LMFDB - Embedded newform 192.2.r.a.157.8

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			157.8
Character	$\chi$	$=$	192.157
Dual form			192.2.r.a.181.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.134977 + 1.40776i) q^{2} +(0.980785 + 0.195090i) q^{3} +(-1.96356 - 0.380029i) q^{4} +(-1.65192 + 2.47227i) q^{5} +(-0.407023 + 1.35438i) q^{6} +(-2.43319 + 1.00786i) q^{7} +(0.800025 - 2.71292i) q^{8} +(0.923880 + 0.382683i) q^{9} +O(q^{10})$	\(q+(-0.134977 + 1.40776i) q^{2} +(0.980785 + 0.195090i) q^{3} +(-1.96356 - 0.380029i) q^{4} +(-1.65192 + 2.47227i) q^{5} +(-0.407023 + 1.35438i) q^{6} +(-2.43319 + 1.00786i) q^{7} +(0.800025 - 2.71292i) q^{8} +(0.923880 + 0.382683i) q^{9} +(-3.25739 - 2.65920i) q^{10} +(0.530629 + 2.66765i) q^{11} +(-1.85169 - 0.755799i) q^{12} +(-0.947516 - 1.41806i) q^{13} +(-1.09040 - 3.56139i) q^{14} +(-2.10249 + 2.10249i) q^{15} +(3.71116 + 1.49242i) q^{16} +(5.29168 + 5.29168i) q^{17} +(-0.663428 + 1.24894i) q^{18} +(-0.475911 + 0.317994i) q^{19} +(4.18318 - 4.22668i) q^{20} +(-2.58307 + 0.513804i) q^{21} +(-3.82703 + 0.386925i) q^{22} +(2.76395 - 6.67276i) q^{23} +(1.31392 - 2.50472i) q^{24} +(-1.46987 - 3.54859i) q^{25} +(2.12417 - 1.14247i) q^{26} +(0.831470 + 0.555570i) q^{27} +(5.16075 - 1.05431i) q^{28} +(-1.06449 + 5.35156i) q^{29} +(-2.67601 - 3.24359i) q^{30} -4.58643i q^{31} +(-2.60189 + 5.02296i) q^{32} +2.71991i q^{33} +(-8.16366 + 6.73515i) q^{34} +(1.52773 - 7.68043i) q^{35} +(-1.66866 - 1.10252i) q^{36} +(2.63143 + 1.75826i) q^{37} +(-0.383421 - 0.712889i) q^{38} +(-0.652660 - 1.57566i) q^{39} +(5.38551 + 6.45941i) q^{40} +(2.02772 - 4.89534i) q^{41} +(-0.374657 - 3.70568i) q^{42} +(3.39035 - 0.674383i) q^{43} +(-0.0281369 - 5.43975i) q^{44} +(-2.47227 + 1.65192i) q^{45} +(9.02056 + 4.79164i) q^{46} +(0.926251 + 0.926251i) q^{47} +(3.34869 + 2.18776i) q^{48} +(-0.0450982 + 0.0450982i) q^{49} +(5.19395 - 1.59025i) q^{50} +(4.15765 + 6.22236i) q^{51} +(1.32160 + 3.14453i) q^{52} +(2.62485 + 13.1960i) q^{53} +(-0.894337 + 1.09552i) q^{54} +(-7.47171 - 3.09488i) q^{55} +(0.787638 + 7.40739i) q^{56} +(-0.528804 + 0.219038i) q^{57} +(-7.39002 - 2.22088i) q^{58} +(6.19622 - 9.27330i) q^{59} +(4.92739 - 3.32937i) q^{60} +(12.2985 + 2.44633i) q^{61} +(6.45659 + 0.619062i) q^{62} -2.63367 q^{63} +(-6.71992 - 4.34081i) q^{64} +5.07105 q^{65} +(-3.82898 - 0.367125i) q^{66} +(-8.67822 - 1.72621i) q^{67} +(-8.37955 - 12.4015i) q^{68} +(4.01263 - 6.00533i) q^{69} +(10.6060 + 3.18736i) q^{70} +(-10.4863 + 4.34359i) q^{71} +(1.77732 - 2.20026i) q^{72} +(-6.18595 - 2.56230i) q^{73} +(-2.83039 + 3.46709i) q^{74} +(-0.749335 - 3.76716i) q^{75} +(1.05533 - 0.443540i) q^{76} +(-3.97975 - 5.95611i) q^{77} +(2.30624 - 0.706110i) q^{78} +(9.17818 - 9.17818i) q^{79} +(-9.82020 + 6.70962i) q^{80} +(0.707107 + 0.707107i) q^{81} +(6.61776 + 3.51529i) q^{82} +(-10.5583 + 7.05480i) q^{83} +(5.26727 - 0.0272447i) q^{84} +(-21.8239 + 4.34105i) q^{85} +(0.491748 + 4.86382i) q^{86} +(-2.08808 + 5.04106i) q^{87} +(7.66165 + 0.694631i) q^{88} +(-3.70422 - 8.94279i) q^{89} +(-1.99180 - 3.70333i) q^{90} +(3.73470 + 2.49545i) q^{91} +(-7.96303 + 12.0520i) q^{92} +(0.894769 - 4.49831i) q^{93} +(-1.42896 + 1.17891i) q^{94} -1.70188i q^{95} +(-3.53183 + 4.41885i) q^{96} -15.4317i q^{97} +(-0.0574001 - 0.0695746i) q^{98} +(-0.530629 + 2.66765i) 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 $

$2$	−0.134977	+	1.40776i	−0.0954431	+	0.995435i
$2$	−0.134977	+	1.40776i	−0.0954431	+	0.995435i
$3$	0.980785	+	0.195090i	0.566257	+	0.112635i
$3$	0.980785	+	0.195090i	0.566257	+	0.112635i
$4$	−1.96356	−	0.380029i	−0.981781	−	0.190015i
$5$	−1.65192	+	2.47227i	−0.738761	+	1.10563i	0.251696	+	0.967806i	$0.419012\pi$
$5$	−1.65192	+	2.47227i	−0.738761	+	1.10563i	−0.990456	+	0.137827i	$0.955988\pi$
$6$	−0.407023	+	1.35438i	−0.166167	+	0.552921i
$7$	−2.43319	+	1.00786i	−0.919661	+	0.380936i	−0.791747	−	0.610849i	$-0.790828\pi$
$7$	−2.43319	+	1.00786i	−0.919661	+	0.380936i	−0.127914	+	0.991785i	$0.540828\pi$
$8$	0.800025	−	2.71292i	0.282851	−	0.959164i
$9$	0.923880	+	0.382683i	0.307960	+	0.127561i
$10$	−3.25739	−	2.65920i	−1.03008	−	0.840913i
$11$	0.530629	+	2.66765i	0.159991	+	0.804327i	0.974537	+	0.224228i	$0.0719860\pi$
$11$	0.530629	+	2.66765i	0.159991	+	0.804327i	−0.814546	+	0.580099i	$0.803014\pi$
$12$	−1.85169	−	0.755799i	−0.534538	−	0.218180i
$13$	−0.947516	−	1.41806i	−0.262794	−	0.393299i	0.676484	−	0.736458i	$-0.263503\pi$
$13$	−0.947516	−	1.41806i	−0.262794	−	0.393299i	−0.939277	+	0.343159i	$0.888503\pi$
$14$	−1.09040	−	3.56139i	−0.291422	−	0.951820i
$15$	−2.10249	+	2.10249i	−0.542862	+	0.542862i
$16$	3.71116	+	1.49242i	0.927789	+	0.373106i
$17$	5.29168	+	5.29168i	1.28342	+	1.28342i	0.938708	+	0.344714i	$0.112024\pi$
$17$	5.29168	+	5.29168i	1.28342	+	1.28342i	0.344714	+	0.938708i	$0.387976\pi$
$18$	−0.663428	+	1.24894i	−0.156371	+	0.294379i
$19$	−0.475911	+	0.317994i	−0.109182	+	0.0729528i	−0.608962	−	0.793199i	$-0.708414\pi$
$19$	−0.475911	+	0.317994i	−0.109182	+	0.0729528i	0.499781	+	0.866152i	$0.333414\pi$
$20$	4.18318	−	4.22668i	0.935388	−	0.945115i
$21$	−2.58307	+	0.513804i	−0.563671	+	0.112121i
$22$	−3.82703	+	0.386925i	−0.815925	+	0.0824927i
$23$	2.76395	−	6.67276i	0.576323	−	1.39137i	−0.319768	−	0.947496i	$-0.603605\pi$
$23$	2.76395	−	6.67276i	0.576323	−	1.39137i	0.896091	−	0.443871i	$-0.146395\pi$
$24$	1.31392	−	2.50472i	0.268202	−	0.511274i
$25$	−1.46987	−	3.54859i	−0.293975	−	0.709718i
$26$	2.12417	−	1.14247i	0.416585	−	0.224056i
$27$	0.831470	+	0.555570i	0.160016	+	0.106920i
$28$	5.16075	−	1.05431i	0.975289	−	0.199247i
$29$	−1.06449	+	5.35156i	−0.197671	+	0.993760i	0.746771	+	0.665081i	$0.231603\pi$
$29$	−1.06449	+	5.35156i	−0.197671	+	0.993760i	−0.944442	+	0.328678i	$0.893397\pi$
$30$	−2.67601	−	3.24359i	−0.488571	−	0.592196i
$31$		−	4.58643i		−	0.823748i	−0.911241	−	0.411874i	$-0.864874\pi$
$31$		−	4.58643i		−	0.823748i	0.911241	−	0.411874i	$-0.135126\pi$
$32$	−2.60189	+	5.02296i	−0.459953	+	0.887943i
$33$			2.71991i			0.473476i
$34$	−8.16366	+	6.73515i	−1.40006	+	1.15507i
$35$	1.52773	−	7.68043i	0.258234	−	1.29823i
$36$	−1.66866	−	1.10252i	−0.278111	−	0.183754i
$37$	2.63143	+	1.75826i	0.432604	+	0.289057i	0.752744	−	0.658313i	$-0.228730\pi$
$37$	2.63143	+	1.75826i	0.432604	+	0.289057i	−0.320140	+	0.947370i	$0.603730\pi$
$38$	−0.383421	−	0.712889i	−0.0621991	−	0.115646i
$39$	−0.652660	−	1.57566i	−0.104509	−	0.252308i
$40$	5.38551	+	6.45941i	0.851524	+	1.02132i
$41$	2.02772	−	4.89534i	0.316676	−	0.764524i	−0.682750	−	0.730652i	$-0.739216\pi$
$41$	2.02772	−	4.89534i	0.316676	−	0.764524i	0.999426	−	0.0338721i	$-0.0107839\pi$
$42$	−0.374657	−	3.70568i	−0.0578108	−	0.571799i
$43$	3.39035	−	0.674383i	0.517024	−	0.102842i	0.0703201	−	0.997524i	$-0.477598\pi$
$43$	3.39035	−	0.674383i	0.517024	−	0.102842i	0.446703	+	0.894682i	$0.352598\pi$
$44$	−0.0281369	−	5.43975i	−0.00424180	−	0.820073i
$45$	−2.47227	+	1.65192i	−0.368545	+	0.246254i
$46$	9.02056	+	4.79164i	1.33001	+	0.706488i
$47$	0.926251	+	0.926251i	0.135108	+	0.135108i	0.771426	−	0.636319i	$-0.219544\pi$
$47$	0.926251	+	0.926251i	0.135108	+	0.135108i	−0.636319	+	0.771426i	$0.719544\pi$
$48$	3.34869	+	2.18776i	0.483342	+	0.315776i
$49$	−0.0450982	+	0.0450982i	−0.00644260	+	0.00644260i
$50$	5.19395	−	1.59025i	0.734536	−	0.224895i
$51$	4.15765	+	6.22236i	0.582187	+	0.871305i
$52$	1.32160	+	3.14453i	0.183273	+	0.436068i
$53$	2.62485	+	13.1960i	0.360551	+	1.81261i	0.555173	+	0.831735i	$0.312652\pi$
$53$	2.62485	+	13.1960i	0.360551	+	1.81261i	−0.194621	+	0.980878i	$0.562348\pi$
$54$	−0.894337	+	1.09552i	−0.121704	+	0.149081i
$55$	−7.47171	−	3.09488i	−1.00749	−	0.417314i
$56$	0.787638	+	7.40739i	0.105253	+	0.989854i
$57$	−0.528804	+	0.219038i	−0.0700418	+	0.0290123i
$58$	−7.39002	−	2.22088i	−0.970357	−	0.291616i
$59$	6.19622	−	9.27330i	0.806679	−	1.20728i	−0.168464	−	0.985708i	$-0.553881\pi$
$59$	6.19622	−	9.27330i	0.806679	−	1.20728i	0.975144	−	0.221573i	$-0.0711192\pi$
$60$	4.92739	−	3.32937i	0.636123	−	0.429820i
$61$	12.2985	+	2.44633i	1.57467	+	0.313221i	0.903667	−	0.428236i	$-0.140865\pi$
$61$	12.2985	+	2.44633i	1.57467	+	0.313221i	0.671000	+	0.741457i	$0.265865\pi$
$62$	6.45659	+	0.619062i	0.819987	+	0.0786210i
$63$	−2.63367			−0.331811
$64$	−6.71992	−	4.34081i	−0.839990	−	0.542602i
$65$	5.07105			0.628986
$66$	−3.82898	−	0.367125i	−0.471314	−	0.0451900i
$67$	−8.67822	−	1.72621i	−1.06021	−	0.210890i	−0.365968	−	0.930627i	$-0.619262\pi$
$67$	−8.67822	−	1.72621i	−1.06021	−	0.210890i	−0.694246	+	0.719738i	$0.744262\pi$
$68$	−8.37955	−	12.4015i	−1.01617	−	1.50391i
$69$	4.01263	−	6.00533i	0.483064	−	0.722956i
$70$	10.6060	+	3.18736i	1.26766	+	0.380962i
$71$	−10.4863	+	4.34359i	−1.24450	+	0.515489i	−0.905118	−	0.425159i	$-0.860218\pi$
$71$	−10.4863	+	4.34359i	−1.24450	+	0.515489i	−0.339382	+	0.940649i	$0.610218\pi$
$72$	1.77732	−	2.20026i	0.209459	−	0.259303i
$73$	−6.18595	−	2.56230i	−0.724010	−	0.299895i	−0.00992235	−	0.999951i	$-0.503158\pi$
$73$	−6.18595	−	2.56230i	−0.724010	−	0.299895i	−0.714088	+	0.700056i	$0.753158\pi$
$74$	−2.83039	+	3.46709i	−0.329026	+	0.403041i
$75$	−0.749335	−	3.76716i	−0.0865258	−	0.434994i
$76$	1.05533	−	0.443540i	0.121054	−	0.0508776i
$77$	−3.97975	−	5.95611i	−0.453534	−	0.678762i
$78$	2.30624	−	0.706110i	0.261131	−	0.0799512i
$79$	9.17818	−	9.17818i	1.03263	−	1.03263i	0.0331769	−	0.999449i	$-0.489438\pi$
$79$	9.17818	−	9.17818i	1.03263	−	1.03263i	0.999449	−	0.0331769i	$-0.0105625\pi$
$80$	−9.82020	+	6.70962i	−1.09793	+	0.750159i
$81$	0.707107	+	0.707107i	0.0785674	+	0.0785674i
$82$	6.61776	+	3.51529i	0.730810	+	0.388199i
$83$	−10.5583	+	7.05480i	−1.15892	+	0.774365i	−0.977891	−	0.209113i	$-0.932942\pi$
$83$	−10.5583	+	7.05480i	−1.15892	+	0.774365i	−0.181027	+	0.983478i	$0.557942\pi$
$84$	5.26727	−	0.0272447i	0.574706	−	0.00297265i
$85$	−21.8239	+	4.34105i	−2.36714	+	0.470853i
$86$	0.491748	+	4.86382i	0.0530266	+	0.524479i
$87$	−2.08808	+	5.04106i	−0.223865	+	0.540458i
$88$	7.66165	+	0.694631i	0.816735	+	0.0740479i
$89$	−3.70422	−	8.94279i	−0.392647	−	0.947934i	−0.989361	−	0.145480i	$-0.953527\pi$
$89$	−3.70422	−	8.94279i	−0.392647	−	0.947934i	0.596714	−	0.802454i	$-0.296473\pi$
$90$	−1.99180	−	3.70333i	−0.209954	−	0.390365i
$91$	3.73470	+	2.49545i	0.391503	+	0.261594i
$92$	−7.96303	+	12.0520i	−0.830203	+	1.25651i
$93$	0.894769	−	4.49831i	0.0927832	−	0.466453i
$94$	−1.42896	+	1.17891i	−0.147386	+	0.121596i
$95$		−	1.70188i		−	0.174609i
$96$	−3.53183	+	4.41885i	−0.360466	+	0.450997i
$97$		−	15.4317i		−	1.56685i	−0.621486	−	0.783425i	$-0.713471\pi$
$97$		−	15.4317i		−	1.56685i	0.621486	−	0.783425i	$-0.286529\pi$
$98$	−0.0574001	−	0.0695746i	−0.00579829	−	0.00702809i
$99$	−0.530629	+	2.66765i	−0.0533302	+	0.268109i
$100$	1.53762	+	7.52647i	0.153762	+	0.752647i
$101$	−1.68352	−	1.12489i	−0.167517	−	0.111931i	0.468986	−	0.883206i	$-0.344620\pi$
$101$	−1.68352	−	1.12489i	−0.167517	−	0.111931i	−0.636503	+	0.771275i	$0.719620\pi$
$102$	−9.32076	+	5.01309i	−0.922893	+	0.496369i
$103$	1.55900	+	3.76376i	0.153613	+	0.370855i	0.981887	−	0.189469i	$-0.0606767\pi$
$103$	1.55900	+	3.76376i	0.153613	+	0.370855i	−0.828274	+	0.560324i	$0.810677\pi$
$104$	−4.60512	+	1.43606i	−0.451569	+	0.140817i
$105$	2.99675	−	7.23480i	0.292453	−	0.706044i
$106$	−18.9311	+	1.91400i	−1.83875	+	0.185904i
$107$	−4.20305	+	0.836039i	−0.406325	+	0.0808230i	−0.394021	−	0.919101i	$-0.628916\pi$
$107$	−4.20305	+	0.836039i	−0.406325	+	0.0808230i	−0.0123033	+	0.999924i	$0.503916\pi$
$108$	−1.42151	−	1.40688i	−0.136785	−	0.135377i
$109$	5.86929	−	3.92173i	0.562176	−	0.375634i	−0.241772	−	0.970333i	$-0.577729\pi$
$109$	5.86929	−	3.92173i	0.562176	−	0.375634i	0.803949	+	0.594699i	$0.202729\pi$
$110$	5.36535	−	10.1006i	0.511566	−	0.963056i
$111$	2.23785	+	2.23785i	0.212407	+	0.212407i
$112$	−10.5341	+	0.108978i	−0.995381	+	0.0102974i
$113$	−11.1426	+	11.1426i	−1.04821	+	1.04821i	−0.0494288	+	0.998778i	$0.515740\pi$
$113$	−11.1426	+	11.1426i	−1.04821	+	1.04821i	−0.998778	+	0.0494288i	$0.984260\pi$
$114$	−0.236976	−	0.773993i	−0.0221948	−	0.0724911i
$115$	11.9311	+	17.8561i	1.11258	+	1.66509i
$116$	4.12395	−	10.1036i	0.382899	−	0.938094i
$117$	−0.332723	−	1.67271i	−0.0307603	−	0.154642i
$118$	12.2182	+	9.97446i	1.12478	+	0.918223i
$119$	−18.2090	−	7.54241i	−1.66921	−	0.691411i
$120$	4.02186	+	7.38596i	0.367144	+	0.674243i
$121$	3.32789	−	1.37846i	0.302535	−	0.125314i
$122$	−5.10386	+	16.9832i	−0.462082	+	1.53758i
$123$	2.94379	−	4.40569i	0.265433	−	0.397248i
$124$	−1.74298	+	9.00575i	−0.156524	+	0.808740i
$125$	−3.38003	−	0.672329i	−0.302319	−	0.0601349i
$126$	0.355485	−	3.70757i	0.0316691	−	0.330297i
$127$	2.61133			0.231718			0.115859	−	0.993266i	$-0.463038\pi$
$127$	2.61133			0.231718			0.115859	+	0.993266i	$0.463038\pi$
$128$	7.01785	−	8.87411i	0.620296	−	0.784368i
$129$	3.45677			0.304352
$130$	−0.684474	+	7.13880i	−0.0600323	+	0.626114i
$131$	13.9604	+	2.77689i	1.21972	+	0.242618i	0.762650	−	0.646812i	$-0.223898\pi$
$131$	13.9604	+	2.77689i	1.21972	+	0.242618i	0.457072	+	0.889430i	$0.348898\pi$
$132$	1.03365	−	5.34072i	0.0899674	−	0.464850i
$133$	0.837491	−	1.25339i	0.0726196	−	0.108683i
$134$	3.60144	−	11.9838i	0.311117	−	1.03525i
$135$	−2.74704	+	1.13786i	−0.236428	+	0.0979316i
$136$	18.5894	−	10.1225i	1.59403	−	0.867994i
$137$	9.40794	+	3.89690i	0.803775	+	0.332934i	0.746467	−	0.665422i	$-0.231748\pi$
$137$	9.40794	+	3.89690i	0.803775	+	0.332934i	0.0573074	+	0.998357i	$0.481748\pi$
$138$	7.91243	+	6.45939i	0.673551	+	0.549860i
$139$	−1.77547	−	8.92590i	−0.150594	−	0.757085i	−0.980087	−	0.198569i	$-0.936371\pi$
$139$	−1.77547	−	8.92590i	−0.150594	−	0.757085i	0.829493	−	0.558516i	$-0.188629\pi$
$140$	−5.91858	+	14.5004i	−0.500212	+	1.22551i
$141$	0.727751	+	1.08916i	0.0612877	+	0.0917235i
$142$	−4.69930	−	15.3485i	−0.394357	−	1.28802i
$143$	3.28010	−	3.28010i	0.274296	−	0.274296i
$144$	2.85753	+	2.79902i	0.238128	+	0.233251i
$145$	−11.4721	−	11.4721i	−0.952702	−	0.952702i
$146$	4.44206	−	8.36246i	0.367628	−	0.692082i
$147$	−0.0530299	+	0.0354334i	−0.00437383	+	0.00292250i
$148$	−4.49878	−	4.45248i	−0.369798	−	0.365992i
$149$	−2.85388	+	0.567673i	−0.233799	+	0.0465056i	−0.310599	−	0.950541i	$-0.600530\pi$
$149$	−2.85388	+	0.567673i	−0.233799	+	0.0465056i	0.0768000	+	0.997047i	$0.475530\pi$
$150$	5.40439	−	0.546403i	0.441267	−	0.0446136i
$151$	6.17658	−	14.9116i	0.502643	−	1.21349i	−0.445396	−	0.895334i	$-0.646937\pi$
$151$	6.17658	−	14.9116i	0.502643	−	1.21349i	0.948039	−	0.318154i	$-0.103063\pi$
$152$	0.481952	+	1.54551i	0.0390915	+	0.125358i
$153$	2.86384	+	6.91392i	0.231528	+	0.558957i
$154$	8.92193	−	4.79858i	0.718950	−	0.386681i
$155$	11.3389	+	7.57642i	0.910763	+	0.608552i
$156$	0.682742	+	3.34194i	0.0546631	+	0.267569i
$157$	−1.11912	+	5.62620i	−0.0893155	+	0.449019i	0.910086	+	0.414420i	$0.136016\pi$
$157$	−1.11912	+	5.62620i	−0.0893155	+	0.449019i	−0.999401	+	0.0345994i	$0.988984\pi$
$158$	11.6818	+	14.1595i	0.929355	+	1.12647i
$159$			13.4546i			1.06702i
$160$	−8.12002	−	14.7301i	−0.641944	−	1.16452i
$161$			19.0218i			1.49913i
$162$	−1.09088	+	0.899992i	−0.0857075	+	0.0707100i
$163$	−3.75828	+	18.8942i	−0.294371	+	1.47990i	0.496562	+	0.868002i	$0.334596\pi$
$163$	−3.75828	+	18.8942i	−0.294371	+	1.47990i	−0.790933	+	0.611903i	$0.790404\pi$
$164$	−5.84193	+	8.84172i	−0.456178	+	0.690422i
$165$	−6.72436	−	4.49308i	−0.523491	−	0.349785i
$166$	−8.50632	−	15.8157i	−0.660219	−	1.22754i
$167$	1.76517	+	4.26149i	0.136593	+	0.329764i	0.977344	−	0.211658i	$-0.0678863\pi$
$167$	1.76517	+	4.26149i	0.136593	+	0.329764i	−0.840751	+	0.541422i	$0.817886\pi$
$168$	−0.672606	+	7.41872i	−0.0518927	+	0.572367i
$169$	3.86178	−	9.32317i	0.297060	−	0.717167i
$170$	−3.16542	−	31.3087i	−0.242776	−	2.40127i
$171$	−0.561376	+	0.111665i	−0.0429295	+	0.00853920i
$172$	−6.91345	+	0.0357595i	−0.527146	+	0.00272664i
$173$	−0.480015	+	0.320736i	−0.0364949	+	0.0243851i	−0.573684	−	0.819077i	$-0.694486\pi$
$173$	−0.480015	+	0.320736i	−0.0364949	+	0.0243851i	0.537189	+	0.843462i	$0.319486\pi$
$174$	−6.81475	−	3.61993i	−0.516625	−	0.274426i
$175$	7.15298	+	7.15298i	0.540714	+	0.540714i
$176$	−2.01202	+	10.6920i	−0.151661	+	0.805939i
$177$	7.88629	−	7.88629i	0.592770	−	0.592770i
$178$	13.0893	−	4.00758i	0.981082	−	0.300381i
$179$	−1.50530	−	2.25284i	−0.112511	−	0.168385i	0.770940	−	0.636907i	$-0.219787\pi$
$179$	−1.50530	−	2.25284i	−0.112511	−	0.168385i	−0.883452	+	0.468522i	$0.844787\pi$
$180$	5.48224	−	2.30411i	0.408622	−	0.171738i
$181$	−0.792065	−	3.98198i	−0.0588737	−	0.295978i	0.940119	−	0.340846i	$-0.110713\pi$
$181$	−0.792065	−	3.98198i	−0.0588737	−	0.295978i	−0.998993	+	0.0448676i	$0.985713\pi$
$182$	−4.01708	+	4.92072i	−0.297766	+	0.364748i
$183$	11.5850	+	4.79865i	0.856386	+	0.354727i
$184$	−15.8915	−	12.8368i	−1.17153	−	0.946338i
$185$	−8.69381	+	3.60110i	−0.639182	+	0.264758i
$186$	6.21175	+	1.86678i	0.455468	+	0.136879i
$187$	−11.3084	+	16.9243i	−0.826955	+	1.23763i
$188$	−1.46675	−	2.17076i	−0.106974	−	0.158319i
$189$	−2.58307	−	0.513804i	−0.187890	−	0.0373737i
$190$	2.39584	+	0.229715i	0.173812	+	0.0166653i
$191$	12.0203			0.869759			0.434880	−	0.900489i	$-0.356791\pi$
$191$	12.0203			0.869759			0.434880	+	0.900489i	$0.356791\pi$
$192$	−5.74395	−	5.56840i	−0.414534	−	0.401865i
$193$	13.0492			0.939303			0.469651	−	0.882852i	$-0.344380\pi$
$193$	13.0492			0.939303			0.469651	+	0.882852i	$0.344380\pi$
$194$	21.7241	+	2.08292i	1.55970	+	0.149545i
$195$	4.97361	+	0.989312i	0.356167	+	0.0708461i
$196$	0.105692	−	0.0714145i	0.00754942	−	0.00510104i
$197$	6.60468	−	9.88460i	0.470564	−	0.704249i	−0.517944	−	0.855414i	$-0.673303\pi$
$197$	6.60468	−	9.88460i	0.470564	−	0.704249i	0.988508	+	0.151165i	$0.0483026\pi$
$198$	−3.68378	−	1.10707i	−0.261795	−	0.0786759i
$199$	5.39618	−	2.23517i	0.382525	−	0.158447i	−0.183130	−	0.983089i	$-0.558623\pi$
$199$	5.39618	−	2.23517i	0.382525	−	0.158447i	0.565656	+	0.824641i	$0.308623\pi$
$200$	−10.8030	+	1.14870i	−0.763887	+	0.0812252i
$201$	−8.17471	−	3.38608i	−0.576599	−	0.238835i
$202$	1.81081	−	2.21816i	0.127408	−	0.156069i
$203$	−2.80352	−	14.0942i	−0.196769	−	0.989222i
$204$	−5.79912	−	13.7980i	−0.406020	−	0.966055i
$205$	8.75299	+	13.0998i	0.611336	+	0.914929i
$206$	−5.50890	+	1.68668i	−0.383823	+	0.117516i
$207$	5.10711	−	5.10711i	0.354969	−	0.354969i
$208$	−1.40004	−	6.67673i	−0.0970751	−	0.462948i
$209$	−1.10083	−	1.10083i	−0.0761459	−	0.0761459i
$210$	9.78036	+	5.19523i	0.674909	+	0.358505i
$211$	−14.7778	+	9.87421i	−1.01735	+	0.679768i	−0.948146	−	0.317834i	$-0.897044\pi$
$211$	−14.7778	+	9.87421i	−1.01735	+	0.679768i	−0.0691991	+	0.997603i	$0.522044\pi$
$212$	−0.139184	−	26.9087i	−0.00955922	−	1.84810i
$213$	−11.1322	+	2.21434i	−0.762769	+	0.151724i
$214$	−0.609626	−	6.02973i	−0.0416732	−	0.412184i
$215$	−3.93333	+	9.49589i	−0.268251	+	0.647615i
$216$	2.17242	−	1.81124i	0.147814	−	0.123240i
$217$	4.62249	+	11.1597i	0.313795	+	0.757569i
$218$	4.72863	+	8.79188i	0.320263	+	0.595461i
$219$	−5.56721	−	3.71989i	−0.376197	−	0.251367i
$220$	13.4950	+	8.91647i	0.909834	+	0.601148i
$221$	2.48996	−	12.5179i	0.167493	−	0.842043i
$222$	−3.45240	+	2.84829i	−0.231710	+	0.191164i
$223$			26.2604i			1.75852i	0.476338	+	0.879262i	$0.341964\pi$
$223$			26.2604i			1.75852i	−0.476338	+	0.879262i	$0.658036\pi$
$224$	1.26845	−	14.8442i	0.0847518	−	0.991819i
$225$		−	3.84097i		−	0.256064i
$226$	−14.1821	−	17.1901i	−0.943377	−	1.14347i
$227$	1.69894	−	8.54116i	0.112763	−	0.566896i	−0.882553	−	0.470214i	$-0.844177\pi$
$227$	1.69894	−	8.54116i	0.112763	−	0.566896i	0.995315	−	0.0966827i	$-0.0308232\pi$
$228$	1.12158	−	0.229133i	0.0742785	−	0.0151747i
$229$	12.4390	+	8.31146i	0.821991	+	0.549237i	0.893948	−	0.448171i	$-0.147924\pi$
$229$	12.4390	+	8.31146i	0.821991	+	0.549237i	−0.0719572	+	0.997408i	$0.522924\pi$
$230$	−26.7475	+	14.3859i	−1.76368	+	0.948577i
$231$	−2.74130	−	6.61808i	−0.180364	−	0.435437i
$232$	13.6668	+	7.16927i	0.897267	+	0.470685i
$233$	6.69929	−	16.1735i	0.438885	−	1.05956i	−0.537449	−	0.843296i	$-0.680612\pi$
$233$	6.69929	−	16.1735i	0.438885	−	1.05956i	0.976334	−	0.216267i	$-0.0693880\pi$
$234$	2.39968	−	0.242616i	0.156872	−	0.0158603i
$235$	−3.82004	+	0.759853i	−0.249192	+	0.0495673i
$236$	−15.6908	+	15.8540i	−1.02138	+	1.03200i
$237$	10.7924	−	7.21125i	0.701042	−	0.468421i
$238$	13.0757	−	24.6158i	0.847570	−	1.59560i
$239$	3.35269	+	3.35269i	0.216867	+	0.216867i	0.807177	−	0.590310i	$-0.200994\pi$
$239$	3.35269	+	3.35269i	0.216867	+	0.216867i	−0.590310	+	0.807177i	$0.700994\pi$
$240$	−10.9405	+	4.66487i	−0.706206	+	0.301116i
$241$	−0.661329	+	0.661329i	−0.0426000	+	0.0426000i	−0.728086	−	0.685486i	$-0.759590\pi$
$241$	−0.661329	+	0.661329i	−0.0426000	+	0.0426000i	0.685486	+	0.728086i	$0.259590\pi$
$242$	1.49134	+	4.87092i	0.0958672	+	0.313114i
$243$	0.555570	+	0.831470i	0.0356398	+	0.0533388i
$244$	−23.2193	−	9.47733i	−1.48646	−	0.606724i
$245$	−0.0369964	−	0.185994i	−0.00236362	−	0.0118827i
$246$	5.80480	+	4.73881i	0.370101	+	0.302135i
$247$	0.901867	+	0.373566i	0.0573844	+	0.0237694i
$248$	−12.4426	−	3.66926i	−0.790109	−	0.232998i
$249$	−11.7317	+	4.85943i	−0.743466	+	0.307954i
$250$	1.40270	−	4.66751i	0.0887146	−	0.295199i
$251$	5.85456	−	8.76197i	0.369536	−	0.553050i	−0.599372	−	0.800471i	$-0.704583\pi$
$251$	5.85456	−	8.76197i	0.369536	−	0.553050i	0.968908	+	0.247420i	$0.0795829\pi$
$252$	5.17138	+	1.00087i	0.325766	+	0.0630490i
$253$	19.2672	+	3.83249i	1.21132	+	0.240946i
$254$	−0.352469	+	3.67612i	−0.0221159	+	0.230660i
$255$	−22.2515			−1.39344
$256$	11.5453	+	11.0772i	0.721584	+	0.692327i
$257$	22.7277			1.41771			0.708856	−	0.705353i	$-0.249211\pi$
$257$	22.7277			1.41771			0.708856	+	0.705353i	$0.249211\pi$
$258$	−0.466584	+	4.86630i	−0.0290483	+	0.302962i
$259$	−8.17486	−	1.62608i	−0.507961	−	0.101040i
$260$	−9.95731	−	1.92715i	−0.617526	−	0.119517i
$261$	−3.03142	+	4.53683i	−0.187640	+	0.280823i
$262$	−5.79351	+	19.2780i	−0.357924	+	1.19100i
$263$	−3.14634	+	1.30326i	−0.194011	+	0.0803622i	−0.477574	−	0.878592i	$-0.658484\pi$
$263$	−3.14634	+	1.30326i	−0.194011	+	0.0803622i	0.283562	+	0.958954i	$0.408484\pi$
$264$	7.37892	+	2.17600i	0.454141	+	0.133923i
$265$	−36.9602	−	15.3094i	−2.27045	−	0.940450i
$266$	1.65143	+	1.34816i	0.101256	+	0.0826612i
$267$	−1.88840	−	9.49362i	−0.115568	−	0.581000i
$268$	16.3842	+	6.68749i	1.00083	+	0.408504i
$269$	−15.1477	−	22.6701i	−0.923570	−	1.38222i	−0.924071	−	0.382221i	$-0.875159\pi$
$269$	−15.1477	−	22.6701i	−0.923570	−	1.38222i	0.000500478	−	1.00000i	$-0.499841\pi$
$270$	−1.23105	−	4.02075i	−0.0749191	−	0.244695i
$271$	1.59521	−	1.59521i	0.0969020	−	0.0969020i	−0.656994	−	0.753896i	$-0.728172\pi$
$271$	1.59521	−	1.59521i	0.0969020	−	0.0969020i	0.753896	+	0.656994i	$0.228172\pi$
$272$	11.7408	+	27.5357i	0.711892	+	1.66960i
$273$	3.17610	+	3.17610i	0.192226	+	0.192226i
$274$	−6.75574	+	12.7181i	−0.408129	+	0.768329i
$275$	8.68644	−	5.80409i	0.523812	−	0.350000i
$276$	−10.1613	+	10.2669i	−0.611636	+	0.617996i
$277$	7.44866	−	1.48163i	0.447547	−	0.0890225i	0.0338286	−	0.999428i	$-0.489230\pi$
$277$	7.44866	−	1.48163i	0.447547	−	0.0890225i	0.413718	+	0.910405i	$0.364230\pi$
$278$	12.8052	−	1.29464i	0.768002	−	0.0776476i
$279$	1.75515	−	4.23731i	0.105078	−	0.253681i
$280$	−19.6142	−	10.2892i	−1.17217	−	0.614894i
$281$	7.33309	+	17.7037i	0.437456	+	1.05611i	0.976825	+	0.214042i	$0.0686628\pi$
$281$	7.33309	+	17.7037i	0.437456	+	1.05611i	−0.539369	+	0.842070i	$0.681337\pi$
$282$	−1.63150	+	0.877486i	−0.0971543	+	0.0522535i
$283$	−0.324521	−	0.216838i	−0.0192908	−	0.0128897i	0.545887	−	0.837859i	$-0.316193\pi$
$283$	−0.324521	−	0.216838i	−0.0192908	−	0.0128897i	−0.565178	+	0.824969i	$0.691193\pi$
$284$	22.2413	−	4.54379i	1.31978	−	0.269624i
$285$	0.332021	−	1.66918i	0.0196672	−	0.0988737i
$286$	4.17485	+	5.06033i	0.246864	+	0.299223i
$287$			13.9550i			0.823737i
$288$	−4.32604	+	3.64491i	−0.254914	+	0.214779i
$289$			39.0038i			2.29434i
$290$	17.6983	−	14.6014i	1.03928	−	0.857424i
$291$	3.01057	−	15.1352i	0.176483	−	0.887239i
$292$	11.1727	+	7.38209i	0.653835	+	0.432004i
$293$	−11.5758	−	7.73470i	−0.676265	−	0.451866i	0.169423	−	0.985543i	$-0.445810\pi$
$293$	−11.5758	−	7.73470i	−0.676265	−	0.451866i	−0.845688	+	0.533678i	$0.820810\pi$
$294$	−0.0427239	−	0.0794359i	−0.00249171	−	0.00463280i
$295$	12.6905	+	30.6375i	0.738867	+	1.78378i
$296$	6.87525	−	5.73221i	0.399616	−	0.333178i
$297$	−1.04087	+	2.51287i	−0.0603971	+	0.145812i
$298$	−0.413937	−	4.09420i	−0.0239787	−	0.237171i
$299$	−12.0812	+	2.40311i	−0.698677	+	0.138975i
$300$	0.0397340	+	7.68183i	0.00229404	+	0.443511i
$301$	−7.56970	+	5.05791i	−0.436310	+	0.291533i
$302$	20.1582	+	10.7078i	1.15997	+	0.616167i
$303$	−1.43172	−	1.43172i	−0.0822501	−	0.0822501i
$304$	−2.24076	+	0.469863i	−0.128516	+	0.0269485i
$305$	−26.3642	+	26.3642i	−1.50961	+	1.50961i
$306$	−10.1197	+	3.09837i	−0.578503	+	0.177122i
$307$	−2.89481	−	4.33239i	−0.165216	−	0.247263i	0.739619	−	0.673026i	$-0.235006\pi$
$307$	−2.89481	−	4.33239i	−0.165216	−	0.247263i	−0.904835	+	0.425763i	$0.860006\pi$
$308$	5.55098	+	13.2076i	0.316297	+	0.752574i
$309$	0.794772	+	3.99559i	0.0452130	+	0.227301i
$310$	−12.1962	+	14.9398i	−0.692700	+	0.848523i
$311$	−16.4790	−	6.82582i	−0.934437	−	0.387057i	−0.137077	−	0.990560i	$-0.543771\pi$
$311$	−16.4790	−	6.82582i	−0.934437	−	0.387057i	−0.797360	+	0.603504i	$0.793771\pi$
$312$	−4.79680	+	0.510050i	−0.271565	+	0.0288759i
$313$	−11.1284	+	4.60955i	−0.629016	+	0.260547i	−0.674335	−	0.738426i	$-0.735570\pi$
$313$	−11.1284	+	4.60955i	−0.629016	+	0.260547i	0.0453189	+	0.998973i	$0.485570\pi$
$314$	−7.76926	−	2.33486i	−0.438445	−	0.131764i
$315$	4.35061	−	6.51115i	0.245129	−	0.366862i
$316$	−21.5099	+	14.5340i	−1.21003	+	0.817599i
$317$	9.87835	+	1.96493i	0.554824	+	0.110361i	0.464536	−	0.885554i	$-0.346221\pi$
$317$	9.87835	+	1.96493i	0.554824	+	0.110361i	0.0902879	+	0.995916i	$0.471221\pi$
$318$	−18.9407	−	1.81605i	−1.06214	−	0.101839i
$319$	−14.8409			−0.830933
$320$	21.8324	−	9.44280i	1.22047	−	0.527868i
$321$	−4.28540			−0.239187
$322$	−26.7781	−	2.56750i	−1.49228	−	0.143081i
$323$	−4.20109	−	0.835649i	−0.233755	−	0.0464968i
$324$	−1.11973	−	1.65717i	−0.0622071	−	0.0920650i
$325$	−3.63938	+	5.44671i	−0.201876	+	0.302129i
$326$	−26.0911	−	7.84102i	−1.44505	−	0.434274i
$327$	6.52161	−	2.70134i	0.360646	−	0.149384i
$328$	−11.6585	−	9.41744i	−0.643732	−	0.519991i
$329$	−3.18728	−	1.32022i	−0.175721	−	0.0727859i
$330$	7.23279	−	8.85981i	0.398152	−	0.487717i
$331$	−6.45326	−	32.4427i	−0.354703	−	1.78321i	−0.585979	−	0.810326i	$-0.699290\pi$
$331$	−6.45326	−	32.4427i	−0.354703	−	1.78321i	0.231275	−	0.972888i	$-0.425710\pi$
$332$	23.4128	−	9.84009i	1.28495	−	0.540045i
$333$	1.75826	+	2.63143i	0.0963523	+	0.144201i
$334$	−6.23740	+	1.90972i	−0.341295	+	0.104495i
$335$	18.6034	−	18.6034i	1.01641	−	1.01641i
$336$	−10.3530	−	1.94822i	−0.564801	−	0.106284i
$337$	−7.91958	−	7.91958i	−0.431407	−	0.431407i	0.457700	−	0.889107i	$-0.348673\pi$
$337$	−7.91958	−	7.91958i	−0.431407	−	0.431407i	−0.889107	+	0.457700i	$0.848673\pi$
$338$	12.6035	+	6.69487i	0.685541	+	0.364153i
$339$	−13.1023	+	8.75467i	−0.711619	+	0.475489i
$340$	44.5023	−	0.230187i	2.41348	−	0.0124836i
$341$	12.2350	−	2.43369i	0.662562	−	0.131792i
$342$	−0.0814239	−	0.805353i	−0.00440290	−	0.0435485i
$343$	7.11932	−	17.1875i	0.384407	−	0.928040i
$344$	0.882815	−	9.73729i	0.0475982	−	0.524999i
$345$	8.21826	+	19.8406i	0.442456	+	1.06818i
$346$	−0.386727	−	0.719036i	−0.0207906	−	0.0386556i
$347$	5.60633	+	3.74603i	0.300964	+	0.201097i	0.696877	−	0.717190i	$-0.254572\pi$
$347$	5.60633	+	3.74603i	0.300964	+	0.201097i	−0.395914	+	0.918288i	$0.629572\pi$
$348$	6.01582	−	9.10490i	0.322482	−	0.488074i
$349$	2.99323	−	15.0480i	0.160224	−	0.805499i	−0.814166	−	0.580633i	$-0.802805\pi$
$349$	2.99323	−	15.0480i	0.160224	−	0.805499i	0.974390	−	0.224867i	$-0.0721947\pi$
$350$	−11.0351	+	9.10417i	−0.589853	+	0.486639i
$351$		−	1.70548i		−	0.0910320i
$352$	−14.7801	−	4.27560i	−0.787784	−	0.227890i
$353$		−	22.4783i		−	1.19640i	−0.801347	−	0.598199i	$-0.795883\pi$
$353$		−	22.4783i		−	1.19640i	0.801347	−	0.598199i	$-0.204117\pi$
$354$	10.0375	+	12.1665i	0.533488	+	0.646640i
$355$	6.58407	−	33.1004i	0.349446	−	1.75678i
$356$	3.87495	+	18.9674i	0.205372	+	1.00527i
$357$	−16.3876	−	10.9499i	−0.867326	−	0.579529i
$358$	3.37463	−	1.81501i	0.178355	−	0.0959265i
$359$	5.93041	+	14.3173i	0.312995	+	0.755637i	0.999591	+	0.0285977i	$0.00910417\pi$
$359$	5.93041	+	14.3173i	0.312995	+	0.755637i	−0.686596	+	0.727039i	$0.740896\pi$
$360$	2.50365	+	8.02866i	0.131954	+	0.423148i
$361$	−7.14561	+	17.2510i	−0.376085	+	0.907949i
$362$	5.71257	−	0.577560i	0.300246	−	0.0303559i
$363$	3.53286	−	0.702731i	0.185427	−	0.0368838i
$364$	−6.38497	−	6.31926i	−0.334663	−	0.331219i
$365$	16.5534	−	11.0606i	0.866445	−	0.578940i
$366$	−8.31904	+	15.6611i	−0.434843	+	0.818620i
$367$	−4.86850	−	4.86850i	−0.254134	−	0.254134i	0.568529	−	0.822663i	$-0.307513\pi$
$367$	−4.86850	−	4.86850i	−0.254134	−	0.254134i	−0.822663	+	0.568529i	$0.807513\pi$
$368$	20.2160	−	20.6387i	1.05383	−	1.07587i
$369$	3.74673	−	3.74673i	0.195047	−	0.195047i
$370$	−3.89601	−	12.7248i	−0.202544	−	0.661533i
$371$	−19.6866	−	29.4630i	−1.02207	−	1.52964i
$372$	−3.46642	+	8.49267i	−0.179726	+	0.440324i
$373$	2.07833	+	10.4485i	0.107612	+	0.541002i	0.996551	+	0.0829772i	$0.0264429\pi$
$373$	2.07833	+	10.4485i	0.107612	+	0.541002i	−0.888939	+	0.458025i	$0.848557\pi$
$374$	−22.2989	−	18.2039i	−1.15305	−	0.941303i
$375$	−3.18391	−	1.31882i	−0.164417	−	0.0681036i
$376$	3.25387	−	1.77183i	0.167806	−	0.0913750i
$377$	8.59745	−	3.56118i	0.442791	−	0.183410i
$378$	1.07197	−	3.56698i	0.0551359	−	0.183466i
$379$	2.50860	−	3.75438i	0.128858	−	0.192850i	−0.761431	−	0.648247i	$-0.775503\pi$
$379$	2.50860	−	3.75438i	0.128858	−	0.192850i	0.890289	+	0.455397i	$0.150503\pi$
$380$	−0.646765	+	3.34175i	−0.0331784	+	0.171428i
$381$	2.56115	+	0.509445i	0.131212	+	0.0260997i
$382$	−1.62246	+	16.9217i	−0.0830125	+	0.865789i
$383$	−3.50112			−0.178899			−0.0894494	−	0.995991i	$-0.528511\pi$
$383$	−3.50112			−0.178899			−0.0894494	+	0.995991i	$0.528511\pi$
$384$	8.61425	−	7.33448i	0.439594	−	0.374286i
$385$	21.2993			1.08552
$386$	−1.76134	+	18.3701i	−0.0896499	+	0.935015i
$387$	3.39035	+	0.674383i	0.172341	+	0.0342808i
$388$	−5.86449	+	30.3011i	−0.297725	+	1.53830i
$389$	3.65674	−	5.47270i	0.185404	−	0.277477i	−0.727111	−	0.686520i	$-0.759137\pi$
$389$	3.65674	−	5.47270i	0.185404	−	0.277477i	0.912515	+	0.409043i	$0.134137\pi$
$390$	−2.06403	+	6.86810i	−0.104516	+	0.347780i
$391$	49.9361	−	20.6842i	2.52538	−	1.04604i
$392$	0.0862684	+	0.158428i	0.00435721	+	0.00800181i
$393$	13.1504	+	5.44706i	0.663348	+	0.274768i
$394$	13.0236	+	10.6320i	0.656122	+	0.535632i
$395$	7.52935	+	37.8526i	0.378843	+	1.90457i
$396$	2.05571	−	5.03644i	0.103303	−	0.253091i
$397$	−17.4036	−	26.0463i	−0.873461	−	1.30723i	−0.950667	−	0.310212i	$-0.899600\pi$
$397$	−17.4036	−	26.0463i	−0.873461	−	1.30723i	0.0772060	−	0.997015i	$-0.475400\pi$
$398$	2.41822	+	7.89822i	0.121214	+	0.395902i
$399$	1.06592	−	1.06592i	0.0533629	−	0.0533629i
$400$	−0.158934	−	15.3630i	−0.00794668	−	0.768152i
$401$	−8.95693	−	8.95693i	−0.447288	−	0.447288i	0.447164	−	0.894452i	$-0.352434\pi$
$401$	−8.95693	−	8.95693i	−0.447288	−	0.447288i	−0.894452	+	0.447164i	$0.852434\pi$
$402$	5.87017	−	11.0510i	0.292777	−	0.551172i
$403$	−6.50383	+	4.34572i	−0.323979	+	0.216476i
$404$	2.87821	+	2.84859i	0.143196	+	0.141722i
$405$	−2.91624	+	0.580077i	−0.144909	+	0.0288243i
$406$	20.2197	−	2.04428i	1.00349	−	0.101456i
$407$	−3.29412	+	7.95271i	−0.163284	+	0.394201i
$408$	20.2070	−	6.30134i	1.00040	−	0.311963i
$409$	−2.54664	−	6.14813i	−0.125923	−	0.304005i	0.848328	−	0.529471i	$-0.177610\pi$
$409$	−2.54664	−	6.14813i	−0.125923	−	0.304005i	−0.974251	+	0.225466i	$0.927610\pi$
$410$	−19.6228	+	10.5539i	−0.969100	+	0.521221i
$411$	8.46692	+	5.65742i	0.417642	+	0.279060i
$412$	−1.63086	−	7.98285i	−0.0803465	−	0.393287i
$413$	−5.73040	+	28.8087i	−0.281975	+	1.41758i
$414$	6.50023	+	7.87892i	0.319469	+	0.387228i
$415$		−	37.7568i		−	1.85341i
$416$	9.58819	−	1.06971i	0.470100	−	0.0524468i
$417$		−	9.10077i		−	0.445667i
$418$	1.69828	−	1.40111i	0.0830658	−	0.0685306i
$419$	3.14329	−	15.8024i	0.153560	−	0.771998i	−0.824855	−	0.565345i	$-0.808743\pi$
$419$	3.14329	−	15.8024i	0.153560	−	0.771998i	0.978414	−	0.206653i	$-0.0662570\pi$
$420$	−8.63375	+	13.0671i	−0.421284	+	0.637611i
$421$	0.717737	+	0.479577i	0.0349804	+	0.0233731i	0.572937	−	0.819599i	$-0.305804\pi$
$421$	0.717737	+	0.479577i	0.0349804	+	0.0233731i	−0.537957	+	0.842972i	$0.680804\pi$
$422$	−11.9058	−	22.1363i	−0.579567	−	1.07758i
$423$	0.501284	+	1.21021i	0.0243732	+	0.0588422i
$424$	37.8998	+	3.43612i	1.84058	+	0.166873i
$425$	10.9999	−	26.5561i	0.533574	−	1.28816i
$426$	−1.61466	−	15.9704i	−0.0782306	−	0.773768i
$427$	−32.3903	+	6.44283i	−1.56748	+	0.311791i
$428$	8.57068	−	0.0443315i	0.414279	−	0.00214284i
$429$	3.85699	−	2.57716i	0.186217	−	0.124426i
$430$	−12.8370	−	6.81890i	−0.619055	−	0.328836i
$431$	14.6897	+	14.6897i	0.707580	+	0.707580i	0.966026	−	0.258446i	$-0.0832104\pi$
$431$	14.6897	+	14.6897i	0.707580	+	0.707580i	−0.258446	+	0.966026i	$0.583210\pi$
$432$	2.25657	+	3.30271i	0.108569	+	0.158902i
$433$	−14.6233	+	14.6233i	−0.702752	+	0.702752i	−0.965000	−	0.262249i	$-0.915536\pi$
$433$	−14.6233	+	14.6233i	−0.702752	+	0.702752i	0.262249	+	0.965000i	$0.415536\pi$
$434$	−16.3341	+	5.00105i	−0.784060	+	0.240058i
$435$	−9.01354	−	13.4897i	−0.432166	−	0.646782i
$436$	−13.0151	+	5.47007i	−0.623310	+	0.261969i
$437$	0.806502	+	4.05456i	0.0385802	+	0.193956i
$438$	5.98814	−	7.33518i	0.286125	−	0.350488i
$439$	−14.8852	−	6.16564i	−0.710430	−	0.294270i	−0.00194745	−	0.999998i	$-0.500620\pi$
$439$	−14.8852	−	6.16564i	−0.710430	−	0.294270i	−0.708482	+	0.705728i	$0.750620\pi$
$440$	−14.3737	+	17.7942i	−0.685241	+	0.848305i
$441$	−0.0589237	+	0.0244070i	−0.00280589	+	0.00116224i
$442$	17.2860	+	5.19488i	0.822213	+	0.247095i
$443$	−11.8396	+	17.7192i	−0.562517	+	0.841867i	−0.998306	−	0.0581824i	$-0.981470\pi$
$443$	−11.8396	+	17.7192i	−0.562517	+	0.841867i	0.435789	+	0.900049i	$0.356470\pi$
$444$	−3.54370	−	5.24460i	−0.168177	−	0.248898i
$445$	28.2281	+	5.61492i	1.33814	+	0.266173i
$446$	−36.9682	−	3.54454i	−1.75050	−	0.167839i
$447$	−2.90979			−0.137629
$448$	20.7258	+	3.78929i	0.979203	+	0.179027i
$449$	−28.6432			−1.35176			−0.675878	−	0.737014i	$-0.736235\pi$
$449$	−28.6432			−1.35176			−0.675878	+	0.737014i	$0.736235\pi$
$450$	5.40715	+	0.518442i	0.254895	+	0.0244396i
$451$	14.1350	+	2.81163i	0.665592	+	0.132395i
$452$	26.1137	−	17.6447i	1.22828	−	0.829935i
$453$	8.96700	−	13.4201i	0.421307	−	0.630530i
$454$	11.7946	+	3.54456i	0.553546	+	0.166354i
$455$	−12.3388	+	5.11091i	−0.578454	+	0.239603i
$456$	0.171177	+	1.60984i	0.00801609	+	0.0753877i
$457$	28.5281	+	11.8167i	1.33449	+	0.552764i	0.931933	−	0.362631i	$-0.118121\pi$
$457$	28.5281	+	11.8167i	1.33449	+	0.552764i	0.402557	+	0.915395i	$0.368121\pi$
$458$	−13.3795	+	16.3892i	−0.625183	+	0.765817i
$459$	1.45997	+	7.33977i	0.0681457	+	0.342591i
$460$	−16.6415	−	39.5957i	−0.775916	−	1.84616i
$461$	−6.46781	−	9.67976i	−0.301236	−	0.450832i	0.649713	−	0.760180i	$-0.274889\pi$
$461$	−6.46781	−	9.67976i	−0.301236	−	0.450832i	−0.950949	+	0.309348i	$0.899889\pi$
$462$	9.68666	−	2.96579i	0.450664	−	0.137981i
$463$	−25.5267	+	25.5267i	−1.18633	+	1.18633i	−0.208252	+	0.978075i	$0.566777\pi$
$463$	−25.5267	+	25.5267i	−1.18633	+	1.18633i	−0.978075	+	0.208252i	$0.933223\pi$
$464$	−11.9373	+	18.2718i	−0.554174	+	0.848247i
$465$	9.64295	+	9.64295i	0.447181	+	0.447181i
$466$	21.8642	+	11.6140i	1.01284	+	0.538010i
$467$	−22.6409	+	15.1282i	−1.04770	+	0.700047i	−0.955289	−	0.295674i	$-0.904456\pi$
$467$	−22.6409	+	15.1282i	−1.04770	+	0.700047i	−0.0924061	+	0.995721i	$0.529456\pi$
$468$	0.0176429	+	3.41092i	0.000815541	+	0.157670i
$469$	22.8556	−	4.54626i	1.05537	−	0.209927i
$470$	−0.554072	−	5.48025i	−0.0255574	−	0.252785i
$471$	−2.19523	+	5.29976i	−0.101151	+	0.244200i
$472$	−20.2006	−	24.2288i	−0.929810	−	1.11522i
$473$	3.59803	+	8.68642i	0.165438	+	0.399402i
$474$	8.69497	+	16.1664i	0.399373	+	0.742549i
$475$	1.82796	+	1.22140i	0.0838725	+	0.0560418i
$476$	32.8881	+	21.7299i	1.50743	+	0.995990i
$477$	−2.62485	+	13.1960i	−0.120184	+	0.604205i
$478$	−5.17231	+	4.26724i	−0.236576	+	0.195179i
$479$		−	15.0477i		−	0.687549i	−0.939052	−	0.343775i	$-0.888294\pi$
$479$		−	15.0477i		−	0.687549i	0.939052	−	0.343775i	$-0.111706\pi$
$480$	−5.09030	−	16.0312i	−0.232339	−	0.731721i
$481$		−	5.39750i		−	0.246105i
$482$	−0.841727	−	1.02026i	−0.0383396	−	0.0464714i
$483$	−3.71097	+	18.6563i	−0.168855	+	0.848891i
$484$	−7.05837	+	1.44199i	−0.320835	+	0.0655450i
$485$	38.1513	+	25.4919i	1.73236	+	1.15753i
$486$	−1.24550	+	0.669879i	−0.0564969	+	0.0303863i
$487$	−8.56436	−	20.6762i	−0.388088	−	0.936927i	−0.990345	−	0.138625i	$-0.955732\pi$
$487$	−8.56436	−	20.6762i	−0.388088	−	0.936927i	0.602257	−	0.798302i	$-0.294268\pi$
$488$	16.4759	−	31.4079i	0.745827	−	1.42177i
$489$	−7.37213	+	17.7979i	−0.333379	+	0.804849i
$490$	0.266828	−	0.0269772i	0.0120540	−	0.00121870i
$491$	4.04017	−	0.803639i	0.182330	−	0.0362677i	−0.103081	−	0.994673i	$-0.532870\pi$
$491$	4.04017	−	0.803639i	0.182330	−	0.0362677i	0.285411	+	0.958405i	$0.407870\pi$
$492$	−7.45461	+	7.53213i	−0.336080	+	0.339574i
$493$	−33.9517	+	22.6858i	−1.52911	+	1.02172i
$494$	−0.647621	+	1.21919i	−0.0291378	+	0.0548538i
$495$	−5.71860	−	5.71860i	−0.257032	−	0.257032i
$496$	6.84490	−	17.0210i	0.307345	−	0.764264i
$497$	21.1376	−	21.1376i	0.948150	−	0.948150i
$498$	−5.25739	−	17.1713i	−0.235589	−	0.769464i
$499$	19.3227	+	28.9185i	0.865003	+	1.29457i	0.954387	+	0.298571i	$0.0965099\pi$
$499$	19.3227	+	28.9185i	0.865003	+	1.29457i	−0.0893848	+	0.995997i	$0.528490\pi$
$500$	6.38139	+	2.60467i	0.285384	+	0.116484i
$501$	0.899873	+	4.52397i	0.0402034	+	0.202116i
$502$	11.5445	+	9.42446i	0.515256	+	0.420634i
$503$	29.3826	+	12.1707i	1.31011	+	0.542664i	0.924915	−	0.380173i	$-0.124135\pi$
$503$	29.3826	+	12.1707i	1.31011	+	0.542664i	0.385191	+	0.922837i	$0.374135\pi$
$504$	−2.10700	+	7.14495i	−0.0938533	+	0.318261i
$505$	5.56209	−	2.30389i	0.247510	−	0.102522i
$506$	−7.99584	+	26.6063i	−0.355459	+	1.18279i
$507$	5.60644	−	8.39063i	0.248991	−	0.372641i
$508$	−5.12751	−	0.992383i	−0.227497	−	0.0440299i
$509$	−38.5882	−	7.67567i	−1.71039	−	0.340218i	−0.759681	−	0.650296i	$-0.774645\pi$
$509$	−38.5882	−	7.67567i	−1.71039	−	0.340218i	−0.950711	+	0.310077i	$0.899645\pi$
$510$	3.00343	−	31.3247i	0.132994	−	1.38708i
$511$	17.6341			0.780085
$512$	−17.1524	+	14.7579i	−0.758036	+	0.652212i
$513$	−0.572374			−0.0252709
$514$	−3.06771	+	31.9950i	−0.135311	+	1.41124i
$515$	−11.8804	−	2.36316i	−0.523513	−	0.104133i
$516$	−6.78759	−	1.31367i	−0.298807	−	0.0578313i
$517$	−1.97942	+	2.96241i	−0.0870547	+	0.130287i
$518$	3.39255	−	11.2887i	0.149060	−	0.495999i
$519$	−0.533364	+	0.220927i	−0.0234121	+	0.00969760i
$520$	4.05696	−	13.7574i	0.177910	−	0.603300i
$521$	−2.82551	−	1.17036i	−0.123788	−	0.0512745i	0.319930	−	0.947441i	$-0.396341\pi$
$521$	−2.82551	−	1.17036i	−0.123788	−	0.0512745i	−0.443718	+	0.896167i	$0.646341\pi$
$522$	−5.97759	−	4.87986i	−0.261632	−	0.213586i
$523$	−4.36719	−	21.9554i	−0.190964	−	0.960041i	−0.950772	−	0.309893i	$-0.899707\pi$
$523$	−4.36719	−	21.9554i	−0.190964	−	0.960041i	0.759808	−	0.650148i	$-0.225293\pi$
$524$	−26.3567	−	10.7579i	−1.15140	−	0.469963i
$525$	5.62006	+	8.41101i	0.245279	+	0.367087i
$526$	−1.40998	−	4.60519i	−0.0614783	−	0.200796i
$527$	24.2699	−	24.2699i	1.05722	−	1.05722i
$528$	−4.05926	+	10.0940i	−0.176657	+	0.439286i
$529$	−20.6229	−	20.6229i	−0.896647	−	0.896647i
$530$	26.5407	−	49.9646i	1.15286	−	2.17032i
$531$	9.27330	−	6.19622i	0.402427	−	0.268893i
$532$	−2.12079	+	2.14285i	−0.0919480	+	0.0929041i
$533$	−8.86318	+	1.76300i	−0.383907	+	0.0763638i
$534$	13.6196	−	1.37699i	0.589378	−	0.0595881i
$535$	4.87619	−	11.7722i	0.210816	−	0.508955i
$536$	−11.6259	+	22.1624i	−0.502161	+	0.957268i
$537$	−1.03687	−	2.50322i	−0.0447441	−	0.108022i
$538$	33.9586	−	18.2643i	1.46406	−	0.787431i
$539$	−0.144237	−	0.0963759i	−0.00621271	−	0.00415120i
$540$	5.82641	−	1.19031i	0.250729	−	0.0512226i
$541$	−4.14114	+	20.8189i	−0.178042	+	0.895076i	0.783705	+	0.621134i	$0.213328\pi$
$541$	−4.14114	+	20.8189i	−0.178042	+	0.895076i	−0.961746	+	0.273942i	$0.911672\pi$
$542$	2.03035	+	2.46098i	0.0872110	+	0.105708i
$543$		−	4.05999i		−	0.174231i
$544$	−40.3483	+	12.8116i	−1.72992	+	0.549291i
$545$			20.9889i			0.899065i
$546$	−4.89988	+	4.04248i	−0.209695	+	0.173002i
$547$	−3.65207	+	18.3602i	−0.156151	+	0.785025i	0.820742	+	0.571298i	$0.193560\pi$
$547$	−3.65207	+	18.3602i	−0.156151	+	0.785025i	−0.976894	+	0.213726i	$0.931440\pi$
$548$	−16.9921	−	11.2271i	−0.725868	−	0.479598i
$549$	10.4262	+	6.96656i	0.444979	+	0.297326i
$550$	6.99829	+	13.0118i	0.298408	+	0.554826i
$551$	−1.19516	−	2.88537i	−0.0509155	−	0.122921i
$552$	−13.0818	−	15.6904i	−0.556798	−	0.667827i
$553$	−13.0820	+	31.5827i	−0.556302	+	1.34303i
$554$	1.08038	+	10.6859i	0.0459009	+	0.454000i
$555$	−9.22930	+	1.83582i	−0.391762	+	0.0779263i
$556$	0.0941455	+	18.2013i	0.00399266	+	0.771907i
$557$	−22.3315	+	14.9214i	−0.946217	+	0.632242i	−0.929974	−	0.367626i	$-0.880171\pi$
$557$	−22.3315	+	14.9214i	−0.946217	+	0.632242i	−0.0162431	+	0.999868i	$0.505171\pi$
$558$	5.72820	+	3.04277i	0.242494	+	0.128811i
$559$	−4.16873	−	4.16873i	−0.176318	−	0.176318i
$560$	17.1321	−	26.2232i	0.723963	−	1.10813i
$561$	−14.3929	+	14.3929i	−0.607669	+	0.607669i
$562$	−25.9122	+	7.93363i	−1.09304	+	0.334660i
$563$	−5.66208	−	8.47391i	−0.238628	−	0.357133i	0.692755	−	0.721173i	$-0.256397\pi$
$563$	−5.66208	−	8.47391i	−0.238628	−	0.357133i	−0.931383	+	0.364041i	$0.881397\pi$
$564$	−1.01507	−	2.41519i	−0.0427423	−	0.101698i
$565$	−9.14085	−	45.9542i	−0.384558	−	1.93331i
$566$	0.349058	−	0.427579i	0.0146720	−	0.0179725i
$567$	−2.43319	−	1.00786i	−0.102185	−	0.0423262i
$568$	3.39449	+	31.9237i	0.142430	+	1.33949i
$569$	−0.943616	+	0.390858i	−0.0395584	+	0.0163856i	−0.402375	−	0.915475i	$-0.631815\pi$
$569$	−0.943616	+	0.390858i	−0.0395584	+	0.0163856i	0.362817	+	0.931861i	$0.381815\pi$
$570$	2.30499	+	0.692705i	0.0965453	+	0.0290142i
$571$	5.69323	−	8.52052i	0.238254	−	0.356573i	−0.693003	−	0.720935i	$-0.743713\pi$
$571$	5.69323	−	8.52052i	0.238254	−	0.356573i	0.931257	+	0.364362i	$0.118713\pi$
$572$	−7.68722	+	5.19415i	−0.321419	+	0.217178i
$573$	11.7893	+	2.34505i	0.492507	+	0.0979657i
$574$	−19.6452	−	1.88360i	−0.819976	−	0.0786199i
$575$	−27.7415			−1.15690
$576$	−4.54724	−	6.58199i	−0.189468	−	0.274250i
$577$	−7.36156			−0.306466			−0.153233	−	0.988190i	$-0.548968\pi$
$577$	−7.36156			−0.306466			−0.153233	+	0.988190i	$0.548968\pi$
$578$	−54.9079	−	5.26461i	−2.28387	−	0.218979i
$579$	12.7985	+	2.54577i	0.531886	+	0.105799i
$580$	18.1664	+	26.8858i	0.754318	+	1.11637i
$581$	18.5800	−	27.8070i	0.770829	−	1.15363i
$582$	20.9003	+	6.28105i	0.866345	+	0.260358i
$583$	−33.8096	+	14.0044i	−1.40025	+	0.580002i
$584$	−11.9002	+	14.7321i	−0.492436	+	0.609619i
$585$	4.68503	+	1.94060i	0.193702	+	0.0802341i
$586$	12.4510	−	15.2519i	0.514348	−	0.630050i
$587$	8.82554	+	44.3690i	0.364269	+	1.83130i	0.533590	+	0.845743i	$0.320843\pi$
$587$	8.82554	+	44.3690i	0.364269	+	1.83130i	−0.169321	+	0.985561i	$0.554157\pi$
$588$	0.117593	−	0.0494229i	0.00484946	−	0.00203816i
$589$	1.45846	+	2.18273i	0.0600947	+	0.0899380i
$590$	−44.8431	+	13.7297i	−1.84616	+	0.565245i
$591$	8.40616	−	8.40616i	0.345783	−	0.345783i
$592$	7.14156	+	10.4524i	0.293516	+	0.429591i
$593$	17.1093	+	17.1093i	0.702593	+	0.702593i	0.964966	−	0.262373i	$-0.0845052\pi$
$593$	17.1093	+	17.1093i	0.702593	+	0.702593i	−0.262373	+	0.964966i	$0.584505\pi$
$594$	−3.39702	−	1.80447i	−0.139381	−	0.0740381i
$595$	48.7266	−	32.5581i	1.99760	−	1.33475i
$596$	5.81951	−	0.0301012i	0.238376	−	0.00123299i
$597$	5.72856	−	1.13948i	0.234454	−	0.0466359i
$598$	−1.75231	−	17.3318i	−0.0716572	−	0.708751i
$599$	−15.2273	+	36.7620i	−0.622172	+	1.50206i	0.226976	+	0.973900i	$0.427116\pi$
$599$	−15.2273	+	36.7620i	−0.622172	+	1.50206i	−0.849148	+	0.528156i	$0.822884\pi$
$600$	−10.8195	−	0.980933i	−0.441705	−	0.0400464i
$601$	−1.25340	−	3.02598i	−0.0511273	−	0.123432i	0.896252	−	0.443545i	$-0.146279\pi$
$601$	−1.25340	−	3.02598i	−0.0511273	−	0.123432i	−0.947380	+	0.320113i	$0.896279\pi$
$602$	−6.09858	−	11.3390i	−0.248559	−	0.462143i
$603$	−7.35704	−	4.91582i	−0.299602	−	0.200188i
$604$	−17.7949	+	26.9325i	−0.724066	+	1.09587i
$605$	−2.08948	+	10.5045i	−0.0849495	+	0.427070i
$606$	2.20876	−	1.82226i	0.0897248	−	0.0740244i
$607$		−	29.3038i		−	1.18940i	−0.803946	−	0.594702i	$-0.797270\pi$
$607$		−	29.3038i		−	1.18940i	0.803946	−	0.594702i	$-0.202730\pi$
$608$	−0.359002	−	3.21787i	−0.0145595	−	0.130502i
$609$		−	14.3704i		−	0.582317i
$610$	−33.5558	−	40.6730i	−1.35864	−	1.64680i
$611$	0.435840	−	2.19112i	0.0176322	−	0.0886431i
$612$	−2.99583	−	14.6642i	−0.121099	−	0.592767i
$613$	15.3167	+	10.2343i	0.618637	+	0.413360i	0.825014	−	0.565112i	$-0.191167\pi$
$613$	15.3167	+	10.2343i	0.618637	+	0.413360i	−0.206377	+	0.978473i	$0.566167\pi$
$614$	6.48969	−	3.49042i	0.261903	−	0.140862i
$615$	6.02917	+	14.5557i	0.243120	+	0.586942i
$616$	−19.3424	+	6.03171i	−0.779326	+	0.243025i
$617$	6.45988	−	15.5955i	0.260065	−	0.627853i	−0.738877	−	0.673840i	$-0.764643\pi$
$617$	6.45988	−	15.5955i	0.260065	−	0.627853i	0.998942	+	0.0459877i	$0.0146435\pi$
$618$	−5.73210	+	0.579534i	−0.230579	+	0.0233123i
$619$	0.475684	−	0.0946195i	0.0191194	−	0.00380308i	−0.185521	−	0.982640i	$-0.559397\pi$
$619$	0.475684	−	0.0946195i	0.0191194	−	0.00380308i	0.204641	+	0.978837i	$0.434397\pi$
$620$	−19.3854	−	19.1859i	−0.778536	−	0.770524i
$621$	6.00533	−	4.01263i	0.240985	−	0.161021i
$622$	11.8334	−	22.2771i	0.474475	−	0.893230i
$623$	18.0262	+	18.0262i	0.722204	+	0.722204i
$624$	−0.0705705	−	6.82157i	−0.00282508	−	0.273081i
$625$	20.8256	−	20.8256i	0.833023	−	0.833023i
$626$	−4.98704	−	16.2883i	−0.199322	−	0.651012i
$627$	−0.864915	−	1.29444i	−0.0345414	−	0.0516948i
$628$	4.33558	−	10.6221i	0.173009	−	0.423868i
$629$	4.62051	+	23.2289i	0.184232	+	0.926195i
$630$	8.57889	+	7.00346i	0.341791	+	0.279025i
$631$	5.03526	+	2.08567i	0.200451	+	0.0830293i	0.480650	−	0.876912i	$-0.340401\pi$
$631$	5.03526	+	2.08567i	0.200451	+	0.0830293i	−0.280200	+	0.959942i	$0.590401\pi$
$632$	−17.5569	−	32.2425i	−0.698378	−	1.28254i
$633$	−16.4202	+	6.80147i	−0.652645	+	0.270334i
$634$	−4.09949	+	13.6411i	−0.162812	+	0.541758i
$635$	−4.31371	+	6.45592i	−0.171184	+	0.256195i
$636$	5.11313	−	26.4189i	0.202749	−	1.04758i
$637$	0.106683	+	0.0212206i	0.00422694	+	0.000840791i
$638$	2.00318	−	20.8924i	0.0793068	−	0.827140i
$639$	−11.3503			−0.449013
$640$	10.3463	+	32.0093i	0.408973	+	1.26528i
$641$	−46.1090			−1.82120			−0.910599	−	0.413291i	$-0.864379\pi$
$641$	−46.1090			−1.82120			−0.910599	+	0.413291i	$0.864379\pi$
$642$	0.578429	−	6.03280i	0.0228288	−	0.238096i
$643$	−31.4699	−	6.25975i	−1.24105	−	0.246861i	−0.469446	−	0.882961i	$-0.655546\pi$
$643$	−31.4699	−	6.25975i	−1.24105	−	0.246861i	−0.771606	+	0.636101i	$0.780546\pi$
$644$	7.22885	−	37.3505i	0.284856	−	1.47182i
$645$	−5.71031	+	8.54608i	−0.224843	+	0.336502i
$646$	1.74344	−	5.80133i	0.0685948	−	0.228250i
$647$	−12.2413	+	5.07052i	−0.481256	+	0.199343i	−0.610103	−	0.792322i	$-0.708872\pi$
$647$	−12.2413	+	5.07052i	−0.481256	+	0.199343i	0.128848	+	0.991664i	$0.458872\pi$
$648$	2.48403	−	1.35262i	0.0975819	−	0.0531361i
$649$	28.0258	+	11.6087i	1.10011	+	0.455680i
$650$	−7.17642	−	5.85854i	−0.281482	−	0.229791i
$651$	2.35653	+	11.8471i	0.0923595	+	0.464323i
$652$	14.5600	−	35.6716i	0.570212	−	1.39701i
$653$	−6.03994	−	9.03941i	−0.236361	−	0.353739i	0.694259	−	0.719725i	$-0.255732\pi$
$653$	−6.03994	−	9.03941i	−0.236361	−	0.353739i	−0.930621	+	0.365985i	$0.880732\pi$
$654$	2.92256	+	9.54546i	0.114281	+	0.373257i
$655$	−29.9266	+	29.9266i	−1.16933	+	1.16933i
$656$	14.8311	−	15.1412i	0.579057	−	0.591163i
$657$	−4.73452	−	4.73452i	−0.184711	−	0.184711i
$658$	2.28875	−	4.30872i	0.0892249	−	0.167972i
$659$	15.5532	−	10.3923i	0.605867	−	0.404827i	−0.214451	−	0.976735i	$-0.568796\pi$
$659$	15.5532	−	10.3923i	0.605867	−	0.404827i	0.820318	+	0.571907i	$0.193796\pi$
$660$	11.4962	+	11.3779i	0.447489	+	0.442884i
$661$	−11.3803	+	2.26368i	−0.442641	+	0.0880468i	−0.411379	−	0.911464i	$-0.634953\pi$
$661$	−11.3803	+	2.26368i	−0.442641	+	0.0880468i	−0.0312624	+	0.999511i	$0.509953\pi$
$662$	46.5426	−	4.70561i	1.80893	−	0.182889i
$663$	4.88423	−	11.7916i	0.189688	−	0.457947i
$664$	10.6923	+	34.2878i	0.414941	+	1.33062i
$665$	1.71526	+	4.14101i	0.0665150	+	0.160581i
$666$	−3.94174	+	2.12003i	−0.152739	+	0.0821494i
$667$	32.7675	+	21.8945i	1.26876	+	0.847760i
$668$	−1.84652	−	9.03851i	−0.0714441	−	0.349710i
$669$	−5.12314	+	25.7558i	−0.198072	+	0.995776i
$670$	23.6780	+	28.7001i	0.914762	+	1.10878i
$671$			34.1063i			1.31666i
$672$	4.14003	−	14.3115i	0.159705	−	0.552078i
$673$		−	22.8817i		−	0.882025i	−0.897501	−	0.441012i	$-0.854620\pi$
$673$		−	22.8817i		−	0.882025i	0.897501	−	0.441012i	$-0.145380\pi$
$674$	12.2178	−	10.0799i	0.470612	−	0.388263i
$675$	0.749335	−	3.76716i	0.0288419	−	0.144998i
$676$	−11.1259	+	16.8390i	−0.427920	+	0.647655i
$677$	−17.3383	−	11.5851i	−0.666365	−	0.445251i	0.175833	−	0.984420i	$-0.443738\pi$
$677$	−17.3383	−	11.5851i	−0.666365	−	0.445251i	−0.842197	+	0.539169i	$0.818738\pi$
$678$	−10.5560	−	19.6265i	−0.405399	−	0.753753i
$679$	15.5530	+	37.5483i	0.596870	+	1.44097i
$680$	−5.68274	+	62.6796i	−0.217923	+	2.40365i
$681$	3.33259	−	8.04559i	0.127705	−	0.308308i
$682$	1.77461	+	17.5524i	0.0679532	+	0.672116i
$683$	−10.1129	+	2.01157i	−0.386958	+	0.0769707i	−0.384735	−	0.923027i	$-0.625707\pi$
$683$	−10.1129	+	2.01157i	−0.386958	+	0.0769707i	−0.00222214	+	0.999998i	$0.500707\pi$
$684$	1.14473	−	0.00592108i	0.0437699	−	0.000226398i
$685$	−25.1753	+	16.8216i	−0.961900	+	0.642721i
$686$	23.2350	+	12.3422i	0.887115	+	0.471227i
$687$	10.5785	+	10.5785i	0.403594	+	0.403594i
$688$	13.5886	+	2.55710i	0.518060	+	0.0974885i
$689$	16.2256	−	16.2256i	0.618148	−	0.618148i
$690$	−29.0401	+	8.89129i	−1.10554	+	0.338486i
$691$	6.74284	+	10.0914i	0.256510	+	0.383894i	0.937265	−	0.348617i	$-0.113348\pi$
$691$	6.74284	+	10.0914i	0.256510	+	0.383894i	−0.680756	+	0.732510i	$0.738348\pi$
$692$	1.06443	−	0.447365i	0.0404635	−	0.0170063i
$693$	−1.39750	−	7.02571i	−0.0530867	−	0.266885i
$694$	−6.03023	+	7.38672i	−0.228904	+	0.280396i
$695$	25.0002	+	10.3554i	0.948311	+	0.392803i
$696$	12.0055	+	9.69776i	0.455067	+	0.367593i
$697$	36.6346	−	15.1746i	1.38764	−	0.574778i
$698$	20.7799	+	6.24487i	0.786530	+	0.236372i
$699$	9.72587	−	14.5558i	0.367866	−	0.550550i
$700$	−11.3270	−	16.7637i	−0.428120	−	0.633607i
$701$	−20.1307	−	4.00425i	−0.760328	−	0.151239i	−0.200325	−	0.979729i	$-0.564200\pi$
$701$	−20.1307	−	4.00425i	−0.760328	−	0.151239i	−0.560003	+	0.828491i	$0.689200\pi$
$702$	2.40091	+	0.230201i	0.0906164	+	0.00868837i
$703$	−1.81144			−0.0683199
$704$	8.01399	−	20.2298i	0.302039	−	0.762438i
$705$	−3.89488			−0.146690
$706$	31.6440	+	3.03405i	1.19094	+	0.114188i
$707$	5.23007	+	1.04033i	0.196697	+	0.0391255i
$708$	−18.4823	+	12.4882i	−0.694606	+	0.469336i
$709$	21.1508	−	31.6544i	0.794336	−	1.18881i	−0.184232	−	0.982883i	$-0.558980\pi$
$709$	21.1508	−	31.6544i	0.794336	−	1.18881i	0.978568	−	0.205925i	$-0.0660202\pi$
$710$	45.7086	+	13.7366i	1.71541	+	0.515524i
$711$	11.9919	−	4.96720i	0.449730	−	0.186284i
$712$	−27.2246	+	2.89483i	−1.02028	+	0.108488i
$713$	−30.6042	−	12.6767i	−1.14614	−	0.474745i
$714$	17.6267	−	21.5919i	0.659664	−	0.808055i
$715$	2.69084	+	13.5278i	0.100632	+	0.505910i
$716$	2.09960	+	4.99565i	0.0784658	+	0.186696i
$717$	2.63419	+	3.94234i	0.0983756	+	0.147230i
$718$	−20.9557	+	6.41608i	−0.782061	+	0.239446i
$719$	−19.8069	+	19.8069i	−0.738673	+	0.738673i	−0.972321	−	0.233648i	$-0.924934\pi$
$719$	−19.8069	+	19.8069i	−0.738673	+	0.738673i	0.233648	+	0.972321i	$0.424934\pi$
$720$	−11.6403	+	2.44085i	−0.433810	+	0.0909652i
$721$	−7.58671	−	7.58671i	−0.282544	−	0.282544i
$722$	−23.3208	−	12.3878i	−0.867910	−	0.461026i
$723$	−0.777641	+	0.519603i	−0.0289208	+	0.0193242i
$724$	0.0419997	+	8.11987i	0.00156091	+	0.301773i
$725$	20.5552	−	4.08868i	0.763399	−	0.151850i
$726$	0.512419	+	5.06827i	0.0190177	+	0.188101i
$727$	0.824920	−	1.99153i	0.0305946	−	0.0738619i	−0.907844	−	0.419309i	$-0.862273\pi$
$727$	0.824920	−	1.99153i	0.0305946	−	0.0738619i	0.938438	+	0.345447i	$0.112273\pi$
$728$	9.75781	−	8.13554i	0.361648	−	0.301523i
$729$	0.382683	+	0.923880i	0.0141735	+	0.0342178i
$730$	13.3364	+	24.7961i	0.493601	+	0.917745i
$731$	21.5093	+	14.3720i	0.795549	+	0.531569i
$732$	−20.9242	−	13.8251i	−0.773380	−	0.510990i
$733$	−1.00827	+	5.06890i	−0.0372412	+	0.187224i	−0.994928	−	0.100588i	$-0.967928\pi$
$733$	−1.00827	+	5.06890i	−0.0372412	+	0.187224i	0.957687	+	0.287812i	$0.0929277\pi$
$734$	7.51080	−	6.19653i	0.277229	−	0.228718i
$735$		−	0.189638i		−	0.00699489i
$736$	26.3256	+	31.2450i	0.970373	+	1.15171i
$737$		−	24.0664i		−	0.886499i
$738$	4.76877	+	5.78022i	0.175541	+	0.212773i
$739$	7.36113	−	37.0069i	0.270783	−	1.36132i	−0.570754	−	0.821121i	$-0.693349\pi$
$739$	7.36113	−	37.0069i	0.270783	−	1.36132i	0.841537	−	0.540199i	$-0.181651\pi$
$740$	18.4394	−	3.76707i	0.677845	−	0.138480i
$741$	0.811659	+	0.542333i	0.0298170	+	0.0199231i
$742$	44.1340	−	23.7371i	1.62021	−	0.871415i
$743$	−10.3429	−	24.9700i	−0.379445	−	0.916060i	−0.992070	−	0.125687i	$-0.959887\pi$
$743$	−10.3429	−	24.9700i	−0.379445	−	0.916060i	0.612625	−	0.790373i	$-0.290113\pi$
$744$	−11.4877	−	6.02620i	−0.421161	−	0.220931i
$745$	3.31094	−	7.99332i	0.121304	−	0.292853i
$746$	−14.9895	+	1.51548i	−0.548803	+	0.0554858i
$747$	−12.4543	+	2.47732i	−0.455679	+	0.0906402i
$748$	28.6365	−	28.9343i	1.04706	−	1.05794i
$749$	9.38423	−	6.27035i	0.342892	−	0.229113i
$750$	2.28633	−	4.30417i	0.0834851	−	0.157166i
$751$	−18.1705	−	18.1705i	−0.663050	−	0.663050i	0.293048	−	0.956098i	$-0.405330\pi$
$751$	−18.1705	−	18.1705i	−0.663050	−	0.663050i	−0.956098	+	0.293048i	$0.905330\pi$
$752$	2.05510	+	4.81982i	0.0749419	+	0.175761i
$753$	7.45144	−	7.45144i	0.271546	−	0.271546i
$754$	3.85282	+	12.5838i	0.140311	+	0.458275i
$755$	26.6623	+	39.9029i	0.970339	+	1.45222i
$756$	4.87675	+	1.99053i	0.177366	+	0.0723947i
$757$	−3.56312	−	17.9130i	−0.129504	−	0.651060i	−0.989938	−	0.141499i	$-0.954808\pi$
$757$	−3.56312	−	17.9130i	−0.129504	−	0.651060i	0.860435	−	0.509561i	$-0.170192\pi$
$758$	4.94666	+	4.03825i	0.179671	+	0.146676i
$759$	18.1493	+	7.51770i	0.658779	+	0.272875i
$760$	−4.61708	−	1.36155i	−0.167479	−	0.0493885i
$761$	31.2922	−	12.9617i	1.13434	−	0.469860i	0.265088	−	0.964224i	$-0.414599\pi$
$761$	31.2922	−	12.9617i	1.13434	−	0.469860i	0.869255	+	0.494364i	$0.164599\pi$
$762$	−1.06287	+	3.53672i	−0.0385038	+	0.128122i
$763$	−10.3286	+	15.4578i	−0.373919	+	0.559609i
$764$	−23.6026	−	4.56807i	−0.853913	−	0.165267i
$765$	−21.8239	−	4.34105i	−0.789045	−	0.156951i
$766$	0.472570	−	4.92872i	0.0170746	−	0.178082i
$767$	−19.0211			−0.686812
$768$	9.16245	+	13.1168i	0.330621	+	0.473311i
$769$	43.6161			1.57284			0.786419	−	0.617694i	$-0.211933\pi$
$769$	43.6161			1.57284			0.786419	+	0.617694i	$0.211933\pi$
$770$	−2.87492	+	29.9843i	−0.103605	+	1.08056i
$771$	22.2910	+	4.43395i	0.802789	+	0.159685i
$772$	−25.6229	−	4.95908i	−0.922190	−	0.178481i
$773$	9.47858	−	14.1857i	0.340921	−	0.510224i	−0.620905	−	0.783886i	$-0.713235\pi$
$773$	9.47858	−	14.1857i	0.340921	−	0.510224i	0.961826	+	0.273662i	$0.0882348\pi$
$774$	−1.40699	+	4.68176i	−0.0505731	+	0.168283i
$775$	−16.2754	+	6.74148i	−0.584628	+	0.242161i
$776$	−41.8650	−	12.3457i	−1.50287	−	0.443186i
$777$	−7.70055	−	3.18967i	−0.276256	−	0.114429i
$778$	7.21066	+	5.88649i	0.258515	+	0.211041i
$779$	0.591675	+	2.97455i	0.0211990	+	0.106574i
$780$	−9.39002	−	3.83269i	−0.336217	−	0.137232i
$781$	−17.1515	−	25.6691i	−0.613730	−	0.918512i
$782$	22.3781	+	73.0898i	0.800240	+	2.61368i
$783$	−3.85826	+	3.85826i	−0.137883	+	0.137883i
$784$	−0.234672	+	0.100061i	−0.00838115	+	0.00357360i
$785$	−12.0608	−	12.0608i	−0.430468	−	0.430468i
$786$	−9.44313	+	17.7773i	−0.336825	+	0.634095i
$787$	2.42923	−	1.62316i	0.0865926	−	0.0578594i	−0.511520	−	0.859271i	$-0.670917\pi$
$787$	2.42923	−	1.62316i	0.0865926	−	0.0578594i	0.598113	+	0.801412i	$0.295917\pi$
$788$	−16.7251	+	16.8991i	−0.595809	+	0.602004i
$789$	−3.34013	+	0.664394i	−0.118912	+	0.0236530i
$790$	−54.3036	+	5.49027i	−1.93203	+	0.195335i
$791$	15.8819	−	38.3423i	0.564695	−	1.36329i
$792$	6.81262	+	3.57374i	0.242076	+	0.126987i
$793$	−8.18403	−	19.7580i	−0.290623	−	0.701627i
$794$	39.0160	−	20.9844i	1.38463	−	0.744708i
$795$	−33.2633	−	22.2258i	−1.17973	−	0.788269i
$796$	−11.4452	+	2.33819i	−0.405663	+	0.0828750i
$797$	9.80200	−	49.2780i	0.347205	−	1.74552i	−0.273871	−	0.961766i	$-0.588304\pi$
$797$	9.80200	−	49.2780i	0.347205	−	1.74552i	0.621076	−	0.783750i	$-0.286696\pi$
$798$	1.35669	+	1.64444i	0.0480262	+	0.0582124i
$799$			9.80286i			0.346800i
$800$	21.6489	+	1.84992i	0.765404	+	0.0654044i
$801$		−	9.67961i		−	0.342012i
$802$	13.8182	−	11.4002i	0.487936	−	0.402555i
$803$	3.55289	−	17.8616i	0.125379	−	0.630321i
$804$	14.7647	+	9.75540i	0.520712	+	0.344046i
$805$	−47.0271	−	31.4225i	−1.65749	−	1.10750i
$806$	−5.23985	−	9.74238i	−0.184566	−	0.343161i
$807$	−10.4339	−	25.1897i	−0.367291	−	0.886719i
$808$	−4.39861	+	3.66733i	−0.154743	+	0.129016i
$809$	−8.06789	+	19.4776i	−0.283652	+	0.684796i	−0.999915	−	0.0130341i	$-0.995851\pi$
$809$	−8.06789	+	19.4776i	−0.283652	+	0.684796i	0.716263	+	0.697830i	$0.245851\pi$
$810$	−0.422982	−	4.18366i	−0.0148621	−	0.146999i
$811$	27.1834	−	5.40711i	0.954538	−	0.189869i	0.306835	−	0.951763i	$-0.400730\pi$
$811$	27.1834	−	5.40711i	0.954538	−	0.189869i	0.647703	+	0.761893i	$0.275730\pi$
$812$	0.148658	+	28.7404i	0.00521688	+	1.00859i
$813$	1.87577	−	1.25335i	0.0657860	−	0.0439568i
$814$	−10.7509	−	5.71076i	−0.376818	−	0.200162i
$815$	−40.5031	−	40.5031i	−1.41876	−	1.41876i
$816$	6.14328	+	29.2971i	0.215058	+	1.02560i
$817$	−1.39906	+	1.39906i	−0.0489468	+	0.0489468i
$818$	8.99881	−	2.75519i	0.314636	−	0.0963331i
$819$	2.49545	+	3.73470i	0.0871979	+	0.130501i
$820$	−12.2087	−	29.0486i	−0.426348	−	1.01442i
$821$	5.30681	+	26.6791i	0.185209	+	0.931108i	0.955854	+	0.293843i	$0.0949343\pi$
$821$	5.30681	+	26.6791i	0.185209	+	0.931108i	−0.770645	+	0.637265i	$0.780066\pi$
$822$	−9.10711	+	11.1558i	−0.317647	+	0.389102i
$823$	−16.7609	−	6.94261i	−0.584250	−	0.242004i	0.0709248	−	0.997482i	$-0.477405\pi$
$823$	−16.7609	−	6.94261i	−0.584250	−	0.242004i	−0.655175	+	0.755477i	$0.727405\pi$
$824$	11.4580	−	1.21835i	0.399160	−	0.0424433i
$825$	9.65185	−	3.99793i	0.336034	−	0.139190i
$826$	−39.7822	−	11.9555i	−1.38420	−	0.415986i
$827$	−9.13963	+	13.6784i	−0.317816	+	0.475645i	−0.955640	−	0.294537i	$-0.904835\pi$
$827$	−9.13963	+	13.6784i	−0.317816	+	0.475645i	0.637824	+	0.770182i	$0.279835\pi$
$828$	−11.9690	+	8.08728i	−0.415951	+	0.281052i
$829$	−13.3023	−	2.64599i	−0.462008	−	0.0918992i	−0.0414024	−	0.999143i	$-0.513183\pi$
$829$	−13.3023	−	2.64599i	−0.462008	−	0.0918992i	−0.420606	+	0.907243i	$0.638183\pi$
$830$	53.1525	+	5.09630i	1.84495	+	0.176895i
$831$	7.59459			0.263453
$832$	0.211707	+	13.6422i	0.00733961	+	0.472959i
$833$	−0.477291			−0.0165372
$834$	12.8117	+	1.22839i	0.443632	+	0.0425358i
$835$	−13.4515	−	2.67566i	−0.465507	−	0.0925951i
$836$	1.74320	+	2.57989i	0.0602897	+	0.0892274i
$837$	2.54809	−	3.81348i	0.0880747	−	0.131813i
$838$	21.8217	+	6.55795i	0.753817	+	0.226541i
$839$	32.5433	−	13.4799i	1.12352	−	0.465377i	0.257946	−	0.966159i	$-0.416954\pi$
$839$	32.5433	−	13.4799i	1.12352	−	0.465377i	0.865573	+	0.500783i	$0.166954\pi$
$840$	−17.2300	−	13.9180i	−0.594491	−	0.480216i
$841$	−0.713544	−	0.295559i	−0.0246050	−	0.0101917i
$842$	−0.772006	+	0.945668i	−0.0266051	+	0.0325899i
$843$	3.73838	+	18.7941i	0.128757	+	0.647303i
$844$	32.7696	−	13.7726i	1.12798	−	0.474073i
$845$	16.6701	+	24.9485i	0.573467	+	0.858254i
$846$	−1.77134	+	0.542336i	−0.0608999	+	0.0186459i
$847$	−6.70810	+	6.70810i	−0.230493	+	0.230493i
$848$	−9.95282	+	52.8899i	−0.341781	+	1.81625i
$849$	−0.275982	−	0.275982i	−0.00947169	−	0.00947169i
$850$	35.8998	+	19.0697i	1.23135	+	0.654084i
$851$	19.0056	−	12.6991i	0.651504	−	0.435321i
$852$	22.7004	−	0.117417i	0.777702	−	0.00402263i
$853$	−11.7668	+	2.34056i	−0.402887	+	0.0801392i	−0.392375	−	0.919806i	$-0.628346\pi$
$853$	−11.7668	+	2.34056i	−0.402887	+	0.0801392i	−0.0105124	+	0.999945i	$0.503346\pi$
$854$	−4.69800	−	46.4673i	−0.160762	−	1.59008i
$855$	0.651282	−	1.57233i	0.0222734	−	0.0537727i
$856$	−1.09444	+	12.0714i	−0.0374070	+	0.412593i
$857$	−8.73092	−	21.0783i	−0.298243	−	0.720021i	−0.999971	−	0.00757707i	$-0.997588\pi$
$857$	−8.73092	−	21.0783i	−0.298243	−	0.720021i	0.701729	−	0.712444i	$-0.252412\pi$
$858$	3.10741	+	5.77757i	0.106085	+	0.197243i
$859$	−12.4249	−	8.30204i	−0.423931	−	0.283262i	0.325248	−	0.945629i	$-0.394552\pi$
$859$	−12.4249	−	8.30204i	−0.423931	−	0.283262i	−0.749180	+	0.662367i	$0.769552\pi$
$860$	11.3321	−	17.1510i	0.386420	−	0.584844i
$861$	−2.72248	+	13.6868i	−0.0927819	+	0.466446i
$862$	−22.6624	+	18.6968i	−0.771883	+	0.636816i
$863$		−	1.20990i		−	0.0411856i	−0.999788	−	0.0205928i	$-0.993445\pi$
$863$		−	1.20990i		−	0.0411856i	0.999788	−	0.0205928i	$-0.00655536\pi$
$864$	−4.95400	+	2.73091i	−0.168539	+	0.0929074i
$865$		−	1.71656i		−	0.0583647i
$866$	−18.6123	−	22.5599i	−0.632471	−	0.766616i
$867$	−7.60927	+	38.2544i	−0.258424	+	1.29919i
$868$	−4.83554	−	23.6694i	−0.164129	−	0.803392i
$869$	29.3544	+	19.6140i	0.995779	+	0.665359i
$870$	20.2069	−	10.8681i	0.685077	−	0.368462i
$871$	5.77490	+	13.9418i	0.195675	+	0.472401i
$872$	−5.94379	−	19.0604i	−0.201282	−	0.645468i
$873$	5.90545	−	14.2570i	0.199869	−	0.482527i
$874$	−5.81670	+	0.588088i	−0.196753	+	0.0198924i
$875$	8.90187	−	1.77069i	0.300938	−	0.0598603i
$876$	9.51789	+	9.41994i	0.321580	+	0.318270i
$877$	10.5779	−	7.06792i	0.357190	−	0.238667i	−0.364008	−	0.931396i	$-0.618592\pi$
$877$	10.5779	−	7.06792i	0.357190	−	0.238667i	0.721198	+	0.692729i	$0.243592\pi$
$878$	10.6889	−	20.1225i	0.360732	−	0.679101i
$879$	−9.84440	−	9.84440i	−0.332043	−	0.332043i
$880$	−23.1098	−	22.6365i	−0.779031	−	0.763078i
$881$	24.1417	−	24.1417i	0.813356	−	0.813356i	−0.171779	−	0.985135i	$-0.554952\pi$
$881$	24.1417	−	24.1417i	0.813356	−	0.813356i	0.985135	+	0.171779i	$0.0549516\pi$
$882$	−0.0264058	−	0.0862446i	−0.000889129	−	0.00290401i
$883$	−16.7527	−	25.0722i	−0.563774	−	0.843747i	0.434608	−	0.900620i	$-0.356887\pi$
$883$	−16.7527	−	25.0722i	−0.563774	−	0.843747i	−0.998381	+	0.0568730i	$0.981887\pi$
$884$	−9.64635	+	23.6334i	−0.324442	+	0.794876i
$885$	6.46954	+	32.5246i	0.217471	+	1.09330i
$886$	−23.3463	−	19.0590i	−0.784335	−	0.640300i
$887$	−1.59297	−	0.659829i	−0.0534866	−	0.0221549i	0.355780	−	0.934570i	$-0.384215\pi$
$887$	−1.59297	−	0.659829i	−0.0534866	−	0.0221549i	−0.409266	+	0.912415i	$0.634215\pi$
$888$	7.86144	−	4.28077i	0.263813	−	0.143653i
$889$	−6.35388	+	2.63186i	−0.213102	+	0.0882698i
$890$	−11.7146	+	38.9804i	−0.392674	+	1.30663i
$891$	−1.51110	+	2.26152i	−0.0506238	+	0.0757639i
$892$	9.97971	−	51.5639i	0.334146	−	1.72649i
$893$	−0.735356	−	0.146271i	−0.0246077	−	0.00489478i
$894$	0.392755	−	4.09628i	0.0131357	−	0.137000i
$895$	8.05626			0.269291
$896$	−8.13191	+	28.6655i	−0.271668	+	0.957646i
$897$	−12.3179			−0.411284
$898$	3.86617	−	40.3227i	0.129016	−	1.34559i
$899$	24.5446	+	4.88222i	0.818607	+	0.162831i
$900$	−1.45968	+	7.54198i	−0.0486560	+	0.251399i
$901$	−55.9393	+	83.7191i	−1.86361	+	2.78909i
$902$	−5.86600	+	19.5192i	−0.195316	+	0.649918i
$903$	−8.41100	+	3.48395i	−0.279900	+	0.115939i
$904$	21.3147	+	39.1433i	0.708915	+	1.30189i
$905$	11.1530	+	4.61971i	0.370737	+	0.153564i
$906$	17.6819	+	14.4348i	0.587441	+	0.479563i
$907$	3.96574	+	19.9371i	0.131680	+	0.662001i	0.989084	+	0.147356i	$0.0470762\pi$
$907$	3.96574	+	19.9371i	0.131680	+	0.662001i	−0.857403	+	0.514645i	$0.827924\pi$
$908$	−6.58187	+	16.1254i	−0.218427	+	0.535142i
$909$	−1.12489	−	1.68352i	−0.0373104	−	0.0558389i
$910$	−5.52947	−	18.0599i	−0.183300	−	0.598681i
$911$	30.9241	−	30.9241i	1.02456	−	1.02456i	0.0248692	−	0.999691i	$-0.492083\pi$
$911$	30.9241	−	30.9241i	1.02456	−	1.02456i	0.999691	−	0.0248692i	$-0.00791693\pi$
$912$	−2.28937	+	0.0236840i	−0.0758087	+	0.000784256i
$913$	−24.4222	−	24.4222i	−0.808258	−	0.808258i
$914$	−20.4858	+	38.5657i	−0.677608	+	1.27564i
$915$	−31.0010	+	20.7142i	−1.02486	+	0.684791i
$916$	−21.2661	−	21.0472i	−0.702652	−	0.695420i
$917$	−36.7670	+	7.31340i	−1.21415	+	0.241510i
$918$	−10.5297	+	1.06459i	−0.347531	+	0.0351366i
$919$	−9.95330	+	24.0294i	−0.328329	+	0.792656i	0.670388	+	0.742011i	$0.266128\pi$
$919$	−9.95330	+	24.0294i	−0.328329	+	0.792656i	−0.998717	+	0.0506453i	$0.983872\pi$
$920$	57.9874	−	18.0828i	1.91179	−	0.596171i
$921$	−1.99398	−	4.81390i	−0.0657039	−	0.158623i
$922$	14.4998	−	7.79857i	0.477524	−	0.256832i
$923$	16.0954	+	10.7546i	0.529788	+	0.353993i
$924$	2.86764	+	14.0368i	0.0943386	+	0.461776i
$925$	2.37149	−	11.9223i	0.0779741	−	0.392002i
$926$	−32.4899	−	39.3809i	−1.06768	−	1.29414i
$927$			4.07387i			0.133803i
$928$	−24.1110	−	19.2711i	−0.791482	−	0.632604i
$929$			1.02099i			0.0334977i	0.999860	+	0.0167489i	$0.00533158\pi$
$929$			1.02099i			0.0334977i	−0.999860	+	0.0167489i	$0.994668\pi$
$930$	−14.8765	+	12.2734i	−0.487820	+	0.402459i
$931$	0.00712180	−	0.0358037i	0.000233408	−	0.00117342i
$932$	−19.3009	+	29.2118i	−0.632222	+	0.956864i
$933$	−14.8307	−	9.90955i	−0.485535	−	0.324424i
$934$	−18.2408	−	33.9148i	−0.596856	−	1.10973i
$935$	−23.1608	−	55.9151i	−0.757439	−	1.82862i
$936$	−4.80413	−	0.435559i	−0.157028	−	0.0142367i
$937$	−17.0396	+	41.1371i	−0.556658	+	1.34389i	0.355739	+	0.934585i	$0.384229\pi$
$937$	−17.0396	+	41.1371i	−0.556658	+	1.34389i	−0.912397	+	0.409306i	$0.865771\pi$
$938$	3.31505	+	32.7888i	0.108240	+	1.07059i
$939$	−11.8139	+	2.34993i	−0.385531	+	0.0766870i
$940$	7.78965	−	0.0402916i	0.254070	−	0.00131417i
$941$	−19.2200	+	12.8424i	−0.626553	+	0.418650i	−0.827904	−	0.560870i	$-0.810467\pi$
$941$	−19.2200	+	12.8424i	−0.626553	+	0.418650i	0.201351	+	0.979519i	$0.435467\pi$
$942$	−7.16447	−	3.80570i	−0.233431	−	0.123996i
$943$	−27.0610	−	27.0610i	−0.881226	−	0.881226i
$944$	36.8348	−	25.1673i	1.19887	−	0.819125i
$945$	5.53728	−	5.53728i	0.180128	−	0.180128i
$946$	−12.7140	+	3.89269i	−0.413369	+	0.126562i
$947$	−1.56596	−	2.34362i	−0.0508868	−	0.0761575i	0.805154	−	0.593066i	$-0.202083\pi$
$947$	−1.56596	−	2.34362i	−0.0508868	−	0.0761575i	−0.856041	+	0.516909i	$0.827083\pi$
$948$	−23.9320	+	10.0583i	−0.777277	+	0.326679i
$949$	2.22779	+	11.1999i	0.0723171	+	0.363563i
$950$	−1.96617	+	2.40846i	−0.0637910	+	0.0781408i
$951$	9.30520	+	3.85434i	0.301742	+	0.124986i
$952$	−35.0296	+	43.3655i	−1.13532	+	1.40548i
$953$	−8.32345	+	3.44768i	−0.269623	+	0.111681i	−0.513399	−	0.858150i	$-0.671614\pi$
$953$	−8.32345	+	3.44768i	−0.269623	+	0.111681i	0.243776	+	0.969832i	$0.421614\pi$
$954$	−18.2225	−	5.47631i	−0.589976	−	0.177302i
$955$	−19.8566	+	29.7175i	−0.642544	+	0.961635i
$956$	−5.30909	−	7.85733i	−0.171708	−	0.254124i
$957$	−14.5558	−	2.89532i	−0.470521	−	0.0935925i
$958$	21.1836	+	2.03110i	0.684410	+	0.0656218i
$959$	−26.8189			−0.866027
$960$	23.2551	−	5.00206i	0.750556	−	0.161441i
$961$	9.96464			0.321440
$962$	7.59837	+	0.728538i	0.244981	+	0.0234890i
$963$	−4.20305	−	0.836039i	−0.135442	−	0.0269410i
$964$	1.54989	−	1.04724i	0.0499185	−	0.0337292i
$965$	−21.5562	+	32.2612i	−0.693920	+	1.03852i
$966$	−25.7627	−	7.74232i	−0.828900	−	0.249105i
$967$	12.9295	−	5.35559i	0.415786	−	0.172224i	−0.164976	−	0.986298i	$-0.552755\pi$
$967$	12.9295	−	5.35559i	0.415786	−	0.172224i	0.580762	+	0.814073i	$0.302755\pi$
$968$	−1.07725	−	10.1311i	−0.0346243	−	0.325626i
$969$	−3.95734	−	1.63919i	−0.127128	−	0.0526582i
$970$	−41.0360	+	50.2670i	−1.31759	+	1.61398i
$971$	−7.80424	−	39.2346i	−0.250450	−	1.25910i	−0.877294	−	0.479953i	$-0.840654\pi$
$971$	−7.80424	−	39.2346i	−0.250450	−	1.25910i	0.626844	−	0.779145i	$-0.284346\pi$
$972$	−0.774914	−	1.84378i	−0.0248554	−	0.0591391i
$973$	13.3161	+	19.9290i	0.426896	+	0.638895i
$974$	30.2630	−	9.26573i	0.969690	−	0.296893i
$975$	−4.63205	+	4.63205i	−0.148344	+	0.148344i
$976$	41.9908	+	27.4333i	1.34409	+	0.878120i
$977$	37.1765	+	37.1765i	1.18938	+	1.18938i	0.977239	+	0.212143i	$0.0680441\pi$
$977$	37.1765	+	37.1765i	1.18938	+	1.18938i	0.212143	+	0.977239i	$0.431956\pi$
$978$	−24.0601	−	12.7805i	−0.769356	−	0.408675i
$979$	21.8907	−	14.6269i	0.699629	−	0.467477i
$980$	0.00196176	+	0.379270i	6.26661e−5	+	0.0121153i
$981$	6.92330	−	1.37713i	0.221044	−	0.0439684i
$982$	0.586000	+	5.79605i	0.0187000	+	0.184959i
$983$	−6.48375	+	15.6532i	−0.206800	+	0.499258i	−0.992916	−	0.118821i	$-0.962089\pi$
$983$	−6.48375	+	15.6532i	−0.206800	+	0.499258i	0.786116	+	0.618079i	$0.212089\pi$
$984$	−9.59721	−	11.5109i	−0.305948	−	0.366955i
$985$	13.5270	+	32.6571i	0.431007	+	1.04054i
$986$	−27.3534	−	50.8578i	−0.871110	−	1.61964i
$987$	−2.86848	−	1.91666i	−0.0913047	−	0.0610079i
$988$	−1.62891	−	1.07626i	−0.0518224	−	0.0342402i
$989$	4.87076	−	24.4870i	0.154881	−	0.778640i
$990$	8.82228	−	7.27852i	0.280391	−	0.231327i
$991$			3.91924i			0.124499i	0.998061	+	0.0622495i	$0.0198274\pi$
$991$			3.91924i			0.124499i	−0.998061	+	0.0622495i	$0.980173\pi$
$992$	23.0375	+	11.9334i	0.731441	+	0.378886i
$993$		−	33.0783i		−	1.04971i
$994$	26.9035	+	32.6097i	0.853328	+	1.03432i
$995$	−3.38811	+	17.0332i	−0.107410	+	0.539987i
$996$	24.8827	−	5.08340i	0.788437	−	0.161074i
$997$	9.74033	+	6.50828i	0.308479	+	0.206119i	0.700167	−	0.713979i	$-0.253109\pi$
$997$	9.74033	+	6.50828i	0.308479	+	0.206119i	−0.391688	+	0.920098i	$0.628109\pi$
$998$	−43.3183	+	23.2983i	−1.37122	+	0.737496i
$999$	1.21111	+	2.92389i	0.0383179	+	0.0925077i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	192.2.r.a.157.8	✓	128
3.2	odd	2		576.2.bd.b.541.9		128
4.3	odd	2		768.2.r.a.721.2		128
64.11	odd	16		768.2.r.a.49.2		128
64.53	even	16	inner	192.2.r.a.181.8	yes	128
192.53	odd	16		576.2.bd.b.181.9		128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
192.2.r.a.157.8	✓	128	1.1	even	1	trivial
192.2.r.a.181.8	yes	128	64.53	even	16	inner
576.2.bd.b.181.9		128	192.53	odd	16
576.2.bd.b.541.9		128	3.2	odd	2
768.2.r.a.49.2		128	64.11	odd	16
768.2.r.a.721.2		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)

\(f(q)\)	\(=\)	\(q+(-0.134977 + 1.40776i) q^{2} +(0.980785 + 0.195090i) q^{3} +(-1.96356 - 0.380029i) q^{4} +(-1.65192 + 2.47227i) q^{5} +(-0.407023 + 1.35438i) q^{6} +(-2.43319 + 1.00786i) q^{7} +(0.800025 - 2.71292i) q^{8} +(0.923880 + 0.382683i) q^{9} +O(q^{10})\)	\(q+(-0.134977 + 1.40776i) q^{2} +(0.980785 + 0.195090i) q^{3} +(-1.96356 - 0.380029i) q^{4} +(-1.65192 + 2.47227i) q^{5} +(-0.407023 + 1.35438i) q^{6} +(-2.43319 + 1.00786i) q^{7} +(0.800025 - 2.71292i) q^{8} +(0.923880 + 0.382683i) q^{9} +(-3.25739 - 2.65920i) q^{10} +(0.530629 + 2.66765i) q^{11} +(-1.85169 - 0.755799i) q^{12} +(-0.947516 - 1.41806i) q^{13} +(-1.09040 - 3.56139i) q^{14} +(-2.10249 + 2.10249i) q^{15} +(3.71116 + 1.49242i) q^{16} +(5.29168 + 5.29168i) q^{17} +(-0.663428 + 1.24894i) q^{18} +(-0.475911 + 0.317994i) q^{19} +(4.18318 - 4.22668i) q^{20} +(-2.58307 + 0.513804i) q^{21} +(-3.82703 + 0.386925i) q^{22} +(2.76395 - 6.67276i) q^{23} +(1.31392 - 2.50472i) q^{24} +(-1.46987 - 3.54859i) q^{25} +(2.12417 - 1.14247i) q^{26} +(0.831470 + 0.555570i) q^{27} +(5.16075 - 1.05431i) q^{28} +(-1.06449 + 5.35156i) q^{29} +(-2.67601 - 3.24359i) q^{30} -4.58643i q^{31} +(-2.60189 + 5.02296i) q^{32} +2.71991i q^{33} +(-8.16366 + 6.73515i) q^{34} +(1.52773 - 7.68043i) q^{35} +(-1.66866 - 1.10252i) q^{36} +(2.63143 + 1.75826i) q^{37} +(-0.383421 - 0.712889i) q^{38} +(-0.652660 - 1.57566i) q^{39} +(5.38551 + 6.45941i) q^{40} +(2.02772 - 4.89534i) q^{41} +(-0.374657 - 3.70568i) q^{42} +(3.39035 - 0.674383i) q^{43} +(-0.0281369 - 5.43975i) q^{44} +(-2.47227 + 1.65192i) q^{45} +(9.02056 + 4.79164i) q^{46} +(0.926251 + 0.926251i) q^{47} +(3.34869 + 2.18776i) q^{48} +(-0.0450982 + 0.0450982i) q^{49} +(5.19395 - 1.59025i) q^{50} +(4.15765 + 6.22236i) q^{51} +(1.32160 + 3.14453i) q^{52} +(2.62485 + 13.1960i) q^{53} +(-0.894337 + 1.09552i) q^{54} +(-7.47171 - 3.09488i) q^{55} +(0.787638 + 7.40739i) q^{56} +(-0.528804 + 0.219038i) q^{57} +(-7.39002 - 2.22088i) q^{58} +(6.19622 - 9.27330i) q^{59} +(4.92739 - 3.32937i) q^{60} +(12.2985 + 2.44633i) q^{61} +(6.45659 + 0.619062i) q^{62} -2.63367 q^{63} +(-6.71992 - 4.34081i) q^{64} +5.07105 q^{65} +(-3.82898 - 0.367125i) q^{66} +(-8.67822 - 1.72621i) q^{67} +(-8.37955 - 12.4015i) q^{68} +(4.01263 - 6.00533i) q^{69} +(10.6060 + 3.18736i) q^{70} +(-10.4863 + 4.34359i) q^{71} +(1.77732 - 2.20026i) q^{72} +(-6.18595 - 2.56230i) q^{73} +(-2.83039 + 3.46709i) q^{74} +(-0.749335 - 3.76716i) q^{75} +(1.05533 - 0.443540i) q^{76} +(-3.97975 - 5.95611i) q^{77} +(2.30624 - 0.706110i) q^{78} +(9.17818 - 9.17818i) q^{79} +(-9.82020 + 6.70962i) q^{80} +(0.707107 + 0.707107i) q^{81} +(6.61776 + 3.51529i) q^{82} +(-10.5583 + 7.05480i) q^{83} +(5.26727 - 0.0272447i) q^{84} +(-21.8239 + 4.34105i) q^{85} +(0.491748 + 4.86382i) q^{86} +(-2.08808 + 5.04106i) q^{87} +(7.66165 + 0.694631i) q^{88} +(-3.70422 - 8.94279i) q^{89} +(-1.99180 - 3.70333i) q^{90} +(3.73470 + 2.49545i) q^{91} +(-7.96303 + 12.0520i) q^{92} +(0.894769 - 4.49831i) q^{93} +(-1.42896 + 1.17891i) q^{94} -1.70188i q^{95} +(-3.53183 + 4.41885i) q^{96} -15.4317i q^{97} +(-0.0574001 - 0.0695746i) q^{98} +(-0.530629 + 2.66765i) 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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