LMFDB - Embedded newform 273.2.bd.a.127.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(43,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("273.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 22x^{14} + 187x^{12} + 774x^{10} + 1619x^{8} + 1618x^{6} + 690x^{4} + 96x^{2} + 1 $ x^16 + 22x^14 + 187x^12 + 774x^10 + 1619x^8 + 1618x^6 + 690x^4 + 96*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			127.1
Root			$2.60802i$ of defining polynomial
Character	$\chi$	$=$	273.127
Dual form			273.2.bd.a.43.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.25861 + 1.30401i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(2.40088 - 4.15844i) q^{4} +1.50528i q^{5} +(2.25861 + 1.30401i) q^{6} +(-0.866025 - 0.500000i) q^{7} +7.30704i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-2.25861 + 1.30401i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(2.40088 - 4.15844i) q^{4} +1.50528i q^{5} +(2.25861 + 1.30401i) q^{6} +(-0.866025 - 0.500000i) q^{7} +7.30704i q^{8} +(-0.500000 + 0.866025i) q^{9} +(-1.96290 - 3.39983i) q^{10} +(0.0753030 - 0.0434762i) q^{11} -4.80176 q^{12} +(-1.30332 - 3.36175i) q^{13} +2.60802 q^{14} +(1.30361 - 0.752639i) q^{15} +(-4.72668 - 8.18685i) q^{16} +(3.24732 - 5.62452i) q^{17} -2.60802i q^{18} +(4.58318 + 2.64610i) q^{19} +(6.25961 + 3.61399i) q^{20} +1.00000i q^{21} +(-0.113387 + 0.196391i) q^{22} +(-2.60110 - 4.50524i) q^{23} +(6.32808 - 3.65352i) q^{24} +2.73414 q^{25} +(7.32743 + 5.89335i) q^{26} +1.00000 q^{27} +(-4.15844 + 2.40088i) q^{28} +(2.98801 + 5.17538i) q^{29} +(-1.96290 + 3.39983i) q^{30} -2.00289i q^{31} +(8.69531 + 5.02024i) q^{32} +(-0.0753030 - 0.0434762i) q^{33} +16.9381i q^{34} +(0.752639 - 1.30361i) q^{35} +(2.40088 + 4.15844i) q^{36} +(8.24566 - 4.76063i) q^{37} -13.8022 q^{38} +(-2.25970 + 2.80958i) q^{39} -10.9991 q^{40} +(5.57631 - 3.21948i) q^{41} +(-1.30401 - 2.25861i) q^{42} +(3.40536 - 5.89825i) q^{43} -0.417524i q^{44} +(-1.30361 - 0.752639i) q^{45} +(11.7498 + 6.78372i) q^{46} -1.83051i q^{47} +(-4.72668 + 8.18685i) q^{48} +(0.500000 + 0.866025i) q^{49} +(-6.17535 + 3.56534i) q^{50} -6.49464 q^{51} +(-17.1088 - 2.65139i) q^{52} -3.28476 q^{53} +(-2.25861 + 1.30401i) q^{54} +(0.0654437 + 0.113352i) q^{55} +(3.65352 - 6.32808i) q^{56} -5.29220i q^{57} +(-13.4975 - 7.79278i) q^{58} +(-2.31669 - 1.33754i) q^{59} -7.22798i q^{60} +(3.27278 - 5.66863i) q^{61} +(2.61179 + 4.52375i) q^{62} +(0.866025 - 0.500000i) q^{63} -7.27901 q^{64} +(5.06037 - 1.96185i) q^{65} +0.226773 q^{66} +(-7.18333 + 4.14730i) q^{67} +(-15.5928 - 27.0076i) q^{68} +(-2.60110 + 4.50524i) q^{69} +3.92579i q^{70} +(-11.1872 - 6.45892i) q^{71} +(-6.32808 - 3.65352i) q^{72} +14.5507i q^{73} +(-12.4158 + 21.5048i) q^{74} +(-1.36707 - 2.36783i) q^{75} +(22.0073 - 12.7059i) q^{76} -0.0869524 q^{77} +(1.44007 - 9.29242i) q^{78} -11.6780 q^{79} +(12.3235 - 7.11497i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-8.39647 + 14.5431i) q^{82} -1.29310i q^{83} +(4.15844 + 2.40088i) q^{84} +(8.46647 + 4.88812i) q^{85} +17.7625i q^{86} +(2.98801 - 5.17538i) q^{87} +(0.317682 + 0.550241i) q^{88} +(13.7225 - 7.92270i) q^{89} +3.92579 q^{90} +(-0.552171 + 3.56302i) q^{91} -24.9797 q^{92} +(-1.73455 + 1.00144i) q^{93} +(2.38701 + 4.13442i) q^{94} +(-3.98312 + 6.89896i) q^{95} -10.0405i q^{96} +(-5.08340 - 2.93490i) q^{97} +(-2.25861 - 1.30401i) q^{98} +0.0869524i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{3} + 6 q^{4} - 8 q^{9}+O(q^{10}) $ 16 * q - 8 * q^3 + 6 * q^4 - 8 * q^9	$ 16 q - 8 q^{3} + 6 q^{4} - 8 q^{9} - 4 q^{10} - 12 q^{11} - 12 q^{12} + 4 q^{13} + 4 q^{14} - 10 q^{16} + 10 q^{17} + 6 q^{20} - 2 q^{22} - 2 q^{23} + 12 q^{25} + 20 q^{26} + 16 q^{27} + 12 q^{29} - 4 q^{30} + 30 q^{32} + 12 q^{33} - 2 q^{35} + 6 q^{36} + 18 q^{37} - 32 q^{38} - 8 q^{39} - 60 q^{40} + 18 q^{41} - 2 q^{42} - 10 q^{43} + 30 q^{46} - 10 q^{48} + 8 q^{49} - 24 q^{50} - 20 q^{51} - 26 q^{52} + 12 q^{53} + 10 q^{55} + 12 q^{56} - 54 q^{58} - 60 q^{59} - 6 q^{61} + 16 q^{62} + 16 q^{64} - 20 q^{65} + 4 q^{66} - 18 q^{67} - 20 q^{68} - 2 q^{69} + 6 q^{71} + 18 q^{74} - 6 q^{75} + 72 q^{76} - 16 q^{77} + 14 q^{78} - 4 q^{79} + 30 q^{80} - 8 q^{81} - 18 q^{82} - 24 q^{85} + 12 q^{87} - 2 q^{88} + 78 q^{89} + 8 q^{90} - 8 q^{91} - 20 q^{92} + 6 q^{93} + 16 q^{94} - 4 q^{95} - 54 q^{97}+O(q^{100}) $ 16 * q - 8 * q^3 + 6 * q^4 - 8 * q^9 - 4 * q^10 - 12 * q^11 - 12 * q^12 + 4 * q^13 + 4 * q^14 - 10 * q^16 + 10 * q^17 + 6 * q^20 - 2 * q^22 - 2 * q^23 + 12 * q^25 + 20 * q^26 + 16 * q^27 + 12 * q^29 - 4 * q^30 + 30 * q^32 + 12 * q^33 - 2 * q^35 + 6 * q^36 + 18 * q^37 - 32 * q^38 - 8 * q^39 - 60 * q^40 + 18 * q^41 - 2 * q^42 - 10 * q^43 + 30 * q^46 - 10 * q^48 + 8 * q^49 - 24 * q^50 - 20 * q^51 - 26 * q^52 + 12 * q^53 + 10 * q^55 + 12 * q^56 - 54 * q^58 - 60 * q^59 - 6 * q^61 + 16 * q^62 + 16 * q^64 - 20 * q^65 + 4 * q^66 - 18 * q^67 - 20 * q^68 - 2 * q^69 + 6 * q^71 + 18 * q^74 - 6 * q^75 + 72 * q^76 - 16 * q^77 + 14 * q^78 - 4 * q^79 + 30 * q^80 - 8 * q^81 - 18 * q^82 - 24 * q^85 + 12 * q^87 - 2 * q^88 + 78 * q^89 + 8 * q^90 - 8 * q^91 - 20 * q^92 + 6 * q^93 + 16 * q^94 - 4 * q^95 - 54 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−2.25861	+	1.30401i	−1.59708	+	0.922074i	−0.605032	+	0.796201i	$0.706840\pi$
$2$	−2.25861	+	1.30401i	−1.59708	+	0.922074i	−0.992046	+	0.125872i	$0.959827\pi$
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	2.40088	−	4.15844i	1.20044	−	2.07922i
$5$			1.50528i			0.673181i	0.941651	+	0.336590i	$0.109274\pi$
$5$			1.50528i			0.673181i	−0.941651	+	0.336590i	$0.890726\pi$
$6$	2.25861	+	1.30401i	0.922074	+	0.532359i
$7$	−0.866025	−	0.500000i	−0.327327	−	0.188982i
$7$	−0.866025	−	0.500000i	−0.327327	−	0.188982i
$8$			7.30704i			2.58343i
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−1.96290	−	3.39983i	−0.620722	−	1.07512i
$11$	0.0753030	−	0.0434762i	0.0227047	−	0.0131086i	−0.488605	−	0.872505i	$-0.662494\pi$
$11$	0.0753030	−	0.0434762i	0.0227047	−	0.0131086i	0.511309	+	0.859397i	$0.329161\pi$
$12$	−4.80176			−1.38615
$13$	−1.30332	−	3.36175i	−0.361475	−	0.932382i
$13$	−1.30332	−	3.36175i	−0.361475	−	0.932382i
$14$	2.60802			0.697022
$15$	1.30361	−	0.752639i	0.336590	−	0.194330i
$16$	−4.72668	−	8.18685i	−1.18167	−	2.04671i
$17$	3.24732	−	5.62452i	0.787591	−	1.36415i	−0.139848	−	0.990173i	$-0.544662\pi$
$17$	3.24732	−	5.62452i	0.787591	−	1.36415i	0.927439	−	0.373974i	$-0.122005\pi$
$18$		−	2.60802i		−	0.614716i
$19$	4.58318	+	2.64610i	1.05145	+	0.607057i	0.923056	−	0.384665i	$-0.125683\pi$
$19$	4.58318	+	2.64610i	1.05145	+	0.607057i	0.128398	+	0.991723i	$0.459016\pi$
$20$	6.25961	+	3.61399i	1.39969	+	0.808113i
$21$			1.00000i			0.218218i
$22$	−0.113387	+	0.196391i	−0.0241741	+	0.0418708i
$23$	−2.60110	−	4.50524i	−0.542367	−	0.939408i	−0.998768	−	0.0496333i	$-0.984195\pi$
$23$	−2.60110	−	4.50524i	−0.542367	−	0.939408i	0.456400	−	0.889775i	$-0.349139\pi$
$24$	6.32808	−	3.65352i	1.29171	−	0.745771i
$25$	2.73414			0.546828
$26$	7.32743	+	5.89335i	1.43703	+	1.15578i
$27$	1.00000			0.192450
$28$	−4.15844	+	2.40088i	−0.785872	+	0.453723i
$29$	2.98801	+	5.17538i	0.554859	+	0.961045i	0.997914	+	0.0645503i	$0.0205613\pi$
$29$	2.98801	+	5.17538i	0.554859	+	0.961045i	−0.443055	+	0.896494i	$0.646105\pi$
$30$	−1.96290	+	3.39983i	−0.358374	+	0.620722i
$31$		−	2.00289i		−	0.359730i	−0.983691	−	0.179865i	$-0.942434\pi$
$31$		−	2.00289i		−	0.359730i	0.983691	−	0.179865i	$-0.0575660\pi$
$32$	8.69531	+	5.02024i	1.53713	+	0.887461i
$33$	−0.0753030	−	0.0434762i	−0.0131086	−	0.00756823i
$34$			16.9381i			2.90487i
$35$	0.752639	−	1.30361i	0.127219	−	0.220350i
$36$	2.40088	+	4.15844i	0.400147	+	0.693074i
$37$	8.24566	−	4.76063i	1.35558	−	0.782643i	0.366554	−	0.930397i	$-0.380538\pi$
$37$	8.24566	−	4.76063i	1.35558	−	0.782643i	0.989024	+	0.147754i	$0.0472042\pi$
$38$	−13.8022			−2.23901
$39$	−2.25970	+	2.80958i	−0.361842	+	0.449893i
$40$	−10.9991			−1.73911
$41$	5.57631	−	3.21948i	0.870873	−	0.502799i	0.00323453	−	0.999995i	$-0.498970\pi$
$41$	5.57631	−	3.21948i	0.870873	−	0.502799i	0.867638	+	0.497196i	$0.165637\pi$
$42$	−1.30401	−	2.25861i	−0.201213	−	0.348511i
$43$	3.40536	−	5.89825i	0.519312	−	0.899475i	−0.480436	−	0.877030i	$-0.659522\pi$
$43$	3.40536	−	5.89825i	0.519312	−	0.899475i	0.999748	−	0.0224449i	$-0.00714502\pi$
$44$		−	0.417524i		−	0.0629441i
$45$	−1.30361	−	0.752639i	−0.194330	−	0.112197i
$46$	11.7498	+	6.78372i	1.73241	+	1.00021i
$47$		−	1.83051i		−	0.267008i	−0.991048	−	0.133504i	$-0.957377\pi$
$47$		−	1.83051i		−	0.267008i	0.991048	−	0.133504i	$-0.0426229\pi$
$48$	−4.72668	+	8.18685i	−0.682238	+	1.18167i
$49$	0.500000	+	0.866025i	0.0714286	+	0.123718i
$50$	−6.17535	+	3.56534i	−0.873327	+	0.504216i
$51$	−6.49464			−0.909431
$52$	−17.1088	−	2.65139i	−2.37256	−	0.367682i
$53$	−3.28476			−0.451197			−0.225598	−	0.974220i	$-0.572434\pi$
$53$	−3.28476			−0.451197			−0.225598	+	0.974220i	$0.572434\pi$
$54$	−2.25861	+	1.30401i	−0.307358	+	0.177453i
$55$	0.0654437	+	0.113352i	0.00882443	+	0.0152844i
$56$	3.65352	−	6.32808i	0.488222	−	0.845625i
$57$		−	5.29220i		−	0.700969i
$58$	−13.4975	−	7.79278i	−1.77231	−	1.02324i
$59$	−2.31669	−	1.33754i	−0.301608	−	0.174133i	0.341557	−	0.939861i	$-0.389046\pi$
$59$	−2.31669	−	1.33754i	−0.301608	−	0.174133i	−0.643165	+	0.765728i	$0.722379\pi$
$60$		−	7.22798i		−	0.933128i
$61$	3.27278	−	5.66863i	0.419037	−	0.725794i	−0.576806	−	0.816881i	$-0.695701\pi$
$61$	3.27278	−	5.66863i	0.419037	−	0.725794i	0.995843	+	0.0910877i	$0.0290344\pi$
$62$	2.61179	+	4.52375i	0.331697	+	0.574516i
$63$	0.866025	−	0.500000i	0.109109	−	0.0629941i
$64$	−7.27901			−0.909876
$65$	5.06037	−	1.96185i	0.627661	−	0.243338i
$66$	0.226773			0.0279139
$67$	−7.18333	+	4.14730i	−0.877583	+	0.506673i	−0.869861	−	0.493297i	$-0.835791\pi$
$67$	−7.18333	+	4.14730i	−0.877583	+	0.506673i	−0.00772242	+	0.999970i	$0.502458\pi$
$68$	−15.5928	−	27.0076i	−1.89091	−	3.27515i
$69$	−2.60110	+	4.50524i	−0.313136	+	0.542367i
$70$			3.92579i			0.469222i
$71$	−11.1872	−	6.45892i	−1.32767	−	0.766533i	−0.342735	−	0.939432i	$-0.611353\pi$
$71$	−11.1872	−	6.45892i	−1.32767	−	0.766533i	−0.984940	+	0.172899i	$0.944687\pi$
$72$	−6.32808	−	3.65352i	−0.745771	−	0.430571i
$73$			14.5507i			1.70303i	0.524334	+	0.851513i	$0.324314\pi$
$73$			14.5507i			1.70303i	−0.524334	+	0.851513i	$0.675686\pi$
$74$	−12.4158	+	21.5048i	−1.44331	+	2.49989i
$75$	−1.36707	−	2.36783i	−0.157856	−	0.273414i
$76$	22.0073	−	12.7059i	2.52441	−	1.45747i
$77$	−0.0869524			−0.00990914
$78$	1.44007	−	9.29242i	0.163056	−	1.05216i
$79$	−11.6780			−1.31387			−0.656936	−	0.753946i	$-0.728148\pi$
$79$	−11.6780			−1.31387			−0.656936	+	0.753946i	$0.728148\pi$
$80$	12.3235	−	7.11497i	1.37781	−	0.795478i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−8.39647	+	14.5431i	−0.927235	+	1.60602i
$83$		−	1.29310i		−	0.141937i	−0.997479	−	0.0709683i	$-0.977391\pi$
$83$		−	1.29310i		−	0.141937i	0.997479	−	0.0709683i	$-0.0226089\pi$
$84$	4.15844	+	2.40088i	0.453723	+	0.261957i
$85$	8.46647	+	4.88812i	0.918317	+	0.530191i
$86$			17.7625i			1.91538i
$87$	2.98801	−	5.17538i	0.320348	−	0.554859i
$88$	0.317682	+	0.550241i	0.0338650	+	0.0586559i
$89$	13.7225	−	7.92270i	1.45458	−	0.839805i	0.455848	−	0.890058i	$-0.349336\pi$
$89$	13.7225	−	7.92270i	1.45458	−	0.839805i	0.998737	+	0.0502531i	$0.0160028\pi$
$90$	3.92579			0.413815
$91$	−0.552171	+	3.56302i	−0.0578833	+	0.373506i
$92$	−24.9797			−2.60432
$93$	−1.73455	+	1.00144i	−0.179865	+	0.103845i
$94$	2.38701	+	4.13442i	0.246201	+	0.426433i
$95$	−3.98312	+	6.89896i	−0.408659	+	0.707819i
$96$		−	10.0405i		−	1.02475i
$97$	−5.08340	−	2.93490i	−0.516141	−	0.297994i	0.219213	−	0.975677i	$-0.429651\pi$
$97$	−5.08340	−	2.93490i	−0.516141	−	0.297994i	−0.735354	+	0.677683i	$0.762984\pi$
$98$	−2.25861	−	1.30401i	−0.228154	−	0.131725i
$99$			0.0869524i			0.00873904i
$100$	6.56434	−	11.3698i	0.656434	−	1.13698i
$101$	−3.34086	−	5.78654i	−0.332428	−	0.575782i	0.650559	−	0.759455i	$-0.274534\pi$
$101$	−3.34086	−	5.78654i	−0.332428	−	0.575782i	−0.982987	+	0.183673i	$0.941201\pi$
$102$	14.6689	−	8.46907i	1.45243	−	0.838563i
$103$	4.52273			0.445637			0.222819	−	0.974860i	$-0.428474\pi$
$103$	4.52273			0.445637			0.222819	+	0.974860i	$0.428474\pi$
$104$	24.5644	−	9.52337i	2.40874	−	0.933843i
$105$	−1.50528			−0.146900
$106$	7.41900	−	4.28336i	0.720597	−	0.416037i
$107$	5.12241	+	8.87227i	0.495202	+	0.857715i	0.999985	−	0.00553163i	$-0.00176078\pi$
$107$	5.12241	+	8.87227i	0.495202	+	0.857715i	−0.504783	+	0.863246i	$0.668427\pi$
$108$	2.40088	−	4.15844i	0.231025	−	0.400147i
$109$			13.5552i			1.29835i	0.760637	+	0.649177i	$0.224887\pi$
$109$			13.5552i			1.29835i	−0.760637	+	0.649177i	$0.775113\pi$
$110$	−0.295624	−	0.170678i	−0.0281866	−	0.0162735i
$111$	−8.24566	−	4.76063i	−0.782643	−	0.451859i
$112$			9.45336i			0.893259i
$113$	−6.69370	+	11.5938i	−0.629691	+	1.09066i	0.357923	+	0.933751i	$0.383485\pi$
$113$	−6.69370	+	11.5938i	−0.629691	+	1.09066i	−0.987614	+	0.156905i	$0.949848\pi$
$114$	6.90108	+	11.9530i	0.646345	+	1.11950i
$115$	6.78164	−	3.91538i	0.632391	−	0.365111i
$116$	28.6954			2.66430
$117$	3.56302	+	0.552171i	0.329401	+	0.0510482i
$118$	6.97667			0.642255
$119$	−5.62452	+	3.24732i	−0.515599	+	0.297681i
$120$	5.49956	+	9.52551i	0.502039	+	0.869556i
$121$	−5.49622	+	9.51973i	−0.499656	+	0.865430i
$122$			17.0710i			1.54553i
$123$	−5.57631	−	3.21948i	−0.502799	−	0.290291i
$124$	−8.32891	−	4.80870i	−0.747958	−	0.431834i
$125$			11.6420i			1.04129i
$126$	−1.30401	+	2.25861i	−0.116170	+	0.201213i
$127$	6.47234	+	11.2104i	0.574328	+	0.994765i	0.996114	+	0.0880695i	$0.0280698\pi$
$127$	6.47234	+	11.2104i	0.574328	+	0.994765i	−0.421787	+	0.906695i	$0.638597\pi$
$128$	−0.950172	+	0.548582i	−0.0839841	+	0.0484883i
$129$	−6.81071			−0.599650
$130$	−8.87113	+	11.0298i	−0.778049	+	0.967379i
$131$	5.84887			0.511018			0.255509	−	0.966807i	$-0.417757\pi$
$131$	5.84887			0.511018			0.255509	+	0.966807i	$0.417757\pi$
$132$	−0.361587	+	0.208762i	−0.0314721	+	0.0181704i
$133$	−2.64610	−	4.58318i	−0.229446	−	0.397412i
$134$	10.8162	−	18.7342i	0.934379	−	1.61839i
$135$			1.50528i			0.129554i
$136$	41.0986	+	23.7283i	3.52417	+	2.03468i
$137$	−4.42616	−	2.55545i	−0.378153	−	0.218327i	0.298862	−	0.954296i	$-0.403393\pi$
$137$	−4.42616	−	2.55545i	−0.378153	−	0.218327i	−0.677014	+	0.735970i	$0.736726\pi$
$138$		−	13.5674i		−	1.15494i
$139$	9.66376	−	16.7381i	0.819669	−	1.41971i	−0.0862564	−	0.996273i	$-0.527490\pi$
$139$	9.66376	−	16.7381i	0.819669	−	1.41971i	0.905926	−	0.423436i	$-0.139176\pi$
$140$	−3.61399	−	6.25961i	−0.305438	−	0.529034i
$141$	−1.58527	+	0.915257i	−0.133504	+	0.0770786i
$142$	33.6900			2.82720
$143$	−0.244300	−	0.196487i	−0.0204294	−	0.0164310i
$144$	9.45336			0.787780
$145$	−7.79039	+	4.49778i	−0.646957	+	0.373521i
$146$	−18.9742	−	32.8643i	−1.57031	−	2.71987i
$147$	0.500000	−	0.866025i	0.0412393	−	0.0714286i
$148$		−	45.7188i		−	3.75806i
$149$	−8.23614	−	4.75514i	−0.674731	−	0.389556i	0.123136	−	0.992390i	$-0.460705\pi$
$149$	−8.23614	−	4.75514i	−0.674731	−	0.389556i	−0.797867	+	0.602834i	$0.794038\pi$
$150$	6.17535	+	3.56534i	0.504216	+	0.291109i
$151$		−	12.7770i		−	1.03977i	−0.854235	−	0.519887i	$-0.825974\pi$
$151$		−	12.7770i		−	1.03977i	0.854235	−	0.519887i	$-0.174026\pi$
$152$	−19.3352	+	33.4895i	−1.56829	+	2.71636i
$153$	3.24732	+	5.62452i	0.262530	+	0.454716i
$154$	0.196391	−	0.113387i	0.0158257	−	0.00913696i
$155$	3.01490			0.242163
$156$	6.25821	+	16.1423i	0.501057	+	1.29242i
$157$	−2.57466			−0.205480			−0.102740	−	0.994708i	$-0.532761\pi$
$157$	−2.57466			−0.205480			−0.102740	+	0.994708i	$0.532761\pi$
$158$	26.3759	−	15.2282i	2.09836	−	1.21149i
$159$	1.64238	+	2.84469i	0.130249	+	0.225598i
$160$	−7.55685	+	13.0888i	−0.597421	+	1.03476i
$161$			5.20221i			0.409991i
$162$	2.25861	+	1.30401i	0.177453	+	0.102453i
$163$	−16.9135	−	9.76499i	−1.32476	−	0.764853i	−0.340280	−	0.940324i	$-0.610522\pi$
$163$	−16.9135	−	9.76499i	−1.32476	−	0.764853i	−0.984485	+	0.175471i	$0.943855\pi$
$164$		−	30.9183i		−	2.41432i
$165$	0.0654437	−	0.113352i	0.00509479	−	0.00882443i
$166$	1.68622	+	2.92062i	0.130876	+	0.226684i
$167$	−1.20942	+	0.698261i	−0.0935881	+	0.0540331i	−0.546064	−	0.837744i	$-0.683874\pi$
$167$	−1.20942	+	0.698261i	−0.0935881	+	0.0540331i	0.452476	+	0.891777i	$0.350541\pi$
$168$	−7.30704			−0.563750
$169$	−9.60274	+	8.76284i	−0.738672	+	0.674065i
$170$	−25.4966			−1.95550
$171$	−4.58318	+	2.64610i	−0.350485	+	0.202352i
$172$	−16.3517	−	28.3220i	−1.24680	−	2.15953i
$173$	8.59070	−	14.8795i	0.653138	−	1.13127i	−0.329219	−	0.944254i	$-0.606785\pi$
$173$	8.59070	−	14.8795i	0.653138	−	1.13127i	0.982357	−	0.187015i	$-0.0598814\pi$
$174$			15.5856i			1.18154i
$175$	−2.36783	−	1.36707i	−0.178991	−	0.103341i
$176$	−0.711866	−	0.410996i	−0.0536589	−	0.0309800i
$177$			2.67509i			0.201072i
$178$	−20.6625	+	35.7886i	−1.54872	+	2.68247i
$179$	−0.718538	−	1.24454i	−0.0537061	−	0.0930216i	0.837923	−	0.545789i	$-0.183770\pi$
$179$	−0.718538	−	1.24454i	−0.0537061	−	0.0930216i	−0.891629	+	0.452768i	$0.850437\pi$
$180$	−6.25961	+	3.61399i	−0.466564	+	0.269371i
$181$	4.31882			0.321015			0.160508	−	0.987035i	$-0.448687\pi$
$181$	4.31882			0.321015			0.160508	+	0.987035i	$0.448687\pi$
$182$	−3.39907	−	8.76751i	−0.251956	−	0.649891i
$183$	−6.54557			−0.483862
$184$	32.9200	−	19.0064i	2.42689	−	1.40117i
$185$	7.16607	+	12.4120i	0.526860	+	0.912549i
$186$	2.61179	−	4.52375i	0.191505	−	0.331697i
$187$		−	0.564724i		−	0.0412967i
$188$	−7.61209	−	4.39484i	−0.555169	−	0.320527i
$189$	−0.866025	−	0.500000i	−0.0629941	−	0.0363696i
$190$		−	20.7761i		−	1.50726i
$191$	3.39359	−	5.87788i	0.245552	−	0.425308i	−0.716735	−	0.697346i	$-0.754364\pi$
$191$	3.39359	−	5.87788i	0.245552	−	0.425308i	0.962287	+	0.272038i	$0.0876975\pi$
$192$	3.63950	+	6.30381i	0.262659	+	0.454938i
$193$	−18.5112	+	10.6875i	−1.33247	+	0.769300i	−0.985677	−	0.168642i	$-0.946062\pi$
$193$	−18.5112	+	10.6875i	−1.33247	+	0.769300i	−0.346790	+	0.937943i	$0.612728\pi$
$194$	15.3085			1.09909
$195$	−4.22920	−	3.40148i	−0.302859	−	0.243585i
$196$	4.80176			0.342983
$197$	19.7438	−	11.3991i	1.40669	−	0.812153i	0.411623	−	0.911354i	$-0.364962\pi$
$197$	19.7438	−	11.3991i	1.40669	−	0.812153i	0.995067	+	0.0992006i	$0.0316286\pi$
$198$	−0.113387	−	0.196391i	−0.00805804	−	0.0139569i
$199$	1.33183	−	2.30679i	0.0944107	−	0.163524i	−0.814952	−	0.579529i	$-0.803237\pi$
$199$	1.33183	−	2.30679i	0.0944107	−	0.163524i	0.909363	+	0.416005i	$0.136570\pi$
$200$			19.9785i			1.41269i
$201$	7.18333	+	4.14730i	0.506673	+	0.292528i
$202$	15.0914	+	8.71302i	1.06183	+	0.613046i
$203$		−	5.97602i		−	0.419434i
$204$	−15.5928	+	27.0076i	−1.09172	+	1.89091i
$205$	4.84621	+	8.39389i	0.338474	+	0.586255i
$206$	−10.2151	+	5.89767i	−0.711718	+	0.410910i
$207$	5.20221			0.361578
$208$	−21.3618	+	26.5600i	−1.48117	+	1.84160i
$209$	0.460170			0.0318306
$210$	3.39983	−	1.96290i	0.234611	−	0.135453i
$211$	12.0916	+	20.9432i	0.832419	+	1.44179i	0.896115	+	0.443823i	$0.146378\pi$
$211$	12.0916	+	20.9432i	0.832419	+	1.44179i	−0.0636958	+	0.997969i	$0.520289\pi$
$212$	−7.88632	+	13.6595i	−0.541635	+	0.938138i
$213$			12.9178i			0.885116i
$214$	−23.1390	−	13.3593i	−1.58175	−	0.913225i
$215$	8.87850	+	5.12601i	0.605509	+	0.349591i
$216$			7.30704i			0.497181i
$217$	−1.00144	+	1.73455i	−0.0679825	+	0.117749i
$218$	−17.6761	−	30.6160i	−1.19718	−	2.07357i
$219$	12.6012	−	7.27533i	0.851513	−	0.491621i
$220$	0.628490			0.0423728
$221$	−23.1405	−	3.58615i	−1.55660	−	0.241231i
$222$	24.8316			1.66659
$223$	−14.6428	+	8.45400i	−0.980551	+	0.566122i	−0.902437	−	0.430823i	$-0.858223\pi$
$223$	−14.6428	+	8.45400i	−0.980551	+	0.566122i	−0.0781148	+	0.996944i	$0.524890\pi$
$224$	−5.02024	−	8.69531i	−0.335429	−	0.580980i
$225$	−1.36707	+	2.36783i	−0.0911380	+	0.157856i
$226$		−	34.9146i		−	2.32248i
$227$	10.0833	+	5.82157i	0.669249	+	0.386391i	0.795792	−	0.605570i	$-0.207055\pi$
$227$	10.0833	+	5.82157i	0.669249	+	0.386391i	−0.126543	+	0.991961i	$0.540388\pi$
$228$	−22.0073	−	12.7059i	−1.45747	−	0.841471i
$229$		−	7.90801i		−	0.522576i	−0.965261	−	0.261288i	$-0.915853\pi$
$229$		−	7.90801i		−	0.522576i	0.965261	−	0.261288i	$-0.0841473\pi$
$230$	−10.2114	+	17.6866i	−0.673319	+	1.16622i
$231$	0.0434762	+	0.0753030i	0.00286052	+	0.00495457i
$232$	−37.8167	+	21.8335i	−2.48279	+	1.43344i
$233$	24.0854			1.57789			0.788945	−	0.614464i	$-0.210628\pi$
$233$	24.0854			1.57789			0.788945	+	0.614464i	$0.210628\pi$
$234$	−8.76751	+	3.39907i	−0.573150	+	0.222204i
$235$	2.75543			0.179745
$236$	−11.1242	+	6.42256i	−0.724124	+	0.418073i
$237$	5.83898	+	10.1134i	0.379282	+	0.656936i
$238$	8.46907	−	14.6689i	0.548968	−	0.950841i
$239$			10.9354i			0.707352i	0.935368	+	0.353676i	$0.115068\pi$
$239$			10.9354i			0.707352i	−0.935368	+	0.353676i	$0.884932\pi$
$240$	−12.3235	−	7.11497i	−0.795478	−	0.459269i
$241$	17.2385	+	9.95268i	1.11043	+	0.641108i	0.938941	−	0.344077i	$-0.111808\pi$
$241$	17.2385	+	9.95268i	1.11043	+	0.641108i	0.171491	+	0.985186i	$0.445142\pi$
$242$		−	28.6685i		−	1.84288i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	−15.7151	−	27.2194i	−1.00606	−	1.74254i
$245$	−1.30361	+	0.752639i	−0.0832845	+	0.0480843i
$246$	16.7929			1.07068
$247$	2.92220	−	18.8562i	0.185935	−	1.19979i
$248$	14.6352			0.929335
$249$	−1.11986	+	0.646552i	−0.0709683	+	0.0409736i
$250$	−15.1813	−	26.2948i	−0.960150	−	1.66303i
$251$	−11.6942	+	20.2549i	−0.738129	+	1.27848i	0.215208	+	0.976568i	$0.430957\pi$
$251$	−11.6942	+	20.2549i	−0.738129	+	1.27848i	−0.953337	+	0.301909i	$0.902376\pi$
$252$		−	4.80176i		−	0.302482i
$253$	−0.391741	−	0.226172i	−0.0246286	−	0.0142193i
$254$	−29.2370	−	16.8800i	−1.83449	−	1.05914i
$255$		−	9.77623i		−	0.612212i
$256$	8.70972	−	15.0857i	0.544357	−	0.942855i
$257$	6.02975	+	10.4438i	0.376125	+	0.651468i	0.990495	−	0.137550i	$-0.0439229\pi$
$257$	6.02975	+	10.4438i	0.376125	+	0.651468i	−0.614369	+	0.789019i	$0.710590\pi$
$258$	15.3827	−	8.88123i	0.957688	−	0.552921i
$259$	−9.52127			−0.591623
$260$	3.99108	−	25.7534i	0.247516	−	1.59716i
$261$	−5.97602			−0.369906
$262$	−13.2103	+	7.62698i	−0.816136	+	0.471196i
$263$	−2.26613	−	3.92505i	−0.139736	−	0.242029i	0.787661	−	0.616109i	$-0.211292\pi$
$263$	−2.26613	−	3.92505i	−0.139736	−	0.242029i	−0.927396	+	0.374080i	$0.877959\pi$
$264$	0.317682	−	0.550241i	0.0195520	−	0.0338650i
$265$		−	4.94448i		−	0.303737i
$266$	11.9530	+	6.90108i	0.732887	+	0.423132i
$267$	−13.7225	−	7.92270i	−0.839805	−	0.484861i
$268$			39.8286i			2.43292i
$269$	13.9800	−	24.2140i	0.852375	−	1.47636i	−0.0266843	−	0.999644i	$-0.508495\pi$
$269$	13.9800	−	24.2140i	0.852375	−	1.47636i	0.879059	−	0.476713i	$-0.158172\pi$
$270$	−1.96290	−	3.39983i	−0.119458	−	0.206907i
$271$	3.62825	−	2.09477i	0.220400	−	0.127248i	−0.385735	−	0.922609i	$-0.626052\pi$
$271$	3.62825	−	2.09477i	0.220400	−	0.127248i	0.606136	+	0.795361i	$0.292719\pi$
$272$	−61.3962			−3.72269
$273$	3.36175	−	1.30332i	0.203462	−	0.0788802i
$274$	13.3293			0.805252
$275$	0.205889	−	0.118870i	0.0124156	−	0.00716813i
$276$	12.4899	+	21.6331i	0.751802	+	1.30216i
$277$	4.93402	−	8.54598i	0.296457	−	0.513478i	−0.678866	−	0.734262i	$-0.737528\pi$
$277$	4.93402	−	8.54598i	0.296457	−	0.513478i	0.975323	+	0.220784i	$0.0708616\pi$
$278$			50.4065i			3.02318i
$279$	1.73455	+	1.00144i	0.103845	+	0.0599549i
$280$	9.52551	+	5.49956i	0.569258	+	0.328661i
$281$		−	2.76496i		−	0.164944i	−0.996593	−	0.0824719i	$-0.973719\pi$
$281$		−	2.76496i		−	0.164944i	0.996593	−	0.0824719i	$-0.0262815\pi$
$282$	2.38701	−	4.13442i	0.142144	−	0.246201i
$283$	−2.87040	−	4.97167i	−0.170627	−	0.295535i	0.768012	−	0.640435i	$-0.221246\pi$
$283$	−2.87040	−	4.97167i	−0.170627	−	0.295535i	−0.938639	+	0.344900i	$0.887913\pi$
$284$	−53.7181	+	31.0142i	−3.18759	+	1.84035i
$285$	7.96623			0.471879
$286$	0.807998	+	0.125218i	0.0477779	+	0.00740428i
$287$	−6.43896			−0.380080
$288$	−8.69531	+	5.02024i	−0.512376	+	0.295820i
$289$	−12.5902	−	21.8068i	−0.740598	−	1.28275i
$290$	11.7303	−	20.3175i	0.688827	−	1.19308i
$291$			5.86980i			0.344094i
$292$	60.5081	+	34.9344i	3.54097	+	2.04438i
$293$	13.6845	+	7.90072i	0.799454	+	0.461565i	0.843280	−	0.537474i	$-0.180621\pi$
$293$	13.6845	+	7.90072i	0.799454	+	0.461565i	−0.0438259	+	0.999039i	$0.513955\pi$
$294$			2.60802i			0.152103i
$295$	2.01337	−	3.48727i	0.117223	−	0.203036i
$296$	34.7861	+	60.2513i	2.02190	+	3.50204i
$297$	0.0753030	−	0.0434762i	0.00436952	−	0.00252274i
$298$	24.8030			1.43680
$299$	−11.7554	+	14.6160i	−0.679835	+	0.845266i
$300$	−13.1287			−0.757985
$301$	−5.89825	+	3.40536i	−0.339969	+	0.196281i
$302$	16.6613	+	28.8582i	0.958749	+	1.66060i
$303$	−3.34086	+	5.78654i	−0.191927	+	0.332428i
$304$		−	50.0291i		−	2.86937i
$305$	8.53286	+	4.92645i	0.488590	+	0.282088i
$306$	−14.6689	−	8.46907i	−0.838563	−	0.484144i
$307$		−	10.1195i		−	0.577549i	−0.957397	−	0.288774i	$-0.906752\pi$
$307$		−	10.1195i		−	0.577549i	0.957397	−	0.288774i	$-0.0932478\pi$
$308$	−0.208762	+	0.361587i	−0.0118953	+	0.0206033i
$309$	−2.26136	−	3.91680i	−0.128644	−	0.222819i
$310$	−6.80949	+	3.93146i	−0.386753	+	0.223292i
$311$	−14.4989			−0.822155			−0.411077	−	0.911600i	$-0.634847\pi$
$311$	−14.4989			−0.822155			−0.411077	+	0.911600i	$0.634847\pi$
$312$	−20.5297	−	16.5117i	−1.16227	−	0.934793i
$313$	13.2670			0.749897			0.374948	−	0.927046i	$-0.377660\pi$
$313$	13.2670			0.749897			0.374948	+	0.927046i	$0.377660\pi$
$314$	5.81516	−	3.35738i	0.328168	−	0.189468i
$315$	0.752639	+	1.30361i	0.0424064	+	0.0734500i
$316$	−28.0374	+	48.5621i	−1.57722	+	2.73183i
$317$			30.4190i			1.70850i	0.519860	+	0.854252i	$0.325984\pi$
$317$			30.4190i			1.70850i	−0.519860	+	0.854252i	$0.674016\pi$
$318$	−7.41900	−	4.28336i	−0.416037	−	0.240199i
$319$	0.450012	+	0.259814i	0.0251958	+	0.0145468i
$320$		−	10.9569i		−	0.612511i
$321$	5.12241	−	8.87227i	0.285905	−	0.495202i
$322$	−6.78372	−	11.7498i	−0.378042	−	0.654788i
$323$	29.7661	−	17.1855i	1.65623	−	0.956226i
$324$	−4.80176			−0.266764
$325$	−3.56345	−	9.19150i	−0.197664	−	0.509852i
$326$	50.9345			2.82100
$327$	11.7392	−	6.77761i	0.649177	−	0.374803i
$328$	23.5249	+	40.7463i	1.29894	+	2.24984i
$329$	−0.915257	+	1.58527i	−0.0504598	+	0.0873989i
$330$			0.341357i			0.0187911i
$331$	8.05659	+	4.65147i	0.442830	+	0.255668i	0.704797	−	0.709409i	$-0.251038\pi$
$331$	8.05659	+	4.65147i	0.442830	+	0.255668i	−0.261967	+	0.965077i	$0.584371\pi$
$332$	−5.37730	−	3.10459i	−0.295118	−	0.170386i
$333$			9.52127i			0.521762i
$334$	1.82108	−	3.15420i	0.0996450	−	0.172590i
$335$	−6.24283	−	10.8129i	−0.341082	−	0.590772i
$336$	8.18685	−	4.72668i	0.446629	−	0.257862i
$337$	−13.3054			−0.724789			−0.362395	−	0.932025i	$-0.618041\pi$
$337$	−13.3054			−0.724789			−0.362395	+	0.932025i	$0.618041\pi$
$338$	10.2620	−	32.3139i	0.558180	−	1.75764i
$339$	13.3874			0.727104
$340$	40.6539	−	23.4716i	2.20477	−	1.27292i
$341$	−0.0870780	−	0.150824i	−0.00471554	−	0.00816755i
$342$	6.90108	−	11.9530i	0.373168	−	0.646345i
$343$		−	1.00000i		−	0.0539949i
$344$	43.0987	+	24.8831i	2.32373	+	1.34160i
$345$	−6.78164	−	3.91538i	−0.365111	−	0.210797i
$346$			44.8094i			2.40897i
$347$	8.43801	−	14.6151i	0.452976	−	0.784578i	−0.545593	−	0.838050i	$-0.683696\pi$
$347$	8.43801	−	14.6151i	0.452976	−	0.784578i	0.998569	+	0.0534723i	$0.0170289\pi$
$348$	−14.3477	−	24.8509i	−0.769117	−	1.33215i
$349$	−2.08469	+	1.20360i	−0.111591	+	0.0644271i	−0.554757	−	0.832013i	$-0.687189\pi$
$349$	−2.08469	+	1.20360i	−0.111591	+	0.0644271i	0.443166	+	0.896440i	$0.353855\pi$
$350$	7.13069			0.381151
$351$	−1.30332	−	3.36175i	−0.0695658	−	0.179437i
$352$	0.873043			0.0465333
$353$	−26.5988	+	15.3568i	−1.41571	+	0.817361i	−0.995918	−	0.0902583i	$-0.971231\pi$
$353$	−26.5988	+	15.3568i	−1.41571	+	0.817361i	−0.419793	+	0.907620i	$0.637897\pi$
$354$	−3.48834	−	6.04198i	−0.185403	−	0.321127i
$355$	9.72247	−	16.8398i	0.516015	−	0.893765i
$356$		−	76.0858i		−	4.03254i
$357$	5.62452	+	3.24732i	0.297681	+	0.171866i
$358$	3.24579	+	1.87396i	0.171546	+	0.0990419i
$359$			10.6322i			0.561145i	0.959833	+	0.280572i	$0.0905243\pi$
$359$			10.6322i			0.561145i	−0.959833	+	0.280572i	$0.909476\pi$
$360$	5.49956	−	9.52551i	0.289852	−	0.502039i
$361$	4.50371	+	7.80065i	0.237037	+	0.410561i
$362$	−9.75453	+	5.63178i	−0.512687	+	0.296000i
$363$	10.9924			0.576953
$364$	13.4909	+	10.8506i	0.707116	+	0.568723i
$365$	−21.9028			−1.14644
$366$	14.7839	−	8.53548i	0.772766	−	0.446157i
$367$	−13.1031	−	22.6953i	−0.683977	−	1.18468i	−0.973757	−	0.227590i	$-0.926915\pi$
$367$	−13.1031	−	22.6953i	−0.683977	−	1.18468i	0.289780	−	0.957093i	$-0.406418\pi$
$368$	−24.5892	+	42.5897i	−1.28180	+	2.22014i
$369$			6.43896i			0.335199i
$370$	−32.3707	−	18.6893i	−1.68287	−	0.971608i
$371$	2.84469	+	1.64238i	0.147689	+	0.0852682i
$372$			9.61739i			0.498639i
$373$	−9.10509	+	15.7705i	−0.471444	+	0.816565i	−0.999466	−	0.0326656i	$-0.989600\pi$
$373$	−9.10509	+	15.7705i	−0.471444	+	0.816565i	0.528022	+	0.849230i	$0.322934\pi$
$374$	0.736405	+	1.27549i	0.0380786	+	0.0659541i
$375$	10.0823	−	5.82101i	0.520647	−	0.300596i
$376$	13.3756			0.689796
$377$	13.5040	−	16.7901i	0.695493	−	0.864734i
$378$	2.60802			0.134142
$379$	−25.0235	+	14.4473i	−1.28537	+	0.742110i	−0.977825	−	0.209423i	$-0.932842\pi$
$379$	−25.0235	+	14.4473i	−1.28537	+	0.742110i	−0.307547	+	0.951533i	$0.599508\pi$
$380$	19.1260	+	33.1271i	0.981141	+	1.69939i
$381$	6.47234	−	11.2104i	0.331588	−	0.574328i
$382$			17.7011i			0.905668i
$383$	−15.0050	−	8.66312i	−0.766718	−	0.442665i	0.0649848	−	0.997886i	$-0.479300\pi$
$383$	−15.0050	−	8.66312i	−0.766718	−	0.442665i	−0.831702	+	0.555222i	$0.812633\pi$
$384$	0.950172	+	0.548582i	0.0484883	+	0.0279947i
$385$		−	0.130887i		−	0.00667064i
$386$	27.8731	−	48.2776i	1.41870	−	2.45727i
$387$	3.40536	+	5.89825i	0.173104	+	0.299825i
$388$	−24.4092	+	14.0927i	−1.23919	+	0.715448i
$389$	−13.6737			−0.693282			−0.346641	−	0.937998i	$-0.612678\pi$
$389$	−13.6737			−0.693282			−0.346641	+	0.937998i	$0.612678\pi$
$390$	13.9877	+	2.16771i	0.708293	+	0.109766i
$391$	−33.7865			−1.70865
$392$	−6.32808	+	3.65352i	−0.319616	+	0.184531i
$393$	−2.92444	−	5.06527i	−0.147518	−	0.255509i
$394$	−29.7291	+	51.4923i	−1.49773	+	2.59415i
$395$		−	17.5786i		−	0.884473i
$396$	0.361587	+	0.208762i	0.0181704	+	0.0104907i
$397$	−13.3743	−	7.72167i	−0.671238	−	0.387540i	0.125307	−	0.992118i	$-0.460008\pi$
$397$	−13.3743	−	7.72167i	−0.671238	−	0.387540i	−0.796546	+	0.604578i	$0.793342\pi$
$398$			6.94686i			0.348215i
$399$	−2.64610	+	4.58318i	−0.132471	+	0.229446i
$400$	−12.9234	−	22.3840i	−0.646170	−	1.11920i
$401$	12.3265	−	7.11671i	0.615556	−	0.355391i	−0.159581	−	0.987185i	$-0.551014\pi$
$401$	12.3265	−	7.11671i	0.615556	−	0.355391i	0.775137	+	0.631794i	$0.217681\pi$
$402$	−21.6324			−1.07893
$403$	−6.73322	+	2.61040i	−0.335405	+	0.130033i
$404$	−32.0840			−1.59624
$405$	1.30361	−	0.752639i	0.0647768	−	0.0373989i
$406$	7.79278	+	13.4975i	0.386749	+	0.669869i
$407$	0.413948	−	0.716979i	0.0205187	−	0.0355394i
$408$		−	47.4566i		−	2.34945i
$409$	12.1987	+	7.04291i	0.603185	+	0.348249i	0.770294	−	0.637689i	$-0.220110\pi$
$409$	12.1987	+	7.04291i	0.603185	+	0.348249i	−0.167108	+	0.985939i	$0.553443\pi$
$410$	−21.8914	−	12.6390i	−1.08114	−	0.624196i
$411$			5.11089i			0.252102i
$412$	10.8585	−	18.8075i	0.534961	−	0.926579i
$413$	1.33754	+	2.31669i	0.0658162	+	0.113997i
$414$	−11.7498	+	6.78372i	−0.577469	+	0.333402i
$415$	1.94648			0.0955489
$416$	5.54406	−	35.7744i	0.271820	−	1.75398i
$417$	−19.3275			−0.946473
$418$	−1.03934	+	0.600065i	−0.0508360	+	0.0293502i
$419$	18.8362	+	32.6252i	0.920207	+	1.59385i	0.799093	+	0.601207i	$0.205313\pi$
$419$	18.8362	+	32.6252i	0.920207	+	1.59385i	0.121114	+	0.992639i	$0.461353\pi$
$420$	−3.61399	+	6.25961i	−0.176345	+	0.305438i
$421$		−	2.28615i		−	0.111420i	−0.998447	−	0.0557101i	$-0.982258\pi$
$421$		−	2.28615i		−	0.111420i	0.998447	−	0.0557101i	$-0.0177423\pi$
$422$	−54.6203	−	31.5351i	−2.65888	−	1.53510i
$423$	1.58527	+	0.915257i	0.0770786	+	0.0445013i
$424$		−	24.0019i		−	1.16563i
$425$	8.87863	−	15.3782i	0.430677	−	0.745954i
$426$	−16.8450	−	29.1764i	−0.816142	−	1.41360i
$427$	−5.66863	+	3.27278i	−0.274324	+	0.158381i
$428$	49.1931			2.37784
$429$	−0.0480126	+	0.309813i	−0.00231807	+	0.0149579i
$430$	−26.7374			−1.28939
$431$	1.71575	−	0.990590i	0.0826449	−	0.0477150i	−0.458108	−	0.888897i	$-0.651473\pi$
$431$	1.71575	−	0.990590i	0.0826449	−	0.0477150i	0.540753	+	0.841181i	$0.318139\pi$
$432$	−4.72668	−	8.18685i	−0.227413	−	0.393890i
$433$	−2.94544	+	5.10165i	−0.141549	+	0.245170i	−0.928080	−	0.372381i	$-0.878542\pi$
$433$	−2.94544	+	5.10165i	−0.141549	+	0.245170i	0.786531	+	0.617550i	$0.211875\pi$
$434$		−	5.22357i		−	0.250740i
$435$	7.79039	+	4.49778i	0.373521	+	0.215652i
$436$	56.3686	+	32.5444i	2.69957	+	1.55860i
$437$		−	27.5311i		−	1.31699i
$438$	−18.9742	+	32.8643i	−0.906622	+	1.57031i
$439$	−4.03281	−	6.98504i	−0.192476	−	0.333378i	0.753594	−	0.657340i	$-0.228318\pi$
$439$	−4.03281	−	6.98504i	−0.192476	−	0.333378i	−0.946070	+	0.323962i	$0.894985\pi$
$440$	−0.828266	+	0.478200i	−0.0394860	+	0.0227973i
$441$	−1.00000			−0.0476190
$442$	56.9418	−	22.0757i	2.70845	−	1.05004i
$443$	6.65984			0.316419			0.158209	−	0.987406i	$-0.449428\pi$
$443$	6.65984			0.316419			0.158209	+	0.987406i	$0.449428\pi$
$444$	−39.5937	+	22.8594i	−1.87903	+	1.08486i
$445$	11.9259	+	20.6562i	0.565340	+	0.979198i
$446$	22.0482	−	38.1886i	1.04401	−	1.80828i
$447$			9.51027i			0.449821i
$448$	6.30381	+	3.63950i	0.297827	+	0.171950i
$449$	−17.1899	−	9.92456i	−0.811239	−	0.468369i	0.0361468	−	0.999346i	$-0.488492\pi$
$449$	−17.1899	−	9.92456i	−0.811239	−	0.468369i	−0.847386	+	0.530977i	$0.821825\pi$
$450$		−	7.13069i		−	0.336144i
$451$	0.279942	−	0.484873i	0.0131819	−	0.0228318i
$452$	32.1415	+	55.6708i	1.51181	+	2.61853i
$453$	−11.0652	+	6.38848i	−0.519887	+	0.300157i
$454$	−30.3655			−1.42512
$455$	−5.36333	−	0.831171i	−0.251437	−	0.0389659i
$456$	38.6703			1.81090
$457$	2.24200	−	1.29442i	0.104876	−	0.0605505i	−0.446644	−	0.894712i	$-0.647381\pi$
$457$	2.24200	−	1.29442i	0.104876	−	0.0605505i	0.551521	+	0.834161i	$0.314048\pi$
$458$	10.3121	+	17.8611i	0.481854	+	0.834595i
$459$	3.24732	−	5.62452i	0.151572	−	0.262530i
$460$		−	37.6014i		−	1.75318i
$461$	22.8342	+	13.1834i	1.06350	+	0.614010i	0.926397	−	0.376547i	$-0.122889\pi$
$461$	22.8342	+	13.1834i	1.06350	+	0.614010i	0.137099	+	0.990557i	$0.456222\pi$
$462$	−0.196391	−	0.113387i	−0.00913696	−	0.00527522i
$463$			29.3082i			1.36207i	0.732252	+	0.681034i	$0.238469\pi$
$463$			29.3082i			1.36207i	−0.732252	+	0.681034i	$0.761531\pi$
$464$	28.2467	−	48.9248i	1.31132	−	2.27128i
$465$	−1.50745	−	2.61098i	−0.0699064	−	0.121081i
$466$	−54.3996	+	31.4076i	−2.52001	+	1.45493i
$467$	−3.23005			−0.149469			−0.0747345	−	0.997203i	$-0.523811\pi$
$467$	−3.23005			−0.149469			−0.0747345	+	0.997203i	$0.523811\pi$
$468$	10.8506	−	13.4909i	0.501567	−	0.623618i
$469$	8.29459			0.383009
$470$	−6.22345	+	3.59311i	−0.287066	+	0.165738i
$471$	1.28733	+	2.22972i	0.0593171	+	0.102740i
$472$	9.77348	−	16.9282i	0.449861	−	0.779182i
$473$		−	0.592207i		−	0.0272297i
$474$	−26.3759	−	15.2282i	−1.21149	−	0.699452i
$475$	12.5311	+	7.23481i	0.574965	+	0.331956i
$476$			31.1857i			1.42939i
$477$	1.64238	−	2.84469i	0.0751995	−	0.130249i
$478$	−14.2599	−	24.6988i	−0.652230	−	1.12970i
$479$	6.85282	−	3.95648i	0.313114	−	0.180776i	−0.335205	−	0.942145i	$-0.608806\pi$
$479$	6.85282	−	3.95648i	0.313114	−	0.180776i	0.648319	+	0.761369i	$0.275472\pi$
$480$	15.1137			0.689843
$481$	−26.7508	−	21.5152i	−1.21973	−	0.981011i
$482$	−51.9135			−2.36460
$483$	4.50524	−	2.60110i	0.204996	−	0.118354i
$484$	26.3915	+	45.7114i	1.19961	+	2.07779i
$485$	4.41784	−	7.65192i	0.200604	−	0.347456i
$486$		−	2.60802i		−	0.118302i
$487$	−13.3758	−	7.72253i	−0.606116	−	0.349941i	0.165328	−	0.986239i	$-0.447132\pi$
$487$	−13.3758	−	7.72253i	−0.606116	−	0.349941i	−0.771444	+	0.636297i	$0.780465\pi$
$488$	41.4209	+	23.9144i	1.87503	+	1.08255i
$489$			19.5300i			0.883176i
$490$	1.96290	−	3.39983i	0.0886746	−	0.153589i
$491$	−7.45311	−	12.9092i	−0.336354	−	0.582582i	0.647390	−	0.762159i	$-0.275861\pi$
$491$	−7.45311	−	12.9092i	−0.336354	−	0.582582i	−0.983744	+	0.179577i	$0.942527\pi$
$492$	−26.7761	+	15.4592i	−1.20716	+	0.696953i
$493$	38.8121			1.74801
$494$	17.9886	+	46.3994i	0.809344	+	2.08761i
$495$	−0.130887			−0.00588295
$496$	−16.3974	+	9.46702i	−0.736263	+	0.425082i
$497$	6.45892	+	11.1872i	0.289722	+	0.501814i
$498$	1.68622	−	2.92062i	0.0755613	−	0.130876i
$499$		−	25.4306i		−	1.13843i	−0.822189	−	0.569214i	$-0.807248\pi$
$499$		−	25.4306i		−	1.13843i	0.822189	−	0.569214i	$-0.192752\pi$
$500$	48.4127	+	27.9511i	2.16508	+	1.25001i
$501$	1.20942	+	0.698261i	0.0540331	+	0.0311960i
$502$		−	60.9972i		−	2.72244i
$503$	−14.3956	+	24.9339i	−0.641867	+	1.11175i	0.343149	+	0.939281i	$0.388507\pi$
$503$	−14.3956	+	24.9339i	−0.641867	+	1.11175i	−0.985016	+	0.172465i	$0.944827\pi$
$504$	3.65352	+	6.32808i	0.162741	+	0.281875i
$505$	8.71034	−	5.02892i	0.387605	−	0.223784i
$506$	1.17972			0.0524450
$507$	12.3902	+	3.93479i	0.550269	+	0.174750i
$508$	62.1573			2.75778
$509$	−13.5662	+	7.83245i	−0.601311	+	0.347167i	−0.769557	−	0.638578i	$-0.779523\pi$
$509$	−13.5662	+	7.83245i	−0.601311	+	0.347167i	0.168246	+	0.985745i	$0.446190\pi$
$510$	12.7483	+	22.0807i	0.564504	+	0.977750i
$511$	7.27533	−	12.6012i	0.321842	−	0.557446i
$512$			43.2359i			1.91077i
$513$	4.58318	+	2.64610i	0.202352	+	0.116828i
$514$	−27.2377	−	15.7257i	−1.20140	−	0.693631i
$515$			6.80796i			0.299994i
$516$	−16.3517	+	28.3220i	−0.719843	+	1.24680i
$517$	−0.0795838	−	0.137843i	−0.00350009	−	0.00606233i
$518$	21.5048	−	12.4158i	0.944868	−	0.545520i
$519$	−17.1814			−0.754179
$520$	14.3353	+	36.9763i	0.628645	+	1.62152i
$521$	4.38082			0.191927			0.0959636	−	0.995385i	$-0.469407\pi$
$521$	4.38082			0.191927			0.0959636	+	0.995385i	$0.469407\pi$
$522$	13.4975	−	7.79278i	0.590769	−	0.341081i
$523$	10.6603	+	18.4643i	0.466144	+	0.807386i	0.999252	−	0.0386616i	$-0.0123094\pi$
$523$	10.6603	+	18.4643i	0.466144	+	0.807386i	−0.533108	+	0.846047i	$0.678976\pi$
$524$	14.0424	−	24.3222i	0.613447	−	1.06252i
$525$			2.73414i			0.119328i
$526$	10.2366	+	5.91011i	0.446337	+	0.257693i
$527$	−11.2653	−	6.50402i	−0.490724	−	0.283320i
$528$			0.821992i			0.0357726i
$529$	−2.03147	+	3.51862i	−0.0883250	+	0.152983i
$530$	6.44765	+	11.1676i	0.280068	+	0.485092i
$531$	2.31669	−	1.33754i	0.100536	−	0.0580444i
$532$	−25.4119			−1.10174
$533$	−18.0908	−	14.5502i	−0.783599	−	0.630237i
$534$	41.3251			1.78831
$535$	−13.3552	+	7.71064i	−0.577397	+	0.333360i
$536$	−30.3044	−	52.4888i	−1.30895	−	2.26717i
$537$	−0.718538	+	1.24454i	−0.0310072	+	0.0537061i
$538$			72.9201i			3.14381i
$539$	0.0753030	+	0.0434762i	0.00324353	+	0.00187265i
$540$	6.25961	+	3.61399i	0.269371	+	0.155521i
$541$			18.7093i			0.804374i	0.915557	+	0.402187i	$0.131750\pi$
$541$			18.7093i			0.804374i	−0.915557	+	0.402187i	$0.868250\pi$
$542$	−5.46320	+	9.46253i	−0.234664	+	0.406451i
$543$	−2.15941	−	3.74021i	−0.0926691	−	0.160508i
$544$	56.4729	−	32.6046i	2.42125	−	1.39791i
$545$	−20.4044			−0.874027
$546$	−5.89335	+	7.32743i	−0.252212	+	0.313585i
$547$	26.4218			1.12972			0.564858	−	0.825188i	$-0.308931\pi$
$547$	26.4218			1.12972			0.564858	+	0.825188i	$0.308931\pi$
$548$	−21.2534	+	12.2706i	−0.907899	+	0.524176i
$549$	3.27278	+	5.66863i	0.139679	+	0.241931i
$550$	−0.310015	+	0.536962i	−0.0132191	+	0.0228961i
$551$			31.6263i			1.34733i
$552$	−32.9200	−	19.0064i	−1.40117	−	0.808964i
$553$	10.1134	+	5.83898i	0.430066	+	0.248299i
$554$			25.7360i			1.09342i
$555$	7.16607	−	12.4120i	0.304183	−	0.526860i
$556$	−46.4030	−	80.3724i	−1.96793	−	3.40855i
$557$	15.6452	−	9.03278i	0.662910	−	0.382731i	−0.130475	−	0.991452i	$-0.541650\pi$
$557$	15.6452	−	9.03278i	0.662910	−	0.382731i	0.793385	+	0.608721i	$0.208317\pi$
$558$	−5.22357			−0.221131
$559$	−24.2667	−	3.76068i	−1.02637	−	0.159060i
$560$	−14.2299			−0.601325
$561$	−0.489066	+	0.282362i	−0.0206484	+	0.0119213i
$562$	3.60554	+	6.24497i	0.152090	+	0.263428i
$563$	−16.4758	+	28.5369i	−0.694371	+	1.20269i	0.276021	+	0.961151i	$0.410984\pi$
$563$	−16.4758	+	28.5369i	−0.694371	+	1.20269i	−0.970392	+	0.241534i	$0.922349\pi$
$564$			8.78969i			0.370113i
$565$	−17.4519	−	10.0759i	−0.734209	−	0.423895i
$566$	12.9662	+	7.48605i	0.545011	+	0.314662i
$567$			1.00000i			0.0419961i
$568$	47.1956	−	81.7451i	1.98028	−	3.42995i
$569$	3.33237	+	5.77184i	0.139700	+	0.241968i	0.927383	−	0.374113i	$-0.122053\pi$
$569$	3.33237	+	5.77184i	0.139700	+	0.241968i	−0.787683	+	0.616081i	$0.788719\pi$
$570$	−17.9926	+	10.3880i	−0.753628	+	0.435107i
$571$	40.5063			1.69513			0.847567	−	0.530688i	$-0.178066\pi$
$571$	40.5063			1.69513			0.847567	+	0.530688i	$0.178066\pi$
$572$	−1.40361	+	0.544166i	−0.0586880	+	0.0227527i
$573$	−6.78719			−0.283539
$574$	14.5431	−	8.39647i	0.607018	−	0.350462i
$575$	−7.11178	−	12.3180i	−0.296582	−	0.513695i
$576$	3.63950	−	6.30381i	0.151646	−	0.262659i
$577$			16.2052i			0.674632i	0.941391	+	0.337316i	$0.109519\pi$
$577$			16.2052i			0.674632i	−0.941391	+	0.337316i	$0.890481\pi$
$578$	56.8726	+	32.8354i	2.36559	+	1.36577i
$579$	18.5112	+	10.6875i	0.769300	+	0.444156i
$580$			43.1945i			1.79356i
$581$	−0.646552	+	1.11986i	−0.0268235	+	0.0464597i
$582$	−7.65427	−	13.2576i	−0.317280	−	0.549545i
$583$	−0.247352	+	0.142809i	−0.0102443	+	0.00591454i
$584$	−106.322			−4.39964
$585$	−0.831171	+	5.36333i	−0.0343647	+	0.221747i
$586$	−41.2105			−1.70239
$587$	15.5385	−	8.97113i	0.641341	−	0.370278i	−0.143790	−	0.989608i	$-0.545929\pi$
$587$	15.5385	−	8.97113i	0.641341	−	0.370278i	0.785131	+	0.619330i	$0.212596\pi$
$588$	−2.40088	−	4.15844i	−0.0990106	−	0.171491i
$589$	5.29985	−	9.17961i	0.218377	−	0.378239i
$590$			10.5018i			0.432354i
$591$	−19.7438	−	11.3991i	−0.812153	−	0.468897i
$592$	−77.9492	−	45.0040i	−3.20369	−	1.84965i
$593$		−	34.1889i		−	1.40397i	−0.712193	−	0.701984i	$-0.752298\pi$
$593$		−	34.1889i		−	1.40397i	0.712193	−	0.701984i	$-0.247702\pi$
$594$	−0.113387	+	0.196391i	−0.00465231	+	0.00805804i
$595$	−4.88812	−	8.46647i	−0.200393	−	0.347091i
$596$	−39.5479	+	22.8330i	−1.61995	+	0.935277i
$597$	−2.66365			−0.109016
$598$	7.49155	−	48.3411i	0.306352	−	1.97681i
$599$	−9.68405			−0.395680			−0.197840	−	0.980234i	$-0.563393\pi$
$599$	−9.68405			−0.395680			−0.197840	+	0.980234i	$0.563393\pi$
$600$	17.3019	−	9.98923i	0.706345	−	0.407809i
$601$	−6.44431	−	11.1619i	−0.262869	−	0.455302i	0.704134	−	0.710067i	$-0.251335\pi$
$601$	−6.44431	−	11.1619i	−0.262869	−	0.455302i	−0.967003	+	0.254765i	$0.918002\pi$
$602$	8.88123	−	15.3827i	0.361972	−	0.626954i
$603$		−	8.29459i		−	0.337782i
$604$	−53.1323	−	30.6760i	−2.16192	−	1.24819i
$605$	−14.3298	−	8.27334i	−0.582591	−	0.336359i
$606$		−	17.4260i		−	0.707884i
$607$	−7.90895	+	13.6987i	−0.321014	+	0.556013i	−0.980698	−	0.195531i	$-0.937357\pi$
$607$	−7.90895	+	13.6987i	−0.321014	+	0.556013i	0.659683	+	0.751544i	$0.270690\pi$
$608$	26.5681	+	46.0173i	1.07748	+	1.86625i
$609$	−5.17538	+	2.98801i	−0.209717	+	0.121080i
$610$	−25.6965			−1.04042
$611$	−6.15373	+	2.38574i	−0.248953	+	0.0965166i
$612$	31.1857			1.26061
$613$	−22.6303	+	13.0656i	−0.914031	+	0.527716i	−0.881726	−	0.471762i	$-0.843618\pi$
$613$	−22.6303	+	13.0656i	−0.914031	+	0.527716i	−0.0323051	+	0.999478i	$0.510285\pi$
$614$	13.1959	+	22.8559i	0.532543	+	0.922391i
$615$	4.84621	−	8.39389i	0.195418	−	0.338474i
$616$		−	0.635364i		−	0.0255995i
$617$	19.7693	+	11.4138i	0.795880	+	0.459502i	0.842029	−	0.539433i	$-0.181361\pi$
$617$	19.7693	+	11.4138i	0.795880	+	0.459502i	−0.0461483	+	0.998935i	$0.514695\pi$
$618$	10.2151	+	5.89767i	0.410910	+	0.237239i
$619$		−	25.4700i		−	1.02373i	−0.859067	−	0.511863i	$-0.828956\pi$
$619$		−	25.4700i		−	1.02373i	0.859067	−	0.511863i	$-0.171044\pi$
$620$	7.23842	−	12.5373i	0.290702	−	0.503511i
$621$	−2.60110	−	4.50524i	−0.104379	−	0.180789i
$622$	32.7473	−	18.9066i	1.31305	−	0.758087i
$623$	−15.8454			−0.634833
$624$	33.6825	+	5.21988i	1.34838	+	0.208962i
$625$	−3.85378			−0.154151
$626$	−29.9650	+	17.3003i	−1.19764	+	0.691460i
$627$	−0.230085	−	0.398519i	−0.00918870	−	0.0159153i
$628$	−6.18145	+	10.7066i	−0.246667	+	0.427239i
$629$		−	61.8372i		−	2.46561i
$630$	−3.39983	−	1.96290i	−0.135453	−	0.0782036i
$631$	13.3886	+	7.72994i	0.532993	+	0.307724i	0.742235	−	0.670140i	$-0.233766\pi$
$631$	13.3886	+	7.72994i	0.532993	+	0.307724i	−0.209241	+	0.977864i	$0.567099\pi$
$632$		−	85.3312i		−	3.39429i
$633$	12.0916	−	20.9432i	0.480597	−	0.832419i
$634$	−39.6667	−	68.7047i	−1.57537	−	2.72861i
$635$	−16.8748	+	9.74267i	−0.669656	+	0.386626i
$636$	15.7726			0.625426
$637$	2.25970	−	2.80958i	0.0895327	−	0.111320i
$638$	−1.35520			−0.0536529
$639$	11.1872	−	6.45892i	0.442558	−	0.255511i
$640$	−0.825768	−	1.43027i	−0.0326414	−	0.0565365i
$641$	−11.6918	+	20.2509i	−0.461800	+	0.799861i	−0.999051	−	0.0435617i	$-0.986129\pi$
$641$	−11.6918	+	20.2509i	−0.461800	+	0.799861i	0.537251	+	0.843422i	$0.319463\pi$
$642$			26.7187i			1.05450i
$643$	−1.05918	−	0.611515i	−0.0417698	−	0.0241158i	0.478970	−	0.877831i	$-0.341010\pi$
$643$	−1.05918	−	0.611515i	−0.0417698	−	0.0241158i	−0.520739	+	0.853716i	$0.674344\pi$
$644$	21.6331	+	12.4899i	0.852463	+	0.492170i
$645$		−	10.2520i		−	0.403673i
$646$	−44.8200	+	77.6306i	−1.76342	+	3.05433i
$647$	6.18090	+	10.7056i	0.242996	+	0.420882i	0.961566	−	0.274573i	$-0.0885363\pi$
$647$	6.18090	+	10.7056i	0.242996	+	0.420882i	−0.718570	+	0.695455i	$0.755203\pi$
$648$	6.32808	−	3.65352i	0.248590	−	0.143524i
$649$	−0.232605			−0.00913055
$650$	20.0342	+	16.1132i	0.785807	+	0.632013i
$651$	2.00289			0.0784994
$652$	−81.2143	+	46.8891i	−3.18060	+	1.83632i
$653$	−4.93154	−	8.54168i	−0.192986	−	0.334262i	0.753252	−	0.657732i	$-0.228484\pi$
$653$	−4.93154	−	8.54168i	−0.192986	−	0.334262i	−0.946238	+	0.323470i	$0.895151\pi$
$654$	−17.6761	+	30.6160i	−0.691191	+	1.19718i
$655$			8.80417i			0.344008i
$656$	−52.7149	−	30.4349i	−2.05817	−	1.18828i
$657$	−12.6012	−	7.27533i	−0.491621	−	0.283838i
$658$		−	4.77401i		−	0.186110i
$659$	−7.27455	+	12.5999i	−0.283376	+	0.490822i	−0.972214	−	0.234093i	$-0.924788\pi$
$659$	−7.27455	+	12.5999i	−0.283376	+	0.490822i	0.688838	+	0.724916i	$0.258121\pi$
$660$	−0.314245	−	0.544288i	−0.0122320	−	0.0211864i
$661$	16.8095	−	9.70496i	0.653813	−	0.377479i	−0.136102	−	0.990695i	$-0.543458\pi$
$661$	16.8095	−	9.70496i	0.653813	−	0.377479i	0.789916	+	0.613216i	$0.210124\pi$
$662$	−24.2622			−0.942979
$663$	8.46456	+	21.8334i	0.328736	+	0.847937i
$664$	9.44876			0.366683
$665$	6.89896	−	3.98312i	0.267530	−	0.154459i
$666$	−12.4158	−	21.5048i	−0.481103	−	0.833295i
$667$	15.5442	−	26.9234i	0.601875	−	1.04248i
$668$			6.70577i			0.259454i
$669$	14.6428	+	8.45400i	0.566122	+	0.326850i
$670$	28.2002	+	16.2814i	1.08947	+	0.629006i
$671$		−	0.569153i		−	0.0219719i
$672$	−5.02024	+	8.69531i	−0.193660	+	0.335429i
$673$	17.6889	+	30.6381i	0.681859	+	1.18101i	0.974413	+	0.224765i	$0.0721614\pi$
$673$	17.6889	+	30.6381i	0.681859	+	1.18101i	−0.292554	+	0.956249i	$0.594505\pi$
$674$	30.0516	−	17.3503i	1.15755	−	0.668309i
$675$	2.73414			0.105237
$676$	13.3848	+	60.9710i	0.514799	+	2.34504i
$677$	10.9841			0.422154			0.211077	−	0.977469i	$-0.432303\pi$
$677$	10.9841			0.422154			0.211077	+	0.977469i	$0.432303\pi$
$678$	−30.2369	+	17.4573i	−1.16124	+	0.670444i
$679$	2.93490	+	5.08340i	0.112631	+	0.195083i
$680$	−35.7176	+	61.8648i	−1.36971	+	2.37241i
$681$		−	11.6431i		−	0.446166i
$682$	0.393350	+	0.227101i	0.0150622	+	0.00869615i
$683$	5.55922	+	3.20962i	0.212718	+	0.122813i	0.602574	−	0.798063i	$-0.294142\pi$
$683$	5.55922	+	3.20962i	0.212718	+	0.122813i	−0.389856	+	0.920876i	$0.627475\pi$
$684$			25.4119i			0.971648i
$685$	3.84666	−	6.66260i	0.146973	−	0.254565i
$686$	1.30401	+	2.25861i	0.0497873	+	0.0862341i
$687$	−6.84854	+	3.95401i	−0.261288	+	0.150855i
$688$	−64.3841			−2.45462
$689$	4.28108	+	11.0426i	0.163096	+	0.420688i
$690$	20.4228			0.777482
$691$	−23.9076	+	13.8031i	−0.909490	+	0.525094i	−0.880267	−	0.474479i	$-0.842637\pi$
$691$	−23.9076	+	13.8031i	−0.909490	+	0.525094i	−0.0292227	+	0.999573i	$0.509303\pi$
$692$	−41.2504	−	71.4479i	−1.56811	−	2.71604i
$693$	0.0434762	−	0.0753030i	0.00165152	−	0.00286052i
$694$			44.0130i			1.67071i
$695$	25.1955	+	14.5466i	0.955721	+	0.551786i
$696$	37.8167	+	21.8335i	1.43344	+	0.827596i
$697$		−	41.8187i		−	1.58400i
$698$	3.13900	−	5.43691i	0.118813	−	0.205790i
$699$	−12.0427	−	20.8586i	−0.455497	−	0.788945i
$700$	−11.3698	+	6.56434i	−0.429737	+	0.248109i
$701$	−15.9426			−0.602144			−0.301072	−	0.953601i	$-0.597344\pi$
$701$	−15.9426			−0.602144			−0.301072	+	0.953601i	$0.597344\pi$
$702$	7.32743	+	5.89335i	0.276556	+	0.222430i
$703$	50.3885			1.90044
$704$	−0.548131	+	0.316463i	−0.0206585	+	0.0119272i
$705$	−1.37772	−	2.38627i	−0.0518878	−	0.0898723i
$706$	40.0509	−	69.3702i	1.50733	−	2.61078i
$707$			6.68172i			0.251292i
$708$	11.1242	+	6.42256i	0.418073	+	0.241375i
$709$	−10.8489	−	6.26364i	−0.407440	−	0.235236i	0.282249	−	0.959341i	$-0.408920\pi$
$709$	−10.8489	−	6.26364i	−0.407440	−	0.235236i	−0.689689	+	0.724105i	$0.742253\pi$
$710$			50.7128i			1.90322i
$711$	5.83898	−	10.1134i	0.218979	−	0.379282i
$712$	57.8915	+	100.271i	2.16957	+	3.75781i
$713$	−9.02350	+	5.20972i	−0.337933	+	0.195106i
$714$	−16.9381			−0.633894
$715$	0.295767	−	0.367739i	0.0110611	−	0.0137526i
$716$	−6.90049			−0.257883
$717$	9.47033	−	5.46770i	0.353676	−	0.204195i
$718$	−13.8645	−	24.0139i	−0.517417	−	0.896192i
$719$	−21.2816	+	36.8608i	−0.793670	+	1.37468i	0.130010	+	0.991513i	$0.458499\pi$
$719$	−21.2816	+	36.8608i	−0.793670	+	1.37468i	−0.923680	+	0.383164i	$0.874834\pi$
$720$			14.2299i			0.530318i
$721$	−3.91680	−	2.26136i	−0.145869	−	0.0842175i
$722$	−20.3442	−	11.7458i	−0.757134	−	0.437132i
$723$		−	19.9054i		−	0.740288i
$724$	10.3690	−	17.9596i	0.385360	−	0.667462i
$725$	8.16964	+	14.1502i	0.303413	+	0.525526i
$726$	−24.8276	+	14.3342i	−0.921440	+	0.531994i
$727$	25.1186			0.931596			0.465798	−	0.884891i	$-0.345767\pi$
$727$	25.1186			0.931596			0.465798	+	0.884891i	$0.345767\pi$
$728$	−26.0351	−	4.03473i	−0.964925	−	0.149537i
$729$	1.00000			0.0370370
$730$	49.4698	−	28.5614i	1.83096	−	1.05711i
$731$	−22.1166	−	38.3070i	−0.818010	−	1.41684i
$732$	−15.7151	+	27.2194i	−0.580848	+	1.00606i
$733$		−	2.32992i		−	0.0860574i	−0.999074	−	0.0430287i	$-0.986299\pi$
$733$		−	2.32992i		−	0.0860574i	0.999074	−	0.0430287i	$-0.0137007\pi$
$734$	59.1897	+	34.1732i	2.18473	+	1.26135i
$735$	1.30361	+	0.752639i	0.0480843	+	0.0277615i
$736$		−	52.2326i		−	1.92532i
$737$	−0.360617	+	0.624607i	−0.0132835	+	0.0230077i
$738$	−8.39647	−	14.5431i	−0.309078	−	0.535339i
$739$	23.2242	−	13.4085i	0.854315	−	0.493239i	−0.00778923	−	0.999970i	$-0.502479\pi$
$739$	23.2242	−	13.4085i	0.854315	−	0.493239i	0.862105	+	0.506731i	$0.169146\pi$
$740$	68.8195			2.52986
$741$	−17.7911	+	6.89741i	−0.653571	+	0.253383i
$742$	−8.56672			−0.314494
$743$	−43.1876	+	24.9344i	−1.58440	+	0.914753i	−0.590192	+	0.807263i	$0.700948\pi$
$743$	−43.1876	+	24.9344i	−1.58440	+	0.914753i	−0.994206	+	0.107490i	$0.965719\pi$
$744$	−7.31759	−	12.6744i	−0.268276	−	0.464668i
$745$	7.15780	−	12.3977i	0.262242	−	0.454216i
$746$		−	47.4925i		−	1.73882i
$747$	1.11986	+	0.646552i	0.0409736	+	0.0236561i
$748$	−2.34837	−	1.35583i	−0.0858651	−	0.0495742i
$749$		−	10.2448i		−	0.374337i
$750$	−15.1813	+	26.2948i	−0.554343	+	0.960150i
$751$	1.39391	+	2.41432i	0.0508645	+	0.0881000i	0.890337	−	0.455303i	$-0.150469\pi$
$751$	1.39391	+	2.41432i	0.0508645	+	0.0881000i	−0.839472	+	0.543403i	$0.817136\pi$
$752$	−14.9862	+	8.65226i	−0.546489	+	0.315515i
$753$	23.3883			0.852318
$754$	−8.60590	+	55.5317i	−0.313408	+	2.02234i
$755$	19.2329			0.699956
$756$	−4.15844	+	2.40088i	−0.151241	+	0.0873191i
$757$	−6.92483	−	11.9941i	−0.251687	−	0.435935i	0.712303	−	0.701872i	$-0.247652\pi$
$757$	−6.92483	−	11.9941i	−0.251687	−	0.435935i	−0.963990	+	0.265937i	$0.914319\pi$
$758$	37.6789	−	65.2618i	1.36856	−	2.37042i
$759$			0.452344i			0.0164191i
$760$	−50.4110	−	29.1048i	−1.82860	−	1.05574i
$761$	−38.7289	−	22.3601i	−1.40392	−	0.810555i	−0.409130	−	0.912476i	$-0.634168\pi$
$761$	−38.7289	−	22.3601i	−1.40392	−	0.810555i	−0.994792	+	0.101922i	$0.967501\pi$
$762$			33.7600i			1.22299i
$763$	6.77761	−	11.7392i	0.245366	−	0.424986i
$764$	−16.2952	−	28.2241i	−0.589540	−	1.02111i
$765$	−8.46647	+	4.88812i	−0.306106	+	0.176730i
$766$	45.1871			1.63268
$767$	−1.47711	+	9.53139i	−0.0533352	+	0.344158i
$768$	−17.4194			−0.628570
$769$	−11.1497	+	6.43728i	−0.402068	+	0.232134i	−0.687376	−

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-2.25861 + 1.30401i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(2.40088 - 4.15844i) q^{4} +1.50528i q^{5} +(2.25861 + 1.30401i) q^{6} +(-0.866025 - 0.500000i) q^{7} +7.30704i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-2.25861 + 1.30401i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(2.40088 - 4.15844i) q^{4} +1.50528i q^{5} +(2.25861 + 1.30401i) q^{6} +(-0.866025 - 0.500000i) q^{7} +7.30704i q^{8} +(-0.500000 + 0.866025i) q^{9} +(-1.96290 - 3.39983i) q^{10} +(0.0753030 - 0.0434762i) q^{11} -4.80176 q^{12} +(-1.30332 - 3.36175i) q^{13} +2.60802 q^{14} +(1.30361 - 0.752639i) q^{15} +(-4.72668 - 8.18685i) q^{16} +(3.24732 - 5.62452i) q^{17} -2.60802i q^{18} +(4.58318 + 2.64610i) q^{19} +(6.25961 + 3.61399i) q^{20} +1.00000i q^{21} +(-0.113387 + 0.196391i) q^{22} +(-2.60110 - 4.50524i) q^{23} +(6.32808 - 3.65352i) q^{24} +2.73414 q^{25} +(7.32743 + 5.89335i) q^{26} +1.00000 q^{27} +(-4.15844 + 2.40088i) q^{28} +(2.98801 + 5.17538i) q^{29} +(-1.96290 + 3.39983i) q^{30} -2.00289i q^{31} +(8.69531 + 5.02024i) q^{32} +(-0.0753030 - 0.0434762i) q^{33} +16.9381i q^{34} +(0.752639 - 1.30361i) q^{35} +(2.40088 + 4.15844i) q^{36} +(8.24566 - 4.76063i) q^{37} -13.8022 q^{38} +(-2.25970 + 2.80958i) q^{39} -10.9991 q^{40} +(5.57631 - 3.21948i) q^{41} +(-1.30401 - 2.25861i) q^{42} +(3.40536 - 5.89825i) q^{43} -0.417524i q^{44} +(-1.30361 - 0.752639i) q^{45} +(11.7498 + 6.78372i) q^{46} -1.83051i q^{47} +(-4.72668 + 8.18685i) q^{48} +(0.500000 + 0.866025i) q^{49} +(-6.17535 + 3.56534i) q^{50} -6.49464 q^{51} +(-17.1088 - 2.65139i) q^{52} -3.28476 q^{53} +(-2.25861 + 1.30401i) q^{54} +(0.0654437 + 0.113352i) q^{55} +(3.65352 - 6.32808i) q^{56} -5.29220i q^{57} +(-13.4975 - 7.79278i) q^{58} +(-2.31669 - 1.33754i) q^{59} -7.22798i q^{60} +(3.27278 - 5.66863i) q^{61} +(2.61179 + 4.52375i) q^{62} +(0.866025 - 0.500000i) q^{63} -7.27901 q^{64} +(5.06037 - 1.96185i) q^{65} +0.226773 q^{66} +(-7.18333 + 4.14730i) q^{67} +(-15.5928 - 27.0076i) q^{68} +(-2.60110 + 4.50524i) q^{69} +3.92579i q^{70} +(-11.1872 - 6.45892i) q^{71} +(-6.32808 - 3.65352i) q^{72} +14.5507i q^{73} +(-12.4158 + 21.5048i) q^{74} +(-1.36707 - 2.36783i) q^{75} +(22.0073 - 12.7059i) q^{76} -0.0869524 q^{77} +(1.44007 - 9.29242i) q^{78} -11.6780 q^{79} +(12.3235 - 7.11497i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-8.39647 + 14.5431i) q^{82} -1.29310i q^{83} +(4.15844 + 2.40088i) q^{84} +(8.46647 + 4.88812i) q^{85} +17.7625i q^{86} +(2.98801 - 5.17538i) q^{87} +(0.317682 + 0.550241i) q^{88} +(13.7225 - 7.92270i) q^{89} +3.92579 q^{90} +(-0.552171 + 3.56302i) q^{91} -24.9797 q^{92} +(-1.73455 + 1.00144i) q^{93} +(2.38701 + 4.13442i) q^{94} +(-3.98312 + 6.89896i) q^{95} -10.0405i q^{96} +(-5.08340 - 2.93490i) q^{97} +(-2.25861 - 1.30401i) q^{98} +0.0869524i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{3} + 6 q^{4} - 8 q^{9}+O(q^{10}) \) 16 * q - 8 * q^3 + 6 * q^4 - 8 * q^9	\( 16 q - 8 q^{3} + 6 q^{4} - 8 q^{9} - 4 q^{10} - 12 q^{11} - 12 q^{12} + 4 q^{13} + 4 q^{14} - 10 q^{16} + 10 q^{17} + 6 q^{20} - 2 q^{22} - 2 q^{23} + 12 q^{25} + 20 q^{26} + 16 q^{27} + 12 q^{29} - 4 q^{30} + 30 q^{32} + 12 q^{33} - 2 q^{35} + 6 q^{36} + 18 q^{37} - 32 q^{38} - 8 q^{39} - 60 q^{40} + 18 q^{41} - 2 q^{42} - 10 q^{43} + 30 q^{46} - 10 q^{48} + 8 q^{49} - 24 q^{50} - 20 q^{51} - 26 q^{52} + 12 q^{53} + 10 q^{55} + 12 q^{56} - 54 q^{58} - 60 q^{59} - 6 q^{61} + 16 q^{62} + 16 q^{64} - 20 q^{65} + 4 q^{66} - 18 q^{67} - 20 q^{68} - 2 q^{69} + 6 q^{71} + 18 q^{74} - 6 q^{75} + 72 q^{76} - 16 q^{77} + 14 q^{78} - 4 q^{79} + 30 q^{80} - 8 q^{81} - 18 q^{82} - 24 q^{85} + 12 q^{87} - 2 q^{88} + 78 q^{89} + 8 q^{90} - 8 q^{91} - 20 q^{92} + 6 q^{93} + 16 q^{94} - 4 q^{95} - 54 q^{97}+O(q^{100}) \) 16 * q - 8 * q^3 + 6 * q^4 - 8 * q^9 - 4 * q^10 - 12 * q^11 - 12 * q^12 + 4 * q^13 + 4 * q^14 - 10 * q^16 + 10 * q^17 + 6 * q^20 - 2 * q^22 - 2 * q^23 + 12 * q^25 + 20 * q^26 + 16 * q^27 + 12 * q^29 - 4 * q^30 + 30 * q^32 + 12 * q^33 - 2 * q^35 + 6 * q^36 + 18 * q^37 - 32 * q^38 - 8 * q^39 - 60 * q^40 + 18 * q^41 - 2 * q^42 - 10 * q^43 + 30 * q^46 - 10 * q^48 + 8 * q^49 - 24 * q^50 - 20 * q^51 - 26 * q^52 + 12 * q^53 + 10 * q^55 + 12 * q^56 - 54 * q^58 - 60 * q^59 - 6 * q^61 + 16 * q^62 + 16 * q^64 - 20 * q^65 + 4 * q^66 - 18 * q^67 - 20 * q^68 - 2 * q^69 + 6 * q^71 + 18 * q^74 - 6 * q^75 + 72 * q^76 - 16 * q^77 + 14 * q^78 - 4 * q^79 + 30 * q^80 - 8 * q^81 - 18 * q^82 - 24 * q^85 + 12 * q^87 - 2 * q^88 + 78 * q^89 + 8 * q^90 - 8 * q^91 - 20 * q^92 + 6 * q^93 + 16 * q^94 - 4 * q^95 - 54 * q^97

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