LMFDB - Embedded newform 322.2.e.a.93.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [322,2,Mod(93,322)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(322, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0]))

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

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

chi := DirichletCharacter("322.93");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 322 = 2 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	322.e (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.57118294509$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.310217769.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 4x^{6} - 2x^{5} + 15x^{4} - 4x^{3} + 5x^{2} + x + 1 $ x^8 + 4x^6 - 2x^5 + 15x^4 - 4x^3 + 5*x^2 + x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			93.4
Root			$-0.198169 - 0.343239i$ of defining polynomial
Character	$\chi$	$=$	322.93
Dual form			322.2.e.a.277.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(0.563379 + 0.975800i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.858079 + 1.48624i) q^{5} -1.12676 q^{6} +(0.779537 + 2.52830i) q^{7} +1.00000 q^{8} +(0.865209 - 1.49859i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(0.563379 + 0.975800i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.858079 + 1.48624i) q^{5} -1.12676 q^{6} +(0.779537 + 2.52830i) q^{7} +1.00000 q^{8} +(0.865209 - 1.49859i) q^{9} +(-0.858079 - 1.48624i) q^{10} +(1.82493 + 3.16087i) q^{11} +(0.563379 - 0.975800i) q^{12} -3.79833 q^{13} +(-2.57934 - 0.589053i) q^{14} -1.93369 q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.08850 - 3.61738i) q^{17} +(0.865209 + 1.49859i) q^{18} +(-4.06135 + 7.03447i) q^{19} +1.71616 q^{20} +(-2.02795 + 2.18506i) q^{21} -3.64985 q^{22} +(0.500000 - 0.866025i) q^{23} +(0.563379 + 0.975800i) q^{24} +(1.02740 + 1.77951i) q^{25} +(1.89916 - 3.28945i) q^{26} +5.33003 q^{27} +(1.79981 - 1.93925i) q^{28} +2.80694 q^{29} +(0.966847 - 1.67463i) q^{30} +(-4.27150 - 7.39846i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-2.05625 + 3.56153i) q^{33} +4.17700 q^{34} +(-4.42656 - 1.01091i) q^{35} -1.73042 q^{36} +(-4.46765 + 7.73820i) q^{37} +(-4.06135 - 7.03447i) q^{38} +(-2.13990 - 3.70641i) q^{39} +(-0.858079 + 1.48624i) q^{40} +10.0518 q^{41} +(-0.878349 - 2.84878i) q^{42} +8.11069 q^{43} +(1.82493 - 3.16087i) q^{44} +(1.48484 + 2.57181i) q^{45} +(0.500000 + 0.866025i) q^{46} +(1.47568 - 2.55596i) q^{47} -1.12676 q^{48} +(-5.78464 + 3.94181i) q^{49} -2.05480 q^{50} +(2.35323 - 4.07591i) q^{51} +(1.89916 + 3.28945i) q^{52} +(-1.52740 - 2.64553i) q^{53} +(-2.66502 + 4.61594i) q^{54} -6.26373 q^{55} +(0.779537 + 2.52830i) q^{56} -9.15232 q^{57} +(-1.40347 + 2.43088i) q^{58} +(-2.09451 - 3.62779i) q^{59} +(0.966847 + 1.67463i) q^{60} +(5.65778 - 9.79957i) q^{61} +8.54301 q^{62} +(4.46335 + 1.01931i) q^{63} +1.00000 q^{64} +(3.25927 - 5.64522i) q^{65} +(-2.05625 - 3.56153i) q^{66} +(6.61841 + 11.4634i) q^{67} +(-2.08850 + 3.61738i) q^{68} +1.12676 q^{69} +(3.08875 - 3.32806i) q^{70} +14.3054 q^{71} +(0.865209 - 1.49859i) q^{72} +(2.13049 + 3.69011i) q^{73} +(-4.46765 - 7.73820i) q^{74} +(-1.15763 + 2.00507i) q^{75} +8.12271 q^{76} +(-6.56903 + 7.07798i) q^{77} +4.27979 q^{78} +(6.72409 - 11.6465i) q^{79} +(-0.858079 - 1.48624i) q^{80} +(0.407198 + 0.705288i) q^{81} +(-5.02592 + 8.70515i) q^{82} +9.43848 q^{83} +(2.90629 + 0.663720i) q^{84} +7.16839 q^{85} +(-4.05534 + 7.02406i) q^{86} +(1.58137 + 2.73901i) q^{87} +(1.82493 + 3.16087i) q^{88} +(-1.97918 + 3.42805i) q^{89} -2.96967 q^{90} +(-2.96094 - 9.60333i) q^{91} -1.00000 q^{92} +(4.81295 - 8.33627i) q^{93} +(1.47568 + 2.55596i) q^{94} +(-6.96993 - 12.0723i) q^{95} +(0.563379 - 0.975800i) q^{96} +0.121105 q^{97} +(-0.521390 - 6.98056i) q^{98} +6.31577 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{2} - 3 q^{3} - 4 q^{4} - 7 q^{5} + 6 q^{6} - q^{7} + 8 q^{8} + q^{9}+O(q^{10}) $ 8 * q - 4 * q^2 - 3 * q^3 - 4 * q^4 - 7 * q^5 + 6 * q^6 - q^7 + 8 * q^8 + q^9	\( 8 q - 4 q^{2} - 3 q^{3} - 4 q^{4} - 7 q^{5} + 6 q^{6} - q^{7} + 8 q^{8} + q^{9} - 7 q^{10} - 2 q^{11} - 3 q^{12} + 2 q^{13} - q^{14} + 18 q^{15} - 4 q^{16} - 5 q^{17} + q^{18} - 11 q^{19} + 14 q^{20} + q^{21} + 4 q^{22} + 4 q^{23} - 3 q^{24} - 3 q^{25} - q^{26} + 6 q^{27} + 2 q^{28} + 4 q^{29} - 9 q^{30} - 6 q^{31} - 4 q^{32} - 15 q^{33} + 10 q^{34} - 8 q^{35} - 2 q^{36} + 8 q^{37} - 11 q^{38} - 3 q^{39} - 7 q^{40} + 18 q^{41} - 2 q^{42} + 8 q^{43} - 2 q^{44} - 3 q^{45} + 4 q^{46} - 11 q^{47} + 6 q^{48} - 19 q^{49} + 6 q^{50} + 18 q^{51} - q^{52} - q^{53} - 3 q^{54} + 20 q^{55} - q^{56} + 6 q^{57} - 2 q^{58} - 12 q^{59} - 9 q^{60} - 21 q^{61} + 12 q^{62} - 15 q^{63} + 8 q^{64} + 24 q^{65} - 15 q^{66} + 3 q^{67} - 5 q^{68} - 6 q^{69} - 8 q^{70} + 22 q^{71} + q^{72} + 16 q^{73} + 8 q^{74} - 18 q^{75} + 22 q^{76} - 19 q^{77} + 6 q^{78} + 21 q^{79} - 7 q^{80} + 8 q^{81} - 9 q^{82} + 8 q^{83} + q^{84} + 20 q^{85} - 4 q^{86} + 7 q^{87} - 2 q^{88} - 27 q^{89} + 6 q^{90} - 54 q^{91} - 8 q^{92} + 27 q^{93} - 11 q^{94} - 5 q^{95} - 3 q^{96} + 12 q^{97} + 14 q^{98} + 26 q^{99}+O(q^{100}) \) 8 * q - 4 * q^2 - 3 * q^3 - 4 * q^4 - 7 * q^5 + 6 * q^6 - q^7 + 8 * q^8 + q^9 - 7 * q^10 - 2 * q^11 - 3 * q^12 + 2 * q^13 - q^14 + 18 * q^15 - 4 * q^16 - 5 * q^17 + q^18 - 11 * q^19 + 14 * q^20 + q^21 + 4 * q^22 + 4 * q^23 - 3 * q^24 - 3 * q^25 - q^26 + 6 * q^27 + 2 * q^28 + 4 * q^29 - 9 * q^30 - 6 * q^31 - 4 * q^32 - 15 * q^33 + 10 * q^34 - 8 * q^35 - 2 * q^36 + 8 * q^37 - 11 * q^38 - 3 * q^39 - 7 * q^40 + 18 * q^41 - 2 * q^42 + 8 * q^43 - 2 * q^44 - 3 * q^45 + 4 * q^46 - 11 * q^47 + 6 * q^48 - 19 * q^49 + 6 * q^50 + 18 * q^51 - q^52 - q^53 - 3 * q^54 + 20 * q^55 - q^56 + 6 * q^57 - 2 * q^58 - 12 * q^59 - 9 * q^60 - 21 * q^61 + 12 * q^62 - 15 * q^63 + 8 * q^64 + 24 * q^65 - 15 * q^66 + 3 * q^67 - 5 * q^68 - 6 * q^69 - 8 * q^70 + 22 * q^71 + q^72 + 16 * q^73 + 8 * q^74 - 18 * q^75 + 22 * q^76 - 19 * q^77 + 6 * q^78 + 21 * q^79 - 7 * q^80 + 8 * q^81 - 9 * q^82 + 8 * q^83 + q^84 + 20 * q^85 - 4 * q^86 + 7 * q^87 - 2 * q^88 - 27 * q^89 + 6 * q^90 - 54 * q^91 - 8 * q^92 + 27 * q^93 - 11 * q^94 - 5 * q^95 - 3 * q^96 + 12 * q^97 + 14 * q^98 + 26 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/322\mathbb{Z}\right)^\times$.

$n$	$185$	$281$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$	0.563379	+	0.975800i	0.325267	+	0.563379i	0.981566	−	0.191122i	$-0.0612126\pi$
$3$	0.563379	+	0.975800i	0.325267	+	0.563379i	−0.656300	+	0.754500i	$0.727879\pi$
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−0.858079	+	1.48624i	−0.383745	+	0.664665i	−0.991594	−	0.129387i	$-0.958699\pi$
$5$	−0.858079	+	1.48624i	−0.383745	+	0.664665i	0.607849	+	0.794052i	$0.292032\pi$
$6$	−1.12676			−0.459997
$7$	0.779537	+	2.52830i	0.294637	+	0.955609i
$7$	0.779537	+	2.52830i	0.294637	+	0.955609i
$8$	1.00000			0.353553
$9$	0.865209	−	1.49859i	0.288403	−	0.499529i
$10$	−0.858079	−	1.48624i	−0.271349	−	0.469989i
$11$	1.82493	+	3.16087i	0.550236	+	0.953037i	0.998257	+	0.0590137i	$0.0187956\pi$
$11$	1.82493	+	3.16087i	0.550236	+	0.953037i	−0.448021	+	0.894023i	$0.647871\pi$
$12$	0.563379	−	0.975800i	0.162633	−	0.281689i
$13$	−3.79833			−1.05347			−0.526733	−	0.850031i	$-0.676583\pi$
$13$	−3.79833			−1.05347			−0.526733	+	0.850031i	$0.676583\pi$
$14$	−2.57934	−	0.589053i	−0.689359	−	0.157431i
$15$	−1.93369			−0.499278
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−2.08850	−	3.61738i	−0.506535	−	0.877345i	−0.999971	−	0.00756264i	$-0.997593\pi$
$17$	−2.08850	−	3.61738i	−0.506535	−	0.877345i	0.493436	−	0.869782i	$-0.335741\pi$
$18$	0.865209	+	1.49859i	0.203932	+	0.353220i
$19$	−4.06135	+	7.03447i	−0.931739	+	1.61382i	−0.151390	+	0.988474i	$0.548375\pi$
$19$	−4.06135	+	7.03447i	−0.931739	+	1.61382i	−0.780349	+	0.625345i	$0.784958\pi$
$20$	1.71616			0.383745
$21$	−2.02795	+	2.18506i	−0.442534	+	0.476820i
$22$	−3.64985			−0.778151
$23$	0.500000	−	0.866025i	0.104257	−	0.180579i
$23$	0.500000	−	0.866025i	0.104257	−	0.180579i
$24$	0.563379	+	0.975800i	0.114999	+	0.199184i
$25$	1.02740	+	1.77951i	0.205480	+	0.355902i
$26$	1.89916	−	3.28945i	0.372457	−	0.645114i
$27$	5.33003			1.02577
$28$	1.79981	−	1.93925i	0.340132	−	0.366484i
$29$	2.80694			0.521235			0.260618	−	0.965442i	$-0.416074\pi$
$29$	2.80694			0.521235			0.260618	+	0.965442i	$0.416074\pi$
$30$	0.966847	−	1.67463i	0.176521	−	0.305744i
$31$	−4.27150	−	7.39846i	−0.767185	−	1.32880i	−0.939084	−	0.343688i	$-0.888324\pi$
$31$	−4.27150	−	7.39846i	−0.767185	−	1.32880i	0.171899	−	0.985115i	$-0.445010\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	−2.05625	+	3.56153i	−0.357947	+	0.619982i
$34$	4.17700			0.716349
$35$	−4.42656	−	1.01091i	−0.748226	−	0.170875i
$36$	−1.73042			−0.288403
$37$	−4.46765	+	7.73820i	−0.734477	+	1.27215i	0.220475	+	0.975393i	$0.429239\pi$
$37$	−4.46765	+	7.73820i	−0.734477	+	1.27215i	−0.954952	+	0.296759i	$0.904094\pi$
$38$	−4.06135	−	7.03447i	−0.658839	−	1.14114i
$39$	−2.13990	−	3.70641i	−0.342658	−	0.593501i
$40$	−0.858079	+	1.48624i	−0.135674	+	0.234995i
$41$	10.0518			1.56983			0.784917	−	0.619601i	$-0.212706\pi$
$41$	10.0518			1.56983			0.784917	+	0.619601i	$0.212706\pi$
$42$	−0.878349	−	2.84878i	−0.135532	−	0.439577i
$43$	8.11069			1.23687			0.618434	−	0.785837i	$-0.287767\pi$
$43$	8.11069			1.23687			0.618434	+	0.785837i	$0.287767\pi$
$44$	1.82493	−	3.16087i	0.275118	−	0.476518i
$45$	1.48484	+	2.57181i	0.221346	+	0.383383i
$46$	0.500000	+	0.866025i	0.0737210	+	0.127688i
$47$	1.47568	−	2.55596i	0.215250	−	0.372825i	−0.738100	−	0.674692i	$-0.764277\pi$
$47$	1.47568	−	2.55596i	0.215250	−	0.372825i	0.953350	+	0.301867i	$0.0976099\pi$
$48$	−1.12676			−0.162633
$49$	−5.78464	+	3.94181i	−0.826378	+	0.563116i
$50$	−2.05480			−0.290593
$51$	2.35323	−	4.07591i	0.329518	−	0.570742i
$52$	1.89916	+	3.28945i	0.263367	+	0.456165i
$53$	−1.52740	−	2.64553i	−0.209804	−	0.363392i	0.741848	−	0.670568i	$-0.233949\pi$
$53$	−1.52740	−	2.64553i	−0.209804	−	0.363392i	−0.951653	+	0.307176i	$0.900616\pi$
$54$	−2.66502	+	4.61594i	−0.362663	+	0.628150i
$55$	−6.26373			−0.844601
$56$	0.779537	+	2.52830i	0.104170	+	0.337859i
$57$	−9.15232			−1.21225
$58$	−1.40347	+	2.43088i	−0.184284	+	0.319190i
$59$	−2.09451	−	3.62779i	−0.272682	−	0.472299i	0.696866	−	0.717201i	$-0.254577\pi$
$59$	−2.09451	−	3.62779i	−0.272682	−	0.472299i	−0.969548	+	0.244903i	$0.921244\pi$
$60$	0.966847	+	1.67463i	0.124819	+	0.216194i
$61$	5.65778	−	9.79957i	0.724405	−	1.25471i	−0.234813	−	0.972040i	$-0.575448\pi$
$61$	5.65778	−	9.79957i	0.724405	−	1.25471i	0.959218	−	0.282666i	$-0.0912188\pi$
$62$	8.54301			1.08496
$63$	4.46335	+	1.01931i	0.562329	+	0.128421i
$64$	1.00000			0.125000
$65$	3.25927	−	5.64522i	0.404262	−	0.700203i
$66$	−2.05625	−	3.56153i	−0.253107	−	0.438394i
$67$	6.61841	+	11.4634i	0.808567	+	1.40048i	0.913856	+	0.406037i	$0.133090\pi$
$67$	6.61841	+	11.4634i	0.808567	+	1.40048i	−0.105290	+	0.994442i	$0.533577\pi$
$68$	−2.08850	+	3.61738i	−0.253268	+	0.438672i
$69$	1.12676			0.135646
$70$	3.08875	−	3.32806i	0.369177	−	0.397780i
$71$	14.3054			1.69773			0.848867	−	0.528607i	$-0.177285\pi$
$71$	14.3054			1.69773			0.848867	+	0.528607i	$0.177285\pi$
$72$	0.865209	−	1.49859i	0.101966	−	0.176610i
$73$	2.13049	+	3.69011i	0.249355	+	0.431895i	0.963347	−	0.268259i	$-0.0864482\pi$
$73$	2.13049	+	3.69011i	0.249355	+	0.431895i	−0.713992	+	0.700154i	$0.753115\pi$
$74$	−4.46765	−	7.73820i	−0.519354	−	0.899547i
$75$	−1.15763	+	2.00507i	−0.133672	+	0.231526i
$76$	8.12271			0.931739
$77$	−6.56903	+	7.07798i	−0.748610	+	0.806611i
$78$	4.27979			0.484591
$79$	6.72409	−	11.6465i	0.756519	−	1.31033i	−0.188096	−	0.982151i	$-0.560232\pi$
$79$	6.72409	−	11.6465i	0.756519	−	1.31033i	0.944615	−	0.328179i	$-0.106435\pi$
$80$	−0.858079	−	1.48624i	−0.0959362	−	0.166166i
$81$	0.407198	+	0.705288i	0.0452442	+	0.0783653i
$82$	−5.02592	+	8.70515i	−0.555020	+	0.961323i
$83$	9.43848			1.03601			0.518004	−	0.855378i	$-0.326675\pi$
$83$	9.43848			1.03601			0.518004	+	0.855378i	$0.326675\pi$
$84$	2.90629	+	0.663720i	0.317103	+	0.0724177i
$85$	7.16839			0.777521
$86$	−4.05534	+	7.02406i	−0.437299	+	0.757424i
$87$	1.58137	+	2.73901i	0.169540	+	0.293653i
$88$	1.82493	+	3.16087i	0.194538	+	0.336949i
$89$	−1.97918	+	3.42805i	−0.209793	+	0.363372i	−0.951649	−	0.307187i	$-0.900612\pi$
$89$	−1.97918	+	3.42805i	−0.209793	+	0.363372i	0.741856	+	0.670559i	$0.233946\pi$
$90$	−2.96967			−0.313031
$91$	−2.96094	−	9.60333i	−0.310391	−	1.00670i
$92$	−1.00000			−0.104257
$93$	4.81295	−	8.33627i	0.499079	−	0.864431i
$94$	1.47568	+	2.55596i	0.152205	+	0.263627i
$95$	−6.96993	−	12.0723i	−0.715100	−	1.23859i
$96$	0.563379	−	0.975800i	0.0574996	−	0.0995922i
$97$	0.121105			0.0122964			0.00614819	−	0.999981i	$-0.498043\pi$
$97$	0.121105			0.0122964			0.00614819	+	0.999981i	$0.498043\pi$
$98$	−0.521390	−	6.98056i	−0.0526683	−	0.705143i
$99$	6.31577			0.634759
$100$	1.02740	−	1.77951i	0.102740	−	0.177951i
$101$	1.86148	+	3.22418i	0.185224	+	0.320818i	0.943652	−	0.330939i	$-0.107366\pi$
$101$	1.86148	+	3.22418i	0.185224	+	0.320818i	−0.758428	+	0.651757i	$0.774032\pi$
$102$	2.35323	+	4.07591i	0.233004	+	0.403576i
$103$	−7.56418	+	13.1015i	−0.745321	+	1.29093i	0.204724	+	0.978820i	$0.434370\pi$
$103$	−7.56418	+	13.1015i	−0.745321	+	1.29093i	−0.950045	+	0.312114i	$0.898963\pi$
$104$	−3.79833			−0.372457
$105$	−1.50739	−	4.88897i	−0.147106	−	0.477114i
$106$	3.05480			0.296708
$107$	6.86772	−	11.8952i	0.663927	−	1.14996i	−0.315648	−	0.948876i	$-0.602222\pi$
$107$	6.86772	−	11.8952i	0.663927	−	1.14996i	0.979575	−	0.201079i	$-0.0644449\pi$
$108$	−2.66502	−	4.61594i	−0.256441	−	0.444169i
$109$	−4.69467	−	8.13140i	−0.449668	−	0.778847i	0.548697	−	0.836022i	$-0.315124\pi$
$109$	−4.69467	−	8.13140i	−0.449668	−	0.778847i	−0.998364	+	0.0571745i	$0.981791\pi$
$110$	3.13186	−	5.42455i	0.298611	−	0.517210i
$111$	−10.0679			−0.955604
$112$	−2.57934	−	0.589053i	−0.243725	−	0.0556603i
$113$	−9.39338			−0.883655			−0.441828	−	0.897100i	$-0.645670\pi$
$113$	−9.39338			−0.883655			−0.441828	+	0.897100i	$0.645670\pi$
$114$	4.57616	−	7.92614i	0.428597	−	0.742351i
$115$	0.858079	+	1.48624i	0.0800163	+	0.138592i
$116$	−1.40347	−	2.43088i	−0.130309	−	0.225701i
$117$	−3.28635	+	5.69212i	−0.303823	+	0.526237i
$118$	4.18902			0.385630
$119$	7.51779	−	8.10024i	0.689154	−	0.742548i
$120$	−1.93369			−0.176521
$121$	−1.16071	+	2.01041i	−0.105519	+	0.182765i
$122$	5.65778	+	9.79957i	0.512232	+	0.887211i
$123$	5.66299	+	9.80859i	0.510615	+	0.884411i
$124$	−4.27150	+	7.39846i	−0.383592	+	0.664401i
$125$	−12.1072			−1.08290
$126$	−3.11442	+	3.35572i	−0.277455	+	0.298951i
$127$	2.53575			0.225012			0.112506	−	0.993651i	$-0.464112\pi$
$127$	2.53575			0.225012			0.112506	+	0.993651i	$0.464112\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	4.56939	+	7.91441i	0.402312	+	0.696825i
$130$	3.25927	+	5.64522i	0.285857	+	0.495118i
$131$	2.63129	−	4.55753i	0.229897	−	0.398193i	−0.727881	−	0.685704i	$-0.759494\pi$
$131$	2.63129	−	4.55753i	0.229897	−	0.398193i	0.957777	+	0.287511i	$0.0928278\pi$
$132$	4.11250			0.357947
$133$	−20.9513	−	4.78471i	−1.81670	−	0.414887i
$134$	−13.2368			−1.14349
$135$	−4.57359	+	7.92169i	−0.393632	+	0.681791i
$136$	−2.08850	−	3.61738i	−0.179087	−	0.310188i
$137$	6.92566	+	11.9956i	0.591699	+	1.02485i	0.994004	+	0.109347i	$0.0348760\pi$
$137$	6.92566	+	11.9956i	0.591699	+	1.02485i	−0.402305	+	0.915506i	$0.631791\pi$
$138$	−0.563379	+	0.975800i	−0.0479580	+	0.0830656i
$139$	−9.65665			−0.819067			−0.409533	−	0.912295i	$-0.634308\pi$
$139$	−9.65665			−0.819067			−0.409533	+	0.912295i	$0.634308\pi$
$140$	1.33781	+	4.33897i	0.113066	+	0.366710i
$141$	3.32547			0.280055
$142$	−7.15268	+	12.3888i	−0.600239	+	1.03965i
$143$	−6.93167	−	12.0060i	−0.579655	−	1.00399i
$144$	0.865209	+	1.49859i	0.0721008	+	0.124882i
$145$	−2.40857	+	4.17177i	−0.200021	+	0.346447i
$146$	−4.26097			−0.352641
$147$	−7.10537	−	3.42392i	−0.586041	−	0.282400i
$148$	8.93530			0.734477
$149$	4.78066	−	8.28034i	0.391647	−	0.678352i	−0.601020	−	0.799234i	$-0.705239\pi$
$149$	4.78066	−	8.28034i	0.391647	−	0.678352i	0.992667	+	0.120882i	$0.0385722\pi$
$150$	−1.15763	−	2.00507i	−0.0945201	−	0.163714i
$151$	−3.62836	−	6.28451i	−0.295272	−	0.511426i	0.679776	−	0.733420i	$-0.262077\pi$
$151$	−3.62836	−	6.28451i	−0.295272	−	0.511426i	−0.975048	+	0.221994i	$0.928744\pi$
$152$	−4.06135	+	7.03447i	−0.329419	+	0.570571i
$153$	−7.22795			−0.584345
$154$	−2.84520	−	9.22794i	−0.229272	−	0.743608i
$155$	14.6612			1.17761
$156$	−2.13990	+	3.70641i	−0.171329	+	0.296750i
$157$	1.37755	+	2.38598i	0.109940	+	0.190422i	0.915746	−	0.401758i	$-0.131601\pi$
$157$	1.37755	+	2.38598i	0.109940	+	0.190422i	−0.805806	+	0.592180i	$0.798267\pi$
$158$	6.72409	+	11.6465i	0.534940	+	0.926543i
$159$	1.72101	−	2.98087i	0.136485	−	0.236399i
$160$	1.71616			0.135674
$161$	2.57934	+	0.589053i	0.203281	+	0.0464239i
$162$	−0.814396			−0.0639850
$163$	−10.1420	+	17.5665i	−0.794386	+	1.37592i	0.128842	+	0.991665i	$0.458874\pi$
$163$	−10.1420	+	17.5665i	−0.794386	+	1.37592i	−0.923228	+	0.384252i	$0.874459\pi$
$164$	−5.02592	−	8.70515i	−0.392459	−	0.679758i
$165$	−3.52885	−	6.11215i	−0.274721	−	0.475830i
$166$	−4.71924	+	8.17397i	−0.366284	+	0.634423i
$167$	−0.325472			−0.0251858			−0.0125929	−	0.999921i	$-0.504009\pi$
$167$	−0.325472			−0.0251858			−0.0125929	+	0.999921i	$0.504009\pi$
$168$	−2.02795	+	2.18506i	−0.156459	+	0.168581i
$169$	1.42730			0.109792
$170$	−3.58419	+	6.20801i	−0.274895	+	0.476132i
$171$	7.02784	+	12.1726i	0.537433	+	0.930861i
$172$	−4.05534	−	7.02406i	−0.309217	−	0.535580i
$173$	−6.70089	+	11.6063i	−0.509459	+	0.882410i	0.490480	+	0.871452i	$0.336821\pi$
$173$	−6.70089	+	11.6063i	−0.509459	+	0.882410i	−0.999940	+	0.0109575i	$0.996512\pi$
$174$	−3.16274			−0.239766
$175$	−3.69824	+	3.98477i	−0.279561	+	0.301220i
$176$	−3.64985			−0.275118
$177$	2.36000	−	4.08764i	0.177389	−	0.307246i
$178$	−1.97918	−	3.42805i	−0.148346	−	0.256943i
$179$	−10.4273	−	18.0606i	−0.779370	−	1.34991i	−0.932305	−	0.361673i	$-0.882206\pi$
$179$	−10.4273	−	18.0606i	−0.779370	−	1.34991i	0.152935	−	0.988236i	$-0.451128\pi$
$180$	1.48484	−	2.57181i	0.110673	−	0.191692i
$181$	1.57738			0.117246			0.0586229	−	0.998280i	$-0.481329\pi$
$181$	1.57738			0.117246			0.0586229	+	0.998280i	$0.481329\pi$
$182$	9.79720	+	2.23742i	0.726217	+	0.165848i
$183$	12.7499			0.942500
$184$	0.500000	−	0.866025i	0.0368605	−	0.0638442i
$185$	−7.66719	−	13.2800i	−0.563703	−	0.976363i
$186$	4.81295	+	8.33627i	0.352902	+	0.611245i
$187$	7.62271	−	13.2029i	0.557428	−	0.965493i
$188$	−2.95137			−0.215250
$189$	4.15496	+	13.4759i	0.302229	+	0.980231i
$190$	13.9399			1.01130
$191$	−3.13049	+	5.42216i	−0.226514	+	0.392334i	−0.956773	−	0.290837i	$-0.906066\pi$
$191$	−3.13049	+	5.42216i	−0.226514	+	0.392334i	0.730259	+	0.683171i	$0.239400\pi$
$192$	0.563379	+	0.975800i	0.0406583	+	0.0704223i
$193$	−6.51789	−	11.2893i	−0.469168	−	0.812623i	0.530211	−	0.847866i	$-0.322113\pi$
$193$	−6.51789	−	11.2893i	−0.469168	−	0.812623i	−0.999379	+	0.0352433i	$0.988779\pi$
$194$	−0.0605527	+	0.104880i	−0.00434743	+	0.00752997i
$195$	7.34481			0.525972
$196$	6.30603	+	3.03874i	0.450431	+	0.217053i
$197$	−21.2551			−1.51436			−0.757182	−	0.653204i	$-0.773425\pi$
$197$	−21.2551			−1.51436			−0.757182	+	0.653204i	$0.773425\pi$
$198$	−3.15789	+	5.46962i	−0.224421	+	0.388709i
$199$	−2.36862	−	4.10257i	−0.167907	−	0.290824i	0.769777	−	0.638313i	$-0.220368\pi$
$199$	−2.36862	−	4.10257i	−0.167907	−	0.290824i	−0.937684	+	0.347490i	$0.887034\pi$
$200$	1.02740	+	1.77951i	0.0726481	+	0.125830i
$201$	−7.45734	+	12.9165i	−0.526000	+	0.911058i
$202$	−3.72296			−0.261947
$203$	2.18811	+	7.09679i	0.153575	+	0.498097i
$204$	−4.70646			−0.329518
$205$	−8.62528	+	14.9394i	−0.602416	+	1.04341i
$206$	−7.56418	−	13.1015i	−0.527021	−	0.912828i
$207$	−0.865209	−	1.49859i	−0.0601362	−	0.104159i
$208$	1.89916	−	3.28945i	0.131683	−	0.228082i
$209$	−29.6467			−2.05070
$210$	4.98766	+	1.13905i	0.344181	+	0.0786018i
$211$	16.7617			1.15392			0.576962	−	0.816771i	$-0.304238\pi$
$211$	16.7617			1.15392			0.576962	+	0.816771i	$0.304238\pi$
$212$	−1.52740	+	2.64553i	−0.104902	+	0.181696i
$213$	8.05933	+	13.9592i	0.552216	+	0.956467i
$214$	6.86772	+	11.8952i	0.469467	+	0.813142i
$215$	−6.95962	+	12.0544i	−0.474642	+	0.822104i
$216$	5.33003			0.362663
$217$	15.3758	−	16.5670i	1.04377	−	1.12464i
$218$	9.38933			0.635926
$219$	−2.40054	+	4.15786i	−0.162214	+	0.280962i
$220$	3.13186	+	5.42455i	0.211150	+	0.365723i
$221$	7.93280	+	13.7400i	0.533618	+	0.924253i
$222$	5.03396	−	8.71907i	0.337857	−	0.585185i
$223$	1.23469			0.0826812			0.0413406	−	0.999145i	$-0.486837\pi$
$223$	1.23469			0.0826812			0.0413406	+	0.999145i	$0.486837\pi$
$224$	1.79981	−	1.93925i	0.120255	−	0.129572i
$225$	3.55566			0.237044
$226$	4.69669	−	8.13491i	0.312419	−	0.541126i
$227$	−11.5210	−	19.9550i	−0.764678	−	1.32446i	−0.940417	−	0.340024i	$-0.889565\pi$
$227$	−11.5210	−	19.9550i	−0.764678	−	1.32446i	0.175739	−	0.984437i	$-0.443768\pi$
$228$	4.57616	+	7.92614i	0.303064	+	0.524922i
$229$	2.41831	−	4.18864i	0.159807	−	0.276793i	−0.774992	−	0.631971i	$-0.782246\pi$
$229$	2.41831	−	4.18864i	0.159807	−	0.276793i	0.934799	+	0.355178i	$0.115580\pi$
$230$	−1.71616			−0.113160
$231$	−10.6075	−	2.42248i	−0.697925	−	0.159387i
$232$	2.80694			0.184284
$233$	6.62724	−	11.4787i	0.434165	−	0.751996i	−0.563062	−	0.826415i	$-0.690377\pi$
$233$	6.62724	−	11.4787i	0.434165	−	0.751996i	0.997227	+	0.0744188i	$0.0237101\pi$
$234$	−3.28635	−	5.69212i	−0.214835	−	0.372106i
$235$	2.53251	+	4.38643i	0.165202	+	0.286139i
$236$	−2.09451	+	3.62779i	−0.136341	+	0.236149i
$237$	15.1528			0.984282
$238$	3.25612	+	10.5607i	0.211063	+	0.684550i
$239$	−5.40250			−0.349459			−0.174729	−	0.984616i	$-0.555905\pi$
$239$	−5.40250			−0.349459			−0.174729	+	0.984616i	$0.555905\pi$
$240$	0.966847	−	1.67463i	0.0624097	−	0.108097i
$241$	8.61037	+	14.9136i	0.554643	+	0.960670i	0.997931	+	0.0642905i	$0.0204784\pi$
$241$	8.61037	+	14.9136i	0.554643	+	0.960670i	−0.443288	+	0.896379i	$0.646188\pi$
$242$	−1.16071	−	2.01041i	−0.0746134	−	0.129234i
$243$	7.53624	−	13.0531i	0.483450	−	0.837359i
$244$	−11.3156			−0.724405
$245$	−0.894788	−	11.9797i	−0.0571659	−	0.765358i
$246$	−11.3260			−0.722118
$247$	15.4264	−	26.7192i	0.981556	−	1.70010i
$248$	−4.27150	−	7.39846i	−0.271241	−	0.469803i
$249$	5.31744	+	9.21007i	0.336979	+	0.583665i
$250$	6.05358	−	10.4851i	0.382862	−	0.663136i
$251$	16.9165			1.06776			0.533879	−	0.845561i	$-0.320734\pi$
$251$	16.9165			1.06776			0.533879	+	0.845561i	$0.320734\pi$
$252$	−1.34893	−	4.37502i	−0.0849743	−	0.275601i
$253$	3.64985			0.229464
$254$	−1.26788	+	2.19602i	−0.0795536	+	0.137791i
$255$	4.03852	+	6.99491i	0.252902	+	0.438039i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	6.13308	−	10.6228i	0.382571	−	0.662633i	−0.608858	−	0.793279i	$-0.708372\pi$
$257$	6.13308	−	10.6228i	0.382571	−	0.662633i	0.991429	+	0.130646i	$0.0417053\pi$
$258$	−9.13878			−0.568955
$259$	−23.0472	−	5.26336i	−1.43208	−	0.327050i
$260$	−6.51854			−0.404262
$261$	2.42859	−	4.20644i	0.150326	−	0.260372i
$262$	2.63129	+	4.55753i	0.162562	+	0.281565i
$263$	−6.52900	−	11.3086i	−0.402596	−	0.697316i	0.591443	−	0.806347i	$-0.298559\pi$
$263$	−6.52900	−	11.3086i	−0.402596	−	0.697316i	−0.994038	+	0.109031i	$0.965225\pi$
$264$	−2.05625	+	3.56153i	−0.126553	+	0.219197i
$265$	5.24252			0.322045
$266$	14.6193	−	15.7520i	0.896367	−	0.965815i
$267$	−4.46012			−0.272955
$268$	6.61841	−	11.4634i	0.404283	−	0.700239i
$269$	−1.78352	−	3.08915i	−0.108743	−	0.188349i	0.806518	−	0.591209i	$-0.201349\pi$
$269$	−1.78352	−	3.08915i	−0.108743	−	0.188349i	−0.915261	+	0.402860i	$0.868016\pi$
$270$	−4.57359	−	7.92169i	−0.278340	−	0.482099i
$271$	−0.988595	+	1.71230i	−0.0600529	+	0.104015i	−0.894489	−	0.447090i	$-0.852460\pi$
$271$	−0.988595	+	1.71230i	−0.0600529	+	0.104015i	0.834436	+	0.551105i	$0.185794\pi$
$272$	4.17700			0.253268
$273$	7.70280	−	8.29959i	0.466195	−	0.502314i
$274$	−13.8513			−0.836789
$275$	−3.74986	+	6.49494i	−0.226125	+	0.391660i
$276$	−0.563379	−	0.975800i	−0.0339114	−	0.0587363i
$277$	5.46819	+	9.47119i	0.328552	+	0.569069i	0.982225	−	0.187709i	$-0.0601061\pi$
$277$	5.46819	+	9.47119i	0.328552	+	0.569069i	−0.653673	+	0.756777i	$0.726773\pi$
$278$	4.82833	−	8.36291i	0.289584	−	0.501574i
$279$	−14.7830			−0.885034
$280$	−4.42656	−	1.01091i	−0.264538	−	0.0604133i
$281$	−4.58034			−0.273240			−0.136620	−	0.990624i	$-0.543624\pi$
$281$	−4.58034			−0.273240			−0.136620	+	0.990624i	$0.543624\pi$
$282$	−1.66274	+	2.87994i	−0.0990145	+	0.171498i
$283$	7.54044	+	13.0604i	0.448233	+	0.776361i	0.998271	−	0.0587778i	$-0.0187203\pi$
$283$	7.54044	+	13.0604i	0.448233	+	0.776361i	−0.550039	+	0.835139i	$0.685387\pi$
$284$	−7.15268	−	12.3888i	−0.424433	−	0.735140i
$285$	7.85342	−	13.6025i	0.465196	−	0.805744i
$286$	13.8633			0.819757
$287$	7.83579	+	25.4141i	0.462532	+	1.50015i
$288$	−1.73042			−0.101966
$289$	−0.223647	+	0.387368i	−0.0131557	+	0.0227863i
$290$	−2.40857	−	4.17177i	−0.141436	−	0.244975i
$291$	0.0682282	+	0.118175i	0.00399961	+	0.00692752i
$292$	2.13049	−	3.69011i	0.124677	−	0.215947i
$293$	14.5555			0.850344			0.425172	−	0.905113i	$-0.360214\pi$
$293$	14.5555			0.850344			0.425172	+	0.905113i	$0.360214\pi$
$294$	6.51789	−	4.44147i	0.380131	−	0.259032i
$295$	7.18902			0.418561
$296$	−4.46765	+	7.73820i	−0.259677	+	0.449773i
$297$	9.72692	+	16.8475i	0.564413	+	0.977592i
$298$	4.78066	+	8.28034i	0.276936	+	0.479667i
$299$	−1.89916	+	3.28945i	−0.109832	+	0.190234i
$300$	2.31526			0.133672
$301$	6.32258	+	20.5063i	0.364428	+	1.18196i
$302$	7.25672			0.417577
$303$	−2.09744	+	3.63286i	−0.120495	+	0.208703i
$304$	−4.06135	−	7.03447i	−0.232935	−	0.403455i
$305$	9.70966	+	16.8176i	0.555973	+	0.962974i
$306$	3.61398	−	6.25959i	0.206597	−	0.357837i
$307$	−12.7024			−0.724965			−0.362482	−	0.931991i	$-0.618071\pi$
$307$	−12.7024			−0.724965			−0.362482	+	0.931991i	$0.618071\pi$
$308$	9.41423	+	2.14996i	0.536425	+	0.122505i
$309$	−17.0460			−0.969712
$310$	−7.33058	+	12.6969i	−0.416349	+	0.721137i
$311$	4.60947	+	7.98383i	0.261379	+	0.452722i	0.966609	−	0.256257i	$-0.0824894\pi$
$311$	4.60947	+	7.98383i	0.261379	+	0.452722i	−0.705230	+	0.708979i	$0.749156\pi$
$312$	−2.13990	−	3.70641i	−0.121148	−	0.209834i
$313$	7.82833	−	13.5591i	0.442483	−	0.766403i	−0.555390	−	0.831590i	$-0.687431\pi$
$313$	7.82833	−	13.5591i	0.442483	−	0.766403i	0.997873	+	0.0651867i	$0.0207643\pi$
$314$	−2.75509			−0.155479
$315$	−5.34484	+	5.75894i	−0.301147	+	0.324480i
$316$	−13.4482			−0.756519
$317$	−5.51911	+	9.55938i	−0.309984	+	0.536908i	−0.978359	−	0.206917i	$-0.933657\pi$
$317$	−5.51911	+	9.55938i	−0.309984	+	0.536908i	0.668374	+	0.743825i	$0.266990\pi$
$318$	1.72101	+	2.98087i	0.0965094	+	0.167159i
$319$	5.12245	+	8.87235i	0.286802	+	0.496756i
$320$	−0.858079	+	1.48624i	−0.0479681	+	0.0830832i
$321$	15.4765			0.863814
$322$	−1.79981	+	1.93925i	−0.100299	+	0.108070i
$323$	33.9285			1.88783
$324$	0.407198	−	0.705288i	0.0226221	−	0.0391827i
$325$	−3.90240	−	6.75916i	−0.216466	−	0.374931i
$326$	−10.1420	−	17.5665i	−0.561716	−	0.972921i
$327$	5.28975	−	9.16211i	0.292524	−	0.506666i
$328$	10.0518			0.555020
$329$	7.61259	+	1.73851i	0.419696	+	0.0958472i
$330$	7.05770			0.388513
$331$	7.84574	−	13.5892i	0.431241	−	0.746931i	−0.565740	−	0.824584i	$-0.691409\pi$
$331$	7.84574	−	13.5892i	0.431241	−	0.746931i	0.996980	+	0.0776528i	$0.0247426\pi$
$332$	−4.71924	−	8.17397i	−0.259002	−	0.448605i
$333$	7.73090	+	13.3903i	0.423651	+	0.733785i
$334$	0.162736	−	0.281867i	0.00890451	−	0.0154231i
$335$	−22.7165			−1.24113
$336$	−0.878349	−	2.84878i	−0.0479179	−	0.155414i
$337$	5.18787			0.282601			0.141301	−	0.989967i	$-0.454872\pi$
$337$	5.18787			0.282601			0.141301	+	0.989967i	$0.454872\pi$
$338$	−0.713651	+	1.23608i	−0.0388175	+	0.0672339i
$339$	−5.29203	−	9.16606i	−0.287424	−	0.497832i
$340$	−3.58419	−	6.20801i	−0.194380	−	0.336676i
$341$	15.5904	−	27.0033i	0.844265	−	1.46231i
$342$	−14.0557			−0.760045
$343$	−14.4755	−	11.5525i	−0.781601	−	0.623779i
$344$	8.11069			0.437299
$345$	−0.966847	+	1.67463i	−0.0520533	+	0.0901589i
$346$	−6.70089	−	11.6063i	−0.360242	−	0.623958i
$347$	8.87970	+	15.3801i	0.476687	+	0.825646i	0.999643	−	0.0267134i	$-0.00850415\pi$
$347$	8.87970	+	15.3801i	0.476687	+	0.825646i	−0.522956	+	0.852360i	$0.675171\pi$
$348$	1.58137	−	2.73901i	0.0847702	−	0.146826i
$349$	−15.3654			−0.822488			−0.411244	−	0.911525i	$-0.634906\pi$
$349$	−15.3654			−0.822488			−0.411244	+	0.911525i	$0.634906\pi$
$350$	−1.60179	−	5.19516i	−0.0856194	−	0.277693i
$351$	−20.2452			−1.08061
$352$	1.82493	−	3.16087i	0.0972689	−	0.168475i
$353$	13.2323	+	22.9190i	0.704283	+	1.21985i	0.966950	+	0.254968i	$0.0820648\pi$
$353$	13.2323	+	22.9190i	0.704283	+	1.21985i	−0.262666	+	0.964887i	$0.584602\pi$
$354$	2.36000	+	4.08764i	0.125433	+	0.217256i
$355$	−12.2751	+	21.2612i	−0.651496	+	1.12842i
$356$	3.95837			0.209793
$357$	12.1396	+	2.77235i	0.642495	+	0.146729i
$358$	20.8545			1.10220
$359$	−3.75001	+	6.49521i	−0.197918	+	0.342804i	−0.947853	−	0.318707i	$-0.896751\pi$
$359$	−3.75001	+	6.49521i	−0.197918	+	0.342804i	0.749935	+	0.661511i	$0.230085\pi$
$360$	1.48484	+	2.57181i	0.0782578	+	0.135546i
$361$	−23.4892	−	40.6845i	−1.23627	−	2.14129i
$362$	−0.788691	+	1.36605i	−0.0414527	+	0.0717981i
$363$	−2.61568			−0.137288
$364$	−6.83626	+	7.36591i	−0.358317	+	0.386079i
$365$	−7.31251			−0.382754
$366$	−6.37495	+	11.0417i	−0.333224	+	0.577161i
$367$	0.805459	+	1.39510i	0.0420446	+	0.0728234i	0.886282	−	0.463146i	$-0.153280\pi$
$367$	0.805459	+	1.39510i	0.0420446	+	0.0728234i	−0.844237	+	0.535970i	$0.819946\pi$
$368$	0.500000	+	0.866025i	0.0260643	+	0.0451447i
$369$	8.69695	−	15.0636i	0.452745	−	0.784177i
$370$	15.3344			0.797197
$371$	5.49805	−	5.92402i	0.285444	−	0.307560i
$372$	−9.62589			−0.499079
$373$	−9.05039	+	15.6757i	−0.468612	+	0.811659i	−0.999356	−	0.0358726i	$-0.988579\pi$
$373$	−9.05039	+	15.6757i	−0.468612	+	0.811659i	0.530745	+	0.847532i	$0.321912\pi$
$374$	7.62271	+	13.2029i	0.394161	+	0.682707i
$375$	−6.82091	−	11.8142i	−0.352230	−	0.610081i
$376$	1.47568	−	2.55596i	0.0761025	−	0.131813i
$377$	−10.6617			−0.549104
$378$	−13.7480	−	3.13967i	−0.707120	−	0.161487i
$379$	−10.3909			−0.533747			−0.266873	−	0.963732i	$-0.585991\pi$
$379$	−10.3909			−0.533747			−0.266873	+	0.963732i	$0.585991\pi$
$380$	−6.96993	+	12.0723i	−0.357550	+	0.619294i
$381$	1.42859	+	2.47439i	0.0731888	+	0.126767i
$382$	−3.13049	−	5.42216i	−0.160170	−	0.277422i
$383$	3.69781	−	6.40480i	0.188949	−	0.327270i	−0.755951	−	0.654628i	$-0.772825\pi$
$383$	3.69781	−	6.40480i	0.188949	−	0.327270i	0.944900	+	0.327359i	$0.106158\pi$
$384$	−1.12676			−0.0574996
$385$	−4.88281	−	15.8366i	−0.248851	−	0.807108i
$386$	13.0358			0.663504
$387$	7.01744	−	12.1546i	0.356717	−	0.617851i
$388$	−0.0605527	−	0.104880i	−0.00307410	−	0.00532449i
$389$	−2.03971	−	3.53288i	−0.103417	−	0.179124i	0.809673	−	0.586881i	$-0.199644\pi$
$389$	−2.03971	−	3.53288i	−0.103417	−	0.179124i	−0.913090	+	0.407757i	$0.866311\pi$
$390$	−3.67240	+	6.36079i	−0.185959	+	0.322091i
$391$	−4.17700			−0.211240
$392$	−5.78464	+	3.94181i	−0.292169	+	0.199092i
$393$	5.92965			0.299111
$394$	10.6276	−	18.4075i	0.535409	−	0.927355i
$395$	11.5396	+	19.9872i	0.580621	+	1.00566i
$396$	−3.15789	−	5.46962i	−0.158690	−	0.274859i
$397$	−4.43055	+	7.67394i	−0.222363	+	0.385144i	−0.955525	−	0.294910i	$-0.904710\pi$
$397$	−4.43055	+	7.67394i	−0.222363	+	0.385144i	0.733162	+	0.680054i	$0.238044\pi$
$398$	4.73724			0.237456
$399$	−7.13457	−	23.1398i	−0.357175	−	1.15844i
$400$	−2.05480			−0.102740
$401$	−8.30173	+	14.3790i	−0.414569	+	0.718054i	−0.995383	−	0.0959821i	$-0.969401\pi$
$401$	−8.30173	+	14.3790i	−0.414569	+	0.718054i	0.580814	+	0.814036i	$0.302734\pi$
$402$	−7.45734	−	12.9165i	−0.371938	−	0.644216i
$403$	16.2246	+	28.1018i	0.808204	+	1.39985i
$404$	1.86148	−	3.22418i	0.0926121	−	0.160409i
$405$	−1.39763			−0.0694489
$406$	−7.24006	−	1.65343i	−0.359318	−	0.0820586i
$407$	−32.6125			−1.61654
$408$	2.35323	−	4.07591i	0.116502	−	0.201788i
$409$	−16.8717	−	29.2227i	−0.834253	−	1.44497i	−0.894637	−	0.446793i	$-0.852566\pi$
$409$	−16.8717	−	29.2227i	−0.834253	−	1.44497i	0.0603848	−	0.998175i	$-0.480767\pi$
$410$	−8.62528	−	14.9394i	−0.425972	−	0.737805i
$411$	−7.80354	+	13.5161i	−0.384920	+	0.666701i
$412$	15.1284			0.745321
$413$	7.53942	−	8.12355i	0.370991	−	0.399734i
$414$	1.73042			0.0850454
$415$	−8.09897	+	14.0278i	−0.397563	+	0.688599i
$416$	1.89916	+	3.28945i	0.0931142	+	0.161279i
$417$	−5.44035	−	9.42296i	−0.266415	−	0.461445i
$418$	14.8233	−	25.6748i	0.725034	−	1.25579i
$419$	36.5806			1.78708			0.893539	−	0.448985i	$-0.148214\pi$
$419$	36.5806			1.78708			0.893539	+	0.448985i	$0.148214\pi$
$420$	−3.48028	+	3.74992i	−0.169820	+	0.182977i
$421$	−32.7603			−1.59664			−0.798321	−	0.602233i	$-0.794278\pi$
$421$	−32.7603			−1.59664			−0.798321	+	0.602233i	$0.794278\pi$
$422$	−8.38086	+	14.5161i	−0.407974	+	0.706631i
$423$	−2.55355	−	4.42288i	−0.124158	−	0.215048i
$424$	−1.52740	−	2.64553i	−0.0741771	−	0.128478i
$425$	4.29144	−	7.43300i	0.208166	−	0.360553i
$426$	−16.1187			−0.780952
$427$	29.1867	+	6.66547i	1.41245	+	0.322565i
$428$	−13.7354			−0.663927
$429$	7.81031	−	13.5279i	0.377085	−	0.653131i
$430$	−6.95962	−	12.0544i	−0.335622	−	0.581315i
$431$	8.85968	+	15.3454i	0.426756	+	0.739163i	0.996583	−	0.0826019i	$-0.0263230\pi$
$431$	8.85968	+	15.3454i	0.426756	+	0.739163i	−0.569827	+	0.821765i	$0.692990\pi$
$432$	−2.66502	+	4.61594i	−0.128221	+	0.222085i
$433$	−4.51989			−0.217212			−0.108606	−	0.994085i	$-0.534639\pi$
$433$	−4.51989			−0.217212			−0.108606	+	0.994085i	$0.534639\pi$
$434$	6.65959	+	21.5993i	0.319671	+	1.03680i
$435$	−5.42776			−0.260241
$436$	−4.69467	+	8.13140i	−0.224834	+	0.389424i
$437$	4.06135	+	7.03447i	0.194281	+	0.336504i
$438$	−2.40054	−	4.15786i	−0.114702	−	0.198670i
$439$	−3.19897	+	5.54078i	−0.152679	+	0.264447i	−0.932211	−	0.361914i	$-0.882123\pi$
$439$	−3.19897	+	5.54078i	−0.152679	+	0.264447i	0.779533	+	0.626361i	$0.215457\pi$
$440$	−6.26373			−0.298611
$441$	0.902222	+	12.0793i	0.0429630	+	0.575204i
$442$	−15.8656			−0.754650
$443$	8.56844	−	14.8410i	0.407099	−	0.705116i	−0.587464	−	0.809250i	$-0.699874\pi$
$443$	8.56844	−	14.8410i	0.407099	−	0.705116i	0.994563	+	0.104134i	$0.0332070\pi$
$444$	5.03396	+	8.71907i	0.238901	+	0.413789i
$445$	−3.39660	−	5.88308i	−0.161014	−	0.278885i
$446$	−0.617347	+	1.06928i	−0.0292322	+	0.0506317i
$447$	10.7733			0.509559
$448$	0.779537	+	2.52830i	0.0368297	+	0.119451i
$449$	−13.2695			−0.626226			−0.313113	−	0.949716i	$-0.601372\pi$
$449$	−13.2695			−0.626226			−0.313113	+	0.949716i	$0.601372\pi$
$450$	−1.77783	+	3.07929i	−0.0838078	+	0.145159i
$451$	18.3439	+	31.7725i	0.863779	+	1.49611i
$452$	4.69669	+	8.13491i	0.220914	+	0.382634i
$453$	4.08828	−	7.08111i	0.192084	−	0.332700i
$454$	23.0421			1.08142
$455$	16.8135	+	3.83976i	0.788231	+	0.180011i
$456$	−9.15232			−0.428597
$457$	15.2314	−	26.3815i	0.712494	−	1.23408i	−0.251424	−	0.967877i	$-0.580899\pi$
$457$	15.2314	−	26.3815i	0.712494	−	1.23408i	0.963918	−	0.266199i	$-0.0857679\pi$
$458$	2.41831	+	4.18864i	0.113000	+	0.195722i
$459$	−11.1318	−	19.2808i	−0.519586	−	0.899950i
$460$	0.858079	−	1.48624i	0.0400082	−	0.0692962i
$461$	13.1239			0.611239			0.305620	−	0.952154i	$-0.401136\pi$
$461$	13.1239			0.611239			0.305620	+	0.952154i	$0.401136\pi$
$462$	7.40170	−	7.97516i	0.344358	−	0.371038i
$463$	−21.3453			−0.991998			−0.495999	−	0.868323i	$-0.665198\pi$
$463$	−21.3453			−0.991998			−0.495999	+	0.868323i	$0.665198\pi$
$464$	−1.40347	+	2.43088i	−0.0651544	+	0.112851i
$465$	8.25978	+	14.3064i	0.383038	+	0.663442i
$466$	6.62724	+	11.4787i	0.307001	+	0.531741i
$467$	−11.1802	+	19.3647i	−0.517358	+	0.896091i	0.482439	+	0.875930i	$0.339751\pi$
$467$	−11.1802	+	19.3647i	−0.517358	+	0.896091i	−0.999797	+	0.0201608i	$0.993582\pi$
$468$	6.57270			0.303823
$469$	−23.8237	+	25.6695i	−1.10008	+	1.18531i
$470$	−5.06501			−0.233632
$471$	−1.55216	+	2.68842i	−0.0715198	+	0.123876i
$472$	−2.09451	−	3.62779i	−0.0964075	−	0.166983i
$473$	14.8014	+	25.6368i	0.680570	+	1.17878i
$474$	−7.57642	+	13.1227i	−0.347996	+	0.602747i
$475$	−16.6905			−0.765814
$476$	−10.7739	−	2.46047i	−0.493821	−	0.112776i
$477$	−5.28608			−0.242033
$478$	2.70125	−	4.67871i	0.123552	−	0.213999i
$479$	8.73350	+	15.1269i	0.399044	+	0.691164i	0.993608	−	0.112884i	$-0.0360088\pi$
$479$	8.73350	+	15.1269i	0.399044	+	0.691164i	−0.594564	+	0.804048i	$0.702675\pi$
$480$	0.966847	+	1.67463i	0.0441303	+	0.0764360i
$481$	16.9696	−	29.3922i	0.773747	−	1.34017i
$482$	−17.2207			−0.784383
$483$	0.878349	+	2.84878i	0.0399663	+	0.129624i
$484$	2.32142			0.105519
$485$	−0.103918	+	0.179991i	−0.00471867	+	0.00817298i
$486$	7.53624	+	13.0531i	0.341851	+	0.592103i
$487$	2.89533	+	5.01486i	0.131200	+	0.227245i	0.924139	−	0.382055i	$-0.124784\pi$
$487$	2.89533	+	5.01486i	0.131200	+	0.227245i	−0.792939	+	0.609301i	$0.791450\pi$
$488$	5.65778	−	9.79957i	0.256116	−	0.443606i
$489$	−22.8552			−1.03355
$490$	10.8222	+	5.21496i	0.488895	+	0.235588i
$491$	−8.47054			−0.382270			−0.191135	−	0.981564i	$-0.561217\pi$
$491$	−8.47054			−0.382270			−0.191135	+	0.981564i	$0.561217\pi$
$492$	5.66299	−	9.80859i	0.255307	−	0.442205i
$493$	−5.86228	−	10.1538i	−0.264024	−	0.457303i
$494$	15.4264	+	26.7192i	0.694065	+	1.20216i
$495$	−5.41943	+	9.38674i	−0.243585	+	0.421902i
$496$	8.54301			0.383592
$497$	11.1516	+	36.1683i	0.500216	+	1.62237i
$498$	−10.6349			−0.476560
$499$	1.26100	−	2.18412i	0.0564502	−	0.0977746i	−0.836419	−	0.548090i	$-0.815355\pi$
$499$	1.26100	−	2.18412i	0.0564502	−	0.0977746i	0.892870	+	0.450315i	$0.148688\pi$
$500$	6.05358	+	10.4851i	0.270724	+	0.468908i
$501$	−0.183364	−	0.317596i	−0.00819209	−	0.0141891i
$502$	−8.45824	+	14.6501i	−0.377510	+	0.653866i
$503$	8.34455			0.372065			0.186033	−	0.982544i	$-0.440437\pi$
$503$	8.34455			0.372065			0.186033	+	0.982544i	$0.440437\pi$
$504$	4.46335	+	1.01931i	0.198813	+	0.0454036i
$505$	−6.38919			−0.284315
$506$	−1.82493	+	3.16087i	−0.0811279	+	0.140518i
$507$	0.804111	+	1.39276i	0.0357118	+	0.0618547i
$508$	−1.26788	−	2.19602i	−0.0562529	−	0.0974329i
$509$	8.43774	−	14.6146i	0.373996	−	0.647781i	−0.616180	−	0.787605i	$-0.711321\pi$
$509$	8.43774	−	14.6146i	0.373996	−	0.647781i	0.990176	+	0.139825i	$0.0446539\pi$
$510$	−8.07703			−0.357657
$511$	−7.66893	+	8.26310i	−0.339253	+	0.365538i
$512$	1.00000			0.0441942
$513$	−21.6472	+	37.4940i	−0.955745	+	1.65540i
$514$	6.13308	+	10.6228i	0.270519	+	0.468552i
$515$	−12.9813	−	22.4843i	−0.572026	−	0.990778i
$516$	4.56939	−	7.91441i	0.201156	−	0.348413i
$517$	10.7720			0.473754
$518$	16.0818	−	17.3278i	0.706594	−	0.761339i
$519$	−15.1006			−0.662841
$520$	3.25927	−	5.64522i	0.142928	−	0.247559i
$521$	−3.43970	−	5.95774i	−0.150696	−	0.261013i	0.780787	−	0.624797i	$-0.214818\pi$
$521$	−3.43970	−	5.95774i	−0.150696	−	0.261013i	−0.931484	+	0.363783i	$0.881485\pi$
$522$	2.42859	+	4.20644i	0.106296	+	0.184111i
$523$	−10.6428	+	18.4338i	−0.465375	+	0.806053i	−0.999218	−	0.0395302i	$-0.987414\pi$
$523$	−10.6428	+	18.4338i	−0.465375	+	0.806053i	0.533843	+	0.845583i	$0.320747\pi$
$524$	−5.26258			−0.229897
$525$	−5.97185	−	1.36381i	−0.260633	−	0.0595216i
$526$	13.0580			0.569356
$527$	−17.8421	+	30.9033i	−0.777212	+	1.34617i
$528$	−2.05625	−	3.56153i	−0.0894867	−	0.154996i
$529$	−0.500000	−	0.866025i	−0.0217391	−	0.0376533i
$530$	−2.62126	+	4.54016i	−0.113860	+	0.197212i
$531$	−7.24875			−0.314569
$532$	6.33195	+	20.5367i	0.274525	+	0.890378i
$533$	−38.1802			−1.65377
$534$	2.23006	−	3.86258i	0.0965041	−	0.167150i
$535$	11.7861	+	20.4141i	0.509557	+	0.882579i
$536$	6.61841	+	11.4634i	0.285872	+	0.495144i
$537$	11.7490	−	20.3499i	0.507007	−	0.878161i
$538$	3.56705			0.153786
$539$	−23.0161	−	11.0910i	−0.991373	−	0.477721i
$540$	9.14718			0.393632
$541$	22.2528	−	38.5429i	0.956721	−	1.65709i	0.226342	−	0.974048i	$-0.427323\pi$
$541$	22.2528	−	38.5429i	0.956721	−	1.65709i	0.730379	−	0.683042i	$-0.239343\pi$
$542$	−0.988595	−	1.71230i	−0.0424638	−	0.0735494i
$543$	0.888663	+	1.53921i	0.0381362	+	0.0660538i
$544$	−2.08850	+	3.61738i	−0.0895436	+	0.155094i
$545$	16.1136			0.690230
$546$	3.33626	+	10.8206i	0.142779	+	0.463080i
$547$	4.70118			0.201008			0.100504	−	0.994937i	$-0.467954\pi$
$547$	4.70118			0.201008			0.100504	+	0.994937i	$0.467954\pi$
$548$	6.92566	−	11.9956i	0.295850	−	0.512426i
$549$	−9.79034	−	16.9574i	−0.417841	−	0.723722i
$550$	−3.74986	−	6.49494i	−0.159894	−	0.276945i
$551$	−11.4000	+	19.7453i	−0.485655	+	0.841179i
$552$	1.12676			0.0479580
$553$	34.6875	+	7.92169i	1.47506	+	0.336865i
$554$	−10.9364			−0.464643
$555$	8.63907	−	14.9633i	0.366708	−	0.635157i
$556$	4.82833	+	8.36291i	0.204767	+	0.354666i
$557$	−11.6577	−	20.1917i	−0.493951	−	0.855548i	0.506025	−	0.862519i	$-0.331114\pi$
$557$	−11.6577	−	20.1917i	−0.493951	−	0.855548i	−0.999976	+	0.00697093i	$0.997781\pi$
$558$	7.39149	−	12.8024i	0.312907	−	0.541970i
$559$	−30.8071			−1.30300
$560$	3.08875	−	3.32806i	0.130524	−	0.140636i
$561$	17.1779			0.725251
$562$	2.29017	−	3.96669i	0.0966050	−	0.167325i
$563$	−19.6307	−	34.0014i	−0.827335	−	1.43299i	−0.900121	−	0.435639i	$-0.856522\pi$
$563$	−19.6307	−	34.0014i	−0.827335	−	1.43299i	0.0727857	−	0.997348i	$-0.476811\pi$
$564$	−1.66274	−	2.87994i	−0.0700138	−	0.121267i
$565$	8.06027	−	13.9608i	0.339098	−	0.587335i
$566$	−15.0809			−0.633896
$567$	−1.46576	+	1.57932i	−0.0615560	+	0.0663251i
$568$	14.3054			0.600239
$569$	−14.2620	+	24.7026i	−0.597895	+	1.03559i	0.395236	+	0.918580i	$0.370663\pi$
$569$	−14.2620	+	24.7026i	−0.597895	+	1.03559i	−0.993131	+	0.117006i	$0.962670\pi$
$570$	7.85342	+	13.6025i	0.328943	+	0.569747i
$571$	−5.73892	−	9.94011i	−0.240167	−	0.415981i	0.720595	−	0.693356i	$-0.243869\pi$
$571$	−5.73892	−	9.94011i	−0.240167	−	0.415981i	−0.960762	+	0.277376i	$0.910535\pi$
$572$	−6.93167	+	12.0060i	−0.289828	+	0.501996i
$573$	−7.05460			−0.294710
$574$	−25.9272	−	5.92107i	−1.08218	−	0.247141i
$575$	2.05480			0.0856911
$576$	0.865209	−	1.49859i	0.0360504	−	0.0624411i
$577$	−11.4092	−	19.7613i	−0.474970	−	0.822672i	0.524619	−	0.851337i	$-0.324208\pi$
$577$	−11.4092	−	19.7613i	−0.474970	−	0.822672i	−0.999589	+	0.0286648i	$0.990874\pi$
$578$	−0.223647	−	0.387368i	−0.00930248	−	0.0161124i
$579$	7.34408	−	12.7203i	0.305209	−	0.528638i
$580$	4.81715			0.200021
$581$	7.35765	+	23.8634i	0.305247	+	0.990019i
$582$	−0.136456			−0.00565630
$583$	5.57478	−	9.65581i	0.230884	−	0.399903i
$584$	2.13049	+	3.69011i	0.0881602	+	0.152698i
$585$	−5.63990	−	9.76859i	−0.233181	−	0.403881i
$586$	−7.27777	+	12.6055i	−0.300642	+	0.520727i
$587$	20.6525			0.852422			0.426211	−	0.904624i	$-0.359848\pi$
$587$	20.6525			0.852422			0.426211	+	0.904624i	$0.359848\pi$
$588$	0.587480	+	7.86539i	0.0242272	+	0.324363i
$589$	69.3924			2.85926
$590$	−3.59451	+	6.22587i	−0.147984	+	0.256315i
$591$	−11.9747	−	20.7407i	−0.492572	−	0.853160i
$592$	−4.46765	−	7.73820i	−0.183619	−	0.318038i
$593$	3.83376	−	6.64027i	0.157434	−	0.272683i	−0.776509	−	0.630106i	$-0.783011\pi$
$593$	3.83376	−	6.64027i	0.157434	−	0.272683i	0.933943	+	0.357423i	$0.116345\pi$
$594$	−19.4538			−0.798200
$595$	5.58803	+	18.1239i	0.229087	+	0.743006i
$596$	−9.56131			−0.391647
$597$	2.66886	−	4.62260i	0.109229	−	0.189190i
$598$	−1.89916	−	3.28945i	−0.0776626	−	0.134516i
$599$	−18.7730	−	32.5158i	−0.767043	−	1.32856i	−0.939160	−	0.343481i	$-0.888394\pi$
$599$	−18.7730	−	32.5158i	−0.767043	−	1.32856i	0.172117	−	0.985077i	$-0.444939\pi$
$600$	−1.15763	+	2.00507i	−0.0472600	+	0.0818568i
$601$	−16.2537			−0.663003			−0.331501	−	0.943455i	$-0.607555\pi$
$601$	−16.2537			−0.663003			−0.331501	+	0.943455i	$0.607555\pi$
$602$	−20.9203	−	4.77763i	−0.852646	−	0.194722i
$603$	22.9052			0.932773
$604$	−3.62836	+	6.28451i	−0.147636	+	0.255713i
$605$	−1.99197	−	3.45019i	−0.0809849	−	0.140270i
$606$	−2.09744	−	3.63286i	−0.0852025	−	0.147575i
$607$	−2.16135	+	3.74356i	−0.0877264	+	0.151947i	−0.906550	−	0.422099i	$-0.861293\pi$
$607$	−2.16135	+	3.74356i	−0.0877264	+	0.151947i	0.818823	+	0.574046i	$0.194627\pi$
$608$	8.12271			0.329419
$609$	−5.69231	+	6.13334i	−0.230664	+	0.248535i
$610$	−19.4193			−0.786265
$611$	−5.60513	+	9.70837i	−0.226759	+	0.392758i
$612$	3.61398	+	6.25959i	0.146086	+	0.253029i
$613$	−20.0725	−	34.7666i	−0.810720	−	1.40421i	−0.912360	−	0.409388i	$-0.865742\pi$
$613$	−20.0725	−	34.7666i	−0.810720	−	1.40421i	0.101640	−	0.994821i	$-0.467591\pi$
$614$	6.35121	−	11.0006i	0.256314	−	0.443949i
$615$	−19.4372			−0.783783
$616$	−6.56903	+	7.07798i	−0.264674	+	0.285180i
$617$	−27.7668			−1.11785			−0.558925	−	0.829218i	$-0.688786\pi$
$617$	−27.7668			−1.11785			−0.558925	+	0.829218i	$0.688786\pi$
$618$	8.52299	−	14.7623i	0.342845	−	0.593825i
$619$	8.36648	+	14.4912i	0.336277	+	0.582450i	0.983729	−	0.179657i	$-0.0574987\pi$
$619$	8.36648	+	14.4912i	0.336277	+	0.582450i	−0.647452	+	0.762106i	$0.724165\pi$
$620$	−7.33058	−	12.6969i	−0.294403	−	0.509921i
$621$	2.66502	−	4.61594i	0.106943	−	0.185231i
$622$	−9.21894			−0.369646
$623$	−10.2100	−	2.33169i	−0.409055	−	0.0934172i
$624$	4.27979			0.171329
$625$	5.25190	−	9.09656i	0.210076	−	0.363862i
$626$	7.82833	+	13.5591i	0.312883	+	0.541929i
$627$	−16.7023	−	28.9292i	−0.667026	−	1.15532i
$628$	1.37755	−	2.38598i	0.0549701	−	0.0952110i
$629$	37.3227			1.48815
$630$	−2.31497	−	7.50824i	−0.0922306	−	0.299135i
$631$	16.4804			0.656073			0.328037	−	0.944665i	$-0.393613\pi$
$631$	16.4804			0.656073			0.328037	+	0.944665i	$0.393613\pi$
$632$	6.72409	−	11.6465i	0.267470	−	0.463272i
$633$	9.44319	+	16.3561i	0.375333	+	0.650096i
$634$	−5.51911	−	9.55938i	−0.219192	−	0.379651i
$635$	−2.17588	+	3.76873i	−0.0863470	+	0.149557i
$636$	−3.44202			−0.136485
$637$	21.9720	−	14.9723i	0.870561	−	0.593224i
$638$	−10.2449			−0.405600
$639$	12.3771	−	21.4378i	0.489632	−	0.848067i
$640$	−0.858079	−	1.48624i	−0.0339186	−	0.0587487i
$641$	−0.882551	−	1.52862i	−0.0348587	−	0.0603770i	0.848070	−	0.529885i	$-0.177765\pi$
$641$	−0.882551	−	1.52862i	−0.0348587	−	0.0603770i	−0.882928	+	0.469508i	$0.844431\pi$
$642$	−7.73825	+	13.4030i	−0.305404	+	0.528976i
$643$	−8.26706			−0.326021			−0.163010	−	0.986624i	$-0.552120\pi$
$643$	−8.26706			−0.326021			−0.163010	+	0.986624i	$0.552120\pi$
$644$	−0.779537	−	2.52830i	−0.0307181	−	0.0996291i
$645$	−15.6836			−0.617541
$646$	−16.9643	+	29.3830i	−0.667450	+	1.15606i
$647$	7.76187	+	13.4439i	0.305150	+	0.528536i	0.977295	−	0.211884i	$-0.0679599\pi$
$647$	7.76187	+	13.4439i	0.305150	+	0.528536i	−0.672144	+	0.740420i	$0.734627\pi$
$648$	0.407198	+	0.705288i	0.0159963	+	0.0277063i
$649$	7.64464	−	13.2409i	0.300079	−	0.519751i
$650$	7.80480			0.306130
$651$	24.8285	+	5.67016i	0.973105	+	0.222231i
$652$	20.2841			0.794386
$653$	−9.92962	+	17.1986i	−0.388576	+	0.673033i	−0.992258	−	0.124192i	$-0.960366\pi$
$653$	−9.92962	+	17.1986i	−0.388576	+	0.673033i	0.603682	+	0.797225i	$0.293700\pi$
$654$	5.28975	+	9.16211i	0.206846	+	0.358267i
$655$	4.51571	+	7.82144i	0.176443	+	0.305609i
$656$	−5.02592	+	8.70515i	−0.196229	+	0.339879i
$657$	7.37327			0.287659
$658$	−5.31189	+	5.72344i	−0.207079	+	0.223123i
$659$	−1.62164			−0.0631702			−0.0315851	−	0.999501i	$-0.510056\pi$
$659$	−1.62164			−0.0631702			−0.0315851	+	0.999501i	$0.510056\pi$
$660$	−3.52885	+	6.11215i	−0.137360	+	0.237915i
$661$	4.53150	+	7.84879i	0.176255	+	0.305283i	0.940595	−	0.339531i	$-0.110268\pi$
$661$	4.53150	+	7.84879i	0.176255	+	0.305283i	−0.764340	+	0.644814i	$0.776935\pi$
$662$	7.84574	+	13.5892i	0.304933	+	0.528160i
$663$	−8.93834	+	15.4817i	−0.347136	+	0.601258i
$664$	9.43848			0.366284
$665$	25.0891	−	27.0329i	0.972912	−	1.04829i
$666$	−15.4618			−0.599133
$667$	1.40347	−	2.43088i	0.0543425	−	0.0941240i
$668$	0.162736	+	0.281867i	0.00629644	+	0.0109058i
$669$	0.695600	+	1.20481i	0.0268934	+	0.0465808i
$670$	11.3582	−	19.6730i	0.438807	−	0.760036i
$671$	41.3002			1.59438
$672$	2.90629	+	0.663720i	0.112113	+	0.0256035i
$673$	8.45539			0.325931			0.162966	−	0.986632i	$-0.447894\pi$
$673$	8.45539			0.325931			0.162966	+	0.986632i	$0.447894\pi$
$674$	−2.59393	+	4.49282i	−0.0999146	+	0.173057i
$675$	5.47607	+	9.48484i	0.210774	+	0.365072i
$676$	−0.713651	−	1.23608i	−0.0274481	−	0.0475415i
$677$	15.3193	−	26.5338i	0.588767	−	1.01978i	−0.405627	−	0.914039i	$-0.632947\pi$
$677$	15.3193	−	26.5338i	0.588767	−	1.01978i	0.994394	−	0.105736i	$-0.0337199\pi$
$678$	10.5841			0.406478
$679$	0.0944061	+	0.306191i	0.00362297	+	0.0117505i
$680$	7.16839			0.274895
$681$	12.9814	−	22.4845i	0.497448	−	0.861606i
$682$	15.5904	+	27.0033i	0.596986	+	1.03401i
$683$	14.5152	+	25.1411i	0.555410	+	0.961998i	0.997872	+	0.0652106i	$0.0207719\pi$
$683$	14.5152	+	25.1411i	0.555410	+	0.961998i	−0.442462	+	0.896787i	$0.645895\pi$
$684$	7.02784	−	12.1726i	0.268716	−	0.465430i
$685$	−23.7711			−0.908246
$686$	17.2425	−	6.75983i	0.658323	−	0.258092i
$687$	5.44971			0.207919
$688$	−4.05534	+	7.02406i	−0.154609	+	0.267790i
$689$	5.80157	+	10.0486i	0.221022	+	0.382821i
$690$	−0.966847	−	1.67463i	−0.0368072	−	0.0637520i
$691$	−11.1056	+	19.2355i	−0.422477	+	0.731751i	−0.996181	−	0.0873113i	$-0.972173\pi$
$691$	−11.1056	+	19.2355i	−0.422477	+	0.731751i	0.573704	+	0.819062i	$0.305506\pi$
$692$	13.4018			0.509459
$693$	4.92338	+	15.9682i	0.187024	+	0.606582i
$694$	−17.7594			−0.674137
$695$	8.28617	−	14.3521i	0.314313	−	0.544405i
$696$	1.58137	+	2.73901i	0.0599416	+	0.103822i
$697$	−20.9933	−	36.3614i	−0.795176	−	1.37729i
$698$	7.68268	−	13.3068i	0.290794	−	0.503669i
$699$	14.9346			0.564878
$700$	5.30003	+	1.21039i	0.200322	+	0.0457483i
$701$	−2.49593			−0.0942699			−0.0471350	−	0.998889i	$-0.515009\pi$
$701$	−2.49593			−0.0942699			−0.0471350	+	0.998889i	$0.515009\pi$
$702$	10.1226	−	17.5329i	0.382053	−	0.661736i
$703$	−36.2894	−	62.8551i	−1.36868	−	2.37063i
$704$	1.82493	+	3.16087i	0.0687795	+	0.119130i
$705$	−2.85352	+	4.94244i	−0.107470	+	0.186143i
$706$	−26.4646			−0.996007
$707$	−6.70061	+	7.21975i	−0.252002	+	0.271527i
$708$	−4.72000			−0.177389
$709$	20.0638	−	34.7515i	0.753510	−	1.30512i	−0.192601	−	0.981277i	$-0.561692\pi$
$709$	20.0638	−	34.7515i	0.753510	−	1.30512i	0.946111	−	0.323841i	$-0.104974\pi$
$710$	−12.2751	−	21.2612i	−0.460677	−	0.797917i
$711$	−11.6355	−	20.1533i	−0.436365	−	0.755806i
$712$	−1.97918	+	3.42805i	−0.0741731	+	0.128472i
$713$	−8.54301			−0.319938
$714$	−8.47072	+	9.12701i	−0.317009	+	0.341570i
$715$	23.7917			0.889759
$716$	−10.4273	+	18.0606i	−0.389685	+	0.674955i
$717$	−3.04365	−	5.27176i	−0.113667	−	0.196878i
$718$	−3.75001	−	6.49521i	−0.139949	−	0.242399i
$719$	−5.69592	+	9.86562i	−0.212422	+	0.367926i	−0.952472	−	0.304626i	$-0.901468\pi$
$719$	−5.69592	+	9.86562i	−0.212422	+	0.367926i	0.740050	+	0.672552i	$0.234802\pi$
$720$	−2.96967			−0.110673
$721$	−39.0213	−	8.91141i	−1.45323	−	0.331878i
$722$	46.9784			1.74836
$723$	−9.70180	+	16.8040i	−0.360814	+	0.624948i
$724$	−0.788691	−	1.36605i	−0.0293115	−	0.0507689i
$725$	2.88385	+	4.99497i	0.107103	+	0.185508i
$726$	1.30784	−	2.26525i	0.0485385	−	0.0840712i
$727$	−22.5154			−0.835051			−0.417526	−	0.908665i	$-0.637103\pi$
$727$	−22.5154			−0.835051			−0.417526	+	0.908665i	$0.637103\pi$
$728$	−2.96094	−	9.60333i	−0.109740	−	0.355923i
$729$	19.4262			0.719489
$730$	3.65625	−	6.33282i	0.135324	−	0.234388i
$731$	−16.9392	−	29.3395i	−0.626517	−	1.08516i
$732$	−6.37495	−	11.0417i	−0.235625	−	0.408114i
$733$	6.17468	−	10.6949i	0.228067	−	0.395024i	−0.729168	−	0.684335i	$-0.760093\pi$
$733$	6.17468	−	10.6949i	0.228067	−	0.395024i	0.957235	+	0.289311i	$0.0934261\pi$
$734$	−1.61092			−0.0594600
$735$	11.1857	−	7.62226i	0.412592	−	0.281151i
$736$	−1.00000			−0.0368605
$737$	−24.1562	+	41.8398i	−0.889805	+	1.54119i
$738$	8.69695	+	15.0636i	0.320139	+	0.554497i
$739$	4.74812	+	8.22398i	0.174662	+	0.302524i	0.940044	−	0.341052i	$-0.110783\pi$
$739$	4.74812	+	8.22398i	0.174662	+	0.302524i	−0.765382	+	0.643576i	$0.777450\pi$
$740$	−7.66719	+	13.2800i	−0.281852	+	0.488181i
$741$	34.7635			1.27707
$742$	2.38133	+	7.72346i	0.0874214	+	0.283537i
$743$	−31.7348			−1.16424			−0.582118	−	0.813104i	$-0.697776\pi$
$743$	−31.7348			−1.16424			−0.582118	+	0.813104i	$0.697776\pi$
$744$	4.81295	−	8.33627i	0.176451	−	0.305622i
$745$	8.20437	+	14.2104i	0.300585	+	0.520628i
$746$	−9.05039	−	15.6757i	−0.331358	−	0.573930i
$747$	8.16626	−	14.1444i	0.298788	−	0.517516i
$748$	−15.2454			−0.557428
$749$	35.4284	+	8.09090i	1.29453	+	0.295635i
$750$	13.6418			0.498129
$751$	0.729462	−	1.26346i	0.0266184	−	0.0461045i	−0.852409	−	0.522875i	$-0.824859\pi$
$751$	0.729462	−	1.26346i	0.0266184	−	0.0461045i	0.879028	+	0.476771i	$0.158193\pi$
$752$	1.47568	+	2.55596i	0.0538126	+	0.0932062i
$753$	9.53038	+	16.5071i	0.347306	+	0.601552i
$754$	5.33083	−	9.23328i	0.194138	−	0.336256i
$755$	12.4537			0.453236
$756$	9.59303	−	10.3363i	0.348895	−	0.375927i
$757$	13.7895			0.501186			0.250593	−	0.968092i	$-0.419374\pi$
$757$	13.7895			0.501186			0.250593	+	0.968092i	$0.419374\pi$
$758$	5.19547	−	8.99882i	0.188708	−	0.326852i
$759$	2.05625	+	3.56153i	0.0746371	+	0.129275i
$760$	−6.96993	−	12.0723i	−0.252826	−	0.437907i
$761$	2.63708	−	4.56756i	0.0955942	−	0.165574i	−0.814262	−	0.580497i	$-0.802858\pi$
$761$	2.63708	−	4.56756i	0.0955942	−	0.165574i	0.909856	+	0.414923i	$0.136192\pi$
$762$	−2.85718			−0.103505
$763$	16.8990	−	18.2083i	0.611785	−	0.659184i
$764$	6.26097			0.226514
$765$	6.20216	−	10.7424i	0.224239	−	0.388394i
$766$	3.69781	+	6.40480i	0.133607	+	0.231415i
$767$	7.95563	+	13.7796i	0.287261	+	0.497551i
$768$	0.563379	−	0.975800i	0.0203292	−	0.0352112i
$769$	−4.68371			−0.168899			−0.0844495	−	0.996428i	$-0.526913\pi$
$769$	−4.68371			−0.168899			−0.0844495	+	0.996428i	$0.526913\pi$
$770$	16.1563	+	3.68967i	0.582233	+	0.132966i
$771$	13.8210			0.497751
$772$	−6.51789	+	11.2893i	−0.234584	+	0.406311i
$773$	4.20158	+	7.27735i	0.151120	+	0.261748i	0.931640	−	0.363384i	$-0.118379\pi$
$773$	4.20158	+	7.27735i	0.151120	+	0.261748i	−0.780519	+	0.625132i	$0.785045\pi$
$774$	7.01744	+	12.1546i	0.252237	+	0.436887i
$775$	8.77708	−	15.2024i	0.315282	−	0.546085i
$776$	0.121105			0.00434743
$777$	−7.84831	−	25.4547i	−0.281557	−	0.913184i
$778$	4.07942			0.146254
$779$	−40.8241	+	70.7094i	−1.46268	+	2.53343i
$780$	−3.67240	−	6.36079i	−0.131493	−	0.227753i
$781$	26.1062	+	45.2173i	0.934154	+	1.61800i
$782$	2.08850	−	3.61738i	0.0746845	−	0.129357i
$783$	14.9611			0.534665
$784$	−0.521390	−	6.98056i	−0.0186211	−	0.249306i
$785$	−4.72818			−0.168756
$786$	−2.96482	+	5.13522i	−0.105752	+	0.183167i
$787$	−12.4682	−	21.5956i	−0.444444	−	0.769800i	0.553569	−	0.832803i	$-0.313265\pi$
$787$	−12.4682	−	21.5956i	−0.444444	−	0.769800i	−0.998013	+	0.0630033i	$0.979932\pi$
$788$	10.6276	+	18.4075i	0.378591	+	0.655739i
$789$	7.35660	−	12.7420i	0.261902	−	0.453627i
$790$	−23.0792			−0.821122
$791$	−7.32249	−	23.7493i	−0.260358	−	0.844429i
$792$	6.31577			0.224421
$793$	−21.4901	+	37.2220i	−0.763137	+	1.32179i
$794$	−4.43055	−	7.67394i	−0.157234	−	0.272338i
$795$	2.95352	+	5.11565i	0.104751	+	0.181434i
$796$	−2.36862	+	4.10257i	−0.0839535	+	0.145412i
$797$	−5.67934			−0.201173			−0.100586	−	0.994928i	$-0.532072\pi$
$797$	−5.67934			−0.201173			−0.100586	+	0.994928i	$0.532072\pi$
$798$	23.6070	+	5.39120i	0.835678	+	0.190846i
$799$	−12.3278			−0.436128
$800$	1.02740	−	1.77951i	0.0363241	−	0.0629151i
$801$	3.42482	+	5.93196i	0.121010	+	0.209595i
$802$	−8.30173	−	14.3790i	−0.293144	−	0.507741i
$803$	−7.77596	+	13.4684i	−0.274408	+	0.475288i
$804$	14.9147			0.526000
$805$	−3.08875	+	3.32806i	−0.108864	+	0.117299i
$806$	−32.4491			−1.14297
$807$	2.00960	−	3.48073i	0.0707412	−	0.122527i
$808$	1.86148	+	3.22418i	0.0654866	+	0.113426i
$809$	9.10604	+	15.7721i	0.320151	+	0.554518i	0.980519	−	0.196424i	$-0.0629329\pi$
$809$	9.10604	+	15.7721i	0.320151	+	0.554518i	−0.660368	+	0.750942i	$0.729600\pi$
$810$	0.698817	−	1.21039i	0.0245539	−	0.0425286i
$811$	39.0257			1.37038			0.685188	−	0.728366i	$-0.259720\pi$
$811$	39.0257			1.37038			0.685188	+	0.728366i	$0.259720\pi$
$812$	5.05194	−	5.44336i	0.177288	−	0.191024i
$813$	−2.22781			−0.0781328
$814$	16.3063	−	28.2433i	0.571534	−	0.989926i
$815$	−17.4054	−	30.1470i	−0.609683	−	1.05600i
$816$	2.35323	+	4.07591i	0.0823795	+	0.142686i
$817$	−32.9404	+	57.0544i	−1.15244	+	1.99608i
$818$	33.7434			1.17981
$819$	−16.9533	−	3.87167i	−0.592395	−	0.135287i
$820$	17.2506			0.602416
$821$	−5.83009	+	10.0980i	−0.203472	+	0.352423i	−0.949645	−	0.313329i	$-0.898556\pi$
$821$	−5.83009	+	10.0980i	−0.203472	+	0.352423i	0.746173	+	0.665752i	$0.231889\pi$
$822$	−7.80354	−	13.5161i	−0.272180	−	0.471429i
$823$	26.8214	+	46.4559i	0.934934	+	1.61935i	0.774752	+	0.632265i	$0.217875\pi$
$823$	26.8214	+	46.4559i	0.934934	+	1.61935i	0.160181	+	0.987088i	$0.448792\pi$
$824$	−7.56418	+	13.1015i	−0.263511	+	0.456414i
$825$	−8.45036			−0.294204
$826$	3.26549	+	10.5911i	0.113621	+	0.368512i
$827$	−8.37095			−0.291086			−0.145543	−	0.989352i	$-0.546493\pi$
$827$	−8.37095			−0.291086			−0.145543	+	0.989352i	$0.546493\pi$
$828$	−0.865209	+	1.49859i	−0.0300681	+	0.0520795i
$829$	21.8638	+	37.8693i	0.759362	+	1.31525i	0.943176	+	0.332293i	$0.107822\pi$
$829$	21.8638	+	37.8693i	0.759362	+	1.31525i	−0.183814	+	0.982961i	$0.558845\pi$
$830$	−8.09897	−	14.0278i	−0.281119	−	0.486913i
$831$	−6.16133	+	10.6717i	−0.213734	+	0.370198i
$832$	−3.79833			−0.131683
$833$	26.3403	+	12.6928i	0.912636	+	0.439780i
$834$	10.8807			0.376768
$835$	0.279281	−	0.483728i	0.00966491	−	0.0167401i
$836$	14.8233	+	25.6748i	0.512676	+	0.887981i
$837$	−22.7673	−	39.4340i	−0.786951	−	1.36304i
$838$	−18.2903	+	31.6797i	−0.631828	+	1.09436i
$839$	−20.3471			−0.702460			−0.351230	−	0.936289i	$-0.614236\pi$
$839$	−20.3471			−0.702460			−0.351230	+	0.936289i	$0.614236\pi$
$840$	−1.50739	−	4.88897i	−0.0520098	−	0.168685i
$841$	−21.1211			−0.728314
$842$	16.3802	−	28.3713i	0.564498	−	0.977739i
$843$	−2.58046	−	4.46950i	−0.0888759	−	0.153938i
$844$	−8.38086	−	14.5161i	−0.288481	−	0.499664i
$845$	−1.22474	+	2.12131i	−0.0421323	+	0.0729752i
$846$	5.10710			0.175586
$847$	−5.98775	−	1.36744i	−0.205742	−	0.0469859i
$848$	3.05480			0.104902
$849$	−8.49624	+	14.7159i	−0.291590	+	0.505049i
$850$	4.29144	+	7.43300i	0.147195	+	0.254950i
$851$	4.46765	+	7.73820i	0.153149	+	0.265262i
$852$	8.05933	−	13.9592i	0.276108	−	0.478233i
$853$	10.3309			0.353724			0.176862	−	0.984236i	$-0.443405\pi$
$853$	10.3309			0.353724			0.176862	+	0.984236i	$0.443405\pi$
$854$	−20.3658	+	21.9437i	−0.696905	+	0.750899i
$855$	−24.1218			−0.824948
$856$	6.86772	−	11.8952i	0.234734	−	0.406571i
$857$	−23.3108	−	40.3756i	−0.796283	−	1.37920i	−0.922021	−	0.387140i	$-0.873463\pi$
$857$	−23.3108	−	40.3756i	−0.796283	−	1.37920i	0.125738	−	0.992064i	$-0.459870\pi$
$858$	7.81031	+	13.5279i	0.266640	+	0.461833i
$859$	5.12762	−	8.88130i	0.174952	−	0.303026i	−0.765193	−	0.643801i	$-0.777356\pi$
$859$	5.12762	−	8.88130i	0.174952	−	0.303026i	0.940145	+	0.340775i	$0.110690\pi$
$860$	13.9192			0.474642
$861$	−20.3846	+	21.9639i	−0.694705	+	0.748529i
$862$	−17.7194			−0.603524
$863$	19.6952	−	34.1130i	0.670431	−	1.16122i	−0.307351	−	0.951596i	$-0.599442\pi$
$863$	19.6952	−	34.1130i	0.670431	−	1.16122i	0.977782	−	0.209625i	$-0.0672242\pi$
$864$	−2.66502	−	4.61594i	−0.0906657	−	0.157038i
$865$	−11.4998	−	19.9182i	−0.391005	−	0.677240i
$866$	2.25994	−	3.91434i	0.0767960	−	0.133015i
$867$	−0.503991			−0.0171164
$868$	−22.0354	−	5.03228i	−0.747929	−	0.170807i
$869$	49.0839			1.66506
$870$	2.71388	−	4.70058i	0.0920091	−	0.159364i
$871$	−25.1389	−	43.5418i	−0.851798	−	1.47536i
$872$	−4.69467	−	8.13140i	−0.158981	−	0.275364i
$873$	0.104781	−	0.181487i	0.00354632	−	0.00614240i
$874$	−8.12271			−0.274755
$875$	−9.43798	−	30.6106i	−0.319062	−	1.03483i
$876$	4.80108			0.162214
$877$	−21.6309	+	37.4659i	−0.730424	+	1.26513i	0.226278	+	0.974063i	$0.427344\pi$
$877$	−21.6309	+	37.4659i	−0.730424	+	1.26513i	−0.956702	+	0.291069i	$0.905989\pi$
$878$	−3.19897	−	5.54078i	−0.107960	−	0.186992i
$879$	8.20028	+	14.2033i	0.276589	+	0.479065i
$880$	3.13186	−	5.42455i	0.105575	−	0.182861i
$881$	27.5229			0.927272			0.463636	−	0.886026i	$-0.346545\pi$
$881$	27.5229			0.927272			0.463636	+	0.886026i	$0.346545\pi$
$882$	−10.9121	−	5.25829i	−0.367429	−	0.177056i
$883$	−20.9321			−0.704421			−0.352210	−	0.935921i	$-0.614570\pi$
$883$	−20.9321			−0.704421			−0.352210	+	0.935921i	$0.614570\pi$
$884$	7.93280	−	13.7400i	0.266809	−	0.462127i
$885$	4.05014	+	7.01504i	0.136144	+	0.235808i
$886$	8.56844	+	14.8410i	0.287863	+	0.498593i
$887$	25.0642	−	43.4125i	0.841575	−	1.45765i	−0.0469884	−	0.998895i	$-0.514962\pi$
$887$	25.0642	−	43.4125i	0.841575	−	1.45765i	0.888563	−	0.458755i	$-0.151704\pi$
$888$	−10.0679			−0.337857
$889$	1.97671	+	6.41115i	0.0662968	+	0.215023i
$890$	6.79319			0.227708
$891$	−1.48621	+	2.57420i	−0.0497900	+	0.0862388i
$892$	−0.617347	−	1.06928i	−0.0206703	−	0.0358020i
$893$	11.9865	+	20.7613i	0.401114	+	0.694750i
$894$	−5.38664	+	9.32993i	−0.180156	+	0.312040i
$895$	35.7897			1.19632
$896$	−2.57934	−	0.589053i	−0.0861698	−	0.0196789i
$897$	−4.27979			−0.142898
$898$	6.63475	−	11.4917i	0.221404	−	0.383484i
$899$	−11.9898	−	20.7670i	−0.399884	−	0.692619i
$900$	−1.77783	−	3.07929i	−0.0592610	−	0.102643i
$901$	−6.37994	+	11.0504i	−0.212547	+	0.368142i
$902$	−36.6877			−1.22157
$903$	−16.4480	+	17.7224i	−0.547356	+	0.589764i
$904$	−9.39338			−0.312419
$905$	−1.35352	+	2.34436i	−0.0449925	+	0.0779293i
$906$	4.08828	+	7.08111i	0.135824	+	0.235254i
$907$	20.8613	+	36.1329i	0.692689	+	1.19977i	0.970954	+	0.239268i	$0.0769073\pi$
$907$	20.8613	+	36.1329i	0.692689	+	1.19977i	−0.278265	+	0.960504i	$0.589759\pi$
$908$	−11.5210	+	19.9550i	−0.382339	+	0.662230i
$909$	6.44228			0.213677
$910$	−11.7321	+	12.6411i	−0.388915	+	0.419048i
$911$	28.5662			0.946440			0.473220	−	0.880944i	$-0.343092\pi$
$911$	28.5662			0.946440			0.473220	+	0.880944i	$0.343092\pi$
$912$	4.57616	−	7.92614i	0.151532	−	0.262461i
$913$	17.2245	+	29.8338i	0.570049	+	0.987354i
$914$	15.2314	+	26.3815i	0.503810	+	0.872624i
$915$	−10.9404	+	18.9494i	−0.361679	+	0.626447i
$916$	−4.83663			−0.159807
$917$	13.5740	+	3.09994i	0.448253	+	0.102369i
$918$	22.2635			0.734806
$919$	−8.48538	+	14.6971i	−0.279907	+	0.484813i	−0.971361	−	0.237607i	$-0.923637\pi$
$919$	−8.48538	+	14.6971i	−0.279907	+	0.484813i	0.691454	+	0.722420i	$0.256970\pi$
$920$	0.858079	+	1.48624i	0.0282900	+	0.0489998i
$921$	−7.15627	−	12.3950i	−0.235807	−	0.408430i
$922$	−6.56193	+	11.3656i	−0.216106	+	0.374306i
$923$	−54.3364			−1.78851
$924$	3.20584	+	10.3976i	0.105465	+	0.342057i
$925$	−18.3602			−0.603681
$926$	10.6726	−	18.4855i	0.350724	−	0.607472i
$927$	13.0892	+	22.6712i	0.429906	+	0.744618i
$928$	−1.40347	−	2.43088i	−0.0460711	−	0.0797975i
$929$	−17.3867	+	30.1146i	−0.570438	+	0.988027i	0.426083	+	0.904684i	$0.359893\pi$
$929$	−17.3867	+	30.1146i	−0.570438	+	0.988027i	−0.996521	+	0.0833434i	$0.973440\pi$
$930$	−16.5196			−0.541698
$931$	−4.23510	−	56.7010i	−0.138800	−	1.85830i
$932$	−13.2545			−0.434165
$933$	−5.19375	+	8.99584i	−0.170036	+	0.294511i
$934$	−11.1802	−	19.3647i	−0.365827	−	0.633632i
$935$	13.0818	+	22.6583i	0.427820	+	0.741006i
$936$	−3.28635	+	5.69212i	−0.107418	+	0.186053i
$937$	−49.0341			−1.60187			−0.800937	−	0.598749i	$-0.795665\pi$
$937$	−49.0341			−1.60187			−0.800937	+	0.598749i	$0.795665\pi$
$938$	−10.3186	−	33.4667i	−0.336914	−	1.09273i
$939$	17.6412			0.575700
$940$	2.53251	−	4.38643i	0.0826012	−	0.143070i
$941$	−17.4632	−	30.2472i	−0.569285	−	0.986030i	−0.996637	−	0.0819447i	$-0.973887\pi$
$941$	−17.4632	−	30.2472i	−0.569285	−	0.986030i	0.427352	−	0.904085i	$-0.359446\pi$
$942$	−1.55216	−	2.68842i	−0.0505721	−	0.0875935i
$943$	5.02592	−	8.70515i	0.163667	−	0.283479i
$944$	4.18902			0.136341
$945$	−23.5937	−	5.38817i	−0.767504	−	0.175277i
$946$	−29.6028			−0.962471
$947$	0.183796	−	0.318345i	0.00597258	−	0.0103448i	−0.863024	−	0.505163i	$-0.831432\pi$
$947$	0.183796	−	0.318345i	0.00597258	−	0.0103448i	0.868996	+	0.494819i	$0.164766\pi$
$948$	−7.57642	−	13.1227i	−0.246071	−	0.426207i
$949$	−8.09229	−	14.0163i	−0.262687	−	0.454987i
$950$	8.34527	−	14.4544i	0.270756	−	0.468964i
$951$	−12.4374			−0.403310
$952$	7.51779	−	8.10024i	0.243653	−	0.262530i
$953$	39.2201			1.27047			0.635233	−	0.772321i	$-0.280904\pi$
$953$	39.2201			1.27047			0.635233	+	0.772321i	$0.280904\pi$
$954$	2.64304	−	4.57788i	0.0855716	−	0.148214i
$955$	−5.37241	−	9.30529i	−0.173847	−	0.301112i
$956$	2.70125	+	4.67871i	0.0873647	+	0.151320i
$957$	−5.77176	+	9.99698i	−0.186575	+	0.323157i
$958$	−17.4670			−0.564333
$959$	−24.9297	+	26.8612i	−0.805022	+	0.867393i
$960$	−1.93369			−0.0624097
$961$	−20.9915	+	36.3583i	−0.677145	+	1.17285i
$962$	16.9696	+	29.3922i	0.547122	+	0.947643i
$963$	−11.8840	−	20.5837i	−0.382957	−	0.663302i
$964$	8.61037	−	14.9136i	0.277321	−	0.480335i
$965$	22.3715			0.720163
$966$	−2.90629	−	0.663720i	−0.0935085	−	0.0213548i
$967$	20.3070			0.653030			0.326515	−	0.945192i	$-0.394126\pi$
$967$	20.3070			0.653030			0.326515	+	0.945192i	$0.394126\pi$
$968$	−1.16071	+	2.01041i	−0.0373067	+	0.0646171i
$969$	19.1146	+	33.1075i	0.614049	+	1.06356i
$970$	−0.103918	−	0.179991i	−0.00333661	−	0.00577917i
$971$	−11.9692	+	20.7312i	−0.384110	+	0.665297i	−0.991645	−	0.128995i	$-0.958825\pi$
$971$	−11.9692	+	20.7312i	−0.384110	+	0.665297i	0.607536	+	0.794292i	$0.292158\pi$
$972$	−15.0725			−0.483450
$973$	−7.52772	−	24.4150i	−0.241328	−	0.782708i
$974$	−5.79067			−0.185545
$975$	4.39706	−	7.61593i	0.140819	−	0.243905i
$976$	5.65778	+	9.79957i	0.181101	+	0.313677i
$977$	−4.27141	−	7.39830i	−0.136655	−	0.236693i	0.789574	−	0.613656i	$-0.210302\pi$
$977$	−4.27141	−	7.39830i	−0.136655	−	0.236693i	−0.926228	+	0.376963i	$0.876968\pi$
$978$	11.4276	−	19.7932i	0.365415	−	0.632917i
$979$	−14.4475			−0.461743
$980$	−9.92737	+	6.76478i	−0.317118	+	0.216093i
$981$	−16.2475			−0.518742
$982$	4.23527	−	7.33570i	0.135153	−	0.234092i
$983$	−15.1512	−	26.2426i	−0.483248	−	0.837011i	0.516567	−	0.856247i	$-0.327210\pi$
$983$	−15.1512	−	26.2426i	−0.483248	−	0.837011i	−0.999815	+	0.0192364i	$0.993876\pi$
$984$	5.66299	+	9.80859i	0.180530	+	0.312686i
$985$	18.2386	−	31.5901i	0.581129	−	1.00655i
$986$	11.7246			0.373386
$987$	2.59233	+	8.40780i	0.0825147	+	0.267623i
$988$	−30.8527			−0.981556
$989$	4.05534	−	7.02406i	0.128952	−	0.223352i
$990$	−5.41943	−	9.38674i	−0.172241	−	0.298330i
$991$	16.2905	+	28.2160i	0.517486	+	0.896311i	0.999794	+	0.0203096i	$0.00646520\pi$
$991$	16.2905	+	28.2160i	0.517486	+	0.896311i	−0.482308	+	0.876002i	$0.660201\pi$
$992$	−4.27150	+	7.39846i	−0.135620	+	0.234901i
$993$	17.6805			0.561073
$994$	−36.8984	−	8.42661i	−1.17035	−	0.267276i
$995$	8.12986			0.257734
$996$	5.31744	−	9.21007i	0.168489	−	0.291832i
$997$	0.465561	+	0.806375i	0.0147445	+	0.0255381i	0.873303	−	0.487177i	$-0.161973\pi$
$997$	0.465561	+	0.806375i	0.0147445	+	0.0255381i	−0.858559	+	0.512715i	$0.828640\pi$
$998$	1.26100	+	2.18412i	0.0399163	+	0.0691371i
$999$	−23.8127	+	41.2448i	−0.753401	+	1.30493i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	322.2.e.a.93.4	✓	8
7.2	even	3		2254.2.a.z.1.1		4
7.4	even	3	inner	322.2.e.a.277.4	yes	8
7.5	odd	6		2254.2.a.x.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
322.2.e.a.93.4	✓	8	1.1	even	1	trivial
322.2.e.a.277.4	yes	8	7.4	even	3	inner
2254.2.a.x.1.4		4	7.5	odd	6
2254.2.a.z.1.1		4	7.2	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 322 = 2 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	322.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(0.563379 + 0.975800i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.858079 + 1.48624i) q^{5} -1.12676 q^{6} +(0.779537 + 2.52830i) q^{7} +1.00000 q^{8} +(0.865209 - 1.49859i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(0.563379 + 0.975800i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.858079 + 1.48624i) q^{5} -1.12676 q^{6} +(0.779537 + 2.52830i) q^{7} +1.00000 q^{8} +(0.865209 - 1.49859i) q^{9} +(-0.858079 - 1.48624i) q^{10} +(1.82493 + 3.16087i) q^{11} +(0.563379 - 0.975800i) q^{12} -3.79833 q^{13} +(-2.57934 - 0.589053i) q^{14} -1.93369 q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.08850 - 3.61738i) q^{17} +(0.865209 + 1.49859i) q^{18} +(-4.06135 + 7.03447i) q^{19} +1.71616 q^{20} +(-2.02795 + 2.18506i) q^{21} -3.64985 q^{22} +(0.500000 - 0.866025i) q^{23} +(0.563379 + 0.975800i) q^{24} +(1.02740 + 1.77951i) q^{25} +(1.89916 - 3.28945i) q^{26} +5.33003 q^{27} +(1.79981 - 1.93925i) q^{28} +2.80694 q^{29} +(0.966847 - 1.67463i) q^{30} +(-4.27150 - 7.39846i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-2.05625 + 3.56153i) q^{33} +4.17700 q^{34} +(-4.42656 - 1.01091i) q^{35} -1.73042 q^{36} +(-4.46765 + 7.73820i) q^{37} +(-4.06135 - 7.03447i) q^{38} +(-2.13990 - 3.70641i) q^{39} +(-0.858079 + 1.48624i) q^{40} +10.0518 q^{41} +(-0.878349 - 2.84878i) q^{42} +8.11069 q^{43} +(1.82493 - 3.16087i) q^{44} +(1.48484 + 2.57181i) q^{45} +(0.500000 + 0.866025i) q^{46} +(1.47568 - 2.55596i) q^{47} -1.12676 q^{48} +(-5.78464 + 3.94181i) q^{49} -2.05480 q^{50} +(2.35323 - 4.07591i) q^{51} +(1.89916 + 3.28945i) q^{52} +(-1.52740 - 2.64553i) q^{53} +(-2.66502 + 4.61594i) q^{54} -6.26373 q^{55} +(0.779537 + 2.52830i) q^{56} -9.15232 q^{57} +(-1.40347 + 2.43088i) q^{58} +(-2.09451 - 3.62779i) q^{59} +(0.966847 + 1.67463i) q^{60} +(5.65778 - 9.79957i) q^{61} +8.54301 q^{62} +(4.46335 + 1.01931i) q^{63} +1.00000 q^{64} +(3.25927 - 5.64522i) q^{65} +(-2.05625 - 3.56153i) q^{66} +(6.61841 + 11.4634i) q^{67} +(-2.08850 + 3.61738i) q^{68} +1.12676 q^{69} +(3.08875 - 3.32806i) q^{70} +14.3054 q^{71} +(0.865209 - 1.49859i) q^{72} +(2.13049 + 3.69011i) q^{73} +(-4.46765 - 7.73820i) q^{74} +(-1.15763 + 2.00507i) q^{75} +8.12271 q^{76} +(-6.56903 + 7.07798i) q^{77} +4.27979 q^{78} +(6.72409 - 11.6465i) q^{79} +(-0.858079 - 1.48624i) q^{80} +(0.407198 + 0.705288i) q^{81} +(-5.02592 + 8.70515i) q^{82} +9.43848 q^{83} +(2.90629 + 0.663720i) q^{84} +7.16839 q^{85} +(-4.05534 + 7.02406i) q^{86} +(1.58137 + 2.73901i) q^{87} +(1.82493 + 3.16087i) q^{88} +(-1.97918 + 3.42805i) q^{89} -2.96967 q^{90} +(-2.96094 - 9.60333i) q^{91} -1.00000 q^{92} +(4.81295 - 8.33627i) q^{93} +(1.47568 + 2.55596i) q^{94} +(-6.96993 - 12.0723i) q^{95} +(0.563379 - 0.975800i) q^{96} +0.121105 q^{97} +(-0.521390 - 6.98056i) q^{98} +6.31577 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{2} - 3 q^{3} - 4 q^{4} - 7 q^{5} + 6 q^{6} - q^{7} + 8 q^{8} + q^{9}+O(q^{10}) \) 8 * q - 4 * q^2 - 3 * q^3 - 4 * q^4 - 7 * q^5 + 6 * q^6 - q^7 + 8 * q^8 + q^9	\( 8 q - 4 q^{2} - 3 q^{3} - 4 q^{4} - 7 q^{5} + 6 q^{6} - q^{7} + 8 q^{8} + q^{9} - 7 q^{10} - 2 q^{11} - 3 q^{12} + 2 q^{13} - q^{14} + 18 q^{15} - 4 q^{16} - 5 q^{17} + q^{18} - 11 q^{19} + 14 q^{20} + q^{21} + 4 q^{22} + 4 q^{23} - 3 q^{24} - 3 q^{25} - q^{26} + 6 q^{27} + 2 q^{28} + 4 q^{29} - 9 q^{30} - 6 q^{31} - 4 q^{32} - 15 q^{33} + 10 q^{34} - 8 q^{35} - 2 q^{36} + 8 q^{37} - 11 q^{38} - 3 q^{39} - 7 q^{40} + 18 q^{41} - 2 q^{42} + 8 q^{43} - 2 q^{44} - 3 q^{45} + 4 q^{46} - 11 q^{47} + 6 q^{48} - 19 q^{49} + 6 q^{50} + 18 q^{51} - q^{52} - q^{53} - 3 q^{54} + 20 q^{55} - q^{56} + 6 q^{57} - 2 q^{58} - 12 q^{59} - 9 q^{60} - 21 q^{61} + 12 q^{62} - 15 q^{63} + 8 q^{64} + 24 q^{65} - 15 q^{66} + 3 q^{67} - 5 q^{68} - 6 q^{69} - 8 q^{70} + 22 q^{71} + q^{72} + 16 q^{73} + 8 q^{74} - 18 q^{75} + 22 q^{76} - 19 q^{77} + 6 q^{78} + 21 q^{79} - 7 q^{80} + 8 q^{81} - 9 q^{82} + 8 q^{83} + q^{84} + 20 q^{85} - 4 q^{86} + 7 q^{87} - 2 q^{88} - 27 q^{89} + 6 q^{90} - 54 q^{91} - 8 q^{92} + 27 q^{93} - 11 q^{94} - 5 q^{95} - 3 q^{96} + 12 q^{97} + 14 q^{98} + 26 q^{99}+O(q^{100}) \) 8 * q - 4 * q^2 - 3 * q^3 - 4 * q^4 - 7 * q^5 + 6 * q^6 - q^7 + 8 * q^8 + q^9 - 7 * q^10 - 2 * q^11 - 3 * q^12 + 2 * q^13 - q^14 + 18 * q^15 - 4 * q^16 - 5 * q^17 + q^18 - 11 * q^19 + 14 * q^20 + q^21 + 4 * q^22 + 4 * q^23 - 3 * q^24 - 3 * q^25 - q^26 + 6 * q^27 + 2 * q^28 + 4 * q^29 - 9 * q^30 - 6 * q^31 - 4 * q^32 - 15 * q^33 + 10 * q^34 - 8 * q^35 - 2 * q^36 + 8 * q^37 - 11 * q^38 - 3 * q^39 - 7 * q^40 + 18 * q^41 - 2 * q^42 + 8 * q^43 - 2 * q^44 - 3 * q^45 + 4 * q^46 - 11 * q^47 + 6 * q^48 - 19 * q^49 + 6 * q^50 + 18 * q^51 - q^52 - q^53 - 3 * q^54 + 20 * q^55 - q^56 + 6 * q^57 - 2 * q^58 - 12 * q^59 - 9 * q^60 - 21 * q^61 + 12 * q^62 - 15 * q^63 + 8 * q^64 + 24 * q^65 - 15 * q^66 + 3 * q^67 - 5 * q^68 - 6 * q^69 - 8 * q^70 + 22 * q^71 + q^72 + 16 * q^73 + 8 * q^74 - 18 * q^75 + 22 * q^76 - 19 * q^77 + 6 * q^78 + 21 * q^79 - 7 * q^80 + 8 * q^81 - 9 * q^82 + 8 * q^83 + q^84 + 20 * q^85 - 4 * q^86 + 7 * q^87 - 2 * q^88 - 27 * q^89 + 6 * q^90 - 54 * q^91 - 8 * q^92 + 27 * q^93 - 11 * q^94 - 5 * q^95 - 3 * q^96 + 12 * q^97 + 14 * q^98 + 26 * q^99

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