LMFDB - Embedded newform 273.2.bd.a.43.1

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			43.1
Root			$-2.60802i$ of defining polynomial
Character	$\chi$	$=$	273.43
Dual form			273.2.bd.a.127.1

$q$-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 $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

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

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	−0.992046	−	0.125872i	$-0.959827\pi$
$2$	−2.25861	−	1.30401i	−1.59708	−	0.922074i	−0.605032	−	0.796201i	$-0.706840\pi$
$3$	−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	$-0.890726\pi$
$5$		−	1.50528i		−	0.673181i	0.941651	−	0.336590i	$-0.109274\pi$
$6$	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	0.511309	−	0.859397i	$-0.329161\pi$
$11$	0.0753030	+	0.0434762i	0.0227047	+	0.0131086i	−0.488605	+	0.872505i	$0.662494\pi$
$12$	−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	0.927439	+	0.373974i	$0.122005\pi$
$17$	3.24732	+	5.62452i	0.787591	+	1.36415i	−0.139848	+	0.990173i	$0.544662\pi$
$18$			2.60802i			0.614716i
$19$	4.58318	−	2.64610i	1.05145	−	0.607057i	0.128398	−	0.991723i	$-0.459016\pi$
$19$	4.58318	−	2.64610i	1.05145	−	0.607057i	0.923056	+	0.384665i	$0.125683\pi$
$20$	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	0.456400	+	0.889775i	$0.349139\pi$
$23$	−2.60110	+	4.50524i	−0.542367	+	0.939408i	−0.998768	+	0.0496333i	$0.984195\pi$
$24$	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	−0.443055	−	0.896494i	$-0.646105\pi$
$29$	2.98801	−	5.17538i	0.554859	−	0.961045i	0.997914	−	0.0645503i	$-0.0205613\pi$
$30$	−1.96290	−	3.39983i	−0.358374	−	0.620722i
$31$			2.00289i			0.359730i	0.983691	+	0.179865i	$0.0575660\pi$
$31$			2.00289i			0.359730i	−0.983691	+	0.179865i	$0.942434\pi$
$32$	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	0.989024	−	0.147754i	$-0.0472042\pi$
$37$	8.24566	+	4.76063i	1.35558	+	0.782643i	0.366554	+	0.930397i	$0.380538\pi$
$38$	−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	0.867638	−	0.497196i	$-0.165637\pi$
$41$	5.57631	+	3.21948i	0.870873	+	0.502799i	0.00323453	+	0.999995i	$0.498970\pi$
$42$	−1.30401	+	2.25861i	−0.201213	+	0.348511i
$43$	3.40536	+	5.89825i	0.519312	+	0.899475i	0.999748	+	0.0224449i	$0.00714502\pi$
$43$	3.40536	+	5.89825i	0.519312	+	0.899475i	−0.480436	+	0.877030i	$0.659522\pi$
$44$			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	$0.0426229\pi$
$47$			1.83051i			0.267008i	−0.991048	+	0.133504i	$0.957377\pi$
$48$	−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	−0.643165	−	0.765728i	$-0.722379\pi$
$59$	−2.31669	+	1.33754i	−0.301608	+	0.174133i	0.341557	+	0.939861i	$0.389046\pi$
$60$			7.22798i			0.933128i
$61$	3.27278	+	5.66863i	0.419037	+	0.725794i	0.995843	−	0.0910877i	$-0.0290344\pi$
$61$	3.27278	+	5.66863i	0.419037	+	0.725794i	−0.576806	+	0.816881i	$0.695701\pi$
$62$	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	−0.00772242	−	0.999970i	$-0.502458\pi$
$67$	−7.18333	−	4.14730i	−0.877583	−	0.506673i	−0.869861	+	0.493297i	$0.835791\pi$
$68$	−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	−0.984940	−	0.172899i	$-0.944687\pi$
$71$	−11.1872	+	6.45892i	−1.32767	+	0.766533i	−0.342735	+	0.939432i	$0.611353\pi$
$72$	−6.32808	+	3.65352i	−0.745771	+	0.430571i
$73$		−	14.5507i		−	1.70303i	−0.524334	−	0.851513i	$-0.675686\pi$
$73$		−	14.5507i		−	1.70303i	0.524334	−	0.851513i	$-0.324314\pi$
$74$	−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	$0.0226089\pi$
$83$			1.29310i			0.141937i	−0.997479	+	0.0709683i	$0.977391\pi$
$84$	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	0.998737	−	0.0502531i	$-0.0160028\pi$
$89$	13.7225	+	7.92270i	1.45458	+	0.839805i	0.455848	+	0.890058i	$0.349336\pi$
$90$	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	−0.735354	−	0.677683i	$-0.762984\pi$
$97$	−5.08340	+	2.93490i	−0.516141	+	0.297994i	0.219213	+	0.975677i	$0.429651\pi$
$98$	−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	−0.982987	−	0.183673i	$-0.941201\pi$
$101$	−3.34086	+	5.78654i	−0.332428	+	0.575782i	0.650559	+	0.759455i	$0.274534\pi$
$102$	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	−0.504783	−	0.863246i	$-0.668427\pi$
$107$	5.12241	−	8.87227i	0.495202	−	0.857715i	0.999985	+	0.00553163i	$0.00176078\pi$
$108$	2.40088	+	4.15844i	0.231025	+	0.400147i
$109$		−	13.5552i		−	1.29835i	−0.760637	−	0.649177i	$-0.775113\pi$
$109$		−	13.5552i		−	1.29835i	0.760637	−	0.649177i	$-0.224887\pi$
$110$	−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	−0.987614	−	0.156905i	$-0.949848\pi$
$113$	−6.69370	−	11.5938i	−0.629691	−	1.09066i	0.357923	−	0.933751i	$-0.383485\pi$
$114$	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	−0.421787	−	0.906695i	$-0.638597\pi$
$127$	6.47234	−	11.2104i	0.574328	−	0.994765i	0.996114	−	0.0880695i	$-0.0280698\pi$
$128$	−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	−0.677014	−	0.735970i	$-0.736726\pi$
$137$	−4.42616	+	2.55545i	−0.378153	+	0.218327i	0.298862	+	0.954296i	$0.403393\pi$
$138$			13.5674i			1.15494i
$139$	9.66376	+	16.7381i	0.819669	+	1.41971i	0.905926	+	0.423436i	$0.139176\pi$
$139$	9.66376	+	16.7381i	0.819669	+	1.41971i	−0.0862564	+	0.996273i	$0.527490\pi$
$140$	−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	−0.797867	−	0.602834i	$-0.794038\pi$
$149$	−8.23614	+	4.75514i	−0.674731	+	0.389556i	0.123136	+	0.992390i	$0.460705\pi$
$150$	6.17535	−	3.56534i	0.504216	−	0.291109i
$151$			12.7770i			1.03977i	0.854235	+	0.519887i	$0.174026\pi$
$151$			12.7770i			1.03977i	−0.854235	+	0.519887i	$0.825974\pi$
$152$	−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	−0.984485	−	0.175471i	$-0.943855\pi$
$163$	−16.9135	+	9.76499i	−1.32476	+	0.764853i	−0.340280	+	0.940324i	$0.610522\pi$
$164$			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	0.452476	−	0.891777i	$-0.350541\pi$
$167$	−1.20942	−	0.698261i	−0.0935881	−	0.0540331i	−0.546064	+	0.837744i	$0.683874\pi$
$168$	−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	0.982357	+	0.187015i	$0.0598814\pi$
$173$	8.59070	+	14.8795i	0.653138	+	1.13127i	−0.329219	+	0.944254i	$0.606785\pi$
$174$		−	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	−0.891629	−	0.452768i	$-0.850437\pi$
$179$	−0.718538	+	1.24454i	−0.0537061	+	0.0930216i	0.837923	+	0.545789i	$0.183770\pi$
$180$	−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	0.962287	−	0.272038i	$-0.0876975\pi$
$191$	3.39359	+	5.87788i	0.245552	+	0.425308i	−0.716735	+	0.697346i	$0.754364\pi$
$192$	3.63950	−	6.30381i	0.262659	−	0.454938i
$193$	−18.5112	−	10.6875i	−1.33247	−	0.769300i	−0.346790	−	0.937943i	$-0.612728\pi$
$193$	−18.5112	−	10.6875i	−1.33247	−	0.769300i	−0.985677	+	0.168642i	$0.946062\pi$
$194$	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	0.995067	−	0.0992006i	$-0.0316286\pi$
$197$	19.7438	+	11.3991i	1.40669	+	0.812153i	0.411623	+	0.911354i	$0.364962\pi$
$198$	−0.113387	+	0.196391i	−0.00805804	+	0.0139569i
$199$	1.33183	+	2.30679i	0.0944107	+	0.163524i	0.909363	−	0.416005i	$-0.136570\pi$
$199$	1.33183	+	2.30679i	0.0944107	+	0.163524i	−0.814952	+	0.579529i	$0.803237\pi$
$200$		−	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	−0.0636958	−	0.997969i	$-0.520289\pi$
$211$	12.0916	−	20.9432i	0.832419	−	1.44179i	0.896115	−	0.443823i	$-0.146378\pi$
$212$	−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	−0.0781148	−	0.996944i	$-0.524890\pi$
$223$	−14.6428	−	8.45400i	−0.980551	−	0.566122i	−0.902437	+	0.430823i	$0.858223\pi$
$224$	−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	−0.126543	−	0.991961i	$-0.540388\pi$
$227$	10.0833	−	5.82157i	0.669249	−	0.386391i	0.795792	+	0.605570i	$0.207055\pi$
$228$	−22.0073	+	12.7059i	−1.45747	+	0.841471i
$229$			7.90801i			0.522576i	0.965261	+	0.261288i	$0.0841473\pi$
$229$			7.90801i			0.522576i	−0.965261	+	0.261288i	$0.915853\pi$
$230$	−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	$-0.884932\pi$
$239$		−	10.9354i		−	0.707352i	0.935368	−	0.353676i	$-0.115068\pi$
$240$	−12.3235	+	7.11497i	−0.795478	+	0.459269i
$241$	17.2385	−	9.95268i	1.11043	−	0.641108i	0.171491	−	0.985186i	$-0.445142\pi$
$241$	17.2385	−	9.95268i	1.11043	−	0.641108i	0.938941	+	0.344077i	$0.111808\pi$
$242$			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	−0.953337	−	0.301909i	$-0.902376\pi$
$251$	−11.6942	−	20.2549i	−0.738129	−	1.27848i	0.215208	−	0.976568i	$-0.430957\pi$
$252$			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	−0.614369	−	0.789019i	$-0.710590\pi$
$257$	6.02975	−	10.4438i	0.376125	−	0.651468i	0.990495	+	0.137550i	$0.0439229\pi$
$258$	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	−0.927396	−	0.374080i	$-0.877959\pi$
$263$	−2.26613	+	3.92505i	−0.139736	+	0.242029i	0.787661	+	0.616109i	$0.211292\pi$
$264$	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	0.879059	+	0.476713i	$0.158172\pi$
$269$	13.9800	+	24.2140i	0.852375	+	1.47636i	−0.0266843	+	0.999644i	$0.508495\pi$
$270$	−1.96290	+	3.39983i	−0.119458	+	0.206907i
$271$	3.62825	+	2.09477i	0.220400	+	0.127248i	0.606136	−	0.795361i	$-0.292719\pi$
$271$	3.62825	+	2.09477i	0.220400	+	0.127248i	−0.385735	+	0.922609i	$0.626052\pi$
$272$	−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	0.975323	−	0.220784i	$-0.0708616\pi$
$277$	4.93402	+	8.54598i	0.296457	+	0.513478i	−0.678866	+	0.734262i	$0.737528\pi$
$278$		−	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	$0.0262815\pi$
$281$			2.76496i			0.164944i	−0.996593	+	0.0824719i	$0.973719\pi$
$282$	2.38701	+	4.13442i	0.142144	+	0.246201i
$283$	−2.87040	+	4.97167i	−0.170627	+	0.295535i	−0.938639	−	0.344900i	$-0.887913\pi$
$283$	−2.87040	+	4.97167i	−0.170627	+	0.295535i	0.768012	+	0.640435i	$0.221246\pi$
$284$	−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	−0.0438259	−	0.999039i	$-0.513955\pi$
$293$	13.6845	−	7.90072i	0.799454	−	0.461565i	0.843280	+	0.537474i	$0.180621\pi$
$294$		−	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	$0.0932478\pi$
$307$			10.1195i			0.577549i	−0.957397	+	0.288774i	$0.906752\pi$
$308$	−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	$-0.674016\pi$
$317$		−	30.4190i		−	1.70850i	0.519860	−	0.854252i	$-0.325984\pi$
$318$	−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	−0.261967	−	0.965077i	$-0.584371\pi$
$331$	8.05659	−	4.65147i	0.442830	−	0.255668i	0.704797	+	0.709409i	$0.251038\pi$
$332$	−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	0.998569	−	0.0534723i	$-0.0170289\pi$
$347$	8.43801	+	14.6151i	0.452976	+	0.784578i	−0.545593	+	0.838050i	$0.683696\pi$
$348$	−14.3477	+	24.8509i	−0.769117	+	1.33215i
$349$	−2.08469	−	1.20360i	−0.111591	−	0.0644271i	0.443166	−	0.896440i	$-0.353855\pi$
$349$	−2.08469	−	1.20360i	−0.111591	−	0.0644271i	−0.554757	+	0.832013i	$0.687189\pi$
$350$	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	−0.419793	−	0.907620i	$-0.637897\pi$
$353$	−26.5988	−	15.3568i	−1.41571	−	0.817361i	−0.995918	+	0.0902583i	$0.971231\pi$
$354$	−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	$-0.909476\pi$
$359$		−	10.6322i		−	0.561145i	0.959833	−	0.280572i	$-0.0905243\pi$
$360$	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	0.289780	+	0.957093i	$0.406418\pi$
$367$	−13.1031	+	22.6953i	−0.683977	+	1.18468i	−0.973757	+	0.227590i	$0.926915\pi$
$368$	−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	0.528022	−	0.849230i	$-0.322934\pi$
$373$	−9.10509	−	15.7705i	−0.471444	−	0.816565i	−0.999466	+	0.0326656i	$0.989600\pi$
$374$	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	−0.307547	−	0.951533i	$-0.599508\pi$
$379$	−25.0235	−	14.4473i	−1.28537	−	0.742110i	−0.977825	+	0.209423i	$0.932842\pi$
$380$	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	−0.831702	−	0.555222i	$-0.812633\pi$
$383$	−15.0050	+	8.66312i	−0.766718	+	0.442665i	0.0649848	+	0.997886i	$0.479300\pi$
$384$	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	−0.796546	−	0.604578i	$-0.793342\pi$
$397$	−13.3743	+	7.72167i	−0.671238	+	0.387540i	0.125307	+	0.992118i	$0.460008\pi$
$398$		−	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	0.775137	−	0.631794i	$-0.217681\pi$
$401$	12.3265	+	7.11671i	0.615556	+	0.355391i	−0.159581	+	0.987185i	$0.551014\pi$
$402$	−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	−0.167108	−	0.985939i	$-0.553443\pi$
$409$	12.1987	−	7.04291i	0.603185	−	0.348249i	0.770294	+	0.637689i	$0.220110\pi$
$410$	−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	0.121114	−	0.992639i	$-0.461353\pi$
$419$	18.8362	−	32.6252i	0.920207	−	1.59385i	0.799093	−	0.601207i	$-0.205313\pi$
$420$	−3.61399	−	6.25961i	−0.176345	−	0.305438i
$421$			2.28615i			0.111420i	0.998447	+	0.0557101i	$0.0177423\pi$
$421$			2.28615i			0.111420i	−0.998447	+	0.0557101i	$0.982258\pi$
$422$	−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	0.540753	−	0.841181i	$-0.318139\pi$
$431$	1.71575	+	0.990590i	0.0826449	+	0.0477150i	−0.458108	+	0.888897i	$0.651473\pi$
$432$	−4.72668	+	8.18685i	−0.227413	+	0.393890i
$433$	−2.94544	−	5.10165i	−0.141549	−	0.245170i	0.786531	−	0.617550i	$-0.211875\pi$
$433$	−2.94544	−	5.10165i	−0.141549	−	0.245170i	−0.928080	+	0.372381i	$0.878542\pi$
$434$			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	−0.946070	−	0.323962i	$-0.894985\pi$
$439$	−4.03281	+	6.98504i	−0.192476	+	0.333378i	0.753594	+	0.657340i	$0.228318\pi$
$440$	−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	−0.847386	−	0.530977i	$-0.821825\pi$
$449$	−17.1899	+	9.92456i	−0.811239	+	0.468369i	0.0361468	+	0.999346i	$0.488492\pi$
$450$			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	0.551521	−	0.834161i	$-0.314048\pi$
$457$	2.24200	+	1.29442i	0.104876	+	0.0605505i	−0.446644	+	0.894712i	$0.647381\pi$
$458$	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	0.137099	−	0.990557i	$-0.456222\pi$
$461$	22.8342	−	13.1834i	1.06350	−	0.614010i	0.926397	+	0.376547i	$0.122889\pi$
$462$	−0.196391	+	0.113387i	−0.00913696	+	0.00527522i
$463$		−	29.3082i		−	1.36207i	−0.732252	−	0.681034i	$-0.761531\pi$
$463$		−	29.3082i		−	1.36207i	0.732252	−	0.681034i	$-0.238469\pi$
$464$	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	0.648319	−	0.761369i	$-0.275472\pi$
$479$	6.85282	+	3.95648i	0.313114	+	0.180776i	−0.335205	+	0.942145i	$0.608806\pi$
$480$	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	−0.771444	−	0.636297i	$-0.780465\pi$
$487$	−13.3758	+	7.72253i	−0.606116	+	0.349941i	0.165328	+	0.986239i	$0.447132\pi$
$488$	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	−0.983744	−	0.179577i	$-0.942527\pi$
$491$	−7.45311	+	12.9092i	−0.336354	+	0.582582i	0.647390	+	0.762159i	$0.275861\pi$
$492$	−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	$0.192752\pi$
$499$			25.4306i			1.13843i	−0.822189	+	0.569214i	$0.807248\pi$
$500$	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	−0.985016	−	0.172465i	$-0.944827\pi$
$503$	−14.3956	−	24.9339i	−0.641867	−	1.11175i	0.343149	−	0.939281i	$-0.388507\pi$
$504$	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	0.168246	−	0.985745i	$-0.446190\pi$
$509$	−13.5662	−	7.83245i	−0.601311	−	0.347167i	−0.769557	+	0.638578i	$0.779523\pi$
$510$	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	−0.533108	−	0.846047i	$-0.678976\pi$
$523$	10.6603	−	18.4643i	0.466144	−	0.807386i	0.999252	+	0.0386616i	$0.0123094\pi$
$524$	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	$-0.868250\pi$
$541$		−	18.7093i		−	0.804374i	0.915557	−	0.402187i	$-0.131750\pi$
$542$	−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	0.793385	−	0.608721i	$-0.208317\pi$
$557$	15.6452	+	9.03278i	0.662910	+	0.382731i	−0.130475	+	0.991452i	$0.541650\pi$
$558$	−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	−0.970392	−	0.241534i	$-0.922349\pi$
$563$	−16.4758	−	28.5369i	−0.694371	−	1.20269i	0.276021	−	0.961151i	$-0.410984\pi$
$564$		−	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	−0.787683	−	0.616081i	$-0.788719\pi$
$569$	3.33237	−	5.77184i	0.139700	−	0.241968i	0.927383	+	0.374113i	$0.122053\pi$
$570$	−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	$-0.890481\pi$
$577$		−	16.2052i		−	0.674632i	0.941391	−	0.337316i	$-0.109519\pi$
$578$	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	0.785131	−	0.619330i	$-0.212596\pi$
$587$	15.5385	+	8.97113i	0.641341	+	0.370278i	−0.143790	+	0.989608i	$0.545929\pi$
$588$	−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	$0.247702\pi$
$593$			34.1889i			1.40397i	−0.712193	+	0.701984i	$0.752298\pi$
$594$	−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	−0.967003	−	0.254765i	$-0.918002\pi$
$601$	−6.44431	+	11.1619i	−0.262869	+	0.455302i	0.704134	+	0.710067i	$0.251335\pi$
$602$	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	0.659683	−	0.751544i	$-0.270690\pi$
$607$	−7.90895	−	13.6987i	−0.321014	−	0.556013i	−0.980698	+	0.195531i	$0.937357\pi$
$608$	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	−0.0323051	−	0.999478i	$-0.510285\pi$
$613$	−22.6303	−	13.0656i	−0.914031	−	0.527716i	−0.881726	+	0.471762i	$0.843618\pi$
$614$	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	−0.0461483	−	0.998935i	$-0.514695\pi$
$617$	19.7693	−	11.4138i	0.795880	−	0.459502i	0.842029	+	0.539433i	$0.181361\pi$
$618$	10.2151	−	5.89767i	0.410910	−	0.237239i
$619$			25.4700i			1.02373i	0.859067	+	0.511863i	$0.171044\pi$
$619$			25.4700i			1.02373i	−0.859067	+	0.511863i	$0.828956\pi$
$620$	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	−0.209241	−	0.977864i	$-0.567099\pi$
$631$	13.3886	−	7.72994i	0.532993	−	0.307724i	0.742235	+	0.670140i	$0.233766\pi$
$632$			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	0.537251	−	0.843422i	$-0.319463\pi$
$641$	−11.6918	−	20.2509i	−0.461800	−	0.799861i	−0.999051	+	0.0435617i	$0.986129\pi$
$642$		−	26.7187i		−	1.05450i
$643$	−1.05918	+	0.611515i	−0.0417698	+	0.0241158i	−0.520739	−	0.853716i	$-0.674344\pi$
$643$	−1.05918	+	0.611515i	−0.0417698	+	0.0241158i	0.478970	+	0.877831i	$0.341010\pi$
$644$	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	−0.718570	−	0.695455i	$-0.755203\pi$
$647$	6.18090	−	10.7056i	0.242996	−	0.420882i	0.961566	+	0.274573i	$0.0885363\pi$
$648$	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	−0.946238	−	0.323470i	$-0.895151\pi$
$653$	−4.93154	+	8.54168i	−0.192986	+	0.334262i	0.753252	+	0.657732i	$0.228484\pi$
$654$	−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	0.688838	−	0.724916i	$-0.258121\pi$
$659$	−7.27455	−	12.5999i	−0.283376	−	0.490822i	−0.972214	+	0.234093i	$0.924788\pi$
$660$	−0.314245	+	0.544288i	−0.0122320	+	0.0211864i
$661$	16.8095	+	9.70496i	0.653813	+	0.377479i	0.789916	−	0.613216i	$-0.210124\pi$
$661$	16.8095	+	9.70496i	0.653813	+	0.377479i	−0.136102	+	0.990695i	$0.543458\pi$
$662$	−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	−0.292554	−	0.956249i	$-0.594505\pi$
$673$	17.6889	−	30.6381i	0.681859	−	1.18101i	0.974413	−	0.224765i	$-0.0721614\pi$
$674$	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	−0.389856	−	0.920876i	$-0.627475\pi$
$683$	5.55922	−	3.20962i	0.212718	−	0.122813i	0.602574	+	0.798063i	$0.294142\pi$
$684$		−	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	−0.0292227	−	0.999573i	$-0.509303\pi$
$691$	−23.9076	−	13.8031i	−0.909490	−	0.525094i	−0.880267	+	0.474479i	$0.842637\pi$
$692$	−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	−0.689689	−	0.724105i	$-0.742253\pi$
$709$	−10.8489	+	6.26364i	−0.407440	+	0.235236i	0.282249	+	0.959341i	$0.408920\pi$
$710$		−	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	−0.923680	−	0.383164i	$-0.874834\pi$
$719$	−21.2816	−	36.8608i	−0.793670	−	1.37468i	0.130010	−	0.991513i	$-0.458499\pi$
$720$		−	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	$0.0137007\pi$
$733$			2.32992i			0.0860574i	−0.999074	+	0.0430287i	$0.986299\pi$
$734$	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	0.862105	−	0.506731i	$-0.169146\pi$
$739$	23.2242	+	13.4085i	0.854315	+	0.493239i	−0.00778923	+	0.999970i	$0.502479\pi$
$740$	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	−0.994206	−	0.107490i	$-0.965719\pi$
$743$	−43.1876	−	24.9344i	−1.58440	−	0.914753i	−0.590192	−	0.807263i	$-0.700948\pi$
$744$	−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	−0.839472	−	0.543403i	$-0.817136\pi$
$751$	1.39391	−	2.41432i	0.0508645	−	0.0881000i	0.890337	+	0.455303i	$0.150469\pi$
$752$	−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	−0.963990	−	0.265937i	$-0.914319\pi$
$757$	−6.92483	+	11.9941i	−0.251687	+	0.435935i	0.712303	+	0.701872i	$0.247652\pi$
$758$	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	−0.994792	−	0.101922i	$-0.967501\pi$
$761$	−38.7289	+	22.3601i	−1.40392	+	0.810555i	−0.409130	+	0.912476i	$0.634168\pi$
$762$		−	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	0.285308	−	0.958436i

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

Introduction

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