LMFDB - Embedded newform 483.2.h.b.160.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,2,Mod(160,483)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(483, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 1]))

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

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

chi := DirichletCharacter("483.160");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	483.h (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.85677441763$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 14x^{10} + 67x^{8} + 141x^{6} + 129x^{4} + 39x^{2} + 1 $ x^12 + 14x^10 + 67x^8 + 141x^6 + 129x^4 + 39*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			160.10
Root			$0.712783i$ of defining polynomial
Character	$\chi$	$=$	483.160
Dual form			483.2.h.b.160.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.86081 q^{2} -1.00000i q^{3} +1.46260 q^{4} +4.10256 q^{5} -1.86081i q^{6} +(0.663393 + 2.56123i) q^{7} -1.00000 q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+1.86081 q^{2} -1.00000i q^{3} +1.46260 q^{4} +4.10256 q^{5} -1.86081i q^{6} +(0.663393 + 2.56123i) q^{7} -1.00000 q^{8} -1.00000 q^{9} +7.63407 q^{10} +1.89784i q^{11} -1.46260i q^{12} -2.18421i q^{13} +(1.23445 + 4.76596i) q^{14} -4.10256i q^{15} -4.78600 q^{16} -1.18482 q^{17} -1.86081 q^{18} -4.98050 q^{19} +6.00040 q^{20} +(2.56123 - 0.663393i) q^{21} +3.53151i q^{22} +(-4.25901 - 2.20472i) q^{23} +1.00000i q^{24} +11.8310 q^{25} -4.06439i q^{26} +1.00000i q^{27} +(0.970278 + 3.74605i) q^{28} +2.39821 q^{29} -7.63407i q^{30} -9.32340i q^{31} -6.90582 q^{32} +1.89784 q^{33} -2.20472 q^{34} +(2.72161 + 10.5076i) q^{35} -1.46260 q^{36} -6.92106i q^{37} -9.26774 q^{38} -2.18421 q^{39} -4.10256 q^{40} +5.60179i q^{41} +(4.76596 - 1.23445i) q^{42} +5.38663i q^{43} +2.77578i q^{44} -4.10256 q^{45} +(-7.92520 - 4.10256i) q^{46} -9.57201i q^{47} +4.78600i q^{48} +(-6.11982 + 3.39821i) q^{49} +22.0152 q^{50} +1.18482i q^{51} -3.19462i q^{52} +5.85844i q^{53} +1.86081i q^{54} +7.78600i q^{55} +(-0.663393 - 2.56123i) q^{56} +4.98050i q^{57} +4.46260 q^{58} +3.50761i q^{59} -6.00040i q^{60} +1.49171 q^{61} -17.3490i q^{62} +(-0.663393 - 2.56123i) q^{63} -3.27839 q^{64} -8.96086i q^{65} +3.53151 q^{66} +3.48879i q^{67} -1.73292 q^{68} +(-2.20472 + 4.25901i) q^{69} +(5.06439 + 19.5526i) q^{70} +1.81579 q^{71} +1.00000 q^{72} +7.97021i q^{73} -12.8787i q^{74} -11.8310i q^{75} -7.28447 q^{76} +(-4.86081 + 1.25901i) q^{77} -4.06439 q^{78} +14.0833i q^{79} -19.6349 q^{80} +1.00000 q^{81} +10.4238i q^{82} +2.51161 q^{83} +(3.74605 - 0.970278i) q^{84} -4.86081 q^{85} +10.0235i q^{86} -2.39821i q^{87} -1.89784i q^{88} -4.57437 q^{89} -7.63407 q^{90} +(5.59427 - 1.44899i) q^{91} +(-6.22923 - 3.22463i) q^{92} -9.32340 q^{93} -17.8116i q^{94} -20.4328 q^{95} +6.90582i q^{96} +7.44939 q^{97} +(-11.3878 + 6.32340i) q^{98} -1.89784i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 8 q^{4} - 12 q^{8} - 12 q^{9}+O(q^{10}) $ 12 * q + 8 * q^4 - 12 * q^8 - 12 * q^9	$ 12 q + 8 q^{4} - 12 q^{8} - 12 q^{9} - 16 q^{16} - 16 q^{23} + 24 q^{25} + 16 q^{29} + 16 q^{32} - 12 q^{35} - 8 q^{36} + 28 q^{39} - 76 q^{46} - 16 q^{49} + 92 q^{50} + 44 q^{58} - 84 q^{64} + 64 q^{70} + 76 q^{71} + 12 q^{72} - 36 q^{77} - 52 q^{78} + 12 q^{81} - 36 q^{85} + 56 q^{92} - 80 q^{93} - 140 q^{95} - 108 q^{98}+O(q^{100}) $ 12 * q + 8 * q^4 - 12 * q^8 - 12 * q^9 - 16 * q^16 - 16 * q^23 + 24 * q^25 + 16 * q^29 + 16 * q^32 - 12 * q^35 - 8 * q^36 + 28 * q^39 - 76 * q^46 - 16 * q^49 + 92 * q^50 + 44 * q^58 - 84 * q^64 + 64 * q^70 + 76 * q^71 + 12 * q^72 - 36 * q^77 - 52 * q^78 + 12 * q^81 - 36 * q^85 + 56 * q^92 - 80 * q^93 - 140 * q^95 - 108 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/483\mathbb{Z}\right)^\times$.

$n$	$323$	$346$	$442$
$\chi(n)$	$1$	$-1$	$-1$

Coefficient data

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

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

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

$2$	1.86081			1.31579			0.657894	−	0.753110i	$-0.271447\pi$
$2$	1.86081			1.31579			0.657894	+	0.753110i	$0.271447\pi$
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$	1.46260			0.731299
$5$	4.10256			1.83472			0.917361	−	0.398057i	$-0.130315\pi$
$5$	4.10256			1.83472			0.917361	+	0.398057i	$0.130315\pi$
$6$		−	1.86081i		−	0.759671i
$7$	0.663393	+	2.56123i	0.250739	+	0.968055i
$7$	0.663393	+	2.56123i	0.250739	+	0.968055i
$8$	−1.00000			−0.353553
$9$	−1.00000			−0.333333
$10$	7.63407			2.41411
$11$			1.89784i			0.572220i	0.958197	+	0.286110i	$0.0923623\pi$
$11$			1.89784i			0.572220i	−0.958197	+	0.286110i	$0.907638\pi$
$12$		−	1.46260i		−	0.422216i
$13$		−	2.18421i		−	0.605791i	−0.953024	−	0.302895i	$-0.902047\pi$
$13$		−	2.18421i		−	0.605791i	0.953024	−	0.302895i	$-0.0979533\pi$
$14$	1.23445	+	4.76596i	0.329920	+	1.27376i
$15$		−	4.10256i		−	1.05928i
$16$	−4.78600			−1.19650
$17$	−1.18482			−0.287362			−0.143681	−	0.989624i	$-0.545894\pi$
$17$	−1.18482			−0.287362			−0.143681	+	0.989624i	$0.545894\pi$
$18$	−1.86081			−0.438596
$19$	−4.98050			−1.14261			−0.571303	−	0.820740i	$-0.693562\pi$
$19$	−4.98050			−1.14261			−0.571303	+	0.820740i	$0.693562\pi$
$20$	6.00040			1.34173
$21$	2.56123	−	0.663393i	0.558907	−	0.144764i
$22$			3.53151i			0.752920i
$23$	−4.25901	−	2.20472i	−0.888066	−	0.459717i
$23$	−4.25901	−	2.20472i	−0.888066	−	0.459717i
$24$			1.00000i			0.204124i
$25$	11.8310			2.36620
$26$		−	4.06439i		−	0.797093i
$27$			1.00000i			0.192450i
$28$	0.970278	+	3.74605i	0.183365	+	0.707938i
$29$	2.39821			0.445336			0.222668	−	0.974894i	$-0.428523\pi$
$29$	2.39821			0.445336			0.222668	+	0.974894i	$0.428523\pi$
$30$		−	7.63407i		−	1.39378i
$31$		−	9.32340i		−	1.67453i	−0.546795	−	0.837266i	$-0.684152\pi$
$31$		−	9.32340i		−	1.67453i	0.546795	−	0.837266i	$-0.315848\pi$
$32$	−6.90582			−1.22079
$33$	1.89784			0.330371
$34$	−2.20472			−0.378107
$35$	2.72161	+	10.5076i	0.460036	+	1.77611i
$36$	−1.46260			−0.243766
$37$		−	6.92106i		−	1.13781i	−0.822402	−	0.568907i	$-0.807366\pi$
$37$		−	6.92106i		−	1.13781i	0.822402	−	0.568907i	$-0.192634\pi$
$38$	−9.26774			−1.50343
$39$	−2.18421			−0.349754
$40$	−4.10256			−0.648672
$41$			5.60179i			0.874853i	0.899254	+	0.437427i	$0.144110\pi$
$41$			5.60179i			0.874853i	−0.899254	+	0.437427i	$0.855890\pi$
$42$	4.76596	−	1.23445i	0.735403	−	0.190479i
$43$			5.38663i			0.821454i	0.911758	+	0.410727i	$0.134725\pi$
$43$			5.38663i			0.821454i	−0.911758	+	0.410727i	$0.865275\pi$
$44$			2.77578i			0.418464i
$45$	−4.10256			−0.611574
$46$	−7.92520	−	4.10256i	−1.16851	−	0.604890i
$47$		−	9.57201i		−	1.39622i	−0.715990	−	0.698110i	$-0.754025\pi$
$47$		−	9.57201i		−	1.39622i	0.715990	−	0.698110i	$-0.245975\pi$
$48$			4.78600i			0.690800i
$49$	−6.11982	+	3.39821i	−0.874260	+	0.485458i
$50$	22.0152			3.11342
$51$			1.18482i			0.165908i
$52$		−	3.19462i		−	0.443014i
$53$			5.85844i			0.804718i	0.915482	+	0.402359i	$0.131810\pi$
$53$			5.85844i			0.804718i	−0.915482	+	0.402359i	$0.868190\pi$
$54$			1.86081i			0.253224i
$55$			7.78600i			1.04986i
$56$	−0.663393	−	2.56123i	−0.0886496	−	0.342259i
$57$			4.98050i			0.659683i
$58$	4.46260			0.585968
$59$			3.50761i			0.456652i	0.973585	+	0.228326i	$0.0733253\pi$
$59$			3.50761i			0.456652i	−0.973585	+	0.228326i	$0.926675\pi$
$60$		−	6.00040i		−	0.774648i
$61$	1.49171			0.190993			0.0954967	−	0.995430i	$-0.469556\pi$
$61$	1.49171			0.190993			0.0954967	+	0.995430i	$0.469556\pi$
$62$		−	17.3490i		−	2.20333i
$63$	−0.663393	−	2.56123i	−0.0835797	−	0.322685i
$64$	−3.27839			−0.409799
$65$		−	8.96086i		−	1.11146i
$66$	3.53151			0.434699
$67$			3.48879i			0.426224i	0.977028	+	0.213112i	$0.0683599\pi$
$67$			3.48879i			0.426224i	−0.977028	+	0.213112i	$0.931640\pi$
$68$	−1.73292			−0.210147
$69$	−2.20472	+	4.25901i	−0.265418	+	0.512725i
$70$	5.06439	+	19.5526i	0.605311	+	2.33699i
$71$	1.81579			0.215495			0.107747	−	0.994178i	$-0.465636\pi$
$71$	1.81579			0.215495			0.107747	+	0.994178i	$0.465636\pi$
$72$	1.00000			0.117851
$73$			7.97021i			0.932843i	0.884563	+	0.466421i	$0.154457\pi$
$73$			7.97021i			0.932843i	−0.884563	+	0.466421i	$0.845543\pi$
$74$		−	12.8787i		−	1.49712i
$75$		−	11.8310i		−	1.36613i
$76$	−7.28447			−0.835586
$77$	−4.86081	+	1.25901i	−0.553940	+	0.143478i
$78$	−4.06439			−0.460202
$79$			14.0833i			1.58450i	0.610198	+	0.792249i	$0.291090\pi$
$79$			14.0833i			1.58450i	−0.610198	+	0.792249i	$0.708910\pi$
$80$	−19.6349			−2.19525
$81$	1.00000			0.111111
$82$			10.4238i			1.15112i
$83$	2.51161			0.275685			0.137842	−	0.990454i	$-0.455983\pi$
$83$	2.51161			0.275685			0.137842	+	0.990454i	$0.455983\pi$
$84$	3.74605	−	0.970278i	0.408728	−	0.105866i
$85$	−4.86081			−0.527228
$86$			10.0235i			1.08086i
$87$		−	2.39821i		−	0.257115i
$88$		−	1.89784i		−	0.202310i
$89$	−4.57437			−0.484882			−0.242441	−	0.970166i	$-0.577948\pi$
$89$	−4.57437			−0.484882			−0.242441	+	0.970166i	$0.577948\pi$
$90$	−7.63407			−0.804702
$91$	5.59427	−	1.44899i	0.586439	−	0.151895i
$92$	−6.22923	−	3.22463i	−0.649442	−	0.336190i
$93$	−9.32340			−0.966792
$94$		−	17.8116i		−	1.83713i
$95$	−20.4328			−2.09636
$96$			6.90582i			0.704822i
$97$	7.44939			0.756371			0.378186	−	0.925730i	$-0.376548\pi$
$97$	7.44939			0.756371			0.378186	+	0.925730i	$0.376548\pi$
$98$	−11.3878	+	6.32340i	−1.15034	+	0.638760i
$99$		−	1.89784i		−	0.190740i
$100$	17.3040			1.73040
$101$		−	17.1004i		−	1.70156i	−0.525524	−	0.850779i	$-0.676131\pi$
$101$		−	17.1004i		−	1.70156i	0.525524	−	0.850779i	$-0.323869\pi$
$102$			2.20472i			0.218300i
$103$	−8.91814			−0.878731			−0.439365	−	0.898308i	$-0.644797\pi$
$103$	−8.91814			−0.878731			−0.439365	+	0.898308i	$0.644797\pi$
$104$			2.18421i			0.214179i
$105$	10.5076	−	2.72161i	1.02544	−	0.265602i
$106$			10.9014i			1.05884i
$107$			6.51492i			0.629821i	0.949121	+	0.314911i	$0.101975\pi$
$107$			6.51492i			0.629821i	−0.949121	+	0.314911i	$0.898025\pi$
$108$			1.46260i			0.140739i
$109$			16.2880i			1.56011i	0.625710	+	0.780056i	$0.284809\pi$
$109$			16.2880i			1.56011i	−0.625710	+	0.780056i	$0.715191\pi$
$110$			14.4882i			1.38140i
$111$	−6.92106			−0.656917
$112$	−3.17500	−	12.2581i	−0.300009	−	1.15828i
$113$		−	15.5750i		−	1.46518i	−0.680673	−	0.732588i	$-0.738312\pi$
$113$		−	15.5750i		−	1.46518i	0.680673	−	0.732588i	$-0.261688\pi$
$114$			9.26774i			0.868004i
$115$	−17.4729	−	9.04502i	−1.62935	−	0.843452i
$116$	3.50761			0.325674
$117$			2.18421i			0.201930i
$118$			6.52699i			0.600858i
$119$	−0.786003	−	3.03460i	−0.0720527	−	0.278182i
$120$			4.10256i			0.374511i
$121$	7.39821			0.672564
$122$	2.77578			0.251307
$123$	5.60179			0.505097
$124$		−	13.6364i		−	1.22458i
$125$	28.0247			2.50660
$126$	−1.23445	−	4.76596i	−0.109973	−	0.424585i
$127$	1.10941			0.0984440			0.0492220	−	0.998788i	$-0.484326\pi$
$127$	1.10941			0.0984440			0.0492220	+	0.998788i	$0.484326\pi$
$128$	7.71120			0.681580
$129$	5.38663			0.474267
$130$		−	16.6744i		−	1.46244i
$131$			3.04502i			0.266044i	0.991113	+	0.133022i	$0.0424681\pi$
$131$			3.04502i			0.266044i	−0.991113	+	0.133022i	$0.957532\pi$
$132$	2.77578			0.241600
$133$	−3.30403	−	12.7562i	−0.286496	−	1.10610i
$134$			6.49197i			0.560821i
$135$			4.10256i			0.353092i
$136$	1.18482			0.101598
$137$			4.45216i			0.380374i	0.981748	+	0.190187i	$0.0609094\pi$
$137$			4.45216i			0.380374i	−0.981748	+	0.190187i	$0.939091\pi$
$138$	−4.10256	+	7.92520i	−0.349233	+	0.674638i
$139$			7.35801i			0.624098i	0.950066	+	0.312049i	$0.101015\pi$
$139$			7.35801i			0.624098i	−0.950066	+	0.312049i	$0.898985\pi$
$140$	3.98062	+	15.3684i	0.336424	+	1.29887i
$141$	−9.57201			−0.806108
$142$	3.37883			0.283545
$143$	4.14528			0.346646
$144$	4.78600			0.398834
$145$	9.83880			0.817068
$146$			14.8310i			1.22742i
$147$	3.39821	+	6.11982i	0.280279	+	0.504754i
$148$		−	10.1227i		−	0.832083i
$149$		−	20.7204i		−	1.69749i	−0.528806	−	0.848743i	$-0.677360\pi$
$149$		−	20.7204i		−	1.69749i	0.528806	−	0.848743i	$-0.322640\pi$
$150$		−	22.0152i		−	1.79754i
$151$	21.6620			1.76283			0.881416	−	0.472341i	$-0.156591\pi$
$151$	21.6620			1.76283			0.881416	+	0.472341i	$0.156591\pi$
$152$	4.98050			0.403972
$153$	1.18482			0.0957872
$154$	−9.04502	+	2.34278i	−0.728868	+	0.188787i
$155$		−	38.2498i		−	3.07230i
$156$	−3.19462			−0.255774
$157$	12.2847			0.980428			0.490214	−	0.871602i	$-0.336919\pi$
$157$	12.2847			0.980428			0.490214	+	0.871602i	$0.336919\pi$
$158$			26.2063i			2.08486i
$159$	5.85844			0.464604
$160$	−28.3316			−2.23981
$161$	2.82141	−	12.3709i	0.222358	−	0.974965i
$162$	1.86081			0.146199
$163$	−10.4328			−0.817161			−0.408580	−	0.912722i	$-0.633976\pi$
$163$	−10.4328			−0.817161			−0.408580	+	0.912722i	$0.633976\pi$
$164$			8.19317i			0.639779i
$165$	7.78600			0.606139
$166$	4.67362			0.362743
$167$			11.9702i			0.926283i	0.886284	+	0.463141i	$0.153278\pi$
$167$			11.9702i			0.926283i	−0.886284	+	0.463141i	$0.846722\pi$
$168$	−2.56123	+	0.663393i	−0.197603	+	0.0511819i
$169$	8.22923			0.633017
$170$	−9.04502			−0.693721
$171$	4.98050			0.380868
$172$			7.87848i			0.600728i
$173$		−	5.17380i		−	0.393357i	−0.980468	−	0.196678i	$-0.936985\pi$
$173$		−	5.17380i		−	0.393357i	0.980468	−	0.196678i	$-0.0630155\pi$
$174$		−	4.46260i		−	0.338309i
$175$	7.84862	+	30.3020i	0.593300	+	2.29061i
$176$		−	9.08306i		−	0.684662i
$177$	3.50761			0.263648
$178$	−8.51201			−0.638002
$179$	−14.5616			−1.08838			−0.544192	−	0.838961i	$-0.683164\pi$
$179$	−14.5616			−1.08838			−0.544192	+	0.838961i	$0.683164\pi$
$180$	−6.00040			−0.447244
$181$	17.4499			1.29704			0.648521	−	0.761197i	$-0.275388\pi$
$181$	17.4499			1.29704			0.648521	+	0.761197i	$0.275388\pi$
$182$	10.4098	−	2.69629i	0.771629	−	0.199862i
$183$		−	1.49171i		−	0.110270i
$184$	4.25901	+	2.20472i	0.313979	+	0.162534i
$185$		−	28.3941i		−	2.08757i
$186$	−17.3490			−1.27209
$187$		−	2.24860i		−	0.164434i
$188$		−	14.0000i		−	1.02105i
$189$	−2.56123	+	0.663393i	−0.186302	+	0.0482547i
$190$	−38.0215			−2.75837
$191$		−	4.07961i		−	0.295190i	−0.989048	−	0.147595i	$-0.952847\pi$
$191$		−	4.07961i		−	0.295190i	0.989048	−	0.147595i	$-0.0471532\pi$
$192$			3.27839i			0.236597i
$193$	22.8864			1.64740			0.823701	−	0.567024i	$-0.191905\pi$
$193$	22.8864			1.64740			0.823701	+	0.567024i	$0.191905\pi$
$194$	13.8619			0.995224
$195$	−8.96086			−0.641700
$196$	−8.95084	+	4.97021i	−0.639346	+	0.355015i
$197$	−0.702237			−0.0500323			−0.0250161	−	0.999687i	$-0.507964\pi$
$197$	−0.702237			−0.0500323			−0.0250161	+	0.999687i	$0.507964\pi$
$198$		−	3.53151i		−	0.250973i
$199$	−23.6947			−1.67967			−0.839837	−	0.542838i	$-0.817350\pi$
$199$	−23.6947			−1.67967			−0.839837	+	0.542838i	$0.817350\pi$
$200$	−11.8310			−0.836579
$201$	3.48879			0.246081
$202$		−	31.8206i		−	2.23889i
$203$	1.59095	+	6.14237i	0.111663	+	0.431110i
$204$			1.73292i			0.121329i
$205$			22.9817i			1.60511i
$206$	−16.5949			−1.15622
$207$	4.25901	+	2.20472i	0.296022	+	0.153239i
$208$			10.4536i			0.724829i
$209$		−	9.45219i		−	0.653821i
$210$	19.5526	−	5.06439i	1.34926	−	0.349476i
$211$	−20.7666			−1.42963			−0.714817	−	0.699312i	$-0.753490\pi$
$211$	−20.7666			−1.42963			−0.714817	+	0.699312i	$0.753490\pi$
$212$			8.56854i			0.588490i
$213$		−	1.81579i		−	0.124416i
$214$			12.1230i			0.828712i
$215$			22.0990i			1.50714i
$216$		−	1.00000i		−	0.0680414i
$217$	23.8794	−	6.18508i	1.62104	−	0.419871i
$218$			30.3089i			2.05278i
$219$	7.97021			0.538577
$220$			11.3878i			0.767765i
$221$			2.58790i			0.174081i
$222$	−12.8787			−0.864364
$223$			24.5228i			1.64217i	0.570805	+	0.821086i	$0.306631\pi$
$223$			24.5228i			1.64217i	−0.570805	+	0.821086i	$0.693369\pi$
$224$	−4.58127	−	17.6874i	−0.306099	−	1.18179i
$225$	−11.8310			−0.788735
$226$		−	28.9821i		−	1.92786i
$227$	21.5098			1.42765			0.713826	−	0.700323i	$-0.246961\pi$
$227$	21.5098			1.42765			0.713826	+	0.700323i	$0.246961\pi$
$228$			7.28447i			0.482426i
$229$	−10.4526			−0.690725			−0.345362	−	0.938469i	$-0.612244\pi$
$229$	−10.4526			−0.690725			−0.345362	+	0.938469i	$0.612244\pi$
$230$	−32.5136	−	16.8310i	−2.14388	−	1.10980i
$231$	1.25901	+	4.86081i	0.0828370	+	0.319818i
$232$	−2.39821			−0.157450
$233$	4.19317			0.274704			0.137352	−	0.990522i	$-0.456141\pi$
$233$	4.19317			0.274704			0.137352	+	0.990522i	$0.456141\pi$
$234$			4.06439i			0.265698i
$235$		−	39.2697i		−	2.56168i
$236$			5.13023i			0.333950i
$237$	14.0833			0.914810
$238$	−1.46260	−	5.64681i	−0.0948062	−	0.366028i
$239$	21.8552			1.41370			0.706848	−	0.707365i	$-0.250116\pi$
$239$	21.8552			1.41370			0.706848	+	0.707365i	$0.250116\pi$
$240$			19.6349i			1.26743i
$241$	−19.8196			−1.27669			−0.638345	−	0.769750i	$-0.720381\pi$
$241$	−19.8196			−1.27669			−0.638345	+	0.769750i	$0.720381\pi$
$242$	13.7666			0.884952
$243$		−	1.00000i		−	0.0641500i
$244$	2.18177			0.139673
$245$	−25.1069	+	13.9414i	−1.60402	+	0.890681i
$246$	10.4238			0.664600
$247$			10.8785i			0.692180i
$248$			9.32340i			0.592037i
$249$		−	2.51161i		−	0.159167i
$250$	52.1485			3.29816
$251$	7.92120			0.499981			0.249991	−	0.968248i	$-0.419572\pi$
$251$	7.92120			0.499981			0.249991	+	0.968248i	$0.419572\pi$
$252$	−0.970278	−	3.74605i	−0.0611218	−	0.235979i
$253$	4.18421	−	8.08292i	0.263059	−	0.508169i
$254$	2.06439			0.129531
$255$			4.86081i			0.304395i
$256$	20.9058			1.30661
$257$		−	12.0900i		−	0.754155i	−0.926182	−	0.377078i	$-0.876929\pi$
$257$		−	12.0900i		−	0.754155i	0.926182	−	0.377078i	$-0.123071\pi$
$258$	10.0235			0.624034
$259$	17.7264	−	4.59138i	1.10147	−	0.285294i
$260$		−	13.1061i		−	0.812808i
$261$	−2.39821			−0.148445
$262$			5.66618i			0.350058i
$263$		−	13.3703i		−	0.824448i	−0.911082	−	0.412224i	$-0.864752\pi$
$263$		−	13.3703i		−	0.824448i	0.911082	−	0.412224i	$-0.135248\pi$
$264$	−1.89784			−0.116804
$265$			24.0346i			1.47643i
$266$	−6.14816	−	23.7368i	−0.376968	−	1.45540i
$267$			4.57437i			0.279947i
$268$			5.10270i			0.311697i
$269$		−	15.6066i		−	0.951552i	−0.879567	−	0.475776i	$-0.842167\pi$
$269$		−	15.6066i		−	0.951552i	0.879567	−	0.475776i	$-0.157833\pi$
$270$			7.63407i			0.464595i
$271$		−	2.78745i		−	0.169326i	−0.996410	−	0.0846628i	$-0.973019\pi$
$271$		−	2.78745i		−	0.169326i	0.996410	−	0.0846628i	$-0.0269813\pi$
$272$	5.67056			0.343828
$273$	−1.44899	−	5.59427i	−0.0876969	−	0.338581i
$274$			8.28461i			0.500492i
$275$			22.4534i			1.35399i
$276$	−3.22463	+	6.22923i	−0.194100	+	0.374955i
$277$	−26.1246			−1.56968			−0.784839	−	0.619700i	$-0.787254\pi$
$277$	−26.1246			−1.56968			−0.784839	+	0.619700i	$0.787254\pi$
$278$			13.6918i			0.821181i
$279$			9.32340i			0.558178i
$280$	−2.72161	−	10.5076i	−0.162647	−	0.627950i
$281$			25.4138i			1.51606i	0.652219	+	0.758031i	$0.273838\pi$
$281$			25.4138i			1.51606i	−0.652219	+	0.758031i	$0.726162\pi$
$282$	−17.8116			−1.06067
$283$	−5.24467			−0.311763			−0.155882	−	0.987776i	$-0.549822\pi$
$283$	−5.24467			−0.311763			−0.155882	+	0.987776i	$0.549822\pi$
$284$	2.65577			0.157591
$285$			20.4328i			1.21034i
$286$	7.71356			0.456112
$287$	−14.3475	+	3.71619i	−0.846906	+	0.219360i
$288$	6.90582			0.406929
$289$	−15.5962			−0.917423
$290$	18.3081			1.07509
$291$		−	7.44939i		−	0.436691i
$292$			11.6572i			0.682187i
$293$	−24.5161			−1.43225			−0.716124	−	0.697973i	$-0.754085\pi$
$293$	−24.5161			−1.43225			−0.716124	+	0.697973i	$0.754085\pi$
$294$	6.32340	+	11.3878i	0.368788	+	0.664150i
$295$			14.3902i			0.837830i
$296$			6.92106i			0.402278i
$297$	−1.89784			−0.110124
$298$		−	38.5567i		−	2.23353i
$299$	−4.81558	+	9.30258i	−0.278492	+	0.537982i
$300$		−	17.3040i		−	0.999049i
$301$	−13.7964	+	3.57345i	−0.795212	+	0.205971i
$302$	40.3088			2.31951
$303$	−17.1004			−0.982395
$304$	23.8367			1.36713
$305$	6.11982			0.350420
$306$	2.20472			0.126036
$307$		−	33.2043i		−	1.89507i	−0.319657	−	0.947533i	$-0.603568\pi$
$307$		−	33.2043i		−	1.89507i	0.319657	−	0.947533i	$-0.396432\pi$
$308$	−7.10941	+	1.84143i	−0.405096	+	0.104925i
$309$			8.91814i			0.507335i
$310$		−	71.1755i		−	4.04250i
$311$		−	22.5526i		−	1.27884i	−0.768857	−	0.639421i	$-0.779174\pi$
$311$		−	22.5526i		−	1.27884i	0.768857	−	0.639421i	$-0.220826\pi$
$312$	2.18421			0.123657
$313$	4.07961			0.230593			0.115296	−	0.993331i	$-0.463218\pi$
$313$	4.07961			0.230593			0.115296	+	0.993331i	$0.463218\pi$
$314$	22.8595			1.29004
$315$	−2.72161	−	10.5076i	−0.153345	−	0.592037i
$316$			20.5982i			1.15874i
$317$	−12.8608			−0.722335			−0.361167	−	0.932501i	$-0.617622\pi$
$317$	−12.8608			−0.722335			−0.361167	+	0.932501i	$0.617622\pi$
$318$	10.9014			0.611321
$319$			4.55141i			0.254830i
$320$	−13.4498			−0.751866
$321$	6.51492			0.363628
$322$	5.25009	−	23.0199i	0.292576	−	1.28285i
$323$	5.90101			0.328341
$324$	1.46260			0.0812555
$325$		−	25.8414i		−	1.43342i
$326$	−19.4134			−1.07521
$327$	16.2880			0.900731
$328$		−	5.60179i		−	0.309307i
$329$	24.5161	−	6.35000i	1.35162	−	0.350087i
$330$	14.4882			0.797551
$331$	24.6081			1.35258			0.676291	−	0.736635i	$-0.263586\pi$
$331$	24.6081			1.35258			0.676291	+	0.736635i	$0.263586\pi$
$332$	3.67347			0.201608
$333$			6.92106i			0.379271i
$334$			22.2742i			1.21879i
$335$			14.3130i			0.782002i
$336$	−12.2581	+	3.17500i	−0.668732	+	0.173211i
$337$			1.77564i			0.0967250i	0.998830	+	0.0483625i	$0.0154003\pi$
$337$			1.77564i			0.0967250i	−0.998830	+	0.0483625i	$0.984600\pi$
$338$	15.3130			0.832917
$339$	−15.5750			−0.845919
$340$	−7.10941			−0.385562
$341$	17.6943			0.958201
$342$	9.26774			0.501142
$343$	−12.7634	−	13.4199i	−0.689161	−	0.724608i
$344$		−	5.38663i		−	0.290428i
$345$	−9.04502	+	17.4729i	−0.486967	+	0.940708i
$346$		−	9.62743i		−	0.517574i
$347$	0.766628			0.0411547			0.0205774	−	0.999788i	$-0.493450\pi$
$347$	0.766628			0.0411547			0.0205774	+	0.999788i	$0.493450\pi$
$348$		−	3.50761i		−	0.188028i
$349$		−	12.9896i		−	0.695317i	−0.937621	−	0.347658i	$-0.886977\pi$
$349$		−	12.9896i		−	0.695317i	0.937621	−	0.347658i	$-0.113023\pi$
$350$	14.6048	+	56.3861i	0.780657	+	3.01396i
$351$	2.18421			0.116585
$352$		−	13.1061i		−	0.698559i
$353$		−	0.736170i		−	0.0391824i	−0.999808	−	0.0195912i	$-0.993764\pi$
$353$		−	0.736170i		−	0.0391824i	0.999808	−	0.0195912i	$-0.00623647\pi$
$354$	6.52699			0.346906
$355$	7.44939			0.395373
$356$	−6.69046			−0.354594
$357$	−3.03460	+	0.786003i	−0.160608	+	0.0415997i
$358$	−27.0963			−1.43208
$359$		−	24.8230i		−	1.31011i	−0.755582	−	0.655054i	$-0.772646\pi$
$359$		−	24.8230i		−	1.31011i	0.755582	−	0.655054i	$-0.227354\pi$
$360$	4.10256			0.216224
$361$	5.80538			0.305546
$362$	32.4709			1.70663
$363$		−	7.39821i		−	0.388305i
$364$	8.18217	−	2.11929i	0.428862	−	0.111081i
$365$			32.6983i			1.71151i
$366$		−	2.77578i		−	0.145092i
$367$	22.7405			1.18704			0.593522	−	0.804818i	$-0.297737\pi$
$367$	22.7405			1.18704			0.593522	+	0.804818i	$0.297737\pi$
$368$	20.3836	+	10.5518i	1.06257	+	0.550051i
$369$		−	5.60179i		−	0.291618i
$370$		−	52.8358i		−	2.74680i
$371$	−15.0048	+	3.88645i	−0.779011	+	0.201774i
$372$	−13.6364			−0.707014
$373$		−	28.9224i		−	1.49754i	−0.662828	−	0.748772i	$-0.730644\pi$
$373$		−	28.9224i		−	1.49754i	0.662828	−	0.748772i	$-0.269356\pi$
$374$		−	4.18421i		−	0.216360i
$375$		−	28.0247i		−	1.44719i
$376$			9.57201i			0.493638i
$377$		−	5.23819i		−	0.269780i
$378$	−4.76596	+	1.23445i	−0.245134	+	0.0634930i
$379$			5.53774i			0.284454i	0.989834	+	0.142227i	$0.0454264\pi$
$379$			5.53774i			0.284454i	−0.989834	+	0.142227i	$0.954574\pi$
$380$	−29.8850			−1.53307
$381$		−	1.10941i		−	0.0568366i
$382$		−	7.59136i		−	0.388408i
$383$	−25.6550			−1.31091			−0.655456	−	0.755234i	$-0.727523\pi$
$383$	−25.6550			−1.31091			−0.655456	+	0.755234i	$0.727523\pi$
$384$		−	7.71120i		−	0.393511i
$385$	−19.9418	+	5.16518i	−1.01633	+	0.263242i
$386$	42.5872			2.16763
$387$		−	5.38663i		−	0.273818i
$388$	10.8955			0.553134
$389$			9.10602i			0.461693i	0.972990	+	0.230847i	$0.0741496\pi$
$389$			9.10602i			0.461693i	−0.972990	+	0.230847i	$0.925850\pi$
$390$	−16.6744			−0.844342
$391$	5.04617	+	2.61220i	0.255196	+	0.132105i
$392$	6.11982	−	3.39821i	0.309098	−	0.171635i
$393$	3.04502			0.153601
$394$	−1.30673			−0.0658319
$395$			57.7777i			2.90711i
$396$		−	2.77578i		−	0.139488i
$397$			18.6468i			0.935856i	0.883766	+	0.467928i	$0.154999\pi$
$397$			18.6468i			0.935856i	−0.883766	+	0.467928i	$0.845001\pi$
$398$	−44.0913			−2.21010
$399$	−12.7562	+	3.30403i	−0.638610	+	0.165408i
$400$	−56.6233			−2.83116
$401$			28.7377i			1.43509i	0.696511	+	0.717546i	$0.254735\pi$
$401$			28.7377i			1.43509i	−0.696511	+	0.717546i	$0.745265\pi$
$402$	6.49197			0.323790
$403$	−20.3643			−1.01442
$404$		−	25.0111i		−	1.24435i
$405$	4.10256			0.203858
$406$	2.96046	+	11.4298i	0.146925	+	0.567249i
$407$	13.1350			0.651080
$408$		−	1.18482i		−	0.0586574i
$409$			20.6170i			1.01945i	0.860339	+	0.509723i	$0.170252\pi$
$409$			20.6170i			1.01945i	−0.860339	+	0.509723i	$0.829748\pi$
$410$			42.7645i			2.11199i
$411$	4.45216			0.219609
$412$	−13.0437			−0.642615
$413$	−8.98381	+	2.32693i	−0.442065	+	0.114501i
$414$	7.92520	+	4.10256i	0.389502	+	0.201630i
$415$	10.3040			0.505805
$416$			15.0838i			0.739542i
$417$	7.35801			0.360323
$418$		−	17.5887i		−	0.860291i
$419$	−36.4940			−1.78285			−0.891424	−	0.453171i	$-0.850293\pi$
$419$	−36.4940			−1.78285			−0.891424	+	0.453171i	$0.850293\pi$
$420$	15.3684	−	3.98062i	0.749902	−	0.194235i
$421$			16.7599i			0.816825i	0.912797	+	0.408413i	$0.133918\pi$
$421$			16.7599i			0.816825i	−0.912797	+	0.408413i	$0.866082\pi$
$422$	−38.6427			−1.88110
$423$			9.57201i			0.465407i
$424$		−	5.85844i		−	0.284511i
$425$	−14.0177			−0.679956
$426$		−	3.37883i		−	0.163705i
$427$	0.989588	+	3.82061i	0.0478895	+	0.184892i
$428$			9.52872i			0.460588i
$429$		−	4.14528i		−	0.200136i
$430$			41.1219i			1.98308i
$431$		−	13.6910i		−	0.659472i	−0.944073	−	0.329736i	$-0.893040\pi$
$431$		−	13.6910i		−	0.659472i	0.944073	−	0.329736i	$-0.106960\pi$
$432$		−	4.78600i		−	0.230267i
$433$	8.81889			0.423809			0.211905	−	0.977290i	$-0.432033\pi$
$433$	8.81889			0.423809			0.211905	+	0.977290i	$0.432033\pi$
$434$	44.4349	−	11.5092i	2.13294	−	0.552461i
$435$		−	9.83880i		−	0.471734i
$436$			23.8229i			1.14091i
$437$	21.2120	+	10.9806i	1.01471	+	0.525275i
$438$	14.8310			0.708653
$439$			19.0034i			0.906981i	0.891261	+	0.453491i	$0.149821\pi$
$439$			19.0034i			0.906981i	−0.891261	+	0.453491i	$0.850179\pi$
$440$		−	7.78600i		−	0.371183i
$441$	6.11982	−	3.39821i	0.291420	−	0.161819i
$442$			4.81558i			0.229054i
$443$	20.3476			0.966743			0.483372	−	0.875415i	$-0.339412\pi$
$443$	20.3476			0.966743			0.483372	+	0.875415i	$0.339412\pi$
$444$	−10.1227			−0.480403
$445$	−18.7666			−0.889623
$446$			45.6323i			2.16075i
$447$	−20.7204			−0.980044
$448$	−2.17486	−	8.39671i	−0.102752	−	0.396707i
$449$	−20.6724			−0.975593			−0.487797	−	0.872957i	$-0.662199\pi$
$449$	−20.6724			−0.975593			−0.487797	+	0.872957i	$0.662199\pi$
$450$	−22.0152			−1.03781
$451$	−10.6313			−0.500608
$452$		−	22.7800i		−	1.07148i
$453$		−	21.6620i		−	1.01777i
$454$	40.0255			1.87849
$455$	22.9508	−	5.94457i	1.07595	−	0.278686i
$456$		−	4.98050i		−	0.233233i
$457$		−	33.5565i		−	1.56971i	−0.619682	−	0.784853i	$-0.712739\pi$
$457$		−	33.5565i		−	1.56971i	0.619682	−	0.784853i	$-0.287261\pi$
$458$	−19.4502			−0.908848
$459$		−	1.18482i		−	0.0553028i
$460$	−25.5558	−	13.2292i	−1.19154	−	0.616816i
$461$			3.26798i			0.152205i	0.997100	+	0.0761024i	$0.0242476\pi$
$461$			3.26798i			0.152205i	−0.997100	+	0.0761024i	$0.975752\pi$
$462$	2.34278	+	9.04502i	0.108996	+	0.420812i
$463$	−4.65577			−0.216372			−0.108186	−	0.994131i	$-0.534504\pi$
$463$	−4.65577			−0.216372			−0.108186	+	0.994131i	$0.534504\pi$
$464$	−11.4778			−0.532845
$465$	−38.2498			−1.77379
$466$	7.80268			0.361452
$467$	−17.2514			−0.798300			−0.399150	−	0.916886i	$-0.630695\pi$
$467$	−17.2514			−0.798300			−0.399150	+	0.916886i	$0.630695\pi$
$468$			3.19462i			0.147671i
$469$	−8.93561	+	2.31444i	−0.412608	+	0.106871i
$470$		−	73.0734i		−	3.37062i
$471$		−	12.2847i		−	0.566051i
$472$		−	3.50761i		−	0.161451i
$473$	−10.2230			−0.470052
$474$	26.2063			1.20370
$475$	−58.9244			−2.70364
$476$	−1.14961	−	4.43841i	−0.0526921	−	0.203434i
$477$		−	5.85844i		−	0.268239i
$478$	40.6683			1.86012
$479$	−20.4333			−0.933622			−0.466811	−	0.884357i	$-0.654597\pi$
$479$	−20.4333			−0.933622			−0.466811	+	0.884357i	$0.654597\pi$
$480$			28.3316i			1.29315i
$481$	−15.1170			−0.689278
$482$	−36.8803			−1.67985
$483$	−12.3709	−	2.82141i	−0.562896	−	0.128379i
$484$	10.8206			0.491846
$485$	30.5616			1.38773
$486$		−	1.86081i		−	0.0844079i
$487$	3.36215			0.152354			0.0761769	−	0.997094i	$-0.475729\pi$
$487$	3.36215			0.152354			0.0761769	+	0.997094i	$0.475729\pi$
$488$	−1.49171			−0.0675264
$489$			10.4328i			0.471788i
$490$	−46.7191	+	25.9422i	−2.11056	+	1.17195i
$491$	2.76181			0.124639			0.0623194	−	0.998056i	$-0.480150\pi$
$491$	2.76181			0.124639			0.0623194	+	0.998056i	$0.480150\pi$
$492$	8.19317			0.369377
$493$	−2.84145			−0.127972
$494$			20.2427i			0.910762i
$495$		−	7.78600i		−	0.349955i
$496$			44.6218i			2.00358i
$497$	1.20458	+	4.65066i	0.0540329	+	0.208611i
$498$		−	4.67362i		−	0.209430i
$499$	38.4328			1.72049			0.860244	−	0.509882i	$-0.170311\pi$
$499$	38.4328			1.72049			0.860244	+	0.509882i	$0.170311\pi$
$500$	40.9889			1.83308
$501$	11.9702			0.534790
$502$	14.7398			0.657870
$503$	11.5092			0.513172			0.256586	−	0.966521i	$-0.417402\pi$
$503$	11.5092			0.513172			0.256586	+	0.966521i	$0.417402\pi$
$504$	0.663393	+	2.56123i	0.0295499	+	0.114086i
$505$		−	70.1556i		−	3.12189i
$506$	7.78600	−	15.0407i	0.346130	−	0.668643i
$507$		−	8.22923i		−	0.365473i
$508$	1.62262			0.0719920
$509$			2.12878i			0.0943566i	0.998886	+	0.0471783i	$0.0150229\pi$
$509$			2.12878i			0.0943566i	−0.998886	+	0.0471783i	$0.984977\pi$
$510$			9.04502i			0.400520i
$511$	−20.4136	+	5.28738i	−0.903043	+	0.233900i
$512$	23.4793			1.03765
$513$		−	4.98050i		−	0.219894i
$514$		−	22.4972i		−	0.992309i
$515$	−36.5872			−1.61223
$516$	7.87848			0.346831
$517$	18.1661			0.798945
$518$	32.9854	−	8.54367i	1.44930	−	0.375387i
$519$	−5.17380			−0.227105
$520$			8.96086i			0.392960i
$521$	−24.4702			−1.07206			−0.536030	−	0.844199i	$-0.680077\pi$
$521$	−24.4702			−1.07206			−0.536030	+	0.844199i	$0.680077\pi$
$522$	−4.46260			−0.195323
$523$	−27.4141			−1.19874			−0.599368	−	0.800474i	$-0.704581\pi$
$523$	−27.4141			−1.19874			−0.599368	+	0.800474i	$0.704581\pi$
$524$			4.45364i			0.194558i
$525$	30.3020	−	7.84862i	1.32249	−	0.342542i
$526$		−	24.8795i		−	1.08480i
$527$			11.0466i			0.481196i
$528$	−9.08306			−0.395290
$529$	13.2784	+	18.7799i	0.577321	+	0.816517i
$530$			44.7237i			1.94267i
$531$		−	3.50761i		−	0.152217i
$532$	−4.83247	−	18.6572i	−0.209514	−	0.808893i
$533$	12.2355			0.529978
$534$			8.51201i			0.368351i
$535$			26.7279i			1.15555i
$536$		−	3.48879i		−	0.150693i
$537$			14.5616i			0.628379i
$538$		−	29.0409i		−	1.25204i
$539$	−6.44925	−	11.6144i	−0.277789	−	0.500269i
$540$			6.00040i			0.258216i
$541$	−22.6468			−0.973662			−0.486831	−	0.873496i	$-0.661847\pi$
$541$	−22.6468			−0.973662			−0.486831	+	0.873496i	$0.661847\pi$
$542$		−	5.18691i		−	0.222797i
$543$		−	17.4499i		−	0.748847i
$544$	8.18217			0.350808
$545$			66.8227i			2.86237i
$546$	−2.69629	−	10.4098i	−0.115391	−	0.445500i
$547$	24.1544			1.03277			0.516384	−	0.856357i	$-0.327278\pi$
$547$	24.1544			1.03277			0.516384	+	0.856357i	$0.327278\pi$
$548$			6.51173i			0.278167i
$549$	−1.49171			−0.0636645
$550$			41.7814i			1.78156i
$551$	−11.9443			−0.508843
$552$	2.20472	−	4.25901i	0.0938393	−	0.181276i
$553$	−36.0707	+	9.34278i	−1.53388	+	0.397295i
$554$	−48.6129			−2.06536
$555$	−28.3941			−1.20526
$556$			10.7618i			0.456402i
$557$		−	12.6008i		−	0.533911i	−0.963709	−	0.266956i	$-0.913982\pi$
$557$		−	12.6008i		−	0.533911i	0.963709	−	0.266956i	$-0.0860177\pi$
$558$			17.3490i			0.734444i
$559$	11.7655			0.497629
$560$	−13.0256	−	50.2895i	−0.550434	−	2.12512i
$561$	−2.24860			−0.0949360
$562$			47.2902i			1.99482i
$563$	2.96365			0.124903			0.0624515	−	0.998048i	$-0.480108\pi$
$563$	2.96365			0.124903			0.0624515	+	0.998048i	$0.480108\pi$
$564$	−14.0000			−0.589506
$565$		−	63.8975i		−	2.68819i
$566$	−9.75931			−0.410214
$567$	0.663393	+	2.56123i	0.0278599	+	0.107562i
$568$	−1.81579			−0.0761889
$569$		−	14.1399i		−	0.592774i	−0.955068	−	0.296387i	$-0.904218\pi$
$569$		−	14.1399i		−	0.592774i	0.955068	−	0.296387i	$-0.0957817\pi$
$570$			38.0215i			1.59255i
$571$			19.0211i			0.796009i	0.917384	+	0.398004i	$0.130297\pi$
$571$			19.0211i			0.796009i	−0.917384	+	0.398004i	$0.869703\pi$
$572$	6.06288			0.253502
$573$	−4.07961			−0.170428
$574$	−26.6979	+	6.91511i	−1.11435	+	0.288631i
$575$	−50.3885	−	26.0841i	−2.10134	−	1.08778i
$576$	3.27839			0.136600
$577$			7.11355i			0.296141i	0.988977	+	0.148071i	$0.0473063\pi$
$577$			7.11355i			0.296141i	−0.988977	+	0.148071i	$0.952694\pi$
$578$	−29.0215			−1.20714
$579$		−	22.8864i		−	0.951128i
$580$	14.3902			0.597521
$581$	1.66618	+	6.43281i	0.0691249	+	0.266878i
$582$		−	13.8619i		−	0.574593i
$583$	−11.1184			−0.460476
$584$		−	7.97021i		−	0.329810i
$585$			8.96086i			0.370486i
$586$	−45.6198			−1.88453
$587$		−	30.9419i		−	1.27711i	−0.769577	−	0.638554i	$-0.779533\pi$
$587$		−	30.9419i		−	1.27711i	0.769577	−	0.638554i	$-0.220467\pi$
$588$	4.97021	+	8.95084i	0.204968	+	0.369126i
$589$			46.4352i			1.91333i
$590$			26.7774i			1.10241i
$591$			0.702237i			0.0288862i
$592$			33.1242i			1.36140i
$593$		−	25.4253i		−	1.04409i	−0.852917	−	0.522046i	$-0.825169\pi$
$593$		−	25.4253i		−	1.04409i	0.852917	−	0.522046i	$-0.174831\pi$
$594$	−3.53151			−0.144900
$595$	−3.22463	−	12.4497i	−0.132197	−	0.510386i
$596$		−	30.3057i		−	1.24137i
$597$			23.6947i			0.969760i
$598$	−8.96086	+	17.3103i	−0.366437	+	0.707871i
$599$	5.08858			0.207914			0.103957	−	0.994582i	$-0.466850\pi$
$599$	5.08858			0.207914			0.103957	+	0.994582i	$0.466850\pi$
$600$			11.8310i			0.482999i
$601$			29.1004i			1.18703i	0.804822	+	0.593516i	$0.202261\pi$
$601$			29.1004i			1.18703i	−0.804822	+	0.593516i	$0.797739\pi$
$602$	−25.6724	+	6.64951i	−1.04633	+	0.271014i
$603$		−	3.48879i		−	0.142075i
$604$	31.6829			1.28916
$605$	30.3516			1.23397
$606$	−31.8206			−1.29262
$607$			19.5679i			0.794235i	0.917768	+	0.397117i	$0.129989\pi$
$607$			19.5679i			0.794235i	−0.917768	+	0.397117i	$0.870011\pi$
$608$	34.3944			1.39488
$609$	6.14237	−	1.59095i	0.248901	−	0.0644687i
$610$	11.3878			0.461078
$611$	−20.9073			−0.845818
$612$	1.73292			0.0700491
$613$		−	1.89784i		−	0.0766530i	−0.999265	−	0.0383265i	$-0.987797\pi$
$613$		−	1.89784i		−	0.0766530i	0.999265	−	0.0383265i	$-0.0122027\pi$
$614$		−	61.7867i		−	2.49351i
$615$	22.9817			0.926712
$616$	4.86081	−	1.25901i	0.195847	−	0.0507271i
$617$			26.4903i			1.06646i	0.845971	+	0.533229i	$0.179022\pi$
$617$			26.4903i			1.06646i	−0.845971	+	0.533229i	$0.820978\pi$
$618$			16.5949i			0.667546i
$619$	28.9058			1.16182			0.580911	−	0.813967i	$-0.302696\pi$
$619$	28.9058			1.16182			0.580911	+	0.813967i	$0.302696\pi$
$620$		−	55.9442i		−	2.24677i
$621$	2.20472	−	4.25901i	0.0884725	−	0.170908i
$622$		−	41.9661i		−	1.68269i
$623$	−3.03460	−	11.7160i	−0.121579	−	0.469392i
$624$	10.4536			0.418480
$625$	55.8179			2.23272
$626$	7.59136			0.303412
$627$	−9.45219			−0.377484
$628$	17.9676			0.716986
$629$			8.20022i			0.326964i
$630$	−5.06439	−	19.5526i	−0.201770	−	0.778995i
$631$			11.9976i			0.477617i	0.971067	+	0.238809i	$0.0767569\pi$
$631$			11.9976i			0.477617i	−0.971067	+	0.238809i	$0.923243\pi$
$632$		−	14.0833i		−	0.560204i
$633$			20.7666i			0.825399i
$634$	−23.9315			−0.950440
$635$	4.55141			0.180617
$636$	8.56854			0.339765
$637$	7.42240	+	13.3670i	0.294086	+	0.529619i
$638$			8.46929i			0.335303i
$639$	−1.81579			−0.0718315
$640$	31.6357			1.25051
$641$			24.2520i			0.957895i	0.877844	+	0.478947i	$0.158982\pi$
$641$			24.2520i			0.957895i	−0.877844	+	0.478947i	$0.841018\pi$
$642$	12.1230			0.478457
$643$	22.8931			0.902815			0.451407	−	0.892318i	$-0.350922\pi$
$643$	22.8931			0.902815			0.451407	+	0.892318i	$0.350922\pi$
$644$	4.12659	−	18.0937i	0.162610	−	0.712991i
$645$	22.0990			0.870147
$646$	10.9806			0.432027
$647$		−	22.0948i		−	0.868638i	−0.900759	−	0.434319i	$-0.856989\pi$
$647$		−	22.0948i		−	0.868638i	0.900759	−	0.434319i	$-0.143011\pi$
$648$	−1.00000			−0.0392837
$649$	−6.65689			−0.261306
$650$		−	48.0859i		−	1.88608i
$651$	−6.18508	−	23.8794i	−0.242412	−	0.935908i
$652$	−15.2590			−0.597589
$653$	0.680742			0.0266395			0.0133197	−	0.999911i	$-0.495760\pi$
$653$	0.680742			0.0266395			0.0133197	+	0.999911i	$0.495760\pi$
$654$	30.3089			1.18517
$655$			12.4924i			0.488117i
$656$		−	26.8102i		−	1.04676i
$657$		−	7.97021i		−	0.310948i
$658$	45.6198	−	11.8161i	1.77844	−	0.460640i
$659$		−	10.1425i		−	0.395095i	−0.980293	−	0.197548i	$-0.936702\pi$
$659$		−	10.1425i		−	0.395095i	0.980293	−	0.197548i	$-0.0632977\pi$
$660$	11.3878			0.443269
$661$	3.93764			0.153157			0.0765783	−	0.997064i	$-0.475600\pi$
$661$	3.93764			0.153157			0.0765783	+	0.997064i	$0.475600\pi$
$662$	45.7908			1.77971
$663$	2.58790			0.100506
$664$	−2.51161			−0.0974693
$665$	−13.5550	−	52.3332i	−0.525640	−	2.02939i
$666$			12.8787i			0.499041i
$667$	−10.2140	−	5.28738i	−0.395488	−	0.204728i
$668$			17.5076i			0.677390i
$669$	24.5228			0.948108
$670$			26.6337i			1.02895i
$671$			2.83102i			0.109290i
$672$	−17.6874	+	4.58127i	−0.682307	+	0.176727i
$673$	14.5062			0.559172			0.279586	−	0.960121i	$-0.409803\pi$
$673$	14.5062			0.559172			0.279586	+	0.960121i	$0.409803\pi$
$674$			3.30411i			0.127270i
$675$			11.8310i			0.455376i
$676$	12.0361			0.462925
$677$	7.46596			0.286940			0.143470	−	0.989655i	$-0.454174\pi$
$677$	7.46596			0.286940			0.143470	+	0.989655i	$0.454174\pi$
$678$	−28.9821			−1.11305
$679$	4.94187	+	19.0796i	0.189652	+	0.732209i
$680$	4.86081			0.186403
$681$		−	21.5098i		−	0.824256i
$682$	32.9257			1.26079
$683$	17.5243			0.670548			0.335274	−	0.942121i	$-0.391171\pi$
$683$	17.5243			0.670548			0.335274	+	0.942121i	$0.391171\pi$
$684$	7.28447			0.278529
$685$			18.2653i			0.697880i
$686$	−23.7503	−	24.9719i	−0.906790	−	0.953431i
$687$			10.4526i			0.398790i
$688$		−	25.7804i		−	0.982870i
$689$	12.7961			0.487491
$690$	−16.8310	+	32.5136i	−0.640746	+	1.23777i
$691$			23.4391i			0.891665i	0.895117	+	0.445832i	$0.147092\pi$
$691$			23.4391i			0.891665i	−0.895117	+	0.445832i	$0.852908\pi$
$692$		−	7.56719i		−	0.287661i
$693$	4.86081	−	1.25901i	0.184647	−	0.0478260i
$694$	1.42655			0.0541509
$695$			30.1867i			1.14505i
$696$			2.39821i			0.0909038i
$697$		−	6.63713i		−	0.251399i
$698$		−	24.1711i		−	0.914890i
$699$		−	4.19317i		−	0.158600i
$700$	11.4794	+	44.3196i	0.433880	+	1.67512i
$701$		−	5.57451i		−	0.210546i	−0.994443	−	0.105273i	$-0.966428\pi$
$701$		−	5.57451i		−	0.210546i	0.994443	−	0.105273i	$-0.0335717\pi$
$702$	4.06439			0.153401
$703$			34.4703i			1.30007i
$704$		−	6.22185i		−	0.234495i
$705$	−39.2697			−1.47898
$706$		−	1.36987i		−	0.0515557i
$707$	43.7982	−	11.3443i	1.64720	−	0.426647i
$708$	5.13023			0.192806
$709$		−	10.9244i		−	0.410273i	−0.978733	−	0.205137i	$-0.934236\pi$
$709$		−	10.9244i		−	0.410273i	0.978733	−	0.205137i	$-0.0657639\pi$
$710$	13.8619			0.520227
$711$		−	14.0833i		−	0.528166i
$712$	4.57437			0.171432
$713$	−20.5555	+	39.7085i	−0.769811	+	1.48710i
$714$	−5.64681	+	1.46260i	−0.211326	+	0.0547364i
$715$	17.0063			0.635998
$716$	−21.2978			−0.795935
$717$		−	21.8552i		−	0.816198i
$718$		−	46.1908i		−	1.72383i
$719$		−	40.9162i		−	1.52592i	−0.646447	−	0.762959i	$-0.723746\pi$
$719$		−	40.9162i		−	1.52592i	0.646447	−	0.762959i	$-0.276254\pi$
$720$	19.6349			0.731749
$721$	−5.91623	−	22.8414i	−0.220332	−	0.850659i
$722$	10.8027			0.402034
$723$			19.8196i			0.737097i
$724$	25.5222			0.948526
$725$	28.3732			1.05376
$726$		−	13.7666i		−	0.510927i
$727$	20.8165			0.772041			0.386021	−	0.922490i	$-0.373849\pi$
$727$	20.8165			0.772041			0.386021	+	0.922490i	$0.373849\pi$
$728$	−5.59427	+	1.44899i	−0.207337	+	0.0537031i
$729$	−1.00000			−0.0370370
$730$			60.8452i			2.25198i
$731$		−	6.38220i		−	0.236054i
$732$		−	2.18177i		−	0.0806405i
$733$	43.2639			1.59799			0.798995	−	0.601338i	$-0.205365\pi$
$733$	43.2639			1.59799			0.798995	+	0.601338i	$0.205365\pi$
$734$	42.3156			1.56190
$735$	13.9414	+	25.1069i	0.514235	+	0.926083i
$736$	29.4120	+	15.2254i	1.08414	+	0.561217i
$737$	−6.62117			−0.243894
$738$		−	10.4238i		−	0.383707i
$739$	−17.4343			−0.641330			−0.320665	−	0.947193i	$-0.603906\pi$
$739$	−17.4343			−0.641330			−0.320665	+	0.947193i	$0.603906\pi$
$740$		−	41.5291i		−	1.52664i
$741$	10.8785			0.399630
$742$	−27.9211	+	7.23192i	−1.02501	+	0.265492i
$743$			45.3129i			1.66237i	0.555998	+	0.831184i	$0.312336\pi$
$743$			45.3129i			1.66237i	−0.555998	+	0.831184i	$0.687664\pi$
$744$	9.32340			0.341813
$745$		−	85.0069i		−	3.11441i
$746$		−	53.8189i		−	1.97045i
$747$	−2.51161			−0.0918949
$748$		−	3.28880i		−	0.120250i
$749$	−16.6862	+	4.32195i	−0.609702	+	0.157921i
$750$		−	52.1485i		−	1.90419i
$751$		−	7.41582i		−	0.270607i	−0.990804	−	0.135303i	$-0.956799\pi$
$751$		−	7.41582i		−	0.270607i	0.990804	−	0.135303i	$-0.0432009\pi$
$752$			45.8116i			1.67058i
$753$		−	7.92120i		−	0.288664i
$754$		−	9.74725i		−	0.354974i
$755$	88.8699			3.23431
$756$	−3.74605	+	0.970278i	−0.136243	+	0.0352887i
$757$			37.6558i			1.36862i	0.729189	+	0.684312i	$0.239898\pi$
$757$			37.6558i			1.36862i	−0.729189	+	0.684312i	$0.760102\pi$
$758$			10.3047i			0.374282i
$759$	−8.08292	−	4.18421i	−0.293391	−	0.151877i
$760$	20.4328			0.741176
$761$			31.7312i			1.15026i	0.818063	+	0.575128i	$0.195048\pi$
$761$			31.7312i			1.15026i	−0.818063	+	0.575128i	$0.804952\pi$
$762$		−	2.06439i		−	0.0747850i
$763$	−41.7175	+	10.8054i	−1.51027	+	0.391181i
$764$		−	5.96683i		−	0.215872i
$765$	4.86081			0.175743
$766$	−47.7390			−1.72488
$767$	7.66137			0.276636
$768$		−	20.9058i		−	0.754374i
$769$	−19.4332			−0.700779			−0.350389	−	0.936604i	$-0.613951\pi$
$769$	−19.4332			−0.700779			−0.350389	+	0.936604i	$0.613951\pi$
$770$	−37.1077	+	9.61140i	−1.33727	+	0.346371i
$771$	−12.0900			−0.435412
$772$	33.4737			1.20474
$773$	25.3849			0.913032			0.456516	−	0.889715i	$-0.349097\pi$
$773$	25.3849			0.913032			0.456516	+	0.889715i	$0.349097\pi$
$774$		−	10.0235i		−	0.360286i
$775$		−	110.305i		−	3.96229i
$776$	−7.44939			−0.267418
$777$	−4.59138	−	17.7264i	−0.164715	−	0.635932i
$778$			16.9445i			0.607491i
$779$		−	27.8997i		−	0.999611i
$780$	−13.1061			−0.469275
$781$			3.44608i			0.123310i
$782$	9.38995	+	4.86081i	0.335784	+	0.173822i
$783$			2.39821i			0.0857049i
$784$	29.2895	−	16.2638i	1.04605	−	0.580851i
$785$	50.3989			1.79881
$786$	5.66618			0.202106
$787$	−25.9054			−0.923427			−0.461714	−	0.887029i	$-0.652765\pi$
$787$	−25.9054			−0.923427			−0.461714	+	0.887029i	$0.652765\pi$
$788$	−1.02709			−0.0365886
$789$	−13.3703			−0.475995
$790$			107.513i			3.82514i
$791$	39.8913	−	10.3324i	1.41837	−	0.367377i
$792$			1.89784i			0.0674368i
$793$		−	3.25820i		−	0.115702i
$794$			34.6981i			1.23139i
$795$	24.0346			0.852420
$796$	−34.6559			−1.22834
$797$	16.5949			0.587823			0.293911	−	0.955833i	$-0.405043\pi$
$797$	16.5949			0.587823			0.293911	+	0.955833i	$0.405043\pi$
$798$	−23.7368	+	6.14816i	−0.840275	+	0.217642i
$799$			11.3411i			0.401220i
$800$	−81.7029			−2.88863
$801$	4.57437			0.161627
$802$			53.4753i			1.88828i
$803$	−15.1262			−0.533791
$804$	5.10270			0.179958
$805$	11.5750	−	50.7525i	0.407965	−	1.78879i
$806$	−37.8940			−1.33476
$807$	−15.6066			−0.549379
$808$			17.1004i			0.601592i
$809$	−32.2742			−1.13470			−0.567351	−	0.823476i	$-0.692032\pi$
$809$	−32.2742			−1.13470			−0.567351	+	0.823476i	$0.692032\pi$
$810$	7.63407			0.268234
$811$			21.3926i			0.751196i	0.926783	+	0.375598i	$0.122563\pi$
$811$			21.3926i			0.751196i	−0.926783	+	0.375598i	$0.877437\pi$
$812$	2.32693	+	8.98381i	0.0816591	+	0.315270i
$813$	−2.78745			−0.0977602
$814$	24.4418			0.856684
$815$	−42.8013			−1.49926
$816$		−	5.67056i		−	0.198509i
$817$		−	26.8281i		−	0.938597i
$818$			38.3643i			1.34138i
$819$	−5.59427	+	1.44899i	−0.195480	+	0.0506318i
$820$			33.6130i			1.17382i
$821$	−1.82957			−0.0638524			−0.0319262	−	0.999490i	$-0.510164\pi$
$821$	−1.82957			−0.0638524			−0.0319262	+	0.999490i	$0.510164\pi$
$822$	8.28461			0.288959
$823$	−15.9564			−0.556206			−0.278103	−	0.960551i	$-0.589706\pi$
$823$	−15.9564			−0.556206			−0.278103	+	0.960551i	$0.589706\pi$
$824$	8.91814			0.310678
$825$	22.4534			0.781726
$826$	−16.7171	+	4.32996i	−0.581663	+	0.150659i
$827$		−	14.5322i		−	0.505333i	−0.967553	−	0.252667i	$-0.918692\pi$
$827$		−	14.5322i		−	0.505333i	0.967553	−	0.252667i	$-0.0813076\pi$
$828$	6.22923	+	3.22463i	0.216481	+	0.112063i
$829$		−	12.7279i		−	0.442057i	−0.975267	−	0.221029i	$-0.929059\pi$
$829$		−	12.7279i		−	0.442057i	0.975267	−	0.221029i	$-0.0709415\pi$
$830$	19.1738			0.665532
$831$			26.1246i			0.906254i
$832$			7.16069i			0.248252i
$833$	7.25090	−	4.02627i	0.251229	−	0.139502i
$834$	13.6918			0.474109
$835$			49.1085i			1.69947i
$836$		−	13.8248i		−	0.478139i
$837$	9.32340			0.322264
$838$	−67.9082			−2.34585
$839$	5.04298			0.174103			0.0870514	−	0.996204i	$-0.472256\pi$
$839$	5.04298			0.174103			0.0870514	+	0.996204i	$0.472256\pi$
$840$	−10.5076	+	2.72161i	−0.362547	+	0.0939045i
$841$	−23.2486			−0.801676
$842$			31.1868i			1.07477i
$843$	25.4138			0.875299
$844$	−30.3732			−1.04549
$845$	33.7609			1.16141
$846$			17.8116i			0.612377i
$847$	4.90792	+	18.9485i	0.168638	+	0.651079i
$848$		−	28.0385i		−	0.962846i
$849$			5.24467i			0.179997i
$850$	−26.0841			−0.894678
$851$	−15.2590	+	29.4769i	−0.523072	+	1.01045i
$852$		−	2.65577i		−	0.0909852i
$853$		−	2.16753i		−	0.0742149i	−0.999311	−	0.0371074i	$-0.988186\pi$
$853$		−	2.16753i		−	0.0742149i	0.999311	−	0.0371074i	$-0.0118144\pi$
$854$	1.84143	+	7.10941i	0.0630125	+	0.243279i
$855$	20.4328			0.698787
$856$		−	6.51492i		−	0.222675i
$857$		−	27.9709i		−	0.955467i	−0.878505	−	0.477734i	$-0.841458\pi$
$857$		−	27.9709i		−	0.955467i	0.878505	−	0.477734i	$-0.158542\pi$
$858$		−	7.71356i		−	0.263337i
$859$		−	9.46405i		−	0.322909i	−0.986880	−	0.161455i	$-0.948381\pi$
$859$		−	9.46405i		−	0.322909i	0.986880	−	0.161455i	$-0.0516185\pi$
$860$			32.3220i			1.10217i
$861$	3.71619	+	14.3475i	0.126647	+	0.488961i
$862$		−	25.4763i		−	0.867726i
$863$	−23.2549			−0.791605			−0.395802	−	0.918336i	$-0.629533\pi$
$863$	−23.2549			−0.791605			−0.395802	+	0.918336i	$0.629533\pi$
$864$		−	6.90582i		−	0.234941i
$865$		−	21.2258i		−	0.721700i
$866$	16.4102			0.557643
$867$			15.5962i			0.529675i
$868$	34.9260	−	9.04629i	1.18546	−	0.307051i
$869$	−26.7279			−0.906681
$870$		−	18.3081i		−	0.620702i
$871$	7.62026			0.258203
$872$		−	16.2880i		−	0.551583i
$873$	−7.44939			−0.252124
$874$	39.4714	+	20.4328i	1.33514	+	0.691150i
$875$	18.5914	+	71.7777i	0.628503	+	2.42653i
$876$	11.6572			0.393861
$877$	32.6981			1.10414			0.552068	−	0.833799i	$-0.313839\pi$
$877$	32.6981			1.10414			0.552068	+	0.833799i	$0.313839\pi$
$878$			35.3616i			1.19340i
$879$			24.5161i			0.826908i
$880$		−	37.2638i		−	1.25616i
$881$	−28.9651			−0.975859			−0.487929	−	0.872883i	$-0.662248\pi$
$881$	−28.9651			−0.975859			−0.487929	+	0.872883i	$0.662248\pi$
$882$	11.3878	−	6.32340i	0.383447	−	0.212920i
$883$	−18.6427			−0.627376			−0.313688	−	0.949526i	$-0.601565\pi$
$883$	−18.6427			−0.627376			−0.313688	+	0.949526i	$0.601565\pi$
$884$			3.78506i			0.127305i
$885$	14.3902			0.483722
$886$	37.8629			1.27203
$887$		−	37.4570i		−	1.25768i	−0.777533	−	0.628842i	$-0.783529\pi$
$887$		−	37.4570i		−	1.25768i	0.777533	−	0.628842i	$-0.216471\pi$
$888$	6.92106			0.232255
$889$	0.735973	+	2.84145i	0.0246837	+	0.0952991i
$890$	−34.9211			−1.17056
$891$			1.89784i			0.0635800i
$892$			35.8671i			1.20092i
$893$			47.6734i			1.59533i
$894$	−38.5567			−1.28953
$895$	−59.7398			−1.99688
$896$	5.11556	+	19.7502i	0.170899	+	0.659807i
$897$	9.30258	+	4.81558i	0.310604	+	0.160788i
$898$	−38.4674			−1.28367
$899$		−	22.3595i		−	0.745730i
$900$	−17.3040			−0.576801
$901$		−	6.94120i		−	0.231245i
$902$	−19.7828			−0.658695
$903$	3.57345	+	13.7964i	0.118917	+	0.459116i
$904$			15.5750i			0.518018i
$905$	71.5894			2.37971
$906$		−	40.3088i		−	1.33917i
$907$		−	32.3151i		−	1.07301i	−0.843898	−	0.536503i	$-0.819745\pi$
$907$		−	32.3151i		−	1.07301i	0.843898	−	0.536503i	$-0.180255\pi$
$908$	31.4601			1.04404
$909$			17.1004i			0.567186i
$910$	42.7071	−	11.0617i	1.41573	−	0.366692i
$911$			19.5922i			0.649117i	0.945866	+	0.324559i	$0.105216\pi$
$911$			19.5922i			0.649117i	−0.945866	+	0.324559i	$0.894784\pi$
$912$		−	23.8367i		−	0.789312i
$913$			4.76663i			0.157752i
$914$		−	62.4421i		−	2.06540i
$915$		−	6.11982i		−	0.202315i
$916$	−15.2879			−0.505127
$917$	−7.79899	+	2.02004i	−0.257545	+	0.0667077i
$918$		−	2.20472i		−	0.0727667i
$919$		−	13.3565i		−	0.440590i	−0.975433	−	0.220295i	$-0.929298\pi$
$919$		−	13.3565i		−	0.440590i	0.975433	−	0.220295i	$-0.0707020\pi$
$920$	17.4729	+	9.04502i	0.576063	+	0.298205i
$921$	−33.2043			−1.09412
$922$			6.08107i			0.200269i
$923$		−	3.96607i		−	0.130545i
$924$	1.84143	+	7.10941i	0.0605786	+	0.233882i
$925$		−	81.8831i		−	2.69230i
$926$	−8.66349			−0.284700
$927$	8.91814			0.292910
$928$	−16.5616			−0.543661
$929$			13.2984i			0.436307i	0.975914	+	0.218154i	$0.0700034\pi$
$929$			13.2984i			0.436307i	−0.975914	+	0.218154i	$0.929997\pi$
$930$	−71.1755			−2.33394
$931$	30.4798	−	16.9248i	0.998934	−	0.554687i
$932$	6.13293			0.200891
$933$	−22.5526			−0.738340
$934$	−32.1015			−1.05039
$935$		−	9.22503i		−	0.301691i
$936$		−	2.18421i		−	0.0713931i
$937$	17.8652			0.583630			0.291815	−	0.956475i	$-0.405741\pi$
$937$	17.8652			0.583630			0.291815	+	0.956475i	$0.405741\pi$
$938$	−16.6274	+	4.30673i	−0.542905	+	0.140620i
$939$		−	4.07961i		−	0.133133i
$940$		−	57.4359i		−	1.87335i
$941$	−49.6994			−1.62015			−0.810076	−	0.586324i	$-0.800574\pi$
$941$	−49.6994			−1.62015			−0.810076	+	0.586324i	$0.800574\pi$
$942$		−	22.8595i		−	0.744803i
$943$	12.3504	−	23.8581i	0.402184	−	0.776927i
$944$		−	16.7875i		−	0.546385i
$945$	−10.5076	+	2.72161i	−0.341813	+	0.0885340i
$946$	−19.0229			−0.618489
$947$	−23.8116			−0.773774			−0.386887	−	0.922127i	$-0.626450\pi$
$947$	−23.8116			−0.773774			−0.386887	+	0.922127i	$0.626450\pi$
$948$	20.5982			0.669000
$949$	17.4086			0.565108
$950$	−109.647			−3.55741
$951$			12.8608i			0.417040i
$952$	0.786003	+	3.03460i	0.0254745	+	0.0983521i
$953$			55.6859i			1.80384i	0.431898	+	0.901922i	$0.357844\pi$
$953$			55.6859i			1.80384i	−0.431898	+	0.901922i	$0.642156\pi$
$954$		−	10.9014i		−	0.352946i
$955$		−	16.7368i		−	0.541591i
$956$	31.9654			1.03383
$957$	4.55141			0.147126
$958$	−38.0225			−1.22845
$959$	−11.4030	+	2.95353i	−0.368223	+	0.0953746i
$960$			13.4498i			0.434090i
$961$	−55.9259			−1.80406
$962$	−28.1299			−0.906944
$963$		−	6.51492i		−	0.209940i
$964$	−28.9881			−0.933642
$965$	93.8931			3.02253
$966$	−23.0199	−	5.25009i	−0.740652	−	0.168919i
$967$	34.2188			1.10040			0.550201	−	0.835032i	$-0.314551\pi$
$967$	34.2188			1.10040			0.550201	+	0.835032i	$0.314551\pi$
$968$	−7.39821			−0.237787
$969$		−	5.90101i		−	0.189568i
$970$	56.8692			1.82596
$971$	−60.1092			−1.92900			−0.964498	−	0.264090i	$-0.914929\pi$
$971$	−60.1092			−1.92900			−0.964498	+	0.264090i	$0.914929\pi$
$972$		−	1.46260i		−	0.0469129i
$973$	−18.8456	+	4.88125i	−0.604161	+	0.156486i
$974$	6.25632			0.200465
$975$	−25.8414			−0.827588
$976$	−7.13931			−0.228524
$977$			50.3329i			1.61029i	0.593077	+	0.805146i	$0.297913\pi$
$977$			50.3329i			1.61029i	−0.593077	+	0.805146i	$0.702087\pi$
$978$			19.4134i			0.620773i
$979$		−	8.68141i		−	0.277459i
$980$	−36.7214	+	20.3906i	−1.17302	+	0.651354i
$981$		−	16.2880i		−	0.520037i
$982$	5.13919			0.163998
$983$	29.3653			0.936607			0.468304	−	0.883568i	$-0.344865\pi$
$983$	29.3653			0.936607			0.468304	+	0.883568i	$0.344865\pi$
$984$	−5.60179			−0.178579
$985$	−2.88097			−0.0917953
$986$	−5.28738			−0.168385
$987$	−6.35000	−	24.5161i	−0.202123	−	0.780357i
$988$			15.9108i			0.506190i
$989$	11.8760	−	22.9417i	0.377636	−	0.729505i
$990$		−	14.4882i		−	0.460466i
$991$	−33.0319			−1.04929			−0.524647	−	0.851320i	$-0.675803\pi$
$991$	−33.0319			−1.04929			−0.524647	+	0.851320i	$0.675803\pi$
$992$			64.3858i			2.04425i
$993$		−	24.6081i		−	0.780913i
$994$	2.24149	+	8.65397i	0.0710959	+	0.274487i
$995$	−97.2091			−3.08173
$996$		−	3.67347i		−	0.116398i
$997$			26.5962i			0.842310i	0.906989	+	0.421155i	$0.138375\pi$
$997$			26.5962i			0.842310i	−0.906989	+	0.421155i	$0.861625\pi$
$998$	71.5160			2.26380
$999$	6.92106			0.218972

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.h.b.160.10	yes	12
3.2	odd	2		1449.2.h.h.1126.2		12
7.6	odd	2	inner	483.2.h.b.160.11	yes	12
21.20	even	2		1449.2.h.h.1126.4		12
23.22	odd	2	inner	483.2.h.b.160.9	✓	12
69.68	even	2		1449.2.h.h.1126.3		12
161.160	even	2	inner	483.2.h.b.160.12	yes	12
483.482	odd	2		1449.2.h.h.1126.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.h.b.160.9	✓	12	23.22	odd	2	inner
483.2.h.b.160.10	yes	12	1.1	even	1	trivial
483.2.h.b.160.11	yes	12	7.6	odd	2	inner
483.2.h.b.160.12	yes	12	161.160	even	2	inner
1449.2.h.h.1126.1		12	483.482	odd	2
1449.2.h.h.1126.2		12	3.2	odd	2
1449.2.h.h.1126.3		12	69.68	even	2
1449.2.h.h.1126.4		12	21.20	even	2

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:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	483.h (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.86081 q^{2} -1.00000i q^{3} +1.46260 q^{4} +4.10256 q^{5} -1.86081i q^{6} +(0.663393 + 2.56123i) q^{7} -1.00000 q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+1.86081 q^{2} -1.00000i q^{3} +1.46260 q^{4} +4.10256 q^{5} -1.86081i q^{6} +(0.663393 + 2.56123i) q^{7} -1.00000 q^{8} -1.00000 q^{9} +7.63407 q^{10} +1.89784i q^{11} -1.46260i q^{12} -2.18421i q^{13} +(1.23445 + 4.76596i) q^{14} -4.10256i q^{15} -4.78600 q^{16} -1.18482 q^{17} -1.86081 q^{18} -4.98050 q^{19} +6.00040 q^{20} +(2.56123 - 0.663393i) q^{21} +3.53151i q^{22} +(-4.25901 - 2.20472i) q^{23} +1.00000i q^{24} +11.8310 q^{25} -4.06439i q^{26} +1.00000i q^{27} +(0.970278 + 3.74605i) q^{28} +2.39821 q^{29} -7.63407i q^{30} -9.32340i q^{31} -6.90582 q^{32} +1.89784 q^{33} -2.20472 q^{34} +(2.72161 + 10.5076i) q^{35} -1.46260 q^{36} -6.92106i q^{37} -9.26774 q^{38} -2.18421 q^{39} -4.10256 q^{40} +5.60179i q^{41} +(4.76596 - 1.23445i) q^{42} +5.38663i q^{43} +2.77578i q^{44} -4.10256 q^{45} +(-7.92520 - 4.10256i) q^{46} -9.57201i q^{47} +4.78600i q^{48} +(-6.11982 + 3.39821i) q^{49} +22.0152 q^{50} +1.18482i q^{51} -3.19462i q^{52} +5.85844i q^{53} +1.86081i q^{54} +7.78600i q^{55} +(-0.663393 - 2.56123i) q^{56} +4.98050i q^{57} +4.46260 q^{58} +3.50761i q^{59} -6.00040i q^{60} +1.49171 q^{61} -17.3490i q^{62} +(-0.663393 - 2.56123i) q^{63} -3.27839 q^{64} -8.96086i q^{65} +3.53151 q^{66} +3.48879i q^{67} -1.73292 q^{68} +(-2.20472 + 4.25901i) q^{69} +(5.06439 + 19.5526i) q^{70} +1.81579 q^{71} +1.00000 q^{72} +7.97021i q^{73} -12.8787i q^{74} -11.8310i q^{75} -7.28447 q^{76} +(-4.86081 + 1.25901i) q^{77} -4.06439 q^{78} +14.0833i q^{79} -19.6349 q^{80} +1.00000 q^{81} +10.4238i q^{82} +2.51161 q^{83} +(3.74605 - 0.970278i) q^{84} -4.86081 q^{85} +10.0235i q^{86} -2.39821i q^{87} -1.89784i q^{88} -4.57437 q^{89} -7.63407 q^{90} +(5.59427 - 1.44899i) q^{91} +(-6.22923 - 3.22463i) q^{92} -9.32340 q^{93} -17.8116i q^{94} -20.4328 q^{95} +6.90582i q^{96} +7.44939 q^{97} +(-11.3878 + 6.32340i) q^{98} -1.89784i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 8 q^{4} - 12 q^{8} - 12 q^{9}+O(q^{10}) \) 12 * q + 8 * q^4 - 12 * q^8 - 12 * q^9	\( 12 q + 8 q^{4} - 12 q^{8} - 12 q^{9} - 16 q^{16} - 16 q^{23} + 24 q^{25} + 16 q^{29} + 16 q^{32} - 12 q^{35} - 8 q^{36} + 28 q^{39} - 76 q^{46} - 16 q^{49} + 92 q^{50} + 44 q^{58} - 84 q^{64} + 64 q^{70} + 76 q^{71} + 12 q^{72} - 36 q^{77} - 52 q^{78} + 12 q^{81} - 36 q^{85} + 56 q^{92} - 80 q^{93} - 140 q^{95} - 108 q^{98}+O(q^{100}) \) 12 * q + 8 * q^4 - 12 * q^8 - 12 * q^9 - 16 * q^16 - 16 * q^23 + 24 * q^25 + 16 * q^29 + 16 * q^32 - 12 * q^35 - 8 * q^36 + 28 * q^39 - 76 * q^46 - 16 * q^49 + 92 * q^50 + 44 * q^58 - 84 * q^64 + 64 * q^70 + 76 * q^71 + 12 * q^72 - 36 * q^77 - 52 * q^78 + 12 * q^81 - 36 * q^85 + 56 * q^92 - 80 * q^93 - 140 * q^95 - 108 * q^98

Introduction

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