LMFDB - Embedded newform 273.2.k.a.22.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(22,273)]

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, 4]))

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

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

chi := DirichletCharacter("273.22");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.k (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:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			22.2
Root			$0.939693 - 0.342020i$ of defining polynomial
Character	$\chi$	$=$	273.22
Dual form			273.2.k.a.211.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.173648 + 0.300767i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.939693 + 1.62760i) q^{4} +3.53209 q^{5} +(-0.173648 - 0.300767i) q^{6} +(0.500000 + 0.866025i) q^{7} -1.34730 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.173648 + 0.300767i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.939693 + 1.62760i) q^{4} +3.53209 q^{5} +(-0.173648 - 0.300767i) q^{6} +(0.500000 + 0.866025i) q^{7} -1.34730 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-0.613341 + 1.06234i) q^{10} +(1.64543 - 2.84997i) q^{11} -1.87939 q^{12} +(-2.99273 - 2.01087i) q^{13} -0.347296 q^{14} +(-1.76604 + 3.05888i) q^{15} +(-1.64543 + 2.84997i) q^{16} +(2.58512 + 4.47756i) q^{17} +0.347296 q^{18} +(-3.03209 - 5.25173i) q^{19} +(3.31908 + 5.74881i) q^{20} -1.00000 q^{21} +(0.571452 + 0.989783i) q^{22} +(-0.745100 + 1.29055i) q^{23} +(0.673648 - 1.16679i) q^{24} +7.47565 q^{25} +(1.12449 - 0.550931i) q^{26} +1.00000 q^{27} +(-0.939693 + 1.62760i) q^{28} +(-2.36824 + 4.10191i) q^{29} +(-0.613341 - 1.06234i) q^{30} -1.59627 q^{31} +(-1.91875 - 3.32337i) q^{32} +(1.64543 + 2.84997i) q^{33} -1.79561 q^{34} +(1.76604 + 3.05888i) q^{35} +(0.939693 - 1.62760i) q^{36} +(-3.95084 + 6.84305i) q^{37} +2.10607 q^{38} +(3.23783 - 1.58634i) q^{39} -4.75877 q^{40} +(5.82295 - 10.0856i) q^{41} +(0.173648 - 0.300767i) q^{42} +(-6.19846 - 10.7361i) q^{43} +6.18479 q^{44} +(-1.76604 - 3.05888i) q^{45} +(-0.258770 - 0.448204i) q^{46} +0.162504 q^{47} +(-1.64543 - 2.84997i) q^{48} +(-0.500000 + 0.866025i) q^{49} +(-1.29813 + 2.24843i) q^{50} -5.17024 q^{51} +(0.460637 - 6.76055i) q^{52} +6.84255 q^{53} +(-0.173648 + 0.300767i) q^{54} +(5.81180 - 10.0663i) q^{55} +(-0.673648 - 1.16679i) q^{56} +6.06418 q^{57} +(-0.822481 - 1.42458i) q^{58} +(-5.80928 - 10.0620i) q^{59} -6.63816 q^{60} +(-0.911474 - 1.57872i) q^{61} +(0.277189 - 0.480105i) q^{62} +(0.500000 - 0.866025i) q^{63} -5.24897 q^{64} +(-10.5706 - 7.10257i) q^{65} -1.14290 q^{66} +(-4.59492 + 7.95864i) q^{67} +(-4.85844 + 8.41507i) q^{68} +(-0.745100 - 1.29055i) q^{69} -1.22668 q^{70} +(2.24510 + 3.88863i) q^{71} +(0.673648 + 1.16679i) q^{72} +14.9436 q^{73} +(-1.37211 - 2.37657i) q^{74} +(-3.73783 + 6.47410i) q^{75} +(5.69846 - 9.87003i) q^{76} +3.29086 q^{77} +(-0.0851223 + 1.24930i) q^{78} -9.22668 q^{79} +(-5.81180 + 10.0663i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(2.02229 + 3.50271i) q^{82} +10.9213 q^{83} +(-0.939693 - 1.62760i) q^{84} +(9.13088 + 15.8152i) q^{85} +4.30541 q^{86} +(-2.36824 - 4.10191i) q^{87} +(-2.21688 + 3.83975i) q^{88} +(-0.0320889 + 0.0555796i) q^{89} +1.22668 q^{90} +(0.245100 - 3.59721i) q^{91} -2.80066 q^{92} +(0.798133 - 1.38241i) q^{93} +(-0.0282185 + 0.0488759i) q^{94} +(-10.7096 - 18.5496i) q^{95} +3.83750 q^{96} +(-0.224155 - 0.388249i) q^{97} +(-0.173648 - 0.300767i) q^{98} -3.29086 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{3} + 12 q^{5} + 3 q^{7} - 6 q^{8} - 3 q^{9}+O(q^{10}) $ 6 * q - 3 * q^3 + 12 * q^5 + 3 * q^7 - 6 * q^8 - 3 * q^9	$ 6 q - 3 q^{3} + 12 q^{5} + 3 q^{7} - 6 q^{8} - 3 q^{9} + 3 q^{10} - 6 q^{11} - 6 q^{15} + 6 q^{16} - 6 q^{17} - 9 q^{19} + 3 q^{20} - 6 q^{21} + 3 q^{22} - 3 q^{23} + 3 q^{24} + 6 q^{25} - 6 q^{26} + 6 q^{27} - 9 q^{29} + 3 q^{30} + 18 q^{31} - 9 q^{32} - 6 q^{33} - 12 q^{34} + 6 q^{35} - 12 q^{37} - 12 q^{38} - 6 q^{40} - 6 q^{41} - 9 q^{43} + 30 q^{44} - 6 q^{45} + 21 q^{46} + 6 q^{47} + 6 q^{48} - 3 q^{49} + 6 q^{50} + 12 q^{51} - 6 q^{52} + 6 q^{53} - 3 q^{56} + 18 q^{57} - 30 q^{58} - 15 q^{59} - 6 q^{60} + 15 q^{61} - 9 q^{62} + 3 q^{63} - 6 q^{64} - 6 q^{65} - 6 q^{66} - 9 q^{67} - 21 q^{68} - 3 q^{69} + 6 q^{70} + 12 q^{71} + 3 q^{72} + 60 q^{73} + 21 q^{74} - 3 q^{75} + 6 q^{76} - 12 q^{77} + 21 q^{78} - 42 q^{79} - 3 q^{81} + 48 q^{83} + 3 q^{85} + 30 q^{86} - 9 q^{87} + 3 q^{88} + 9 q^{89} - 6 q^{90} + 12 q^{92} - 9 q^{93} - 15 q^{94} - 30 q^{95} + 18 q^{96} - 3 q^{97} + 12 q^{99}+O(q^{100}) $ 6 * q - 3 * q^3 + 12 * q^5 + 3 * q^7 - 6 * q^8 - 3 * q^9 + 3 * q^10 - 6 * q^11 - 6 * q^15 + 6 * q^16 - 6 * q^17 - 9 * q^19 + 3 * q^20 - 6 * q^21 + 3 * q^22 - 3 * q^23 + 3 * q^24 + 6 * q^25 - 6 * q^26 + 6 * q^27 - 9 * q^29 + 3 * q^30 + 18 * q^31 - 9 * q^32 - 6 * q^33 - 12 * q^34 + 6 * q^35 - 12 * q^37 - 12 * q^38 - 6 * q^40 - 6 * q^41 - 9 * q^43 + 30 * q^44 - 6 * q^45 + 21 * q^46 + 6 * q^47 + 6 * q^48 - 3 * q^49 + 6 * q^50 + 12 * q^51 - 6 * q^52 + 6 * q^53 - 3 * q^56 + 18 * q^57 - 30 * q^58 - 15 * q^59 - 6 * q^60 + 15 * q^61 - 9 * q^62 + 3 * q^63 - 6 * q^64 - 6 * q^65 - 6 * q^66 - 9 * q^67 - 21 * q^68 - 3 * q^69 + 6 * q^70 + 12 * q^71 + 3 * q^72 + 60 * q^73 + 21 * q^74 - 3 * q^75 + 6 * q^76 - 12 * q^77 + 21 * q^78 - 42 * q^79 - 3 * q^81 + 48 * q^83 + 3 * q^85 + 30 * q^86 - 9 * q^87 + 3 * q^88 + 9 * q^89 - 6 * q^90 + 12 * q^92 - 9 * q^93 - 15 * q^94 - 30 * q^95 + 18 * q^96 - 3 * q^97 + 12 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−0.173648	+	0.300767i	−0.122788	+	0.212675i	−0.920866	−	0.389879i	$-0.872517\pi$
$2$	−0.173648	+	0.300767i	−0.122788	+	0.212675i	0.798078	+	0.602554i	$0.205850\pi$
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$4$	0.939693	+	1.62760i	0.469846	+	0.813798i
$5$	3.53209			1.57960			0.789799	−	0.613366i	$-0.210185\pi$
$5$	3.53209			1.57960			0.789799	+	0.613366i	$0.210185\pi$
$6$	−0.173648	−	0.300767i	−0.0708916	−	0.122788i
$7$	0.500000	+	0.866025i	0.188982	+	0.327327i
$7$	0.500000	+	0.866025i	0.188982	+	0.327327i
$8$	−1.34730			−0.476341
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	−0.613341	+	1.06234i	−0.193955	+	0.335941i
$11$	1.64543	−	2.84997i	0.496116	−	0.859298i	−0.503874	−	0.863777i	$-0.668093\pi$
$11$	1.64543	−	2.84997i	0.496116	−	0.859298i	0.999990	+	0.00447939i	$0.00142584\pi$
$12$	−1.87939			−0.542532
$13$	−2.99273	−	2.01087i	−0.830033	−	0.557714i
$13$	−2.99273	−	2.01087i	−0.830033	−	0.557714i
$14$	−0.347296			−0.0928189
$15$	−1.76604	+	3.05888i	−0.455991	+	0.789799i
$16$	−1.64543	+	2.84997i	−0.411357	+	0.712492i
$17$	2.58512	+	4.47756i	0.626984	+	1.08597i	0.988154	+	0.153468i	$0.0490443\pi$
$17$	2.58512	+	4.47756i	0.626984	+	1.08597i	−0.361169	+	0.932500i	$0.617622\pi$
$18$	0.347296			0.0818585
$19$	−3.03209	−	5.25173i	−0.695609	−	1.20483i	−0.969975	−	0.243205i	$-0.921801\pi$
$19$	−3.03209	−	5.25173i	−0.695609	−	1.20483i	0.274366	−	0.961625i	$-0.411532\pi$
$20$	3.31908	+	5.74881i	0.742168	+	1.28547i
$21$	−1.00000			−0.218218
$22$	0.571452	+	0.989783i	0.121834	+	0.211023i
$23$	−0.745100	+	1.29055i	−0.155364	+	0.269098i	−0.933192	−	0.359379i	$-0.882988\pi$
$23$	−0.745100	+	1.29055i	−0.155364	+	0.269098i	0.777827	+	0.628478i	$0.216322\pi$
$24$	0.673648	−	1.16679i	0.137508	−	0.238171i
$25$	7.47565			1.49513
$26$	1.12449	−	0.550931i	0.220530	−	0.108046i
$27$	1.00000			0.192450
$28$	−0.939693	+	1.62760i	−0.177585	+	0.307587i
$29$	−2.36824	+	4.10191i	−0.439771	+	0.761706i	−0.997672	−	0.0682018i	$-0.978274\pi$
$29$	−2.36824	+	4.10191i	−0.439771	+	0.761706i	0.557900	+	0.829908i	$0.311607\pi$
$30$	−0.613341	−	1.06234i	−0.111980	−	0.193955i
$31$	−1.59627			−0.286698			−0.143349	−	0.989672i	$-0.545787\pi$
$31$	−1.59627			−0.286698			−0.143349	+	0.989672i	$0.545787\pi$
$32$	−1.91875	−	3.32337i	−0.339190	−	0.587494i
$33$	1.64543	+	2.84997i	0.286433	+	0.496116i
$34$	−1.79561			−0.307944
$35$	1.76604	+	3.05888i	0.298516	+	0.517045i
$36$	0.939693	−	1.62760i	0.156615	−	0.271266i
$37$	−3.95084	+	6.84305i	−0.649514	+	1.12499i	0.333726	+	0.942670i	$0.391694\pi$
$37$	−3.95084	+	6.84305i	−0.649514	+	1.12499i	−0.983239	+	0.182320i	$0.941639\pi$
$38$	2.10607			0.341649
$39$	3.23783	−	1.58634i	0.518467	−	0.254018i
$40$	−4.75877			−0.752428
$41$	5.82295	−	10.0856i	0.909392	−	1.57511i	0.0944806	−	0.995527i	$-0.469881\pi$
$41$	5.82295	−	10.0856i	0.909392	−	1.57511i	0.814911	−	0.579586i	$-0.196786\pi$
$42$	0.173648	−	0.300767i	0.0267945	−	0.0464094i
$43$	−6.19846	−	10.7361i	−0.945257	−	1.63723i	−0.755236	−	0.655453i	$-0.772478\pi$
$43$	−6.19846	−	10.7361i	−0.945257	−	1.63723i	−0.190020	−	0.981780i	$-0.560855\pi$
$44$	6.18479			0.932393
$45$	−1.76604	−	3.05888i	−0.263266	−	0.455991i
$46$	−0.258770	−	0.448204i	−0.0381536	−	0.0660840i
$47$	0.162504			0.0237036			0.0118518	−	0.999930i	$-0.496227\pi$
$47$	0.162504			0.0237036			0.0118518	+	0.999930i	$0.496227\pi$
$48$	−1.64543	−	2.84997i	−0.237497	−	0.411357i
$49$	−0.500000	+	0.866025i	−0.0714286	+	0.123718i
$50$	−1.29813	+	2.24843i	−0.183584	+	0.317976i
$51$	−5.17024			−0.723979
$52$	0.460637	−	6.76055i	0.0638789	−	0.937519i
$53$	6.84255			0.939896			0.469948	−	0.882694i	$-0.344273\pi$
$53$	6.84255			0.939896			0.469948	+	0.882694i	$0.344273\pi$
$54$	−0.173648	+	0.300767i	−0.0236305	+	0.0409293i
$55$	5.81180	−	10.0663i	0.783663	−	1.35734i
$56$	−0.673648	−	1.16679i	−0.0900200	−	0.155919i
$57$	6.06418			0.803220
$58$	−0.822481	−	1.42458i	−0.107997	−	0.187056i
$59$	−5.80928	−	10.0620i	−0.756304	−	1.30996i	−0.944724	−	0.327868i	$-0.893670\pi$
$59$	−5.80928	−	10.0620i	−0.756304	−	1.30996i	0.188420	−	0.982089i	$-0.439663\pi$
$60$	−6.63816			−0.856982
$61$	−0.911474	−	1.57872i	−0.116702	−	0.202134i	0.801757	−	0.597651i	$-0.203899\pi$
$61$	−0.911474	−	1.57872i	−0.116702	−	0.202134i	−0.918459	+	0.395516i	$0.870566\pi$
$62$	0.277189	−	0.480105i	0.0352030	−	0.0609734i
$63$	0.500000	−	0.866025i	0.0629941	−	0.109109i
$64$	−5.24897			−0.656121
$65$	−10.5706	−	7.10257i	−1.31112	−	0.880965i
$66$	−1.14290			−0.140682
$67$	−4.59492	+	7.95864i	−0.561359	+	0.972303i	0.436019	+	0.899937i	$0.356388\pi$
$67$	−4.59492	+	7.95864i	−0.561359	+	0.972303i	−0.997378	+	0.0723651i	$0.976945\pi$
$68$	−4.85844	+	8.41507i	−0.589172	+	1.02048i
$69$	−0.745100	−	1.29055i	−0.0896995	−	0.155364i
$70$	−1.22668			−0.146616
$71$	2.24510	+	3.88863i	0.266444	+	0.461495i	0.967941	−	0.251178i	$-0.0808178\pi$
$71$	2.24510	+	3.88863i	0.266444	+	0.461495i	−0.701497	+	0.712673i	$0.747484\pi$
$72$	0.673648	+	1.16679i	0.0793902	+	0.137508i
$73$	14.9436			1.74901			0.874506	−	0.485015i	$-0.161186\pi$
$73$	14.9436			1.74901			0.874506	+	0.485015i	$0.161186\pi$
$74$	−1.37211	−	2.37657i	−0.159505	−	0.276270i
$75$	−3.73783	+	6.47410i	−0.431607	+	0.747565i
$76$	5.69846	−	9.87003i	0.653659	−	1.13217i
$77$	3.29086			0.375028
$78$	−0.0851223	+	1.24930i	−0.00963820	+	0.141455i
$79$	−9.22668			−1.03808			−0.519041	−	0.854749i	$-0.673711\pi$
$79$	−9.22668			−1.03808			−0.519041	+	0.854749i	$0.673711\pi$
$80$	−5.81180	+	10.0663i	−0.649779	+	1.12545i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	2.02229	+	3.50271i	0.223324	+	0.386809i
$83$	10.9213			1.19877			0.599383	−	0.800463i	$-0.295413\pi$
$83$	10.9213			1.19877			0.599383	+	0.800463i	$0.295413\pi$
$84$	−0.939693	−	1.62760i	−0.102529	−	0.177585i
$85$	9.13088	+	15.8152i	0.990383	+	1.71539i
$86$	4.30541			0.464264
$87$	−2.36824	−	4.10191i	−0.253902	−	0.439771i
$88$	−2.21688	+	3.83975i	−0.236320	+	0.409319i
$89$	−0.0320889	+	0.0555796i	−0.00340142	+	0.00589142i	−0.867721	−	0.497051i	$-0.834416\pi$
$89$	−0.0320889	+	0.0555796i	−0.00340142	+	0.00589142i	0.864320	+	0.502943i	$0.167749\pi$
$90$	1.22668			0.129304
$91$	0.245100	−	3.59721i	0.0256935	−	0.377090i
$92$	−2.80066			−0.291989
$93$	0.798133	−	1.38241i	0.0827626	−	0.143349i
$94$	−0.0282185	+	0.0488759i	−0.00291052	+	0.00504116i
$95$	−10.7096	−	18.5496i	−1.09878	−	1.90315i
$96$	3.83750			0.391663
$97$	−0.224155	−	0.388249i	−0.0227595	−	0.0394207i	0.854421	−	0.519581i	$-0.173912\pi$
$97$	−0.224155	−	0.388249i	−0.0227595	−	0.0394207i	−0.877181	+	0.480160i	$0.840579\pi$
$98$	−0.173648	−	0.300767i	−0.0175411	−	0.0303821i
$99$	−3.29086			−0.330744
$100$	7.02481	+	12.1673i	0.702481	+	1.21673i
$101$	6.31908	−	10.9450i	0.628772	−	1.08906i	−0.359027	−	0.933327i	$-0.616891\pi$
$101$	6.31908	−	10.9450i	0.628772	−	1.08906i	0.987799	−	0.155737i	$-0.0497753\pi$
$102$	0.897804	−	1.55504i	0.0888958	−	0.153972i
$103$	4.06418			0.400455			0.200228	−	0.979749i	$-0.435832\pi$
$103$	4.06418			0.400455			0.200228	+	0.979749i	$0.435832\pi$
$104$	4.03209	+	2.70924i	0.395379	+	0.265662i
$105$	−3.53209			−0.344697
$106$	−1.18820	+	2.05802i	−0.115408	+	0.199892i
$107$	−6.00387	+	10.3990i	−0.580416	+	1.00531i	0.415014	+	0.909815i	$0.363777\pi$
$107$	−6.00387	+	10.3990i	−0.580416	+	1.00531i	−0.995430	+	0.0954950i	$0.969557\pi$
$108$	0.939693	+	1.62760i	0.0904220	+	0.156615i
$109$	2.78106			0.266377			0.133189	−	0.991091i	$-0.457478\pi$
$109$	2.78106			0.266377			0.133189	+	0.991091i	$0.457478\pi$
$110$	2.01842	+	3.49600i	0.192449	+	0.333331i
$111$	−3.95084	−	6.84305i	−0.374997	−	0.649514i
$112$	−3.29086			−0.310957
$113$	0.145430	+	0.251892i	0.0136809	+	0.0236960i	0.872785	−	0.488105i	$-0.162312\pi$
$113$	0.145430	+	0.251892i	0.0136809	+	0.0236960i	−0.859104	+	0.511801i	$0.828978\pi$
$114$	−1.05303	+	1.82391i	−0.0986256	+	0.170825i
$115$	−2.63176	+	4.55834i	−0.245413	+	0.425067i
$116$	−8.90167			−0.826500
$117$	−0.245100	+	3.59721i	−0.0226595	+	0.332562i
$118$	4.03508			0.371459
$119$	−2.58512	+	4.47756i	−0.236978	+	0.410458i
$120$	2.37939	−	4.12122i	0.217207	−	0.376214i
$121$	0.0851223	+	0.147436i	0.00773839	+	0.0134033i
$122$	0.633103			0.0573185
$123$	5.82295	+	10.0856i	0.525038	+	0.909392i
$124$	−1.50000	−	2.59808i	−0.134704	−	0.233314i
$125$	8.74422			0.782107
$126$	0.173648	+	0.300767i	0.0154698	+	0.0267945i
$127$	3.23396	−	5.60138i	0.286967	−	0.497042i	−0.686117	−	0.727491i	$-0.740686\pi$
$127$	3.23396	−	5.60138i	0.286967	−	0.497042i	0.973084	+	0.230449i	$0.0740196\pi$
$128$	4.74897	−	8.22546i	0.419754	−	0.727035i
$129$	12.3969			1.09149
$130$	3.97178	−	1.94594i	0.348348	−	0.170670i
$131$	−6.27126			−0.547922			−0.273961	−	0.961741i	$-0.588334\pi$
$131$	−6.27126			−0.547922			−0.273961	+	0.961741i	$0.588334\pi$
$132$	−3.09240	+	5.35619i	−0.269159	+	0.466196i
$133$	3.03209	−	5.25173i	0.262915	−	0.455383i
$134$	−1.59580	−	2.76401i	−0.137856	−	0.238774i
$135$	3.53209			0.303994
$136$	−3.48293	−	6.03260i	−0.298658	−	0.517292i
$137$	0.926022	+	1.60392i	0.0791154	+	0.137032i	0.902869	−	0.429917i	$-0.141457\pi$
$137$	0.926022	+	1.60392i	0.0791154	+	0.137032i	−0.823753	+	0.566949i	$0.808124\pi$
$138$	0.517541			0.0440560
$139$	7.80200	+	13.5135i	0.661757	+	1.14620i	0.980154	+	0.198240i	$0.0635224\pi$
$139$	7.80200	+	13.5135i	0.661757	+	1.14620i	−0.318396	+	0.947958i	$0.603144\pi$
$140$	−3.31908	+	5.74881i	−0.280513	+	0.485863i
$141$	−0.0812519	+	0.140732i	−0.00684265	+	0.0118518i
$142$	−1.55943			−0.130864
$143$	−10.6552	+	5.22043i	−0.891035	+	0.436554i
$144$	3.29086			0.274238
$145$	−8.36484	+	14.4883i	−0.694662	+	1.20319i
$146$	−2.59492	+	4.49454i	−0.214757	+	0.371971i
$147$	−0.500000	−	0.866025i	−0.0412393	−	0.0714286i
$148$	−14.8503			−1.22069
$149$	0.539363	+	0.934204i	0.0441863	+	0.0765330i	0.887273	−	0.461245i	$-0.152597\pi$
$149$	0.539363	+	0.934204i	0.0441863	+	0.0765330i	−0.843086	+	0.537778i	$0.819264\pi$
$150$	−1.29813	−	2.24843i	−0.105992	−	0.183584i
$151$	5.01960			0.408489			0.204245	−	0.978920i	$-0.434526\pi$
$151$	5.01960			0.408489			0.204245	+	0.978920i	$0.434526\pi$
$152$	4.08512	+	7.07564i	0.331347	+	0.573910i
$153$	2.58512	−	4.47756i	0.208995	−	0.361990i
$154$	−0.571452	+	0.989783i	−0.0460489	+	0.0797590i
$155$	−5.63816			−0.452868
$156$	5.62449	+	3.77920i	0.450319	+	0.302578i
$157$	−17.0692			−1.36227			−0.681136	−	0.732157i	$-0.738514\pi$
$157$	−17.0692			−1.36227			−0.681136	+	0.732157i	$0.738514\pi$
$158$	1.60220	−	2.77509i	0.127464	−	0.220774i
$159$	−3.42127	+	5.92582i	−0.271325	+	0.469948i
$160$	−6.77719	−	11.7384i	−0.535784	−	0.928005i
$161$	−1.49020			−0.117444
$162$	−0.173648	−	0.300767i	−0.0136431	−	0.0236305i
$163$	3.62836	+	6.28450i	0.284195	+	0.492240i	0.972414	−	0.233263i	$-0.0749404\pi$
$163$	3.62836	+	6.28450i	0.284195	+	0.492240i	−0.688219	+	0.725503i	$0.741607\pi$
$164$	21.8871			1.70910
$165$	5.81180	+	10.0663i	0.452448	+	0.783663i
$166$	−1.89646	+	3.28476i	−0.147194	+	0.254947i
$167$	−4.48545	+	7.76903i	−0.347095	+	0.601186i	−0.985732	−	0.168322i	$-0.946165\pi$
$167$	−4.48545	+	7.76903i	−0.347095	+	0.601186i	0.638637	+	0.769508i	$0.279498\pi$
$168$	1.34730			0.103946
$169$	4.91282	+	12.0360i	0.377909	+	0.925843i
$170$	−6.34224			−0.486428
$171$	−3.03209	+	5.25173i	−0.231870	+	0.401610i
$172$	11.6493	−	20.1772i	0.888251	−	1.53850i
$173$	−7.85117	−	13.5986i	−0.596913	−	1.03388i	−0.993274	−	0.115789i	$-0.963060\pi$
$173$	−7.85117	−	13.5986i	−0.596913	−	1.03388i	0.396361	−	0.918095i	$-0.370273\pi$
$174$	1.64496			0.124704
$175$	3.73783	+	6.47410i	0.282553	+	0.489396i
$176$	5.41488	+	9.37884i	0.408162	+	0.706957i
$177$	11.6186			0.873304
$178$	−0.0111444	−	0.0193026i	−0.000835305	−	0.00144679i
$179$	8.00640	−	13.8675i	0.598426	−	1.03650i	−0.394627	−	0.918841i	$-0.629126\pi$
$179$	8.00640	−	13.8675i	0.598426	−	1.03650i	0.993054	−	0.117663i	$-0.0375404\pi$
$180$	3.31908	−	5.74881i	0.247389	−	0.428491i
$181$	−14.9786			−1.11335			−0.556677	−	0.830729i	$-0.687924\pi$
$181$	−14.9786			−1.11335			−0.556677	+	0.830729i	$0.687924\pi$
$182$	1.03936	+	0.698367i	0.0770427	+	0.0517664i
$183$	1.82295			0.134756
$184$	1.00387	−	1.73875i	0.0740063	−	0.128183i
$185$	−13.9547	+	24.1703i	−1.02597	+	1.77703i
$186$	0.277189	+	0.480105i	0.0203245	+	0.0352030i
$187$	17.0145			1.24423
$188$	0.152704	+	0.264490i	0.0111371	+	0.0192900i
$189$	0.500000	+	0.866025i	0.0363696	+	0.0629941i
$190$	7.43882			0.539668
$191$	0.148833	+	0.257787i	0.0107692	+	0.0186528i	0.871360	−	0.490645i	$-0.163239\pi$
$191$	0.148833	+	0.257787i	0.0107692	+	0.0186528i	−0.860591	+	0.509297i	$0.829905\pi$
$192$	2.62449	−	4.54574i	0.189406	−	0.328061i
$193$	−7.70826	+	13.3511i	−0.554853	+	0.961033i	0.443062	+	0.896491i	$0.353892\pi$
$193$	−7.70826	+	13.3511i	−0.554853	+	0.961033i	−0.997915	+	0.0645425i	$0.979441\pi$
$194$	0.155697			0.0111784
$195$	11.4363	−	5.60310i	0.818970	−	0.401247i
$196$	−1.87939			−0.134242
$197$	−9.57785	+	16.5893i	−0.682393	+	1.18194i	0.291855	+	0.956463i	$0.405728\pi$
$197$	−9.57785	+	16.5893i	−0.682393	+	1.18194i	−0.974248	+	0.225478i	$0.927606\pi$
$198$	0.571452	−	0.989783i	0.0406113	−	0.0703408i
$199$	−0.698463	−	1.20977i	−0.0495127	−	0.0857586i	0.840207	−	0.542266i	$-0.182434\pi$
$199$	−0.698463	−	1.20977i	−0.0495127	−	0.0857586i	−0.889720	+	0.456507i	$0.849100\pi$
$200$	−10.0719			−0.712192
$201$	−4.59492	−	7.95864i	−0.324101	−	0.561359i
$202$	2.19459	+	3.80115i	0.154411	+	0.267448i
$203$	−4.73648			−0.332436
$204$	−4.85844	−	8.41507i	−0.340159	−	0.589172i
$205$	20.5672	−	35.6234i	1.43647	−	2.48805i
$206$	−0.705737	+	1.22237i	−0.0491710	+	0.0851667i
$207$	1.49020			0.103576
$208$	10.6552	−	5.22043i	0.738807	−	0.361972i
$209$	−19.9564			−1.38041
$210$	0.613341	−	1.06234i	0.0423245	−	0.0733082i
$211$	−0.461981	+	0.800175i	−0.0318041	+	0.0550863i	−0.881489	−	0.472204i	$-0.843459\pi$
$211$	−0.461981	+	0.800175i	−0.0318041	+	0.0550863i	0.849685	+	0.527290i	$0.176792\pi$
$212$	6.42989	+	11.1369i	0.441607	+	0.764885i
$213$	−4.49020			−0.307663
$214$	−2.08512	−	3.61154i	−0.142536	−	0.246880i
$215$	−21.8935	−	37.9207i	−1.49313	−	2.58617i
$216$	−1.34730			−0.0916719
$217$	−0.798133	−	1.38241i	−0.0541808	−	0.0938439i
$218$	−0.482926	+	0.836452i	−0.0327079	+	0.0566517i
$219$	−7.47178	+	12.9415i	−0.504896	+	0.874506i
$220$	21.8452			1.47281
$221$	1.26723	−	18.5985i	0.0852429	−	1.25107i
$222$	2.74422			0.184180
$223$	−3.91147	+	6.77487i	−0.261932	+	0.453679i	−0.966755	−	0.255704i	$-0.917693\pi$
$223$	−3.91147	+	6.77487i	−0.261932	+	0.453679i	0.704824	+	0.709383i	$0.251026\pi$
$224$	1.91875	−	3.32337i	0.128202	−	0.222052i
$225$	−3.73783	−	6.47410i	−0.249188	−	0.431607i
$226$	−0.101014			−0.00671938
$227$	4.26604	+	7.38901i	0.283147	+	0.490426i	0.972158	−	0.234325i	$-0.0752881\pi$
$227$	4.26604	+	7.38901i	0.283147	+	0.490426i	−0.689011	+	0.724751i	$0.741955\pi$
$228$	5.69846	+	9.87003i	0.377390	+	0.653659i
$229$	3.16519			0.209162			0.104581	−	0.994516i	$-0.466650\pi$
$229$	3.16519			0.209162			0.104581	+	0.994516i	$0.466650\pi$
$230$	−0.914000	−	1.58310i	−0.0602674	−	0.104386i
$231$	−1.64543	+	2.84997i	−0.108261	+	0.187514i
$232$	3.19072	−	5.52649i	0.209481	−	0.362832i
$233$	−22.8580			−1.49748			−0.748740	−	0.662864i	$-0.769341\pi$
$233$	−22.8580			−1.49748			−0.748740	+	0.662864i	$0.769341\pi$
$234$	−1.03936	−	0.698367i	−0.0679453	−	0.0456537i
$235$	0.573978			0.0374422
$236$	10.9179	−	18.9103i	0.710693	−	1.23096i
$237$	4.61334	−	7.99054i	0.299669	−	0.519041i
$238$	−0.897804	−	1.55504i	−0.0581960	−	0.100798i
$239$	6.82295			0.441340			0.220670	−	0.975349i	$-0.429176\pi$
$239$	6.82295			0.441340			0.220670	+	0.975349i	$0.429176\pi$
$240$	−5.81180	−	10.0663i	−0.375150	−	0.649779i
$241$	−10.5424	−	18.2599i	−0.679093	−	1.17622i	−0.975254	−	0.221085i	$-0.929040\pi$
$241$	−10.5424	−	18.2599i	−0.679093	−	1.17622i	0.296162	−	0.955138i	$-0.404293\pi$
$242$	−0.0591253			−0.00380072
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	1.71301	−	2.96702i	0.109664	−	0.189944i
$245$	−1.76604	+	3.05888i	−0.112828	+	0.195425i
$246$	−4.04458			−0.257873
$247$	−1.48633	+	21.8141i	−0.0945729	+	1.38800i
$248$	2.15064			0.136566
$249$	−5.46064	+	9.45810i	−0.346054	+	0.599383i
$250$	−1.51842	+	2.62998i	−0.0960332	+	0.166334i
$251$	−1.91875	−	3.32337i	−0.121110	−	0.209769i	0.799095	−	0.601204i	$-0.205312\pi$
$251$	−1.91875	−	3.32337i	−0.121110	−	0.209769i	−0.920206	+	0.391435i	$0.871979\pi$
$252$	1.87939			0.118390
$253$	2.45202	+	4.24702i	0.154157	+	0.267008i
$254$	1.12314	+	1.94534i	0.0704721	+	0.122061i
$255$	−18.2618			−1.14360
$256$	−3.59967	−	6.23481i	−0.224979	−	0.389676i
$257$	0.116744	−	0.202207i	0.00728231	−	0.0126133i	−0.862361	−	0.506293i	$-0.831015\pi$
$257$	0.116744	−	0.202207i	0.00728231	−	0.0126133i	0.869644	+	0.493680i	$0.164349\pi$
$258$	−2.15270	+	3.72859i	−0.134021	+	0.232132i
$259$	−7.90167			−0.490986
$260$	1.62701	−	23.8788i	0.100903	−	1.48090i
$261$	4.73648			0.293181
$262$	1.08899	−	1.88619i	0.0672782	−	0.116529i
$263$	−3.52822	+	6.11105i	−0.217559	+	0.376824i	−0.954061	−	0.299612i	$-0.903143\pi$
$263$	−3.52822	+	6.11105i	−0.217559	+	0.376824i	0.736502	+	0.676435i	$0.236476\pi$
$264$	−2.21688	−	3.83975i	−0.136440	−	0.236320i
$265$	24.1685			1.48466
$266$	1.05303	+	1.82391i	0.0645656	+	0.111831i
$267$	−0.0320889	−	0.0555796i	−0.00196381	−	0.00340142i
$268$	−17.2713			−1.05501
$269$	8.45084	+	14.6373i	0.515257	+	0.892451i	0.999843	+	0.0177074i	$0.00563672\pi$
$269$	8.45084	+	14.6373i	0.515257	+	0.892451i	−0.484587	+	0.874743i	$0.661030\pi$
$270$	−0.613341	+	1.06234i	−0.0373267	+	0.0646518i
$271$	−6.40033	+	11.0857i	−0.388792	+	0.673408i	−0.992287	−	0.123959i	$-0.960441\pi$
$271$	−6.40033	+	11.0857i	−0.388792	+	0.673408i	0.603495	+	0.797367i	$0.293774\pi$
$272$	−17.0145			−1.03166
$273$	2.99273	+	2.01087i	0.181128	+	0.121703i
$274$	−0.643208			−0.0388576
$275$	12.3007	−	21.3054i	0.741758	−	1.28476i
$276$	1.40033	−	2.42544i	0.0842899	−	0.145994i
$277$	−0.815207	−	1.41198i	−0.0489811	−	0.0848377i	0.840495	−	0.541819i	$-0.182264\pi$
$277$	−0.815207	−	1.41198i	−0.0489811	−	0.0848377i	−0.889476	+	0.456981i	$0.848931\pi$
$278$	−5.41921			−0.325023
$279$	0.798133	+	1.38241i	0.0477830	+	0.0827626i
$280$	−2.37939	−	4.12122i	−0.142195	−	0.246290i
$281$	−5.19759			−0.310062			−0.155031	−	0.987910i	$-0.549548\pi$
$281$	−5.19759			−0.310062			−0.155031	+	0.987910i	$0.549548\pi$
$282$	−0.0282185	−	0.0488759i	−0.00168039	−	0.00291052i
$283$	1.73009	−	2.99660i	0.102843	−	0.178129i	−0.810012	−	0.586413i	$-0.800539\pi$
$283$	1.73009	−	2.99660i	0.102843	−	0.178129i	0.912855	+	0.408284i	$0.133873\pi$
$284$	−4.21941	+	7.30823i	−0.250376	+	0.433664i
$285$	21.4192			1.26876
$286$	0.280126	−	4.11126i	0.0165642	−	0.243104i
$287$	11.6459			0.687436
$288$	−1.91875	+	3.32337i	−0.113063	+	0.195831i
$289$	−4.86571	+	8.42767i	−0.286219	+	0.495745i
$290$	−2.90508	−	5.03174i	−0.170592	−	0.295474i
$291$	0.448311			0.0262804
$292$	14.0424	+	24.3221i	0.821767	+	1.42334i
$293$	11.5326	+	19.9750i	0.673739	+	1.16695i	0.976836	+	0.213991i	$0.0686462\pi$
$293$	11.5326	+	19.9750i	0.673739	+	1.16695i	−0.303097	+	0.952960i	$0.598020\pi$
$294$	0.347296			0.0202547
$295$	−20.5189	−	35.5398i	−1.19466	−	2.06920i
$296$	5.32295	−	9.21962i	0.309390	−	0.535879i
$297$	1.64543	−	2.84997i	0.0954775	−	0.165372i
$298$	−0.374638			−0.0217022
$299$	4.82501	−	2.36397i	0.279037	−	0.136712i
$300$	−14.0496			−0.811156
$301$	6.19846	−	10.7361i	0.357273	−	0.618816i
$302$	−0.871644	+	1.50973i	−0.0501575	+	0.0868753i
$303$	6.31908	+	10.9450i	0.363022	+	0.628772i
$304$	19.9564			1.14458
$305$	−3.21941	−	5.57618i	−0.184343	−	0.319291i
$306$	0.897804	+	1.55504i	0.0513240	+	0.0888958i
$307$	−27.7716			−1.58501			−0.792503	−	0.609867i	$-0.791223\pi$
$307$	−27.7716			−1.58501			−0.792503	+	0.609867i	$0.791223\pi$
$308$	3.09240	+	5.35619i	0.176206	+	0.305197i
$309$	−2.03209	+	3.51968i	−0.115601	+	0.200228i
$310$	0.979055	−	1.69577i	0.0556066	−	0.0963135i
$311$	20.3628			1.15467			0.577334	−	0.816508i	$-0.304093\pi$
$311$	20.3628			1.15467			0.577334	+	0.816508i	$0.304093\pi$
$312$	−4.36231	+	2.13727i	−0.246967	+	0.120999i
$313$	2.56717			0.145105			0.0725525	−	0.997365i	$-0.476886\pi$
$313$	2.56717			0.145105			0.0725525	+	0.997365i	$0.476886\pi$
$314$	2.96404	−	5.13387i	0.167270	−	0.289721i
$315$	1.76604	−	3.05888i	0.0995053	−	0.172348i
$316$	−8.67024	−	15.0173i	−0.487739	−	0.844789i
$317$	5.99319			0.336611			0.168306	−	0.985735i	$-0.446170\pi$
$317$	5.99319			0.336611			0.168306	+	0.985735i	$0.446170\pi$
$318$	−1.18820	−	2.05802i	−0.0666307	−	0.115408i
$319$	7.79355	+	13.4988i	0.436355	+	0.755789i
$320$	−18.5398			−1.03641
$321$	−6.00387	−	10.3990i	−0.335103	−	0.580416i
$322$	0.258770	−	0.448204i	0.0144207	−	0.0249774i
$323$	15.6766	−	27.1527i	0.872272	−	1.51082i
$324$	−1.87939			−0.104410
$325$	−22.3726	−	15.0326i	−1.24101	−	0.833856i
$326$	−2.52023			−0.139583
$327$	−1.39053	+	2.40847i	−0.0768965	+	0.133189i
$328$	−7.84524	+	13.5883i	−0.433181	+	0.750291i
$329$	0.0812519	+	0.140732i	0.00447956	+	0.00775883i
$330$	−4.03684			−0.222221
$331$	−15.2135	−	26.3505i	−0.836208	−	1.44836i	−0.893043	−	0.449972i	$-0.851434\pi$
$331$	−15.2135	−	26.3505i	−0.836208	−	1.44836i	0.0568344	−	0.998384i	$-0.481899\pi$
$332$	10.2626	+	17.7754i	0.563236	+	0.975553i
$333$	7.90167			0.433009
$334$	−1.55778	−	2.69816i	−0.0852380	−	0.147637i
$335$	−16.2297	+	28.1106i	−0.886722	+	1.53585i
$336$	1.64543	−	2.84997i	0.0897655	−	0.155478i
$337$	20.3901			1.11072			0.555360	−	0.831610i	$-0.312580\pi$
$337$	20.3901			1.11072			0.555360	+	0.831610i	$0.312580\pi$
$338$	−4.47313	−	0.612406i	−0.243306	−	0.0333105i
$339$	−0.290859			−0.0157973
$340$	−17.1604	+	29.7228i	−0.930656	+	1.61194i
$341$	−2.62654	+	4.54931i	−0.142235	+	0.246359i
$342$	−1.05303	−	1.82391i	−0.0569415	−	0.0986256i
$343$	−1.00000			−0.0539949
$344$	8.35117	+	14.4646i	0.450265	+	0.779881i
$345$	−2.63176	−	4.55834i	−0.141689	−	0.245413i
$346$	5.45336			0.293175
$347$	4.75743	+	8.24010i	0.255392	+	0.442352i	0.965002	−	0.262243i	$-0.0844621\pi$
$347$	4.75743	+	8.24010i	0.255392	+	0.442352i	−0.709610	+	0.704595i	$0.751129\pi$
$348$	4.45084	−	7.70908i	0.238590	−	0.413250i
$349$	−1.05778	+	1.83213i	−0.0566217	+	0.0980717i	−0.892947	−	0.450162i	$-0.851366\pi$
$349$	−1.05778	+	1.83213i	−0.0566217	+	0.0980717i	0.836325	+	0.548234i	$0.184700\pi$
$350$	−2.59627			−0.138776
$351$	−2.99273	−	2.01087i	−0.159740	−	0.107332i
$352$	−12.6287			−0.673110
$353$	8.37211	−	14.5009i	0.445603	−	0.771806i	−0.552491	−	0.833519i	$-0.686323\pi$
$353$	8.37211	−	14.5009i	0.445603	−	0.771806i	0.998094	+	0.0617124i	$0.0196561\pi$
$354$	−2.01754	+	3.49448i	−0.107231	+	0.185730i
$355$	7.92989	+	13.7350i	0.420875	+	0.728977i
$356$	−0.120615			−0.00639257
$357$	−2.58512	−	4.47756i	−0.136819	−	0.236978i
$358$	2.78059	+	4.81613i	0.146959	+	0.254540i
$359$	13.3500			0.704585			0.352293	−	0.935890i	$-0.385402\pi$
$359$	13.3500			0.704585			0.352293	+	0.935890i	$0.385402\pi$
$360$	2.37939	+	4.12122i	0.125405	+	0.217207i
$361$	−8.88713	+	15.3930i	−0.467743	+	0.810155i
$362$	2.60101	−	4.50509i	0.136706	−	0.236782i
$363$	−0.170245			−0.00893552
$364$	6.08512	−	2.98135i	0.318947	−	0.156265i
$365$	52.7820			2.76274
$366$	−0.316552	+	0.548284i	−0.0165464	+	0.0286592i
$367$	−17.5535	+	30.4036i	−0.916285	+	1.58705i	−0.111277	+	0.993789i	$0.535494\pi$
$367$	−17.5535	+	30.4036i	−0.916285	+	1.58705i	−0.805009	+	0.593263i	$0.797839\pi$
$368$	−2.45202	−	4.24702i	−0.127820	−	0.221391i
$369$	−11.6459			−0.606261
$370$	−4.84642	−	8.39424i	−0.251953	−	0.436396i
$371$	3.42127	+	5.92582i	0.177624	+	0.307653i
$372$	3.00000			0.155543
$373$	7.61674	+	13.1926i	0.394380	+	0.683086i	0.993022	−	0.117931i	$-0.0376260\pi$
$373$	7.61674	+	13.1926i	0.394380	+	0.683086i	−0.598642	+	0.801017i	$0.704293\pi$
$374$	−2.95455	+	5.11742i	−0.152776	+	0.264616i
$375$	−4.37211	+	7.57272i	−0.225775	+	0.391054i
$376$	−0.218941			−0.0112910
$377$	15.3359	−	7.51368i	0.789839	−	0.386974i
$378$	−0.347296			−0.0178630
$379$	−2.89393	+	5.01244i	−0.148651	+	0.257472i	−0.930729	−	0.365709i	$-0.880827\pi$
$379$	−2.89393	+	5.01244i	−0.148651	+	0.257472i	0.782078	+	0.623181i	$0.214160\pi$
$380$	20.1275	−	34.8618i	1.03252	−	1.78837i
$381$	3.23396	+	5.60138i	0.165681	+	0.286967i
$382$	−0.103378			−0.00528930
$383$	−3.91622	−	6.78310i	−0.200110	−	0.346600i	0.748454	−	0.663187i	$-0.230796\pi$
$383$	−3.91622	−	6.78310i	−0.200110	−	0.346600i	−0.948564	+	0.316587i	$0.897463\pi$
$384$	4.74897	+	8.22546i	0.242345	+	0.419754i
$385$	11.6236			0.592394
$386$	−2.67705	−	4.63679i	−0.136258	−	0.236006i
$387$	−6.19846	+	10.7361i	−0.315086	+	0.545744i
$388$	0.421274	−	0.729669i	0.0213870	−	0.0370433i
$389$	−6.86215			−0.347925			−0.173962	−	0.984752i	$-0.555657\pi$
$389$	−6.86215			−0.347925			−0.173962	+	0.984752i	$0.555657\pi$
$390$	−0.300660	+	4.41263i	−0.0152245	+	0.223442i
$391$	−7.70470			−0.389643
$392$	0.673648	−	1.16679i	0.0340244	−	0.0589319i
$393$	3.13563	−	5.43107i	0.158172	−	0.273961i
$394$	−3.32635	−	5.76141i	−0.167579	−	0.290256i
$395$	−32.5895			−1.63975
$396$	−3.09240	−	5.35619i	−0.155399	−	0.269159i
$397$	−12.6454	−	21.9025i	−0.634656	−	1.09926i	−0.986588	−	0.163231i	$-0.947809\pi$
$397$	−12.6454	−	21.9025i	−0.634656	−	1.09926i	0.351932	−	0.936026i	$-0.385525\pi$
$398$	0.485147			0.0243182
$399$	3.03209	+	5.25173i	0.151794	+	0.262915i
$400$	−12.3007	+	21.3054i	−0.615033	+	1.06527i
$401$	−17.3195	+	29.9983i	−0.864897	+	1.49805i	0.00225284	+	0.999997i	$0.499283\pi$
$401$	−17.3195	+	29.9983i	−0.864897	+	1.49805i	−0.867150	+	0.498048i	$0.834050\pi$
$402$	3.19160			0.159183
$403$	4.77719	+	3.20988i	0.237969	+	0.159896i
$404$	23.7520			1.18170
$405$	−1.76604	+	3.05888i	−0.0877555	+	0.151997i
$406$	0.822481	−	1.42458i	0.0408191	−	0.0707007i
$407$	13.0016	+	22.5195i	0.644468	+	1.11625i
$408$	6.96585			0.344861
$409$	−2.34090	−	4.05456i	−0.115750	−	0.200485i	0.802329	−	0.596882i	$-0.203594\pi$
$409$	−2.34090	−	4.05456i	−0.115750	−	0.200485i	−0.918079	+	0.396397i	$0.870260\pi$
$410$	7.14290	+	12.3719i	0.352763	+	0.611003i
$411$	−1.85204			−0.0913546
$412$	3.81908	+	6.61484i	0.188152	+	0.325890i
$413$	5.80928	−	10.0620i	0.285856	−	0.495117i
$414$	−0.258770	+	0.448204i	−0.0127179	+	0.0220280i
$415$	38.5749			1.89357
$416$	−0.940570	+	13.8043i	−0.0461152	+	0.676811i
$417$	−15.6040			−0.764132
$418$	3.46538	−	6.00222i	0.169498	−	0.293578i
$419$	−12.4829	+	21.6211i	−0.609831	+	1.05626i	0.381437	+	0.924395i	$0.375429\pi$
$419$	−12.4829	+	21.6211i	−0.609831	+	1.05626i	−0.991268	+	0.131863i	$0.957904\pi$
$420$	−3.31908	−	5.74881i	−0.161954	−	0.280513i
$421$	5.18210			0.252560			0.126280	−	0.991995i	$-0.459696\pi$
$421$	5.18210			0.252560			0.126280	+	0.991995i	$0.459696\pi$
$422$	−0.160444	−	0.277898i	−0.00781031	−	0.0135279i
$423$	−0.0812519	−	0.140732i	−0.00395060	−	0.00684265i
$424$	−9.21894			−0.447711
$425$	19.3255	+	33.4727i	0.937423	+	1.62366i
$426$	0.779715	−	1.35051i	0.0377773	−	0.0654322i
$427$	0.911474	−	1.57872i	0.0441093	−	0.0763996i
$428$	−22.5672			−1.09083
$429$	0.806589	−	11.8379i	0.0389425	−	0.571540i
$430$	15.2071			0.733351
$431$	10.3525	−	17.9311i	0.498663	−	0.863709i	−0.501336	−	0.865253i	$-0.667158\pi$
$431$	10.3525	−	17.9311i	0.498663	−	0.863709i	0.999999	+	0.00154326i	$0.000491234\pi$
$432$	−1.64543	+	2.84997i	−0.0791658	+	0.137119i
$433$	18.1236	+	31.3910i	0.870965	+	1.50856i	0.861000	+	0.508605i	$0.169839\pi$
$433$	18.1236	+	31.3910i	0.870965	+	1.50856i	0.00996521	+	0.999950i	$0.496828\pi$
$434$	0.554378			0.0266110
$435$	−8.36484	−	14.4883i	−0.401063	−	0.694662i
$436$	2.61334	+	4.52644i	0.125156	+	0.216777i
$437$	9.03684			0.432291
$438$	−2.59492	−	4.49454i	−0.123990	−	0.214757i
$439$	−8.30675	+	14.3877i	−0.396460	+	0.686688i	−0.993286	−	0.115682i	$-0.963095\pi$
$439$	−8.30675	+	14.3877i	−0.396460	+	0.686688i	0.596827	+	0.802370i	$0.296428\pi$
$440$	−7.83022	+	13.5623i	−0.373291	+	0.646559i
$441$	1.00000			0.0476190
$442$	5.37376	+	3.61073i	0.255604	+	0.171745i
$443$	−18.1925			−0.864353			−0.432177	−	0.901789i	$-0.642254\pi$
$443$	−18.1925			−0.864353			−0.432177	+	0.901789i	$0.642254\pi$
$444$	7.42514	−	12.8607i	0.352382	−	0.610343i
$445$	−0.113341	+	0.196312i	−0.00537287	+	0.00930608i
$446$	−1.35844	−	2.35289i	−0.0643240	−	0.111412i
$447$	−1.07873			−0.0510220
$448$	−2.62449	−	4.54574i	−0.123995	−	0.214766i
$449$	17.3478	+	30.0472i	0.818692	+	1.41802i	0.906647	+	0.421891i	$0.138633\pi$
$449$	17.3478	+	30.0472i	0.818692	+	1.41802i	−0.0879550	+	0.996124i	$0.528033\pi$
$450$	2.59627			0.122389
$451$	−19.1625	−	33.1904i	−0.902327	−	1.56288i
$452$	−0.273318	+	0.473401i	−0.0128558	+	0.0222669i
$453$	−2.50980	+	4.34710i	−0.117921	+	0.204245i
$454$	−2.96316			−0.139068
$455$	0.865715	−	12.7057i	0.0405853	−	0.595651i
$456$	−8.17024			−0.382607
$457$	14.7306	−	25.5141i	0.689066	−	1.19350i	−0.283074	−	0.959098i	$-0.591354\pi$
$457$	14.7306	−	25.5141i	0.689066	−	1.19350i	0.972140	−	0.234400i	$-0.0753124\pi$
$458$	−0.549630	+	0.951987i	−0.0256825	+	0.0444834i
$459$	2.58512	+	4.47756i	0.120663	+	0.208995i
$460$	−9.89218			−0.461225
$461$	10.9684	+	18.9978i	0.510848	+	0.884815i	0.999921	+	0.0125722i	$0.00400195\pi$
$461$	10.9684	+	18.9978i	0.510848	+	0.884815i	−0.489073	+	0.872243i	$0.662665\pi$
$462$	−0.571452	−	0.989783i	−0.0265863	−	0.0460489i
$463$	−6.11112			−0.284008			−0.142004	−	0.989866i	$-0.545355\pi$
$463$	−6.11112			−0.284008			−0.142004	+	0.989866i	$0.545355\pi$
$464$	−7.79355	−	13.4988i	−0.361806	−	0.626667i
$465$	2.81908	−	4.88279i	0.130732	−	0.226434i
$466$	3.96926	−	6.87495i	0.183872	−	0.318476i
$467$	−4.00269			−0.185222			−0.0926112	−	0.995702i	$-0.529521\pi$
$467$	−4.00269			−0.185222			−0.0926112	+	0.995702i	$0.529521\pi$
$468$	−6.08512	+	2.98135i	−0.281285	+	0.137813i
$469$	−9.18984			−0.424348
$470$	−0.0996702	+	0.172634i	−0.00459744	+	0.00796301i
$471$	8.53462	−	14.7824i	0.393254	−	0.681136i
$472$	7.82682	+	13.5564i	0.360259	+	0.623986i
$473$	−40.7965			−1.87583
$474$	1.60220	+	2.77509i	0.0735913	+	0.127464i
$475$	−22.6668	−	39.2601i	−1.04003	−	1.80138i
$476$	−9.71688			−0.445373
$477$	−3.42127	−	5.92582i	−0.156649	−	0.271325i
$478$	−1.18479	+	2.05212i	−0.0541911	+	0.0938618i
$479$	19.1518	−	33.1719i	0.875069	−	1.51566i	0.0183804	−	0.999831i	$-0.494149\pi$
$479$	19.1518	−	33.1719i	0.875069	−	1.51566i	0.856689	−	0.515833i	$-0.172518\pi$
$480$	13.5544			0.618670
$481$	25.5842	−	12.5348i	1.16654	−	0.571536i
$482$	7.32264			0.333537
$483$	0.745100	−	1.29055i	0.0339032	−	0.0587221i
$484$	−0.159978	+	0.277089i	−0.00727171	+	0.0125950i
$485$	−0.791737	−	1.37133i	−0.0359509	−	0.0622688i
$486$	0.347296			0.0157537
$487$	6.68139	+	11.5725i	0.302763	+	0.524400i	0.976761	−	0.214333i	$-0.0687577\pi$
$487$	6.68139	+	11.5725i	0.302763	+	0.524400i	−0.673998	+	0.738733i	$0.735424\pi$
$488$	1.22803	+	2.12700i	0.0555901	+	0.0962849i
$489$	−7.25671			−0.328160
$490$	−0.613341	−	1.06234i	−0.0277079	−	0.0479915i
$491$	11.9158	−	20.6388i	0.537753	−	0.931416i	−0.461272	−	0.887259i	$-0.652607\pi$
$491$	11.9158	−	20.6388i	0.537753	−	0.931416i	0.999025	−	0.0441566i	$-0.0140601\pi$
$492$	−10.9436	+	18.9548i	−0.493374	+	0.854549i
$493$	−24.4888			−1.10292
$494$	−6.30288	−	4.23502i	−0.283580	−	0.190543i
$495$	−11.6236			−0.522442
$496$	2.62654	−	4.54931i	0.117935	−	0.204270i
$497$	−2.24510	+	3.88863i	−0.100706	+	0.174429i
$498$	−1.89646	−	3.28476i	−0.0849824	−	0.147194i
$499$	11.9385			0.534441			0.267221	−	0.963635i	$-0.413895\pi$
$499$	11.9385			0.534441			0.267221	+	0.963635i	$0.413895\pi$
$500$	8.21688	+	14.2321i	0.367470	+	0.636477i
$501$	−4.48545	−	7.76903i	−0.200395	−	0.347095i
$502$	1.33275			0.0594835
$503$	7.96791	+	13.8008i	0.355272	+	0.615348i	0.987164	−	0.159707i	$-0.0510551\pi$
$503$	7.96791	+	13.8008i	0.355272	+	0.615348i	−0.631893	+	0.775056i	$0.717722\pi$
$504$	−0.673648	+	1.16679i	−0.0300067	+	0.0519731i
$505$	22.3195	−	38.6586i	0.993207	−	1.72028i
$506$	−1.70315			−0.0757145
$507$	−12.8799	−	1.76335i	−0.572014	−	0.0783132i
$508$	12.1557			0.539322
$509$	7.01455	−	12.1496i	0.310914	−	0.538519i	−0.667646	−	0.744479i	$-0.732698\pi$
$509$	7.01455	−	12.1496i	0.310914	−	0.538519i	0.978561	+	0.205959i	$0.0660314\pi$
$510$	3.17112	−	5.49254i	0.140420	−	0.243214i
$511$	7.47178	+	12.9415i	0.330532	+	0.572498i
$512$	21.4962			0.950006
$513$	−3.03209	−	5.25173i	−0.133870	−	0.231870i
$514$	0.0405449	+	0.0702258i	0.00178836	+	0.00309753i
$515$	14.3550			0.632559
$516$	11.6493	+	20.1772i	0.512832	+	0.888251i
$517$	0.267389	−	0.463131i	0.0117597	−	0.0203685i
$518$	1.37211	−	2.37657i	0.0602871	−	0.104420i
$519$	15.7023			0.689256
$520$	14.2417	+	9.56926i	0.624540	+	0.419640i
$521$	−13.4466			−0.589104			−0.294552	−	0.955635i	$-0.595170\pi$
$521$	−13.4466			−0.589104			−0.294552	+	0.955635i	$0.595170\pi$
$522$	−0.822481	+	1.42458i	−0.0359990	+	0.0623522i
$523$	1.56876	−	2.71718i	0.0685972	−	0.118814i	−0.829687	−	0.558229i	$-0.811481\pi$
$523$	1.56876	−	2.71718i	0.0685972	−	0.118814i	0.898284	+	0.439415i	$0.144814\pi$
$524$	−5.89306	−	10.2071i	−0.257439	−	0.445898i
$525$	−7.47565			−0.326264
$526$	−1.22534	−	2.12235i	−0.0534273	−	0.0925387i
$527$	−4.12654	−	7.14738i	−0.179755	−	0.311345i
$528$	−10.8298			−0.471305
$529$	10.3897	+	17.9954i	0.451724	+	0.782409i
$530$	−4.19681	+	7.26910i	−0.182298	+	0.315749i
$531$	−5.80928	+	10.0620i	−0.252101	+	0.436652i
$532$	11.3969			0.494119
$533$	−37.7074	+	18.4744i	−1.63329	+	0.800214i
$534$	0.0222887			0.000964527
$535$	−21.2062	+	36.7302i	−0.916824	+	1.58799i
$536$	6.19072	−	10.7226i	0.267398	−	0.463148i
$537$	8.00640	+	13.8675i	0.345502	+	0.598426i
$538$	−5.86989			−0.253069
$539$	1.64543	+	2.84997i	0.0708737	+	0.122757i
$540$	3.31908	+	5.74881i	0.142830	+	0.247389i
$541$	−27.3236			−1.17473			−0.587366	−	0.809321i	$-0.699835\pi$
$541$	−27.3236			−1.17473			−0.587366	+	0.809321i	$0.699835\pi$
$542$	−2.22281	−	3.85002i	−0.0954779	−	0.165373i
$543$	7.48932	−	12.9719i	0.321398	−	0.556677i
$544$	9.92040	−	17.1826i	0.425334	−	0.736699i
$545$	9.82295			0.420769
$546$	−1.12449	+	0.550931i	−0.0481235	+	0.0235777i
$547$	−6.19522			−0.264889			−0.132444	−	0.991190i	$-0.542283\pi$
$547$	−6.19522			−0.264889			−0.132444	+	0.991190i	$0.542283\pi$
$548$	−1.74035	+	3.01438i	−0.0743442	+	0.128768i
$549$	−0.911474	+	1.57872i	−0.0389008	+	0.0673781i
$550$	4.27197	+	7.39928i	0.182158	+	0.315506i
$551$	28.7229			1.22364
$552$	1.00387	+	1.73875i	0.0427276	+	0.0740063i
$553$	−4.61334	−	7.99054i	−0.196179	−	0.339792i
$554$	0.566237			0.0240571
$555$	−13.9547	−	24.1703i	−0.592344	−	1.02597i
$556$	−14.6630	+	25.3970i	−0.621848	+	1.07707i
$557$	15.2999	−	26.5003i	0.648279	−	1.12285i	−0.335254	−	0.942128i	$-0.608822\pi$
$557$	15.2999	−	26.5003i	0.648279	−	1.12285i	0.983534	−	0.180725i	$-0.0578445\pi$
$558$	−0.554378			−0.0234687
$559$	−3.03849	+	44.5944i	−0.128514	+	1.88614i
$560$	−11.6236			−0.491187
$561$	−8.50727	+	14.7350i	−0.359177	+	0.622113i
$562$	0.902551	−	1.56326i	0.0380718	−	0.0659423i
$563$	−3.75537	−	6.50449i	−0.158270	−	0.274131i	0.775975	−	0.630764i	$-0.217258\pi$
$563$	−3.75537	−	6.50449i	−0.158270	−	0.274131i	−0.934245	+	0.356632i	$0.883925\pi$
$564$	−0.305407			−0.0128600
$565$	0.513671	+	0.889704i	0.0216103	+	0.0374301i
$566$	0.600852	+	1.04071i	0.0252557	+	0.0437442i
$567$	−1.00000			−0.0419961
$568$	−3.02481	−	5.23913i	−0.126918	−	0.219829i
$569$	5.07011	−	8.78168i	0.212550	−	0.368147i	−0.739962	−	0.672649i	$-0.765157\pi$
$569$	5.07011	−	8.78168i	0.212550	−	0.368147i	0.952512	+	0.304501i	$0.0984898\pi$
$570$	−3.71941	+	6.44220i	−0.155789	+	0.269834i
$571$	−35.1019			−1.46897			−0.734485	−	0.678624i	$-0.762576\pi$
$571$	−35.1019			−1.46897			−0.734485	+	0.678624i	$0.762576\pi$
$572$	−18.5094	−	12.4368i	−0.773916	−	0.520009i
$573$	−0.297667			−0.0124352
$574$	−2.02229	+	3.50271i	−0.0844087	+	0.146200i
$575$	−5.57011	+	9.64771i	−0.232290	+	0.402337i
$576$	2.62449	+	4.54574i	0.109354	+	0.189406i
$577$	−4.31315			−0.179559			−0.0897794	−	0.995962i	$-0.528616\pi$
$577$	−4.31315			−0.179559			−0.0897794	+	0.995962i	$0.528616\pi$
$578$	−1.68984	−	2.92690i	−0.0702883	−	0.121743i
$579$	−7.70826	−	13.3511i	−0.320344	−	0.554853i
$580$	−31.4415			−1.30554
$581$	5.46064	+	9.45810i	0.226545	+	0.392388i
$582$	−0.0778483	+	0.134837i	−0.00322692	+	0.00558919i
$583$	11.2589	−	19.5010i	0.466297	−	0.807651i
$584$	−20.1334			−0.833126
$585$	−0.865715	+	12.7057i	−0.0357929	+	0.525315i
$586$	−8.01043			−0.330908
$587$	10.5123	−	18.2079i	0.433890	−	0.751520i	−0.563314	−	0.826243i	$-0.690474\pi$
$587$	10.5123	−	18.2079i	0.433890	−	0.751520i	0.997204	+	0.0747230i	$0.0238073\pi$
$588$	0.939693	−	1.62760i	0.0387523	−	0.0671209i
$589$	4.84002	+	8.38316i	0.199430	+	0.345422i
$590$	14.2523			0.586757
$591$	−9.57785	−	16.5893i	−0.393980	−	0.682393i
$592$	−13.0016	−	22.5195i	−0.534364	−	0.925546i
$593$	−7.55943			−0.310429			−0.155214	−	0.987881i	$-0.549607\pi$
$593$	−7.55943			−0.310429			−0.155214	+	0.987881i	$0.549607\pi$
$594$	0.571452	+	0.989783i	0.0234469	+	0.0406113i
$595$	−9.13088	+	15.8152i	−0.374330	+	0.648358i
$596$	−1.01367	+	1.75573i	−0.0415216	+	0.0719175i
$597$	1.39693			0.0571724
$598$	−0.126849	+	1.86170i	−0.00518725	+	0.0761307i
$599$	37.0547			1.51401			0.757007	−	0.653407i	$-0.226661\pi$
$599$	37.0547			1.51401			0.757007	+	0.653407i	$0.226661\pi$
$600$	5.03596	−	8.72254i	0.205592	−	0.356096i
$601$	20.3974	−	35.3293i	0.832027	−	1.44111i	−0.0644012	−	0.997924i	$-0.520514\pi$
$601$	20.3974	−	35.3293i	0.832027	−	1.44111i	0.896428	−	0.443189i	$-0.146153\pi$
$602$	2.15270	+	3.72859i	0.0877377	+	0.151966i
$603$	9.18984			0.374239
$604$	4.71688	+	8.16988i	0.191927	+	0.332428i
$605$	0.300660	+	0.520758i	0.0122235	+	0.0211718i
$606$	−4.38919			−0.178298
$607$	−21.6716	−	37.5363i	−0.879623	−	1.52355i	−0.851755	−	0.523939i	$-0.824462\pi$
$607$	−21.6716	−	37.5363i	−0.879623	−	1.52355i	−0.0278672	−	0.999612i	$-0.508872\pi$
$608$	−11.6356	+	20.1535i	−0.471887	+	0.817332i
$609$	2.36824	−	4.10191i	0.0959660	−	0.166218i
$610$	2.23618			0.0905402
$611$	−0.486329	−	0.326774i	−0.0196748	−	0.0132199i
$612$	9.71688			0.392782
$613$	16.8576	−	29.1982i	0.680871	−	1.17930i	−0.293845	−	0.955853i	$-0.594935\pi$
$613$	16.8576	−	29.1982i	0.680871	−	1.17930i	0.974716	−	0.223449i	$-0.0717317\pi$
$614$	4.82248	−	8.35278i	0.194620	−	0.337091i
$615$	20.5672	+	35.6234i	0.829348	+	1.43647i
$616$	−4.43376			−0.178641
$617$	−20.9217	−	36.2375i	−0.842278	−	1.45887i	−0.887965	−	0.459912i	$-0.847881\pi$
$617$	−20.9217	−	36.2375i	−0.842278	−	1.45887i	0.0456870	−	0.998956i	$-0.485452\pi$
$618$	−0.705737	−	1.22237i	−0.0283889	−	0.0491710i
$619$	35.2472			1.41671			0.708353	−	0.705859i	$-0.249439\pi$
$619$	35.2472			1.41671			0.708353	+	0.705859i	$0.249439\pi$
$620$	−5.29813	−	9.17664i	−0.212778	−	0.368543i
$621$	−0.745100	+	1.29055i	−0.0298998	+	0.0517880i
$622$	−3.53596	+	6.12446i	−0.141779	+	0.245569i
$623$	−0.0641778			−0.00257123
$624$	−0.806589	+	11.8379i	−0.0322894	+	0.473896i
$625$	−6.49289			−0.259716
$626$	−0.445785	+	0.772121i	−0.0178171	+	0.0308602i
$627$	9.97818	−	17.2827i	0.398490	−	0.690205i
$628$	−16.0398	−	27.7818i	−0.640059	−	1.10861i
$629$	−40.8536			−1.62894
$630$	0.613341	+	1.06234i	0.0244361	+	0.0423245i
$631$	−0.154048	−	0.266819i	−0.00613255	−	0.0106219i	0.862943	−	0.505302i	$-0.168619\pi$
$631$	−0.154048	−	0.266819i	−0.00613255	−	0.0106219i	−0.869075	+	0.494680i	$0.835285\pi$
$632$	12.4311			0.494482
$633$	−0.461981	−	0.800175i	−0.0183621	−	0.0318041i
$634$	−1.04071	+	1.80256i	−0.0413318	+	0.0715887i
$635$	11.4226	−	19.7846i	0.453293	−	0.785126i
$636$	−12.8598			−0.509924
$637$	3.23783	−	1.58634i	0.128287	−	0.0628532i
$638$	−5.41334			−0.214316
$639$	2.24510	−	3.88863i	0.0888148	−	0.153832i
$640$	16.7738	−	29.0530i	0.663042	−	1.14842i
$641$	−9.92040	−	17.1826i	−0.391832	−	0.678673i	0.600859	−	0.799355i	$-0.294825\pi$
$641$	−9.92040	−	17.1826i	−0.391832	−	0.678673i	−0.992691	+	0.120682i	$0.961492\pi$
$642$	4.17024			0.164586
$643$	−7.79355	−	13.4988i	−0.307348	−	0.532342i	0.670434	−	0.741969i	$-0.266108\pi$
$643$	−7.79355	−	13.4988i	−0.307348	−	0.532342i	−0.977781	+	0.209628i	$0.932775\pi$
$644$	−1.40033	−	2.42544i	−0.0551807	−	0.0955758i
$645$	43.7870			1.72411
$646$	5.44444	+	9.43005i	0.214209	+	0.371020i
$647$	−13.9722	+	24.2006i	−0.549306	+	0.951425i	0.449017	+	0.893523i	$0.351774\pi$
$647$	−13.9722	+	24.2006i	−0.549306	+	0.951425i	−0.998322	+	0.0579020i	$0.981559\pi$
$648$	0.673648	−	1.16679i	0.0264634	−	0.0458360i
$649$	−38.2350			−1.50086
$650$	8.40626	−	4.11857i	0.329721	−	0.161544i
$651$	1.59627			0.0625626
$652$	−6.81908	+	11.8110i	−0.267056	+	0.462554i
$653$	10.5496	−	18.2725i	0.412839	−	0.715058i	−0.582360	−	0.812931i	$-0.697871\pi$
$653$	10.5496	−	18.2725i	0.412839	−	0.715058i	0.995199	+	0.0978730i	$0.0312039\pi$
$654$	−0.482926	−	0.836452i	−0.0188839	−	0.0327079i
$655$	−22.1506			−0.865497
$656$	19.1625	+	33.1904i	0.748170	+	1.29587i
$657$	−7.47178	−	12.9415i	−0.291502	−	0.504896i
$658$	−0.0564370			−0.00220014
$659$	−11.0394	−	19.1207i	−0.430033	−	0.744838i	0.566843	−	0.823826i	$-0.308165\pi$
$659$	−11.0394	−	19.1207i	−0.430033	−	0.744838i	−0.996876	+	0.0789876i	$0.974831\pi$
$660$	−10.9226	+	18.9185i	−0.425162	+	0.736403i
$661$	−16.4440	+	28.4819i	−0.639599	+	1.10782i	0.345922	+	0.938263i	$0.387566\pi$
$661$	−16.4440	+	28.4819i	−0.639599	+	1.10782i	−0.985521	+	0.169554i	$0.945767\pi$
$662$	10.5672			0.410705
$663$	15.4731	+	10.3967i	0.600926	+	0.403774i
$664$	−14.7142			−0.571021
$665$	10.7096	−	18.5496i	0.415301	−	0.719322i
$666$	−1.37211	+	2.37657i	−0.0531682	+	0.0920901i
$667$	−3.52915	−	6.11267i	−0.136649	−	0.236684i
$668$	−16.8598			−0.652325
$669$	−3.91147	−	6.77487i	−0.151226	−	0.261932i
$670$	−5.63651	−	9.76272i	−0.217757	−	0.377167i
$671$	−5.99907			−0.231591
$672$	1.91875	+	3.32337i	0.0740173	+	0.128202i
$673$	20.0805	−	34.7805i	0.774048	−	1.34069i	−0.161280	−	0.986909i	$-0.551562\pi$
$673$	20.0805	−	34.7805i	0.774048	−	1.34069i	0.935328	−	0.353781i	$-0.115104\pi$
$674$	−3.54071	+	6.13268i	−0.136383	+	0.236222i
$675$	7.47565			0.287738
$676$	−14.9731	+	19.3062i	−0.575889	+	0.742545i
$677$	−37.3473			−1.43537			−0.717687	−	0.696366i	$-0.754799\pi$
$677$	−37.3473			−1.43537			−0.717687	+	0.696366i	$0.754799\pi$
$678$	0.0505072	−	0.0874810i	0.00193972	−	0.00335969i
$679$	0.224155	−	0.388249i	0.00860229	−	0.0148996i
$680$	−12.3020	−	21.3077i	−0.471760	−	0.817113i
$681$	−8.53209			−0.326950
$682$	−0.912189	−	1.57996i	−0.0349295	−	0.0604997i
$683$	−1.19341	−	2.06705i	−0.0456646	−	0.0790934i	0.842290	−	0.539025i	$-0.181207\pi$
$683$	−1.19341	−	2.06705i	−0.0456646	−	0.0790934i	−0.887954	+	0.459932i	$0.847874\pi$
$684$	−11.3969			−0.435772
$685$	3.27079	+	5.66518i	0.124971	+	0.216455i
$686$	0.173648	−	0.300767i	0.00662992	−	0.0114834i
$687$	−1.58260	+	2.74114i	−0.0603798	+	0.104581i
$688$	40.7965			1.55535
$689$	−20.4779	−	13.7595i	−0.780145	−	0.524194i
$690$	1.82800			0.0695908
$691$	14.3764	−	24.9007i	0.546906	−	0.947269i	−0.451578	−	0.892231i	$-0.649139\pi$
$691$	14.3764	−	24.9007i	0.546906	−	0.947269i	0.998484	−	0.0550373i	$-0.0175278\pi$
$692$	14.7554	−	25.5570i	0.560915	−	0.971533i
$693$	−1.64543	−	2.84997i	−0.0625047	−	0.108261i
$694$	−3.30447			−0.125436
$695$	27.5574	+	47.7308i	1.04531	+	1.81053i
$696$	3.19072	+	5.52649i	0.120944	+	0.209481i
$697$	60.2121			2.28070
$698$	−0.367364	−	0.636292i	−0.0139049	−	0.0240840i
$699$	11.4290	−	19.7956i	0.432285	−	0.748740i
$700$	−7.02481	+	12.1673i	−0.265513	+	0.459882i
$701$	−3.50475			−0.132372			−0.0661862	−	0.997807i	$-0.521083\pi$
$701$	−3.50475			−0.132372			−0.0661862	+	0.997807i	$0.521083\pi$
$702$	1.12449	−	0.550931i	0.0424410	−	0.0207936i
$703$	47.9172			1.80723
$704$	−8.63681	+	14.9594i	−0.325512	+	0.563803i
$705$	−0.286989	+	0.497079i	−0.0108086	+	0.0187211i
$706$	2.90760	+	5.03612i	0.109429	+	0.189537i
$707$	12.6382			0.475307
$708$	10.9179	+	18.9103i	0.410319	+	0.710693i
$709$	1.72756	+	2.99222i	0.0648798	+	0.112375i	0.896641	−	0.442759i	$-0.146000\pi$
$709$	1.72756	+	2.99222i	0.0648798	+	0.112375i	−0.831761	+	0.555134i	$0.812667\pi$
$710$	−5.50805			−0.206713
$711$	4.61334	+	7.99054i	0.173014	+	0.299669i
$712$	0.0432332	−	0.0748822i	0.00162023	−	0.00280633i
$713$	1.18938	−	2.06006i	0.0445426	−	0.0771500i
$714$	1.79561			0.0671989
$715$	−37.6352	+	18.4390i	−1.40748	+	0.689580i
$716$	30.0942			1.12467
$717$	−3.41147	+	5.90885i	−0.127404	+	0.220670i
$718$	−2.31820	+	4.01524i	−0.0865145	+	0.149847i
$719$	19.2528	+	33.3469i	0.718010	+	1.24363i	0.961787	+	0.273798i	$0.0882801\pi$
$719$	19.2528	+	33.3469i	0.718010	+	1.24363i	−0.243777	+	0.969831i	$0.578387\pi$
$720$	11.6236			0.433186
$721$	2.03209	+	3.51968i	0.0756789	+	0.131080i
$722$	−3.08647	−	5.34592i	−0.114866	−	0.198954i
$723$	21.0847			0.784149
$724$	−14.0753	−	24.3792i	−0.523105	−	0.906045i
$725$	−17.7041	+	30.6645i	−0.657515	+	1.13885i
$726$	0.0295627	−	0.0512040i	0.00109717	−	0.00190036i
$727$	50.1121			1.85855			0.929277	−	0.369385i	$-0.120432\pi$
$727$	50.1121			1.85855			0.929277	+	0.369385i	$0.120432\pi$
$728$	−0.330222	+	4.84651i	−0.0122388	+	0.179624i
$729$	1.00000			0.0370370
$730$	−9.16550	+	15.8751i	−0.339230	+	0.587564i
$731$	32.0476	−	55.5080i	1.18532	−	2.05304i
$732$	1.71301	+	2.96702i	0.0633147	+	0.109664i
$733$	27.3979			1.01196			0.505982	−	0.862544i	$-0.331130\pi$
$733$	27.3979			1.01196			0.505982	+	0.862544i	$0.331130\pi$
$734$	−6.09627	−	10.5590i	−0.225017	−	0.389741i
$735$	−1.76604	−	3.05888i	−0.0651415	−	0.112828i
$736$	5.71864			0.210792
$737$	15.1212	+	26.1908i	0.556998	+	0.964749i
$738$	2.02229	−	3.50271i	0.0744415	−	0.128936i
$739$	−3.87077	+	6.70437i	−0.142388	+	0.246624i	−0.928396	−	0.371593i	$-0.878812\pi$
$739$	−3.87077	+	6.70437i	−0.142388	+	0.246624i	0.786007	+	0.618217i	$0.212145\pi$
$740$	−52.4525			−1.92819
$741$	−18.1484	−	12.1943i	−0.666699	−	0.447967i
$742$	−2.37639			−0.0872401
$743$	−12.4179	+	21.5084i	−0.455567	+	0.789066i	−0.998721	−	0.0505676i	$-0.983897\pi$
$743$	−12.4179	+	21.5084i	−0.455567	+	0.789066i	0.543153	+	0.839634i	$0.317230\pi$
$744$	−1.07532	+	1.86251i	−0.0394232	+	0.0682830i
$745$	1.90508	+	3.29969i	0.0697966	+	0.120891i
$746$	−5.29054			−0.193700
$747$	−5.46064	−	9.45810i	−0.199794	−	0.346054i
$748$	15.9884	+	27.6928i	0.584595	+	1.01255i
$749$	−12.0077			−0.438753
$750$	−1.51842	−	2.62998i	−0.0554448	−	0.0960332i
$751$	−14.1125	+	24.4435i	−0.514971	+	0.891956i	0.484878	+	0.874582i	$0.338864\pi$
$751$	−14.1125	+	24.4435i	−0.514971	+	0.891956i	−0.999849	+	0.0173743i	$0.994469\pi$
$752$	−0.267389	+	0.463131i	−0.00975066	+	0.0168886i
$753$	3.83750			0.139846
$754$	−0.403180	+	5.91728i	−0.0146830	+	0.215495i
$755$	17.7297			0.645249
$756$	−0.939693	+	1.62760i	−0.0341763	+	0.0591951i
$757$	1.82888	−	3.16771i	0.0664717	−	0.115132i	−0.830874	−	0.556460i	$-0.812159\pi$
$757$	1.82888	−	3.16771i	0.0664717	−	0.115132i	0.897346	+	0.441328i	$0.145492\pi$
$758$	−1.00505	−	1.74080i	−0.0365051	−	0.0632288i
$759$	−4.90404			−0.178005
$760$	14.4290	+	24.9918i	0.523395	+	0.906547i
$761$	10.4390	+	18.0808i	0.378413	+	0.655430i	0.990831	−	0.135104i	$-0.0431367\pi$
$761$	10.4390	+	18.0808i	0.378413	+	0.655430i	−0.612419	+	0.790533i	$0.709803\pi$
$762$	−2.24628			−0.0813742
$763$	1.39053	+	2.40847i	0.0503406	+	0.0871924i
$764$	−0.279715	+	0.484481i	−0.0101197	+	0.0175279i
$765$	9.13088	−	15.8152i	0.330128	−	0.571798i
$766$	2.72018			0.0982841
$767$	−2.84771	+	41.7944i	−0.102825	+	1.50911i
$768$	7.19934			0.259784
$769$	14.9659	−	25.9216i	0.539682	−	0.934757i	−0.459238	−	0.888313i	$-0.651878\pi$
$769$	14.9659	−	25.9216i	0.539682	−	0.934757i	0.998921	−	0.0464443i	$-0.0147890\pi$
$770$	−2.01842	+	3.49600i	−0.0727387	+	0.125987i
$771$	0.116744	+	0.202207i	0.00420445	+	0.00728231i
$772$	−28.9736			−1.04278
$773$	18.2574	+	31.6228i	0.656674	+	1.13739i	0.981471	+	0.191609i	$0.0613706\pi$
$773$	18.2574	+	31.6228i	0.656674	+	1.13739i	−0.324797	+	0.945784i	$0.605296\pi$
$774$	−2.15270	−	3.72859i	−0.0773773	−	0.134021i
$775$	−11.9331			−0.428651
$776$	0.302004	+	0.523086i	0.0108413	+	0.0187777i
$777$	3.95084	−	6.84305i	0.141735	−	0.245493i
$778$	1.19160	−	2.06391i	0.0427209	−	0.0739948i
$779$	−70.6228			−2.53032
$780$	19.8662	+	13.3485i	0.711323	+	0.477951i
$781$	14.7766			0.528749
$782$	1.33791	−	2.31732i	0.0478434	−	0.0828673i
$783$	−2.36824	+	4.10191i	−0.0846340	+	0.146590i
$784$	−1.64543	−	2.84997i	−0.0587653	−	0.101785i
$785$	−60.2900			−2.15184
$786$	1.08899	+	1.88619i	0.0388431	+	0.0672782i
$787$	21.3195	+	36.9265i	0.759960	+	1.31629i	0.942871	+	0.333159i	$0.108115\pi$
$787$	21.3195	+	36.9265i	0.759960	+	1.31629i	−0.182911	+	0.983130i	$0.558552\pi$
$788$	−36.0009			−1.28248
$789$	−3.52822	−	6.11105i	−0.125608	−	0.217559i
$790$	5.65910	−	9.80185i	0.201342	−	0.348734i
$791$	−0.145430	+	0.251892i	−0.00517088	+	0.00895623i
$792$	4.43376			0.157547
$793$	−0.446804	+	6.55753i	−0.0158665	+	0.232865i
$794$	8.78342			0.311712
$795$	−12.0842	+	20.9305i	−0.428584	+	0.742329i
$796$	1.31268	−	2.27363i	0.0465268	−	0.0805867i
$797$	8.27925	+	14.3401i	0.293266	+	0.507952i	0.974580	−	0.224040i	$-0.0719245\pi$
$797$	8.27925	+	14.3401i	0.293266	+	0.507952i	−0.681314	+	0.731991i	$0.738591\pi$
$798$	−2.10607			−0.0745540
$799$	0.420092	+	0.727621i	0.0148618	+	0.0257414i
$800$	−14.3439	−	24.8444i	−0.507133	−	0.878380i
$801$	0.0641778			0.00226761
$802$	−6.01501	−	10.4183i	−0.212398	−	0.367883i
$803$	24.5886	−	42.5887i	0.867712	−	1.50292i
$804$	8.63563	−	14.9573i	0.304555	−	0.527505i
$805$	−5.26352			−0.185515
$806$	−1.79498	+	0.879433i	−0.0632254	+	0.0309767i
$807$	−16.9017			−0.594967
$808$	−8.51367	+	14.7461i	−0.299510	+	0.518766i
$809$	−27.2456	+	47.1907i	−0.957903	+	1.65914i	−0.230323	+	0.973114i	$0.573978\pi$
$809$	−27.2456	+	47.1907i	−0.957903	+	1.65914i	−0.727580	+	0.686023i	$0.759355\pi$
$810$	−0.613341	−	1.06234i	−0.0215506	−	0.0373267i
$811$	2.78611			0.0978336			0.0489168	−	0.998803i	$-0.484423\pi$
$811$	2.78611			0.0978336			0.0489168	+	0.998803i	$0.484423\pi$
$812$	−4.45084	−	7.70908i	−0.156194	−	0.270536i
$813$	−6.40033	−	11.0857i	−0.224469	−	0.388792i
$814$	−9.03085			−0.316531
$815$	12.8157	+	22.1974i	0.448913	+	0.777541i
$816$	8.50727	−	14.7350i	0.297814	−	0.515829i
$817$	−37.5886	+	65.1053i	−1.31506	+	2.27775i
$818$	1.62597			0.0568508
$819$	−3.23783	+	1.58634i	−0.113139	+	0.0554313i
$820$	77.3073			2.69969
$821$	−13.4543	+	23.3035i	−0.469558	+	0.813299i	−0.999394	−	0.0348014i	$-0.988920\pi$
$821$	−13.4543	+	23.3035i	−0.469558	+	0.813299i	0.529836	+	0.848100i	$0.322253\pi$
$822$	0.321604	−	0.557035i	0.0112172	−	0.0194288i
$823$	16.4736	+	28.5331i	0.574233	+	0.994601i	0.996124	+	0.0879548i	$0.0280331\pi$
$823$	16.4736	+	28.5331i	0.574233	+	0.994601i	−0.421891	+	0.906646i	$0.638634\pi$
$824$	−5.47565			−0.190753
$825$	12.3007	+	21.3054i	0.428254	+	0.741758i
$826$	2.01754	+	3.49448i	0.0701992	+	0.121589i
$827$	15.6628			0.544649			0.272325	−	0.962205i	$-0.412208\pi$
$827$	15.6628			0.544649			0.272325	+	0.962205i	$0.412208\pi$
$828$	1.40033	+	2.42544i	0.0486648	+	0.0842899i
$829$	9.85803	−	17.0746i	0.342384	−	0.593026i	−0.642491	−	0.766293i	$-0.722099\pi$
$829$	9.85803	−	17.0746i	0.342384	−	0.593026i	0.984875	+	0.173267i	$0.0554325\pi$
$830$	−6.69846	+	11.6021i	−0.232507	+	0.402714i
$831$	1.63041			0.0565585
$832$	15.7087	+	10.5550i	0.544602	+	0.365928i
$833$	−5.17024			−0.179138
$834$	2.70961	−	4.69318i	0.0938260	−	0.162511i
$835$	−15.8430	+	27.4409i	−0.548270	+	0.949632i
$836$	−18.7528	−	32.4809i	−0.648581	−	1.12337i
$837$	−1.59627			−0.0551750
$838$	−4.33527	−	7.50892i	−0.149760	−	0.259391i
$839$	−27.6395	−	47.8730i	−0.954222	−	1.65276i	−0.736140	−	0.676830i	$-0.763353\pi$
$839$	−27.6395	−	47.8730i	−0.954222	−	1.65276i	−0.218082	−	0.975930i	$-0.569980\pi$
$840$	4.75877			0.164193
$841$	3.28287	+	5.68610i	0.113202	+	0.196072i
$842$	−0.899863	+	1.55861i	−0.0310113	+	0.0537132i
$843$	2.59879	−	4.50124i	0.0895072	−	0.155031i
$844$	−1.73648			−0.0597722
$845$	17.3525	+	42.5121i	0.596945	+	1.46246i
$846$	0.0564370			0.00194034
$847$	−0.0851223	+	0.147436i	−0.00292484	+	0.00506597i
$848$	−11.2589	+	19.5010i	−0.386633	+	0.669669i
$849$	1.73009	+	2.99660i	0.0593764	+	0.102843i
$850$	−13.4233			−0.460417
$851$	−5.88754	−	10.1975i	−0.201822	−	0.349566i
$852$	−4.21941	−	7.30823i	−0.144555	−	0.250376i
$853$	−12.6970			−0.434736			−0.217368	−	0.976090i	$-0.569747\pi$
$853$	−12.6970			−0.434736			−0.217368	+	0.976090i	$0.569747\pi$
$854$	0.316552	+	0.548284i	0.0108322	+	0.0187619i
$855$	−10.7096	+	18.5496i	−0.366261	+	0.634382i
$856$	8.08899	−	14.0105i	0.276476	−	0.478871i
$857$	−34.3824			−1.17448			−0.587240	−	0.809413i	$-0.699785\pi$
$857$	−34.3824			−1.17448			−0.587240	+	0.809413i	$0.699785\pi$
$858$	3.42040	+	2.29823i	0.116770	+	0.0784602i
$859$	−7.10370			−0.242375			−0.121188	−	0.992630i	$-0.538670\pi$
$859$	−7.10370			−0.242375			−0.121188	+	0.992630i	$0.538670\pi$
$860$	41.1464	−	71.2676i	1.40308	−	2.43020i
$861$	−5.82295	+	10.0856i	−0.198446	+	0.343718i
$862$	3.59539	+	6.22740i	0.122459	+	0.212106i
$863$	−18.0820			−0.615519			−0.307760	−	0.951464i	$-0.599579\pi$
$863$	−18.0820			−0.615519			−0.307760	+	0.951464i	$0.599579\pi$
$864$	−1.91875	−	3.32337i	−0.0652771	−	0.113063i
$865$	−27.7310	−	48.0315i	−0.942883	−	1.63312i
$866$	−12.5885			−0.427776
$867$	−4.86571	−	8.42767i	−0.165248	−	0.286219i
$868$	1.50000	−	2.59808i	0.0509133	−	0.0881845i
$869$	−15.1819	+	26.2957i	−0.515009	+	0.892022i
$870$	5.81016			0.196983
$871$	29.7551	−	14.5782i	1.00821	−	0.493965i
$872$	−3.74691			−0.126886
$873$	−0.224155	+	0.388249i	−0.00758651	+	0.0131402i
$874$	−1.56923	+	2.71799i	−0.0530800	+	0.0919373i
$875$	4.37211	+	7.57272i	0.147804	+	0.256005i
$876$	−28.0847			−0.948894
$877$	−16.5881	−	28.7315i	−0.560141	−	0.970192i	−0.997484	−	0.0708975i	$-0.977414\pi$
$877$	−16.5881	−	28.7315i	−0.560141	−	0.970192i	0.437343	−	0.899295i	$-0.355920\pi$
$878$	−2.88490	−	4.99680i	−0.0973608	−	0.168634i
$879$	−23.0651			−0.777967
$880$	19.1258	+	33.1269i	0.644732	+	1.11671i
$881$	−5.26991	+	9.12776i	−0.177548	+	0.307522i	−0.941040	−	0.338295i	$-0.890150\pi$
$881$	−5.26991	+	9.12776i	−0.177548	+	0.307522i	0.763492	+	0.645817i	$0.223483\pi$
$882$	−0.173648	+	0.300767i	−0.00584704	+	0.0101274i
$883$	29.1429			0.980737			0.490368	−	0.871515i	$-0.336862\pi$
$883$	29.1429			0.980737			0.490368	+	0.871515i	$0.336862\pi$
$884$	31.4616	−	15.4143i	1.05817	−	0.518439i
$885$	41.0378			1.37947
$886$	3.15910	−	5.47172i	0.106132	−	0.183826i
$887$	4.67499	−	8.09732i	0.156971	−	0.271882i	−0.776804	−	0.629742i	$-0.783160\pi$
$887$	4.67499	−	8.09732i	0.156971	−	0.271882i	0.933775	+	0.357861i	$0.116494\pi$
$888$	5.32295	+	9.21962i	0.178626	+	0.309390i
$889$	6.46791			0.216927
$890$	−0.0393628	−	0.0681784i	−0.00131945	−	0.00228535i
$891$	1.64543	+	2.84997i	0.0551240	+	0.0954775i
$892$	−14.7023			−0.492271
$893$	−0.492726	−	0.853427i	−0.0164884	−	0.0285588i
$894$	0.187319	−	0.324446i	0.00626488	−	0.0108511i
$895$	28.2793	−	48.9812i	0.945273	−	1.63726i
$896$	9.49794			0.317304
$897$	−0.365248	+	5.36056i	−0.0121953	+	0.178984i
$898$	−12.0496			−0.402101
$899$	3.78034	−	6.54775i	0.126082	−	0.218380i
$900$	7.02481	−	12.1673i	0.234160	−	0.405578i
$901$	17.6888	+	30.6379i	0.589300	+	1.02070i
$902$	13.3101			0.443179
$903$	6.19846	+	10.7361i	0.206272	+	0.357273i
$904$	−0.195937	−	0.339373i	−0.00651676	−	0.0112874i
$905$	−52.9059			−1.75865
$906$	−0.871644	−	1.50973i	−0.0289584	−	0.0501575i
$907$	25.9149	−	44.8860i	0.860491	−	1.49041i	−0.0109642	−	0.999940i	$-0.503490\pi$
$907$	25.9149	−	44.8860i	0.860491	−	1.49041i	0.871455	−	0.490475i	$-0.163177\pi$
$908$	−8.01754	+	13.8868i	−0.266071	+	0.460849i
$909$	−12.6382			−0.419181
$910$	3.67112	+	2.46669i	0.121697	+	0.0817701i
$911$	56.5485			1.87354			0.936768	−	0.349952i	$-0.113802\pi$
$911$	56.5485			1.87354			0.936768	+	0.349952i	$0.113802\pi$
$912$	−9.97818	+	17.2827i	−0.330410	+	0.572288i
$913$	17.9702	−	31.1253i	0.594726	−	1.03010i
$914$	5.11587	+	8.86094i	0.169218	+	0.293094i
$915$	6.43882			0.212861
$916$	2.97431	+	5.15165i	0.0982739	+	0.170215i
$917$	−3.13563	−	5.43107i	−0.103548	−	0.179350i
$918$	−1.79561			−0.0592639
$919$	16.6930	+	28.9131i	0.550651	+	0.953756i	0.998228	+	0.0595103i	$0.0189539\pi$
$919$	16.6930	+	28.9131i	0.550651	+	0.953756i	−0.447576	+	0.894246i	$0.647713\pi$
$920$	3.54576	−	6.14144i	0.116900	−	0.202477i
$921$	13.8858	−	24.0509i	0.457552	−	0.792503i
$922$	−7.61856			−0.250904
$923$	1.10055	−	16.1522i	0.0362250	−	0.531656i
$924$	−6.18479			−0.203465
$925$	−29.5351	+	51.1563i	−0.971108	+	1.68201i
$926$	1.06118	−	1.83803i	0.0348727	−	0.0604013i
$927$	−2.03209	−	3.51968i	−0.0667426	−	0.115601i
$928$	18.1762			0.596664
$929$	15.6643	+	27.1314i	0.513929	+	0.890152i	0.999869	+	0.0161598i	$0.00514404\pi$
$929$	15.6643	+	27.1314i	0.513929	+	0.890152i	−0.485940	+	0.873992i	$0.661523\pi$
$930$	0.979055	+	1.69577i	0.0321045	+	0.0556066i
$931$	6.06418			0.198745
$932$	−21.4795	−	37.2036i	−0.703585	−	1.21865i
$933$	−10.1814	+	17.6347i	−0.333324	+	0.577334i
$934$	0.695060	−	1.20388i	0.0227430	−	0.0393921i
$935$	60.0969			1.96538
$936$	0.330222	−	4.84651i	0.0107937	−	0.158413i
$937$	−32.3904			−1.05815			−0.529075	−	0.848575i	$-0.677461\pi$
$937$	−32.3904			−1.05815			−0.529075	+	0.848575i	$0.677461\pi$
$938$	1.59580	−	2.76401i	0.0521047	−	0.0902480i
$939$	−1.28359	+	2.22324i	−0.0418882	+	0.0725525i
$940$	0.539363	+	0.934204i	0.0175921	+	0.0304704i
$941$	−3.20708			−0.104548			−0.0522739	−	0.998633i	$-0.516647\pi$
$941$	−3.20708			−0.104548			−0.0522739	+	0.998633i	$0.516647\pi$
$942$	2.96404	+	5.13387i	0.0965737	+	0.167270i
$943$	8.67736	+	15.0296i	0.282574	+	0.489432i
$944$	38.2350			1.24444
$945$	1.76604	+	3.05888i	0.0574494	+	0.0995053i
$946$	7.08424	−	12.2703i	0.230329	−	0.398941i
$947$	−8.37211	+	14.5009i	−0.272057	+	0.471217i	−0.969388	−	0.245532i	$-0.921037\pi$
$947$	−8.37211	+	14.5009i	−0.272057	+	0.471217i	0.697331	+	0.716749i	$0.254371\pi$
$948$	17.3405			0.563193
$949$	−44.7220	−	30.0495i	−1.45174	−	0.975449i
$950$	15.7442			0.510810
$951$	−2.99660	+	5.19026i	−0.0971713	+	0.168306i
$952$	3.48293	−	6.03260i	0.112882	−	0.195518i
$953$	−3.40538	−	5.89830i	−0.110311	−	0.191065i	0.805585	−	0.592481i	$-0.201851\pi$
$953$	−3.40538	−	5.89830i	−0.110311	−	0.191065i	−0.915896	+	0.401416i	$0.868518\pi$
$954$	2.37639			0.0769385
$955$	0.525692	+	0.910526i	0.0170110	+	0.0294639i
$956$	6.41147	+	11.1050i	0.207362	+	0.359161i
$957$	−15.5871			−0.503859
$958$	6.65136	+	11.5205i	0.214896	+	0.372210i
$959$	−0.926022	+	1.60392i	−0.0299028	+	0.0517932i
$960$	9.26991	−	16.0560i	0.299185	−	0.518204i
$961$	−28.4519			−0.917804
$962$	−0.672609	+	9.87155i	−0.0216858	+	0.318271i
$963$	12.0077			0.386944
$964$	19.8131	−	34.3174i	0.638139	−	1.10529i
$965$	−27.2263	+	47.1573i	−0.876445	+	1.51805i
$966$	0.258770	+	0.448204i	0.00832580	+	0.0144207i
$967$	−40.6013			−1.30565			−0.652825	−	0.757509i	$-0.726416\pi$
$967$	−40.6013			−1.30565			−0.652825	+	0.757509i	$0.726416\pi$
$968$	−0.114685	−	0.198640i	−0.00368611	−	0.00638454i
$969$	15.6766	+	27.1527i	0.503606	+	0.872272i
$970$	0.549935			0.0176573
$971$	−21.4641	−	37.1769i	−0.688816	−	1.19306i	−0.972221	−	0.234064i	$-0.924798\pi$
$971$	−21.4641	−	37.1769i	−0.688816	−	1.19306i	0.283406	−	0.959000i	$-0.408536\pi$
$972$	0.939693	−	1.62760i	0.0301407	−	0.0522051i
$973$	−7.80200	+	13.5135i	−0.250121	+	0.433222i
$974$	−4.64084			−0.148702
$975$	24.2049	−	11.8589i	0.775176	−	0.379790i
$976$	5.99907			0.192025
$977$	11.1488	−	19.3103i	0.356683	−	0.617793i	−0.630722	−	0.776009i	$-0.717241\pi$
$977$	11.1488	−	19.3103i	0.356683	−	0.617793i	0.987404	+	0.158216i	$0.0505744\pi$
$978$	1.26011	−	2.18258i	0.0402940	−	0.0697913i
$979$	0.105600	+	0.182905i	0.00337499	+	0.00584566i
$980$	−6.63816			−0.212048
$981$	−1.39053	−	2.40847i	−0.0443962	−	0.0768965i
$982$	4.13832	+	7.16778i	0.132059	+	0.228733i
$983$	−9.35948			−0.298521			−0.149261	−	0.988798i	$-0.547689\pi$
$983$	−9.35948			−0.298521			−0.149261	+	0.988798i	$0.547689\pi$
$984$	−7.84524	−	13.5883i	−0.250097	−	0.433181i
$985$	−33.8298	+	58.5950i	−1.07791	+	1.86699i
$986$	4.25243	−	7.36543i	0.135425	−	0.234563i
$987$	−0.162504			−0.00517255
$988$	−36.9013	+	18.0794i	−1.17399	+	0.575183i
$989$	18.4739			0.587436
$990$	2.01842	−	3.49600i	0.0641495	−	0.111110i
$991$	−12.6077	+	21.8372i	−0.400497	+	0.693682i	−0.993786	−	0.111308i	$-0.964496\pi$
$991$	−12.6077	+	21.8372i	−0.400497	+	0.693682i	0.593289	+	0.804990i	$0.297829\pi$
$992$	3.06283	+	5.30498i	0.0972451	+	0.168433i
$993$	30.4270			0.965570
$994$	−0.779715	−	1.35051i	−0.0247311	−	0.0428354i
$995$	−2.46703	−	4.27303i	−0.0782102	−	0.135464i
$996$	−20.5253			−0.650368
$997$	−15.0351	−	26.0415i	−0.476166	−	0.824743i	0.523461	−	0.852049i	$-0.324640\pi$
$997$	−15.0351	−	26.0415i	−0.476166	−	0.824743i	−0.999627	+	0.0273061i	$0.991307\pi$
$998$	−2.07310	+	3.59072i	−0.0656229	+	0.113662i
$999$	−3.95084	+	6.84305i	−0.124999	+	0.216505i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.k.a.22.2	✓	6
3.2	odd	2		819.2.o.g.568.2		6
13.3	even	3	inner	273.2.k.a.211.2	yes	6
13.4	even	6		3549.2.a.n.1.2		3
13.9	even	3		3549.2.a.o.1.2		3
39.29	odd	6		819.2.o.g.757.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.k.a.22.2	✓	6	1.1	even	1	trivial
273.2.k.a.211.2	yes	6	13.3	even	3	inner
819.2.o.g.568.2		6	3.2	odd	2
819.2.o.g.757.2		6	39.29	odd	6
3549.2.a.n.1.2		3	13.4	even	6
3549.2.a.o.1.2		3	13.9	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.173648 + 0.300767i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.939693 + 1.62760i) q^{4} +3.53209 q^{5} +(-0.173648 - 0.300767i) q^{6} +(0.500000 + 0.866025i) q^{7} -1.34730 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.173648 + 0.300767i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.939693 + 1.62760i) q^{4} +3.53209 q^{5} +(-0.173648 - 0.300767i) q^{6} +(0.500000 + 0.866025i) q^{7} -1.34730 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-0.613341 + 1.06234i) q^{10} +(1.64543 - 2.84997i) q^{11} -1.87939 q^{12} +(-2.99273 - 2.01087i) q^{13} -0.347296 q^{14} +(-1.76604 + 3.05888i) q^{15} +(-1.64543 + 2.84997i) q^{16} +(2.58512 + 4.47756i) q^{17} +0.347296 q^{18} +(-3.03209 - 5.25173i) q^{19} +(3.31908 + 5.74881i) q^{20} -1.00000 q^{21} +(0.571452 + 0.989783i) q^{22} +(-0.745100 + 1.29055i) q^{23} +(0.673648 - 1.16679i) q^{24} +7.47565 q^{25} +(1.12449 - 0.550931i) q^{26} +1.00000 q^{27} +(-0.939693 + 1.62760i) q^{28} +(-2.36824 + 4.10191i) q^{29} +(-0.613341 - 1.06234i) q^{30} -1.59627 q^{31} +(-1.91875 - 3.32337i) q^{32} +(1.64543 + 2.84997i) q^{33} -1.79561 q^{34} +(1.76604 + 3.05888i) q^{35} +(0.939693 - 1.62760i) q^{36} +(-3.95084 + 6.84305i) q^{37} +2.10607 q^{38} +(3.23783 - 1.58634i) q^{39} -4.75877 q^{40} +(5.82295 - 10.0856i) q^{41} +(0.173648 - 0.300767i) q^{42} +(-6.19846 - 10.7361i) q^{43} +6.18479 q^{44} +(-1.76604 - 3.05888i) q^{45} +(-0.258770 - 0.448204i) q^{46} +0.162504 q^{47} +(-1.64543 - 2.84997i) q^{48} +(-0.500000 + 0.866025i) q^{49} +(-1.29813 + 2.24843i) q^{50} -5.17024 q^{51} +(0.460637 - 6.76055i) q^{52} +6.84255 q^{53} +(-0.173648 + 0.300767i) q^{54} +(5.81180 - 10.0663i) q^{55} +(-0.673648 - 1.16679i) q^{56} +6.06418 q^{57} +(-0.822481 - 1.42458i) q^{58} +(-5.80928 - 10.0620i) q^{59} -6.63816 q^{60} +(-0.911474 - 1.57872i) q^{61} +(0.277189 - 0.480105i) q^{62} +(0.500000 - 0.866025i) q^{63} -5.24897 q^{64} +(-10.5706 - 7.10257i) q^{65} -1.14290 q^{66} +(-4.59492 + 7.95864i) q^{67} +(-4.85844 + 8.41507i) q^{68} +(-0.745100 - 1.29055i) q^{69} -1.22668 q^{70} +(2.24510 + 3.88863i) q^{71} +(0.673648 + 1.16679i) q^{72} +14.9436 q^{73} +(-1.37211 - 2.37657i) q^{74} +(-3.73783 + 6.47410i) q^{75} +(5.69846 - 9.87003i) q^{76} +3.29086 q^{77} +(-0.0851223 + 1.24930i) q^{78} -9.22668 q^{79} +(-5.81180 + 10.0663i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(2.02229 + 3.50271i) q^{82} +10.9213 q^{83} +(-0.939693 - 1.62760i) q^{84} +(9.13088 + 15.8152i) q^{85} +4.30541 q^{86} +(-2.36824 - 4.10191i) q^{87} +(-2.21688 + 3.83975i) q^{88} +(-0.0320889 + 0.0555796i) q^{89} +1.22668 q^{90} +(0.245100 - 3.59721i) q^{91} -2.80066 q^{92} +(0.798133 - 1.38241i) q^{93} +(-0.0282185 + 0.0488759i) q^{94} +(-10.7096 - 18.5496i) q^{95} +3.83750 q^{96} +(-0.224155 - 0.388249i) q^{97} +(-0.173648 - 0.300767i) q^{98} -3.29086 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{3} + 12 q^{5} + 3 q^{7} - 6 q^{8} - 3 q^{9}+O(q^{10}) \) 6 * q - 3 * q^3 + 12 * q^5 + 3 * q^7 - 6 * q^8 - 3 * q^9	\( 6 q - 3 q^{3} + 12 q^{5} + 3 q^{7} - 6 q^{8} - 3 q^{9} + 3 q^{10} - 6 q^{11} - 6 q^{15} + 6 q^{16} - 6 q^{17} - 9 q^{19} + 3 q^{20} - 6 q^{21} + 3 q^{22} - 3 q^{23} + 3 q^{24} + 6 q^{25} - 6 q^{26} + 6 q^{27} - 9 q^{29} + 3 q^{30} + 18 q^{31} - 9 q^{32} - 6 q^{33} - 12 q^{34} + 6 q^{35} - 12 q^{37} - 12 q^{38} - 6 q^{40} - 6 q^{41} - 9 q^{43} + 30 q^{44} - 6 q^{45} + 21 q^{46} + 6 q^{47} + 6 q^{48} - 3 q^{49} + 6 q^{50} + 12 q^{51} - 6 q^{52} + 6 q^{53} - 3 q^{56} + 18 q^{57} - 30 q^{58} - 15 q^{59} - 6 q^{60} + 15 q^{61} - 9 q^{62} + 3 q^{63} - 6 q^{64} - 6 q^{65} - 6 q^{66} - 9 q^{67} - 21 q^{68} - 3 q^{69} + 6 q^{70} + 12 q^{71} + 3 q^{72} + 60 q^{73} + 21 q^{74} - 3 q^{75} + 6 q^{76} - 12 q^{77} + 21 q^{78} - 42 q^{79} - 3 q^{81} + 48 q^{83} + 3 q^{85} + 30 q^{86} - 9 q^{87} + 3 q^{88} + 9 q^{89} - 6 q^{90} + 12 q^{92} - 9 q^{93} - 15 q^{94} - 30 q^{95} + 18 q^{96} - 3 q^{97} + 12 q^{99}+O(q^{100}) \) 6 * q - 3 * q^3 + 12 * q^5 + 3 * q^7 - 6 * q^8 - 3 * q^9 + 3 * q^10 - 6 * q^11 - 6 * q^15 + 6 * q^16 - 6 * q^17 - 9 * q^19 + 3 * q^20 - 6 * q^21 + 3 * q^22 - 3 * q^23 + 3 * q^24 + 6 * q^25 - 6 * q^26 + 6 * q^27 - 9 * q^29 + 3 * q^30 + 18 * q^31 - 9 * q^32 - 6 * q^33 - 12 * q^34 + 6 * q^35 - 12 * q^37 - 12 * q^38 - 6 * q^40 - 6 * q^41 - 9 * q^43 + 30 * q^44 - 6 * q^45 + 21 * q^46 + 6 * q^47 + 6 * q^48 - 3 * q^49 + 6 * q^50 + 12 * q^51 - 6 * q^52 + 6 * q^53 - 3 * q^56 + 18 * q^57 - 30 * q^58 - 15 * q^59 - 6 * q^60 + 15 * q^61 - 9 * q^62 + 3 * q^63 - 6 * q^64 - 6 * q^65 - 6 * q^66 - 9 * q^67 - 21 * q^68 - 3 * q^69 + 6 * q^70 + 12 * q^71 + 3 * q^72 + 60 * q^73 + 21 * q^74 - 3 * q^75 + 6 * q^76 - 12 * q^77 + 21 * q^78 - 42 * q^79 - 3 * q^81 + 48 * q^83 + 3 * q^85 + 30 * q^86 - 9 * q^87 + 3 * q^88 + 9 * q^89 - 6 * q^90 + 12 * q^92 - 9 * q^93 - 15 * q^94 - 30 * q^95 + 18 * q^96 - 3 * q^97 + 12 * q^99

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