LMFDB - Embedded newform 637.2.e.o.508.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(79,637)]

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([2, 0]))

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

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

chi := DirichletCharacter("637.79");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.e (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:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2 x^{11} + 9 x^{10} - 6 x^{9} + 34 x^{8} - 18 x^{7} + 85 x^{6} - 2 x^{5} + 92 x^{4} - 26 x^{3} + \cdots + 1 $ x^12 - 2x^11 + 9x^10 - 6x^9 + 34x^8 - 18x^7 + 85x^6 - 2x^5 + 92x^4 - 26x^3 + 43x^2 + 6*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			508.4
Root			$-0.602377 - 1.04335i$ of defining polynomial
Character	$\chi$	$=$	637.508
Dual form			637.2.e.o.79.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.328092 + 0.568272i) q^{2} +(-0.102377 + 0.177322i) q^{3} +(0.784711 - 1.35916i) q^{4} +(-0.679981 - 1.17776i) q^{5} -0.134356 q^{6} +2.34220 q^{8} +(1.47904 + 2.56177i) q^{9} +O(q^{10})$	\(q+(0.328092 + 0.568272i) q^{2} +(-0.102377 + 0.177322i) q^{3} +(0.784711 - 1.35916i) q^{4} +(-0.679981 - 1.17776i) q^{5} -0.134356 q^{6} +2.34220 q^{8} +(1.47904 + 2.56177i) q^{9} +(0.446193 - 0.772828i) q^{10} +(0.952756 - 1.65022i) q^{11} +(0.160672 + 0.278293i) q^{12} -1.00000 q^{13} +0.278457 q^{15} +(-0.800966 - 1.38731i) q^{16} +(1.78317 - 3.08854i) q^{17} +(-0.970521 + 1.68099i) q^{18} +(0.492627 + 0.853255i) q^{19} -2.13436 q^{20} +1.25037 q^{22} +(-0.848026 - 1.46882i) q^{23} +(-0.239786 + 0.415322i) q^{24} +(1.57525 - 2.72841i) q^{25} +(-0.328092 - 0.568272i) q^{26} -1.21994 q^{27} +6.54835 q^{29} +(0.0913595 + 0.158239i) q^{30} +(3.84775 - 6.66450i) q^{31} +(2.86778 - 4.96714i) q^{32} +(0.195080 + 0.337889i) q^{33} +2.34017 q^{34} +4.64247 q^{36} +(1.01003 + 1.74942i) q^{37} +(-0.323254 + 0.559893i) q^{38} +(0.102377 - 0.177322i) q^{39} +(-1.59265 - 2.75855i) q^{40} -9.88779 q^{41} -3.16639 q^{43} +(-1.49528 - 2.58990i) q^{44} +(2.01144 - 3.48391i) q^{45} +(0.556461 - 0.963819i) q^{46} +(3.88208 + 6.72396i) q^{47} +0.328001 q^{48} +2.06731 q^{50} +(0.365109 + 0.632388i) q^{51} +(-0.784711 + 1.35916i) q^{52} +(-0.177097 + 0.306741i) q^{53} +(-0.400251 - 0.693255i) q^{54} -2.59143 q^{55} -0.201734 q^{57} +(2.14846 + 3.72124i) q^{58} +(1.08192 - 1.87395i) q^{59} +(0.218508 - 0.378467i) q^{60} +(6.10010 + 10.5657i) q^{61} +5.04967 q^{62} +0.559715 q^{64} +(0.679981 + 1.17776i) q^{65} +(-0.128008 + 0.221717i) q^{66} +(-5.65670 + 9.79769i) q^{67} +(-2.79854 - 4.84722i) q^{68} +0.347272 q^{69} -9.05268 q^{71} +(3.46420 + 6.00017i) q^{72} +(-3.56809 + 6.18012i) q^{73} +(-0.662763 + 1.14794i) q^{74} +(0.322538 + 0.558652i) q^{75} +1.54628 q^{76} +0.134356 q^{78} +(2.69815 + 4.67333i) q^{79} +(-1.08928 + 1.88670i) q^{80} +(-4.31222 + 7.46899i) q^{81} +(-3.24411 - 5.61896i) q^{82} +2.03494 q^{83} -4.85008 q^{85} +(-1.03887 - 1.79937i) q^{86} +(-0.670398 + 1.16116i) q^{87} +(2.23154 - 3.86515i) q^{88} +(-3.44932 - 5.97440i) q^{89} +2.63974 q^{90} -2.66182 q^{92} +(0.787840 + 1.36458i) q^{93} +(-2.54736 + 4.41216i) q^{94} +(0.669955 - 1.16040i) q^{95} +(0.587187 + 1.01704i) q^{96} +14.6223 q^{97} +5.63665 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 8 q^{3} - 4 q^{4} + 6 q^{5} - 8 q^{6} - 6 q^{9}+O(q^{10}) $ 12 * q + 8 * q^3 - 4 * q^4 + 6 * q^5 - 8 * q^6 - 6 * q^9	$ 12 q + 8 q^{3} - 4 q^{4} + 6 q^{5} - 8 q^{6} - 6 q^{9} + 4 q^{10} - 4 q^{11} - 4 q^{12} - 12 q^{13} + 24 q^{15} + 16 q^{17} + 4 q^{18} + 2 q^{19} - 32 q^{20} - 24 q^{22} + 6 q^{23} + 12 q^{24} + 4 q^{25} - 40 q^{27} - 12 q^{29} + 6 q^{31} + 20 q^{32} + 4 q^{33} - 48 q^{36} + 8 q^{38} - 8 q^{39} + 4 q^{40} + 16 q^{41} + 4 q^{43} + 4 q^{44} + 14 q^{45} - 8 q^{46} + 30 q^{47} + 16 q^{48} + 16 q^{50} + 4 q^{51} + 4 q^{52} + 14 q^{53} - 48 q^{54} + 16 q^{55} + 8 q^{57} + 8 q^{58} + 24 q^{59} - 12 q^{60} - 56 q^{62} - 40 q^{64} - 6 q^{65} - 4 q^{66} - 16 q^{67} + 28 q^{68} + 40 q^{69} + 16 q^{71} - 28 q^{72} - 6 q^{73} + 12 q^{74} + 12 q^{75} + 32 q^{76} + 8 q^{78} + 22 q^{79} - 28 q^{80} - 46 q^{81} - 40 q^{82} - 100 q^{83} - 16 q^{85} + 16 q^{86} - 16 q^{87} + 44 q^{88} + 26 q^{89} + 80 q^{90} + 40 q^{92} - 16 q^{93} - 32 q^{94} + 6 q^{95} - 20 q^{96} + 28 q^{97} + 24 q^{99}+O(q^{100}) $ 12 * q + 8 * q^3 - 4 * q^4 + 6 * q^5 - 8 * q^6 - 6 * q^9 + 4 * q^10 - 4 * q^11 - 4 * q^12 - 12 * q^13 + 24 * q^15 + 16 * q^17 + 4 * q^18 + 2 * q^19 - 32 * q^20 - 24 * q^22 + 6 * q^23 + 12 * q^24 + 4 * q^25 - 40 * q^27 - 12 * q^29 + 6 * q^31 + 20 * q^32 + 4 * q^33 - 48 * q^36 + 8 * q^38 - 8 * q^39 + 4 * q^40 + 16 * q^41 + 4 * q^43 + 4 * q^44 + 14 * q^45 - 8 * q^46 + 30 * q^47 + 16 * q^48 + 16 * q^50 + 4 * q^51 + 4 * q^52 + 14 * q^53 - 48 * q^54 + 16 * q^55 + 8 * q^57 + 8 * q^58 + 24 * q^59 - 12 * q^60 - 56 * q^62 - 40 * q^64 - 6 * q^65 - 4 * q^66 - 16 * q^67 + 28 * q^68 + 40 * q^69 + 16 * q^71 - 28 * q^72 - 6 * q^73 + 12 * q^74 + 12 * q^75 + 32 * q^76 + 8 * q^78 + 22 * q^79 - 28 * q^80 - 46 * q^81 - 40 * q^82 - 100 * q^83 - 16 * q^85 + 16 * q^86 - 16 * q^87 + 44 * q^88 + 26 * q^89 + 80 * q^90 + 40 * q^92 - 16 * q^93 - 32 * q^94 + 6 * q^95 - 20 * q^96 + 28 * q^97 + 24 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	0.328092	+	0.568272i	0.231996	+	0.401829i	0.958395	−	0.285444i	$-0.0921410\pi$
$2$	0.328092	+	0.568272i	0.231996	+	0.401829i	−0.726399	+	0.687273i	$0.758808\pi$
$3$	−0.102377	+	0.177322i	−0.0591072	+	0.102377i	−0.894065	−	0.447937i	$-0.852159\pi$
$3$	−0.102377	+	0.177322i	−0.0591072	+	0.102377i	0.834958	+	0.550314i	$0.185492\pi$
$4$	0.784711	−	1.35916i	0.392356	−	0.679580i
$5$	−0.679981	−	1.17776i	−0.304097	−	0.526711i	0.672963	−	0.739676i	$-0.265021\pi$
$5$	−0.679981	−	1.17776i	−0.304097	−	0.526711i	−0.977060	+	0.212965i	$0.931688\pi$
$6$	−0.134356			−0.0548505
$7$		0			0
$7$		0			0
$8$	2.34220			0.828092
$9$	1.47904	+	2.56177i	0.493013	+	0.853923i
$10$	0.446193	−	0.772828i	0.141099	−	0.244390i
$11$	0.952756	−	1.65022i	0.287267	−	0.497561i	−0.685890	−	0.727706i	$-0.740587\pi$
$11$	0.952756	−	1.65022i	0.287267	−	0.497561i	0.973156	+	0.230145i	$0.0739200\pi$
$12$	0.160672	+	0.278293i	0.0463821	+	0.0803361i
$13$	−1.00000			−0.277350
$13$	−1.00000			−0.277350
$14$		0			0
$15$	0.278457			0.0718972
$16$	−0.800966	−	1.38731i	−0.200242	−	0.346829i
$17$	1.78317	−	3.08854i	0.432482	−	0.749080i	−0.564605	−	0.825361i	$-0.690971\pi$
$17$	1.78317	−	3.08854i	0.432482	−	0.749080i	0.997086	+	0.0762814i	$0.0243047\pi$
$18$	−0.970521	+	1.68099i	−0.228754	+	0.396214i
$19$	0.492627	+	0.853255i	0.113016	+	0.195750i	0.916985	−	0.398921i	$-0.130615\pi$
$19$	0.492627	+	0.853255i	0.113016	+	0.195750i	−0.803969	+	0.594672i	$0.797282\pi$
$20$	−2.13436			−0.477256
$21$		0			0
$22$	1.25037			0.266579
$23$	−0.848026	−	1.46882i	−0.176826	−	0.306271i	0.763966	−	0.645257i	$-0.223250\pi$
$23$	−0.848026	−	1.46882i	−0.176826	−	0.306271i	−0.940792	+	0.338986i	$0.889916\pi$
$24$	−0.239786	+	0.415322i	−0.0489462	+	0.0847773i
$25$	1.57525	−	2.72841i	0.315050	−	0.545683i
$26$	−0.328092	−	0.568272i	−0.0643441	−	0.111447i
$27$	−1.21994			−0.234777
$28$		0			0
$29$	6.54835			1.21600			0.607999	−	0.793938i	$-0.291972\pi$
$29$	6.54835			1.21600			0.607999	+	0.793938i	$0.291972\pi$
$30$	0.0913595	+	0.158239i	0.0166799	+	0.0288904i
$31$	3.84775	−	6.66450i	0.691077	−	1.19698i	−0.280409	−	0.959881i	$-0.590470\pi$
$31$	3.84775	−	6.66450i	0.691077	−	1.19698i	0.971485	−	0.237099i	$-0.0761966\pi$
$32$	2.86778	−	4.96714i	0.506957	−	0.878074i
$33$	0.195080	+	0.337889i	0.0339591	+	0.0588188i
$34$	2.34017			0.401336
$35$		0			0
$36$	4.64247			0.773745
$37$	1.01003	+	1.74942i	0.166047	+	0.287602i	0.937027	−	0.349258i	$-0.113566\pi$
$37$	1.01003	+	1.74942i	0.166047	+	0.287602i	−0.770979	+	0.636860i	$0.780233\pi$
$38$	−0.323254	+	0.559893i	−0.0524387	+	0.0908266i
$39$	0.102377	−	0.177322i	0.0163934	−	0.0283942i
$40$	−1.59265	−	2.75855i	−0.251820	−	0.436165i
$41$	−9.88779			−1.54421			−0.772107	−	0.635493i	$-0.780797\pi$
$41$	−9.88779			−1.54421			−0.772107	+	0.635493i	$0.780797\pi$
$42$		0			0
$43$	−3.16639			−0.482869			−0.241435	−	0.970417i	$-0.577618\pi$
$43$	−3.16639			−0.482869			−0.241435	+	0.970417i	$0.577618\pi$
$44$	−1.49528	−	2.58990i	−0.225422	−	0.390442i
$45$	2.01144	−	3.48391i	0.299847	−	0.519351i
$46$	0.556461	−	0.963819i	0.0820457	−	0.142107i
$47$	3.88208	+	6.72396i	0.566260	+	0.980791i	0.996931	+	0.0782818i	$0.0249434\pi$
$47$	3.88208	+	6.72396i	0.566260	+	0.980791i	−0.430672	+	0.902509i	$0.641723\pi$
$48$	0.328001			0.0473429
$49$		0			0
$50$	2.06731			0.292362
$51$	0.365109	+	0.632388i	0.0511255	+	0.0885520i
$52$	−0.784711	+	1.35916i	−0.108820	+	0.188482i
$53$	−0.177097	+	0.306741i	−0.0243261	+	0.0421341i	−0.877932	−	0.478785i	$-0.841077\pi$
$53$	−0.177097	+	0.306741i	−0.0243261	+	0.0421341i	0.853606	+	0.520919i	$0.174411\pi$
$54$	−0.400251	−	0.693255i	−0.0544673	−	0.0943401i
$55$	−2.59143			−0.349428
$56$		0			0
$57$	−0.201734			−0.0267203
$58$	2.14846	+	3.72124i	0.282107	+	0.488623i
$59$	1.08192	−	1.87395i	0.140854	−	0.243967i	−0.786964	−	0.616999i	$-0.788348\pi$
$59$	1.08192	−	1.87395i	0.140854	−	0.243967i	0.927819	+	0.373032i	$0.121682\pi$
$60$	0.218508	−	0.378467i	0.0282093	−	0.0488599i
$61$	6.10010	+	10.5657i	0.781037	+	1.35280i	0.931338	+	0.364156i	$0.118642\pi$
$61$	6.10010	+	10.5657i	0.781037	+	1.35280i	−0.150301	+	0.988640i	$0.548024\pi$
$62$	5.04967			0.641308
$63$		0			0
$64$	0.559715			0.0699644
$65$	0.679981	+	1.17776i	0.0843413	+	0.146083i
$66$	−0.128008	+	0.221717i	−0.0157567	+	0.0272915i
$67$	−5.65670	+	9.79769i	−0.691076	+	1.19698i	0.280410	+	0.959880i	$0.409530\pi$
$67$	−5.65670	+	9.79769i	−0.691076	+	1.19698i	−0.971486	+	0.237098i	$0.923804\pi$
$68$	−2.79854	−	4.84722i	−0.339373	−	0.587812i
$69$	0.347272			0.0418067
$70$		0			0
$71$	−9.05268			−1.07436			−0.537178	−	0.843469i	$-0.680510\pi$
$71$	−9.05268			−1.07436			−0.537178	+	0.843469i	$0.680510\pi$
$72$	3.46420	+	6.00017i	0.408260	+	0.707127i
$73$	−3.56809	+	6.18012i	−0.417614	+	0.723328i	−0.995699	−	0.0926481i	$-0.970467\pi$
$73$	−3.56809	+	6.18012i	−0.417614	+	0.723328i	0.578085	+	0.815977i	$0.303800\pi$
$74$	−0.662763	+	1.14794i	−0.0770447	+	0.133445i
$75$	0.322538	+	0.558652i	0.0372435	+	0.0645076i
$76$	1.54628			0.177371
$77$		0			0
$78$	0.134356			0.0152128
$79$	2.69815	+	4.67333i	0.303565	+	0.525790i	0.976941	−	0.213510i	$-0.0684897\pi$
$79$	2.69815	+	4.67333i	0.303565	+	0.525790i	−0.673376	+	0.739300i	$0.735156\pi$
$80$	−1.08928	+	1.88670i	−0.121786	+	0.210939i
$81$	−4.31222	+	7.46899i	−0.479136	+	0.829887i
$82$	−3.24411	−	5.61896i	−0.358251	−	0.620510i
$83$	2.03494			0.223364			0.111682	−	0.993744i	$-0.464376\pi$
$83$	2.03494			0.223364			0.111682	+	0.993744i	$0.464376\pi$
$84$		0			0
$85$	−4.85008			−0.526065
$86$	−1.03887	−	1.79937i	−0.112024	−	0.194031i
$87$	−0.670398	+	1.16116i	−0.0718743	+	0.124490i
$88$	2.23154	−	3.86515i	0.237883	−	0.412026i
$89$	−3.44932	−	5.97440i	−0.365627	−	0.633285i	0.623249	−	0.782023i	$-0.285812\pi$
$89$	−3.44932	−	5.97440i	−0.365627	−	0.633285i	−0.988877	+	0.148738i	$0.952479\pi$
$90$	2.63974			0.278253
$91$		0			0
$92$	−2.66182			−0.277514
$93$	0.787840	+	1.36458i	0.0816952	+	0.141500i
$94$	−2.54736	+	4.41216i	−0.262740	+	0.455079i
$95$	0.669955	−	1.16040i	0.0687359	−	0.119054i
$96$	0.587187	+	1.01704i	0.0599296	+	0.103801i
$97$	14.6223			1.48467			0.742334	−	0.670030i	$-0.233719\pi$
$97$	14.6223			1.48467			0.742334	+	0.670030i	$0.233719\pi$
$98$		0			0
$99$	5.63665			0.566505
$100$	−2.47223	−	4.28204i	−0.247223	−	0.428204i
$101$	1.40684	−	2.43672i	0.139986	−	0.242463i	−0.787505	−	0.616308i	$-0.788628\pi$
$101$	1.40684	−	2.43672i	0.139986	−	0.242463i	0.927491	+	0.373845i	$0.121961\pi$
$102$	−0.239579	+	0.414963i	−0.0237218	+	0.0410874i
$103$	3.02494	+	5.23935i	0.298056	+	0.516248i	0.975691	−	0.219150i	$-0.0703285\pi$
$103$	3.02494	+	5.23935i	0.298056	+	0.516248i	−0.677635	+	0.735398i	$0.736995\pi$
$104$	−2.34220			−0.229671
$105$		0			0
$106$	−0.232416			−0.0225743
$107$	−8.66018	−	14.9999i	−0.837211	−	1.45009i	−0.892218	−	0.451606i	$-0.850851\pi$
$107$	−8.66018	−	14.9999i	−0.837211	−	1.45009i	0.0550067	−	0.998486i	$-0.482482\pi$
$108$	−0.957298	+	1.65809i	−0.0921160	+	0.159550i
$109$	−5.28811	+	9.15928i	−0.506509	+	0.877300i	0.493462	+	0.869767i	$0.335731\pi$
$109$	−5.28811	+	9.15928i	−0.506509	+	0.877300i	−0.999972	+	0.00753267i	$0.997602\pi$
$110$	−0.850226	−	1.47263i	−0.0810659	−	0.140410i
$111$	−0.413613			−0.0392584
$112$		0			0
$113$	−2.34665			−0.220755			−0.110377	−	0.993890i	$-0.535206\pi$
$113$	−2.34665			−0.220755			−0.110377	+	0.993890i	$0.535206\pi$
$114$	−0.0661874	−	0.114640i	−0.00619901	−	0.0107370i
$115$	−1.15328	+	1.99755i	−0.107544	+	0.186272i
$116$	5.13857	−	8.90026i	0.477104	−	0.826368i
$117$	−1.47904	−	2.56177i	−0.136737	−	0.236836i
$118$	1.41988			0.130711
$119$		0			0
$120$	0.652201			0.0595375
$121$	3.68451	+	6.38176i	0.334956	+	0.580160i
$122$	−4.00278	+	6.93303i	−0.362395	+	0.627687i
$123$	1.01228	−	1.75332i	0.0912741	−	0.158091i
$124$	−6.03875	−	10.4594i	−0.542296	−	0.939284i
$125$	−11.0844			−0.991417
$126$		0			0
$127$	−18.1639			−1.61179			−0.805894	−	0.592060i	$-0.798315\pi$
$127$	−18.1639			−1.61179			−0.805894	+	0.592060i	$0.798315\pi$
$128$	−5.55192	−	9.61621i	−0.490725	−	0.849961i
$129$	0.324164	−	0.561469i	0.0285411	−	0.0494346i
$130$	−0.446193	+	0.772828i	−0.0391337	+	0.0677815i
$131$	5.05068	+	8.74804i	0.441280	+	0.764320i	0.997785	−	0.0665248i	$-0.0211911\pi$
$131$	5.05068	+	8.74804i	0.441280	+	0.764320i	−0.556505	+	0.830845i	$0.687858\pi$
$132$	0.612326			0.0532961
$133$		0			0
$134$	−7.42367			−0.641308
$135$	0.829534	+	1.43679i	0.0713949	+	0.123660i
$136$	4.17653	−	7.23396i	0.358134	−	0.620307i
$137$	−3.27800	+	5.67767i	−0.280059	+	0.485076i	−0.971399	−	0.237453i	$-0.923687\pi$
$137$	−3.27800	+	5.67767i	−0.280059	+	0.485076i	0.691340	+	0.722529i	$0.257021\pi$
$138$	0.113937	+	0.197345i	0.00969899	+	0.0167991i
$139$	13.8243			1.17256			0.586281	−	0.810108i	$-0.300591\pi$
$139$	13.8243			1.17256			0.586281	+	0.810108i	$0.300591\pi$
$140$		0			0
$141$	−1.58974			−0.133880
$142$	−2.97011	−	5.14439i	−0.249246	−	0.431707i
$143$	−0.952756	+	1.65022i	−0.0796735	+	0.137999i
$144$	2.36932	−	4.10378i	0.197443	−	0.341982i
$145$	−4.45276	−	7.71240i	−0.369781	−	0.640480i
$146$	−4.68265			−0.387539
$147$		0			0
$148$	3.17032			0.260598
$149$	−4.04695	−	7.00952i	−0.331539	−	0.574242i	0.651275	−	0.758842i	$-0.274234\pi$
$149$	−4.04695	−	7.00952i	−0.331539	−	0.574242i	−0.982814	+	0.184600i	$0.940901\pi$
$150$	−0.211644	+	0.366578i	−0.0172807	+	0.0299310i
$151$	−6.01827	+	10.4239i	−0.489760	+	0.848289i	−0.999931	−	0.0117843i	$-0.996249\pi$
$151$	−6.01827	+	10.4239i	−0.489760	+	0.848289i	0.510171	+	0.860073i	$0.329582\pi$
$152$	1.15383	+	1.99849i	0.0935880	+	0.162099i
$153$	10.5495			0.852876
$154$		0			0
$155$	−10.4656			−0.840617
$156$	−0.160672	−	0.278293i	−0.0128641	−	0.0222812i
$157$	−9.19677	+	15.9293i	−0.733982	+	1.27129i	0.221186	+	0.975232i	$0.429007\pi$
$157$	−9.19677	+	15.9293i	−0.733982	+	1.27129i	−0.955168	+	0.296063i	$0.904326\pi$
$158$	−1.77048	+	3.06656i	−0.140852	+	0.243963i
$159$	−0.0362612	−	0.0628062i	−0.00287570	−	0.00498085i
$160$	−7.80014			−0.616655
$161$		0			0
$162$	−5.65922			−0.444630
$163$	−1.25643	−	2.17620i	−0.0984114	−	0.170454i	0.812616	−	0.582800i	$-0.198043\pi$
$163$	−1.25643	−	2.17620i	−0.0984114	−	0.170454i	−0.911027	+	0.412346i	$0.864709\pi$
$164$	−7.75906	+	13.4391i	−0.605881	+	1.04942i
$165$	0.265302	−	0.459516i	0.0206537	−	0.0357732i
$166$	0.667649	+	1.15640i	0.0518196	+	0.0897542i
$167$	−17.9095			−1.38588			−0.692941	−	0.720995i	$-0.743685\pi$
$167$	−17.9095			−1.38588			−0.692941	+	0.720995i	$0.743685\pi$
$168$		0			0
$169$	1.00000			0.0769231
$170$	−1.59127	−	2.75616i	−0.122045	−	0.211388i
$171$	−1.45723	+	2.52399i	−0.111437	+	0.193015i
$172$	−2.48470	+	4.30363i	−0.189457	+	0.328148i
$173$	3.25991	+	5.64632i	0.247846	+	0.429282i	0.962928	−	0.269759i	$-0.0869439\pi$
$173$	3.25991	+	5.64632i	0.247846	+	0.429282i	−0.715082	+	0.699041i	$0.753611\pi$
$174$	−0.879809			−0.0666982
$175$		0			0
$176$	−3.05250			−0.230091
$177$	0.221527	+	0.383697i	0.0166510	+	0.0288404i
$178$	2.26339	−	3.92030i	0.169648	−	0.293839i
$179$	13.3007	−	23.0375i	0.994141	−	1.72190i	0.403461	−	0.914997i	$-0.367807\pi$
$179$	13.3007	−	23.0375i	0.994141	−	1.72190i	0.590680	−	0.806906i	$-0.298859\pi$
$180$	−3.15679	−	5.46773i	−0.235293	−	0.407540i
$181$	24.6402			1.83149			0.915746	−	0.401758i	$-0.131601\pi$
$181$	24.6402			1.83149			0.915746	+	0.401758i	$0.131601\pi$
$182$		0			0
$183$	−2.49803			−0.184660
$184$	−1.98625	−	3.44028i	−0.146428	−	0.253621i
$185$	1.37360	−	2.37914i	0.100989	−	0.174918i
$186$	−0.516968	+	0.895415i	−0.0379059	+	0.0656550i
$187$	−3.39785	−	5.88524i	−0.248475	−	0.430372i
$188$	12.1853			0.888701
$189$		0			0
$190$	0.879227			0.0637858
$191$	−1.51049	−	2.61625i	−0.109295	−	0.189305i	0.806190	−	0.591657i	$-0.201526\pi$
$191$	−1.51049	−	2.61625i	−0.109295	−	0.189305i	−0.915485	+	0.402352i	$0.868193\pi$
$192$	−0.0573018	+	0.0992496i	−0.00413540	+	0.00716273i
$193$	−10.6261	+	18.4050i	−0.764884	+	1.32482i	0.175424	+	0.984493i	$0.443870\pi$
$193$	−10.6261	+	18.4050i	−0.764884	+	1.32482i	−0.940308	+	0.340325i	$0.889463\pi$
$194$	4.79746	+	8.30944i	0.344437	+	0.596583i
$195$	−0.278457			−0.0199407
$196$		0			0
$197$	−2.72191			−0.193928			−0.0969639	−	0.995288i	$-0.530913\pi$
$197$	−2.72191			−0.193928			−0.0969639	+	0.995288i	$0.530913\pi$
$198$	1.84934	+	3.20315i	0.131427	+	0.227638i
$199$	−10.8335	+	18.7642i	−0.767967	+	1.33016i	0.170697	+	0.985324i	$0.445398\pi$
$199$	−10.8335	+	18.7642i	−0.767967	+	1.33016i	−0.938664	+	0.344834i	$0.887935\pi$
$200$	3.68955	−	6.39049i	0.260891	−	0.451876i
$201$	−1.15823	−	2.00611i	−0.0816951	−	0.141500i
$202$	1.84629			0.129905
$203$		0			0
$204$	1.14602			0.0802376
$205$	6.72351	+	11.6455i	0.469591	+	0.813355i
$206$	−1.98492	+	3.43797i	−0.138296	+	0.239535i
$207$	2.50853	−	4.34489i	0.174355	−	0.301991i
$208$	0.800966	+	1.38731i	0.0555370	+	0.0961930i
$209$	1.87741			0.129864
$210$		0			0
$211$	18.3885			1.26592			0.632959	−	0.774186i	$-0.281840\pi$
$211$	18.3885			1.26592			0.632959	+	0.774186i	$0.281840\pi$
$212$	0.277940	+	0.481406i	0.0190890	+	0.0330631i
$213$	0.926784	−	1.60524i	0.0635022	−	0.109989i
$214$	5.68267	−	9.84267i	0.388459	−	0.672831i
$215$	2.15308	+	3.72925i	0.146839	+	0.254333i
$216$	−2.85733			−0.194417
$217$		0			0
$218$	−6.93995			−0.470033
$219$	−0.730579	−	1.26540i	−0.0493680	−	0.0855078i
$220$	−2.03352	+	3.52216i	−0.137100	+	0.237464i
$221$	−1.78317	+	3.08854i	−0.119949	+	0.207757i
$222$	−0.135703	−	0.235044i	−0.00910779	−	0.0157752i
$223$	−22.2216			−1.48807			−0.744035	−	0.668141i	$-0.767090\pi$
$223$	−22.2216			−1.48807			−0.744035	+	0.668141i	$0.767090\pi$
$224$		0			0
$225$	9.31943			0.621295
$226$	−0.769918	−	1.33354i	−0.0512142	−	0.0887056i
$227$	13.3687	−	23.1553i	0.887313	−	1.53687i	0.0442740	−	0.999019i	$-0.485903\pi$
$227$	13.3687	−	23.1553i	0.887313	−	1.53687i	0.843039	−	0.537852i	$-0.180764\pi$
$228$	−0.158303	+	0.274189i	−0.0104839	+	0.0181586i
$229$	−8.35039	−	14.4633i	−0.551809	−	0.955761i	−0.998144	−	0.0608954i	$-0.980604\pi$
$229$	−8.35039	−	14.4633i	−0.551809	−	0.955761i	0.446335	−	0.894866i	$-0.352729\pi$
$230$	−1.51353			−0.0997994
$231$		0			0
$232$	15.3375			1.00696
$233$	6.93878	+	12.0183i	0.454575	+	0.787346i	0.998664	−	0.0516812i	$-0.0164580\pi$
$233$	6.93878	+	12.0183i	0.454575	+	0.787346i	−0.544089	+	0.839027i	$0.683125\pi$
$234$	0.970521	−	1.68099i	0.0634449	−	0.109890i
$235$	5.27948	−	9.14433i	0.344396	−	0.596511i
$236$	−1.69800	−	2.94101i	−0.110530	−	0.191444i
$237$	−1.10491			−0.0717715
$238$		0			0
$239$	0.465845			0.0301330			0.0150665	−	0.999886i	$-0.495204\pi$
$239$	0.465845			0.0301330			0.0150665	+	0.999886i	$0.495204\pi$
$240$	−0.223035	−	0.386307i	−0.0143968	−	0.0249360i
$241$	2.84657	−	4.93040i	0.183364	−	0.317595i	−0.759660	−	0.650320i	$-0.774635\pi$
$241$	2.84657	−	4.93040i	0.183364	−	0.317595i	0.943024	+	0.332725i	$0.107968\pi$
$242$	−2.41772	+	4.18761i	−0.155417	+	0.269190i
$243$	−2.71285	−	4.69879i	−0.174029	−	0.301427i
$244$	19.1473			1.22578
$245$		0			0
$246$	1.32848			0.0847010
$247$	−0.492627	−	0.853255i	−0.0313451	−	0.0542913i
$248$	9.01220	−	15.6096i	0.572275	−	0.991209i
$249$	−0.208331	+	0.360840i	−0.0132024	+	0.0228673i
$250$	−3.63669	−	6.29894i	−0.230005	−	0.398380i
$251$	−17.9066			−1.13025			−0.565126	−	0.825005i	$-0.691172\pi$
$251$	−17.9066			−1.13025			−0.565126	+	0.825005i	$0.691172\pi$
$252$		0			0
$253$	−3.23185			−0.203185
$254$	−5.95944	−	10.3221i	−0.373929	−	0.647663i
$255$	0.496535	−	0.860024i	0.0310942	−	0.0538568i
$256$	4.20280	−	7.27946i	0.262675	−	0.454966i
$257$	12.9878	+	22.4955i	0.810156	+	1.40323i	0.912754	+	0.408509i	$0.133951\pi$
$257$	12.9878	+	22.4955i	0.810156	+	1.40323i	−0.102598	+	0.994723i	$0.532715\pi$
$258$	0.425423			0.0264857
$259$		0			0
$260$	2.13436			0.132367
$261$	9.68526	+	16.7754i	0.599503	+	1.03837i
$262$	−3.31418	+	5.74032i	−0.204751	+	0.354638i
$263$	−13.9201	+	24.1103i	−0.858349	+	1.48670i	0.0151543	+	0.999885i	$0.495176\pi$
$263$	−13.9201	+	24.1103i	−0.858349	+	1.48670i	−0.873503	+	0.486819i	$0.838157\pi$
$264$	0.456916	+	0.791402i	0.0281212	+	0.0487074i
$265$	0.481690			0.0295900
$266$		0			0
$267$	1.41252			0.0864448
$268$	8.87775	+	15.3767i	0.542295	+	0.939283i
$269$	2.95243	−	5.11375i	0.180013	−	0.311791i	−0.761872	−	0.647728i	$-0.775719\pi$
$269$	2.95243	−	5.11375i	0.180013	−	0.311791i	0.941885	+	0.335937i	$0.109053\pi$
$270$	−0.544327	+	0.942801i	−0.0331267	+	0.0573771i
$271$	−2.17466	−	3.76662i	−0.132101	−	0.228806i	0.792385	−	0.610021i	$-0.208839\pi$
$271$	−2.17466	−	3.76662i	−0.132101	−	0.228806i	−0.924486	+	0.381215i	$0.875506\pi$
$272$	−5.71303			−0.346403
$273$		0			0
$274$	−4.30195			−0.259890
$275$	−3.00166	−	5.19903i	−0.181007	−	0.313513i
$276$	0.272509	−	0.471999i	0.0164031	−	0.0284110i
$277$	−0.540257	+	0.935752i	−0.0324609	+	0.0562239i	−0.881799	−	0.471625i	$-0.843668\pi$
$277$	−0.540257	+	0.935752i	−0.0324609	+	0.0562239i	0.849339	+	0.527848i	$0.177001\pi$
$278$	4.53564	+	7.85596i	0.272030	+	0.471169i
$279$	22.7639			1.36284
$280$		0			0
$281$	14.4912			0.864473			0.432236	−	0.901760i	$-0.357725\pi$
$281$	14.4912			0.864473			0.432236	+	0.901760i	$0.357725\pi$
$282$	−0.521580	−	0.903403i	−0.0310597	−	0.0537969i
$283$	12.2489	−	21.2158i	0.728123	−	1.26115i	−0.229552	−	0.973296i	$-0.573726\pi$
$283$	12.2489	−	21.2158i	0.728123	−	1.26115i	0.957676	−	0.287850i	$-0.0929404\pi$
$284$	−7.10374	+	12.3040i	−0.421530	+	0.730111i
$285$	0.137175	+	0.237595i	0.00812557	+	0.0140739i
$286$	−1.25037			−0.0739357
$287$		0			0
$288$	16.9662			0.999744
$289$	2.14063	+	3.70768i	0.125919	+	0.218099i
$290$	2.92183	−	5.06075i	0.171576	−	0.297178i
$291$	−1.49698	+	2.59285i	−0.0877546	+	0.151995i
$292$	5.59985	+	9.69922i	0.327706	+	0.567604i
$293$	−1.16105			−0.0678296			−0.0339148	−	0.999425i	$-0.510797\pi$
$293$	−1.16105			−0.0678296			−0.0339148	+	0.999425i	$0.510797\pi$
$294$		0			0
$295$	−2.94275			−0.171334
$296$	2.36568	+	4.09748i	0.137502	+	0.238161i
$297$	−1.16230	+	2.01317i	−0.0674436	+	0.116816i
$298$	2.65554	−	4.59953i	0.153831	−	0.266444i
$299$	0.848026	+	1.46882i	0.0490426	+	0.0849443i
$300$	1.01240			0.0584507
$301$		0			0
$302$	−7.89818			−0.454489
$303$	0.288055	+	0.498926i	0.0165483	+	0.0286626i
$304$	0.789156	−	1.36686i	0.0452612	−	0.0783947i
$305$	8.29590	−	14.3689i	0.475022	−	0.822762i
$306$	3.46120	+	5.99498i	0.197864	+	0.342710i
$307$	−25.3731			−1.44812			−0.724060	−	0.689737i	$-0.757726\pi$
$307$	−25.3731			−1.44812			−0.724060	+	0.689737i	$0.757726\pi$
$308$		0			0
$309$	−1.23873			−0.0704690
$310$	−3.43368	−	5.94730i	−0.195020	−	0.337784i
$311$	12.2323	−	21.1869i	0.693628	−	1.20140i	−0.277012	−	0.960866i	$-0.589344\pi$
$311$	12.2323	−	21.1869i	0.693628	−	1.20140i	0.970641	−	0.240533i	$-0.0773224\pi$
$312$	0.239786	−	0.415322i	0.0135752	−	0.0235130i
$313$	3.30832	+	5.73018i	0.186997	+	0.323889i	0.944248	−	0.329236i	$-0.106791\pi$
$313$	3.30832	+	5.73018i	0.186997	+	0.323889i	−0.757250	+	0.653125i	$0.773458\pi$
$314$	−12.0695			−0.681124
$315$		0			0
$316$	8.46906			0.476422
$317$	−4.09901	−	7.09970i	−0.230224	−	0.398759i	0.727650	−	0.685948i	$-0.240612\pi$
$317$	−4.09901	−	7.09970i	−0.230224	−	0.398759i	−0.957874	+	0.287189i	$0.907279\pi$
$318$	0.0237940	−	0.0412124i	0.00133430	−	0.00231108i
$319$	6.23898	−	10.8062i	0.349316	−	0.605033i
$320$	−0.380596	−	0.659212i	−0.0212760	−	0.0368510i
$321$	3.54640			0.197941
$322$		0			0
$323$	3.51375			0.195510
$324$	6.76770	+	11.7220i	0.375983	+	0.651222i
$325$	−1.57525	+	2.72841i	−0.0873792	+	0.151345i
$326$	0.824451	−	1.42799i	0.0456621	−	0.0790891i
$327$	−1.08276	−	1.87539i	−0.0598767	−	0.103709i
$328$	−23.1592			−1.27875
$329$		0			0
$330$	0.348173			0.0191663
$331$	0.362357	+	0.627621i	0.0199170	+	0.0344972i	0.875812	−	0.482652i	$-0.160326\pi$
$331$	0.362357	+	0.627621i	0.0199170	+	0.0344972i	−0.855895	+	0.517149i	$0.826993\pi$
$332$	1.59684	−	2.76581i	0.0876382	−	0.151794i
$333$	−2.98774	+	5.17491i	−0.163727	+	0.283583i
$334$	−5.87597	−	10.1775i	−0.321519	−	0.556887i
$335$	15.3858			0.840616
$336$		0			0
$337$	−8.58299			−0.467545			−0.233773	−	0.972291i	$-0.575107\pi$
$337$	−8.58299			−0.467545			−0.233773	+	0.972291i	$0.575107\pi$
$338$	0.328092	+	0.568272i	0.0178459	+	0.0309099i
$339$	0.240243	−	0.416112i	0.0130482	−	0.0226001i
$340$	−3.80591	+	6.59203i	−0.206405	+	0.357503i
$341$	−7.33194	−	12.6993i	−0.397047	−	0.687705i
$342$	−1.91242			−0.103412
$343$		0			0
$344$	−7.41630			−0.399860
$345$	−0.236139	−	0.409004i	−0.0127133	−	0.0220200i
$346$	−2.13910	+	3.70503i	−0.114999	+	0.199183i
$347$	12.9625	−	22.4517i	0.695864	−	1.20527i	−0.274024	−	0.961723i	$-0.588355\pi$
$347$	12.9625	−	22.4517i	0.695864	−	1.20527i	0.969888	−	0.243550i	$-0.0783119\pi$
$348$	1.05214	+	1.82236i	0.0564005	+	0.0976886i
$349$	−17.1403			−0.917501			−0.458750	−	0.888565i	$-0.651703\pi$
$349$	−17.1403			−0.917501			−0.458750	+	0.888565i	$0.651703\pi$
$350$		0			0
$351$	1.21994			0.0651154
$352$	−5.46459	−	9.46495i	−0.291264	−	0.504483i
$353$	−9.45506	+	16.3766i	−0.503242	+	0.871641i	0.496751	+	0.867893i	$0.334526\pi$
$353$	−9.45506	+	16.3766i	−0.503242	+	0.871641i	−0.999993	+	0.00374752i	$0.998807\pi$
$354$	−0.145363	+	0.251776i	−0.00772594	+	0.0133817i
$355$	6.15566	+	10.6619i	0.326708	+	0.565875i
$356$	−10.8269			−0.573823
$357$		0			0
$358$	17.4554			0.922547
$359$	−7.05247	−	12.2152i	−0.372215	−	0.644696i	0.617691	−	0.786421i	$-0.288068\pi$
$359$	−7.05247	−	12.2152i	−0.372215	−	0.644696i	−0.989906	+	0.141725i	$0.954735\pi$
$360$	4.71118	−	8.16001i	0.248301	−	0.430070i
$361$	9.01464	−	15.6138i	0.474455	−	0.821779i
$362$	8.08425	+	14.0023i	0.424899	+	0.735946i
$363$	−1.50883			−0.0791931
$364$		0			0
$365$	9.70495			0.507980
$366$	−0.819584	−	1.41956i	−0.0428403	−	0.0742016i
$367$	0.180129	−	0.311993i	0.00940266	−	0.0162859i	−0.861286	−	0.508121i	$-0.830340\pi$
$367$	0.180129	−	0.311993i	0.00940266	−	0.0162859i	0.870688	+	0.491835i	$0.163674\pi$
$368$	−1.35848	+	2.35296i	−0.0708157	+	0.122656i
$369$	−14.6244	−	25.3302i	−0.761317	−	1.31864i
$370$	1.80267			0.0937162
$371$		0			0
$372$	2.47291			0.128214
$373$	12.5840	+	21.7961i	0.651575	+	1.12856i	0.982741	+	0.184989i	$0.0592249\pi$
$373$	12.5840	+	21.7961i	0.651575	+	1.12856i	−0.331165	+	0.943573i	$0.607442\pi$
$374$	2.22961	−	3.86180i	0.115291	−	0.199689i
$375$	1.13478	−	1.96550i	0.0585999	−	0.101498i
$376$	9.09260	+	15.7488i	0.468915	+	0.812185i
$377$	−6.54835			−0.337257
$378$		0			0
$379$	31.8947			1.63832			0.819161	−	0.573564i	$-0.194440\pi$
$379$	31.8947			1.63832			0.819161	+	0.573564i	$0.194440\pi$
$380$	−1.05144	−	1.82115i	−0.0539378	−	0.0934231i
$381$	1.85956	−	3.22086i	0.0952683	−	0.165010i
$382$	0.991161	−	1.71674i	0.0507122	−	0.0878361i
$383$	16.4086	+	28.4205i	0.838440	+	1.45222i	0.891199	+	0.453613i	$0.149865\pi$
$383$	16.4086	+	28.4205i	0.838440	+	1.45222i	−0.0527590	+	0.998607i	$0.516801\pi$
$384$	2.27355			0.116022
$385$		0			0
$386$	−13.9454			−0.709800
$387$	−4.68321	−	8.11155i	−0.238061	−	0.412333i
$388$	11.4743	−	19.8740i	0.582518	−	1.00895i
$389$	12.6543	−	21.9179i	0.641600	−	1.11128i	−0.343476	−	0.939162i	$-0.611604\pi$
$389$	12.6543	−	21.9179i	0.641600	−	1.11128i	0.985076	−	0.172122i	$-0.0550623\pi$
$390$	−0.0913595	−	0.158239i	−0.00462617	−	0.00801275i
$391$	−6.04869			−0.305895
$392$		0			0
$393$	−2.06829			−0.104331
$394$	−0.893035	−	1.54678i	−0.0449905	−	0.0779258i
$395$	3.66938	−	6.35555i	0.184626	−	0.319782i
$396$	4.42314	−	7.66111i	0.222271	−	0.384985i
$397$	−2.64698	−	4.58470i	−0.132848	−	0.230099i	0.791925	−	0.610618i	$-0.209079\pi$
$397$	−2.64698	−	4.58470i	−0.132848	−	0.230099i	−0.924773	+	0.380518i	$0.875746\pi$
$398$	−14.2175			−0.712661
$399$		0			0
$400$	−5.04689			−0.252345
$401$	12.3168	+	21.3333i	0.615070	+	1.06533i	0.990372	+	0.138430i	$0.0442055\pi$
$401$	12.3168	+	21.3333i	0.615070	+	1.06533i	−0.375303	+	0.926902i	$0.622461\pi$
$402$	0.760011	−	1.31638i	0.0379059	−	0.0656549i
$403$	−3.84775	+	6.66450i	−0.191670	+	0.331982i
$404$	−2.20793	−	3.82424i	−0.109849	−	0.190263i
$405$	11.7289			0.582815
$406$		0			0
$407$	3.84924			0.190800
$408$	0.855158	+	1.48118i	0.0423366	+	0.0733292i
$409$	5.11113	−	8.85273i	0.252729	−	0.437739i	−0.711547	−	0.702638i	$-0.752005\pi$
$409$	5.11113	−	8.85273i	0.252729	−	0.437739i	0.964276	+	0.264899i	$0.0853386\pi$
$410$	−4.41186	+	7.64157i	−0.217886	+	0.377390i
$411$	−0.671182	−	1.16252i	−0.0331070	−	0.0573430i
$412$	9.49481			0.467776
$413$		0			0
$414$	3.29211			0.161798
$415$	−1.38372	−	2.39668i	−0.0679243	−	0.117648i
$416$	−2.86778	+	4.96714i	−0.140604	+	0.243534i
$417$	−1.41529	+	2.45135i	−0.0693069	+	0.120043i
$418$	0.615965	+	1.06688i	0.0301278	+	0.0521829i
$419$	−30.6503			−1.49736			−0.748682	−	0.662929i	$-0.769313\pi$
$419$	−30.6503			−1.49736			−0.748682	+	0.662929i	$0.769313\pi$
$420$		0			0
$421$	25.9764			1.26601			0.633007	−	0.774146i	$-0.281820\pi$
$421$	25.9764			1.26601			0.633007	+	0.774146i	$0.281820\pi$
$422$	6.03312	+	10.4497i	0.293688	+	0.508682i
$423$	−11.4835	+	19.8900i	−0.558346	+	0.967084i
$424$	−0.414796	+	0.718447i	−0.0201443	+	0.0348909i
$425$	−5.61787	−	9.73044i	−0.272507	−	0.471996i
$426$	1.21628			0.0589290
$427$		0			0
$428$	−27.1830			−1.31394
$429$	−0.195080	−	0.337889i	−0.00941855	−	0.0163134i
$430$	−1.41282	+	2.44707i	−0.0681322	+	0.118008i
$431$	−7.44088	+	12.8880i	−0.358415	+	0.620792i	−0.987696	−	0.156385i	$-0.950016\pi$
$431$	−7.44088	+	12.8880i	−0.358415	+	0.620792i	0.629282	+	0.777177i	$0.283349\pi$
$432$	0.977128	+	1.69243i	0.0470121	+	0.0814273i
$433$	40.0871			1.92647			0.963233	−	0.268669i	$-0.0865837\pi$
$433$	40.0871			1.92647			0.963233	+	0.268669i	$0.0865837\pi$
$434$		0			0
$435$	1.82343			0.0874269
$436$	8.29928	+	14.3748i	0.397464	+	0.688427i
$437$	0.835522	−	1.44717i	0.0399684	−	0.0692273i
$438$	0.479394	−	0.830335i	0.0229063	−	0.0396750i
$439$	−1.50121	−	2.60018i	−0.0716491	−	0.124100i	0.827975	−	0.560765i	$-0.189493\pi$
$439$	−1.50121	−	2.60018i	−0.0716491	−	0.124100i	−0.899624	+	0.436665i	$0.856159\pi$
$440$	−6.06963			−0.289358
$441$		0			0
$442$	−2.34017			−0.111311
$443$	−0.717828	−	1.24332i	−0.0341051	−	0.0590717i	0.848469	−	0.529245i	$-0.177525\pi$
$443$	−0.717828	−	1.24332i	−0.0341051	−	0.0590717i	−0.882574	+	0.470173i	$0.844191\pi$
$444$	−0.324567	+	0.562166i	−0.0154032	+	0.0266792i
$445$	−4.69094	+	8.12495i	−0.222372	+	0.385160i
$446$	−7.29073	−	12.6279i	−0.345226	−	0.597949i
$447$	1.65725			0.0783853
$448$		0			0
$449$	19.6313			0.926460			0.463230	−	0.886238i	$-0.346690\pi$
$449$	19.6313			0.926460			0.463230	+	0.886238i	$0.346690\pi$
$450$	3.05763	+	5.29597i	0.144138	+	0.249654i
$451$	−9.42066	+	16.3171i	−0.443601	+	0.768340i
$452$	−1.84145	+	3.18948i	−0.0866143	+	0.150020i
$453$	−1.23226	−	2.13434i	−0.0578967	−	0.100280i
$454$	17.5447			0.823413
$455$		0			0
$456$	−0.472501			−0.0221269
$457$	−5.32103	−	9.21630i	−0.248907	−	0.431120i	0.714316	−	0.699824i	$-0.246738\pi$
$457$	−5.32103	−	9.21630i	−0.248907	−	0.431120i	−0.963223	+	0.268703i	$0.913405\pi$
$458$	5.47939	−	9.49058i	0.256035	−	0.443466i
$459$	−2.17535	+	3.76782i	−0.101537	+	0.175867i
$460$	1.80999	+	3.13499i	0.0843912	+	0.146170i
$461$	38.5930			1.79745			0.898727	−	0.438509i	$-0.144493\pi$
$461$	38.5930			1.79745			0.898727	+	0.438509i	$0.144493\pi$
$462$		0			0
$463$	−27.9993			−1.30124			−0.650618	−	0.759405i	$-0.725490\pi$
$463$	−27.9993			−1.30124			−0.650618	+	0.759405i	$0.725490\pi$
$464$	−5.24501	−	9.08462i	−0.243493	−	0.421743i
$465$	1.07143	−	1.85578i	0.0496865	−	0.0860596i
$466$	−4.55312	+	7.88623i	−0.210919	+	0.365322i
$467$	−12.9099	−	22.3607i	−0.597401	−	1.03473i	−0.993203	−	0.116393i	$-0.962867\pi$
$467$	−12.9099	−	22.3607i	−0.597401	−	1.03473i	0.395802	−	0.918336i	$-0.370467\pi$
$468$	−4.64247			−0.214598
$469$		0			0
$470$	6.92862			0.319594
$471$	−1.88307	−	3.26157i	−0.0867673	−	0.150285i
$472$	2.53408	−	4.38915i	0.116640	−	0.202027i
$473$	−3.01679	+	5.22524i	−0.138712	+	0.240257i
$474$	−0.362512	−	0.627889i	−0.0166507	−	0.0288399i
$475$	3.10405			0.142423
$476$		0			0
$477$	−1.04773			−0.0479723
$478$	0.152840	+	0.264726i	0.00699073	+	0.0121083i
$479$	−19.7035	+	34.1275i	−0.900277	+	1.55933i	−0.0731431	+	0.997321i	$0.523303\pi$
$479$	−19.7035	+	34.1275i	−0.900277	+	1.55933i	−0.827134	+	0.562005i	$0.810030\pi$
$480$	0.798553	−	1.38313i	0.0364488	−	0.0631311i
$481$	−1.01003	−	1.74942i	−0.0460533	−	0.0797666i
$482$	3.73575			0.170159
$483$		0			0
$484$	11.5651			0.525687
$485$	−9.94288	−	17.2216i	−0.451483	−	0.781991i
$486$	1.78013	−	3.08327i	0.0807481	−	0.139860i
$487$	17.0480	−	29.5280i	0.772517	−	1.33804i	−0.163662	−	0.986516i	$-0.552331\pi$
$487$	17.0480	−	29.5280i	0.772517	−	1.33804i	0.936179	−	0.351523i	$-0.114336\pi$
$488$	14.2876	+	24.7469i	0.646771	+	1.12024i
$489$	0.514517			0.0232673
$490$		0			0
$491$	−9.70414			−0.437942			−0.218971	−	0.975731i	$-0.570270\pi$
$491$	−9.70414			−0.437942			−0.218971	+	0.975731i	$0.570270\pi$
$492$	−1.58869	−	2.75170i	−0.0716239	−	0.124056i
$493$	11.6768	−	20.2248i	0.525897	−	0.910880i
$494$	0.323254	−	0.559893i	0.0145439	−	0.0251908i
$495$	−3.83282	−	6.63863i	−0.172272	−	0.298384i
$496$	−12.3277			−0.553529
$497$		0			0
$498$	−0.273407			−0.0122516
$499$	−9.02313	−	15.6285i	−0.403931	−	0.699629i	0.590265	−	0.807209i	$-0.299023\pi$
$499$	−9.02313	−	15.6285i	−0.403931	−	0.699629i	−0.994196	+	0.107580i	$0.965690\pi$
$500$	−8.69804	+	15.0654i	−0.388988	+	0.673747i
$501$	1.83352	−	3.17575i	0.0819156	−	0.141882i
$502$	−5.87500	−	10.1758i	−0.262214	−	0.454168i
$503$	−16.4922			−0.735352			−0.367676	−	0.929954i	$-0.619846\pi$
$503$	−16.4922			−0.735352			−0.367676	+	0.929954i	$0.619846\pi$
$504$		0			0
$505$	−3.82650			−0.170277
$506$	−1.06034	−	1.83657i	−0.0471380	−	0.0816455i
$507$	−0.102377	+	0.177322i	−0.00454671	+	0.00787513i
$508$	−14.2534	+	24.6877i	−0.632394	+	1.09534i
$509$	−9.59883	−	16.6257i	−0.425460	−	0.736919i	0.571003	−	0.820948i	$-0.306555\pi$
$509$	−9.59883	−	16.6257i	−0.425460	−	0.736919i	−0.996463	+	0.0840290i	$0.973221\pi$
$510$	0.651637			0.0288550
$511$		0			0
$512$	−16.6921			−0.737692
$513$	−0.600974	−	1.04092i	−0.0265336	−	0.0459576i
$514$	−8.52238	+	14.7612i	−0.375906	+	0.651089i
$515$	4.11380	−	7.12531i	0.181276	−	0.313979i
$516$	−0.508750	−	0.881182i	−0.0223965	−	0.0387919i
$517$	14.7947			0.650670
$518$		0			0
$519$	−1.33495			−0.0585979
$520$	1.59265	+	2.75855i	0.0698423	+	0.120970i
$521$	−4.38017	+	7.58668i	−0.191899	+	0.332378i	−0.945879	−	0.324518i	$-0.894798\pi$
$521$	−4.38017	+	7.58668i	−0.191899	+	0.332378i	0.753981	+	0.656897i	$0.228131\pi$
$522$	−6.35531	+	11.0077i	−0.278164	+	0.481795i
$523$	−5.87030	−	10.1677i	−0.256690	−	0.444601i	0.708663	−	0.705547i	$-0.249299\pi$
$523$	−5.87030	−	10.1677i	−0.256690	−	0.444601i	−0.965353	+	0.260946i	$0.915965\pi$
$524$	15.8533			0.692555
$525$		0			0
$526$	−18.2683			−0.796534
$527$	−13.7224	−	23.7678i	−0.597756	−	1.03534i
$528$	0.312505	−	0.541275i	0.0136000	−	0.0235560i
$529$	10.0617	−	17.4274i	0.437465	−	0.757712i
$530$	0.158039	+	0.273731i	0.00686476	+	0.0118901i
$531$	6.40082			0.277772
$532$		0			0
$533$	9.88779			0.428288
$534$	0.463436	+	0.802695i	0.0200548	+	0.0347360i
$535$	−11.7775	+	20.3993i	−0.509186	+	0.881937i
$536$	−13.2491	+	22.9481i	−0.572274	+	0.991208i
$537$	2.72336	+	4.71700i	0.117522	+	0.203554i
$538$	3.87467			0.167049
$539$		0			0
$540$	2.60378			0.112049
$541$	−8.22934	−	14.2536i	−0.353807	−	0.612812i	0.633106	−	0.774065i	$-0.281780\pi$
$541$	−8.22934	−	14.2536i	−0.353807	−	0.612812i	−0.986913	+	0.161253i	$0.948446\pi$
$542$	1.42698	−	2.47160i	0.0612939	−	0.106164i
$543$	−2.52258	+	4.36924i	−0.108254	+	0.187502i
$544$	−10.2275	−	17.7145i	−0.438499	−	0.759502i
$545$	14.3833			0.616112
$546$		0			0
$547$	−8.19375			−0.350339			−0.175170	−	0.984538i	$-0.556047\pi$
$547$	−8.19375			−0.350339			−0.175170	+	0.984538i	$0.556047\pi$
$548$	5.14457	+	8.91066i	0.219765	+	0.380645i
$549$	−18.0445	+	31.2541i	−0.770123	+	1.33389i
$550$	1.96964	−	3.41152i	0.0839858	−	0.145468i
$551$	3.22590	+	5.58742i	0.137428	+	0.238032i
$552$	0.813381			0.0346198
$553$		0			0
$554$	−0.709015			−0.0301232
$555$	0.281249	+	0.487137i	0.0119383	+	0.0206778i
$556$	10.8481	−	18.7894i	0.460061	−	0.796850i
$557$	6.90720	−	11.9636i	0.292667	−	0.506915i	−0.681772	−	0.731565i	$-0.738790\pi$
$557$	6.90720	−	11.9636i	0.292667	−	0.506915i	0.974440	+	0.224650i	$0.0721238\pi$
$558$	7.46865	+	12.9361i	0.316173	+	0.547628i
$559$	3.16639			0.133924
$560$		0			0
$561$	1.39144			0.0587467
$562$	4.75445	+	8.23494i	0.200554	+	0.347370i
$563$	4.87780	−	8.44859i	0.205575	−	0.356066i	−0.744741	−	0.667354i	$-0.767427\pi$
$563$	4.87780	−	8.44859i	0.205575	−	0.356066i	0.950316	+	0.311288i	$0.100760\pi$
$564$	−1.24749	+	2.16071i	−0.0525286	+	0.0909822i
$565$	1.59568	+	2.76380i	0.0671308	+	0.116274i
$566$	16.0751			0.675687
$567$		0			0
$568$	−21.2032			−0.889666
$569$	0.716319	+	1.24070i	0.0300296	+	0.0520129i	0.880650	−	0.473768i	$-0.157106\pi$
$569$	0.716319	+	1.24070i	0.0300296	+	0.0520129i	−0.850620	+	0.525781i	$0.823773\pi$
$570$	−0.0900123	+	0.155906i	−0.00377020	+	0.00653018i
$571$	−8.14359	+	14.1051i	−0.340799	+	0.590281i	−0.984581	−	0.174928i	$-0.944031\pi$
$571$	−8.14359	+	14.1051i	−0.340799	+	0.590281i	0.643783	+	0.765209i	$0.277364\pi$
$572$	1.49528	+	2.58990i	0.0625207	+	0.108289i
$573$	0.618557			0.0258406
$574$		0			0
$575$	−5.34342			−0.222836
$576$	0.827840	+	1.43386i	0.0344934	+	0.0597442i
$577$	−2.40923	+	4.17291i	−0.100297	+	0.173720i	−0.911807	−	0.410619i	$-0.865313\pi$
$577$	−2.40923	+	4.17291i	−0.100297	+	0.173720i	0.811510	+	0.584339i	$0.198646\pi$
$578$	−1.40465	+	2.43292i	−0.0584256	+	0.101196i
$579$	−2.17573	−	3.76848i	−0.0904203	−	0.156613i
$580$	−13.9765			−0.580343
$581$		0			0
$582$	−1.96459			−0.0814349
$583$	0.337460	+	0.584498i	0.0139762	+	0.0242074i
$584$	−8.35718	+	14.4751i	−0.345823	+	0.598982i
$585$	−2.01144	+	3.48391i	−0.0831626	+	0.144042i
$586$	−0.380933	−	0.659795i	−0.0157362	−	0.0272559i
$587$	−36.6215			−1.51153			−0.755765	−	0.654843i	$-0.772735\pi$
$587$	−36.6215			−1.51153			−0.755765	+	0.654843i	$0.772735\pi$
$588$		0			0
$589$	7.58203			0.312412
$590$	−0.965493	−	1.67228i	−0.0397487	−	0.0688468i
$591$	0.278660	−	0.482653i	0.0114625	−	0.0198537i
$592$	1.61799	−	2.80245i	0.0664992	−	0.115180i
$593$	−9.35407	−	16.2017i	−0.384125	−	0.665325i	0.607522	−	0.794303i	$-0.292164\pi$
$593$	−9.35407	−	16.2017i	−0.384125	−	0.665325i	−0.991647	+	0.128978i	$0.958830\pi$
$594$	−1.52537			−0.0625866
$595$		0			0
$596$	−12.7027			−0.520325
$597$	−2.21820	−	3.84203i	−0.0907847	−	0.157244i
$598$	−0.556461	+	0.963819i	−0.0227554	+	0.0394135i
$599$	12.7097	−	22.0139i	0.519305	−	0.899463i	−0.480443	−	0.877026i	$-0.659524\pi$
$599$	12.7097	−	22.0139i	0.519305	−	0.899463i	0.999748	−	0.0224368i	$-0.00714245\pi$
$600$	0.755448	+	1.30847i	0.0308410	+	0.0534182i
$601$	−17.7790			−0.725219			−0.362609	−	0.931941i	$-0.618114\pi$
$601$	−17.7790			−0.725219			−0.362609	+	0.931941i	$0.618114\pi$
$602$		0			0
$603$	−33.4659			−1.36284
$604$	9.44521	+	16.3596i	0.384320	+	0.665662i
$605$	5.01080	−	8.67895i	0.203718	−	0.352850i
$606$	−0.189017	+	0.327388i	−0.00767830	+	0.0132992i
$607$	13.0024	+	22.5208i	0.527750	+	0.914089i	0.999477	+	0.0323446i	$0.0102974\pi$
$607$	13.0024	+	22.5208i	0.527750	+	0.914089i	−0.471727	+	0.881745i	$0.656369\pi$
$608$	5.65098			0.229178
$609$		0			0
$610$	10.8873			0.440813
$611$	−3.88208	−	6.72396i	−0.157052	−	0.272022i
$612$	8.27830	−	14.3384i	0.334631	−	0.579597i
$613$	−13.4115	+	23.2294i	−0.541685	+	0.938226i	0.457123	+	0.889404i	$0.348880\pi$
$613$	−13.4115	+	23.2294i	−0.541685	+	0.938226i	−0.998807	+	0.0488222i	$0.984453\pi$
$614$	−8.32471	−	14.4188i	−0.335958	−	0.581896i
$615$	−2.75332			−0.111025
$616$		0			0
$617$	−18.6491			−0.750784			−0.375392	−	0.926866i	$-0.622492\pi$
$617$	−18.6491			−0.750784			−0.375392	+	0.926866i	$0.622492\pi$
$618$	−0.406418	−	0.703937i	−0.0163485	−	0.0283165i
$619$	6.53427	−	11.3177i	0.262634	−	0.454896i	−0.704307	−	0.709896i	$-0.748742\pi$
$619$	6.53427	−	11.3177i	0.262634	−	0.454896i	0.966941	+	0.255000i	$0.0820753\pi$
$620$	−8.21247	+	14.2244i	−0.329821	+	0.571266i
$621$	1.03454	+	1.79187i	0.0415146	+	0.0719053i
$622$	16.0532			0.643676
$623$		0			0
$624$	−0.328001			−0.0131306
$625$	−0.339088	−	0.587317i	−0.0135635	−	0.0234927i
$626$	−2.17087	+	3.76005i	−0.0867654	+	0.150282i
$627$	−0.192203	+	0.332906i	−0.00767587	+	0.0132950i
$628$	14.4336	+	24.9998i	0.575964	+	0.997599i
$629$	7.20418			0.287250
$630$		0			0
$631$	−49.1745			−1.95761			−0.978804	−	0.204801i	$-0.934345\pi$
$631$	−49.1745			−1.95761			−0.978804	+	0.204801i	$0.934345\pi$
$632$	6.31959	+	10.9459i	0.251380	+	0.435403i
$633$	−1.88255	+	3.26068i	−0.0748248	+	0.129600i
$634$	2.68971	−	4.65871i	0.106822	−	0.185021i
$635$	12.3511	+	21.3928i	0.490140	+	0.848947i
$636$	−0.113818			−0.00451318
$637$		0			0
$638$	8.18784			0.324160
$639$	−13.3893	−	23.1909i	−0.529671	−	0.917417i
$640$	−7.55040	+	13.0777i	−0.298456	+	0.516941i
$641$	−2.18751	+	3.78888i	−0.0864016	+	0.149652i	−0.905988	−	0.423304i	$-0.860870\pi$
$641$	−2.18751	+	3.78888i	−0.0864016	+	0.149652i	0.819586	+	0.572956i	$0.194203\pi$
$642$	1.16355	+	2.01532i	0.0459215	+	0.0795383i
$643$	5.34651			0.210846			0.105423	−	0.994427i	$-0.466380\pi$
$643$	5.34651			0.210846			0.105423	+	0.994427i	$0.466380\pi$
$644$		0			0
$645$	−0.881702			−0.0347170
$646$	1.15283	+	1.99676i	0.0453576	+	0.0785616i
$647$	−14.8673	+	25.7509i	−0.584493	+	1.01237i	0.410445	+	0.911885i	$0.365373\pi$
$647$	−14.8673	+	25.7509i	−0.584493	+	1.01237i	−0.994938	+	0.100487i	$0.967960\pi$
$648$	−10.1001	+	17.4938i	−0.396768	+	0.687223i
$649$	−2.06162	−	3.57083i	−0.0809256	−	0.140167i
$650$	−2.06731			−0.0810865
$651$		0			0
$652$	−3.94375			−0.154449
$653$	1.27131	+	2.20198i	0.0497503	+	0.0861700i	0.889828	−	0.456296i	$-0.150824\pi$
$653$	1.27131	+	2.20198i	0.0497503	+	0.0861700i	−0.840078	+	0.542466i	$0.817491\pi$
$654$	0.710489	−	1.23060i	0.0277823	−	0.0481204i
$655$	6.86874	−	11.8970i	0.268384	−	0.464854i
$656$	7.91979	+	13.7175i	0.309216	+	0.535578i
$657$	−21.1094			−0.823556
$658$		0			0
$659$	1.87019			0.0728523			0.0364261	−	0.999336i	$-0.488403\pi$
$659$	1.87019			0.0728523			0.0364261	+	0.999336i	$0.488403\pi$
$660$	−0.416370	−	0.721174i	−0.0162072	−	0.0280717i
$661$	−6.03815	+	10.4584i	−0.234857	+	0.406784i	−0.959231	−	0.282623i	$-0.908795\pi$
$661$	−6.03815	+	10.4584i	−0.234857	+	0.406784i	0.724374	+	0.689407i	$0.242129\pi$
$662$	−0.237773	+	0.411835i	−0.00924131	+	0.0160064i
$663$	−0.365109	−	0.632388i	−0.0141797	−	0.0245599i
$664$	4.76624			0.184966
$665$		0			0
$666$	−3.92101			−0.151936
$667$	−5.55317	−	9.61838i	−0.215020	−	0.372425i
$668$	−14.0538	+	24.3419i	−0.543758	+	0.941817i
$669$	2.27498	−	3.94037i	0.0879556	−	0.152344i
$670$	5.04796	+	8.74332i	0.195020	+	0.337784i
$671$	23.2476			0.897464
$672$		0			0
$673$	−7.81691			−0.301320			−0.150660	−	0.988586i	$-0.548140\pi$
$673$	−7.81691			−0.301320			−0.150660	+	0.988586i	$0.548140\pi$
$674$	−2.81601	−	4.87747i	−0.108469	−	0.187873i
$675$	−1.92171	+	3.32849i	−0.0739665	+	0.128114i
$676$	0.784711	−	1.35916i	0.0301812	−	0.0522754i
$677$	3.12814	+	5.41809i	0.120224	+	0.208234i	0.919856	−	0.392256i	$-0.128305\pi$
$677$	3.12814	+	5.41809i	0.120224	+	0.208234i	−0.799632	+	0.600491i	$0.794972\pi$
$678$	0.315287			0.0121085
$679$		0			0
$680$	−11.3598			−0.435630
$681$	2.73729	+	4.74113i	0.104893	+	0.181680i
$682$	4.81110	−	8.33307i	0.184227	−	0.319090i
$683$	−11.1828	+	19.3692i	−0.427898	+	0.741140i	−0.996686	−	0.0813435i	$-0.974079\pi$
$683$	−11.1828	+	19.3692i	−0.427898	+	0.741140i	0.568789	+	0.822484i	$0.307412\pi$
$684$	2.28701	+	3.96121i	0.0874459	+	0.151461i
$685$	8.91593			0.340660
$686$		0			0
$687$	3.41954			0.130464
$688$	2.53617	+	4.39277i	0.0966905	+	0.167473i
$689$	0.177097	−	0.306741i	0.00674685	−	0.0116859i
$690$	0.154950	−	0.268382i	0.00589886	−	0.0102171i
$691$	−1.90385	−	3.29757i	−0.0724260	−	0.125445i	0.827538	−	0.561410i	$-0.189741\pi$
$691$	−1.90385	−	3.29757i	−0.0724260	−	0.125445i	−0.899964	+	0.435964i	$0.856407\pi$
$692$	10.2323			0.388975
$693$		0			0
$694$	17.0116			0.645751
$695$	−9.40027	−	16.2817i	−0.356572	−	0.617602i
$696$	−1.57021	+	2.71968i	−0.0595185	+	0.103089i
$697$	−17.6316	+	30.5388i	−0.667844	+	1.15674i
$698$	−5.62360	−	9.74037i	−0.212857	−	0.368678i
$699$	−2.84148			−0.107475
$700$		0			0
$701$	−8.14218			−0.307526			−0.153763	−	0.988108i	$-0.549139\pi$
$701$	−8.14218			−0.307526			−0.153763	+	0.988108i	$0.549139\pi$
$702$	0.400251	+	0.693255i	0.0151065	+	0.0261652i
$703$	−0.995133	+	1.72362i	−0.0375322	+	0.0650076i
$704$	0.533272	−	0.923655i	0.0200985	−	0.0348116i
$705$	1.08099	+	1.87233i	0.0407125	+	0.0705161i
$706$	−12.4085			−0.467001
$707$		0			0
$708$	0.695340			0.0261325
$709$	12.0159	+	20.8122i	0.451268	+	0.781619i	0.998465	−	0.0553845i	$-0.0176385\pi$
$709$	12.0159	+	20.8122i	0.451268	+	0.781619i	−0.547197	+	0.837004i	$0.684305\pi$
$710$	−4.03924	+	6.99617i	−0.151590	+	0.262562i
$711$	−7.98132	+	13.8241i	−0.299323	+	0.518442i
$712$	−8.07899	−	13.9932i	−0.302773	−	0.524418i
$713$	−13.0520			−0.488800
$714$		0			0
$715$	2.59143			0.0969138
$716$	−20.8744	−	36.1556i	−0.780114	−	1.35120i
$717$	−0.0476916	+	0.0826043i	−0.00178108	+	0.00308492i
$718$	4.62772	−	8.01544i	0.172705	−	0.299134i
$719$	−16.3480	−	28.3156i	−0.609678	−	1.05599i	−0.991293	−	0.131672i	$-0.957965\pi$
$719$	−16.3480	−	28.3156i	−0.609678	−	1.05599i	0.381615	−	0.924321i	$-0.375368\pi$
$720$	−6.44437			−0.240168
$721$		0			0
$722$	11.8305			0.440286
$723$	0.582845	+	1.00952i	0.0216762	+	0.0375443i
$724$	19.3354	−	33.4900i	0.718596	−	1.24465i
$725$	10.3153	−	17.8666i	0.383101	−	0.663550i
$726$	−0.495036	−	0.857427i	−0.0183725	−	0.0318221i
$727$	15.7712			0.584921			0.292460	−	0.956278i	$-0.405526\pi$
$727$	15.7712			0.584921			0.292460	+	0.956278i	$0.405526\pi$
$728$		0			0
$729$	−24.7624			−0.917126
$730$	3.18412	+	5.51505i	0.117849	+	0.204121i
$731$	−5.64620	+	9.77950i	−0.208832	+	0.361708i
$732$	−1.96023	+	3.39522i	−0.0724523	+	0.125491i
$733$	11.7547	+	20.3598i	0.434170	+	0.752005i	0.997228	−	0.0744131i	$-0.0237083\pi$
$733$	11.7547	+	20.3598i	0.434170	+	0.752005i	−0.563057	+	0.826418i	$0.690375\pi$
$734$	0.236396			0.00872552
$735$		0			0
$736$	−9.72781			−0.358572
$737$	10.7789	+	18.6696i	0.397046	+	0.687705i
$738$	9.59631	−	16.6213i	0.353245	−	0.611838i
$739$	11.2633	−	19.5087i	0.414329	−	0.717639i	−0.581029	−	0.813883i	$-0.697350\pi$
$739$	11.2633	−	19.5087i	0.414329	−	0.717639i	0.995358	+	0.0962443i	$0.0306830\pi$
$740$	−2.15576	−	3.73388i	−0.0792472	−	0.137260i
$741$	0.201734			0.00741089
$742$		0			0
$743$	−13.9795			−0.512857			−0.256429	−	0.966563i	$-0.582546\pi$
$743$	−13.9795			−0.512857			−0.256429	+	0.966563i	$0.582546\pi$
$744$	1.84528	+	3.19611i	0.0676511	+	0.117175i
$745$	−5.50370	+	9.53268i	−0.201640	+	0.349250i
$746$	−8.25743	+	14.3023i	−0.302326	+	0.523644i
$747$	3.00976	+	5.21306i	0.110121	+	0.190736i
$748$	−10.6653			−0.389963
$749$		0			0
$750$	1.48925			0.0543798
$751$	−1.27296	−	2.20483i	−0.0464509	−	0.0804552i	0.841865	−	0.539688i	$-0.181458\pi$
$751$	−1.27296	−	2.20483i	−0.0464509	−	0.0804552i	−0.888316	+	0.459233i	$0.848124\pi$
$752$	6.21883	−	10.7713i	0.226777	−	0.392790i
$753$	1.83321	−	3.17522i	0.0668060	−	0.115711i
$754$	−2.14846	−	3.72124i	−0.0782424	−	0.135520i
$755$	16.3692			0.595738
$756$		0			0
$757$	19.6921			0.715721			0.357861	−	0.933775i	$-0.383506\pi$
$757$	19.6921			0.715721			0.357861	+	0.933775i	$0.383506\pi$
$758$	10.4644	+	18.1249i	0.380084	+	0.658325i
$759$	0.330866	−	0.573077i	0.0120097	−	0.0208014i
$760$	1.56917	−	2.71788i	0.0569196	−	0.0985877i
$761$	−19.5453	−	33.8534i	−0.708515	−	1.22718i	−0.965408	−	0.260744i	$-0.916032\pi$
$761$	−19.5453	−	33.8534i	−0.708515	−	1.22718i	0.256893	−	0.966440i	$-0.417301\pi$
$762$	2.44043			0.0884075
$763$		0			0
$764$	−4.74120			−0.171531
$765$	−7.17345	−	12.4248i	−0.259357	−	0.449219i
$766$	−10.7671	+	18.6491i	−0.389029	+	0.673819i
$767$	−1.08192	+	1.87395i	−0.0390660	+	0.0676643i
$768$	0.860536	+	1.49049i	0.0310519	+	0.0537835i
$769$	21.7389			0.783926			0.391963	−	0.919981i	$-0.371796\pi$
$769$	21.7389			0.783926			0.391963	+	0.919981i	$0.371796\pi$
$770$		0			0
$771$	−5.31859			−0.191544
$772$	16.6769	+	28.8852i	0.600213	+	1.03960i
$773$	2.06403	−	3.57501i	0.0742381	−	0.128584i	−0.826517	−	0.562912i	$-0.809681\pi$
$773$	2.06403	−	3.57501i	0.0742381	−	0.128584i	0.900755	+	0.434328i	$0.143014\pi$
$774$	3.07304	−	5.32267i	0.110458	−	0.191319i
$775$	−12.1224	−	20.9965i	−0.435448	−	0.754218i
$776$	34.2483

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.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.328092 + 0.568272i) q^{2} +(-0.102377 + 0.177322i) q^{3} +(0.784711 - 1.35916i) q^{4} +(-0.679981 - 1.17776i) q^{5} -0.134356 q^{6} +2.34220 q^{8} +(1.47904 + 2.56177i) q^{9} +O(q^{10})\)	\(q+(0.328092 + 0.568272i) q^{2} +(-0.102377 + 0.177322i) q^{3} +(0.784711 - 1.35916i) q^{4} +(-0.679981 - 1.17776i) q^{5} -0.134356 q^{6} +2.34220 q^{8} +(1.47904 + 2.56177i) q^{9} +(0.446193 - 0.772828i) q^{10} +(0.952756 - 1.65022i) q^{11} +(0.160672 + 0.278293i) q^{12} -1.00000 q^{13} +0.278457 q^{15} +(-0.800966 - 1.38731i) q^{16} +(1.78317 - 3.08854i) q^{17} +(-0.970521 + 1.68099i) q^{18} +(0.492627 + 0.853255i) q^{19} -2.13436 q^{20} +1.25037 q^{22} +(-0.848026 - 1.46882i) q^{23} +(-0.239786 + 0.415322i) q^{24} +(1.57525 - 2.72841i) q^{25} +(-0.328092 - 0.568272i) q^{26} -1.21994 q^{27} +6.54835 q^{29} +(0.0913595 + 0.158239i) q^{30} +(3.84775 - 6.66450i) q^{31} +(2.86778 - 4.96714i) q^{32} +(0.195080 + 0.337889i) q^{33} +2.34017 q^{34} +4.64247 q^{36} +(1.01003 + 1.74942i) q^{37} +(-0.323254 + 0.559893i) q^{38} +(0.102377 - 0.177322i) q^{39} +(-1.59265 - 2.75855i) q^{40} -9.88779 q^{41} -3.16639 q^{43} +(-1.49528 - 2.58990i) q^{44} +(2.01144 - 3.48391i) q^{45} +(0.556461 - 0.963819i) q^{46} +(3.88208 + 6.72396i) q^{47} +0.328001 q^{48} +2.06731 q^{50} +(0.365109 + 0.632388i) q^{51} +(-0.784711 + 1.35916i) q^{52} +(-0.177097 + 0.306741i) q^{53} +(-0.400251 - 0.693255i) q^{54} -2.59143 q^{55} -0.201734 q^{57} +(2.14846 + 3.72124i) q^{58} +(1.08192 - 1.87395i) q^{59} +(0.218508 - 0.378467i) q^{60} +(6.10010 + 10.5657i) q^{61} +5.04967 q^{62} +0.559715 q^{64} +(0.679981 + 1.17776i) q^{65} +(-0.128008 + 0.221717i) q^{66} +(-5.65670 + 9.79769i) q^{67} +(-2.79854 - 4.84722i) q^{68} +0.347272 q^{69} -9.05268 q^{71} +(3.46420 + 6.00017i) q^{72} +(-3.56809 + 6.18012i) q^{73} +(-0.662763 + 1.14794i) q^{74} +(0.322538 + 0.558652i) q^{75} +1.54628 q^{76} +0.134356 q^{78} +(2.69815 + 4.67333i) q^{79} +(-1.08928 + 1.88670i) q^{80} +(-4.31222 + 7.46899i) q^{81} +(-3.24411 - 5.61896i) q^{82} +2.03494 q^{83} -4.85008 q^{85} +(-1.03887 - 1.79937i) q^{86} +(-0.670398 + 1.16116i) q^{87} +(2.23154 - 3.86515i) q^{88} +(-3.44932 - 5.97440i) q^{89} +2.63974 q^{90} -2.66182 q^{92} +(0.787840 + 1.36458i) q^{93} +(-2.54736 + 4.41216i) q^{94} +(0.669955 - 1.16040i) q^{95} +(0.587187 + 1.01704i) q^{96} +14.6223 q^{97} +5.63665 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 8 q^{3} - 4 q^{4} + 6 q^{5} - 8 q^{6} - 6 q^{9}+O(q^{10}) \) 12 * q + 8 * q^3 - 4 * q^4 + 6 * q^5 - 8 * q^6 - 6 * q^9	\( 12 q + 8 q^{3} - 4 q^{4} + 6 q^{5} - 8 q^{6} - 6 q^{9} + 4 q^{10} - 4 q^{11} - 4 q^{12} - 12 q^{13} + 24 q^{15} + 16 q^{17} + 4 q^{18} + 2 q^{19} - 32 q^{20} - 24 q^{22} + 6 q^{23} + 12 q^{24} + 4 q^{25} - 40 q^{27} - 12 q^{29} + 6 q^{31} + 20 q^{32} + 4 q^{33} - 48 q^{36} + 8 q^{38} - 8 q^{39} + 4 q^{40} + 16 q^{41} + 4 q^{43} + 4 q^{44} + 14 q^{45} - 8 q^{46} + 30 q^{47} + 16 q^{48} + 16 q^{50} + 4 q^{51} + 4 q^{52} + 14 q^{53} - 48 q^{54} + 16 q^{55} + 8 q^{57} + 8 q^{58} + 24 q^{59} - 12 q^{60} - 56 q^{62} - 40 q^{64} - 6 q^{65} - 4 q^{66} - 16 q^{67} + 28 q^{68} + 40 q^{69} + 16 q^{71} - 28 q^{72} - 6 q^{73} + 12 q^{74} + 12 q^{75} + 32 q^{76} + 8 q^{78} + 22 q^{79} - 28 q^{80} - 46 q^{81} - 40 q^{82} - 100 q^{83} - 16 q^{85} + 16 q^{86} - 16 q^{87} + 44 q^{88} + 26 q^{89} + 80 q^{90} + 40 q^{92} - 16 q^{93} - 32 q^{94} + 6 q^{95} - 20 q^{96} + 28 q^{97} + 24 q^{99}+O(q^{100}) \) 12 * q + 8 * q^3 - 4 * q^4 + 6 * q^5 - 8 * q^6 - 6 * q^9 + 4 * q^10 - 4 * q^11 - 4 * q^12 - 12 * q^13 + 24 * q^15 + 16 * q^17 + 4 * q^18 + 2 * q^19 - 32 * q^20 - 24 * q^22 + 6 * q^23 + 12 * q^24 + 4 * q^25 - 40 * q^27 - 12 * q^29 + 6 * q^31 + 20 * q^32 + 4 * q^33 - 48 * q^36 + 8 * q^38 - 8 * q^39 + 4 * q^40 + 16 * q^41 + 4 * q^43 + 4 * q^44 + 14 * q^45 - 8 * q^46 + 30 * q^47 + 16 * q^48 + 16 * q^50 + 4 * q^51 + 4 * q^52 + 14 * q^53 - 48 * q^54 + 16 * q^55 + 8 * q^57 + 8 * q^58 + 24 * q^59 - 12 * q^60 - 56 * q^62 - 40 * q^64 - 6 * q^65 - 4 * q^66 - 16 * q^67 + 28 * q^68 + 40 * q^69 + 16 * q^71 - 28 * q^72 - 6 * q^73 + 12 * q^74 + 12 * q^75 + 32 * q^76 + 8 * q^78 + 22 * q^79 - 28 * q^80 - 46 * q^81 - 40 * q^82 - 100 * q^83 - 16 * q^85 + 16 * q^86 - 16 * q^87 + 44 * q^88 + 26 * q^89 + 80 * q^90 + 40 * q^92 - 16 * q^93 - 32 * q^94 + 6 * q^95 - 20 * q^96 + 28 * q^97 + 24 * q^99

Introduction

L-functions

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