LMFDB - Embedded newform 637.2.k.i.459.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(459,637)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 1]))

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

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

chi := DirichletCharacter("637.459");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.k (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.2346760387617129.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} + x^{10} + 10 x^{9} - 15 x^{8} - 10 x^{7} + 45 x^{6} - 20 x^{5} - 60 x^{4} + 80 x^{3} + \cdots + 64 $ x^12 - 3x^11 + x^10 + 10x^9 - 15x^8 - 10x^7 + 45x^6 - 20x^5 - 60x^4 + 80x^3 + 16x^2 - 96x + 64
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			459.2
Root			$-1.38488 - 0.286553i$ of defining polynomial
Character	$\chi$	$=$	637.459
Dual form			637.2.k.i.569.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.37905i q^{2} +(1.44060 + 2.49520i) q^{3} +0.0982074 q^{4} +(0.697972 - 0.402974i) q^{5} +(3.44101 - 1.98667i) q^{6} -2.89354i q^{8} +(-2.65067 + 4.59109i) q^{9} +O(q^{10})$	\(q-1.37905i q^{2} +(1.44060 + 2.49520i) q^{3} +0.0982074 q^{4} +(0.697972 - 0.402974i) q^{5} +(3.44101 - 1.98667i) q^{6} -2.89354i q^{8} +(-2.65067 + 4.59109i) q^{9} +(-0.555723 - 0.962541i) q^{10} +(4.56532 - 2.63579i) q^{11} +(0.141478 + 0.245047i) q^{12} +(2.36581 + 2.72084i) q^{13} +(2.01100 + 1.16105i) q^{15} -3.79394 q^{16} -0.560102 q^{17} +(6.33136 + 3.65541i) q^{18} +(-5.06165 - 2.92234i) q^{19} +(0.0685460 - 0.0395750i) q^{20} +(-3.63490 - 6.29583i) q^{22} +1.60488 q^{23} +(7.21995 - 4.16844i) q^{24} +(-2.17522 + 3.76760i) q^{25} +(3.75219 - 3.26258i) q^{26} -6.63060 q^{27} +(-1.14008 + 1.97467i) q^{29} +(1.60115 - 2.77328i) q^{30} +(-3.01022 - 1.73795i) q^{31} -0.555034i q^{32} +(13.1536 + 7.59424i) q^{33} +0.772411i q^{34} +(-0.260315 + 0.450879i) q^{36} +1.24196i q^{37} +(-4.03007 + 6.98029i) q^{38} +(-3.38084 + 9.82279i) q^{39} +(-1.16602 - 2.01961i) q^{40} +(-0.803413 - 0.463851i) q^{41} +(2.22356 + 3.85131i) q^{43} +(0.448348 - 0.258854i) q^{44} +4.27260i q^{45} -2.21321i q^{46} +(3.32915 - 1.92209i) q^{47} +(-5.46556 - 9.46662i) q^{48} +(5.19572 + 2.99975i) q^{50} +(-0.806883 - 1.39756i) q^{51} +(0.232340 + 0.267207i) q^{52} +(-2.72727 + 4.72377i) q^{53} +9.14396i q^{54} +(2.12431 - 3.67941i) q^{55} -16.8397i q^{57} +(2.72318 + 1.57223i) q^{58} +10.9940i q^{59} +(0.197495 + 0.114024i) q^{60} +(3.65107 - 6.32385i) q^{61} +(-2.39673 + 4.15126i) q^{62} -8.35330 q^{64} +(2.74769 + 0.945710i) q^{65} +(10.4729 - 18.1396i) q^{66} +(6.36144 - 3.67278i) q^{67} -0.0550061 q^{68} +(2.31199 + 4.00448i) q^{69} +(-8.06668 + 4.65730i) q^{71} +(13.2845 + 7.66982i) q^{72} +(-4.33139 - 2.50073i) q^{73} +1.71273 q^{74} -12.5345 q^{75} +(-0.497091 - 0.286996i) q^{76} +(13.5462 + 4.66237i) q^{78} +(-5.68437 - 9.84562i) q^{79} +(-2.64806 + 1.52886i) q^{80} +(-1.60006 - 2.77138i) q^{81} +(-0.639676 + 1.10795i) q^{82} -5.81962i q^{83} +(-0.390935 + 0.225707i) q^{85} +(5.31117 - 3.06641i) q^{86} -6.56959 q^{87} +(-7.62677 - 13.2100i) q^{88} -5.00946i q^{89} +5.89215 q^{90} +0.157611 q^{92} -10.0148i q^{93} +(-2.65067 - 4.59109i) q^{94} -4.71051 q^{95} +(1.38492 - 0.799583i) q^{96} +(-9.22171 + 5.32416i) q^{97} +27.9464i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 3 q^{3} - 8 q^{4} + 3 q^{5} + 9 q^{6} - q^{9}+O(q^{10}) $ 12 * q + 3 * q^3 - 8 * q^4 + 3 * q^5 + 9 * q^6 - q^9	$ 12 q + 3 q^{3} - 8 q^{4} + 3 q^{5} + 9 q^{6} - q^{9} - 12 q^{10} + 12 q^{11} + q^{12} + 2 q^{13} - 12 q^{15} + 16 q^{16} + 34 q^{17} + 3 q^{18} - 9 q^{19} + 3 q^{20} - 15 q^{22} - 6 q^{23} - 15 q^{24} - 5 q^{25} + 6 q^{26} - 12 q^{27} - q^{29} + 11 q^{30} - 18 q^{31} + 6 q^{33} - 13 q^{36} - 19 q^{38} - 4 q^{39} + q^{40} + 6 q^{41} + 11 q^{43} - 33 q^{44} + 15 q^{47} - 19 q^{48} + 18 q^{50} + 4 q^{51} + 7 q^{52} - 8 q^{53} + 15 q^{55} - 24 q^{58} - 30 q^{60} - 5 q^{61} - 41 q^{62} + 2 q^{64} + 21 q^{65} + 34 q^{66} + 15 q^{67} - 22 q^{68} - 7 q^{69} + 30 q^{71} + 57 q^{72} - 42 q^{73} + 66 q^{74} + 2 q^{75} + 45 q^{76} + 44 q^{78} - 35 q^{79} + 63 q^{80} + 14 q^{81} - 5 q^{82} - 21 q^{85} - 57 q^{86} + 20 q^{87} - 14 q^{88} - 66 q^{92} - q^{94} - 4 q^{95} - 21 q^{96} + 3 q^{97}+O(q^{100}) $ 12 * q + 3 * q^3 - 8 * q^4 + 3 * q^5 + 9 * q^6 - q^9 - 12 * q^10 + 12 * q^11 + q^12 + 2 * q^13 - 12 * q^15 + 16 * q^16 + 34 * q^17 + 3 * q^18 - 9 * q^19 + 3 * q^20 - 15 * q^22 - 6 * q^23 - 15 * q^24 - 5 * q^25 + 6 * q^26 - 12 * q^27 - q^29 + 11 * q^30 - 18 * q^31 + 6 * q^33 - 13 * q^36 - 19 * q^38 - 4 * q^39 + q^40 + 6 * q^41 + 11 * q^43 - 33 * q^44 + 15 * q^47 - 19 * q^48 + 18 * q^50 + 4 * q^51 + 7 * q^52 - 8 * q^53 + 15 * q^55 - 24 * q^58 - 30 * q^60 - 5 * q^61 - 41 * q^62 + 2 * q^64 + 21 * q^65 + 34 * q^66 + 15 * q^67 - 22 * q^68 - 7 * q^69 + 30 * q^71 + 57 * q^72 - 42 * q^73 + 66 * q^74 + 2 * q^75 + 45 * q^76 + 44 * q^78 - 35 * q^79 + 63 * q^80 + 14 * q^81 - 5 * q^82 - 21 * q^85 - 57 * q^86 + 20 * q^87 - 14 * q^88 - 66 * q^92 - q^94 - 4 * q^95 - 21 * q^96 + 3 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

$n$	$197$	$248$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$		−	1.37905i		−	0.975139i	−0.873084	−	0.487570i	$-0.837884\pi$
$2$		−	1.37905i		−	0.975139i	0.873084	−	0.487570i	$-0.162116\pi$
$3$	1.44060	+	2.49520i	0.831732	+	1.44060i	0.896664	+	0.442712i	$0.145984\pi$
$3$	1.44060	+	2.49520i	0.831732	+	1.44060i	−0.0649323	+	0.997890i	$0.520683\pi$
$4$	0.0982074			0.0491037
$5$	0.697972	−	0.402974i	0.312142	−	0.180216i	−0.335742	−	0.941954i	$-0.608987\pi$
$5$	0.697972	−	0.402974i	0.312142	−	0.180216i	0.647885	+	0.761738i	$0.275654\pi$
$6$	3.44101	−	1.98667i	1.40479	−	0.811054i
$7$		0			0
$7$		0			0
$8$		−	2.89354i		−	1.02302i
$9$	−2.65067	+	4.59109i	−0.883555	+	1.53036i
$10$	−0.555723	−	0.962541i	−0.175735	−	0.304382i
$11$	4.56532	−	2.63579i	1.37650	−	0.794720i	0.384760	−	0.923017i	$-0.374284\pi$
$11$	4.56532	−	2.63579i	1.37650	−	0.794720i	0.991736	+	0.128296i	$0.0409508\pi$
$12$	0.141478	+	0.245047i	0.0408411	+	0.0707389i
$13$	2.36581	+	2.72084i	0.656156	+	0.754625i
$13$	2.36581	+	2.72084i	0.656156	+	0.754625i
$14$		0			0
$15$	2.01100	+	1.16105i	0.519237	+	0.299782i
$16$	−3.79394			−0.948485
$17$	−0.560102			−0.135845			−0.0679223	−	0.997691i	$-0.521637\pi$
$17$	−0.560102			−0.135845			−0.0679223	+	0.997691i	$0.521637\pi$
$18$	6.33136	+	3.65541i	1.49232	+	0.861589i
$19$	−5.06165	−	2.92234i	−1.16122	−	0.670431i	−0.209625	−	0.977782i	$-0.567224\pi$
$19$	−5.06165	−	2.92234i	−1.16122	−	0.670431i	−0.951596	+	0.307351i	$0.900558\pi$
$20$	0.0685460	−	0.0395750i	0.0153273	−	0.00884925i
$21$		0			0
$22$	−3.63490	−	6.29583i	−0.774963	−	1.34228i
$23$	1.60488			0.334640			0.167320	−	0.985903i	$-0.446489\pi$
$23$	1.60488			0.334640			0.167320	+	0.985903i	$0.446489\pi$
$24$	7.21995	−	4.16844i	1.47377	−	0.850880i
$25$	−2.17522	+	3.76760i	−0.435045	+	0.753520i
$26$	3.75219	−	3.26258i	0.735864	−	0.639844i
$27$	−6.63060			−1.27606
$28$		0			0
$29$	−1.14008	+	1.97467i	−0.211707	+	0.366687i	−0.952249	−	0.305323i	$-0.901236\pi$
$29$	−1.14008	+	1.97467i	−0.211707	+	0.366687i	0.740542	+	0.672010i	$0.234569\pi$
$30$	1.60115	−	2.77328i	0.292329	−	0.506329i
$31$	−3.01022	−	1.73795i	−0.540651	−	0.312145i	0.204692	−	0.978827i	$-0.434381\pi$
$31$	−3.01022	−	1.73795i	−0.540651	−	0.312145i	−0.745343	+	0.666681i	$0.767714\pi$
$32$		−	0.555034i		−	0.0981171i
$33$	13.1536	+	7.59424i	2.28975	+	1.32199i
$34$			0.772411i			0.132467i
$35$		0			0
$36$	−0.260315	+	0.450879i	−0.0433858	+	0.0751464i
$37$			1.24196i			0.204177i	0.994775	+	0.102088i	$0.0325524\pi$
$37$			1.24196i			0.204177i	−0.994775	+	0.102088i	$0.967448\pi$
$38$	−4.03007	+	6.98029i	−0.653764	+	1.13235i
$39$	−3.38084	+	9.82279i	−0.541368	+	1.57291i
$40$	−1.16602	−	2.01961i	−0.184364	−	0.319329i
$41$	−0.803413	−	0.463851i	−0.125472	−	0.0724413i	0.435950	−	0.899971i	$-0.356412\pi$
$41$	−0.803413	−	0.463851i	−0.125472	−	0.0724413i	−0.561422	+	0.827529i	$0.689746\pi$
$42$		0			0
$43$	2.22356	+	3.85131i	0.339089	+	0.587320i	0.984262	−	0.176717i	$-0.0565478\pi$
$43$	2.22356	+	3.85131i	0.339089	+	0.587320i	−0.645172	+	0.764037i	$0.723214\pi$
$44$	0.448348	−	0.258854i	0.0675910	−	0.0390237i
$45$			4.27260i			0.636921i
$46$		−	2.21321i		−	0.326320i
$47$	3.32915	−	1.92209i	0.485607	−	0.280365i	−0.237143	−	0.971475i	$-0.576211\pi$
$47$	3.32915	−	1.92209i	0.485607	−	0.280365i	0.722750	+	0.691109i	$0.242878\pi$
$48$	−5.46556	−	9.46662i	−0.788885	−	1.36639i
$49$		0			0
$50$	5.19572	+	2.99975i	0.734786	+	0.424229i
$51$	−0.806883	−	1.39756i	−0.112986	−	0.195698i
$52$	0.232340	+	0.267207i	0.0322197	+	0.0370549i
$53$	−2.72727	+	4.72377i	−0.374620	+	0.648860i	−0.990270	−	0.139159i	$-0.955560\pi$
$53$	−2.72727	+	4.72377i	−0.374620	+	0.648860i	0.615650	+	0.788019i	$0.288893\pi$
$54$			9.14396i			1.24434i
$55$	2.12431	−	3.67941i	0.286442	−	0.496132i
$56$		0			0
$57$		−	16.8397i		−	2.23048i
$58$	2.72318	+	1.57223i	0.357571	+	0.206444i
$59$			10.9940i			1.43129i	0.698463	+	0.715646i	$0.253868\pi$
$59$			10.9940i			1.43129i	−0.698463	+	0.715646i	$0.746132\pi$
$60$	0.197495	+	0.114024i	0.0254965	+	0.0147204i
$61$	3.65107	−	6.32385i	0.467472	−	0.809686i	−0.531837	−	0.846847i	$-0.678498\pi$
$61$	3.65107	−	6.32385i	0.467472	−	0.809686i	0.999309	+	0.0371610i	$0.0118314\pi$
$62$	−2.39673	+	4.15126i	−0.304385	+	0.527210i
$63$		0			0
$64$	−8.35330			−1.04416
$65$	2.74769	+	0.945710i	0.340809	+	0.117301i
$66$	10.4729	−	18.1396i	1.28912	−	2.23283i
$67$	6.36144	−	3.67278i	0.777174	−	0.448701i	−0.0582541	−	0.998302i	$-0.518553\pi$
$67$	6.36144	−	3.67278i	0.777174	−	0.448701i	0.835428	+	0.549600i	$0.185220\pi$
$68$	−0.0550061			−0.00667047
$69$	2.31199	+	4.00448i	0.278330	+	0.482083i
$70$		0			0
$71$	−8.06668	+	4.65730i	−0.957339	+	0.552720i	−0.895353	−	0.445357i	$-0.853077\pi$
$71$	−8.06668	+	4.65730i	−0.957339	+	0.552720i	−0.0619857	+	0.998077i	$0.519743\pi$
$72$	13.2845	+	7.66982i	1.56559	+	0.903896i
$73$	−4.33139	−	2.50073i	−0.506951	−	0.292688i	0.224629	−	0.974444i	$-0.427883\pi$
$73$	−4.33139	−	2.50073i	−0.506951	−	0.292688i	−0.731579	+	0.681756i	$0.761216\pi$
$74$	1.71273			0.199101
$75$	−12.5345			−1.44736
$76$	−0.497091	−	0.286996i	−0.0570202	−	0.0329207i
$77$		0			0
$78$	13.5462	+	4.66237i	1.53380	+	0.527909i
$79$	−5.68437	−	9.84562i	−0.639542	−	1.10772i	−0.985533	−	0.169481i	$-0.945791\pi$
$79$	−5.68437	−	9.84562i	−0.639542	−	1.10772i	0.345992	−	0.938238i	$-0.387543\pi$
$80$	−2.64806	+	1.52886i	−0.296062	+	0.170932i
$81$	−1.60006	−	2.77138i	−0.177784	−	0.307931i
$82$	−0.639676	+	1.10795i	−0.0706404	+	0.122353i
$83$		−	5.81962i		−	0.638786i	−0.947622	−	0.319393i	$-0.896521\pi$
$83$		−	5.81962i		−	0.638786i	0.947622	−	0.319393i	$-0.103479\pi$
$84$		0			0
$85$	−0.390935	+	0.225707i	−0.0424029	+	0.0244813i
$86$	5.31117	−	3.06641i	0.572719	−	0.330659i
$87$	−6.56959			−0.704334
$88$	−7.62677	−	13.2100i	−0.813016	−	1.40819i
$89$		−	5.00946i		−	0.531001i	−0.964111	−	0.265501i	$-0.914463\pi$
$89$		−	5.00946i		−	0.531001i	0.964111	−	0.265501i	$-0.0855373\pi$
$90$	5.89215			0.621087
$91$		0			0
$92$	0.157611			0.0164320
$93$		−	10.0148i		−	1.03848i
$94$	−2.65067	−	4.59109i	−0.273395	−	0.473534i
$95$	−4.71051			−0.483289
$96$	1.38492	−	0.799583i	0.141348	−	0.0816071i
$97$	−9.22171	+	5.32416i	−0.936323	+	0.540586i	−0.888806	−	0.458284i	$-0.848464\pi$
$97$	−9.22171	+	5.32416i	−0.936323	+	0.540586i	−0.0475172	+	0.998870i	$0.515131\pi$
$98$		0			0
$99$			27.9464i			2.80872i
$100$	−0.213623	+	0.370006i	−0.0213623	+	0.0370006i
$101$	−1.95777	−	3.39096i	−0.194805	−	0.337413i	0.752031	−	0.659127i	$-0.229074\pi$
$101$	−1.95777	−	3.39096i	−0.194805	−	0.337413i	−0.946837	+	0.321715i	$0.895741\pi$
$102$	−1.92732	+	1.11274i	−0.190833	+	0.110177i
$103$	−4.22690	−	7.32120i	−0.416488	−	0.721379i	0.579095	−	0.815260i	$-0.303406\pi$
$103$	−4.22690	−	7.32120i	−0.416488	−	0.721379i	−0.995583	+	0.0938810i	$0.970073\pi$
$104$	7.87287	−	6.84556i	0.771998	−	0.671262i
$105$		0			0
$106$	6.51434	+	3.76106i	0.632729	+	0.365306i
$107$	−9.67522			−0.935339			−0.467670	−	0.883903i	$-0.654906\pi$
$107$	−9.67522			−0.935339			−0.467670	+	0.883903i	$0.654906\pi$
$108$	−0.651174			−0.0626592
$109$	−12.6126	−	7.28189i	−1.20807	−	0.697478i	−0.245731	−	0.969338i	$-0.579028\pi$
$109$	−12.6126	−	7.28189i	−1.20807	−	0.697478i	−0.962337	+	0.271860i	$0.912361\pi$
$110$	−5.07411	−	2.92954i	−0.483798	−	0.279321i
$111$	−3.09893	+	1.78917i	−0.294137	+	0.169820i
$112$		0			0
$113$	−9.75572	−	16.8974i	−0.917741	−	1.58957i	−0.802838	−	0.596197i	$-0.796678\pi$
$113$	−9.75572	−	16.8974i	−0.917741	−	1.58957i	−0.114903	−	0.993377i	$-0.536656\pi$
$114$	−23.2229			−2.17502
$115$	1.12016	−	0.646723i	0.104455	−	0.0603073i
$116$	−0.111964	+	0.193927i	−0.0103956	+	0.0180057i
$117$	−18.7626	+	3.64958i	−1.73460	+	0.337404i
$118$	15.1613			1.39571
$119$		0			0
$120$	3.35955	−	5.81891i	0.306683	−	0.531191i
$121$	8.39477	−	14.5402i	0.763161	−	1.32183i
$122$	−8.72093	−	5.03503i	−0.789556	−	0.455850i
$123$		−	2.67290i		−	0.241007i
$124$	−0.295626	−	0.170680i	−0.0265480	−	0.0153275i
$125$			7.53598i			0.674038i
$126$		0			0
$127$	−0.958656	+	1.66044i	−0.0850670	+	0.147340i	−0.905420	−	0.424517i	$-0.860444\pi$
$127$	−0.958656	+	1.66044i	−0.0850670	+	0.147340i	0.820353	+	0.571858i	$0.193777\pi$
$128$			10.4096i			0.920087i
$129$	−6.40652	+	11.0964i	−0.564063	+	0.976985i
$130$	1.30419	−	3.78922i	0.114385	−	0.332337i
$131$	7.79078	+	13.4940i	0.680684	+	1.17898i	0.974772	+	0.223201i	$0.0716506\pi$
$131$	7.79078	+	13.4940i	0.680684	+	1.17898i	−0.294089	+	0.955778i	$0.595016\pi$
$132$	1.29178	+	0.745811i	0.112435	+	0.0649145i
$133$		0			0
$134$	−5.06496	−	8.77278i	−0.437546	−	0.757852i
$135$	−4.62797	+	2.67196i	−0.398312	+	0.229966i
$136$			1.62068i			0.138972i
$137$		−	7.85105i		−	0.670761i	−0.942083	−	0.335380i	$-0.891135\pi$
$137$		−	7.85105i		−	0.670761i	0.942083	−	0.335380i	$-0.108865\pi$
$138$	5.52240	−	3.18836i	0.470098	−	0.271411i
$139$	4.96241	+	8.59514i	0.420906	+	0.729030i	0.996028	−	0.0890370i	$-0.0283789\pi$
$139$	4.96241	+	8.59514i	0.420906	+	0.729030i	−0.575122	+	0.818067i	$0.695046\pi$
$140$		0			0
$141$	9.59197	+	5.53793i	0.807790	+	0.466378i
$142$	6.42267	+	11.1244i	0.538979	+	0.933538i
$143$	17.9722	+	6.18574i	1.50291	+	0.517278i
$144$	10.0565	−	17.4183i	0.838039	−	1.45153i
$145$			1.83769i			0.152612i
$146$	−3.44864	+	5.97322i	−0.285412	+	0.494347i
$147$		0			0
$148$			0.121969i			0.0100258i
$149$	6.85827	+	3.95962i	0.561851	+	0.324385i	0.753888	−	0.657003i	$-0.228176\pi$
$149$	6.85827	+	3.95962i	0.561851	+	0.324385i	−0.192037	+	0.981388i	$0.561509\pi$
$150$			17.2858i			1.41138i
$151$	1.30005	+	0.750582i	0.105796	+	0.0610815i	0.551965	−	0.833868i	$-0.313878\pi$
$151$	1.30005	+	0.750582i	0.105796	+	0.0610815i	−0.446168	+	0.894949i	$0.647212\pi$
$152$	−8.45592	+	14.6461i	−0.685866	+	1.18795i
$153$	1.48464	−	2.57148i	0.120026	−	0.207892i
$154$		0			0
$155$	−2.80140			−0.225014
$156$	−0.332024	+	0.964671i	−0.0265832	+	0.0772355i
$157$	1.92846	−	3.34019i	0.153908	−	0.266576i	−0.778753	−	0.627331i	$-0.784147\pi$
$157$	1.92846	−	3.34019i	0.153908	−	0.266576i	0.932661	+	0.360754i	$0.117481\pi$
$158$	−13.5777	+	7.83906i	−1.08018	+	0.623642i
$159$	−15.7156			−1.24633
$160$	−0.223664	−	0.387398i	−0.0176822	−	0.0306265i
$161$		0			0
$162$	−3.82189	+	2.20657i	−0.300276	+	0.173364i
$163$	12.4369	+	7.18042i	0.974130	+	0.562414i	0.900493	−	0.434871i	$-0.143206\pi$
$163$	12.4369	+	7.18042i	0.974130	+	0.562414i	0.0736372	+	0.997285i	$0.476539\pi$
$164$	−0.0789011	−	0.0455536i	−0.00616114	−	0.00355714i
$165$	12.2411			0.952971
$166$	−8.02557			−0.622905
$167$	3.91563	+	2.26069i	0.303000	+	0.174937i	0.643790	−	0.765202i	$-0.277361\pi$
$167$	3.91563	+	2.26069i	0.303000	+	0.174937i	−0.340790	+	0.940140i	$0.610694\pi$
$168$		0			0
$169$	−1.80593	+	12.8740i	−0.138918	+	0.990304i
$170$	0.311262	+	0.539121i	0.0238727	+	0.0413487i
$171$	26.8335	−	15.4923i	2.05201	−	1.18473i
$172$	0.218370	+	0.378227i	0.0166505	+	0.0288396i
$173$	9.75896	−	16.9030i	0.741960	−	1.28511i	−0.209642	−	0.977778i	$-0.567230\pi$
$173$	9.75896	−	16.9030i	0.741960	−	1.28511i	0.951602	−	0.307334i	$-0.0994369\pi$
$174$			9.05982i			0.686823i
$175$		0			0
$176$	−17.3206	+	10.0000i	−1.30559	+	0.753780i
$177$	−27.4321	+	15.8379i	−2.06192	+	1.19045i
$178$	−6.90832			−0.517800
$179$	10.4098	+	18.0303i	0.778065	+	1.34765i	0.933055	+	0.359733i	$0.117132\pi$
$179$	10.4098	+	18.0303i	0.778065	+	1.34765i	−0.154990	+	0.987916i	$0.549535\pi$
$180$			0.419601i			0.0312752i
$181$	−16.5522			−1.23031			−0.615157	−	0.788405i	$-0.710907\pi$
$181$	−16.5522			−1.23031			−0.615157	+	0.788405i	$0.710907\pi$
$182$		0			0
$183$	21.0390			1.55525
$184$		−	4.64378i		−	0.342344i
$185$	0.500477	+	0.866851i	0.0367958	+	0.0637322i
$186$	−13.8109			−1.01267
$187$	−2.55704	+	1.47631i	−0.186990	+	0.107958i
$188$	0.326948	−	0.188763i	0.0238451	−	0.0137670i
$189$		0			0
$190$			6.49606i			0.471274i
$191$	2.12504	−	3.68068i	0.153762	−	0.266324i	−0.778845	−	0.627216i	$-0.784194\pi$
$191$	2.12504	−	3.68068i	0.153762	−	0.266324i	0.932608	+	0.360892i	$0.117528\pi$
$192$	−12.0338	−	20.8431i	−0.868463	−	1.50422i
$193$	−10.0435	+	5.79861i	−0.722946	+	0.417393i	−0.815836	−	0.578283i	$-0.803723\pi$
$193$	−10.0435	+	5.79861i	−0.722946	+	0.417393i	0.0928898	+	0.995676i	$0.470390\pi$
$194$	7.34231	+	12.7172i	0.527147	+	0.913045i
$195$	1.59860	+	8.21842i	0.114478	+	0.588533i
$196$		0			0
$197$	−12.4892	−	7.21066i	−0.889821	−	0.513738i	−0.0159371	−	0.999873i	$-0.505073\pi$
$197$	−12.4892	−	7.21066i	−0.889821	−	0.513738i	−0.873884	+	0.486135i	$0.838406\pi$
$198$	38.5396			2.73889
$199$	7.05924			0.500416			0.250208	−	0.968192i	$-0.419501\pi$
$199$	7.05924			0.500416			0.250208	+	0.968192i	$0.419501\pi$
$200$	10.9017	+	6.29410i	0.770867	+	0.445060i
$201$	18.3286	+	10.5820i	1.29280	+	0.746398i
$202$	−4.67632	+	2.69987i	−0.329024	+	0.189962i
$203$		0			0
$204$	−0.0792419	−	0.137251i	−0.00554804	−	0.00960949i
$205$	−0.747680			−0.0522202
$206$	−10.0963	+	5.82912i	−0.703445	+	0.406134i
$207$	−4.25399	+	7.36812i	−0.295673	+	0.512120i
$208$	−8.97572	−	10.3227i	−0.622354	−	0.715751i
$209$	−30.8107			−2.13122
$210$		0			0
$211$	13.2113	−	22.8827i	0.909505	−	1.57531i	0.0947513	−	0.995501i	$-0.469794\pi$
$211$	13.2113	−	22.8827i	0.909505	−	1.57531i	0.814754	−	0.579807i	$-0.196872\pi$
$212$	−0.267838	+	0.463909i	−0.0183952	+	0.0318614i
$213$	−23.2417	−	13.4186i	−1.59250	−	0.919429i
$214$			13.3427i			0.912086i
$215$	3.10396	+	1.79207i	0.211688	+	0.122218i
$216$			19.1859i			1.30544i
$217$		0			0
$218$	−10.0421	+	17.3935i	−0.680138	+	1.17803i
$219$		−	14.4102i		−	0.973752i
$220$	0.208623	−	0.361345i	0.0140654	−	0.0243619i
$221$	−1.32509	−	1.52395i	−0.0891353	−	0.102512i
$222$	2.46736	+	4.27359i	0.165598	+	0.286825i
$223$	−19.9191	−	11.5003i	−1.33388	−	0.770115i	−0.347987	−	0.937499i	$-0.613135\pi$
$223$	−19.9191	−	11.5003i	−1.33388	−	0.770115i	−0.985892	+	0.167384i	$0.946468\pi$
$224$		0			0
$225$	−11.5316	−	19.9733i	−0.768772	−	1.33155i
$226$	−23.3024	+	13.4537i	−1.55006	+	0.894925i
$227$		−	0.453367i		−	0.0300911i	−0.999887	−	0.0150455i	$-0.995211\pi$
$227$		−	0.453367i		−	0.0300911i	0.999887	−	0.0150455i	$-0.00478932\pi$
$228$		−	1.65379i		−	0.109525i
$229$	−15.0112	+	8.66674i	−0.991970	+	0.572714i	−0.905863	−	0.423571i	$-0.860776\pi$
$229$	−15.0112	+	8.66674i	−0.991970	+	0.572714i	−0.0861077	+	0.996286i	$0.527443\pi$
$230$	−0.891867	−	1.54476i	−0.0588080	−	0.101858i
$231$		0			0
$232$	5.71380	+	3.29886i	0.375129	+	0.216581i
$233$	3.90756	+	6.76809i	0.255992	+	0.443392i	0.965165	−	0.261643i	$-0.0842644\pi$
$233$	3.90756	+	6.76809i	0.255992	+	0.443392i	−0.709172	+	0.705035i	$0.750931\pi$
$234$	5.03298	+	25.8746i	0.329016	+	1.69148i
$235$	1.54910	−	2.68313i	0.101052	−	0.175028i
$236$			1.07969i			0.0702818i
$237$	16.3778	−	28.3672i	1.06385	−	1.84265i
$238$		0			0
$239$			13.5314i			0.875276i	0.899151	+	0.437638i	$0.144185\pi$
$239$			13.5314i			0.875276i	−0.899151	+	0.437638i	$0.855815\pi$
$240$	−7.62961	−	4.40496i	−0.492489	−	0.284339i
$241$		−	22.5592i		−	1.45317i	−0.687078	−	0.726583i	$-0.741107\pi$
$241$		−	22.5592i		−	1.45317i	0.687078	−	0.726583i	$-0.258893\pi$
$242$	−20.0517	−	11.5768i	−1.28897	−	0.744188i
$243$	−5.33581	+	9.24189i	−0.342292	+	0.592868i
$244$	0.358563	−	0.621049i	0.0229546	−	0.0397586i
$245$		0			0
$246$	−3.68607			−0.235015
$247$	−4.02364	−	20.6856i	−0.256018	−	1.31619i
$248$	−5.02884	+	8.71020i	−0.319331	+	0.553098i
$249$	14.5211	−	8.38375i	0.920236	−	0.531299i
$250$	10.3925			0.657281
$251$	3.36618	+	5.83039i	0.212471	+	0.368011i	0.952487	−	0.304578i	$-0.0985154\pi$
$251$	3.36618	+	5.83039i	0.212471	+	0.368011i	−0.740016	+	0.672589i	$0.765182\pi$
$252$		0			0
$253$	7.32677	−	4.23011i	0.460630	−	0.265945i
$254$	2.28984	+	1.32204i	0.143677	+	0.0829521i
$255$	−1.12636	−	0.650306i	−0.0705356	−	0.0407238i
$256$	−2.35120			−0.146950
$257$	16.5381			1.03162			0.515811	−	0.856703i	$-0.327491\pi$
$257$	16.5381			1.03162			0.515811	+	0.856703i	$0.327491\pi$
$258$	15.3026	+	8.83494i	0.952696	+	0.550039i
$259$		0			0
$260$	0.269844	+	0.0928757i	0.0167350	+	0.00575991i
$261$	−6.04392	−	10.4684i	−0.374110	−	0.647977i
$262$	18.6090	−	10.7439i	1.14967	−	0.663761i
$263$	5.01137	+	8.67994i	0.309014	+	0.535228i	0.978147	−	0.207915i	$-0.0666676\pi$
$263$	5.01137	+	8.67994i	0.309014	+	0.535228i	−0.669133	+	0.743143i	$0.733334\pi$
$264$	21.9743	−	38.0606i	1.35242	−	2.34247i
$265$			4.39608i			0.270049i
$266$		0			0
$267$	12.4996	−	7.21663i	0.764962	−	0.441651i
$268$	0.624740	−	0.360694i	0.0381621	−	0.0220329i
$269$	15.7230			0.958647			0.479323	−	0.877638i	$-0.340882\pi$
$269$	15.7230			0.958647			0.479323	+	0.877638i	$0.340882\pi$
$270$	3.68478	+	6.38223i	0.224249	+	0.388410i
$271$			5.21618i			0.316860i	0.987370	+	0.158430i	$0.0506433\pi$
$271$			5.21618i			0.316860i	−0.987370	+	0.158430i	$0.949357\pi$
$272$	2.12499			0.128847
$273$		0			0
$274$	−10.8270			−0.654085
$275$			22.9337i			1.38296i
$276$	0.227054	+	0.393269i	0.0136671	+	0.0236720i
$277$	19.2724			1.15797			0.578983	−	0.815340i	$-0.303450\pi$
$277$	19.2724			1.15797			0.578983	+	0.815340i	$0.303450\pi$
$278$	11.8532	−	6.84343i	0.710906	−	0.410442i
$279$	15.9582	−	9.21345i	0.955390	−	0.551595i
$280$		0			0
$281$			2.14283i			0.127831i	0.997955	+	0.0639153i	$0.0203588\pi$
$281$			2.14283i			0.127831i	−0.997955	+	0.0639153i	$0.979641\pi$
$282$	7.63711	−	13.2279i	0.454783	−	0.787707i
$283$	7.87512	+	13.6401i	0.468127	+	0.810820i	0.999337	−	0.0364203i	$-0.0115955\pi$
$283$	7.87512	+	13.6401i	0.468127	+	0.810820i	−0.531209	+	0.847241i	$0.678262\pi$
$284$	−0.792207	+	0.457381i	−0.0470089	+	0.0271406i
$285$	−6.78597	−	11.7537i	−0.401966	−	0.696226i
$286$	8.53048	−	24.7847i	0.504418	−	1.46555i
$287$		0			0
$288$	2.54821	+	1.47121i	0.150155	+	0.0866919i
$289$	−16.6863			−0.981546
$290$	2.53427			0.148817
$291$	−26.5696	−	15.3400i	−1.55754	−	0.899246i
$292$	−0.425374	−	0.245590i	−0.0248932	−	0.0143721i
$293$	20.0474	−	11.5744i	1.17118	−	0.676182i	0.217223	−	0.976122i	$-0.430300\pi$
$293$	20.0474	−	11.5744i	1.17118	−	0.676182i	0.953958	+	0.299940i	$0.0969668\pi$
$294$		0			0
$295$	4.43029	+	7.67348i	0.257941	+	0.446767i
$296$	3.59366			0.208877
$297$	−30.2708	+	17.4769i	−1.75649	+	1.01411i
$298$	5.46054	−	9.45793i	0.316320	−	0.547883i
$299$	3.79682	+	4.36661i	0.219576	+	0.252528i
$300$	−1.23098			−0.0710708
$301$		0			0
$302$	1.03509	−	1.79283i	0.0595629	−	0.103166i
$303$	5.64073	−	9.77003i	0.324052	−	0.561274i
$304$	19.2036	+	11.0872i	1.10140	+	0.635894i
$305$		−	5.88515i		−	0.336983i
$306$	−3.54621	−	2.04740i	−0.202723	−	0.117042i
$307$			4.23590i			0.241756i	0.992667	+	0.120878i	$0.0385709\pi$
$307$			4.23590i			0.241756i	−0.992667	+	0.120878i	$0.961429\pi$
$308$		0			0
$309$	12.1785	−	21.0939i	0.692813	−	1.19999i
$310$			3.86328i			0.219420i
$311$	−13.6251	+	23.5993i	−0.772606	+	1.33819i	0.163524	+	0.986539i	$0.447714\pi$
$311$	−13.6251	+	23.5993i	−0.772606	+	1.33819i	−0.936130	+	0.351654i	$0.885619\pi$
$312$	28.4227	+	9.78261i	1.60912	+	0.553831i
$313$	1.34849	+	2.33565i	0.0762209	+	0.132018i	0.901617	−	0.432536i	$-0.142381\pi$
$313$	1.34849	+	2.33565i	0.0762209	+	0.132018i	−0.825396	+	0.564555i	$0.809048\pi$
$314$	−4.60631	−	2.65945i	−0.259949	−	0.150082i
$315$		0			0
$316$	−0.558247	−	0.966913i	−0.0314039	−	0.0543931i
$317$	20.8456	−	12.0352i	1.17081	−	0.675966i	0.216937	−	0.976186i	$-0.430393\pi$
$317$	20.8456	−	12.0352i	1.17081	−	0.675966i	0.953870	+	0.300220i	$0.0970600\pi$
$318$			21.6727i			1.21535i
$319$			12.0200i			0.672991i
$320$	−5.83037	+	3.36617i	−0.325928	+	0.188174i
$321$	−13.9381	−	24.1416i	−0.777951	−	1.34745i
$322$		0			0
$323$	2.83504	+	1.63681i	0.157746	+	0.0910745i
$324$	−0.157138	−	0.272170i	−0.00872986	−	0.0151206i
$325$	−15.3972	+	2.99497i	−0.854082	+	0.166131i
$326$	9.90220	−	17.1511i	0.548432	−	0.949912i
$327$		−	41.9612i		−	2.32046i
$328$	−1.34217	+	2.32471i	−0.0741091	+	0.128361i
$329$		0			0
$330$		−	16.8812i		−	0.929279i
$331$	0.536696	+	0.309862i	0.0294995	+	0.0170315i	0.514677	−	0.857384i	$-0.327912\pi$
$331$	0.536696	+	0.309862i	0.0294995	+	0.0170315i	−0.485178	+	0.874416i	$0.661245\pi$
$332$		−	0.571530i		−	0.0313668i
$333$	−5.70194	−	3.29201i	−0.312464	−	0.180401i
$334$	3.11762	−	5.39987i	0.170588	−	0.295468i
$335$	2.96007	−	5.12699i	0.161726	−	0.280117i
$336$		0			0
$337$	−5.72118			−0.311652			−0.155826	−	0.987784i	$-0.549804\pi$
$337$	−5.72118			−0.311652			−0.155826	+	0.987784i	$0.549804\pi$
$338$	17.7539	+	2.49048i	0.965684	+	0.135464i
$339$	28.1082	−	48.6848i	1.52663	−	2.64420i
$340$	−0.0383927	+	0.0221660i	−0.00208214	+	0.00120212i
$341$	−18.3235			−0.992272
$342$	−21.3647	−	37.0048i	−1.15527	−	2.00099i
$343$		0			0
$344$	11.1439	−	6.43396i	0.600841	−	0.346896i
$345$	3.22740	+	1.86334i	0.173757	+	0.100319i
$346$	−23.3102	−	13.4581i	−1.25316	−	0.723514i
$347$	−1.86486			−0.100111			−0.0500554	−	0.998746i	$-0.515940\pi$
$347$	−1.86486			−0.100111			−0.0500554	+	0.998746i	$0.515940\pi$
$348$	−0.645182			−0.0345854
$349$	19.3273	+	11.1586i	1.03457	+	0.597307i	0.918290	−	0.395909i	$-0.129571\pi$
$349$	19.3273	+	11.1586i	1.03457	+	0.597307i	0.116277	+	0.993217i	$0.462904\pi$
$350$		0			0
$351$	−15.6867	−	18.0408i	−0.837295	−	0.962947i
$352$	−1.46295	−	2.53391i	−0.0779756	−	0.135058i
$353$	−2.01956	+	1.16600i	−0.107491	+	0.0620597i	−0.552781	−	0.833326i	$-0.686434\pi$
$353$	−2.01956	+	1.16600i	−0.107491	+	0.0620597i	0.445291	+	0.895386i	$0.353100\pi$
$354$	21.8414	+	37.8304i	1.16086	+	2.01066i
$355$	−3.75354	+	6.50133i	−0.199217	+	0.345055i
$356$		−	0.491966i		−	0.0260741i
$357$		0			0
$358$	24.8648	−	14.3557i	1.31415	−	0.758722i
$359$	−2.83281	+	1.63553i	−0.149510	+	0.0863197i	−0.572889	−	0.819633i	$-0.694177\pi$
$359$	−2.83281	+	1.63553i	−0.149510	+	0.0863197i	0.423379	+	0.905953i	$0.360844\pi$
$360$	12.3629			0.651585
$361$	7.58017	+	13.1292i	0.398956	+	0.691013i
$362$			22.8264i			1.19973i
$363$	48.3741			2.53898
$364$		0			0
$365$	−4.03092			−0.210988
$366$		−	29.0139i		−	1.51658i
$367$	2.07645	+	3.59652i	0.108390	+	0.187737i	0.915118	−	0.403186i	$-0.132097\pi$
$367$	2.07645	+	3.59652i	0.108390	+	0.187737i	−0.806728	+	0.590923i	$0.798764\pi$
$368$	−6.08880			−0.317401
$369$	4.25916	−	2.45903i	0.221723	−	0.128012i
$370$	1.19544	−	0.690185i	0.0621477	−	0.0358810i
$371$		0			0
$372$		−	0.983525i		−	0.0509934i
$373$	5.55446	−	9.62061i	0.287599	−	0.498136i	−0.685637	−	0.727944i	$-0.740476\pi$
$373$	5.55446	−	9.62061i	0.287599	−	0.498136i	0.973236	+	0.229807i	$0.0738096\pi$
$374$	2.03591	+	3.52630i	0.105275	+	0.182341i
$375$	−18.8037	+	10.8563i	−0.971021	+	0.560619i
$376$	−5.56165	−	9.63305i	−0.286820	−	0.496787i
$377$	−8.06996	+	1.56972i	−0.415624	+	0.0808447i
$378$		0			0
$379$	−4.01862	−	2.32015i	−0.206422	−	0.119178i	0.393225	−	0.919442i	$-0.371359\pi$
$379$	−4.01862	−	2.32015i	−0.206422	−	0.119178i	−0.599648	+	0.800264i	$0.704693\pi$
$380$	−0.462607			−0.0237312
$381$	−5.52416			−0.283012
$382$	−5.07586	−	2.93055i	−0.259703	−	0.149940i
$383$	3.17773	+	1.83466i	0.162374	+	0.0937469i	0.578985	−	0.815338i	$-0.303449\pi$
$383$	3.17773	+	1.83466i	0.162374	+	0.0937469i	−0.416611	+	0.909085i	$0.636782\pi$
$384$	−25.9740	+	14.9961i	−1.32548	+	0.765266i
$385$		0			0
$386$	7.99661	+	13.8505i	0.407017	+	0.704973i
$387$	−23.5756			−1.19842
$388$	−0.905640	+	0.522872i	−0.0459769	+	0.0265448i
$389$	8.44156	−	14.6212i	0.428004	−	0.741324i	−0.568692	−	0.822551i	$-0.692550\pi$
$389$	8.44156	−	14.6212i	0.428004	−	0.741324i	0.996696	+	0.0812262i	$0.0258836\pi$
$390$	11.3337	−	2.20455i	0.573902	−	0.111632i
$391$	−0.898894			−0.0454590
$392$		0			0
$393$	−22.4468	+	38.8790i	−1.13229	+	1.96119i
$394$	−9.94390	+	17.2233i	−0.500966	+	0.867699i
$395$	−7.93506	−	4.58131i	−0.399256	−	0.230511i
$396$			2.74454i			0.137918i
$397$	14.4700	+	8.35428i	0.726230	+	0.419289i	0.817041	−	0.576579i	$-0.195613\pi$
$397$	14.4700	+	8.35428i	0.726230	+	0.419289i	−0.0908114	+	0.995868i	$0.528946\pi$
$398$		−	9.73508i		−	0.487976i
$399$		0			0
$400$	8.25267	−	14.2940i	0.412633	−	0.714702i
$401$			25.3134i			1.26409i	0.774931	+	0.632046i	$0.217785\pi$
$401$			25.3134i			1.26409i	−0.774931	+	0.632046i	$0.782215\pi$
$402$	14.5932	−	25.2761i	0.727842	−	1.26066i
$403$	−2.39291	−	12.3020i	−0.119199	−	0.612805i
$404$	−0.192267	−	0.333017i	−0.00956566	−	0.0165682i
$405$	−2.23359	−	1.28956i	−0.110988	−	0.0640789i
$406$		0			0
$407$	3.27354	+	5.66994i	0.162263	+	0.281048i
$408$	−4.04391	+	2.33475i	−0.200203	+	0.115587i
$409$			5.73343i			0.283500i	0.989903	+	0.141750i	$0.0452729\pi$
$409$			5.73343i			0.283500i	−0.989903	+	0.141750i	$0.954727\pi$
$410$			1.03109i			0.0509220i
$411$	19.5899	−	11.3102i	0.966299	−	0.557893i
$412$	−0.415112	−	0.718996i	−0.0204511	−	0.0354224i
$413$		0			0
$414$	10.1610	+	5.86648i	0.499388	+	0.288322i
$415$	−2.34516	−	4.06193i	−0.115119	−	0.199392i
$416$	1.51016	−	1.31310i	0.0740416	−	0.0643801i
$417$	−14.2977	+	24.7643i	−0.700161	+	1.21272i
$418$			42.4897i			2.07824i
$419$	−17.1729	+	29.7443i	−0.838950	+	1.45310i	0.0518229	+	0.998656i	$0.483497\pi$
$419$	−17.1729	+	29.7443i	−0.838950	+	1.45310i	−0.890773	+	0.454448i	$0.849836\pi$
$420$		0			0
$421$			2.94167i			0.143368i	0.997427	+	0.0716842i	$0.0228374\pi$
$421$			2.94167i			0.143368i	−0.997427	+	0.0716842i	$0.977163\pi$
$422$	−31.5565	−	18.2191i	−1.53614	−	0.886894i
$423$			20.3793i			0.990873i
$424$	13.6684	+	7.89148i	0.663798	+	0.383244i
$425$	1.21835	−	2.11024i	0.0590985	−	0.102362i
$426$	−18.5050	+	32.0516i	−0.896571	+	1.55291i
$427$		0			0
$428$	−0.950178			−0.0459286
$429$	10.4562	+	53.7554i	0.504829	+	2.59533i
$430$	2.47137	−	4.28053i	0.119180	−	0.206426i
$431$	34.3773	−	19.8478i	1.65590	−	0.956033i	0.681321	−	0.731985i	$-0.261406\pi$
$431$	34.3773	−	19.8478i	1.65590	−	0.956033i	0.974578	−	0.224048i	$-0.0719273\pi$
$432$	25.1561			1.21032
$433$	4.91827	+	8.51869i	0.236357	+	0.409382i	0.959666	−	0.281142i	$-0.0907133\pi$
$433$	4.91827	+	8.51869i	0.236357	+	0.409382i	−0.723309	+	0.690524i	$0.757380\pi$
$434$		0			0
$435$	−4.58538	+	2.64737i	−0.219852	+	0.126932i
$436$	−1.23865	−	0.715135i	−0.0593206	−	0.0342488i
$437$	−8.12331	−	4.69000i	−0.388591	−	0.224353i
$438$	−19.8725			−0.949544
$439$	28.5465			1.36245			0.681226	−	0.732073i	$-0.261447\pi$
$439$	28.5465			1.36245			0.681226	+	0.732073i	$0.261447\pi$
$440$	−10.6465	−	6.14678i	−0.507554	−	0.293036i
$441$		0			0
$442$	−2.10161	+	1.82737i	−0.0999632	+	0.0869193i
$443$	−1.66951	−	2.89167i	−0.0793207	−	0.137387i	0.823636	−	0.567118i	$-0.191942\pi$
$443$	−1.66951	−	2.89167i	−0.0793207	−	0.137387i	−0.902957	+	0.429731i	$0.858608\pi$
$444$	−0.304337	+	0.175709i	−0.0144432	+	0.00833880i
$445$	−2.01868	−	3.49646i	−0.0956947	−	0.165748i
$446$	−15.8595	+	27.4695i	−0.750969	+	1.30072i
$447$			22.8170i			1.07921i
$448$		0			0
$449$	15.7487	−	9.09253i	0.743228	−	0.429103i	−0.0800136	−	0.996794i	$-0.525496\pi$
$449$	15.7487	−	9.09253i	0.743228	−	0.429103i	0.823242	+	0.567691i	$0.192163\pi$
$450$	−27.5443	+	15.9027i	−1.29845	+	0.749660i
$451$	−4.89045			−0.230282
$452$	−0.958084	−	1.65945i	−0.0450645	−	0.0780539i
$453$			4.32516i			0.203214i
$454$	−0.625219			−0.0293430
$455$		0			0
$456$	−48.7265			−2.28183
$457$			8.72932i			0.408341i	0.978935	+	0.204170i	$0.0654496\pi$
$457$			8.72932i			0.408341i	−0.978935	+	0.204170i	$0.934550\pi$
$458$	11.9519	+	20.7013i	0.558476	+	0.967309i
$459$	3.71381			0.173346
$460$	0.110008	−	0.0635130i	0.00512914	−	0.00296131i
$461$	1.96695	−	1.13562i	0.0916099	−	0.0528910i	−0.453495	−	0.891259i	$-0.649823\pi$
$461$	1.96695	−	1.13562i	0.0916099	−	0.0528910i	0.545105	+	0.838368i	$0.316490\pi$
$462$		0			0
$463$			5.48326i			0.254829i	0.991850	+	0.127414i	$0.0406678\pi$
$463$			5.48326i			0.254829i	−0.991850	+	0.127414i	$0.959332\pi$
$464$	4.32538	−	7.49178i	0.200801	−	0.347797i
$465$	−4.03570	−	6.99003i	−0.187151	−	0.324155i
$466$	9.33356	−	5.38873i	0.432369	−	0.249628i
$467$	−9.44095	−	16.3522i	−0.436875	−	0.756690i	0.560572	−	0.828106i	$-0.310581\pi$
$467$	−9.44095	−	16.3522i	−0.436875	−	0.756690i	−0.997447	+	0.0714164i	$0.977248\pi$
$468$	−1.84262	+	0.358416i	−0.0851753	+	0.0165678i
$469$		0			0
$470$	−3.70018	−	2.13630i	−0.170677	−	0.0985401i
$471$	11.1126			0.512040
$472$	31.8115			1.46424
$473$	20.3025	+	11.7217i	0.933510	+	0.538962i
$474$	−39.1200	−	22.5859i	−1.79684	−	1.03741i
$475$	22.0204	−	12.7135i	1.01037	−	0.583335i
$476$		0			0
$477$	−14.4582	−	25.0423i	−0.661994	−	1.14661i
$478$	18.6606			0.853516
$479$	28.6961	−	16.5677i	1.31116	−	0.756997i	0.328869	−	0.944375i	$-0.393332\pi$
$479$	28.6961	−	16.5677i	1.31116	−	0.756997i	0.982288	+	0.187378i	$0.0599991\pi$
$480$	0.644422	−	1.11617i	0.0294137	−	0.0509461i
$481$	−3.37917	+	2.93823i	−0.154077	+	0.133972i
$482$	−31.1104			−1.41704
$483$		0			0
$484$	0.824428	−	1.42795i	0.0374740	−	0.0649069i
$485$	−4.29100	+	7.43222i	−0.194844	+	0.337480i
$486$	12.7451	+	7.35838i	0.578129	+	0.333783i
$487$			15.9563i			0.723048i	0.932363	+	0.361524i	$0.117743\pi$
$487$			15.9563i			0.723048i	−0.932363	+	0.361524i	$0.882257\pi$
$488$	−18.2983	−	10.5645i	−0.828326	−	0.478234i
$489$			41.3765i			1.87111i
$490$		0			0
$491$	−15.8464	+	27.4468i	−0.715138	+	1.23866i	0.247769	+	0.968819i	$0.420303\pi$
$491$	−15.8464	+	27.4468i	−0.715138	+	1.23866i	−0.962906	+	0.269836i	$0.913031\pi$
$492$		−	0.262498i		−	0.0118343i
$493$	0.638559	−	1.10602i	0.0287593	−	0.0498125i
$494$	−28.5266	+	5.54882i	−1.28347	+	0.249653i
$495$	11.2617	+	19.5058i	0.506174	+	0.876720i
$496$	11.4206	+	6.59368i	0.512800	+	0.296065i
$497$		0			0
$498$	−11.5617	−	20.0254i	−0.518090	−	0.897358i
$499$	20.9738	−	12.1092i	0.938916	−	0.542083i	0.0492955	−	0.998784i	$-0.484302\pi$
$499$	20.9738	−	12.1092i	0.938916	−	0.542083i	0.889620	+	0.456701i	$0.150969\pi$
$500$			0.740089i			0.0330978i
$501$			13.0270i			0.582004i
$502$	8.04043	−	4.64215i	0.358862	−	0.207189i
$503$	0.427249	+	0.740017i	0.0190501	+	0.0329957i	0.875393	−	0.483411i	$-0.160602\pi$
$503$	0.427249	+	0.740017i	0.0190501	+	0.0329957i	−0.856343	+	0.516407i	$0.827269\pi$
$504$		0			0
$505$	−2.73294	−	1.57786i	−0.121614	−	0.0702139i
$506$	−5.83356	−	10.1040i	−0.259333	−	0.449179i
$507$	−34.7246	+	14.0401i	−1.54218	+	0.623542i
$508$	−0.0941471	+	0.163068i	−0.00417710	+	0.00723495i
$509$			1.30000i			0.0576215i	0.999585	+	0.0288108i	$0.00917202\pi$
$509$			1.30000i			0.0576215i	−0.999585	+	0.0288108i	$0.990828\pi$
$510$	−0.896808	+	1.55332i	−0.0397113	+	0.0687820i
$511$		0			0
$512$			24.0616i			1.06338i
$513$	33.5618	+	19.3769i	1.48179	+	0.855511i
$514$		−	22.8070i		−	1.00597i
$515$	−5.90051	−	3.40666i	−0.260007	−	0.150115i
$516$	−0.629167	+	1.08975i	−0.0276976	+	0.0479736i
$517$	10.1324	−	17.5499i	0.445624	−	0.771844i
$518$		0			0
$519$	56.2351			2.46845
$520$	2.73645	−	7.95057i	0.120001	−	0.348655i
$521$	−12.5228	+	21.6901i	−0.548632	+	0.950259i	0.449736	+	0.893161i	$0.351518\pi$
$521$	−12.5228	+	21.6901i	−0.548632	+	0.950259i	−0.998369	+	0.0570974i	$0.981815\pi$
$522$	−14.4365	+	8.33490i	−0.631867	+	0.364809i
$523$	−12.8239			−0.560752			−0.280376	−	0.959890i	$-0.590459\pi$
$523$	−12.8239			−0.560752			−0.280376	+	0.959890i	$0.590459\pi$
$524$	0.765112	+	1.32521i	0.0334241	+	0.0578922i
$525$		0			0
$526$	11.9701	−	6.91095i	0.521922	−	0.301332i
$527$	1.68603	+	0.973429i	0.0734446	+	0.0424032i
$528$	−49.9040	−	28.8121i	−2.17179	−	1.25389i
$529$	−20.4244			−0.888016
$530$	6.06244			0.263335
$531$	−50.4743	−	29.1413i	−2.19040	−	1.26463i
$532$		0			0
$533$	−0.638656	−	3.28334i	−0.0276632	−	0.142217i
$534$	−9.95213	−	17.2376i	−0.430671	−	0.745944i
$535$	−6.75303	+	3.89886i	−0.291959	+	0.168563i
$536$	−10.6273	−	18.4071i	−0.459031	−	0.795066i
$537$	−29.9928	+	51.9490i	−1.29428	+	2.24176i
$538$		−	21.6828i		−	0.934814i
$539$		0			0
$540$	−0.454501	+	0.262406i	−0.0195586	+	0.0112922i
$541$	−24.8938	+	14.3725i	−1.07027	+	0.617920i	−0.928255	−	0.371944i	$-0.878691\pi$
$541$	−24.8938	+	14.3725i	−1.07027	+	0.617920i	−0.142014	+	0.989865i	$0.545358\pi$
$542$	7.19340			0.308983
$543$	−23.8451	−	41.3009i	−1.02329	−	1.77239i
$544$			0.310876i			0.0133287i
$545$	−11.7376			−0.502785
$546$		0			0
$547$	−8.88085			−0.379718			−0.189859	−	0.981811i	$-0.560803\pi$
$547$	−8.88085			−0.379718			−0.189859	+	0.981811i	$0.560803\pi$
$548$		−	0.771031i		−	0.0329368i
$549$	19.3556	+	33.5248i	0.826075	+	1.43080i
$550$	31.6269			1.34857
$551$	11.5413	−	6.66339i	0.491677	−	0.283870i
$552$	11.5871	−	6.68983i	0.493181	−	0.284738i
$553$		0			0
$554$		−	26.5777i		−	1.12918i
$555$	−1.44198	+	2.49757i	−0.0612084	+	0.106016i
$556$	0.487345	+	0.844106i	0.0206680	+	0.0357981i
$557$	33.5389	−	19.3637i	1.42109	−	0.820465i	0.424695	−	0.905336i	$-0.360381\pi$
$557$	33.5389	−	19.3637i	1.42109	−	0.820465i	0.996392	+	0.0848711i	$0.0270478\pi$
$558$	−12.7059	−	22.0072i	−0.537882	−	0.931639i
$559$	−5.21830	+	15.1614i	−0.220711	+	0.641259i
$560$		0			0
$561$	−7.36736	−	4.25355i	−0.311050	−	0.179585i
$562$	2.95508			0.124653
$563$	6.90882			0.291172			0.145586	−	0.989346i	$-0.453493\pi$
$563$	6.90882			0.291172			0.145586	+	0.989346i	$0.453493\pi$
$564$	0.942002	+	0.543865i	0.0396655	+	0.0229009i
$565$	−13.6184	−	7.86260i	−0.572932	−	0.330782i
$566$	18.8105	−	10.8602i	0.790663	−	0.456489i
$567$		0			0
$568$	13.4761	+	23.3413i	0.565444	+	0.979379i
$569$	2.83745			0.118952			0.0594759	−	0.998230i	$-0.481057\pi$
$569$	2.83745			0.118952			0.0594759	+	0.998230i	$0.481057\pi$
$570$	−16.2089	+	9.35823i	−0.678917	+	0.391973i
$571$	−23.3362	+	40.4195i	−0.976589	+	1.69150i	−0.302001	+	0.953307i	$0.597655\pi$
$571$	−23.3362	+	40.4195i	−0.976589	+	1.69150i	−0.674588	+	0.738195i	$0.735679\pi$
$572$	1.76500	+	0.607485i	0.0737985	+	0.0254002i
$573$	12.2453			0.511557
$574$		0			0
$575$	−3.49096	+	6.04653i	−0.145583	+	0.252158i
$576$	22.1418	−	38.3507i	0.922576	−	1.59795i
$577$	9.88033	+	5.70441i	0.411323	+	0.237478i	0.691358	−	0.722512i	$-0.257013\pi$
$577$	9.88033	+	5.70441i	0.411323	+	0.237478i	−0.280035	+	0.959990i	$0.590346\pi$
$578$			23.0113i			0.957144i
$579$	−28.9373	−	16.7070i	−1.20259	−	0.694318i
$580$			0.180474i			0.00749379i
$581$		0			0
$582$	−21.1547	+	36.6410i	−0.876890	+	1.51882i
$583$			28.7541i			1.19087i
$584$	−7.23597	+	12.5331i	−0.299426	+	0.518622i
$585$	−11.6251	+	10.1081i	−0.480637	+	0.417920i
$586$	−15.9617	−	27.6465i	−0.659371	−	1.14206i
$587$	40.2191	+	23.2205i	1.66002	+	0.958413i	0.972702	+	0.232057i	$0.0745456\pi$
$587$	40.2191	+	23.2205i	1.66002	+	0.958413i	0.687318	+	0.726356i	$0.258788\pi$
$588$		0			0
$589$	10.1578	+	17.5938i	0.418544	+	0.724939i
$590$	10.5821	−	6.10961i	0.435660	−	0.251529i
$591$		−	41.5508i		−	1.70917i
$592$		−	4.71191i		−	0.193658i
$593$	−17.5462	+	10.1303i	−0.720535	+	0.416001i	−0.814950	−	0.579532i	$-0.803235\pi$
$593$	−17.5462	+	10.1303i	−0.720535	+	0.416001i	0.0944146	+	0.995533i	$0.469902\pi$
$594$	24.1016	+	41.7451i	0.988899	+	1.71282i
$595$		0			0
$596$	0.673533	+	0.388864i	0.0275890	+	0.0159285i
$597$	10.1696	+	17.6142i	0.416212	+	0.720901i
$598$	6.02179	−	5.23603i	0.246249	−	0.214117i
$599$	19.4938	−	33.7642i	0.796494	−	1.37957i	−0.125391	−	0.992107i	$-0.540019\pi$
$599$	19.4938	−	33.7642i	0.796494	−	1.37957i	0.921886	−	0.387462i	$-0.126648\pi$
$600$			36.2692i			1.48068i
$601$	9.56951	−	16.5749i	0.390348	−	0.676103i	−0.602147	−	0.798385i	$-0.705688\pi$
$601$	9.56951	−	16.5749i	0.390348	−	0.676103i	0.992495	+	0.122282i	$0.0390212\pi$
$602$		0			0
$603$			38.9412i			1.58581i
$604$	0.127674	+	0.0737127i	0.00519499	+	0.00299933i
$605$		−	13.5315i		−	0.550134i
$606$	−13.4734	−	7.77888i	−0.547320	−	0.315995i
$607$	21.6668	−	37.5280i	0.879428	−	1.52321i	0.0274572	−	0.999623i	$-0.491259\pi$
$607$	21.6668	−	37.5280i	0.879428	−	1.52321i	0.851970	−	0.523590i	$-0.175408\pi$
$608$	−1.62200	+	2.80939i	−0.0657808	+	0.113936i
$609$		0			0
$610$	−8.11595			−0.328605
$611$	13.1058	+	4.51081i	0.530205	+	0.182488i
$612$	0.145803	−	0.252538i	0.00589373	−	0.0102082i
$613$	8.92834	−	5.15478i	0.360612	−	0.208200i	−0.308737	−	0.951147i	$-0.599906\pi$
$613$	8.92834	−	5.15478i	0.360612	−	0.208200i	0.669349	+	0.742948i	$0.266573\pi$
$614$	5.84154			0.235745
$615$	−1.07711	−	1.86561i	−0.0434332	−	0.0752285i
$616$		0			0
$617$	−9.58684	+	5.53497i	−0.385952	+	0.222829i	−0.680405	−	0.732837i	$-0.738196\pi$
$617$	−9.58684	+	5.53497i	−0.385952	+	0.222829i	0.294453	+	0.955666i	$0.404863\pi$
$618$	−29.0896	−	16.7949i	−1.17015	−	0.675589i
$619$	−29.2384	−	16.8808i	−1.17519	−	0.678498i	−0.220295	−	0.975433i	$-0.570702\pi$
$619$	−29.2384	−	16.8808i	−1.17519	−	0.678498i	−0.954897	+	0.296936i	$0.904035\pi$
$620$	−0.275118			−0.0110490
$621$	−10.6413			−0.427020
$622$	32.5447	+	18.7897i	1.30492	+	0.753399i
$623$		0			0
$624$	12.8267	−	37.2671i	0.513480	−	1.49188i
$625$	−7.83931	−	13.5781i	−0.313573	−	0.543124i
$626$	3.22098	−	1.85964i	0.128736	−	0.0743260i
$627$	−44.3860	−	76.8787i	−1.77260	−	3.07024i
$628$	0.189389	−	0.328031i	0.00755745	−	0.0130899i
$629$		−	0.695623i		−	0.0277363i
$630$		0			0
$631$	33.4264	−	19.2987i	1.33068	−	0.768271i	0.345280	−	0.938500i	$-0.387784\pi$
$631$	33.4264	−	19.2987i	1.33068	−	0.768271i	0.985405	+	0.170229i	$0.0544507\pi$
$632$	−28.4887	+	16.4480i	−1.13322	+	0.654265i
$633$	76.1290			3.02586
$634$	−16.5972	−	28.7473i	−0.659161	−	1.14170i
$635$			1.54525i			0.0613215i
$636$	−1.54339			−0.0611995
$637$		0			0
$638$	16.5763			0.656260
$639$		−	49.3798i		−	1.95343i
$640$	4.19480	+	7.26560i	0.165814	+	0.287198i
$641$	−19.5228			−0.771105			−0.385553	−	0.922686i	$-0.625989\pi$
$641$	−19.5228			−0.771105			−0.385553	+	0.922686i	$0.625989\pi$
$642$	−33.2926	+	19.2215i	−1.31395	+	0.758611i
$643$	−10.8009	+	6.23589i	−0.425945	+	0.245920i	−0.697618	−	0.716470i	$-0.745757\pi$
$643$	−10.8009	+	6.23589i	−0.425945	+	0.245920i	0.271673	+	0.962390i	$0.412423\pi$
$644$		0			0
$645$			10.3266i			0.406611i
$646$	2.25725	−	3.90967i	0.0888103	−	0.153824i
$647$	−17.9695	−	31.1241i	−0.706455	−	1.22362i	−0.966164	−	0.257929i	$-0.916960\pi$
$647$	−17.9695	−	31.1241i	−0.706455	−	1.22362i	0.259709	−	0.965687i	$-0.416373\pi$
$648$	−8.01911	+	4.62984i	−0.315021	+	0.181877i
$649$	28.9778	+	50.1910i	1.13748	+	1.97017i
$650$	4.13023	+	21.2336i	0.162001	+	0.832849i
$651$		0			0
$652$	1.22139	+	0.705171i	0.0478334	+	0.0276166i
$653$	4.85888			0.190143			0.0950713	−	0.995470i	$-0.469692\pi$
$653$	4.85888			0.190143			0.0950713	+	0.995470i	$0.469692\pi$
$654$	−57.8668			−2.26277
$655$	10.8755	+	6.27897i	0.424941	+	0.245340i
$656$	3.04810	+	1.75982i	0.119008	+	0.0687095i
$657$	22.9621	−	13.2572i	0.895838	−	0.517212i
$658$		0			0
$659$	11.8103	+	20.4560i	0.460063	+	0.796853i	0.998964	−	0.0455166i	$-0.0144934\pi$
$659$	11.8103	+	20.4560i	0.460063	+	0.796853i	−0.538900	+	0.842370i	$0.681160\pi$
$660$	1.20217			0.0467944
$661$	−14.1970	+	8.19662i	−0.552198	+	0.318812i	−0.750008	−	0.661429i	$-0.769950\pi$
$661$	−14.1970	+	8.19662i	−0.552198	+	0.318812i	0.197810	+	0.980240i	$0.436617\pi$
$662$	0.427316	−	0.740134i	0.0166081	−	0.0287661i
$663$	1.89362	−	5.50176i	0.0735419	−	0.213671i
$664$	−16.8393			−0.653492
$665$		0			0
$666$	−4.53987	+	7.86328i	−0.175916	+	0.304696i
$667$	−1.82968	+	3.16910i	−0.0708456	+	0.122708i
$668$	0.384544	+	0.222016i	0.0148784	+	0.00859007i
$669$		−	66.2692i		−	2.56212i
$670$	−7.07040	−	4.08210i	−0.273154	−	0.157705i
$671$		−	38.4939i		−	1.48604i
$672$		0			0
$673$	−7.12678	+	12.3439i	−0.274717	+	0.475824i	−0.970064	−	0.242851i	$-0.921918\pi$
$673$	−7.12678	+	12.3439i	−0.274717	+	0.475824i	0.695347	+	0.718675i	$0.255251\pi$
$674$			7.88982i			0.303904i
$675$	14.4230	−	24.9814i	0.555143	−	0.961536i
$676$	−0.177356	+	1.26432i	−0.00682138	+	0.0486276i
$677$	−5.13574	−	8.89537i	−0.197383	−	0.341877i	0.750296	−	0.661102i	$-0.229911\pi$
$677$	−5.13574	−	8.89537i	−0.197383	−	0.341877i	−0.947679	+	0.319225i	$0.896577\pi$
$678$	−67.1391	−	38.7628i	−2.57846	−	1.48867i
$679$		0			0
$680$	0.653092	+	1.13119i	0.0250449	+	0.0433791i
$681$	1.13124	−	0.653122i	0.0433492	−	0.0250277i
$682$			25.2691i			0.967604i
$683$		−	2.22201i		−	0.0850230i	−0.999096	−	0.0425115i	$-0.986464\pi$
$683$		−	2.22201i		−	0.0850230i	0.999096	−	0.0425115i	$-0.0135359\pi$
$684$	2.63524	−	1.52146i	0.100761	−	0.0581744i
$685$	−3.16377	−	5.47981i	−0.120881	−	0.209373i
$686$		0			0
$687$	−43.2504	−	24.9706i	−1.65011	−	0.952689i
$688$	−8.43604	−	14.6117i	−0.321621	−	0.557064i
$689$	−19.3048	+	3.75506i	−0.735455	+	0.143056i
$690$	2.56965	−	4.45076i	0.0978249	−	0.169438i
$691$		−	2.64015i		−	0.100436i	−0.998738	−	0.0502179i	$-0.984008\pi$
$691$		−	2.64015i		−	0.100436i	0.998738	−	0.0502179i	$-0.0159916\pi$
$692$	0.958402	−	1.66000i	0.0364330	−	0.0631038i
$693$		0			0
$694$			2.57174i			0.0976220i
$695$	6.92724	+	3.99944i	0.262765	+	0.151708i
$696$			19.0094i			0.720549i
$697$	0.449993	+	0.259804i	0.0170447	+	0.00984077i
$698$	15.3884	−	26.6534i	0.582458	−	1.00885i
$699$	−11.2585	+	19.5002i	−0.425834	+	0.737566i
$700$		0			0
$701$	−8.89991			−0.336145			−0.168072	−	0.985775i	$-0.553754\pi$
$701$	−8.89991			−0.336145			−0.168072	+	0.985775i	$0.553754\pi$
$702$	−24.8793	+	21.6328i	−0.939007	+	0.816479i
$703$	3.62943	−	6.28635i	0.136886	−	0.237094i
$704$	−38.1355	+	22.0175i	−1.43729	+	0.829818i
$705$	8.92656			0.336194
$706$	1.60797	+	2.78509i	0.0605168	+	0.104818i
$707$		0			0
$708$	−2.69403	+	1.55540i	−0.101248	+	0.0584556i
$709$	−35.1558	−	20.2972i	−1.32030	−	0.762278i	−0.336527	−	0.941674i	$-0.609252\pi$
$709$	−35.1558	−	20.2972i	−1.32030	−	0.762278i	−0.983777	+	0.179396i	$0.942586\pi$
$710$	8.96569	+	5.17634i	0.336476	+	0.194265i
$711$	60.2695			2.26028
$712$	−14.4951			−0.543226
$713$	−4.83103	−	2.78920i	−0.180923	−	0.104456i
$714$		0			0
$715$	15.0368	−	2.92487i	0.562344	−	0.109384i
$716$	1.02232	+	1.77071i	0.0382059	+	0.0661745i
$717$	−33.7636	+	19.4934i	−1.26092	+	0.727995i
$718$	2.25548	+	3.90661i	0.0841738	+	0.145793i
$719$	−7.25674	+	12.5690i	−0.270631	+	0.468746i	−0.969024	−	0.246968i	$-0.920566\pi$
$719$	−7.25674	+	12.5690i	−0.270631	+	0.468746i	0.698393	+	0.715715i	$0.253899\pi$
$720$		−	16.2100i		−	0.604110i
$721$		0			0
$722$	18.1059	−	10.4535i	0.673834	−	0.389038i
$723$	56.2896	−	32.4988i	2.09343	−	1.20864i
$724$	−1.62555			−0.0604129
$725$	−4.95984	−	8.59070i	−0.184204	−	0.319051i
$726$		−	66.7105i		−	2.47586i
$727$	−30.6942			−1.13839			−0.569193	−	0.822204i	$-0.692744\pi$
$727$	−30.6942			−1.13839			−0.569193	+	0.822204i	$0.692744\pi$
$728$		0			0
$729$	−40.3475			−1.49435
$730$			5.55885i			0.205742i
$731$	−1.24542	−	2.15713i	−0.0460635	−	0.0797842i
$732$	2.06618			0.0763683
$733$	11.4873	−	6.63218i	0.424292	−	0.244965i	−0.272620	−	0.962122i	$-0.587890\pi$
$733$	11.4873	−	6.63218i	0.424292	−	0.244965i	0.696912	+	0.717157i	$0.254557\pi$
$734$	4.95980	−	2.86354i	0.183069	−	0.105695i
$735$		0			0
$736$		−	0.890761i		−	0.0328339i
$737$	19.3613	−	33.5348i	0.713184	−	1.23527i
$738$	−3.39113	−	5.87361i	−0.124829	−	0.216211i
$739$	−6.28279	+	3.62737i	−0.231116	+	0.133435i	−0.611087	−	0.791564i	$-0.709267\pi$
$739$	−6.28279	+	3.62737i	−0.231116	+	0.133435i	0.379971	+	0.924999i	$0.375934\pi$
$740$	0.0491505	+	0.0851312i	0.00180681	+	0.00312948i
$741$	45.8182	−	39.8395i	1.68317	−	1.46354i
$742$		0			0
$743$	−40.0705	−	23.1347i	−1.47004	−	0.848730i	−0.470608	−	0.882342i	$-0.655965\pi$
$743$	−40.0705	−	23.1347i	−1.47004	−	0.848730i	−0.999435	+	0.0336128i	$0.989299\pi$
$744$	−28.9782			−1.06239
$745$	6.38250			0.233837
$746$	−13.2673	−	7.65991i	−0.485752	−	0.280449i
$747$	26.7184	+	15.4259i	0.977574	+	0.564403i
$748$	−0.251121	+	0.144985i	−0.00918188	+	0.00530116i
$749$		0			0
$750$	14.9715	+	25.9314i	0.546681	+	0.946880i
$751$	36.0260			1.31461			0.657305	−	0.753625i	$-0.271697\pi$
$751$	36.0260			1.31461			0.657305	+	0.753625i	$0.271697\pi$
$752$	−12.6306	+	7.29229i	−0.460591	+	0.265922i
$753$	−9.69865	+	16.7985i	−0.353438	+	0.612173i
$754$	2.16473	+	11.1289i	0.0788349	+	0.405291i
$755$	1.20986			0.0440313
$756$		0			0
$757$	5.28132	−	9.14751i	0.191953	−	0.332472i	−0.753945	−	0.656938i	$-0.771851\pi$
$757$	5.28132	−	9.14751i	0.191953	−	0.332472i	0.945897	+	0.324466i	$0.105185\pi$
$758$	−3.19961	+	5.54189i	−0.116215	+	0.201291i
$759$	21.1099	+	12.1878i	0.766242	+	0.442390i
$760$			13.6301i			0.494415i
$761$	−6.76541	−	3.90601i	−0.245246	−	0.141593i	0.372340	−	0.928097i	$-0.378556\pi$
$761$	−6.76541	−	3.90601i	−0.245246	−	0.141593i	−0.617585	+	0.786504i	$0.711889\pi$
$762$			7.61813i			0.275976i
$763$		0			0
$764$	0.208695	−	0.361470i	0.00755031	−	0.0130775i
$765$		−	2.39309i		−	0.0865223i
$766$	2.53010	−	4.38226i	0.0914163	−	0.158338i
$767$	−29.9128	+	26.0096i	−1.08009	+	0.939152i
$768$	−3.38714	−	5.86671i	−0.122223	−	0.211696i
$769$	−21.9030	−	12.6457i	−0.789844	−	0.456017i	0.0500637	−	0.998746i	$-0.484058\pi$
$769$	−21.9030	−	12.6457i	−0.789844	−	0.456017i	−0.839908	+	0.542729i	$0.817391\pi$
$770$		0			0
$771$	23.8249	+	41.2659i	0.858032	+	1.48615i
$772$	−0.986345	+	0.569467i	−0.0354993	+	0.0204956i
$773$		−	46.6004i		−	1.67610i	−0.545592	−	0.838051i	$-0.683695\pi$
$773$		−	46.6004i		−	1.67610i	0.545592	−	0.838051i	$-0.316305\pi$
$774$			32.5121i			1.16862i
$775$	13.0958	−	7.56086i	0.470415	−	0.271594i
$776$	15.4057	+	26.6834i	0.553032	+	0.957879i
$777$		0			0
$778$	−20.1634	−	11.6414i	−0.722895	−	0.417363i
$779$	2.71106	+	4.69570i	0.0971339	+	0.168241i
$780$	0.156994	+	0.807110i	0.00562129	+	0.0288992i
$781$	−24.5513	+	42.5241i	−0.878515	+	1.52163i
$782$			1.23962i			0.0443289i
$783$	7.55940	−	13.0933i	0.270151	−	0.467915i
$784$		0			0
$785$		−	3.10848i		−	0.110946i
$786$	53.6163	+	30.9554i	1.91243	+	1.10414i
$787$			39.7332i			1.41633i	0.706045	+	0.708167i	$0.250478\pi$
$787$			39.7332i			1.41633i	−0.706045	+	0.708167i	$0.749522\pi$
$788$	−1.22653	−	0.708140i	−0.0436935	−	0.0252265i
$789$	−14.4388	+	25.0087i	−0.514034	+	0.890333i
$790$	−6.31788	+	10.9429i	−0.224780	+	0.389330i
$791$		0			0
$792$	80.8641			2.87338
$793$	25.8439	−	5.02700i	0.917744	−	0.178514i
$794$	11.5210	−	19.9550i	0.408865	−	0.708175i
$795$	−10.9691	+	6.33300i	−0.389033	+	0.224608i
$796$	0.693270			0.0245723
$797$	1.39299	+	2.41273i	0.0493422	+	0.0854632i	0.889642	−	0.456659i	$-0.150954\pi$
$797$	1.39299	+	2.41273i	0.0493422	+	0.0854632i	−0.840299	+	0.542123i	$0.817621\pi$
$798$		0			0
$799$	−1.86467	+	1.07656i	−0.0659671	+	0.0380861i
$800$	2.09115	+	1.20732i	0.0739332	+	0.0426853i
$801$	22.9989	+	13.2784i	0.812625	+	0.469169i
$802$	34.9086			1.23267
$803$	−26.3656			−0.930421
$804$	1.80000	+	1.03923i	0.0634812	+	0.0366509i
$805$		0			0
$806$	−16.9651	+	3.29995i	−0.597570	+	0.116236i
$807$	22.6505	+	39.2319i	0.797337	+	1.38103i
$808$	−9.81188	+	5.66489i	−0.345181	+	0.199290i
$809$	20.7293	+	35.9042i	0.728803	+	1.26232i	0.957389	+	0.288801i	$0.0932565\pi$
$809$	20.7293	+	35.9042i	0.728803	+	1.26232i	−0.228586	+	0.973524i	$0.573410\pi$
$810$	−1.77838	+	3.08024i	−0.0624859	+	0.108229i
$811$			27.8622i			0.978375i	0.872179	+	0.489188i	$0.162707\pi$
$811$			27.8622i			0.978375i	−0.872179	+	0.489188i	$0.837293\pi$
$812$		0			0
$813$	−13.0154	+	7.51443i	−0.456469	+	0.263543i
$814$	7.81915	−	4.51439i	0.274061	−	0.158229i
$815$	11.5741			0.405423
$816$	3.06127	+	5.30227i	0.107166	+	0.185617i
$817$		−	25.9920i		−	0.909344i
$818$	7.90671			0.276452
$819$		0			0
$820$	−0.0734276			−0.00256420
$821$		−	22.4202i		−	0.782469i	−0.920291	−	0.391235i	$-0.872048\pi$
$821$		−	22.4202i		−	0.782469i	0.920291	−	0.391235i	$-0.127952\pi$
$822$	−15.5974	−	27.0156i	−0.544023	−	0.942276i
$823$	2.36166			0.0823221			0.0411611	−	0.999153i	$-0.486894\pi$
$823$	2.36166			0.0823221			0.0411611	+	0.999153i	$0.486894\pi$
$824$	−21.1842	+	12.2307i	−0.737987	+	0.426077i
$825$	−57.2241	+	33.0384i	−1.99229	+	1.15025i
$826$		0			0
$827$		−	43.3148i		−	1.50620i	−0.657904	−	0.753102i	$-0.728557\pi$
$827$		−	43.3148i		−	1.50620i	0.657904	−	0.753102i	$-0.271443\pi$
$828$	−0.417773	+	0.723604i	−0.0145186	+	0.0251470i
$829$	27.4640	+	47.5690i	0.953864	+	1.65214i	0.736947	+	0.675951i	$0.236267\pi$
$829$	27.4640	+	47.5690i	0.953864	+	1.65214i	0.216917	+	0.976190i	$0.430400\pi$
$830$	−5.60162	+	3.23410i	−0.194435	+	0.112257i
$831$	27.7638	+	48.0884i	0.963117	+	1.66817i
$832$	−19.7623	−	22.7280i	−0.685134	−	0.787951i
$833$		0			0
$834$	34.1514	+	19.7173i	1.18257	+	0.682755i
$835$	3.64400			0.126106
$836$	−3.02584			−0.104651
$837$	19.9596	+	11.5237i	0.689903	+	0.398316i
$838$	41.0190	+	23.6824i	1.41698	+	0.818093i
$839$	12.7661	−	7.37052i	0.440735	−	0.254459i	−0.263174	−	0.964748i	$-0.584769\pi$
$839$	12.7661	−	7.37052i	0.440735	−	0.254459i	0.703910	+	0.710290i	$0.251436\pi$
$840$		0			0
$841$	11.9004	+	20.6122i	0.410360	+	0.710765i
$842$	4.05673			0.139804
$843$	−5.34678	+	3.08697i	−0.184153	+	0.106321i
$844$	1.29745	−	2.24725i	0.0446600	−	0.0773535i
$845$	3.92738	+	9.71340i	0.135106	+	0.334151i
$846$	28.1041			0.966239
$847$		0			0
$848$	10.3471	−	17.9217i	0.355321	−	0.615434i
$849$	−22.6898	+	39.2999i	−0.778713	+	1.34877i
$850$	−2.91013	−	1.68017i	−0.0998168	−	0.0576292i
$851$			1.99319i			0.0683256i
$852$	−2.28251	−	1.31781i	−0.0781975	−	0.0451474i
$853$			24.1038i			0.825297i	0.910890	+	0.412649i	$0.135396\pi$
$853$			24.1038i			0.825297i	−0.910890	+	0.412649i	$0.864604\pi$
$854$		0			0
$855$	12.4860	−	21.6264i	0.427012	−	0.739607i
$856$			27.9957i			0.956873i
$857$	9.29249	−	16.0951i	0.317425	−	0.549797i	−0.662525	−	0.749040i	$-0.730515\pi$
$857$	9.29249	−	16.0951i	0.317425	−	0.549797i	0.979950	+	0.199243i	$0.0638483\pi$
$858$	74.1316	−	14.4196i	2.53081	−	0.492278i
$859$	14.7487	+	25.5456i	0.503221	+	0.871604i	0.999993	+	0.00372294i	$0.00118505\pi$
$859$	14.7487	+	25.5456i	0.503221	+	0.871604i	−0.496772	+	0.867881i	$0.665482\pi$
$860$	0.304832	+	0.175995i	0.0103947	+	0.00600137i
$861$		0			0
$862$	−27.3712	−	47.4083i	−0.932266	−	1.61473i
$863$	−16.1457	+	9.32173i	−0.549606	+	0.317315i	−0.748963	−	0.662612i	$-0.769448\pi$
$863$	−16.1457	+	9.32173i	−0.549606	+	0.317315i	0.199357	+	0.979927i	$0.436115\pi$
$864$			3.68021i			0.125203i
$865$		−	15.7304i		−	0.534851i
$866$	11.7477	−	6.78256i	0.399204	−	0.230481i
$867$	−24.0383	−	41.6355i	−0.816383	−	1.41402i
$868$		0			0
$869$	−51.9020	−	29.9656i	−1.76065	−	1.01651i
$870$	3.65087	+	6.32350i	0.123776	+	0.214387i
$871$	25.0430	+	8.61938i	0.848549	+	0.292056i
$872$	−21.0705	+	36.4951i	−0.713536	+	1.23588i
$873$		−	56.4502i		−	1.91055i
$874$	−6.46776	+	11.2025i	−0.218775	+	0.378930i
$875$		0			0
$876$		−	1.41519i		−	0.0478148i
$877$	−32.6941	−	18.8759i	−1.10400	−	0.637395i	−0.166731	−	0.986002i	$-0.553321\pi$
$877$	−32.6941	−	18.8759i	−1.10400	−	0.637395i	−0.937269	+	0.348608i	$0.886655\pi$
$878$		−	39.3673i		−	1.32858i
$879$	57.7606	+	33.3481i	1.94822	+	1.12480i
$880$	−8.05950	+	13.9595i	−0.271686	+	0.470574i
$881$	−14.9149	+	25.8334i	−0.502497	+	0.870350i	0.497499	+	0.867464i	$0.334252\pi$
$881$	−14.9149	+	25.8334i	−0.502497	+	0.870350i	−0.999996	+	0.00288515i	$0.999082\pi$
$882$		0			0
$883$	−32.3979			−1.09028			−0.545138	−	0.838346i	$-0.683523\pi$
$883$	−32.3979			−1.09028			−0.545138	+	0.838346i	$0.683523\pi$
$884$	−0.130134	−	0.149663i	−0.00437687	−	0.00503371i
$885$	−12.7646	+	22.1089i	−0.429076	+	0.743181i
$886$	−3.98777	+	2.30234i	−0.133972	+	0.0773487i
$887$	25.9198			0.870302			0.435151	−	0.900358i	$-0.356695\pi$
$887$	25.9198			0.870302			0.435151	+	0.900358i	$0.356695\pi$
$888$	5.17703	+	8.96688i	0.173730	+	0.300909i
$889$		0			0
$890$	−4.82181	+	2.78387i	−0.161627	+	0.0933156i
$891$	−14.6096	−	8.43483i	−0.489439	−	0.282577i
$892$	−1.95620	−	1.12941i	−0.0654984	−	0.0378155i
$893$	−22.4680			−0.751863
$894$	31.4658			1.05238
$895$	14.5315	+	8.38976i	0.485734	+	0.280439i
$896$		0			0
$897$	−5.42583	+	15.7644i	−0.181163	+	0.526357i
$898$	−12.5391	−	21.7184i	−0.418435	−	0.724751i
$899$	6.86376	−	3.96280i	0.228919	−	0.132167i
$900$	−1.13249	−	1.96152i	−0.0377495	−	0.0653841i
$901$	1.52755	−	2.64579i	0.0508901	−	0.0881442i
$902$			6.74420i			0.224557i
$903$		0			0
$904$	−48.8934	+	28.2286i	−1.62617	+	0.938869i
$905$	−11.5529	+	6.67010i	−0.384033	+	0.221722i
$906$	5.96463			0.198162
$907$	7.77113	+	13.4600i	0.258036	+	0.446931i	0.965716	−	0.259602i	$-0.0835914\pi$
$907$	7.77113	+	13.4600i	0.258036	+	0.446931i	−0.707680	+	0.706533i	$0.750258\pi$
$908$		−	0.0445240i		−	0.00147758i
$909$	20.7576			0.688485
$910$		0			0
$911$	23.6358			0.783090			0.391545	−	0.920159i	$-0.371941\pi$
$911$	23.6358			0.783090			0.391545	+	0.920159i	$0.371941\pi$
$912$			63.8889i			2.11557i
$913$	−15.3393	−	26.5684i	−0.507656	−	0.879287i
$914$	12.0382			0.398189
$915$	14.6846	−	8.47816i	0.485458	−	0.280279i
$916$	−1.47421	+	0.851138i	−0.0487094	+	0.0281224i
$917$		0			0
$918$		−	5.12155i		−	0.169036i
$919$	−22.2409	+	38.5223i	−0.733659	+	1.27073i	0.221651	+	0.975126i	$0.428856\pi$
$919$	−22.2409	+	38.5223i	−0.733659	+	1.27073i	−0.955309	+	0.295608i	$0.904478\pi$
$920$	−1.87132	−	3.24123i	−0.0616957	−	0.106860i
$921$	−10.5694	+	6.10224i	−0.348273	+	0.201076i
$922$	−1.56608	−	2.71253i	−0.0515761	−	0.0893324i
$923$	−31.7560	−	10.9299i	−1.04526	−	0.359761i
$924$		0			0
$925$	−4.67920	−	2.70154i	−0.153851	−	0.0888259i
$926$	7.56171			0.248493
$927$	44.8163			1.47196
$928$	1.09601	+	0.632782i	0.0359783	+	0.0207721i
$929$	2.54846	+	1.47135i	0.0836121	+	0.0482735i	0.541223	−	0.840879i	$-0.317961\pi$
$929$	2.54846	+	1.47135i	0.0836121	+	0.0482735i	−0.457611	+	0.889152i	$0.651295\pi$
$930$	−9.63964	+	5.56545i	−0.316096	+	0.182498i
$931$		0			0
$932$	0.383751	+	0.664676i	0.0125702	+	0.0217722i
$933$	−78.5131			−2.57040
$934$	−22.5506	+	13.0196i	−0.737878	+	0.426014i
$935$	−1.18983	+	2.06085i	−0.0389116	+	0.0673968i
$936$	10.5602	+	54.2903i	0.345172	+	1.77453i
$937$	0.951020			0.0310685			0.0155342	−	0.999879i	$-0.495055\pi$
$937$	0.951020			0.0310685			0.0155342	+	0.999879i	$0.495055\pi$
$938$		0			0
$939$	−3.88526	+	6.72947i	−0.126791	+	0.219608i
$940$	0.152133	−	0.263503i	0.00496205	−	0.00859451i
$941$	19.1125	+	11.0346i	0.623050	+	0.359718i	0.778056	−	0.628196i	$-0.216206\pi$
$941$	19.1125	+	11.0346i	0.623050	+	0.359718i	−0.155006	+	0.987914i	$0.549540\pi$
$942$		−	15.3248i		−	0.499311i
$943$	−1.28938	−	0.744423i	−0.0419879	−	0.0242417i
$944$		−	41.7105i		−	1.35756i
$945$		0			0
$946$	16.1648	−	27.9983i	0.525563	−	0.910302i
$947$		−	51.1717i		−	1.66286i	−0.555631	−	0.831429i	$-0.687523\pi$
$947$		−	51.1717i		−	1.66286i	0.555631	−	0.831429i	$-0.312477\pi$
$948$	1.60842	−	2.78587i	0.0522392	−	0.0904809i
$949$	−3.44314	−	17.7012i	−0.111769	−	0.574607i
$950$	−17.5326	−	30.3674i	−0.568833	−	0.985248i
$951$	60.0605	+	34.6759i	1.94759	+	1.12444i
$952$		0			0
$953$	22.9235	+	39.7047i	0.742565	+	1.28616i	0.951324	+	0.308194i	$0.0997245\pi$
$953$	22.9235	+	39.7047i	0.742565	+	1.28616i	−0.208758	+	0.977967i	$0.566942\pi$
$954$	−34.5347	+	19.9386i	−1.11810	+	0.645536i
$955$		−	3.42534i		−	0.110842i
$956$			1.32889i			0.0429793i
$957$	−29.9923	+	17.3160i	−0.969512	+	0.559748i
$958$	−22.8478	−	39.5735i	−0.738177	−	1.27856i
$959$		0			0
$960$	−16.7985	−	9.69861i	−0.542169	−	0.313021i
$961$	−9.45905	−	16.3836i	−0.305131	−	0.528502i
$962$	4.05198	+	4.66006i	0.130641	+	0.150246i
$963$	25.6458	−	44.4198i	0.826424	−	1.43141i
$964$		−	2.21548i		−	0.0713559i
$965$	−4.67338	+	8.09453i	−0.150441	+	0.260572i
$966$		0			0
$967$		−	19.2609i		−	0.619387i	−0.950836	−	0.309694i	$-0.899773\pi$
$967$		−	19.2609i		−	0.619387i	0.950836	−	0.309694i	$-0.100227\pi$
$968$	−42.0726	−	24.2906i	−1.35226	−	0.780730i
$969$			9.43196i			0.302998i
$970$	10.2494	+	5.91752i	0.329090	+	0.190000i
$971$	23.6663	−	40.9912i	0.759487	−	1.31547i	−0.183625	−	0.982996i	$-0.558783\pi$
$971$	23.6663	−	40.9912i	0.759487	−	1.31547i	0.943112	−	0.332474i	$-0.107883\pi$
$972$	−0.524016	+	0.907622i	−0.0168078	+	0.0291120i
$973$		0			0
$974$	22.0046			0.705072
$975$	−29.6542	−	34.1044i	−0.949696	−	1.09222i
$976$	−13.8520	+	23.9923i	−0.443390	+	0.767975i
$977$	41.4454	−	23.9285i	1.32596	−	0.765541i	0.341285	−	0.939960i	$-0.389138\pi$
$977$	41.4454	−	23.9285i	1.32596	−	0.765541i	0.984672	+	0.174418i	$0.0558045\pi$
$978$	57.0605			1.82459
$979$	−13.2039	−	22.8698i	−0.421998	−	0.730921i
$980$		0			0
$981$	66.8635	−	38.6037i	2.13479	−	1.23252i
$982$	37.8506	+	21.8531i	1.20786	+	0.697359i
$983$	−13.6560	−	7.88432i	−0.435560	−	0.251471i	0.266152	−	0.963931i	$-0.414248\pi$
$983$	−13.6560	−	7.88432i	−0.435560	−	0.251471i	−0.701712	+	0.712460i	$0.747581\pi$
$984$	−7.73414			−0.246555
$985$	−11.6228			−0.370335
$986$	−1.52526	−	0.880608i	−0.0485741	−	0.0280443i
$987$		0			0
$988$	−0.395151	−	2.03148i	−0.0125714	−	0.0646300i
$989$	3.56853	+	6.18088i	0.113473	+	0.196541i
$990$	26.8995	−	15.5305i	0.854924	−	0.493590i
$991$	6.06892	+	10.5117i	0.192786	+	0.333914i	0.946172	−	0.323663i	$-0.104914\pi$
$991$	6.06892	+	10.5117i	0.192786	+	0.333914i	−0.753387	+	0.657578i	$0.771581\pi$
$992$	−0.964622	+	1.67077i	−0.0306268	+	0.0530471i
$993$			1.78555i			0.0566627i
$994$		0			0
$995$	4.92715	−	2.84469i	0.156201	−	0.0901828i
$996$	1.42608	−	0.823346i	0.0451870	−	0.0260887i
$997$	−33.7876			−1.07006			−0.535032	−	0.844832i	$-0.679701\pi$
$997$	−33.7876			−1.07006			−0.535032	+	0.844832i	$0.679701\pi$
$998$	−16.6993	−	28.9240i	−0.528607	−	0.915574i
$999$		−	8.23493i		−	0.260542i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.k.i.459.2		12
7.2	even	3		637.2.u.g.30.2		12
7.3	odd	6		637.2.q.g.589.5		12
7.4	even	3		637.2.q.i.589.5		12
7.5	odd	6		91.2.u.b.30.2	yes	12
7.6	odd	2		91.2.k.b.4.2	✓	12
13.10	even	6		637.2.u.g.361.2		12
21.5	even	6		819.2.do.e.667.5		12
21.20	even	2		819.2.bm.f.550.5		12
91.6	even	12		1183.2.e.j.508.10		24
91.10	odd	6		637.2.q.g.491.5		12
91.19	even	12		1183.2.e.j.170.10		24
91.20	even	12		1183.2.e.j.508.3		24
91.23	even	6	inner	637.2.k.i.569.5		12
91.32	odd	12		8281.2.a.co.1.3		12
91.33	even	12		1183.2.e.j.170.3		24
91.45	even	12		8281.2.a.cp.1.3		12
91.46	odd	12		8281.2.a.co.1.10		12
91.59	even	12		8281.2.a.cp.1.10		12
91.62	odd	6		91.2.u.b.88.2	yes	12
91.75	odd	6		91.2.k.b.23.5	yes	12
91.88	even	6		637.2.q.i.491.5		12
273.62	even	6		819.2.do.e.361.5		12
273.257	even	6		819.2.bm.f.478.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.k.b.4.2	✓	12	7.6	odd	2
91.2.k.b.23.5	yes	12	91.75	odd	6
91.2.u.b.30.2	yes	12	7.5	odd	6
91.2.u.b.88.2	yes	12	91.62	odd	6
637.2.k.i.459.2		12	1.1	even	1	trivial
637.2.k.i.569.5		12	91.23	even	6	inner
637.2.q.g.491.5		12	91.10	odd	6
637.2.q.g.589.5		12	7.3	odd	6
637.2.q.i.491.5		12	91.88	even	6
637.2.q.i.589.5		12	7.4	even	3
637.2.u.g.30.2		12	7.2	even	3
637.2.u.g.361.2		12	13.10	even	6
819.2.bm.f.478.2		12	273.257	even	6
819.2.bm.f.550.5		12	21.20	even	2
819.2.do.e.361.5		12	273.62	even	6
819.2.do.e.667.5		12	21.5	even	6
1183.2.e.j.170.3		24	91.33	even	12
1183.2.e.j.170.10		24	91.19	even	12
1183.2.e.j.508.3		24	91.20	even	12
1183.2.e.j.508.10		24	91.6	even	12
8281.2.a.co.1.3		12	91.32	odd	12
8281.2.a.co.1.10		12	91.46	odd	12
8281.2.a.cp.1.3		12	91.45	even	12
8281.2.a.cp.1.10		12	91.59	even	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.k (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-1.37905i q^{2} +(1.44060 + 2.49520i) q^{3} +0.0982074 q^{4} +(0.697972 - 0.402974i) q^{5} +(3.44101 - 1.98667i) q^{6} -2.89354i q^{8} +(-2.65067 + 4.59109i) q^{9} +O(q^{10})\)	\(q-1.37905i q^{2} +(1.44060 + 2.49520i) q^{3} +0.0982074 q^{4} +(0.697972 - 0.402974i) q^{5} +(3.44101 - 1.98667i) q^{6} -2.89354i q^{8} +(-2.65067 + 4.59109i) q^{9} +(-0.555723 - 0.962541i) q^{10} +(4.56532 - 2.63579i) q^{11} +(0.141478 + 0.245047i) q^{12} +(2.36581 + 2.72084i) q^{13} +(2.01100 + 1.16105i) q^{15} -3.79394 q^{16} -0.560102 q^{17} +(6.33136 + 3.65541i) q^{18} +(-5.06165 - 2.92234i) q^{19} +(0.0685460 - 0.0395750i) q^{20} +(-3.63490 - 6.29583i) q^{22} +1.60488 q^{23} +(7.21995 - 4.16844i) q^{24} +(-2.17522 + 3.76760i) q^{25} +(3.75219 - 3.26258i) q^{26} -6.63060 q^{27} +(-1.14008 + 1.97467i) q^{29} +(1.60115 - 2.77328i) q^{30} +(-3.01022 - 1.73795i) q^{31} -0.555034i q^{32} +(13.1536 + 7.59424i) q^{33} +0.772411i q^{34} +(-0.260315 + 0.450879i) q^{36} +1.24196i q^{37} +(-4.03007 + 6.98029i) q^{38} +(-3.38084 + 9.82279i) q^{39} +(-1.16602 - 2.01961i) q^{40} +(-0.803413 - 0.463851i) q^{41} +(2.22356 + 3.85131i) q^{43} +(0.448348 - 0.258854i) q^{44} +4.27260i q^{45} -2.21321i q^{46} +(3.32915 - 1.92209i) q^{47} +(-5.46556 - 9.46662i) q^{48} +(5.19572 + 2.99975i) q^{50} +(-0.806883 - 1.39756i) q^{51} +(0.232340 + 0.267207i) q^{52} +(-2.72727 + 4.72377i) q^{53} +9.14396i q^{54} +(2.12431 - 3.67941i) q^{55} -16.8397i q^{57} +(2.72318 + 1.57223i) q^{58} +10.9940i q^{59} +(0.197495 + 0.114024i) q^{60} +(3.65107 - 6.32385i) q^{61} +(-2.39673 + 4.15126i) q^{62} -8.35330 q^{64} +(2.74769 + 0.945710i) q^{65} +(10.4729 - 18.1396i) q^{66} +(6.36144 - 3.67278i) q^{67} -0.0550061 q^{68} +(2.31199 + 4.00448i) q^{69} +(-8.06668 + 4.65730i) q^{71} +(13.2845 + 7.66982i) q^{72} +(-4.33139 - 2.50073i) q^{73} +1.71273 q^{74} -12.5345 q^{75} +(-0.497091 - 0.286996i) q^{76} +(13.5462 + 4.66237i) q^{78} +(-5.68437 - 9.84562i) q^{79} +(-2.64806 + 1.52886i) q^{80} +(-1.60006 - 2.77138i) q^{81} +(-0.639676 + 1.10795i) q^{82} -5.81962i q^{83} +(-0.390935 + 0.225707i) q^{85} +(5.31117 - 3.06641i) q^{86} -6.56959 q^{87} +(-7.62677 - 13.2100i) q^{88} -5.00946i q^{89} +5.89215 q^{90} +0.157611 q^{92} -10.0148i q^{93} +(-2.65067 - 4.59109i) q^{94} -4.71051 q^{95} +(1.38492 - 0.799583i) q^{96} +(-9.22171 + 5.32416i) q^{97} +27.9464i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 3 q^{3} - 8 q^{4} + 3 q^{5} + 9 q^{6} - q^{9}+O(q^{10}) \) 12 * q + 3 * q^3 - 8 * q^4 + 3 * q^5 + 9 * q^6 - q^9	\( 12 q + 3 q^{3} - 8 q^{4} + 3 q^{5} + 9 q^{6} - q^{9} - 12 q^{10} + 12 q^{11} + q^{12} + 2 q^{13} - 12 q^{15} + 16 q^{16} + 34 q^{17} + 3 q^{18} - 9 q^{19} + 3 q^{20} - 15 q^{22} - 6 q^{23} - 15 q^{24} - 5 q^{25} + 6 q^{26} - 12 q^{27} - q^{29} + 11 q^{30} - 18 q^{31} + 6 q^{33} - 13 q^{36} - 19 q^{38} - 4 q^{39} + q^{40} + 6 q^{41} + 11 q^{43} - 33 q^{44} + 15 q^{47} - 19 q^{48} + 18 q^{50} + 4 q^{51} + 7 q^{52} - 8 q^{53} + 15 q^{55} - 24 q^{58} - 30 q^{60} - 5 q^{61} - 41 q^{62} + 2 q^{64} + 21 q^{65} + 34 q^{66} + 15 q^{67} - 22 q^{68} - 7 q^{69} + 30 q^{71} + 57 q^{72} - 42 q^{73} + 66 q^{74} + 2 q^{75} + 45 q^{76} + 44 q^{78} - 35 q^{79} + 63 q^{80} + 14 q^{81} - 5 q^{82} - 21 q^{85} - 57 q^{86} + 20 q^{87} - 14 q^{88} - 66 q^{92} - q^{94} - 4 q^{95} - 21 q^{96} + 3 q^{97}+O(q^{100}) \) 12 * q + 3 * q^3 - 8 * q^4 + 3 * q^5 + 9 * q^6 - q^9 - 12 * q^10 + 12 * q^11 + q^12 + 2 * q^13 - 12 * q^15 + 16 * q^16 + 34 * q^17 + 3 * q^18 - 9 * q^19 + 3 * q^20 - 15 * q^22 - 6 * q^23 - 15 * q^24 - 5 * q^25 + 6 * q^26 - 12 * q^27 - q^29 + 11 * q^30 - 18 * q^31 + 6 * q^33 - 13 * q^36 - 19 * q^38 - 4 * q^39 + q^40 + 6 * q^41 + 11 * q^43 - 33 * q^44 + 15 * q^47 - 19 * q^48 + 18 * q^50 + 4 * q^51 + 7 * q^52 - 8 * q^53 + 15 * q^55 - 24 * q^58 - 30 * q^60 - 5 * q^61 - 41 * q^62 + 2 * q^64 + 21 * q^65 + 34 * q^66 + 15 * q^67 - 22 * q^68 - 7 * q^69 + 30 * q^71 + 57 * q^72 - 42 * q^73 + 66 * q^74 + 2 * q^75 + 45 * q^76 + 44 * q^78 - 35 * q^79 + 63 * q^80 + 14 * q^81 - 5 * q^82 - 21 * q^85 - 57 * q^86 + 20 * q^87 - 14 * q^88 - 66 * q^92 - q^94 - 4 * q^95 - 21 * q^96 + 3 * q^97

Introduction

L-functions

Modular forms

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Database

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