pi$
$242$	16.0386			1.03100
$243$	8.33782	+	13.1712i	0.534871	+	0.844934i
$244$	4.50299			0.288274
$245$		0			0
$246$	3.24130	+	28.5948i	0.206658	+	1.82314i
$247$	−6.48091	+	11.2253i	−0.412370	+	0.714247i
$248$	2.16023	−	3.74163i	0.137175	−	0.237594i
$249$	−7.80341	+	5.76728i	−0.494521	+	0.365486i
$250$	−10.0988	−	17.4917i	−0.638705	−	1.10627i
$251$	−3.26628			−0.206166			−0.103083	−	0.994673i	$-0.532871\pi$
$251$	−3.26628			−0.206166			−0.103083	+	0.994673i	$0.532871\pi$
$252$		0			0
$253$	−11.1370			−0.700176
$254$	7.82531	+	13.5538i	0.491004	+	0.850443i
$255$	3.28308	+	1.42977i	0.205594	+	0.0895357i
$256$	−10.4896	+	18.1686i	−0.655603	+	1.13554i
$257$	2.34787	−	4.06663i	0.146456	−	0.253669i	−0.783459	−	0.621443i	$-0.786547\pi$
$257$	2.34787	−	4.06663i	0.146456	−	0.253669i	0.929915	+	0.367774i	$0.119880\pi$
$258$	−29.8229	−	12.9878i	−1.85669	−	0.808584i
$259$		0			0
$260$	9.60421			0.595628
$261$	0.126578	+	0.136052i	0.00783498	+	0.00842139i
$262$	3.70727			0.229036
$263$	−9.77491	−	16.9306i	−0.602747	−	1.04399i	−0.992403	−	0.123028i	$-0.960740\pi$
$263$	−9.77491	−	16.9306i	−0.602747	−	1.04399i	0.389656	−	0.920960i	$-0.372594\pi$
$264$	2.36640	−	1.74894i	0.145642	−	0.107640i
$265$	1.00824	−	1.74632i	0.0619355	−	0.107276i
$266$		0			0
$267$	−0.274400	−	2.42076i	−0.0167930	−	0.148148i
$268$	−4.81929	−	8.34725i	−0.294385	−	0.509890i
$269$	−15.7673			−0.961349			−0.480675	−	0.876899i	$-0.659608\pi$
$269$	−15.7673			−0.961349			−0.480675	+	0.876899i	$0.659608\pi$
$270$	4.24196	+	12.0449i	0.258157	+	0.733032i
$271$	−14.7976			−0.898893			−0.449446	−	0.893307i	$-0.648379\pi$
$271$	−14.7976			−0.898893			−0.449446	+	0.893307i	$0.648379\pi$
$272$	−3.75442	−	6.50285i	−0.227645	−	0.394293i
$273$		0			0
$274$	2.04138	−	3.53578i	0.123324	−	0.213604i
$275$	2.43477	−	4.21715i	0.146822	−	0.254304i
$276$	−14.2533	+	10.5342i	−0.857948	+	0.634084i
$277$	3.72561	+	6.45295i	0.223850	+	0.387720i	0.955974	−	0.293452i	$-0.0948040\pi$
$277$	3.72561	+	6.45295i	0.223850	+	0.387720i	−0.732124	+	0.681172i	$0.761471\pi$
$278$	1.39076			0.0834123
$279$	−3.38764	+	11.0350i	−0.202812	+	0.660650i
$280$		0			0
$281$	−12.9938	−	22.5060i	−0.775146	−	1.34259i	−0.934712	−	0.355406i	$-0.884343\pi$
$281$	−12.9938	−	22.5060i	−0.775146	−	1.34259i	0.159566	−	0.987187i	$-0.448991\pi$
$282$	−27.8310	−	12.1203i	−1.65731	−	0.721754i
$283$	−9.37768	+	16.2426i	−0.557445	+	0.965524i	0.440263	+	0.897869i	$0.354885\pi$
$283$	−9.37768	+	16.2426i	−0.557445	+	0.965524i	−0.997709	+	0.0676550i	$0.978448\pi$
$284$	8.57064	−	14.8448i	0.508574	−	0.880876i
$285$	−5.30790	−	2.31157i	−0.314413	−	0.136926i
$286$	7.20971	+	12.4876i	0.426319	+	0.738406i
$287$		0			0
$288$	5.88136	−	19.1582i	0.346563	−	1.12891i
$289$	−14.6008			−0.858872
$290$	0.0761152	+	0.131835i	0.00446964	+	0.00774165i
$291$	16.9856	−	12.5535i	0.995711	−	0.735901i
$292$	−1.91754	+	3.32127i	−0.112215	+	0.194363i
$293$	−1.23089	+	2.13196i	−0.0719093	+	0.124551i	−0.899738	−	0.436430i	$-0.856243\pi$
$293$	−1.23089	+	2.13196i	−0.0719093	+	0.124551i	0.827829	+	0.560981i	$0.189576\pi$
$294$		0			0
$295$	5.63487	+	9.75988i	0.328075	+	0.568242i
$296$	0.632407			0.0367579
$297$	−5.11618	+	5.96939i	−0.296871	+	0.346379i
$298$	−12.1245			−0.702356
$299$	19.0497	+	32.9950i	1.10167	+	1.90815i
$300$	−0.872835	−	7.70016i	−0.0503932	−	0.444569i
$301$		0			0
$302$	11.6616	−	20.1985i	0.671050	−	1.16229i
$303$	1.55821	−	1.15163i	0.0895170	−	0.0661594i
$304$	6.06994	+	10.5134i	0.348135	+	0.602987i
$305$	4.32349			0.247562
$306$	5.82787	+	6.26405i	0.333157	+	0.358092i
$307$	−4.66277			−0.266118			−0.133059	−	0.991108i	$-0.542480\pi$
$307$	−4.66277			−0.266118			−0.133059	+	0.991108i	$0.542480\pi$
$308$		0			0
$309$	−3.06555	−	1.33503i	−0.174393	−	0.0759475i
$310$	−4.72814	+	8.18938i	−0.268541	+	0.465126i
$311$	−13.7410	+	23.8002i	−0.779183	+	1.34958i	0.153231	+	0.988190i	$0.451032\pi$
$311$	−13.7410	+	23.8002i	−0.779183	+	1.34958i	−0.932413	+	0.361393i	$0.882301\pi$
$312$	−9.22921	−	4.01929i	−0.522501	−	0.227548i
$313$	−2.74666	−	4.75735i	−0.155250	−	0.268901i	0.777900	−	0.628388i	$-0.216285\pi$
$313$	−2.74666	−	4.75735i	−0.155250	−	0.268901i	−0.933150	+	0.359487i	$0.882952\pi$
$314$	31.8671			1.79837
$315$		0			0
$316$	−8.22893			−0.462914
$317$	−4.93879	−	8.55424i	−0.277390	−	0.480454i	0.693345	−	0.720606i	$-0.256136\pi$
$317$	−4.93879	−	8.55424i	−0.277390	−	0.480454i	−0.970735	+	0.240152i	$0.922803\pi$
$318$	3.87460	−	2.86360i	0.217277	−	0.160583i
$319$	−0.0468601	+	0.0811641i	−0.00262366	+	0.00454432i
$320$	1.73808	−	3.01044i	0.0971614	−	0.168288i
$321$	−1.12746	−	9.94649i	−0.0629288	−	0.555159i
$322$		0			0
$323$	−3.87885			−0.215825
$324$	−0.901478	+	12.4790i	−0.0500821	+	0.693277i
$325$	−16.6586			−0.924052
$326$	−11.2493	−	19.4844i	−0.623041	−	1.07914i
$327$	1.60790	+	14.1849i	0.0889172	+	0.784428i
$328$	5.06616	−	8.77485i	0.279732	−	0.484510i
$329$		0			0
$330$	−5.17940	+	3.82794i	−0.285116	+	0.210721i
$331$	10.3471	+	17.9217i	0.568729	+	0.985067i	0.996692	+	0.0812710i	$0.0258979\pi$
$331$	10.3471	+	17.9217i	0.568729	+	0.985067i	−0.427963	+	0.903796i	$0.640769\pi$
$332$	−7.78803			−0.427424
$333$	−1.64678	+	0.378194i	−0.0902430	+	0.0207249i
$334$	6.49029			0.355133
$335$	−4.62718	−	8.01452i	−0.252810	−	0.437880i
$336$		0			0
$337$	0.748747	−	1.29687i	0.0407869	−	0.0706449i	−0.844911	−	0.534906i	$-0.820347\pi$
$337$	0.748747	−	1.29687i	0.0407869	−	0.0706449i	0.885698	+	0.464261i	$0.153680\pi$
$338$	12.6962	−	21.9905i	0.690582	−	1.19612i
$339$	23.0293	+	10.0292i	1.25078	+	0.544710i
$340$	1.43704	+	2.48903i	0.0779344	+	0.134986i
$341$	−5.82174			−0.315265
$342$	−9.42217	−	10.1274i	−0.509493	−	0.547626i
$343$		0			0
$344$	5.72639	+	9.91840i	0.308746	+	0.534764i
$345$	−13.6851	+	10.1143i	−0.736783	+	0.544535i
$346$	9.33593	−	16.1703i	0.501903	−	0.869321i
$347$	14.7694	−	25.5813i	0.792862	−	1.37328i	−0.131326	−	0.991339i	$-0.541923\pi$
$347$	14.7694	−	25.5813i	0.792862	−	1.37328i	0.924188	−	0.381938i	$-0.124743\pi$
$348$	0.0167988	+	0.148199i	0.000900509	+	0.00794430i
$349$	18.0006	+	31.1780i	0.963551	+	1.66892i	0.713458	+	0.700698i	$0.247128\pi$
$349$	18.0006	+	31.1780i	0.963551	+	1.66892i	0.250094	+	0.968222i	$0.419539\pi$
$350$		0			0
$351$	26.4364	+	4.94691i	1.41107	+	0.264046i
$352$	10.1073			0.538719
$353$	14.7465	+	25.5417i	0.784877	+	1.35945i	0.929073	+	0.369897i	$0.120607\pi$
$353$	14.7465	+	25.5417i	0.784877	+	1.35945i	−0.144196	+	0.989549i	$0.546060\pi$
$354$	3.03280	+	26.7554i	0.161192	+	1.42203i
$355$	8.22900	−	14.2530i	0.436750	−	0.756473i
$356$	0.977687	−	1.69340i	0.0518173	−	0.0897502i
$357$		0			0
$358$	−1.56612	−	2.71260i	−0.0827720	−	0.143365i
$359$	−5.41069			−0.285566			−0.142783	−	0.989754i	$-0.545605\pi$
$359$	−5.41069			−0.285566			−0.142783	+	0.989754i	$0.545605\pi$
$360$	1.31950	−	4.29820i	0.0695439	−	0.226535i
$361$	−12.7289			−0.669942
$362$	−15.6451	−	27.0981i	−0.822289	−	1.42425i
$363$	13.8327	+	6.02409i	0.726028	+	0.316183i
$364$		0			0
$365$	−1.84110	+	3.18888i	−0.0963676	+	0.166914i
$366$	9.47096	+	4.12457i	0.495055	+	0.215595i
$367$	11.5422	+	19.9916i	0.602496	+	1.04355i	0.992442	+	0.122715i	$0.0391602\pi$
$367$	11.5422	+	19.9916i	0.602496	+	1.04355i	−0.389946	+	0.920838i	$0.627506\pi$
$368$	35.6834			1.86013
$369$	−7.94466	+	25.8793i	−0.413583	+	1.34722i
$370$	−1.38416			−0.0719591
$371$		0			0
$372$	−7.45075	+	5.50664i	−0.386304	+	0.285506i
$373$	−10.7515	+	18.6222i	−0.556692	+	0.964219i	0.441078	+	0.897469i	$0.354596\pi$
$373$	−10.7515	+	18.6222i	−0.556692	+	0.964219i	−0.997770	+	0.0667498i	$0.978737\pi$
$374$	−2.15752	+	3.73694i	−0.111563	+	0.193232i
$375$	−2.13999	−	18.8790i	−0.110508	−	0.974906i
$376$	5.34392	+	9.25595i	0.275592	+	0.477339i
$377$	0.320615			0.0165125
$378$		0			0
$379$	5.72168			0.293903			0.146952	−	0.989144i	$-0.453054\pi$
$379$	5.72168			0.293903			0.146952	+	0.989144i	$0.453054\pi$
$380$	−2.32333	−	4.02412i	−0.119184	−	0.206433i
$381$	1.65822	+	14.6288i	0.0849531	+	0.749457i
$382$	20.8925	−	36.1869i	1.06895	−	1.85148i
$383$	17.4604	−	30.2424i	0.892187	−	1.54531i	0.0549390	−	0.998490i	$-0.482504\pi$
$383$	17.4604	−	30.2424i	0.892187	−	1.54531i	0.837248	−	0.546823i	$-0.184163\pi$
$384$	−11.9306	+	8.81756i	−0.608831	+	0.449969i
$385$		0			0
$386$	−11.3917			−0.579823
$387$	−20.8429	−	22.4029i	−1.05950	−	1.13880i
$388$	16.9521			0.860611
$389$	14.4411	+	25.0127i	0.732192	+	1.26819i	0.955944	+	0.293548i	$0.0948361\pi$
$389$	14.4411	+	25.0127i	0.732192	+	1.26819i	−0.223752	+	0.974646i	$0.571831\pi$
$390$	20.2002	+	8.79711i	1.02288	+	0.445459i
$391$	−5.70066	+	9.87383i	−0.288295	+	0.499341i
$392$		0			0
$393$	3.19737	+	1.39244i	0.161286	+	0.0702395i
$394$	8.99455	+	15.5790i	0.453139	+	0.784860i
$395$	−7.90091			−0.397538
$396$	−6.14994	+	1.41237i	−0.309046	+	0.0709745i
$397$	−11.1845			−0.561335			−0.280667	−	0.959805i	$-0.590556\pi$
$397$	−11.1845			−0.561335			−0.280667	+	0.959805i	$0.590556\pi$
$398$	7.99049	+	13.8399i	0.400527	+	0.693734i
$399$		0			0
$400$	−7.80111	+	13.5119i	−0.390056	+	0.675596i
$401$	0.541061	−	0.937146i	0.0270193	−	0.0467988i	−0.852200	−	0.523217i	$-0.824732\pi$
$401$	0.541061	−	0.937146i	0.0270193	−	0.0467988i	0.879219	+	0.476418i	$0.158065\pi$
$402$	−2.49045	−	21.9707i	−0.124212	−	1.09580i
$403$	9.95802	+	17.2478i	0.496044	+	0.859174i
$404$	1.55514			0.0773711
$405$	−0.865544	+	11.9816i	−0.0430092	+	0.595368i
$406$		0			0
$407$	−0.426078	−	0.737988i	−0.0211199	−	0.0365807i
$408$	−0.339291	−	2.99323i	−0.0167974	−	0.148187i
$409$	10.8674	−	18.8229i	0.537360	−	0.930735i	−0.461685	−	0.887044i	$-0.652755\pi$
$409$	10.8674	−	18.8229i	0.537360	−	0.930735i	0.999045	−	0.0436908i	$-0.0139116\pi$
$410$	−11.0884	+	19.2057i	−0.547618	+	0.948501i
$411$	3.08864	−	2.28273i	0.152351	−	0.112599i
$412$	−1.34182	−	2.32410i	−0.0661069	−	0.114500i
$413$		0			0
$414$	−39.6273	+	9.10068i	−1.94758	+	0.447274i
$415$	−7.47759			−0.367060
$416$	−17.2884	−	29.9443i	−0.847632	−	1.46814i
$417$	1.19948	+	0.522368i	0.0587386	+	0.0255805i
$418$	3.48816	−	6.04167i	0.170611	−	0.295508i
$419$	12.5906	−	21.8075i	0.615090	−	1.06537i	−0.375279	−	0.926912i	$-0.622453\pi$
$419$	12.5906	−	21.8075i	0.615090	−	1.06537i	0.990369	−	0.138455i	$-0.0442135\pi$
$420$		0			0
$421$	−14.8304	−	25.6869i	−0.722788	−	1.25191i	−0.959878	−	0.280418i	$-0.909527\pi$
$421$	−14.8304	−	25.6869i	−0.722788	−	1.25191i	0.237090	−	0.971488i	$-0.423806\pi$
$422$	−10.4663			−0.509493
$423$	−19.4508	−	20.9066i	−0.945729	−	1.01651i
$424$	−1.69634			−0.0823816
$425$	−2.49256	−	4.31724i	−0.120907	−	0.209417i
$426$	31.6236	−	23.3721i	1.53217	−	1.13238i
$427$		0			0
$428$	4.01715	−	6.95791i	0.194176	−	0.336323i
$429$	1.52777	+	13.4780i	0.0737615	+	0.650724i
$430$	−12.5335	−	21.7086i	−0.604418	−	1.04688i
$431$	−4.89034			−0.235559			−0.117780	−	0.993040i	$-0.537578\pi$
$431$	−4.89034			−0.235559			−0.117780	+	0.993040i	$0.537578\pi$
$432$	16.3925	−	19.1262i	0.788683	−	0.920208i
$433$	9.71430			0.466839			0.233420	−	0.972376i	$-0.425008\pi$
$433$	9.71430			0.466839			0.233420	+	0.972376i	$0.425008\pi$
$434$		0			0
$435$	0.0161292	+	0.142292i	0.000773334	+	0.00682236i
$436$	−5.72896	+	9.92285i	−0.274367	+	0.475218i
$437$	9.21651	−	15.9635i	0.440885	−	0.763636i
$438$	−7.07524	+	5.22911i	−0.338068	+	0.249856i
$439$	7.41176	+	12.8375i	0.353744	+	0.612703i	0.986902	−	0.161320i	$-0.0515751\pi$
$439$	7.41176	+	12.8375i	0.353744	+	0.612703i	−0.633158	+	0.774022i	$0.718242\pi$
$440$	2.26760			0.108103
$441$		0			0
$442$	14.7617			0.702141
$443$	10.9510	+	18.9676i	0.520297	+	0.901180i	0.999722	+	0.0235972i	$0.00751192\pi$
$443$	10.9510	+	18.9676i	0.520297	+	0.901180i	−0.479425	+	0.877583i	$0.659155\pi$
$444$	−1.24335	−	0.541473i	−0.0590066	−	0.0256972i
$445$	0.938715	−	1.62590i	0.0444994	−	0.0770751i
$446$	−10.7921	+	18.6925i	−0.511021	+	0.885115i
$447$	−10.4569	−	4.55396i	−0.494596	−	0.215395i
$448$		0			0
$449$	21.4952			1.01442			0.507212	−	0.861822i	$-0.330676\pi$
$449$	21.4952			1.01442			0.507212	+	0.861822i	$0.330676\pi$
$450$	5.21726	−	16.9949i	0.245944	−	0.801149i
$451$	−13.6531			−0.642899
$452$	10.0802	+	17.4594i	0.474131	+	0.821220i
$453$	17.6442	−	13.0403i	0.828996	−	0.612687i
$454$	10.2954	−	17.8321i	0.483185	−	0.836902i
$455$		0			0
$456$	0.548548	+	4.83929i	0.0256881	+	0.226621i
$457$	−20.3128	−	35.1827i	−0.950190	−	1.64578i	−0.745009	−	0.667054i	$-0.767555\pi$
$457$	−20.3128	−	35.1827i	−0.950190	−	1.64578i	−0.205181	−	0.978724i	$-0.565778\pi$
$458$	17.7799			0.830800
$459$	2.67353	+	7.59144i	0.124790	+	0.354338i
$460$	−13.6582			−0.636815
$461$	1.41541	+	2.45155i	0.0659220	+	0.114180i	0.897103	−	0.441822i	$-0.145668\pi$
$461$	1.41541	+	2.45155i	0.0659220	+	0.114180i	−0.831181	+	0.556003i	$0.812334\pi$
$462$		0			0
$463$	−13.9324	+	24.1317i	−0.647494	+	1.12149i	0.336225	+	0.941782i	$0.390850\pi$
$463$	−13.9324	+	24.1317i	−0.647494	+	1.12149i	−0.983719	+	0.179711i	$0.942484\pi$
$464$	0.150142	−	0.260053i	0.00697016	−	0.0120727i
$465$	−7.15376	+	5.28714i	−0.331748	+	0.245185i
$466$	17.7586	+	30.7588i	0.822653	+	1.42488i
$467$	26.6438			1.23293			0.616464	−	0.787383i	$-0.288564\pi$
$467$	26.6438			1.23293			0.616464	+	0.787383i	$0.288564\pi$
$468$	14.7038	+	15.8043i	0.679682	+	0.730554i
$469$		0			0
$470$	−11.6964	−	20.2587i	−0.539513	−	0.934463i
$471$	27.4842	+	11.9693i	1.26640	+	0.551514i
$472$	4.74028	−	8.21041i	0.218189	−	0.377915i
$473$	7.71620	−	13.3648i	0.354791	−	0.614516i
$474$	−17.3076	−	7.53740i	−0.794964	−	0.346204i
$475$	4.02983	+	6.97987i	0.184901	+	0.320258i
$476$		0			0
$477$	4.41725	−	1.01445i	0.202252	−	0.0464485i
$478$	−0.716762			−0.0327839
$479$	15.7895	+	27.3483i	0.721443	+	1.24958i	0.960422	+	0.278551i	$0.0898540\pi$
$479$	15.7895	+	27.3483i	0.721443	+	1.24958i	−0.238979	+	0.971025i	$0.576813\pi$
$480$	12.4198	−	9.17913i	0.566885	−	0.418968i
$481$	−1.45760	+	2.52464i	−0.0664609	+	0.115114i
$482$	9.79185	−	16.9600i	0.446007	−	0.772506i
$483$		0			0
$484$	6.05472	+	10.4871i	0.275215	+	0.476686i
$485$	16.2763			0.739070
$486$	−13.3263	+	25.4208i	−0.604495	+	1.15311i
$487$	0.306174			0.0138741			0.00693703	−	0.999976i	$-0.497792\pi$
$487$	0.306174			0.0138741			0.00693703	+	0.999976i	$0.497792\pi$
$488$	−1.81855	−	3.14982i	−0.0823218	−	0.142586i
$489$	−2.38378	−	21.0297i	−0.107798	−	0.950996i
$490$		0			0
$491$	−9.06981	+	15.7094i	−0.409315	+	0.708954i	−0.994813	−	0.101720i	$-0.967566\pi$
$491$	−9.06981	+	15.7094i	−0.409315	+	0.708954i	0.585498	+	0.810674i	$0.300899\pi$
$492$	−17.4735	+	12.9141i	−0.787764	+	0.582214i
$493$	0.0479723	+	0.0830905i	0.00216057	+	0.00374221i
$494$	−23.8658			−1.07377
$495$	−5.90480	+	1.35607i	−0.265401	+	0.0609510i
$496$	18.6531			0.837549
$497$		0			0
$498$	−16.3803	−	7.13355i	−0.734017	−	0.319662i
$499$	10.6546	−	18.4543i	0.476964	−	0.826126i	−0.522687	−	0.852524i	$-0.675070\pi$
$499$	10.6546	−	18.4543i	0.476964	−	0.826126i	0.999652	+	0.0263983i	$0.00840381\pi$
$500$	7.62478	−	13.2065i	0.340990	−	0.590613i
$501$	5.59762	+	2.43774i	0.250083	+	0.108910i
$502$	−3.00701	−	5.20829i	−0.134209	−	0.232457i
$503$	−17.0738			−0.761285			−0.380642	−	0.924722i	$-0.624297\pi$
$503$	−17.0738			−0.761285			−0.380642	+	0.924722i	$0.624297\pi$
$504$		0			0
$505$	1.49315			0.0664443
$506$	−10.2529	−	17.7586i	−0.455799	−	0.789466i
$507$	19.2096	−	14.1972i	0.853126	−	0.630521i
$508$	−5.90824	+	10.2334i	−0.262136	+	0.454032i
$509$	−18.3868	+	31.8468i	−0.814979	+	1.41159i	0.0943635	+	0.995538i	$0.469918\pi$
$509$	−18.3868	+	31.8468i	−0.814979	+	1.41159i	−0.909343	+	0.416048i	$0.863415\pi$
$510$	0.742614	+	6.55135i	0.0328835	+	0.290099i
$511$		0			0
$512$	−21.4975			−0.950065
$513$	−4.32242	−	12.2734i	−0.190839	−	0.541884i
$514$	8.64598			0.381358
$515$	−1.28834	−	2.23146i	−0.0567709	−	0.0983300i
$516$	−2.76616	−	24.4031i	−0.121774	−	1.07429i
$517$	7.20083	−	12.4722i	0.316692	−	0.548527i
$518$		0			0
$519$	14.1254	−	10.4397i	0.620037	−	0.458251i
$520$	−3.87870	−	6.71810i	−0.170092	−	0.294608i
$521$	19.1507			0.839008			0.419504	−	0.907754i	$-0.362204\pi$
$521$	19.1507			0.839008			0.419504	+	0.907754i	$0.362204\pi$
$522$	−0.100413	+	0.327088i	−0.00439494	+	0.0143163i
$523$	41.9429			1.83404			0.917018	−	0.398847i	$-0.130589\pi$
$523$	41.9429			1.83404			0.917018	+	0.398847i	$0.130589\pi$
$524$	1.39952	+	2.42405i	0.0611385	+	0.105895i
$525$		0			0
$526$	17.9980	−	31.1734i	0.784749	−	1.35922i
$527$	−2.97996	+	5.16144i	−0.129809	+	0.224836i
$528$	11.6476	+	5.07248i	0.506895	+	0.220751i
$529$	−15.5906	−	27.0037i	−0.677851	−	1.17407i
$530$	3.71282			0.161274
$531$	−7.43362	+	24.2146i	−0.322592	+	1.05082i
$532$		0			0
$533$	23.3535	+	40.4494i	1.01155	+	1.75206i
$534$	3.60743	−	2.66614i	0.156109	−	0.115375i
$535$	3.85702	−	6.68056i	0.166754	−	0.288826i
$536$	−3.89258	+	6.74214i	−0.168134	+	0.291216i
$537$	−0.331868	−	2.92774i	−0.0143212	−	0.126341i
$538$	−14.5157	−	25.1419i	−0.625816	−	1.08395i
$539$		0			0
$540$	−6.27438	+	7.32073i	−0.270006	+	0.315034i
$541$	2.88544			0.124055			0.0620273	−	0.998074i	$-0.480243\pi$
$541$	2.88544			0.124055			0.0620273	+	0.998074i	$0.480243\pi$
$542$	−13.6230	−	23.5957i	−0.585158	−	1.01352i
$543$	−3.31527	−	29.2474i	−0.142272	−	1.25512i
$544$	5.17358	−	8.96090i	0.221815	−	0.384196i
$545$	−5.50059	+	9.52731i	−0.235620	+	0.408105i
$546$		0			0
$547$	1.38738	+	2.40301i	0.0593201	+	0.102745i	0.894160	−	0.447747i	$-0.147773\pi$
$547$	1.38738	+	2.40301i	0.0593201	+	0.102745i	−0.834840	+	0.550492i	$0.814440\pi$
$548$	3.08255			0.131680
$549$	6.61914	+	7.11456i	0.282498	+	0.303642i
$550$	8.96600			0.382311
$551$	−0.0775590	−	0.134336i	−0.00330413	−	0.00572291i
$552$	13.1249	+	5.71584i	0.558632	+	0.243282i
$553$		0			0
$554$	−6.85975	+	11.8814i	−0.291443	+	0.504794i
$555$	−1.19378	−	0.519889i	−0.0506733	−	0.0220681i
$556$	0.525024	+	0.909368i	0.0222660	+	0.0385658i
$557$	−31.0688			−1.31643			−0.658214	−	0.752831i	$-0.728688\pi$
$557$	−31.0688			−1.31643			−0.658214	+	0.752831i	$0.728688\pi$
$558$	−20.7148	+	4.75728i	−0.876926	+	0.201392i
$559$	−52.7939			−2.23294
$560$		0			0
$561$	−3.26436	+	2.41260i	−0.137822	+	0.101860i
$562$	23.9248	−	41.4389i	1.00920	−	1.74799i
$563$	−0.144020	+	0.249451i	−0.00606973	+	0.0105131i	−0.869044	−	0.494734i	$-0.835265\pi$
$563$	−0.144020	+	0.249451i	−0.00606973	+	0.0105131i	0.862975	+	0.505247i	$0.168599\pi$
$564$	−2.58141	−	22.7732i	−0.108697	−	0.958925i
$565$	9.67836	+	16.7634i	0.407172	+	0.705242i
$566$	−34.5331			−1.45154
$567$		0			0
$568$	−13.8451			−0.580929
$569$	8.04004	+	13.9258i	0.337056	+	0.583798i	0.983878	−	0.178843i	$-0.0572354\pi$
$569$	8.04004	+	13.9258i	0.337056	+	0.583798i	−0.646821	+	0.762641i	$0.723902\pi$
$570$	−1.20062	−	10.5919i	−0.0502883	−	0.443644i
$571$	7.64289	−	13.2379i	0.319845	−	0.553988i	−0.660610	−	0.750729i	$-0.729702\pi$
$571$	7.64289	−	13.2379i	0.319845	−	0.553988i	0.980456	+	0.196741i	$0.0630358\pi$
$572$	−5.44345	+	9.42834i	−0.227602	+	0.394218i
$573$	31.6107	−	23.3626i	1.32056	−	0.975985i
$574$		0			0
$575$	23.6902			0.987950
$576$	7.61479	−	1.74879i	0.317283	−	0.0728661i
$577$	−24.1625			−1.00590			−0.502949	−	0.864316i	$-0.667752\pi$
$577$	−24.1625			−1.00590			−0.502949	+	0.864316i	$0.667752\pi$
$578$	−13.4418	−	23.2819i	−0.559106	−	0.968400i
$579$	−9.82490	−	4.27871i	−0.408309	−	0.177817i
$580$	−0.0574683	+	0.0995380i	−0.00238624	+	0.00413309i
$581$		0			0
$582$	35.6546	+	15.5275i	1.47793	+	0.643634i
$583$	1.14289	+	1.97955i	0.0473338	+	0.0819845i
$584$	3.09762			0.128180
$585$	14.1177	+	15.1743i	0.583694	+	0.627381i
$586$	−4.53273			−0.187245
$587$	18.0145	+	31.2020i	0.743537	+	1.28784i	0.950875	+	0.309574i	$0.100186\pi$
$587$	18.0145	+	31.2020i	0.743537	+	1.28784i	−0.207339	+	0.978269i	$0.566480\pi$
$588$		0			0
$589$	4.81783	−	8.34472i	0.198515	−	0.343838i
$590$	−10.3752	+	17.9703i	−0.427138	+	0.739825i
$591$	1.90599	+	16.8146i	0.0784018	+	0.691661i
$592$	1.36517	+	2.36455i	0.0561082	+	0.0971823i
$593$	−24.9337			−1.02390			−0.511951	−	0.859014i	$-0.671077\pi$
$593$	−24.9337			−1.02390			−0.511951	+	0.859014i	$0.671077\pi$
$594$	−14.2286	−	2.66253i	−0.583807	−	0.109245i
$595$		0			0
$596$	−4.57712	−	7.92780i	−0.187486	−	0.324735i
$597$	1.69322	+	14.9376i	0.0692990	+	0.611356i
$598$	−35.0751	+	60.7518i	−1.43433	+	2.48433i
$599$	−19.7642	+	34.2325i	−0.807542	+	1.39870i	0.107019	+	0.994257i	$0.465869\pi$
$599$	−19.7642	+	34.2325i	−0.807542	+	1.39870i	−0.914561	+	0.404447i	$0.867464\pi$
$600$	−5.03373	+	3.72028i	−0.205501	+	0.151880i
$601$	1.86447	+	3.22936i	0.0760534	+	0.131728i	0.901544	−	0.432688i	$-0.142435\pi$
$601$	1.86447	+	3.22936i	0.0760534	+	0.131728i	−0.825490	+	0.564416i	$0.809101\pi$
$602$		0			0
$603$	6.10427	−	19.8843i	0.248585	−	0.809751i
$604$	17.6094			0.716516
$605$	5.81337	+	10.0691i	0.236347	+	0.409365i
$606$	3.27087	+	1.42445i	0.132870	+	0.0578644i
$607$	−11.8264	+	20.4839i	−0.480018	+	0.831415i	−0.999737	−	0.0229218i	$-0.992703\pi$
$607$	−11.8264	+	20.4839i	−0.480018	+	0.831415i	0.519719	+	0.854337i	$0.326036\pi$
$608$	−8.36436	+	14.4875i	−0.339219	+	0.587545i
$609$		0			0
$610$	3.98029	+	6.89407i	0.161157	+	0.279133i
$611$	−49.2677			−1.99316
$612$	−1.89577	+	6.17536i	−0.0766320	+	0.249624i
$613$	−3.79903			−0.153442			−0.0767208	−	0.997053i	$-0.524445\pi$
$613$	−3.79903			−0.153442			−0.0767208	+	0.997053i	$0.524445\pi$
$614$	−4.29264	−	7.43507i	−0.173237	−	0.300055i
$615$	−16.7769	+	12.3994i	−0.676512	+	0.499990i
$616$		0			0
$617$	−17.5615	+	30.4174i	−0.706999	+	1.22456i	0.258966	+	0.965886i	$0.416618\pi$
$617$	−17.5615	+	30.4174i	−0.706999	+	1.22456i	−0.965965	+	0.258672i	$0.916715\pi$
$618$	−0.693409	−	6.11726i	−0.0278930	−	0.246072i
$619$	10.5816	+	18.3279i	0.425311	+	0.736660i	0.996449	−	0.0841934i	$-0.0268314\pi$
$619$	10.5816	+	18.3279i	0.425311	+	0.736660i	−0.571138	+	0.820854i	$0.693498\pi$
$620$	−7.13965			−0.286735
$621$	−37.5952	−	7.03500i	−1.50864	−	0.282305i
$622$	−50.6011			−2.02892
$623$		0			0
$624$	−4.89504	−	43.1841i	−0.195959	−	1.72875i
$625$	−0.725240	+	1.25615i	−0.0290096	+	0.0502461i
$626$	5.05726	−	8.75943i	0.202129	−	0.350097i
$627$	5.27764	−	3.90055i	0.210769	−	0.155773i
$628$	12.0301	+	20.8368i	0.480054	+	0.831477i
$629$	−0.872381			−0.0347841
$630$		0			0
$631$	4.74845			0.189033			0.0945164	−	0.995523i	$-0.469870\pi$
$631$	4.74845			0.189033			0.0945164	+	0.995523i	$0.469870\pi$
$632$	3.32329	+	5.75610i	0.132193	+	0.228965i
$633$	−9.02679	−	3.93114i	−0.358783	−	0.156249i
$634$	9.09350	−	15.7504i	0.361149	−	0.625529i
$635$	−5.67273	+	9.82546i	−0.225115	+	0.389911i
$636$	3.33510	+	1.45242i	0.132245	+	0.0575924i
$637$		0			0
$638$	−0.172562			−0.00683178
$639$	36.0526	−	8.27971i	1.42622	−	0.327540i
$640$	−11.4324			−0.451907
$641$	4.93735	+	8.55174i	0.195013	+	0.337773i	0.946905	−	0.321514i	$-0.104192\pi$
$641$	4.93735	+	8.55174i	0.195013	+	0.337773i	−0.751891	+	0.659287i	$0.770858\pi$
$642$	14.8223	−	10.9547i	0.584990	−	0.432349i
$643$	21.9748	−	38.0615i	0.866602	−	1.50100i	0.00115462	−	0.999999i	$-0.499632\pi$
$643$	21.9748	−	38.0615i	0.866602	−	1.50100i	0.865448	−	0.501000i	$-0.167034\pi$
$644$		0			0
$645$	−2.65590	−	23.4304i	−0.104576	−	0.922570i
$646$	−3.57095	−	6.18507i	−0.140497	−	0.243348i
$647$	−44.3872			−1.74504			−0.872521	−	0.488577i	$-0.837516\pi$
$647$	−44.3872			−1.74504			−0.872521	+	0.488577i	$0.837516\pi$
$648$	9.09306	−	4.40911i	0.357209	−	0.173206i
$649$	−12.7749			−0.501457
$650$	−15.3362	−	26.5631i	−0.601537	−	1.04189i
$651$		0			0
$652$	8.49341	−	14.7110i	0.332628	−	0.576128i
$653$	−20.9956	+	36.3655i	−0.821622	+	1.42309i	0.0828523	+	0.996562i	$0.473597\pi$
$653$	−20.9956	+	36.3655i	−0.821622	+	1.42309i	−0.904474	+	0.426529i	$0.859736\pi$
$654$	−21.1385	+	15.6228i	−0.826579	+	0.610901i
$655$	1.34374	+	2.32742i	0.0525042	+	0.0909399i
$656$	43.7451			1.70796
$657$	−8.06616	+	1.85245i	−0.314691	+	0.0722708i
$658$		0			0
$659$	−19.6365	−	34.0114i	−0.764928	−	1.32489i	−0.940284	−	0.340390i	$-0.889441\pi$
$659$	−19.6365	−	34.0114i	−0.764928	−	1.32489i	0.175356	−	0.984505i	$-0.443892\pi$
$660$	−4.45822	−	1.94154i	−0.173536	−	0.0755743i
$661$	0.0933694	−	0.161721i	0.00363165	−	0.00629020i	−0.864204	−	0.503142i	$-0.832177\pi$
$661$	0.0933694	−	0.161721i	0.00363165	−	0.00629020i	0.867836	+	0.496852i	$0.165511\pi$
$662$	−19.0515	+	32.9982i	−0.740459	+	1.28251i
$663$	12.7313	+	5.54446i	0.494444	+	0.215329i
$664$	3.14522	+	5.44769i	0.122058	+	0.211411i
$665$		0			0
$666$	−2.11911	−	2.27772i	−0.0821139	−	0.0882598i
$667$	−0.455947			−0.0176543
$668$	2.45014	+	4.24376i	0.0947987	+	0.164196i
$669$	−16.3286	+	12.0680i	−0.631302	+	0.466577i
$670$	8.51976	−	14.7567i	0.329147	−	0.570099i
$671$	−2.45046	+	4.24432i	−0.0945989	+	0.163850i
$672$		0			0
$673$	−5.43382	−	9.41166i	−0.209458	−	0.362793i	0.742086	−	0.670305i	$-0.233837\pi$
$673$	−5.43382	−	9.41166i	−0.209458	−	0.362793i	−0.951544	+	0.307512i	$0.900503\pi$
$674$	2.75725			0.106205
$675$	10.8830	−	12.6979i	0.418885	−	0.488741i
$676$	19.1717			0.737372
$677$	−14.1950	−	24.5865i	−0.545560	−	0.944937i	−0.998571	−	0.0534326i	$-0.982984\pi$
$677$	−14.1950	−	24.5865i	−0.545560	−	0.944937i	0.453012	−	0.891505i	$-0.350350\pi$
$678$	5.20910	+	45.9547i	0.200054	+	1.76488i
$679$		0			0
$680$	1.16071	−	2.01041i	0.0445111	−	0.0770956i
$681$	15.5771	−	11.5125i	0.596914	−	0.441162i
$682$	−5.35961	−	9.28312i	−0.205230	−	0.355469i
$683$	−11.8407			−0.453071			−0.226536	−	0.974003i	$-0.572740\pi$
$683$	−11.8407			−0.453071			−0.226536	+	0.974003i	$0.572740\pi$
$684$	3.06498	−	9.98398i	0.117192	−	0.381747i
$685$	2.95968			0.113083
$686$		0			0
$687$	15.3345	+	6.67810i	0.585046	+	0.254786i
$688$	−24.7230	+	42.8216i	−0.942557	+	1.63256i
$689$	3.90981	−	6.77199i	0.148952	−	0.257992i
$690$	−28.7267	−	12.5104i	−1.09361	−	0.476262i
$691$	−5.95416	−	10.3129i	−0.226507	−	0.392321i	0.730264	−	0.683165i	$-0.239397\pi$
$691$	−5.95416	−	10.3129i	−0.226507	−	0.392321i	−0.956770	+	0.290844i	$0.906064\pi$
$692$	14.0976			0.535909
$693$		0			0
$694$	54.3880			2.06454
$695$	0.504096	+	0.873119i	0.0191214	+	0.0331193i
$696$	0.0968803	−	0.0716014i	0.00367224	−	0.00271405i
$697$	−6.98857	+	12.1046i	−0.264711	+	0.458493i
$698$	−33.1435	+	57.4062i	−1.25450	+	2.17286i
$699$	3.76313	+	33.1984i	0.142335	+	1.25568i
$700$		0			0
$701$	−31.3902			−1.18559			−0.592795	−	0.805353i	$-0.701976\pi$
$701$	−31.3902			−1.18559			−0.592795	+	0.805353i	$0.701976\pi$
$702$	16.4497	+	46.7087i	0.620855	+	1.76291i
$703$	1.41042			0.0531949
$704$	1.97020	+	3.41249i	0.0742549	+	0.128613i
$705$	−2.47851	−	21.8654i	−0.0933461	−	0.823500i
$706$	−27.1518	+	47.0284i	−1.02187	+	1.76994i
$707$		0			0
$708$	−16.3495	+	12.0834i	−0.614451	+	0.454123i
$709$	−0.312609	−	0.541455i	−0.0117403	−	0.0203348i	0.860096	−	0.510133i	$-0.170404\pi$
$709$	−0.312609	−	0.541455i	−0.0117403	−	0.0203348i	−0.871836	+	0.489798i	$0.837070\pi$
$710$	30.3031			1.13726
$711$	−12.0961	−	13.0014i	−0.453638	−	0.487591i
$712$	−1.57937			−0.0591894
$713$	−14.1613	−	24.5281i	−0.530345	−	0.918584i
$714$		0			0
$715$	−5.22647	+	9.05251i	−0.195459	+	0.338545i
$716$	1.18245	−	2.04806i	0.0441901	−	0.0765395i
$717$	−0.618179	−	0.269215i	−0.0230863	−	0.0100540i
$718$	−4.98119	−	8.62768i	−0.185897	−	0.321982i
$719$	−24.3939			−0.909739			−0.454869	−	0.890558i	$-0.650314\pi$
$719$	−24.3939			−0.909739			−0.454869	+	0.890558i	$0.650314\pi$
$720$	18.9192	−	4.34492i	0.705078	−	0.161926i
$721$		0			0
$722$	−11.7185	−	20.2970i	−0.436116	−	0.755376i
$723$	14.8152	−	10.9495i	0.550984	−	0.407217i
$724$	11.8123	−	20.4595i	0.439002	−	0.760373i
$725$	0.0996792	−	0.172649i	0.00370199	−	0.00641204i
$726$	3.12888	+	27.6030i	0.116124	+	1.02444i
$727$	−18.9253	−	32.7796i	−0.701900	−	1.21573i	−0.967799	−	0.251726i	$-0.919002\pi$
$727$	−18.9253	−	32.7796i	−0.701900	−	1.21573i	0.265899	−	0.964001i	$-0.414331\pi$
$728$		0			0
$729$	−21.0415	+	16.9191i	−0.779314	+	0.626634i
$730$	−6.77982			−0.250932
$731$	−7.89934	−	13.6821i	−0.292168	−	0.506049i
$732$	0.878459	+	7.74977i	0.0324688	+	0.286440i
$733$	−1.20077	+	2.07980i	−0.0443516	+	0.0768193i	−0.887349	−	0.461098i	$-0.847456\pi$
$733$	−1.20077	+	2.07980i	−0.0443516	+	0.0768193i	0.842997	+	0.537918i	$0.180789\pi$
$734$	−21.2519	+	36.8093i	−0.784421	+	1.35866i
$735$		0			0
$736$	24.5858	+	42.5839i	0.906245	+	1.56966i
$737$	10.4903			0.386416
$738$	−48.5801	+	11.1567i	−1.78826	+	0.410685i
$739$	30.3880			1.11784			0.558920	−	0.829222i	$-0.311216\pi$
$739$	30.3880			1.11784			0.558920	+	0.829222i	$0.311216\pi$
$740$	−0.522533	−	0.905053i	−0.0192087	−	0.0332704i
$741$	−20.5833	−	8.96397i	−0.756148	−	0.329300i
$742$		0			0
$743$	−2.54785	+	4.41300i	−0.0934715	+	0.161897i	−0.908970	−	0.416862i	$-0.863130\pi$
$743$	−2.54785	+	4.41300i	−0.0934715	+	0.161897i	0.815498	+	0.578760i	$0.196463\pi$
$744$	6.86088	+	2.98789i	0.251532	+	0.109541i
$745$	−4.39467	−	7.61179i	−0.161008	−	0.278874i
$746$	−39.5922			−1.44957
$747$	−11.4480	−	12.3048i	−0.418859	−	0.450209i
$748$	−3.25793			−0.119122
$749$		0			0
$750$	28.1336	−	20.7927i	1.02729	−	0.759242i
$751$	0.487506	−	0.844384i	0.0177893	−	0.0308120i	−0.856994	−	0.515327i	$-0.827671\pi$
$751$	0.487506	−	0.844384i	0.0177893	−	0.0308120i	0.874783	+	0.484515i	$0.161004\pi$
$752$	−23.0718	+	39.9615i	−0.841341	+	1.45724i
$753$	−0.637198	−	5.62137i	−0.0232208	−	0.204854i
$754$	0.295165	+	0.511240i	0.0107493	+	0.0186183i
$755$	16.9075			0.615326
$756$		0			0
$757$	11.6346			0.422865			0.211433	−	0.977393i	$-0.432187\pi$
$757$	11.6346			0.422865			0.211433	+	0.977393i	$0.432187\pi$
$758$	5.26750	+	9.12357i	0.191324	+	0.331383i
$759$	−2.17264	−	19.1671i	−0.0788620	−	0.695721i
$760$	−1.87657	+	3.25031i	−0.0680703	+	0.117901i
$761$	27.0875	−	46.9169i	0.981920	−	1.70073i	0.327023	−	0.945016i	$-0.393955\pi$
$761$	27.0875	−	46.9169i	0.981920	−	1.70073i	0.654897	−	0.755718i	$-0.272712\pi$
$762$	−21.8000	+	16.1117i	−0.789729	+	0.583666i
$763$		0			0
$764$	31.5484			1.14138
$765$	−1.82020	+	5.92920i	−0.0658095	+	0.214371i
$766$	64.2978			2.32317
$767$	21.8513	+	37.8475i	0.789004	+	1.36659i
$768$	−33.3151	−	14.5086i	−1.20215	−	0.523534i
$769$	−10.4326	+	18.0698i	−0.376208	+	0.651612i	−0.990507	−	0.137462i	$-0.956106\pi$
$769$	−10.4326	+	18.0698i	−0.376208	+	0.651612i	0.614299	+	0.789074i	$0.289439\pi$
$770$		0			0
$771$	7.45681	+	3.24742i	0.268551	+	0.116953i
$772$	−4.30047	−	7.44863i	−0.154777	−	0.268082i
$773$	54.9945			1.97801			0.989007	−	0.147868i	$-0.0472409\pi$
$773$	54.9945			1.97801			0.989007	+	0.147868i	$0.0472409\pi$
$774$	16.5344	−	53.8598i	0.594316	−	1.93595i
$775$	12.3838			0.444839
$776$	−6.84616	−	11.8579i	−0.245763	−	0.425674i
$777$		0			0
$778$	−26.5895	+	46.0544i	−0.953281	+	1.65113i
$779$	11.2987	−	19.5700i	0.404819	−	0.701168i
$780$	1.87363	+	16.5291i	0.0670865	+	0.591838i
$781$	9.32802	+	16.1566i	0.333783	+	0.578129i
$782$	−20.9926			−0.750693
$783$	−0.209456	+	0.244386i	−0.00748534	+	0.00873364i
$784$		0			0
$785$	11.5506	+	20.0062i	0.412258	+	0.714051i
$786$	0.723227	+	6.38032i	0.0257967	+	0.227578i
$787$	−4.59475	+	7.95833i	−0.163785	+	0.283684i	−0.936223	−	0.351406i	$-0.885704\pi$
$787$	−4.59475	+	7.95833i	−0.163785	+	0.283684i	0.772438	+	0.635090i	$0.219037\pi$
$788$	−6.79103	+	11.7624i	−0.241921	+	0.419019i
$789$	27.2312	−	20.1258i	0.969457	−	0.716498i
$790$	−7.27374	−	12.5985i	−0.258788	−	0.448234i
$791$		0			0
$792$	3.47163	+	3.73146i	0.123359	+	0.132592i
$793$	16.7659			0.595375
$794$	−10.2967	−	17.8344i	−0.365416	−	0.632919i
$795$	3.20216	+	1.39453i	0.113569	+	0.0494588i
$796$	−6.03296	+	10.4494i	−0.213832	+	0.370369i
$797$	3.53774	−	6.12754i	0.125313	−	0.217049i	−0.796542	−	0.604583i	$-0.793340\pi$
$797$	3.53774	−	6.12754i	0.125313	−	0.217049i	0.921855	+	0.387534i	$0.126673\pi$
$798$		0			0
$799$	−7.37174	−	12.7682i	−0.260793	−	0.451707i
$800$	−21.4998			−0.760133
$801$	4.11266	−	0.944500i	0.145314	−	0.0333723i
$802$	1.99245			0.0703558
$803$	−2.08699	−	3.61477i	−0.0736483	−	0.127563i
$804$	13.4257	−	9.92255i	0.473488	−	0.349941i
$805$		0			0
$806$	−18.3351	+	31.7573i	−0.645827	+	1.11860i
$807$	−3.07594	−	27.1360i	−0.108278	−	0.955232i
$808$	−0.628050	−	1.08781i	−0.0220947	−	0.0382692i
$809$	5.94119			0.208881			0.104441	−	0.994531i	$-0.466695\pi$
$809$	5.94119			0.208881			0.104441	+	0.994531i	$0.466695\pi$
$810$	−19.9022	+	9.65030i	−0.699291	+	0.339077i
$811$	44.4139			1.55958			0.779791	−	0.626039i	$-0.215325\pi$
$811$	44.4139			1.55958			0.779791	+	0.626039i	$0.215325\pi$
$812$		0			0
$813$	−2.88678	−	25.4672i	−0.101244	−	0.893173i
$814$	0.784512	−	1.35881i	0.0274971	−	0.0476264i
$815$	8.15485	−	14.1246i	0.285652	−	0.494764i
$816$	10.4592	−	7.73007i	0.366144	−	0.270606i
$817$	12.7712	+	22.1204i	0.446808	+	0.773894i
$818$	40.0191			1.39924
$819$		0			0
$820$	−16.7439			−0.584721
$821$	−3.17761	−	5.50378i	−0.110899	−	0.192083i	0.805234	−	0.592958i	$-0.202040\pi$
$821$	−3.17761	−	5.50378i	−0.110899	−	0.192083i	−0.916133	+	0.400874i	$0.868706\pi$
$822$	6.48341	+	2.82350i	0.226135	+	0.0984810i
$823$	4.73216	−	8.19635i	0.164953	−	0.285707i	−0.771686	−	0.636004i	$-0.780586\pi$
$823$	4.73216	−	8.19635i	0.164953	−	0.285707i	0.936639	+	0.350297i	$0.113919\pi$
$824$	−1.08380	+	1.87720i	−0.0377560	+	0.0653953i
$825$	7.73282	+	3.36762i	0.269222	+	0.117245i
$826$		0			0
$827$	−4.86261			−0.169090			−0.0845448	−	0.996420i	$-0.526944\pi$
$827$	−4.86261			−0.169090			−0.0845448	+	0.996420i	$0.526944\pi$
$828$	−20.9103	−	22.4753i	−0.726682	−	0.781070i
$829$	−40.7853			−1.41653			−0.708266	−	0.705946i	$-0.750522\pi$
$829$	−40.7853			−1.41653			−0.708266	+	0.705946i	$0.750522\pi$
$830$	−6.88402	−	11.9235i	−0.238948	−	0.413870i
$831$	−10.3789	+	7.67075i	−0.360040	+	0.266095i
$832$	6.74003	−	11.6741i	0.233668	−	0.404725i
$833$		0			0
$834$	0.271315	+	2.39354i	0.00939486	+	0.0828815i
$835$	2.35247	+	4.07460i	0.0814107	+	0.141007i
$836$	5.26724			0.182171
$837$	−19.6525	−	3.67747i	−0.679289	−	0.127112i
$838$	46.3645			1.60164
$839$	9.60171	+	16.6307i	0.331488	+	0.574154i	0.982804	−	0.184653i	$-0.0591161\pi$
$839$	9.60171	+	16.6307i	0.331488	+	0.574154i	−0.651316	+	0.758807i	$0.725783\pi$
$840$		0			0
$841$	14.4981	−	25.1114i	0.499934	−	0.865911i
$842$	27.3063	−	47.2959i	0.941036	−	1.62992i
$843$	36.1985	−	26.7533i	1.24674	−	0.921432i
$844$	−3.95113	−	6.84355i	−0.136003	−	0.235565i
$845$	18.4075			0.633236
$846$	15.4300	−	50.2625i	0.530496	−	1.72806i
$847$		0			0
$848$	−3.66188	−	6.34256i	−0.125749	−	0.217804i
$849$	−29.7835	−	12.9706i	−1.02217	−	0.445150i
$850$	4.58940	−	7.94907i	0.157415	−	0.272651i
$851$	2.07286	−	3.59029i	0.0710566	−	0.123074i
$852$	27.2203	+	11.8543i	0.932552	+	0.406123i
$853$	−6.95055	−	12.0387i	−0.237982	−	0.412198i	0.722153	−	0.691734i	$-0.243153\pi$
$853$	−6.95055	−	12.0387i	−0.237982	−	0.412198i	−0.960135	+	0.279536i	$0.909819\pi$
$854$		0			0
$855$	2.94280	−	9.58601i	0.100642	−	0.327835i
$856$	−6.48937			−0.221802
$857$	−28.4919	−	49.3494i	−0.973265	−	1.68574i	−0.685547	−	0.728029i	$-0.740437\pi$
$857$	−28.4919	−	49.3494i	−0.973265	−	1.68574i	−0.287718	−	0.957715i	$-0.592897\pi$
$858$	−20.0850	+	14.8442i	−0.685691	+	0.506774i
$859$	10.0501	−	17.4073i	0.342905	−	0.593929i	−0.642066	−	0.766650i	$-0.721922\pi$
$859$	10.0501	−	17.4073i	0.342905	−	0.593929i	0.984971	+	0.172721i	$0.0552557\pi$
$860$	9.46298	−	16.3904i	0.322685	−	0.558907i
$861$		0			0
$862$	−4.50214	−	7.79794i	−0.153344	−	0.265599i
$863$	6.17786			0.210297			0.105148	−	0.994457i	$-0.466468\pi$
$863$	6.17786			0.210297			0.105148	+	0.994457i	$0.466468\pi$
$864$	34.1192	+	6.38455i	1.16076	+	0.217207i
$865$	13.5356			0.460225
$866$	8.94318	+	15.4900i	0.303902	+	0.526373i
$867$	−2.84838	−	25.1285i	−0.0967361	−	0.853407i
$868$		0			0
$869$	4.47806	−	7.75623i	0.151908	−	0.263112i
$870$	−0.212044	+	0.156716i	−0.00718896	+	0.00531315i
$871$	−17.9436	−	31.0792i	−0.607996	−	1.05308i
$872$	9.25465			0.313402
$873$	24.9186	+	26.7837i	0.843367	+	0.906489i
$874$	33.9396			1.14802
$875$		0			0
$876$	−6.09009	−	2.65221i	−0.205765	−	0.0896099i
$877$	18.6287	−	32.2658i	0.629046	−	1.08954i	−0.358697	−	0.933454i	$-0.616779\pi$
$877$	18.6287	−	32.2658i	0.629046	−	1.08954i	0.987743	−	0.156086i	$-0.0498877\pi$
$878$	−13.6468	+	23.6370i	−0.460558	+	0.797710i
$879$	−3.90930	−	1.70249i	−0.131857	−	0.0574234i
$880$	4.89504	+	8.47846i	0.165012	+	0.285809i
$881$	−11.7848			−0.397041			−0.198520	−	0.980097i	$-0.563614\pi$
$881$	−11.7848			−0.397041			−0.198520	+	0.980097i	$0.563614\pi$
$882$		0			0
$883$	−29.2308			−0.983693			−0.491847	−	0.870682i	$-0.663678\pi$
$883$	−29.2308			−0.983693			−0.491847	+	0.870682i	$0.663678\pi$
$884$	5.57265	+	9.65211i	0.187428	+	0.324636i
$885$	−15.6978	+	11.6018i	−0.527675	+	0.389989i
$886$	−20.1634	+	34.9240i	−0.677402	+	1.17329i
$887$	−14.2581	+	24.6957i	−0.478739	+	0.829201i	−0.999703	−	0.0243782i	$-0.992239\pi$
$887$	−14.2581	+	24.6957i	−0.478739	+	0.829201i	0.520964	+	0.853579i	$0.325573\pi$
$888$	0.123372	+	1.08839i	0.00414010	+	0.0365240i
$889$		0			0
$890$	3.45680			0.115872
$891$	−11.2716	−	7.64057i	−0.377612	−	0.255969i
$892$	−16.2964			−0.545645
$893$	11.9182	+	20.6430i	0.398828	+	0.690790i
$894$	−2.36530	−	20.8667i	−0.0791075	−	0.697887i
$895$	1.13531	−	1.96642i	0.0379493	−	0.0657301i
$896$		0			0
$897$	−53.0691	+	39.2219i	−1.77193	+	1.30958i
$898$	19.7890	+	34.2755i	0.660366	+	1.14379i
$899$	−0.238341			−0.00794912
$900$	13.0819	−	3.00435i	0.436064	−	0.100145i
$901$	2.34004			0.0779579
$902$	−12.5693	−	21.7707i	−0.418513	−	0.724885i
$903$		0			0
$904$	8.14183	−	14.1021i	0.270793	−	0.469028i
$905$	11.3415	−	19.6440i	0.377003	−	0.652989i
$906$	37.0372	+	16.1296i	1.23048	+	0.535869i
$907$	3.94577	+	6.83428i	0.131017	+	0.226929i	0.924069	−	0.382226i	$-0.124842\pi$
$907$	3.94577	+	6.83428i	0.131017	+	0.226929i	−0.793052	+	0.609154i	$0.791509\pi$
$908$	15.5463			0.515923
$909$	2.28597	+	2.45707i	0.0758209	+	0.0814957i
$910$		0			0
$911$	−14.2206	−	24.6308i	−0.471150	−	0.816055i	0.528306	−	0.849054i	$-0.322827\pi$
$911$	−14.2206	−	24.6308i	−0.471150	−	0.816055i	−0.999455	+	0.0329991i	$0.989494\pi$
$912$	−16.9098	+	12.4975i	−0.559939	+	0.413835i
$913$	4.23813	−	7.34065i	0.140262	−	0.242940i
$914$	37.4007	−	64.7798i	1.23710	−	2.14273i
$915$	0.843442	+	7.44086i	0.0278833	+	0.245987i
$916$	6.71206	+	11.6256i	0.221773	+	0.384121i
$917$		0			0
$918$	−9.64370	+	11.2519i	−0.318290	+	0.371369i
$919$	−7.98542			−0.263415			−0.131707	−	0.991289i	$-0.542046\pi$
$919$	−7.98542			−0.263415			−0.131707	+	0.991289i	$0.542046\pi$
$920$	5.51590	+	9.55382i	0.181854	+	0.314980i
$921$	−0.909630	−	8.02476i	−0.0299733	−	0.264425i
$922$	−2.60610	+	4.51390i	−0.0858274	+	0.148657i
$923$	31.9110	−	55.2714i	1.05036	−	1.81928i
$924$		0			0
$925$	0.906337	+	1.56982i	0.0298002	+	0.0516154i
$926$	−51.3059			−1.68602
$927$	1.69960	−	5.53634i	0.0558221	−	0.181837i
$928$	0.413790			0.0135833
$929$	−9.40031	−	16.2818i	−0.308414	−	0.534189i	0.669601	−	0.742721i	$-0.266465\pi$
$929$	−9.40031	−	16.2818i	−0.308414	−	0.534189i	−0.978016	+	0.208531i	$0.933132\pi$
$930$	−15.0166	−	6.53966i	−0.492412	−	0.214444i
$931$		0			0
$932$	−13.4081	+	23.2234i	−0.439196	+	0.760709i
$933$	−43.6414	−	19.0057i	−1.42876	−	0.622219i
$934$	24.5288	+	42.4852i	0.802608	+	1.39016i
$935$	−3.12806			−0.102299
$936$	5.11685	−	16.6678i	0.167250	−	0.544806i
$937$	48.5788			1.58700			0.793500	−	0.608570i	$-0.208256\pi$
$937$	48.5788			1.58700			0.793500	+	0.608570i	$0.208256\pi$
$938$		0			0
$939$	7.65172	−	5.65516i	0.249704	−	0.184549i
$940$	8.83094	−	15.2956i	0.288034	−	0.498889i
$941$	−10.2425	+	17.7406i	−0.333898	+	0.578328i	−0.983272	−	0.182141i	$-0.941697\pi$
$941$	−10.2425	+	17.7406i	−0.333898	+	0.578328i	0.649375	+	0.760468i	$0.275031\pi$
$942$	6.21676	+	54.8443i	0.202553	+	1.78692i
$943$	−33.2110	−	57.5231i	−1.08150	−	1.87321i
$944$	40.9312			1.33220
$945$		0			0
$946$	28.4148			0.923843
$947$	7.42524	+	12.8609i	0.241288	+	0.417923i	0.961081	−	0.276265i	$-0.0890969\pi$
$947$	7.42524	+	12.8609i	0.241288	+	0.417923i	−0.719793	+	0.694188i	$0.755764\pi$
$948$	−1.60533	−	14.1622i	−0.0521387	−	0.459968i
$949$	−7.13954	+	12.3661i	−0.231759	+	0.401419i
$950$	−7.41989	+	12.8516i	−0.240733	+	0.416962i
$951$	13.7586	−	10.1686i	0.446154	−	0.329739i
$952$		0			0
$953$	46.4678			1.50524			0.752620	−	0.658456i	$-0.228790\pi$
$953$	46.4678			1.50524			0.752620	+	0.658456i	$0.228790\pi$
$954$	5.68422	+	6.10965i	0.184033	+	0.197807i
$955$	30.2908			0.980188
$956$	−0.270584	−	0.468665i	−0.00875130	−	0.0151577i
$957$	−0.148828	−	0.0648139i	−0.00481091	−	0.00209514i
$958$	−29.0724	+	50.3548i	−0.939285	+	1.62689i
$959$		0			0
$960$	5.52012	+	2.40399i	0.178161	+	0.0775886i
$961$	8.09733	+	14.0250i	0.261204	+	0.452419i
$962$	−5.36759			−0.173058
$963$	16.8982	−	3.88079i	0.544538	−	0.125057i
$964$	14.7860			0.476226
$965$	−4.12905	−	7.15172i	−0.132919	−	0.230222i
$966$		0			0
$967$	0.863670	−	1.49592i	0.0277738	−	0.0481056i	−0.851804	−	0.523860i	$-0.824492\pi$
$967$	0.863670	−	1.49592i	0.0277738	−	0.0481056i	0.879578	+	0.475754i	$0.157825\pi$
$968$	4.89045	−	8.47050i	0.157185	−	0.272252i
$969$	−0.756700	−	6.67562i	−0.0243087	−	0.214452i
$970$	14.9843	+	25.9536i	0.481118	+	0.833320i
$971$	7.56171			0.242667			0.121333	−	0.992612i	$-0.461283\pi$
$971$	7.56171			0.242667			0.121333	+	0.992612i	$0.461283\pi$
$972$	−21.6526	+	0.882976i	−0.694506	+	0.0283215i
$973$		0			0
$974$	0.281870	+	0.488213i	0.00903169	+	0.0156434i
$975$	−3.24982	−	28.6699i	−0.104077	−	0.918173i
$976$	7.85137	−	13.5990i	0.251316	−	0.435293i
$977$	28.3101	−	49.0345i	0.905721	−	1.56875i	0.0857737	−	0.996315i	$-0.472664\pi$
$977$	28.3101	−	49.0345i	0.905721	−	1.56875i	0.819947	−	0.572440i	$-0.194003\pi$
$978$	31.3386	−	23.1615i	1.00210	−	0.740622i
$979$	1.06408	+	1.84305i	0.0340083	+	0.0589041i
$980$		0			0
$981$	−24.0990	+	5.53449i	−0.769422	+	0.176703i
$982$	−33.3994			−1.06582
$983$	−16.1486	−	27.9702i	−0.515061	−	0.892112i	−0.999847	−	0.0174790i	$-0.994436\pi$
$983$	−16.1486	−	27.9702i	−0.515061	−	0.892112i	0.484786	−	0.874633i	$-0.338897\pi$
$984$	16.0901	+	7.00718i	0.512934	+	0.223381i
$985$	−6.52033	+	11.2936i	−0.207755	+	0.359842i
$986$	−0.0883286	+	0.152990i	−0.00281296	+	0.00487218i
$987$		0			0
$988$	−9.00955	−	15.6050i	−0.286632	−	0.496461i
$989$	75.0782			2.38735
$990$	−7.59842	−	8.16713i	−0.241494	−	0.259568i
$991$	14.3100			0.454573			0.227287	−	0.973828i	$-0.427015\pi$
$991$	14.3100			0.454573			0.227287	+	0.973828i	$0.427015\pi$
$992$	12.8520	+	22.2602i	0.408050	+	0.706764i
$993$	−28.8253	+	21.3039i	−0.914742	+	0.676059i
$994$		0			0
$995$	−5.79247	+	10.0329i	−0.183634	+	0.318063i
$996$	−1.51932	−	13.4034i	−0.0481414	−	0.424704i
$997$	−28.1262	−	48.7160i	−0.890765	−	1.54285i	−0.838960	−	0.544194i	$-0.816836\pi$
$997$	−28.1262	−	48.7160i	−0.890765	−	1.54285i	−0.0518058	−	0.998657i	$-0.516498\pi$
$998$	39.2353			1.24197
$999$	−0.972142	−	2.76038i	−0.0307572	−	0.0873345i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.f.e.148.4		10
3.2	odd	2		1323.2.f.e.442.2		10
7.2	even	3		63.2.g.b.4.4	✓	10
7.3	odd	6		441.2.h.f.373.2		10
7.4	even	3		63.2.h.b.58.2	yes	10
7.5	odd	6		441.2.g.f.67.4		10
7.6	odd	2		441.2.f.f.148.4		10
9.2	odd	6		1323.2.f.e.883.2		10
9.4	even	3		3969.2.a.z.1.2		5
9.5	odd	6		3969.2.a.bc.1.4		5
9.7	even	3	inner	441.2.f.e.295.4		10
21.2	odd	6		189.2.g.b.172.2		10
21.5	even	6		1323.2.g.f.361.2		10
21.11	odd	6		189.2.h.b.37.4		10
21.17	even	6		1323.2.h.f.226.4		10
21.20	even	2		1323.2.f.f.442.2		10
28.11	odd	6		1008.2.q.i.625.2		10
28.23	odd	6		1008.2.t.i.193.5		10
63.2	odd	6		189.2.h.b.46.4		10
63.4	even	3		567.2.e.f.163.4		10
63.11	odd	6		189.2.g.b.100.2		10
63.13	odd	6		3969.2.a.ba.1.2		5
63.16	even	3		63.2.h.b.25.2	yes	10
63.20	even	6		1323.2.f.f.883.2		10
63.23	odd	6		567.2.e.e.487.2		10
63.25	even	3		63.2.g.b.16.4	yes	10
63.32	odd	6		567.2.e.e.163.2		10
63.34	odd	6		441.2.f.f.295.4		10
63.38	even	6		1323.2.g.f.667.2		10
63.41	even	6		3969.2.a.bb.1.4		5
63.47	even	6		1323.2.h.f.802.4		10
63.52	odd	6		441.2.g.f.79.4		10
63.58	even	3		567.2.e.f.487.4		10
63.61	odd	6		441.2.h.f.214.2		10
84.11	even	6		3024.2.q.i.2305.4		10
84.23	even	6		3024.2.t.i.1873.2		10
252.11	even	6		3024.2.t.i.289.2		10
252.79	odd	6		1008.2.q.i.529.2		10
252.151	odd	6		1008.2.t.i.961.5		10
252.191	even	6		3024.2.q.i.2881.4		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.g.b.4.4	✓	10	7.2	even	3
63.2.g.b.16.4	yes	10	63.25	even	3
63.2.h.b.25.2	yes	10	63.16	even	3
63.2.h.b.58.2	yes	10	7.4	even	3
189.2.g.b.100.2		10	63.11	odd	6
189.2.g.b.172.2		10	21.2	odd	6
189.2.h.b.37.4		10	21.11	odd	6
189.2.h.b.46.4		10	63.2	odd	6
441.2.f.e.148.4		10	1.1	even	1	trivial
441.2.f.e.295.4		10	9.7	even	3	inner
441.2.f.f.148.4		10	7.6	odd	2
441.2.f.f.295.4		10	63.34	odd	6
441.2.g.f.67.4		10	7.5	odd	6
441.2.g.f.79.4		10	63.52	odd	6
441.2.h.f.214.2		10	63.61	odd	6
441.2.h.f.373.2		10	7.3	odd	6
567.2.e.e.163.2		10	63.32	odd	6
567.2.e.e.487.2		10	63.23	odd	6
567.2.e.f.163.4		10	63.4	even	3
567.2.e.f.487.4		10	63.58	even	3
1008.2.q.i.529.2		10	252.79	odd	6
1008.2.q.i.625.2		10	28.11	odd	6
1008.2.t.i.193.5		10	28.23	odd	6
1008.2.t.i.961.5		10	252.151	odd	6
1323.2.f.e.442.2		10	3.2	odd	2
1323.2.f.e.883.2		10	9.2	odd	6
1323.2.f.f.442.2		10	21.20	even	2
1323.2.f.f.883.2		10	63.20	even	6
1323.2.g.f.361.2		10	21.5	even	6
1323.2.g.f.667.2		10	63.38	even	6
1323.2.h.f.226.4		10	21.17	even	6
1323.2.h.f.802.4		10	63.47	even	6
3024.2.q.i.2305.4		10	84.11	even	6
3024.2.q.i.2881.4		10	252.191	even	6
3024.2.t.i.289.2		10	252.11	even	6
3024.2.t.i.1873.2		10	84.23	even	6
3969.2.a.z.1.2		5	9.4	even	3
3969.2.a.ba.1.2		5	63.13	odd	6
3969.2.a.bb.1.4		5	63.41	even	6
3969.2.a.bc.1.4		5	9.5	odd	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:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	441.f (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.920620 + 1.59456i) q^{2} +(0.195084 + 1.72103i) q^{3} +(-0.695084 + 1.20392i) q^{4} +(-0.667377 + 1.15593i) q^{5} +(-2.56469 + 1.89549i) q^{6} +1.12285 q^{8} +(-2.92388 + 0.671489i) q^{9} +O(q^{10})\)	\(q+(0.920620 + 1.59456i) q^{2} +(0.195084 + 1.72103i) q^{3} +(-0.695084 + 1.20392i) q^{4} +(-0.667377 + 1.15593i) q^{5} +(-2.56469 + 1.89549i) q^{6} +1.12285 q^{8} +(-2.92388 + 0.671489i) q^{9} -2.45760 q^{10} +(-0.756508 - 1.31031i) q^{11} +(-2.20758 - 0.961394i) q^{12} +(-2.58800 + 4.48254i) q^{13} +(-2.11958 - 0.923072i) q^{15} +(2.42388 + 4.19829i) q^{16} -1.54893 q^{17} +(-3.76252 - 4.04413i) q^{18} +2.50422 q^{19} +(-0.927765 - 1.60694i) q^{20} +(1.39291 - 2.41260i) q^{22} +(3.68039 - 6.37463i) q^{23} +(0.219049 + 1.93246i) q^{24} +(1.60922 + 2.78725i) q^{25} -9.53025 q^{26} +(-1.72605 - 4.90110i) q^{27} +(-0.0309713 - 0.0536439i) q^{29} +(-0.479438 - 4.22961i) q^{30} +(1.92388 - 3.33227i) q^{31} +(-3.34011 + 5.78523i) q^{32} +(2.10750 - 1.55759i) q^{33} +(-1.42597 - 2.46986i) q^{34} +(1.22392 - 3.98687i) q^{36} +0.563216 q^{37} +(2.30543 + 3.99313i) q^{38} +(-8.21946 - 3.57955i) q^{39} +(-0.749363 + 1.29794i) q^{40} +(4.51188 - 7.81481i) q^{41} +(5.09988 + 8.83325i) q^{43} +2.10335 q^{44} +(1.17514 - 3.82794i) q^{45} +13.5530 q^{46} +(4.75925 + 8.24327i) q^{47} +(-6.75252 + 4.99060i) q^{48} +(-2.96296 + 5.13199i) q^{50} +(-0.302170 - 2.66575i) q^{51} +(-3.59775 - 6.23148i) q^{52} -1.51075 q^{53} +(6.22605 - 7.26435i) q^{54} +2.01950 q^{55} +(0.488532 + 4.30983i) q^{57} +(0.0570257 - 0.0987714i) q^{58} +(4.22166 - 7.31212i) q^{59} +(2.58459 - 1.91020i) q^{60} +(-1.61958 - 2.80520i) q^{61} +7.08467 q^{62} -2.60434 q^{64} +(-3.45434 - 5.98309i) q^{65} +(4.42388 + 1.92659i) q^{66} +(-3.46670 + 6.00449i) q^{67} +(1.07663 - 1.86478i) q^{68} +(11.6889 + 5.09048i) q^{69} -12.3304 q^{71} +(-3.28308 + 0.753981i) q^{72} +2.75871 q^{73} +(0.518508 + 0.898083i) q^{74} +(-4.48300 + 3.31326i) q^{75} +(-1.74064 + 3.01488i) q^{76} +(-1.85920 - 16.4018i) q^{78} +(2.95969 + 5.12633i) q^{79} -6.47058 q^{80} +(8.09820 - 3.92671i) q^{81} +16.6149 q^{82} +(2.80111 + 4.85167i) q^{83} +(1.03372 - 1.79045i) q^{85} +(-9.39010 + 16.2641i) q^{86} +(0.0862808 - 0.0637676i) q^{87} +(-0.849444 - 1.47128i) q^{88} -1.40657 q^{89} +(7.18575 - 1.65025i) q^{90} +(5.11636 + 8.86180i) q^{92} +(6.11025 + 2.66099i) q^{93} +(-8.76293 + 15.1778i) q^{94} +(-1.67126 + 2.89470i) q^{95} +(-10.6082 - 4.61982i) q^{96} +(-6.09713 - 10.5605i) q^{97} +(3.09180 + 3.32321i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 2 q^{2} - q^{3} - 4 q^{4} + 4 q^{5} - 2 q^{6} - 6 q^{8} - 7 q^{9}+O(q^{10}) \) 10 * q + 2 * q^2 - q^3 - 4 * q^4 + 4 * q^5 - 2 * q^6 - 6 * q^8 - 7 * q^9	\( 10 q + 2 q^{2} - q^{3} - 4 q^{4} + 4 q^{5} - 2 q^{6} - 6 q^{8} - 7 q^{9} + 14 q^{10} + 4 q^{11} - 2 q^{12} - 8 q^{13} - 19 q^{15} + 2 q^{16} - 24 q^{17} - 2 q^{18} - 2 q^{19} + 5 q^{20} - q^{22} + 3 q^{23} - 9 q^{24} - q^{25} - 22 q^{26} - 7 q^{27} + 7 q^{29} + 10 q^{30} - 3 q^{31} - 2 q^{32} - 13 q^{33} + 3 q^{34} + 34 q^{36} + 20 q^{38} - 22 q^{39} - 3 q^{40} + 5 q^{41} - 7 q^{43} + 20 q^{44} + 17 q^{45} - 6 q^{46} + 27 q^{47} - 5 q^{48} + 19 q^{50} - 15 q^{51} - 10 q^{52} + 42 q^{53} + 52 q^{54} + 4 q^{55} - 4 q^{57} - 10 q^{58} + 30 q^{59} + 31 q^{60} - 14 q^{61} - 12 q^{62} - 50 q^{64} - 11 q^{65} + 22 q^{66} - 2 q^{67} + 27 q^{68} + 15 q^{69} - 6 q^{71} - 12 q^{72} - 30 q^{73} - 36 q^{74} - 17 q^{75} + 5 q^{76} - 20 q^{78} - 4 q^{79} - 40 q^{80} - 31 q^{81} + 10 q^{82} + 9 q^{83} - 6 q^{85} - 8 q^{86} - 34 q^{87} - 18 q^{88} - 56 q^{89} + 28 q^{90} + 27 q^{92} + 18 q^{93} - 3 q^{94} - 14 q^{95} - 58 q^{96} - 12 q^{97} + 35 q^{99}+O(q^{100}) \) 10 * q + 2 * q^2 - q^3 - 4 * q^4 + 4 * q^5 - 2 * q^6 - 6 * q^8 - 7 * q^9 + 14 * q^10 + 4 * q^11 - 2 * q^12 - 8 * q^13 - 19 * q^15 + 2 * q^16 - 24 * q^17 - 2 * q^18 - 2 * q^19 + 5 * q^20 - q^22 + 3 * q^23 - 9 * q^24 - q^25 - 22 * q^26 - 7 * q^27 + 7 * q^29 + 10 * q^30 - 3 * q^31 - 2 * q^32 - 13 * q^33 + 3 * q^34 + 34 * q^36 + 20 * q^38 - 22 * q^39 - 3 * q^40 + 5 * q^41 - 7 * q^43 + 20 * q^44 + 17 * q^45 - 6 * q^46 + 27 * q^47 - 5 * q^48 + 19 * q^50 - 15 * q^51 - 10 * q^52 + 42 * q^53 + 52 * q^54 + 4 * q^55 - 4 * q^57 - 10 * q^58 + 30 * q^59 + 31 * q^60 - 14 * q^61 - 12 * q^62 - 50 * q^64 - 11 * q^65 + 22 * q^66 - 2 * q^67 + 27 * q^68 + 15 * q^69 - 6 * q^71 - 12 * q^72 - 30 * q^73 - 36 * q^74 - 17 * q^75 + 5 * q^76 - 20 * q^78 - 4 * q^79 - 40 * q^80 - 31 * q^81 + 10 * q^82 + 9 * q^83 - 6 * q^85 - 8 * q^86 - 34 * q^87 - 18 * q^88 - 56 * q^89 + 28 * q^90 + 27 * q^92 + 18 * q^93 - 3 * q^94 - 14 * q^95 - 58 * q^96 - 12 * q^97 + 35 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more