LMFDB - Embedded newform 441.2.g.f.67.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,2,Mod(67,441)]

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, 4]))

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

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

chi := DirichletCharacter("441.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.g (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.52140272914$
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:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			67.4
Root			$0.920620 - 1.59456i$ of defining polynomial
Character	$\chi$	$=$	441.67
Dual form			441.2.g.f.79.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.920620 - 1.59456i) q^{2} +(1.58800 + 0.691567i) q^{3} +(-0.695084 - 1.20392i) q^{4} -1.33475 q^{5} +(2.56469 - 1.89549i) q^{6} +1.12285 q^{8} +(2.04347 + 2.19641i) q^{9} +O(q^{10})$	\(q+(0.920620 - 1.59456i) q^{2} +(1.58800 + 0.691567i) q^{3} +(-0.695084 - 1.20392i) q^{4} -1.33475 q^{5} +(2.56469 - 1.89549i) q^{6} +1.12285 q^{8} +(2.04347 + 2.19641i) q^{9} +(-1.22880 + 2.12835i) q^{10} +1.51302 q^{11} +(-0.271199 - 2.39252i) q^{12} +(2.58800 - 4.48254i) q^{13} +(-2.11958 - 0.923072i) q^{15} +(2.42388 - 4.19829i) q^{16} +(-0.774463 + 1.34141i) q^{17} +(5.38358 - 1.23637i) q^{18} +(1.25211 + 2.16872i) q^{19} +(0.927765 + 1.60694i) q^{20} +(1.39291 - 2.41260i) q^{22} -7.36079 q^{23} +(1.78308 + 0.776526i) q^{24} -3.21843 q^{25} +(-4.76513 - 8.25344i) q^{26} +(1.72605 + 4.90110i) q^{27} +(-0.0309713 - 0.0536439i) q^{29} +(-3.42323 + 2.53001i) q^{30} +(-1.92388 - 3.33227i) q^{31} +(-3.34011 - 5.78523i) q^{32} +(2.40267 + 1.04635i) q^{33} +(1.42597 + 2.46986i) q^{34} +(1.22392 - 3.98687i) q^{36} +(-0.281608 - 0.487760i) q^{37} +4.61087 q^{38} +(7.20971 - 5.32849i) q^{39} -1.49873 q^{40} +(-4.51188 + 7.81481i) q^{41} +(5.09988 + 8.83325i) q^{43} +(-1.05167 - 1.82155i) q^{44} +(-2.72753 - 2.93167i) q^{45} +(-6.77649 + 11.7372i) q^{46} +(-4.75925 + 8.24327i) q^{47} +(6.75252 - 4.99060i) q^{48} +(-2.96296 + 5.13199i) q^{50} +(-2.15752 + 1.59456i) q^{51} -7.19550 q^{52} +(0.755374 - 1.30835i) q^{53} +(9.40414 + 1.75975i) q^{54} -2.01950 q^{55} +(0.488532 + 4.30983i) q^{57} -0.114051 q^{58} +(-4.22166 - 7.31212i) q^{59} +(0.361984 + 3.19342i) q^{60} +(1.61958 - 2.80520i) q^{61} -7.08467 q^{62} -2.60434 q^{64} +(-3.45434 + 5.98309i) q^{65} +(3.88042 - 2.86790i) q^{66} +(-3.46670 - 6.00449i) q^{67} +2.15327 q^{68} +(-11.6889 - 5.09048i) q^{69} -12.3304 q^{71} +(2.29451 + 2.46624i) q^{72} +(1.37936 - 2.38912i) q^{73} -1.03702 q^{74} +(-5.11086 - 2.22576i) q^{75} +(1.74064 - 3.01488i) q^{76} +(-1.85920 - 16.4018i) q^{78} +(2.95969 - 5.12633i) q^{79} +(-3.23529 + 5.60368i) q^{80} +(-0.648467 + 8.97661i) q^{81} +(8.30746 + 14.3889i) q^{82} +(-2.80111 - 4.85167i) q^{83} +(1.03372 - 1.79045i) q^{85} +18.7802 q^{86} +(-0.0120840 - 0.106605i) q^{87} +1.69889 q^{88} +(-0.703287 - 1.21813i) q^{89} +(-7.18575 + 1.65025i) q^{90} +(5.11636 + 8.86180i) q^{92} +(-0.750637 - 6.62212i) q^{93} +(8.76293 + 15.1778i) q^{94} +(-1.67126 - 2.89470i) q^{95} +(-1.30320 - 11.4968i) 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} - 2 q^{3} - 4 q^{4} + 8 q^{5} + 2 q^{6} - 6 q^{8} - 4 q^{9}+O(q^{10}) $ 10 * q + 2 * q^2 - 2 * q^3 - 4 * q^4 + 8 * q^5 + 2 * q^6 - 6 * q^8 - 4 * q^9	$ 10 q + 2 q^{2} - 2 q^{3} - 4 q^{4} + 8 q^{5} + 2 q^{6} - 6 q^{8} - 4 q^{9} + 7 q^{10} - 8 q^{11} - 22 q^{12} + 8 q^{13} - 19 q^{15} + 2 q^{16} - 12 q^{17} - 2 q^{18} - q^{19} - 5 q^{20} - q^{22} - 6 q^{23} - 3 q^{24} + 2 q^{25} - 11 q^{26} + 7 q^{27} + 7 q^{29} - 26 q^{30} + 3 q^{31} - 2 q^{32} + q^{33} - 3 q^{34} + 34 q^{36} + 40 q^{38} + 20 q^{39} - 6 q^{40} - 5 q^{41} - 7 q^{43} - 10 q^{44} + q^{45} + 3 q^{46} - 27 q^{47} + 5 q^{48} + 19 q^{50} + 24 q^{51} - 20 q^{52} - 21 q^{53} + 53 q^{54} - 4 q^{55} - 4 q^{57} + 20 q^{58} - 30 q^{59} - 41 q^{60} + 14 q^{61} + 12 q^{62} - 50 q^{64} - 11 q^{65} + 41 q^{66} - 2 q^{67} + 54 q^{68} - 15 q^{69} - 6 q^{71} + 48 q^{72} - 15 q^{73} + 72 q^{74} - 31 q^{75} - 5 q^{76} - 20 q^{78} - 4 q^{79} - 20 q^{80} + 8 q^{81} + 5 q^{82} - 9 q^{83} - 6 q^{85} + 16 q^{86} - 32 q^{87} + 36 q^{88} - 28 q^{89} - 28 q^{90} + 27 q^{92} - 12 q^{93} + 3 q^{94} - 14 q^{95} + q^{96} + 12 q^{97} + 35 q^{99}+O(q^{100}) $ 10 * q + 2 * q^2 - 2 * q^3 - 4 * q^4 + 8 * q^5 + 2 * q^6 - 6 * q^8 - 4 * q^9 + 7 * q^10 - 8 * q^11 - 22 * q^12 + 8 * q^13 - 19 * q^15 + 2 * q^16 - 12 * q^17 - 2 * q^18 - q^19 - 5 * q^20 - q^22 - 6 * q^23 - 3 * q^24 + 2 * q^25 - 11 * q^26 + 7 * q^27 + 7 * q^29 - 26 * q^30 + 3 * q^31 - 2 * q^32 + q^33 - 3 * q^34 + 34 * q^36 + 40 * q^38 + 20 * q^39 - 6 * q^40 - 5 * q^41 - 7 * q^43 - 10 * q^44 + q^45 + 3 * q^46 - 27 * q^47 + 5 * q^48 + 19 * q^50 + 24 * q^51 - 20 * q^52 - 21 * q^53 + 53 * q^54 - 4 * q^55 - 4 * q^57 + 20 * q^58 - 30 * q^59 - 41 * q^60 + 14 * q^61 + 12 * q^62 - 50 * q^64 - 11 * q^65 + 41 * q^66 - 2 * q^67 + 54 * q^68 - 15 * q^69 - 6 * q^71 + 48 * q^72 - 15 * q^73 + 72 * q^74 - 31 * q^75 - 5 * q^76 - 20 * q^78 - 4 * q^79 - 20 * q^80 + 8 * q^81 + 5 * q^82 - 9 * q^83 - 6 * q^85 + 16 * q^86 - 32 * q^87 + 36 * q^88 - 28 * q^89 - 28 * q^90 + 27 * q^92 - 12 * q^93 + 3 * q^94 - 14 * q^95 + q^96 + 12 * q^97 + 35 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	0.920620	−	1.59456i	0.650977	−	1.12753i	−0.331909	−	0.943311i	$-0.607693\pi$
$2$	0.920620	−	1.59456i	0.650977	−	1.12753i	0.982886	−	0.184214i	$-0.0589739\pi$
$3$	1.58800	+	0.691567i	0.916831	+	0.399277i
$3$	1.58800	+	0.691567i	0.916831	+	0.399277i
$4$	−0.695084	−	1.20392i	−0.347542	−	0.601960i
$5$	−1.33475			−0.596920			−0.298460	−	0.954422i	$-0.596473\pi$
$5$	−1.33475			−0.596920			−0.298460	+	0.954422i	$0.596473\pi$
$6$	2.56469	−	1.89549i	1.04703	−	0.773830i
$7$		0			0
$7$		0			0
$8$	1.12285			0.396987
$9$	2.04347	+	2.19641i	0.681156	+	0.732138i
$10$	−1.22880	+	2.12835i	−0.388581	+	0.673042i
$11$	1.51302			0.456192			0.228096	−	0.973639i	$-0.426750\pi$
$11$	1.51302			0.456192			0.228096	+	0.973639i	$0.426750\pi$
$12$	−0.271199	−	2.39252i	−0.0782884	−	0.690661i
$13$	2.58800	−	4.48254i	0.717781	−	1.24323i	−0.244096	−	0.969751i	$-0.578491\pi$
$13$	2.58800	−	4.48254i	0.717781	−	1.24323i	0.961877	−	0.273482i	$-0.0881755\pi$
$14$		0			0
$15$	−2.11958	−	0.923072i	−0.547274	−	0.238336i
$16$	2.42388	−	4.19829i	0.605971	−	1.04957i
$17$	−0.774463	+	1.34141i	−0.187835	+	0.325340i	−0.944528	−	0.328430i	$-0.893480\pi$
$17$	−0.774463	+	1.34141i	−0.187835	+	0.325340i	0.756693	+	0.653770i	$0.226814\pi$
$18$	5.38358	−	1.23637i	1.26892	−	0.291416i
$19$	1.25211	+	2.16872i	0.287254	+	0.497538i	0.973153	−	0.230158i	$-0.0739244\pi$
$19$	1.25211	+	2.16872i	0.287254	+	0.497538i	−0.685900	+	0.727696i	$0.740591\pi$
$20$	0.927765	+	1.60694i	0.207455	+	0.359322i
$21$		0			0
$22$	1.39291	−	2.41260i	0.296970	−	0.514367i
$23$	−7.36079			−1.53483			−0.767415	−	0.641151i	$-0.778457\pi$
$23$	−7.36079			−1.53483			−0.767415	+	0.641151i	$0.778457\pi$
$24$	1.78308	+	0.776526i	0.363970	+	0.158508i
$25$	−3.21843			−0.643687
$26$	−4.76513	−	8.25344i	−0.934518	−	1.61863i
$27$	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	$0.835164\pi$
$30$	−3.42323	+	2.53001i	−0.624993	+	0.461914i
$31$	−1.92388	−	3.33227i	−0.345540	−	0.598493i	0.639912	−	0.768448i	$-0.278971\pi$
$31$	−1.92388	−	3.33227i	−0.345540	−	0.598493i	−0.985452	+	0.169956i	$0.945638\pi$
$32$	−3.34011	−	5.78523i	−0.590453	−	1.02269i
$33$	2.40267	+	1.04635i	0.418250	+	0.182147i
$34$	1.42597	+	2.46986i	0.244552	+	0.423577i
$35$		0			0
$36$	1.22392	−	3.98687i	0.203987	−	0.664478i
$37$	−0.281608	−	0.487760i	−0.0462961	−	0.0801872i	0.841949	−	0.539557i	$-0.181408\pi$
$37$	−0.281608	−	0.487760i	−0.0462961	−	0.0801872i	−0.888245	+	0.459370i	$0.848075\pi$
$38$	4.61087			0.747982
$39$	7.20971	−	5.32849i	1.15448	−	0.853241i
$40$	−1.49873			−0.236969
$41$	−4.51188	+	7.81481i	−0.704638	+	1.22047i	0.262185	+	0.965018i	$0.415557\pi$
$41$	−4.51188	+	7.81481i	−0.704638	+	1.22047i	−0.966822	+	0.255450i	$0.917776\pi$
$42$		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	$0.549707\pi$
$44$	−1.05167	−	1.82155i	−0.158546	−	0.274609i
$45$	−2.72753	−	2.93167i	−0.406596	−	0.437028i
$46$	−6.77649	+	11.7372i	−0.999139	+	1.73056i
$47$	−4.75925	+	8.24327i	−0.694209	+	1.20240i	0.276238	+	0.961089i	$0.410912\pi$
$47$	−4.75925	+	8.24327i	−0.694209	+	1.20240i	−0.970447	+	0.241315i	$0.922421\pi$
$48$	6.75252	−	4.99060i	0.974643	−	0.720330i
$49$		0			0
$50$	−2.96296	+	5.13199i	−0.419025	+	0.725773i
$51$	−2.15752	+	1.59456i	−0.302113	+	0.223283i
$52$	−7.19550			−0.997836
$53$	0.755374	−	1.30835i	0.103759	−	0.179715i	−0.809472	−	0.587159i	$-0.800246\pi$
$53$	0.755374	−	1.30835i	0.103759	−	0.179715i	0.913230	+	0.407444i	$0.133580\pi$
$54$	9.40414	+	1.75975i	1.27974	+	0.239471i
$55$	−2.01950			−0.272310
$56$		0			0
$57$	0.488532	+	4.30983i	0.0647077	+	0.570851i
$58$	−0.114051			−0.0149757
$59$	−4.22166	−	7.31212i	−0.549613	−	0.951957i	−0.998301	−	0.0582689i	$-0.981442\pi$
$59$	−4.22166	−	7.31212i	−0.549613	−	0.951957i	0.448688	−	0.893688i	$-0.351891\pi$
$60$	0.361984	+	3.19342i	0.0467319	+	0.412269i
$61$	1.61958	−	2.80520i	0.207367	−	0.359169i	−0.743518	−	0.668716i	$-0.766844\pi$
$61$	1.61958	−	2.80520i	0.207367	−	0.359169i	0.950884	+	0.309547i	$0.100177\pi$
$62$	−7.08467			−0.899754
$63$		0			0
$64$	−2.60434			−0.325543
$65$	−3.45434	+	5.98309i	−0.428458	+	0.742111i
$66$	3.88042	−	2.86790i	0.477646	−	0.353014i
$67$	−3.46670	−	6.00449i	−0.423524	−	0.733566i	0.572757	−	0.819725i	$-0.305874\pi$
$67$	−3.46670	−	6.00449i	−0.423524	−	0.733566i	−0.996281	+	0.0861595i	$0.972541\pi$
$68$	2.15327			0.261122
$69$	−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	$0.761260\pi$
$72$	2.29451	+	2.46624i	0.270410	+	0.290649i
$73$	1.37936	−	2.38912i	0.161442	−	0.279625i	−0.773944	−	0.633254i	$-0.781719\pi$
$73$	1.37936	−	2.38912i	0.161442	−	0.279625i	0.935386	+	0.353629i	$0.115052\pi$
$74$	−1.03702			−0.120551
$75$	−5.11086	−	2.22576i	−0.590152	−	0.257009i
$76$	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	−0.650106	−	0.759844i	$-0.725275\pi$
$79$	2.95969	−	5.12633i	0.332991	−	0.576758i	0.983097	+	0.183086i	$0.0586087\pi$
$80$	−3.23529	+	5.60368i	−0.361716	+	0.626511i
$81$	−0.648467	+	8.97661i	−0.0720519	+	0.997401i
$82$	8.30746	+	14.3889i	0.917406	+	1.58899i
$83$	−2.80111	−	4.85167i	−0.307462	−	0.532540i	0.670344	−	0.742050i	$-0.266146\pi$
$83$	−2.80111	−	4.85167i	−0.307462	−	0.532540i	−0.977806	+	0.209510i	$0.932813\pi$
$84$		0			0
$85$	1.03372	−	1.79045i	0.112122	−	0.194202i
$86$	18.7802			2.02512
$87$	−0.0120840	−	0.106605i	−0.00129554	−	0.0114293i
$88$	1.69889			0.181102
$89$	−0.703287	−	1.21813i	−0.0745483	−	0.129121i	0.826341	−	0.563169i	$-0.190418\pi$
$89$	−0.703287	−	1.21813i	−0.0745483	−	0.129121i	−0.900890	+	0.434048i	$0.857085\pi$
$90$	−7.18575	+	1.65025i	−0.757444	+	0.173952i
$91$		0			0
$92$	5.11636	+	8.86180i	0.533418	+	0.923906i
$93$	−0.750637	−	6.62212i	−0.0778374	−	0.686682i
$94$	8.76293	+	15.1778i	0.903827	+	1.56548i
$95$	−1.67126	−	2.89470i	−0.171467	−	0.296990i
$96$	−1.30320	−	11.4968i	−0.133007	−	1.17339i
$97$	6.09713	+	10.5605i	0.619070	+	1.07226i	0.989656	+	0.143462i	$0.0458236\pi$
$97$	6.09713	+	10.5605i	0.619070	+	1.07226i	−0.370586	+	0.928798i	$0.620843\pi$
$98$		0			0
$99$	3.09180	+	3.32321i	0.310738	+	0.333995i
$100$	2.23708	+	3.87474i	0.223708	+	0.387474i
$101$	−1.11867			−0.111312			−0.0556560	−	0.998450i	$-0.517725\pi$
$101$	−1.11867			−0.111312			−0.0556560	+	0.998450i	$0.517725\pi$
$102$	0.556368	+	4.90828i	0.0550886	+	0.485993i
$103$	−1.93045			−0.190213			−0.0951063	−	0.995467i	$-0.530319\pi$
$103$	−1.93045			−0.190213			−0.0951063	+	0.995467i	$0.530319\pi$
$104$	2.90593	−	5.03322i	0.284950	−	0.493548i
$105$		0			0
$106$	−1.39082	−	2.40898i	−0.135089	−	0.233981i
$107$	2.88969	+	5.00509i	0.279357	+	0.483860i	0.971225	−	0.238163i	$-0.0765454\pi$
$107$	2.88969	+	5.00509i	0.279357	+	0.483860i	−0.691868	+	0.722024i	$0.743212\pi$
$108$	4.70077	−	5.48470i	0.452332	−	0.527766i
$109$	−4.12106	+	7.13788i	−0.394726	+	0.683685i	−0.993066	−	0.117557i	$-0.962494\pi$
$109$	−4.12106	+	7.13788i	−0.394726	+	0.683685i	0.598340	+	0.801242i	$0.295827\pi$
$110$	−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	$-0.0722758\pi$
$114$	7.32205	+	3.18873i	0.685773	+	0.298652i
$115$	9.82483			0.916170
$116$	−0.0430553	+	0.0745740i	−0.00399759	+	0.00692403i
$117$	15.1340	−	3.47562i	1.39914	−	0.321322i
$118$	−15.5462			−1.43114
$119$		0			0
$120$	−2.37997	−	1.03647i	−0.217261	−	0.0946164i
$121$	−8.71078			−0.791889
$122$	−2.98204	−	5.16505i	−0.269982	−	0.467622i
$123$	−12.5693	+	9.28962i	−1.13334	+	0.837617i
$124$	−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
$129$	1.98981	+	17.5541i	0.175193	+	1.54555i
$130$	6.36027	+	11.0163i	0.557832	+	0.966194i
$131$	2.01346			0.175917			0.0879585	−	0.996124i	$-0.471966\pi$
$131$	2.01346			0.175917			0.0879585	+	0.996124i	$0.471966\pi$
$132$	−0.410328	−	3.61992i	−0.0357145	−	0.315074i
$133$		0			0
$134$	−12.7660			−1.10282
$135$	−2.30386	−	6.54175i	−0.198285	−	0.563024i
$136$	−0.869605	+	1.50620i	−0.0745680	+	0.129156i
$137$	2.21740			0.189445			0.0947225	−	0.995504i	$-0.469804\pi$
$137$	2.21740			0.189445			0.0947225	+	0.995504i	$0.469804\pi$
$138$	−18.8781	+	13.9523i	−1.60701	+	1.18770i
$139$	−0.377669	+	0.654143i	−0.0320335	+	0.0554836i	−0.881598	−	0.472002i	$-0.843532\pi$
$139$	−0.377669	+	0.654143i	−0.0320335	+	0.0554836i	0.849564	+	0.527485i	$0.176865\pi$
$140$		0			0
$141$	−13.2585	+	9.79894i	−1.11656	+	0.825220i
$142$	−11.3516	+	19.6615i	−0.952604	+	1.64996i
$143$	3.91568	−	6.78216i	0.327446	−	0.567153i
$144$	14.1743	−	3.25523i	1.18119	−	0.271269i
$145$	0.0413391	+	0.0716014i	0.00343303	+	0.00594618i
$146$	−2.53973	−	4.39894i	−0.210189	−	0.364059i
$147$		0			0
$148$	−0.391482	+	0.678068i	−0.0321797	+	0.0557368i
$149$	6.58499			0.539463			0.269732	−	0.962936i	$-0.413065\pi$
$149$	6.58499			0.539463			0.269732	+	0.962936i	$0.413065\pi$
$150$	−8.25428	+	6.10050i	−0.673959	+	0.498104i
$151$	12.6671			1.03083			0.515417	−	0.856939i	$-0.327637\pi$
$151$	12.6671			1.03083			0.515417	+	0.856939i	$0.327637\pi$
$152$	1.40593	+	2.43514i	0.114036	+	0.197516i
$153$	−4.52888	+	1.04009i	−0.366138	+	0.0840861i
$154$		0			0
$155$	2.56791	+	4.44775i	0.206260	+	0.357252i
$156$	−11.4264	−	4.97617i	−0.914846	−	0.398413i
$157$	−8.65372	−	14.9887i	−0.690642	−	1.19623i	−0.971628	−	0.236515i	$-0.923995\pi$
$157$	−8.65372	−	14.9887i	−0.690642	−	1.19623i	0.280986	−	0.959712i	$-0.409338\pi$
$158$	−5.44950	−	9.43882i	−0.433539	−	0.750912i
$159$	2.10434	−	1.55526i	0.166885	−	0.123340i
$160$	4.45822	+	7.72186i	0.352453	+	0.610467i
$161$		0			0
$162$	13.7168	+	9.29807i	1.07769	+	0.730525i
$163$	6.10963	+	10.5822i	0.478543	+	0.828861i	0.999697	−	0.0246014i	$-0.00783167\pi$
$163$	6.10963	+	10.5822i	0.478543	+	0.828861i	−0.521154	+	0.853463i	$0.674498\pi$
$164$	12.5445			0.979564
$165$	−3.20697	−	1.39662i	−0.249662	−	0.108727i
$166$	−10.3150			−0.800602
$167$	−1.76248	+	3.05270i	−0.136385	+	0.236225i	−0.926126	−	0.377215i	$-0.876882\pi$
$167$	−1.76248	+	3.05270i	−0.136385	+	0.236225i	0.789741	+	0.613440i	$0.210215\pi$
$168$		0			0
$169$	−6.89546	−	11.9433i	−0.530420	−	0.918714i
$170$	−1.90332	−	3.29665i	−0.145978	−	0.252842i
$171$	−2.20475	+	7.18186i	−0.168602	+	0.549210i
$172$	7.08968	−	12.2797i	0.540583	−	0.936318i
$173$	5.07046	−	8.78229i	0.385500	−	0.667705i	−0.606339	−	0.795206i	$-0.707362\pi$
$173$	5.07046	−	8.78229i	0.385500	−	0.667705i	0.991838	+	0.127502i	$0.0406958\pi$
$174$	−0.181113	−	0.0788742i	−0.0137302	−	0.00597944i
$175$		0			0
$176$	3.66738	−	6.35208i	0.276439	−	0.478806i
$177$	−1.64715	−	14.5312i	−0.123808	−	1.09223i
$178$	−2.58984			−0.194117
$179$	0.850579	−	1.47325i	0.0635752	−	0.110116i	−0.832486	−	0.554046i	$-0.813083\pi$
$179$	0.850579	−	1.47325i	0.0635752	−	0.110116i	0.896061	+	0.443931i	$0.146416\pi$
$180$	−1.63364	+	5.32148i	−0.121764	+	0.396640i
$181$	16.9941			1.26316			0.631581	−	0.775310i	$-0.282406\pi$
$181$	16.9941			1.26316			0.631581	+	0.775310i	$0.282406\pi$
$182$		0			0
$183$	4.51188	−	3.33460i	0.333528	−	0.246501i
$184$	−8.26505			−0.609308
$185$	0.375877	+	0.651039i	0.0276351	+	0.0478653i
$186$	−11.2504	−	4.89953i	−0.824922	−	0.359251i
$187$	−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	0.0838717	+	0.996477i	$0.473271\pi$
$191$	−11.3470	+	19.6535i	−0.821038	+	1.42208i	−0.904910	+	0.425603i	$0.860062\pi$
$192$	−4.13568	−	1.80108i	−0.298467	−	0.129982i
$193$	−3.09349	−	5.35808i	−0.222674	−	0.385683i	0.732945	−	0.680288i	$-0.238145\pi$
$193$	−3.09349	−	5.35808i	−0.222674	−	0.385683i	−0.955619	+	0.294605i	$0.904812\pi$
$194$	22.4526			1.61200
$195$	−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	$0.386846\pi$
$198$	8.14544	−	1.87065i	0.578871	−	0.132942i
$199$	4.33973	−	7.51664i	0.307636	−	0.532840i	−0.670209	−	0.742172i	$-0.733796\pi$
$199$	4.33973	−	7.51664i	0.307636	−	0.532840i	0.977845	+	0.209332i	$0.0671289\pi$
$200$	−3.61381			−0.255535
$201$	−1.35259	−	11.9326i	−0.0954044	−	0.841659i
$202$	−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
$206$	−1.77721	+	3.07822i	−0.123824	+	0.214470i
$207$	−15.0415	−	16.1673i	−1.04546	−	1.12371i
$208$	−12.5460	−	21.7303i	−0.869909	−	1.50673i
$209$	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	$0.229353\pi$
$212$	−2.10019			−0.144242
$213$	−19.5806	−	8.52728i	−1.34164	−	0.584280i
$214$	10.6412			0.727420
$215$	−6.80708	−	11.7902i	−0.464239	−	0.804086i
$216$	1.93810	+	5.50319i	0.131871	+	0.374445i
$217$		0			0
$218$	7.58786	+	13.1426i	0.513915	+	0.890126i
$219$	3.84265	−	2.83999i	0.259662	−	0.191909i
$220$	1.40372	+	2.43132i	0.0946390	+	0.163920i
$221$	4.00862	+	6.94313i	0.269649	+	0.467045i
$222$	−1.64678	−	0.717167i	−0.110525	−	0.0481331i
$223$	−5.86133	−	10.1521i	−0.392503	−	0.679836i	0.600276	−	0.799793i	$-0.295058\pi$
$223$	−5.86133	−	10.1521i	−0.392503	−	0.679836i	−0.992779	+	0.119957i	$0.961724\pi$
$224$		0			0
$225$	−6.57677	−	7.06901i	−0.438451	−	0.471267i
$226$	−13.3509	−	23.1245i	−0.888091	−	1.53822i
$227$	−11.1831			−0.742247			−0.371123	−	0.928584i	$-0.621027\pi$
$227$	−11.1831			−0.742247			−0.371123	+	0.928584i	$0.621027\pi$
$228$	4.84913	−	3.58385i	0.321141	−	0.237346i
$229$	9.65647			0.638118			0.319059	−	0.947735i	$-0.396633\pi$
$229$	9.65647			0.638118			0.319059	+	0.947735i	$0.396633\pi$
$230$	9.04494	−	15.6663i	0.596406	−	1.03301i
$231$		0			0
$232$	−0.0347761	−	0.0602340i	−0.00228317	−	0.00395456i
$233$	−9.64492	−	16.7055i	−0.631860	−	1.09441i	−0.987171	−	0.159666i	$-0.948958\pi$
$233$	−9.64492	−	16.7055i	−0.631860	−	1.09441i	0.355311	−	0.934748i	$-0.384375\pi$
$234$	8.39058	−	27.3318i	0.548509	−	1.78674i
$235$	6.35243	−	11.0027i	0.414387	−	0.717739i
$236$	−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	$0.170674\pi$
$240$	−9.01295	+	6.66121i	−0.581784	+	0.429979i
$241$	−10.6361			−0.685134			−0.342567	−	0.939493i	$-0.611296\pi$
$241$	−10.6361			−0.685134			−0.342567	+	0.939493i	$0.611296\pi$
$242$	−8.01932	+	13.8899i	−0.515502	+	0.892875i
$243$	−7.23769	+	13.8064i	−0.464298	+	0.885679i
$244$	−4.50299			−0.288274
$245$		0			0
$246$	3.24130	+	28.5948i	0.206658	+	1.82314i
$247$	12.9618			0.824741
$248$	−2.16023	−	3.74163i	−0.137175	−	0.237594i
$249$	−1.09290	−	9.64159i	−0.0692599	−	0.611011i
$250$	10.0988	−	17.4917i	0.638705	−	1.10627i
$251$	3.26628			0.206166			0.103083	−	0.994673i	$-0.467129\pi$
$251$	3.26628			0.206166			0.103083	+	0.994673i	$0.467129\pi$
$252$		0			0
$253$	−11.1370			−0.700176
$254$	7.82531	−	13.5538i	0.491004	−	0.850443i
$255$	2.87976	−	2.12835i	0.180337	−	0.133282i
$256$	−10.4896	−	18.1686i	−0.655603	−	1.13554i
$257$	4.69573			0.292912			0.146456	−	0.989217i	$-0.453213\pi$
$257$	4.69573			0.292912			0.146456	+	0.989217i	$0.453213\pi$
$258$	29.8229	+	12.9878i	1.85669	+	0.808584i
$259$		0			0
$260$	9.60421			0.595628
$261$	0.0545353	−	0.177646i	0.00337565	−	0.0109960i
$262$	1.85363	−	3.21059i	0.114518	−	0.198351i
$263$	19.5498			1.20549			0.602747	−	0.797932i	$-0.294073\pi$
$263$	19.5498			1.20549			0.602747	+	0.797932i	$0.294073\pi$
$264$	2.69783	+	1.17490i	0.166040	+	0.0723098i
$265$	−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
$269$	−7.88365	+	13.6549i	−0.480675	+	0.832553i	−0.999754	−	0.0221730i	$-0.992942\pi$
$269$	−7.88365	+	13.6549i	−0.480675	+	0.832553i	0.519079	+	0.854726i	$0.326275\pi$
$270$	−12.5522	−	2.34883i	−0.763903	−	0.142945i
$271$	−7.39882	−	12.8151i	−0.449446	−	0.778464i	0.548904	−	0.835886i	$-0.315045\pi$
$271$	−7.39882	−	12.8151i	−0.449446	−	0.778464i	−0.998350	+	0.0574218i	$0.981712\pi$
$272$	3.75442	+	6.50285i	0.227645	+	0.394293i
$273$		0			0
$274$	2.04138	−	3.53578i	0.123324	−	0.213604i
$275$	−4.86954			−0.293644
$276$	1.99624	+	17.6108i	0.120159	+	1.06005i
$277$	−7.45122			−0.447701			−0.223850	−	0.974624i	$-0.571863\pi$
$277$	−7.45122			−0.447701			−0.223850	+	0.974624i	$0.571863\pi$
$278$	0.695380	+	1.20443i	0.0417061	+	0.0722371i
$279$	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	$-0.448991\pi$
$282$	3.41901	+	30.1625i	0.203599	+	1.79615i
$283$	9.37768	+	16.2426i	0.557445	+	0.965524i	0.997709	+	0.0676550i	$0.0215517\pi$
$283$	9.37768	+	16.2426i	0.557445	+	0.965524i	−0.440263	+	0.897869i	$0.645115\pi$
$284$	8.57064	+	14.8448i	0.508574	+	0.880876i
$285$	−0.652070	−	5.75257i	−0.0386253	−	0.340753i
$286$	−7.20971	−	12.4876i	−0.426319	−	0.738406i
$287$		0			0
$288$	5.88136	−	19.1582i	0.346563	−	1.12891i
$289$	7.30041	+	12.6447i	0.429436	+	0.743805i
$290$	0.152230			0.00893928
$291$	2.37890	+	20.9867i	0.139454	+	1.23026i
$292$	−3.83507			−0.224431
$293$	1.23089	−	2.13196i	0.0719093	−	0.124551i	−0.827829	−	0.560981i	$-0.810424\pi$
$293$	1.23089	−	2.13196i	0.0719093	−	0.124551i	0.899738	+	0.436430i	$0.143757\pi$
$294$		0			0
$295$	5.63487	+	9.75988i	0.328075	+	0.568242i
$296$	−0.316203	−	0.547680i	−0.0183790	−	0.0318333i
$297$	2.61155	+	7.41544i	0.151537	+	0.430287i
$298$	6.06227	−	10.5002i	0.351178	−	0.608258i
$299$	−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
$303$	−1.77645	−	0.773637i	−0.102054	−	0.0444443i
$304$	12.1399			0.696270
$305$	−2.16175	+	3.74425i	−0.123781	+	0.214395i
$306$	−2.51090	+	8.17911i	−0.143538	+	0.467568i
$307$	4.66277			0.266118			0.133059	−	0.991108i	$-0.457520\pi$
$307$	4.66277			0.266118			0.133059	+	0.991108i	$0.457520\pi$
$308$		0			0
$309$	−3.06555	−	1.33503i	−0.174393	−	0.0759475i
$310$	9.45629			0.537081
$311$	13.7410	+	23.8002i	0.779183	+	1.34958i	0.932413	+	0.361393i	$0.117699\pi$
$311$	13.7410	+	23.8002i	0.779183	+	1.34958i	−0.153231	+	0.988190i	$0.548968\pi$
$312$	8.09542	−	5.98309i	0.458313	−	0.338726i
$313$	2.74666	−	4.75735i	0.155250	−	0.268901i	−0.777900	−	0.628388i	$-0.783715\pi$
$313$	2.74666	−	4.75735i	0.155250	−	0.268901i	0.933150	+	0.359487i	$0.117048\pi$
$314$	−31.8671			−1.79837
$315$		0			0
$316$	−8.22893			−0.462914
$317$	−4.93879	+	8.55424i	−0.277390	+	0.480454i	−0.970735	−	0.240152i	$-0.922803\pi$
$317$	−4.93879	+	8.55424i	−0.277390	+	0.480454i	0.693345	+	0.720606i	$0.256136\pi$
$318$	−0.542654	−	4.78730i	−0.0304305	−	0.268459i
$319$	−0.0468601	−	0.0811641i	−0.00262366	−	0.00454432i
$320$	3.47615			0.194323
$321$	1.12746	+	9.94649i	0.0629288	+	0.555159i
$322$		0			0
$323$	−3.87885			−0.215825
$324$	11.2579	−	5.45879i	0.625437	−	0.303266i
$325$	−8.32930	+	14.4268i	−0.462026	+	0.800253i
$326$	22.4986			1.24608
$327$	−11.4806	+	8.48494i	−0.634876	+	0.469218i
$328$	−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	−0.427963	−	0.903796i	$-0.640769\pi$
$331$	10.3471	−	17.9217i	0.568729	−	0.985067i	0.996692	−	0.0812710i	$-0.0258979\pi$
$332$	−3.89401	+	6.74463i	−0.213712	+	0.370160i
$333$	0.495864	−	1.61525i	0.0271732	−	0.0885152i
$334$	3.24514	+	5.62076i	0.177566	+	0.307554i
$335$	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	$0.153680\pi$
$338$	−25.3924			−1.38116
$339$	20.2002	−	14.9294i	1.09712	−	0.810852i
$340$	−2.87408			−0.155869
$341$	−2.91087	−	5.04177i	−0.157632	−	0.273027i
$342$	9.42217	+	10.1274i	0.509493	+	0.547626i
$343$		0			0
$344$	5.72639	+	9.91840i	0.308746	+	0.534764i
$345$	15.6018	+	6.79453i	0.839973	+	0.365805i
$346$	−9.33593	−	16.1703i	−0.501903	−	0.869321i
$347$	14.7694	+	25.5813i	0.792862	+	1.37328i	0.924188	+	0.381938i	$0.124743\pi$
$347$	14.7694	+	25.5813i	0.792862	+	1.37328i	−0.131326	+	0.991339i	$0.541923\pi$
$348$	−0.119945	+	0.0886477i	−0.00642971	+	0.00475202i
$349$	−18.0006	−	31.1780i	−0.963551	−	1.66892i	−0.713458	−	0.700698i	$-0.752872\pi$
$349$	−18.0006	−	31.1780i	−0.963551	−	1.66892i	−0.250094	−	0.968222i	$-0.580461\pi$
$350$		0			0
$351$	26.4364	+	4.94691i	1.41107	+	0.264046i
$352$	−5.05363	−	8.75315i	−0.269360	−	0.466545i
$353$	29.4930			1.56975			0.784877	−	0.619652i	$-0.212726\pi$
$353$	29.4930			1.56975			0.784877	+	0.619652i	$0.212726\pi$
$354$	−24.6873	−	10.7512i	−1.31211	−	0.571421i
$355$	16.4580			0.873500
$356$	−0.977687	+	1.69340i	−0.0518173	+	0.0897502i
$357$		0			0
$358$	−1.56612	−	2.71260i	−0.0827720	−	0.143365i
$359$	2.70535	+	4.68580i	0.142783	+	0.247307i	0.928544	−	0.371224i	$-0.121062\pi$
$359$	2.70535	+	4.68580i	0.142783	+	0.247307i	−0.785761	+	0.618531i	$0.787728\pi$
$360$	−3.06260	−	3.29182i	−0.161413	−	0.173494i
$361$	6.36444	−	11.0235i	0.334971	−	0.580186i
$362$	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
$366$	−1.16350	−	10.2644i	−0.0608169	−	0.536527i
$367$	23.0843			1.20499			0.602496	−	0.798122i	$-0.294173\pi$
$367$	23.0843			1.20499			0.602496	+	0.798122i	$0.294173\pi$
$368$	−17.8417	+	30.9027i	−0.930063	+	1.61092i
$369$	−26.3844	+	6.05936i	−1.37352	+	0.315438i
$370$	1.38416			0.0719591
$371$		0			0
$372$	−7.45075	+	5.50664i	−0.386304	+	0.285506i
$373$	21.5030			1.11338			0.556692	−	0.830719i	$-0.312070\pi$
$373$	21.5030			1.11338			0.556692	+	0.830719i	$0.312070\pi$
$374$	2.15752	+	3.73694i	0.111563	+	0.193232i
$375$	17.4197	+	7.58620i	0.899548	+	0.391750i
$376$	−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
$381$	13.4980	+	5.87835i	0.691526	+	0.301157i
$382$	20.8925	+	36.1869i	1.06895	+	1.85148i
$383$	34.9209			1.78437			0.892187	−	0.451666i	$-0.149170\pi$
$383$	34.9209			1.78437			0.892187	+	0.451666i	$0.149170\pi$
$384$	11.9306	−	8.81756i	0.608831	−	0.449969i
$385$		0			0
$386$	−11.3917			−0.579823
$387$	−8.98003	+	29.2519i	−0.456480	+	1.48696i
$388$	8.47603	−	14.6809i	0.430305	−	0.745311i
$389$	−28.8822			−1.46438			−0.732192	−	0.681098i	$-0.761503\pi$
$389$	−28.8822			−1.46438			−0.732192	+	0.681098i	$0.761503\pi$
$390$	2.48157	+	21.8924i	0.125659	+	1.10857i
$391$	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
$395$	−3.95046	+	6.84239i	−0.198769	+	0.344278i
$396$	1.85182	−	6.03219i	0.0930574	−	0.303129i
$397$	−5.59226	−	9.68607i	−0.280667	−	0.486130i	0.690882	−	0.722968i	$-0.257222\pi$
$397$	−5.59226	−	9.68607i	−0.280667	−	0.486130i	−0.971549	+	0.236838i	$0.923889\pi$
$398$	−7.99049	−	13.8399i	−0.400527	−	0.693734i
$399$		0			0
$400$	−7.80111	+	13.5119i	−0.390056	+	0.675596i
$401$	−1.08212			−0.0540386			−0.0270193	−	0.999635i	$-0.508602\pi$
$401$	−1.08212			−0.0540386			−0.0270193	+	0.999635i	$0.508602\pi$
$402$	−20.2724	−	8.82858i	−1.01110	−	0.440330i
$403$	−19.9160			−0.992088
$404$	0.777570	+	1.34679i	0.0386856	+	0.0670054i
$405$	0.865544	−	11.9816i	0.0430092	−	0.595368i
$406$		0			0
$407$	−0.426078	−	0.737988i	−0.0211199	−	0.0365807i
$408$	−2.42257	+	1.79045i	−0.119935	+	0.0886405i
$409$	−10.8674	−	18.8229i	−0.537360	−	0.930735i	−0.999045	−	0.0436908i	$-0.986088\pi$
$409$	−10.8674	−	18.8229i	−0.537360	−	0.930735i	0.461685	−	0.887044i	$-0.347245\pi$
$410$	−11.0884	−	19.2057i	−0.547618	−	0.948501i
$411$	3.52122	+	1.53348i	0.173689	+	0.0756410i
$412$	1.34182	+	2.32410i	0.0661069	+	0.114500i
$413$		0			0
$414$	−39.6273	+	9.10068i	−1.94758	+	0.447274i
$415$	3.73879	+	6.47578i	0.183530	+	0.317884i
$416$	−34.5767			−1.69526
$417$	−1.05212	+	0.777593i	−0.0515226	+	0.0380789i
$418$	6.97632			0.341223
$419$	−12.5906	+	21.8075i	−0.615090	+	1.06537i	0.375279	+	0.926912i	$0.377547\pi$
$419$	−12.5906	+	21.8075i	−0.615090	+	1.06537i	−0.990369	+	0.138455i	$0.955787\pi$
$420$		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	$-0.423806\pi$
$422$	5.23316	+	9.06411i	0.254746	+	0.441234i
$423$	−27.8310	+	6.39158i	−1.35319	+	0.310769i
$424$	0.848171	−	1.46907i	0.0411908	−	0.0713446i
$425$	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
$429$	10.9084	−	8.06209i	0.526663	−	0.389241i
$430$	−25.0669			−1.20884
$431$	2.44517	−	4.23516i	0.117780	−	0.204000i	−0.801108	−	0.598520i	$-0.795756\pi$
$431$	2.44517	−	4.23516i	0.117780	−	0.204000i	0.918887	+	0.394520i	$0.129089\pi$
$432$	24.7600	+	4.63321i	1.19127	+	0.222915i
$433$	−9.71430			−0.466839			−0.233420	−	0.972376i	$-0.574992\pi$
$433$	−9.71430			−0.466839			−0.233420	+	0.972376i	$0.574992\pi$
$434$		0			0
$435$	0.0161292	+	0.142292i	0.000773334	+	0.00682236i
$436$	11.4579			0.548735
$437$	−9.21651	−	15.9635i	−0.440885	−	0.763636i
$438$	−0.990919	−	8.74189i	−0.0473479	−	0.417704i
$439$	−7.41176	+	12.8375i	−0.353744	+	0.612703i	−0.986902	−	0.161320i	$-0.948425\pi$
$439$	−7.41176	+	12.8375i	−0.353744	+	0.612703i	0.633158	+	0.774022i	$0.281758\pi$
$440$	−2.26760			−0.108103
$441$		0			0
$442$	14.7617			0.702141
$443$	10.9510	−	18.9676i	0.520297	−	0.901180i	−0.479425	−	0.877583i	$-0.659155\pi$
$443$	10.9510	−	18.9676i	0.520297	−	0.901180i	0.999722	−	0.0235972i	$-0.00751192\pi$
$444$	−1.09060	+	0.806033i	−0.0517577	+	0.0382526i
$445$	0.938715	+	1.62590i	0.0444994	+	0.0770751i
$446$	−21.5842			−1.02204
$447$	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	$0.330676\pi$
$450$	−17.3267	+	3.97919i	−0.816787	+	0.187581i
$451$	−6.82655	+	11.8239i	−0.321450	+	0.556767i
$452$	−20.1603			−0.948263
$453$	20.1153	+	8.76016i	0.945101	+	0.411588i
$454$	−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	−0.205181	+	0.978724i	$0.565778\pi$
$457$	−20.3128	+	35.1827i	−0.950190	+	1.64578i	−0.745009	+	0.667054i	$0.767555\pi$
$458$	8.88995	−	15.3978i	0.415400	−	0.719494i
$459$	−7.91114	−	1.48037i	−0.369261	−	0.0690978i
$460$	−6.82908	−	11.8283i	−0.318408	−	0.551498i
$461$	−1.41541	−	2.45155i	−0.0659220	−	0.114180i	0.831181	−	0.556003i	$-0.187666\pi$
$461$	−1.41541	−	2.45155i	−0.0659220	−	0.114180i	−0.897103	+	0.441822i	$0.854332\pi$
$462$		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	$0.942484\pi$
$464$	−0.300284			−0.0139403
$465$	1.00192	+	8.83890i	0.0464627	+	0.409894i
$466$	−35.5173			−1.64531
$467$	13.3219	+	23.0742i	0.616464	+	1.06775i	0.990126	+	0.140182i	$0.0447689\pi$
$467$	13.3219	+	23.0742i	0.616464	+	1.06775i	−0.373661	+	0.927565i	$0.621898\pi$
$468$	−14.7038	−	15.8043i	−0.679682	−	0.730554i
$469$		0			0
$470$	−11.6964	−	20.2587i	−0.539513	−	0.934463i
$471$	−3.37640	−	29.7866i	−0.155576	−	1.37249i
$472$	−4.74028	−	8.21041i	−0.218189	−	0.377915i
$473$	7.71620	+	13.3648i	0.354791	+	0.614516i
$474$	−2.12622	−	18.7575i	−0.0976604	−	0.861561i
$475$	−4.02983	−	6.97987i	−0.184901	−	0.320258i
$476$		0			0
$477$	4.41725	−	1.01445i	0.202252	−	0.0464485i
$478$	0.358381	+	0.620734i	0.0163920	+	0.0283917i
$479$	31.5791			1.44289			0.721443	−	0.692474i	$-0.243479\pi$
$479$	31.5791			1.44289			0.721443	+	0.692474i	$0.243479\pi$
$480$	1.73945	+	15.3455i	0.0793947	+	0.700421i
$481$	−2.91520			−0.132922
$482$	−9.79185	+	16.9600i	−0.446007	+	0.772506i
$483$		0			0
$484$	6.05472	+	10.4871i	0.275215	+	0.476686i
$485$	−8.13817	−	14.0957i	−0.369535	−	0.640054i
$486$	15.3519	+	24.2514i	0.696378	+	1.10006i
$487$	−0.153087	+	0.265154i	−0.00693703	+	0.0120153i	−0.869473	−	0.493980i	$-0.835541\pi$
$487$	−0.153087	+	0.265154i	−0.00693703	+	0.0120153i	0.862536	+	0.505996i	$0.168875\pi$
$488$	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	$0.300899\pi$
$492$	19.9207	+	8.67539i	0.898094	+	0.391117i
$493$	0.0959447			0.00432113
$494$	11.9329	−	20.6684i	0.536887	−	0.929916i
$495$	−4.12679	−	4.43567i	−0.185486	−	0.199368i
$496$	−18.6531			−0.837549
$497$		0			0
$498$	−16.3803	−	7.13355i	−0.734017	−	0.319662i
$499$	−21.3091			−0.953928			−0.476964	−	0.878923i	$-0.658263\pi$
$499$	−21.3091			−0.953928			−0.476964	+	0.878923i	$0.658263\pi$
$500$	−7.62478	−	13.2065i	−0.340990	−	0.590613i
$501$	−4.90996	+	3.62881i	−0.219361	+	0.162123i
$502$	3.00701	−	5.20829i	0.134209	−	0.232457i
$503$	17.0738			0.761285			0.380642	−	0.924722i	$-0.375703\pi$
$503$	17.0738			0.761285			0.380642	+	0.924722i	$0.375703\pi$
$504$		0			0
$505$	1.49315			0.0664443
$506$	−10.2529	+	17.7586i	−0.455799	+	0.789466i
$507$	−2.69038	−	23.7346i	−0.119484	−	1.05409i
$508$	−5.90824	−	10.2334i	−0.262136	−	0.454032i
$509$	−36.7735			−1.62996			−0.814979	−	0.579490i	$-0.803252\pi$
$509$	−36.7735			−1.62996			−0.814979	+	0.579490i	$0.803252\pi$
$510$	−0.742614	−	6.55135i	−0.0328835	−	0.290099i
$511$		0			0
$512$	−21.4975			−0.950065
$513$	−8.46788	+	9.88003i	−0.373866	+	0.436214i
$514$	4.32299	−	7.48764i	0.190679	−	0.330265i
$515$	2.57667			0.113542
$516$	19.7506	−	14.5971i	0.869473	−	0.642603i
$517$	−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
$521$	9.57535	−	16.5850i	0.419504	−	0.726602i	−0.576386	−	0.817178i	$-0.695537\pi$
$521$	9.57535	−	16.5850i	0.419504	−	0.726602i	0.995890	+	0.0905758i	$0.0288707\pi$
$522$	−0.233061	−	0.250504i	−0.0102008	−	0.0109643i
$523$	20.9715	+	36.3236i	0.917018	+	1.58832i	0.803920	+	0.594737i	$0.202744\pi$
$523$	20.9715	+	36.3236i	0.917018	+	1.58832i	0.113097	+	0.993584i	$0.463923\pi$
$524$	−1.39952	−	2.42405i	−0.0611385	−	0.105895i
$525$		0			0
$526$	17.9980	−	31.1734i	0.784749	−	1.35922i
$527$	5.95991			0.259618
$528$	10.2167	−	7.55085i	0.444624	−	0.328609i
$529$	31.1812			1.35570
$530$	1.85641	+	3.21539i	0.0806372	+	0.139668i
$531$	7.43362	−	24.2146i	0.322592	−	1.05082i
$532$		0			0
$533$	23.3535	+	40.4494i	1.01155	+	1.75206i
$534$	−4.11266	−	1.79105i	−0.177972	−	0.0775063i
$535$	−3.85702	−	6.68056i	−0.166754	−	0.288826i
$536$	−3.89258	−	6.74214i	−0.168134	−	0.291216i
$537$	2.36956	−	1.75128i	0.102254	−	0.0755732i
$538$	14.5157	+	25.1419i	0.625816	+	1.08395i
$539$		0			0
$540$	−6.27438	+	7.32073i	−0.270006	+	0.315034i
$541$	−1.44272	−	2.49886i	−0.0620273	−	0.107434i	0.833344	−	0.552754i	$-0.186423\pi$
$541$	−1.44272	−	2.49886i	−0.0620273	−	0.107434i	−0.895371	+	0.445320i	$0.853090\pi$
$542$	−27.2460			−1.17032
$543$	26.9866	+	11.7526i	1.15811	+	0.504351i
$544$	10.3472			0.443631
$545$	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	$0.814440\pi$
$548$	−1.54128	−	2.66957i	−0.0658401	−	0.114038i
$549$	9.47096	−	2.17507i	0.404211	−	0.0928296i
$550$	−4.48300	+	7.76478i	−0.191156	+	0.331091i
$551$	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
$555$	0.146655	+	1.29379i	0.00622516	+	0.0549184i
$556$	1.05005			0.0445319
$557$	15.5344	−	26.9064i	0.658214	−	1.14006i	−0.322864	−	0.946445i	$-0.604646\pi$
$557$	15.5344	−	26.9064i	0.658214	−	1.14006i	0.981078	−	0.193614i	$-0.0620211\pi$
$558$	−14.4773	−	15.5609i	−0.612873	−	0.658744i
$559$	52.7939			2.23294
$560$		0			0
$561$	−3.26436	+	2.41260i	−0.137822	+	0.101860i
$562$	−47.8495			−2.01841
$563$	0.144020	+	0.249451i	0.00606973	+	0.0105131i	0.869044	−	0.494734i	$-0.164735\pi$
$563$	0.144020	+	0.249451i	0.00606973	+	0.0105131i	−0.862975	+	0.505247i	$0.831401\pi$
$564$	21.0129	+	9.15104i	0.884802	+	0.385328i
$565$	−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	−0.646821	−	0.762641i	$-0.723902\pi$
$569$	8.04004	−	13.9258i	0.337056	−	0.583798i	0.983878	+	0.178843i	$0.0572354\pi$
$570$	−9.77313	−	4.25616i	−0.409351	−	0.178271i
$571$	7.64289	+	13.2379i	0.319845	+	0.553988i	0.980456	−	0.196741i	$-0.0630358\pi$
$571$	7.64289	+	13.2379i	0.319845	+	0.553988i	−0.660610	+	0.750729i	$0.729702\pi$
$572$	−10.8869			−0.455204
$573$	−31.6107	+	23.3626i	−1.32056	+	0.975985i
$574$		0			0
$575$	23.6902			0.987950
$576$	−5.32189	−	5.72021i	−0.221745	−	0.238342i
$577$	−12.0812	+	20.9253i	−0.502949	+	0.871133i	0.497045	+	0.867725i	$0.334418\pi$
$577$	−12.0812	+	20.9253i	−0.502949	+	0.871133i	−0.999994	+	0.00340833i	$0.998915\pi$
$578$	26.8836			1.11821
$579$	−1.20698	−	10.6480i	−0.0501603	−	0.442515i
$580$	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
$584$	1.54881	−	2.68262i	0.0640902	−	0.111007i
$585$	−20.2002	+	4.63910i	−0.835174	+	0.191803i
$586$	−2.26636	−	3.92546i	−0.0936226	−	0.162159i
$587$	−18.0145	−	31.2020i	−0.743537	−	1.28784i	−0.950875	−	0.309574i	$-0.899814\pi$
$587$	−18.0145	−	31.2020i	−0.743537	−	1.28784i	0.207339	−	0.978269i	$-0.433520\pi$
$588$		0			0
$589$	4.81783	−	8.34472i	0.198515	−	0.343838i
$590$	20.7503			0.854276
$591$	15.5149	+	6.75668i	0.638197	+	0.277933i
$592$	−2.73034			−0.112216
$593$	−12.4668	−	21.5932i	−0.511951	−	0.886726i	−0.999904	−	0.0138558i	$-0.995589\pi$
$593$	−12.4668	−	21.5932i	−0.511951	−	0.886726i	0.487953	−	0.872870i	$-0.337744\pi$
$594$	14.2286	+	2.66253i	0.583807	+	0.109245i
$595$		0			0
$596$	−4.57712	−	7.92780i	−0.187486	−	0.324735i
$597$	12.0897	−	8.93518i	0.494800	−	0.365693i
$598$	35.0751	+	60.7518i	1.43433	+	2.48433i
$599$	−19.7642	−	34.2325i	−0.807542	−	1.39870i	−0.914561	−	0.404447i	$-0.867464\pi$
$599$	−19.7642	−	34.2325i	−0.807542	−	1.39870i	0.107019	−	0.994257i	$-0.465869\pi$
$600$	−5.73873	−	2.49920i	−0.234283	−	0.102029i
$601$	−1.86447	−	3.22936i	−0.0760534	−	0.131728i	0.825490	−	0.564416i	$-0.190899\pi$
$601$	−1.86447	−	3.22936i	−0.0760534	−	0.131728i	−0.901544	+	0.432688i	$0.857565\pi$
$602$		0			0
$603$	6.10427	−	19.8843i	0.248585	−	0.809751i
$604$	−8.80470	−	15.2502i	−0.358258	−	0.620521i
$605$	11.6267			0.472694
$606$	−2.86904	+	2.12043i	−0.116547	+	0.0861365i
$607$	−23.6528			−0.960036			−0.480018	−	0.877259i	$-0.659370\pi$
$607$	−23.6528			−0.960036			−0.480018	+	0.877259i	$0.659370\pi$
$608$	8.36436	−	14.4875i	0.339219	−	0.587545i
$609$		0			0
$610$	3.98029	+	6.89407i	0.161157	+	0.279133i
$611$	24.6339	+	42.6671i	0.996580	+	1.72613i
$612$	4.40013	+	4.72947i	0.177865	+	0.191177i
$613$	1.89952	−	3.29006i	0.0767208	−	0.132884i	−0.825113	−	0.564968i	$-0.808888\pi$
$613$	1.89952	−	3.29006i	0.0767208	−	0.132884i	0.901833	+	0.432084i	$0.142222\pi$
$614$	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	$0.916715\pi$
$618$	−4.95100	+	3.65914i	−0.199158	+	0.147192i
$619$	21.1632			0.850622			0.425311	−	0.905047i	$-0.360165\pi$
$619$	21.1632			0.850622			0.425311	+	0.905047i	$0.360165\pi$
$620$	3.56983	−	6.18312i	0.143368	−	0.248320i
$621$	−12.7051	−	36.0759i	−0.509839	−	1.44768i
$622$	50.6011			2.02892
$623$		0			0
$624$	−4.89504	−	43.1841i	−0.195959	−	1.72875i
$625$	1.45048			0.0580192
$626$	−5.05726	−	8.75943i	−0.202129	−	0.350097i
$627$	0.739157	+	6.52085i	0.0295191	+	0.260418i
$628$	−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
$633$	−7.91786	+	5.85186i	−0.314707	+	0.232591i
$634$	9.09350	+	15.7504i	0.361149	+	0.625529i
$635$	−11.3455			−0.450231
$636$	−3.33510	−	1.45242i	−0.132245	−	0.0575924i
$637$		0			0
$638$	−0.172562			−0.00683178
$639$	−25.1967	−	27.0826i	−0.996767	−	1.07137i
$640$	−5.71622	+	9.90078i	−0.225953	+	0.391363i
$641$	−9.87469			−0.390027			−0.195013	−	0.980801i	$-0.562475\pi$
$641$	−9.87469			−0.390027			−0.195013	+	0.980801i	$0.562475\pi$
$642$	16.8982	+	7.35913i	0.666921	+	0.290442i
$643$	−21.9748	+	38.0615i	−0.866602	+	1.50100i	−0.00115462	+	0.999999i	$0.500368\pi$
$643$	−21.9748	+	38.0615i	−0.866602	+	1.50100i	−0.865448	+	0.501000i	$0.832966\pi$
$644$		0			0
$645$	−2.65590	−	23.4304i	−0.104576	−	0.922570i
$646$	−3.57095	+	6.18507i	−0.140497	+	0.243348i
$647$	−22.1936	+	38.4404i	−0.872521	+	1.51125i	−0.0131398	+	0.999914i	$0.504183\pi$
$647$	−22.1936	+	38.4404i	−0.872521	+	1.51125i	−0.859381	+	0.511336i	$0.829151\pi$
$648$	−0.728131	+	10.0794i	−0.0286037	+	0.395955i
$649$	−6.38743	−	11.0634i	−0.250729	−	0.434275i
$650$	15.3362	+	26.5631i	0.601537	+	1.04189i
$651$		0			0
$652$	8.49341	−	14.7110i	0.332628	−	0.576128i
$653$	41.9912			1.64324			0.821622	−	0.570033i	$-0.193070\pi$
$653$	41.9912			1.64324			0.821622	+	0.570033i	$0.193070\pi$
$654$	2.96053	+	26.1179i	0.115766	+	1.02129i
$655$	−2.68748			−0.105008
$656$	21.8726	+	37.8844i	0.853980	+	1.47914i
$657$	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	$-0.443892\pi$
$660$	0.547687	+	4.83170i	0.0213187	+	0.188074i
$661$	−0.0933694	−	0.161721i	−0.00363165	−	0.00629020i	0.864204	−	0.503142i	$-0.167823\pi$
$661$	−0.0933694	−	0.161721i	−0.00363165	−	0.00629020i	−0.867836	+	0.496852i	$0.834489\pi$
$662$	−19.0515	−	32.9982i	−0.740459	−	1.28251i
$663$	1.56403	+	13.7979i	0.0607419	+	0.535866i
$664$	−3.14522	−	5.44769i	−0.122058	−	0.211411i
$665$		0			0
$666$	−2.11911	−	2.27772i	−0.0821139	−	0.0882598i
$667$	0.227973	+	0.394862i	0.00882717	+	0.0152891i
$668$	4.90028			0.189597
$669$	−2.28690	−	20.1750i	−0.0884166	−	0.780012i
$670$	17.0395			0.658294
$671$	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	$0.900503\pi$
$674$	−1.37862	−	2.38785i	−0.0531026	−	0.0919764i
$675$	−5.55519	−	15.7738i	−0.213819	−	0.607136i
$676$	−9.58584	+	16.6032i	−0.368686	+	0.638583i
$677$	14.1950	−	24.5865i	0.545560	−	0.944937i	−0.453012	−	0.891505i	$-0.649650\pi$
$677$	14.1950	−	24.5865i	0.545560	−	0.944937i	0.998571	−	0.0534326i	$-0.0170162\pi$
$678$	−5.20910	−	45.9547i	−0.200054	−	1.76488i
$679$		0			0
$680$	1.16071	−	2.01041i	0.0445111	−	0.0770956i
$681$	−17.7587	−	7.73385i	−0.680514	−	0.296362i
$682$	−10.7192			−0.410460
$683$	5.92034	−	10.2543i	0.226536	−	0.392371i	−0.730243	−	0.683187i	$-0.760593\pi$
$683$	5.92034	−	10.2543i	0.226536	−	0.392371i	0.956779	+	0.290816i	$0.0939267\pi$
$684$	10.1789	−	2.33764i	0.389199	−	0.0893821i
$685$	−2.95968			−0.113083
$686$		0			0
$687$	15.3345	+	6.67810i	0.585046	+	0.254786i
$688$	49.4461			1.88511
$689$	−3.90981	−	6.77199i	−0.148952	−	0.257992i
$690$	25.1976	−	18.6228i	0.959258	−	0.708960i
$691$	5.95416	−	10.3129i	0.226507	−	0.392321i	−0.730264	−	0.683165i	$-0.760603\pi$
$691$	5.95416	−	10.3129i	0.226507	−	0.392321i	0.956770	+	0.290844i	$0.0939361\pi$
$692$	−14.0976			−0.535909
$693$		0			0
$694$	54.3880			2.06454
$695$	0.504096	−	0.873119i	0.0191214	−	0.0331193i
$696$	−0.0135685	−	0.119702i	−0.000514313	−	0.00453727i
$697$	−6.98857	−	12.1046i	−0.264711	−	0.458493i
$698$	−66.2870			−2.50900
$699$	−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	$0.701976\pi$
$702$	32.2260	−	37.6002i	1.21629	−	1.41913i
$703$	0.705208	−	1.22146i	0.0265974	−	0.0460681i
$704$	−3.94041			−0.148510
$705$	17.6968	−	13.0792i	0.666499	−	0.492590i
$706$	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	−0.871836	−	0.489798i	$-0.837070\pi$
$709$	−0.312609	+	0.541455i	−0.0117403	+	0.0203348i	0.860096	+	0.510133i	$0.170404\pi$
$710$	15.1516	−	26.2433i	0.568628	−	0.984893i
$711$	17.3076	−	3.97480i	0.649085	−	0.149067i
$712$	−0.789685	−	1.36777i	−0.0295947	−	0.0512595i
$713$	14.1613	+	24.5281i	0.530345	+	0.918584i
$714$		0			0
$715$	−5.22647	+	9.05251i	−0.195459	+	0.338545i
$716$	−2.36489			−0.0883802
$717$	−0.542236	+	0.400751i	−0.0202502	+	0.0149663i
$718$	9.96239			0.371793
$719$	−12.1969	−	21.1257i	−0.454869	−	0.787857i	0.543811	−	0.839208i	$-0.316981\pi$
$719$	−12.1969	−	21.1257i	−0.454869	−	0.787857i	−0.998681	+	0.0513506i	$0.983647\pi$
$720$	−18.9192	+	4.34492i	−0.705078	+	0.161926i
$721$		0			0
$722$	−11.7185	−	20.2970i	−0.436116	−	0.755376i
$723$	−16.8902	−	7.35561i	−0.628152	−	0.273558i
$724$	−11.8123	−	20.4595i	−0.439002	−	0.760373i
$725$	0.0996792	+	0.172649i	0.00370199	+	0.00641204i
$726$	−22.3404	+	16.5112i	−0.829132	+	0.612787i
$727$	18.9253	+	32.7796i	0.701900	+	1.21573i	0.967799	+	0.251726i	$0.0809980\pi$
$727$	18.9253	+	32.7796i	0.701900	+	1.21573i	−0.265899	+	0.964001i	$0.585669\pi$
$728$		0			0
$729$	−21.0415	+	16.9191i	−0.779314	+	0.626634i
$730$	3.38991	+	5.87150i	0.125466	+	0.217314i
$731$	−15.7987			−0.584335
$732$	−7.15073	−	3.11412i	−0.264299	−	0.115101i
$733$	−2.40155			−0.0887033			−0.0443516	−	0.999016i	$-0.514122\pi$
$733$	−2.40155			−0.0887033			−0.0443516	+	0.999016i	$0.514122\pi$
$734$	21.2519	−	36.8093i	0.784421	−	1.35866i
$735$		0			0
$736$	24.5858	+	42.5839i	0.906245	+	1.56966i
$737$	−5.24517	−	9.08490i	−0.193208	−	0.334646i
$738$	−14.6280	+	47.6500i	−0.538465	+	1.75402i
$739$	−15.1940	+	26.3167i	−0.558920	+	0.968077i	0.438667	+	0.898650i	$0.355451\pi$
$739$	−15.1940	+	26.3167i	−0.558920	+	0.968077i	−0.997587	+	0.0694277i	$0.977883\pi$
$740$	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	$0.196463\pi$
$744$	−0.842852	−	7.43565i	−0.0309004	−	0.272604i
$745$	−8.78934			−0.322016
$746$	19.7961	−	34.2879i	0.724787	−	1.25537i
$747$	4.93228	−	16.0666i	0.180463	−	0.587847i
$748$	3.25793			0.119122
$749$		0			0
$750$	28.1336	−	20.7927i	1.02729	−	0.759242i
$751$	−0.975011			−0.0355787			−0.0177893	−	0.999842i	$-0.505663\pi$
$751$	−0.975011			−0.0355787			−0.0177893	+	0.999842i	$0.505663\pi$
$752$	23.0718	+	39.9615i	0.841341	+	1.45724i
$753$	5.18685	+	2.25885i	0.189019	+	0.0823172i
$754$	−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
$759$	−17.6855	−	7.70198i	−0.641943	−	0.279564i
$760$	−1.87657	−	3.25031i	−0.0680703	−	0.117901i
$761$	54.1749			1.96384			0.981920	−	0.189298i	$-0.0606213\pi$
$761$	54.1749			1.96384			0.981920	+	0.189298i	$0.0606213\pi$
$762$	21.8000	−	16.1117i	0.789729	−	0.583666i
$763$		0			0
$764$	31.5484			1.14138
$765$	6.04494	−	1.38826i	0.218555	−	0.0501927i
$766$	32.1489	−	55.6835i	1.16159	−	2.01193i
$767$	−43.7025			−1.57801
$768$	−4.09272	−	36.1060i	−0.147683	−	1.30286i
$769$	10.4326	−	18.0698i	0.376208	−	0.651612i	−0.614299	−	0.789074i	$-0.710561\pi$
$769$	10.4326	−	18.0698i	0.376208	−	0.651612i	0.990507	+	0.137462i	$0.0438943\pi$
$770$		0			0
$771$	7.45681	+	3.24742i	0.268551	+	0.116953i
$772$	−4.30047	+	7.44863i	−0.154777	+	0.268082i
$773$	27.4972	−	47.6266i	0.989007	−	1.71301i	0.366447	−	0.930439i	$-0.380574\pi$
$773$	27.4972	−	47.6266i	0.989007	−	1.71301i	0.622561	−	0.782572i	$-0.286092\pi$
$774$	38.3768	+	41.2491i	1.37942	+	1.48267i
$775$	6.19189	+	10.7247i	0.222419	+	0.385242i
$776$	6.84616	+	11.8579i	0.245763	+	0.425674i
$777$		0			0
$778$	−26.5895	+	46.0544i	−0.953281	+	1.65113i
$779$	−22.5975			−0.809639
$780$	15.2515	+	6.64196i	0.546090	+	0.237820i
$781$	−18.6560			−0.667566
$782$	−10.4963	−	18.1801i	−0.375346	−	0.650119i
$783$	0.209456	−	0.244386i	0.00748534	−	0.00873364i
$784$		0			0
$785$	11.5506	+	20.0062i	0.412258	+	0.714051i
$786$	5.16390	−	3.81649i	0.184190	−	0.136130i
$787$	4.59475	+	7.95833i	0.163785	+	0.283684i	0.936223	−	0.351406i	$-0.114296\pi$
$787$	4.59475	+	7.95833i	0.163785	+	0.283684i	−0.772438	+	0.635090i	$0.780963\pi$
$788$	−6.79103	−	11.7624i	−0.241921	−	0.419019i
$789$	31.0451	+	13.5200i	1.10523	+	0.481325i
$790$	7.27374	+	12.5985i	0.258788	+	0.448234i
$791$		0			0
$792$	3.47163	+	3.73146i	0.123359	+	0.132592i
$793$	−8.38296	−	14.5197i	−0.297688	−	0.515610i
$794$	−20.5934			−0.730832
$795$	−2.80878	+	2.07588i	−0.0996170	+	0.0736241i
$796$	−12.0659			−0.427665
$797$	−3.53774	+	6.12754i	−0.125313	+	0.217049i	−0.921855	−	0.387534i	$-0.873327\pi$
$797$	−3.53774	+	6.12754i	−0.125313	+	0.217049i	0.796542	+	0.604583i	$0.206660\pi$
$798$		0			0
$799$	−7.37174	−	12.7682i	−0.260793	−	0.451707i
$800$	10.7499	+	18.6194i	0.380067	+	0.658295i
$801$	1.23837	−	4.03392i	0.0437556	−	0.142532i
$802$	−0.996224	+	1.72551i	−0.0351779	+	0.0609299i
$803$	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
$807$	−21.9625	+	16.2318i	−0.773116	+	0.571388i
$808$	−1.25610			−0.0441894
$809$	−2.97060	+	5.14522i	−0.104441	+	0.180896i	−0.913510	−	0.406817i	$-0.866639\pi$
$809$	−2.97060	+	5.14522i	−0.104441	+	0.180896i	0.809069	+	0.587714i	$0.199972\pi$
$810$	−18.3085	−	12.4106i	−0.643295	−	0.436065i
$811$	−44.4139			−1.55958			−0.779791	−	0.626039i	$-0.784675\pi$
$811$	−44.4139			−1.55958			−0.779791	+	0.626039i	$0.784675\pi$
$812$		0			0
$813$	−2.88678	−	25.4672i	−0.101244	−	0.893173i
$814$	−1.56902			−0.0549942
$815$	−8.15485	−	14.1246i	−0.285652	−	0.494764i
$816$	1.46485	+	12.9229i	0.0512801	+	0.452393i
$817$	−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	−0.916133	−	0.400874i	$-0.868706\pi$
$821$	−3.17761	+	5.50378i	−0.110899	+	0.192083i	0.805234	+	0.592958i	$0.202040\pi$
$822$	5.68693	−	4.20305i	0.198355	−	0.146598i
$823$	4.73216	+	8.19635i	0.164953	+	0.285707i	0.936639	−	0.350297i	$-0.113919\pi$
$823$	4.73216	+	8.19635i	0.164953	+	0.285707i	−0.771686	+	0.636004i	$0.780586\pi$
$824$	−2.16760			−0.0755120
$825$	−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	$0.526944\pi$
$828$	−9.00905	+	29.3465i	−0.313086	+	1.01986i
$829$	−20.3926	+	35.3211i	−0.708266	+	1.22675i	0.257234	+	0.966349i	$0.417189\pi$
$829$	−20.3926	+	35.3211i	−0.708266	+	1.22675i	−0.965500	+	0.260403i	$0.916145\pi$
$830$	13.7680			0.477896
$831$	−11.8325	−	5.15302i	−0.410466	−	0.178756i
$832$	−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
$836$	2.63362	−	4.56156i	0.0910856	−	0.157765i
$837$	13.0110	−	15.1808i	0.449727	−	0.524726i
$838$	23.1823	+	40.1529i	0.800818	+	1.38706i
$839$	−9.60171	−	16.6307i	−0.331488	−	0.574154i	0.651316	−	0.758807i	$-0.274217\pi$
$839$	−9.60171	−	16.6307i	−0.331488	−	0.574154i	−0.982804	+	0.184653i	$0.940884\pi$
$840$		0			0
$841$	14.4981	−	25.1114i	0.499934	−	0.865911i
$842$	−54.6126			−1.88207
$843$	−5.06976	−	44.7255i	−0.174612	−	1.54043i
$844$	7.90225			0.272007
$845$	9.20374	+	15.9413i	0.316618	+	0.548399i
$846$	−15.4300	+	50.2625i	−0.530496	+	1.72806i
$847$		0			0
$848$	−3.66188	−	6.34256i	−0.125749	−	0.217804i
$849$	3.65886	+	32.2785i	0.125572	+	1.10780i
$850$	−4.58940	−	7.94907i	−0.157415	−	0.272651i
$851$	2.07286	+	3.59029i	0.0710566	+	0.123074i
$852$	3.34398	+	29.5006i	0.114563	+	1.01068i
$853$	6.95055	+	12.0387i	0.237982	+	0.412198i	0.960135	−	0.279536i	$-0.0901806\pi$
$853$	6.95055	+	12.0387i	0.237982	+	0.412198i	−0.722153	+	0.691734i	$0.756847\pi$
$854$		0			0
$855$	2.94280	−	9.58601i	0.100642	−	0.327835i
$856$	3.24469	+	5.61996i	0.110901	+	0.192086i
$857$	−56.9838			−1.94653			−0.973265	−	0.229686i	$-0.926230\pi$
$857$	−56.9838			−1.94653			−0.973265	+	0.229686i	$0.926230\pi$
$858$	−2.81299	−	24.8163i	−0.0960340	−	0.847213i
$859$	20.1002			0.685810			0.342905	−	0.939370i	$-0.388589\pi$
$859$	20.1002			0.685810			0.342905	+	0.939370i	$0.388589\pi$
$860$	−9.46298	+	16.3904i	−0.322685	+	0.558907i
$861$		0			0
$862$	−4.50214	−	7.79794i	−0.153344	−	0.265599i
$863$	−3.08893	−	5.35018i	−0.105148	−	0.182122i	0.808650	−	0.588289i	$-0.200198\pi$
$863$	−3.08893	−	5.35018i	−0.105148	−	0.182122i	−0.913799	+	0.406167i	$0.866865\pi$
$864$	22.5888	−	26.3558i	0.768486	−	0.896643i
$865$	−6.76781	+	11.7222i	−0.230112	+	0.398566i
$866$	−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
$870$	0.241742	+	0.105278i	0.00819581	+	0.00356925i
$871$	−35.8872			−1.21599
$872$	−4.62732	+	8.01476i	−0.156701	+	0.271414i
$873$	−10.7360	+	34.9720i	−0.363359	+	1.18362i
$874$	−33.9396			−1.14802
$875$		0			0
$876$	−6.09009	−	2.65221i	−0.205765	−	0.0896099i
$877$	−37.2574			−1.25809			−0.629046	−	0.777368i	$-0.716554\pi$
$877$	−37.2574			−1.25809			−0.629046	+	0.777368i	$0.716554\pi$
$878$	13.6468	+	23.6370i	0.460558	+	0.797710i
$879$	3.42905	−	2.53431i	0.115659	−	0.0854801i
$880$	−4.89504	+	8.47846i	−0.165012	+	0.285809i
$881$	11.7848			0.397041			0.198520	−	0.980097i	$-0.436386\pi$
$881$	11.7848			0.397041			0.198520	+	0.980097i	$0.436386\pi$
$882$		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
$885$	2.19854	+	19.3956i	0.0739032	+	0.651974i
$886$	−20.1634	−	34.9240i	−0.677402	−	1.17329i
$887$	−28.5161			−0.957479			−0.478739	−	0.877957i	$-0.658906\pi$
$887$	−28.5161			−0.957479			−0.478739	+	0.877957i	$0.658906\pi$
$888$	−0.123372	−	1.08839i	−0.00414010	−	0.0365240i
$889$		0			0
$890$	3.45680			0.115872
$891$	−0.981141	+	13.5818i	−0.0328695	+	0.455006i
$892$	−8.14822	+	14.1131i	−0.272823	+	0.472543i
$893$	−23.8364			−0.797656
$894$	16.8884	−	12.4818i	0.564834	−	0.417453i
$895$	−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
$899$	−0.119171	+	0.206410i	−0.00397456	+	0.00688414i
$900$	−3.93912	+	12.8315i	−0.131304	+	0.427715i
$901$	1.17002	+	2.02653i	0.0389790	+	0.0675135i
$902$	12.5693	+	21.7707i	0.418513	+	0.724885i
$903$		0			0
$904$	8.14183	−	14.1021i	0.270793	−	0.469028i
$905$	−22.6829			−0.754006
$906$	32.4872	−	24.0104i	1.07931	−	0.797690i
$907$	−7.89155			−0.262035			−0.131017	−	0.991380i	$-0.541824\pi$
$907$	−7.89155			−0.262035			−0.131017	+	0.991380i	$0.541824\pi$
$908$	7.77317	+	13.4635i	0.257962	+	0.446803i
$909$	−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	$0.989494\pi$
$912$	19.2781	+	8.39554i	0.638361	+	0.278004i
$913$	−4.23813	−	7.34065i	−0.140262	−	0.242940i
$914$	37.4007	+	64.7798i	1.23710	+	2.14273i
$915$	−6.02225	+	4.45087i	−0.199089	+	0.147141i
$916$	−6.71206	−	11.6256i	−0.221773	−	0.384121i
$917$		0			0
$918$	−9.64370	+	11.2519i	−0.318290	+	0.371369i
$919$	3.99271	+	6.91558i	0.131707	+	0.228124i	0.924335	−	0.381582i	$-0.124621\pi$
$919$	3.99271	+	6.91558i	0.131707	+	0.228124i	−0.792627	+	0.609706i	$0.791287\pi$
$920$	11.0318			0.363708
$921$	7.40446	+	3.22462i	0.243985	+	0.106255i
$922$	−5.21221			−0.171655
$923$	−31.9110	+	55.2714i	−1.05036	+	1.81928i
$924$		0			0
$925$	0.906337	+	1.56982i	0.0298002	+	0.0516154i
$926$	25.6529	+	44.4322i	0.843008	+	1.46013i
$927$	−3.94481	−	4.24006i	−0.129565	−	0.139262i
$928$	−0.206895	+	0.358353i	−0.00679167	+	0.0117635i
$929$	9.40031	−	16.2818i	0.308414	−	0.534189i	−0.669601	−	0.742721i	$-0.733535\pi$
$929$	9.40031	−	16.2818i	0.308414	−	0.534189i	0.978016	+	0.208531i	$0.0668684\pi$
$930$	15.0166	+	6.53966i	0.492412	+	0.214444i
$931$		0			0
$932$	−13.4081	+	23.2234i	−0.439196	+	0.760709i
$933$	5.36130	+	47.2974i	0.175521	+	1.54845i
$934$	49.0577			1.60522
$935$	1.56403	−	2.70898i	0.0511493	−	0.0885932i
$936$	16.9932	−	3.90260i	0.555440	−	0.127561i
$937$	−48.5788			−1.58700			−0.793500	−	0.608570i	$-0.791744\pi$
$937$	−48.5788			−1.58700			−0.793500	+	0.608570i	$0.791744\pi$
$938$		0			0
$939$	7.65172	−	5.65516i	0.249704	−	0.184549i
$940$	−17.6619			−0.576067
$941$	10.2425	+	17.7406i	0.333898	+	0.578328i	0.983272	−	0.182141i	$-0.0583027\pi$
$941$	10.2425	+	17.7406i	0.333898	+	0.578328i	−0.649375	+	0.760468i	$0.724969\pi$
$942$	−50.6049	−	22.0383i	−1.64880	−	0.718046i
$943$	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	−0.719793	−	0.694188i	$-0.755764\pi$
$947$	7.42524	−	12.8609i	0.241288	−	0.417923i	0.961081	+	0.276265i	$0.0890969\pi$
$948$	−13.0675	−	5.69086i	−0.424413	−	0.184831i
$949$	−7.13954	−	12.3661i	−0.231759	−	0.401419i
$950$	−14.8398			−0.481466
$951$	−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	$0.228790\pi$
$954$	2.44901	−	7.97750i	0.0792896	−	0.258281i
$955$	15.1454	−	26.2326i	0.490094	−	0.848868i
$956$	0.541167			0.0175026
$957$	−0.0182833	−	0.161295i	−0.000591015	−	0.00521394i
$958$	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
$962$	−2.68380	+	4.64847i	−0.0865291	+	0.149873i
$963$	−5.08826	+	16.5747i	−0.163967	+	0.534112i
$964$	7.39301	+	12.8051i	0.238113	+	0.412423i
$965$	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	$0.157825\pi$
$968$	−9.78089			−0.314370
$969$	−6.15960	−	2.68249i	−0.197875	−	0.0861739i
$970$	−29.9687			−0.962235
$971$	3.78085	+	6.54863i	0.121333	+	0.210156i	0.920294	−	0.391228i	$-0.127950\pi$
$971$	3.78085	+	6.54863i	0.121333	+	0.210156i	−0.798960	+	0.601384i	$0.794616\pi$
$972$	21.6526	−	0.882976i	0.694506	−	0.0283215i
$973$		0			0
$974$	0.281870	+	0.488213i	0.00903169	+	0.0156434i
$975$	−23.2040	+	17.1494i	−0.743122	+	0.549220i
$976$	−7.85137	−	13.5990i	−0.251316	−	0.435293i
$977$	28.3101	+	49.0345i	0.905721	+	1.56875i	0.819947	+	0.572440i	$0.194003\pi$
$977$	28.3101	+	49.0345i	0.905721	+	1.56875i	0.0857737	+	0.996315i	$0.472664\pi$
$978$	35.7277	+	15.5593i	1.14245	+	0.497531i
$979$	−1.06408	−	1.84305i	−0.0340083	−	0.0589041i
$980$		0			0
$981$	−24.0990	+	5.53449i	−0.769422	+	0.176703i
$982$	16.6997	+	28.9247i	0.532909	+	0.923025i
$983$	−32.2972			−1.03012			−0.515061	−	0.857154i	$-0.672231\pi$
$983$	−32.2972			−1.03012			−0.515061	+	0.857154i	$0.672231\pi$
$984$	−14.1134	+	10.4308i	−0.449920	+	0.332523i
$985$	−13.0407			−0.415510
$986$	0.0883286	−	0.152990i	0.00281296	−	0.00487218i
$987$		0			0
$988$	−9.00955	−	15.6050i	−0.286632	−	0.496461i
$989$	−37.5391	−	65.0197i	−1.19367	−	2.06750i
$990$	−10.8721	+	2.49686i	−0.345540	+	0.0793554i
$991$	−7.15502	+	12.3929i	−0.227287	+	0.393672i	−0.957003	−	0.290078i	$-0.906319\pi$
$991$	−7.15502	+	12.3929i	−0.227287	+	0.393672i	0.729716	+	0.683750i	$0.239652\pi$
$992$	−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
$996$	−10.8480	+	8.01748i	−0.343734	+	0.254044i
$997$	−56.2524			−1.78153			−0.890765	−	0.454463i	$-0.849831\pi$
$997$	−56.2524			−1.78153			−0.890765	+	0.454463i	$0.849831\pi$
$998$	−19.6176	+	33.9787i	−0.620985	+	1.07558i
$999$	1.90449	−	2.22209i	0.0602553	−	0.0703038i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.g.b.4.4	✓	10	7.6	odd	2
63.2.g.b.16.4	yes	10	63.61	odd	6
63.2.h.b.25.2	yes	10	63.34	odd	6
63.2.h.b.58.2	yes	10	7.5	odd	6
189.2.g.b.100.2		10	63.47	even	6
189.2.g.b.172.2		10	21.20	even	2
189.2.h.b.37.4		10	21.5	even	6
189.2.h.b.46.4		10	63.20	even	6
441.2.f.e.148.4		10	7.3	odd	6
441.2.f.e.295.4		10	63.52	odd	6
441.2.f.f.148.4		10	7.4	even	3
441.2.f.f.295.4		10	63.25	even	3
441.2.g.f.67.4		10	1.1	even	1	trivial
441.2.g.f.79.4		10	63.16	even	3	inner
441.2.h.f.214.2		10	9.7	even	3
441.2.h.f.373.2		10	7.2	even	3
567.2.e.e.163.2		10	63.5	even	6
567.2.e.e.487.2		10	63.41	even	6
567.2.e.f.163.4		10	63.40	odd	6
567.2.e.f.487.4		10	63.13	odd	6
1008.2.q.i.529.2		10	252.223	even	6
1008.2.q.i.625.2		10	28.19	even	6
1008.2.t.i.193.5		10	28.27	even	2
1008.2.t.i.961.5		10	252.187	even	6
1323.2.f.e.442.2		10	21.17	even	6
1323.2.f.e.883.2		10	63.38	even	6
1323.2.f.f.442.2		10	21.11	odd	6
1323.2.f.f.883.2		10	63.11	odd	6
1323.2.g.f.361.2		10	3.2	odd	2
1323.2.g.f.667.2		10	63.2	odd	6
1323.2.h.f.226.4		10	21.2	odd	6
1323.2.h.f.802.4		10	9.2	odd	6
3024.2.q.i.2305.4		10	84.47	odd	6
3024.2.q.i.2881.4		10	252.83	odd	6
3024.2.t.i.289.2		10	252.47	odd	6
3024.2.t.i.1873.2		10	84.83	odd	2
3969.2.a.z.1.2		5	63.31	odd	6
3969.2.a.ba.1.2		5	63.4	even	3
3969.2.a.bb.1.4		5	63.32	odd	6
3969.2.a.bc.1.4		5	63.59	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	441.g (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.920620 - 1.59456i) q^{2} +(1.58800 + 0.691567i) q^{3} +(-0.695084 - 1.20392i) q^{4} -1.33475 q^{5} +(2.56469 - 1.89549i) q^{6} +1.12285 q^{8} +(2.04347 + 2.19641i) q^{9} +O(q^{10})\)	\(q+(0.920620 - 1.59456i) q^{2} +(1.58800 + 0.691567i) q^{3} +(-0.695084 - 1.20392i) q^{4} -1.33475 q^{5} +(2.56469 - 1.89549i) q^{6} +1.12285 q^{8} +(2.04347 + 2.19641i) q^{9} +(-1.22880 + 2.12835i) q^{10} +1.51302 q^{11} +(-0.271199 - 2.39252i) q^{12} +(2.58800 - 4.48254i) q^{13} +(-2.11958 - 0.923072i) q^{15} +(2.42388 - 4.19829i) q^{16} +(-0.774463 + 1.34141i) q^{17} +(5.38358 - 1.23637i) q^{18} +(1.25211 + 2.16872i) q^{19} +(0.927765 + 1.60694i) q^{20} +(1.39291 - 2.41260i) q^{22} -7.36079 q^{23} +(1.78308 + 0.776526i) q^{24} -3.21843 q^{25} +(-4.76513 - 8.25344i) q^{26} +(1.72605 + 4.90110i) q^{27} +(-0.0309713 - 0.0536439i) q^{29} +(-3.42323 + 2.53001i) q^{30} +(-1.92388 - 3.33227i) q^{31} +(-3.34011 - 5.78523i) q^{32} +(2.40267 + 1.04635i) q^{33} +(1.42597 + 2.46986i) q^{34} +(1.22392 - 3.98687i) q^{36} +(-0.281608 - 0.487760i) q^{37} +4.61087 q^{38} +(7.20971 - 5.32849i) q^{39} -1.49873 q^{40} +(-4.51188 + 7.81481i) q^{41} +(5.09988 + 8.83325i) q^{43} +(-1.05167 - 1.82155i) q^{44} +(-2.72753 - 2.93167i) q^{45} +(-6.77649 + 11.7372i) q^{46} +(-4.75925 + 8.24327i) q^{47} +(6.75252 - 4.99060i) q^{48} +(-2.96296 + 5.13199i) q^{50} +(-2.15752 + 1.59456i) q^{51} -7.19550 q^{52} +(0.755374 - 1.30835i) q^{53} +(9.40414 + 1.75975i) q^{54} -2.01950 q^{55} +(0.488532 + 4.30983i) q^{57} -0.114051 q^{58} +(-4.22166 - 7.31212i) q^{59} +(0.361984 + 3.19342i) q^{60} +(1.61958 - 2.80520i) q^{61} -7.08467 q^{62} -2.60434 q^{64} +(-3.45434 + 5.98309i) q^{65} +(3.88042 - 2.86790i) q^{66} +(-3.46670 - 6.00449i) q^{67} +2.15327 q^{68} +(-11.6889 - 5.09048i) q^{69} -12.3304 q^{71} +(2.29451 + 2.46624i) q^{72} +(1.37936 - 2.38912i) q^{73} -1.03702 q^{74} +(-5.11086 - 2.22576i) q^{75} +(1.74064 - 3.01488i) q^{76} +(-1.85920 - 16.4018i) q^{78} +(2.95969 - 5.12633i) q^{79} +(-3.23529 + 5.60368i) q^{80} +(-0.648467 + 8.97661i) q^{81} +(8.30746 + 14.3889i) q^{82} +(-2.80111 - 4.85167i) q^{83} +(1.03372 - 1.79045i) q^{85} +18.7802 q^{86} +(-0.0120840 - 0.106605i) q^{87} +1.69889 q^{88} +(-0.703287 - 1.21813i) q^{89} +(-7.18575 + 1.65025i) q^{90} +(5.11636 + 8.86180i) q^{92} +(-0.750637 - 6.62212i) q^{93} +(8.76293 + 15.1778i) q^{94} +(-1.67126 - 2.89470i) q^{95} +(-1.30320 - 11.4968i) q^{96} +(6.09713 + 10.5605i) q^{97} +(3.09180 + 3.32321i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 2 q^{2} - 2 q^{3} - 4 q^{4} + 8 q^{5} + 2 q^{6} - 6 q^{8} - 4 q^{9}+O(q^{10}) \) 10 * q + 2 * q^2 - 2 * q^3 - 4 * q^4 + 8 * q^5 + 2 * q^6 - 6 * q^8 - 4 * q^9	\( 10 q + 2 q^{2} - 2 q^{3} - 4 q^{4} + 8 q^{5} + 2 q^{6} - 6 q^{8} - 4 q^{9} + 7 q^{10} - 8 q^{11} - 22 q^{12} + 8 q^{13} - 19 q^{15} + 2 q^{16} - 12 q^{17} - 2 q^{18} - q^{19} - 5 q^{20} - q^{22} - 6 q^{23} - 3 q^{24} + 2 q^{25} - 11 q^{26} + 7 q^{27} + 7 q^{29} - 26 q^{30} + 3 q^{31} - 2 q^{32} + q^{33} - 3 q^{34} + 34 q^{36} + 40 q^{38} + 20 q^{39} - 6 q^{40} - 5 q^{41} - 7 q^{43} - 10 q^{44} + q^{45} + 3 q^{46} - 27 q^{47} + 5 q^{48} + 19 q^{50} + 24 q^{51} - 20 q^{52} - 21 q^{53} + 53 q^{54} - 4 q^{55} - 4 q^{57} + 20 q^{58} - 30 q^{59} - 41 q^{60} + 14 q^{61} + 12 q^{62} - 50 q^{64} - 11 q^{65} + 41 q^{66} - 2 q^{67} + 54 q^{68} - 15 q^{69} - 6 q^{71} + 48 q^{72} - 15 q^{73} + 72 q^{74} - 31 q^{75} - 5 q^{76} - 20 q^{78} - 4 q^{79} - 20 q^{80} + 8 q^{81} + 5 q^{82} - 9 q^{83} - 6 q^{85} + 16 q^{86} - 32 q^{87} + 36 q^{88} - 28 q^{89} - 28 q^{90} + 27 q^{92} - 12 q^{93} + 3 q^{94} - 14 q^{95} + q^{96} + 12 q^{97} + 35 q^{99}+O(q^{100}) \) 10 * q + 2 * q^2 - 2 * q^3 - 4 * q^4 + 8 * q^5 + 2 * q^6 - 6 * q^8 - 4 * q^9 + 7 * q^10 - 8 * q^11 - 22 * q^12 + 8 * q^13 - 19 * q^15 + 2 * q^16 - 12 * q^17 - 2 * q^18 - q^19 - 5 * q^20 - q^22 - 6 * q^23 - 3 * q^24 + 2 * q^25 - 11 * q^26 + 7 * q^27 + 7 * q^29 - 26 * q^30 + 3 * q^31 - 2 * q^32 + q^33 - 3 * q^34 + 34 * q^36 + 40 * q^38 + 20 * q^39 - 6 * q^40 - 5 * q^41 - 7 * q^43 - 10 * q^44 + q^45 + 3 * q^46 - 27 * q^47 + 5 * q^48 + 19 * q^50 + 24 * q^51 - 20 * q^52 - 21 * q^53 + 53 * q^54 - 4 * q^55 - 4 * q^57 + 20 * q^58 - 30 * q^59 - 41 * q^60 + 14 * q^61 + 12 * q^62 - 50 * q^64 - 11 * q^65 + 41 * q^66 - 2 * q^67 + 54 * q^68 - 15 * q^69 - 6 * q^71 + 48 * q^72 - 15 * q^73 + 72 * q^74 - 31 * q^75 - 5 * q^76 - 20 * q^78 - 4 * q^79 - 20 * q^80 + 8 * q^81 + 5 * q^82 - 9 * q^83 - 6 * q^85 + 16 * q^86 - 32 * q^87 + 36 * q^88 - 28 * q^89 - 28 * q^90 + 27 * q^92 - 12 * q^93 + 3 * q^94 - 14 * q^95 + q^96 + 12 * q^97 + 35 * q^99

Introduction

L-functions

Modular forms

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