LMFDB - Embedded newform 189.2.e.e.163.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,2,Mod(109,189)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(189, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("189.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	189.e (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.50917259820$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.309123.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 $ x^6 - 3x^5 + 10x^4 - 15x^3 + 19x^2 - 12*x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			163.3
Root			$0.500000 + 2.05195i$ of defining polynomial
Character	$\chi$	$=$	189.163
Dual form			189.2.e.e.109.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.730252 - 1.26483i) q^{2} +(-0.0665372 - 0.115246i) q^{4} +(0.296790 - 0.514055i) q^{5} +(2.32383 + 1.26483i) q^{7} +2.72665 q^{8} +O(q^{10})$	\(q+(0.730252 - 1.26483i) q^{2} +(-0.0665372 - 0.115246i) q^{4} +(0.296790 - 0.514055i) q^{5} +(2.32383 + 1.26483i) q^{7} +2.72665 q^{8} +(-0.433463 - 0.750780i) q^{10} +(-2.23025 - 3.86291i) q^{11} -4.51459 q^{13} +(3.29679 - 2.01561i) q^{14} +(2.12422 - 3.67926i) q^{16} +(0.136673 + 0.236725i) q^{17} +(-1.43346 + 2.48283i) q^{19} -0.0789903 q^{20} -6.51459 q^{22} +(-2.52704 + 4.37697i) q^{23} +(2.32383 + 4.02499i) q^{25} +(-3.29679 + 5.71021i) q^{26} +(-0.00885441 - 0.351971i) q^{28} +0.352336 q^{29} +(-1.25729 - 2.17770i) q^{31} +(-0.375780 - 0.650870i) q^{32} +0.399223 q^{34} +(1.33988 - 0.819187i) q^{35} +(3.32383 - 5.75705i) q^{37} +(2.09358 + 3.62619i) q^{38} +(0.809243 - 1.40165i) q^{40} -10.8961 q^{41} +3.38151 q^{43} +(-0.296790 + 0.514055i) q^{44} +(3.69076 + 6.39258i) q^{46} +(-6.21780 + 10.7695i) q^{47} +(3.80039 + 5.87852i) q^{49} +6.78794 q^{50} +(0.300388 + 0.520288i) q^{52} +(-5.66372 - 9.80984i) q^{53} -2.64766 q^{55} +(6.33628 + 3.44877i) q^{56} +(0.257295 - 0.445647i) q^{58} +(4.02704 + 6.97504i) q^{59} +(1.36693 - 2.36758i) q^{61} -3.67257 q^{62} +7.39922 q^{64} +(-1.33988 + 2.32075i) q^{65} +(-2.93346 - 5.08091i) q^{67} +(0.0181877 - 0.0315020i) q^{68} +(-0.0576828 - 2.29294i) q^{70} +2.60078 q^{71} +(-5.55768 - 9.62619i) q^{73} +(-4.85447 - 8.40819i) q^{74} +0.381515 q^{76} +(-0.296790 - 11.7977i) q^{77} +(-5.58113 + 9.66679i) q^{79} +(-1.26089 - 2.18393i) q^{80} +(-7.95691 + 13.7818i) q^{82} +16.5438 q^{83} +0.162253 q^{85} +(2.46936 - 4.27706i) q^{86} +(-6.08113 - 10.5328i) q^{88} +(2.68716 - 4.65430i) q^{89} +(-10.4911 - 5.71021i) q^{91} +0.672570 q^{92} +(9.08113 + 15.7290i) q^{94} +(0.850874 + 1.47376i) q^{95} -2.26615 q^{97} +(10.2106 - 0.514055i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 2 q^{2} - 4 q^{4} - q^{5} + 2 q^{7} + 18 q^{8}+O(q^{10}) $ 6 * q - 2 * q^2 - 4 * q^4 - q^5 + 2 * q^7 + 18 * q^8	$ 6 q - 2 q^{2} - 4 q^{4} - q^{5} + 2 q^{7} + 18 q^{8} + q^{10} - 7 q^{11} + 4 q^{13} + 17 q^{14} - 10 q^{16} - 5 q^{19} - 26 q^{20} - 8 q^{22} - 6 q^{23} + 2 q^{25} - 17 q^{26} - 30 q^{28} + 26 q^{29} + 8 q^{31} - 25 q^{32} + 24 q^{34} + 10 q^{35} + 8 q^{37} + 7 q^{38} + 24 q^{40} + 4 q^{41} - 18 q^{43} + q^{44} + 3 q^{46} - 9 q^{47} + 12 q^{49} + 8 q^{50} - 9 q^{52} - 24 q^{53} + 8 q^{55} + 48 q^{56} - 14 q^{58} + 15 q^{59} + q^{61} - 42 q^{62} + 66 q^{64} - 10 q^{65} - 14 q^{67} - 39 q^{68} + 26 q^{70} - 6 q^{71} - 7 q^{73} - 36 q^{76} + q^{77} - 6 q^{79} + 16 q^{80} - 43 q^{82} + 6 q^{83} - 54 q^{85} + 32 q^{86} - 9 q^{88} + 5 q^{89} - 33 q^{91} + 24 q^{92} + 27 q^{94} - 16 q^{95} - 28 q^{97} + 49 q^{98}+O(q^{100}) $ 6 * q - 2 * q^2 - 4 * q^4 - q^5 + 2 * q^7 + 18 * q^8 + q^10 - 7 * q^11 + 4 * q^13 + 17 * q^14 - 10 * q^16 - 5 * q^19 - 26 * q^20 - 8 * q^22 - 6 * q^23 + 2 * q^25 - 17 * q^26 - 30 * q^28 + 26 * q^29 + 8 * q^31 - 25 * q^32 + 24 * q^34 + 10 * q^35 + 8 * q^37 + 7 * q^38 + 24 * q^40 + 4 * q^41 - 18 * q^43 + q^44 + 3 * q^46 - 9 * q^47 + 12 * q^49 + 8 * q^50 - 9 * q^52 - 24 * q^53 + 8 * q^55 + 48 * q^56 - 14 * q^58 + 15 * q^59 + q^61 - 42 * q^62 + 66 * q^64 - 10 * q^65 - 14 * q^67 - 39 * q^68 + 26 * q^70 - 6 * q^71 - 7 * q^73 - 36 * q^76 + q^77 - 6 * q^79 + 16 * q^80 - 43 * q^82 + 6 * q^83 - 54 * q^85 + 32 * q^86 - 9 * q^88 + 5 * q^89 - 33 * q^91 + 24 * q^92 + 27 * q^94 - 16 * q^95 - 28 * q^97 + 49 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/189\mathbb{Z}\right)^\times$.

$n$	$29$	$136$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	0.730252	−	1.26483i	0.516366	−	0.894373i	−0.483453	−	0.875370i	$-0.660618\pi$
$2$	0.730252	−	1.26483i	0.516366	−	0.894373i	0.999819	−	0.0190026i	$-0.00604908\pi$
$3$		0			0
$3$		0			0
$4$	−0.0665372	−	0.115246i	−0.0332686	−	0.0576229i
$5$	0.296790	−	0.514055i	0.132728	−	0.229892i	−0.791999	−	0.610522i	$-0.790960\pi$
$5$	0.296790	−	0.514055i	0.132728	−	0.229892i	0.924727	+	0.380630i	$0.124293\pi$
$6$		0			0
$7$	2.32383	+	1.26483i	0.878326	+	0.478062i
$7$	2.32383	+	1.26483i	0.878326	+	0.478062i
$8$	2.72665			0.964018
$9$		0			0
$10$	−0.433463	−	0.750780i	−0.137073	−	0.237417i
$11$	−2.23025	−	3.86291i	−0.672446	−	1.16471i	−0.977208	−	0.212283i	$-0.931910\pi$
$11$	−2.23025	−	3.86291i	−0.672446	−	1.16471i	0.304762	−	0.952429i	$-0.401423\pi$
$12$		0			0
$13$	−4.51459			−1.25212			−0.626061	−	0.779774i	$-0.715334\pi$
$13$	−4.51459			−1.25212			−0.626061	+	0.779774i	$0.715334\pi$
$14$	3.29679	−	2.01561i	0.881104	−	0.538695i
$15$		0			0
$16$	2.12422	−	3.67926i	0.531055	−	0.919814i
$17$	0.136673	+	0.236725i	0.0331481	+	0.0574142i	0.882124	−	0.471018i	$-0.156113\pi$
$17$	0.136673	+	0.236725i	0.0331481	+	0.0574142i	−0.848975	+	0.528432i	$0.822780\pi$
$18$		0			0
$19$	−1.43346	+	2.48283i	−0.328859	+	0.569600i	−0.982286	−	0.187389i	$-0.939997\pi$
$19$	−1.43346	+	2.48283i	−0.328859	+	0.569600i	0.653427	+	0.756990i	$0.273331\pi$
$20$	−0.0789903			−0.0176628
$21$		0			0
$22$	−6.51459			−1.38892
$23$	−2.52704	+	4.37697i	−0.526925	+	0.912660i	0.472583	+	0.881286i	$0.343322\pi$
$23$	−2.52704	+	4.37697i	−0.526925	+	0.912660i	−0.999508	+	0.0313742i	$0.990012\pi$
$24$		0			0
$25$	2.32383	+	4.02499i	0.464766	+	0.804999i
$26$	−3.29679	+	5.71021i	−0.646554	+	1.11986i
$27$		0			0
$28$	−0.00885441	−	0.351971i	−0.00167333	−	0.0665162i
$29$	0.352336			0.0654272			0.0327136	−	0.999465i	$-0.489585\pi$
$29$	0.352336			0.0654272			0.0327136	+	0.999465i	$0.489585\pi$
$30$		0			0
$31$	−1.25729	−	2.17770i	−0.225817	−	0.391126i	0.730747	−	0.682648i	$-0.239172\pi$
$31$	−1.25729	−	2.17770i	−0.225817	−	0.391126i	−0.956564	+	0.291522i	$0.905838\pi$
$32$	−0.375780	−	0.650870i	−0.0664291	−	0.115059i
$33$		0			0
$34$	0.399223			0.0684663
$35$	1.33988	−	0.819187i	0.226482	−	0.138468i
$36$		0			0
$37$	3.32383	−	5.75705i	0.546435	−	0.946452i	−0.452081	−	0.891977i	$-0.649318\pi$
$37$	3.32383	−	5.75705i	0.546435	−	0.946452i	0.998515	−	0.0544753i	$-0.0173486\pi$
$38$	2.09358	+	3.62619i	0.339623	+	0.588245i
$39$		0			0
$40$	0.809243	−	1.40165i	0.127953	−	0.221620i
$41$	−10.8961			−1.70169			−0.850843	−	0.525420i	$-0.823908\pi$
$41$	−10.8961			−1.70169			−0.850843	+	0.525420i	$0.823908\pi$
$42$		0			0
$43$	3.38151			0.515676			0.257838	−	0.966188i	$-0.416990\pi$
$43$	3.38151			0.515676			0.257838	+	0.966188i	$0.416990\pi$
$44$	−0.296790	+	0.514055i	−0.0447427	+	0.0774967i
$45$		0			0
$46$	3.69076	+	6.39258i	0.544172	+	0.942534i
$47$	−6.21780	+	10.7695i	−0.906959	+	1.57090i	−0.0886938	+	0.996059i	$0.528269\pi$
$47$	−6.21780	+	10.7695i	−0.906959	+	1.57090i	−0.818265	+	0.574841i	$0.805064\pi$
$48$		0			0
$49$	3.80039	+	5.87852i	0.542913	+	0.839789i
$50$	6.78794			0.959959
$51$		0			0
$52$	0.300388	+	0.520288i	0.0416564	+	0.0721509i
$53$	−5.66372	−	9.80984i	−0.777971	−	1.34749i	−0.933109	−	0.359593i	$-0.882916\pi$
$53$	−5.66372	−	9.80984i	−0.777971	−	1.34749i	0.155138	−	0.987893i	$-0.450418\pi$
$54$		0			0
$55$	−2.64766			−0.357011
$56$	6.33628	+	3.44877i	0.846722	+	0.460861i
$57$		0			0
$58$	0.257295	−	0.445647i	0.0337844	−	0.0585163i
$59$	4.02704	+	6.97504i	0.524276	+	0.908073i	0.999601	+	0.0282624i	$0.00899740\pi$
$59$	4.02704	+	6.97504i	0.524276	+	0.908073i	−0.475324	+	0.879811i	$0.657669\pi$
$60$		0			0
$61$	1.36693	−	2.36758i	0.175017	−	0.303138i	−0.765150	−	0.643852i	$-0.777335\pi$
$61$	1.36693	−	2.36758i	0.175017	−	0.303138i	0.940167	+	0.340714i	$0.110669\pi$
$62$	−3.67257			−0.466417
$63$		0			0
$64$	7.39922			0.924903
$65$	−1.33988	+	2.32075i	−0.166192	+	0.287853i
$66$		0			0
$67$	−2.93346	−	5.08091i	−0.358380	−	0.620732i	0.629311	−	0.777154i	$-0.283337\pi$
$67$	−2.93346	−	5.08091i	−0.358380	−	0.620732i	−0.987690	+	0.156422i	$0.950004\pi$
$68$	0.0181877	−	0.0315020i	0.00220558	−	0.00382018i
$69$		0			0
$70$	−0.0576828	−	2.29294i	−0.00689442	−	0.274059i
$71$	2.60078			0.308655			0.154328	−	0.988020i	$-0.450679\pi$
$71$	2.60078			0.308655			0.154328	+	0.988020i	$0.450679\pi$
$72$		0			0
$73$	−5.55768	−	9.62619i	−0.650478	−	1.12666i	−0.983007	−	0.183567i	$-0.941235\pi$
$73$	−5.55768	−	9.62619i	−0.650478	−	1.12666i	0.332530	−	0.943093i	$-0.392098\pi$
$74$	−4.85447	−	8.40819i	−0.564321	−	0.977433i
$75$		0			0
$76$	0.381515			0.0437627
$77$	−0.296790	−	11.7977i	−0.0338223	−	1.34447i
$78$		0			0
$79$	−5.58113	+	9.66679i	−0.627926	+	1.08760i	0.360042	+	0.932936i	$0.382763\pi$
$79$	−5.58113	+	9.66679i	−0.627926	+	1.08760i	−0.987967	+	0.154663i	$0.950571\pi$
$80$	−1.26089	−	2.18393i	−0.140972	−	0.244171i
$81$		0			0
$82$	−7.95691	+	13.7818i	−0.878693	+	1.52194i
$83$	16.5438			1.81591			0.907957	−	0.419063i	$-0.137641\pi$
$83$	16.5438			1.81591			0.907957	+	0.419063i	$0.137641\pi$
$84$		0			0
$85$	0.162253			0.0175988
$86$	2.46936	−	4.27706i	0.266278	−	0.461207i
$87$		0			0
$88$	−6.08113	−	10.5328i	−0.648250	−	1.12280i
$89$	2.68716	−	4.65430i	0.284838	−	0.493354i	−0.687732	−	0.725965i	$-0.741393\pi$
$89$	2.68716	−	4.65430i	0.284838	−	0.493354i	0.972570	+	0.232611i	$0.0747268\pi$
$90$		0			0
$91$	−10.4911	−	5.71021i	−1.09977	−	0.598592i
$92$	0.672570			0.0701202
$93$		0			0
$94$	9.08113	+	15.7290i	0.936647	+	1.62232i
$95$	0.850874	+	1.47376i	0.0872978	+	0.151204i
$96$		0			0
$97$	−2.26615			−0.230093			−0.115046	−	0.993360i	$-0.536702\pi$
$97$	−2.26615			−0.230093			−0.115046	+	0.993360i	$0.536702\pi$
$98$	10.2106	−	0.514055i	1.03143	−	0.0519274i
$99$		0			0
$100$	0.309243	−	0.535624i	0.0309243	−	0.0535624i
$101$	−4.67830	−	8.10306i	−0.465509	−	0.806285i	0.533716	−	0.845664i	$-0.320795\pi$
$101$	−4.67830	−	8.10306i	−0.465509	−	0.806285i	−0.999224	+	0.0393793i	$0.987462\pi$
$102$		0			0
$103$	7.88151	−	13.6512i	0.776589	−	1.34509i	−0.157309	−	0.987550i	$-0.550282\pi$
$103$	7.88151	−	13.6512i	0.776589	−	1.34509i	0.933897	−	0.357542i	$-0.116385\pi$
$104$	−12.3097			−1.20707
$105$		0			0
$106$	−16.5438			−1.60687
$107$	−0.512453	+	0.887595i	−0.0495407	+	0.0858070i	−0.889732	−	0.456483i	$-0.849109\pi$
$107$	−0.512453	+	0.887595i	−0.0495407	+	0.0858070i	0.840192	+	0.542290i	$0.182442\pi$
$108$		0			0
$109$	−0.647664	−	1.12179i	−0.0620349	−	0.107448i	0.833340	−	0.552761i	$-0.186426\pi$
$109$	−0.647664	−	1.12179i	−0.0620349	−	0.107448i	−0.895375	+	0.445313i	$0.853092\pi$
$110$	−1.93346	+	3.34886i	−0.184348	+	0.319301i
$111$		0			0
$112$	9.58998	−	5.86319i	0.906168	−	0.554019i
$113$	14.2953			1.34479			0.672396	−	0.740192i	$-0.265265\pi$
$113$	14.2953			1.34479			0.672396	+	0.740192i	$0.265265\pi$
$114$		0			0
$115$	1.50000	+	2.59808i	0.139876	+	0.242272i
$116$	−0.0234435	−	0.0406053i	−0.00217667	−	0.00377011i
$117$		0			0
$118$	11.7630			1.08287
$119$	0.0181877	+	0.722977i	0.00166726	+	0.0662752i
$120$		0			0
$121$	−4.44805	+	7.70425i	−0.404368	+	0.700387i
$122$	−1.99640	−	3.45787i	−0.180746	−	0.313061i
$123$		0			0
$124$	−0.167314	+	0.289796i	−0.0150252	+	0.0260245i
$125$	5.72665			0.512207
$126$		0			0
$127$	12.3346			1.09452			0.547261	−	0.836962i	$-0.315671\pi$
$127$	12.3346			1.09452			0.547261	+	0.836962i	$0.315671\pi$
$128$	6.15486	−	10.6605i	0.544018	−	0.942267i
$129$		0			0
$130$	1.95691	+	3.38946i	0.171632	+	0.297275i
$131$	1.59718	−	2.76639i	0.139546	−	0.241701i	−0.787779	−	0.615958i	$-0.788769\pi$
$131$	1.59718	−	2.76639i	0.139546	−	0.241701i	0.927325	+	0.374257i	$0.122102\pi$
$132$		0			0
$133$	−6.47150	+	3.95659i	−0.561150	+	0.343080i
$134$	−8.56867			−0.740221
$135$		0			0
$136$	0.372660	+	0.645466i	0.0319553	+	0.0553483i
$137$	−5.05408	−	8.75393i	−0.431800	−	0.747899i	0.565229	−	0.824934i	$-0.308788\pi$
$137$	−5.05408	−	8.75393i	−0.431800	−	0.747899i	−0.997028	+	0.0770354i	$0.975455\pi$
$138$		0			0
$139$	18.0761			1.53319			0.766596	−	0.642130i	$-0.221949\pi$
$139$	18.0761			1.53319			0.766596	+	0.642130i	$0.221949\pi$
$140$	−0.183560	−	0.0999096i	−0.0155137	−	0.00844390i
$141$		0			0
$142$	1.89922	−	3.28955i	0.159379	−	0.276053i
$143$	10.0687	+	17.4395i	0.841985	+	1.45836i
$144$		0			0
$145$	0.104570	−	0.181120i	0.00868405	−	0.0150412i
$146$	−16.2340			−1.34354
$147$		0			0
$148$	−0.884634			−0.0727165
$149$	−7.02704	+	12.1712i	−0.575678	+	0.997103i	0.420290	+	0.907390i	$0.361928\pi$
$149$	−7.02704	+	12.1712i	−0.575678	+	0.997103i	−0.995968	+	0.0897132i	$0.971405\pi$
$150$		0			0
$151$	−0.190757	−	0.330401i	−0.0155236	−	0.0268877i	0.858159	−	0.513384i	$-0.171608\pi$
$151$	−0.190757	−	0.330401i	−0.0155236	−	0.0268877i	−0.873683	+	0.486496i	$0.838275\pi$
$152$	−3.90856	+	6.76982i	−0.317026	+	0.549105i
$153$		0			0
$154$	−15.1388	−	8.23988i	−1.21992	−	0.663988i
$155$	−1.49261			−0.119889
$156$		0			0
$157$	3.75729	+	6.50783i	0.299865	+	0.519381i	0.976105	−	0.217300i	$-0.0697251\pi$
$157$	3.75729	+	6.50783i	0.299865	+	0.519381i	−0.676240	+	0.736681i	$0.736392\pi$
$158$	8.15126	+	14.1184i	0.648480	+	1.12320i
$159$		0			0
$160$	−0.446110			−0.0352681
$161$	−11.4086	+	6.97504i	−0.899120	+	0.549710i
$162$		0			0
$163$	−7.59572	+	13.1562i	−0.594942	+	1.03047i	0.398613	+	0.917119i	$0.369492\pi$
$163$	−7.59572	+	13.1562i	−0.594942	+	1.03047i	−0.993555	+	0.113351i	$0.963842\pi$
$164$	0.724997	+	1.25573i	0.0566127	+	0.0980561i
$165$		0			0
$166$	12.0811	−	20.9251i	0.937677	−	1.62410i
$167$	8.95311			0.692813			0.346406	−	0.938085i	$-0.387402\pi$
$167$	8.95311			0.692813			0.346406	+	0.938085i	$0.387402\pi$
$168$		0			0
$169$	7.38151			0.567809
$170$	0.118485	−	0.205223i	0.00908741	−	0.0157399i
$171$		0			0
$172$	−0.224997	−	0.389706i	−0.0171558	−	0.0297148i
$173$	5.23025	−	9.05906i	0.397649	−	0.688748i	−0.595787	−	0.803143i	$-0.703160\pi$
$173$	5.23025	−	9.05906i	0.397649	−	0.688748i	0.993435	+	0.114395i	$0.0364929\pi$
$174$		0			0
$175$	0.309243	+	12.2927i	0.0233766	+	0.929239i
$176$	−18.9502			−1.42842
$177$		0			0
$178$	−3.92461	−	6.79762i	−0.294162	−	0.509503i
$179$	4.48395	+	7.76643i	0.335146	+	0.580490i	0.983513	−	0.180838i	$-0.0578810\pi$
$179$	4.48395	+	7.76643i	0.335146	+	0.580490i	−0.648367	+	0.761328i	$0.724548\pi$
$180$		0			0
$181$	5.04689			0.375132			0.187566	−	0.982252i	$-0.439940\pi$
$181$	5.04689			0.375132			0.187566	+	0.982252i	$0.439940\pi$
$182$	−14.8837	+	9.09967i	−1.10325	+	0.674512i
$183$		0			0
$184$	−6.89037	+	11.9345i	−0.507965	+	0.879821i
$185$	−1.97296	−	3.41726i	−0.145055	−	0.251242i
$186$		0			0
$187$	0.609631	−	1.05591i	0.0445806	−	0.0772159i
$188$	1.65486			0.120693
$189$		0			0
$190$	2.48541			0.180311
$191$	−6.06507	+	10.5050i	−0.438853	+	0.760116i	−0.997601	−	0.0692211i	$-0.977949\pi$
$191$	−6.06507	+	10.5050i	−0.438853	+	0.760116i	0.558748	+	0.829338i	$0.311282\pi$
$192$		0			0
$193$	−8.58113	−	14.8629i	−0.617683	−	1.06986i	−0.989907	−	0.141716i	$-0.954738\pi$
$193$	−8.58113	−	14.8629i	−0.617683	−	1.06986i	0.372224	−	0.928143i	$-0.378595\pi$
$194$	−1.65486	+	2.86630i	−0.118812	+	0.205789i
$195$		0			0
$196$	0.424608	−	0.829120i	0.0303292	−	0.0592228i
$197$	0.751560			0.0535464			0.0267732	−	0.999642i	$-0.491477\pi$
$197$	0.751560			0.0535464			0.0267732	+	0.999642i	$0.491477\pi$
$198$		0			0
$199$	−5.14766	−	8.91601i	−0.364908	−	0.632040i	0.623853	−	0.781542i	$-0.285566\pi$
$199$	−5.14766	−	8.91601i	−0.364908	−	0.632040i	−0.988761	+	0.149502i	$0.952233\pi$
$200$	6.33628	+	10.9748i	0.448043	+	0.776033i
$201$		0			0
$202$	−13.6654			−0.961492
$203$	0.818771	+	0.445647i	0.0574664	+	0.0312783i
$204$		0			0
$205$	−3.23385	+	5.60119i	−0.225862	+	0.391204i
$206$	−11.5110	−	19.9376i	−0.802009	−	1.38912i
$207$		0			0
$208$	−9.58998	+	16.6103i	−0.664946	+	1.15172i
$209$	12.7879			0.884560
$210$		0			0
$211$	−16.1154			−1.10943			−0.554714	−	0.832041i	$-0.687172\pi$
$211$	−16.1154			−1.10943			−0.554714	+	0.832041i	$0.687172\pi$
$212$	−0.753696	+	1.30544i	−0.0517640	+	0.0896580i
$213$		0			0
$214$	0.748440	+	1.29634i	0.0511623	+	0.0886157i
$215$	1.00360	−	1.73828i	0.0684449	−	0.118550i
$216$		0			0
$217$	−0.167314	−	6.65087i	−0.0113580	−	0.451491i
$218$	−1.89183			−0.128131
$219$		0			0
$220$	0.176168	+	0.305132i	0.0118773	+	0.0205720i
$221$	−0.617023	−	1.06871i	−0.0415054	−	0.0718895i
$222$		0			0
$223$	−6.95311			−0.465615			−0.232807	−	0.972523i	$-0.574791\pi$
$223$	−6.95311			−0.465615			−0.232807	+	0.972523i	$0.574791\pi$
$224$	−0.0500067	−	1.98781i	−0.00334121	−	0.132816i
$225$		0			0
$226$	10.4392	−	18.0812i	0.694405	−	1.20274i
$227$	2.64553	+	4.58219i	0.175590	+	0.304131i	0.940365	−	0.340166i	$-0.110483\pi$
$227$	2.64553	+	4.58219i	0.175590	+	0.304131i	−0.764775	+	0.644297i	$0.777150\pi$
$228$		0			0
$229$	−5.86186	+	10.1530i	−0.387363	+	0.670932i	−0.992094	−	0.125498i	$-0.959947\pi$
$229$	−5.86186	+	10.1530i	−0.387363	+	0.670932i	0.604731	+	0.796430i	$0.293281\pi$
$230$	4.38151			0.288909
$231$		0			0
$232$	0.960699			0.0630730
$233$	1.93560	−	3.35256i	0.126805	−	0.219633i	−0.795632	−	0.605780i	$-0.792861\pi$
$233$	1.93560	−	3.35256i	0.126805	−	0.219633i	0.922437	+	0.386147i	$0.126194\pi$
$234$		0			0
$235$	3.69076	+	6.39258i	0.240758	+	0.417006i
$236$	0.535897	−	0.928200i	0.0348839	−	0.0604207i
$237$		0			0
$238$	0.927728	+	0.504951i	0.0601357	+	0.0327311i
$239$	−12.3992			−0.802039			−0.401020	−	0.916069i	$-0.631344\pi$
$239$	−12.3992			−0.802039			−0.401020	+	0.916069i	$0.631344\pi$
$240$		0			0
$241$	8.28074	+	14.3427i	0.533409	+	0.923892i	0.999239	+	0.0390173i	$0.0124227\pi$
$241$	8.28074	+	14.3427i	0.533409	+	0.923892i	−0.465829	+	0.884875i	$0.654244\pi$
$242$	6.49640	+	11.2521i	0.417604	+	0.723312i
$243$		0			0
$244$	−0.363806			−0.0232903
$245$	4.14980	−	0.208922i	0.265121	−	0.0133476i
$246$		0			0
$247$	6.47150	−	11.2090i	0.411771	−	0.713209i
$248$	−3.42821	−	5.93783i	−0.217691	−	0.377052i
$249$		0			0
$250$	4.18190	−	7.24327i	0.264487	−	0.458105i
$251$	−1.84922			−0.116722			−0.0583608	−	0.998296i	$-0.518587\pi$
$251$	−1.84922			−0.116722			−0.0583608	+	0.998296i	$0.518587\pi$
$252$		0			0
$253$	22.5438			1.41731
$254$	9.00739	−	15.6013i	0.565174	−	0.978910i
$255$		0			0
$256$	−1.58998	−	2.75393i	−0.0993738	−	0.172120i
$257$	13.4210	−	23.2459i	0.837180	−	1.45004i	−0.0550638	−	0.998483i	$-0.517536\pi$
$257$	13.4210	−	23.2459i	0.837180	−	1.45004i	0.892243	−	0.451555i	$-0.149130\pi$
$258$		0			0
$259$	15.0057	−	9.17431i	0.932411	−	0.570064i
$260$	0.356609			0.0221159
$261$		0			0
$262$	−2.33269	−	4.04033i	−0.144114	−	0.249612i
$263$	10.1424	+	17.5672i	0.625408	+	1.08324i	0.988462	+	0.151470i	$0.0484006\pi$
$263$	10.1424	+	17.5672i	0.625408	+	1.08324i	−0.363054	+	0.931768i	$0.618266\pi$
$264$		0			0
$265$	−6.72373			−0.413035
$266$	0.278602	+	11.0747i	0.0170822	+	0.679032i
$267$		0			0
$268$	−0.390369	+	0.676139i	−0.0238456	+	0.0413018i
$269$	−4.36333	−	7.55750i	−0.266037	−	0.460789i	0.701798	−	0.712376i	$-0.252381\pi$
$269$	−4.36333	−	7.55750i	−0.266037	−	0.460789i	−0.967835	+	0.251587i	$0.919048\pi$
$270$		0			0
$271$	−12.0957	+	20.9504i	−0.734762	+	1.27265i	0.220065	+	0.975485i	$0.429373\pi$
$271$	−12.0957	+	20.9504i	−0.734762	+	1.27265i	−0.954828	+	0.297161i	$0.903960\pi$
$272$	1.16129			0.0704138
$273$		0			0
$274$	−14.7630			−0.891867
$275$	10.3655	−	17.9535i	0.625061	−	1.08264i
$276$		0			0
$277$	3.55768	+	6.16209i	0.213760	+	0.370244i	0.952888	−	0.303321i	$-0.0980955\pi$
$277$	3.55768	+	6.16209i	0.213760	+	0.370244i	−0.739128	+	0.673565i	$0.764762\pi$
$278$	13.2001	−	22.8632i	0.791689	−	1.37125i
$279$		0			0
$280$	3.65340	−	2.23364i	0.218332	−	0.133485i
$281$	−7.89610			−0.471042			−0.235521	−	0.971869i	$-0.575680\pi$
$281$	−7.89610			−0.471042			−0.235521	+	0.971869i	$0.575680\pi$
$282$		0			0
$283$	−1.10457	−	1.91317i	−0.0656599	−	0.113726i	0.831327	−	0.555784i	$-0.187582\pi$
$283$	−1.10457	−	1.91317i	−0.0656599	−	0.113726i	−0.896987	+	0.442058i	$0.854249\pi$
$284$	−0.173048	−	0.299729i	−0.0102685	−	0.0177856i
$285$		0			0
$286$	29.4107			1.73909
$287$	−25.3207	−	13.7818i	−1.49463	−	0.813512i
$288$		0			0
$289$	8.46264	−	14.6577i	0.497802	−	0.862219i
$290$	−0.152725	−	0.264527i	−0.00896830	−	0.0155336i
$291$		0			0
$292$	−0.739586	+	1.28100i	−0.0432810	+	0.0749649i
$293$	19.1914			1.12118			0.560588	−	0.828095i	$-0.310575\pi$
$293$	19.1914			1.12118			0.560588	+	0.828095i	$0.310575\pi$
$294$		0			0
$295$	4.78074			0.278345
$296$	9.06294	−	15.6975i	0.526773	−	0.912397i
$297$		0			0
$298$	10.2630	+	17.7761i	0.594521	+	1.02974i
$299$	11.4086	−	19.7602i	0.659774	−	1.14276i
$300$		0			0
$301$	7.85807	+	4.27706i	0.452932	+	0.246525i
$302$	−0.557204			−0.0320635
$303$		0			0
$304$	6.08998	+	10.5482i	0.349284	+	0.604978i
$305$	−0.811379	−	1.40535i	−0.0464594	−	0.0804701i
$306$		0			0
$307$	−13.9138			−0.794103			−0.397052	−	0.917796i	$-0.629967\pi$
$307$	−13.9138			−0.794103			−0.397052	+	0.917796i	$0.629967\pi$
$308$	−1.33988	+	0.819187i	−0.0763469	+	0.0466775i
$309$		0			0
$310$	−1.08998	+	1.88790i	−0.0619067	+	0.107226i
$311$	5.32743	+	9.22738i	0.302091	+	0.523237i	0.976609	−	0.215021i	$-0.0689821\pi$
$311$	5.32743	+	9.22738i	0.302091	+	0.523237i	−0.674519	+	0.738258i	$0.735649\pi$
$312$		0			0
$313$	8.28074	−	14.3427i	0.468055	−	0.810695i	−0.531279	−	0.847197i	$-0.678288\pi$
$313$	8.28074	−	14.3427i	0.468055	−	0.810695i	0.999334	+	0.0365022i	$0.0116216\pi$
$314$	10.9751			0.619360
$315$		0			0
$316$	1.48541			0.0835609
$317$	−13.3186	+	23.0685i	−0.748046	+	1.29565i	0.200712	+	0.979650i	$0.435674\pi$
$317$	−13.3186	+	23.0685i	−0.748046	+	1.29565i	−0.948758	+	0.316003i	$0.897659\pi$
$318$		0			0
$319$	−0.785799	−	1.36104i	−0.0439963	−	0.0762038i
$320$	2.19601	−	3.80361i	0.122761	−	0.212628i
$321$		0			0
$322$	0.491146	+	19.5235i	0.0273705	+	1.08800i
$323$	−0.783663			−0.0436042
$324$		0			0
$325$	−10.4911	−	18.1712i	−0.581944	−	1.00796i
$326$	11.0936	+	19.2146i	0.614417	+	1.06420i
$327$		0			0
$328$	−29.7099			−1.64045
$329$	−28.0708	+	17.1621i	−1.54759	+	0.946179i
$330$		0			0
$331$	11.6534	−	20.1843i	0.640529	−	1.10943i	−0.344786	−	0.938681i	$-0.612049\pi$
$331$	11.6534	−	20.1843i	0.640529	−	1.10943i	0.985315	−	0.170747i	$-0.0546181\pi$
$332$	−1.10078	−	1.90660i	−0.0604130	−	0.104638i
$333$		0			0
$334$	6.53803	−	11.3242i	0.357745	−	0.619633i
$335$	−3.48249			−0.190269
$336$		0			0
$337$	−23.2383			−1.26587			−0.632936	−	0.774204i	$-0.718150\pi$
$337$	−23.2383			−1.26587			−0.632936	+	0.774204i	$0.718150\pi$
$338$	5.39037	−	9.33639i	0.293197	−	0.507833i
$339$		0			0
$340$	−0.0107958	−	0.0186989i	−0.000585487	−	0.00101409i
$341$	−5.60817	+	9.71363i	−0.303699	+	0.526023i
$342$		0			0
$343$	1.39610	+	18.4676i	0.0753825	+	0.997155i
$344$	9.22022			0.497121
$345$		0			0
$346$	−7.63881	−	13.2308i	−0.410665	−	0.711293i
$347$	−8.56867	−	14.8414i	−0.459990	−	0.796727i	0.538969	−	0.842325i	$-0.318814\pi$
$347$	−8.56867	−	14.8414i	−0.459990	−	0.796727i	−0.998960	+	0.0455985i	$0.985481\pi$
$348$		0			0
$349$	−19.5146			−1.04459			−0.522296	−	0.852764i	$-0.674924\pi$
$349$	−19.5146			−1.04459			−0.522296	+	0.852764i	$0.674924\pi$
$350$	15.7740	+	8.58561i	0.843157	+	0.458920i
$351$		0			0
$352$	−1.67617	+	2.90321i	−0.0893401	+	0.154742i
$353$	−8.03064	−	13.9095i	−0.427428	−	0.740327i	0.569216	−	0.822188i	$-0.307247\pi$
$353$	−8.03064	−	13.9095i	−0.427428	−	0.740327i	−0.996644	+	0.0818613i	$0.973914\pi$
$354$		0			0
$355$	0.771884	−	1.33694i	0.0409673	−	0.0709575i
$356$	−0.715184			−0.0379047
$357$		0			0
$358$	13.0977			0.692233
$359$	−6.93200	+	12.0066i	−0.365857	+	0.633683i	−0.988913	−	0.148494i	$-0.952557\pi$
$359$	−6.93200	+	12.0066i	−0.365857	+	0.633683i	0.623056	+	0.782177i	$0.285891\pi$
$360$		0			0
$361$	5.39037	+	9.33639i	0.283704	+	0.491389i
$362$	3.68550	−	6.38348i	0.193706	−	0.335508i
$363$		0			0
$364$	0.0399740	+	1.58900i	0.00209521	+	0.0832864i
$365$	−6.59785			−0.345347
$366$		0			0
$367$	−12.6477	−	21.9064i	−0.660203	−	1.14350i	−0.980562	−	0.196209i	$-0.937137\pi$
$367$	−12.6477	−	21.9064i	−0.660203	−	1.14350i	0.320360	−	0.947296i	$-0.396196\pi$
$368$	10.7360	+	18.5953i	0.559652	+	0.969346i
$369$		0			0
$370$	−5.76303			−0.299606
$371$	−0.753696	−	29.9601i	−0.0391299	−	1.55545i
$372$		0			0
$373$	−1.00000	+	1.73205i	−0.0517780	+	0.0896822i	−0.890753	−	0.454488i	$-0.849822\pi$
$373$	−1.00000	+	1.73205i	−0.0517780	+	0.0896822i	0.838975	+	0.544170i	$0.183156\pi$
$374$	−0.890369	−	1.54216i	−0.0460399	−	0.0797434i
$375$		0			0
$376$	−16.9538	+	29.3648i	−0.874325	+	1.51437i
$377$	−1.59065			−0.0819229
$378$		0			0
$379$	−18.8099			−0.966200			−0.483100	−	0.875565i	$-0.660489\pi$
$379$	−18.8099			−0.966200			−0.483100	+	0.875565i	$0.660489\pi$
$380$	0.113230	−	0.196119i	0.00580856	−	0.0100607i
$381$		0			0
$382$	8.85807	+	15.3426i	0.453218	+	0.784997i
$383$	−17.5708	+	30.4335i	−0.897826	+	1.55508i	−0.0675593	+	0.997715i	$0.521521\pi$
$383$	−17.5708	+	30.4335i	−0.897826	+	1.55508i	−0.830267	+	0.557366i	$0.811812\pi$
$384$		0			0
$385$	−6.15272	−	3.34886i	−0.313572	−	0.170673i
$386$	−25.0656			−1.27580
$387$		0			0
$388$	0.150783	+	0.261164i	0.00765486	+	0.0132586i
$389$	4.18929	+	7.25607i	0.212406	+	0.367897i	0.952467	−	0.304642i	$-0.0985368\pi$
$389$	4.18929	+	7.25607i	0.212406	+	0.367897i	−0.740061	+	0.672539i	$0.765204\pi$
$390$		0			0
$391$	−1.38151			−0.0698662
$392$	10.3623	+	16.0287i	0.523377	+	0.809572i
$393$		0			0
$394$	0.548828	−	0.950599i	0.0276496	−	0.0478905i
$395$	3.31284	+	5.73801i	0.166687	+	0.288711i
$396$		0			0
$397$	4.62422	−	8.00938i	0.232083	−	0.401979i	−0.726338	−	0.687338i	$-0.758779\pi$
$397$	4.62422	−	8.00938i	0.232083	−	0.401979i	0.958421	+	0.285358i	$0.0921126\pi$
$398$	−15.0364			−0.753705
$399$		0			0
$400$	19.7453			0.987266
$401$	0.0737345	−	0.127712i	0.00368212	−	0.00637763i	−0.864178	−	0.503185i	$-0.832161\pi$
$401$	0.0737345	−	0.127712i	0.00368212	−	0.00637763i	0.867861	+	0.496808i	$0.165495\pi$
$402$		0			0
$403$	5.67617	+	9.83141i	0.282750	+	0.489738i
$404$	−0.622563	+	1.07831i	−0.0309737	+	0.0536480i
$405$		0			0
$406$	1.16158	−	0.710174i	0.0576482	−	0.0352454i
$407$	−29.6519			−1.46979
$408$		0			0
$409$	1.96264	+	3.39939i	0.0970463	+	0.168089i	0.910461	−	0.413595i	$-0.135727\pi$
$409$	1.96264	+	3.39939i	0.0970463	+	0.168089i	−0.813414	+	0.581685i	$0.802394\pi$
$410$	4.72306	+	8.18057i	0.233255	+	0.404010i
$411$		0			0
$412$	−2.09766			−0.103344
$413$	0.535897	+	21.3024i	0.0263697	+	1.04822i
$414$		0			0
$415$	4.91002	−	8.50440i	0.241023	−	0.417465i
$416$	1.69649	+	2.93841i	0.0831774	+	0.144067i
$417$		0			0
$418$	9.33842	−	16.1746i	0.456757	−	0.791126i
$419$	21.0000			1.02592			0.512959	−	0.858413i	$-0.328549\pi$
$419$	21.0000			1.02592			0.512959	+	0.858413i	$0.328549\pi$
$420$		0			0
$421$	−24.6883			−1.20323			−0.601617	−	0.798784i	$-0.705477\pi$
$421$	−24.6883			−1.20323			−0.601617	+	0.798784i	$0.705477\pi$
$422$	−11.7683	+	20.3833i	−0.572871	+	0.992242i
$423$		0			0
$424$	−15.4430	−	26.7480i	−0.749978	−	1.29900i
$425$	−0.635211	+	1.10022i	−0.0308122	+	0.0533684i
$426$		0			0
$427$	6.17111	−	3.77293i	0.298641	−	0.182585i
$428$	0.136389			0.00659260
$429$		0			0
$430$	−1.46576	−	2.53877i	−0.0706853	−	0.122430i
$431$	2.73745	+	4.74140i	0.131858	+	0.228385i	0.924393	−	0.381442i	$-0.124572\pi$
$431$	2.73745	+	4.74140i	0.131858	+	0.228385i	−0.792535	+	0.609827i	$0.791239\pi$
$432$		0			0
$433$	23.6300			1.13558			0.567792	−	0.823172i	$-0.307798\pi$
$433$	23.6300			1.13558			0.567792	+	0.823172i	$0.307798\pi$
$434$	−8.53443	−	4.64519i	−0.409666	−	0.222976i
$435$		0			0
$436$	−0.0861875	+	0.149281i	−0.00412763	+	0.00714927i
$437$	−7.24484	−	12.5484i	−0.346568	−	0.600273i
$438$		0			0
$439$	2.63307	−	4.56062i	0.125670	−	0.217666i	−0.796325	−	0.604869i	$-0.793225\pi$
$439$	2.63307	−	4.56062i	0.125670	−	0.217666i	0.921995	+	0.387203i	$0.126559\pi$
$440$	−7.21926			−0.344165
$441$		0			0
$442$	−1.80233			−0.0857281
$443$	−3.01819	+	5.22765i	−0.143398	+	0.248373i	−0.928774	−	0.370646i	$-0.879136\pi$
$443$	−3.01819	+	5.22765i	−0.143398	+	0.248373i	0.785376	+	0.619019i	$0.212470\pi$
$444$		0			0
$445$	−1.59504	−	2.76269i	−0.0756122	−	0.130964i
$446$	−5.07753	+	8.79454i	−0.240428	+	0.416433i
$447$		0			0
$448$	17.1946	+	9.35879i	0.812366	+	0.442161i
$449$	22.1445			1.04507			0.522533	−	0.852619i	$-0.324987\pi$
$449$	22.1445			1.04507			0.522533	+	0.852619i	$0.324987\pi$
$450$		0			0
$451$	24.3011	+	42.0907i	1.14429	+	1.98197i
$452$	−0.951172	−	1.64748i	−0.0447393	−	0.0774908i
$453$		0			0
$454$	7.72761			0.362675
$455$	−6.04902	+	3.69829i	−0.283583	+	0.173379i
$456$		0			0
$457$	2.66731	−	4.61992i	0.124772	−	0.216111i	−0.796872	−	0.604148i	$-0.793513\pi$
$457$	2.66731	−	4.61992i	0.124772	−	0.216111i	0.921644	+	0.388037i	$0.126847\pi$
$458$	8.56128	+	14.8286i	0.400042	+	0.692894i
$459$		0			0
$460$	0.199612	−	0.345738i	0.00930694	−	0.0161201i
$461$	−29.6946			−1.38301			−0.691507	−	0.722370i	$-0.743053\pi$
$461$	−29.6946			−1.38301			−0.691507	+	0.722370i	$0.743053\pi$
$462$		0			0
$463$	18.5907			0.863981			0.431990	−	0.901878i	$-0.357811\pi$
$463$	18.5907			0.863981			0.431990	+	0.901878i	$0.357811\pi$
$464$	0.748440	−	1.29634i	0.0347455	−	0.0601809i
$465$		0			0
$466$	−2.82695	−	4.89642i	−0.130956	−	0.226822i
$467$	12.3063	−	21.3152i	0.569468	−	0.986348i	−0.427150	−	0.904181i	$-0.640482\pi$
$467$	12.3063	−	21.3152i	0.569468	−	0.986348i	0.996619	−	0.0821676i	$-0.0261843\pi$
$468$		0			0
$469$	−0.390369	−	15.5175i	−0.0180256	−	0.716532i
$470$	10.7807			0.497278
$471$		0			0
$472$	10.9803	+	19.0185i	0.505412	+	0.875399i
$473$	−7.54163	−	13.0625i	−0.346765	−	0.600614i
$474$		0			0
$475$	−13.3245			−0.611370
$476$	0.0821100	−	0.0502010i	0.00376351	−	0.00230096i
$477$		0			0
$478$	−9.05456	+	15.6830i	−0.414146	+	0.717322i
$479$	−0.178304	−	0.308832i	−0.00814693	−	0.0141109i	0.861923	−	0.507039i	$-0.169260\pi$
$479$	−0.178304	−	0.308832i	−0.00814693	−	0.0141109i	−0.870070	+	0.492928i	$0.835927\pi$
$480$		0			0
$481$	−15.0057	+	25.9907i	−0.684203	+	1.18507i
$482$	24.1881			1.10174
$483$		0			0
$484$	1.18384			0.0538111
$485$	−0.672570	+	1.16492i	−0.0305398	+	0.0528965i
$486$		0			0
$487$	6.43920	+	11.1530i	0.291788	+	0.505391i	0.974233	−	0.225546i	$-0.0724165\pi$
$487$	6.43920	+	11.1530i	0.291788	+	0.505391i	−0.682445	+	0.730937i	$0.739083\pi$
$488$	3.72713	−	6.45558i	0.168719	−	0.292231i
$489$		0			0
$490$	2.76615	−	5.40138i	0.124962	−	0.244009i
$491$	−5.55389			−0.250644			−0.125322	−	0.992116i	$-0.539996\pi$
$491$	−5.55389			−0.250644			−0.125322	+	0.992116i	$0.539996\pi$
$492$		0			0
$493$	0.0481549	+	0.0834068i	0.00216879	+	0.00375645i
$494$	−9.45165	−	16.3707i	−0.425250	−	0.736554i
$495$		0			0
$496$	−10.6831			−0.479685
$497$	6.04377	+	3.28955i	0.271100	+	0.147557i
$498$		0			0
$499$	14.0577	−	24.3486i	0.629308	−	1.08999i	−0.358382	−	0.933575i	$-0.616672\pi$
$499$	14.0577	−	24.3486i	0.629308	−	1.08999i	0.987691	−	0.156419i	$-0.0499951\pi$
$500$	−0.381036	−	0.659973i	−0.0170404	−	0.0295149i
$501$		0			0
$502$	−1.35040	+	2.33895i	−0.0602711	+	0.104393i
$503$	−16.9430			−0.755451			−0.377725	−	0.925918i	$-0.623294\pi$
$503$	−16.9430			−0.755451			−0.377725	+	0.925918i	$0.623294\pi$
$504$		0			0
$505$	−5.55389			−0.247145
$506$	16.4626	−	28.5141i	0.731854	−	1.26761i
$507$		0			0
$508$	−0.820712	−	1.42151i	−0.0364132	−	0.0630695i
$509$	−11.1513	+	19.3146i	−0.494271	+	0.856102i	−0.999978	−	0.00660269i	$-0.997898\pi$
$509$	−11.1513	+	19.3146i	−0.494271	+	0.856102i	0.505707	+	0.862705i	$0.331232\pi$
$510$		0			0
$511$	−0.739586	−	29.3992i	−0.0327173	−	1.30054i
$512$	19.9751			0.882783
$513$		0			0
$514$	−19.6015	−	33.9507i	−0.864583	−	1.49750i
$515$	−4.67830	−	8.10306i	−0.206151	−	0.357064i
$516$		0			0
$517$	55.4690			2.43953
$518$	−0.646006	−	25.6793i	−0.0283839	−	1.12828i
$519$		0			0
$520$	−3.65340	+	6.32787i	−0.160212	+	0.277496i
$521$	6.18044	+	10.7048i	0.270770	+	0.468987i	0.969059	−	0.246828i	$-0.0793884\pi$
$521$	6.18044	+	10.7048i	0.270770	+	0.468987i	−0.698289	+	0.715816i	$0.746055\pi$
$522$		0			0
$523$	−3.09572	+	5.36194i	−0.135366	+	0.234461i	−0.925737	−	0.378167i	$-0.876554\pi$
$523$	−3.09572	+	5.36194i	−0.135366	+	0.234461i	0.790371	+	0.612628i	$0.209888\pi$
$524$	−0.425087			−0.0185700
$525$		0			0
$526$	29.6261			1.29176
$527$	0.343677	−	0.595265i	0.0149708	−	0.0259302i
$528$		0			0
$529$	−1.27188	−	2.20297i	−0.0552993	−	0.0957812i
$530$	−4.91002	+	8.50440i	−0.213278	+	0.369408i
$531$		0			0
$532$	0.886576	+	0.482553i	0.0384379	+	0.0209213i
$533$	49.1914			2.13072
$534$		0			0
$535$	0.304182	+	0.526858i	0.0131509	+	0.0227781i
$536$	−7.99854	−	13.8539i	−0.345484	−	0.598396i
$537$		0			0
$538$	−12.7453			−0.549490
$539$	14.2324	−	27.7912i	0.613032	−	1.19705i
$540$		0			0
$541$	−13.4100	+	23.2268i	−0.576542	+	0.998600i	0.419330	+	0.907834i	$0.362265\pi$
$541$	−13.4100	+	23.2268i	−0.576542	+	0.998600i	−0.995872	+	0.0907660i	$0.971068\pi$
$542$	17.6659	+	30.5982i	0.758813	+	1.31430i
$543$		0			0
$544$	0.102718	−	0.177913i	0.00440400	−	0.00762795i
$545$	−0.768879			−0.0329352
$546$		0			0
$547$	−14.6591			−0.626779			−0.313390	−	0.949625i	$-0.601465\pi$
$547$	−14.6591			−0.626779			−0.313390	+	0.949625i	$0.601465\pi$
$548$	−0.672570	+	1.16492i	−0.0287307	+	0.0497631i
$549$		0			0
$550$	−15.1388	−	26.2212i	−0.645521	−	1.11808i
$551$	−0.505061	+	0.874792i	−0.0215163	+	0.0372674i
$552$		0			0
$553$	−25.1965	+	15.4048i	−1.07146	+	0.655079i
$554$	10.3920			0.441515
$555$		0			0
$556$	−1.20273	−	2.08319i	−0.0510072	−	0.0883470i
$557$	−11.8399	−	20.5073i	−0.501672	−	0.868921i	−0.999998	−	0.00193169i	$-0.999385\pi$
$557$	−11.8399	−	20.5073i	−0.501672	−	0.868921i	0.498326	−	0.866990i	$-0.333948\pi$
$558$		0			0
$559$	−15.2661			−0.645689
$560$	−0.167793	−	6.66991i	−0.00709054	−	0.281855i
$561$		0			0
$562$	−5.76615	+	9.98726i	−0.243230	+	0.421287i
$563$	−8.19289	−	14.1905i	−0.345289	−	0.598059i	0.640117	−	0.768277i	$-0.278886\pi$
$563$	−8.19289	−	14.1905i	−0.345289	−	0.598059i	−0.985406	+	0.170219i	$0.945553\pi$
$564$		0			0
$565$	4.24271	−	7.34858i	0.178492	−	0.309157i
$566$	−3.22646			−0.135618
$567$		0			0
$568$	7.09142			0.297549
$569$	−7.89397	+	13.6728i	−0.330932	+	0.573192i	−0.982695	−	0.185231i	$-0.940697\pi$
$569$	−7.89397	+	13.6728i	−0.330932	+	0.573192i	0.651763	+	0.758423i	$0.274030\pi$
$570$		0			0
$571$	−3.19076	−	5.52655i	−0.133529	−	0.231279i	0.791506	−	0.611162i	$-0.209298\pi$
$571$	−3.19076	−	5.52655i	−0.133529	−	0.231279i	−0.925035	+	0.379883i	$0.875964\pi$
$572$	1.33988	−	2.32075i	0.0560233	−	0.0970353i
$573$		0			0
$574$	−35.9222	+	21.9623i	−1.49936	+	0.916690i
$575$	−23.4897			−0.979587
$576$		0			0
$577$	18.5203	+	32.0781i	0.771011	+	1.33543i	0.937009	+	0.349304i	$0.113582\pi$
$577$	18.5203	+	32.0781i	0.771011	+	1.33543i	−0.165998	+	0.986126i	$0.553085\pi$
$578$	−12.3597	−	21.4077i	−0.514097	−	0.890442i
$579$		0			0
$580$	−0.0278311			−0.00115563
$581$	38.4449	+	20.9251i	1.59496	+	0.868120i
$582$		0			0
$583$	−25.2630	+	43.7569i	−1.04629	+	1.81222i
$584$	−15.1539	−	26.2473i	−0.627072	−	1.08612i
$585$		0			0
$586$	14.0146	−	24.2740i	0.578937	−	1.00275i
$587$	12.0938			0.499163			0.249582	−	0.968354i	$-0.419707\pi$
$587$	12.0938			0.499163			0.249582	+	0.968354i	$0.419707\pi$
$588$		0			0
$589$	7.20914			0.297047
$590$	3.49115	−	6.04684i	0.143728	−	0.248945i
$591$		0			0
$592$	−14.1211	−	24.4585i	−0.580374	−	1.00524i
$593$	8.26449	−	14.3145i	0.339382	−	0.587827i	−0.644935	−	0.764238i	$-0.723115\pi$
$593$	8.26449	−	14.3145i	0.339382	−	0.587827i	0.984317	+	0.176411i	$0.0564487\pi$
$594$		0			0
$595$	0.377048	+	0.205223i	0.0154575	+	0.00841331i
$596$	1.87024			0.0766080
$597$		0			0
$598$	−16.6623	−	28.8599i	−0.681370	−	1.18017i
$599$	−4.37412	−	7.57620i	−0.178722	−	0.309555i	0.762721	−	0.646727i	$-0.223863\pi$
$599$	−4.37412	−	7.57620i	−0.178722	−	0.309555i	−0.941443	+	0.337172i	$0.890530\pi$
$600$		0			0
$601$	−5.92393			−0.241642			−0.120821	−	0.992674i	$-0.538553\pi$
$601$	−5.92393			−0.241642			−0.120821	+	0.992674i	$0.538553\pi$
$602$	11.1481	−	6.81583i	0.454364	−	0.277792i
$603$		0			0
$604$	−0.0253849	+	0.0439680i	−0.00103290	+	0.00178903i
$605$	2.64027	+	4.57308i	0.107342	+	0.185922i
$606$		0			0
$607$	0.370719	−	0.642104i	0.0150470	−	0.0260622i	−0.858404	−	0.512974i	$-0.828544\pi$
$607$	0.370719	−	0.642104i	0.0150470	−	0.0260622i	0.873451	+	0.486912i	$0.161877\pi$
$608$	2.15467			0.0873833
$609$		0			0
$610$	−2.37005			−0.0959603
$611$	28.0708	−	48.6201i	1.13562	−	1.96696i
$612$		0			0
$613$	−2.25350	−	3.90318i	−0.0910181	−	0.157648i	0.816922	−	0.576749i	$-0.195679\pi$
$613$	−2.25350	−	3.90318i	−0.0910181	−	0.157648i	−0.907940	+	0.419101i	$0.862345\pi$
$614$	−10.1606	+	17.5987i	−0.410048	+	0.710224i
$615$		0			0
$616$	−0.809243	−	32.1681i	−0.0326053	−	1.29609i
$617$	17.2016			0.692508			0.346254	−	0.938141i	$-0.387453\pi$
$617$	17.2016			0.692508			0.346254	+	0.938141i	$0.387453\pi$
$618$		0			0
$619$	−2.24271	−	3.88448i	−0.0901419	−	0.156130i	0.817429	−	0.576030i	$-0.195399\pi$
$619$	−2.24271	−	3.88448i	−0.0901419	−	0.156130i	−0.907571	+	0.419899i	$0.862065\pi$
$620$	0.0993140	+	0.172017i	0.00398855	+	0.00690837i
$621$		0			0
$622$	15.5615			0.623958
$623$	12.1314	−	7.41699i	0.486035	−	0.297155i
$624$		0			0
$625$	−9.91955	+	17.1812i	−0.396782	+	0.687246i
$626$	−12.0941	−	20.9475i	−0.483376	−	0.837231i
$627$		0			0
$628$	0.500000	−	0.866025i	0.0199522	−	0.0345582i
$629$	1.81711			0.0724531
$630$		0			0
$631$	−17.3068			−0.688973			−0.344486	−	0.938791i	$-0.611947\pi$
$631$	−17.3068			−0.688973			−0.344486	+	0.938791i	$0.611947\pi$
$632$	−15.2178	+	26.3580i	−0.605332	+	1.04847i
$633$		0			0
$634$	19.4518	+	33.6916i	0.772531	+	1.33806i
$635$	3.66079	−	6.34067i	0.145274	−	0.251622i
$636$		0			0
$637$	−17.1572	−	26.5391i	−0.679793	−	1.05152i
$638$	−2.29533			−0.0908729
$639$		0			0
$640$	−3.65340	−	6.32787i	−0.144413	−	0.250131i
$641$	21.6608	+	37.5176i	0.855550	+	1.48186i	0.876134	+	0.482068i	$0.160114\pi$
$641$	21.6608	+	37.5176i	0.855550	+	1.48186i	−0.0205843	+	0.999788i	$0.506553\pi$
$642$		0			0
$643$	29.9823			1.18239			0.591193	−	0.806530i	$-0.298657\pi$
$643$	29.9823			1.18239			0.591193	+	0.806530i	$0.298657\pi$
$644$	1.56294	+	0.850689i	0.0615884	+	0.0335218i
$645$		0			0
$646$	−0.572272	+	0.991204i	−0.0225157	+	0.0389984i
$647$	7.08472	+	12.2711i	0.278529	+	0.482427i	0.971019	−	0.239000i	$-0.0768197\pi$
$647$	7.08472	+	12.2711i	0.278529	+	0.482427i	−0.692490	+	0.721427i	$0.743486\pi$
$648$		0			0
$649$	17.9626	−	31.1122i	0.705095	−	1.22126i
$650$	−30.6447			−1.20199
$651$		0			0
$652$	2.02159			0.0791716
$653$	−14.1981	+	24.5919i	−0.555617	+	0.962356i	0.442239	+	0.896897i	$0.354184\pi$
$653$	−14.1981	+	24.5919i	−0.555617	+	0.962356i	−0.997855	+	0.0654587i	$0.979149\pi$
$654$		0			0
$655$	−0.948052	−	1.64207i	−0.0370435	−	0.0641611i
$656$	−23.1457	+	40.0896i	−0.903689	+	1.56523i
$657$		0			0
$658$	1.20847	+	48.0376i	0.0471109	+	1.87270i
$659$	−9.39922			−0.366142			−0.183071	−	0.983100i	$-0.558604\pi$
$659$	−9.39922			−0.366142			−0.183071	+	0.983100i	$0.558604\pi$
$660$		0			0
$661$	6.35807	+	11.0125i	0.247300	+	0.428337i	0.962776	−	0.270301i	$-0.0871232\pi$
$661$	6.35807	+	11.0125i	0.247300	+	0.428337i	−0.715476	+	0.698638i	$0.753790\pi$
$662$	−17.0198	−	29.4792i	−0.661495	−	1.14574i
$663$		0			0
$664$	45.1091			1.75057
$665$	0.113230	+	4.50098i	0.00439086	+	0.174540i
$666$		0			0
$667$	−0.890369	+	1.54216i	−0.0344752	+	0.0597128i
$668$	−0.595715	−	1.03181i	−0.0230489	−	0.0399219i
$669$		0			0
$670$	−2.54309	+	4.40477i	−0.0982483	+	0.170171i
$671$	−12.1944			−0.470758
$672$		0			0
$673$	35.7922			1.37969			0.689844	−	0.723958i	$-0.257679\pi$
$673$	35.7922			1.37969			0.689844	+	0.723958i	$0.257679\pi$
$674$	−16.9698	+	29.3926i	−0.653654	+	1.13216i
$675$		0			0
$676$	−0.491146	−	0.850689i	−0.0188902	−	0.0327188i
$677$	−5.44592	+	9.43260i	−0.209304	+	0.362524i	−0.951495	−	0.307663i	$-0.900453\pi$
$677$	−5.44592	+	9.43260i	−0.209304	+	0.362524i	0.742192	+	0.670188i	$0.233786\pi$
$678$		0			0
$679$	−5.26615	−	2.86630i	−0.202096	−	0.109999i
$680$	0.442407			0.0169655
$681$		0			0
$682$	8.19076	+	14.1868i	0.313640	+	0.543241i
$683$	−17.5079	−	30.3245i	−0.669920	−	1.16034i	−0.977926	−	0.208951i	$-0.932995\pi$
$683$	−17.5079	−	30.3245i	−0.669920	−	1.16034i	0.308006	−	0.951384i	$-0.400338\pi$
$684$		0			0
$685$	−6.00000			−0.229248
$686$	24.3779	+	11.7201i	0.930753	+	0.447477i
$687$		0			0
$688$	7.18308	−	12.4415i	0.273852	−	0.474326i
$689$	25.5693	+	44.2874i	0.974115	+	1.68722i
$690$		0			0
$691$	−4.21041	+	7.29264i	−0.160171	+	0.277425i	−0.934930	−	0.354832i	$-0.884538\pi$
$691$	−4.21041	+	7.29264i	−0.160171	+	0.277425i	0.774759	+	0.632257i	$0.217871\pi$
$692$	−1.39203			−0.0529169
$693$		0			0
$694$	−25.0292			−0.950095
$695$	5.36479	−	9.29209i	0.203498	−	0.352469i
$696$		0			0
$697$	−1.48920	−	2.57938i	−0.0564076	−	0.0977009i
$698$	−14.2506	+	24.6827i	−0.539392	+	0.934255i
$699$		0			0
$700$	1.39610	−	0.853559i	0.0527678	−	0.0322615i
$701$	42.7453			1.61447			0.807234	−	0.590231i	$-0.200963\pi$
$701$	42.7453			1.61447			0.807234	+	0.590231i	$0.200963\pi$
$702$		0			0
$703$	9.52918	+	16.5050i	0.359400	+	0.622499i
$704$	−16.5021	−	28.5825i	−0.621948	−	1.07724i
$705$		0			0
$706$	−23.4576			−0.882838
$707$	−0.622563	−	24.7474i	−0.0234139	−	0.930723i
$708$		0			0
$709$	12.0431	−	20.8593i	0.452288	−	0.783386i	−0.546240	−	0.837629i	$-0.683941\pi$
$709$	12.0431	−	20.8593i	0.452288	−	0.783386i	0.998528	+	0.0542432i	$0.0172746\pi$
$710$	−1.12734	−	1.95261i	−0.0423083	−	0.0732801i
$711$		0			0
$712$	7.32695	−	12.6907i	0.274589	−	0.475602i
$713$	12.7089			0.475954
$714$		0			0
$715$	11.9531			0.447021
$716$	0.596699	−	1.03351i	0.0222997	−	0.0386242i
$717$		0			0
$718$	10.1242	+	17.5357i	0.377833	+	0.654425i
$719$	−21.0512	+	36.4617i	−0.785076	+	1.35979i	0.143878	+	0.989595i	$0.454043\pi$
$719$	−21.0512	+	36.4617i	−0.785076	+	1.35979i	−0.928954	+	0.370196i	$0.879291\pi$
$720$		0			0
$721$	35.5818	−	21.7542i	1.32514	−	0.810170i
$722$	15.7453			0.585980
$723$		0			0
$724$	−0.335806	−	0.581633i	−0.0124801	−	0.0216162i
$725$	0.818771	+	1.41815i	0.0304084	+	0.0526689i
$726$		0			0
$727$	36.0698			1.33776			0.668878	−	0.743372i	$-0.266775\pi$
$727$	36.0698			1.33776			0.668878	+	0.743372i	$0.266775\pi$
$728$	−28.6057	−	15.5698i	−1.06020	−	0.577054i
$729$		0			0
$730$	−4.81810	+	8.34519i	−0.178326	+	0.308869i
$731$	0.462162	+	0.800488i	0.0170937	+	0.0296071i
$732$		0			0
$733$	−17.0665	+	29.5601i	−0.630367	+	1.09183i	0.357110	+	0.934062i	$0.383762\pi$
$733$	−17.0665	+	29.5601i	−0.630367	+	1.09183i	−0.987477	+	0.157765i	$0.949571\pi$
$734$	−36.9439			−1.36363
$735$		0			0
$736$	3.79845			0.140013
$737$	−13.0847	+	22.6634i	−0.481982	+	0.834817i
$738$		0			0
$739$	−10.9481	−	18.9626i	−0.402731	−	0.697550i	0.591324	−	0.806434i	$-0.298606\pi$
$739$	−10.9481	−	18.9626i	−0.402731	−	0.697550i	−0.994054	+	0.108884i	$0.965272\pi$
$740$	−0.262550	+	0.454751i	−0.00965154	+	0.0167170i
$741$		0			0
$742$	−38.4449	−	20.9251i	−1.41136	−	0.768185i
$743$	−28.2852			−1.03768			−0.518842	−	0.854870i	$-0.673637\pi$
$743$	−28.2852			−1.03768			−0.518842	+	0.854870i	$0.673637\pi$
$744$		0			0
$745$	4.17111	+	7.22457i	0.152818	+	0.264688i
$746$	1.46050	+	2.52967i	0.0534729	+	0.0926177i
$747$		0			0
$748$	−0.162253			−0.00593254
$749$	−2.31351	+	1.41445i	−0.0845340	+	0.0516830i
$750$		0			0
$751$	7.24844	−	12.5547i	0.264499	−	0.458126i	−0.702933	−	0.711256i	$-0.748127\pi$
$751$	7.24844	−	12.5547i	0.264499	−	0.458126i	0.967432	+	0.253130i	$0.0814600\pi$
$752$	26.4159	+	45.7538i	0.963291	+	1.66847i
$753$		0			0
$754$	−1.16158	+	2.01191i	−0.0423022	+	0.0732696i
$755$	−0.226459			−0.00824169
$756$		0			0
$757$	−38.9646			−1.41619			−0.708096	−	0.706116i	$-0.750446\pi$
$757$	−38.9646			−1.41619			−0.708096	+	0.706116i	$0.750446\pi$
$758$	−13.7360	+	23.7914i	−0.498914	+	0.864144i
$759$		0			0
$760$	2.32004	+	4.01842i	0.0841566	+	0.145764i
$761$	−0.627819	+	1.08741i	−0.0227584	+	0.0394187i	−0.877180	−	0.480161i	$-0.840578\pi$
$761$	−0.627819	+	1.08741i	−0.0227584	+	0.0394187i	0.854422	+	0.519580i	$0.173912\pi$
$762$		0			0
$763$	−0.0861875	−	3.42603i	−0.00312020	−	0.124031i
$764$	1.61421			0.0584002
$765$		0			0
$766$	25.6623	+	44.4483i	0.927215	+	1.60598i
$767$	−18.1804	−	31.4894i	−0.656458	−	1.13702i
$768$		0			0
$769$	−27.6883			−0.998466			−0.499233	−	0.866468i	$-0.666385\pi$
$769$	−27.6883			−0.998466			−0.499233	+	0.866468i	$0.666385\pi$
$770$	−8.72879	+	5.33667i	−0.314564	+	0.192320i
$771$		0			0
$772$	−1.14193	+	1.97788i	−0.0410989	+	0.0711854i
$773$	3.95544	+	6.85103i	0.142267	+	0.246414i	0.928350	−	0.371707i	$-0.121227\pi$
$773$	3.95544	+	6.85103i	0.142267	+	0.246414i	−0.786083	+	0.618121i	$0.787894\pi$
$774$		0			0
$775$	5.84348	−	10.1212i	0.209904	−	0.363565i
$776$	−6.17900			−0.221813
$777$		0			0
$778$	12.2370			0.438717
$779$	15.6192	−	27.0532i	0.559614	−	0.969281i
$780$		0			0
$781$	−5.80039	−	10.0466i	−0.207554	−	0.359494i
$782$	−1.00885	+	1.74739i	−0.0360766	+	0.0624864i
$783$		0			0
$784$	29.7015	−	1.49533i	1.06077	−	0.0534045i
$785$	4.46050			0.159202
$786$		0			0
$787$	−15.8346	−	27.4264i	−0.564444	−	0.977645i	−0.997101	−	0.0760866i	$-0.975757\pi$
$787$	−15.8346	−	27.4264i	−0.564444	−	0.977645i	0.432658	−	0.901558i	$-0.357576\pi$
$788$	−0.0500067	−	0.0866142i	−0.00178142	−	0.00308550i
$789$		0			0
$790$	9.67684			0.344287
$791$	33.2199	+	18.0812i	1.18116	+	0.642894i
$792$		0			0
$793$	−6.17111	+	10.6887i	−0.219142	+	0.379566i
$794$	−6.75370	−	11.6977i	−0.239680	−	0.415137i
$795$		0			0
$796$	−0.685023	+	1.18649i	−0.0242800	+	0.0420542i
$797$	−33.7922			−1.19698			−0.598491	−	0.801130i	$-0.704233\pi$
$797$	−33.7922			−1.19698			−0.598491	+	0.801130i	$0.704233\pi$
$798$		0			0
$799$	−3.39922			−0.120256
$800$	1.74650	−	3.02502i	0.0617481	−	0.106951i
$801$		0			0
$802$	−0.107690	−	0.186524i	−0.00380265	−	0.00658638i
$803$	−24.7901	+	42.9377i	−0.874823	+	1.51524i
$804$		0			0
$805$	0.199612	+	7.93474i	0.00703539	+	0.279663i
$806$	16.5801			0.584011
$807$		0			0
$808$	−12.7561	−	22.0942i	−0.448759	−	0.777273i
$809$	18.3801	+	31.8352i	0.646208	+	1.11927i	0.984021	+	0.178052i	$0.0569796\pi$
$809$	18.3801	+	31.8352i	0.646208	+	1.11927i	−0.337813	+	0.941213i	$0.609687\pi$
$810$		0			0
$811$	3.54377			0.124438			0.0622192	−	0.998063i	$-0.480182\pi$
$811$	3.54377			0.124438			0.0622192	+	0.998063i	$0.480182\pi$
$812$	−0.00311973	−	0.124012i	−0.000109481	−	0.00435197i
$813$		0			0
$814$	−21.6534	+	37.5048i	−0.758951	+	1.31454i
$815$	4.50866	+	7.80923i	0.157931	+	0.273545i
$816$		0			0
$817$	−4.84728	+	8.39573i	−0.169585	+	0.293729i
$818$	5.73289			0.200446
$819$		0			0
$820$	0.860686			0.0300565
$821$	10.4318	−	18.0684i	0.364073	−	0.630592i	−0.624554	−	0.780981i	$-0.714719\pi$
$821$	10.4318	−	18.0684i	0.364073	−	0.630592i	0.988627	+	0.150389i	$0.0480527\pi$
$822$		0			0
$823$	−22.7003	−	39.3180i	−0.791282	−	1.37054i	−0.925173	−	0.379545i	$-0.876081\pi$
$823$	−22.7003	−	39.3180i	−0.791282	−	1.37054i	0.133891	−	0.990996i	$-0.457253\pi$
$824$	21.4902	−	37.2221i	0.748645	−	1.29669i
$825$		0			0
$826$	27.3353	+	14.8783i	0.951117	+	0.517682i
$827$	5.34221			0.185767			0.0928835	−	0.995677i	$-0.470392\pi$
$827$	5.34221			0.185767			0.0928835	+	0.995677i	$0.470392\pi$
$828$		0			0
$829$	−8.45185	−	14.6390i	−0.293545	−	0.508434i	0.681101	−	0.732190i	$-0.261502\pi$
$829$	−8.45185	−	14.6390i	−0.293545	−	0.508434i	−0.974645	+	0.223755i	$0.928168\pi$
$830$	−7.17111	−	12.4207i	−0.248913	−	0.431130i
$831$		0			0
$832$	−33.4045			−1.15809
$833$	−0.872181	+	1.70308i	−0.0302193	+	0.0590083i
$834$		0			0
$835$	2.65719	−	4.60239i	0.0919559	−	0.159272i
$836$	−0.850874	−	1.47376i	−0.0294281	−	0.0509709i
$837$		0			0
$838$	15.3353	−	26.5615i	0.529749	−	0.917553i
$839$	9.83909			0.339683			0.169842	−	0.985471i	$-0.445674\pi$
$839$	9.83909			0.339683			0.169842	+	0.985471i	$0.445674\pi$
$840$		0			0
$841$	−28.8759			−0.995719
$842$	−18.0287	+	31.2266i	−0.621310	+	1.07614i
$843$		0			0
$844$	1.07227	+	1.85723i	0.0369091	+	0.0639285i
$845$	2.19076	−	3.79450i	0.0753643	−	0.130535i
$846$		0			0
$847$	−20.0811	+	12.2773i	−0.689996	+	0.421854i
$848$	−48.1239			−1.65258
$849$		0			0
$850$	0.927728	+	1.60687i	0.0318208	+	0.0551153i
$851$	16.7989	+	29.0966i	0.575860	+	0.997418i
$852$		0			0
$853$	−55.4868			−1.89983			−0.949915	−	0.312508i	$-0.898831\pi$
$853$	−55.4868			−1.89983			−0.949915	+	0.312508i	$0.898831\pi$
$854$	−0.265670	−	10.5606i	−0.00909104	−	0.361377i
$855$		0			0
$856$	−1.39728	+	2.42016i	−0.0477581	+	0.0827195i
$857$	−28.1732	−	48.7975i	−0.962380	−	1.66689i	−0.716496	−	0.697591i	$-0.754255\pi$
$857$	−28.1732	−	48.7975i	−0.962380	−	1.66689i	−0.245884	−	0.969299i	$-0.579078\pi$
$858$		0			0
$859$	−21.9626	+	38.0404i	−0.749356	+	1.29792i	0.198776	+	0.980045i	$0.436303\pi$
$859$	−21.9626	+	38.0404i	−0.749356	+	1.29792i	−0.948132	+	0.317877i	$0.897030\pi$
$860$	−0.267107			−0.00910826
$861$		0			0
$862$	7.99612			0.272349
$863$	5.66372	−	9.80984i	0.192795	−	0.333931i	−0.753380	−	0.657585i	$-0.771578\pi$
$863$	5.66372	−	9.80984i	0.192795	−	0.333931i	0.946175	+	0.323654i	$0.104911\pi$
$864$		0			0
$865$	−3.10457	−	5.37727i	−0.105559	−	0.182833i
$866$	17.2558	−	29.8880i	0.586377	−	1.01563i
$867$		0			0
$868$	−0.755353	+	0.461813i	−0.0256384	+	0.0156750i
$869$	49.7893			1.68899
$870$		0			0
$871$	13.2434	+	22.9382i	0.448735	+	0.777231i
$872$	−1.76595	−	3.05872i	−0.0598028	−	0.103581i
$873$		0			0
$874$	−21.1623			−0.715824
$875$	13.3078	+	7.24327i	0.449885	+	0.244867i
$876$		0			0
$877$	23.2307	−	40.2368i	0.784446	−	1.35870i	−0.144883	−	0.989449i	$-0.546281\pi$
$877$	23.2307	−	40.2368i	0.784446	−	1.35870i	0.929329	−	0.369252i	$-0.120386\pi$
$878$	−3.84562	−	6.66081i	−0.129783	−	0.224791i
$879$		0			0
$880$	−5.62422	+	9.74143i	−0.189592	+	0.328384i
$881$	−21.6578			−0.729669			−0.364835	−	0.931072i	$-0.618874\pi$
$881$	−21.6578			−0.729669			−0.364835	+	0.931072i	$0.618874\pi$
$882$		0			0
$883$	11.4868			0.386560			0.193280	−	0.981144i	$-0.438087\pi$
$883$	11.4868			0.386560			0.193280	+	0.981144i	$0.438087\pi$
$884$	−0.0821100	+	0.142219i	−0.00276166	+	0.00478333i
$885$		0			0
$886$	4.40808	+	7.63501i	0.148092	+	0.256503i
$887$	8.92101	−	15.4516i	0.299538	−	0.518815i	−0.676492	−	0.736450i	$-0.736501\pi$
$887$	8.92101	−	15.4516i	0.299538	−	0.518815i	0.976030	+	0.217634i	$0.0698341\pi$
$888$		0			0
$889$	28.6636	+	15.6013i	0.961346	+	0.523249i
$890$	−4.65913			−0.156174
$891$		0			0
$892$	0.462641	+	0.801318i	0.0154904	+	0.0268301i
$893$	−17.8260	−	30.8755i	−0.596523	−	1.03321i
$894$		0			0
$895$	5.32316			0.177934
$896$	27.7867	−	16.9884i	0.928287	−	0.567543i
$897$		0			0
$898$	16.1711	−	28.0092i	0.539637	−	0.934678i
$899$	−0.442991	−	0.767282i	−0.0147746	−	0.0255903i
$900$		0			0
$901$	1.54815	−	2.68148i	0.0515765	−	0.0893331i
$902$	70.9836			2.36350
$903$		0			0
$904$	38.9784			1.29640
$905$	1.49786	−	2.59438i	0.0497907	−	0.0862400i
$906$		0			0
$907$	25.9253	+	44.9039i	0.860835	+	1.49101i	0.871124	+	0.491063i	$0.163391\pi$
$907$	25.9253	+	44.9039i	0.860835	+	1.49101i	−0.0102894	+	0.999947i	$0.503275\pi$
$908$	0.352052	−	0.609772i	0.0116833	−	0.0202360i
$909$		0			0
$910$	0.260414	+	10.3517i	0.00863265	+	0.343155i
$911$	6.48676			0.214916			0.107458	−	0.994210i	$-0.465729\pi$
$911$	6.48676			0.214916			0.107458	+	0.994210i	$0.465729\pi$
$912$		0			0
$913$	−36.8968	−	63.9071i	−1.22111	−	2.11502i
$914$	−3.89562	−	6.74742i	−0.128856	−	0.223185i
$915$		0			0
$916$	1.56013			0.0515481
$917$	7.21060	−	4.40847i	0.238115	−	0.145580i
$918$		0			0
$919$	5.84221	−	10.1190i	0.192717	−	0.333795i	−0.753433	−	0.657525i	$-0.771603\pi$
$919$	5.84221	−	10.1190i	0.192717	−	0.333795i	0.946150	+	0.323730i	$0.104937\pi$
$920$	4.08998	+	7.08405i	0.134843	+	0.233554i
$921$		0			0
$922$	−21.6845	+	37.5587i	−0.714142	+	1.23693i
$923$	−11.7414			−0.386474
$924$		0			0
$925$	30.8961			1.01586
$926$	13.5759	−	23.5141i	0.446131	−	0.772721i
$927$		0			0
$928$	−0.132401	−	0.229325i	−0.00434627	−	0.00752797i
$929$	0.730252	−	1.26483i	0.0239588	−	0.0414979i	−0.853797	−	0.520605i	$-0.825706\pi$
$929$	0.730252	−	1.26483i	0.0239588	−	0.0414979i	0.877756	+	0.479108i	$0.159040\pi$
$930$		0			0
$931$	−20.0431	+	1.00907i	−0.656886	+	0.0330710i
$932$	−0.515158			−0.0168745
$933$		0			0
$934$	−17.9734	−	31.1309i	−0.588109	−	1.01863i
$935$	−0.361864	−	0.626767i	−0.0118342	−	0.0204975i
$936$		0			0
$937$	9.87451			0.322586			0.161293	−	0.986907i	$-0.448434\pi$
$937$	9.87451			0.322586			0.161293	+	0.986907i	$0.448434\pi$
$938$	−19.9122	−	10.8380i	−0.650155	−	0.353872i
$939$		0			0
$940$	0.491146	−	0.850689i	0.0160194	−	0.0277464i
$941$	−27.0972	−	46.9337i	−0.883343	−	1.52999i	−0.847601	−	0.530633i	$-0.821954\pi$
$941$	−27.0972	−	46.9337i	−0.883343	−	1.52999i	−0.0357414	−	0.999361i	$-0.511379\pi$
$942$		0			0
$943$	27.5349	−	47.6919i	0.896660	−	1.55306i
$944$	34.2173			1.11368
$945$		0			0
$946$	−22.0292			−0.716230
$947$	27.4451	−	47.5364i	0.891847	−	1.54472i	0.0541875	−	0.998531i	$-0.482743\pi$
$947$	27.4451	−	47.5364i	0.891847	−	1.54472i	0.837659	−	0.546193i	$-0.183924\pi$
$948$		0			0
$949$	25.0907	+	43.4583i	0.814477	+	1.41072i
$950$	−9.73025	+	16.8533i	−0.315691	+	0.546793i
$951$		0			0
$952$	0.0495916	+	1.97131i	0.00160727	+	0.0638905i
$953$	−27.0406			−0.875932			−0.437966	−	0.898991i	$-0.644301\pi$
$953$	−27.0406			−0.875932			−0.437966	+	0.898991i	$0.644301\pi$
$954$		0			0
$955$	3.60010	+	6.23556i	0.116497	+	0.201778i
$956$	0.825010	+	1.42896i	0.0266827	+	0.0462158i
$957$		0			0
$958$	−0.520829			−0.0168272
$959$	−0.672570	−	26.7352i	−0.0217184	−	0.863326i
$960$		0			0
$961$	12.3384	−	21.3708i	0.398014	−	0.689380i
$962$	21.9159	+	37.9595i	0.706599	+	1.22386i
$963$		0			0
$964$	1.10195	−	1.90864i	0.0354916	−	0.0614732i
$965$	−10.1872			−0.327936
$966$		0			0
$967$	−13.5146			−0.434600			−0.217300	−	0.976105i	$-0.569725\pi$
$967$	−13.5146			−0.434600			−0.217300	+	0.976105i	$0.569725\pi$
$968$	−12.1283	+	21.0068i	−0.389818	+	0.675185i
$969$		0			0
$970$	0.982291	+	1.70138i	0.0315395	+	0.0546280i
$971$	−6.46557	+	11.1987i	−0.207490	+	0.359383i	−0.950923	−	0.309427i	$-0.899863\pi$
$971$	−6.46557	+	11.1987i	−0.207490	+	0.359383i	0.743433	+	0.668810i	$0.233196\pi$
$972$		0			0
$973$	42.0057	+	22.8632i	1.34664	+	0.732961i
$974$	18.8090			0.602678
$975$		0			0
$976$	−5.80730	−	10.0585i	−0.185887	−	0.321966i
$977$	18.2989	+	31.6947i	0.585435	+	1.01400i	0.994821	+	0.101641i	$0.0324094\pi$
$977$	18.2989	+	31.6947i	0.585435	+	1.01400i	−0.409387	+	0.912361i	$0.634257\pi$
$978$		0			0
$979$	−23.9722			−0.766154
$980$	−0.300194	−	0.464346i	−0.00958933	−	0.0148330i
$981$		0			0
$982$	−4.05574	+	7.02475i	−0.129424	+	0.224169i
$983$	8.61896	+	14.9285i	0.274902	+	0.476145i	0.970110	−	0.242664i	$-0.0780212\pi$
$983$	8.61896	+	14.9285i	0.274902	+	0.476145i	−0.695208	+	0.718808i	$0.744688\pi$
$984$		0			0
$985$	0.223055	−	0.386343i	0.00710713	−	0.0123099i
$986$	0.140661			0.00447956
$987$		0			0
$988$	−1.72238			−0.0547963
$989$	−8.54523	+	14.8008i	−0.271722	+	0.470637i
$990$		0			0
$991$	7.67111	+	13.2867i	0.243681	+	0.422067i	0.961760	−	0.273894i	$-0.0883118\pi$
$991$	7.67111	+	13.2867i	0.243681	+	0.422067i	−0.718079	+	0.695961i	$0.754978\pi$
$992$	−0.944932	+	1.63667i	−0.0300016	+	0.0519643i
$993$		0			0
$994$	8.57421	−	5.24216i	0.271958	−	0.166271i
$995$	−6.11109			−0.193735
$996$		0			0
$997$	17.0577	+	29.5448i	0.540222	+	0.935692i	0.998891	+	0.0470850i	$0.0149932\pi$
$997$	17.0577	+	29.5448i	0.540222	+	0.935692i	−0.458669	+	0.888607i	$0.651674\pi$
$998$	−20.5313	−	35.5613i	−0.649907	−	1.12567i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.2.e.e.163.3	yes	6
3.2	odd	2		189.2.e.f.163.1	yes	6
7.2	even	3		1323.2.a.ba.1.1		3
7.4	even	3	inner	189.2.e.e.109.3	✓	6
7.5	odd	6		1323.2.a.z.1.1		3
9.2	odd	6		567.2.h.h.352.3		6
9.4	even	3		567.2.g.h.541.3		6
9.5	odd	6		567.2.g.i.541.1		6
9.7	even	3		567.2.h.i.352.1		6
21.2	odd	6		1323.2.a.x.1.3		3
21.5	even	6		1323.2.a.y.1.3		3
21.11	odd	6		189.2.e.f.109.1	yes	6
63.4	even	3		567.2.h.i.298.1		6
63.11	odd	6		567.2.g.i.109.1		6
63.25	even	3		567.2.g.h.109.3		6
63.32	odd	6		567.2.h.h.298.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.e.e.109.3	✓	6	7.4	even	3	inner
189.2.e.e.163.3	yes	6	1.1	even	1	trivial
189.2.e.f.109.1	yes	6	21.11	odd	6
189.2.e.f.163.1	yes	6	3.2	odd	2
567.2.g.h.109.3		6	63.25	even	3
567.2.g.h.541.3		6	9.4	even	3
567.2.g.i.109.1		6	63.11	odd	6
567.2.g.i.541.1		6	9.5	odd	6
567.2.h.h.298.3		6	63.32	odd	6
567.2.h.h.352.3		6	9.2	odd	6
567.2.h.i.298.1		6	63.4	even	3
567.2.h.i.352.1		6	9.7	even	3
1323.2.a.x.1.3		3	21.2	odd	6
1323.2.a.y.1.3		3	21.5	even	6
1323.2.a.z.1.1		3	7.5	odd	6
1323.2.a.ba.1.1		3	7.2	even	3

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:	\( N \)	\(=\)	\( 189 = 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	189.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.730252 - 1.26483i) q^{2} +(-0.0665372 - 0.115246i) q^{4} +(0.296790 - 0.514055i) q^{5} +(2.32383 + 1.26483i) q^{7} +2.72665 q^{8} +O(q^{10})\)	\(q+(0.730252 - 1.26483i) q^{2} +(-0.0665372 - 0.115246i) q^{4} +(0.296790 - 0.514055i) q^{5} +(2.32383 + 1.26483i) q^{7} +2.72665 q^{8} +(-0.433463 - 0.750780i) q^{10} +(-2.23025 - 3.86291i) q^{11} -4.51459 q^{13} +(3.29679 - 2.01561i) q^{14} +(2.12422 - 3.67926i) q^{16} +(0.136673 + 0.236725i) q^{17} +(-1.43346 + 2.48283i) q^{19} -0.0789903 q^{20} -6.51459 q^{22} +(-2.52704 + 4.37697i) q^{23} +(2.32383 + 4.02499i) q^{25} +(-3.29679 + 5.71021i) q^{26} +(-0.00885441 - 0.351971i) q^{28} +0.352336 q^{29} +(-1.25729 - 2.17770i) q^{31} +(-0.375780 - 0.650870i) q^{32} +0.399223 q^{34} +(1.33988 - 0.819187i) q^{35} +(3.32383 - 5.75705i) q^{37} +(2.09358 + 3.62619i) q^{38} +(0.809243 - 1.40165i) q^{40} -10.8961 q^{41} +3.38151 q^{43} +(-0.296790 + 0.514055i) q^{44} +(3.69076 + 6.39258i) q^{46} +(-6.21780 + 10.7695i) q^{47} +(3.80039 + 5.87852i) q^{49} +6.78794 q^{50} +(0.300388 + 0.520288i) q^{52} +(-5.66372 - 9.80984i) q^{53} -2.64766 q^{55} +(6.33628 + 3.44877i) q^{56} +(0.257295 - 0.445647i) q^{58} +(4.02704 + 6.97504i) q^{59} +(1.36693 - 2.36758i) q^{61} -3.67257 q^{62} +7.39922 q^{64} +(-1.33988 + 2.32075i) q^{65} +(-2.93346 - 5.08091i) q^{67} +(0.0181877 - 0.0315020i) q^{68} +(-0.0576828 - 2.29294i) q^{70} +2.60078 q^{71} +(-5.55768 - 9.62619i) q^{73} +(-4.85447 - 8.40819i) q^{74} +0.381515 q^{76} +(-0.296790 - 11.7977i) q^{77} +(-5.58113 + 9.66679i) q^{79} +(-1.26089 - 2.18393i) q^{80} +(-7.95691 + 13.7818i) q^{82} +16.5438 q^{83} +0.162253 q^{85} +(2.46936 - 4.27706i) q^{86} +(-6.08113 - 10.5328i) q^{88} +(2.68716 - 4.65430i) q^{89} +(-10.4911 - 5.71021i) q^{91} +0.672570 q^{92} +(9.08113 + 15.7290i) q^{94} +(0.850874 + 1.47376i) q^{95} -2.26615 q^{97} +(10.2106 - 0.514055i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 2 q^{2} - 4 q^{4} - q^{5} + 2 q^{7} + 18 q^{8}+O(q^{10}) \) 6 * q - 2 * q^2 - 4 * q^4 - q^5 + 2 * q^7 + 18 * q^8	\( 6 q - 2 q^{2} - 4 q^{4} - q^{5} + 2 q^{7} + 18 q^{8} + q^{10} - 7 q^{11} + 4 q^{13} + 17 q^{14} - 10 q^{16} - 5 q^{19} - 26 q^{20} - 8 q^{22} - 6 q^{23} + 2 q^{25} - 17 q^{26} - 30 q^{28} + 26 q^{29} + 8 q^{31} - 25 q^{32} + 24 q^{34} + 10 q^{35} + 8 q^{37} + 7 q^{38} + 24 q^{40} + 4 q^{41} - 18 q^{43} + q^{44} + 3 q^{46} - 9 q^{47} + 12 q^{49} + 8 q^{50} - 9 q^{52} - 24 q^{53} + 8 q^{55} + 48 q^{56} - 14 q^{58} + 15 q^{59} + q^{61} - 42 q^{62} + 66 q^{64} - 10 q^{65} - 14 q^{67} - 39 q^{68} + 26 q^{70} - 6 q^{71} - 7 q^{73} - 36 q^{76} + q^{77} - 6 q^{79} + 16 q^{80} - 43 q^{82} + 6 q^{83} - 54 q^{85} + 32 q^{86} - 9 q^{88} + 5 q^{89} - 33 q^{91} + 24 q^{92} + 27 q^{94} - 16 q^{95} - 28 q^{97} + 49 q^{98}+O(q^{100}) \) 6 * q - 2 * q^2 - 4 * q^4 - q^5 + 2 * q^7 + 18 * q^8 + q^10 - 7 * q^11 + 4 * q^13 + 17 * q^14 - 10 * q^16 - 5 * q^19 - 26 * q^20 - 8 * q^22 - 6 * q^23 + 2 * q^25 - 17 * q^26 - 30 * q^28 + 26 * q^29 + 8 * q^31 - 25 * q^32 + 24 * q^34 + 10 * q^35 + 8 * q^37 + 7 * q^38 + 24 * q^40 + 4 * q^41 - 18 * q^43 + q^44 + 3 * q^46 - 9 * q^47 + 12 * q^49 + 8 * q^50 - 9 * q^52 - 24 * q^53 + 8 * q^55 + 48 * q^56 - 14 * q^58 + 15 * q^59 + q^61 - 42 * q^62 + 66 * q^64 - 10 * q^65 - 14 * q^67 - 39 * q^68 + 26 * q^70 - 6 * q^71 - 7 * q^73 - 36 * q^76 + q^77 - 6 * q^79 + 16 * q^80 - 43 * q^82 + 6 * q^83 - 54 * q^85 + 32 * q^86 - 9 * q^88 + 5 * q^89 - 33 * q^91 + 24 * q^92 + 27 * q^94 - 16 * q^95 - 28 * q^97 + 49 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more