LMFDB - Embedded newform 273.2.bh.a.131.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(131,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 5, 0]))

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

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

chi := DirichletCharacter("273.131");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.bh (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$32$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			131.16
Character	$\chi$	$=$	273.131
Dual form			273.2.bh.a.248.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0408006 - 0.0235563i) q^{2} +(0.539158 + 1.64600i) q^{3} +(-0.998890 - 1.73013i) q^{4} +(0.697336 - 1.20782i) q^{5} +(0.0167755 - 0.0798583i) q^{6} +(0.623634 - 2.57120i) q^{7} +0.188345i q^{8} +(-2.41862 + 1.77491i) q^{9} +O(q^{10})$	\(q+(-0.0408006 - 0.0235563i) q^{2} +(0.539158 + 1.64600i) q^{3} +(-0.998890 - 1.73013i) q^{4} +(0.697336 - 1.20782i) q^{5} +(0.0167755 - 0.0798583i) q^{6} +(0.623634 - 2.57120i) q^{7} +0.188345i q^{8} +(-2.41862 + 1.77491i) q^{9} +(-0.0569035 + 0.0328532i) q^{10} +(5.15885 - 2.97846i) q^{11} +(2.30923 - 2.57698i) q^{12} -1.00000i q^{13} +(-0.0860125 + 0.0902162i) q^{14} +(2.36405 + 0.496606i) q^{15} +(-1.99334 + 3.45257i) q^{16} +(0.255100 + 0.441847i) q^{17} +(0.140491 - 0.0154438i) q^{18} +(-3.26922 - 1.88748i) q^{19} -2.78625 q^{20} +(4.56843 - 0.359786i) q^{21} -0.280646 q^{22} +(6.05965 + 3.49854i) q^{23} +(-0.310016 + 0.101548i) q^{24} +(1.52745 + 2.64561i) q^{25} +(-0.0235563 + 0.0408006i) q^{26} +(-4.22551 - 3.02408i) q^{27} +(-5.07145 + 1.48938i) q^{28} +2.11360i q^{29} +(-0.0847564 - 0.0759499i) q^{30} +(1.48020 - 0.854596i) q^{31} +(0.488883 - 0.282257i) q^{32} +(7.68398 + 6.88559i) q^{33} -0.0240368i q^{34} +(-2.67067 - 2.54623i) q^{35} +(5.48675 + 2.41158i) q^{36} +(3.33819 - 5.78191i) q^{37} +(0.0889241 + 0.154021i) q^{38} +(1.64600 - 0.539158i) q^{39} +(0.227488 + 0.131340i) q^{40} -5.70663 q^{41} +(-0.194870 - 0.0929356i) q^{42} -8.94548 q^{43} +(-10.3062 - 5.95031i) q^{44} +(0.457182 + 4.15896i) q^{45} +(-0.164825 - 0.285485i) q^{46} +(-5.67842 + 9.83531i) q^{47} +(-6.75765 - 1.41956i) q^{48} +(-6.22216 - 3.20698i) q^{49} -0.143924i q^{50} +(-0.589739 + 0.658120i) q^{51} +(-1.73013 + 0.998890i) q^{52} +(3.31629 - 1.91466i) q^{53} +(0.101167 + 0.222922i) q^{54} -8.30796i q^{55} +(0.484274 + 0.117459i) q^{56} +(1.34417 - 6.39878i) q^{57} +(0.0497885 - 0.0862362i) q^{58} +(3.17081 + 5.49200i) q^{59} +(-1.50223 - 4.58616i) q^{60} +(-4.85718 - 2.80429i) q^{61} -0.0805244 q^{62} +(3.05531 + 7.32564i) q^{63} +7.94678 q^{64} +(-1.20782 - 0.697336i) q^{65} +(-0.151312 - 0.461942i) q^{66} +(3.53248 + 6.11844i) q^{67} +(0.509634 - 0.882712i) q^{68} +(-2.49148 + 11.8604i) q^{69} +(0.0489854 + 0.166799i) q^{70} +7.65396i q^{71} +(-0.334296 - 0.455535i) q^{72} +(8.58793 - 4.95824i) q^{73} +(-0.272400 + 0.157270i) q^{74} +(-3.53114 + 3.94057i) q^{75} +7.54156i q^{76} +(-4.44100 - 15.1219i) q^{77} +(-0.0798583 - 0.0167755i) q^{78} +(-6.18461 + 10.7121i) q^{79} +(2.78006 + 4.81521i) q^{80} +(2.69941 - 8.58564i) q^{81} +(0.232834 + 0.134427i) q^{82} -0.936995 q^{83} +(-5.18584 - 7.54459i) q^{84} +0.711562 q^{85} +(0.364981 + 0.210722i) q^{86} +(-3.47898 + 1.13957i) q^{87} +(0.560980 + 0.971645i) q^{88} +(-1.42346 + 2.46551i) q^{89} +(0.0793163 - 0.180458i) q^{90} +(-2.57120 - 0.623634i) q^{91} -13.9786i q^{92} +(2.20473 + 1.97565i) q^{93} +(0.463366 - 0.267525i) q^{94} +(-4.55949 + 2.63242i) q^{95} +(0.728180 + 0.652519i) q^{96} +9.56933i q^{97} +(0.178324 + 0.277417i) q^{98} +(-7.19078 + 16.3602i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 32 q^{4} - 4 q^{7} - 4 q^{9}+O(q^{10}) $ 64 * q + 32 * q^4 - 4 * q^7 - 4 * q^9	$ 64 q + 32 q^{4} - 4 q^{7} - 4 q^{9} - 12 q^{10} - 30 q^{12} + 12 q^{15} - 16 q^{16} - 10 q^{18} + 10 q^{21} - 8 q^{22} + 36 q^{24} - 36 q^{25} - 20 q^{28} - 22 q^{30} + 12 q^{31} + 36 q^{36} - 36 q^{40} + 48 q^{42} - 32 q^{43} - 6 q^{45} - 48 q^{46} + 36 q^{49} - 16 q^{51} - 54 q^{54} - 8 q^{57} - 12 q^{58} + 16 q^{60} - 72 q^{61} - 86 q^{63} - 48 q^{64} - 78 q^{66} + 32 q^{67} - 4 q^{70} + 62 q^{72} + 48 q^{73} + 48 q^{75} - 20 q^{78} - 64 q^{79} + 28 q^{81} + 72 q^{82} - 18 q^{84} + 64 q^{85} + 60 q^{87} + 44 q^{88} + 8 q^{91} - 38 q^{93} + 72 q^{94} + 66 q^{96} - 68 q^{99}+O(q^{100}) $ 64 * q + 32 * q^4 - 4 * q^7 - 4 * q^9 - 12 * q^10 - 30 * q^12 + 12 * q^15 - 16 * q^16 - 10 * q^18 + 10 * q^21 - 8 * q^22 + 36 * q^24 - 36 * q^25 - 20 * q^28 - 22 * q^30 + 12 * q^31 + 36 * q^36 - 36 * q^40 + 48 * q^42 - 32 * q^43 - 6 * q^45 - 48 * q^46 + 36 * q^49 - 16 * q^51 - 54 * q^54 - 8 * q^57 - 12 * q^58 + 16 * q^60 - 72 * q^61 - 86 * q^63 - 48 * q^64 - 78 * q^66 + 32 * q^67 - 4 * q^70 + 62 * q^72 + 48 * q^73 + 48 * q^75 - 20 * q^78 - 64 * q^79 + 28 * q^81 + 72 * q^82 - 18 * q^84 + 64 * q^85 + 60 * q^87 + 44 * q^88 + 8 * q^91 - 38 * q^93 + 72 * q^94 + 66 * q^96 - 68 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

$n$	$92$	$106$	$157$
$\chi(n)$	$-1$	$1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−0.0408006	−	0.0235563i	−0.0288504	−	0.0166568i	0.485505	−	0.874234i	$-0.338636\pi$
$2$	−0.0408006	−	0.0235563i	−0.0288504	−	0.0166568i	−0.514356	+	0.857577i	$0.671969\pi$
$3$	0.539158	+	1.64600i	0.311283	+	0.950317i
$3$	0.539158	+	1.64600i	0.311283	+	0.950317i
$4$	−0.998890	−	1.73013i	−0.499445	−	0.865064i
$5$	0.697336	−	1.20782i	0.311858	−	0.540154i	−0.666907	−	0.745141i	$-0.732382\pi$
$5$	0.697336	−	1.20782i	0.311858	−	0.540154i	0.978765	+	0.204987i	$0.0657153\pi$
$6$	0.0167755	−	0.0798583i	0.00684858	−	0.0326020i
$7$	0.623634	−	2.57120i	0.235711	−	0.971823i
$7$	0.623634	−	2.57120i	0.235711	−	0.971823i
$8$			0.188345i			0.0665902i
$9$	−2.41862	+	1.77491i	−0.806206	+	0.591636i
$10$	−0.0569035	+	0.0328532i	−0.0179945	+	0.0103891i
$11$	5.15885	−	2.97846i	1.55545	−	0.898040i	0.557769	−	0.829996i	$-0.311658\pi$
$11$	5.15885	−	2.97846i	1.55545	−	0.898040i	0.997682	−	0.0680438i	$-0.0216758\pi$
$12$	2.30923	−	2.57698i	0.666617	−	0.743911i
$13$		−	1.00000i		−	0.277350i
$13$		−	1.00000i		−	0.277350i
$14$	−0.0860125	+	0.0902162i	−0.0229878	+	0.0241113i
$15$	2.36405	+	0.496606i	0.610394	+	0.128223i
$16$	−1.99334	+	3.45257i	−0.498336	+	0.863143i
$17$	0.255100	+	0.441847i	0.0618709	+	0.107164i	0.895302	−	0.445460i	$-0.146960\pi$
$17$	0.255100	+	0.441847i	0.0618709	+	0.107164i	−0.833431	+	0.552624i	$0.813627\pi$
$18$	0.140491	−	0.0154438i	0.0331141	−	0.00364013i
$19$	−3.26922	−	1.88748i	−0.750010	−	0.433019i	0.0756875	−	0.997132i	$-0.475885\pi$
$19$	−3.26922	−	1.88748i	−0.750010	−	0.433019i	−0.825698	+	0.564113i	$0.809218\pi$
$20$	−2.78625			−0.623024
$21$	4.56843	−	0.359786i	0.996913	−	0.0785117i
$22$	−0.280646			−0.0598338
$23$	6.05965	+	3.49854i	1.26352	+	0.729496i	0.973755	−	0.227600i	$-0.0730878\pi$
$23$	6.05965	+	3.49854i	1.26352	+	0.729496i	0.289770	+	0.957096i	$0.406421\pi$
$24$	−0.310016	+	0.101548i	−0.0632818	+	0.0207284i
$25$	1.52745	+	2.64561i	0.305489	+	0.529122i
$26$	−0.0235563	+	0.0408006i	−0.00461976	+	0.00800166i
$27$	−4.22551	−	3.02408i	−0.813200	−	0.581985i
$28$	−5.07145	+	1.48938i	−0.958414	+	0.281467i
$29$			2.11360i			0.392486i	0.980555	+	0.196243i	$0.0628741\pi$
$29$			2.11360i			0.392486i	−0.980555	+	0.196243i	$0.937126\pi$
$30$	−0.0847564	−	0.0759499i	−0.0154743	−	0.0138665i
$31$	1.48020	−	0.854596i	0.265853	−	0.153490i	−0.361149	−	0.932508i	$-0.617615\pi$
$31$	1.48020	−	0.854596i	0.265853	−	0.153490i	0.627001	+	0.779018i	$0.284282\pi$
$32$	0.488883	−	0.282257i	0.0864232	−	0.0498964i
$33$	7.68398	+	6.88559i	1.33761	+	1.19863i
$34$		−	0.0240368i		−	0.00412228i
$35$	−2.67067	−	2.54623i	−0.451426	−	0.430391i
$36$	5.48675	+	2.41158i	0.914458	+	0.401930i
$37$	3.33819	−	5.78191i	0.548795	−	0.950540i	−0.449563	−	0.893249i	$-0.648420\pi$
$37$	3.33819	−	5.78191i	0.548795	−	0.950540i	0.998358	−	0.0572914i	$-0.0182464\pi$
$38$	0.0889241	+	0.154021i	0.0144254	+	0.0249855i
$39$	1.64600	−	0.539158i	0.263571	−	0.0863344i
$40$	0.227488	+	0.131340i	0.0359690	+	0.0207667i
$41$	−5.70663			−0.891226			−0.445613	−	0.895226i	$-0.647014\pi$
$41$	−5.70663			−0.891226			−0.445613	+	0.895226i	$0.647014\pi$
$42$	−0.194870	−	0.0929356i	−0.0300691	−	0.0143403i
$43$	−8.94548			−1.36417			−0.682087	−	0.731271i	$-0.738927\pi$
$43$	−8.94548			−1.36417			−0.682087	+	0.731271i	$0.738927\pi$
$44$	−10.3062	−	5.95031i	−1.55372	−	0.897044i
$45$	0.457182	+	4.15896i	0.0681526	+	0.619982i
$46$	−0.164825	−	0.285485i	−0.0243021	−	0.0420925i
$47$	−5.67842	+	9.83531i	−0.828283	+	1.43463i	0.0711020	+	0.997469i	$0.477348\pi$
$47$	−5.67842	+	9.83531i	−0.828283	+	1.43463i	−0.899385	+	0.437158i	$0.855985\pi$
$48$	−6.75765	−	1.41956i	−0.975383	−	0.204895i
$49$	−6.22216	−	3.20698i	−0.888880	−	0.458139i
$50$		−	0.143924i		−	0.0203539i
$51$	−0.589739	+	0.658120i	−0.0825800	+	0.0921552i
$52$	−1.73013	+	0.998890i	−0.239926	+	0.138521i
$53$	3.31629	−	1.91466i	0.455528	−	0.262999i	−0.254634	−	0.967037i	$-0.581955\pi$
$53$	3.31629	−	1.91466i	0.455528	−	0.262999i	0.710162	+	0.704038i	$0.248622\pi$
$54$	0.101167	+	0.222922i	0.0137671	+	0.0303358i
$55$		−	8.30796i		−	1.12024i
$56$	0.484274	+	0.117459i	0.0647139	+	0.0156961i
$57$	1.34417	−	6.39878i	0.178039	−	0.847539i
$58$	0.0497885	−	0.0862362i	0.00653755	−	0.0113234i
$59$	3.17081	+	5.49200i	0.412804	+	0.714998i	0.995195	−	0.0979111i	$-0.0312161\pi$
$59$	3.17081	+	5.49200i	0.412804	+	0.714998i	−0.582391	+	0.812909i	$0.697883\pi$
$60$	−1.50223	−	4.58616i	−0.193937	−	0.592070i
$61$	−4.85718	−	2.80429i	−0.621898	−	0.359053i	0.155709	−	0.987803i	$-0.450234\pi$
$61$	−4.85718	−	2.80429i	−0.621898	−	0.359053i	−0.777608	+	0.628750i	$0.783567\pi$
$62$	−0.0805244			−0.0102266
$63$	3.05531	+	7.32564i	0.384933	+	0.922944i
$64$	7.94678			0.993347
$65$	−1.20782	−	0.697336i	−0.149812	−	0.0864939i
$66$	−0.151312	−	0.461942i	−0.0186253	−	0.0568611i
$67$	3.53248	+	6.11844i	0.431561	+	0.747486i	0.997008	−	0.0772989i	$-0.0246296\pi$
$67$	3.53248	+	6.11844i	0.431561	+	0.747486i	−0.565447	+	0.824785i	$0.691296\pi$
$68$	0.509634	−	0.882712i	0.0618022	−	0.107045i
$69$	−2.49148	+	11.8604i	−0.299939	+	1.42783i
$70$	0.0489854	+	0.166799i	0.00585488	+	0.0199363i
$71$			7.65396i			0.908358i	0.890910	+	0.454179i	$0.150067\pi$
$71$			7.65396i			0.908358i	−0.890910	+	0.454179i	$0.849933\pi$
$72$	−0.334296	−	0.455535i	−0.0393971	−	0.0536854i
$73$	8.58793	−	4.95824i	1.00514	−	0.580318i	0.0953756	−	0.995441i	$-0.469595\pi$
$73$	8.58793	−	4.95824i	1.00514	−	0.580318i	0.909765	+	0.415123i	$0.136261\pi$
$74$	−0.272400	+	0.157270i	−0.0316659	+	0.0182823i
$75$	−3.53114	+	3.94057i	−0.407741	+	0.455018i
$76$			7.54156i			0.865076i
$77$	−4.44100	−	15.1219i	−0.506099	−	1.72330i
$78$	−0.0798583	−	0.0167755i	−0.00904217	−	0.00189946i
$79$	−6.18461	+	10.7121i	−0.695823	+	1.20520i	0.274079	+	0.961707i	$0.411627\pi$
$79$	−6.18461	+	10.7121i	−0.695823	+	1.20520i	−0.969902	+	0.243494i	$0.921706\pi$
$80$	2.78006	+	4.81521i	0.310820	+	0.538356i
$81$	2.69941	−	8.58564i	0.299935	−	0.953960i
$82$	0.232834	+	0.134427i	0.0257122	+	0.0148450i
$83$	−0.936995			−0.102849			−0.0514243	−	0.998677i	$-0.516376\pi$
$83$	−0.936995			−0.102849			−0.0514243	+	0.998677i	$0.516376\pi$
$84$	−5.18584	−	7.54459i	−0.565821	−	0.823182i
$85$	0.711562			0.0771798
$86$	0.364981	+	0.210722i	0.0393569	+	0.0227227i
$87$	−3.47898	+	1.13957i	−0.372986	+	0.122174i
$88$	0.560980	+	0.971645i	0.0598006	+	0.103578i
$89$	−1.42346	+	2.46551i	−0.150887	+	0.261343i	−0.931554	−	0.363604i	$-0.881546\pi$
$89$	−1.42346	+	2.46551i	−0.150887	+	0.261343i	0.780667	+	0.624947i	$0.214879\pi$
$90$	0.0793163	−	0.180458i	0.00836067	−	0.0190219i
$91$	−2.57120	−	0.623634i	−0.269535	−	0.0653746i
$92$		−	13.9786i		−	1.45737i
$93$	2.20473	+	1.97565i	0.228620	+	0.204865i
$94$	0.463366	−	0.267525i	0.0477926	−	0.0275930i
$95$	−4.55949	+	2.63242i	−0.467793	+	0.270081i
$96$	0.728180	+	0.652519i	0.0743195	+	0.0665975i
$97$			9.56933i			0.971619i	0.874065	+	0.485809i	$0.161475\pi$
$97$			9.56933i			0.971619i	−0.874065	+	0.485809i	$0.838525\pi$
$98$	0.178324	+	0.277417i	0.0180134	+	0.0280234i
$99$	−7.19078	+	16.3602i	−0.722701	+	1.64427i
$100$	3.05150	−	5.28535i	0.305150	−	0.528535i
$101$	9.41087	+	16.3001i	0.936416	+	1.62192i	0.772089	+	0.635515i	$0.219212\pi$
$101$	9.41087	+	16.3001i	0.936416	+	1.62192i	0.164327	+	0.986406i	$0.447455\pi$
$102$	0.0395646	−	0.0129597i	0.00391747	−	0.00128320i
$103$	−8.09092	−	4.67129i	−0.797222	−	0.460276i	0.0452770	−	0.998974i	$-0.485583\pi$
$103$	−8.09092	−	4.67129i	−0.797222	−	0.460276i	−0.842499	+	0.538698i	$0.818916\pi$
$104$	0.188345			0.0184688
$105$	2.75117	−	5.76874i	0.268487	−	0.562971i
$106$	−0.180409			−0.0175229
$107$	−1.63019	−	0.941191i	−0.157597	−	0.0909884i	0.419128	−	0.907927i	$-0.362336\pi$
$107$	−1.63019	−	0.941191i	−0.157597	−	0.0909884i	−0.576724	+	0.816939i	$0.695669\pi$
$108$	−1.01123	+	10.3314i	−0.0973056	+	0.994139i
$109$	0.661161	+	1.14516i	0.0633277	+	0.109687i	0.895951	−	0.444153i	$-0.146495\pi$
$109$	0.661161	+	1.14516i	0.0633277	+	0.109687i	−0.832623	+	0.553840i	$0.813162\pi$
$110$	−0.195704	+	0.338970i	−0.0186597	+	0.0323195i
$111$	11.3168	+	2.37728i	1.07415	+	0.225642i
$112$	7.63415	+	7.27843i	0.721359	+	0.687747i
$113$		−	12.0329i		−	1.13196i	−0.824420	−	0.565978i	$-0.808499\pi$
$113$		−	12.0329i		−	1.13196i	0.824420	−	0.565978i	$-0.191501\pi$
$114$	−0.205574	+	0.229411i	−0.0192538	+	0.0214863i
$115$	8.45123	−	4.87932i	0.788081	−	0.454999i
$116$	3.65680	−	2.11125i	0.339525	−	0.196025i
$117$	1.77491	+	2.41862i	0.164090	+	0.223601i
$118$		−	0.298769i		−	0.0275040i
$119$	1.29517	−	0.380364i	0.118728	−	0.0348679i
$120$	−0.0935336	+	0.445257i	−0.00853841	+	0.0406462i
$121$	12.2425	−	21.2046i	1.11295	−	1.92769i
$122$	0.132117	+	0.228834i	0.0119613	+	0.0207176i
$123$	−3.07678	−	9.39310i	−0.277424	−	0.846947i
$124$	−2.95712	−	1.70730i	−0.265558	−	0.153320i
$125$	11.2339			1.00479
$126$	0.0479060	−	0.370863i	0.00426781	−	0.0330391i
$127$	9.81825			0.871229			0.435614	−	0.900133i	$-0.356531\pi$
$127$	9.81825			0.871229			0.435614	+	0.900133i	$0.356531\pi$
$128$	−1.30200	−	0.751710i	−0.115082	−	0.0664424i
$129$	−4.82303	−	14.7242i	−0.424644	−	1.29640i
$130$	0.0328532	+	0.0569035i	0.00288142	+	0.00499077i
$131$	−1.61775	+	2.80202i	−0.141343	+	0.244814i	−0.928003	−	0.372573i	$-0.878475\pi$
$131$	−1.61775	+	2.80202i	−0.141343	+	0.244814i	0.786659	+	0.617387i	$0.211809\pi$
$132$	4.23750	−	20.1722i	0.368827	−	1.75577i
$133$	−6.89190	+	7.22872i	−0.597603	+	0.626810i
$134$		−	0.332848i		−	0.0287537i
$135$	−6.59915	+	2.99486i	−0.567964	+	0.257756i
$136$	−0.0832198	+	0.0480470i	−0.00713604	+	0.00411999i
$137$	13.5607	−	7.82928i	1.15857	−	0.668900i	0.207609	−	0.978212i	$-0.433432\pi$
$137$	13.5607	−	7.82928i	1.15857	−	0.668900i	0.950961	+	0.309311i	$0.100099\pi$
$138$	0.381042	−	0.425224i	0.0324364	−	0.0361974i
$139$			10.8590i			0.921051i	0.887646	+	0.460525i	$0.152339\pi$
$139$			10.8590i			0.921051i	−0.887646	+	0.460525i	$0.847661\pi$
$140$	−1.73760	+	7.16401i	−0.146854	+	0.605469i
$141$	−19.2505	−	4.04387i	−1.62118	−	0.340556i
$142$	0.180299	−	0.312286i	0.0151303	−	0.0262065i
$143$	−2.97846	−	5.15885i	−0.249072	−	0.431405i
$144$	−1.30686	−	11.8884i	−0.108905	−	0.990704i
$145$	2.55285	+	1.47389i	0.212003	+	0.122400i
$146$	−0.467190			−0.0386650
$147$	1.92394	−	11.9707i	0.158684	−	0.987329i
$148$	−13.3379			−1.09637
$149$	0.798927	+	0.461261i	0.0654507	+	0.0377880i	0.532368	−	0.846513i	$-0.321302\pi$
$149$	0.798927	+	0.461261i	0.0654507	+	0.0377880i	−0.466918	+	0.884301i	$0.654636\pi$
$150$	0.236898	−	0.0775976i	0.0193426	−	0.00633581i
$151$	0.280490	+	0.485822i	0.0228259	+	0.0395357i	0.877213	−	0.480102i	$-0.159400\pi$
$151$	0.280490	+	0.485822i	0.0228259	+	0.0395357i	−0.854387	+	0.519638i	$0.826067\pi$
$152$	0.355499	−	0.615742i	0.0288348	−	0.0499433i
$153$	−1.40123	−	0.615878i	−0.113282	−	0.0497908i
$154$	−0.175020	+	0.721597i	−0.0141035	+	0.0581479i
$155$		−	2.38376i		−	0.191468i
$156$	−2.57698	−	2.30923i	−0.206324	−	0.184886i
$157$	−0.524784	+	0.302984i	−0.0418823	+	0.0241808i	−0.520795	−	0.853682i	$-0.674364\pi$
$157$	−0.524784	+	0.302984i	−0.0418823	+	0.0241808i	0.478913	+	0.877863i	$0.341031\pi$
$158$	0.504672	−	0.291373i	0.0401496	−	0.0231804i
$159$	4.93954	+	4.42630i	0.391731	+	0.351029i
$160$		−	0.787311i		−	0.0622424i
$161$	12.7745	−	13.3988i	1.00677	−	1.05597i
$162$	−0.312383	+	0.286711i	−0.0245431	+	0.0225262i
$163$	5.37199	−	9.30455i	0.420766	−	0.728789i	−0.575248	−	0.817979i	$-0.695095\pi$
$163$	5.37199	−	9.30455i	0.420766	−	0.728789i	0.996015	+	0.0891901i	$0.0284279\pi$
$164$	5.70030	+	9.87321i	0.445118	+	0.770968i
$165$	13.6749	−	4.47930i	1.06459	−	0.348713i
$166$	0.0382300	+	0.0220721i	0.00296722	+	0.00171313i
$167$	−20.7092			−1.60253			−0.801264	−	0.598311i	$-0.795839\pi$
$167$	−20.7092			−1.60253			−0.801264	+	0.598311i	$0.795839\pi$
$168$	0.0677640	+	0.860443i	0.00522811	+	0.0663846i
$169$	−1.00000			−0.0769231
$170$	−0.0290322	−	0.0167617i	−0.00222667	−	0.00128557i
$171$	11.2571	−	1.23746i	0.860851	−	0.0946307i
$172$	8.93555	+	15.4768i	0.681330	+	1.18010i
$173$	7.06681	−	12.2401i	0.537279	−	0.930595i	−0.461770	−	0.887000i	$-0.652785\pi$
$173$	7.06681	−	12.2401i	0.537279	−	0.930595i	0.999049	−	0.0435953i	$-0.0138812\pi$
$174$	0.168788	+	0.0354568i	0.0127958	+	0.00268797i
$175$	7.75497	−	2.27748i	0.586221	−	0.172161i
$176$			23.7484i			1.79010i
$177$	−7.33025	+	8.18020i	−0.550976	+	0.614862i
$178$	0.116156	−	0.0670628i	0.00870628	−	0.00502657i
$179$	−6.72527	+	3.88284i	−0.502671	+	0.290217i	−0.729816	−	0.683644i	$-0.760394\pi$
$179$	−6.72527	+	3.88284i	−0.502671	+	0.290217i	0.227145	+	0.973861i	$0.427061\pi$
$180$	6.73887	−	4.94533i	0.502285	−	0.368603i
$181$			8.95701i			0.665769i	0.942968	+	0.332885i	$0.108022\pi$
$181$			8.95701i			0.665769i	−0.942968	+	0.332885i	$0.891978\pi$
$182$	0.0902162	+	0.0860125i	0.00668727	+	0.00637567i
$183$	1.99707	−	9.50687i	0.147628	−	0.702768i
$184$	−0.658934	+	1.14131i	−0.0485773	+	0.0841383i
$185$	−4.65568	−	8.06387i	−0.342292	−	0.592867i
$186$	−0.0434154	−	0.132543i	−0.00318337	−	0.00971852i
$187$	2.63205	+	1.51961i	0.192474	+	0.111125i
$188$	22.6885			1.65473
$189$	−10.4107	+	8.97872i	−0.757267	+	0.653106i
$190$	0.248040			0.0179947
$191$	11.3877	+	6.57469i	0.823985	+	0.475728i	0.851789	−	0.523886i	$-0.175518\pi$
$191$	11.3877	+	6.57469i	0.823985	+	0.475728i	−0.0278039	+	0.999613i	$0.508851\pi$
$192$	4.28457	+	13.0804i	0.309212	+	0.943995i
$193$	−6.10661	−	10.5770i	−0.439563	−	0.761346i	0.558092	−	0.829779i	$-0.311533\pi$
$193$	−6.10661	−	10.5770i	−0.439563	−	0.761346i	−0.997656	+	0.0684328i	$0.978200\pi$
$194$	0.225418	−	0.390435i	0.0161840	−	0.0280316i
$195$	0.496606	−	2.36405i	0.0355627	−	0.169293i
$196$	0.666776	+	13.9686i	0.0476269	+	0.997754i
$197$			17.5933i			1.25347i	0.779232	+	0.626736i	$0.215610\pi$
$197$			17.5933i			1.25347i	−0.779232	+	0.626736i	$0.784390\pi$
$198$	0.678774	−	0.498120i	0.0482384	−	0.0353998i
$199$	10.7669	−	6.21627i	0.763244	−	0.440659i	−0.0672150	−	0.997739i	$-0.521411\pi$
$199$	10.7669	−	6.21627i	0.763244	−	0.440659i	0.830459	+	0.557079i	$0.188078\pi$
$200$	−0.498289	+	0.287687i	−0.0352344	+	0.0203426i
$201$	−8.16636	+	9.11326i	−0.576011	+	0.642800i
$202$		−	0.886739i		−	0.0623907i
$203$	5.43449	+	1.31811i	0.381427	+	0.0925133i
$204$	1.72772	+	0.362935i	0.120964	+	0.0254105i
$205$	−3.97944	+	6.89259i	−0.277936	+	0.481399i
$206$	0.220076	+	0.381183i	0.0153334	+	0.0265583i
$207$	−20.8656	+	2.29369i	−1.45026	+	0.159422i
$208$	3.45257	+	1.99334i	0.239393	+	0.138214i
$209$	−22.4872			−1.55547
$210$	−0.248139	+	0.170561i	−0.0171233	+	0.0117698i
$211$	−3.36287			−0.231510			−0.115755	−	0.993278i	$-0.536929\pi$
$211$	−3.36287			−0.231510			−0.115755	+	0.993278i	$0.536929\pi$
$212$	−6.62522	−	3.82507i	−0.455022	−	0.262707i
$213$	−12.5984	+	4.12670i	−0.863229	+	0.282757i
$214$	0.0443419	+	0.0768024i	0.00303115	+	0.00525010i
$215$	−6.23801	+	10.8045i	−0.425429	+	0.736864i
$216$	0.569572	−	0.795855i	0.0387545	−	0.0541511i
$217$	−1.27424	−	4.33886i	−0.0865007	−	0.294541i
$218$		−	0.0622979i		−	0.00421935i
$219$	12.7915	+	11.4624i	0.864370	+	0.774559i
$220$	−14.3738	+	8.29874i	−0.969084	+	0.559501i
$221$	0.441847	−	0.255100i	0.0297218	−	0.0171599i
$222$	−0.405733	−	0.363576i	−0.0272310	−	0.0244017i
$223$			4.62898i			0.309979i	0.987916	+	0.154990i	$0.0495344\pi$
$223$			4.62898i			0.309979i	−0.987916	+	0.154990i	$0.950466\pi$
$224$	−0.420855	−	1.43304i	−0.0281196	−	0.0957492i
$225$	−8.39002	−	3.68765i	−0.559335	−	0.245843i
$226$	−0.283449	+	0.490948i	−0.0188548	+	0.0326574i
$227$	−12.2312	−	21.1851i	−0.811813	−	1.40610i	−0.911594	−	0.411092i	$-0.865147\pi$
$227$	−12.2312	−	21.1851i	−0.811813	−	1.40610i	0.0997806	−	0.995009i	$-0.468186\pi$
$228$	−12.4134	+	4.06609i	−0.822096	+	0.269284i
$229$	0.339161	+	0.195815i	0.0224124	+	0.0129398i	0.511164	−	0.859483i	$-0.329214\pi$
$229$	0.339161	+	0.195815i	0.0224124	+	0.0129398i	−0.488752	+	0.872423i	$0.662548\pi$
$230$	−0.459754			−0.0303153
$231$	22.4962	−	15.4630i	1.48014	−	1.01739i
$232$	−0.398087			−0.0261357
$233$	−12.3209	−	7.11345i	−0.807167	−	0.466018i	0.0388043	−	0.999247i	$-0.487645\pi$
$233$	−12.3209	−	7.11345i	−0.807167	−	0.466018i	−0.845971	+	0.533229i	$0.820978\pi$
$234$	−0.0154438	−	0.140491i	−0.00100959	−	0.00918420i
$235$	7.91953	+	13.7170i	0.516613	+	0.894800i
$236$	6.33458	−	10.9718i	0.412346	−	0.714204i
$237$	−20.9665	−	4.40436i	−1.36192	−	0.286094i
$238$	−0.0618035	−	0.0149902i	−0.00400613	−	0.000971668i
$239$		−	11.9836i		−	0.775155i	−0.921837	−	0.387578i	$-0.873312\pi$
$239$		−	11.9836i		−	0.775155i	0.921837	−	0.387578i	$-0.126688\pi$
$240$	−6.42693	+	7.17213i	−0.414856	+	0.462959i
$241$	−13.4671	+	7.77526i	−0.867495	+	0.500848i	−0.866515	−	0.499151i	$-0.833645\pi$
$241$	−13.4671	+	7.77526i	−0.867495	+	0.500848i	−0.000979872		1.00000i	$0.500312\pi$
$242$	−0.999001	+	0.576774i	−0.0642182	+	0.0370764i
$243$	15.5874	−	0.185792i	0.999929	−	0.0119185i
$244$			11.2047i			0.717309i
$245$	−8.21239	+	5.27892i	−0.524670	+	0.337258i
$246$	−0.0957318	+	0.455722i	−0.00610364	+	0.0290558i
$247$	−1.88748	+	3.26922i	−0.120098	+	0.208015i
$248$	0.160959	+	0.278790i	0.0102209	+	0.0177032i
$249$	−0.505189	−	1.54229i	−0.0320150	−	0.0977387i
$250$	−0.458351	−	0.264629i	−0.0289887	−	0.0167366i
$251$	−3.43050			−0.216531			−0.108266	−	0.994122i	$-0.534530\pi$
$251$	−3.43050			−0.216531			−0.108266	+	0.994122i	$0.534530\pi$
$252$	9.62238	−	12.6036i	0.606153	−	0.793952i
$253$	41.6811			2.62047
$254$	−0.400591	−	0.231281i	−0.0251353	−	0.0145119i
$255$	0.383645	+	1.17123i	0.0240248	+	0.0733453i
$256$	−7.91136	−	13.7029i	−0.494460	−	0.856430i
$257$	−2.75251	+	4.76749i	−0.171697	+	0.297388i	−0.939013	−	0.343881i	$-0.888258\pi$
$257$	−2.75251	+	4.76749i	−0.171697	+	0.297388i	0.767316	+	0.641269i	$0.221592\pi$
$258$	−0.150065	+	0.714371i	−0.00934266	+	0.0444748i
$259$	−12.7847	−	12.1889i	−0.794400	−	0.757384i
$260$			2.78625i			0.172796i
$261$	−3.75144	−	5.11199i	−0.232209	−	0.316424i
$262$	0.132010	−	0.0762162i	0.00815562	−	0.00470865i
$263$	−16.2877	+	9.40369i	−1.00434	+	0.579857i	−0.909530	−	0.415639i	$-0.863558\pi$
$263$	−16.2877	+	9.40369i	−1.00434	+	0.579857i	−0.0948112	+	0.995495i	$0.530225\pi$
$264$	−1.29687	+	1.44724i	−0.0798168	+	0.0890716i
$265$		−	5.34065i		−	0.328074i
$266$	0.451475	−	0.132589i	0.0276817	−	0.00812956i
$267$	−4.82569	−	1.01372i	−0.295327	−	0.0620384i
$268$	7.05712	−	12.2233i	0.431082	−	0.746656i
$269$	−13.2097	−	22.8799i	−0.805410	−	1.39501i	−0.916014	−	0.401147i	$-0.868612\pi$
$269$	−13.2097	−	22.8799i	−0.805410	−	1.39501i	0.110604	−	0.993865i	$-0.464722\pi$
$270$	0.339797	+	0.0332591i	0.0206794	+	0.00202408i
$271$	4.91099	+	2.83536i	0.298321	+	0.172236i	0.641689	−	0.766965i	$-0.278234\pi$
$271$	4.91099	+	2.83536i	0.298321	+	0.172236i	−0.343367	+	0.939201i	$0.611568\pi$
$272$	−2.03401			−0.123330
$273$	−0.359786	−	4.56843i	−0.0217752	−	0.276494i
$274$	−0.737714			−0.0445669
$275$	15.7597	+	9.09887i	0.950346	+	0.548683i
$276$	23.0088	−	7.53670i	1.38497	−	0.453656i
$277$	7.83627	+	13.5728i	0.470836	+	0.815512i	0.999444	−	0.0333546i	$-0.0106191\pi$
$277$	7.83627	+	13.5728i	0.470836	+	0.815512i	−0.528608	+	0.848866i	$0.677286\pi$
$278$	0.255798	−	0.443055i	0.0153417	−	0.0265727i
$279$	−2.06322	+	4.69417i	−0.123522	+	0.281032i
$280$	0.479571	−	0.503009i	0.0286598	−	0.0300605i
$281$			21.8321i			1.30239i	0.758908	+	0.651197i	$0.225733\pi$
$281$			21.8321i			1.30239i	−0.758908	+	0.651197i	$0.774267\pi$
$282$	0.690172	+	0.618461i	0.0410992	+	0.0368288i
$283$	−10.5400	+	6.08526i	−0.626537	+	0.361731i	−0.779410	−	0.626515i	$-0.784481\pi$
$283$	−10.5400	+	6.08526i	−0.626537	+	0.361731i	0.152873	+	0.988246i	$0.451147\pi$
$284$	13.2423	−	7.64547i	0.785788	−	0.453675i
$285$	−6.79124	−	6.08561i	−0.402279	−	0.360481i
$286$			0.280646i			0.0165949i
$287$	−3.55885	+	14.6729i	−0.210072	+	0.866114i
$288$	−0.681441	+	1.55039i	−0.0401543	+	0.0913578i
$289$	8.36985	−	14.4970i	0.492344	−	0.852765i
$290$	−0.0694386	−	0.120271i	−0.00407758	−	0.00706257i
$291$	−15.7511	+	5.15939i	−0.923346	+	0.302449i
$292$	−17.1568	−	9.90548i	−1.00403	−	0.579674i
$293$	1.17555			0.0686761			0.0343381	−	0.999410i	$-0.489068\pi$
$293$	1.17555			0.0686761			0.0343381	+	0.999410i	$0.489068\pi$
$294$	−0.360484	+	0.443092i	−0.0210238	+	0.0258417i
$295$	8.84448			0.514945
$296$	1.08900	+	0.628732i	0.0632966	+	0.0365443i
$297$	−30.8059	−	3.01526i	−1.78754	−	0.174963i
$298$	−0.0217311	−	0.0376395i	−0.00125885	−	0.00218039i
$299$	3.49854	−	6.05965i	0.202326	−	0.350439i
$300$	10.3449	+	2.17312i	0.597264	+	0.125465i
$301$	−5.57870	+	23.0006i	−0.321551	+	1.32574i
$302$		−	0.0264291i		−	0.00152083i
$303$	−21.7560	+	24.2786i	−1.24985	+	1.39477i
$304$	13.0334	−	7.52481i	0.747514	−	0.431577i
$305$	−6.77417	+	3.91107i	−0.387888	+	0.223947i
$306$	0.0426631	+	0.0581359i	0.00243889	+	0.00332341i
$307$		−	27.8692i		−	1.59058i	−0.606229	−	0.795290i	$-0.707318\pi$
$307$		−	27.8692i		−	1.59058i	0.606229	−	0.795290i	$-0.292682\pi$
$308$	−21.7268	+	22.7886i	−1.23800	+	1.29850i
$309$	3.32665	−	15.8362i	0.189247	−	0.900890i
$310$	−0.0561525	+	0.0972590i	−0.00318925	+	0.00552394i
$311$	4.11692	+	7.13071i	0.233449	+	0.404345i	0.958821	−	0.284012i	$-0.0916655\pi$
$311$	4.11692	+	7.13071i	0.233449	+	0.404345i	−0.725372	+	0.688357i	$0.758332\pi$
$312$	0.101548	+	0.310016i	0.00574902	+	0.0175512i
$313$	−25.1480	−	14.5192i	−1.42145	−	0.820675i	−0.425028	−	0.905180i	$-0.639736\pi$
$313$	−25.1480	−	14.5192i	−1.42145	−	0.820675i	−0.996423	+	0.0845047i	$0.973069\pi$
$314$	0.0285487			0.00161109
$315$	10.9786	+	1.41816i	0.618577	+	0.0799044i
$316$	24.7110			1.39010
$317$	−9.95440	−	5.74717i	−0.559095	−	0.322793i	0.193687	−	0.981063i	$-0.437955\pi$
$317$	−9.95440	−	5.74717i	−0.559095	−	0.322793i	−0.752782	+	0.658270i	$0.771289\pi$
$318$	−0.0972690	−	0.296953i	−0.00545458	−	0.0166523i
$319$	6.29528	+	10.9037i	0.352468	+	0.610492i
$320$	5.54158	−	9.59829i	0.309783	−	0.536561i
$321$	0.670268	−	3.19074i	0.0374107	−	0.178090i
$322$	−0.836831	+	0.245760i	−0.0466348	+	0.0136957i
$323$		−	1.92599i		−	0.107165i
$324$	−17.5507	+	3.90578i	−0.975037	+	0.216988i
$325$	2.64561	−	1.52745i	0.146752	−	0.0847274i
$326$	−0.438361	+	0.253088i	−0.0242786	+	0.0140172i
$327$	−1.52847	+	1.70569i	−0.0845245	+	0.0943251i
$328$		−	1.07482i		−	0.0593469i
$329$	21.7473	+	20.7340i	1.19897	+	1.14310i
$330$	−0.663459	−	0.139370i	−0.0365222	−	0.00767209i
$331$	−3.40247	+	5.89325i	−0.187017	+	0.323922i	−0.944254	−	0.329217i	$-0.893215\pi$
$331$	−3.40247	+	5.89325i	−0.187017	+	0.323922i	0.757238	+	0.653139i	$0.226548\pi$
$332$	0.935955	+	1.62112i	0.0513672	+	0.0889706i
$333$	2.18856	+	19.9092i	0.119932	+	1.09102i
$334$	0.844949	+	0.487832i	0.0462336	+	0.0266930i
$335$	9.85330			0.538343
$336$	−7.86427	+	16.4900i	−0.429031	+	0.899604i
$337$	−0.0340775			−0.00185632			−0.000928159	−	1.00000i	$-0.500295\pi$
$337$	−0.0340775			−0.00185632			−0.000928159		1.00000i	$0.500295\pi$
$338$	0.0408006	+	0.0235563i	0.00221926	+	0.00128129i
$339$	19.8061	−	6.48762i	1.07572	−	0.352359i
$340$	−0.710773	−	1.23109i	−0.0385471	−	0.0667655i
$341$	5.09077	−	8.81747i	0.275680	−	0.477493i
$342$	−0.488446	−	0.214686i	−0.0264121	−	0.0116089i
$343$	−12.1261	+	13.9985i	−0.654750	+	0.755846i
$344$		−	1.68484i		−	0.0908405i
$345$	12.5879	+	11.2800i	0.677710	+	0.607294i
$346$	−0.576660	+	0.332935i	−0.0310014	+	0.0178987i
$347$	18.0074	−	10.3966i	0.966686	−	0.558117i	0.0684619	−	0.997654i	$-0.478191\pi$
$347$	18.0074	−	10.3966i	0.966686	−	0.558117i	0.898224	+	0.439537i	$0.144858\pi$
$348$	5.44671	+	4.88078i	0.291975	+	0.261638i
$349$		−	32.6374i		−	1.74704i	−0.486786	−	0.873521i	$-0.661831\pi$
$349$		−	32.6374i		−	1.74704i	0.486786	−	0.873521i	$-0.338169\pi$
$350$	−0.370056	−	0.0897555i	−0.0197804	−	0.00479764i
$351$	−3.02408	+	4.22551i	−0.161414	+	0.225541i
$352$	1.68138	−	2.91224i	0.0896180	−	0.155223i
$353$	−9.54834	−	16.5382i	−0.508207	−	0.880240i	−0.999955	−	0.00950230i	$-0.996975\pi$
$353$	−9.54834	−	16.5382i	−0.508207	−	0.880240i	0.491748	−	0.870737i	$-0.336358\pi$
$354$	0.491774	−	0.161084i	0.0261375	−	0.00856152i
$355$	9.24462	+	5.33738i	0.490654	+	0.283279i
$356$	5.68753			0.301438
$357$	1.32438	+	1.92676i	0.0700935	+	0.101975i
$358$	0.365860			0.0193363
$359$	−3.32321	−	1.91866i	−0.175392	−	0.101263i	0.409734	−	0.912205i	$-0.365622\pi$
$359$	−3.32321	−	1.91866i	−0.175392	−	0.101263i	−0.585126	+	0.810942i	$0.698955\pi$
$360$	−0.783322	+	0.0861081i	−0.0412847	+	0.00453830i
$361$	−2.37481	−	4.11329i	−0.124990	−	0.216489i
$362$	0.210994	−	0.365452i	0.0110896	−	0.0192077i
$363$	41.5033	+	8.71845i	2.17836	+	0.457600i
$364$	1.48938	+	5.07145i	0.0780649	+	0.265816i
$365$		−	13.8302i		−	0.723908i
$366$	−0.305428	+	0.340843i	−0.0159650	+	0.0178161i
$367$	−23.2384	+	13.4167i	−1.21304	+	0.700346i	−0.963419	−	0.267998i	$-0.913638\pi$
$367$	−23.2384	+	13.4167i	−1.21304	+	0.700346i	−0.249616	+	0.968345i	$0.580304\pi$
$368$	−24.1579	+	13.9476i	−1.25932	+	0.727069i
$369$	13.8022	−	10.1287i	0.718511	−	0.527281i
$370$			0.438681i			0.0228059i
$371$	−2.85483	−	9.72090i	−0.148216	−	0.504684i
$372$	1.21585	−	5.78792i	0.0630388	−	0.300090i
$373$	5.83099	−	10.0996i	0.301917	−	0.522936i	−0.674653	−	0.738135i	$-0.735707\pi$
$373$	5.83099	−	10.0996i	0.301917	−	0.522936i	0.976570	+	0.215199i	$0.0690400\pi$
$374$	−0.0715928	−	0.124002i	−0.00370197	−	0.00641201i
$375$	6.05687	+	18.4910i	0.312775	+	0.954872i
$376$	−1.85244	−	1.06950i	−0.0955321	−	0.0551555i
$377$	2.11360			0.108856
$378$	0.636268	−	0.121100i	0.0327261	−	0.00622874i
$379$	−30.1532			−1.54886			−0.774432	−	0.632657i	$-0.781964\pi$
$379$	−30.1532			−1.54886			−0.774432	+	0.632657i	$0.781964\pi$
$380$	9.10885	+	5.25900i	0.467274	+	0.269781i
$381$	5.29359	+	16.1608i	0.271199	+	0.827944i
$382$	−0.309750	−	0.536503i	−0.0158482	−	0.0274499i
$383$	−12.8829	+	22.3138i	−0.658284	+	1.14018i	0.322775	+	0.946476i	$0.395384\pi$
$383$	−12.8829	+	22.3138i	−0.658284	+	1.14018i	−0.981060	+	0.193706i	$0.937949\pi$
$384$	0.535329	−	2.54838i	0.0273184	−	0.130046i
$385$	−21.3614	−	5.18112i	−1.08868	−	0.264054i
$386$			0.575395i			0.0292868i
$387$	21.6357	−	15.8774i	1.09980	−	0.807093i
$388$	16.5562	−	9.55871i	0.840513	−	0.485270i
$389$	8.93634	−	5.15940i	0.453091	−	0.261592i	−0.256044	−	0.966665i	$-0.582419\pi$
$389$	8.93634	−	5.15940i	0.453091	−	0.261592i	0.709135	+	0.705073i	$0.249086\pi$
$390$	−0.0759499	+	0.0847564i	−0.00384587	+	0.00429180i
$391$			3.56992i			0.180538i
$392$	0.604019	−	1.17192i	0.0305076	−	0.0591907i
$393$	−5.48434	−	1.15208i	−0.276649	−	0.0581145i
$394$	0.414433	−	0.717818i	0.0208788	−	0.0361632i
$395$	8.62551	+	14.9398i	0.433996	+	0.751704i
$396$	35.4881	−	3.90110i	1.78334	−	0.196038i
$397$	−5.77444	−	3.33387i	−0.289811	−	0.167322i	0.348046	−	0.937478i	$-0.386845\pi$
$397$	−5.77444	−	3.33387i	−0.289811	−	0.167322i	−0.637857	+	0.770155i	$0.720179\pi$
$398$	−0.585728			−0.0293599
$399$	−15.6143	−	7.44662i	−0.781692	−	0.372797i
$400$	−12.1789			−0.608945
$401$	22.1362	+	12.7803i	1.10543	+	0.638220i	0.937642	−	0.347604i	$-0.113005\pi$
$401$	22.1362	+	12.7803i	1.10543	+	0.638220i	0.167787	+	0.985823i	$0.446338\pi$
$402$	0.547867	−	0.179458i	0.0273251	−	0.00895054i
$403$	−0.854596	−	1.48020i	−0.0425705	−	0.0737342i
$404$	18.8008	−	32.5640i	0.935377	−	1.62012i
$405$	−8.48752	−	9.24748i	−0.421748	−	0.459511i
$406$	−0.190681	−	0.181796i	−0.00946334	−	0.00902239i
$407$		−	39.7707i		−	1.97136i
$408$	−0.123954	−	0.111075i	−0.00613663	−	0.00549901i
$409$	−4.09676	+	2.36527i	−0.202572	+	0.116955i	−0.597855	−	0.801605i	$-0.703980\pi$
$409$	−4.09676	+	2.36527i	−0.202572	+	0.116955i	0.395283	+	0.918560i	$0.370647\pi$
$410$	0.324727	−	0.187481i	0.0160371	−	0.00925904i
$411$	20.1983	+	18.0997i	0.996311	+	0.892791i
$412$			18.6644i			0.919531i
$413$	16.0985	−	4.72779i	0.792154	−	0.232640i
$414$	0.905359	+	0.397931i	0.0444959	+	0.0195572i
$415$	−0.653400	+	1.13172i	−0.0320742	+	0.0555541i
$416$	−0.282257	−	0.488883i	−0.0138388	−	0.0239695i
$417$	−17.8739	+	5.85474i	−0.875291	+	0.286708i
$418$	0.917492	+	0.529714i	0.0448760	+	0.0259092i
$419$	34.1086			1.66631			0.833157	−	0.553037i	$-0.186531\pi$
$419$	34.1086			1.66631			0.833157	+	0.553037i	$0.186531\pi$
$420$	−12.7288	+	1.00245i	−0.621101	+	0.0489147i
$421$	19.6855			0.959411			0.479705	−	0.877430i	$-0.340744\pi$
$421$	19.6855			0.959411			0.479705	+	0.877430i	$0.340744\pi$
$422$	0.137207	+	0.0792166i	0.00667914	+	0.00385621i
$423$	−3.72284	−	33.8665i	−0.181011	−	1.64665i
$424$	0.360618	+	0.624608i	0.0175132	+	0.0303337i
$425$	−0.779303	+	1.34979i	−0.0378018	+	0.0654746i
$426$	0.611232	+	0.128399i	0.0296143	+	0.00622097i
$427$	−10.2395	+	10.7399i	−0.495525	+	0.519742i
$428$			3.76059i			0.181775i
$429$	6.88559	−	7.68398i	0.332439	−	0.370986i
$430$	0.509029	−	0.293888i	0.0245476	−	0.0141725i
$431$	−5.51191	+	3.18230i	−0.265499	+	0.153286i	−0.626841	−	0.779148i	$-0.715652\pi$
$431$	−5.51191	+	3.18230i	−0.265499	+	0.153286i	0.361341	+	0.932434i	$0.382319\pi$
$432$	18.8638	−	8.56084i	0.907583	−	0.411884i
$433$		−	34.2620i		−	1.64653i	−0.567660	−	0.823263i	$-0.692151\pi$
$433$		−	34.2620i		−	1.64653i	0.567660	−	0.823263i	$-0.307849\pi$
$434$	−0.0502177	+	0.207044i	−0.00241053	+	0.00993845i
$435$	−1.04963	+	4.99665i	−0.0503258	+	0.239571i
$436$	1.32085	−	2.28779i	0.0632575	−	0.109565i
$437$	−13.2069	−	22.8750i	−0.631771	−	1.09426i
$438$	−0.251890	−	0.768994i	−0.0120358	−	0.0367440i
$439$	−19.2073	−	11.0894i	−0.916717	−	0.529267i	−0.0341306	−	0.999417i	$-0.510866\pi$
$439$	−19.2073	−	11.0894i	−0.916717	−	0.529267i	−0.882586	+	0.470151i	$0.844200\pi$
$440$	1.56477			0.0745973
$441$	20.7411	−	3.28731i	0.987672	−	0.156539i
$442$	−0.0240368			−0.00114332
$443$	20.1068	+	11.6087i	0.955305	+	0.551546i	0.894725	−	0.446618i	$-0.147372\pi$
$443$	20.1068	+	11.6087i	0.955305	+	0.551546i	0.0605802	+	0.998163i	$0.480705\pi$
$444$	−7.19126	−	21.9542i	−0.341282	−	1.04190i
$445$	1.98526	+	3.43857i	0.0941104	+	0.163004i
$446$	0.109041	−	0.188865i	0.00516326	−	0.00894303i
$447$	−0.328486	+	1.56372i	−0.0155369	+	0.0739616i
$448$	4.95588	−	20.4328i	0.234143	−	0.965358i
$449$		−	11.5322i		−	0.544240i	−0.962263	−	0.272120i	$-0.912275\pi$
$449$		−	11.5322i		−	0.544240i	0.962263	−	0.272120i	$-0.0877247\pi$
$450$	0.255451	+	0.348096i	0.0120421	+	0.0164094i
$451$	−29.4396	+	16.9970i	−1.38626	+	0.800357i
$452$	−20.8184	+	12.0195i	−0.979215	+	0.565350i
$453$	−0.648434	+	0.723620i	−0.0304661	+	0.0339987i
$454$			1.15248i			0.0540888i
$455$	−2.54623	+	2.67067i	−0.119369	+	0.125203i
$456$	1.20518	+	0.253168i	0.0564378	+	0.0118557i
$457$	2.40598	−	4.16728i	0.112547	−	0.194937i	−0.804249	−	0.594292i	$-0.797432\pi$
$457$	2.40598	−	4.16728i	0.112547	−	0.194937i	0.916797	+	0.399355i	$0.130766\pi$
$458$	−0.00922531	−	0.0159787i	−0.000431071	−	0.000746636i
$459$	0.258252	−	2.63847i	0.0120542	−	0.123153i
$460$	−16.8837	−	9.74781i	−0.787206	−	0.454494i
$461$	19.7845			0.921455			0.460728	−	0.887542i	$-0.347589\pi$
$461$	19.7845			0.921455			0.460728	+	0.887542i	$0.347589\pi$
$462$	−1.28211	+	0.100972i	−0.0596492	+	0.00469766i
$463$	12.0040			0.557872			0.278936	−	0.960310i	$-0.410018\pi$
$463$	12.0040			0.557872			0.278936	+	0.960310i	$0.410018\pi$
$464$	−7.29736	−	4.21313i	−0.338771	−	0.195590i
$465$	3.92367	−	1.28523i	0.181956	−	0.0596009i
$466$	0.335133	+	0.580467i	0.0155247	+	0.0268896i
$467$	−10.2459	+	17.7464i	−0.474124	+	0.821207i	−0.999561	−	0.0296256i	$-0.990568\pi$
$467$	−10.2459	+	17.7464i	−0.474124	+	0.821207i	0.525437	+	0.850832i	$0.323902\pi$
$468$	2.41158	−	5.48675i	0.111475	−	0.253625i
$469$	17.9347	−	5.26706i	0.828148	−	0.243210i
$470$		−	0.746218i		−	0.0344205i
$471$	−0.781653	−	0.700436i	−0.0360166	−	0.0322744i
$472$	−1.03439	+	0.597207i	−0.0476118	+	0.0274887i
$473$	−46.1484	+	26.6438i	−2.12190	+	1.22508i
$474$	0.751697	+	0.673593i	0.0345266	+	0.0309392i
$475$		−	11.5321i		−	0.529130i
$476$	−1.95181	−	1.86086i	−0.0894609	−	0.0852925i
$477$	−4.62249	+	10.5169i	−0.211649	+	0.481538i
$478$	−0.282289	+	0.488939i	−0.0129116	+	0.0223635i
$479$	4.02095	+	6.96449i	0.183722	+	0.318216i	0.943145	−	0.332381i	$-0.107852\pi$
$479$	4.02095	+	6.96449i	0.183722	+	0.318216i	−0.759423	+	0.650597i	$0.774519\pi$
$480$	1.29591	−	0.424486i	0.0591501	−	0.0193750i
$481$	−5.78191	−	3.33819i	−0.263632	−	0.152208i
$482$	0.732624			0.0333701
$483$	28.9418	+	13.8027i	1.31690	+	0.628043i
$484$	−48.9156			−2.22343
$485$	11.5580	+	6.67304i	0.524824	+	0.303007i
$486$	−0.640350	−	0.359599i	−0.0290469	−	0.0163117i
$487$	−13.1627	−	22.7984i	−0.596457	−	1.03309i	−0.993339	−	0.115225i	$-0.963241\pi$
$487$	−13.1627	−	22.7984i	−0.596457	−	1.03309i	0.396882	−	0.917869i	$-0.370092\pi$
$488$	0.528176	−	0.914828i	0.0239094	−	0.0414123i
$489$	18.2116	+	3.82565i	0.823558	+	0.173002i
$490$	0.459422	−	0.0219301i	0.0207546	−	0.000990701i
$491$		−	40.4161i		−	1.82395i	−0.410243	−	0.911976i	$-0.634556\pi$
$491$		−	40.4161i		−	1.82395i	0.410243	−	0.911976i	$-0.365444\pi$
$492$	−13.1779	+	14.7059i	−0.594106	+	0.662993i
$493$	−0.933887	+	0.539180i	−0.0420602	+	0.0242834i
$494$	0.154021	−	0.0889241i	0.00692973	−	0.00400088i
$495$	14.7458	+	20.0938i	0.662776	+	0.903147i
$496$			6.81402i			0.305958i
$497$	19.6799	+	4.77327i	0.882764	+	0.214110i
$498$	−0.0157186	+	0.0748268i	−0.000704367	+	0.00335307i
$499$	−0.749571	+	1.29829i	−0.0335554	+	0.0581196i	−0.882315	−	0.470659i	$-0.844016\pi$
$499$	−0.749571	+	1.29829i	−0.0335554	+	0.0581196i	0.848760	+	0.528778i	$0.177350\pi$
$500$	−11.2215	−	19.4361i	−0.501839	−	0.869211i
$501$	−11.1655	−	34.0873i	−0.498840	−	1.52291i
$502$	0.139967	+	0.0808098i	0.00624702	+	0.00360672i
$503$	8.23344			0.367111			0.183555	−	0.983009i	$-0.441239\pi$
$503$	8.23344			0.367111			0.183555	+	0.983009i	$0.441239\pi$
$504$	−1.37975	+	0.575454i	−0.0614590	+	0.0256328i
$505$	26.2501			1.16812
$506$	−1.70062	−	0.981851i	−0.0756016	−	0.0436486i
$507$	−0.539158	−	1.64600i	−0.0239449	−	0.0731013i
$508$	−9.80736	−	16.9868i	−0.435131	−	0.753669i
$509$	−10.1538	+	17.5869i	−0.450060	+	0.779527i	−0.998389	−	0.0567355i	$-0.981931\pi$
$509$	−10.1538	+	17.5869i	−0.450060	+	0.779527i	0.548329	+	0.836263i	$0.315264\pi$
$510$	0.0119368	−	0.0568241i	0.000528572	−	0.00251622i
$511$	−7.39292	−	25.1734i	−0.327044	−	1.11361i
$512$			3.75229i			0.165829i
$513$	8.10621	+	17.8620i	0.357898	+	0.788625i
$514$	0.224609	−	0.129678i	0.00990706	−	0.00571984i
$515$	−11.2842	+	6.51492i	−0.497240	+	0.287082i
$516$	−20.6572	+	23.0524i	−0.909381	+	1.01482i
$517$			67.6518i			2.97532i
$518$	0.234496	+	0.798475i	0.0103032	+	0.0350830i
$519$	23.9572	+	5.03261i	1.05161	+	0.220907i
$520$	0.131340	−	0.227488i	0.00575964	−	0.00997599i
$521$	10.8916	+	18.8648i	0.477170	+	0.826483i	0.999658	−	0.0261641i	$-0.00832925\pi$
$521$	10.8916	+	18.8648i	0.477170	+	0.826483i	−0.522488	+	0.852647i	$0.674996\pi$
$522$	0.0326419	+	0.296942i	0.00142870	+	0.0129968i
$523$	21.8027	+	12.5878i	0.953367	+	0.550427i	0.894125	−	0.447817i	$-0.147798\pi$
$523$	21.8027	+	12.5878i	0.953367	+	0.550427i	0.0592415	+	0.998244i	$0.481132\pi$
$524$	6.46381			0.282373
$525$	7.92988	+	11.5367i	0.346088	+	0.503505i
$526$	0.886063			0.0386342
$527$	0.755201	+	0.436016i	0.0328971	+	0.0189931i
$528$	−39.0898	+	12.8041i	−1.70117	+	0.557229i
$529$	12.9796	+	22.4813i	0.564330	+	0.977449i
$530$	−0.125806	+	0.217902i	−0.00546465	+	0.00946505i
$531$	−17.4168	−	7.65516i	−0.755823	−	0.332205i
$532$	19.3909	+	4.70317i	0.840701	+	0.203908i
$533$			5.70663i			0.247182i
$534$	0.173012	+	0.155035i	0.00748695	+	0.00670904i
$535$	−2.27358	+	1.31265i	−0.0982955	+	0.0567509i
$536$	−1.15238	+	0.665327i	−0.0497752	+	0.0287377i
$537$	−10.0171	−	8.97632i	−0.432271	−	0.387357i
$538$			1.24468i			0.0536622i
$539$	−41.6510	+	1.98817i	−1.79404	+	0.0856367i
$540$	11.7733	+	8.42584i	0.506643	+	0.362591i
$541$	−3.28601	+	5.69153i	−0.141277	+	0.244698i	−0.927978	−	0.372636i	$-0.878454\pi$
$541$	−3.28601	+	5.69153i	−0.141277	+	0.244698i	0.786701	+	0.617334i	$0.211787\pi$
$542$	−0.133581	−	0.231369i	−0.00573779	−	0.00993815i
$543$	−14.7432	+	4.82925i	−0.632692	+	0.207243i
$544$	0.249428	+	0.144008i	0.0106942	+	0.00617427i
$545$	1.84421			0.0789971
$546$	−0.0929356	+	0.194870i	−0.00397728	+	0.00833967i
$547$	−29.0225			−1.24091			−0.620456	−	0.784241i	$-0.713052\pi$
$547$	−29.0225			−1.24091			−0.620456	+	0.784241i	$0.713052\pi$
$548$	−27.0913	−	15.6412i	−1.15728	−	0.668158i
$549$	16.7250	−	1.83853i	0.713806	−	0.0784665i
$550$	−0.428671	−	0.742480i	−0.0182786	−	0.0316594i
$551$	3.98939	−	6.90982i	0.169954	−	0.294368i
$552$	−2.23386	−	0.469259i	−0.0950794	−	0.0199730i
$553$	23.6860	+	22.5823i	1.00723	+	0.960297i
$554$		−	0.738373i		−	0.0313704i
$555$	10.7630	−	12.0109i	0.456862	−	0.509836i
$556$	18.7875	−	10.8470i	0.796768	−	0.460014i
$557$	20.5511	−	11.8652i	0.870777	−	0.502743i	0.00317056	−	0.999995i	$-0.498991\pi$
$557$	20.5511	−	11.8652i	0.870777	−	0.502743i	0.867606	+	0.497252i	$0.165657\pi$
$558$	0.194758	−	0.142923i	0.00824474	−	0.00605042i
$559$			8.94548i			0.378354i
$560$	14.1146	−	4.14517i	0.596451	−	0.175166i
$561$	−1.08219	+	5.15165i	−0.0456901	+	0.217503i
$562$	0.514283	−	0.890764i	0.0216937	−	0.0375746i
$563$	7.56363	+	13.1006i	0.318769	+	0.552124i	0.980231	−	0.197854i	$-0.0633973\pi$
$563$	7.56363	+	13.1006i	0.318769	+	0.552124i	−0.661462	+	0.749978i	$0.730064\pi$
$564$	12.2327	+	37.3452i	0.515089	+	1.57252i
$565$	−14.5335	−	8.39095i	−0.611431	−	0.353010i
$566$	0.573384			0.0241011
$567$	−20.3920	−	12.2950i	−0.856382	−	0.516343i
$568$	−1.44159			−0.0604877
$569$	−30.2650	−	17.4735i	−1.26877	−	0.732527i	−0.294018	−	0.955800i	$-0.594992\pi$
$569$	−30.2650	−	17.4735i	−1.26877	−	0.732527i	−0.974756	+	0.223273i	$0.928326\pi$
$570$	0.133733	+	0.408273i	0.00560145	+	0.0171007i
$571$	−1.05572	−	1.82856i	−0.0441805	−	0.0765228i	0.843090	−	0.537773i	$-0.180734\pi$
$571$	−1.05572	−	1.82856i	−0.0441805	−	0.0765228i	−0.887270	+	0.461250i	$0.847401\pi$
$572$	−5.95031	+	10.3062i	−0.248795	+	0.430926i
$573$	−4.68215	+	22.2889i	−0.195600	+	0.931133i
$574$	0.490842	−	0.514831i	0.0204873	−	0.0214886i
$575$			21.3753i			0.891413i
$576$	−19.2202	+	14.1048i	−0.800842	+	0.587700i
$577$	20.9456	−	12.0929i	0.871975	−	0.503435i	0.00397109	−	0.999992i	$-0.498736\pi$
$577$	20.9456	−	12.0929i	0.871975	−	0.503435i	0.868004	+	0.496557i	$0.165403\pi$
$578$	−0.682990	+	0.394324i	−0.0284086	+	0.0164017i
$579$	14.1172	−	15.7541i	0.586692	−	0.654719i
$580$		−	5.88902i		−	0.244528i
$581$	−0.584341	+	2.40920i	−0.0242426	+	0.0999506i
$582$	0.764190	+	0.160531i	0.0316767	+	0.00665421i
$583$	11.4055	−	19.7549i	0.472367	−	0.818164i
$584$	0.933862	+	1.61750i	0.0386435	+	0.0669325i
$585$	4.15896	−	0.457182i	0.171952	−	0.0189021i
$586$	−0.0479630	−	0.0276914i	−0.00198133	−	0.00114392i
$587$	2.64918			0.109344			0.0546718	−	0.998504i	$-0.482589\pi$
$587$	2.64918			0.109344			0.0546718	+	0.998504i	$0.482589\pi$
$588$	−22.6327	+	8.62878i	−0.933357	+	0.355845i
$589$	−6.45215			−0.265856
$590$	−0.360860	−	0.208343i	−0.0148564	−	0.00857733i
$591$	−28.9586	+	9.48559i	−1.19120	+	0.390185i
$592$	13.3083	+	23.0507i	0.546968	+	0.947376i
$593$	14.5932	−	25.2762i	0.599271	−	1.03797i	−0.393658	−	0.919257i	$-0.628790\pi$
$593$	14.5932	−	25.2762i	0.599271	−	1.03797i	0.992929	−	0.118711i	$-0.0378762\pi$
$594$	1.18587	+	0.848695i	0.0486569	+	0.0348224i
$595$	0.443754	−	1.82957i	0.0181921	−	0.0750051i
$596$		−	1.84300i		−	0.0754920i
$597$	16.0370	+	14.3707i	0.656351	+	0.588154i
$598$	−0.285485	+	0.164825i	−0.0116744	+	0.00674020i
$599$	−22.0715	+	12.7430i	−0.901819	+	0.520665i	−0.877790	−	0.479046i	$-0.840983\pi$
$599$	−22.0715	+	12.7430i	−0.901819	+	0.520665i	−0.0240290	+	0.999711i	$0.507649\pi$
$600$	−0.742189	−	0.665074i	−0.0302998	−	0.0271515i
$601$		−	2.11855i		−	0.0864174i	−0.999066	−	0.0432087i	$-0.986242\pi$
$601$		−	2.11855i		−	0.0864174i	0.999066	−	0.0432087i	$-0.0137580\pi$
$602$	0.769424	−	0.807027i	0.0313594	−	0.0328920i
$603$	−19.4034	−	8.52833i	−0.790166	−	0.347300i
$604$	0.560357	−	0.970566i	0.0228006	−	0.0394918i
$605$	−17.0742	−	29.5734i	−0.694166	−	1.20233i
$606$	1.45957	−	0.478093i	0.0592910	−	0.0194212i
$607$	−2.85584	−	1.64882i	−0.115915	−	0.0669236i	0.440921	−	0.897546i	$-0.354652\pi$
$607$	−2.85584	−	1.64882i	−0.115915	−	0.0669236i	−0.556837	+	0.830622i	$0.687985\pi$
$608$	−2.13102			−0.0864243
$609$	0.760443	+	9.65584i	0.0308147	+	0.391274i
$610$	0.368521			0.0149210
$611$	9.83531	+	5.67842i	0.397894	+	0.229724i
$612$	0.334122	+	3.03950i	0.0135061	+	0.122864i
$613$	−6.85785	−	11.8781i	−0.276986	−	0.479754i	0.693648	−	0.720314i	$-0.256002\pi$
$613$	−6.85785	−	11.8781i	−0.276986	−	0.479754i	−0.970634	+	0.240560i	$0.922669\pi$
$614$	−0.656494	+	1.13708i	−0.0264940	+	0.0458889i
$615$	−13.4907	−	2.83395i	−0.543999	−	0.114276i
$616$	2.84814	−	0.836442i	0.114755	−	0.0337012i
$617$			30.9556i			1.24622i	0.782133	+	0.623112i	$0.214132\pi$
$617$			30.9556i			1.24622i	−0.782133	+	0.623112i	$0.785868\pi$
$618$	−0.508771	+	0.567763i	−0.0204658	+	0.0228388i
$619$	26.4917	−	15.2950i	1.06479	−	0.614758i	0.138038	−	0.990427i	$-0.455920\pi$
$619$	26.4917	−	15.2950i	1.06479	−	0.614758i	0.926754	+	0.375669i	$0.122587\pi$
$620$	−4.12422	+	2.38112i	−0.165633	+	0.0956280i
$621$	−15.0252	−	33.1080i	−0.602942	−	1.32858i
$622$		−	0.387916i		−	0.0155540i
$623$	5.45160	+	5.19758i	0.218414	+	0.208237i
$624$	−1.41956	+	6.75765i	−0.0568277	+	0.270523i
$625$	0.196598	−	0.340518i	0.00786392	−	0.0136207i
$626$	0.684037	+	1.18479i	0.0273396	+	0.0473536i
$627$	−12.1242	−	37.0139i	−0.484192	−	1.47819i
$628$	1.04840	+	0.605296i	0.0418358	+	0.0241539i
$629$	3.40629			0.135818
$630$	−0.414529	−	0.316478i	−0.0165152	−	0.0126088i
$631$	2.96288			0.117951			0.0589753	−	0.998259i	$-0.481217\pi$
$631$	2.96288			0.117951			0.0589753	+	0.998259i	$0.481217\pi$
$632$	−2.01757	−	1.16484i	−0.0802546	−	0.0463350i
$633$	−1.81312	−	5.53528i	−0.0720651	−	0.220008i
$634$	0.270764	+	0.468977i	0.0107534	+	0.0186254i
$635$	6.84662	−	11.8587i	0.271700	−	0.470598i
$636$	2.72402	−	12.9674i	0.108014	−	0.514192i
$637$	−3.20698	+	6.22216i	−0.127065	+	0.246531i
$638$		−	0.593173i		−	0.0234839i
$639$	−13.5851	−	18.5120i	−0.537417	−	0.732324i
$640$	−1.81586	+	1.04839i	−0.0717783	+	0.0414412i
$641$	−14.6925	+	8.48274i	−0.580320	+	0.335048i	−0.761261	−	0.648446i	$-0.775419\pi$
$641$	−14.6925	+	8.48274i	−0.580320	+	0.335048i	0.180940	+	0.983494i	$0.442086\pi$
$642$	−0.102509	+	0.114395i	−0.00404572	+	0.00451482i
$643$		−	3.63792i		−	0.143465i	−0.997424	−	0.0717327i	$-0.977147\pi$
$643$		−	3.63792i		−	0.143465i	0.997424	−	0.0717327i	$-0.0228529\pi$
$644$	−35.9419	−	8.71755i	−1.41631	−	0.343520i
$645$	−21.1475	−	4.44238i	−0.832683	−	0.174919i
$646$	−0.0453691	+	0.0785816i	−0.00178502	+	0.00309175i
$647$	1.40125	+	2.42704i	0.0550889	+	0.0954168i	0.892255	−	0.451532i	$-0.149122\pi$
$647$	1.40125	+	2.42704i	0.0550889	+	0.0954168i	−0.837166	+	0.546949i	$0.815789\pi$
$648$	1.61707	+	0.508422i	0.0635243	+	0.0199727i
$649$	32.7154	+	18.8883i	1.28419	+	0.741429i
$650$	−0.143924			−0.00564514
$651$	6.45474	−	4.43672i	0.252981	−	0.173889i
$652$	−21.4641			−0.840599
$653$	−37.2552	−	21.5093i	−1.45791	−	0.841723i	−0.458999	−	0.888437i	$-0.651792\pi$
$653$	−37.2552	−	21.5093i	−1.45791	−	0.841723i	−0.998908	+	0.0467132i	$0.985125\pi$
$654$	0.102542	−	0.0335884i	0.00400972	−	0.00131341i
$655$	2.25623	+	3.90790i	0.0881581	+	0.152694i
$656$	11.3753	−	19.7026i	0.444130	−	0.769256i
$657$	−11.9705	+	27.2349i	−0.467013	+	1.06253i
$658$	−0.398889	−	1.35825i	−0.0155503	−	0.0529499i
$659$			44.9591i			1.75136i	0.482892	+	0.875680i	$0.339586\pi$
$659$			44.9591i			1.75136i	−0.482892	+	0.875680i	$0.660414\pi$
$660$	−21.4095	−	19.1850i	−0.833362	−	0.746774i
$661$	10.6321	−	6.13846i	0.413542	−	0.238758i	−0.278769	−	0.960358i	$-0.589926\pi$
$661$	10.6321	−	6.13846i	0.413542	−	0.238758i	0.692310	+	0.721600i	$0.256593\pi$
$662$	0.277646	−	0.160299i	0.0107910	−	0.00623019i
$663$	0.658120	+	0.589739i	0.0255593	+	0.0229036i
$664$		−	0.176479i		−	0.00684870i
$665$	3.92504	+	13.3650i	0.152206	+	0.518274i
$666$	0.379691	−	0.863862i	0.0147127	−	0.0334740i
$667$	−7.39452	+	12.8077i	−0.286317	+	0.495916i
$668$	20.6862	+	35.8296i	0.800375	+	1.38629i
$669$	−7.61929	+	2.49575i	−0.294579	+	0.0964914i
$670$	−0.402021	−	0.232107i	−0.0155314	−	0.00896707i
$671$	−33.4099			−1.28978
$672$	2.13188	−	1.46536i	0.0822389	−	0.0565276i
$673$	−6.55223			−0.252570			−0.126285	−	0.991994i	$-0.540305\pi$
$673$	−6.55223			−0.252570			−0.126285	+	0.991994i	$0.540305\pi$
$674$	0.00139038		0.000802737i	5.35555e−5		3.09203e-5i
$675$	1.54631	−	15.7982i	0.0595176	−	0.608072i
$676$	0.998890	+	1.73013i	0.0384189	+	0.0665434i
$677$	−23.1392	+	40.0783i	−0.889312	+	1.54033i	−0.0486212	+	0.998817i	$0.515483\pi$
$677$	−23.1392	+	40.0783i	−0.889312	+	1.54033i	−0.840691	+	0.541516i	$0.817851\pi$
$678$	−0.960923	−	0.201858i	−0.0369040	−	0.00775230i
$679$	24.6047	+	5.96776i	0.944241	+	0.229022i
$680$			0.134020i			0.00513941i
$681$	28.2760	−	31.5546i	1.08354	−	1.20918i
$682$	−0.415413	+	0.239839i	−0.0159070	+	0.00918390i
$683$	26.2137	−	15.1345i	1.00304	−	0.579106i	0.0938944	−	0.995582i	$-0.470068\pi$
$683$	26.2137	−	15.1345i	1.00304	−	0.579106i	0.909147	+	0.416476i	$0.136735\pi$
$684$	−13.3856	−	18.2401i	−0.511810	−	0.697429i
$685$		−	21.8386i		−	0.834408i
$686$	0.824505	−	0.285500i	0.0314797	−	0.0109004i
$687$	−0.139449	+	0.663833i	−0.00532031	+	0.0253268i
$688$	17.8314	−	30.8849i	0.679817	−	1.17748i
$689$	−1.91466	−	3.31629i	−0.0729428	−	0.126341i
$690$	−0.247880	−	0.756754i	−0.00943663	−	0.0288091i
$691$	26.6158	+	15.3667i	1.01251	+	0.584575i	0.911927	−	0.410353i	$-0.134595\pi$
$691$	26.6158	+	15.3667i	1.01251	+	0.584575i	0.100587	+	0.994928i	$0.467928\pi$
$692$	−28.2359			−1.07337
$693$	37.5811	+	28.6917i	1.42759	+	1.08991i
$694$	−0.979616			−0.0371857
$695$	13.1158	+	7.57239i	0.497510	+	0.287237i
$696$	−0.214632	−	0.655250i	−0.00813560	−	0.0248372i
$697$	−1.45576	−	2.52146i	−0.0551410	−	0.0955069i
$698$	−0.768816	+	1.33163i	−0.0291001	+	0.0504029i
$699$	5.06583	−	24.1154i	0.191607	−	0.912128i
$700$	−11.6867	−	11.1421i	−0.441715	−	0.421134i
$701$			12.1625i			0.459370i	0.973265	+	0.229685i	$0.0737696\pi$
$701$			12.1625i			0.459370i	−0.973265	+	0.229685i	$0.926230\pi$
$702$	0.222922	−	0.101167i	0.00841363	−	0.00381832i
$703$	−21.8265	+	12.6015i	−0.823203	+	0.475276i
$704$	40.9962	−	23.6692i	1.54510	−	0.892066i
$705$	−18.3083	+	20.4312i	−0.689531	+	0.769483i
$706$			0.899692i			0.0338604i
$707$	47.7798	−	14.0320i	1.79694	−	0.527726i
$708$	21.4749	+	4.51116i	0.807077	+	0.169540i
$709$	−15.7202	+	27.2282i	−0.590384	+	1.02258i	0.403796	+	0.914849i	$0.367690\pi$
$709$	−15.7202	+	27.2282i	−0.590384	+	1.02258i	−0.994181	+	0.107727i	$0.965643\pi$
$710$	−0.251458	−	0.435537i	−0.00943703	−	0.0163454i
$711$	−4.05471	−	36.8855i	−0.152063	−	1.38331i
$712$	−0.464367	−	0.268102i	−0.0174029	−	0.0100476i
$713$	11.9594			0.447882
$714$	−0.00864811	−	0.109811i	−0.000323647	−	0.00410956i
$715$	−8.30796			−0.310700
$716$	13.4356	+	7.75706i	0.502113	+	0.289895i
$717$	19.7250	−	6.46106i	0.736643	−	0.241293i
$718$	0.0903927	+	0.156565i	0.00337343	+	0.00584295i
$719$	−7.15809	+	12.3982i	−0.266952	+	0.462374i	−0.968073	−	0.250668i	$-0.919350\pi$
$719$	−7.15809	+	12.3982i	−0.266952	+	0.462374i	0.701121	+	0.713042i	$0.252683\pi$
$720$	−15.2704	−	6.71179i	−0.569096	−	0.250134i
$721$	−17.0566	+	17.8902i	−0.635221	+	0.666266i
$722$			0.223766i			0.00832772i
$723$	−20.0590	−	17.9748i	−0.746001	−	0.668490i
$724$	15.4968	−	8.94707i	0.575933	−	0.332515i
$725$	−5.59177	+	3.22841i	−0.207673	+	0.119900i
$726$	−1.48799	−	1.33338i	−0.0552244	−	0.0494864i
$727$			24.8097i			0.920140i	0.887883	+	0.460070i	$0.152176\pi$
$727$			24.8097i			0.920140i	−0.887883	+	0.460070i	$0.847824\pi$
$728$	0.117459	−	0.484274i	0.00435330	−	0.0179484i
$729$	8.70986	+	25.5566i	0.322587	+	0.946540i
$730$	−0.325789	+	0.564283i	−0.0120580	+	0.0208850i
$731$	−2.28199	−	3.95253i	−0.0844026	−	0.146190i
$732$	−18.4430	+	6.04112i	−0.681671	+	0.223286i
$733$	3.85134	+	2.22357i	0.142253	+	0.0821296i	0.569437	−	0.822035i	$-0.307161\pi$
$733$	3.85134	+	2.22357i	0.142253	+	0.0821296i	−0.427185	+	0.904164i	$0.640495\pi$
$734$	1.26419			0.0466621
$735$	−13.1169	−	10.6714i	−0.483823	−	0.393621i
$736$	3.94995			0.145597
$737$	36.4471	+	21.0427i	1.34254	+	0.775118i
$738$	−0.801732	+	0.0881318i	−0.0295121	+	0.00324418i
$739$	4.12989	+	7.15319i	0.151921	+	0.263134i	0.931933	−	0.362629i	$-0.118121\pi$
$739$	4.12989	+	7.15319i	0.151921	+	0.263134i	−0.780013	+	0.625763i	$0.784788\pi$
$740$	−9.30102	+	16.1098i	−0.341912	+	0.592209i
$741$	−6.39878	−	1.34417i	−0.235065	−	0.0493792i
$742$	−0.112509	+	0.463868i	−0.00413034	+	0.0170291i
$743$		−	32.7399i		−	1.20111i	−0.799583	−	0.600556i	$-0.794946\pi$
$743$		−	32.7399i		−	1.20111i	0.799583	−	0.600556i	$-0.205054\pi$
$744$	−0.372105	+	0.415251i	−0.0136420	+	0.0152238i
$745$	1.11424	−	0.643307i	0.0408226	−	0.0235690i
$746$	−0.475816	+	0.274713i	−0.0174209	+	0.0100579i
$747$	2.26623	−	1.66308i	0.0829171	−	0.0608489i
$748$		−	6.07171i		−	0.222004i
$749$	−3.43664	+	3.60459i	−0.125572	+	0.131709i
$750$	0.188455	−	0.897122i	0.00688141	−	0.0327583i
$751$	−14.2807	+	24.7349i	−0.521110	+	0.902590i	0.478588	+	0.878039i	$0.341149\pi$
$751$	−14.2807	+	24.7349i	−0.521110	+	0.902590i	−0.999699	+	0.0245502i	$0.992185\pi$
$752$	−22.6381	−	39.2103i	−0.825526	−	1.42985i
$753$	−1.84958	−	5.64660i	−0.0674026	−	0.205773i
$754$	−0.0862362	−	0.0497885i	−0.00314054	−	0.00181319i
$755$	0.782382			0.0284738
$756$	25.9335	+	9.04308i	0.943192	+	0.328894i
$757$	21.3186			0.774839			0.387420	−	0.921903i	$-0.373366\pi$
$757$	21.3186			0.774839			0.387420	+	0.921903i	$0.373366\pi$
$758$	1.23027	+	0.710296i	0.0446853	+	0.0257991i
$759$	22.4727	+	68.6070i	0.815708	+	2.49028i
$760$	−0.495804	−	0.858759i	−0.0179847	−	0.0311504i
$761$	6.75158	−	11.6941i	0.244745	−	0.423910i	−0.717315	−	0.696749i	$-0.754629\pi$
$761$	6.75158	−	11.6941i	0.244745	−	0.423910i	0.962060	+	0.272839i	$0.0879626\pi$
$762$	0.164706	−	0.784069i	0.00596669	−	0.0284038i
$763$	3.35677	−	0.985816i	0.121523	−	0.0356889i
$764$		−	26.2696i		−	0.950400i
$765$	−1.72100	+	1.26296i	−0.0622228	+	0.0456623i
$766$	1.05126	−	0.606945i	0.0379835	−	0.0219298i
$767$	5.49200	−	3.17081i	0.198305	−	0.114491i
$768$	18.2894	−	20.4101i	0.659963	−	0.736486i
$769$			9.41375i			0.339469i	0.985490	+	0.169734i	$0.0542910\pi$
$769$			9.41375i			0.339469i	−0.985490	+	0.169734i	$0.945709\pi$
$770$	0.749512	+	0.714588i	0.0270105	+	0.0257520i
$771$	−9.33132	−	1.96020i	−0.336059	−	0.0705948i
$772$	−12.1997	+	21.1304i	−0.439075	+	0.760501i
$773$	−2.45165	−	4.24639i	−0.0881799	−	0.152732i	0.818562	−	0.574418i	$-0.194772\pi$
$773$	−2.45165	−	4.24639i	−0.0881799	−	0.152732i	−0.906742	+	0.421686i	$0.861438\pi$
$774$	−1.25676	+	0.138152i	−0.0451734	+	0.00496577i
$775$	4.52186	+	2.61070i	0.162430	+	0.0937790i
$776$	−1.80234			−0.0647002
$777$	13.1700	−	27.6153i	0.472472	−	0.990693i
$778$	−0.486144			−0.0174291
$779$	18.6562	+	10.7712i	0.668429	+	0.385917i
$780$	−4.58616	+	1.50223i	−0.164211	+	0.0537884i
$781$	22.7970	+	39.4856i	0.815742	+	1.41291i
$782$	0.0840938	−	0.145655i	0.00300719	−	0.00520860i
$783$	6.39170	−	8.93104i	0.228421	−	0.319169i
$784$	23.4752	−	15.0899i	0.838401	−	0.538924i
$785$			0.845127i			0.0301639i
$786$	0.196626	+	0.176196i	0.00701342	+	0.00628470i
$787$	−2.94317	+	1.69924i	−0.104913	+	0.0605714i	−0.551538	−	0.834150i	$-0.685959\pi$
$787$	−2.94317	+	1.69924i	−0.104913	+	0.0605714i	0.446626	+	0.894721i	$0.352626\pi$
$788$	30.4387	−	17.5738i	1.08433	−	0.626041i
$789$	−24.2601	−	21.7394i	−0.863682	−	0.773943i
$790$		−	0.812738i		−	0.0289159i
$791$	−30.9389	−	7.50409i	−1.10006	−	0.266815i
$792$	−3.08138	−	1.35435i	−0.109492	−	0.0481248i
$793$	−2.80429	+	4.85718i	−0.0995834	+	0.172484i
$794$	0.157067	+	0.272048i	0.00557410	+	0.00965463i
$795$	8.79070	−	2.87946i	0.311774	−	0.102124i
$796$	−21.5099	−	12.4187i	−0.762397	−	0.440170i
$797$	−17.2587			−0.611334			−0.305667	−	0.952138i	$-0.598879\pi$
$797$	−17.2587			−0.611334			−0.305667	+	0.952138i	$0.598879\pi$
$798$	0.461658	+	0.671641i	0.0163425	+	0.0237758i
$799$	−5.79426			−0.204986
$800$	1.49348	+	0.862264i	0.0528026	+	0.0304856i
$801$	−0.933238	−	8.48963i	−0.0329744	−	0.299966i
$802$	−0.602114	−	1.04289i	−0.0212614	−	0.0368258i
$803$	29.5359	−	51.1576i	1.04230	−	1.80531i
$804$	23.9244	+	5.02571i	0.843749	+	0.177243i
$805$	−7.27525	−	24.7727i	−0.256419	−	0.873124i
$806$			0.0805244i			0.00283635i
$807$	30.5381	−	34.0790i	1.07499	−	1.19964i
$808$	−3.07005	+	1.77249i	−0.108004	+	0.0623561i
$809$	19.8615	−	11.4670i	0.698293	−	0.403159i	−0.108419	−	0.994105i	$-0.534579\pi$
$809$	19.8615	−	11.4670i	0.698293	−	0.403159i	0.806711	+	0.590946i	$0.201245\pi$
$810$	0.128460	+	0.577237i	0.00451363	+	0.0202820i
$811$			9.49798i			0.333519i	0.985998	+	0.166760i	$0.0533304\pi$
$811$			9.49798i			0.333519i	−0.985998	+	0.166760i	$0.946670\pi$
$812$	−3.14796	−	10.7190i	−0.110472	−	0.376164i
$813$	−2.01920	+	9.61219i	−0.0708163	+	0.337114i
$814$	−0.936847	+	1.62267i	−0.0328365	+	0.0568745i
$815$	−7.49216	−	12.9768i	−0.262439	−	0.454557i
$816$	−1.09665	−	3.34798i	−0.0383905	−	0.117203i
$817$	29.2447	+	16.8845i	1.02314	+	0.590712i
$818$	0.222867			0.00779237
$819$	7.32564	−	3.05531i	0.255979	−	0.106761i
$820$	15.9001			0.555255
$821$	−8.72565	−	5.03775i	−0.304527	−	0.175819i	0.339948	−	0.940444i	$-0.389591\pi$
$821$	−8.72565	−	5.03775i	−0.304527	−	0.175819i	−0.644475	+	0.764626i	$0.722924\pi$
$822$	−0.397745	−	1.21428i	−0.0138729	−	0.0423527i
$823$	1.40958	+	2.44147i	0.0491349	+	0.0851042i	0.889547	−	0.456844i	$-0.151020\pi$
$823$	1.40958	+	2.44147i	0.0491349	+	0.0851042i	−0.840412	+	0.541948i	$0.817687\pi$
$824$	0.879817	−	1.52389i	0.0306499	−	0.0530871i
$825$	−6.47975	+	30.8462i	−0.225596	+	1.07393i
$826$	−0.768197	−	0.186323i	−0.0267290	−	0.00648299i
$827$		−	46.2282i		−	1.60751i	−0.594959	−	0.803756i	$-0.702832\pi$
$827$		−	46.2282i		−	1.60751i	0.594959	−	0.803756i	$-0.297168\pi$
$828$	24.8108	+	33.8090i	0.862234	+	1.17494i
$829$	−16.9441	+	9.78266i	−0.588492	+	0.339766i	−0.764501	−	0.644623i	$-0.777014\pi$
$829$	−16.9441	+	9.78266i	−0.588492	+	0.339766i	0.176009	+	0.984389i	$0.443681\pi$
$830$	0.0533183	−	0.0307833i	0.00185070	−	0.00106850i
$831$	−18.1158	+	20.2164i	−0.628431	+	0.701299i
$832$		−	7.94678i		−	0.275505i
$833$	−0.170284	−	3.56734i	−0.00589998	−	0.123601i
$834$	0.867184	+	0.182166i	0.0300281	+	0.00630790i
$835$	−14.4413	+	25.0130i	−0.499761	+	0.865612i
$836$	22.4622	+	38.9057i	0.776873	+	1.34558i
$837$	−8.83899	−	0.865153i	−0.305520	−	0.0299041i
$838$	−1.39165	−	0.803471i	−0.0480738	−	0.0277554i
$839$	4.21576			0.145544			0.0727720	−	0.997349i	$-0.476815\pi$
$839$	4.21576			0.145544			0.0727720	+	0.997349i	$0.476815\pi$
$840$	1.08652	+	0.518171i	0.0374884	+	0.0178786i
$841$	24.5327			0.845955
$842$	−0.803179	−	0.463716i	−0.0276794	−	0.0159807i
$843$	−35.9356	+	11.7710i	−1.23769	+	0.405414i
$844$	3.35914	+	5.81820i	0.115626	+	0.200271i
$845$	−0.697336	+	1.20782i	−0.0239891	+	0.0415503i
$846$	−0.645874	+	1.46947i	−0.0222056	+	0.0505214i
$847$	−46.8865	−	44.7018i	−1.61104	−	1.53597i
$848$			15.2663i			0.524247i
$849$	−15.6990	−	14.0679i	−0.538790	−	0.482808i
$850$	0.0635921	−	0.0367149i	0.00218119	−	0.00125931i
$851$	40.4565	−	23.3576i	1.38683	−	0.800687i
$852$	19.7241	+	17.6747i	0.675738	+	0.605527i
$853$			8.63160i			0.295541i	0.989022	+	0.147770i	$0.0472096\pi$
$853$			8.63160i			0.295541i	−0.989022	+	0.147770i	$0.952790\pi$
$854$	0.670771	−	0.196992i	0.0229533	−	0.00674092i
$855$	6.35535	−	14.4595i	0.217348	−	0.494504i
$856$	0.177269	−	0.307039i	0.00605893	−	0.0104944i
$857$	9.20833	+	15.9493i	0.314550	+	0.544817i	0.979342	−	0.202212i	$-0.0648129\pi$
$857$	9.20833	+	15.9493i	0.314550	+	0.544817i	−0.664791	+	0.747029i	$0.731480\pi$
$858$	−0.461942	+	0.151312i	−0.0157704	+	0.00516572i
$859$	−26.5396	−	15.3226i	−0.905518	−	0.522801i	−0.0265319	−	0.999648i	$-0.508446\pi$
$859$	−26.5396	−	15.3226i	−0.905518	−	0.522801i	−0.878986	+	0.476847i	$0.841780\pi$
$860$	24.9243			0.849913
$861$	−26.0703	+	2.05316i	−0.888475	+	0.0699717i
$862$	0.299853			0.0102130
$863$	6.85369	+	3.95698i	0.233302	+	0.134697i	0.612095	−	0.790785i	$-0.290327\pi$
$863$	6.85369	+	3.95698i	0.233302	+	0.134697i	−0.378792	+	0.925482i	$0.623661\pi$
$864$	−2.91935	−	0.285744i	−0.0993182	−	0.00972120i
$865$	−9.85588	−	17.0709i	−0.335110	−	0.580427i
$866$	−0.807084	+	1.39791i	−0.0274258	+	0.0475029i
$867$	28.3747	+	5.96057i	0.963655	+	0.202432i
$868$	−6.23396	+	6.53864i	−0.211595	+	0.221936i
$869$			73.6825i			2.49951i
$870$	0.160528	−	0.179141i	0.00544240	−	0.00607345i
$871$	6.11844	−	3.53248i	0.207315	−	0.119694i
$872$	−0.215687	+	0.124527i	−0.00730407	+	0.00421701i
$873$	−16.9847	−	23.1445i	−0.574844	−	0.783324i
$874$			1.24442i			0.0420931i
$875$	7.00586	−	28.8847i	0.236841	−	0.976481i
$876$	7.05417	−	33.5807i	0.238338	−	1.13459i
$877$	18.2634	−	31.6332i	0.616712	−	1.06818i	−0.373369	−	0.927683i	$-0.621798\pi$
$877$	18.2634	−	31.6332i	0.616712	−	1.06818i	0.990082	−	0.140494i	$-0.0448691\pi$
$878$	0.522448	+	0.904906i	0.0176318	+	0.0305391i
$879$	0.633805	+	1.93495i	0.0213777	+	0.0652641i
$880$	28.6838	+	16.5606i	0.966931	+	0.558258i
$881$	−45.9203			−1.54709			−0.773547	−	0.633739i	$-0.781519\pi$
$881$	−45.9203			−1.54709			−0.773547	+	0.633739i	$0.781519\pi$
$882$	−0.923687	−	0.354458i	−0.0311022	−	0.0119352i
$883$	7.06173			0.237646			0.118823	−	0.992915i	$-0.462088\pi$
$883$	7.06173			0.237646			0.118823	+	0.992915i	$0.462088\pi$
$884$	−0.882712	−	0.509634i	−0.0296888	−	0.0171409i
$885$	4.76857	+	14.5580i	0.160294	+	0.489361i
$886$	−0.546915	−	0.947284i	−0.0183740	−	0.0318246i
$887$	−3.80222	+	6.58565i	−0.127666	+	0.221124i	−0.922772	−	0.385346i	$-0.874082\pi$
$887$	−3.80222	+	6.58565i	−0.127666	+	0.221124i	0.795106	+	0.606471i	$0.207415\pi$
$888$	−0.447750	+	2.13147i	−0.0150255	+	0.0715275i
$889$	6.12299	−	25.2447i	0.205359	−	0.846680i
$890$		−	0.187061i		−	0.00627031i
$891$	−11.6461	−	52.3321i	−0.390160	−	1.75319i
$892$	8.00873	−	4.62384i	0.268152	−	0.154818i
$893$	37.1280	−	21.4358i	1.24244	−	0.717323i
$894$	0.0502379	−	0.0560630i	0.00168021	−	0.00187503i
$895$			10.8306i			0.362026i
$896$	−2.74477	+	2.87891i	−0.0916963	+	0.0961778i
$897$	11.8604	+	2.49148i	0.396009	+	0.0831881i
$898$	−0.271656	+	0.470522i	−0.00906528	+	0.0157015i
$899$	1.80628	+	3.12856i	0.0602427	+	0.104343i
$900$	2.00060	+	18.1994i	0.0666867	+	0.606646i
$901$	1.69197	+	0.976861i	0.0563678	+	0.0325440i
$902$	1.60154			0.0533255
$903$	−40.8668	+	3.21846i	−1.35996	+	0.107104i
$904$	2.26633			0.0753772
$905$	10.8185	+	6.24605i	0.359618	+	0.207626i
$906$	0.0435023	−	0.0142495i	0.00144527	−	0.000473408i
$907$	−7.37930	−	12.7813i	−0.245026	−	0.424397i	0.717113	−	0.696957i	$-0.245463\pi$
$907$	−7.37930	−	12.7813i	−0.245026	−	0.424397i	−0.962139	+	0.272560i	$0.912130\pi$
$908$	−24.4352	+	42.3231i	−0.810912	+	1.40454i
$909$	−51.6924	−	22.7203i	−1.71453	−	0.753584i
$910$	0.166799	−	0.0489854i	0.00552933	−	0.00162385i
$911$			6.09339i			0.201883i	0.994892	+	0.100942i	$0.0321855\pi$
$911$			6.09339i			0.201883i	−0.994892	+	0.100942i	$0.967814\pi$
$912$	19.4129	+	17.3958i	0.642824	+	0.576033i
$913$	−4.83381	+	2.79080i	−0.159976	+	0.0923621i
$914$	−0.196331	+	0.113352i	−0.00649406	+	0.00374935i
$915$	−10.0900	−	9.04159i	−0.333564	−	0.298906i
$916$		−	0.782389i		−	0.0258509i
$917$	6.19568	+	5.90699i	0.204599	+	0.195066i
$918$	−0.0726893	+	0.101568i	−0.00239910	+	0.00335224i
$919$	−19.8834	+	34.4391i	−0.655894	+	1.13604i	0.325775	+	0.945447i	$0.394375\pi$
$919$	−19.8834	+	34.4391i	−0.655894	+	1.13604i	−0.981669	+	0.190594i	$0.938959\pi$
$920$	0.918997	+	1.59175i	0.0302984	+	0.0524785i
$921$	45.8727	−	15.0259i	1.51156	−	0.495121i
$922$	−0.807219	−	0.466048i	−0.0265843	−	0.0153485i
$923$	7.65396			0.251933
$924$	−49.2242	−	23.4756i	−1.61936	−	0.772289i
$925$	20.3956			0.670603
$926$	−0.489769	−	0.282768i	−0.0160948	−	0.00929235i
$927$	27.8599	−	3.06256i	0.915040	−	0.100588i
$928$	0.596578	+	1.03330i	0.0195836	+	0.0339199i
$929$	−7.29075	+	12.6279i	−0.239202	+	0.414310i	−0.960485	−	0.278330i	$-0.910219\pi$
$929$	−7.29075	+	12.6279i	−0.239202	+	0.414310i	0.721284	+	0.692640i	$0.243552\pi$
$930$	−0.190363	−	0.0399889i	−0.00624226	−	0.00131129i
$931$	14.2885	+	22.2285i	0.468286	+	0.728511i
$932$			28.4222i			0.931001i
$933$	−9.51746	+	10.6210i	−0.311588	+	0.347716i
$934$	0.836079	−	0.482710i	0.0273573	−	0.0157948i
$935$	3.67084	−	2.11936i	0.120049	−	0.0693105i
$936$	−0.455535	+	0.334296i	−0.0148896	+	0.0109268i
$937$		−	29.0746i		−	0.949825i	−0.880033	−	0.474913i	$-0.842480\pi$
$937$		−	29.0746i		−	0.949825i	0.880033	−	0.474913i	$-0.157520\pi$
$938$	−0.855819	−	0.207575i	−0.0279435	−	0.00677757i
$939$	10.3398	−	49.2218i	0.337428	−	1.60629i
$940$	15.8215	−	27.4036i	0.516040	−	0.893807i
$941$	27.1990	+	47.1100i	0.886661	+	1.53574i	0.843798	+	0.536661i	$0.180315\pi$
$941$	27.1990	+	47.1100i	0.886661	+	1.53574i	0.0428636	+	0.999081i	$0.486352\pi$
$942$	0.0153923	+	0.0469910i	0.000501507	+	0.00153105i
$943$	−34.5802	−	19.9649i	−1.12609	−	0.650146i
$944$	−25.2820			−0.822860
$945$	3.58494	+	18.8354i	0.116618	+	0.612717i
$946$	2.51051			0.0816237
$947$	−30.9506	−	17.8694i	−1.00576	−	0.580676i	−0.0958132	−	0.995399i	$-0.530545\pi$
$947$	−30.9506	−	17.8694i	−1.00576	−	0.580676i	−0.909948	+	0.414723i	$0.863878\pi$
$948$	13.3231	+	40.6742i	0.432715	+	1.32104i
$949$	−4.95824	−	8.58793i	−0.160951	−	0.278776i
$950$	−0.271653	+	0.470517i	−0.00881360	+	0.0152656i
$951$	4.09284	−	19.4835i	0.132719	−	0.631797i
$952$	0.0716398	+	0.243939i	0.00232186	+	0.00790610i
$953$		−	37.6492i		−	1.21958i	−0.792564	−	0.609789i	$-0.791254\pi$
$953$		−	37.6492i		−	1.21958i	0.792564	−	0.609789i	$-0.208746\pi$
$954$	0.436340	−	0.320209i	0.0141270	−	0.0103672i
$955$	15.8821	−	9.16954i	0.513933	−	0.296719i
$956$	−20.7332	+	11.9703i	−0.670559	+	0.387148i
$957$	−14.5534	+	16.2409i	−0.470444	+	0.524992i
$958$		−	0.378874i		−	0.0122409i
$959$	−11.6737	−	39.7499i	−0.376965	−	1.28359i
$960$	18.7865	+	3.94642i	0.606333	+	0.127370i
$961$	−14.0393	+	24.3168i	−0.452882	+	0.784414i
$962$	0.157270	+	0.272400i	0.00507060	+	0.00878254i
$963$	5.61333	−	0.617056i	0.180887	−	0.0198844i
$964$	26.9044	+	15.5333i	0.866532	+	0.500293i
$965$	−17.0334			−0.548326
$966$	−0.855705	−	1.24492i	−0.0275319	−	0.0400546i
$967$	8.46304			0.272153			0.136076	−	0.990698i	$-0.456551\pi$
$967$	8.46304			0.272153			0.136076	+	0.990698i	$0.456551\pi$
$968$	3.99379	+	2.30581i	0.128365	+	0.0741117i
$969$	3.17018	−	1.03841i	0.101841	−	0.0333587i
$970$	−0.314384	−	0.544528i	−0.0100942	−	0.0174838i
$971$	−19.1309	+	33.1358i	−0.613941	+	1.06338i	0.376628	+	0.926365i	$0.377083\pi$
$971$	−19.1309	+	33.1358i	−0.613941	+	1.06338i	−0.990569	+	0.137013i	$0.956250\pi$
$972$	−15.8915	−	26.7825i	−0.509720	−	0.859050i
$973$	27.9208	+	6.77206i	0.895099	+	0.217102i
$974$			1.24025i			0.0397402i
$975$	3.94057	+	3.53114i	0.126199	+	0.113087i
$976$	19.3641	−	11.1798i	0.619828	−	0.357858i
$977$	−18.2978	+	10.5643i	−0.585400	+	0.337981i	−0.763277	−	0.646072i	$-0.776411\pi$
$977$	−18.2978	+	10.5643i	−0.585400	+	0.337981i	0.177876	+	0.984053i	$0.443077\pi$
$978$	−0.652928	−	0.585086i	−0.0208783	−	0.0187090i
$979$			16.9589i			0.542009i
$980$	17.3365	+	8.93543i	0.553794	+	0.285432i
$981$	−3.63166	−	1.59621i	−0.115950	−	0.0509632i
$982$	−0.952051	+	1.64900i	−0.0303812	+	0.0526217i
$983$	−3.40625	−	5.89980i	−0.108643	−	0.188174i	0.806578	−	0.591128i	$-0.201317\pi$
$983$	−3.40625	−	5.89980i	−0.108643	−	0.188174i	−0.915221	+	0.402953i	$0.867984\pi$
$984$	1.76915	−	0.579497i	0.0563984	−	0.0184737i
$985$	21.2496	+	12.2685i	0.677068	+	0.390906i
$986$	0.0508042			0.00161794
$987$	−22.4029	+	46.9749i	−0.713091	+	1.49523i
$988$	7.54156			0.239929
$989$	−54.2065	−	31.2961i	−1.72367	−	0.995160i
$990$	−0.128306	−	1.16719i	−0.00407784	−	0.0370959i
$991$	23.8940	+	41.3857i	0.759019	+	1.31466i	0.943351	+	0.331795i	$0.107654\pi$
$991$	23.8940	+	41.3857i	0.759019	+	1.31466i	−0.184333	+	0.982864i	$0.559012\pi$
$992$	0.482431	−	0.835596i	0.0153172	−	0.0265302i
$993$	−11.5347	−	2.42306i	−0.366044	−	0.0768935i
$994$	−0.690511	−	0.658337i	−0.0219017	−	0.0208812i
$995$		−	17.3393i		−	0.549693i
$996$	−2.16373	+	2.41462i	−0.0685605	+	0.0765102i
$997$	32.1799	−	18.5791i	1.01915	−	0.588404i	0.105290	−	0.994442i	$-0.466423\pi$
$997$	32.1799	−	18.5791i	1.01915	−	0.588404i	0.913857	+	0.406037i	$0.133090\pi$
$998$	0.0611659	−	0.0353141i	0.00193617	−	0.00111785i
$999$	−31.5905	+	14.3366i	−0.999479	+	0.453589i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.bh.a.131.16	✓	64
3.2	odd	2	inner	273.2.bh.a.131.17	yes	64
7.3	odd	6	inner	273.2.bh.a.248.17	yes	64
21.17	even	6	inner	273.2.bh.a.248.16	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.bh.a.131.16	✓	64	1.1	even	1	trivial
273.2.bh.a.131.17	yes	64	3.2	odd	2	inner
273.2.bh.a.248.16	yes	64	21.17	even	6	inner
273.2.bh.a.248.17	yes	64	7.3	odd	6	inner

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:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.bh (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0408006 - 0.0235563i) q^{2} +(0.539158 + 1.64600i) q^{3} +(-0.998890 - 1.73013i) q^{4} +(0.697336 - 1.20782i) q^{5} +(0.0167755 - 0.0798583i) q^{6} +(0.623634 - 2.57120i) q^{7} +0.188345i q^{8} +(-2.41862 + 1.77491i) q^{9} +O(q^{10})\)	\(q+(-0.0408006 - 0.0235563i) q^{2} +(0.539158 + 1.64600i) q^{3} +(-0.998890 - 1.73013i) q^{4} +(0.697336 - 1.20782i) q^{5} +(0.0167755 - 0.0798583i) q^{6} +(0.623634 - 2.57120i) q^{7} +0.188345i q^{8} +(-2.41862 + 1.77491i) q^{9} +(-0.0569035 + 0.0328532i) q^{10} +(5.15885 - 2.97846i) q^{11} +(2.30923 - 2.57698i) q^{12} -1.00000i q^{13} +(-0.0860125 + 0.0902162i) q^{14} +(2.36405 + 0.496606i) q^{15} +(-1.99334 + 3.45257i) q^{16} +(0.255100 + 0.441847i) q^{17} +(0.140491 - 0.0154438i) q^{18} +(-3.26922 - 1.88748i) q^{19} -2.78625 q^{20} +(4.56843 - 0.359786i) q^{21} -0.280646 q^{22} +(6.05965 + 3.49854i) q^{23} +(-0.310016 + 0.101548i) q^{24} +(1.52745 + 2.64561i) q^{25} +(-0.0235563 + 0.0408006i) q^{26} +(-4.22551 - 3.02408i) q^{27} +(-5.07145 + 1.48938i) q^{28} +2.11360i q^{29} +(-0.0847564 - 0.0759499i) q^{30} +(1.48020 - 0.854596i) q^{31} +(0.488883 - 0.282257i) q^{32} +(7.68398 + 6.88559i) q^{33} -0.0240368i q^{34} +(-2.67067 - 2.54623i) q^{35} +(5.48675 + 2.41158i) q^{36} +(3.33819 - 5.78191i) q^{37} +(0.0889241 + 0.154021i) q^{38} +(1.64600 - 0.539158i) q^{39} +(0.227488 + 0.131340i) q^{40} -5.70663 q^{41} +(-0.194870 - 0.0929356i) q^{42} -8.94548 q^{43} +(-10.3062 - 5.95031i) q^{44} +(0.457182 + 4.15896i) q^{45} +(-0.164825 - 0.285485i) q^{46} +(-5.67842 + 9.83531i) q^{47} +(-6.75765 - 1.41956i) q^{48} +(-6.22216 - 3.20698i) q^{49} -0.143924i q^{50} +(-0.589739 + 0.658120i) q^{51} +(-1.73013 + 0.998890i) q^{52} +(3.31629 - 1.91466i) q^{53} +(0.101167 + 0.222922i) q^{54} -8.30796i q^{55} +(0.484274 + 0.117459i) q^{56} +(1.34417 - 6.39878i) q^{57} +(0.0497885 - 0.0862362i) q^{58} +(3.17081 + 5.49200i) q^{59} +(-1.50223 - 4.58616i) q^{60} +(-4.85718 - 2.80429i) q^{61} -0.0805244 q^{62} +(3.05531 + 7.32564i) q^{63} +7.94678 q^{64} +(-1.20782 - 0.697336i) q^{65} +(-0.151312 - 0.461942i) q^{66} +(3.53248 + 6.11844i) q^{67} +(0.509634 - 0.882712i) q^{68} +(-2.49148 + 11.8604i) q^{69} +(0.0489854 + 0.166799i) q^{70} +7.65396i q^{71} +(-0.334296 - 0.455535i) q^{72} +(8.58793 - 4.95824i) q^{73} +(-0.272400 + 0.157270i) q^{74} +(-3.53114 + 3.94057i) q^{75} +7.54156i q^{76} +(-4.44100 - 15.1219i) q^{77} +(-0.0798583 - 0.0167755i) q^{78} +(-6.18461 + 10.7121i) q^{79} +(2.78006 + 4.81521i) q^{80} +(2.69941 - 8.58564i) q^{81} +(0.232834 + 0.134427i) q^{82} -0.936995 q^{83} +(-5.18584 - 7.54459i) q^{84} +0.711562 q^{85} +(0.364981 + 0.210722i) q^{86} +(-3.47898 + 1.13957i) q^{87} +(0.560980 + 0.971645i) q^{88} +(-1.42346 + 2.46551i) q^{89} +(0.0793163 - 0.180458i) q^{90} +(-2.57120 - 0.623634i) q^{91} -13.9786i q^{92} +(2.20473 + 1.97565i) q^{93} +(0.463366 - 0.267525i) q^{94} +(-4.55949 + 2.63242i) q^{95} +(0.728180 + 0.652519i) q^{96} +9.56933i q^{97} +(0.178324 + 0.277417i) q^{98} +(-7.19078 + 16.3602i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 32 q^{4} - 4 q^{7} - 4 q^{9}+O(q^{10}) \) 64 * q + 32 * q^4 - 4 * q^7 - 4 * q^9	\( 64 q + 32 q^{4} - 4 q^{7} - 4 q^{9} - 12 q^{10} - 30 q^{12} + 12 q^{15} - 16 q^{16} - 10 q^{18} + 10 q^{21} - 8 q^{22} + 36 q^{24} - 36 q^{25} - 20 q^{28} - 22 q^{30} + 12 q^{31} + 36 q^{36} - 36 q^{40} + 48 q^{42} - 32 q^{43} - 6 q^{45} - 48 q^{46} + 36 q^{49} - 16 q^{51} - 54 q^{54} - 8 q^{57} - 12 q^{58} + 16 q^{60} - 72 q^{61} - 86 q^{63} - 48 q^{64} - 78 q^{66} + 32 q^{67} - 4 q^{70} + 62 q^{72} + 48 q^{73} + 48 q^{75} - 20 q^{78} - 64 q^{79} + 28 q^{81} + 72 q^{82} - 18 q^{84} + 64 q^{85} + 60 q^{87} + 44 q^{88} + 8 q^{91} - 38 q^{93} + 72 q^{94} + 66 q^{96} - 68 q^{99}+O(q^{100}) \) 64 * q + 32 * q^4 - 4 * q^7 - 4 * q^9 - 12 * q^10 - 30 * q^12 + 12 * q^15 - 16 * q^16 - 10 * q^18 + 10 * q^21 - 8 * q^22 + 36 * q^24 - 36 * q^25 - 20 * q^28 - 22 * q^30 + 12 * q^31 + 36 * q^36 - 36 * q^40 + 48 * q^42 - 32 * q^43 - 6 * q^45 - 48 * q^46 + 36 * q^49 - 16 * q^51 - 54 * q^54 - 8 * q^57 - 12 * q^58 + 16 * q^60 - 72 * q^61 - 86 * q^63 - 48 * q^64 - 78 * q^66 + 32 * q^67 - 4 * q^70 + 62 * q^72 + 48 * q^73 + 48 * q^75 - 20 * q^78 - 64 * q^79 + 28 * q^81 + 72 * q^82 - 18 * q^84 + 64 * q^85 + 60 * q^87 + 44 * q^88 + 8 * q^91 - 38 * q^93 + 72 * q^94 + 66 * q^96 - 68 * q^99

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