LMFDB - Embedded newform 273.2.j.b.172.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(100,273)]

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, 2, 4]))

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

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

chi := DirichletCharacter("273.100");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
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} + 11 x^{14} - 4 x^{13} + 87 x^{12} - 35 x^{11} + 326 x^{10} - 205 x^{9} + 895 x^{8} - 481 x^{7} + \cdots + 1 $ x^16 + 11x^14 - 4x^13 + 87x^12 - 35x^11 + 326x^10 - 205x^9 + 895x^8 - 481x^7 + 1005x^6 - 544x^5 + 811x^4 - 312x^3 + 195x^2 + 13x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			172.8
Root			$1.21707 - 2.10803i$ of defining polynomial
Character	$\chi$	$=$	273.172
Dual form			273.2.j.b.100.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.21707 - 2.10803i) q^{2} -1.00000 q^{3} +(-1.96253 - 3.39920i) q^{4} +(-0.613891 - 1.06329i) q^{5} +(-1.21707 + 2.10803i) q^{6} +(-2.37183 - 1.17236i) q^{7} -4.68588 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+(1.21707 - 2.10803i) q^{2} -1.00000 q^{3} +(-1.96253 - 3.39920i) q^{4} +(-0.613891 - 1.06329i) q^{5} +(-1.21707 + 2.10803i) q^{6} +(-2.37183 - 1.17236i) q^{7} -4.68588 q^{8} +1.00000 q^{9} -2.98860 q^{10} +3.49255 q^{11} +(1.96253 + 3.39920i) q^{12} +(-2.87580 + 2.17480i) q^{13} +(-5.35806 + 3.57304i) q^{14} +(0.613891 + 1.06329i) q^{15} +(-1.77799 + 3.07957i) q^{16} +(-2.26353 - 3.92054i) q^{17} +(1.21707 - 2.10803i) q^{18} +1.35541 q^{19} +(-2.40956 + 4.17348i) q^{20} +(2.37183 + 1.17236i) q^{21} +(4.25069 - 7.36241i) q^{22} +(0.336664 - 0.583119i) q^{23} +4.68588 q^{24} +(1.74628 - 3.02464i) q^{25} +(1.08449 + 8.70917i) q^{26} -1.00000 q^{27} +(0.669691 + 10.3631i) q^{28} +(2.64824 + 4.58688i) q^{29} +2.98860 q^{30} +(4.99846 - 8.65759i) q^{31} +(-0.357986 - 0.620050i) q^{32} -3.49255 q^{33} -11.0195 q^{34} +(0.209483 + 3.24164i) q^{35} +(-1.96253 - 3.39920i) q^{36} +(1.54118 - 2.66940i) q^{37} +(1.64963 - 2.85725i) q^{38} +(2.87580 - 2.17480i) q^{39} +(2.87662 + 4.98245i) q^{40} +(3.61102 + 6.25447i) q^{41} +(5.35806 - 3.57304i) q^{42} +(4.48886 - 7.77494i) q^{43} +(-6.85424 - 11.8719i) q^{44} +(-0.613891 - 1.06329i) q^{45} +(-0.819488 - 1.41940i) q^{46} +(2.58008 + 4.46883i) q^{47} +(1.77799 - 3.07957i) q^{48} +(4.25114 + 5.56128i) q^{49} +(-4.25069 - 7.36241i) q^{50} +(2.26353 + 3.92054i) q^{51} +(13.0364 + 5.50732i) q^{52} +(-4.95271 + 8.57835i) q^{53} +(-1.21707 + 2.10803i) q^{54} +(-2.14405 - 3.71360i) q^{55} +(11.1141 + 5.49354i) q^{56} -1.35541 q^{57} +12.8924 q^{58} +(-0.401721 - 0.695802i) q^{59} +(2.40956 - 4.17348i) q^{60} +4.64974 q^{61} +(-12.1670 - 21.0738i) q^{62} +(-2.37183 - 1.17236i) q^{63} -8.85475 q^{64} +(4.07787 + 1.72272i) q^{65} +(-4.25069 + 7.36241i) q^{66} -2.12136 q^{67} +(-8.88448 + 15.3884i) q^{68} +(-0.336664 + 0.583119i) q^{69} +(7.08845 + 3.50372i) q^{70} +(-2.52793 + 4.37850i) q^{71} -4.68588 q^{72} +(-6.04227 + 10.4655i) q^{73} +(-3.75145 - 6.49771i) q^{74} +(-1.74628 + 3.02464i) q^{75} +(-2.66004 - 4.60732i) q^{76} +(-8.28373 - 4.09453i) q^{77} +(-1.08449 - 8.70917i) q^{78} +(-5.90140 - 10.2215i) q^{79} +4.36598 q^{80} +1.00000 q^{81} +17.5795 q^{82} +12.6805 q^{83} +(-0.669691 - 10.3631i) q^{84} +(-2.77912 + 4.81357i) q^{85} +(-10.9265 - 18.9253i) q^{86} +(-2.64824 - 4.58688i) q^{87} -16.3657 q^{88} +(1.55233 - 2.68871i) q^{89} -2.98860 q^{90} +(9.37056 - 1.78677i) q^{91} -2.64285 q^{92} +(-4.99846 + 8.65759i) q^{93} +12.5606 q^{94} +(-0.832075 - 1.44120i) q^{95} +(0.357986 + 0.620050i) q^{96} +(-3.59585 + 6.22820i) q^{97} +(16.8973 - 2.19305i) q^{98} +3.49255 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 16 q^{3} - 6 q^{4} + q^{7} + 12 q^{8} + 16 q^{9}+O(q^{10}) $ 16 * q - 16 * q^3 - 6 * q^4 + q^7 + 12 * q^8 + 16 * q^9	\( 16 q - 16 q^{3} - 6 q^{4} + q^{7} + 12 q^{8} + 16 q^{9} + 8 q^{10} + 4 q^{11} + 6 q^{12} + 5 q^{13} - 7 q^{14} - 6 q^{16} - 2 q^{17} + 22 q^{19} - 20 q^{20} - q^{21} + 7 q^{22} + 4 q^{23} - 12 q^{24} + 2 q^{25} - 6 q^{26} - 16 q^{27} - 7 q^{28} + 15 q^{29} - 8 q^{30} + 3 q^{31} + 3 q^{32} - 4 q^{33} - 68 q^{34} - 12 q^{35} - 6 q^{36} + 4 q^{37} + 2 q^{38} - 5 q^{39} - 25 q^{40} + 19 q^{41} + 7 q^{42} + 11 q^{43} - 16 q^{44} + 2 q^{46} + 5 q^{47} + 6 q^{48} + 13 q^{49} - 7 q^{50} + 2 q^{51} + 36 q^{52} + 36 q^{53} - 15 q^{55} + 39 q^{56} - 22 q^{57} - 40 q^{58} - 17 q^{59} + 20 q^{60} + 44 q^{61} - 6 q^{62} + q^{63} - 20 q^{64} - 21 q^{65} - 7 q^{66} - 52 q^{67} + 5 q^{68} - 4 q^{69} + 46 q^{70} + 9 q^{71} + 12 q^{72} - 6 q^{73} + 15 q^{74} - 2 q^{75} - 16 q^{76} - 36 q^{77} + 6 q^{78} + 16 q^{79} + 56 q^{80} + 16 q^{81} + 2 q^{82} + 36 q^{83} + 7 q^{84} - 4 q^{85} + 16 q^{86} - 15 q^{87} - 48 q^{88} + 20 q^{89} + 8 q^{90} - 7 q^{91} - 94 q^{92} - 3 q^{93} + 40 q^{94} - 3 q^{96} + 7 q^{97} - 3 q^{98} + 4 q^{99}+O(q^{100}) \) 16 * q - 16 * q^3 - 6 * q^4 + q^7 + 12 * q^8 + 16 * q^9 + 8 * q^10 + 4 * q^11 + 6 * q^12 + 5 * q^13 - 7 * q^14 - 6 * q^16 - 2 * q^17 + 22 * q^19 - 20 * q^20 - q^21 + 7 * q^22 + 4 * q^23 - 12 * q^24 + 2 * q^25 - 6 * q^26 - 16 * q^27 - 7 * q^28 + 15 * q^29 - 8 * q^30 + 3 * q^31 + 3 * q^32 - 4 * q^33 - 68 * q^34 - 12 * q^35 - 6 * q^36 + 4 * q^37 + 2 * q^38 - 5 * q^39 - 25 * q^40 + 19 * q^41 + 7 * q^42 + 11 * q^43 - 16 * q^44 + 2 * q^46 + 5 * q^47 + 6 * q^48 + 13 * q^49 - 7 * q^50 + 2 * q^51 + 36 * q^52 + 36 * q^53 - 15 * q^55 + 39 * q^56 - 22 * q^57 - 40 * q^58 - 17 * q^59 + 20 * q^60 + 44 * q^61 - 6 * q^62 + q^63 - 20 * q^64 - 21 * q^65 - 7 * q^66 - 52 * q^67 + 5 * q^68 - 4 * q^69 + 46 * q^70 + 9 * q^71 + 12 * q^72 - 6 * q^73 + 15 * q^74 - 2 * q^75 - 16 * q^76 - 36 * q^77 + 6 * q^78 + 16 * q^79 + 56 * q^80 + 16 * q^81 + 2 * q^82 + 36 * q^83 + 7 * q^84 - 4 * q^85 + 16 * q^86 - 15 * q^87 - 48 * q^88 + 20 * q^89 + 8 * q^90 - 7 * q^91 - 94 * q^92 - 3 * q^93 + 40 * q^94 - 3 * q^96 + 7 * q^97 - 3 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$92$	$106$	$157$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	1.21707	−	2.10803i	0.860600	−	1.49060i	−0.0107503	−	0.999942i	$-0.503422\pi$
$2$	1.21707	−	2.10803i	0.860600	−	1.49060i	0.871351	−	0.490661i	$-0.163245\pi$
$3$	−1.00000			−0.577350
$3$	−1.00000			−0.577350
$4$	−1.96253	−	3.39920i	−0.981265	−	1.69960i
$5$	−0.613891	−	1.06329i	−0.274540	−	0.475518i	0.695479	−	0.718547i	$-0.255192\pi$
$5$	−0.613891	−	1.06329i	−0.274540	−	0.475518i	−0.970019	+	0.243029i	$0.921859\pi$
$6$	−1.21707	+	2.10803i	−0.496868	+	0.860600i
$7$	−2.37183	−	1.17236i	−0.896467	−	0.443111i
$7$	−2.37183	−	1.17236i	−0.896467	−	0.443111i
$8$	−4.68588			−1.65671
$9$	1.00000			0.333333
$10$	−2.98860			−0.945078
$11$	3.49255			1.05304			0.526522	−	0.850162i	$-0.323496\pi$
$11$	3.49255			1.05304			0.526522	+	0.850162i	$0.323496\pi$
$12$	1.96253	+	3.39920i	0.566534	+	0.981265i
$13$	−2.87580	+	2.17480i	−0.797604	+	0.603181i
$13$	−2.87580	+	2.17480i	−0.797604	+	0.603181i
$14$	−5.35806	+	3.57304i	−1.43200	+	0.954935i
$15$	0.613891	+	1.06329i	0.158506	+	0.274540i
$16$	−1.77799	+	3.07957i	−0.444498	+	0.769894i
$17$	−2.26353	−	3.92054i	−0.548986	−	0.950871i	−0.998344	−	0.0575196i	$-0.981681\pi$
$17$	−2.26353	−	3.92054i	−0.548986	−	0.950871i	0.449359	−	0.893351i	$-0.351653\pi$
$18$	1.21707	−	2.10803i	0.286867	−	0.496868i
$19$	1.35541			0.310953			0.155476	−	0.987840i	$-0.450309\pi$
$19$	1.35541			0.310953			0.155476	+	0.987840i	$0.450309\pi$
$20$	−2.40956	+	4.17348i	−0.538794	+	0.933219i
$21$	2.37183	+	1.17236i	0.517575	+	0.255830i
$22$	4.25069	−	7.36241i	0.906250	−	1.56967i
$23$	0.336664	−	0.583119i	0.0701992	−	0.121589i	−0.828789	−	0.559561i	$-0.810970\pi$
$23$	0.336664	−	0.583119i	0.0701992	−	0.121589i	0.898989	+	0.437972i	$0.144303\pi$
$24$	4.68588			0.956501
$25$	1.74628	−	3.02464i	0.349255	−	0.604928i
$26$	1.08449	+	8.70917i	0.212686	+	1.70801i
$27$	−1.00000			−0.192450
$28$	0.669691	+	10.3631i	0.126560	+	1.95845i
$29$	2.64824	+	4.58688i	0.491766	+	0.851763i	0.999955	−	0.00948238i	$-0.00301838\pi$
$29$	2.64824	+	4.58688i	0.491766	+	0.851763i	−0.508189	+	0.861245i	$0.669685\pi$
$30$	2.98860			0.545641
$31$	4.99846	−	8.65759i	0.897750	−	1.55495i	0.0673864	−	0.997727i	$-0.478534\pi$
$31$	4.99846	−	8.65759i	0.897750	−	1.55495i	0.830364	−	0.557222i	$-0.188133\pi$
$32$	−0.357986	−	0.620050i	−0.0632836	−	0.109610i
$33$	−3.49255			−0.607975
$34$	−11.0195			−1.88983
$35$	0.209483	+	3.24164i	0.0354091	+	0.547938i
$36$	−1.96253	−	3.39920i	−0.327088	−	0.566534i
$37$	1.54118	−	2.66940i	0.253368	−	0.438847i	−0.711083	−	0.703108i	$-0.751795\pi$
$37$	1.54118	−	2.66940i	0.253368	−	0.438847i	0.964451	+	0.264262i	$0.0851282\pi$
$38$	1.64963	−	2.85725i	0.267606	−	0.463507i
$39$	2.87580	−	2.17480i	0.460497	−	0.348247i
$40$	2.87662	+	4.98245i	0.454834	+	0.787795i
$41$	3.61102	+	6.25447i	0.563947	+	0.976784i	0.997147	+	0.0754865i	$0.0240510\pi$
$41$	3.61102	+	6.25447i	0.563947	+	0.976784i	−0.433200	+	0.901298i	$0.642616\pi$
$42$	5.35806	−	3.57304i	0.826767	−	0.551332i
$43$	4.48886	−	7.77494i	0.684545	−	1.18567i	−0.289034	−	0.957319i	$-0.593334\pi$
$43$	4.48886	−	7.77494i	0.684545	−	1.18567i	0.973579	−	0.228348i	$-0.0733325\pi$
$44$	−6.85424	−	11.8719i	−1.03332	−	1.78975i
$45$	−0.613891	−	1.06329i	−0.0915135	−	0.158506i
$46$	−0.819488	−	1.41940i	−0.120827	−	0.209278i
$47$	2.58008	+	4.46883i	0.376344	+	0.651846i	0.990527	−	0.137317i	$-0.0438479\pi$
$47$	2.58008	+	4.46883i	0.376344	+	0.651846i	−0.614184	+	0.789163i	$0.710515\pi$
$48$	1.77799	−	3.07957i	0.256631	−	0.444498i
$49$	4.25114	+	5.56128i	0.607305	+	0.794469i
$50$	−4.25069	−	7.36241i	−0.601138	−	1.04120i
$51$	2.26353	+	3.92054i	0.316957	+	0.548986i
$52$	13.0364	+	5.50732i	1.80783	+	0.763728i
$53$	−4.95271	+	8.57835i	−0.680308	+	1.17833i	0.294579	+	0.955627i	$0.404820\pi$
$53$	−4.95271	+	8.57835i	−0.680308	+	1.17833i	−0.974887	+	0.222700i	$0.928513\pi$
$54$	−1.21707	+	2.10803i	−0.165623	+	0.286867i
$55$	−2.14405	−	3.71360i	−0.289103	−	0.500741i
$56$	11.1141	+	5.49354i	1.48518	+	0.734106i
$57$	−1.35541			−0.179529
$58$	12.8924			1.69285
$59$	−0.401721	−	0.695802i	−0.0522997	−	0.0905857i	0.838690	−	0.544609i	$-0.183322\pi$
$59$	−0.401721	−	0.695802i	−0.0522997	−	0.0905857i	−0.890990	+	0.454023i	$0.849988\pi$
$60$	2.40956	−	4.17348i	0.311073	−	0.538794i
$61$	4.64974			0.595339			0.297669	−	0.954669i	$-0.403791\pi$
$61$	4.64974			0.595339			0.297669	+	0.954669i	$0.403791\pi$
$62$	−12.1670	−	21.0738i	−1.54521	−	2.67638i
$63$	−2.37183	−	1.17236i	−0.298822	−	0.147704i
$64$	−8.85475			−1.10684
$65$	4.07787	+	1.72272i	0.505798	+	0.213677i
$66$	−4.25069	+	7.36241i	−0.523223	+	0.906250i
$67$	−2.12136			−0.259165			−0.129583	−	0.991569i	$-0.541364\pi$
$67$	−2.12136			−0.259165			−0.129583	+	0.991569i	$0.541364\pi$
$68$	−8.88448	+	15.3884i	−1.07740	+	1.86611i
$69$	−0.336664	+	0.583119i	−0.0405295	+	0.0701992i
$70$	7.08845	+	3.50372i	0.847231	+	0.418775i
$71$	−2.52793	+	4.37850i	−0.300010	+	0.519632i	−0.976138	−	0.217152i	$-0.930323\pi$
$71$	−2.52793	+	4.37850i	−0.300010	+	0.519632i	0.676128	+	0.736784i	$0.263657\pi$
$72$	−4.68588			−0.552236
$73$	−6.04227	+	10.4655i	−0.707194	+	1.22490i	0.258699	+	0.965958i	$0.416706\pi$
$73$	−6.04227	+	10.4655i	−0.707194	+	1.22490i	−0.965894	+	0.258939i	$0.916627\pi$
$74$	−3.75145	−	6.49771i	−0.436098	−	0.755343i
$75$	−1.74628	+	3.02464i	−0.201643	+	0.349255i
$76$	−2.66004	−	4.60732i	−0.305127	−	0.528496i
$77$	−8.28373	−	4.09453i	−0.944019	−	0.466615i
$78$	−1.08449	−	8.70917i	−0.122794	−	0.986120i
$79$	−5.90140	−	10.2215i	−0.663960	−	1.15001i	−0.979566	−	0.201122i	$-0.935541\pi$
$79$	−5.90140	−	10.2215i	−0.663960	−	1.15001i	0.315607	−	0.948890i	$-0.397792\pi$
$80$	4.36598			0.488131
$81$	1.00000			0.111111
$82$	17.5795			1.94133
$83$	12.6805			1.39187			0.695935	−	0.718105i	$-0.254990\pi$
$83$	12.6805			1.39187			0.695935	+	0.718105i	$0.254990\pi$
$84$	−0.669691	−	10.3631i	−0.0730693	−	1.13071i
$85$	−2.77912	+	4.81357i	−0.301438	+	0.522105i
$86$	−10.9265	−	18.9253i	−1.17824	−	2.04077i
$87$	−2.64824	−	4.58688i	−0.283921	−	0.491766i
$88$	−16.3657			−1.74459
$89$	1.55233	−	2.68871i	0.164546	−	0.285003i	−0.771948	−	0.635686i	$-0.780717\pi$
$89$	1.55233	−	2.68871i	0.164546	−	0.285003i	0.936494	+	0.350683i	$0.114051\pi$
$90$	−2.98860			−0.315026
$91$	9.37056	−	1.78677i	0.982302	−	0.187305i
$92$	−2.64285			−0.275536
$93$	−4.99846	+	8.65759i	−0.518316	+	0.897750i
$94$	12.5606			1.29553
$95$	−0.832075	−	1.44120i	−0.0853691	−	0.147864i
$96$	0.357986	+	0.620050i	0.0365368	+	0.0632836i
$97$	−3.59585	+	6.22820i	−0.365104	+	0.632378i	−0.988793	−	0.149294i	$-0.952300\pi$
$97$	−3.59585	+	6.22820i	−0.365104	+	0.632378i	0.623689	+	0.781672i	$0.285633\pi$
$98$	16.8973	−	2.19305i	1.70688	−	0.221531i
$99$	3.49255			0.351015
$100$	−13.7085			−1.37085
$101$	−1.54577			−0.153810			−0.0769050	−	0.997038i	$-0.524504\pi$
$101$	−1.54577			−0.153810			−0.0769050	+	0.997038i	$0.524504\pi$
$102$	11.0195			1.09109
$103$	−2.75895	−	4.77865i	−0.271848	−	0.470854i	0.697487	−	0.716597i	$-0.254301\pi$
$103$	−2.75895	−	4.77865i	−0.271848	−	0.470854i	−0.969335	+	0.245743i	$0.920968\pi$
$104$	13.4757	−	10.1909i	1.32140	−	0.999296i
$105$	−0.209483	−	3.24164i	−0.0204435	−	0.316352i
$106$	12.0556	+	20.8810i	1.17095	+	2.02814i
$107$	−0.724187	+	1.25433i	−0.0700098	+	0.121261i	−0.898905	−	0.438143i	$-0.855636\pi$
$107$	−0.724187	+	1.25433i	−0.0700098	+	0.121261i	0.828896	+	0.559403i	$0.188970\pi$
$108$	1.96253	+	3.39920i	0.188845	+	0.327088i
$109$	−8.20485	+	14.2112i	−0.785882	+	1.36119i	0.142588	+	0.989782i	$0.454458\pi$
$109$	−8.20485	+	14.2112i	−0.785882	+	1.36119i	−0.928471	+	0.371406i	$0.878876\pi$
$110$	−10.4378			−0.995209
$111$	−1.54118	+	2.66940i	−0.146282	+	0.253368i
$112$	7.82747	−	5.21977i	0.739626	−	0.493222i
$113$	5.38049	−	9.31929i	0.506154	−	0.876685i	−0.493820	−	0.869564i	$-0.664400\pi$
$113$	5.38049	−	9.31929i	0.506154	−	0.876685i	0.999975	−	0.00712097i	$-0.00226669\pi$
$114$	−1.64963	+	2.85725i	−0.154502	+	0.267606i
$115$	−0.826699			−0.0770901
$116$	10.3945	−	18.0038i	0.965105	−	1.67161i
$117$	−2.87580	+	2.17480i	−0.265868	+	0.201060i
$118$	−1.95570			−0.180036
$119$	0.772402	+	11.9525i	0.0708060	+	1.09569i
$120$	−2.87662	−	4.98245i	−0.262598	−	0.454834i
$121$	1.19791			0.108901
$122$	5.65908	−	9.80181i	0.512349	−	0.887414i
$123$	−3.61102	−	6.25447i	−0.325595	−	0.563947i
$124$	−39.2385			−3.52372
$125$	−10.4270			−0.932619
$126$	−5.35806	+	3.57304i	−0.477334	+	0.318312i
$127$	8.24568	+	14.2819i	0.731686	+	1.26732i	0.956162	+	0.292838i	$0.0945996\pi$
$127$	8.24568	+	14.2819i	0.731686	+	1.26732i	−0.224476	+	0.974480i	$0.572067\pi$
$128$	−10.0609	+	17.4260i	−0.889267	+	1.54026i
$129$	−4.48886	+	7.77494i	−0.395222	+	0.684545i
$130$	8.59462	−	6.49961i	0.753798	−	0.570053i
$131$	3.52172	+	6.09979i	0.307694	+	0.532942i	0.977857	−	0.209272i	$-0.0671094\pi$
$131$	3.52172	+	6.09979i	0.307694	+	0.532942i	−0.670164	+	0.742213i	$0.733776\pi$
$132$	6.85424	+	11.8719i	0.596585	+	1.03332i
$133$	−3.21480	−	1.58903i	−0.278759	−	0.137787i
$134$	−2.58185	+	4.47189i	−0.223038	+	0.386312i
$135$	0.613891	+	1.06329i	0.0528353	+	0.0915135i
$136$	10.6066	+	18.3712i	0.909509	+	1.57532i
$137$	9.66065	+	16.7327i	0.825365	+	1.42957i	0.901640	+	0.432487i	$0.142364\pi$
$137$	9.66065	+	16.7327i	0.825365	+	1.42957i	−0.0762752	+	0.997087i	$0.524303\pi$
$138$	0.819488	+	1.41940i	0.0697595	+	0.120827i
$139$	7.76176	−	13.4438i	0.658343	−	1.14028i	−0.322701	−	0.946501i	$-0.604591\pi$
$139$	7.76176	−	13.4438i	0.658343	−	1.14028i	0.981044	−	0.193783i	$-0.0620759\pi$
$140$	10.6079	−	7.07390i	0.896530	−	0.597854i
$141$	−2.58008	−	4.46883i	−0.217282	−	0.376344i
$142$	6.15334	+	10.6579i	0.516377	+	0.894392i
$143$	−10.0439	+	7.59560i	−0.839912	+	0.635176i
$144$	−1.77799	+	3.07957i	−0.148166	+	0.256631i
$145$	3.25146	−	5.63169i	0.270019	−	0.467687i
$146$	14.7078	+	25.4746i	1.21722	+	2.10829i
$147$	−4.25114	−	5.56128i	−0.350628	−	0.458687i
$148$	−12.0984			−0.994486
$149$	17.5332			1.43637			0.718187	−	0.695850i	$-0.244972\pi$
$149$	17.5332			1.43637			0.718187	+	0.695850i	$0.244972\pi$
$150$	4.25069	+	7.36241i	0.347067	+	0.601138i
$151$	−7.01950	+	12.1581i	−0.571239	+	0.989415i	0.425200	+	0.905099i	$0.360204\pi$
$151$	−7.01950	+	12.1581i	−0.571239	+	0.989415i	−0.996439	+	0.0843154i	$0.973130\pi$
$152$	−6.35130			−0.515158
$153$	−2.26353	−	3.92054i	−0.182995	−	0.316957i
$154$	−18.7133	+	12.4790i	−1.50796	+	1.00559i
$155$	−12.2740			−0.985875
$156$	−13.0364	−	5.50732i	−1.04375	−	0.440939i
$157$	5.62295	−	9.73923i	0.448760	−	0.777275i	−0.549545	−	0.835464i	$-0.685199\pi$
$157$	5.62295	−	9.73923i	0.448760	−	0.777275i	0.998306	+	0.0581884i	$0.0185324\pi$
$158$	−28.7297			−2.28562
$159$	4.95271	−	8.57835i	0.392776	−	0.680308i
$160$	−0.439529	+	0.761287i	−0.0347478	+	0.0601850i
$161$	−1.48213	+	0.988365i	−0.116809	+	0.0778941i
$162$	1.21707	−	2.10803i	0.0956222	−	0.165623i
$163$	11.6079			0.909205			0.454602	−	0.890695i	$-0.349781\pi$
$163$	11.6079			0.909205			0.454602	+	0.890695i	$0.349781\pi$
$164$	14.1735	−	24.5492i	1.10676	−	1.91697i
$165$	2.14405	+	3.71360i	0.166914	+	0.289103i
$166$	15.4331	−	26.7310i	1.19784	−	2.07472i
$167$	3.44594	+	5.96855i	0.266655	+	0.461860i	0.967996	−	0.250966i	$-0.0807482\pi$
$167$	3.44594	+	5.96855i	0.266655	+	0.461860i	−0.701341	+	0.712826i	$0.747415\pi$
$168$	−11.1141	−	5.49354i	−0.857471	−	0.423836i
$169$	3.54048	−	12.5086i	0.272345	−	0.962200i
$170$	6.76477	+	11.7169i	0.518834	+	0.898648i
$171$	1.35541			0.103651
$172$	−35.2381			−2.68688
$173$	−15.8386			−1.20419			−0.602093	−	0.798426i	$-0.705666\pi$
$173$	−15.8386			−1.20419			−0.602093	+	0.798426i	$0.705666\pi$
$174$	−12.8924			−0.977370
$175$	−7.68783	+	5.12665i	−0.581146	+	0.387539i
$176$	−6.20973	+	10.7556i	−0.468076	+	0.810732i
$177$	0.401721	+	0.695802i	0.0301952	+	0.0522997i
$178$	−3.77859	−	6.54471i	−0.283217	−	0.490547i
$179$	21.1031			1.57732			0.788658	−	0.614832i	$-0.210776\pi$
$179$	21.1031			1.57732			0.788658	+	0.614832i	$0.210776\pi$
$180$	−2.40956	+	4.17348i	−0.179598	+	0.311073i
$181$	15.0685			1.12003			0.560015	−	0.828483i	$-0.310796\pi$
$181$	15.0685			1.12003			0.560015	+	0.828483i	$0.310796\pi$
$182$	7.63808	−	21.9281i	0.566172	−	1.62542i
$183$	−4.64974			−0.343719
$184$	−1.57757	+	2.73242i	−0.116300	+	0.201437i
$185$	−3.78446			−0.278239
$186$	12.1670	+	21.0738i	0.892126	+	1.54521i
$187$	−7.90548	−	13.6927i	−0.578106	−	1.00131i
$188$	10.1270	−	17.5404i	0.738586	−	1.27927i
$189$	2.37183	+	1.17236i	0.172525	+	0.0852768i
$190$	−4.05078			−0.293875
$191$	−9.49806			−0.687255			−0.343628	−	0.939106i	$-0.611656\pi$
$191$	−9.49806			−0.687255			−0.343628	+	0.939106i	$0.611656\pi$
$192$	8.85475			0.639037
$193$	−18.5435			−1.33479			−0.667395	−	0.744704i	$-0.732591\pi$
$193$	−18.5435			−1.33479			−0.667395	+	0.744704i	$0.732591\pi$
$194$	8.75283	+	15.1603i	0.628416	+	1.08845i
$195$	−4.07787	−	1.72272i	−0.292023	−	0.123367i
$196$	10.5609	−	25.3647i	0.754352	−	1.81176i
$197$	−12.8786	−	22.3065i	−0.917565	−	1.58927i	−0.803102	−	0.595842i	$-0.796819\pi$
$197$	−12.8786	−	22.3065i	−0.917565	−	1.58927i	−0.114463	−	0.993427i	$-0.536515\pi$
$198$	4.25069	−	7.36241i	0.302083	−	0.523223i
$199$	−8.84779	−	15.3248i	−0.627203	−	1.08635i	−0.988110	−	0.153746i	$-0.950866\pi$
$199$	−8.84779	−	15.3248i	−0.627203	−	1.08635i	0.360907	−	0.932602i	$-0.382467\pi$
$200$	−8.18284	+	14.1731i	−0.578614	+	1.00219i
$201$	2.12136			0.149629
$202$	−1.88132	+	3.25854i	−0.132369	+	0.229270i
$203$	−0.903681	−	13.9840i	−0.0634259	−	0.981484i
$204$	8.88448	−	15.3884i	0.622038	−	1.07740i
$205$	4.43355	−	7.67913i	0.309652	−	0.536334i
$206$	−13.4314			−0.935809
$207$	0.336664	−	0.583119i	0.0233997	−	0.0405295i
$208$	−1.58430	−	12.7230i	−0.109852	−	0.882183i
$209$	4.73385			0.327447
$210$	−7.08845	−	3.50372i	−0.489149	−	0.241780i
$211$	−6.23896	−	10.8062i	−0.429508	−	0.743929i	0.567322	−	0.823496i	$-0.307980\pi$
$211$	−6.23896	−	10.8062i	−0.429508	−	0.743929i	−0.996830	+	0.0795669i	$0.974646\pi$
$212$	38.8794			2.67025
$213$	2.52793	−	4.37850i	0.173211	−	0.300010i
$214$	1.76278	+	3.05322i	0.120501	+	0.208714i
$215$	−11.0227			−0.751741
$216$	4.68588			0.318834
$217$	−22.0053	+	14.6743i	−1.49382	+	0.996157i
$218$	19.9718	+	34.5922i	1.35266	+	2.34288i
$219$	6.04227	−	10.4655i	0.408299	−	0.707194i
$220$	−8.41551	+	14.5761i	−0.567374	+	0.982720i
$221$	15.0359	+	6.35199i	1.01142	+	0.427281i
$222$	3.75145	+	6.49771i	0.251781	+	0.436098i
$223$	−4.65232	−	8.05805i	−0.311542	−	0.539607i	0.667154	−	0.744920i	$-0.267512\pi$
$223$	−4.65232	−	8.05805i	−0.311542	−	0.539607i	−0.978696	+	0.205313i	$0.934179\pi$
$224$	0.122159	+	1.89034i	0.00816207	+	0.126304i
$225$	1.74628	−	3.02464i	0.116418	−	0.201643i
$226$	−13.0969	−	22.6845i	−0.871193	−	1.50895i
$227$	−4.76651	−	8.25583i	−0.316364	−	0.547959i	0.663362	−	0.748298i	$-0.269129\pi$
$227$	−4.76651	−	8.25583i	−0.316364	−	0.547959i	−0.979727	+	0.200340i	$0.935795\pi$
$228$	2.66004	+	4.60732i	0.176165	+	0.305127i
$229$	3.22423	+	5.58453i	0.213063	+	0.369036i	0.952672	−	0.304001i	$-0.0983226\pi$
$229$	3.22423	+	5.58453i	0.213063	+	0.369036i	−0.739608	+	0.673037i	$0.764989\pi$
$230$	−1.00615	+	1.74271i	−0.0663438	+	0.114911i
$231$	8.28373	+	4.09453i	0.545029	+	0.269400i
$232$	−12.4093	−	21.4936i	−0.814712	−	1.41112i
$233$	12.2379	+	21.1967i	0.801733	+	1.38864i	0.918475	+	0.395479i	$0.129421\pi$
$233$	12.2379	+	21.1967i	0.801733	+	1.38864i	−0.116742	+	0.993162i	$0.537245\pi$
$234$	1.08449	+	8.70917i	0.0708952	+	0.569336i
$235$	3.16778	−	5.48675i	0.206643	−	0.357916i
$236$	−1.57678	+	2.73107i	−0.102640	+	0.177777i
$237$	5.90140	+	10.2215i	0.383337	+	0.663960i
$238$	26.1364	+	12.9188i	1.69417	+	0.837404i
$239$	3.62130			0.234242			0.117121	−	0.993118i	$-0.462633\pi$
$239$	3.62130			0.234242			0.117121	+	0.993118i	$0.462633\pi$
$240$	−4.36598			−0.281823
$241$	−12.5649	−	21.7631i	−0.809377	−	1.40188i	−0.913296	−	0.407297i	$-0.866471\pi$
$241$	−12.5649	−	21.7631i	−0.809377	−	1.40188i	0.103919	−	0.994586i	$-0.466862\pi$
$242$	1.45795	−	2.52524i	0.0937203	−	0.162328i
$243$	−1.00000			−0.0641500
$244$	−9.12527	−	15.8054i	−0.584185	−	1.01184i
$245$	3.30352	−	7.93421i	0.211054	−	0.506898i
$246$	−17.5795			−1.12083
$247$	−3.89790	+	2.94775i	−0.248017	+	0.187561i
$248$	−23.4222	+	40.5684i	−1.48731	+	2.57610i
$249$	−12.6805			−0.803596
$250$	−12.6904	+	21.9804i	−0.802613	+	1.39017i
$251$	0.280269	−	0.485440i	0.0176904	−	0.0306407i	−0.857045	−	0.515242i	$-0.827702\pi$
$251$	0.280269	−	0.485440i	0.0176904	−	0.0306407i	0.874735	+	0.484601i	$0.161035\pi$
$252$	0.669691	+	10.3631i	0.0421866	+	0.652815i
$253$	1.17581	−	2.03657i	0.0739229	−	0.128038i
$254$	40.1424			2.51876
$255$	2.77912	−	4.81357i	0.174035	−	0.301438i
$256$	15.6349	+	27.0805i	0.977184	+	1.69253i
$257$	11.8793	−	20.5756i	0.741013	−	1.28347i	−0.211021	−	0.977482i	$-0.567679\pi$
$257$	11.8793	−	20.5756i	0.741013	−	1.28347i	0.952034	−	0.305991i	$-0.0989879\pi$
$258$	10.9265	+	18.9253i	0.680257	+	1.17824i
$259$	−6.78491	+	4.52454i	−0.421594	+	0.281141i
$260$	−2.14707	−	17.2424i	−0.133156	−	1.06933i
$261$	2.64824	+	4.58688i	0.163922	+	0.283921i
$262$	17.1447			1.05921
$263$	−7.07522			−0.436277			−0.218138	−	0.975918i	$-0.569998\pi$
$263$	−7.07522			−0.436277			−0.218138	+	0.975918i	$0.569998\pi$
$264$	16.3657			1.00724
$265$	12.1617			0.747088
$266$	−7.26238	+	4.84294i	−0.445285	+	0.296940i
$267$	−1.55233	+	2.68871i	−0.0950009	+	0.164546i
$268$	4.16323	+	7.21093i	0.254310	+	0.440478i
$269$	5.19422	+	8.99665i	0.316697	+	0.548536i	0.979797	−	0.199996i	$-0.0640928\pi$
$269$	5.19422	+	8.99665i	0.316697	+	0.548536i	−0.663100	+	0.748531i	$0.730759\pi$
$270$	2.98860			0.181880
$271$	0.0613862	−	0.106324i	0.00372894	−	0.00645872i	−0.864155	−	0.503226i	$-0.832146\pi$
$271$	0.0613862	−	0.106324i	0.00372894	−	0.00645872i	0.867884	+	0.496767i	$0.165480\pi$
$272$	16.0981			0.976093
$273$	−9.37056	+	1.78677i	−0.567132	+	0.108140i
$274$	47.0308			2.84124
$275$	6.09896	−	10.5637i	0.367781	−	0.637015i
$276$	2.64285			0.159081
$277$	2.68599	+	4.65228i	0.161386	+	0.279528i	0.935366	−	0.353682i	$-0.115070\pi$
$277$	2.68599	+	4.65228i	0.161386	+	0.279528i	−0.773980	+	0.633210i	$0.781737\pi$
$278$	−18.8932	−	32.7240i	−1.13314	−	1.96266i
$279$	4.99846	−	8.65759i	0.299250	−	0.518316i
$280$	−0.981613	−	15.1900i	−0.0586626	−	0.907774i
$281$	−14.8847			−0.887945			−0.443972	−	0.896040i	$-0.646431\pi$
$281$	−14.8847			−0.887945			−0.443972	+	0.896040i	$0.646431\pi$
$282$	−12.5606			−0.747972
$283$	4.48537			0.266628			0.133314	−	0.991074i	$-0.457438\pi$
$283$	4.48537			0.266628			0.133314	+	0.991074i	$0.457438\pi$
$284$	19.8446			1.17756
$285$	0.832075	+	1.44120i	0.0492879	+	0.0853691i
$286$	3.78763	+	30.4172i	0.223967	+	1.79861i
$287$	−1.23222	−	19.0680i	−0.0727356	−	1.12555i
$288$	−0.357986	−	0.620050i	−0.0210945	−	0.0365368i
$289$	−1.74710	+	3.02606i	−0.102770	+	0.178004i
$290$	−7.91453	−	13.7084i	−0.464757	−	0.804983i
$291$	3.59585	−	6.22820i	0.210793	−	0.365104i
$292$	47.4326			2.77578
$293$	−11.0016	+	19.0553i	−0.642719	+	1.11322i	0.342105	+	0.939662i	$0.388860\pi$
$293$	−11.0016	+	19.0553i	−0.642719	+	1.11322i	−0.984823	+	0.173560i	$0.944473\pi$
$294$	−16.8973	+	2.19305i	−0.985470	+	0.127901i
$295$	−0.493226	+	0.854293i	−0.0287168	+	0.0497389i
$296$	−7.22178	+	12.5085i	−0.419757	+	0.727041i
$297$	−3.49255			−0.202658
$298$	21.3392	−	36.9605i	1.23614	−	2.14106i
$299$	0.299989	+	2.40911i	0.0173488	+	0.139322i
$300$	13.7085			0.791459
$301$	−19.7619	+	13.1782i	−1.13905	+	0.759582i
$302$	17.0865	+	29.5947i	0.983217	+	1.70298i
$303$	1.54577			0.0888023
$304$	−2.40991	+	4.17409i	−0.138218	+	0.239401i
$305$	−2.85444	−	4.94403i	−0.163445	−	0.283094i
$306$	−11.0195			−0.629943
$307$	32.9959			1.88318			0.941589	−	0.336764i	$-0.109333\pi$
$307$	32.9959			1.88318			0.941589	+	0.336764i	$0.109333\pi$
$308$	2.33893	+	36.1937i	0.133273	+	2.06233i
$309$	2.75895	+	4.77865i	0.156951	+	0.271848i
$310$	−14.9384	+	25.8741i	−0.848444	+	1.46955i
$311$	4.11532	−	7.12794i	0.233358	−	0.404188i	−0.725436	−	0.688290i	$-0.758362\pi$
$311$	4.11532	−	7.12794i	0.233358	−	0.404188i	0.958794	+	0.284101i	$0.0916952\pi$
$312$	−13.4757	+	10.1909i	−0.762909	+	0.576944i
$313$	7.14348	+	12.3729i	0.403773	+	0.699356i	0.994178	−	0.107752i	$-0.0343651\pi$
$313$	7.14348	+	12.3729i	0.403773	+	0.699356i	−0.590405	+	0.807107i	$0.701032\pi$
$314$	−13.6871	−	23.7067i	−0.772406	−	1.33785i
$315$	0.209483	+	3.24164i	0.0118030	+	0.182646i
$316$	−23.1634	+	40.1201i	−1.30304	+	2.25693i
$317$	4.68195	+	8.10938i	0.262965	+	0.455468i	0.967028	−	0.254669i	$-0.0819664\pi$
$317$	4.68195	+	8.10938i	0.262965	+	0.455468i	−0.704064	+	0.710137i	$0.748633\pi$
$318$	−12.0556	−	20.8810i	−0.676046	−	1.17095i
$319$	9.24911	+	16.0199i	0.517851	+	0.896944i
$320$	5.43585	+	9.41518i	0.303874	+	0.526324i
$321$	0.724187	−	1.25433i	0.0404202	−	0.0700098i
$322$	0.279641	+	4.32730i	0.0155838	+	0.241151i
$323$	−3.06801	−	5.31395i	−0.170709	−	0.295676i
$324$	−1.96253	−	3.39920i	−0.109029	−	0.188845i
$325$	1.55604	+	12.4961i	0.0863137	+	0.693157i
$326$	14.1277	−	24.4699i	0.782462	−	1.35526i
$327$	8.20485	−	14.2112i	0.453729	−	0.785882i
$328$	−16.9208	−	29.3077i	−0.934295	−	1.61825i
$329$	−0.880423	−	13.6241i	−0.0485393	−	0.751121i
$330$	10.4378			0.574584
$331$	−24.4779			−1.34543			−0.672714	−	0.739903i	$-0.734871\pi$
$331$	−24.4779			−1.34543			−0.672714	+	0.739903i	$0.734871\pi$
$332$	−24.8859	−	43.1037i	−1.36579	−	2.36562i
$333$	1.54118	−	2.66940i	0.0844561	−	0.146282i
$334$	16.7759			0.917934
$335$	1.30228	+	2.25562i	0.0711513	+	0.123238i
$336$	−7.82747	+	5.21977i	−0.427023	+	0.284762i
$337$	−13.1685			−0.717334			−0.358667	−	0.933466i	$-0.616769\pi$
$337$	−13.1685			−0.717334			−0.358667	+	0.933466i	$0.616769\pi$
$338$	−22.0595	−	22.6873i	−1.19988	−	1.23403i
$339$	−5.38049	+	9.31929i	−0.292228	+	0.506154i
$340$	21.8164			1.18316
$341$	17.4574	−	30.2371i	0.945370	−	1.63743i
$342$	1.64963	−	2.85725i	0.0892020	−	0.154502i
$343$	−3.56314	−	18.1743i	−0.192391	−	0.981318i
$344$	−21.0343	+	36.4324i	−1.13409	+	1.96430i
$345$	0.826699			0.0445080
$346$	−19.2767	+	33.3882i	−1.03632	+	1.79496i
$347$	−7.33666	−	12.7075i	−0.393853	−	0.682173i	0.599101	−	0.800673i	$-0.295525\pi$
$347$	−7.33666	−	12.7075i	−0.393853	−	0.682173i	−0.992954	+	0.118501i	$0.962191\pi$
$348$	−10.3945	+	18.0038i	−0.557204	+	0.965105i
$349$	12.1698	+	21.0787i	0.651433	+	1.12831i	0.982775	+	0.184804i	$0.0591652\pi$
$349$	12.1698	+	21.0787i	0.651433	+	1.12831i	−0.331342	+	0.943511i	$0.607502\pi$
$350$	1.45050	+	22.4457i	0.0775324	+	1.19977i
$351$	2.87580	−	2.17480i	0.153499	−	0.116082i
$352$	−1.25029	−	2.16556i	−0.0666404	−	0.115425i
$353$	−0.669625			−0.0356405			−0.0178203	−	0.999841i	$-0.505673\pi$
$353$	−0.669625			−0.0356405			−0.0178203	+	0.999841i	$0.505673\pi$
$354$	1.95570			0.103944
$355$	6.20749			0.329459
$356$	−12.1860			−0.645855
$357$	−0.772402	−	11.9525i	−0.0408798	−	0.632595i
$358$	25.6840	−	44.4859i	1.35744	−	2.35115i
$359$	17.8146	+	30.8557i	0.940216	+	1.62850i	0.765058	+	0.643962i	$0.222710\pi$
$359$	17.8146	+	30.8557i	0.940216	+	1.62850i	0.175158	+	0.984540i	$0.443956\pi$
$360$	2.87662	+	4.98245i	0.151611	+	0.262598i
$361$	−17.1629			−0.903308
$362$	18.3394	−	31.7648i	0.963897	−	1.66952i
$363$	−1.19791			−0.0628741
$364$	−24.4636	−	28.3458i	−1.28224	−	1.48573i
$365$	14.8372			0.776614
$366$	−5.65908	+	9.80181i	−0.295805	+	0.512349i
$367$	10.2224			0.533602			0.266801	−	0.963752i	$-0.414033\pi$
$367$	10.2224			0.533602			0.266801	+	0.963752i	$0.414033\pi$
$368$	1.19717	+	2.07356i	0.0624069	+	0.108092i
$369$	3.61102	+	6.25447i	0.187982	+	0.325595i
$370$	−4.60597	+	7.97777i	−0.239453	+	0.414745i
$371$	21.8039	−	14.5400i	1.13200	−	0.754879i
$372$	39.2385			2.03442
$373$	4.95108			0.256357			0.128179	−	0.991751i	$-0.459087\pi$
$373$	4.95108			0.256357			0.128179	+	0.991751i	$0.459087\pi$
$374$	−38.4862			−1.99007
$375$	10.4270			0.538448
$376$	−12.0900	−	20.9404i	−0.623492	−	1.07992i
$377$	−17.5914	−	7.43158i	−0.906002	−	0.382746i
$378$	5.35806	−	3.57304i	0.275589	−	0.183777i
$379$	6.33641	+	10.9750i	0.325479	+	0.563747i	0.981609	−	0.190901i	$-0.0611410\pi$
$379$	6.33641	+	10.9750i	0.325479	+	0.563747i	−0.656130	+	0.754648i	$0.727808\pi$
$380$	−3.26595	+	5.65679i	−0.167540	+	0.290187i
$381$	−8.24568	−	14.2819i	−0.422439	−	0.731686i
$382$	−11.5598	+	20.0222i	−0.591452	+	1.02442i
$383$	−23.7902			−1.21562			−0.607810	−	0.794082i	$-0.707952\pi$
$383$	−23.7902			−1.21562			−0.607810	+	0.794082i	$0.707952\pi$
$384$	10.0609	−	17.4260i	0.513418	−	0.889267i
$385$	0.731631	+	11.3216i	0.0372874	+	0.577003i
$386$	−22.5688	+	39.0903i	−1.14872	+	1.98964i
$387$	4.48886	−	7.77494i	0.228182	−	0.395222i
$388$	28.2279			1.43305
$389$	12.7721	−	22.1218i	0.647569	−	1.12162i	−0.336133	−	0.941815i	$-0.609119\pi$
$389$	12.7721	−	22.1218i	0.647569	−	1.12162i	0.983702	−	0.179808i	$-0.0575475\pi$
$390$	−8.59462	+	6.49961i	−0.435206	+	0.329121i
$391$	−3.04819			−0.154153
$392$	−19.9203	−	26.0595i	−1.00613	−	1.31620i
$393$	−3.52172	−	6.09979i	−0.177647	−	0.307694i
$394$	−62.6969			−3.15863
$395$	−7.24564	+	12.5498i	−0.364568	+	0.631450i
$396$	−6.85424	−	11.8719i	−0.344438	−	0.596585i
$397$	−2.12736			−0.106769			−0.0533846	−	0.998574i	$-0.517001\pi$
$397$	−2.12736			−0.106769			−0.0533846	+	0.998574i	$0.517001\pi$
$398$	−43.0736			−2.15908
$399$	3.21480	+	1.58903i	0.160942	+	0.0795511i
$400$	6.20973	+	10.7556i	0.310487	+	0.537779i
$401$	−0.293644	+	0.508607i	−0.0146639	+	0.0253986i	−0.873264	−	0.487247i	$-0.838001\pi$
$401$	−0.293644	+	0.508607i	−0.0146639	+	0.0253986i	0.858600	+	0.512646i	$0.171334\pi$
$402$	2.58185	−	4.47189i	0.128771	−	0.223038i
$403$	4.45394	+	35.7682i	0.221867	+	1.78174i
$404$	3.03362	+	5.25439i	0.150928	+	0.261416i
$405$	−0.613891	−	1.06329i	−0.0305045	−	0.0528353i
$406$	−30.5785	−	15.1145i	−1.51759	−	0.750122i
$407$	5.38265	−	9.32302i	0.266808	−	0.462125i
$408$	−10.6066	−	18.3712i	−0.525105	−	0.909509i
$409$	2.17228	+	3.76249i	0.107412	+	0.186043i	0.914721	−	0.404086i	$-0.132410\pi$
$409$	2.17228	+	3.76249i	0.107412	+	0.186043i	−0.807309	+	0.590129i	$0.799077\pi$
$410$	−10.7919	−	18.6921i	−0.532974	−	0.923138i
$411$	−9.66065	−	16.7327i	−0.476525	−	0.825365i
$412$	−10.8291	+	18.7565i	−0.533510	+	0.924066i
$413$	0.137083	+	2.12129i	0.00674540	+	0.104382i
$414$	−0.819488	−	1.41940i	−0.0402756	−	0.0697595i
$415$	−7.78446	−	13.4831i	−0.382124	−	0.661859i
$416$	2.37798	+	1.00459i	0.116590	+	0.0492543i
$417$	−7.76176	+	13.4438i	−0.380095	+	0.658343i
$418$	5.76143	−	9.97909i	0.281801	−	0.488093i
$419$	−4.72818	−	8.18946i	−0.230987	−	0.400081i	0.727112	−	0.686519i	$-0.240862\pi$
$419$	−4.72818	−	8.18946i	−0.230987	−	0.400081i	−0.958099	+	0.286438i	$0.907529\pi$
$420$	−10.6079	+	7.07390i	−0.517612	+	0.345171i
$421$	−11.9569			−0.582741			−0.291371	−	0.956610i	$-0.594111\pi$
$421$	−11.9569			−0.582741			−0.291371	+	0.956610i	$0.594111\pi$
$422$	−30.3731			−1.47854
$423$	2.58008	+	4.46883i	0.125448	+	0.217282i
$424$	23.2078	−	40.1971i	1.12707	−	1.95214i
$425$	−15.8110			−0.766944
$426$	−6.15334	−	10.6579i	−0.298131	−	0.516377i
$427$	−11.0284	−	5.45118i	−0.533701	−	0.263801i
$428$	5.68496			0.274793
$429$	10.0439	−	7.59560i	0.484923	−	0.366719i
$430$	−13.4154	+	23.2362i	−0.646949	+	1.12055i
$431$	−26.4705			−1.27504			−0.637519	−	0.770435i	$-0.720039\pi$
$431$	−26.4705			−1.27504			−0.637519	+	0.770435i	$0.720039\pi$
$432$	1.77799	−	3.07957i	0.0855437	−	0.148166i
$433$	4.13088	−	7.15489i	0.198517	−	0.343842i	−0.749531	−	0.661970i	$-0.769721\pi$
$433$	4.13088	−	7.15489i	0.198517	−	0.343842i	0.948048	+	0.318128i	$0.103054\pi$
$434$	4.15184	+	64.2476i	0.199295	+	3.08398i
$435$	−3.25146	+	5.63169i	−0.155896	+	0.270019i
$436$	64.4091			3.08464
$437$	0.456318	−	0.790366i	0.0218286	−	0.0378083i
$438$	−14.7078	−	25.4746i	−0.702764	−	1.21722i
$439$	−17.5522	+	30.4012i	−0.837719	+	1.45097i	0.0540784	+	0.998537i	$0.482778\pi$
$439$	−17.5522	+	30.4012i	−0.837719	+	1.45097i	−0.891797	+	0.452435i	$0.850555\pi$
$440$	10.0467	+	17.4015i	0.478960	+	0.829582i
$441$	4.25114	+	5.56128i	0.202435	+	0.264823i
$442$	31.6899	−	23.9652i	1.50734	−	1.13991i
$443$	0.192275	+	0.333030i	0.00913525	+	0.0158227i	0.870557	−	0.492068i	$-0.163759\pi$
$443$	0.192275	+	0.333030i	0.00913525	+	0.0158227i	−0.861422	+	0.507890i	$0.830425\pi$
$444$	12.0984			0.574167
$445$	−3.81184			−0.180699
$446$	−22.6488			−1.07245
$447$	−17.5332			−0.829291
$448$	21.0020	+	10.3810i	0.992249	+	0.490455i
$449$	−18.9728	+	32.8619i	−0.895382	+	1.55085i	−0.0620505	+	0.998073i	$0.519764\pi$
$449$	−18.9728	+	32.8619i	−0.895382	+	1.55085i	−0.833331	+	0.552774i	$0.813569\pi$
$450$	−4.25069	−	7.36241i	−0.200379	−	0.347067i
$451$	12.6117	+	21.8441i	0.593860	+	1.02860i
$452$	−42.2375			−1.98669
$453$	7.01950	−	12.1581i	0.329805	−	0.571239i
$454$	−23.2047			−1.08905
$455$	−7.65236	−	8.86675i	−0.358748	−	0.415679i
$456$	6.35130			0.297427
$457$	7.19474	−	12.4617i	0.336556	−	0.582932i	−0.647227	−	0.762298i	$-0.724071\pi$
$457$	7.19474	−	12.4617i	0.336556	−	0.582932i	0.983782	+	0.179366i	$0.0574046\pi$
$458$	15.6965			0.733449
$459$	2.26353	+	3.92054i	0.105652	+	0.182995i
$460$	1.62242	+	2.81012i	0.0756459	+	0.131022i
$461$	1.79501	−	3.10905i	0.0836019	−	0.144803i	−0.821193	−	0.570651i	$-0.806691\pi$
$461$	1.79501	−	3.10905i	0.0836019	−	0.144803i	0.904795	+	0.425848i	$0.140024\pi$
$462$	18.7133	−	12.4790i	0.870622	−	0.580577i
$463$	4.69484			0.218188			0.109094	−	0.994031i	$-0.465205\pi$
$463$	4.69484			0.218188			0.109094	+	0.994031i	$0.465205\pi$
$464$	−18.8342			−0.874356
$465$	12.2740			0.569195
$466$	59.5777			2.75988
$467$	20.0343	+	34.7003i	0.927075	+	1.60574i	0.788190	+	0.615432i	$0.211018\pi$
$467$	20.0343	+	34.7003i	0.927075	+	1.60574i	0.138885	+	0.990309i	$0.455648\pi$
$468$	13.0364	+	5.50732i	0.602610	+	0.254576i
$469$	5.03150	+	2.48700i	0.232333	+	0.114839i
$470$	−7.71083	−	13.3556i	−0.355674	−	0.616046i
$471$	−5.62295	+	9.73923i	−0.259092	+	0.448760i
$472$	1.88242	+	3.26044i	0.0866453	+	0.150074i
$473$	15.6776	−	27.1544i	0.720856	−	1.24856i
$474$	28.7297			1.31960
$475$	2.36692	−	4.09963i	0.108602	−	0.188104i
$476$	39.1132	−	26.0827i	1.79275	−	1.19550i
$477$	−4.95271	+	8.57835i	−0.226769	+	0.392776i
$478$	4.40738	−	7.63381i	0.201589	−	0.349162i
$479$	20.4700			0.935300			0.467650	−	0.883914i	$-0.345101\pi$
$479$	20.4700			0.935300			0.467650	+	0.883914i	$0.345101\pi$
$480$	0.439529	−	0.761287i	0.0200617	−	0.0347478i
$481$	1.37329	+	11.0284i	0.0626165	+	0.502853i
$482$	−61.1696			−2.78620
$483$	1.48213	−	0.988365i	0.0674394	−	0.0449722i
$484$	−2.35094	−	4.07195i	−0.106861	−	0.185088i
$485$	8.82985			0.400943
$486$	−1.21707	+	2.10803i	−0.0552075	+	0.0956222i
$487$	−16.7968	−	29.0930i	−0.761138	−	1.31833i	−0.942264	−	0.334870i	$-0.891308\pi$
$487$	−16.7968	−	29.0930i	−0.761138	−	1.31833i	0.181127	−	0.983460i	$-0.442026\pi$
$488$	−21.7881			−0.986303
$489$	−11.6079			−0.524930
$490$	−12.7049	−	16.6204i	−0.573951	−	0.750835i
$491$	20.2312	+	35.0415i	0.913021	+	1.58140i	0.809773	+	0.586743i	$0.199590\pi$
$491$	20.2312	+	35.0415i	0.913021	+	1.58140i	0.103248	+	0.994656i	$0.467077\pi$
$492$	−14.1735	+	24.5492i	−0.638990	+	1.10676i
$493$	11.9887	−	20.7651i	0.539944	−	0.935211i
$494$	1.46993	+	11.8045i	0.0661352	+	0.531110i
$495$	−2.14405	−	3.71360i	−0.0963677	−	0.166914i
$496$	17.7745	+	30.7863i	0.798097	+	1.38234i
$497$	11.1290	−	7.42140i	0.499204	−	0.332896i
$498$	−15.4331	+	26.7310i	−0.691575	+	1.19784i
$499$	−2.38204	−	4.12581i	−0.106635	−	0.184697i	0.807770	−	0.589498i	$-0.200674\pi$
$499$	−2.38204	−	4.12581i	−0.106635	−	0.184697i	−0.914405	+	0.404801i	$0.867341\pi$
$500$	20.4633	+	35.4435i	0.915147	+	1.58508i
$501$	−3.44594	−	5.96855i	−0.153953	−	0.266655i
$502$	−0.682215	−	1.18163i	−0.0304487	−	0.0527388i
$503$	−0.350346	+	0.606817i	−0.0156212	+	0.0270567i	−0.873730	−	0.486411i	$-0.838306\pi$
$503$	−0.350346	+	0.606817i	−0.0156212	+	0.0270567i	0.858109	+	0.513467i	$0.171639\pi$
$504$	11.1141	+	5.49354i	0.495061	+	0.244702i
$505$	0.948935	+	1.64360i	0.0422271	+	0.0731394i
$506$	−2.86210	−	4.95731i	−0.127236	−	0.220379i
$507$	−3.54048	+	12.5086i	−0.157238	+	0.555526i
$508$	32.3648	−	56.0575i	1.43596	−	2.48715i
$509$	−13.4457	+	23.2886i	−0.595970	+	1.03225i	0.397439	+	0.917628i	$0.369899\pi$
$509$	−13.4457	+	23.2886i	−0.595970	+	1.03225i	−0.993409	+	0.114622i	$0.963434\pi$
$510$	−6.76477	−	11.7169i	−0.299549	−	0.518834i
$511$	26.6006	−	17.7387i	1.17674	−	0.784713i
$512$	35.8718			1.58533
$513$	−1.35541			−0.0598429
$514$	−28.9161	−	50.0841i	−1.27543	−	2.20911i
$515$	−3.38739	+	5.86714i	−0.149266	+	0.258537i
$516$	35.2381			1.55127
$517$	9.01107	+	15.6076i	0.396306	+	0.686423i
$518$	1.28014	+	19.8095i	0.0562461	+	0.870380i
$519$	15.8386			0.695237
$520$	−19.1084	−	8.07247i	−0.837960	−	0.354001i
$521$	−15.4700	+	26.7948i	−0.677753	+	1.17390i	0.297903	+	0.954596i	$0.403713\pi$
$521$	−15.4700	+	26.7948i	−0.677753	+	1.17390i	−0.975656	+	0.219306i	$0.929621\pi$
$522$	12.8924			0.564285
$523$	0.851131	−	1.47420i	0.0372173	−	0.0644623i	−0.846817	−	0.531885i	$-0.821484\pi$
$523$	0.851131	−	1.47420i	0.0372173	−	0.0644623i	0.884034	+	0.467422i	$0.154817\pi$
$524$	13.8230	−	23.9421i	0.603859	−	1.04591i
$525$	7.68783	−	5.12665i	0.335525	−	0.223746i
$526$	−8.61105	+	14.9148i	−0.375460	+	0.650315i
$527$	−45.2566			−1.97141
$528$	6.20973	−	10.7556i	0.270244	−	0.468076i
$529$	11.2733	+	19.5260i	0.490144	+	0.848955i
$530$	14.8017	−	25.6373i	0.642944	−	1.11361i
$531$	−0.401721	−	0.695802i	−0.0174332	−	0.0301952i
$532$	0.907707	+	14.0463i	0.0393541	+	0.608984i
$533$	−23.9868	−	10.1334i	−1.03898	−	0.438925i
$534$	3.77859	+	6.54471i	0.163516	+	0.283217i
$535$	1.77829			0.0768821
$536$	9.94043			0.429361
$537$	−21.1031			−0.910664
$538$	25.2870			1.09020
$539$	14.8473	+	19.4231i	0.639519	+	0.836610i
$540$	2.40956	−	4.17348i	0.103691	−	0.179598i
$541$	1.00845	+	1.74668i	0.0433566	+	0.0750958i	0.886889	−	0.461982i	$-0.152862\pi$
$541$	1.00845	+	1.74668i	0.0433566	+	0.0750958i	−0.843533	+	0.537078i	$0.819528\pi$
$542$	−0.149423	−	0.258808i	−0.00641826	−	0.0111168i
$543$	−15.0685			−0.646649
$544$	−1.62062	+	2.80700i	−0.0694836	+	0.120349i
$545$	20.1475			0.863026
$546$	−7.63808	+	21.9281i	−0.326880	+	0.938435i
$547$	−2.08074			−0.0889658			−0.0444829	−	0.999010i	$-0.514164\pi$
$547$	−2.08074			−0.0889658			−0.0444829	+	0.999010i	$0.514164\pi$
$548$	37.9186	−	65.6770i	1.61980	−	2.80558i
$549$	4.64974			0.198446
$550$	−14.8457	−	25.7136i	−0.633025	−	1.09643i
$551$	3.58945	+	6.21712i	0.152916	+	0.264858i
$552$	1.57757	−	2.73242i	0.0671456	−	0.116300i
$553$	2.01379	+	31.1623i	0.0856349	+	1.32516i
$554$	13.0762			0.555554
$555$	3.78446			0.160642
$556$	−60.9307			−2.58404
$557$	19.6341			0.831922			0.415961	−	0.909383i	$-0.363445\pi$
$557$	19.6341			0.831922			0.415961	+	0.909383i	$0.363445\pi$
$558$	−12.1670	−	21.0738i	−0.515069	−	0.892126i
$559$	3.99986	+	32.1216i	0.169176	+	1.35860i
$560$	−10.3553	−	5.11850i	−0.437593	−	0.216296i
$561$	7.90548	+	13.6927i	0.333770	+	0.578106i
$562$	−18.1157	+	31.3773i	−0.764166	+	1.32357i
$563$	11.6699	+	20.2128i	0.491826	+	0.851868i	0.999956	−	0.00941281i	$-0.00299623\pi$
$563$	11.6699	+	20.2128i	0.491826	+	0.851868i	−0.508130	+	0.861281i	$0.669663\pi$
$564$	−10.1270	+	17.5404i	−0.426423	+	0.738586i
$565$	−13.2121			−0.555839
$566$	5.45902	−	9.45531i	0.229460	−	0.397436i
$567$	−2.37183	−	1.17236i	−0.0996074	−	0.0492346i
$568$	11.8456	−	20.5171i	0.497029	−	0.860880i
$569$	10.8206	−	18.7419i	0.453625	−	0.785702i	−0.544983	−	0.838447i	$-0.683464\pi$
$569$	10.8206	−	18.7419i	0.453625	−	0.785702i	0.998608	+	0.0527455i	$0.0167972\pi$
$570$	4.05078			0.169669
$571$	−3.91282	+	6.77720i	−0.163746	+	0.283617i	−0.936209	−	0.351443i	$-0.885691\pi$
$571$	−3.91282	+	6.77720i	−0.163746	+	0.283617i	0.772463	+	0.635060i	$0.219025\pi$
$572$	45.5304	+	19.2346i	1.90372	+	0.804239i
$573$	9.49806			0.396787
$574$	−41.6955	−	20.6095i	−1.74034	−	0.860225i
$575$	−1.17581	−	2.03657i	−0.0490349	−	0.0849309i
$576$	−8.85475			−0.368948
$577$	5.92244	−	10.2580i	0.246555	−	0.427045i	−0.716013	−	0.698087i	$-0.754035\pi$
$577$	5.92244	−	10.2580i	0.246555	−	0.427045i	0.962568	+	0.271042i	$0.0873682\pi$
$578$	4.25269	+	7.36587i	0.176889	+	0.306380i
$579$	18.5435			0.770642
$580$	−25.5244			−1.05984
$581$	−30.0760	−	14.8662i	−1.24776	−	0.616752i
$582$	−8.75283	−	15.1603i	−0.362816	−	0.628416i
$583$	−17.2976	+	29.9603i	−0.716394	+	1.24083i
$584$	28.3134	−	49.0402i	1.17161	−	2.02930i
$585$	4.07787	+	1.72272i	0.168599	+	0.0712258i
$586$	26.7794	+	46.3833i	1.10625	+	1.91608i
$587$	−2.24869	−	3.89484i	−0.0928134	−	0.160757i	0.815881	−	0.578220i	$-0.196253\pi$
$587$	−2.24869	−	3.89484i	−0.0928134	−	0.160757i	−0.908694	+	0.417463i	$0.862919\pi$
$588$	−10.5609	+	25.3647i	−0.435526	+	1.04602i
$589$	6.77497	−	11.7346i	0.279158	−	0.483516i
$590$	1.20058	+	2.07947i	0.0494273	+	0.0856106i
$591$	12.8786	+	22.3065i	0.529756	+	0.917565i
$592$	5.48041	+	9.49235i	0.225244	+	0.390133i
$593$	17.8835	+	30.9751i	0.734388	+	1.27200i	0.954992	+	0.296633i	$0.0958638\pi$
$593$	17.8835	+	30.9751i	0.734388	+	1.27200i	−0.220604	+	0.975363i	$0.570803\pi$
$594$	−4.25069	+	7.36241i	−0.174408	+	0.302083i
$595$	12.2348	−	8.15883i	0.501579	−	0.334480i
$596$	−34.4094	−	59.5988i	−1.40946	−	2.44126i
$597$	8.84779	+	15.3248i	0.362116	+	0.627203i
$598$	5.44359	+	2.29968i	0.222605	+	0.0940408i
$599$	−9.70429	+	16.8083i	−0.396507	+	0.686769i	−0.993292	−	0.115631i	$-0.963111\pi$
$599$	−9.70429	+	16.8083i	−0.396507	+	0.686769i	0.596786	+	0.802401i	$0.296444\pi$
$600$	8.18284	−	14.1731i	0.334063	−	0.578614i
$601$	−20.4135	−	35.3571i	−0.832682	−	1.44225i	−0.895904	−	0.444248i	$-0.853471\pi$
$601$	−20.4135	−	35.3571i	−0.832682	−	1.44225i	0.0632213	−	0.998000i	$-0.479863\pi$
$602$	3.72856	+	57.6975i	0.151965	+	2.35157i
$603$	−2.12136			−0.0863884
$604$	55.1039			2.24215
$605$	−0.735387	−	1.27373i	−0.0298977	−	0.0517844i
$606$	1.88132	−	3.25854i	0.0764232	−	0.132369i
$607$	0.942690			0.0382626			0.0191313	−	0.999817i	$-0.493910\pi$
$607$	0.942690			0.0382626			0.0191313	+	0.999817i	$0.493910\pi$
$608$	−0.485219	−	0.840424i	−0.0196782	−	0.0340837i
$609$	0.903681	+	13.9840i	0.0366190	+	0.566660i
$610$	−13.8962			−0.562642
$611$	−17.1386	−	7.24032i	−0.693355	−	0.292912i
$612$	−8.88448	+	15.3884i	−0.359134	+	0.622038i
$613$	0.921093			0.0372026			0.0186013	−	0.999827i	$-0.494079\pi$
$613$	0.921093			0.0372026			0.0186013	+	0.999827i	$0.494079\pi$
$614$	40.1585	−	69.5565i	1.62066	−	2.80707i
$615$	−4.43355	+	7.67913i	−0.178778	+	0.309652i
$616$	38.8166	+	19.1865i	1.56396	+	0.773045i
$617$	12.3732	−	21.4311i	0.498127	−	0.862782i	−0.501870	−	0.864943i	$-0.667355\pi$
$617$	12.3732	−	21.4311i	0.498127	−	0.862782i	0.999998	+	0.00216105i	$0.000687883\pi$
$618$	13.4314			0.540290
$619$	−12.0229	+	20.8243i	−0.483242	+	0.836999i	−0.999815	−	0.0192441i	$-0.993874\pi$
$619$	−12.0229	+	20.8243i	−0.483242	+	0.836999i	0.516573	+	0.856243i	$0.327207\pi$
$620$	24.0882	+	41.7220i	0.967405	+	1.67559i
$621$	−0.336664	+	0.583119i	−0.0135098	+	0.0233997i
$622$	−10.0173	−	17.3504i	−0.401656	−	0.695689i
$623$	−6.83400	+	4.55727i	−0.273798	+	0.182583i
$624$	1.58430	+	12.7230i	0.0634229	+	0.509329i
$625$	−2.33033	−	4.03626i	−0.0932133	−	0.161450i
$626$	34.7765			1.38995
$627$	−4.73385			−0.189052
$628$	−44.1408			−1.76141
$629$	−13.9540			−0.556382
$630$	7.08845	+	3.50372i	0.282410	+	0.139592i
$631$	−14.7428	+	25.5353i	−0.586902	+	1.01654i	0.407734	+	0.913101i	$0.366319\pi$
$631$	−14.7428	+	25.5353i	−0.586902	+	1.01654i	−0.994635	+	0.103443i	$0.967014\pi$
$632$	27.6533	+	47.8969i	1.09999	+	1.90523i
$633$	6.23896	+	10.8062i	0.247976	+	0.429508i
$634$	22.7931			0.905229
$635$	10.1239	−	17.5351i	0.401755	−	0.695860i
$636$	−38.8794			−1.54167
$637$	−24.3201	−	6.74777i	−0.963598	−	0.267356i
$638$	45.0273			1.78265
$639$	−2.52793	+	4.37850i	−0.100003	+	0.173211i
$640$	24.7052			0.976559
$641$	−1.09270	−	1.89260i	−0.0431589	−	0.0747534i	0.843639	−	0.536911i	$-0.180409\pi$
$641$	−1.09270	−	1.89260i	−0.0431589	−	0.0747534i	−0.886798	+	0.462157i	$0.847075\pi$
$642$	−1.76278	−	3.05322i	−0.0695712	−	0.120501i
$643$	5.19137	−	8.99172i	0.204728	−	0.354599i	−0.745318	−	0.666709i	$-0.767702\pi$
$643$	5.19137	−	8.99172i	0.204728	−	0.354599i	0.950046	+	0.312110i	$0.101036\pi$
$644$	6.26839	+	3.09838i	0.247009	+	0.122093i
$645$	11.0227			0.434018
$646$	−14.9360			−0.587648
$647$	−12.1316			−0.476943			−0.238471	−	0.971150i	$-0.576646\pi$
$647$	−12.1316			−0.476943			−0.238471	+	0.971150i	$0.576646\pi$
$648$	−4.68588			−0.184079
$649$	−1.40303	−	2.43012i	−0.0550738	−	0.0953907i
$650$	28.2359	+	11.9284i	1.10750	+	0.467872i
$651$	22.0053	−	14.6743i	0.862456	−	0.575131i
$652$	−22.7810	−	39.4578i	−0.892171	−	1.54529i
$653$	12.0127	−	20.8065i	0.470091	−	0.814222i	−0.529324	−	0.848420i	$-0.677554\pi$
$653$	12.0127	−	20.8065i	0.470091	−	0.814222i	0.999415	+	0.0341978i	$0.0108876\pi$
$654$	−19.9718	−	34.5922i	−0.780959	−	1.35266i
$655$	4.32390	−	7.48922i	0.168949	−	0.292628i
$656$	−25.6815			−1.00269
$657$	−6.04227	+	10.4655i	−0.235731	+	0.408299i
$658$	−29.7916	−	14.7255i	−1.16140	−	0.574062i
$659$	10.4678	−	18.1307i	0.407766	−	0.706272i	−0.586873	−	0.809679i	$-0.699641\pi$
$659$	10.4678	−	18.1307i	0.407766	−	0.706272i	0.994639	+	0.103407i	$0.0329744\pi$
$660$	8.41551	−	14.5761i	0.327573	−	0.567374i
$661$	−21.4780			−0.835398			−0.417699	−	0.908586i	$-0.637163\pi$
$661$	−21.4780			−0.835398			−0.417699	+	0.908586i	$0.637163\pi$
$662$	−29.7914	+	51.6002i	−1.15787	+	2.00550i
$663$	−15.0359	−	6.35199i	−0.583944	−	0.246691i
$664$	−59.4194			−2.30592
$665$	0.283936	+	4.39376i	0.0110106	+	0.170383i
$666$	−3.75145	−	6.49771i	−0.145366	−	0.251781i
$667$	3.56626			0.138086
$668$	13.5255	−	23.4269i	0.523319	−	0.906415i
$669$	4.65232	+	8.05805i	0.179869	+	0.311542i
$670$	6.33989			0.244931
$671$	16.2395			0.626918
$672$	−0.122159	−	1.89034i	−0.00471237	−	0.0729215i
$673$	−0.483978	−	0.838274i	−0.0186560	−	0.0323131i	0.856547	−	0.516070i	$-0.172605\pi$
$673$	−0.483978	−	0.838274i	−0.0186560	−	0.0323131i	−0.875203	+	0.483756i	$0.839272\pi$
$674$	−16.0270	+	27.7596i	−0.617338	+	1.06926i
$675$	−1.74628	+	3.02464i	−0.0672142	+	0.116418i
$676$	−49.4676	+	12.5137i	−1.90260	+	0.481296i
$677$	−23.4146	−	40.5552i	−0.899895	−	1.55866i	−0.827626	−	0.561279i	$-0.810309\pi$
$677$	−23.4146	−	40.5552i	−0.899895	−	1.55866i	−0.0722691	−	0.997385i	$-0.523024\pi$
$678$	13.0969	+	22.6845i	0.502983	+	0.871193i
$679$	15.8304	−	10.5566i	0.607517	−	0.405124i
$680$	13.0226	−	22.5558i	0.499394	−	0.864976i
$681$	4.76651	+	8.25583i	0.182653	+	0.316364i
$682$	−42.4938	−	73.6014i	−1.62717	−	2.81834i
$683$	−8.94014	−	15.4848i	−0.342085	−	0.592509i	0.642735	−	0.766089i	$-0.277800\pi$
$683$	−8.94014	−	15.4848i	−0.342085	−	0.592509i	−0.984820	+	0.173580i	$0.944466\pi$
$684$	−2.66004	−	4.60732i	−0.101709	−	0.176165i
$685$	11.8612	−	20.5442i	0.453192	−	0.784952i
$686$	−42.6485	−	14.6082i	−1.62833	−	0.557744i
$687$	−3.22423	−	5.58453i	−0.123012	−	0.213063i
$688$	15.9623	+	27.6476i	0.608558	+	1.05405i
$689$	−4.41318	−	35.4408i	−0.168129	−	1.35019i
$690$	1.00615	−	1.74271i	0.0383036	−	0.0663438i
$691$	16.6082	−	28.7663i	0.631806	−	1.09432i	−0.355377	−	0.934723i	$-0.615647\pi$
$691$	16.6082	−	28.7663i	0.631806	−	1.09432i	0.987182	−	0.159597i	$-0.0510193\pi$
$692$	31.0837	+	53.8386i	1.18163	+	2.04664i
$693$	−8.28373	−	4.09453i	−0.314673	−	0.155538i
$694$	−35.7170			−1.35580
$695$	−19.0595			−0.722968
$696$	12.4093	+	21.4936i	0.470374	+	0.814712i
$697$	16.3473	−	28.3143i	0.619197	−	1.07248i
$698$	59.2460			2.24249
$699$	−12.2379	−	21.1967i	−0.462881	−	0.801733i
$700$	32.5142	+	16.0713i	1.22892	+	0.607438i
$701$	29.1267			1.10010			0.550050	−	0.835132i	$-0.314609\pi$
$701$	29.1267			1.10010			0.550050	+	0.835132i	$0.314609\pi$
$702$	−1.08449	−	8.70917i	−0.0409314	−	0.328707i
$703$	2.08893	−	3.61814i	0.0787856	−	0.136461i
$704$	−30.9257			−1.16556
$705$	−3.16778	+	5.48675i	−0.119305	+	0.206643i
$706$	−0.814982	+	1.41159i	−0.0306723	+	0.0531259i
$707$	3.66630	+	1.81220i	0.137886	+	0.0681549i
$708$	1.57678	−	2.73107i	0.0592591	−	0.102640i
$709$	11.4015			0.428191			0.214096	−	0.976813i	$-0.431320\pi$
$709$	11.4015			0.428191			0.214096	+	0.976813i	$0.431320\pi$
$710$	7.55497	−	13.0856i	0.283533	−	0.491093i
$711$	−5.90140	−	10.2215i	−0.221320	−	0.383337i
$712$	−7.27402	+	12.5990i	−0.272605	+	0.472166i
$713$	−3.36560	−	5.82939i	−0.126043	−	0.218312i
$714$	−26.1364	−	12.9188i	−0.978129	−	0.483475i
$715$	14.2422	+	6.01670i	0.532628	+	0.225012i
$716$	−41.4154	−	71.7336i	−1.54777	−	2.68081i
$717$	−3.62130			−0.135240
$718$	86.7264			3.23660
$719$	−36.2517			−1.35196			−0.675980	−	0.736920i	$-0.736280\pi$
$719$	−36.2517			−1.35196			−0.675980	+	0.736920i	$0.736280\pi$
$720$	4.36598			0.162710
$721$	0.941461	+	14.5686i	0.0350618	+	0.542564i
$722$	−20.8884	+	36.1798i	−0.777387	+	1.34647i
$723$	12.5649	+	21.7631i	0.467294	+	0.809377i
$724$	−29.5723	−	51.2207i	−1.09905	−	1.90360i
$725$	18.4982			0.687006
$726$	−1.45795	+	2.52524i	−0.0541094	+	0.0937203i
$727$	4.46075			0.165440			0.0827200	−	0.996573i	$-0.473639\pi$
$727$	4.46075			0.165440			0.0827200	+	0.996573i	$0.473639\pi$
$728$	−43.9093	+	8.37261i	−1.62739	+	0.310309i
$729$	1.00000			0.0370370
$730$	18.0579	−	31.2773i	0.668354	−	1.15762i
$731$	−40.6426			−1.50322
$732$	9.12527	+	15.8054i	0.337280	+	0.584185i
$733$	5.24983	+	9.09297i	0.193907	+	0.335856i	0.946542	−	0.322582i	$-0.104551\pi$
$733$	5.24983	+	9.09297i	0.193907	+	0.335856i	−0.752635	+	0.658438i	$0.771217\pi$
$734$	12.4413	−	21.5490i	0.459218	−	0.795390i
$735$	−3.30352	+	7.93421i	−0.121852	+	0.292658i
$736$	−0.482084			−0.0177698
$737$	−7.40895			−0.272912
$738$	17.5795			0.647110
$739$	−4.64923			−0.171025			−0.0855123	−	0.996337i	$-0.527253\pi$
$739$	−4.64923			−0.171025			−0.0855123	+	0.996337i	$0.527253\pi$
$740$	7.42713	+	12.8642i	0.273027	+	0.472896i
$741$	3.89790	−	2.94775i	0.143193	−	0.108288i
$742$	−4.11384	−	63.6596i	−0.151024	−	2.33702i
$743$	9.95236	+	17.2380i	0.365117	+	0.632400i	0.988795	−	0.149281i	$-0.0476958\pi$
$743$	9.95236	+	17.2380i	0.365117	+	0.632400i	−0.623678	+	0.781681i	$0.714362\pi$
$744$	23.4222	−	40.5684i	0.858699	−	1.48731i
$745$	−10.7635	−	18.6429i	−0.394343	−	0.683022i
$746$	6.02582	−	10.4370i	0.220621	−	0.382127i
$747$	12.6805			0.463956
$748$	−31.0295	+	53.7447i	−1.13455	+	1.96510i
$749$	3.18817	−	2.12604i	0.116493	−	0.0776839i
$750$	12.6904	−	21.9804i	0.463389	−	0.802613i
$751$	20.9950	−	36.3645i	0.766120	−	1.32696i	−0.173532	−	0.984828i	$-0.555518\pi$
$751$	20.9950	−	36.3645i	0.766120	−	1.32696i	0.939652	−	0.342131i	$-0.111149\pi$
$752$	−18.3495			−0.669136
$753$	−0.280269	+	0.485440i	−0.0102136	+	0.0176904i
$754$	−37.0760	+	28.0384i	−1.35023	+	1.02110i
$755$	17.2368			0.627313
$756$	−0.669691	−	10.3631i	−0.0243564	−	0.376903i
$757$	21.8795	+	37.8965i	0.795225	+	1.37737i	0.922696	+	0.385528i	$0.125981\pi$
$757$	21.8795	+	37.8965i	0.795225	+	1.37737i	−0.127471	+	0.991842i	$0.540686\pi$
$758$	30.8475			1.12043
$759$	−1.17581	+	2.03657i	−0.0426794	+	0.0739229i
$760$	3.89900	+	6.75327i	0.141432	+	0.244967i
$761$	12.0389			0.436411			0.218206	−	0.975903i	$-0.429980\pi$
$761$	12.0389			0.436411			0.218206	+	0.975903i	$0.429980\pi$
$762$	−40.1424			−1.45420
$763$	36.1212	−	24.0875i	1.30767	−	0.872027i
$764$	18.6402	+	32.2858i	0.674380	+	1.16806i
$765$	−2.77912	+	4.81357i	−0.100479	+	0.174035i
$766$	−28.9544	+	50.1504i	−1.04616	+	1.81201i
$767$	2.66850	+	1.12732i	0.0963540	+	0.0407053i
$768$	−15.6349	−	27.0805i	−0.564178	−	0.977184i
$769$	13.1918	+	22.8489i	0.475708	+	0.823951i	0.999613	−	0.0278261i	$-0.00885848\pi$
$769$	13.1918	+	22.8489i	0.475708	+	0.823951i	−0.523905	+	0.851777i	$0.675525\pi$
$770$	24.7568	+	12.2369i	0.892172	+	0.440988i
$771$	−11.8793	+	20.5756i	−0.427824	+	0.741013i
$772$	36.3922	+	63.0331i	1.30978	+	2.26861i
$773$	4.94438	+	8.56392i	0.177837	+	0.308023i	0.941139	−	0.338018i	$-0.109757\pi$
$773$	4.94438	+	8.56392i	0.177837	+	0.308023i	−0.763302	+	0.646041i	$0.776423\pi$
$774$	−10.9265	−	18.9253i	−0.392747	−	0.680257i
$775$	−17.4574	−	30.2371i	−0.627088	−	1.08615i
$776$	16.8497	−	29.1846i	0.604870	−	1.04767i
$777$	6.78491	−	4.52454i	0.243407	−	0.162317i
$778$	−31.0890	−	53.8478i	−1.11460	−	1.93054i
$779$	4.89442	+	8.47738i	0.175361	+	0.303734i
$780$	2.14707	+	17.2424i	0.0768775	+	0.617378i
$781$	−8.82892	+	15.2921i	−0.315924	+	0.547196i
$782$	−3.70987	+	6.42567i	−0.132665	+	0.229782i
$783$	−2.64824	−	4.58688i	−0.0946403	−	0.163922i
$784$	−24.6849	+	3.20378i	−0.881602	+	0.114421i
$785$	−13.8075			−0.492811
$786$	−17.1447			−0.611533
$787$	19.2333	+	33.3130i	0.685593	+	1.18748i	0.973250	+	0.229748i	$0.0737902\pi$
$787$	19.2333	+	33.3130i	0.685593	+	1.18748i	−0.287657	+	0.957733i	$0.592876\pi$
$788$	−50.5495	+	87.5542i	−1.80075	+	3.11899i
$789$	7.07522			0.251884
$790$	17.6369	+	30.5481i	0.627494	+	1.08685i
$791$	−23.6872	+	15.7959i	−0.842219	+	0.561636i
$792$	−16.3657			−0.581529
$793$	−13.3717	+	10.1123i	−0.474845	+	0.359097i
$794$	−2.58915	+	4.48454i	−0.0918856	+	0.159151i
$795$	−12.1617			−0.431331
$796$	−34.7281	+	60.1509i	−1.23091	+	2.13199i
$797$	4.91617	−	8.51506i	0.174140	−	0.301619i	−0.765723	−	0.643170i	$-0.777619\pi$
$797$	4.91617	−	8.51506i	0.174140	−	0.301619i	0.939863	+	0.341551i	$0.110952\pi$
$798$	7.26238	−	4.84294i	0.257086	−	0.171438i
$799$	11.6802	−	20.2306i	0.413214	−	0.715709i
$800$	−2.50057			−0.0884085
$801$	1.55233	−	2.68871i	0.0548488	−	0.0950009i
$802$	0.714773	+	1.23802i	0.0252395	+	0.0437161i
$803$	−21.1029	+	36.5514i	−0.744707	+	1.28987i
$804$	−4.16323	−	7.21093i	−0.146826	−	0.254310i
$805$	1.96079	+	0.969190i	0.0691087	+	0.0341595i
$806$	80.8212	+	34.1434i	2.84681	+	1.20265i
$807$	−5.19422	−	8.99665i	−0.182845	−	0.316697i
$808$	7.24330			0.254818
$809$	−21.2555			−0.747305			−0.373653	−	0.927569i	$-0.621895\pi$
$809$	−21.2555			−0.747305			−0.373653	+	0.927569i	$0.621895\pi$
$810$	−2.98860			−0.105009
$811$	35.9695			1.26306			0.631531	−	0.775351i	$-0.282427\pi$
$811$	35.9695			1.26306			0.631531	+	0.775351i	$0.282427\pi$
$812$	−45.7609	+	30.5158i	−1.60589	+	1.07090i
$813$	−0.0613862	+	0.106324i	−0.00215291	+	0.00372894i
$814$	−13.1021	−	22.6936i	−0.459230	−	0.795409i
$815$	−7.12602	−	12.3426i	−0.249613	−	0.432343i
$816$	−16.0981			−0.563547
$817$	6.08426	−	10.5382i	0.212861	−	0.368687i
$818$	10.5753			0.369756
$819$	9.37056	−	1.78677i	0.327434	−	0.0624349i
$820$	−34.8039			−1.21540
$821$	−18.4057	+	31.8795i	−0.642362	+	1.11260i	0.342542	+	0.939503i	$0.388712\pi$
$821$	−18.4057	+	31.8795i	−0.642362	+	1.11260i	−0.984904	+	0.173101i	$0.944621\pi$
$822$	−47.0308			−1.64039
$823$	18.8162	+	32.5906i	0.655892	+	1.13604i	0.981669	+	0.190592i	$0.0610407\pi$
$823$	18.8162	+	32.5906i	0.655892	+	1.13604i	−0.325777	+	0.945447i	$0.605626\pi$
$824$	12.9281	+	22.3922i	0.450373	+	0.780068i
$825$	−6.09896	+	10.5637i	−0.212338	+	0.367781i
$826$	4.63858	+	2.29278i	0.161397	+	0.0797761i
$827$	−28.9693			−1.00736			−0.503681	−	0.863890i	$-0.668021\pi$
$827$	−28.9693			−1.00736			−0.503681	+	0.863890i	$0.668021\pi$
$828$	−2.64285			−0.0918454
$829$	8.86111			0.307759			0.153880	−	0.988090i	$-0.450823\pi$
$829$	8.86111			0.307759			0.153880	+	0.988090i	$0.450823\pi$
$830$	−37.8970			−1.31543
$831$	−2.68599	−	4.65228i	−0.0931761	−	0.161386i
$832$	25.4645	−	19.2573i	0.882824	−	0.667628i
$833$	12.1807	−	29.2549i	0.422035	−	1.01362i
$834$	18.8932	+	32.7240i	0.654219	+	1.13314i
$835$	4.23087	−	7.32808i	0.146415	−	0.253599i
$836$	−9.29032	−	16.0913i	−0.321312	−	0.556529i
$837$	−4.99846	+	8.65759i	−0.172772	+	0.299250i
$838$	−23.0182			−0.795150
$839$	15.9655	−	27.6530i	0.551190	−	0.954689i	−0.446999	−	0.894534i	$-0.647507\pi$
$839$	15.9655	−	27.6530i	0.551190	−	0.954689i	0.998189	−	0.0601547i	$-0.0191594\pi$
$840$	0.981613	+	15.1900i	0.0338689	+	0.524103i
$841$	0.473666	−	0.820413i	0.0163333	−	0.0282901i
$842$	−14.5524	+	25.2054i	−0.501507	+	0.868636i
$843$	14.8847			0.512655
$844$	−24.4883	+	42.4150i	−0.842922	+	1.45998i
$845$	−15.4737	+	3.91436i	−0.532313	+	0.134658i
$846$	12.5606			0.431842
$847$	−2.84124	−	1.40439i	−0.0976262	−	0.0482553i
$848$	−17.6118	−	30.5045i	−0.604791	−	1.04753i
$849$	−4.48537			−0.153938
$850$	−19.2431	+	33.3300i	−0.660032	+	1.14321i
$851$	−1.03772	−	1.79738i	−0.0355725	−	0.0616134i
$852$	−19.8446			−0.679863
$853$	5.62395			0.192560			0.0962801	−	0.995354i	$-0.469306\pi$
$853$	5.62395			0.192560			0.0962801	+	0.995354i	$0.469306\pi$
$854$	−24.9136	+	16.6137i	−0.852526	+	0.568510i
$855$	−0.832075	−	1.44120i	−0.0284564	−	0.0492879i
$856$	3.39345	−	5.87763i	0.115986	−	0.200893i
$857$	23.8452	−	41.3011i	0.814537	−	1.41082i	−0.0951229	−	0.995466i	$-0.530324\pi$
$857$	23.8452	−	41.3011i	0.814537	−	1.41082i	0.909660	−	0.415354i	$-0.136342\pi$
$858$	−3.78763	−	30.4172i	−0.129308	−	1.03843i
$859$	−24.8420	−	43.0276i	−0.847598	−	1.46808i	−0.883345	−	0.468723i	$-0.844714\pi$
$859$	−24.8420	−	43.0276i	−0.847598	−	1.46808i	0.0357469	−	0.999361i	$-0.488619\pi$
$860$	21.6324	+	37.4684i	0.737658	+	1.27766i
$861$	1.23222	+	19.0680i	0.0419939	+	0.649834i
$862$	−32.2165	+	55.8006i	−1.09730	+	1.90058i
$863$	11.4553	+	19.8412i	0.389944	+	0.675402i	0.992442	−	0.122718i	$-0.0391611\pi$
$863$	11.4553	+	19.8412i	0.389944	+	0.675402i	−0.602498	+	0.798121i	$0.705828\pi$
$864$	0.357986	+	0.620050i	0.0121789	+	0.0210945i
$865$	9.72317	+	16.8410i	0.330598	+	0.572612i
$866$	−10.0552	−	17.4160i	−0.341688	−	0.591821i
$867$	1.74710	−	3.02606i	0.0593346	−	0.102770i
$868$	93.0671	+	46.0018i	3.15890	+	1.56140i
$869$	−20.6109	−	35.6992i	−0.699179	−	1.21101i
$870$	7.91453	+	13.7084i	0.268328	+	0.464757i
$871$	6.10061	−	4.61353i	0.206711	−	0.156324i
$872$	38.4470	−	66.5921i	1.30198	−	2.25509i
$873$	−3.59585	+	6.22820i	−0.121701	+	0.210793i
$874$	−1.11074	−	1.92387i	−0.0375715	−	0.0650757i
$875$	24.7311	+	12.2242i	0.836062	+	0.413254i
$876$	−47.4326			−1.60260
$877$	−32.3047			−1.09085			−0.545427	−	0.838158i	$-0.683632\pi$
$877$	−32.3047			−1.09085			−0.545427	+	0.838158i	$0.683632\pi$
$878$	42.7245	+	74.0010i	1.44188	+	2.49741i
$879$	11.0016	−	19.0553i	0.371074	−	0.642719i
$880$	15.2484			0.514023
$881$	18.8690	+	32.6821i	0.635714	+	1.10109i	0.986363	+	0.164582i	$0.0526274\pi$
$881$	18.8690	+	32.6821i	0.635714	+	1.10109i	−0.350650	+	0.936507i	$0.614039\pi$
$882$	16.8973	−	2.19305i	0.568962	−	0.0738438i
$883$	−34.3867			−1.15720			−0.578602	−	0.815610i	$-0.696401\pi$
$883$	−34.3867			−1.15720			−0.578602	+	0.815610i	$0.696401\pi$
$884$	−7.91663	−	63.5759i	−0.266265	−	2.13829i
$885$	0.493226	−	0.854293i	0.0165796	−	0.0287168i
$886$	0.936050			0.0314472
$887$	−11.8396	+	20.5069i	−0.397536	+	0.688553i	−0.993421	−	0.114517i	$-0.963468\pi$
$887$	−11.8396	+	20.5069i	−0.397536	+	0.688553i	0.595885	+	0.803070i	$0.296801\pi$
$888$	7.22178	−	12.5085i	0.242347	−	0.419757i
$889$	−2.81374	−	43.5412i	−0.0943699	−	1.46033i
$890$	−4.63929	+	8.03548i	−0.155509	+	0.269350i
$891$	3.49255			0.117005
$892$	−18.2606	+	31.6284i	−0.611412	+	1.05900i
$893$	3.49707	+	6.05711i	0.117025	+	0.202693i
$894$	−21.3392	+	36.9605i	−0.713688	+	1.23614i
$895$	−12.9550	−	22.4387i	−0.433037	−	0.750043i
$896$	44.2923	−	29.5365i	1.47970	−	0.986744i
$897$	−0.299989	−	2.40911i	−0.0100163	−	0.0804379i
$898$	46.1825	+	79.9905i	1.54113	+	2.66932i
$899$	52.9485			1.76593
$900$	−13.7085			−0.456949
$901$	44.8424			1.49392
$902$	61.3973			2.04431
$903$	19.7619	−	13.1782i	0.657633	−	0.438545i
$904$	−25.2123	+	43.6691i	−0.838550	+	1.45241i
$905$	−9.25039	−	16.0221i	−0.307493	−	0.532594i
$906$	−17.0865	−	29.5947i	−0.567660	−	0.983217i
$907$	−9.26733			−0.307717			−0.153858	−	0.988093i	$-0.549170\pi$
$907$	−9.26733			−0.307717			−0.153858	+	0.988093i	$0.549170\pi$
$908$	−18.7088	+	32.4046i	−0.620874	+	1.07539i
$909$	−1.54577			−0.0512700
$910$	−28.0049	+	5.33995i	−0.928352	+	0.177018i
$911$	−10.2739			−0.340390			−0.170195	−	0.985410i	$-0.554440\pi$
$911$	−10.2739			−0.340390			−0.170195	+	0.985410i	$0.554440\pi$
$912$	2.40991	−	4.17409i	0.0798002	−	0.138218i
$913$	44.2874			1.46570
$914$	−17.5130	−	30.3335i	−0.579280	−	1.00334i
$915$	2.85444	+	4.94403i	0.0943648	+	0.163445i
$916$	12.6553	−	21.9196i	0.418143	−	0.724245i
$917$	−1.20175	−	18.5964i	−0.0396851	−	0.614107i
$918$	11.0195			0.363698
$919$	−4.63206			−0.152797			−0.0763987	−	0.997077i	$-0.524342\pi$
$919$	−4.63206			−0.152797			−0.0763987	+	0.997077i	$0.524342\pi$
$920$	3.87381			0.127716
$921$	−32.9959			−1.08725
$922$	−4.36931	−	7.56787i	−0.143896	−	0.249235i
$923$	−2.25254	−	18.0894i	−0.0741434	−	0.595421i
$924$	−2.33893	−	36.1937i	−0.0769451	−	1.19069i
$925$	−5.38265	−	9.32302i	−0.176980	−	0.306539i
$926$	5.71396	−	9.89687i	0.187772	−	0.325231i
$927$	−2.75895	−	4.77865i	−0.0906159	−	0.156951i
$928$	1.89607	−	3.28408i	0.0622414	−	0.107805i
$929$	3.09036			0.101392			0.0506958	−	0.998714i	$-0.483856\pi$
$929$	3.09036			0.101392			0.0506958	+	0.998714i	$0.483856\pi$
$930$	14.9384	−	25.8741i	0.489849	−	0.848444i
$931$	5.76204	+	7.53783i	0.188843	+	0.247042i
$932$	48.0346	−	83.1983i	1.57342	−	2.72525i
$933$	−4.11532	+	7.12794i	−0.134729	+	0.233358i
$934$	97.5326			3.19136
$935$	−9.70621	+	16.8116i	−0.317427	+	0.549800i
$936$	13.4757	−	10.1909i	0.440466	−	0.333099i
$937$	−41.8382			−1.36680			−0.683398	−	0.730046i	$-0.739498\pi$
$937$	−41.8382			−1.36680			−0.683398	+	0.730046i	$0.739498\pi$
$938$	11.3664	−	7.57970i	0.371125	−	0.247486i
$939$	−7.14348	−	12.3729i	−0.233119	−	0.403773i
$940$	−24.8675			−0.811087
$941$	−18.9382	+	32.8019i	−0.617368	+	1.06931i	0.372596	+	0.927994i	$0.378468\pi$
$941$	−18.9382	+	32.8019i	−0.617368	+	1.06931i	−0.989964	+	0.141319i	$0.954866\pi$
$942$	13.6871	+	23.7067i	0.445949	+	0.772406i
$943$	4.86280			0.158354
$944$	2.85703			0.0929885
$945$	−0.209483	−	3.24164i	−0.00681449	−	0.105451i
$946$	−38.1615	−	66.0977i	−1.24074	−	2.14902i
$947$	0.390777	−	0.676846i	0.0126986	−	0.0219946i	−0.859606	−	0.510957i	$-0.829291\pi$
$947$	0.390777	−	0.676846i	0.0126986	−	0.0219946i	0.872305	+	0.488962i	$0.162624\pi$
$948$	23.1634	−	40.1201i	0.752311	−	1.30304i
$949$	−5.38405	−	43.2375i	−0.174773	−	1.40355i
$950$	−5.76143	−	9.97909i	−0.186926	−	0.323765i
$951$	−4.68195	−	8.10938i	−0.151823	−	0.262965i
$952$	−3.61938	−	56.0081i	−0.117305	−	1.81523i
$953$	14.6233	−	25.3283i	0.473695	−	0.820463i	−0.525852	−	0.850576i	$-0.676253\pi$
$953$	14.6233	−	25.3283i	0.473695	−	0.820463i	0.999547	+	0.0301129i	$0.00958667\pi$
$954$	12.0556	+	20.8810i	0.390315	+	0.676046i
$955$	5.83077	+	10.0992i	0.188679	+	0.326802i
$956$	−7.10691	−	12.3095i	−0.229854	−	0.398119i
$957$	−9.24911	−	16.0199i	−0.298981	−	0.517851i
$958$	24.9135	−	43.1515i	0.804919	−	1.39416i
$959$	−3.29658	−	51.0129i	−0.106452	−	1.64729i
$960$	−5.43585	−	9.41518i	−0.175441	−	0.303874i
$961$	−34.4692	−	59.7025i	−1.11191	−	1.92589i
$962$	24.9197	+	10.5275i	0.803442	+	0.339419i
$963$	−0.724187	+	1.25433i	−0.0233366	+	0.0404202i
$964$	−49.3181	+	85.4214i	−1.58843	+	2.75124i
$965$	11.3837	+	19.7171i	0.366454	+	0.634717i
$966$	−0.279641	−	4.32730i	−0.00899730	−	0.139229i
$967$	−30.4010			−0.977631			−0.488816	−	0.872387i	$-0.662571\pi$
$967$	−30.4010			−0.977631			−0.488816	+	0.872387i	$0.662571\pi$
$968$	−5.61327			−0.180417
$969$	3.06801	+	5.31395i	0.0985587	+	0.170709i
$970$	10.7466	−	18.6136i	0.345051	−	0.597647i
$971$	8.91863			0.286212			0.143106	−	0.989707i	$-0.454291\pi$
$971$	8.91863			0.286212			0.143106	+	0.989707i	$0.454291\pi$
$972$	1.96253	+	3.39920i	0.0629482	+	0.109029i
$973$	−34.1705	+	22.7867i	−1.09546	+	0.730508i
$974$	−81.7719			−2.62014
$975$	−1.55604	−	12.4961i	−0.0498332	−	0.400194i
$976$	−8.26721	+	14.3192i	−0.264627	+	0.458348i
$977$	23.6062			0.755229			0.377615	−	0.925963i	$-0.376744\pi$
$977$	23.6062			0.755229			0.377615	+	0.925963i	$0.376744\pi$
$978$	−14.1277	+	24.4699i	−0.451754	+	0.782462i
$979$	5.42158	−	9.39046i	0.173275	−	0.300120i
$980$	−33.4533	+	4.34180i	−1.06863	+	0.138694i
$981$	−8.20485	+	14.2112i	−0.261961	+	0.453729i
$982$	98.4913			3.14298
$983$	−10.1644	+	17.6053i	−0.324195	+	0.561523i	−0.981349	−	0.192234i	$-0.938427\pi$
$983$	−10.1644	+	17.6053i	−0.324195	+	0.561523i	0.657154	+	0.753756i	$0.271760\pi$
$984$	16.9208	+	29.3077i	0.539416	+	0.934295i
$985$	−15.8122	+	27.3875i	−0.503817	+	0.872637i
$986$	−29.1823	−	50.5452i	−0.929353	−	1.60969i
$987$	0.880423	+	13.6241i	0.0280242	+	0.433660i
$988$	17.6698	+	7.46469i	0.562150	+	0.237484i
$989$	−3.02247	−	5.23508i	−0.0961091	−	0.166466i
$990$	−10.4378			−0.331736
$991$	−45.2804			−1.43838			−0.719190	−	0.694813i	$-0.755487\pi$
$991$	−45.2804			−1.43838			−0.719190	+	0.694813i	$0.755487\pi$
$992$	−7.15752			−0.227252
$993$	24.4779			0.776783
$994$	−2.09976	−	32.4927i	−0.0666003	−	1.03060i
$995$	−10.8632	+	18.8155i	−0.344385	+	0.596493i
$996$	24.8859	+	43.1037i	0.788541	+	1.36579i
$997$	9.65104	+	16.7161i	0.305652	+	0.529404i	0.977406	−	0.211370i	$-0.0677924\pi$
$997$	9.65104	+	16.7161i	0.305652	+	0.529404i	−0.671755	+	0.740774i	$0.734459\pi$
$998$	−11.5965			−0.367079
$999$	−1.54118	+	2.66940i	−0.0487607	+	0.0844561i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.j.b.172.8	yes	16
3.2	odd	2		819.2.n.e.172.1		16
7.2	even	3		273.2.l.b.16.1	yes	16
13.9	even	3		273.2.l.b.256.1	yes	16
21.2	odd	6		819.2.s.e.289.8		16
39.35	odd	6		819.2.s.e.802.8		16
91.9	even	3	inner	273.2.j.b.100.8	✓	16
273.191	odd	6		819.2.n.e.100.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.j.b.100.8	✓	16	91.9	even	3	inner
273.2.j.b.172.8	yes	16	1.1	even	1	trivial
273.2.l.b.16.1	yes	16	7.2	even	3
273.2.l.b.256.1	yes	16	13.9	even	3
819.2.n.e.100.1		16	273.191	odd	6
819.2.n.e.172.1		16	3.2	odd	2
819.2.s.e.289.8		16	21.2	odd	6
819.2.s.e.802.8		16	39.35	odd	6

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.j (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.21707 - 2.10803i) q^{2} -1.00000 q^{3} +(-1.96253 - 3.39920i) q^{4} +(-0.613891 - 1.06329i) q^{5} +(-1.21707 + 2.10803i) q^{6} +(-2.37183 - 1.17236i) q^{7} -4.68588 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+(1.21707 - 2.10803i) q^{2} -1.00000 q^{3} +(-1.96253 - 3.39920i) q^{4} +(-0.613891 - 1.06329i) q^{5} +(-1.21707 + 2.10803i) q^{6} +(-2.37183 - 1.17236i) q^{7} -4.68588 q^{8} +1.00000 q^{9} -2.98860 q^{10} +3.49255 q^{11} +(1.96253 + 3.39920i) q^{12} +(-2.87580 + 2.17480i) q^{13} +(-5.35806 + 3.57304i) q^{14} +(0.613891 + 1.06329i) q^{15} +(-1.77799 + 3.07957i) q^{16} +(-2.26353 - 3.92054i) q^{17} +(1.21707 - 2.10803i) q^{18} +1.35541 q^{19} +(-2.40956 + 4.17348i) q^{20} +(2.37183 + 1.17236i) q^{21} +(4.25069 - 7.36241i) q^{22} +(0.336664 - 0.583119i) q^{23} +4.68588 q^{24} +(1.74628 - 3.02464i) q^{25} +(1.08449 + 8.70917i) q^{26} -1.00000 q^{27} +(0.669691 + 10.3631i) q^{28} +(2.64824 + 4.58688i) q^{29} +2.98860 q^{30} +(4.99846 - 8.65759i) q^{31} +(-0.357986 - 0.620050i) q^{32} -3.49255 q^{33} -11.0195 q^{34} +(0.209483 + 3.24164i) q^{35} +(-1.96253 - 3.39920i) q^{36} +(1.54118 - 2.66940i) q^{37} +(1.64963 - 2.85725i) q^{38} +(2.87580 - 2.17480i) q^{39} +(2.87662 + 4.98245i) q^{40} +(3.61102 + 6.25447i) q^{41} +(5.35806 - 3.57304i) q^{42} +(4.48886 - 7.77494i) q^{43} +(-6.85424 - 11.8719i) q^{44} +(-0.613891 - 1.06329i) q^{45} +(-0.819488 - 1.41940i) q^{46} +(2.58008 + 4.46883i) q^{47} +(1.77799 - 3.07957i) q^{48} +(4.25114 + 5.56128i) q^{49} +(-4.25069 - 7.36241i) q^{50} +(2.26353 + 3.92054i) q^{51} +(13.0364 + 5.50732i) q^{52} +(-4.95271 + 8.57835i) q^{53} +(-1.21707 + 2.10803i) q^{54} +(-2.14405 - 3.71360i) q^{55} +(11.1141 + 5.49354i) q^{56} -1.35541 q^{57} +12.8924 q^{58} +(-0.401721 - 0.695802i) q^{59} +(2.40956 - 4.17348i) q^{60} +4.64974 q^{61} +(-12.1670 - 21.0738i) q^{62} +(-2.37183 - 1.17236i) q^{63} -8.85475 q^{64} +(4.07787 + 1.72272i) q^{65} +(-4.25069 + 7.36241i) q^{66} -2.12136 q^{67} +(-8.88448 + 15.3884i) q^{68} +(-0.336664 + 0.583119i) q^{69} +(7.08845 + 3.50372i) q^{70} +(-2.52793 + 4.37850i) q^{71} -4.68588 q^{72} +(-6.04227 + 10.4655i) q^{73} +(-3.75145 - 6.49771i) q^{74} +(-1.74628 + 3.02464i) q^{75} +(-2.66004 - 4.60732i) q^{76} +(-8.28373 - 4.09453i) q^{77} +(-1.08449 - 8.70917i) q^{78} +(-5.90140 - 10.2215i) q^{79} +4.36598 q^{80} +1.00000 q^{81} +17.5795 q^{82} +12.6805 q^{83} +(-0.669691 - 10.3631i) q^{84} +(-2.77912 + 4.81357i) q^{85} +(-10.9265 - 18.9253i) q^{86} +(-2.64824 - 4.58688i) q^{87} -16.3657 q^{88} +(1.55233 - 2.68871i) q^{89} -2.98860 q^{90} +(9.37056 - 1.78677i) q^{91} -2.64285 q^{92} +(-4.99846 + 8.65759i) q^{93} +12.5606 q^{94} +(-0.832075 - 1.44120i) q^{95} +(0.357986 + 0.620050i) q^{96} +(-3.59585 + 6.22820i) q^{97} +(16.8973 - 2.19305i) q^{98} +3.49255 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 16 q^{3} - 6 q^{4} + q^{7} + 12 q^{8} + 16 q^{9}+O(q^{10}) \) 16 * q - 16 * q^3 - 6 * q^4 + q^7 + 12 * q^8 + 16 * q^9	\( 16 q - 16 q^{3} - 6 q^{4} + q^{7} + 12 q^{8} + 16 q^{9} + 8 q^{10} + 4 q^{11} + 6 q^{12} + 5 q^{13} - 7 q^{14} - 6 q^{16} - 2 q^{17} + 22 q^{19} - 20 q^{20} - q^{21} + 7 q^{22} + 4 q^{23} - 12 q^{24} + 2 q^{25} - 6 q^{26} - 16 q^{27} - 7 q^{28} + 15 q^{29} - 8 q^{30} + 3 q^{31} + 3 q^{32} - 4 q^{33} - 68 q^{34} - 12 q^{35} - 6 q^{36} + 4 q^{37} + 2 q^{38} - 5 q^{39} - 25 q^{40} + 19 q^{41} + 7 q^{42} + 11 q^{43} - 16 q^{44} + 2 q^{46} + 5 q^{47} + 6 q^{48} + 13 q^{49} - 7 q^{50} + 2 q^{51} + 36 q^{52} + 36 q^{53} - 15 q^{55} + 39 q^{56} - 22 q^{57} - 40 q^{58} - 17 q^{59} + 20 q^{60} + 44 q^{61} - 6 q^{62} + q^{63} - 20 q^{64} - 21 q^{65} - 7 q^{66} - 52 q^{67} + 5 q^{68} - 4 q^{69} + 46 q^{70} + 9 q^{71} + 12 q^{72} - 6 q^{73} + 15 q^{74} - 2 q^{75} - 16 q^{76} - 36 q^{77} + 6 q^{78} + 16 q^{79} + 56 q^{80} + 16 q^{81} + 2 q^{82} + 36 q^{83} + 7 q^{84} - 4 q^{85} + 16 q^{86} - 15 q^{87} - 48 q^{88} + 20 q^{89} + 8 q^{90} - 7 q^{91} - 94 q^{92} - 3 q^{93} + 40 q^{94} - 3 q^{96} + 7 q^{97} - 3 q^{98} + 4 q^{99}+O(q^{100}) \) 16 * q - 16 * q^3 - 6 * q^4 + q^7 + 12 * q^8 + 16 * q^9 + 8 * q^10 + 4 * q^11 + 6 * q^12 + 5 * q^13 - 7 * q^14 - 6 * q^16 - 2 * q^17 + 22 * q^19 - 20 * q^20 - q^21 + 7 * q^22 + 4 * q^23 - 12 * q^24 + 2 * q^25 - 6 * q^26 - 16 * q^27 - 7 * q^28 + 15 * q^29 - 8 * q^30 + 3 * q^31 + 3 * q^32 - 4 * q^33 - 68 * q^34 - 12 * q^35 - 6 * q^36 + 4 * q^37 + 2 * q^38 - 5 * q^39 - 25 * q^40 + 19 * q^41 + 7 * q^42 + 11 * q^43 - 16 * q^44 + 2 * q^46 + 5 * q^47 + 6 * q^48 + 13 * q^49 - 7 * q^50 + 2 * q^51 + 36 * q^52 + 36 * q^53 - 15 * q^55 + 39 * q^56 - 22 * q^57 - 40 * q^58 - 17 * q^59 + 20 * q^60 + 44 * q^61 - 6 * q^62 + q^63 - 20 * q^64 - 21 * q^65 - 7 * q^66 - 52 * q^67 + 5 * q^68 - 4 * q^69 + 46 * q^70 + 9 * q^71 + 12 * q^72 - 6 * q^73 + 15 * q^74 - 2 * q^75 - 16 * q^76 - 36 * q^77 + 6 * q^78 + 16 * q^79 + 56 * q^80 + 16 * q^81 + 2 * q^82 + 36 * q^83 + 7 * q^84 - 4 * q^85 + 16 * q^86 - 15 * q^87 - 48 * q^88 + 20 * q^89 + 8 * q^90 - 7 * q^91 - 94 * q^92 - 3 * q^93 + 40 * q^94 - 3 * q^96 + 7 * q^97 - 3 * q^98 + 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more