LMFDB - Embedded newform 192.2.r.a.157.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [192,2,Mod(13,192)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(192, base_ring=CyclotomicField(16))

chi = DirichletCharacter(H, H._module([0, 15, 0]))

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

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

chi := DirichletCharacter("192.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 192 = 2^{6} \cdot 3 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	192.r (of order $16$, degree $8$, 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:	$1.53312771881$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$16$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			157.11
Character	$\chi$	$=$	192.157
Dual form			192.2.r.a.181.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.898585 + 1.09204i) q^{2} +(0.980785 + 0.195090i) q^{3} +(-0.385091 + 1.96258i) q^{4} +(0.988484 - 1.47937i) q^{5} +(0.668273 + 1.24636i) q^{6} +(0.0771711 - 0.0319653i) q^{7} +(-2.48924 + 1.34301i) q^{8} +(0.923880 + 0.382683i) q^{9} +O(q^{10})$	\(q+(0.898585 + 1.09204i) q^{2} +(0.980785 + 0.195090i) q^{3} +(-0.385091 + 1.96258i) q^{4} +(0.988484 - 1.47937i) q^{5} +(0.668273 + 1.24636i) q^{6} +(0.0771711 - 0.0319653i) q^{7} +(-2.48924 + 1.34301i) q^{8} +(0.923880 + 0.382683i) q^{9} +(2.50377 - 0.249879i) q^{10} +(0.319217 + 1.60481i) q^{11} +(-0.760571 + 1.84974i) q^{12} +(-1.00438 - 1.50317i) q^{13} +(0.104252 + 0.0555502i) q^{14} +(1.25810 - 1.25810i) q^{15} +(-3.70341 - 1.51154i) q^{16} +(-3.24971 - 3.24971i) q^{17} +(0.412280 + 1.35278i) q^{18} +(-3.79804 + 2.53777i) q^{19} +(2.52272 + 2.50967i) q^{20} +(0.0819244 - 0.0162958i) q^{21} +(-1.46567 + 1.79066i) q^{22} +(2.39973 - 5.79347i) q^{23} +(-2.70342 + 0.831575i) q^{24} +(0.701978 + 1.69473i) q^{25} +(0.738989 - 2.44755i) q^{26} +(0.831470 + 0.555570i) q^{27} +(0.0330165 + 0.163764i) q^{28} +(1.15817 - 5.82249i) q^{29} +(2.50441 + 0.243383i) q^{30} +5.85544i q^{31} +(-1.67717 - 5.40251i) q^{32} +1.63625i q^{33} +(0.628664 - 6.46894i) q^{34} +(0.0289939 - 0.145762i) q^{35} +(-1.10682 + 1.66582i) q^{36} +(-3.44947 - 2.30487i) q^{37} +(-6.18420 - 1.86720i) q^{38} +(-0.691831 - 1.67023i) q^{39} +(-0.473770 + 5.01006i) q^{40} +(2.13458 - 5.15334i) q^{41} +(0.0914116 + 0.0748214i) q^{42} +(3.97932 - 0.791536i) q^{43} +(-3.27250 + 0.00848954i) q^{44} +(1.47937 - 0.988484i) q^{45} +(8.48305 - 2.58533i) q^{46} +(7.75629 + 7.75629i) q^{47} +(-3.33736 - 2.20500i) q^{48} +(-4.94481 + 4.94481i) q^{49} +(-1.21992 + 2.28944i) q^{50} +(-2.55328 - 3.82125i) q^{51} +(3.33686 - 1.39232i) q^{52} +(-1.74539 - 8.77469i) q^{53} +(0.140443 + 1.40722i) q^{54} +(2.68966 + 1.11409i) q^{55} +(-0.149168 + 0.183211i) q^{56} +(-4.22016 + 1.74805i) q^{57} +(7.39909 - 3.96724i) q^{58} +(-6.80186 + 10.1797i) q^{59} +(1.98464 + 2.95360i) q^{60} +(-1.16747 - 0.232224i) q^{61} +(-6.39436 + 5.26161i) q^{62} +0.0835294 q^{63} +(4.39266 - 6.68615i) q^{64} -3.21656 q^{65} +(-1.78685 + 1.47031i) q^{66} +(-6.59208 - 1.31125i) q^{67} +(7.62923 - 5.12637i) q^{68} +(3.48387 - 5.21398i) q^{69} +(0.185231 - 0.0993171i) q^{70} +(2.11094 - 0.874381i) q^{71} +(-2.81371 + 0.288185i) q^{72} +(10.8446 + 4.49199i) q^{73} +(-0.582647 - 5.83807i) q^{74} +(0.357866 + 1.79911i) q^{75} +(-3.51798 - 8.43122i) q^{76} +(0.0759327 + 0.113641i) q^{77} +(1.20228 - 2.25635i) q^{78} +(-0.0685134 + 0.0685134i) q^{79} +(-5.89689 + 3.98459i) q^{80} +(0.707107 + 0.707107i) q^{81} +(7.54575 - 2.29967i) q^{82} +(-7.79791 + 5.21040i) q^{83} +(0.000433384 + 0.167058i) q^{84} +(-8.01981 + 1.59524i) q^{85} +(4.44014 + 3.63430i) q^{86} +(2.27182 - 5.48467i) q^{87} +(-2.94989 - 3.56606i) q^{88} +(1.01445 + 2.44910i) q^{89} +(2.40880 + 0.727292i) q^{90} +(-0.125559 - 0.0838955i) q^{91} +(10.4460 + 6.94067i) q^{92} +(-1.14234 + 5.74293i) q^{93} +(-1.50047 + 15.4398i) q^{94} +8.12726i q^{95} +(-0.590968 - 5.62590i) q^{96} +16.9414i q^{97} +(-9.84326 - 0.956586i) q^{98} +(-0.319217 + 1.60481i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q+O(q^{10}) $ 128 * q	$ 128 q - 16 q^{22} - 80 q^{26} - 80 q^{28} - 80 q^{32} - 80 q^{34} - 80 q^{38} - 80 q^{40} - 16 q^{44} + 48 q^{50} - 32 q^{51} + 48 q^{52} + 16 q^{54} - 64 q^{55} + 112 q^{56} - 128 q^{59} + 96 q^{60} + 96 q^{62} - 32 q^{63} + 96 q^{64} + 96 q^{66} - 32 q^{67} + 96 q^{68} + 96 q^{70} - 128 q^{71} + 112 q^{74} - 64 q^{75} + 16 q^{76} + 48 q^{78} - 32 q^{79} + 48 q^{80} - 80 q^{82} - 80 q^{88} - 96 q^{94}+O(q^{100}) $ 128 * q - 16 * q^22 - 80 * q^26 - 80 * q^28 - 80 * q^32 - 80 * q^34 - 80 * q^38 - 80 * q^40 - 16 * q^44 + 48 * q^50 - 32 * q^51 + 48 * q^52 + 16 * q^54 - 64 * q^55 + 112 * q^56 - 128 * q^59 + 96 * q^60 + 96 * q^62 - 32 * q^63 + 96 * q^64 + 96 * q^66 - 32 * q^67 + 96 * q^68 + 96 * q^70 - 128 * q^71 + 112 * q^74 - 64 * q^75 + 16 * q^76 + 48 * q^78 - 32 * q^79 + 48 * q^80 - 80 * q^82 - 80 * q^88 - 96 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/192\mathbb{Z}\right)^\times$.

$n$	$65$	$127$	$133$
$\chi(n)$	$1$	$1$	$e\left(\frac{11}{16}\right)$

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 $

$2$	0.898585	+	1.09204i	0.635395	+	0.772187i
$2$	0.898585	+	1.09204i	0.635395	+	0.772187i
$3$	0.980785	+	0.195090i	0.566257	+	0.112635i
$3$	0.980785	+	0.195090i	0.566257	+	0.112635i
$4$	−0.385091	+	1.96258i	−0.192545	+	0.981288i
$5$	0.988484	−	1.47937i	0.442064	−	0.661595i	−0.541801	−	0.840506i	$-0.682258\pi$
$5$	0.988484	−	1.47937i	0.442064	−	0.661595i	0.983865	+	0.178911i	$0.0572575\pi$
$6$	0.668273	+	1.24636i	0.272821	+	0.508824i
$7$	0.0771711	−	0.0319653i	0.0291679	−	0.0120818i	−0.368052	−	0.929805i	$-0.619975\pi$
$7$	0.0771711	−	0.0319653i	0.0291679	−	0.0120818i	0.397220	+	0.917724i	$0.369975\pi$
$8$	−2.48924	+	1.34301i	−0.880080	+	0.474825i
$9$	0.923880	+	0.382683i	0.307960	+	0.127561i
$10$	2.50377	−	0.249879i	0.791760	−	0.0790187i
$11$	0.319217	+	1.60481i	0.0962476	+	0.483869i	0.998601	+	0.0528730i	$0.0168379\pi$
$11$	0.319217	+	1.60481i	0.0962476	+	0.483869i	−0.902354	+	0.430996i	$0.858162\pi$
$12$	−0.760571	+	1.84974i	−0.219558	+	0.533973i
$13$	−1.00438	−	1.50317i	−0.278566	−	0.416903i	0.665633	−	0.746279i	$-0.268162\pi$
$13$	−1.00438	−	1.50317i	−0.278566	−	0.416903i	−0.944199	+	0.329376i	$0.893162\pi$
$14$	0.104252	+	0.0555502i	0.0278625	+	0.0148464i
$15$	1.25810	−	1.25810i	0.324841	−	0.324841i
$16$	−3.70341	−	1.51154i	−0.925853	−	0.377885i
$17$	−3.24971	−	3.24971i	−0.788170	−	0.788170i	0.193024	−	0.981194i	$-0.438171\pi$
$17$	−3.24971	−	3.24971i	−0.788170	−	0.788170i	−0.981194	+	0.193024i	$0.938171\pi$
$18$	0.412280	+	1.35278i	0.0971752	+	0.318854i
$19$	−3.79804	+	2.53777i	−0.871331	+	0.582205i	−0.908865	−	0.417091i	$-0.863050\pi$
$19$	−3.79804	+	2.53777i	−0.871331	+	0.582205i	0.0375340	+	0.999295i	$0.488050\pi$
$20$	2.52272	+	2.50967i	0.564098	+	0.561179i
$21$	0.0819244	−	0.0162958i	0.0178774	−	0.00355603i
$22$	−1.46567	+	1.79066i	−0.312482	+	0.381770i
$23$	2.39973	−	5.79347i	0.500379	−	1.20802i	−0.448899	−	0.893583i	$-0.648184\pi$
$23$	2.39973	−	5.79347i	0.500379	−	1.20802i	0.949278	−	0.314439i	$-0.101816\pi$
$24$	−2.70342	+	0.831575i	−0.551833	+	0.169745i
$25$	0.701978	+	1.69473i	0.140396	+	0.338945i
$26$	0.738989	−	2.44755i	0.144928	−	0.480003i
$27$	0.831470	+	0.555570i	0.160016	+	0.106920i
$28$	0.0330165	+	0.163764i	0.00623953	+	0.0309484i
$29$	1.15817	−	5.82249i	0.215066	−	1.08121i	−0.710811	−	0.703383i	$-0.751672\pi$
$29$	1.15817	−	5.82249i	0.215066	−	1.08121i	0.925877	−	0.377826i	$-0.123328\pi$
$30$	2.50441	+	0.243383i	0.457240	+	0.0444354i
$31$			5.85544i			1.05167i	0.850587	+	0.525834i	$0.176247\pi$
$31$			5.85544i			1.05167i	−0.850587	+	0.525834i	$0.823753\pi$
$32$	−1.67717	−	5.40251i	−0.296485	−	0.955038i
$33$			1.63625i			0.284835i
$34$	0.628664	−	6.46894i	0.107815	−	1.10941i
$35$	0.0289939	−	0.145762i	0.00490086	−	0.0246383i
$36$	−1.10682	+	1.66582i	−0.184470	+	0.277636i
$37$	−3.44947	−	2.30487i	−0.567090	−	0.378917i	0.238723	−	0.971088i	$-0.423271\pi$
$37$	−3.44947	−	2.30487i	−0.567090	−	0.378917i	−0.805813	+	0.592170i	$0.798271\pi$
$38$	−6.18420	−	1.86720i	−1.00321	−	0.302900i
$39$	−0.691831	−	1.67023i	−0.110782	−	0.267451i
$40$	−0.473770	+	5.01006i	−0.0749097	+	0.792160i
$41$	2.13458	−	5.15334i	0.333366	−	0.804817i	−0.664954	−	0.746884i	$-0.731549\pi$
$41$	2.13458	−	5.15334i	0.333366	−	0.804817i	0.998320	−	0.0579331i	$-0.0184510\pi$
$42$	0.0914116	+	0.0748214i	0.0141051	+	0.0115452i
$43$	3.97932	−	0.791536i	0.606841	−	0.120708i	0.117900	−	0.993025i	$-0.462384\pi$
$43$	3.97932	−	0.791536i	0.606841	−	0.120708i	0.488940	+	0.872317i	$0.337384\pi$
$44$	−3.27250	+	0.00848954i	−0.493347	+	0.00127985i
$45$	1.47937	−	0.988484i	0.220532	−	0.147355i
$46$	8.48305	−	2.58533i	1.25076	−	0.381185i
$47$	7.75629	+	7.75629i	1.13137	+	1.13137i	0.989949	+	0.141422i	$0.0451673\pi$
$47$	7.75629	+	7.75629i	1.13137	+	1.13137i	0.141422	+	0.989949i	$0.454833\pi$
$48$	−3.33736	−	2.20500i	−0.481707	−	0.318264i
$49$	−4.94481	+	4.94481i	−0.706402	+	0.706402i
$50$	−1.21992	+	2.28944i	−0.172522	+	0.323776i
$51$	−2.55328	−	3.82125i	−0.357531	−	0.535083i
$52$	3.33686	−	1.39232i	0.462739	−	0.193081i
$53$	−1.74539	−	8.77469i	−0.239748	−	1.20530i	−0.893667	−	0.448731i	$-0.851876\pi$
$53$	−1.74539	−	8.77469i	−0.239748	−	1.20530i	0.653918	−	0.756565i	$-0.273124\pi$
$54$	0.140443	+	1.40722i	0.0191118	+	0.191499i
$55$	2.68966	+	1.11409i	0.362673	+	0.150224i
$56$	−0.149168	+	0.183211i	−0.0199334	+	0.0244826i
$57$	−4.22016	+	1.74805i	−0.558974	+	0.231535i
$58$	7.39909	−	3.96724i	0.971548	−	0.520924i
$59$	−6.80186	+	10.1797i	−0.885527	+	1.32528i	0.0594786	+	0.998230i	$0.481056\pi$
$59$	−6.80186	+	10.1797i	−0.885527	+	1.32528i	−0.945005	+	0.327055i	$0.893944\pi$
$60$	1.98464	+	2.95360i	0.256216	+	0.381309i
$61$	−1.16747	−	0.232224i	−0.149479	−	0.0297333i	0.119783	−	0.992800i	$-0.461780\pi$
$61$	−1.16747	−	0.232224i	−0.149479	−	0.0297333i	−0.269263	+	0.963067i	$0.586780\pi$
$62$	−6.39436	+	5.26161i	−0.812084	+	0.668225i
$63$	0.0835294			0.0105237
$64$	4.39266	−	6.68615i	0.549082	−	0.835768i
$65$	−3.21656			−0.398965
$66$	−1.78685	+	1.47031i	−0.219946	+	0.180983i
$67$	−6.59208	−	1.31125i	−0.805351	−	0.160194i	−0.224786	−	0.974408i	$-0.572168\pi$
$67$	−6.59208	−	1.31125i	−0.805351	−	0.160194i	−0.580565	+	0.814214i	$0.697168\pi$
$68$	7.62923	−	5.12637i	0.925181	−	0.621664i
$69$	3.48387	−	5.21398i	0.419409	−	0.627690i
$70$	0.185231	−	0.0993171i	0.0221393	−	0.0118707i
$71$	2.11094	−	0.874381i	0.250523	−	0.103770i	−0.253888	−	0.967234i	$-0.581710\pi$
$71$	2.11094	−	0.874381i	0.250523	−	0.103770i	0.504411	+	0.863464i	$0.331710\pi$
$72$	−2.81371	+	0.288185i	−0.331599	+	0.0339630i
$73$	10.8446	+	4.49199i	1.26927	+	0.525748i	0.912741	−	0.408538i	$-0.133961\pi$
$73$	10.8446	+	4.49199i	1.26927	+	0.525748i	0.356526	+	0.934286i	$0.383961\pi$
$74$	−0.582647	−	5.83807i	−0.0677313	−	0.678662i
$75$	0.357866	+	1.79911i	0.0413228	+	0.207743i
$76$	−3.51798	−	8.43122i	−0.403540	−	0.967127i
$77$	0.0759327	+	0.113641i	0.00865334	+	0.0129506i
$78$	1.20228	−	2.25635i	0.136132	−	0.255481i
$79$	−0.0685134	+	0.0685134i	−0.00770836	+	0.00770836i	−0.710950	−	0.703242i	$-0.751735\pi$
$79$	−0.0685134	+	0.0685134i	−0.00770836	+	0.00770836i	0.703242	+	0.710950i	$0.251735\pi$
$80$	−5.89689	+	3.98459i	−0.659293	+	0.445490i
$81$	0.707107	+	0.707107i	0.0785674	+	0.0785674i
$82$	7.54575	−	2.29967i	0.833289	−	0.253956i
$83$	−7.79791	+	5.21040i	−0.855932	+	0.571916i	−0.904292	−	0.426914i	$-0.859601\pi$
$83$	−7.79791	+	5.21040i	−0.855932	+	0.571916i	0.0483598	+	0.998830i	$0.484601\pi$
$84$	0.000433384		0.167058i	4.72861e−5		0.0182275i
$85$	−8.01981	+	1.59524i	−0.869871	+	0.173028i
$86$	4.44014	+	3.63430i	0.478793	+	0.391897i
$87$	2.27182	−	5.48467i	0.243565	−	0.588018i
$88$	−2.94989	−	3.56606i	−0.314459	−	0.380143i
$89$	1.01445	+	2.44910i	0.107532	+	0.259604i	0.968481	−	0.249086i	$-0.0801300\pi$
$89$	1.01445	+	2.44910i	0.107532	+	0.259604i	−0.860950	+	0.508690i	$0.830130\pi$
$90$	2.40880	+	0.727292i	0.253910	+	0.0766633i
$91$	−0.125559	−	0.0838955i	−0.0131621	−	0.00879464i
$92$	10.4460	+	6.94067i	1.08907	+	0.723615i
$93$	−1.14234	+	5.74293i	−0.118455	+	0.595514i
$94$	−1.50047	+	15.4398i	−0.154762	+	1.59250i
$95$			8.12726i			0.833840i
$96$	−0.590968	−	5.62590i	−0.0603154	−	0.574191i
$97$			16.9414i			1.72013i	0.510181	+	0.860067i	$0.329579\pi$
$97$			16.9414i			1.72013i	−0.510181	+	0.860067i	$0.670421\pi$
$98$	−9.84326	−	0.956586i	−0.994319	−	0.0966298i
$99$	−0.319217	+	1.60481i	−0.0320825	+	0.161290i
$100$	−3.59635	+	0.725063i	−0.359635	+	0.0725063i
$101$	2.50708	+	1.67518i	0.249464	+	0.166687i	0.674015	−	0.738717i	$-0.264568\pi$
$101$	2.50708	+	1.67518i	0.249464	+	0.166687i	−0.424551	+	0.905404i	$0.639568\pi$
$102$	1.87861	−	6.22200i	0.186010	−	0.616070i
$103$	4.53718	+	10.9537i	0.447061	+	1.07930i	0.973418	+	0.229037i	$0.0735578\pi$
$103$	4.53718	+	10.9537i	0.447061	+	1.07930i	−0.526356	+	0.850264i	$0.676442\pi$
$104$	4.51892	+	2.39285i	0.443116	+	0.234638i
$105$	0.0568735	−	0.137305i	0.00555028	−	0.0133996i
$106$	8.01390	−	9.79084i	0.778379	−	0.950970i
$107$	−0.668992	+	0.133071i	−0.0646739	+	0.0128644i	−0.227321	−	0.973820i	$-0.572997\pi$
$107$	−0.668992	+	0.133071i	−0.0646739	+	0.0128644i	0.162647	+	0.986684i	$0.447997\pi$
$108$	−1.41054	+	1.41788i	−0.135729	+	0.136435i
$109$	−4.09756	+	2.73790i	−0.392475	+	0.262243i	−0.736113	−	0.676859i	$-0.763341\pi$
$109$	−4.09756	+	2.73790i	−0.392475	+	0.262243i	0.343638	+	0.939102i	$0.388341\pi$
$110$	1.20025	+	3.93831i	0.114440	+	0.375503i
$111$	−2.93354	−	2.93354i	−0.278439	−	0.278439i
$112$	−0.334113	+	0.00173353i	−0.0315707	+	0.000163803i
$113$	−5.62191	+	5.62191i	−0.528865	+	0.528865i	−0.920234	−	0.391369i	$-0.872002\pi$
$113$	−5.62191	+	5.62191i	−0.528865	+	0.528865i	0.391369	+	0.920234i	$0.372002\pi$
$114$	−5.70110	−	3.03780i	−0.533957	−	0.284516i
$115$	−6.19859	−	9.27685i	−0.578022	−	0.865071i
$116$	10.9811	+	4.51517i	1.01957	+	0.419223i
$117$	−0.352692	−	1.77310i	−0.0326064	−	0.163924i
$118$	−17.2287	+	1.71944i	−1.58603	+	0.158287i
$119$	−0.354662	−	0.146906i	−0.0325118	−	0.0134668i
$120$	−1.44208	+	4.82136i	−0.131643	+	0.440128i
$121$	7.68915	−	3.18495i	0.699013	−	0.289541i
$122$	−0.795474	−	1.48360i	−0.0720188	−	0.134318i
$123$	3.09894	−	4.63789i	0.279422	−	0.418184i
$124$	−11.4917	−	2.25487i	−1.03199	−	0.202494i
$125$	11.9262	+	2.37227i	1.06671	+	0.212182i
$126$	0.0750582	+	0.0912172i	0.00668672	+	0.00812627i
$127$	−4.26606			−0.378551			−0.189276	−	0.981924i	$-0.560614\pi$
$127$	−4.26606			−0.378551			−0.189276	+	0.981924i	$0.560614\pi$
$128$	11.2487	−	1.21112i	0.994254	−	0.107049i
$129$	4.05728			0.357224
$130$	−2.89035	−	3.51260i	−0.253500	−	0.308075i
$131$	7.18899	+	1.42998i	0.628105	+	0.124938i	0.498871	−	0.866676i	$-0.333748\pi$
$131$	7.18899	+	1.42998i	0.628105	+	0.124938i	0.129234	+	0.991614i	$0.458748\pi$
$132$	−3.21127	−	0.630106i	−0.279505	−	0.0548437i
$133$	−0.211978	+	0.317248i	−0.0183809	+	0.0275089i
$134$	−4.49161	−	8.37707i	−0.388016	−	0.723668i
$135$	1.64379	−	0.680880i	0.141475	−	0.0586008i
$136$	12.4537	+	3.72493i	1.06790	+	0.319410i
$137$	12.7157	+	5.26701i	1.08638	+	0.449991i	0.852741	−	0.522333i	$-0.174938\pi$
$137$	12.7157	+	5.26701i	1.08638	+	0.449991i	0.233634	+	0.972325i	$0.424938\pi$
$138$	8.82442	−	0.880688i	0.751185	−	0.0749692i
$139$	−2.96745	−	14.9184i	−0.251696	−	1.26536i	−0.875285	−	0.483607i	$-0.839326\pi$
$139$	−2.96745	−	14.9184i	−0.251696	−	1.26536i	0.623590	−	0.781752i	$-0.285674\pi$
$140$	0.274904	+	0.113034i	0.0232336	+	0.00955313i
$141$	6.09408	+	9.12043i	0.513214	+	0.768079i
$142$	2.85172	+	1.51952i	0.239311	+	0.127515i
$143$	2.09168	−	2.09168i	0.174915	−	0.174915i
$144$	−2.84306	−	2.81371i	−0.236922	−	0.234476i
$145$	−7.46880	−	7.46880i	−0.620250	−	0.620250i
$146$	4.83939	+	15.8792i	0.400511	+	1.31417i
$147$	−5.81449	+	3.88512i	−0.479571	+	0.320439i
$148$	5.85183	−	5.88227i	0.481018	−	0.483520i
$149$	−19.8957	+	3.95750i	−1.62992	+	0.324211i	−0.923505	−	0.383586i	$-0.874689\pi$
$149$	−19.8957	+	3.95750i	−1.62992	+	0.324211i	−0.706415	+	0.707797i	$0.749689\pi$
$150$	−1.64312	+	2.00746i	−0.134161	+	0.163908i
$151$	8.12710	−	19.6206i	0.661374	−	1.59670i	−0.134277	−	0.990944i	$-0.542871\pi$
$151$	8.12710	−	19.6206i	0.661374	−	1.59670i	0.795651	−	0.605755i	$-0.207129\pi$
$152$	6.04600	−	11.4179i	0.490396	−	0.926116i
$153$	−1.75873	−	4.24595i	−0.142185	−	0.343265i
$154$	−0.0558686	+	0.185038i	−0.00450202	+	0.0149108i
$155$	8.66237	+	5.78801i	0.695778	+	0.464904i
$156$	3.54437	−	0.714582i	0.283777	−	0.0572124i
$157$	−4.47575	+	22.5011i	−0.357204	+	1.79578i	0.216024	+	0.976388i	$0.430691\pi$
$157$	−4.47575	+	22.5011i	−0.357204	+	1.79578i	−0.573228	+	0.819396i	$0.694309\pi$
$158$	−0.136384	−	0.0132541i	−0.0108501	−	0.00105444i
$159$		−	8.94660i		−	0.709511i
$160$	−9.65018	−	2.85914i	−0.762913	−	0.226035i
$161$		−	0.523797i		−	0.0412810i
$162$	−0.136792	+	1.40758i	−0.0107474	+	0.110590i
$163$	3.79619	−	19.0848i	0.297341	−	1.49483i	−0.486395	−	0.873739i	$-0.661688\pi$
$163$	3.79619	−	19.0848i	0.297341	−	1.49483i	0.783736	−	0.621094i	$-0.213312\pi$
$164$	9.29182	+	6.17379i	0.725569	+	0.482092i
$165$	2.42063	+	1.61741i	0.188446	+	0.125915i
$166$	−12.6970	−	3.83363i	−0.985481	−	0.297547i
$167$	−5.61122	−	13.5467i	−0.434210	−	1.04827i	−0.977916	−	0.208999i	$-0.932979\pi$
$167$	−5.61122	−	13.5467i	−0.434210	−	1.04827i	0.543706	−	0.839276i	$-0.317021\pi$
$168$	−0.182044	+	0.150589i	−0.0140450	+	0.0116182i
$169$	3.72416	−	8.99092i	0.286474	−	0.691610i
$170$	−8.94855	−	7.32448i	−0.686322	−	0.561762i
$171$	−4.48010	+	0.891147i	−0.342602	+	0.0681477i
$172$	0.0210508	+	8.11453i	0.00160511	+	0.618727i
$173$	9.81318	−	6.55696i	0.746082	−	0.498516i	−0.123475	−	0.992348i	$-0.539404\pi$
$173$	9.81318	−	6.55696i	0.746082	−	0.498516i	0.869558	+	0.493831i	$0.164404\pi$
$174$	8.03089	−	2.44752i	0.608820	−	0.185546i
$175$	0.108345	+	0.108345i	0.00819010	+	0.00819010i
$176$	1.24355	−	6.42579i	0.0937358	−	0.484362i
$177$	−8.65713	+	8.65713i	−0.650709	+	0.650709i
$178$	−1.76294	+	3.30854i	−0.132138	+	0.247986i
$179$	1.87012	+	2.79883i	0.139779	+	0.209194i	0.894754	−	0.446560i	$-0.147351\pi$
$179$	1.87012	+	2.79883i	0.139779	+	0.209194i	−0.754975	+	0.655754i	$0.772351\pi$
$180$	1.37028	+	3.28404i	0.102135	+	0.244778i
$181$	−3.68071	−	18.5042i	−0.273585	−	1.37540i	−0.836082	−	0.548604i	$-0.815159\pi$
$181$	−3.68071	−	18.5042i	−0.273585	−	1.37540i	0.562497	−	0.826799i	$-0.309841\pi$
$182$	−0.0212079	−	0.212502i	−0.00157204	−	0.0157517i
$183$	−1.09973	−	0.455525i	−0.0812947	−	0.0336734i
$184$	1.80716	+	17.6442i	0.133225	+	1.30075i
$185$	−6.81950	+	2.82473i	−0.501380	+	0.207678i
$186$	−7.29798	+	3.91303i	−0.535114	+	0.286917i
$187$	4.17781	−	6.25254i	0.305512	−	0.457231i
$188$	−18.2092	+	12.2354i	−1.32804	+	0.892361i
$189$	0.0819244	+	0.0162958i	0.00595912	+	0.00118534i
$190$	−8.87528	+	7.30304i	−0.643880	+	0.529818i
$191$	−21.6289			−1.56501			−0.782507	−	0.622642i	$-0.786059\pi$
$191$	−21.6289			−1.56501			−0.782507	+	0.622642i	$0.786059\pi$
$192$	5.61266	−	5.70071i	0.405059	−	0.411413i
$193$	24.3844			1.75523			0.877613	−	0.479370i	$-0.159135\pi$
$193$	24.3844			1.75523			0.877613	+	0.479370i	$0.159135\pi$
$194$	−18.5006	+	15.2232i	−1.32827	+	1.09297i
$195$	−3.15475	−	0.627519i	−0.225917	−	0.0449376i
$196$	−7.80037	−	11.6088i	−0.557169	−	0.829198i
$197$	8.05759	−	12.0590i	0.574079	−	0.859170i	−0.424858	−	0.905260i	$-0.639676\pi$
$197$	8.05759	−	12.0590i	0.574079	−	0.859170i	0.998937	+	0.0460896i	$0.0146760\pi$
$198$	−2.03936	+	1.09346i	−0.144931	+	0.0777091i
$199$	−12.9847	+	5.37846i	−0.920465	+	0.381269i	−0.792053	−	0.610452i	$-0.790988\pi$
$199$	−12.9847	+	5.37846i	−0.920465	+	0.381269i	−0.128411	+	0.991721i	$0.540988\pi$
$200$	−4.02343	−	3.27582i	−0.284499	−	0.231636i
$201$	−6.20961	−	2.57210i	−0.437992	−	0.181422i
$202$	0.423469	+	4.24312i	0.0297952	+	0.298545i
$203$	−0.0967408	−	0.486349i	−0.00678988	−	0.0341350i
$204$	8.48275	−	3.53948i	0.593911	−	0.247813i
$205$	−5.51371	−	8.25184i	−0.385094	−	0.576334i
$206$	−7.88483	+	14.7976i	−0.549362	+	1.03100i
$207$	4.43413	−	4.43413i	0.308193	−	0.308193i
$208$	1.44755	+	7.08500i	0.100369	+	0.491257i
$209$	−5.28505	−	5.28505i	−0.365575	−	0.365575i
$210$	0.201048	−	0.0612720i	0.0138736	−	0.00422817i
$211$	−12.1986	+	8.15083i	−0.839785	+	0.561127i	−0.899416	−	0.437094i	$-0.856008\pi$
$211$	−12.1986	+	8.15083i	−0.839785	+	0.561127i	0.0596306	+	0.998221i	$0.481008\pi$
$212$	17.8931	−	0.0464185i	1.22891	−	0.00318804i
$213$	2.24096	−	0.445755i	0.153548	−	0.0305427i
$214$	−0.746465	−	0.610989i	−0.0510273	−	0.0417664i
$215$	2.76252	−	6.66931i	0.188402	−	0.454843i
$216$	−2.81586	−	0.266279i	−0.191595	−	0.0181180i
$217$	0.187171	+	0.451871i	0.0127060	+	0.0306750i
$218$	−6.67189	−	2.01445i	−0.451878	−	0.136436i
$219$	9.75990	+	6.52136i	0.659513	+	0.440673i
$220$	−3.22225	+	4.84963i	−0.217244	+	0.326962i
$221$	−1.62090	+	8.14881i	−0.109033	+	0.548148i
$222$	0.567500	−	5.83956i	0.0380881	−	0.391926i
$223$		−	10.7458i		−	0.719592i	−0.933031	−	0.359796i	$-0.882846\pi$
$223$		−	10.7458i		−	0.719592i	0.933031	−	0.359796i	$-0.117154\pi$
$224$	−0.302122	−	0.363306i	−0.0201864	−	0.0242744i
$225$			1.83436i			0.122291i
$226$	−11.1911	−	1.08757i	−0.744420	−	0.0723442i
$227$	3.07100	−	15.4389i	0.203829	−	1.02472i	−0.734403	−	0.678713i	$-0.762538\pi$
$227$	3.07100	−	15.4389i	0.203829	−	1.02472i	0.938233	−	0.346005i	$-0.112462\pi$
$228$	−1.80553	−	8.95554i	−0.119574	−	0.593095i
$229$	8.68021	+	5.79993i	0.573604	+	0.383270i	0.808275	−	0.588805i	$-0.200401\pi$
$229$	8.68021	+	5.79993i	0.573604	+	0.383270i	−0.234671	+	0.972075i	$0.575401\pi$
$230$	4.56071	−	15.1051i	0.300724	−	0.996003i
$231$	0.0523034	+	0.126271i	0.00344131	+	0.00830805i
$232$	4.93670	+	16.0490i	0.324110	+	1.05367i
$233$	6.88685	−	16.6263i	0.451172	−	1.08923i	−0.520704	−	0.853737i	$-0.674331\pi$
$233$	6.88685	−	16.6263i	0.451172	−	1.08923i	0.971877	−	0.235490i	$-0.0756694\pi$
$234$	1.61937	−	1.97844i	0.105862	−	0.129335i
$235$	19.1414	−	3.80746i	1.24865	−	0.248371i
$236$	−17.3591	−	17.2693i	−1.12998	−	1.12413i
$237$	−0.0805632	+	0.0538306i	−0.00523314	+	0.00349667i
$238$	−0.158267	−	0.519311i	−0.0102589	−	0.0336619i
$239$	13.1459	+	13.1459i	0.850340	+	0.850340i	0.990175	−	0.139835i	$-0.0446572\pi$
$239$	13.1459	+	13.1459i	0.850340	+	0.850340i	−0.139835	+	0.990175i	$0.544657\pi$
$240$	−6.56094	+	2.75760i	−0.423507	+	0.178002i
$241$	14.5543	−	14.5543i	0.937523	−	0.937523i	−0.0606369	−	0.998160i	$-0.519313\pi$
$241$	14.5543	−	14.5543i	0.937523	−	0.937523i	0.998160	+	0.0606369i	$0.0193132\pi$
$242$	10.3874	+	5.53489i	0.667730	+	0.355796i
$243$	0.555570	+	0.831470i	0.0356398	+	0.0533388i
$244$	0.905340	−	2.20182i	0.0579585	−	0.140957i
$245$	2.42735	+	12.2031i	0.155077	+	0.779627i
$246$	7.84940	−	0.783380i	0.500460	−	0.0499465i
$247$	7.62938	+	3.16019i	0.485446	+	0.201078i
$248$	−7.86390	−	14.5756i	−0.499358	−	0.925552i
$249$	−8.66458	+	3.58899i	−0.549095	+	0.227443i
$250$	8.12611	+	15.1556i	0.513940	+	0.958521i
$251$	0.895742	−	1.34057i	0.0565387	−	0.0846162i	−0.802123	−	0.597159i	$-0.796296\pi$
$251$	0.895742	−	1.34057i	0.0565387	−	0.0846162i	0.858662	+	0.512542i	$0.171296\pi$
$252$	−0.0321664	+	0.163933i	−0.00202629	+	0.0103268i
$253$	10.0635	+	2.00175i	0.632685	+	0.125849i
$254$	−3.83341	−	4.65869i	−0.240530	−	0.292312i
$255$	−8.17693			−0.512059
$256$	11.4305	+	11.1957i	0.714406	+	0.699731i
$257$	−29.2778			−1.82630			−0.913150	−	0.407624i	$-0.866358\pi$
$257$	−29.2778			−1.82630			−0.913150	+	0.407624i	$0.866358\pi$
$258$	3.64581	+	4.43070i	0.226978	+	0.275843i
$259$	−0.339875	−	0.0676054i	−0.0211188	−	0.00420080i
$260$	1.23867	−	6.31274i	0.0768188	−	0.391500i
$261$	3.29818	−	4.93607i	0.204152	−	0.305535i
$262$	4.89833	+	9.13560i	0.302620	+	0.564399i
$263$	−1.57775	+	0.653525i	−0.0972882	+	0.0402981i	−0.430797	−	0.902449i	$-0.641767\pi$
$263$	−1.57775	+	0.653525i	−0.0972882	+	0.0402981i	0.333509	+	0.942747i	$0.391767\pi$
$264$	−2.19750	−	4.07303i	−0.135247	−	0.250678i
$265$	−14.7063	−	6.09156i	−0.903402	−	0.374201i
$266$	−0.536928	+	0.0535860i	−0.0329211	+	0.00328557i
$267$	0.517163	+	2.59995i	0.0316498	+	0.159114i
$268$	5.11197	−	12.4325i	0.312263	−	0.759437i
$269$	−0.295283	−	0.441923i	−0.0180037	−	0.0269445i	0.822359	−	0.568970i	$-0.192658\pi$
$269$	−0.295283	−	0.441923i	−0.0180037	−	0.0269445i	−0.840362	+	0.542025i	$0.817658\pi$
$270$	2.22063	+	1.18325i	0.135143	+	0.0720104i
$271$	−16.1098	+	16.1098i	−0.978600	+	0.978600i	−0.999776	−	0.0211756i	$-0.993259\pi$
$271$	−16.1098	+	16.1098i	−0.978600	+	0.978600i	0.0211756	+	0.999776i	$0.493259\pi$
$272$	7.12294	+	16.9471i	0.431892	+	1.02757i
$273$	−0.106779	−	0.106779i	−0.00646254	−	0.00646254i
$274$	5.67436	+	18.6189i	0.342800	+	1.12481i
$275$	−2.49564	+	1.66753i	−0.150492	+	0.100556i
$276$	8.89124	+	8.84522i	0.535189	+	0.532420i
$277$	0.930094	−	0.185007i	0.0558839	−	0.0111160i	−0.167069	−	0.985945i	$-0.553430\pi$
$277$	0.930094	−	0.185007i	0.0558839	−	0.0111160i	0.222953	+	0.974829i	$0.428430\pi$
$278$	13.6249	−	16.6460i	0.817167	−	0.998359i
$279$	−2.24078	+	5.40972i	−0.134152	+	0.323871i
$280$	0.123587	+	0.401776i	0.00738572	+	0.0240107i
$281$	6.07073	+	14.6560i	0.362150	+	0.874306i	0.994985	+	0.100020i	$0.0318908\pi$
$281$	6.07073	+	14.6560i	0.362150	+	0.874306i	−0.632836	+	0.774286i	$0.718109\pi$
$282$	−4.48380	+	14.8504i	−0.267007	+	0.884331i
$283$	21.0408	+	14.0590i	1.25074	+	0.835720i	0.991502	−	0.130092i	$-0.0415273\pi$
$283$	21.0408	+	14.0590i	1.25074	+	0.835720i	0.259242	+	0.965812i	$0.416527\pi$
$284$	0.903135	+	4.47960i	0.0535912	+	0.265815i
$285$	−1.58555	+	7.97110i	−0.0939199	+	0.472167i
$286$	4.16375	+	0.404641i	0.246208	+	0.0239269i
$287$		−	0.465922i		−	0.0275025i
$288$	0.517946	−	5.63309i	0.0305203	−	0.331933i
$289$			4.12122i			0.242425i
$290$	1.44486	−	14.8676i	0.0848449	−	0.873053i
$291$	−3.30510	+	16.6158i	−0.193748	+	0.974038i
$292$	−12.9920	+	19.5536i	−0.760301	+	1.14429i
$293$	12.6693	+	8.46537i	0.740150	+	0.494552i	0.867581	−	0.497295i	$-0.165673\pi$
$293$	12.6693	+	8.46537i	0.740150	+	0.494552i	−0.127432	+	0.991847i	$0.540673\pi$
$294$	−9.46750	−	2.85853i	−0.552156	−	0.166713i
$295$	8.33603	+	20.1250i	0.485342	+	1.17172i
$296$	11.6820	+	1.10470i	0.679004	+	0.0642092i
$297$	−0.626167	+	1.51170i	−0.0363339	+	0.0877178i
$298$	−22.1997	−	18.1707i	−1.28600	−	1.05260i
$299$	−11.1188	+	2.21167i	−0.643017	+	0.127904i
$300$	−3.66870	+	0.00951739i	−0.211813	+	0.000549487i
$301$	0.281787	−	0.188284i	0.0162419	−	0.0108525i
$302$	28.7293	−	8.75564i	1.65318	−	0.503831i
$303$	2.13210	+	2.13210i	0.122486	+	0.122486i
$304$	17.9017	−	3.65752i	1.02673	−	0.209773i
$305$	−1.49757	+	1.49757i	−0.0857508	+	0.0857508i
$306$	3.05637	−	5.73594i	0.174721	−	0.327902i
$307$	4.77082	+	7.14003i	0.272285	+	0.407503i	0.942261	−	0.334880i	$-0.108696\pi$
$307$	4.77082	+	7.14003i	0.272285	+	0.407503i	−0.669976	+	0.742383i	$0.733696\pi$
$308$	−0.252271	+	0.105262i	−0.0143745	+	0.00599783i
$309$	2.31303	+	11.6284i	0.131584	+	0.661517i
$310$	1.46315	+	14.6606i	0.0831014	+	0.832669i
$311$	−13.1320	−	5.43946i	−0.744648	−	0.308443i	−0.0220924	−	0.999756i	$-0.507033\pi$
$311$	−13.1320	−	5.43946i	−0.744648	−	0.308443i	−0.722556	+	0.691313i	$0.757033\pi$
$312$	3.96527	+	3.22847i	0.224489	+	0.182776i
$313$	2.79547	−	1.15792i	0.158009	−	0.0654497i	−0.302277	−	0.953220i	$-0.597747\pi$
$313$	2.79547	−	1.15792i	0.158009	−	0.0654497i	0.460286	+	0.887770i	$0.347747\pi$
$314$	−28.5939	+	15.3315i	−1.61365	+	0.865205i
$315$	0.0825675	−	0.123571i	0.00465215	−	0.00696244i
$316$	−0.108079	−	0.160847i	−0.00607991	−	0.00904833i
$317$	−9.76710	−	1.94280i	−0.548575	−	0.109118i	−0.0869814	−	0.996210i	$-0.527722\pi$
$317$	−9.76710	−	1.94280i	−0.548575	−	0.109118i	−0.461593	+	0.887092i	$0.652722\pi$
$318$	9.77002	−	8.03928i	0.547875	−	0.450820i
$319$	9.71372			0.543864
$320$	−5.54922	−	13.1075i	−0.310211	−	0.732733i
$321$	−0.682099			−0.0380710
$322$	0.572005	−	0.470676i	0.0318766	−	0.0262297i
$323$	20.5896	+	4.09552i	1.14563	+	0.227881i
$324$	−1.66005	+	1.11545i	−0.0922251	+	0.0619695i
$325$	1.84240	−	2.75734i	0.102198	−	0.152950i
$326$	24.2525	−	13.0037i	1.34322	−	0.720208i
$327$	−4.55296	+	1.88590i	−0.251779	+	0.104290i
$328$	1.60748	+	15.6947i	0.0887583	+	0.866594i
$329$	0.846494	+	0.350629i	0.0466687	+	0.0193308i
$330$	0.408865	+	4.09680i	0.0225073	+	0.225521i
$331$	−4.48646	−	22.5550i	−0.246598	−	1.23973i	−0.883369	−	0.468679i	$-0.844730\pi$
$331$	−4.48646	−	22.5550i	−0.246598	−	1.23973i	0.636770	−	0.771053i	$-0.280270\pi$
$332$	−7.22290	−	17.3105i	−0.396408	−	0.950036i
$333$	−2.30487	−	3.44947i	−0.126306	−	0.189030i
$334$	9.75133	−	18.3005i	0.533569	−	1.00136i
$335$	−8.45599	+	8.45599i	−0.462000	+	0.462000i
$336$	−0.328031	−	0.0634820i	−0.0178956	−	0.00346323i
$337$	−1.66468	−	1.66468i	−0.0906808	−	0.0906808i	0.660311	−	0.750992i	$-0.270424\pi$
$337$	−1.66468	−	1.66468i	−0.0906808	−	0.0906808i	−0.750992	+	0.660311i	$0.770424\pi$
$338$	13.1649	−	4.01218i	0.716076	−	0.218234i
$339$	−6.61066	+	4.41710i	−0.359042	+	0.239904i
$340$	−0.0424252	−	16.3538i	−0.00230083	−	0.886910i
$341$	−9.39689	+	1.86916i	−0.508870	+	0.101221i
$342$	−4.99891	−	4.09166i	−0.270310	−	0.221252i
$343$	−0.447291	+	1.07986i	−0.0241515	+	0.0583068i
$344$	−8.84245	+	7.31458i	−0.476753	+	0.394376i
$345$	−4.26967	−	10.3079i	−0.229871	−	0.554958i
$346$	15.9784	+	4.82438i	0.859005	+	0.259360i
$347$	2.21705	+	1.48139i	0.119018	+	0.0795250i	0.613654	−	0.789575i	$-0.289699\pi$
$347$	2.21705	+	1.48139i	0.119018	+	0.0795250i	−0.494637	+	0.869100i	$0.664699\pi$
$348$	9.88922	+	6.57072i	0.530118	+	0.352228i
$349$	−5.79847	+	29.1509i	−0.310385	+	1.56041i	0.439130	+	0.898423i	$0.355287\pi$
$349$	−5.79847	+	29.1509i	−0.310385	+	1.56041i	−0.749515	+	0.661987i	$0.769713\pi$
$350$	−0.0209596	+	0.215674i	−0.00112034	+	0.0115282i
$351$		−	1.80784i		−	0.0964955i
$352$	8.13464	−	4.41612i	0.433578	−	0.235380i
$353$		−	10.7508i		−	0.572206i	−0.958199	−	0.286103i	$-0.907640\pi$
$353$		−	10.7508i		−	0.572206i	0.958199	−	0.286103i	$-0.0923599\pi$
$354$	−17.2331	−	1.67474i	−0.915927	−	0.0890115i
$355$	0.793099	−	3.98718i	0.0420933	−	0.211618i
$356$	−5.19720	+	1.04781i	−0.275451	+	0.0555339i
$357$	−0.319187	−	0.213274i	−0.0168932	−	0.0112877i
$358$	−1.37596	+	4.55722i	−0.0727220	+	0.240857i
$359$	−8.35727	−	20.1762i	−0.441080	−	1.06486i	−0.975570	−	0.219687i	$-0.929496\pi$
$359$	−8.35727	−	20.1762i	−0.441080	−	1.06486i	0.534490	−	0.845175i	$-0.320504\pi$
$360$	−2.35497	+	4.44739i	−0.124118	+	0.234398i
$361$	0.713863	−	1.72342i	0.0375718	−	0.0907063i
$362$	16.8998	−	20.6470i	0.888234	−	1.08518i
$363$	8.16276	−	1.62367i	0.428434	−	0.0852207i
$364$	0.213003	−	0.214111i	0.0111644	−	0.0112225i
$365$	17.3651	−	11.6030i	0.908929	−	0.607327i
$366$	−0.490754	−	1.61028i	−0.0256521	−	0.0841706i
$367$	1.61948	+	1.61948i	0.0845362	+	0.0845362i	0.748110	−	0.663574i	$-0.230961\pi$
$367$	1.61948	+	1.61948i	0.0845362	+	0.0845362i	−0.663574	+	0.748110i	$0.730961\pi$
$368$	−17.6443	+	17.8283i	−0.919770	+	0.929365i
$369$	3.94420	−	3.94420i	0.205327	−	0.205327i
$370$	−9.21261	−	4.90889i	−0.478941	−	0.255201i
$371$	−0.415180	−	0.621360i	−0.0215551	−	0.0322594i
$372$	−10.8310	−	4.45348i	−0.561563	−	0.230902i
$373$	−2.62925	−	13.2182i	−0.136138	−	0.684410i	−0.987218	−	0.159375i	$-0.949052\pi$
$373$	−2.62925	−	13.2182i	−0.136138	−	0.684410i	0.851080	−	0.525035i	$-0.175948\pi$
$374$	10.5821	−	1.05611i	0.547189	−	0.0546101i
$375$	11.2342	+	4.65338i	0.580134	+	0.240299i
$376$	−29.7240	−	8.89053i	−1.53290	−	0.458494i
$377$	−9.91541	+	4.10710i	−0.510670	+	0.211526i
$378$	0.0558204	+	0.104108i	0.00287109	+	0.00535472i
$379$	−8.39709	+	12.5671i	−0.431330	+	0.645531i	−0.981931	−	0.189238i	$-0.939398\pi$
$379$	−8.39709	+	12.5671i	−0.431330	+	0.645531i	0.550602	+	0.834768i	$0.314398\pi$
$380$	−15.9504	−	3.12973i	−0.818237	−	0.160552i
$381$	−4.18409	−	0.832266i	−0.214357	−	0.0426383i
$382$	−19.4354	−	23.6196i	−0.994403	−	1.20848i
$383$	−10.3997			−0.531399			−0.265699	−	0.964056i	$-0.585603\pi$
$383$	−10.3997			−0.531399			−0.265699	+	0.964056i	$0.585603\pi$
$384$	11.2688	+	1.00666i	0.575060	+	0.0513710i
$385$	0.243176			0.0123934
$386$	21.9114	+	26.6287i	1.11526	+	1.35536i
$387$	3.97932	+	0.791536i	0.202280	+	0.0402360i
$388$	−33.2487	−	6.52396i	−1.68795	−	0.331204i
$389$	−16.8093	+	25.1570i	−0.852268	+	1.27551i	0.107356	+	0.994221i	$0.465762\pi$
$389$	−16.8093	+	25.1570i	−0.852268	+	1.27551i	−0.959623	+	0.281288i	$0.909238\pi$
$390$	−2.14954	−	4.00899i	−0.108846	−	0.203003i
$391$	−26.6255	+	11.0287i	−1.34651	+	0.557743i
$392$	5.66792	−	18.9498i	0.286273	−	0.957108i
$393$	6.77188	+	2.80500i	0.341596	+	0.141494i
$394$	20.4093	−	2.03688i	1.02821	−	0.102616i
$395$	0.0336323	+	0.169081i	0.00169223	+	0.00850739i
$396$	−3.02664	−	1.24449i	−0.152094	−	0.0625378i
$397$	−10.6617	−	15.9564i	−0.535096	−	0.800828i	0.461157	−	0.887319i	$-0.347435\pi$
$397$	−10.6617	−	15.9564i	−0.535096	−	0.800828i	−0.996253	+	0.0864910i	$0.972435\pi$
$398$	−17.5414	−	9.34683i	−0.879270	−	0.468514i
$399$	−0.269797	+	0.269797i	−0.0135068	+	0.0135068i
$400$	−0.0380694	−	7.33733i	−0.00190347	−	0.366867i
$401$	−20.4440	−	20.4440i	−1.02092	−	1.02092i	−0.999776	−	0.0211485i	$-0.993268\pi$
$401$	−20.4440	−	20.4440i	−1.02092	−	1.02092i	−0.0211485	−	0.999776i	$-0.506732\pi$
$402$	−2.77103	−	9.09237i	−0.138206	−	0.453486i
$403$	8.80169	−	5.88110i	0.438444	−	0.292959i
$404$	−4.25312	+	4.27525i	−0.211601	+	0.212701i
$405$	1.74504	−	0.347110i	0.0867116	−	0.0172480i
$406$	0.444181	−	0.542671i	0.0220444	−	0.0269323i
$407$	2.59775	−	6.27152i	0.128766	−	0.310867i
$408$	11.4877	+	6.08295i	0.568726	+	0.301151i
$409$	−3.88409	−	9.37703i	−0.192056	−	0.463664i	0.798291	−	0.602271i	$-0.205737\pi$
$409$	−3.88409	−	9.37703i	−0.192056	−	0.463664i	−0.990347	+	0.138607i	$0.955737\pi$
$410$	4.05679	−	13.4362i	0.200351	−	0.663564i
$411$	11.4438	+	7.64652i	0.564482	+	0.377175i
$412$	−23.2447	+	4.68638i	−1.14519	+	0.230882i
$413$	−0.199510	+	1.00300i	−0.00981722	+	0.0493545i
$414$	8.82668	+	0.857793i	0.433807	+	0.0421582i
$415$			16.6864i			0.819104i
$416$	−6.43634	+	7.94726i	−0.315568	+	0.389646i
$417$		−	15.2106i		−	0.744868i
$418$	1.02241	−	10.5205i	0.0500075	−	0.514576i
$419$	−3.56612	+	17.9281i	−0.174216	+	0.875845i	0.790482	+	0.612486i	$0.209830\pi$
$419$	−3.56612	+	17.9281i	−0.174216	+	0.875845i	−0.964698	+	0.263359i	$0.915170\pi$
$420$	0.247570	+	0.164493i	0.0120802	+	0.00802645i
$421$	−13.5835	−	9.07619i	−0.662018	−	0.442346i	0.178639	−	0.983915i	$-0.442831\pi$
$421$	−13.5835	−	9.07619i	−0.662018	−	0.442346i	−0.840657	+	0.541568i	$0.817831\pi$
$422$	−19.8625	−	5.99709i	−0.966890	−	0.291934i
$423$	4.19767	+	10.1341i	0.204098	+	0.492736i
$424$	16.1292	+	19.4983i	0.783303	+	0.946919i
$425$	3.22614	−	7.78859i	0.156491	−	0.377802i
$426$	2.50048	+	2.04667i	0.121149	+	0.0991614i
$427$	−0.0975182	+	0.0193976i	−0.00471923	+	0.000938714i
$428$	−0.00353900	−	1.36419i	−0.000171064	−	0.0659407i
$429$	2.45956	−	1.64343i	0.118749	−	0.0793453i
$430$	9.76550	−	2.97617i	0.470934	−	0.143524i
$431$	11.0209	+	11.0209i	0.530859	+	0.530859i	0.920828	−	0.389969i	$-0.127514\pi$
$431$	11.0209	+	11.0209i	0.530859	+	0.530859i	−0.389969	+	0.920828i	$0.627514\pi$
$432$	−2.23951	−	3.31430i	−0.107748	−	0.159460i
$433$	13.0346	−	13.0346i	0.626401	−	0.626401i	−0.320760	−	0.947161i	$-0.603938\pi$
$433$	13.0346	−	13.0346i	0.626401	−	0.626401i	0.947161	+	0.320760i	$0.103938\pi$
$434$	−0.325271	+	0.610442i	−0.0156135	+	0.0293021i
$435$	−5.86820	−	8.78238i	−0.281359	−	0.421083i
$436$	−3.79541	−	9.09611i	−0.181767	−	0.435625i
$437$	5.58821	+	28.0938i	0.267320	+	1.34391i
$438$	1.64853	+	16.5182i	0.0787700	+	0.789269i
$439$	−19.9535	−	8.26499i	−0.952326	−	0.394467i	−0.148222	−	0.988954i	$-0.547355\pi$
$439$	−19.9535	−	8.26499i	−0.952326	−	0.394467i	−0.804105	+	0.594488i	$0.797355\pi$
$440$	−8.19144	+	0.838984i	−0.390512	+	0.0399970i
$441$	−6.46071	+	2.67611i	−0.307653	+	0.127434i
$442$	−10.3553	+	5.55231i	−0.492552	+	0.264097i
$443$	−1.15844	+	1.73373i	−0.0550391	+	0.0823718i	−0.857968	−	0.513702i	$-0.828274\pi$
$443$	−1.15844	+	1.73373i	−0.0550391	+	0.0823718i	0.802929	+	0.596074i	$0.203274\pi$
$444$	6.88697	−	4.62761i	0.326841	−	0.219617i
$445$	4.62590	+	0.920149i	0.219289	+	0.0436192i
$446$	11.7348	−	9.65601i	0.555659	−	0.457225i
$447$	−20.2855			−0.959471
$448$	0.125262	−	0.656390i	0.00591806	−	0.0310115i
$449$	32.4423			1.53105			0.765523	−	0.643409i	$-0.222480\pi$
$449$	32.4423			1.53105			0.765523	+	0.643409i	$0.222480\pi$
$450$	−2.00319	+	1.64833i	−0.0944312	+	0.0777029i
$451$	8.95155	+	1.78057i	0.421512	+	0.0838440i
$452$	−8.86848	−	13.1984i	−0.417138	−	0.620799i
$453$	11.7987	−	17.6580i	0.554353	−	0.829647i
$454$	19.6194	−	10.5196i	0.920786	−	0.493707i
$455$	−0.248225	+	0.102818i	−0.0116370	+	0.00482020i
$456$	8.15736	−	10.0190i	0.382003	−	0.469184i
$457$	−26.2552	−	10.8752i	−1.22816	−	0.508722i	−0.328168	−	0.944619i	$-0.606431\pi$
$457$	−26.2552	−	10.8752i	−1.22816	−	0.508722i	−0.899997	+	0.435897i	$0.856431\pi$
$458$	1.46616	+	14.6908i	0.0685093	+	0.686458i
$459$	−0.896593	−	4.50748i	−0.0418494	−	0.210391i
$460$	20.5936	−	8.59279i	0.960179	−	0.400641i
$461$	−9.81173	−	14.6843i	−0.456978	−	0.683916i	0.529407	−	0.848368i	$-0.322414\pi$
$461$	−9.81173	−	14.6843i	−0.456978	−	0.683916i	−0.986385	+	0.164452i	$0.947414\pi$
$462$	−0.0908942	+	0.170583i	−0.00422878	+	0.00793623i
$463$	8.80899	−	8.80899i	0.409389	−	0.409389i	−0.472137	−	0.881525i	$-0.656517\pi$
$463$	8.80899	−	8.80899i	0.409389	−	0.409389i	0.881525	+	0.472137i	$0.156517\pi$
$464$	−13.0901	+	19.8125i	−0.607692	+	0.919770i
$465$	7.36674	+	7.36674i	0.341624	+	0.341624i
$466$	24.3450	−	7.41947i	1.12776	−	0.343700i
$467$	25.1096	−	16.7777i	1.16194	−	0.776381i	0.183518	−	0.983016i	$-0.441251\pi$
$467$	25.1096	−	16.7777i	1.16194	−	0.776381i	0.978418	+	0.206636i	$0.0662514\pi$
$468$	3.61567	−	0.00937981i	0.167134	−	0.000433582i
$469$	−0.550633	+	0.109528i	−0.0254259	+	0.00505752i
$470$	21.3581	+	17.4818i	0.985174	+	0.806375i
$471$	−8.77950	+	21.1956i	−0.404538	+	0.976641i
$472$	3.26006	−	34.4747i	0.150056	−	1.58683i
$473$	2.54054	+	6.13339i	0.116814	+	0.282014i
$474$	−0.131178	−	0.0396066i	−0.00602520	−	0.00181919i
$475$	−6.96697	−	4.65518i	−0.319667	−	0.213594i
$476$	0.424890	−	0.639478i	0.0194748	−	0.0293104i
$477$	1.74539	−	8.77469i	0.0799161	−	0.401765i
$478$	−2.54311	+	26.1686i	−0.116319	+	1.19692i
$479$		−	18.0515i		−	0.824792i	−0.911005	−	0.412396i	$-0.864692\pi$
$479$		−	18.0515i		−	0.824792i	0.911005	−	0.412396i	$-0.135308\pi$
$480$	−8.90696	−	4.68685i	−0.406545	−	0.213925i
$481$			7.50010i			0.341975i
$482$	28.9721	+	2.81556i	1.31964	+	0.128245i
$483$	0.102188	−	0.513732i	0.00464970	−	0.0233756i
$484$	3.28969	+	16.3170i	0.149531	+	0.741683i
$485$	25.0626	+	16.7463i	1.13803	+	0.760409i
$486$	−0.408769	+	1.35385i	−0.0185421	+	0.0614119i
$487$	11.1231	+	26.8535i	0.504036	+	1.21685i	0.947268	+	0.320443i	$0.103832\pi$
$487$	11.1231	+	26.8535i	0.504036	+	1.21685i	−0.443232	+	0.896407i	$0.646168\pi$
$488$	3.21800	−	0.989860i	0.145672	−	0.0448089i
$489$	7.44650	−	17.9774i	0.336743	−	0.812968i
$490$	−11.1451	+	13.6163i	−0.503482	+	0.615120i
$491$	−33.6744	+	6.69825i	−1.51970	+	0.302288i	−0.883203	−	0.468990i	$-0.844618\pi$
$491$	−33.6744	+	6.69825i	−1.51970	+	0.302288i	−0.636499	+	0.771278i	$0.719618\pi$
$492$	7.90883	+	7.86791i	0.356558	+	0.354713i
$493$	−22.6851	+	15.1577i	−1.02169	+	0.682668i
$494$	3.40460	+	11.1713i	0.153180	+	0.502619i
$495$	2.05857	+	2.05857i	0.0925260	+	0.0925260i
$496$	8.85072	−	21.6851i	0.397409	−	0.973689i
$497$	0.134954	−	0.134954i	0.00605351	−	0.00605351i
$498$	−11.7052	−	6.23703i	−0.524521	−	0.279488i
$499$	11.9330	+	17.8590i	0.534193	+	0.799477i	0.996172	−	0.0874143i	$-0.0278604\pi$
$499$	11.9330	+	17.8590i	0.534193	+	0.799477i	−0.461979	+	0.886891i	$0.652860\pi$
$500$	−9.24844	+	22.4926i	−0.413603	+	1.00590i
$501$	−2.86058	−	14.3811i	−0.127801	−	0.642500i
$502$	2.26886	−	0.226435i	0.101264	−	0.0101063i
$503$	2.44604	+	1.01318i	0.109064	+	0.0451756i	0.436548	−	0.899681i	$-0.356201\pi$
$503$	2.44604	+	1.01318i	0.109064	+	0.0451756i	−0.327484	+	0.944857i	$0.606201\pi$
$504$	−0.207925	+	0.112181i	−0.00926171	+	0.00499692i
$505$	4.95643	−	2.05302i	0.220558	−	0.0913582i
$506$	6.85690	+	12.7884i	0.304826	+	0.568515i
$507$	5.40665	−	8.09162i	0.240118	−	0.359361i
$508$	1.64282	−	8.37246i	0.0728883	−	0.371468i
$509$	5.37286	+	1.06873i	0.238148	+	0.0473705i	0.312721	−	0.949845i	$-0.398759\pi$
$509$	5.37286	+	1.06873i	0.238148	+	0.0473705i	−0.0745734	+	0.997216i	$0.523759\pi$
$510$	−7.34767	−	8.92951i	−0.325360	−	0.395406i
$511$	0.980479			0.0433738
$512$	−1.95485	+	22.5428i	−0.0863930	+	0.996261i
$513$	−4.56787			−0.201676
$514$	−26.3086	−	31.9725i	−1.16042	−	1.41025i
$515$	20.6895	+	4.11541i	0.911690	+	0.181346i
$516$	−1.56242	+	7.96272i	−0.0687817	+	0.350539i
$517$	−9.97146	+	14.9233i	−0.438544	+	0.656328i
$518$	−0.231579	−	0.431906i	−0.0101750	−	0.0189769i
$519$	10.9038	−	4.51651i	0.478625	−	0.198253i
$520$	8.00679	−	4.31986i	0.351121	−	0.189439i
$521$	23.2095	+	9.61371i	1.01683	+	0.421184i	0.827941	−	0.560814i	$-0.189512\pi$
$521$	23.2095	+	9.61371i	1.01683	+	0.421184i	0.188887	+	0.981999i	$0.439512\pi$
$522$	8.35406	−	0.833746i	0.365647	−	0.0364921i
$523$	2.92531	+	14.7065i	0.127915	+	0.643072i	0.990540	+	0.137227i	$0.0438190\pi$
$523$	2.92531	+	14.7065i	0.127915	+	0.643072i	−0.862625	+	0.505844i	$0.831181\pi$
$524$	−5.57486	+	13.5583i	−0.243539	+	0.592296i
$525$	0.0851260	+	0.127400i	0.00371520	+	0.00556020i
$526$	−2.13142	−	1.13571i	−0.0929341	−	0.0495194i
$527$	19.0285	−	19.0285i	0.828893	−	0.828893i
$528$	2.47326	−	6.05972i	0.107635	−	0.263715i
$529$	−11.5421	−	11.5421i	−0.501831	−	0.501831i
$530$	−6.56267	−	21.5336i	−0.285064	−	0.935361i
$531$	−10.1797	+	6.80186i	−0.441761	+	0.295176i
$532$	−0.540993	−	0.538193i	−0.0234550	−	0.0233336i
$533$	−9.89027	+	1.96730i	−0.428395	+	0.0852131i
$534$	−2.37453	+	2.90104i	−0.102756	+	0.125540i
$535$	−0.464427	+	1.12123i	−0.0200789	+	0.0484749i
$536$	18.1703	−	5.58921i	0.784838	−	0.241417i
$537$	1.28816	+	3.10989i	0.0555881	+	0.134202i
$538$	0.217259	−	0.719566i	0.00936670	−	0.0310227i
$539$	−9.51397	−	6.35703i	−0.409796	−	0.273817i
$540$	0.703271	+	3.48826i	0.0302640	+	0.150111i
$541$	5.76206	−	28.9678i	0.247730	−	1.24542i	−0.633874	−	0.773436i	$-0.718536\pi$
$541$	5.76206	−	28.9678i	0.247730	−	1.24542i	0.881605	−	0.471988i	$-0.156464\pi$
$542$	−32.0685	−	3.11648i	−1.37746	−	0.133864i
$543$		−	18.8667i		−	0.809647i
$544$	−12.1063	+	23.0069i	−0.519052	+	0.986413i
$545$			8.76818i			0.375588i
$546$	0.0206566	−	0.212556i	0.000884021	−	0.00909656i
$547$	3.52062	−	17.6994i	0.150531	−	0.756770i	−0.829591	−	0.558372i	$-0.811426\pi$
$547$	3.52062	−	17.6994i	0.150531	−	0.756770i	0.980122	−	0.198398i	$-0.0635739\pi$
$548$	−15.2336	+	22.9272i	−0.650748	+	0.979403i
$549$	−0.989734	−	0.661319i	−0.0422408	−	0.0282244i
$550$	−4.06355	−	1.22691i	−0.173270	−	0.0523156i
$551$	10.3774	+	25.0532i	0.442092	+	1.06730i
$552$	−1.66978	+	17.6577i	−0.0710707	+	0.751563i
$553$	−0.00309720	+	0.00747730i	−0.000131706	+	0.000317967i
$554$	1.03780	+	0.849453i	0.0440920	+	0.0360898i
$555$	−7.23955	+	1.44004i	−0.307302	+	0.0611261i
$556$	30.4212	−	0.0789189i	1.29014	−	0.00334691i
$557$	10.3031	−	6.88430i	0.436556	−	0.291697i	−0.317807	−	0.948156i	$-0.602946\pi$
$557$	10.3031	−	6.88430i	0.436556	−	0.291697i	0.754362	+	0.656458i	$0.227946\pi$
$558$	−7.92114	+	2.41408i	−0.335329	+	0.102196i
$559$	−5.18657	−	5.18657i	−0.219369	−	0.219369i
$560$	−0.327701	+	0.495991i	−0.0138479	+	0.0209594i
$561$	5.31735	−	5.31735i	0.224499	−	0.224499i
$562$	−10.5499	+	19.7992i	−0.445020	+	0.835178i
$563$	−4.21708	−	6.31131i	−0.177729	−	0.265990i	0.731900	−	0.681412i	$-0.238634\pi$
$563$	−4.21708	−	6.31131i	−0.177729	−	0.265990i	−0.909629	+	0.415422i	$0.863634\pi$
$564$	−20.2463	+	8.44790i	−0.852524	+	0.355721i
$565$	2.75972	+	13.8741i	0.116102	+	0.583686i
$566$	3.55397	+	35.6105i	0.149385	+	1.49682i
$567$	0.0771711	+	0.0319653i	0.00324088	+	0.00134242i
$568$	−4.08035	+	5.01156i	−0.171208	+	0.210280i
$569$	−1.66164	+	0.688272i	−0.0696594	+	0.0288539i	−0.417241	−	0.908796i	$-0.637003\pi$
$569$	−1.66164	+	0.688272i	−0.0696594	+	0.0288539i	0.347582	+	0.937650i	$0.387003\pi$
$570$	−10.1295	+	5.43123i	−0.424278	+	0.227489i
$571$	−22.2220	+	33.2576i	−0.929964	+	1.39179i	−0.00992985	+	0.999951i	$0.503161\pi$
$571$	−22.2220	+	33.2576i	−0.929964	+	1.39179i	−0.920034	+	0.391839i	$0.871839\pi$
$572$	3.29960	+	4.91058i	0.137963	+	0.205322i
$573$	−21.2133	−	4.21959i	−0.886199	−	0.176276i
$574$	0.508804	−	0.418670i	0.0212371	−	0.0174750i
$575$	11.5029			0.479704
$576$	6.61697	−	4.49619i	0.275707	−	0.187341i
$577$	15.3515			0.639091			0.319546	−	0.947571i	$-0.396470\pi$
$577$	15.3515			0.639091			0.319546	+	0.947571i	$0.396470\pi$
$578$	−4.50053	+	3.70327i	−0.187197	+	0.154036i
$579$	23.9158	+	4.75716i	0.993908	+	0.197701i
$580$	17.5343	−	11.7819i	0.728070	−	0.489218i
$581$	−0.435221	+	0.651355i	−0.0180560	+	0.0270228i
$582$	−21.1150	+	11.3215i	−0.875246	+	0.469289i
$583$	13.5246	−	5.60207i	0.560131	−	0.232014i
$584$	−33.0277	+	3.38276i	−1.36669	+	0.139980i
$585$	−2.97171	−	1.23092i	−0.122865	−	0.0508924i
$586$	2.13996	+	21.4422i	0.0884010	+	0.885770i
$587$	−8.52668	−	42.8665i	−0.351934	−	1.76929i	−0.599455	−	0.800408i	$-0.704616\pi$
$587$	−8.52668	−	42.8665i	−0.351934	−	1.76929i	0.247521	−	0.968882i	$-0.420384\pi$
$588$	−5.38573	−	12.9075i	−0.222104	−	0.532296i
$589$	−14.8598	−	22.2392i	−0.612286	−	0.916351i
$590$	−14.4866	+	27.1872i	−0.596403	+	1.11928i
$591$	10.2554	−	10.2554i	0.421849	−	0.421849i
$592$	9.29092	+	13.7499i	0.381855	+	0.565116i
$593$	1.80339	+	1.80339i	0.0740563	+	0.0740563i	0.743165	−	0.669108i	$-0.233324\pi$
$593$	1.80339	+	1.80339i	0.0740563	+	0.0740563i	−0.669108	+	0.743165i	$0.733324\pi$
$594$	−2.21350	+	0.674594i	−0.0908209	+	0.0276789i
$595$	−0.567905	+	0.379462i	−0.0232819	+	0.0155564i
$596$	−0.105249	−	40.5709i	−0.00431118	−	1.66185i
$597$	−13.7845	+	2.74191i	−0.564164	+	0.112219i
$598$	−12.4064	−	10.1548i	−0.507336	−	0.415259i
$599$	1.74765	−	4.21921i	0.0714072	−	0.172392i	−0.884146	−	0.467210i	$-0.845259\pi$
$599$	1.74765	−	4.21921i	0.0714072	−	0.172392i	0.955553	+	0.294818i	$0.0952591\pi$
$600$	−3.30704	−	3.99781i	−0.135009	−	0.163210i
$601$	9.99642	+	24.1335i	0.407763	+	0.984426i	0.985725	+	0.168363i	$0.0538480\pi$
$601$	9.99642	+	24.1335i	0.407763	+	0.984426i	−0.577963	+	0.816063i	$0.696152\pi$
$602$	0.458822	+	0.138533i	0.0187002	+	0.00564617i
$603$	−5.58850	−	3.73411i	−0.227581	−	0.152065i
$604$	35.3772	+	23.5058i	1.43948	+	0.956436i
$605$	2.88888	−	14.5234i	0.117450	−	0.590459i
$606$	−0.412460	+	4.24420i	−0.0167550	+	0.172409i
$607$		−	12.5801i		−	0.510612i	−0.966860	−	0.255306i	$-0.917824\pi$
$607$		−	12.5801i		−	0.510612i	0.966860	−	0.255306i	$-0.0821762\pi$
$608$	20.0803	+	16.2627i	0.814364	+	0.659539i
$609$		−	0.495877i		−	0.0200940i
$610$	−2.98110	−	0.289709i	−0.120701	−	0.0117300i
$611$	3.86870	−	19.4493i	0.156511	−	0.786833i
$612$	9.01027	−	1.81657i	0.364219	−	0.0734303i
$613$	15.2470	+	10.1877i	0.615819	+	0.411477i	0.823981	−	0.566617i	$-0.191748\pi$
$613$	15.2470	+	10.1877i	0.615819	+	0.411477i	−0.208162	+	0.978094i	$0.566748\pi$
$614$	−3.51020	+	11.6258i	−0.141660	+	0.469181i
$615$	−3.79791	−	9.16896i	−0.153146	−	0.369728i
$616$	−0.341636	−	0.180903i	−0.0137649	−	0.00728878i
$617$	−9.04572	+	21.8383i	−0.364167	+	0.879177i	0.630514	+	0.776178i	$0.282844\pi$
$617$	−9.04572	+	21.8383i	−0.364167	+	0.879177i	−0.994681	+	0.102999i	$0.967156\pi$
$618$	−10.6202	+	12.9750i	−0.427207	+	0.521932i
$619$	9.28437	−	1.84678i	0.373170	−	0.0742282i	−0.00494239	−	0.999988i	$-0.501573\pi$
$619$	9.28437	−	1.84678i	0.373170	−	0.0742282i	0.378113	+	0.925760i	$0.376573\pi$
$620$	−14.6952	+	14.7716i	−0.590174	+	0.593244i
$621$	5.21398	−	3.48387i	0.209230	−	0.139803i
$622$	−5.86014	−	19.2285i	−0.234970	−	0.770991i
$623$	0.156573	+	0.156573i	0.00627295	+	0.00627295i
$624$	0.0375191	+	7.23127i	0.00150197	+	0.289483i
$625$	8.81291	−	8.81291i	0.352516	−	0.352516i
$626$	3.77646	+	2.01227i	0.150938	+	0.0804264i
$627$	−4.15244	−	6.21456i	−0.165832	−	0.248186i
$628$	−42.4366	−	17.4490i	−1.69340	−	0.696290i
$629$	3.71965	+	18.6999i	0.148312	+	0.745615i
$630$	0.209138	−	0.0208722i	0.00833226	−	0.000831570i
$631$	−7.59591	−	3.14633i	−0.302388	−	0.125253i	0.226330	−	0.974051i	$-0.427327\pi$
$631$	−7.59591	−	3.14633i	−0.302388	−	0.125253i	−0.528718	+	0.848797i	$0.677327\pi$
$632$	0.0785324	−	0.262560i	0.00312385	−	0.0104441i
$633$	−13.5543	+	5.61439i	−0.538737	+	0.223152i
$634$	−6.65496	−	12.4118i	−0.264302	−	0.492935i
$635$	−4.21693	+	6.31108i	−0.167344	+	0.250448i
$636$	17.5584	+	3.44525i	0.696235	+	0.136613i
$637$	12.3994	+	2.46639i	0.491281	+	0.0977218i
$638$	8.72860	+	10.6077i	0.345569	+	0.419965i
$639$	2.28487			0.0903880
$640$	9.32746	−	17.8382i	0.368700	−	0.705116i
$641$	−22.6717			−0.895478			−0.447739	−	0.894164i	$-0.647771\pi$
$641$	−22.6717			−0.895478			−0.447739	+	0.894164i	$0.647771\pi$
$642$	−0.612924	−	0.744877i	−0.0241902	−	0.0293980i
$643$	−23.2840	−	4.63147i	−0.918230	−	0.182647i	−0.286719	−	0.958015i	$-0.592565\pi$
$643$	−23.2840	−	4.63147i	−0.918230	−	0.182647i	−0.631510	+	0.775367i	$0.717565\pi$
$644$	1.02799	+	0.201709i	0.0405085	+	0.00794845i
$645$	4.01056	−	6.00222i	0.157916	−	0.236337i
$646$	14.0290	+	26.1647i	0.551964	+	1.02944i
$647$	11.0606	−	4.58146i	0.434838	−	0.180116i	−0.154517	−	0.987990i	$-0.549382\pi$
$647$	11.0606	−	4.58146i	0.434838	−	0.180116i	0.589355	+	0.807874i	$0.299382\pi$
$648$	−2.70981	−	0.810511i	−0.106451	−	0.0318399i
$649$	−18.5078	−	7.66618i	−0.726495	−	0.300924i
$650$	4.66667	−	0.465740i	0.183042	−	0.0182678i
$651$	0.0954189	+	0.479703i	0.00373976	+	0.0188011i
$652$	35.9934	+	14.7997i	1.40961	+	0.579600i
$653$	8.21835	+	12.2996i	0.321609	+	0.481321i	0.956684	−	0.291129i	$-0.0940309\pi$
$653$	8.21835	+	12.2996i	0.321609	+	0.481321i	−0.635075	+	0.772450i	$0.719031\pi$
$654$	−6.15069	−	3.27736i	−0.240511	−	0.128155i
$655$	9.22168	−	9.22168i	0.360321	−	0.360321i
$656$	−15.6947	+	15.8584i	−0.612776	+	0.619168i
$657$	8.30011	+	8.30011i	0.323818	+	0.323818i
$658$	0.377746	+	1.23947i	0.0147261	+	0.0483197i
$659$	21.3093	−	14.2384i	0.830091	−	0.554649i	−0.0663583	−	0.997796i	$-0.521138\pi$
$659$	21.3093	−	14.2384i	0.830091	−	0.554649i	0.896449	+	0.443147i	$0.146138\pi$
$660$	−4.10645	+	4.12782i	−0.159843	+	0.160675i
$661$	49.6370	−	9.87341i	1.93066	−	0.384031i	0.930828	−	0.365458i	$-0.119087\pi$
$661$	49.6370	−	9.87341i	1.93066	−	0.384031i	0.999827	−	0.0185736i	$-0.00591251\pi$
$662$	20.5994	−	25.1669i	0.800618	−	0.978140i
$663$	−3.17951	+	7.67601i	−0.123482	+	0.298111i
$664$	12.4133	−	23.4426i	0.481729	−	0.909750i
$665$	0.259791	+	0.627190i	0.0100742	+	0.0243214i
$666$	1.69584	−	5.61664i	0.0657124	−	0.217641i
$667$	−30.9531	−	20.6822i	−1.19851	−	0.800819i
$668$	28.7472	−	5.79575i	1.11226	−	0.224244i
$669$	2.09640	−	10.5393i	0.0810515	−	0.407474i
$670$	−16.8327	−	1.63583i	−0.650303	−	0.0631977i
$671$		−	1.94770i		−	0.0751903i
$672$	−0.225439	−	0.415266i	−0.00869651	−	0.0160193i
$673$			50.1817i			1.93436i	0.254088	+	0.967181i	$0.418225\pi$
$673$			50.1817i			1.93436i	−0.254088	+	0.967181i	$0.581775\pi$
$674$	0.322036	−	3.31375i	0.0124044	−	0.127641i
$675$	−0.357866	+	1.79911i	−0.0137743	+	0.0692478i
$676$	16.2112	+	10.7713i	0.623509	+	0.414280i
$677$	−35.2201	−	23.5333i	−1.35362	−	0.904459i	−0.354092	−	0.935211i	$-0.615210\pi$
$677$	−35.2201	−	23.5333i	−1.35362	−	0.904459i	−0.999527	+	0.0307514i	$0.990210\pi$
$678$	−10.7639	−	3.24995i	−0.413384	−	0.124813i
$679$	0.541536	+	1.30738i	0.0207822	+	0.0501728i
$680$	17.8208	−	14.7416i	0.683398	−	0.565315i
$681$	6.02398	−	14.5432i	0.230839	−	0.557295i
$682$	−10.4851	−	8.58215i	−0.401495	−	0.328628i
$683$	−20.7139	+	4.12024i	−0.792593	+	0.157657i	−0.574752	−	0.818328i	$-0.694902\pi$
$683$	−20.7139	+	4.12024i	−0.792593	+	0.157657i	−0.217841	+	0.975984i	$0.569902\pi$
$684$	−0.0236999	−	9.13570i	−0.000906190	−	0.349312i
$685$	20.3611	−	13.6049i	0.777959	−	0.519816i
$686$	−1.58117	+	0.481884i	−0.0603695	+	0.0183984i
$687$	7.38191	+	7.38191i	0.281637	+	0.281637i
$688$	−15.9335	−	3.08352i	−0.607459	−	0.117558i
$689$	−11.4368	+	11.4368i	−0.435706	+	0.435706i
$690$	7.41994	−	13.9251i	0.282472	−	0.530121i
$691$	12.4279	+	18.5996i	0.472779	+	0.707564i	0.988839	−	0.148989i	$-0.0476018\pi$
$691$	12.4279	+	18.5996i	0.472779	+	0.707564i	−0.516060	+	0.856553i	$0.672602\pi$
$692$	9.08956	+	21.7841i	0.345533	+	0.828108i
$693$	0.0266640	+	0.134049i	0.00101288	+	0.00509210i
$694$	0.374480	+	3.75225i	0.0142151	+	0.142434i
$695$	−25.0031	−	10.3566i	−0.948421	−	0.392849i
$696$	1.71083	+	16.7037i	0.0648489	+	0.633154i
$697$	−23.6836	+	9.81009i	−0.897082	+	0.371584i
$698$	−37.0443	+	19.8624i	−1.40215	+	0.751802i
$699$	9.99815	−	14.9633i	0.378165	−	0.565964i
$700$	−0.254358	+	0.170912i	−0.00961382	+	0.00645989i
$701$	−13.3567	−	2.65681i	−0.504475	−	0.100346i	−0.0637091	−	0.997969i	$-0.520293\pi$
$701$	−13.3567	−	2.65681i	−0.504475	−	0.100346i	−0.440766	+	0.897622i	$0.645293\pi$
$702$	1.97423	−	1.62450i	0.0745125	−	0.0613128i
$703$	18.9505			0.714731
$704$	12.1322	+	4.91507i	0.457251	+	0.185244i
$705$	19.5164			0.735030
$706$	11.7402	−	9.66048i	0.441850	−	0.363577i
$707$	0.247022	+	0.0491357i	0.00929022	+	0.00184794i
$708$	−13.6565	−	20.3240i	−0.513242	−	0.763824i
$709$	−5.62837	+	8.42345i	−0.211378	+	0.316349i	−0.921975	−	0.387250i	$-0.873425\pi$
$709$	−5.62837	+	8.42345i	−0.211378	+	0.316349i	0.710597	+	0.703599i	$0.248425\pi$
$710$	5.06682	−	2.71673i	0.190154	−	0.101957i
$711$	−0.0895170	+	0.0370792i	−0.00335715	+	0.00139058i
$712$	−5.81438	−	4.73399i	−0.217903	−	0.177414i
$713$	33.9233	+	14.0515i	1.27044	+	0.526232i
$714$	−0.0539135	−	0.540209i	−0.00201766	−	0.0202168i
$715$	−1.02678	−	5.16198i	−0.0383994	−	0.193047i
$716$	−6.21307	+	2.59244i	−0.232193	+	0.0968842i
$717$	10.3287	+	15.4580i	0.385732	+	0.577289i
$718$	14.5235	−	27.2565i	0.542012	−	1.01720i
$719$	3.90775	−	3.90775i	0.145735	−	0.145735i	−0.630475	−	0.776210i	$-0.717140\pi$
$719$	3.90775	−	3.90775i	0.145735	−	0.145735i	0.776210	+	0.630475i	$0.217140\pi$
$720$	−6.97285	+	1.42464i	−0.259863	+	0.0530930i
$721$	0.700278	+	0.700278i	0.0260797	+	0.0260797i
$722$	2.52350	−	0.769073i	0.0939151	−	0.0286219i
$723$	17.1140	−	11.4352i	0.636477	−	0.425280i
$724$	37.7332	−	0.0978879i	1.40234	−	0.00363798i
$725$	10.6805	−	2.12449i	0.396665	−	0.0789016i
$726$	9.10804	+	7.45503i	0.338031	+	0.276682i
$727$	−2.17829	+	5.25885i	−0.0807882	+	0.195040i	−0.959112	−	0.283026i	$-0.908662\pi$
$727$	−2.17829	+	5.25885i	−0.0807882	+	0.195040i	0.878324	+	0.478066i	$0.158662\pi$
$728$	0.425218	+	0.0402102i	0.0157596	+	0.00149029i
$729$	0.382683	+	0.923880i	0.0141735	+	0.0342178i
$730$	28.2749	+	8.53705i	1.04650	+	0.315970i
$731$	−15.5039	−	10.3594i	−0.573432	−	0.383155i
$732$	1.31750	−	1.98289i	0.0486962	−	0.0732898i
$733$	−2.07450	+	10.4292i	−0.0766234	+	0.385212i	0.923376	+	0.383897i	$0.125418\pi$
$733$	−2.07450	+	10.4292i	−0.0766234	+	0.385212i	−0.999999	+	0.00131444i	$0.999582\pi$
$734$	−0.313292	+	3.22377i	−0.0115638	+	0.118992i
$735$			12.4422i			0.458936i
$736$	−35.3240	−	3.24794i	−1.30206	−	0.119721i
$737$		−	10.9976i		−	0.405103i
$738$	7.85141	+	0.763015i	0.289014	+	0.0280870i
$739$	−8.94601	+	44.9747i	−0.329084	+	1.65442i	0.362396	+	0.932024i	$0.381959\pi$
$739$	−8.94601	+	44.9747i	−0.329084	+	1.65442i	−0.691480	+	0.722395i	$0.743041\pi$
$740$	−2.91762	−	14.4716i	−0.107254	−	0.531986i
$741$	6.86626	+	4.58789i	0.252238	+	0.168540i
$742$	0.305474	−	1.01174i	0.0112143	−	0.0371420i
$743$	−8.30094	−	20.0402i	−0.304532	−	0.735205i	−0.999864	−	0.0165159i	$-0.994743\pi$
$743$	−8.30094	−	20.0402i	−0.304532	−	0.735205i	0.695332	−	0.718689i	$-0.255257\pi$
$744$	−4.86924	−	15.8297i	−0.178515	−	0.580345i
$745$	−13.8120	+	33.3451i	−0.506032	+	1.22167i
$746$	12.0721	−	14.7489i	0.441991	−	0.539995i
$747$	−9.19827	+	1.82965i	−0.336547	+	0.0669434i
$748$	10.6622	+	10.6071i	0.389850	+	0.387833i
$749$	−0.0473732	+	0.0316538i	−0.00173098	+	0.00115660i
$750$	5.01326	+	16.4497i	0.183058	+	0.600657i
$751$	−27.4363	−	27.4363i	−1.00117	−	1.00117i	−0.999999	−	0.00116606i	$-0.999629\pi$
$751$	−27.4363	−	27.4363i	−1.00117	−	1.00117i	−0.00116606	−	0.999999i	$-0.500371\pi$
$752$	−17.0008	−	40.4487i	−0.619955	−	1.47501i
$753$	1.14006	−	1.14006i	0.0415462	−	0.0415462i
$754$	−13.3949	−	7.13742i	−0.487815	−	0.259930i
$755$	−20.9926	−	31.4176i	−0.763999	−	1.14340i
$756$	−0.0635300	+	0.154508i	−0.00231056	+	0.00561938i
$757$	−3.79534	−	19.0804i	−0.137944	−	0.693490i	−0.986418	−	0.164254i	$-0.947478\pi$
$757$	−3.79534	−	19.0804i	−0.137944	−	0.693490i	0.848474	−	0.529237i	$-0.177522\pi$
$758$	−21.2693	+	2.12270i	−0.772535	+	0.0771000i
$759$	9.47959	+	3.92657i	0.344087	+	0.142526i
$760$	−10.9150	−	20.2307i	−0.395928	−	0.733846i
$761$	−12.8737	+	5.33248i	−0.466673	+	0.193302i	−0.603613	−	0.797277i	$-0.706273\pi$
$761$	−12.8737	+	5.33248i	−0.466673	+	0.193302i	0.136941	+	0.990579i	$0.456273\pi$
$762$	−2.85089	−	5.31704i	−0.103277	−	0.192616i
$763$	−0.228695	+	0.342266i	−0.00827932	+	0.0123909i
$764$	8.32909	−	42.4484i	0.301336	−	1.53573i
$765$	−8.01981	−	1.59524i	−0.289957	−	0.0576760i
$766$	−9.34500	−	11.3568i	−0.337648	−	0.410339i
$767$	22.1335			0.799193
$768$	9.02669	+	13.2106i	0.325723	+	0.476695i
$769$	−7.54592			−0.272113			−0.136056	−	0.990701i	$-0.543443\pi$
$769$	−7.54592			−0.272113			−0.136056	+	0.990701i	$0.543443\pi$
$770$	0.218514	+	0.265557i	0.00787471	+	0.00957002i
$771$	−28.7153	−	5.71182i	−1.03415	−	0.205706i
$772$	−9.39020	+	47.8562i	−0.337961	+	1.72238i
$773$	−0.978093	+	1.46382i	−0.0351796	+	0.0526500i	−0.848643	−	0.528967i	$-0.822580\pi$
$773$	−0.978093	+	1.46382i	−0.0351796	+	0.0526500i	0.813463	+	0.581617i	$0.197580\pi$
$774$	2.71137	+	5.05683i	0.0974582	+	0.181764i
$775$	−9.92336	+	4.11039i	−0.356458	+	0.147650i
$776$	−22.7524	−	42.1712i	−0.816763	−	1.51386i
$777$	−0.320156	−	0.132613i	−0.0114855	−	0.00475746i
$778$	−42.5770	+	4.24923i	−1.52646	+	0.152342i
$779$	4.97076	+	24.9897i	0.178096	+	0.895349i
$780$	2.44642	−	5.94979i	0.0875959	−	0.213037i
$781$	2.07707	+	3.10855i	0.0743233	+	0.111233i
$782$	−35.9690	−	19.1659i	−1.28625	−	0.685371i
$783$	4.19778	−	4.19778i	0.150016	−	0.150016i
$784$	25.7870	−	10.8384i	0.920963	−	0.387086i
$785$	28.8633	+	28.8633i	1.03018	+	1.03018i
$786$	3.02194	+	9.91568i	0.107789	+	0.353681i
$787$	−17.1189	+	11.4385i	−0.610223	+	0.407738i	−0.821925	−	0.569596i	$-0.807100\pi$
$787$	−17.1189	+	11.4385i	−0.610223	+	0.407738i	0.211701	+	0.977334i	$0.432100\pi$
$788$	20.5639	+	20.4574i	0.732557	+	0.728766i
$789$	−1.67493	+	0.333164i	−0.0596291	+	0.0118610i
$790$	−0.154421	+	0.188661i	−0.00549407	+	0.00671227i
$791$	−0.254143	+	0.613555i	−0.00903627	+	0.0218155i
$792$	−1.36067	−	4.42348i	−0.0483492	−	0.157182i
$793$	0.823517	+	1.98815i	0.0292439	+	0.0706011i
$794$	7.84451	−	25.9811i	0.278391	−	0.922036i
$795$	−13.2353	−	8.84357i	−0.469409	−	0.313649i
$796$	−5.55533	−	27.5548i	−0.196903	−	0.976652i
$797$	5.75833	−	28.9491i	0.203971	−	1.02543i	−0.734115	−	0.679026i	$-0.762403\pi$
$797$	5.75833	−	28.9491i	0.203971	−	1.02543i	0.938085	−	0.346404i	$-0.112597\pi$
$798$	−0.537065	−	0.0521930i	−0.0190119	−	0.00184761i
$799$		−	50.4114i		−	1.78343i
$800$	7.97843	−	6.63479i	0.282080	−	0.234575i
$801$			2.65089i			0.0936645i
$802$	3.95494	−	40.6963i	0.139654	−	1.43704i
$803$	−3.74702	+	18.8375i	−0.132229	+	0.664762i
$804$	7.43921	−	11.1963i	0.262361	−	0.394864i
$805$	−0.774890	−	0.517765i	−0.0273113	−	0.0182488i
$806$	14.3315	+	4.32711i	0.504804	+	0.152416i
$807$	−0.203395	−	0.491038i	−0.00715983	−	0.0172854i
$808$	−8.49052	−	0.802896i	−0.298695	−	0.0282458i
$809$	−12.3013	+	29.6979i	−0.432490	+	1.04412i	0.545992	+	0.837791i	$0.316153\pi$
$809$	−12.3013	+	29.6979i	−0.432490	+	1.04412i	−0.978482	+	0.206333i	$0.933847\pi$
$810$	1.94712	+	1.59374i	0.0684149	+	0.0559983i
$811$	−4.39380	+	0.873981i	−0.154287	+	0.0306896i	−0.271629	−	0.962402i	$-0.587563\pi$
$811$	−4.39380	+	0.873981i	−0.154287	+	0.0306896i	0.117342	+	0.993092i	$0.462563\pi$
$812$	0.991751	−	0.00257281i	0.0348036	−	9.02880e-5i
$813$	−18.9431	+	12.6574i	−0.664364	+	0.443914i
$814$	9.18302	−	2.79865i	0.321865	−	0.0980927i
$815$	−24.4810	−	24.4810i	−0.857531	−	0.857531i
$816$	3.67987	+	18.0111i	0.128821	+	0.630513i
$817$	−13.1049	+	13.1049i	−0.458482	+	0.458482i
$818$	6.74988	−	12.6676i	0.236004	−	0.442913i
$819$	−0.0838955	−	0.125559i	−0.00293155	−	0.00438737i
$820$	18.3182	−	7.64336i	0.639698	−	0.266918i
$821$	3.07098	+	15.4389i	0.107178	+	0.538820i	0.996647	+	0.0818240i	$0.0260745\pi$
$821$	3.07098	+	15.4389i	0.107178	+	0.538820i	−0.889469	+	0.456996i	$0.848925\pi$
$822$	1.93296	+	19.3681i	0.0674198	+	0.675541i
$823$	37.0438	+	15.3441i	1.29127	+	0.534860i	0.919363	−	0.393411i	$-0.128705\pi$
$823$	37.0438	+	15.3441i	1.29127	+	0.534860i	0.371904	+	0.928271i	$0.378705\pi$
$824$	−26.0051	−	21.1730i	−0.905929	−	0.737596i
$825$	−2.77300	+	1.14861i	−0.0965435	+	0.0399896i
$826$	−1.27459	+	0.683411i	−0.0443487	+	0.0237789i
$827$	9.88669	−	14.7965i	0.343794	−	0.514524i	−0.618772	−	0.785570i	$-0.712370\pi$
$827$	9.88669	−	14.7965i	0.343794	−	0.514524i	0.962566	+	0.271047i	$0.0873697\pi$
$828$	6.99478	+	10.4099i	0.243085	+	0.361768i
$829$	6.86119	+	1.36478i	0.238299	+	0.0474006i	0.312795	−	0.949821i	$-0.398735\pi$
$829$	6.86119	+	1.36478i	0.238299	+	0.0474006i	−0.0744958	+	0.997221i	$0.523735\pi$
$830$	−18.2222	+	14.9942i	−0.632501	+	0.520455i
$831$	0.948316			0.0328967
$832$	−14.4623	+	0.112557i	−0.501390	+	0.00390220i
$833$	32.1384			1.11353
$834$	16.6106	−	13.6680i	0.575177	−	0.473286i
$835$	−25.5872	−	5.08961i	−0.885482	−	0.176133i
$836$	12.4075	−	8.33709i	0.429124	−	0.288344i
$837$	−3.25311	+	4.86862i	−0.112444	+	0.168284i
$838$	−22.7826	+	12.2156i	−0.787012	+	0.421980i
$839$	−10.5047	+	4.35120i	−0.362664	+	0.150220i	−0.556572	−	0.830800i	$-0.687884\pi$
$839$	−10.5047	+	4.35120i	−0.362664	+	0.150220i	0.193908	+	0.981020i	$0.437884\pi$
$840$	0.0428294	+	0.418166i	0.00147776	+	0.0144281i
$841$	−5.76754	−	2.38899i	−0.198881	−	0.0823791i
$842$	−2.29437	−	22.9894i	−0.0790692	−	0.792266i
$843$	3.09483	+	15.5588i	0.106592	+	0.535873i
$844$	−11.2991	−	27.0795i	−0.388930	−	0.932113i
$845$	−9.61964	−	14.3968i	−0.330926	−	0.495265i
$846$	−7.29483	+	13.6903i	−0.250801	+	0.470684i
$847$	0.491572	−	0.491572i	0.0168906	−	0.0168906i
$848$	−6.79938	+	35.1345i	−0.233492	+	1.20652i
$849$	17.8937	+	17.8937i	0.614110	+	0.614110i
$850$	11.4044	−	3.47565i	0.391167	−	0.119214i
$851$	−21.6310	+	14.4534i	−0.741501	+	0.495455i
$852$	0.0118548	+	4.56972i	0.000406139	+	0.156556i
$853$	22.7521	−	4.52567i	0.779016	−	0.154956i	0.210462	−	0.977602i	$-0.432503\pi$
$853$	22.7521	−	4.52567i	0.779016	−	0.154956i	0.568554	+	0.822646i	$0.307503\pi$
$854$	−0.108811	−	0.0890631i	−0.00372344	−	0.00304768i
$855$	−3.11017	+	7.50861i	−0.106366	+	0.256789i
$856$	1.48657	−	1.22971i	0.0508099	−	0.0420305i
$857$	5.92242	+	14.2980i	0.202306	+	0.488410i	0.992173	−	0.124868i	$-0.0398507\pi$
$857$	5.92242	+	14.2980i	0.202306	+	0.488410i	−0.789867	+	0.613278i	$0.789851\pi$
$858$	4.00481	+	1.20917i	0.136722	+	0.0412805i
$859$	−9.52306	−	6.36311i	−0.324923	−	0.217106i	0.382401	−	0.923997i	$-0.375097\pi$
$859$	−9.52306	−	6.36311i	−0.324923	−	0.217106i	−0.707323	+	0.706890i	$0.750097\pi$
$860$	12.0252	+	7.98995i	0.410056	+	0.272455i
$861$	0.0908968	−	0.456969i	0.00309776	−	0.0155735i
$862$	−2.13202	+	21.9385i	−0.0726170	+	0.747227i
$863$			34.3516i			1.16934i	0.811270	+	0.584672i	$0.198777\pi$
$863$			34.3516i			1.16934i	−0.811270	+	0.584672i	$0.801223\pi$
$864$	1.60696	−	5.42381i	0.0546698	−	0.184522i
$865$		−	20.9988i		−	0.713980i
$866$	25.9469	+	2.52157i	0.881711	+	0.0856863i
$867$	−0.804010	+	4.04203i	−0.0273056	+	0.137275i
$868$	−0.958908	+	0.193326i	−0.0325475	+	0.00656191i
$869$	−0.131822	−	0.0880805i	−0.00447175	−	0.00298793i
$870$	4.31761	−	14.3000i	0.146381	−	0.484815i
$871$	4.64996	+	11.2260i	0.157558	+	0.380378i
$872$	6.52279	−	12.3184i	0.220890	−	0.417152i
$873$	−6.48318	+	15.6518i	−0.219422	+	0.529732i
$874$	−25.6580	+	31.3472i	−0.867896	+	1.06034i
$875$	0.996189	−	0.198154i	0.0336773	−	0.00669884i
$876$	−16.5571	+	16.6432i	−0.559413	+	0.562323i
$877$	−13.9331	+	9.30979i	−0.470487	+	0.314369i	−0.768114	−	0.640313i	$-0.778805\pi$
$877$	−13.9331	+	9.30979i	−0.470487	+	0.314369i	0.297627	+	0.954682i	$0.403805\pi$
$878$	−8.90419	−	29.2167i	−0.300502	−	0.986016i
$879$	10.7744	+	10.7744i	0.363411	+	0.363411i
$880$	−8.27691	−	8.19146i	−0.279015	−	0.276134i
$881$	16.9439	−	16.9439i	0.570854	−	0.570854i	−0.361513	−	0.932367i	$-0.617740\pi$
$881$	16.9439	−	16.9439i	0.570854	−	0.570854i	0.932367	+	0.361513i	$0.117740\pi$
$882$	−8.72791	−	4.65062i	−0.293884	−	0.156595i
$883$	27.6610	+	41.3977i	0.930868	+	1.39314i	0.919450	+	0.393208i	$0.128635\pi$
$883$	27.6610	+	41.3977i	0.930868	+	1.39314i	0.0114184	+	0.999935i	$0.496365\pi$
$884$	−15.3685	−	6.31916i	−0.516897	−	0.212536i
$885$	4.24967	+	21.3645i	0.142851	+	0.718161i
$886$	−2.93425	+	0.292842i	−0.0985780	+	0.00983821i
$887$	31.5535	+	13.0699i	1.05946	+	0.438844i	0.843261	−	0.537504i	$-0.180633\pi$
$887$	31.5535	+	13.0699i	1.05946	+	0.438844i	0.216203	+	0.976349i	$0.430633\pi$
$888$	11.2420	+	3.36252i	0.377258	+	0.112839i
$889$	−0.329216	+	0.136366i	−0.0110416	+	0.00457356i
$890$	3.15193	+	5.87849i	0.105653	+	0.197047i
$891$	−0.909054	+	1.36050i	−0.0304544	+	0.0455783i
$892$	21.0894	+	4.13811i	0.706127	+	0.138554i
$893$	−49.1424	−	9.77503i	−1.64449	−	0.327109i
$894$	−18.2282	−	22.1525i	−0.609644	−	0.740891i
$895$	5.98908			0.200193
$896$	0.829360	−	0.453032i	0.0277070	−	0.0151347i
$897$	−11.3366			−0.378519
$898$	29.1521	+	35.4282i	0.972819	+	1.18225i
$899$	34.0932	+	6.78157i	1.13707	+	0.226178i
$900$	−3.60007	−	0.706394i	−0.120002	−	0.0235465i
$901$	−22.8432	+	34.1872i	−0.761016	+	1.13894i
$902$	6.09928	+	11.3754i	0.203084	+	0.378760i
$903$	0.313105	−	0.129692i	0.0104195	−	0.00431589i
$904$	6.44403	−	21.5446i	0.214325	−	0.716561i
$905$	−31.0129	−	12.8459i	−1.03090	−	0.427014i
$906$	29.8854	−	2.98260i	0.992876	−	0.0990903i
$907$	0.388609	+	1.95367i	0.0129036	+	0.0648706i	0.986701	−	0.162548i	$-0.0519713\pi$
$907$	0.388609	+	1.95367i	0.0129036	+	0.0648706i	−0.973797	+	0.227419i	$0.926971\pi$
$908$	29.1175	+	11.9725i	0.966298	+	0.397320i
$909$	1.67518	+	2.50708i	0.0555622	+	0.0831547i
$910$	−0.335333	−	0.178680i	−0.0111162	−	0.00592319i
$911$	−0.574069	+	0.574069i	−0.0190198	+	0.0190198i	−0.716553	−	0.697533i	$-0.754281\pi$
$911$	−0.574069	+	0.574069i	−0.0190198	+	0.0190198i	0.697533	+	0.716553i	$0.254281\pi$
$912$	18.2712	−	0.0947994i	0.605021	−	0.00313912i
$913$	−10.8509	−	10.8509i	−0.359114	−	0.359114i
$914$	−11.7163	−	38.4439i	−0.387541	−	1.27161i
$915$	−1.76096	+	1.17664i	−0.0582155	+	0.0388984i
$916$	−14.7255	+	14.8021i	−0.486543	+	0.489074i
$917$	0.600492	−	0.119445i	0.0198300	−	0.00394443i
$918$	4.11667	−	5.02946i	0.135870	−	0.165997i
$919$	16.9039	−	40.8095i	0.557607	−	1.34618i	−0.354049	−	0.935227i	$-0.615195\pi$
$919$	16.9039	−	40.8095i	0.557607	−	1.34618i	0.911656	−	0.410955i	$-0.134805\pi$
$920$	27.8887	+	14.7676i	0.919463	+	0.486873i
$921$	3.28620	+	7.93358i	0.108284	+	0.261420i
$922$	7.21912	−	23.9099i	0.237749	−	0.787429i
$923$	−3.43453	−	2.29488i	−0.113049	−	0.0755370i
$924$	−0.267959	+	0.0540234i	−0.00881520	+	0.00177724i
$925$	1.48466	−	7.46388i	0.0488152	−	0.245411i
$926$	17.5354	+	1.70412i	0.576248	+	0.0560009i
$927$			11.8562i			0.389409i
$928$	−33.3985	+	3.50832i	−1.09636	+	0.115166i
$929$		−	20.3782i		−	0.668587i	−0.942469	−	0.334293i	$-0.891502\pi$
$929$		−	20.3782i		−	0.668587i	0.942469	−	0.334293i	$-0.108498\pi$
$930$	−1.42511	+	14.6644i	−0.0467313	+	0.480864i
$931$	6.23181	−	31.3294i	0.204239	−	1.02678i
$932$	29.9784	+	19.9186i	0.981974	+	0.652456i
$933$	−11.8185	−	7.89687i	−0.386920	−	0.258532i
$934$	40.8851	+	12.3445i	1.33780	+	0.403923i
$935$	−5.12013	−	12.3611i	−0.167446	−	0.404250i
$936$	3.25923	+	3.94002i	0.106531	+	0.128784i
$937$	−18.1095	+	43.7202i	−0.591611	+	1.42828i	0.290335	+	0.956925i	$0.406233\pi$
$937$	−18.1095	+	43.7202i	−0.591611	+	1.42828i	−0.881946	+	0.471350i	$0.843767\pi$
$938$	−0.614398	−	0.502891i	−0.0200608	−	0.0164200i
$939$	2.96766	−	0.590304i	0.0968459	−	0.0192638i
$940$	0.101259	+	39.0327i	0.00330270	+	1.27311i
$941$	−10.6498	+	7.11595i	−0.347173	+	0.231973i	−0.716914	−	0.697161i	$-0.754446\pi$
$941$	−10.6498	+	7.11595i	−0.347173	+	0.231973i	0.369742	+	0.929135i	$0.379446\pi$
$942$	−31.0355	+	9.45849i	−1.01119	+	0.308174i
$943$	−24.7333	−	24.7333i	−0.805427	−	0.805427i
$944$	40.5771	−	27.4183i	1.32067	−	0.892391i
$945$	0.105088	−	0.105088i	0.00341853	−	0.00341853i
$946$	−4.41501	+	8.28573i	−0.143544	+	0.269392i
$947$	−6.45667	−	9.66308i	−0.209813	−	0.314008i	0.711605	−	0.702580i	$-0.247969\pi$
$947$	−6.45667	−	9.66308i	−0.209813	−	0.314008i	−0.921418	+	0.388572i	$0.872969\pi$
$948$	−0.0746225	−	0.178841i	−0.00242363	−	0.00580849i
$949$	−4.13995	−	20.8129i	−0.134389	−	0.675617i
$950$	−1.17678	−	11.7913i	−0.0381799	−	0.382559i
$951$	−9.20040	−	3.81093i	−0.298343	−	0.123578i
$952$	1.08013	−	0.110629i	0.0350074	−	0.00358552i
$953$	17.2732	−	7.15481i	0.559535	−	0.231767i	−0.0849484	−	0.996385i	$-0.527073\pi$
$953$	17.2732	−	7.15481i	0.559535	−	0.231767i	0.644483	+	0.764618i	$0.277073\pi$
$954$	11.1507	−	5.97877i	0.361016	−	0.193570i
$955$	−21.3799	+	31.9972i	−0.691836	+	1.03541i
$956$	−30.8623	+	20.7375i	−0.998157	+	0.670699i
$957$	9.52707	+	1.89505i	0.307966	+	0.0612583i
$958$	19.7129	−	16.2208i	0.636894	−	0.524069i
$959$	1.14965			0.0371240
$960$	−2.88544	−	13.9383i	−0.0931271	−	0.449856i
$961$	−3.28615			−0.106005
$962$	−8.19039	+	6.73948i	−0.264069	+	0.217289i
$963$	−0.668992	−	0.133071i	−0.0215580	−	0.00428815i
$964$	22.9592	+	34.1686i	0.739465	+	1.10050i
$965$	24.1036	−	36.0736i	0.775922	−	1.16125i
$966$	0.652839	−	0.350039i	0.0210047	−	0.0112623i
$967$	18.5232	−	7.67256i	0.595666	−	0.246733i	−0.0644200	−	0.997923i	$-0.520520\pi$
$967$	18.5232	−	7.67256i	0.595666	−	0.246733i	0.660086	+	0.751190i	$0.270520\pi$
$968$	−14.8627	+	18.2547i	−0.477707	+	0.586728i
$969$	19.3949	+	8.03365i	0.623055	+	0.258078i
$970$	4.23329	+	42.4172i	0.135923	+	1.36193i
$971$	6.52528	+	32.8048i	0.209406	+	1.05276i	0.932270	+	0.361764i	$0.117826\pi$
$971$	6.52528	+	32.8048i	0.209406	+	1.05276i	−0.722863	+	0.690991i	$0.757174\pi$
$972$	−1.84577	+	0.770158i	−0.0592030	+	0.0247028i
$973$	−0.705871	−	1.05641i	−0.0226292	−	0.0338670i
$974$	−19.3300	+	36.2770i	−0.619373	+	1.16239i
$975$	2.34493	−	2.34493i	0.0750978	−	0.0750978i
$976$	3.97261	+	2.62470i	0.127160	+	0.0840146i
$977$	21.0998	+	21.0998i	0.675044	+	0.675044i	0.958874	−	0.283831i	$-0.0916054\pi$
$977$	21.0998	+	21.0998i	0.675044	+	0.675044i	−0.283831	+	0.958874i	$0.591605\pi$
$978$	26.3234	−	8.02240i	0.841728	−	0.256528i
$979$	−3.60652	+	2.40980i	−0.115265	+	0.0770175i
$980$	−24.8842	+	0.0645549i	−0.794898	+	0.00206213i
$981$	−4.83340	+	0.961423i	−0.154319	+	0.0306959i
$982$	−37.5740	−	30.7547i	−1.19903	−	0.981422i
$983$	−20.7119	+	50.0029i	−0.660606	+	1.59484i	0.136250	+	0.990674i	$0.456495\pi$
$983$	−20.7119	+	50.0029i	−0.660606	+	1.59484i	−0.796856	+	0.604169i	$0.793505\pi$
$984$	−1.48529	+	15.7067i	−0.0473493	+	0.500712i
$985$	−9.87499	−	23.8403i	−0.314643	−	0.759616i
$986$	−36.9373	−	11.1525i	−1.17632	−	0.355168i
$987$	0.761824	+	0.509035i	0.0242491	+	0.0162027i
$988$	−9.14012	+	13.7563i	−0.290786	+	0.437646i
$989$	4.96357	−	24.9535i	0.157832	−	0.793477i
$990$	−0.398236	+	4.09784i	−0.0126568	+	0.130238i
$991$			21.2322i			0.674463i	0.941422	+	0.337232i	$0.109491\pi$
$991$			21.2322i			0.674463i	−0.941422	+	0.337232i	$0.890509\pi$
$992$	31.6341	−	9.82057i	1.00438	−	0.311803i
$993$		−	22.9968i		−	0.729782i
$994$	0.268642	+	0.0261071i	0.00852081	+	0.000828068i
$995$	−4.87848	+	24.5258i	−0.154658	+	0.777520i
$996$	−3.70701	−	18.3870i	−0.117461	−	0.582614i
$997$	50.0100	+	33.4156i	1.58383	+	1.05828i	0.961231	+	0.275745i	$0.0889246\pi$
$997$	50.0100	+	33.4156i	1.58383	+	1.05828i	0.622602	+	0.782538i	$0.286075\pi$
$998$	−8.77986	+	29.0790i	−0.277922	+	0.920481i
$999$	−1.58762	−	3.83285i	−0.0502300	−	0.121266i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	192.2.r.a.157.11	✓	128
3.2	odd	2		576.2.bd.b.541.6		128
4.3	odd	2		768.2.r.a.721.6		128
64.11	odd	16		768.2.r.a.49.6		128
64.53	even	16	inner	192.2.r.a.181.11	yes	128
192.53	odd	16		576.2.bd.b.181.6		128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
192.2.r.a.157.11	✓	128	1.1	even	1	trivial
192.2.r.a.181.11	yes	128	64.53	even	16	inner
576.2.bd.b.181.6		128	192.53	odd	16
576.2.bd.b.541.6		128	3.2	odd	2
768.2.r.a.49.6		128	64.11	odd	16
768.2.r.a.721.6		128	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 192 = 2^{6} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	192.r (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.898585 + 1.09204i) q^{2} +(0.980785 + 0.195090i) q^{3} +(-0.385091 + 1.96258i) q^{4} +(0.988484 - 1.47937i) q^{5} +(0.668273 + 1.24636i) q^{6} +(0.0771711 - 0.0319653i) q^{7} +(-2.48924 + 1.34301i) q^{8} +(0.923880 + 0.382683i) q^{9} +O(q^{10})\)	\(q+(0.898585 + 1.09204i) q^{2} +(0.980785 + 0.195090i) q^{3} +(-0.385091 + 1.96258i) q^{4} +(0.988484 - 1.47937i) q^{5} +(0.668273 + 1.24636i) q^{6} +(0.0771711 - 0.0319653i) q^{7} +(-2.48924 + 1.34301i) q^{8} +(0.923880 + 0.382683i) q^{9} +(2.50377 - 0.249879i) q^{10} +(0.319217 + 1.60481i) q^{11} +(-0.760571 + 1.84974i) q^{12} +(-1.00438 - 1.50317i) q^{13} +(0.104252 + 0.0555502i) q^{14} +(1.25810 - 1.25810i) q^{15} +(-3.70341 - 1.51154i) q^{16} +(-3.24971 - 3.24971i) q^{17} +(0.412280 + 1.35278i) q^{18} +(-3.79804 + 2.53777i) q^{19} +(2.52272 + 2.50967i) q^{20} +(0.0819244 - 0.0162958i) q^{21} +(-1.46567 + 1.79066i) q^{22} +(2.39973 - 5.79347i) q^{23} +(-2.70342 + 0.831575i) q^{24} +(0.701978 + 1.69473i) q^{25} +(0.738989 - 2.44755i) q^{26} +(0.831470 + 0.555570i) q^{27} +(0.0330165 + 0.163764i) q^{28} +(1.15817 - 5.82249i) q^{29} +(2.50441 + 0.243383i) q^{30} +5.85544i q^{31} +(-1.67717 - 5.40251i) q^{32} +1.63625i q^{33} +(0.628664 - 6.46894i) q^{34} +(0.0289939 - 0.145762i) q^{35} +(-1.10682 + 1.66582i) q^{36} +(-3.44947 - 2.30487i) q^{37} +(-6.18420 - 1.86720i) q^{38} +(-0.691831 - 1.67023i) q^{39} +(-0.473770 + 5.01006i) q^{40} +(2.13458 - 5.15334i) q^{41} +(0.0914116 + 0.0748214i) q^{42} +(3.97932 - 0.791536i) q^{43} +(-3.27250 + 0.00848954i) q^{44} +(1.47937 - 0.988484i) q^{45} +(8.48305 - 2.58533i) q^{46} +(7.75629 + 7.75629i) q^{47} +(-3.33736 - 2.20500i) q^{48} +(-4.94481 + 4.94481i) q^{49} +(-1.21992 + 2.28944i) q^{50} +(-2.55328 - 3.82125i) q^{51} +(3.33686 - 1.39232i) q^{52} +(-1.74539 - 8.77469i) q^{53} +(0.140443 + 1.40722i) q^{54} +(2.68966 + 1.11409i) q^{55} +(-0.149168 + 0.183211i) q^{56} +(-4.22016 + 1.74805i) q^{57} +(7.39909 - 3.96724i) q^{58} +(-6.80186 + 10.1797i) q^{59} +(1.98464 + 2.95360i) q^{60} +(-1.16747 - 0.232224i) q^{61} +(-6.39436 + 5.26161i) q^{62} +0.0835294 q^{63} +(4.39266 - 6.68615i) q^{64} -3.21656 q^{65} +(-1.78685 + 1.47031i) q^{66} +(-6.59208 - 1.31125i) q^{67} +(7.62923 - 5.12637i) q^{68} +(3.48387 - 5.21398i) q^{69} +(0.185231 - 0.0993171i) q^{70} +(2.11094 - 0.874381i) q^{71} +(-2.81371 + 0.288185i) q^{72} +(10.8446 + 4.49199i) q^{73} +(-0.582647 - 5.83807i) q^{74} +(0.357866 + 1.79911i) q^{75} +(-3.51798 - 8.43122i) q^{76} +(0.0759327 + 0.113641i) q^{77} +(1.20228 - 2.25635i) q^{78} +(-0.0685134 + 0.0685134i) q^{79} +(-5.89689 + 3.98459i) q^{80} +(0.707107 + 0.707107i) q^{81} +(7.54575 - 2.29967i) q^{82} +(-7.79791 + 5.21040i) q^{83} +(0.000433384 + 0.167058i) q^{84} +(-8.01981 + 1.59524i) q^{85} +(4.44014 + 3.63430i) q^{86} +(2.27182 - 5.48467i) q^{87} +(-2.94989 - 3.56606i) q^{88} +(1.01445 + 2.44910i) q^{89} +(2.40880 + 0.727292i) q^{90} +(-0.125559 - 0.0838955i) q^{91} +(10.4460 + 6.94067i) q^{92} +(-1.14234 + 5.74293i) q^{93} +(-1.50047 + 15.4398i) q^{94} +8.12726i q^{95} +(-0.590968 - 5.62590i) q^{96} +16.9414i q^{97} +(-9.84326 - 0.956586i) q^{98} +(-0.319217 + 1.60481i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q+O(q^{10}) \) 128 * q	\( 128 q - 16 q^{22} - 80 q^{26} - 80 q^{28} - 80 q^{32} - 80 q^{34} - 80 q^{38} - 80 q^{40} - 16 q^{44} + 48 q^{50} - 32 q^{51} + 48 q^{52} + 16 q^{54} - 64 q^{55} + 112 q^{56} - 128 q^{59} + 96 q^{60} + 96 q^{62} - 32 q^{63} + 96 q^{64} + 96 q^{66} - 32 q^{67} + 96 q^{68} + 96 q^{70} - 128 q^{71} + 112 q^{74} - 64 q^{75} + 16 q^{76} + 48 q^{78} - 32 q^{79} + 48 q^{80} - 80 q^{82} - 80 q^{88} - 96 q^{94}+O(q^{100}) \) 128 * q - 16 * q^22 - 80 * q^26 - 80 * q^28 - 80 * q^32 - 80 * q^34 - 80 * q^38 - 80 * q^40 - 16 * q^44 + 48 * q^50 - 32 * q^51 + 48 * q^52 + 16 * q^54 - 64 * q^55 + 112 * q^56 - 128 * q^59 + 96 * q^60 + 96 * q^62 - 32 * q^63 + 96 * q^64 + 96 * q^66 - 32 * q^67 + 96 * q^68 + 96 * q^70 - 128 * q^71 + 112 * q^74 - 64 * q^75 + 16 * q^76 + 48 * q^78 - 32 * q^79 + 48 * q^80 - 80 * q^82 - 80 * q^88 - 96 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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