LMFDB - Embedded newform 143.2.h.c.92.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [143,2,Mod(14,143)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(143, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([8, 0]))

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

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

chi := DirichletCharacter("143.14");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 143 = 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	143.h (of order $5$, degree $4$, 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:	$1.14186074890$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$7$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			92.7
Character	$\chi$	$=$	143.92
Dual form			143.2.h.c.14.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.91124 + 1.38860i) q^{2} +(0.562838 - 1.73224i) q^{3} +(1.10660 + 3.40577i) q^{4} +(-1.72715 + 1.25485i) q^{5} +(3.48110 - 2.52917i) q^{6} +(-0.333124 - 1.02525i) q^{7} +(-1.15421 + 3.55228i) q^{8} +(-0.256810 - 0.186583i) q^{9} +O(q^{10})$	\(q+(1.91124 + 1.38860i) q^{2} +(0.562838 - 1.73224i) q^{3} +(1.10660 + 3.40577i) q^{4} +(-1.72715 + 1.25485i) q^{5} +(3.48110 - 2.52917i) q^{6} +(-0.333124 - 1.02525i) q^{7} +(-1.15421 + 3.55228i) q^{8} +(-0.256810 - 0.186583i) q^{9} -5.04348 q^{10} +(-2.78205 - 1.80561i) q^{11} +6.52245 q^{12} +(-0.809017 - 0.587785i) q^{13} +(0.786980 - 2.42208i) q^{14} +(1.20159 + 3.69811i) q^{15} +(-1.34441 + 0.976772i) q^{16} +(-0.957512 + 0.695673i) q^{17} +(-0.231736 - 0.713210i) q^{18} +(0.317680 - 0.977717i) q^{19} +(-6.18500 - 4.49367i) q^{20} -1.96347 q^{21} +(-2.80989 - 7.31409i) q^{22} -5.23055 q^{23} +(5.50377 + 3.99872i) q^{24} +(-0.136680 + 0.420658i) q^{25} +(-0.730029 - 2.24680i) q^{26} +(3.95284 - 2.87191i) q^{27} +(3.12314 - 2.26909i) q^{28} +(2.18567 + 6.72681i) q^{29} +(-2.83866 + 8.73651i) q^{30} +(-4.19129 - 3.04515i) q^{31} +3.54435 q^{32} +(-4.69359 + 3.80290i) q^{33} -2.79605 q^{34} +(1.86189 + 1.35274i) q^{35} +(0.351274 - 1.08111i) q^{36} +(3.05471 + 9.40142i) q^{37} +(1.96482 - 1.42752i) q^{38} +(-1.47353 + 1.07058i) q^{39} +(-2.46409 - 7.58368i) q^{40} +(0.446709 - 1.37483i) q^{41} +(-3.75267 - 2.72647i) q^{42} +12.3409 q^{43} +(3.07088 - 11.4731i) q^{44} +0.677682 q^{45} +(-9.99683 - 7.26312i) q^{46} +(2.39049 - 7.35718i) q^{47} +(0.935315 + 2.87860i) q^{48} +(4.72295 - 3.43142i) q^{49} +(-0.845354 + 0.614185i) q^{50} +(0.666147 + 2.05019i) q^{51} +(1.10660 - 3.40577i) q^{52} +(-6.19010 - 4.49737i) q^{53} +11.5427 q^{54} +(7.07078 - 0.372486i) q^{55} +4.02648 q^{56} +(-1.51484 - 1.10059i) q^{57} +(-5.16349 + 15.8916i) q^{58} +(3.87769 + 11.9343i) q^{59} +(-11.2653 + 8.18468i) q^{60} +(4.15573 - 3.01931i) q^{61} +(-3.78207 - 11.6400i) q^{62} +(-0.105745 + 0.325450i) q^{63} +(9.46293 + 6.87522i) q^{64} +2.13488 q^{65} +(-14.2513 + 0.750752i) q^{66} -4.78456 q^{67} +(-3.42889 - 2.49124i) q^{68} +(-2.94395 + 9.06055i) q^{69} +(1.68011 + 5.17083i) q^{70} +(-12.3107 + 8.94423i) q^{71} +(0.959208 - 0.696905i) q^{72} +(-1.55638 - 4.79003i) q^{73} +(-7.21651 + 22.2101i) q^{74} +(0.651751 + 0.473525i) q^{75} +3.68143 q^{76} +(-0.924436 + 3.45379i) q^{77} -4.30288 q^{78} +(0.522678 + 0.379747i) q^{79} +(1.09630 - 3.37406i) q^{80} +(-3.04429 - 9.36937i) q^{81} +(2.76285 - 2.00733i) q^{82} +(0.368309 - 0.267592i) q^{83} +(-2.17279 - 6.68715i) q^{84} +(0.780803 - 2.40306i) q^{85} +(23.5865 + 17.1366i) q^{86} +12.8826 q^{87} +(9.62509 - 7.79857i) q^{88} -13.3715 q^{89} +(1.29521 + 0.941028i) q^{90} +(-0.333124 + 1.02525i) q^{91} +(-5.78814 - 17.8141i) q^{92} +(-7.63394 + 5.54638i) q^{93} +(14.7850 - 10.7419i) q^{94} +(0.678206 + 2.08730i) q^{95} +(1.99490 - 6.13966i) q^{96} +(-9.53931 - 6.93072i) q^{97} +13.7916 q^{98} +(0.377560 + 0.982780i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 3 q^{2} - 7 q^{3} - 5 q^{4} - 7 q^{5} - 4 q^{6} - 7 q^{7} + q^{8} - 6 q^{9}+O(q^{10}) $ 28 * q - 3 * q^2 - 7 * q^3 - 5 * q^4 - 7 * q^5 - 4 * q^6 - 7 * q^7 + q^8 - 6 * q^9	\( 28 q - 3 q^{2} - 7 q^{3} - 5 q^{4} - 7 q^{5} - 4 q^{6} - 7 q^{7} + q^{8} - 6 q^{9} - 24 q^{10} - 5 q^{11} + 38 q^{12} - 7 q^{13} - 7 q^{14} + 8 q^{15} - 19 q^{16} + 7 q^{17} + 5 q^{18} + 5 q^{19} + 9 q^{20} - 33 q^{22} + 50 q^{23} - 7 q^{24} - 34 q^{25} + 2 q^{26} - 19 q^{27} + 30 q^{28} + 8 q^{29} - 6 q^{30} + 17 q^{31} + 24 q^{32} - 26 q^{33} + 26 q^{34} - 4 q^{35} - 27 q^{36} + 17 q^{37} - 51 q^{38} - 2 q^{39} + 39 q^{40} - 23 q^{41} + 80 q^{42} - 32 q^{43} + q^{44} + 78 q^{45} - 31 q^{46} - 29 q^{47} + 52 q^{48} - 52 q^{49} + 6 q^{50} + 7 q^{51} - 5 q^{52} - 16 q^{53} - 42 q^{54} - 5 q^{55} + 34 q^{56} - 7 q^{57} - 13 q^{58} - 11 q^{59} - 74 q^{60} + 37 q^{61} + 23 q^{62} - 38 q^{63} + 67 q^{64} + 18 q^{65} - 65 q^{66} + 58 q^{67} - 68 q^{68} - 28 q^{69} + 44 q^{70} - 47 q^{71} + 10 q^{72} + 44 q^{73} - 46 q^{74} + 17 q^{75} + 6 q^{76} + 21 q^{77} + 26 q^{78} + 51 q^{79} + 23 q^{80} - 14 q^{81} - 47 q^{82} - 13 q^{83} - 107 q^{84} - q^{85} + 38 q^{86} - 12 q^{87} + 9 q^{88} + 38 q^{89} - 74 q^{90} - 7 q^{91} - 41 q^{92} - 51 q^{93} - 5 q^{94} + 47 q^{95} - 71 q^{96} - 20 q^{97} + 162 q^{98} + 60 q^{99}+O(q^{100}) \) 28 * q - 3 * q^2 - 7 * q^3 - 5 * q^4 - 7 * q^5 - 4 * q^6 - 7 * q^7 + q^8 - 6 * q^9 - 24 * q^10 - 5 * q^11 + 38 * q^12 - 7 * q^13 - 7 * q^14 + 8 * q^15 - 19 * q^16 + 7 * q^17 + 5 * q^18 + 5 * q^19 + 9 * q^20 - 33 * q^22 + 50 * q^23 - 7 * q^24 - 34 * q^25 + 2 * q^26 - 19 * q^27 + 30 * q^28 + 8 * q^29 - 6 * q^30 + 17 * q^31 + 24 * q^32 - 26 * q^33 + 26 * q^34 - 4 * q^35 - 27 * q^36 + 17 * q^37 - 51 * q^38 - 2 * q^39 + 39 * q^40 - 23 * q^41 + 80 * q^42 - 32 * q^43 + q^44 + 78 * q^45 - 31 * q^46 - 29 * q^47 + 52 * q^48 - 52 * q^49 + 6 * q^50 + 7 * q^51 - 5 * q^52 - 16 * q^53 - 42 * q^54 - 5 * q^55 + 34 * q^56 - 7 * q^57 - 13 * q^58 - 11 * q^59 - 74 * q^60 + 37 * q^61 + 23 * q^62 - 38 * q^63 + 67 * q^64 + 18 * q^65 - 65 * q^66 + 58 * q^67 - 68 * q^68 - 28 * q^69 + 44 * q^70 - 47 * q^71 + 10 * q^72 + 44 * q^73 - 46 * q^74 + 17 * q^75 + 6 * q^76 + 21 * q^77 + 26 * q^78 + 51 * q^79 + 23 * q^80 - 14 * q^81 - 47 * q^82 - 13 * q^83 - 107 * q^84 - q^85 + 38 * q^86 - 12 * q^87 + 9 * q^88 + 38 * q^89 - 74 * q^90 - 7 * q^91 - 41 * q^92 - 51 * q^93 - 5 * q^94 + 47 * q^95 - 71 * q^96 - 20 * q^97 + 162 * q^98 + 60 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/143\mathbb{Z}\right)^\times$.

$n$	$67$	$79$
$\chi(n)$	$1$	$e\left(\frac{1}{5}\right)$

Coefficient data

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

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

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

$2$	1.91124	+	1.38860i	1.35145	+	0.981887i	0.998938	+	0.0460799i	$0.0146729\pi$
$2$	1.91124	+	1.38860i	1.35145	+	0.981887i	0.352513	+	0.935807i	$0.385327\pi$
$3$	0.562838	−	1.73224i	0.324955	−	1.00011i	−0.646506	−	0.762909i	$-0.723771\pi$
$3$	0.562838	−	1.73224i	0.324955	−	1.00011i	0.971461	−	0.237199i	$-0.0762294\pi$
$4$	1.10660	+	3.40577i	0.553302	+	1.70289i
$5$	−1.72715	+	1.25485i	−0.772405	+	0.561185i	−0.902690	−	0.430291i	$-0.858411\pi$
$5$	−1.72715	+	1.25485i	−0.772405	+	0.561185i	0.130285	+	0.991477i	$0.458411\pi$
$6$	3.48110	−	2.52917i	1.42115	−	1.03253i
$7$	−0.333124	−	1.02525i	−0.125909	−	0.387508i	0.868156	−	0.496291i	$-0.165305\pi$
$7$	−0.333124	−	1.02525i	−0.125909	−	0.387508i	−0.994066	+	0.108782i	$0.965305\pi$
$8$	−1.15421	+	3.55228i	−0.408074	+	1.25592i
$9$	−0.256810	−	0.186583i	−0.0856032	−	0.0621944i
$10$	−5.04348			−1.59489
$11$	−2.78205	−	1.80561i	−0.838818	−	0.544412i
$11$	−2.78205	−	1.80561i	−0.838818	−	0.544412i
$12$	6.52245			1.88287
$13$	−0.809017	−	0.587785i	−0.224381	−	0.163022i
$13$	−0.809017	−	0.587785i	−0.224381	−	0.163022i
$14$	0.786980	−	2.42208i	0.210329	−	0.647327i
$15$	1.20159	+	3.69811i	0.310249	+	0.954848i
$16$	−1.34441	+	0.976772i	−0.336103	+	0.244193i
$17$	−0.957512	+	0.695673i	−0.232231	+	0.168725i	−0.697815	−	0.716278i	$-0.745844\pi$
$17$	−0.957512	+	0.695673i	−0.232231	+	0.168725i	0.465584	+	0.885004i	$0.345844\pi$
$18$	−0.231736	−	0.713210i	−0.0546207	−	0.168105i
$19$	0.317680	−	0.977717i	0.0728807	−	0.224304i	−0.907980	−	0.419013i	$-0.862376\pi$
$19$	0.317680	−	0.977717i	0.0728807	−	0.224304i	0.980861	+	0.194709i	$0.0623763\pi$
$20$	−6.18500	−	4.49367i	−1.38301	−	1.00481i
$21$	−1.96347			−0.428465
$22$	−2.80989	−	7.31409i	−0.599071	−	1.55937i
$23$	−5.23055			−1.09064			−0.545322	−	0.838227i	$-0.683593\pi$
$23$	−5.23055			−1.09064			−0.545322	+	0.838227i	$0.683593\pi$
$24$	5.50377	+	3.99872i	1.12345	+	0.816236i
$25$	−0.136680	+	0.420658i	−0.0273360	+	0.0841316i
$26$	−0.730029	−	2.24680i	−0.143170	−	0.440633i
$27$	3.95284	−	2.87191i	0.760724	−	0.552699i
$28$	3.12314	−	2.26909i	0.590217	−	0.428818i
$29$	2.18567	+	6.72681i	0.405870	+	1.24914i	0.920167	+	0.391526i	$0.128053\pi$
$29$	2.18567	+	6.72681i	0.405870	+	1.24914i	−0.514297	+	0.857612i	$0.671947\pi$
$30$	−2.83866	+	8.73651i	−0.518267	+	1.59506i
$31$	−4.19129	−	3.04515i	−0.752777	−	0.546925i	0.143909	−	0.989591i	$-0.454033\pi$
$31$	−4.19129	−	3.04515i	−0.752777	−	0.546925i	−0.896687	+	0.442666i	$0.854033\pi$
$32$	3.54435			0.626559
$33$	−4.69359	+	3.80290i	−0.817048	+	0.662000i
$34$	−2.79605			−0.479518
$35$	1.86189	+	1.35274i	0.314717	+	0.228655i
$36$	0.351274	−	1.08111i	0.0585456	−	0.180185i
$37$	3.05471	+	9.40142i	0.502191	+	1.54558i	0.805443	+	0.592673i	$0.201928\pi$
$37$	3.05471	+	9.40142i	0.502191	+	1.54558i	−0.303252	+	0.952910i	$0.598072\pi$
$38$	1.96482	−	1.42752i	0.318736	−	0.231575i
$39$	−1.47353	+	1.07058i	−0.235954	+	0.171430i
$40$	−2.46409	−	7.58368i	−0.389607	−	1.19909i
$41$	0.446709	−	1.37483i	0.0697642	−	0.214712i	−0.910096	−	0.414398i	$-0.863992\pi$
$41$	0.446709	−	1.37483i	0.0697642	−	0.214712i	0.979860	+	0.199686i	$0.0639922\pi$
$42$	−3.75267	−	2.72647i	−0.579050	−	0.420704i
$43$	12.3409			1.88197			0.940987	−	0.338444i	$-0.109900\pi$
$43$	12.3409			1.88197			0.940987	+	0.338444i	$0.109900\pi$
$44$	3.07088	−	11.4731i	0.462952	−	1.72964i
$45$	0.677682			0.101023
$46$	−9.99683	−	7.26312i	−1.47395	−	1.07089i
$47$	2.39049	−	7.35718i	0.348689	−	1.07315i	−0.610890	−	0.791715i	$-0.709188\pi$
$47$	2.39049	−	7.35718i	0.348689	−	1.07315i	0.959579	−	0.281439i	$-0.0908117\pi$
$48$	0.935315	+	2.87860i	0.135001	+	0.415491i
$49$	4.72295	−	3.43142i	0.674707	−	0.490204i
$50$	−0.845354	+	0.614185i	−0.119551	+	0.0868589i
$51$	0.666147	+	2.05019i	0.0932792	+	0.287084i
$52$	1.10660	−	3.40577i	0.153458	−	0.472296i
$53$	−6.19010	−	4.49737i	−0.850275	−	0.617761i	0.0749468	−	0.997188i	$-0.476121\pi$
$53$	−6.19010	−	4.49737i	−0.850275	−	0.617761i	−0.925222	+	0.379427i	$0.876121\pi$
$54$	11.5427			1.57077
$55$	7.07078	−	0.372486i	0.953423	−	0.0502260i
$56$	4.02648			0.538061
$57$	−1.51484	−	1.10059i	−0.200645	−	0.145777i
$58$	−5.16349	+	15.8916i	−0.677999	+	2.08667i
$59$	3.87769	+	11.9343i	0.504832	+	1.55371i	0.801053	+	0.598594i	$0.204274\pi$
$59$	3.87769	+	11.9343i	0.504832	+	1.55371i	−0.296221	+	0.955119i	$0.595726\pi$
$60$	−11.2653	+	8.18468i	−1.45434	+	1.05664i
$61$	4.15573	−	3.01931i	0.532086	−	0.386583i	−0.289051	−	0.957314i	$-0.593340\pi$
$61$	4.15573	−	3.01931i	0.532086	−	0.386583i	0.821138	+	0.570730i	$0.193340\pi$
$62$	−3.78207	−	11.6400i	−0.480324	−	1.47828i
$63$	−0.105745	+	0.325450i	−0.0133226	+	0.0410028i
$64$	9.46293	+	6.87522i	1.18287	+	0.859402i
$65$	2.13488			0.264799
$66$	−14.2513	+	0.750752i	−1.75421	+	0.0924111i
$67$	−4.78456			−0.584527			−0.292263	−	0.956338i	$-0.594408\pi$
$67$	−4.78456			−0.584527			−0.292263	+	0.956338i	$0.594408\pi$
$68$	−3.42889	−	2.49124i	−0.415814	−	0.302107i
$69$	−2.94395	+	9.06055i	−0.354410	+	1.09076i
$70$	1.68011	+	5.17083i	0.200811	+	0.618033i
$71$	−12.3107	+	8.94423i	−1.46101	+	1.06148i	−0.477909	+	0.878409i	$0.658605\pi$
$71$	−12.3107	+	8.94423i	−1.46101	+	1.06148i	−0.983099	+	0.183075i	$0.941395\pi$
$72$	0.959208	−	0.696905i	0.113044	−	0.0821311i
$73$	−1.55638	−	4.79003i	−0.182160	−	0.560631i	0.817728	−	0.575605i	$-0.195233\pi$
$73$	−1.55638	−	4.79003i	−0.182160	−	0.560631i	−0.999888	+	0.0149741i	$0.995233\pi$
$74$	−7.21651	+	22.2101i	−0.838902	+	2.58188i
$75$	0.651751	+	0.473525i	0.0752577	+	0.0546780i
$76$	3.68143			0.422289
$77$	−0.924436	+	3.45379i	−0.105349	+	0.393596i
$78$	−4.30288			−0.487205
$79$	0.522678	+	0.379747i	0.0588058	+	0.0427249i	0.616800	−	0.787120i	$-0.288429\pi$
$79$	0.522678	+	0.379747i	0.0588058	+	0.0427249i	−0.557994	+	0.829845i	$0.688429\pi$
$80$	1.09630	−	3.37406i	0.122570	−	0.377232i
$81$	−3.04429	−	9.36937i	−0.338255	−	1.04104i
$82$	2.76285	−	2.00733i	0.305106	−	0.221672i
$83$	0.368309	−	0.267592i	0.0404272	−	0.0293721i	−0.567388	−	0.823450i	$-0.692046\pi$
$83$	0.368309	−	0.267592i	0.0404272	−	0.0293721i	0.607815	+	0.794078i	$0.292046\pi$
$84$	−2.17279	−	6.68715i	−0.237070	−	0.729628i
$85$	0.780803	−	2.40306i	0.0846900	−	0.260649i
$86$	23.5865	+	17.1366i	2.54339	+	1.84788i
$87$	12.8826			1.38116
$88$	9.62509	−	7.79857i	1.02604	−	0.831330i
$89$	−13.3715			−1.41738			−0.708688	−	0.705522i	$-0.750713\pi$
$89$	−13.3715			−1.41738			−0.708688	+	0.705522i	$0.750713\pi$
$90$	1.29521	+	0.941028i	0.136528	+	0.0991931i
$91$	−0.333124	+	1.02525i	−0.0349209	+	0.107476i
$92$	−5.78814	−	17.8141i	−0.603455	−	1.85724i
$93$	−7.63394	+	5.54638i	−0.791602	+	0.575133i
$94$	14.7850	−	10.7419i	1.52495	−	1.10794i
$95$	0.678206	+	2.08730i	0.0695825	+	0.214153i
$96$	1.99490	−	6.13966i	0.203603	−	0.626626i
$97$	−9.53931	−	6.93072i	−0.968571	−	0.703708i	−0.0134453	−	0.999910i	$-0.504280\pi$
$97$	−9.53931	−	6.93072i	−0.968571	−	0.703708i	−0.955125	+	0.296202i	$0.904280\pi$
$98$	13.7916			1.39316
$99$	0.377560	+	0.982780i	0.0379462	+	0.0987731i
$100$	−1.58392			−0.158392
$101$	5.12247	+	3.72169i	0.509705	+	0.370322i	0.812712	−	0.582666i	$-0.197990\pi$
$101$	5.12247	+	3.72169i	0.509705	+	0.370322i	−0.303007	+	0.952988i	$0.597990\pi$
$102$	−1.57372	+	4.84341i	−0.155822	+	0.479570i
$103$	−1.18803	−	3.65637i	−0.117060	−	0.360272i	0.875311	−	0.483560i	$-0.160656\pi$
$103$	−1.18803	−	3.65637i	−0.117060	−	0.360272i	−0.992371	+	0.123287i	$0.960656\pi$
$104$	3.02175	−	2.19543i	0.296307	−	0.215280i
$105$	3.39121	−	2.46386i	0.330949	−	0.240448i
$106$	−5.58573	−	17.1911i	−0.542534	−	1.66975i
$107$	1.17315	−	3.61060i	0.113413	−	0.349050i	−0.878200	−	0.478294i	$-0.841255\pi$
$107$	1.17315	−	3.61060i	0.113413	−	0.349050i	0.991613	+	0.129245i	$0.0412553\pi$
$108$	14.1553	+	10.2844i	1.36209	+	0.989619i
$109$	−10.8273			−1.03707			−0.518534	−	0.855057i	$-0.673522\pi$
$109$	−10.8273			−1.03707			−0.518534	+	0.855057i	$0.673522\pi$
$110$	14.0312	+	9.10655i	1.33782	+	0.868276i
$111$	18.0048			1.70894
$112$	1.44929	+	1.05297i	0.136945	+	0.0994965i
$113$	1.87857	−	5.78165i	0.176721	−	0.543892i	−0.822987	−	0.568061i	$-0.807694\pi$
$113$	1.87857	−	5.78165i	0.176721	−	0.543892i	0.999708	+	0.0241688i	$0.00769391\pi$
$114$	−1.36694	−	4.20700i	−0.128025	−	0.394021i
$115$	9.03394	−	6.56354i	0.842419	−	0.612053i
$116$	−20.4913	+	14.8878i	−1.90257	+	1.38230i
$117$	0.0980925	+	0.301898i	0.00906866	+	0.0279105i
$118$	−9.16074	+	28.1939i	−0.843314	+	2.59545i
$119$	1.03221	+	0.749944i	0.0946225	+	0.0687473i
$120$	−14.5236			−1.32582
$121$	4.47955	+	10.0466i	0.407232	+	0.913325i
$122$	12.1352			1.09867
$123$	−2.13010	−	1.54761i	−0.192065	−	0.139543i
$124$	5.73300	−	17.6444i	0.514838	−	1.58451i
$125$	−3.59036	−	11.0500i	−0.321131	−	0.988341i
$126$	−0.654023	+	0.475175i	−0.0582650	+	0.0423320i
$127$	−1.14582	+	0.832484i	−0.101675	+	0.0738710i	−0.637461	−	0.770483i	$-0.720015\pi$
$127$	−1.14582	+	0.832484i	−0.101675	+	0.0738710i	0.535786	+	0.844354i	$0.320015\pi$
$128$	6.34849	+	19.5386i	0.561132	+	1.72699i
$129$	6.94594	−	21.3774i	0.611556	−	1.88218i
$130$	4.08026	+	2.96448i	0.357863	+	0.260002i
$131$	5.34497			0.466992			0.233496	−	0.972358i	$-0.424983\pi$
$131$	5.34497			0.466992			0.233496	+	0.972358i	$0.424983\pi$
$132$	−18.1457	−	11.7770i	−1.57938	−	1.02506i
$133$	−1.10823			−0.0960959
$134$	−9.14444	−	6.64382i	−0.789959	−	0.573939i
$135$	−3.22334	+	9.92043i	−0.277421	+	0.853815i
$136$	−1.36606	−	4.20430i	−0.117139	−	0.360516i
$137$	−0.518306	+	0.376571i	−0.0442818	+	0.0321726i	−0.609706	−	0.792628i	$-0.708712\pi$
$137$	−0.518306	+	0.376571i	−0.0442818	+	0.0321726i	0.565424	+	0.824800i	$0.308712\pi$
$138$	−18.2081	+	13.2289i	−1.54997	+	1.12612i
$139$	−5.51383	−	16.9698i	−0.467677	−	1.43936i	−0.855585	−	0.517663i	$-0.826802\pi$
$139$	−5.51383	−	16.9698i	−0.467677	−	1.43936i	0.387908	−	0.921698i	$-0.373198\pi$
$140$	−2.54676	+	7.83813i	−0.215241	+	0.662443i
$141$	−11.3989	−	8.28180i	−0.959962	−	0.697453i
$142$	−35.9486			−3.01674
$143$	1.18941	+	3.09601i	0.0994636	+	0.258902i
$144$	0.527507			0.0439589
$145$	−12.2161	−	8.87553i	−1.01449	−	0.737073i
$146$	3.67682	−	11.3161i	0.304296	−	0.936526i
$147$	−3.28579	−	10.1126i	−0.271007	−	0.834074i
$148$	−28.6388	+	20.8073i	−2.35409	+	1.71035i
$149$	−5.84759	+	4.24852i	−0.479053	+	0.348053i	−0.800959	−	0.598719i	$-0.795677\pi$
$149$	−5.84759	+	4.24852i	−0.479053	+	0.348053i	0.321906	+	0.946772i	$0.395677\pi$
$150$	0.588118	+	1.81004i	0.0480196	+	0.147789i
$151$	5.07162	−	15.6088i	0.412723	−	1.27023i	−0.501550	−	0.865129i	$-0.667237\pi$
$151$	5.07162	−	15.6088i	0.412723	−	1.27023i	0.914272	−	0.405100i	$-0.132763\pi$
$152$	3.10646	+	2.25698i	0.251967	+	0.183065i
$153$	0.375699			0.0303735
$154$	−6.56274	+	5.31735i	−0.528841	+	0.428484i
$155$	11.0602			0.888375
$156$	−5.27677	−	3.83380i	−0.422480	−	0.306950i
$157$	0.0476578	−	0.146676i	0.00380351	−	0.0117060i	−0.949137	−	0.314864i	$-0.898041\pi$
$157$	0.0476578	−	0.146676i	0.00380351	−	0.0117060i	0.952940	+	0.303158i	$0.0980410\pi$
$158$	0.471646	+	1.45158i	0.0375221	+	0.115481i
$159$	−11.2745	+	8.19143i	−0.894129	+	0.649622i
$160$	−6.12163	+	4.44762i	−0.483957	+	0.351615i
$161$	1.74242	+	5.36262i	0.137322	+	0.422634i
$162$	7.19191	−	22.1344i	0.565050	−	1.73904i
$163$	4.66442	+	3.38890i	0.365345	+	0.265439i	0.755278	−	0.655404i	$-0.227502\pi$
$163$	4.66442	+	3.38890i	0.365345	+	0.265439i	−0.389933	+	0.920843i	$0.627502\pi$
$164$	5.17668			0.404231
$165$	3.33447	−	12.4579i	0.259588	−	0.969847i
$166$	1.07551			0.0834755
$167$	16.1422	+	11.7280i	1.24912	+	0.907542i	0.998171	−	0.0604569i	$-0.0192558\pi$
$167$	16.1422	+	11.7280i	1.24912	+	0.907542i	0.250954	+	0.967999i	$0.419256\pi$
$168$	2.26626	−	6.97482i	0.174845	−	0.538119i
$169$	0.309017	+	0.951057i	0.0237705	+	0.0731582i
$170$	4.82919	−	3.50861i	0.370382	−	0.269098i
$171$	−0.264009	+	0.191814i	−0.0201892	+	0.0146683i
$172$	13.6565	+	42.0304i	1.04130	+	3.20479i
$173$	−3.69053	+	11.3583i	−0.280586	+	0.863554i	0.707101	+	0.707112i	$0.250002\pi$
$173$	−3.69053	+	11.3583i	−0.280586	+	0.863554i	−0.987687	+	0.156442i	$0.949998\pi$
$174$	24.6218	+	17.8888i	1.86657	+	1.35614i
$175$	0.476812			0.0360436
$176$	5.50388	−	0.289942i	0.414870	−	0.0218552i
$177$	22.8555			1.71793
$178$	−25.5561	−	18.5676i	−1.91551	−	1.39170i
$179$	1.03850	−	3.19618i	0.0776212	−	0.238893i	−0.904715	−	0.426017i	$-0.859916\pi$
$179$	1.03850	−	3.19618i	0.0776212	−	0.238893i	0.982336	+	0.187123i	$0.0599164\pi$
$180$	0.749925	+	2.30803i	0.0558961	+	0.172031i
$181$	3.95188	−	2.87121i	0.293741	−	0.213415i	−0.431148	−	0.902281i	$-0.641891\pi$
$181$	3.95188	−	2.87121i	0.293741	−	0.213415i	0.724889	+	0.688866i	$0.241891\pi$
$182$	−2.06034	+	1.49693i	−0.152723	+	0.110960i
$183$	−2.89117	−	8.89809i	−0.213721	−	0.657766i
$184$	6.03713	−	18.5804i	0.445063	−	1.36976i
$185$	−17.0733	−	12.4045i	−1.25525	−	0.911995i
$186$	−22.2920			−1.63453
$187$	3.91995	−	0.206502i	0.286655	−	0.0151009i
$188$	27.7022			2.02039
$189$	−4.26121	−	3.09595i	−0.309958	−	0.225197i
$190$	−1.60221	+	4.93110i	−0.116237	+	0.357739i
$191$	7.35891	+	22.6484i	0.532472	+	1.63878i	0.749049	+	0.662515i	$0.230511\pi$
$191$	7.35891	+	22.6484i	0.532472	+	1.63878i	−0.216577	+	0.976266i	$0.569489\pi$
$192$	17.2356	−	12.5224i	1.24387	−	0.903727i
$193$	16.6219	−	12.0765i	1.19647	−	0.869289i	0.202540	−	0.979274i	$-0.435080\pi$
$193$	16.6219	−	12.0765i	1.19647	−	0.869289i	0.993933	+	0.109985i	$0.0350804\pi$
$194$	−8.60795	−	26.4925i	−0.618015	−	1.90205i
$195$	1.20159	−	3.69811i	0.0860476	−	0.264827i
$196$	16.9131	+	12.2881i	1.20808	+	0.877720i
$197$	15.4653			1.10185			0.550927	−	0.834553i	$-0.314274\pi$
$197$	15.4653			1.10185			0.550927	+	0.834553i	$0.314274\pi$
$198$	−0.643079	+	2.40261i	−0.0457016	+	0.170746i
$199$	−21.3373			−1.51256			−0.756280	−	0.654248i	$-0.772985\pi$
$199$	−21.3373			−1.51256			−0.756280	+	0.654248i	$0.772985\pi$
$200$	−1.33654	−	0.971053i	−0.0945077	−	0.0686638i
$201$	−2.69293	+	8.28799i	−0.189945	+	0.584590i
$202$	4.62234	+	14.2261i	0.325227	+	1.00094i
$203$	6.16857	−	4.48173i	0.432949	−	0.314556i
$204$	−6.24532	+	4.53749i	−0.437260	+	0.317688i
$205$	0.953667	+	2.93509i	0.0666070	+	0.204995i
$206$	2.80662	−	8.63788i	0.195546	−	0.601830i
$207$	1.34325	+	0.975931i	0.0933626	+	0.0678319i
$208$	1.66178			0.115224
$209$	−2.64917	+	2.14645i	−0.183247	+	0.148473i
$210$	9.90274			0.683354
$211$	−2.96205	−	2.15206i	−0.203916	−	0.148154i	0.481141	−	0.876643i	$-0.340223\pi$
$211$	−2.96205	−	2.15206i	−0.203916	−	0.148154i	−0.685057	+	0.728490i	$0.740223\pi$
$212$	8.46704	−	26.0589i	0.581519	−	1.78973i
$213$	8.56461	+	26.3592i	0.586837	+	1.80610i
$214$	7.25585	−	5.27168i	0.495999	−	0.360365i
$215$	−21.3146	+	15.4860i	−1.45365	+	1.05614i
$216$	5.63943	+	17.3564i	0.383715	+	1.18095i
$217$	−1.72582	+	5.31153i	−0.117156	+	0.360570i
$218$	−20.6936	−	15.0348i	−1.40155	−	1.01828i
$219$	−9.17346			−0.619885
$220$	9.09315	+	23.6693i	0.613060	+	1.59578i
$221$	1.18355			0.0796142
$222$	34.4115	+	25.0014i	2.30955	+	1.67799i
$223$	−0.637405	+	1.96173i	−0.0426838	+	0.131367i	−0.970128	−	0.242596i	$-0.922001\pi$
$223$	−0.637405	+	1.96173i	−0.0426838	+	0.131367i	0.927444	+	0.373963i	$0.122001\pi$
$224$	−1.18071	−	3.63385i	−0.0788895	−	0.242797i
$225$	0.113588	−	0.0825269i	0.00757256	−	0.00550179i
$226$	11.6188	−	8.44154i	0.772870	−	0.561523i
$227$	1.76510	+	5.43241i	0.117154	+	0.360562i	0.992390	−	0.123133i	$-0.0392943\pi$
$227$	1.76510	+	5.43241i	0.117154	+	0.360562i	−0.875236	+	0.483695i	$0.839294\pi$
$228$	2.07205	−	6.37711i	0.137225	−	0.422334i
$229$	9.53500	+	6.92758i	0.630091	+	0.457788i	0.856432	−	0.516260i	$-0.172676\pi$
$229$	9.53500	+	6.92758i	0.630091	+	0.457788i	−0.226341	+	0.974048i	$0.572676\pi$
$230$	26.3801			1.73946
$231$	5.46247	+	3.54527i	0.359404	+	0.233261i
$232$	−26.4183			−1.73444
$233$	−21.6427	−	15.7243i	−1.41786	−	1.03013i	−0.992121	−	0.125287i	$-0.960015\pi$
$233$	−21.6427	−	15.7243i	−1.41786	−	1.03013i	−0.425737	−	0.904847i	$-0.639985\pi$
$234$	−0.231736	+	0.713210i	−0.0151491	+	0.0466240i
$235$	5.10340	+	15.7067i	0.332909	+	1.02459i
$236$	−36.3545	+	26.4131i	−2.36647	+	1.71934i
$237$	0.951996	−	0.691665i	0.0618388	−	0.0449285i
$238$	0.931430	+	2.86665i	0.0603757	+	0.185817i
$239$	7.05409	−	21.7103i	0.456291	−	1.40432i	−0.413321	−	0.910585i	$-0.635631\pi$
$239$	7.05409	−	21.7103i	0.456291	−	1.40432i	0.869613	−	0.493735i	$-0.164369\pi$
$240$	−5.22764	−	3.79810i	−0.337443	−	0.245166i
$241$	−18.4323			−1.18733			−0.593664	−	0.804713i	$-0.702319\pi$
$241$	−18.4323			−1.18733			−0.593664	+	0.804713i	$0.702319\pi$
$242$	−5.38915	+	25.4217i	−0.346427	+	1.63417i
$243$	−3.28548			−0.210764
$244$	14.8818	+	10.8123i	0.952712	+	0.692186i
$245$	−3.85133	+	11.8532i	−0.246052	+	0.757272i
$246$	−1.92213	−	5.91571i	−0.122551	−	0.377172i
$247$	−0.831696	+	0.604263i	−0.0529195	+	0.0384483i
$248$	15.6548	−	11.3739i	0.994084	−	0.722244i
$249$	−0.256235	−	0.788611i	−0.0162382	−	0.0499762i
$250$	8.48195	−	26.1048i	0.536445	−	1.65101i
$251$	−9.69946	−	7.04707i	−0.612224	−	0.444807i	0.237972	−	0.971272i	$-0.423517\pi$
$251$	−9.69946	−	7.04707i	−0.612224	−	0.444807i	−0.850197	+	0.526465i	$0.823517\pi$
$252$	−1.22543			−0.0771946
$253$	14.5516	+	9.44432i	0.914852	+	0.593759i
$254$	−3.34591			−0.209941
$255$	−3.72321	−	2.70507i	−0.233157	−	0.169398i
$256$	−7.76878	+	23.9099i	−0.485549	+	1.49437i
$257$	−1.86292	−	5.73346i	−0.116205	−	0.357644i	0.875991	−	0.482327i	$-0.160208\pi$
$257$	−1.86292	−	5.73346i	−0.116205	−	0.357644i	−0.992197	+	0.124684i	$0.960208\pi$
$258$	42.9600	−	31.2123i	2.67457	−	1.94319i
$259$	8.62122	−	6.26368i	0.535696	−	0.389206i
$260$	2.36246	+	7.27090i	0.146514	+	0.450922i
$261$	0.693808	−	2.13532i	0.0429456	−	0.132173i
$262$	10.2155	+	7.42201i	0.631117	+	0.458533i
$263$	−9.26488			−0.571297			−0.285648	−	0.958334i	$-0.592209\pi$
$263$	−9.26488			−0.571297			−0.285648	+	0.958334i	$0.592209\pi$
$264$	−8.09160	−	21.0623i	−0.498004	−	1.29629i
$265$	16.3347			1.00344
$266$	−2.11810	−	1.53889i	−0.129869	−	0.0943553i
$267$	−7.52599	+	23.1626i	−0.460583	+	1.41753i
$268$	−5.29461	−	16.2951i	−0.323420	−	0.995383i
$269$	−7.44671	+	5.41035i	−0.454034	+	0.329875i	−0.791186	−	0.611575i	$-0.790536\pi$
$269$	−7.44671	+	5.41035i	−0.454034	+	0.329875i	0.337153	+	0.941450i	$0.390536\pi$
$270$	−19.9361	+	14.4844i	−1.21327	+	0.881492i
$271$	2.71775	+	8.36438i	0.165092	+	0.508100i	0.999043	−	0.0437381i	$-0.0139267\pi$
$271$	2.71775	+	8.36438i	0.165092	+	0.508100i	−0.833951	+	0.551838i	$0.813927\pi$
$272$	0.607775	−	1.87054i	0.0368518	−	0.113418i
$273$	1.58848	+	1.15410i	0.0961394	+	0.0698494i
$274$	−1.51351			−0.0914346
$275$	1.13979	−	0.923499i	0.0687322	−	0.0556891i
$276$	−34.1160			−2.05354
$277$	15.2930	+	11.1110i	0.918870	+	0.667598i	0.943243	−	0.332105i	$-0.107759\pi$
$277$	15.2930	+	11.1110i	0.918870	+	0.667598i	−0.0243725	+	0.999703i	$0.507759\pi$
$278$	13.0260	−	40.0899i	0.781247	−	2.40443i
$279$	0.508190	+	1.56405i	0.0304245	+	0.0936370i
$280$	−6.95433	+	5.05262i	−0.415601	+	0.301952i
$281$	−4.24483	+	3.08405i	−0.253225	+	0.183979i	−0.707155	−	0.707059i	$-0.750022\pi$
$281$	−4.24483	+	3.08405i	−0.253225	+	0.183979i	0.453930	+	0.891038i	$0.350022\pi$
$282$	−10.2860	−	31.6570i	−0.612522	−	1.88515i
$283$	−2.72557	+	8.38843i	−0.162018	+	0.498640i	−0.998804	−	0.0488895i	$-0.984432\pi$
$283$	−2.72557	+	8.38843i	−0.162018	+	0.498640i	0.836786	+	0.547530i	$0.184432\pi$
$284$	−44.0850	−	32.0297i	−2.61597	−	1.90061i
$285$	3.99743			0.236787
$286$	−2.02587	+	7.56884i	−0.119792	+	0.447555i
$287$	−1.55835			−0.0919867
$288$	−0.910223	−	0.661316i	−0.0536354	−	0.0389684i
$289$	−4.82042	+	14.8357i	−0.283554	+	0.872690i
$290$	−11.0234	−	33.9265i	−0.647317	−	1.99224i
$291$	−17.3747	+	12.6235i	−1.01853	+	0.740002i
$292$	14.5915	−	10.6013i	0.853902	−	0.620396i
$293$	2.99033	+	9.20329i	0.174697	+	0.537662i	0.999619	−	0.0275838i	$-0.00878131\pi$
$293$	2.99033	+	9.20329i	0.174697	+	0.537662i	−0.824923	+	0.565246i	$0.808781\pi$
$294$	7.76242	−	23.8903i	0.452713	−	1.39331i
$295$	−21.6731	−	15.7464i	−1.26186	−	0.916792i
$296$	−36.9223			−2.14606
$297$	−16.1825	+	0.852489i	−0.939005	+	0.0494665i
$298$	−17.0756			−0.989165
$299$	4.23160	+	3.07444i	0.244720	+	0.177799i
$300$	−0.891489	+	2.74372i	−0.0514702	+	0.158409i
$301$	−4.11106	−	12.6525i	−0.236958	−	0.729281i
$302$	31.3675	−	22.7898i	1.80500	−	1.31141i
$303$	9.32998	−	6.77862i	0.535993	−	0.389422i
$304$	0.527915	+	1.62475i	0.0302780	+	0.0931860i
$305$	−3.38879	+	10.4296i	−0.194041	+	0.597198i
$306$	0.718051	+	0.521695i	0.0410483	+	0.0298233i
$307$	25.1565			1.43576			0.717879	−	0.696168i	$-0.245113\pi$
$307$	25.1565			1.43576			0.717879	+	0.696168i	$0.245113\pi$
$308$	−12.7858	+	0.673552i	−0.728539	+	0.0383792i
$309$	−7.00236			−0.398350
$310$	21.1387	+	15.3581i	1.20060	+	0.872284i
$311$	−9.00110	+	27.7025i	−0.510405	+	1.57087i	0.281084	+	0.959683i	$0.409306\pi$
$311$	−9.00110	+	27.7025i	−0.510405	+	1.57087i	−0.791489	+	0.611183i	$0.790694\pi$
$312$	−2.10225	−	6.47007i	−0.119017	−	0.366295i
$313$	18.3329	−	13.3196i	1.03624	−	0.752870i	0.0666891	−	0.997774i	$-0.478756\pi$
$313$	18.3329	−	13.3196i	1.03624	−	0.752870i	0.969547	+	0.244904i	$0.0787564\pi$
$314$	0.294759	−	0.214155i	0.0166342	−	0.0120855i
$315$	−0.225752	−	0.694795i	−0.0127197	−	0.0391472i
$316$	−0.714938	+	2.20035i	−0.0402184	+	0.123779i
$317$	−5.54620	−	4.02955i	−0.311506	−	0.226322i	0.421037	−	0.907044i	$-0.361666\pi$
$317$	−5.54620	−	4.02955i	−0.311506	−	0.226322i	−0.732542	+	0.680722i	$0.761666\pi$
$318$	−32.9229			−1.84623
$319$	6.06535	−	22.6608i	0.339595	−	1.26876i
$320$	−24.9713			−1.39594
$321$	−5.59412	−	4.06436i	−0.312233	−	0.226851i
$322$	−4.11634	+	12.6688i	−0.229395	+	0.706004i
$323$	0.375990	+	1.15718i	0.0209206	+	0.0643870i
$324$	28.5411	−	20.7363i	1.58562	−	1.15202i
$325$	0.357833	−	0.259981i	0.0198490	−	0.0144212i
$326$	4.20901	+	12.9540i	0.233116	+	0.717456i
$327$	−6.09402	+	18.7555i	−0.337000	+	1.03718i
$328$	4.36818	+	3.17367i	0.241193	+	0.175237i
$329$	−8.33928			−0.459760
$330$	23.6720	−	19.1798i	1.30310	−	1.05582i
$331$	−1.87735			−0.103189			−0.0515944	−	0.998668i	$-0.516430\pi$
$331$	−1.87735			−0.103189			−0.0515944	+	0.998668i	$0.516430\pi$
$332$	1.31893	+	0.958260i	0.0723858	+	0.0525914i
$333$	0.969668	−	2.98433i	0.0531375	−	0.163540i
$334$	14.5662	+	44.8302i	0.797027	+	2.45300i
$335$	8.26365	−	6.00389i	0.451492	−	0.328028i
$336$	2.63971	−	1.91787i	0.144008	−	0.104628i
$337$	10.4342	+	32.1131i	0.568385	+	1.74931i	0.657673	+	0.753304i	$0.271541\pi$
$337$	10.4342	+	32.1131i	0.568385	+	1.74931i	−0.0892876	+	0.996006i	$0.528459\pi$
$338$	−0.730029	+	2.24680i	−0.0397083	+	0.122210i
$339$	−8.95786	−	6.50827i	−0.486524	−	0.353480i
$340$	9.04833			0.490715
$341$	6.16200	+	16.0396i	0.333691	+	0.868591i
$342$	−0.770936			−0.0416874
$343$	−11.1963	−	8.13460i	−0.604544	−	0.439227i
$344$	−14.2440	+	43.8385i	−0.767984	+	2.36361i
$345$	−6.28497	−	19.3431i	−0.338371	−	1.04140i
$346$	−22.8256	+	16.5837i	−1.22711	+	0.891548i
$347$	17.4818	−	12.7012i	0.938471	−	0.681839i	−0.00958149	−	0.999954i	$-0.503050\pi$
$347$	17.4818	−	12.7012i	0.938471	−	0.681839i	0.948052	+	0.318115i	$0.103050\pi$
$348$	14.2560	+	43.8753i	0.764199	+	2.35196i
$349$	−7.94035	+	24.4379i	−0.425037	+	1.30813i	0.477922	+	0.878402i	$0.341390\pi$
$349$	−7.94035	+	24.4379i	−0.425037	+	1.30813i	−0.902959	+	0.429727i	$0.858610\pi$
$350$	0.911302	+	0.662100i	0.0487111	+	0.0353907i
$351$	−4.88598			−0.260794
$352$	−9.86054	−	6.39971i	−0.525569	−	0.341106i
$353$	12.8401			0.683410			0.341705	−	0.939807i	$-0.388996\pi$
$353$	12.8401			0.683410			0.341705	+	0.939807i	$0.388996\pi$
$354$	43.6824	+	31.7372i	2.32170	+	1.68681i
$355$	10.0387	−	30.8960i	0.532801	−	1.63979i
$356$	−14.7969	−	45.5403i	−0.784236	−	2.41363i
$357$	1.88005	−	1.36594i	0.0995028	−	0.0722930i
$358$	6.42303	−	4.66660i	0.339467	−	0.246638i
$359$	−5.02299	−	15.4592i	−0.265104	−	0.815905i	−0.991670	−	0.128808i	$-0.958885\pi$
$359$	−5.02299	−	15.4592i	−0.265104	−	0.815905i	0.726566	−	0.687097i	$-0.241115\pi$
$360$	−0.782186	+	2.40732i	−0.0412248	+	0.126877i
$361$	14.5163	+	10.5467i	0.764016	+	0.555090i
$362$	11.5400			0.606527
$363$	19.9243	−	2.10505i	1.04576	−	0.110487i
$364$	−3.86041			−0.202340
$365$	8.69886	+	6.32009i	0.455319	+	0.330809i
$366$	6.83016	−	21.0211i	0.357018	−	1.09879i
$367$	0.582455	+	1.79261i	0.0304039	+	0.0935736i	0.965107	−	0.261856i	$-0.0843346\pi$
$367$	0.582455	+	1.79261i	0.0304039	+	0.0935736i	−0.934703	+	0.355430i	$0.884335\pi$
$368$	7.03200	−	5.10905i	0.366568	−	0.266328i
$369$	−0.371239	+	0.269721i	−0.0193259	+	0.0140411i
$370$	−15.4063	−	47.4159i	−0.800938	−	2.46503i
$371$	−2.54886	+	7.84459i	−0.132330	+	0.407271i
$372$	−27.3375	−	19.8618i	−1.41738	−	1.02979i
$373$	20.2429			1.04814			0.524070	−	0.851675i	$-0.324413\pi$
$373$	20.2429			1.04814			0.524070	+	0.851675i	$0.324413\pi$
$374$	7.77872	+	5.04856i	0.402228	+	0.261055i
$375$	−21.1620			−1.09280
$376$	23.3757	+	16.9834i	1.20551	+	0.875852i
$377$	2.18567	−	6.72681i	0.112568	−	0.346449i
$378$	−3.84517	−	11.8342i	−0.197774	−	0.608686i
$379$	−21.4830	+	15.6083i	−1.10351	+	0.801745i	−0.981629	−	0.190800i	$-0.938892\pi$
$379$	−21.4830	+	15.6083i	−1.10351	+	0.801745i	−0.121878	+	0.992545i	$0.538892\pi$
$380$	−6.35838	+	4.61964i	−0.326178	+	0.236982i
$381$	0.797151	+	2.45338i	0.0408393	+	0.125690i
$382$	−17.3849	+	53.5051i	−0.889487	+	2.73756i
$383$	−1.86232	−	1.35306i	−0.0951603	−	0.0691380i	0.539188	−	0.842186i	$-0.318731\pi$
$383$	−1.86232	−	1.35306i	−0.0951603	−	0.0691380i	−0.634348	+	0.773048i	$0.718731\pi$
$384$	37.4187			1.90952
$385$	−2.73734	−	7.12524i	−0.139508	−	0.363136i
$386$	48.5380			2.47052
$387$	−3.16927	−	2.30261i	−0.161103	−	0.117048i
$388$	13.0482	−	40.1583i	0.662423	−	2.03873i
$389$	−9.98018	−	30.7158i	−0.506015	−	1.55735i	−0.799057	−	0.601255i	$-0.794668\pi$
$389$	−9.98018	−	30.7158i	−0.506015	−	1.55735i	0.293042	−	0.956099i	$-0.405332\pi$
$390$	7.43172	−	5.39946i	0.376320	−	0.273412i
$391$	5.00831	−	3.63875i	0.253281	−	0.184019i
$392$	6.73813	+	20.7378i	0.340327	+	1.04742i
$393$	3.00835	−	9.25875i	0.151751	−	0.467042i
$394$	29.5578	+	21.4750i	1.48910	+	1.08190i
$395$	−1.37927			−0.0693985
$396$	−2.92932	+	2.37343i	−0.147204	+	0.119269i
$397$	−19.5159			−0.979474			−0.489737	−	0.871870i	$-0.662907\pi$
$397$	−19.5159			−0.979474			−0.489737	+	0.871870i	$0.662907\pi$
$398$	−40.7807	−	29.6289i	−2.04415	−	1.48516i
$399$	−0.623755	+	1.91972i	−0.0312268	+	0.0961063i
$400$	−0.227133	−	0.699043i	−0.0113566	−	0.0349521i
$401$	13.2360	−	9.61649i	0.660973	−	0.480225i	−0.206019	−	0.978548i	$-0.566051\pi$
$401$	13.2360	−	9.61649i	0.660973	−	0.480225i	0.866991	+	0.498323i	$0.166051\pi$
$402$	−16.6555	+	12.1009i	−0.830702	+	0.603540i
$403$	1.60093	+	4.92715i	0.0797480	+	0.245439i
$404$	−7.00670	+	21.5644i	−0.348596	+	1.07287i
$405$	17.0151	+	12.3622i	0.845487	+	0.614282i
$406$	18.0129			0.893967
$407$	8.47696	−	31.6708i	0.420187	−	1.56986i
$408$	−8.05173			−0.398620
$409$	3.10172	+	2.25353i	0.153370	+	0.111430i	0.661824	−	0.749659i	$-0.269783\pi$
$409$	3.10172	+	2.25353i	0.153370	+	0.111430i	−0.508454	+	0.861089i	$0.669783\pi$
$410$	−2.25297	+	6.93392i	−0.111266	+	0.342442i
$411$	0.360588	+	1.10978i	0.0177865	+	0.0547413i
$412$	11.1381	−	8.09229i	0.548734	−	0.398679i
$413$	10.9439	−	7.95121i	0.538514	−	0.391253i
$414$	1.21211	+	3.73048i	0.0595718	+	0.183343i
$415$	−0.300338	+	0.924345i	−0.0147430	+	0.0453743i
$416$	−2.86744	−	2.08332i	−0.140588	−	0.102143i
$417$	−32.4991			−1.59149
$418$	−8.04376	+	0.423743i	−0.393433	+	0.0207259i
$419$	−31.1596			−1.52225			−0.761124	−	0.648606i	$-0.775352\pi$
$419$	−31.1596			−1.52225			−0.761124	+	0.648606i	$0.775352\pi$
$420$	12.1441	+	8.82319i	0.592571	+	0.430528i
$421$	−1.07310	+	3.30266i	−0.0522996	+	0.160962i	−0.973795	−	0.227428i	$-0.926968\pi$
$421$	−1.07310	+	3.30266i	−0.0522996	+	0.160962i	0.921495	+	0.388389i	$0.126968\pi$
$422$	−2.67286	−	8.22620i	−0.130113	−	0.400445i
$423$	−1.98663	+	1.44337i	−0.0965931	+	0.0701790i
$424$	23.1206	−	16.7981i	1.12283	−	0.815787i
$425$	−0.161768	−	0.497870i	−0.00784689	−	0.0241502i
$426$	−20.2332	+	62.2715i	−0.980303	+	3.01706i
$427$	−4.47993	−	3.25486i	−0.216799	−	0.157514i
$428$	13.5951			0.657144
$429$	6.03248	−	0.317789i	0.291251	−	0.0153430i
$430$	−62.2412			−3.00154
$431$	5.93593	+	4.31271i	0.285924	+	0.207736i	0.721497	−	0.692417i	$-0.243454\pi$
$431$	5.93593	+	4.31271i	0.285924	+	0.207736i	−0.435573	+	0.900153i	$0.643454\pi$
$432$	−2.50904	+	7.72204i	−0.120716	+	0.371527i
$433$	10.9199	+	33.6080i	0.524777	+	1.61510i	0.764757	+	0.644319i	$0.222859\pi$
$433$	10.9199	+	33.6080i	0.524777	+	1.61510i	−0.239981	+	0.970778i	$0.577141\pi$
$434$	−10.6740	+	7.75515i	−0.512371	+	0.372259i
$435$	−22.2502	+	16.1657i	−1.06682	+	0.775088i
$436$	−11.9815	−	36.8754i	−0.573812	−	1.76601i
$437$	−1.66164	+	5.11399i	−0.0794869	+	0.244636i
$438$	−17.5327	−	12.7382i	−0.837745	−	0.608657i
$439$	−22.2003			−1.05956			−0.529782	−	0.848134i	$-0.677726\pi$
$439$	−22.2003			−1.05956			−0.529782	+	0.848134i	$0.677726\pi$
$440$	−6.83796	+	25.5473i	−0.325987	+	1.21792i
$441$	−1.85314			−0.0882450
$442$	2.26205	+	1.64347i	0.107595	+	0.0781721i
$443$	2.29436	−	7.06133i	0.109009	−	0.335494i	−0.881642	−	0.471919i	$-0.843561\pi$
$443$	2.29436	−	7.06133i	0.109009	−	0.335494i	0.990650	+	0.136425i	$0.0435614\pi$
$444$	19.9242	+	61.3203i	0.945559	+	2.91013i
$445$	23.0946	−	16.7792i	1.09479	−	0.795411i
$446$	−3.94229	+	2.86424i	−0.186673	+	0.135626i
$447$	4.06820	+	12.5206i	0.192419	+	0.592206i
$448$	3.89650	−	11.9922i	0.184092	−	0.566577i
$449$	12.9188	+	9.38605i	0.609676	+	0.442955i	0.849300	−	0.527910i	$-0.177024\pi$
$449$	12.9188	+	9.38605i	0.609676	+	0.442955i	−0.239624	+	0.970866i	$0.577024\pi$
$450$	0.331691			0.0156361
$451$	−3.72517	+	3.01825i	−0.175411	+	0.142124i
$452$	21.7698			1.02397
$453$	−24.1837	−	17.5705i	−1.13625	−	0.825534i
$454$	−4.16991	+	12.8337i	−0.195703	+	0.602313i
$455$	−0.711179	−	2.18878i	−0.0333406	−	0.102612i
$456$	5.65805	−	4.11082i	0.264963	−	0.192507i
$457$	19.2501	−	13.9860i	0.900483	−	0.654239i	−0.0381068	−	0.999274i	$-0.512133\pi$
$457$	19.2501	−	13.9860i	0.900483	−	0.654239i	0.938590	+	0.345034i	$0.112133\pi$
$458$	8.60406	+	26.4806i	0.402041	+	1.23736i
$459$	−1.78698	+	5.49977i	−0.0834092	+	0.256707i
$460$	32.3509	+	23.5043i	1.50837	+	1.09589i
$461$	−0.0626903			−0.00291978			−0.00145989	−	0.999999i	$-0.500465\pi$
$461$	−0.0626903			−0.00291978			−0.00145989	+	0.999999i	$0.500465\pi$
$462$	5.51715	+	14.3610i	0.256681	+	0.668136i
$463$	−10.0284			−0.466061			−0.233031	−	0.972469i	$-0.574864\pi$
$463$	−10.0284			−0.466061			−0.233031	+	0.972469i	$0.574864\pi$
$464$	−9.50900	−	6.90870i	−0.441444	−	0.320728i
$465$	6.22509	−	19.1589i	0.288682	−	0.888471i
$466$	−19.5296	−	60.1059i	−0.904691	−	2.78435i
$467$	10.8660	−	7.89462i	0.502819	−	0.365319i	−0.307274	−	0.951621i	$-0.599417\pi$
$467$	10.8660	−	7.89462i	0.502819	−	0.365319i	0.810093	+	0.586302i	$0.199417\pi$
$468$	−0.919646	+	0.668162i	−0.0425107	+	0.0308858i
$469$	1.59385	+	4.90537i	0.0735973	+	0.226509i
$470$	−12.0564	+	37.1058i	−0.556120	+	1.71156i
$471$	−0.227254	−	0.165109i	−0.0104713	−	0.00760784i
$472$	−46.8697			−2.15735
$473$	−34.3330	−	22.2829i	−1.57863	−	1.02457i
$474$	2.77994			0.127687
$475$	0.367864	+	0.267269i	0.0168788	+	0.0122631i
$476$	−1.41189	+	4.34537i	−0.0647141	+	0.199169i
$477$	0.750543	+	2.30993i	0.0343650	+	0.105765i
$478$	43.6289	−	31.6982i	1.99554	−	1.44984i
$479$	31.4286	−	22.8342i	1.43601	−	1.04332i	0.447151	−	0.894458i	$-0.352439\pi$
$479$	31.4286	−	22.8342i	1.43601	−	1.04332i	0.988858	−	0.148863i	$-0.0475614\pi$
$480$	4.25885	+	13.1074i	0.194389	+	0.598268i
$481$	3.05471	−	9.40142i	0.139283	−	0.428668i
$482$	−35.2286	−	25.5950i	−1.60462	−	1.16582i
$483$	10.2700			0.467303
$484$	−29.2593	+	26.3739i	−1.32997	+	1.19881i
$485$	25.1728			1.14304
$486$	−6.27935	−	4.56221i	−0.284837	−	0.206946i
$487$	10.9921	−	33.8303i	0.498102	−	1.53300i	−0.313965	−	0.949434i	$-0.601658\pi$
$487$	10.9921	−	33.8303i	0.498102	−	1.53300i	0.812067	−	0.583564i	$-0.198342\pi$
$488$	5.92889	+	18.2472i	0.268388	+	0.826014i
$489$	8.49569	−	6.17248i	0.384188	−	0.279129i
$490$	−23.8201	+	17.3063i	−1.07608	+	0.781820i
$491$	−1.65232	−	5.08531i	−0.0745680	−	0.229497i	0.906825	−	0.421508i	$-0.138499\pi$
$491$	−1.65232	−	5.08531i	−0.0745680	−	0.229497i	−0.981393	+	0.192011i	$0.938499\pi$
$492$	2.91363	−	8.96724i	0.131357	−	0.404275i
$493$	−6.77247	−	4.92049i	−0.305017	−	0.221608i
$494$	−2.42865			−0.109270
$495$	−1.88534	−	1.22363i	−0.0847399	−	0.0549981i
$496$	8.60923			0.386566
$497$	13.2711	+	9.64199i	0.595288	+	0.432502i
$498$	0.605336	−	1.86303i	0.0271257	−	0.0834845i
$499$	−0.659646	−	2.03018i	−0.0295298	−	0.0908834i	0.935205	−	0.354106i	$-0.115215\pi$
$499$	−0.659646	−	2.03018i	−0.0295298	−	0.0908834i	−0.964735	+	0.263222i	$0.915215\pi$
$500$	33.6607	−	24.4559i	1.50535	−	1.09370i
$501$	29.4012	−	21.3612i	1.31355	−	0.954349i
$502$	−8.75246	−	26.9373i	−0.390641	−	1.20227i
$503$	4.94289	−	15.2127i	0.220393	−	0.678299i	−0.778334	−	0.627850i	$-0.783935\pi$
$503$	4.94289	−	15.2127i	0.220393	−	0.678299i	0.998727	−	0.0504485i	$-0.0160651\pi$
$504$	−1.03404	−	0.751273i	−0.0460597	−	0.0334643i
$505$	−13.5174			−0.601518
$506$	14.6973	+	38.2567i	0.653374	+	1.70072i
$507$	1.82138			0.0808904
$508$	−4.10322	−	2.98116i	−0.182051	−	0.132268i
$509$	−0.840055	+	2.58542i	−0.0372348	+	0.114597i	−0.967946	−	0.251157i	$-0.919189\pi$
$509$	−0.840055	+	2.58542i	−0.0372348	+	0.114597i	0.930712	+	0.365754i	$0.119189\pi$
$510$	−3.35970	−	10.3401i	−0.148770	−	0.457867i
$511$	−4.39252	+	3.19135i	−0.194314	+	0.141177i
$512$	−14.8081	+	10.7587i	−0.654430	+	0.475471i
$513$	−1.55218	−	4.77711i	−0.0685302	−	0.210914i
$514$	4.40099	−	13.5449i	0.194120	−	0.597438i
$515$	6.64008	+	4.82430i	0.292597	+	0.212584i
$516$	80.4930			3.54351
$517$	−19.9346	+	16.1517i	−0.876724	+	0.710351i
$518$	25.1750			1.10612
$519$	17.5981	+	12.7857i	0.772469	+	0.561232i
$520$	−2.46409	+	7.58368i	−0.108057	+	0.332567i
$521$	2.17046	+	6.68000i	0.0950898	+	0.292656i	0.987277	−	0.159009i	$-0.0508300\pi$
$521$	2.17046	+	6.68000i	0.0950898	+	0.292656i	−0.892187	+	0.451666i	$0.850830\pi$
$522$	4.29113	−	3.11769i	0.187818	−	0.136458i
$523$	−32.5296	+	23.6341i	−1.42242	+	1.03345i	−0.431054	+	0.902326i	$0.641858\pi$
$523$	−32.5296	+	23.6341i	−1.42242	+	1.03345i	−0.991366	+	0.131123i	$0.958142\pi$
$524$	5.91476	+	18.2038i	0.258387	+	0.795235i
$525$	0.268368	−	0.825951i	0.0117125	−	0.0360475i
$526$	−17.7074	−	12.8652i	−0.772080	−	0.560949i
$527$	6.13164			0.267098
$528$	2.59554	−	9.69722i	0.112957	−	0.422017i
$529$	4.35861			0.189505
$530$	31.2196	+	22.6824i	1.35609	+	0.985260i
$531$	1.23091	−	3.78835i	0.0534170	−	0.164400i
$532$	−1.22637	−	3.77439i	−0.0531700	−	0.163641i
$533$	−1.16950	+	0.849690i	−0.0506566	+	0.0368042i
$534$	−46.5475	+	33.8188i	−2.01431	+	1.46348i
$535$	2.50454	+	7.70818i	0.108281	+	0.333253i
$536$	5.52237	−	16.9961i	0.238530	−	0.734120i
$537$	−4.95203	−	3.59786i	−0.213696	−	0.155259i
$538$	−21.7452			−0.937504
$539$	−19.3353	+	1.01858i	−0.832829	+	0.0438732i
$540$	−37.3537			−1.60745
$541$	14.9189	+	10.8392i	0.641415	+	0.466015i	0.860336	−	0.509727i	$-0.170254\pi$
$541$	14.9189	+	10.8392i	0.641415	+	0.466015i	−0.218921	+	0.975743i	$0.570254\pi$
$542$	−6.42048	+	19.7602i	−0.275783	+	0.848773i
$543$	−2.74935	−	8.46163i	−0.117986	−	0.363123i
$544$	−3.39376	+	2.46571i	−0.145506	+	0.105716i
$545$	18.7004	−	13.5866i	0.801037	−	0.581987i
$546$	1.43339	+	4.41153i	0.0613435	+	0.188796i
$547$	4.30555	−	13.2511i	0.184092	−	0.566577i	−0.815839	−	0.578279i	$-0.803725\pi$
$547$	4.30555	−	13.2511i	0.184092	−	0.566577i	0.999932	+	0.0117012i	$0.00372470\pi$
$548$	−1.85607	−	1.34852i	−0.0792876	−	0.0576058i
$549$	−1.63058			−0.0695916
$550$	3.46079	−	0.182313i	0.147569	−	0.00777386i
$551$	7.27127			0.309766
$552$	−28.7877	−	20.9155i	−1.22529	−	0.890223i
$553$	0.215220	−	0.662379i	0.00915208	−	0.0281672i
$554$	13.7999	+	42.4718i	0.586302	+	1.80445i
$555$	−31.0970	+	22.5933i	−1.31999	+	0.959032i
$556$	51.6937	−	37.5577i	2.19230	−	1.59280i
$557$	7.18803	+	22.1225i	0.304567	+	0.937360i	0.979839	+	0.199791i	$0.0640264\pi$
$557$	7.18803	+	22.1225i	0.304567	+	0.937360i	−0.675272	+	0.737569i	$0.735974\pi$
$558$	−1.20056	+	3.69494i	−0.0508237	+	0.156419i
$559$	−9.98402	−	7.25381i	−0.422279	−	0.306804i
$560$	−3.82447			−0.161613
$561$	1.84859	−	6.90652i	0.0780475	−	0.291594i
$562$	−12.3954			−0.522868
$563$	6.79763	+	4.93877i	0.286486	+	0.208144i	0.721741	−	0.692163i	$-0.243342\pi$
$563$	6.79763	+	4.93877i	0.286486	+	0.208144i	−0.435256	+	0.900307i	$0.643342\pi$
$564$	15.5919	−	47.9868i	0.656536	−	2.02061i
$565$	4.01052	+	12.3431i	0.168724	+	0.519278i
$566$	−16.8574	+	12.2476i	−0.708568	+	0.514805i
$567$	−8.59183	+	6.24233i	−0.360823	+	0.262153i
$568$	−17.5634	−	54.0545i	−0.736943	−	2.26808i
$569$	7.22637	−	22.2405i	0.302945	−	0.932370i	−0.677491	−	0.735531i	$-0.736933\pi$
$569$	7.22637	−	22.2405i	0.302945	−	0.932370i	0.980436	−	0.196839i	$-0.0630675\pi$
$570$	7.64005	+	5.55082i	0.320006	+	0.232498i
$571$	−11.1741			−0.467623			−0.233812	−	0.972282i	$-0.575120\pi$
$571$	−11.1741			−0.467623			−0.233812	+	0.972282i	$0.575120\pi$
$572$	−9.22812	+	7.47693i	−0.385847	+	0.312626i
$573$	43.3743			1.81199
$574$	−2.97839	−	2.16393i	−0.124316	−	0.0903205i
$575$	0.714912	−	2.20027i	0.0298139	−	0.0917577i
$576$	−1.14737	−	3.53124i	−0.0478071	−	0.147135i
$577$	−25.5100	+	18.5341i	−1.06199	+	0.771584i	−0.974456	−	0.224577i	$-0.927900\pi$
$577$	−25.5100	+	18.5341i	−1.06199	+	0.771584i	−0.0875383	+	0.996161i	$0.527900\pi$
$578$	−29.8138	+	21.6610i	−1.24009	+	0.900980i
$579$	−11.5640	−	35.5903i	−0.480583	−	1.47908i
$580$	16.7097	−	51.4270i	0.693831	−	2.13539i
$581$	−0.397042	−	0.288468i	−0.0164721	−	0.0119677i
$582$	−50.7363			−2.10309
$583$	9.10064	+	23.6888i	0.376910	+	0.981089i
$584$	18.8119			0.778444
$585$	−0.548257	−	0.398332i	−0.0226676	−	0.0164690i
$586$	−7.06443	+	21.7421i	−0.291829	+	0.898157i
$587$	−2.92217	−	8.99352i	−0.120611	−	0.371202i	0.872465	−	0.488677i	$-0.162520\pi$
$587$	−2.92217	−	8.99352i	−0.120611	−	0.371202i	−0.993076	+	0.117474i	$0.962520\pi$
$588$	30.8052	−	22.3813i	1.27039	−	0.922989i
$589$	−4.30878	+	3.13051i	−0.177540	+	0.128991i
$590$	−19.5570	−	60.1904i	−0.805151	−	2.47800i
$591$	8.70444	−	26.7895i	0.358053	−	1.10197i
$592$	−13.2898	−	9.65562i	−0.546208	−	0.396843i
$593$	−29.0535			−1.19308			−0.596541	−	0.802582i	$-0.703459\pi$
$593$	−29.0535			−1.19308			−0.596541	+	0.802582i	$0.703459\pi$
$594$	−32.1124	−	20.8417i	−1.31759	−	0.855145i
$595$	−2.72385			−0.111667
$596$	−20.9405	−	15.2141i	−0.857755	−	0.623196i
$597$	−12.0094	+	36.9612i	−0.491514	+	1.51272i
$598$	3.81845	+	11.7520i	0.156148	+	0.480574i
$599$	−24.4131	+	17.7372i	−0.997492	+	0.724721i	−0.961549	−	0.274633i	$-0.911444\pi$
$599$	−24.4131	+	17.7372i	−0.997492	+	0.724721i	−0.0359432	+	0.999354i	$0.511444\pi$
$600$	−2.43435	+	1.76866i	−0.0993820	+	0.0722052i
$601$	3.14377	+	9.67553i	0.128237	+	0.394673i	0.994477	−	0.104955i	$-0.0334699\pi$
$601$	3.14377	+	9.67553i	0.128237	+	0.394673i	−0.866240	+	0.499628i	$0.833470\pi$
$602$	9.71207	−	29.8907i	0.395834	−	1.21825i
$603$	1.22872	+	0.892717i	0.0500374	+	0.0363543i
$604$	58.7725			2.39142
$605$	−20.3438	−	11.7308i	−0.827092	−	0.476924i
$606$	27.2446			1.10674
$607$	9.31195	+	6.76553i	0.377960	+	0.274604i	0.760504	−	0.649333i	$-0.224952\pi$
$607$	9.31195	+	6.76553i	0.377960	+	0.274604i	−0.382544	+	0.923937i	$0.624952\pi$
$608$	1.12597	−	3.46537i	0.0456640	−	0.140539i
$609$	−4.29151	−	13.2079i	−0.173901	−	0.535212i
$610$	−20.9593	+	15.2278i	−0.848618	+	0.616557i
$611$	−6.25839	+	4.54699i	−0.253187	+	0.183951i
$612$	0.415750	+	1.27955i	0.0168057	+	0.0517226i
$613$	−0.0545547	+	0.167902i	−0.00220344	+	0.00678151i	−0.952152	−	0.305624i	$-0.901135\pi$
$613$	−0.0545547	+	0.167902i	−0.00220344	+	0.00678151i	0.949949	+	0.312406i	$0.101135\pi$
$614$	48.0802	+	34.9323i	1.94036	+	1.40975i
$615$	5.62103			0.226662
$616$	−11.2018	−	7.27024i	−0.451335	−	0.292926i
$617$	14.4909			0.583380			0.291690	−	0.956513i	$-0.405782\pi$
$617$	14.4909			0.583380			0.291690	+	0.956513i	$0.405782\pi$
$618$	−13.3832	−	9.72346i	−0.538351	−	0.391135i
$619$	5.10756	−	15.7195i	0.205290	−	0.631818i	−0.794411	−	0.607380i	$-0.792220\pi$
$619$	5.10756	−	15.7195i	0.205290	−	0.631818i	0.999701	−	0.0244379i	$-0.00777961\pi$
$620$	12.2392	+	37.6685i	0.491540	+	1.51280i
$621$	−20.6755	+	15.0216i	−0.829680	+	0.602797i
$622$	−55.6709	+	40.4473i	−2.23220	+	1.62179i
$623$	4.45437	+	13.7091i	0.178461	+	0.549245i
$624$	0.935315	−	2.87860i	0.0374426	−	0.115236i
$625$	18.2780	+	13.2797i	0.731119	+	0.531189i
$626$	53.5342			2.13966
$627$	2.22710	+	5.79710i	0.0889419	+	0.231514i
$628$	0.552283			0.0220385
$629$	−9.46523	−	6.87689i	−0.377403	−	0.274200i
$630$	0.533323	−	1.64140i	0.0212481	−	0.0653949i
$631$	0.761555	+	2.34383i	0.0303170	+	0.0933062i	0.965070	−	0.261992i	$-0.0843794\pi$
$631$	0.761555	+	2.34383i	0.0303170	+	0.0933062i	−0.934753	+	0.355298i	$0.884379\pi$
$632$	−1.95225	+	1.41839i	−0.0776563	+	0.0564206i
$633$	−5.39503	+	3.91972i	−0.214433	+	0.155795i
$634$	−5.00470	−	15.4029i	−0.198762	−	0.611726i
$635$	0.934355	−	2.87565i	0.0370788	−	0.114117i
$636$	−40.3746	−	29.3339i	−1.60096	−	1.16316i
$637$	−5.83789			−0.231306
$638$	43.0590	−	34.8879i	1.70472	−	1.38122i
$639$	4.83034			0.191085
$640$	−35.4828	−	25.7798i	−1.40258	−	1.01904i
$641$	1.31383	−	4.04355i	0.0518931	−	0.159711i	−0.921751	−	0.387781i	$-0.873242\pi$
$641$	1.31383	−	4.04355i	0.0518931	−	0.159711i	0.973645	+	0.228070i	$0.0732416\pi$
$642$	−5.04794	−	15.5360i	−0.199226	−	0.613155i
$643$	1.68448	−	1.22384i	0.0664293	−	0.0482637i	−0.554075	−	0.832467i	$-0.686928\pi$
$643$	1.68448	−	1.22384i	0.0664293	−	0.0482637i	0.620504	+	0.784203i	$0.286928\pi$
$644$	−16.3357	+	11.8686i	−0.643717	+	0.467688i
$645$	14.8287	+	45.6381i	0.583880	+	1.79700i
$646$	−0.888246	+	2.73374i	−0.0349476	+	0.107558i
$647$	19.8136	+	14.3954i	0.778953	+	0.565942i	0.904665	−	0.426125i	$-0.140121\pi$
$647$	19.8136	+	14.3954i	0.778953	+	0.565942i	−0.125712	+	0.992067i	$0.540121\pi$
$648$	36.7964			1.44550
$649$	10.7608	−	40.2033i	0.422397	−	1.57812i
$650$	1.04491			0.0409849
$651$	8.22948	+	5.97907i	0.322539	+	0.234338i
$652$	−6.38016	+	19.6361i	−0.249866	+	0.769010i
$653$	2.10334	+	6.47340i	0.0823099	+	0.253324i	0.983739	−	0.179602i	$-0.0574811\pi$
$653$	2.10334	+	6.47340i	0.0823099	+	0.253324i	−0.901429	+	0.432926i	$0.857481\pi$
$654$	−37.6910	+	27.3841i	−1.47383	+	1.07080i
$655$	−9.23156	+	6.70712i	−0.360707	+	0.262069i
$656$	0.742333	+	2.28467i	0.0289832	+	0.0892012i
$657$	−0.494047	+	1.52052i	−0.0192746	+	0.0593211i
$658$	−15.9384	−	11.5799i	−0.621343	−	0.451432i
$659$	−43.2019			−1.68291			−0.841453	−	0.540331i	$-0.818299\pi$
$659$	−43.2019			−1.68291			−0.841453	+	0.540331i	$0.818299\pi$
$660$	46.1188	−	2.42952i	1.79517	−	0.0945690i
$661$	−24.8882			−0.968040			−0.484020	−	0.875057i	$-0.660824\pi$
$661$	−24.8882			−0.968040			−0.484020	+	0.875057i	$0.660824\pi$
$662$	−3.58808	−	2.60689i	−0.139455	−	0.101320i
$663$	0.666147	−	2.05019i	0.0258710	−	0.0796228i
$664$	0.525459	+	1.61720i	0.0203918	+	0.0627594i
$665$	1.91408	−	1.39066i	0.0742250	−	0.0539276i
$666$	5.99730	−	4.35730i	0.232391	−	0.168842i
$667$	−11.4323	−	35.1849i	−0.442659	−	1.36237i
$668$	−22.0800	+	67.9551i	−0.854299	+	2.62926i
$669$	3.03943	+	2.20827i	0.117511	+	0.0853768i
$670$	24.1308			0.932255
$671$	−17.0131	+	0.896245i	−0.656784	+	0.0345992i
$672$	−6.95924			−0.268458
$673$	−5.09736	−	3.70345i	−0.196489	−	0.142757i	0.485191	−	0.874408i	$-0.338750\pi$
$673$	−5.09736	−	3.70345i	−0.196489	−	0.142757i	−0.681679	+	0.731651i	$0.738750\pi$
$674$	−24.6499	+	75.8646i	−0.949479	+	2.92220i
$675$	0.667816	+	2.05533i	0.0257043	+	0.0791096i
$676$	−2.89712	+	2.10488i	−0.111428	+	0.0809571i
$677$	39.2169	−	28.4928i	1.50723	−	1.09507i	0.539840	−	0.841768i	$-0.318485\pi$
$677$	39.2169	−	28.4928i	1.50723	−	1.09507i	0.967388	−	0.253298i	$-0.0815153\pi$
$678$	−8.08326	−	24.8777i	−0.310436	−	0.955423i
$679$	−3.92795	+	12.0890i	−0.150741	+	0.463933i
$680$	7.63516	+	5.54727i	0.292795	+	0.212728i
$681$	10.4037			0.398670
$682$	−10.4954	+	39.2120i	−0.401891	+	1.50151i
$683$	27.0779			1.03611			0.518054	−	0.855348i	$-0.326657\pi$
$683$	27.0779			1.03611			0.518054	+	0.855348i	$0.326657\pi$
$684$	−0.945426	−	0.686892i	−0.0361493	−	0.0262640i
$685$	0.422652	−	1.30079i	0.0161487	−	0.0497006i
$686$	−10.1032	−	31.0944i	−0.385741	−	1.18719i
$687$	17.3669	−	12.6178i	0.662588	−	0.481398i
$688$	−16.5913	+	12.0543i	−0.632536	+	0.459564i
$689$	2.36441	+	7.27689i	0.0900767	+	0.277228i
$690$	14.8478	−	45.6967i	0.565244	−	1.73964i
$691$	25.6831	+	18.6598i	0.977030	+	0.709854i	0.957043	−	0.289946i	$-0.0936375\pi$
$691$	25.6831	+	18.6598i	0.977030	+	0.709854i	0.0199870	+	0.999800i	$0.493638\pi$
$692$	−42.7677			−1.62578
$693$	0.881822	−	0.714482i	0.0334977	−	0.0271409i
$694$	51.0488			1.93779
$695$	30.8177	+	22.3904i	1.16898	+	0.849316i
$696$	−14.8692	+	45.7627i	−0.563616	+	1.73463i
$697$	0.528702	+	1.62718i	0.0200260	+	0.0616337i
$698$	−49.1103	+	35.6807i	−1.85885	+	1.35053i
$699$	−39.4196	+	28.6400i	−1.49098	+	1.08326i
$700$	0.527641	+	1.62391i	0.0199430	+	0.0613781i
$701$	−1.80963	+	5.56946i	−0.0683486	+	0.210355i	−0.979397	−	0.201944i	$-0.935274\pi$
$701$	−1.80963	+	5.56946i	−0.0683486	+	0.210355i	0.911048	+	0.412299i	$0.135274\pi$
$702$	−9.33828	−	6.78466i	−0.352451	−	0.256070i
$703$	10.1623			0.383280
$704$	−13.9123	−	36.2135i	−0.524341	−	1.36485i
$705$	30.0801			1.13288
$706$	24.5405	+	17.8297i	0.923595	+	0.671031i
$707$	2.10925	−	6.49160i	0.0793265	−	0.244142i
$708$	25.2920	+	77.8408i	0.950532	+	2.92544i
$709$	37.0559	−	26.9227i	1.39166	−	1.01110i	0.395981	−	0.918259i	$-0.370405\pi$
$709$	37.0559	−	26.9227i	1.39166	−	1.01110i	0.995681	−	0.0928428i	$-0.0295954\pi$
$710$	62.0886	−	45.1100i	2.33014	−	1.69295i
$711$	−0.0633742	−	0.195046i	−0.00237672	−	0.00731478i
$712$	15.4335	−	47.4994i	0.578394	−	1.78011i
$713$	21.9227	+	15.9278i	0.821012	+	0.596500i
$714$	5.48996			0.205457
$715$	−5.93932	−	3.85475i	−0.222118	−	0.144160i
$716$	12.0347			0.449756
$717$	−33.6370	−	24.4387i	−1.25620	−	0.912681i
$718$	11.8664	−	36.5211i	0.442852	−	1.36296i
$719$	−5.82741	−	17.9349i	−0.217326	−	0.668859i	−0.998980	−	0.0451480i	$-0.985624\pi$
$719$	−5.82741	−	17.9349i	−0.217326	−	0.668859i	0.781655	−	0.623711i	$-0.214376\pi$
$720$	−0.911083	+	0.661941i	−0.0339541	+	0.0246691i
$721$	−3.35293	+	2.43605i	−0.124870	+	0.0907232i
$722$	13.0990	+	40.3146i	0.487495	+	1.50036i
$723$	−10.3744	+	31.9291i	−0.385828	+	1.18746i
$724$	14.1519	+	10.2819i	0.525950	+	0.382125i
$725$	−3.12843			−0.116187
$726$	41.0032	+	23.6436i	1.52177	+	0.877496i
$727$	−18.7319			−0.694727			−0.347363	−	0.937731i	$-0.612923\pi$
$727$	−18.7319			−0.694727			−0.347363	+	0.937731i	$0.612923\pi$
$728$	−3.25749	−	2.36670i	−0.120731	−	0.0877159i
$729$	7.28368	−	22.4169i	0.269766	−	0.830254i
$730$	7.84955	+	24.1584i	0.290525	+	0.894144i
$731$	−11.8166	+	8.58525i	−0.437052	+	0.317537i
$732$	27.1055	−	19.6933i	1.00185	−	0.727886i
$733$	−0.861473	−	2.65134i	−0.0318192	−	0.0979295i	0.933886	−	0.357572i	$-0.116395\pi$
$733$	−0.861473	−	2.65134i	−0.0318192	−	0.0979295i	−0.965705	+	0.259642i	$0.916395\pi$
$734$	−1.37601	+	4.23491i	−0.0507893	+	0.156313i
$735$	18.3648	+	13.3428i	0.677397	+	0.492158i
$736$	−18.5389			−0.683352
$737$	13.3109	+	8.63904i	0.490312	+	0.318223i
$738$	−1.08406			−0.0399048
$739$	−8.97530	−	6.52094i	−0.330162	−	0.239877i	0.410337	−	0.911934i	$-0.365411\pi$
$739$	−8.97530	−	6.52094i	−0.330162	−	0.239877i	−0.740499	+	0.672057i	$0.765411\pi$
$740$	23.3535	−	71.8746i	0.858491	−	2.64216i
$741$	0.578616	+	1.78080i	0.0212560	+	0.0654192i
$742$	−15.7645	+	11.4535i	−0.578731	+	0.420473i
$743$	−18.4611	+	13.4128i	−0.677271	+	0.492066i	−0.872451	−	0.488701i	$-0.837471\pi$
$743$	−18.4611	+	13.4128i	−0.677271	+	0.492066i	0.195180	+	0.980767i	$0.437471\pi$
$744$	−10.8912	−	33.5196i	−0.399290	−	1.22889i
$745$	4.76842	−	14.6757i	0.174701	−	0.537675i
$746$	38.6891	+	28.1093i	1.41651	+	1.02915i
$747$	−0.144514			−0.00528748
$748$	5.04113	+	13.1220i	0.184322	+	0.479787i
$749$	−4.09257			−0.149539
$750$	−40.4457	−	29.3855i	−1.47687	−	1.07301i
$751$	3.82642	−	11.7765i	0.139628	−	0.429731i	−0.856653	−	0.515893i	$-0.827460\pi$
$751$	3.82642	−	11.7765i	0.139628	−	0.429731i	0.996281	+	0.0861620i	$0.0274603\pi$
$752$	3.97248	+	12.2260i	0.144861	+	0.445837i
$753$	−17.6664	+	12.8354i	−0.643800	+	0.467748i
$754$	13.5182	−	9.82154i	0.492303	−	0.357679i
$755$	10.8273	+	33.3229i	0.394045	+	1.21275i
$756$	5.82864	−	17.9387i	0.211986	−	0.652425i
$757$	10.0637	+	7.31173i	0.365773	+	0.265749i	0.755456	−	0.655200i	$-0.227415\pi$
$757$	10.0637	+	7.31173i	0.365773	+	0.265749i	−0.389683	+	0.920949i	$0.627415\pi$
$758$	−62.7328			−2.27856
$759$	24.5500	−	19.8912i	0.891109	−	0.722006i
$760$	−8.19749			−0.297354
$761$	−34.6120	−	25.1471i	−1.25468	−	0.911581i	−0.256199	−	0.966624i	$-0.582470\pi$
$761$	−34.6120	−	25.1471i	−1.25468	−	0.911581i	−0.998484	+	0.0550435i	$0.982470\pi$
$762$	−1.88321	+	5.79592i	−0.0682214	+	0.209964i
$763$	3.60684	+	11.1007i	0.130576	+	0.401873i
$764$	−68.9919	+	50.1256i	−2.49604	+	1.81348i
$765$	−0.648889	+	0.471445i	−0.0234606	+	0.0170451i
$766$	−1.68050	−	5.17204i	−0.0607188	−	0.186873i
$767$	3.87769	−	11.9343i	0.140015	−	0.430922i
$768$	37.0450	+	26.9148i	1.33675	+	0.971203i
$769$	3.24436			0.116994			0.0584972	−	0.998288i	$-0.481369\pi$
$769$	3.24436			0.116994			0.0584972	+	0.998288i	$0.481369\pi$
$770$	4.66237	−	17.4191i	0.168020	−	0.627741i
$771$	−10.9802			−0.395444
$772$	59.5239	+	43.2466i	2.14231	+	1.55648i
$773$	−2.56930	+	7.90749i	−0.0924113	+	0.284413i	−0.986570	−	0.163337i	$-0.947774\pi$
$773$	−2.56930	+	7.90749i	−0.0924113	+	0.284413i	0.894159	+	0.447749i	$0.147774\pi$
$774$	−2.85984	−	8.80167i	−0.102795	−	0.316370i
$775$	1.85383	−	1.34689i	0.0665916	−	0.0483816i
$776$	35.6302	−	25.8869i	1.27905	−	0.929285i
$777$	−5.99784	−	18.4594i	−0.215171	−	0.662229i
$778$	23.5774	−	72.5638i	0.845291	−	2.60154i
$779$	−1.20228	−	0.873510i	−0.0430762	−	0.0312967i
$780$	13.9246			0.498581
$781$	50.3986	−	2.65498i	1.80340	−	0.0950027i
$782$	14.6248			0.522983
$783$	27.9584	+	20.3130i	0.999152	+	0.725926i
$784$	−2.99787	+	9.22649i	−0.107067	+	0.329517i
$785$	0.101744	+	0.313134i	0.00363138	+	0.0111762i
$786$	18.6064	−	13.5183i	0.663667	−	0.482182i
$787$	9.93935	−	7.22136i	0.354299	−	0.257414i	−0.396371	−	0.918090i	$-0.629731\pi$
$787$	9.93935	−	7.22136i	0.354299	−	0.257414i	0.750670	+	0.660677i	$0.229731\pi$
$788$	17.1139	+	52.6712i	0.609658	+	1.87633i
$789$	−5.21463	+	16.0490i	−0.185646	+	0.571359i
$790$	−2.63611	−	1.91525i	−0.0937887	−	0.0681415i
$791$	−6.55344			−0.233013
$792$	−3.92690	+	0.206868i	−0.139536	+	0.00735072i
$793$	−5.13676			−0.182412
$794$	−37.2995	−	27.0997i	−1.32371	−	0.961732i
$795$	9.19382	−	28.2957i	0.326071	−	1.00354i
$796$	−23.6119	−	72.6700i	−0.836902	−	2.57572i
$797$	8.01025	−	5.81979i	0.283738	−	0.206147i	−0.436808	−	0.899555i	$-0.643891\pi$
$797$	8.01025	−	5.81979i	0.283738	−	0.206147i	0.720546	+	0.693407i	$0.243891\pi$
$798$	−3.85787	+	2.80291i	−0.136567	+	0.0992218i
$799$	2.82927	+	8.70758i	0.100092	+	0.308052i
$800$	−0.484442	+	1.49096i	−0.0171276	+	0.0527134i
$801$	3.43393	+	2.49490i	0.121332	+	0.0881528i
$802$	38.6505			1.36480
$803$	−4.31902	+	16.1363i	−0.152415	+	0.569437i
$804$	−31.2070			−1.10059
$805$	−9.73870	−	7.07558i	−0.343244	−	0.249381i
$806$	−3.78207	+	11.6400i	−0.133218	+	0.410002i
$807$	5.18072	+	15.9446i	0.182370	+	0.561277i
$808$	−19.1329	+	13.9009i	−0.673093	+	0.489031i
$809$	−21.9721	+	15.9637i	−0.772498	+	0.561253i	−0.902718	−	0.430233i	$-0.858432\pi$
$809$	−21.9721	+	15.9637i	−0.772498	+	0.561253i	0.130220	+	0.991485i	$0.458432\pi$
$810$	15.3538	+	47.2542i	0.539479	+	1.66034i
$811$	−14.4497	+	44.4716i	−0.507398	+	1.56161i	0.289304	+	0.957237i	$0.406576\pi$
$811$	−14.4497	+	44.4716i	−0.507398	+	1.56161i	−0.796702	+	0.604373i	$0.793424\pi$
$812$	22.0899	+	16.0493i	0.775204	+	0.563219i
$813$	16.0187			0.561802
$814$	60.1795	−	48.7594i	2.10929	−	1.70902i
$815$	−12.3087			−0.431155
$816$	−2.89814	−	2.10562i	−0.101455	−	0.0737116i
$817$	3.92046	−	12.0659i	0.137160	−	0.422134i
$818$	2.79888	+	8.61407i	0.0978606	+	0.301184i
$819$	0.276844	−	0.201139i	0.00967371	−	0.00702836i
$820$	−8.94091	+	6.49595i	−0.312230	+	0.226848i
$821$	−11.4073	−	35.1079i	−0.398116	−	1.22528i	−0.926508	−	0.376275i	$-0.877205\pi$
$821$	−11.4073	−	35.1079i	−0.398116	−	1.22528i	0.528392	−	0.849001i	$-0.322795\pi$
$822$	−0.851862	+	2.62176i	−0.0297121	+	0.0914445i
$823$	−42.5735	−	30.9315i	−1.48402	−	1.07820i	−0.976234	−	0.216719i	$-0.930464\pi$
$823$	−42.5735	−	30.9315i	−1.48402	−	1.07820i	−0.507785	−	0.861484i	$-0.669536\pi$
$824$	14.3597			0.500243
$825$	−0.958200	−	2.49418i	−0.0333603	−	0.0868361i
$826$	31.9574			1.11194
$827$	15.2315	+	11.0663i	0.529651	+	0.384814i	0.820227	−	0.572038i	$-0.193847\pi$
$827$	15.2315	+	11.0663i	0.529651	+	0.384814i	−0.290576	+	0.956852i	$0.593847\pi$
$828$	−1.83735	+	5.65479i	−0.0638524	+	0.196518i
$829$	−8.65374	−	26.6335i	−0.300557	−	0.925019i	−0.981298	−	0.192495i	$-0.938342\pi$
$829$	−8.65374	−	26.6335i	−0.300557	−	0.925019i	0.680741	−	0.732524i	$-0.261658\pi$
$830$	−1.85756	+	1.34960i	−0.0644769	+	0.0468452i
$831$	27.8545	−	20.2375i	0.966261	−	0.702030i
$832$	−3.61452	−	11.1243i	−0.125311	−	0.385667i
$833$	−2.13513	+	6.57126i	−0.0739779	+	0.227681i
$834$	−62.1137	−	45.1282i	−2.15082	−	1.56266i
$835$	−42.5970			−1.47413
$836$	−10.2419	−	6.64722i	−0.354224	−	0.229899i
$837$	−25.3129			−0.874941
$838$	−59.5536	−	43.2682i	−2.05724	−	1.49468i
$839$	−4.34360	+	13.3682i	−0.149958	+	0.461522i	−0.997615	−	0.0690216i	$-0.978012\pi$
$839$	−4.34360	+	13.3682i	−0.149958	+	0.461522i	0.847657	+	0.530544i	$0.178012\pi$
$840$	4.83817	+	14.8904i	0.166933	+	0.513766i
$841$	−17.0114	+	12.3595i	−0.586599	+	0.426189i
$842$	−6.63701	+	4.82207i	−0.228727	+	0.166180i
$843$	2.95316	+	9.08888i	0.101712	+	0.313038i
$844$	4.05161	−	12.4696i	0.139462	−	0.429220i
$845$	−1.72715	−	1.25485i	−0.0594158	−	0.0431681i
$846$	−5.80118			−0.199449
$847$	8.80801	−	7.93942i	0.302647	−	0.272802i
$848$	12.7149			0.436633
$849$	12.9967	+	9.44266i	0.446046	+	0.324071i
$850$	0.382164	−	1.17618i	0.0131081	−	0.0403426i
$851$	−15.9778	−	49.1746i	−0.547711	−	1.68568i
$852$	−80.2957	+	58.3383i	−2.75089	+	1.99864i
$853$	−40.3398	+	29.3086i	−1.38121	+	1.00351i	−0.384443	+	0.923149i	$0.625606\pi$
$853$	−40.3398	+	29.3086i	−1.38121	+	1.00351i	−0.996766	+	0.0803584i	$0.974394\pi$
$854$	−4.04253	−	12.4416i	−0.138333	−	0.425744i
$855$	0.215286	−	0.662582i	0.00736262	−	0.0226598i
$856$	11.4718	+	8.33475i	0.392098	+	0.284876i
$857$	−43.3736			−1.48161			−0.740807	−	0.671718i	$-0.765557\pi$
$857$	−43.3736			−1.48161			−0.740807	+	0.671718i	$0.765557\pi$
$858$	11.9708	+	7.76931i	0.408676	+	0.265240i
$859$	−7.89562			−0.269395			−0.134698	−	0.990887i	$-0.543006\pi$
$859$	−7.89562			−0.269395			−0.134698	+	0.990887i	$0.543006\pi$
$860$	−76.3286	−	55.4560i	−2.60278	−	1.89103i
$861$	−0.877101	+	2.69944i	−0.0298915	+	0.0919966i
$862$	5.35638	+	16.4852i	0.182439	+	0.561490i
$863$	10.8409	−	7.87638i	0.369029	−	0.268115i	−0.387779	−	0.921752i	$-0.626758\pi$
$863$	10.8409	−	7.87638i	0.369029	−	0.268115i	0.756808	+	0.653637i	$0.226758\pi$
$864$	14.0102	−	10.1790i	0.476638	−	0.346298i
$865$	−7.87882	−	24.2485i	−0.267888	−	0.824474i
$866$	−25.7974	+	79.3963i	−0.876632	+	2.69799i
$867$	22.9859	+	16.7002i	0.780642	+	0.567170i
$868$	−19.9997			−0.678834
$869$	−0.768437	−	2.00023i	−0.0260674	−	0.0678530i
$870$	−64.9732			−2.20280
$871$	3.87079	+	2.81229i	0.131157	+	0.0952909i
$872$	12.4970	−	38.4617i	0.423200	−	1.30248i
$873$	1.15663	+	3.55975i	0.0391461	+	0.120479i
$874$	−10.2771	+	7.46673i	−0.347627	+	0.252566i
$875$	−10.1330	+	7.36204i	−0.342557	+	0.248882i
$876$	−10.1514	−	31.2427i	−0.342983	−	1.05559i
$877$	−12.3547	+	38.0238i	−0.417188	+	1.28397i	0.493090	+	0.869978i	$0.335867\pi$
$877$	−12.3547	+	38.0238i	−0.417188	+	1.28397i	−0.910279	+	0.413996i	$0.864133\pi$
$878$	−42.4301	−	30.8273i	−1.43195	−	1.04037i
$879$	17.6254			0.594489
$880$	−9.14219	+	7.40731i	−0.308183	+	0.249700i
$881$	21.3954			0.720828			0.360414	−	0.932792i	$-0.382635\pi$
$881$	21.3954			0.720828			0.360414	+	0.932792i	$0.382635\pi$
$882$	−3.54181	−	2.57327i	−0.119259	−	0.0866466i
$883$	−6.91058	+	21.2686i	−0.232559	+	0.715744i	0.764876	+	0.644177i	$0.222800\pi$
$883$	−6.91058	+	21.2686i	−0.232559	+	0.715744i	−0.997436	+	0.0715673i	$0.977200\pi$
$884$	1.30972	+	4.03090i	0.0440506	+	0.135574i
$885$	−39.4750	+	28.6802i	−1.32694	+	0.964076i
$886$	14.1904	−	10.3099i	0.476737	−	0.346369i
$887$	−13.7026	−	42.1723i	−0.460089	−	1.41601i	−0.865055	−	0.501676i	$-0.832717\pi$
$887$	−13.7026	−	42.1723i	−0.460089	−	1.41601i	0.404967	−	0.914331i	$-0.367283\pi$
$888$	−20.7813	+	63.9582i	−0.697374	+	2.14630i
$889$	1.23520	+	0.897428i	0.0414274	+	0.0300988i
$890$	67.4389			2.26056
$891$	−8.44806	+	31.5628i	−0.283021	+	1.05739i
$892$	−7.38657			−0.247321
$893$	−6.43383	−	4.67445i	−0.215300	−	0.156424i
$894$	−9.61082	+	29.5791i	−0.321434	+	0.989272i
$895$	2.21707	+	6.82344i	0.0741085	+	0.228082i
$896$	17.9172	−	13.0176i	0.598571	−	0.434887i
$897$	7.70736	−	5.59973i	0.257341	−	0.186969i
$898$	11.6575	+	35.8780i	0.389015	+	1.19726i
$899$	11.3234	−	34.8497i	0.377655	−	1.16230i
$900$	0.406765	+	0.295532i	0.0135588	+	0.00985107i
$901$	9.05579			0.301692
$902$	−11.3108	+	0.595850i	−0.376609	+	0.0198396i
$903$	−24.2311			−0.806360
$904$	18.3698	+	13.3464i	0.610970	+	0.443896i
$905$	−3.22256	+	9.91803i	−0.107122	+	0.329686i
$906$	−21.8225	−	67.1629i	−0.725006	−	2.23134i
$907$	6.29318	−	4.57226i	0.208962	−	0.151820i	−0.478382	−	0.878152i	$-0.658777\pi$
$907$	6.29318	−	4.57226i	0.208962	−	0.151820i	0.687344	+	0.726332i	$0.258777\pi$
$908$	−16.5483	+	12.0230i	−0.549175	+	0.398999i
$909$	−0.621094	−	1.91153i	−0.0206004	−	0.0634015i
$910$	1.68011	−	5.17083i	0.0556950	−	0.171411i
$911$	−21.4734	−	15.6013i	−0.711445	−	0.516895i	0.172194	−	0.985063i	$-0.444914\pi$
$911$	−21.4734	−	15.6013i	−0.711445	−	0.516895i	−0.883640	+	0.468168i	$0.844914\pi$
$912$	3.11159			0.103035
$913$	−1.50782	+	0.0794315i	−0.0499016	+	0.00262880i
$914$	56.2126			1.85935
$915$	16.1592	+	11.7404i	0.534208	+	0.388125i
$916$	−13.0423	+	40.1402i	−0.430931	+	1.32627i
$917$	−1.78054	−	5.47993i	−0.0587986	−	0.180963i
$918$	−11.0523	+	8.02998i	−0.364781	+	0.265029i
$919$	−16.6734	+	12.1139i	−0.550004	+	0.399601i	−0.827787	−	0.561042i	$-0.810400\pi$
$919$	−16.6734	+	12.1139i	−0.550004	+	0.399601i	0.277783	+	0.960644i	$0.410400\pi$
$920$	12.8885	+	39.6668i	0.424922	+	1.30778i
$921$	14.1590	−	43.5771i	0.466557	−	1.43591i
$922$	−0.119816	−	0.0870516i	−0.00394594	−	0.00286689i
$923$	15.2168			0.500868
$924$	−6.02959	+	22.5272i	−0.198359	+	0.741089i
$925$	−4.37230			−0.143760
$926$	−19.1668	−	13.9255i	−0.629859	−	0.457619i
$927$	−0.377120	+	1.16066i	−0.0123862	+	0.0381209i
$928$	7.74680	+	23.8422i	0.254301	+	0.782658i
$929$	31.8394	−	23.1327i	1.04462	−	0.758959i	0.0734362	−	0.997300i	$-0.476603\pi$
$929$	31.8394	−	23.1327i	1.04462	−	0.758959i	0.971182	+	0.238341i	$0.0766035\pi$
$930$	38.5016	−	27.9731i	1.26252	−	0.917273i
$931$	−1.85458	−	5.70780i	−0.0607813	−	0.187066i
$932$	29.6036	−	91.1106i	0.969699	−	2.98443i
$933$	42.9212	+	31.1841i	1.40518	+	1.02092i
$934$	31.7300			1.03824
$935$	−6.51122	+	5.27561i	−0.212940	+	0.172531i
$936$	−1.18565			−0.0387540
$937$	−24.7633	−	17.9916i	−0.808980	−	0.587759i	0.104555	−	0.994519i	$-0.466658\pi$
$937$	−24.7633	−	17.9916i	−0.808980	−	0.587759i	−0.913535	+	0.406761i	$0.866658\pi$
$938$	−3.76535	+	11.5886i	−0.122943	+	0.378380i
$939$	−12.7543	−	39.2537i	−0.416221	−	1.28100i
$940$	−47.8459	+	34.7621i	−1.56056	+	1.13381i
$941$	40.9751	−	29.7702i	1.33575	−	0.970479i	0.336161	−	0.941804i	$-0.390871\pi$
$941$	40.9751	−	29.7702i	1.33575	−	0.970479i	0.999589	−	0.0286748i	$-0.00912873\pi$
$942$	−0.205066	−	0.631127i	−0.00668140	−	0.0205632i
$943$	−2.33653	+	7.19110i	−0.0760879	+	0.234174i
$944$	−16.8703	−	12.2570i	−0.549081	−	0.398931i
$945$	11.2447			0.365790
$946$	−34.6767	−	90.2627i	−1.12744	−	2.93469i
$947$	33.0294			1.07331			0.536655	−	0.843802i	$-0.319688\pi$
$947$	33.0294			1.07331			0.536655	+	0.843802i	$0.319688\pi$
$948$	3.40914	+	2.47688i	0.110724	+	0.0804454i
$949$	−1.55638	+	4.79003i	−0.0505221	+	0.155491i
$950$	0.331948	+	1.02163i	0.0107698	+	0.0331461i
$951$	−10.1017	+	7.33935i	−0.327572	+	0.237995i
$952$	−3.85540	+	2.80111i	−0.124954	+	0.0907846i
$953$	4.09683	+	12.6088i	0.132709	+	0.408438i	0.995227	−	0.0975899i	$-0.0311133\pi$
$953$	4.09683	+	12.6088i	0.132709	+	0.408438i	−0.862517	+	0.506028i	$0.831113\pi$
$954$	−1.77310	+	5.45704i	−0.0574063	+	0.176678i
$955$	−41.1302	−	29.8829i	−1.33094	−	0.966987i
$956$	81.7463			2.64386
$957$	−35.8400	−	23.2610i	−1.15854	−	0.751921i
$958$	91.7751			2.96512
$959$	0.558740	+	0.405948i	0.0180427	+	0.0131088i
$960$	−14.0548	+	43.2562i	−0.453616	+	1.39609i
$961$	−1.28557	−	3.95657i	−0.0414699	−	0.127631i
$962$	18.8931	−	13.7266i	0.609137	−	0.442564i
$963$	−0.974954	+	0.708345i	−0.0314174	+	0.0228261i
$964$	−20.3972	−	62.7762i	−0.656951	−	2.02189i
$965$	−13.5544	+	41.7160i	−0.436330	+	1.34289i
$966$	19.6285	+	14.2609i	0.631537	+	0.458838i
$967$	12.3240			0.396314			0.198157	−	0.980170i	$-0.436504\pi$
$967$	12.3240			0.396314			0.198157	+	0.980170i	$0.436504\pi$
$968$	−40.8586	+	4.31681i	−1.31325	+	0.138748i
$969$	2.21613			0.0711922
$970$	48.1113	+	34.9549i	1.54476	+	1.12234i
$971$	14.4307	−	44.4130i	0.463102	−	1.42528i	−0.398252	−	0.917276i	$-0.630383\pi$
$971$	14.4307	−	44.4130i	0.463102	−	1.42528i	0.861354	−	0.508005i	$-0.169617\pi$
$972$	−3.63573	−	11.1896i	−0.116616	−	0.358907i
$973$	−15.5615	+	11.3061i	−0.498880	+	0.362457i
$974$	67.9854	−	49.3942i	2.17839	−	1.58269i
$975$	−0.248947	−	0.766179i	−0.00797268	−	0.0245374i
$976$	−2.63783	+	8.11839i	−0.0844347	+	0.259863i
$977$	−22.6496	−	16.4559i	−0.724625	−	0.526471i	0.163233	−	0.986588i	$-0.447808\pi$
$977$	−22.6496	−	16.4559i	−0.724625	−	0.526471i	−0.887859	+	0.460116i	$0.847808\pi$
$978$	24.8084			0.793285
$979$	37.2001	+	24.1437i	1.18892	+	0.771636i
$980$	−44.6311			−1.42569
$981$	2.78056	+	2.02019i	0.0887764	+	0.0644998i
$982$	3.90347	−	12.0137i	0.124565	−	0.383371i
$983$	2.45340	+	7.55079i	0.0782514	+	0.240833i	0.982528	−	0.186114i	$-0.0595893\pi$
$983$	2.45340	+	7.55079i	0.0782514	+	0.240833i	−0.904277	+	0.426947i	$0.859589\pi$
$984$	7.95614	−	5.78047i	0.253632	−	0.184275i
$985$	−26.7108	+	19.4066i	−0.851078	+	0.618344i
$986$	−6.11124	−	18.8085i	−0.194622	−	0.598984i
$987$	−4.69367	+	14.4456i	−0.149401	+	0.459809i
$988$	−2.97834	−	2.16389i	−0.0947536	−	0.0688425i
$989$	−64.5498			−2.05256
$990$	−1.90421	−	4.95663i	−0.0605199	−	0.157532i
$991$	30.0106			0.953317			0.476659	−	0.879089i	$-0.341848\pi$
$991$	30.0106			0.953317			0.476659	+	0.879089i	$0.341848\pi$
$992$	−14.8554	−	10.7931i	−0.471659	−	0.342680i
$993$	−1.05665	+	3.25202i	−0.0335317	+	0.103200i
$994$	11.9753	+	36.8563i	0.379835	+	1.16901i
$995$	36.8527	−	26.7751i	1.16831	−	0.848826i
$996$	2.40228	−	1.74536i	0.0761191	−	0.0553038i
$997$	6.40082	+	19.6997i	0.202716	+	0.623896i	0.999799	+	0.0200267i	$0.00637513\pi$
$997$	6.40082	+	19.6997i	0.202716	+	0.623896i	−0.797083	+	0.603869i	$0.793625\pi$
$998$	1.55836	−	4.79615i	0.0493291	−	0.151819i
$999$	39.0748	+	28.3895i	1.23627	+	0.898203i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	143.2.h.c.92.7	yes	28
11.3	even	5	inner	143.2.h.c.14.7	✓	28
11.5	even	5		1573.2.a.s.1.2		14
11.6	odd	10		1573.2.a.r.1.13		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.2.h.c.14.7	✓	28	11.3	even	5	inner
143.2.h.c.92.7	yes	28	1.1	even	1	trivial
1573.2.a.r.1.13		14	11.6	odd	10
1573.2.a.s.1.2		14	11.5	even	5

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:	\( N \)	\(=\)	\( 143 = 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	143.h (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.91124 + 1.38860i) q^{2} +(0.562838 - 1.73224i) q^{3} +(1.10660 + 3.40577i) q^{4} +(-1.72715 + 1.25485i) q^{5} +(3.48110 - 2.52917i) q^{6} +(-0.333124 - 1.02525i) q^{7} +(-1.15421 + 3.55228i) q^{8} +(-0.256810 - 0.186583i) q^{9} +O(q^{10})\)	\(q+(1.91124 + 1.38860i) q^{2} +(0.562838 - 1.73224i) q^{3} +(1.10660 + 3.40577i) q^{4} +(-1.72715 + 1.25485i) q^{5} +(3.48110 - 2.52917i) q^{6} +(-0.333124 - 1.02525i) q^{7} +(-1.15421 + 3.55228i) q^{8} +(-0.256810 - 0.186583i) q^{9} -5.04348 q^{10} +(-2.78205 - 1.80561i) q^{11} +6.52245 q^{12} +(-0.809017 - 0.587785i) q^{13} +(0.786980 - 2.42208i) q^{14} +(1.20159 + 3.69811i) q^{15} +(-1.34441 + 0.976772i) q^{16} +(-0.957512 + 0.695673i) q^{17} +(-0.231736 - 0.713210i) q^{18} +(0.317680 - 0.977717i) q^{19} +(-6.18500 - 4.49367i) q^{20} -1.96347 q^{21} +(-2.80989 - 7.31409i) q^{22} -5.23055 q^{23} +(5.50377 + 3.99872i) q^{24} +(-0.136680 + 0.420658i) q^{25} +(-0.730029 - 2.24680i) q^{26} +(3.95284 - 2.87191i) q^{27} +(3.12314 - 2.26909i) q^{28} +(2.18567 + 6.72681i) q^{29} +(-2.83866 + 8.73651i) q^{30} +(-4.19129 - 3.04515i) q^{31} +3.54435 q^{32} +(-4.69359 + 3.80290i) q^{33} -2.79605 q^{34} +(1.86189 + 1.35274i) q^{35} +(0.351274 - 1.08111i) q^{36} +(3.05471 + 9.40142i) q^{37} +(1.96482 - 1.42752i) q^{38} +(-1.47353 + 1.07058i) q^{39} +(-2.46409 - 7.58368i) q^{40} +(0.446709 - 1.37483i) q^{41} +(-3.75267 - 2.72647i) q^{42} +12.3409 q^{43} +(3.07088 - 11.4731i) q^{44} +0.677682 q^{45} +(-9.99683 - 7.26312i) q^{46} +(2.39049 - 7.35718i) q^{47} +(0.935315 + 2.87860i) q^{48} +(4.72295 - 3.43142i) q^{49} +(-0.845354 + 0.614185i) q^{50} +(0.666147 + 2.05019i) q^{51} +(1.10660 - 3.40577i) q^{52} +(-6.19010 - 4.49737i) q^{53} +11.5427 q^{54} +(7.07078 - 0.372486i) q^{55} +4.02648 q^{56} +(-1.51484 - 1.10059i) q^{57} +(-5.16349 + 15.8916i) q^{58} +(3.87769 + 11.9343i) q^{59} +(-11.2653 + 8.18468i) q^{60} +(4.15573 - 3.01931i) q^{61} +(-3.78207 - 11.6400i) q^{62} +(-0.105745 + 0.325450i) q^{63} +(9.46293 + 6.87522i) q^{64} +2.13488 q^{65} +(-14.2513 + 0.750752i) q^{66} -4.78456 q^{67} +(-3.42889 - 2.49124i) q^{68} +(-2.94395 + 9.06055i) q^{69} +(1.68011 + 5.17083i) q^{70} +(-12.3107 + 8.94423i) q^{71} +(0.959208 - 0.696905i) q^{72} +(-1.55638 - 4.79003i) q^{73} +(-7.21651 + 22.2101i) q^{74} +(0.651751 + 0.473525i) q^{75} +3.68143 q^{76} +(-0.924436 + 3.45379i) q^{77} -4.30288 q^{78} +(0.522678 + 0.379747i) q^{79} +(1.09630 - 3.37406i) q^{80} +(-3.04429 - 9.36937i) q^{81} +(2.76285 - 2.00733i) q^{82} +(0.368309 - 0.267592i) q^{83} +(-2.17279 - 6.68715i) q^{84} +(0.780803 - 2.40306i) q^{85} +(23.5865 + 17.1366i) q^{86} +12.8826 q^{87} +(9.62509 - 7.79857i) q^{88} -13.3715 q^{89} +(1.29521 + 0.941028i) q^{90} +(-0.333124 + 1.02525i) q^{91} +(-5.78814 - 17.8141i) q^{92} +(-7.63394 + 5.54638i) q^{93} +(14.7850 - 10.7419i) q^{94} +(0.678206 + 2.08730i) q^{95} +(1.99490 - 6.13966i) q^{96} +(-9.53931 - 6.93072i) q^{97} +13.7916 q^{98} +(0.377560 + 0.982780i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 3 q^{2} - 7 q^{3} - 5 q^{4} - 7 q^{5} - 4 q^{6} - 7 q^{7} + q^{8} - 6 q^{9}+O(q^{10}) \) 28 * q - 3 * q^2 - 7 * q^3 - 5 * q^4 - 7 * q^5 - 4 * q^6 - 7 * q^7 + q^8 - 6 * q^9	\( 28 q - 3 q^{2} - 7 q^{3} - 5 q^{4} - 7 q^{5} - 4 q^{6} - 7 q^{7} + q^{8} - 6 q^{9} - 24 q^{10} - 5 q^{11} + 38 q^{12} - 7 q^{13} - 7 q^{14} + 8 q^{15} - 19 q^{16} + 7 q^{17} + 5 q^{18} + 5 q^{19} + 9 q^{20} - 33 q^{22} + 50 q^{23} - 7 q^{24} - 34 q^{25} + 2 q^{26} - 19 q^{27} + 30 q^{28} + 8 q^{29} - 6 q^{30} + 17 q^{31} + 24 q^{32} - 26 q^{33} + 26 q^{34} - 4 q^{35} - 27 q^{36} + 17 q^{37} - 51 q^{38} - 2 q^{39} + 39 q^{40} - 23 q^{41} + 80 q^{42} - 32 q^{43} + q^{44} + 78 q^{45} - 31 q^{46} - 29 q^{47} + 52 q^{48} - 52 q^{49} + 6 q^{50} + 7 q^{51} - 5 q^{52} - 16 q^{53} - 42 q^{54} - 5 q^{55} + 34 q^{56} - 7 q^{57} - 13 q^{58} - 11 q^{59} - 74 q^{60} + 37 q^{61} + 23 q^{62} - 38 q^{63} + 67 q^{64} + 18 q^{65} - 65 q^{66} + 58 q^{67} - 68 q^{68} - 28 q^{69} + 44 q^{70} - 47 q^{71} + 10 q^{72} + 44 q^{73} - 46 q^{74} + 17 q^{75} + 6 q^{76} + 21 q^{77} + 26 q^{78} + 51 q^{79} + 23 q^{80} - 14 q^{81} - 47 q^{82} - 13 q^{83} - 107 q^{84} - q^{85} + 38 q^{86} - 12 q^{87} + 9 q^{88} + 38 q^{89} - 74 q^{90} - 7 q^{91} - 41 q^{92} - 51 q^{93} - 5 q^{94} + 47 q^{95} - 71 q^{96} - 20 q^{97} + 162 q^{98} + 60 q^{99}+O(q^{100}) \) 28 * q - 3 * q^2 - 7 * q^3 - 5 * q^4 - 7 * q^5 - 4 * q^6 - 7 * q^7 + q^8 - 6 * q^9 - 24 * q^10 - 5 * q^11 + 38 * q^12 - 7 * q^13 - 7 * q^14 + 8 * q^15 - 19 * q^16 + 7 * q^17 + 5 * q^18 + 5 * q^19 + 9 * q^20 - 33 * q^22 + 50 * q^23 - 7 * q^24 - 34 * q^25 + 2 * q^26 - 19 * q^27 + 30 * q^28 + 8 * q^29 - 6 * q^30 + 17 * q^31 + 24 * q^32 - 26 * q^33 + 26 * q^34 - 4 * q^35 - 27 * q^36 + 17 * q^37 - 51 * q^38 - 2 * q^39 + 39 * q^40 - 23 * q^41 + 80 * q^42 - 32 * q^43 + q^44 + 78 * q^45 - 31 * q^46 - 29 * q^47 + 52 * q^48 - 52 * q^49 + 6 * q^50 + 7 * q^51 - 5 * q^52 - 16 * q^53 - 42 * q^54 - 5 * q^55 + 34 * q^56 - 7 * q^57 - 13 * q^58 - 11 * q^59 - 74 * q^60 + 37 * q^61 + 23 * q^62 - 38 * q^63 + 67 * q^64 + 18 * q^65 - 65 * q^66 + 58 * q^67 - 68 * q^68 - 28 * q^69 + 44 * q^70 - 47 * q^71 + 10 * q^72 + 44 * q^73 - 46 * q^74 + 17 * q^75 + 6 * q^76 + 21 * q^77 + 26 * q^78 + 51 * q^79 + 23 * q^80 - 14 * q^81 - 47 * q^82 - 13 * q^83 - 107 * q^84 - q^85 + 38 * q^86 - 12 * q^87 + 9 * q^88 + 38 * q^89 - 74 * q^90 - 7 * q^91 - 41 * q^92 - 51 * q^93 - 5 * q^94 + 47 * q^95 - 71 * q^96 - 20 * q^97 + 162 * q^98 + 60 * q^99

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