LMFDB - Embedded newform 231.2.y.b.37.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [231,2,Mod(4,231)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(231, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 20, 6]))

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

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

chi := DirichletCharacter("231.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 231 = 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	231.y (of order $15$, degree $8$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.84454428669$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$8$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			37.2
Character	$\chi$	$=$	231.37
Dual form			231.2.y.b.25.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.43967 + 0.640984i) q^{2} +(-0.978148 + 0.207912i) q^{3} +(0.323537 - 0.359324i) q^{4} +(0.433772 + 4.12706i) q^{5} +(1.27494 - 0.926302i) q^{6} +(-2.64557 - 0.0310171i) q^{7} +(0.738505 - 2.27288i) q^{8} +(0.913545 - 0.406737i) q^{9} +O(q^{10})$	\(q+(-1.43967 + 0.640984i) q^{2} +(-0.978148 + 0.207912i) q^{3} +(0.323537 - 0.359324i) q^{4} +(0.433772 + 4.12706i) q^{5} +(1.27494 - 0.926302i) q^{6} +(-2.64557 - 0.0310171i) q^{7} +(0.738505 - 2.27288i) q^{8} +(0.913545 - 0.406737i) q^{9} +(-3.26987 - 5.66358i) q^{10} +(2.14258 + 2.53167i) q^{11} +(-0.241759 + 0.418739i) q^{12} +(-1.57878 - 1.14705i) q^{13} +(3.82864 - 1.65111i) q^{14} +(-1.28236 - 3.94669i) q^{15} +(0.494759 + 4.70732i) q^{16} +(-4.15061 - 1.84797i) q^{17} +(-1.05450 + 1.17114i) q^{18} +(-3.37641 - 3.74988i) q^{19} +(1.62329 + 1.17939i) q^{20} +(2.59421 - 0.519706i) q^{21} +(-4.70737 - 2.27142i) q^{22} +(0.495419 - 0.858091i) q^{23} +(-0.249807 + 2.37676i) q^{24} +(-11.9537 + 2.54085i) q^{25} +(3.00817 + 0.639406i) q^{26} +(-0.809017 + 0.587785i) q^{27} +(-0.867085 + 0.940582i) q^{28} +(0.853348 + 2.62634i) q^{29} +(4.37594 + 4.85997i) q^{30} +(0.485833 - 4.62239i) q^{31} +(-1.33975 - 2.32052i) q^{32} +(-2.62212 - 2.03088i) q^{33} +7.16004 q^{34} +(-1.01956 - 10.9319i) q^{35} +(0.149415 - 0.459853i) q^{36} +(3.11960 + 0.663091i) q^{37} +(7.26453 + 3.23438i) q^{38} +(1.78277 + 0.793738i) q^{39} +(9.70067 + 2.06194i) q^{40} +(-3.23441 + 9.95449i) q^{41} +(-3.40169 + 2.41105i) q^{42} +3.83062 q^{43} +(1.60289 + 0.0492102i) q^{44} +(2.07490 + 3.59383i) q^{45} +(-0.163219 + 1.55293i) q^{46} +(-4.00875 - 4.45217i) q^{47} +(-1.46265 - 4.50159i) q^{48} +(6.99808 + 0.164116i) q^{49} +(15.5808 - 11.3201i) q^{50} +(4.44413 + 0.944628i) q^{51} +(-0.922957 + 0.196181i) q^{52} +(-1.01426 + 9.65000i) q^{53} +(0.787959 - 1.36479i) q^{54} +(-9.51898 + 9.94071i) q^{55} +(-2.02426 + 5.99016i) q^{56} +(4.08227 + 2.96594i) q^{57} +(-2.91198 - 3.23408i) q^{58} +(-4.39787 + 4.88433i) q^{59} +(-1.83303 - 0.816118i) q^{60} +(0.790124 + 7.51753i) q^{61} +(2.26344 + 6.96614i) q^{62} +(-2.42946 + 1.04771i) q^{63} +(-4.24233 - 3.08223i) q^{64} +(4.04912 - 7.01328i) q^{65} +(5.07676 + 1.24307i) q^{66} +(-0.922802 - 1.59834i) q^{67} +(-2.00690 + 0.893529i) q^{68} +(-0.306186 + 0.942343i) q^{69} +(8.47500 + 15.0848i) q^{70} +(3.33445 - 2.42262i) q^{71} +(-0.249807 - 2.37676i) q^{72} +(-3.15290 + 3.50165i) q^{73} +(-4.91623 + 1.04498i) q^{74} +(11.1642 - 4.97064i) q^{75} -2.43982 q^{76} +(-5.58981 - 6.76417i) q^{77} -3.07537 q^{78} +(-1.18499 + 0.527591i) q^{79} +(-19.2128 + 4.08380i) q^{80} +(0.669131 - 0.743145i) q^{81} +(-1.72417 - 16.4044i) q^{82} +(1.10236 - 0.800908i) q^{83} +(0.652579 - 1.10031i) q^{84} +(5.82627 - 17.9314i) q^{85} +(-5.51483 + 2.45536i) q^{86} +(-1.38075 - 2.39152i) q^{87} +(7.33650 - 3.00017i) q^{88} +(-7.79893 + 13.5081i) q^{89} +(-5.29076 - 3.84396i) q^{90} +(4.14119 + 3.08357i) q^{91} +(-0.148047 - 0.455640i) q^{92} +(0.485833 + 4.62239i) q^{93} +(8.62506 + 3.84013i) q^{94} +(14.0114 - 15.5612i) q^{95} +(1.79294 + 1.99126i) q^{96} +(3.00835 + 2.18569i) q^{97} +(-10.1801 + 4.24938i) q^{98} +(2.98706 + 1.44133i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 4 q^{2} + 8 q^{3} + 10 q^{4} - 4 q^{5} - 8 q^{6} - q^{7} + 8 q^{8} + 8 q^{9}+O(q^{10}) $ 64 * q + 4 * q^2 + 8 * q^3 + 10 * q^4 - 4 * q^5 - 8 * q^6 - q^7 + 8 * q^8 + 8 * q^9	\( 64 q + 4 q^{2} + 8 q^{3} + 10 q^{4} - 4 q^{5} - 8 q^{6} - q^{7} + 8 q^{8} + 8 q^{9} - 14 q^{10} + 11 q^{11} - 30 q^{12} - 8 q^{13} + 6 q^{14} - 12 q^{15} - 4 q^{17} - q^{18} - 2 q^{19} + 24 q^{20} - 2 q^{21} - 14 q^{22} + 16 q^{24} - 10 q^{25} + 4 q^{26} - 16 q^{27} + 29 q^{28} - 58 q^{29} + 11 q^{30} - 19 q^{31} - 64 q^{32} + 6 q^{33} - 88 q^{34} + 17 q^{35} - 20 q^{36} - 20 q^{37} + 29 q^{38} + 4 q^{39} + 51 q^{40} - 68 q^{41} - 11 q^{42} + 92 q^{43} - 21 q^{44} - 4 q^{45} - 5 q^{46} - 26 q^{47} - 10 q^{48} + 37 q^{49} - 10 q^{50} + 6 q^{51} - 14 q^{52} - 3 q^{53} - 6 q^{54} - 32 q^{55} + 24 q^{56} - 36 q^{57} + 52 q^{58} + 7 q^{59} - 12 q^{60} - 21 q^{61} + 92 q^{62} - 7 q^{63} - 72 q^{64} - 66 q^{65} - 23 q^{66} - 4 q^{67} - 17 q^{68} + 40 q^{69} - q^{70} + 58 q^{71} + 16 q^{72} - 3 q^{73} - 28 q^{74} + 20 q^{75} + 168 q^{76} - 34 q^{77} + 132 q^{78} + 9 q^{79} - 5 q^{80} + 8 q^{81} - 42 q^{82} + 60 q^{83} - 39 q^{84} + 110 q^{85} + 13 q^{86} - 46 q^{87} + 92 q^{88} - 10 q^{89} + 8 q^{90} + 10 q^{91} + 110 q^{92} - 19 q^{93} - 46 q^{94} + 43 q^{95} - 4 q^{96} + 64 q^{97} - 88 q^{98} + 28 q^{99}+O(q^{100}) \) 64 * q + 4 * q^2 + 8 * q^3 + 10 * q^4 - 4 * q^5 - 8 * q^6 - q^7 + 8 * q^8 + 8 * q^9 - 14 * q^10 + 11 * q^11 - 30 * q^12 - 8 * q^13 + 6 * q^14 - 12 * q^15 - 4 * q^17 - q^18 - 2 * q^19 + 24 * q^20 - 2 * q^21 - 14 * q^22 + 16 * q^24 - 10 * q^25 + 4 * q^26 - 16 * q^27 + 29 * q^28 - 58 * q^29 + 11 * q^30 - 19 * q^31 - 64 * q^32 + 6 * q^33 - 88 * q^34 + 17 * q^35 - 20 * q^36 - 20 * q^37 + 29 * q^38 + 4 * q^39 + 51 * q^40 - 68 * q^41 - 11 * q^42 + 92 * q^43 - 21 * q^44 - 4 * q^45 - 5 * q^46 - 26 * q^47 - 10 * q^48 + 37 * q^49 - 10 * q^50 + 6 * q^51 - 14 * q^52 - 3 * q^53 - 6 * q^54 - 32 * q^55 + 24 * q^56 - 36 * q^57 + 52 * q^58 + 7 * q^59 - 12 * q^60 - 21 * q^61 + 92 * q^62 - 7 * q^63 - 72 * q^64 - 66 * q^65 - 23 * q^66 - 4 * q^67 - 17 * q^68 + 40 * q^69 - q^70 + 58 * q^71 + 16 * q^72 - 3 * q^73 - 28 * q^74 + 20 * q^75 + 168 * q^76 - 34 * q^77 + 132 * q^78 + 9 * q^79 - 5 * q^80 + 8 * q^81 - 42 * q^82 + 60 * q^83 - 39 * q^84 + 110 * q^85 + 13 * q^86 - 46 * q^87 + 92 * q^88 - 10 * q^89 + 8 * q^90 + 10 * q^91 + 110 * q^92 - 19 * q^93 - 46 * q^94 + 43 * q^95 - 4 * q^96 + 64 * q^97 - 88 * q^98 + 28 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/231\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{5}\right)$

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 $

$2$	−1.43967	+	0.640984i	−1.01800	+	0.453244i	−0.846754	−	0.531984i	$-0.821447\pi$
$2$	−1.43967	+	0.640984i	−1.01800	+	0.453244i	−0.171248	+	0.985228i	$0.554780\pi$
$3$	−0.978148	+	0.207912i	−0.564734	+	0.120038i
$3$	−0.978148	+	0.207912i	−0.564734	+	0.120038i
$4$	0.323537	−	0.359324i	0.161769	−	0.179662i
$5$	0.433772	+	4.12706i	0.193989	+	1.84568i	0.467726	+	0.883873i	$0.345073\pi$
$5$	0.433772	+	4.12706i	0.193989	+	1.84568i	−0.273738	+	0.961804i	$0.588260\pi$
$6$	1.27494	−	0.926302i	0.520494	−	0.378161i
$7$	−2.64557	−	0.0310171i	−0.999931	−	0.0117234i
$7$	−2.64557	−	0.0310171i	−0.999931	−	0.0117234i
$8$	0.738505	−	2.27288i	0.261101	−	0.803586i
$9$	0.913545	−	0.406737i	0.304515	−	0.135579i
$10$	−3.26987	−	5.66358i	−1.03402	−	1.79098i
$11$	2.14258	+	2.53167i	0.646011	+	0.763328i
$11$	2.14258	+	2.53167i	0.646011	+	0.763328i
$12$	−0.241759	+	0.418739i	−0.0697899	+	0.120880i
$13$	−1.57878	−	1.14705i	−0.437875	−	0.318135i	0.346915	−	0.937897i	$-0.387229\pi$
$13$	−1.57878	−	1.14705i	−0.437875	−	0.318135i	−0.784790	+	0.619762i	$0.787229\pi$
$14$	3.82864	−	1.65111i	1.02325	−	0.441278i
$15$	−1.28236	−	3.94669i	−0.331103	−	1.01903i
$16$	0.494759	+	4.70732i	0.123690	+	1.17683i
$17$	−4.15061	−	1.84797i	−1.00667	−	0.448199i	−0.163904	−	0.986476i	$-0.552409\pi$
$17$	−4.15061	−	1.84797i	−1.00667	−	0.448199i	−0.842768	+	0.538277i	$0.819075\pi$
$18$	−1.05450	+	1.17114i	−0.248547	+	0.276039i
$19$	−3.37641	−	3.74988i	−0.774601	−	0.860281i	0.218705	−	0.975791i	$-0.429817\pi$
$19$	−3.37641	−	3.74988i	−0.774601	−	0.860281i	−0.993306	+	0.115509i	$0.963150\pi$
$20$	1.62329	+	1.17939i	0.362980	+	0.263720i
$21$	2.59421	−	0.519706i	0.566102	−	0.113409i
$22$	−4.70737	−	2.27142i	−1.00361	−	0.484269i
$23$	0.495419	−	0.858091i	0.103302	−	0.178924i	−0.809741	−	0.586787i	$-0.800393\pi$
$23$	0.495419	−	0.858091i	0.103302	−	0.178924i	0.913043	+	0.407863i	$0.133726\pi$
$24$	−0.249807	+	2.37676i	−0.0509917	+	0.485154i
$25$	−11.9537	+	2.54085i	−2.39075	+	0.508169i
$26$	3.00817	+	0.639406i	0.589950	+	0.125398i
$27$	−0.809017	+	0.587785i	−0.155695	+	0.113119i
$28$	−0.867085	+	0.940582i	−0.163864	+	0.177753i
$29$	0.853348	+	2.62634i	0.158463	+	0.487698i	0.998495	−	0.0548378i	$-0.0174642\pi$
$29$	0.853348	+	2.62634i	0.158463	+	0.487698i	−0.840032	+	0.542536i	$0.817464\pi$
$30$	4.37594	+	4.85997i	0.798933	+	0.887305i
$31$	0.485833	−	4.62239i	0.0872582	−	0.830206i	−0.860120	−	0.510091i	$-0.829612\pi$
$31$	0.485833	−	4.62239i	0.0872582	−	0.830206i	0.947379	−	0.320115i	$-0.103722\pi$
$32$	−1.33975	−	2.32052i	−0.236837	−	0.410214i
$33$	−2.62212	−	2.03088i	−0.456453	−	0.353531i
$34$	7.16004			1.22794
$35$	−1.01956	−	10.9319i	−0.172338	−	1.84783i
$36$	0.149415	−	0.459853i	0.0249026	−	0.0766422i
$37$	3.11960	+	0.663091i	0.512859	+	0.109011i	0.457069	−	0.889431i	$-0.348899\pi$
$37$	3.11960	+	0.663091i	0.512859	+	0.109011i	0.0557894	+	0.998443i	$0.482232\pi$
$38$	7.26453	+	3.23438i	1.17846	+	0.524686i
$39$	1.78277	+	0.793738i	0.285471	+	0.127100i
$40$	9.70067	+	2.06194i	1.53381	+	0.326022i
$41$	−3.23441	+	9.95449i	−0.505130	+	1.55463i	0.295422	+	0.955367i	$0.404540\pi$
$41$	−3.23441	+	9.95449i	−0.505130	+	1.55463i	−0.800552	+	0.599263i	$0.795460\pi$
$42$	−3.40169	+	2.41105i	−0.524892	+	0.372033i
$43$	3.83062			0.584163			0.292082	−	0.956393i	$-0.405652\pi$
$43$	3.83062			0.584163			0.292082	+	0.956393i	$0.405652\pi$
$44$	1.60289	+	0.0492102i	0.241645	+	0.00741871i
$45$	2.07490	+	3.59383i	0.309307	+	0.535736i
$46$	−0.163219	+	1.55293i	−0.0240653	+	0.228966i
$47$	−4.00875	−	4.45217i	−0.584737	−	0.649416i	0.376084	−	0.926585i	$-0.377270\pi$
$47$	−4.00875	−	4.45217i	−0.584737	−	0.649416i	−0.960821	+	0.277169i	$0.910604\pi$
$48$	−1.46265	−	4.50159i	−0.211116	−	0.649748i
$49$	6.99808	+	0.164116i	0.999725	+	0.0234451i
$50$	15.5808	−	11.3201i	2.20346	−	1.60091i
$51$	4.44413	+	0.944628i	0.622302	+	0.132274i
$52$	−0.922957	+	0.196181i	−0.127991	+	0.0272054i
$53$	−1.01426	+	9.65000i	−0.139319	+	1.32553i	0.671837	+	0.740699i	$0.265506\pi$
$53$	−1.01426	+	9.65000i	−0.139319	+	1.32553i	−0.811155	+	0.584831i	$0.801161\pi$
$54$	0.787959	−	1.36479i	0.107228	−	0.185724i
$55$	−9.51898	+	9.94071i	−1.28354	+	1.34041i
$56$	−2.02426	+	5.99016i	−0.270504	+	0.800469i
$57$	4.08227	+	2.96594i	0.540710	+	0.392849i
$58$	−2.91198	−	3.23408i	−0.382362	−	0.424656i
$59$	−4.39787	+	4.88433i	−0.572554	+	0.635886i	−0.957974	−	0.286856i	$-0.907390\pi$
$59$	−4.39787	+	4.88433i	−0.572554	+	0.635886i	0.385420	+	0.922741i	$0.374057\pi$
$60$	−1.83303	−	0.816118i	−0.236643	−	0.105360i
$61$	0.790124	+	7.51753i	0.101165	+	0.962521i	0.920906	+	0.389786i	$0.127451\pi$
$61$	0.790124	+	7.51753i	0.101165	+	0.962521i	−0.819741	+	0.572735i	$0.805882\pi$
$62$	2.26344	+	6.96614i	0.287457	+	0.884701i
$63$	−2.42946	+	1.04771i	−0.306084	+	0.132000i
$64$	−4.24233	−	3.08223i	−0.530291	−	0.385279i
$65$	4.04912	−	7.01328i	0.502231	−	0.869890i
$66$	5.07676	+	1.24307i	0.624906	+	0.153011i
$67$	−0.922802	−	1.59834i	−0.112738	−	0.195268i	0.804135	−	0.594446i	$-0.202629\pi$
$67$	−0.922802	−	1.59834i	−0.112738	−	0.195268i	−0.916873	+	0.399178i	$0.869295\pi$
$68$	−2.00690	+	0.893529i	−0.243372	+	0.108356i
$69$	−0.306186	+	0.942343i	−0.0368604	+	0.113445i
$70$	8.47500	+	15.0848i	1.01296	+	1.80298i
$71$	3.33445	−	2.42262i	0.395726	−	0.287512i	−0.372072	−	0.928204i	$-0.621352\pi$
$71$	3.33445	−	2.42262i	0.395726	−	0.287512i	0.767798	+	0.640692i	$0.221352\pi$
$72$	−0.249807	−	2.37676i	−0.0294401	−	0.280104i
$73$	−3.15290	+	3.50165i	−0.369019	+	0.409837i	−0.898843	−	0.438270i	$-0.855591\pi$
$73$	−3.15290	+	3.50165i	−0.369019	+	0.409837i	0.529824	+	0.848108i	$0.322258\pi$
$74$	−4.91623	+	1.04498i	−0.571500	+	0.121476i
$75$	11.1642	−	4.97064i	1.28914	−	0.573960i
$76$	−2.43982			−0.279866
$77$	−5.58981	−	6.76417i	−0.637018	−	0.770849i
$78$	−3.07537			−0.348217
$79$	−1.18499	+	0.527591i	−0.133322	+	0.0593587i	−0.472313	−	0.881431i	$-0.656581\pi$
$79$	−1.18499	+	0.527591i	−0.133322	+	0.0593587i	0.338991	+	0.940789i	$0.389914\pi$
$80$	−19.2128	+	4.08380i	−2.14805	+	0.456583i
$81$	0.669131	−	0.743145i	0.0743478	−	0.0825716i
$82$	−1.72417	−	16.4044i	−0.190403	−	1.81156i
$83$	1.10236	−	0.800908i	0.120999	−	0.0879111i	−0.525640	−	0.850707i	$-0.676174\pi$
$83$	1.10236	−	0.800908i	0.120999	−	0.0879111i	0.646639	+	0.762796i	$0.276174\pi$
$84$	0.652579	−	1.10031i	0.0712022	−	0.120053i
$85$	5.82627	−	17.9314i	0.631948	−	1.94494i
$86$	−5.51483	+	2.45536i	−0.594680	+	0.264769i
$87$	−1.38075	−	2.39152i	−0.148032	−	0.256398i
$88$	7.33650	−	3.00017i	0.782073	−	0.319820i
$89$	−7.79893	+	13.5081i	−0.826685	+	1.43186i	0.0739396	+	0.997263i	$0.476443\pi$
$89$	−7.79893	+	13.5081i	−0.826685	+	1.43186i	−0.900625	+	0.434598i	$0.856891\pi$
$90$	−5.29076	−	3.84396i	−0.557695	−	0.405189i
$91$	4.14119	+	3.08357i	0.434115	+	0.323246i
$92$	−0.148047	−	0.455640i	−0.0154349	−	0.0475038i
$93$	0.485833	+	4.62239i	0.0503785	+	0.479320i
$94$	8.62506	+	3.84013i	0.889607	+	0.396079i
$95$	14.0114	−	15.5612i	1.43754	−	1.59655i
$96$	1.79294	+	1.99126i	0.182991	+	0.203232i
$97$	3.00835	+	2.18569i	0.305451	+	0.221923i	0.729942	−	0.683509i	$-0.239547\pi$
$97$	3.00835	+	2.18569i	0.305451	+	0.221923i	−0.424491	+	0.905432i	$0.639547\pi$
$98$	−10.1801	+	4.24938i	−1.02835	+	0.429252i
$99$	2.98706	+	1.44133i	0.300211	+	0.144859i
$100$	−2.95449	+	5.11733i	−0.295449	+	0.511733i
$101$	1.19986	−	11.4159i	0.119391	−	1.13592i	−0.756695	−	0.653768i	$-0.773187\pi$
$101$	1.19986	−	11.4159i	0.119391	−	1.13592i	0.876085	−	0.482156i	$-0.160146\pi$
$102$	−7.00358	+	1.48866i	−0.693458	+	0.147399i
$103$	−5.84111	−	1.24157i	−0.575542	−	0.122335i	−0.0890605	−	0.996026i	$-0.528386\pi$
$103$	−5.84111	−	1.24157i	−0.575542	−	0.122335i	−0.486481	+	0.873691i	$0.661720\pi$
$104$	−3.77305	+	2.74128i	−0.369978	+	0.268805i
$105$	3.27015	+	10.4810i	0.319134	+	1.02284i
$106$	−4.72530	−	14.5430i	−0.458962	−	1.41254i
$107$	−2.55515	−	2.83778i	−0.247016	−	0.274339i	0.606868	−	0.794803i	$-0.292426\pi$
$107$	−2.55515	−	2.83778i	−0.247016	−	0.274339i	−0.853884	+	0.520464i	$0.825759\pi$
$108$	−0.0505414	+	0.480870i	−0.00486335	+	0.0462717i
$109$	−2.52250	−	4.36909i	−0.241611	−	0.418483i	0.719562	−	0.694428i	$-0.244343\pi$
$109$	−2.52250	−	4.36909i	−0.241611	−	0.418483i	−0.961173	+	0.275945i	$0.911009\pi$
$110$	7.33238	−	20.4129i	0.699115	−	1.94629i
$111$	−3.18929			−0.302714
$112$	−1.16291	−	12.4689i	−0.109885	−	1.17820i
$113$	−4.75887	+	14.6463i	−0.447677	+	1.37781i	0.431844	+	0.901949i	$0.357863\pi$
$113$	−4.75887	+	14.6463i	−0.447677	+	1.37781i	−0.879521	+	0.475860i	$0.842137\pi$
$114$	−7.77825	−	1.65332i	−0.728500	−	0.154847i
$115$	3.75629	+	1.67241i	0.350276	+	0.155953i
$116$	1.21980	+	0.543088i	0.113255	+	0.0504245i
$117$	−1.90884	−	0.405735i	−0.176472	−	0.0375103i
$118$	3.20072	−	9.85080i	0.294650	−	0.906840i
$119$	10.9234	+	5.01768i	1.00135	+	0.459970i
$120$	−9.91739			−0.905330
$121$	−1.81873	+	10.8486i	−0.165339	+	0.986237i
$122$	−5.95613	−	10.3163i	−0.539243	−	0.933996i
$123$	1.09408	−	10.4094i	0.0986494	−	0.938587i
$124$	−1.50375	−	1.67009i	−0.135041	−	0.149978i
$125$	−9.25963	−	28.4982i	−0.828206	−	2.54896i
$126$	2.82607	−	3.06561i	0.251766	−	0.273107i
$127$	−12.6872	+	9.21782i	−1.12581	+	0.817949i	−0.985080	−	0.172099i	$-0.944945\pi$
$127$	−12.6872	+	9.21782i	−1.12581	+	0.817949i	−0.140731	+	0.990048i	$0.544945\pi$
$128$	13.3251	+	2.83235i	1.17779	+	0.250346i
$129$	−3.74691	+	0.796430i	−0.329897	+	0.0701217i
$130$	−1.33401	+	12.6922i	−0.117000	+	1.11318i
$131$	−5.39188	+	9.33900i	−0.471090	+	0.815952i	−0.999453	−	0.0330662i	$-0.989473\pi$
$131$	−5.39188	+	9.33900i	−0.471090	+	0.815952i	0.528363	+	0.849019i	$0.322806\pi$
$132$	−1.57810	+	0.285126i	−0.137356	+	0.0248170i
$133$	8.81621	+	10.0253i	0.764462	+	0.869303i
$134$	2.35304	+	1.70958i	0.203272	+	0.147686i
$135$	−2.77675	−	3.08390i	−0.238985	−	0.265420i
$136$	−7.26547	+	8.06912i	−0.623009	+	0.691922i
$137$	−14.2311	−	6.33611i	−1.21585	−	0.541330i	−0.304320	−	0.952570i	$-0.598429\pi$
$137$	−14.2311	−	6.33611i	−1.21585	−	0.541330i	−0.911527	+	0.411240i	$0.865096\pi$
$138$	−0.163219	−	1.55293i	−0.0138941	−	0.132194i
$139$	5.54456	+	17.0644i	0.470284	+	1.44738i	0.852214	+	0.523193i	$0.175259\pi$
$139$	5.54456	+	17.0644i	0.470284	+	1.44738i	−0.381930	+	0.924191i	$0.624741\pi$
$140$	−4.25796	−	3.17051i	−0.359863	−	0.267957i
$141$	4.84681	+	3.52141i	0.408175	+	0.296557i
$142$	−3.24766	+	5.62511i	−0.272537	+	0.472048i
$143$	−0.478700	−	6.45460i	−0.0400309	−	0.539761i
$144$	2.36662	+	4.09911i	0.197219	+	0.341593i
$145$	−10.4689	+	4.66105i	−0.869394	+	0.387079i
$146$	2.29465	−	7.06219i	0.189906	−	0.584471i
$147$	−6.87927	+	1.29445i	−0.567393	+	0.106765i
$148$	1.24757	−	0.906413i	0.102550	−	0.0745067i
$149$	−0.406831	−	3.87074i	−0.0333289	−	0.317103i	−0.998466	−	0.0553600i	$-0.982369\pi$
$149$	−0.406831	−	3.87074i	−0.0333289	−	0.317103i	0.965138	−	0.261743i	$-0.0842973\pi$
$150$	−12.8868	+	14.3122i	−1.05220	+	1.16859i
$151$	−1.58865	+	0.337678i	−0.129282	+	0.0274798i	−0.272098	−	0.962269i	$-0.587718\pi$
$151$	−1.58865	+	0.337678i	−0.129282	+	0.0274798i	0.142816	+	0.989749i	$0.454384\pi$
$152$	−11.0165	+	4.90488i	−0.893559	+	0.397838i
$153$	−4.54341			−0.367313
$154$	12.3832	+	6.15522i	0.997869	+	0.496002i
$155$	19.2876			1.54922
$156$	0.862000	−	0.383787i	0.0690152	−	0.0307276i
$157$	8.10823	−	1.72346i	0.647107	−	0.137547i	0.127346	−	0.991858i	$-0.459354\pi$
$157$	8.10823	−	1.72346i	0.647107	−	0.137547i	0.519761	+	0.854312i	$0.326021\pi$
$158$	1.36782	−	1.51912i	0.108818	−	0.120855i
$159$	−1.01426	−	9.65000i	−0.0804358	−	0.765295i
$160$	8.99579	−	6.53582i	0.711180	−	0.516702i
$161$	−1.33728	+	2.25477i	−0.105393	+	0.177701i
$162$	−0.486986	+	1.49879i	−0.0382612	+	0.117756i
$163$	−2.35298	+	1.04762i	−0.184300	+	0.0820556i	−0.496812	−	0.867858i	$-0.665496\pi$
$163$	−2.35298	+	1.04762i	−0.184300	+	0.0820556i	0.312512	+	0.949914i	$0.398830\pi$
$164$	2.53044	+	4.38285i	0.197594	+	0.342243i
$165$	7.24418	−	11.7026i	0.563958	−	0.911045i
$166$	−1.07366	+	1.85964i	−0.0833324	+	0.144336i
$167$	10.9144	+	7.92980i	0.844584	+	0.613626i	0.923647	−	0.383243i	$-0.125193\pi$
$167$	10.9144	+	7.92980i	0.844584	+	0.613626i	−0.0790634	+	0.996870i	$0.525193\pi$
$168$	0.734603	−	6.28013i	0.0566759	−	0.484523i
$169$	−2.84040	−	8.74185i	−0.218492	−	0.672450i
$170$	3.10582	+	29.5499i	0.238206	+	2.26638i
$171$	−4.60971	−	2.05238i	−0.352514	−	0.156949i
$172$	1.23935	−	1.37643i	0.0944992	−	0.104952i
$173$	0.339703	+	0.377278i	0.0258271	+	0.0286839i	0.755920	−	0.654664i	$-0.227190\pi$
$173$	0.339703	+	0.377278i	0.0258271	+	0.0286839i	−0.730093	+	0.683348i	$0.760523\pi$
$174$	3.52075	+	2.55797i	0.266907	+	0.193920i
$175$	31.7033	−	6.35121i	2.39654	−	0.480107i
$176$	−10.8573	+	11.3384i	−0.818402	+	0.854661i
$177$	3.28626	−	5.69196i	0.247010	−	0.427834i
$178$	2.56941	−	24.4463i	0.192585	−	1.83233i
$179$	15.0606	−	3.20122i	1.12568	−	0.239270i	0.392796	−	0.919626i	$-0.371508\pi$
$179$	15.0606	−	3.20122i	1.12568	−	0.239270i	0.732882	+	0.680355i	$0.238175\pi$
$180$	1.96266	+	0.417175i	0.146288	+	0.0310944i
$181$	18.9457	−	13.7649i	1.40822	−	1.02313i	0.414646	−	0.909983i	$-0.363905\pi$
$181$	18.9457	−	13.7649i	1.40822	−	1.02313i	0.993578	−	0.113152i	$-0.0360946\pi$
$182$	−7.93849	−	1.78490i	−0.588440	−	0.132305i
$183$	−2.33584	−	7.18897i	−0.172670	−	0.531424i
$184$	−1.58447	−	1.75973i	−0.116809	−	0.129729i
$185$	−1.38342	+	13.1624i	−0.101711	+	0.967719i
$186$	−3.66232	−	6.34332i	−0.268534	−	0.465115i
$187$	−4.21454	−	14.4674i	−0.308198	−	1.05796i
$188$	−2.89675			−0.211267
$189$	2.15854	−	1.52993i	0.157011	−	0.111286i
$190$	−10.1973	+	31.3842i	−0.739792	+	2.27685i
$191$	23.0020	+	4.88923i	1.66437	+	0.353772i	0.941448	−	0.337158i	$-0.109466\pi$
$191$	23.0020	+	4.88923i	1.66437	+	0.353772i	0.722921	+	0.690931i	$0.242799\pi$
$192$	4.79046	+	2.13285i	0.345721	+	0.153925i
$193$	19.7783	+	8.80585i	1.42367	+	0.633859i	0.966767	−	0.255657i	$-0.0822919\pi$
$193$	19.7783	+	8.80585i	1.42367	+	0.633859i	0.456903	+	0.889516i	$0.348959\pi$
$194$	−5.73203	−	1.21838i	−0.411536	−	0.0874746i
$195$	−2.50249	+	7.70188i	−0.179207	+	0.551543i
$196$	2.32311	−	2.46148i	0.165936	−	0.175820i
$197$	−15.2088			−1.08358			−0.541790	−	0.840514i	$-0.682253\pi$
$197$	−15.2088			−1.08358			−0.541790	+	0.840514i	$0.682253\pi$
$198$	−5.22427	−	0.160389i	−0.371273	−	0.0113984i
$199$	−6.60469	−	11.4397i	−0.468194	−	0.810936i	0.531145	−	0.847281i	$-0.321762\pi$
$199$	−6.60469	−	11.4397i	−0.468194	−	0.810936i	−0.999339	+	0.0363450i	$0.988428\pi$
$200$	−3.05284	+	29.0459i	−0.215869	+	2.05385i
$201$	1.23495	+	1.37155i	0.0871066	+	0.0967417i
$202$	5.59000	+	17.2043i	0.393311	+	1.21049i
$203$	−2.17613	−	6.97462i	−0.152734	−	0.489522i
$204$	1.77727	−	1.29126i	0.124434	−	0.0904063i
$205$	−42.4858	−	9.03063i	−2.96733	−	0.630727i
$206$	9.20511	−	1.95661i	0.641351	−	0.136323i
$207$	0.103571	−	0.985410i	0.00719867	−	0.0684908i
$208$	4.61842	−	7.99933i	0.320230	−	0.554654i
$209$	2.25926	−	16.5824i	0.156276	−	1.14703i
$210$	−11.4261	−	12.9931i	−0.788476	−	0.896610i
$211$	9.82946	+	7.14152i	0.676688	+	0.491643i	0.872257	−	0.489047i	$-0.162655\pi$
$211$	9.82946	+	7.14152i	0.676688	+	0.491643i	−0.195569	+	0.980690i	$0.562655\pi$
$212$	3.13933	+	3.48658i	0.215610	+	0.239459i
$213$	−2.75789	+	3.06295i	−0.188968	+	0.209870i
$214$	5.49756	+	2.44767i	0.375805	+	0.167319i
$215$	1.66161	+	15.8092i	0.113321	+	1.07818i
$216$	0.738505	+	2.27288i	0.0502489	+	0.154650i
$217$	−1.42868	+	12.2138i	−0.0969850	+	0.829126i
$218$	6.43209	+	4.67319i	0.435636	+	0.316508i
$219$	2.35597	−	4.08066i	0.159202	−	0.275745i
$220$	0.492197	+	6.63659i	0.0331839	+	0.447439i
$221$	4.43319	+	7.67851i	0.298208	+	0.516512i
$222$	4.59154	−	2.04428i	0.308164	−	0.137203i
$223$	−3.00327	+	9.24310i	−0.201114	+	0.618964i	0.798737	+	0.601680i	$0.205502\pi$
$223$	−3.00327	+	9.24310i	−0.201114	+	0.618964i	−0.999851	+	0.0172836i	$0.994498\pi$
$224$	3.47244	+	6.18066i	0.232012	+	0.412963i
$225$	−9.88683	+	7.18320i	−0.659122	+	0.478880i
$226$	−2.53682	−	24.1363i	−0.168747	−	1.60552i
$227$	−13.1067	+	14.5565i	−0.869925	+	0.966149i	−0.999677	−	0.0253973i	$-0.991915\pi$
$227$	−13.1067	+	14.5565i	−0.869925	+	0.966149i	0.129753	+	0.991546i	$0.458582\pi$
$228$	2.38650	−	0.507266i	0.158050	−	0.0335945i
$229$	−2.97206	+	1.32325i	−0.196399	+	0.0874426i	−0.502580	−	0.864531i	$-0.667616\pi$
$229$	−2.97206	+	1.32325i	−0.196399	+	0.0874426i	0.306180	+	0.951974i	$0.400949\pi$
$230$	−6.47982			−0.427267
$231$	6.87401	+	5.45417i	0.452277	+	0.358858i
$232$	6.59956			0.433282
$233$	26.0359	−	11.5919i	1.70567	−	0.759414i	0.707036	−	0.707178i	$-0.250032\pi$
$233$	26.0359	−	11.5919i	1.70567	−	0.759414i	0.998635	−	0.0522360i	$-0.0166348\pi$
$234$	3.00817	−	0.639406i	0.196650	−	0.0417993i
$235$	16.6355	−	18.4756i	1.08518	−	1.20521i
$236$	0.332184	+	3.16052i	0.0216234	+	0.205733i
$237$	1.04940	−	0.762435i	0.0681660	−	0.0495255i
$238$	−18.9424	−	0.222084i	−1.22785	−	0.0143956i
$239$	0.503891	−	1.55082i	0.0325940	−	0.100314i	−0.933436	−	0.358744i	$-0.883205\pi$
$239$	0.503891	−	1.55082i	0.0325940	−	0.100314i	0.966030	+	0.258430i	$0.0832051\pi$
$240$	17.9439	−	7.98912i	1.15827	−	0.515696i
$241$	−2.73011	−	4.72869i	−0.175862	−	0.304602i	0.764597	−	0.644508i	$-0.222938\pi$
$241$	−2.73011	−	4.72869i	−0.175862	−	0.304602i	−0.940459	+	0.339907i	$0.889605\pi$
$242$	−4.33540	−	16.7842i	−0.278690	−	1.07893i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	2.95686	+	2.14829i	0.189294	+	0.137530i
$245$	2.35825	+	28.9527i	0.150663	+	1.84972i
$246$	5.09716	+	15.6875i	0.324983	+	1.00020i
$247$	1.02930	+	9.79315i	0.0654929	+	0.623123i
$248$	−10.1474	−	4.51790i	−0.644358	−	0.286887i
$249$	−0.911749	+	1.01260i	−0.0577797	+	0.0641709i
$250$	31.5977	+	35.0928i	1.99842	+	2.21947i
$251$	−15.8982	−	11.5507i	−1.00348	−	0.729073i	−0.0406509	−	0.999173i	$-0.512943\pi$
$251$	−15.8982	−	11.5507i	−1.00348	−	0.729073i	−0.962832	+	0.270100i	$0.912943\pi$
$252$	−0.409552	+	1.21194i	−0.0257994	+	0.0763450i
$253$	3.23388	−	0.584287i	0.203312	−	0.0367338i
$254$	12.3570	−	21.4030i	0.775347	−	1.34294i
$255$	−1.97080	+	18.7509i	−0.123416	+	1.17423i
$256$	−10.7409	+	2.28305i	−0.671306	+	0.142690i
$257$	9.78629	+	2.08014i	0.610452	+	0.129756i	0.502756	−	0.864428i	$-0.332319\pi$
$257$	9.78629	+	2.08014i	0.610452	+	0.129756i	0.107696	+	0.994184i	$0.465653\pi$
$258$	4.88382	−	3.54830i	0.304054	−	0.220908i
$259$	−8.23255	−	1.85101i	−0.511546	−	0.115016i
$260$	−1.21000	−	3.72400i	−0.0750411	−	0.230953i
$261$	1.84780	+	2.05219i	0.114376	+	0.127027i
$262$	1.77639	−	16.9012i	0.109746	−	1.04416i
$263$	3.33921	+	5.78367i	0.205904	+	0.356637i	0.950420	−	0.310968i	$-0.100653\pi$
$263$	3.33921	+	5.78367i	0.205904	+	0.356637i	−0.744516	+	0.667604i	$0.767320\pi$
$264$	−6.55241	+	4.45996i	−0.403273	+	0.274491i
$265$	−40.2661			−2.47353
$266$	−19.1185	−	8.78210i	−1.17223	−	0.538465i
$267$	4.82000	−	14.8344i	0.294979	−	0.907854i
$268$	−0.872883	−	0.185537i	−0.0533198	−	0.0113335i
$269$	25.1952	+	11.2176i	1.53618	+	0.683951i	0.988288	−	0.152599i	$-0.0487643\pi$
$269$	25.1952	+	11.2176i	1.53618	+	0.683951i	0.547891	+	0.836550i	$0.315431\pi$
$270$	5.97435	+	2.65995i	0.363587	+	0.161879i
$271$	−4.24166	−	0.901594i	−0.257663	−	0.0547679i	0.0772690	−	0.997010i	$-0.475380\pi$
$271$	−4.24166	−	0.901594i	−0.257663	−	0.0547679i	−0.334932	+	0.942242i	$0.608713\pi$
$272$	6.64544	−	20.4526i	0.402939	−	1.24012i
$273$	−4.69181	−	2.15519i	−0.283961	−	0.130438i
$274$	24.5495			1.48309
$275$	−32.0444	−	24.8190i	−1.93235	−	1.49664i
$276$	0.239544	+	0.414903i	0.0144189	+	0.0249742i
$277$	0.799494	−	7.60667i	0.0480369	−	0.457041i	−0.943893	−	0.330252i	$-0.892866\pi$
$277$	0.799494	−	7.60667i	0.0480369	−	0.457041i	0.991930	−	0.126789i	$-0.0404671\pi$
$278$	−18.9204	−	21.0132i	−1.13477	−	1.26029i
$279$	−1.43627	−	4.42037i	−0.0859870	−	0.264641i
$280$	−25.5998	−	5.75590i	−1.52988	−	0.343981i
$281$	9.49612	−	6.89934i	0.566491	−	0.411580i	−0.267338	−	0.963603i	$-0.586144\pi$
$281$	9.49612	−	6.89934i	0.566491	−	0.411580i	0.833829	+	0.552023i	$0.186144\pi$
$282$	−9.23499	−	1.96296i	−0.549936	−	0.116892i
$283$	7.39881	−	1.57267i	0.439813	−	0.0934852i	0.0173175	−	0.999850i	$-0.494487\pi$
$283$	7.39881	−	1.57267i	0.439813	−	0.0934852i	0.422496	+	0.906365i	$0.361154\pi$
$284$	0.208312	−	1.98196i	0.0123610	−	0.117607i
$285$	−10.4698	+	18.1343i	−0.620180	+	1.07418i
$286$	4.82646	+	8.98567i	0.285395	+	0.531334i
$287$	8.86561	−	26.2350i	0.523321	−	1.54860i
$288$	−2.16777	−	1.57498i	−0.127737	−	0.0928063i
$289$	2.43736	+	2.70697i	0.143374	+	0.159233i
$290$	12.0841	−	13.4208i	0.709604	−	0.788095i
$291$	−3.39704	−	1.51246i	−0.199138	−	0.0886619i
$292$	0.238148	+	2.26583i	0.0139366	+	0.132598i
$293$	4.69184	+	14.4400i	0.274100	+	0.843594i	0.989456	+	0.144834i	$0.0462647\pi$
$293$	4.69184	+	14.4400i	0.274100	+	0.843594i	−0.715356	+	0.698760i	$0.753735\pi$
$294$	9.07418	−	6.27309i	0.529217	−	0.365854i
$295$	−22.0656	−	16.0316i	−1.28471	−	0.933396i
$296$	3.81097	−	6.60079i	0.221508	−	0.383663i
$297$	−3.22146	−	0.788791i	−0.186928	−	0.0457703i
$298$	3.06678	+	5.31182i	0.177654	+	0.307706i
$299$	−1.76643	+	0.786466i	−0.102155	+	0.0454825i
$300$	1.82597	−	5.61977i	0.105423	−	0.324458i
$301$	−10.1342	−	0.118815i	−0.584123	−	0.00684836i
$302$	2.07069	−	1.50444i	0.119155	−	0.0865711i
$303$	1.19986	+	11.4159i	0.0689301	+	0.655827i
$304$	15.9814	−	17.7491i	0.916594	−	1.01798i
$305$	−30.6826	+	6.52178i	−1.75688	+	0.373436i
$306$	6.54103	−	2.91225i	0.373926	−	0.166482i
$307$	−11.8851			−0.678321			−0.339161	−	0.940729i	$-0.610143\pi$
$307$	−11.8851			−0.678321			−0.339161	+	0.940729i	$0.610143\pi$
$308$	−4.23904	−	0.179906i	−0.241542	−	0.0102511i
$309$	5.97160			0.339713
$310$	−27.7679	+	12.3631i	−1.57711	+	0.702175i
$311$	17.3291	−	3.68340i	0.982641	−	0.208867i	0.311540	−	0.950233i	$-0.399155\pi$
$311$	17.3291	−	3.68340i	0.982641	−	0.208867i	0.671101	+	0.741366i	$0.265822\pi$
$312$	3.12065	−	3.46584i	0.176672	−	0.196214i
$313$	−1.36213	−	12.9598i	−0.0769924	−	0.732534i	−0.963116	−	0.269085i	$-0.913279\pi$
$313$	−1.36213	−	12.9598i	−0.0769924	−	0.732534i	0.886124	−	0.463448i	$-0.153388\pi$
$314$	−10.5685	+	7.67846i	−0.596414	+	0.433320i
$315$	−5.37781	−	9.57208i	−0.303005	−	0.539325i
$316$	−0.193812	+	0.596491i	−0.0109028	+	0.0335552i
$317$	−14.9625	+	6.66174i	−0.840379	+	0.374161i	−0.781348	−	0.624095i	$-0.785468\pi$
$317$	−14.9625	+	6.66174i	−0.840379	+	0.374161i	−0.0590307	+	0.998256i	$0.518801\pi$
$318$	7.64569	+	13.2427i	0.428749	+	0.742615i
$319$	−4.82066	+	7.78752i	−0.269905	+	0.436018i
$320$	10.8804	−	18.8453i	0.608231	−	1.05349i
$321$	3.08932	+	2.24453i	0.172429	+	0.125277i
$322$	0.479975	−	4.10331i	0.0267480	−	0.228669i
$323$	7.08449	+	21.8038i	0.394191	+	1.21320i
$324$	−0.0505414	−	0.480870i	−0.00280786	−	0.0267150i
$325$	21.7868	+	9.70011i	1.20851	+	0.538065i
$326$	2.71602	−	3.01645i	0.150427	−	0.167066i
$327$	3.37576	+	3.74916i	0.186680	+	0.207329i
$328$	20.2368	+	14.7029i	1.11739	+	0.811830i
$329$	10.4673	+	11.9029i	0.577083	+	0.656226i
$330$	−2.92808	+	21.4913i	−0.161185	+	1.18306i
$331$	1.64859	−	2.85543i	0.0906145	−	0.156949i	−0.817155	−	0.576417i	$-0.804450\pi$
$331$	1.64859	−	2.85543i	0.0906145	−	0.156949i	0.907770	+	0.419469i	$0.137784\pi$
$332$	0.0688671	−	0.655227i	0.00377957	−	0.0359602i
$333$	3.11960	−	0.663091i	0.170953	−	0.0363372i
$334$	−20.7961	−	4.42034i	−1.13791	−	0.241870i
$335$	6.19616	−	4.50177i	0.338532	−	0.245958i
$336$	3.72993	+	11.9546i	0.203484	+	0.652178i
$337$	9.76850	+	30.0644i	0.532124	+	1.63771i	0.749782	+	0.661685i	$0.230158\pi$
$337$	9.76850	+	30.0644i	0.532124	+	1.63771i	−0.217658	+	0.976025i	$0.569842\pi$
$338$	9.69263	+	10.7648i	0.527210	+	0.585526i
$339$	1.60974	−	15.3157i	0.0874292	−	0.831833i
$340$	−4.55818	−	7.89500i	−0.247202	−	0.428167i
$341$	12.7433	−	8.67386i	0.690089	−	0.469716i
$342$	7.95202			0.429996
$343$	−18.5088	−	0.651240i	−0.999382	−	0.0351636i
$344$	2.82893	−	8.70654i	0.152526	−	0.469425i
$345$	−4.02192	−	0.854886i	−0.216533	−	0.0460255i
$346$	−0.730890	−	0.325413i	−0.0392929	−	0.0174943i
$347$	−30.6627	−	13.6519i	−1.64606	−	0.732873i	−0.646512	−	0.762904i	$-0.723773\pi$
$347$	−30.6627	−	13.6519i	−1.64606	−	0.732873i	−0.999549	+	0.0300308i	$0.990439\pi$
$348$	−1.30605	−	0.277611i	−0.0700119	−	0.0148815i
$349$	3.38656	−	10.4228i	0.181279	−	0.557918i	−0.818586	−	0.574384i	$-0.805242\pi$
$349$	3.38656	−	10.4228i	0.181279	−	0.557918i	0.999864	+	0.0164660i	$0.00524152\pi$
$350$	−41.5713	+	29.4649i	−2.22208	+	1.57497i
$351$	1.95148			0.104162
$352$	3.00428	−	8.36372i	0.160129	−	0.445788i
$353$	15.1279	+	26.2023i	0.805177	+	1.39461i	0.916172	+	0.400786i	$0.131263\pi$
$353$	15.1279	+	26.2023i	0.805177	+	1.39461i	−0.110995	+	0.993821i	$0.535404\pi$
$354$	−1.08268	+	10.3010i	−0.0575438	+	0.547492i
$355$	11.4447	+	12.7106i	0.607421	+	0.674609i
$356$	2.33056	+	7.17273i	0.123520	+	0.380154i
$357$	−11.7279	−	2.63692i	−0.620709	−	0.139561i
$358$	−19.6303	+	14.2623i	−1.03750	+	0.753785i
$359$	−19.7846	−	4.20534i	−1.04419	−	0.221949i	−0.346277	−	0.938132i	$-0.612554\pi$
$359$	−19.7846	−	4.20534i	−1.04419	−	0.221949i	−0.697913	+	0.716183i	$0.745888\pi$
$360$	9.70067	−	2.06194i	0.511270	−	0.108674i
$361$	−0.675434	+	6.42633i	−0.0355492	+	0.338228i
$362$	−18.4526	+	31.9608i	−0.969846	+	1.67982i
$363$	−0.476562	−	10.9897i	−0.0250130	−	0.576808i
$364$	2.44783	−	0.490382i	0.128301	−	0.0257030i
$365$	−15.8192	−	11.4933i	−0.828013	−	0.601587i
$366$	7.97086	+	8.85254i	0.416644	+	0.462729i
$367$	1.57767	−	1.75218i	0.0823537	−	0.0914631i	−0.700560	−	0.713594i	$-0.747066\pi$
$367$	1.57767	−	1.75218i	0.0823537	−	0.0914631i	0.782913	+	0.622131i	$0.213733\pi$
$368$	4.28442	+	1.90755i	0.223341	+	0.0994378i
$369$	1.09408	+	10.4094i	0.0569553	+	0.541893i
$370$	−6.44521	−	19.8363i	−0.335070	−	1.03124i
$371$	2.98260	−	25.4983i	0.154849	−	1.32381i
$372$	1.81812	+	1.32094i	0.0942653	+	0.0684877i
$373$	8.05587	−	13.9532i	0.417117	−	0.722468i	−0.578531	−	0.815660i	$-0.696374\pi$
$373$	8.05587	−	13.9532i	0.417117	−	0.722468i	0.995648	+	0.0931924i	$0.0297072\pi$
$374$	15.3409	+	18.1269i	0.793261	+	0.937319i
$375$	14.9824	+	25.9503i	0.773688	+	1.34007i
$376$	−13.0797	+	5.82348i	−0.674537	+	0.300323i
$377$	1.66529	−	5.12524i	0.0857669	−	0.263963i
$378$	−2.12693	+	3.58619i	−0.109398	+	0.184454i
$379$	−22.4027	+	16.2765i	−1.15075	+	0.836069i	−0.988581	−	0.150694i	$-0.951849\pi$
$379$	−22.4027	+	16.2765i	−1.15075	+	0.836069i	−0.162170	+	0.986763i	$0.551849\pi$
$380$	−1.05832	−	10.0693i	−0.0542908	−	0.516543i
$381$	10.4935	−	11.6542i	0.537598	−	0.597063i
$382$	−36.2493	+	7.70503i	−1.85468	+	0.394224i
$383$	13.9016	−	6.18940i	0.710340	−	0.316264i	−0.0195688	−	0.999809i	$-0.506229\pi$
$383$	13.9016	−	6.18940i	0.710340	−	0.316264i	0.729908	+	0.683545i	$0.239563\pi$
$384$	−13.6228			−0.695187
$385$	25.4915	−	26.0036i	1.29916	−	1.32527i
$386$	−34.1186			−1.73659
$387$	3.49944	−	1.55805i	0.177887	−	0.0792002i
$388$	1.75868	−	0.373820i	0.0892836	−	0.0189778i
$389$	−3.88654	+	4.31644i	−0.197055	+	0.218852i	−0.833572	−	0.552411i	$-0.813708\pi$
$389$	−3.88654	+	4.31644i	−0.197055	+	0.218852i	0.636517	+	0.771263i	$0.280375\pi$
$390$	−1.33401	−	12.6922i	−0.0675502	−	0.642697i
$391$	−3.64202	+	2.64608i	−0.184185	+	0.133818i
$392$	5.54113	−	15.7846i	0.279869	−	0.797243i
$393$	3.33236	−	10.2560i	0.168095	−	0.517345i
$394$	21.8957	−	9.74858i	1.10309	−	0.491126i
$395$	−2.69142	−	4.66167i	−0.135420	−	0.234554i
$396$	1.48433	−	0.607000i	0.0745905	−	0.0305029i
$397$	10.5158	−	18.2139i	0.527772	−	0.914127i	−0.471704	−	0.881757i	$-0.656361\pi$
$397$	10.5158	−	18.2139i	0.527772	−	0.914127i	0.999476	−	0.0323706i	$-0.0103057\pi$
$398$	16.8412	+	12.2359i	0.844174	+	0.613329i
$399$	−10.7079	−	7.97322i	−0.536067	−	0.399160i
$400$	−17.8748	−	55.0129i	−0.893739	−	2.75065i
$401$	0.0334066	+	0.317843i	0.00166825	+	0.0158723i	0.995324	−	0.0965890i	$-0.0307932\pi$
$401$	0.0334066	+	0.317843i	0.00166825	+	0.0158723i	−0.993656	+	0.112461i	$0.964127\pi$
$402$	−2.65706	−	1.18300i	−0.132522	−	0.0590028i
$403$	−6.06914	+	6.74047i	−0.302326	+	0.335767i
$404$	−3.71381	−	4.12461i	−0.184769	−	0.205207i
$405$	3.35725	+	2.43919i	0.166823	+	0.121204i
$406$	7.60354	+	8.64631i	0.377357	+	0.429109i
$407$	5.00525	+	9.31852i	0.248101	+	0.461902i
$408$	5.42904	−	9.40337i	0.268777	−	0.465536i
$409$	1.02405	−	9.74319i	0.0506360	−	0.481770i	−0.939590	−	0.342301i	$-0.888794\pi$
$409$	1.02405	−	9.74319i	0.0506360	−	0.481770i	0.990226	−	0.139469i	$-0.0445395\pi$
$410$	66.9541	−	14.2315i	3.30663	−	0.702845i
$411$	15.2375	+	3.23883i	0.751610	+	0.159760i
$412$	−2.33594	+	1.69716i	−0.115084	+	0.0836131i
$413$	11.7864	−	12.7854i	0.579969	−	0.629130i
$414$	0.482524	+	1.48506i	0.0237148	+	0.0729865i
$415$	3.78357	+	4.20208i	0.185728	+	0.206272i
$416$	−0.546580	+	5.20036i	−0.0267983	+	0.254969i
$417$	−8.97129	−	15.5387i	−0.439326	−	0.760935i
$418$	7.37643	+	25.3213i	0.360793	+	1.23851i
$419$	−24.4796			−1.19591			−0.597953	−	0.801531i	$-0.704019\pi$
$419$	−24.4796			−1.19591			−0.597953	+	0.801531i	$0.704019\pi$
$420$	4.82410	+	2.21595i	0.235392	+	0.108127i
$421$	−2.19524	+	6.75624i	−0.106989	+	0.329279i	−0.990192	−	0.139712i	$-0.955382\pi$
$421$	−2.19524	+	6.75624i	−0.106989	+	0.329279i	0.883203	+	0.468991i	$0.155382\pi$
$422$	−18.7288	−	3.98093i	−0.911704	−	0.193789i
$423$	−5.47304	−	2.43675i	−0.266108	−	0.118479i
$424$	21.1843	+	9.43186i	1.02880	+	0.458052i
$425$	54.3107	+	11.5441i	2.63446	+	0.559971i
$426$	2.00716	−	6.17741i	0.0972473	−	0.299296i
$427$	−1.85716	−	19.9126i	−0.0898741	−	0.963640i
$428$	−1.84637			−0.0892477
$429$	1.81023	+	6.21402i	0.0873985	+	0.300016i
$430$	−12.5256	−	21.6950i	−0.604038	−	1.04623i
$431$	0.802324	−	7.63360i	0.0386466	−	0.367698i	−0.958058	−	0.286576i	$-0.907483\pi$
$431$	0.802324	−	7.63360i	0.0386466	−	0.367698i	0.996704	−	0.0811220i	$-0.0258504\pi$
$432$	−3.16716	−	3.51749i	−0.152380	−	0.169235i
$433$	1.06654	+	3.28247i	0.0512547	+	0.157746i	0.973408	−	0.229080i	$-0.0735716\pi$
$433$	1.06654	+	3.28247i	0.0512547	+	0.157746i	−0.922153	+	0.386825i	$0.873572\pi$
$434$	−5.77201	−	18.4996i	−0.277065	−	0.888010i
$435$	9.27103	−	6.73580i	0.444512	−	0.322957i
$436$	−2.38604	−	0.507169i	−0.114271	−	0.0242890i
$437$	−4.89048	+	1.03950i	−0.233943	+	0.0497262i
$438$	−0.776190	+	7.38495i	−0.0370878	+	0.352867i
$439$	−15.7554	+	27.2892i	−0.751965	+	1.30244i	0.194905	+	0.980822i	$0.437560\pi$
$439$	−15.7554	+	27.2892i	−0.751965	+	1.30244i	−0.946869	+	0.321619i	$0.895773\pi$
$440$	15.5643	+	28.9768i	0.741997	+	1.38141i
$441$	6.45981	−	2.69645i	0.307610	−	0.128402i
$442$	−11.3041	−	8.21294i	−0.537683	−	0.390650i
$443$	−6.53109	−	7.25351i	−0.310301	−	0.344625i	0.567741	−	0.823207i	$-0.307817\pi$
$443$	−6.53109	−	7.25351i	−0.310301	−	0.344625i	−0.878043	+	0.478582i	$0.841151\pi$
$444$	−1.03185	+	1.14599i	−0.0489696	+	0.0543863i
$445$	−59.1319	−	26.3272i	−2.80312	−	1.24803i
$446$	−1.60096	−	15.2321i	−0.0758075	−	0.721260i
$447$	1.20271	+	3.70157i	0.0568863	+	0.175078i
$448$	11.1278	+	8.28584i	0.525738	+	0.391469i
$449$	−13.4686	−	9.78552i	−0.635623	−	0.461807i	0.222720	−	0.974882i	$-0.428506\pi$
$449$	−13.4686	−	9.78552i	−0.635623	−	0.461807i	−0.858344	+	0.513075i	$0.828506\pi$
$450$	9.62948	−	16.6788i	0.453938	−	0.786244i
$451$	−32.1315	+	13.1398i	−1.51301	+	0.618728i
$452$	3.72310	+	6.44860i	0.175120	+	0.303317i
$453$	1.48373	−	0.660598i	0.0697116	−	0.0310376i
$454$	9.53893	−	29.3578i	0.447684	−	1.37783i
$455$	−10.9298	+	18.4285i	−0.512395	+	0.863943i
$456$	9.75601	−	7.08816i	0.456867	−	0.331933i
$457$	1.33196	+	12.6728i	0.0623067	+	0.592809i	0.980479	+	0.196626i	$0.0629985\pi$
$457$	1.33196	+	12.6728i	0.0623067	+	0.592809i	−0.918172	+	0.396182i	$0.870335\pi$
$458$	3.43062	−	3.81009i	0.160302	−	0.178034i
$459$	4.44413	−	0.944628i	0.207434	−	0.0440915i
$460$	1.81624	−	0.808641i	0.0846825	−	0.0377031i
$461$	5.21592			0.242929			0.121465	−	0.992596i	$-0.461241\pi$
$461$	5.21592			0.242929			0.121465	+	0.992596i	$0.461241\pi$
$462$	−13.3924	−	3.44610i	−0.623069	−	0.160327i
$463$	−10.6551			−0.495186			−0.247593	−	0.968864i	$-0.579640\pi$
$463$	−10.6551			−0.495186			−0.247593	+	0.968864i	$0.579640\pi$
$464$	−11.9408	+	5.31638i	−0.554337	+	0.246807i
$465$	−18.8662	+	4.01012i	−0.874897	+	0.185965i
$466$	−30.0530	+	33.3772i	−1.39218	+	1.54617i
$467$	3.10324	+	29.5253i	0.143601	+	1.36627i	0.794573	+	0.607169i	$0.207695\pi$
$467$	3.10324	+	29.5253i	0.143601	+	1.36627i	−0.650972	+	0.759102i	$0.725639\pi$
$468$	−0.763369	+	0.554620i	−0.0352868	+	0.0256373i
$469$	2.39176	+	4.25714i	0.110441	+	0.196576i
$470$	−12.1071	+	37.2619i	−0.558460	+	1.71876i
$471$	−7.57272	+	3.37159i	−0.348932	+	0.155355i
$472$	7.85367	+	13.6029i	0.361494	+	0.626126i
$473$	8.20739	+	9.69786i	0.377376	+	0.445908i
$474$	−1.02209	+	1.77031i	−0.0469460	+	0.0813129i
$475$	49.8885	+	36.2461i	2.28904	+	1.66309i
$476$	5.33710	−	2.30164i	0.244626	−	0.105496i
$477$	2.99844	+	9.22825i	0.137289	+	0.422533i
$478$	0.268610	+	2.55566i	0.0122859	+	0.116893i
$479$	−20.1742	−	8.98211i	−0.921780	−	0.410403i	−0.109711	−	0.993964i	$-0.534992\pi$
$479$	−20.1742	−	8.98211i	−0.921780	−	0.410403i	−0.812070	+	0.583560i	$0.801659\pi$
$480$	−7.44034	+	8.26333i	−0.339603	+	0.377168i
$481$	−4.16456	−	4.62521i	−0.189888	−	0.210892i
$482$	6.96148	+	5.05781i	0.317087	+	0.230377i
$483$	0.839265	−	2.48354i	0.0381879	−	0.113005i
$484$	3.30974	+	4.16344i	0.150443	+	0.189247i
$485$	−7.71555	+	13.3637i	−0.350345	+	0.606815i
$486$	0.164728	−	1.56729i	0.00747223	−	0.0710935i
$487$	31.7266	−	6.74370i	1.43767	−	0.305586i	0.577833	−	0.816155i	$-0.303898\pi$
$487$	31.7266	−	6.74370i	1.43767	−	0.305586i	0.859837	+	0.510569i	$0.170565\pi$
$488$	17.6700	+	3.75587i	0.799882	+	0.170020i
$489$	2.08375	−	1.51394i	0.0942306	−	0.0684626i
$490$	−21.9533	−	40.1708i	−0.991749	−	1.81473i
$491$	−1.64832	−	5.07301i	−0.0743877	−	0.228942i	0.906949	−	0.421241i	$-0.138405\pi$
$491$	−1.64832	−	5.07301i	−0.0743877	−	0.228942i	−0.981336	+	0.192300i	$0.938405\pi$
$492$	−3.38639	−	3.76096i	−0.152670	−	0.169557i
$493$	1.31148	−	12.4779i	0.0590659	−	0.561975i
$494$	−7.75911	−	13.4392i	−0.349099	−	0.604657i
$495$	−4.65277	+	12.9530i	−0.209126	+	0.582194i
$496$	21.9994			0.987804
$497$	−8.89666	+	6.30578i	−0.399070	+	0.282853i
$498$	0.663560	−	2.04223i	0.0297348	−	0.0915144i
$499$	36.5148	+	7.76145i	1.63462	+	0.347450i	0.931535	−	0.363651i	$-0.118470\pi$
$499$	36.5148	+	7.76145i	1.63462	+	0.347450i	0.703090	+	0.711101i	$0.251803\pi$
$500$	−13.2359	−	5.89302i	−0.591929	−	0.263544i
$501$	−12.3246	−	5.48727i	−0.550623	−	0.245153i
$502$	30.2920	+	6.43876i	1.35200	+	0.287376i
$503$	−1.78265	+	5.48642i	−0.0794843	+	0.244627i	−0.982901	−	0.184137i	$-0.941051\pi$
$503$	−1.78265	+	5.48642i	−0.0794843	+	0.244627i	0.903416	+	0.428764i	$0.141051\pi$
$504$	0.587163	+	6.29563i	0.0261543	+	0.280430i
$505$	47.6346			2.11971
$506$	−4.28121	+	2.91405i	−0.190323	+	0.129545i
$507$	4.59586	+	7.96027i	0.204109	+	0.353528i
$508$	−0.792606	+	7.54114i	−0.0351662	+	0.334584i
$509$	2.23691	+	2.48434i	0.0991494	+	0.110117i	0.790677	−	0.612233i	$-0.209729\pi$
$509$	2.23691	+	2.48434i	0.0991494	+	0.110117i	−0.691528	+	0.722350i	$0.743062\pi$
$510$	−9.18173	−	28.2585i	−0.406574	−	1.25131i
$511$	8.44983	−	9.16607i	0.373799	−	0.405483i
$512$	−8.04222	+	5.84302i	−0.355419	+	0.258227i
$513$	4.93569	+	1.04911i	0.217916	+	0.0463195i
$514$	−15.4224	+	3.27813i	−0.680253	+	0.144592i
$515$	2.59031	−	24.6452i	0.114143	−	1.08600i
$516$	−0.926087	+	1.60403i	−0.0407687	+	0.0706135i
$517$	2.68238	−	19.6880i	0.117971	−	0.865876i
$518$	13.0386	−	2.61207i	0.572885	−	0.114768i
$519$	−0.410720	−	0.298405i	−0.0180286	−	0.0130985i
$520$	−12.9501	−	14.3825i	−0.567898	−	0.630715i
$521$	6.50638	−	7.22607i	0.285050	−	0.316580i	−0.583566	−	0.812065i	$-0.698343\pi$
$521$	6.50638	−	7.22607i	0.285050	−	0.316580i	0.868616	+	0.495486i	$0.165010\pi$
$522$	−3.97565	−	1.77007i	−0.174009	−	0.0774739i
$523$	−1.19187	−	11.3399i	−0.0521169	−	0.495859i	−0.989181	−	0.146701i	$-0.953134\pi$
$523$	−1.19187	−	11.3399i	−0.0521169	−	0.495859i	0.937064	−	0.349158i	$-0.113532\pi$
$524$	1.61126	+	4.95895i	0.0703882	+	0.216633i
$525$	−29.6900	+	12.8039i	−1.29578	+	0.558808i
$526$	−8.51461	−	6.18622i	−0.371254	−	0.269732i
$527$	−10.5586	+	18.2880i	−0.459938	+	0.796636i
$528$	8.26269	−	13.3480i	0.359588	−	0.580895i
$529$	11.0091	+	19.0684i	0.478657	+	0.829059i
$530$	57.9700	−	25.8099i	2.51806	−	1.12111i
$531$	−2.03102	+	6.25083i	−0.0881387	+	0.271263i
$532$	6.45470	+	0.0756760i	0.279847	+	0.00328097i
$533$	16.5247	−	12.0059i	0.715765	−	0.520034i
$534$	2.56941	+	24.4463i	0.111189	+	1.05789i
$535$	10.6034	−	11.7762i	0.458423	−	0.509130i
$536$	−4.31433	+	0.917039i	−0.186351	+	0.0396101i
$537$	−14.0659	+	6.26253i	−0.606987	+	0.270248i
$538$	−43.4632			−1.87383
$539$	14.5784	+	18.0685i	0.627937	+	0.778264i
$540$	−2.00650			−0.0863461
$541$	10.9349	−	4.86851i	0.470126	−	0.209314i	−0.157979	−	0.987443i	$-0.550498\pi$
$541$	10.9349	−	4.86851i	0.470126	−	0.209314i	0.628105	+	0.778129i	$0.283831\pi$
$542$	6.68452	−	1.42084i	0.287125	−	0.0610302i
$543$	−15.6698	+	17.4031i	−0.672457	+	0.746839i
$544$	1.27254	+	12.1074i	0.0545597	+	0.519101i
$545$	16.9373	−	12.3057i	0.725515	−	0.527118i
$546$	8.13611	+	0.0953891i	0.348193	+	0.00408228i
$547$	0.385883	−	1.18762i	0.0164991	−	0.0507791i	−0.942468	−	0.334296i	$-0.891501\pi$
$547$	0.385883	−	1.18762i	0.0164991	−	0.0507791i	0.958967	+	0.283517i	$0.0915013\pi$
$548$	−6.88101	+	3.06363i	−0.293942	+	0.130872i
$549$	3.77947	+	6.54623i	0.161304	+	0.279386i
$550$	62.0420	+	15.1913i	2.64548	+	0.647760i
$551$	6.96719	−	12.0675i	0.296812	−	0.514094i
$552$	1.91572	+	1.39185i	0.0815383	+	0.0592410i
$553$	3.15134	−	1.35902i	0.134008	−	0.0577916i
$554$	3.72475	+	11.4636i	0.158249	+	0.487041i
$555$	−1.38342	−	13.1624i	−0.0587231	−	0.558713i
$556$	7.92553	+	3.52867i	0.336117	+	0.149649i
$557$	0.905939	−	1.00615i	0.0383859	−	0.0426318i	−0.723646	−	0.690171i	$-0.757535\pi$
$557$	0.905939	−	1.00615i	0.0383859	−	0.0426318i	0.762032	+	0.647539i	$0.224202\pi$
$558$	4.90114	+	5.44327i	0.207482	+	0.230432i
$559$	−6.04770	−	4.39391i	−0.255790	−	0.185843i
$560$	50.9554	−	10.2081i	2.15326	−	0.431369i
$561$	7.13039	+	13.2750i	0.301045	+	0.560471i
$562$	−9.24895	+	16.0197i	−0.390143	+	0.675748i
$563$	−2.73488	+	26.0207i	−0.115262	+	1.09664i	0.772079	+	0.635526i	$0.219217\pi$
$563$	−2.73488	+	26.0207i	−0.115262	+	1.09664i	−0.887341	+	0.461114i	$0.847450\pi$
$564$	2.83345	−	0.602269i	0.119310	−	0.0253601i
$565$	−62.5105	−	13.2870i	−2.62984	−	0.558989i
$566$	−9.64381	+	7.00664i	−0.405360	+	0.294511i
$567$	−1.79328	+	1.94529i	−0.0753108	+	0.0816944i
$568$	−3.04382	−	9.36793i	−0.127716	−	0.393070i
$569$	7.16986	+	7.96294i	0.300576	+	0.333824i	0.874446	−	0.485123i	$-0.161225\pi$
$569$	7.16986	+	7.96294i	0.300576	+	0.333824i	−0.573870	+	0.818947i	$0.694558\pi$
$570$	3.44936	−	32.8185i	0.144478	−	1.37461i
$571$	−0.748830	−	1.29701i	−0.0313376	−	0.0542783i	0.849931	−	0.526894i	$-0.176643\pi$
$571$	−0.748830	−	1.29701i	−0.0313376	−	0.0542783i	−0.881269	+	0.472615i	$0.843310\pi$
$572$	−2.47417	−	1.91629i	−0.103450	−	0.0801243i
$573$	−23.5159			−0.982391
$574$	4.05260	+	43.4525i	0.169152	+	1.81367i
$575$	−3.74183	+	11.5162i	−0.156045	+	0.480258i
$576$	−5.12922	−	1.09025i	−0.213717	−	0.0454270i
$577$	23.8569	+	10.6218i	0.993177	+	0.442191i	0.837985	−	0.545694i	$-0.183734\pi$
$577$	23.8569	+	10.6218i	0.993177	+	0.442191i	0.155192	+	0.987884i	$0.450400\pi$
$578$	−5.24413	−	2.33484i	−0.218127	−	0.0971164i
$579$	−21.1769	−	4.50129i	−0.880082	−	0.187067i
$580$	−1.71225	+	5.26975i	−0.0710971	+	0.218814i
$581$	−2.94120	+	2.08467i	−0.122022	+	0.0864866i
$582$	5.86008			0.242908
$583$	−26.6038	+	18.1081i	−1.10182	+	0.749961i
$584$	5.63041	+	9.75216i	0.232988	+	0.403547i
$585$	0.846496	−	8.05388i	0.0349983	−	0.332987i
$586$	−16.0105	−	17.7815i	−0.661389	−	0.734547i
$587$	−6.81855	−	20.9853i	−0.281432	−	0.866158i	−0.987446	−	0.157960i	$-0.949508\pi$
$587$	−6.81855	−	20.9853i	−0.281432	−	0.866158i	0.706014	−	0.708198i	$-0.250492\pi$
$588$	−1.76057	+	2.89069i	−0.0726047	+	0.119210i
$589$	−18.9738	+	13.7853i	−0.781801	+	0.568012i
$590$	42.0432	+	8.93657i	1.73089	+	0.367913i
$591$	14.8764	−	3.16208i	0.611935	−	0.130071i
$592$	−1.57793	+	15.0130i	−0.0648526	+	0.617031i
$593$	−5.52727	+	9.57352i	−0.226978	+	0.393137i	−0.956911	−	0.290381i	$-0.906218\pi$
$593$	−5.52727	+	9.57352i	−0.226978	+	0.393137i	0.729933	+	0.683519i	$0.239551\pi$
$594$	5.14345	−	0.929302i	0.211038	−	0.0381297i
$595$	−15.9700	+	47.2581i	−0.654706	+	1.93739i
$596$	−1.52247	−	1.10614i	−0.0623630	−	0.0453094i
$597$	8.83880	+	9.81648i	0.361748	+	0.401762i
$598$	2.03897	−	2.26451i	0.0833798	−	0.0926026i
$599$	−2.18297	−	0.971919i	−0.0891936	−	0.0397115i	0.361655	−	0.932312i	$-0.382212\pi$
$599$	−2.18297	−	0.971919i	−0.0891936	−	0.0397115i	−0.450848	+	0.892600i	$0.648879\pi$
$600$	−3.05284	−	29.0459i	−0.124632	−	1.18579i
$601$	5.39235	+	16.5959i	0.219959	+	0.676963i	0.998764	+	0.0496976i	$0.0158257\pi$
$601$	5.39235	+	16.5959i	0.219959	+	0.676963i	−0.778806	+	0.627265i	$0.784174\pi$
$602$	14.6660	−	6.32478i	0.597743	−	0.257779i
$603$	−1.49312	−	1.08482i	−0.0608047	−	0.0441772i
$604$	−0.392651	+	0.680092i	−0.0159768	+	0.0276725i
$605$	−45.5618	−	2.80021i	−1.85235	−	0.113845i
$606$	−9.04481	−	15.6661i	−0.367420	−	0.636391i
$607$	44.2709	−	19.7107i	1.79690	−	0.800031i	0.824812	−	0.565406i	$-0.191281\pi$
$607$	44.2709	−	19.7107i	1.79690	−	0.800031i	0.972086	−	0.234624i	$-0.0753860\pi$
$608$	−4.17813	+	12.8589i	−0.169445	+	0.521499i
$609$	3.57868	+	6.36977i	0.145016	+	0.258116i
$610$	39.9925	−	29.0562i	1.61925	−	1.17645i
$611$	1.22207	+	11.6272i	0.0494398	+	0.470388i
$612$	−1.46996	+	1.63256i	−0.0594197	+	0.0659922i
$613$	−4.85729	+	1.03245i	−0.196184	+	0.0417002i	−0.304956	−	0.952367i	$-0.598642\pi$
$613$	−4.85729	+	1.03245i	−0.196184	+	0.0417002i	0.108772	+	0.994067i	$0.465308\pi$
$614$	17.1107	−	7.61818i	0.690533	−	0.307445i
$615$	43.4349			1.75147
$616$	−19.5023	+	7.70961i	−0.785769	+	0.310629i
$617$	−22.2393			−0.895322			−0.447661	−	0.894203i	$-0.647743\pi$
$617$	−22.2393			−0.895322			−0.447661	+	0.894203i	$0.647743\pi$
$618$	−8.59716	+	3.82770i	−0.345828	+	0.153973i
$619$	28.6331	−	6.08616i	1.15086	−	0.244623i	0.407303	−	0.913293i	$-0.366469\pi$
$619$	28.6331	−	6.08616i	1.15086	−	0.244623i	0.743560	+	0.668670i	$0.233136\pi$
$620$	6.24026	−	6.93052i	0.250615	−	0.278336i
$621$	0.103571	+	0.985410i	0.00415615	+	0.0395432i
$622$	−22.5872	+	16.4105i	−0.905663	+	0.658003i
$623$	21.0516	−	35.4948i	0.843414	−	1.42207i
$624$	−2.85434	+	8.78475i	−0.114265	+	0.351672i
$625$	57.7760	−	25.7236i	2.31104	−	1.02894i
$626$	10.2681	+	17.7848i	0.410395	+	0.710825i
$627$	1.23778	+	16.6897i	0.0494321	+	0.666523i
$628$	2.00403	−	3.47109i	0.0799696	−	0.138511i
$629$	−11.7229	−	8.51716i	−0.467421	−	0.339602i
$630$	13.8778	+	10.3336i	0.552906	+	0.411699i
$631$	10.5313	+	32.4119i	0.419243	+	1.29030i	0.908401	+	0.418101i	$0.137304\pi$
$631$	10.5313	+	32.4119i	0.419243	+	1.29030i	−0.489158	+	0.872195i	$0.662696\pi$
$632$	0.324033	+	3.08297i	0.0128894	+	0.122634i
$633$	−11.0995	−	4.94180i	−0.441164	−	0.196419i
$634$	17.2711	−	19.1815i	0.685922	−	0.761793i
$635$	−43.5459	−	48.3626i	−1.72806	−	1.91921i
$636$	−3.79563	−	2.75769i	−0.150507	−	0.109349i
$637$	−10.8602	−	8.28625i	−0.430296	−	0.328313i
$638$	1.94850	−	14.3015i	0.0771417	−	0.566200i
$639$	2.06080	−	3.56941i	0.0815241	−	0.141204i
$640$	−5.90920	+	56.2222i	−0.233581	+	2.22238i
$641$	−27.6062	+	5.86788i	−1.09038	+	0.231767i	−0.717812	−	0.696237i	$-0.754856\pi$
$641$	−27.6062	+	5.86788i	−1.09038	+	0.231767i	−0.372568	+	0.928005i	$0.621523\pi$
$642$	−5.88632	−	1.25118i	−0.232315	−	0.0493800i
$643$	−4.28751	+	3.11506i	−0.169083	+	0.122846i	−0.669109	−	0.743165i	$-0.733324\pi$
$643$	−4.28751	+	3.11506i	−0.169083	+	0.122846i	0.500026	+	0.866011i	$0.333324\pi$
$644$	0.377535	+	1.21002i	0.0148770	+	0.0476815i
$645$	−4.91222	−	15.1182i	−0.193418	−	0.595280i
$646$	−24.1752	−	26.8493i	−0.951162	−	1.05637i
$647$	−2.41816	+	23.0072i	−0.0950675	+	0.904507i	0.838209	+	0.545349i	$0.183603\pi$
$647$	−2.41816	+	23.0072i	−0.0950675	+	0.904507i	−0.933277	+	0.359158i	$0.883064\pi$
$648$	−1.19493	−	2.06967i	−0.0469411	−	0.0813044i
$649$	−21.7883	−	0.668918i	−0.855266	−	0.0262573i
$650$	−37.5835			−1.47415
$651$	−1.14193	−	12.2439i	−0.0447558	−	0.479877i
$652$	−0.384844	+	1.18443i	−0.0150716	+	0.0463857i
$653$	5.03855	+	1.07098i	0.197174	+	0.0419106i	0.305440	−	0.952211i	$-0.401197\pi$
$653$	5.03855	+	1.07098i	0.197174	+	0.0419106i	−0.108266	+	0.994122i	$0.534530\pi$
$654$	−7.26314	−	3.23376i	−0.284011	−	0.126450i
$655$	−40.8815	−	18.2016i	−1.59737	−	0.711196i
$656$	−48.4592	−	10.3003i	−1.89201	−	0.402160i
$657$	−1.45607	+	4.48132i	−0.0568067	+	0.174833i
$658$	−22.6991	−	10.4268i	−0.884903	−	0.406481i
$659$	−3.97856			−0.154983			−0.0774913	−	0.996993i	$-0.524691\pi$
$659$	−3.97856			−0.154983			−0.0774913	+	0.996993i	$0.524691\pi$
$660$	−1.86127	−	6.38923i	−0.0724497	−	0.248700i
$661$	−9.08125	−	15.7292i	−0.353220	−	0.611794i	0.633592	−	0.773667i	$-0.281580\pi$
$661$	−9.08125	−	15.7292i	−0.353220	−	0.611794i	−0.986812	+	0.161873i	$0.948246\pi$
$662$	−0.543138	+	5.16761i	−0.0211096	+	0.200845i
$663$	−5.93276	−	6.58900i	−0.230409	−	0.255896i
$664$	−1.00628	−	3.09700i	−0.0390511	−	0.120187i
$665$	−37.5508	+	40.7337i	−1.45616	+	1.57959i
$666$	−4.06617	+	2.95425i	−0.157561	+	0.114475i
$667$	2.67640	+	0.568886i	0.103631	+	0.0220274i
$668$	6.38059	−	1.35624i	0.246872	−	0.0524744i
$669$	1.01589	−	9.66553i	0.0392765	−	0.373691i
$670$	−6.03488	+	10.4527i	−0.233148	+	0.403824i
$671$	−17.3390	+	18.1072i	−0.669365	+	0.699021i
$672$	−4.68159	−	5.32364i	−0.180596	−	0.205364i
$673$	−8.98748	−	6.52978i	−0.346442	−	0.251705i	0.400933	−	0.916107i	$-0.368686\pi$
$673$	−8.98748	−	6.52978i	−0.346442	−	0.251705i	−0.747375	+	0.664403i	$0.768686\pi$
$674$	−33.3342	−	37.0214i	−1.28399	−	1.42601i
$675$	8.17730	−	9.08182i	0.314745	−	0.349559i
$676$	−4.06013	−	1.80769i	−0.156159	−	0.0695265i
$677$	−2.15837	−	20.5355i	−0.0829529	−	0.789244i	−0.954355	−	0.298675i	$-0.903455\pi$
$677$	−2.15837	−	20.5355i	−0.0829529	−	0.789244i	0.871402	−	0.490570i	$-0.163211\pi$
$678$	7.49960	+	23.0814i	0.288020	+	0.886435i
$679$	−7.89099	−	5.87571i	−0.302829	−	0.225489i
$680$	−36.4533	−	26.4849i	−1.39792	−	1.01565i
$681$	9.79385	−	16.9635i	0.375301	−	0.650041i
$682$	−12.7864	+	20.6558i	−0.489617	+	0.790951i
$683$	11.4215	+	19.7826i	0.437032	+	0.756961i	0.997459	−	0.0712425i	$-0.0226964\pi$
$683$	11.4215	+	19.7826i	0.437032	+	0.756961i	−0.560427	+	0.828204i	$0.689363\pi$
$684$	−2.22888	+	0.992362i	−0.0852235	+	0.0379439i
$685$	19.9764	−	61.4812i	0.763261	−	2.34907i
$686$	27.0641	−	10.9263i	1.03331	−	0.417167i
$687$	2.63200	−	1.91226i	0.100417	−	0.0729572i
$688$	1.89523	+	18.0319i	0.0722550	+	0.687461i
$689$	12.6703	−	14.0718i	0.482701	−	0.536094i
$690$	6.33822	−	1.34723i	0.241292	−	0.0512882i
$691$	16.2753	−	7.24623i	0.619142	−	0.275660i	−0.0731008	−	0.997325i	$-0.523289\pi$
$691$	16.2753	−	7.24623i	0.619142	−	0.275660i	0.692243	+	0.721665i	$0.256623\pi$
$692$	0.245472			0.00933143
$693$	−7.85778	−	3.90580i	−0.298492	−	0.148369i
$694$	52.8949			2.00786
$695$	−68.0208	+	30.2848i	−2.58018	+	1.14877i
$696$	−6.45534	+	1.37212i	−0.244689	+	0.0520103i
$697$	31.8204	−	35.3401i	1.20528	−	1.33860i
$698$	1.80528	+	17.1761i	0.0683310	+	0.650126i
$699$	−23.0569	+	16.7518i	−0.872092	+	0.633612i
$700$	7.97503	−	13.4466i	0.301428	−	0.508234i
$701$	11.2347	−	34.5768i	0.424328	−	1.30595i	−0.479308	−	0.877647i	$-0.659112\pi$
$701$	11.2347	−	34.5768i	0.424328	−	1.30595i	0.903636	−	0.428301i	$-0.140888\pi$
$702$	−2.80949	+	1.25087i	−0.106037	+	0.0472109i
$703$	−8.04652	−	13.9370i	−0.303480	−	0.525643i
$704$	−1.28631	−	17.3441i	−0.0484796	−	0.653681i
$705$	−12.4307	+	21.5306i	−0.468167	+	0.810888i
$706$	−38.5745	−	28.0260i	−1.45177	−	1.05477i
$707$	−3.52840	+	30.1644i	−0.132699	+	1.13445i
$708$	−0.982035	−	3.02239i	−0.0369071	−	0.113589i
$709$	2.05233	+	19.5266i	0.0770770	+	0.733338i	0.962999	+	0.269504i	$0.0868599\pi$
$709$	2.05233	+	19.5266i	0.0770770	+	0.733338i	−0.885922	+	0.463834i	$0.846473\pi$
$710$	−24.6239	−	10.9633i	−0.924118	−	0.411444i
$711$	−0.867951	+	0.963957i	−0.0325507	+	0.0361512i
$712$	24.9429	+	27.7019i	0.934774	+	1.03817i
$713$	−3.72574	−	2.70691i	−0.139530	−	0.101375i
$714$	18.5746	−	3.72111i	0.695138	−	0.139259i
$715$	26.4309	−	4.77544i	0.988459	−	0.178591i
$716$	3.72237	−	6.44733i	0.139112	−	0.240948i
$717$	−0.170447	+	1.62169i	−0.00636545	+	0.0605632i
$718$	31.1789	−	6.62727i	1.16359	−	0.247328i
$719$	−28.1362	−	5.98053i	−1.04930	−	0.223036i	−0.349178	−	0.937057i	$-0.613539\pi$
$719$	−28.1362	−	5.98053i	−1.04930	−	0.223036i	−0.700125	+	0.714021i	$0.746872\pi$
$720$	−15.8907	+	11.5453i	−0.592212	+	0.430267i
$721$	15.4146	+	3.46582i	0.574068	+	0.129074i
$722$	−3.14677	−	9.68475i	−0.117111	−	0.360429i
$723$	3.65360	+	4.05773i	0.135879	+	0.150909i
$724$	1.18359	−	11.2611i	0.0439878	−	0.418515i
$725$	−16.8738	−	29.2263i	−0.626678	−	1.08544i
$726$	7.73029	+	15.5161i	0.286898	+	0.575855i
$727$	37.1335			1.37721			0.688603	−	0.725139i	$-0.258224\pi$
$727$	37.1335			1.37721			0.688603	+	0.725139i	$0.258224\pi$
$728$	10.0669	−	7.13522i	0.373104	−	0.264449i
$729$	0.309017	−	0.951057i	0.0114451	−	0.0352243i
$730$	30.1415	+	6.40676i	1.11559	+	0.237125i
$731$	−15.8994	−	7.07887i	−0.588061	−	0.261821i
$732$	−3.33890	−	1.48658i	−0.123409	−	0.0549454i
$733$	−27.5778	−	5.86183i	−1.01861	−	0.216512i	−0.331799	−	0.943350i	$-0.607656\pi$
$733$	−27.5778	−	5.86183i	−1.01861	−	0.216512i	−0.686809	+	0.726838i	$0.740989\pi$
$734$	−1.14821	+	3.53383i	−0.0423812	+	0.130436i
$735$	−8.32632	−	27.8297i	−0.307121	−	1.02651i
$736$	−2.65496			−0.0978631
$737$	2.06930	−	5.76080i	0.0762236	−	0.212202i
$738$	−8.24739	−	14.2849i	−0.303590	−	0.525834i
$739$	0.853356	−	8.11914i	0.0313912	−	0.298667i	−0.967551	−	0.252677i	$-0.918689\pi$
$739$	0.853356	−	8.11914i	0.0313912	−	0.298667i	0.998942	−	0.0459904i	$-0.0146443\pi$
$740$	4.28198	+	4.75562i	0.157409	+	0.174820i
$741$	−3.04292	−	9.36514i	−0.111784	−	0.344037i
$742$	12.0500	+	38.6210i	0.442370	+	1.41782i
$743$	19.2134	−	13.9593i	0.704871	−	0.512119i	−0.176644	−	0.984275i	$-0.556524\pi$
$743$	19.2134	−	13.9593i	0.704871	−	0.512119i	0.881515	+	0.472156i	$0.156524\pi$
$744$	10.8649	+	2.30942i	0.398328	+	0.0846673i
$745$	15.7983	−	3.35803i	0.578805	−	0.123029i
$746$	−2.65406	+	25.2517i	−0.0971720	+	0.924530i
$747$	0.681293	−	1.18003i	0.0249272	−	0.0431752i
$748$	−6.56205	−	3.16636i	−0.239932	−	0.115773i
$749$	6.67181	+	7.58681i	0.243783	+	0.277216i
$750$	−38.2035	−	27.7564i	−1.39499	−	1.01352i
$751$	−28.9990	−	32.2067i	−1.05819	−	1.17524i	−0.984032	−	0.177992i	$-0.943040\pi$
$751$	−28.9990	−	32.2067i	−1.05819	−	1.17524i	−0.0741578	−	0.997247i	$-0.523627\pi$
$752$	18.9744	−	21.0732i	0.691926	−	0.768462i
$753$	17.9523	+	7.99287i	0.654217	+	0.291276i
$754$	0.887720	+	8.44610i	0.0323289	+	0.307589i
$755$	−2.08273	−	6.40998i	−0.0757983	−	0.233283i
$756$	0.148626	−	1.27061i	0.00540548	−	0.0462115i
$757$	23.5693	+	17.1241i	0.856643	+	0.622387i	0.926969	−	0.375137i	$-0.122404\pi$
$757$	23.5693	+	17.1241i	0.856643	+	0.622387i	−0.0703269	+	0.997524i	$0.522404\pi$
$758$	21.8196	−	37.7927i	0.792524	−	1.37269i
$759$	−3.04173	+	1.24388i	−0.110408	+	0.0451500i
$760$	−25.0214	−	43.3383i	−0.907621	−	1.57205i
$761$	−22.6054	+	10.0646i	−0.819446	+	0.364841i	−0.773258	−	0.634092i	$-0.781374\pi$
$761$	−22.6054	+	10.0646i	−0.819446	+	0.364841i	−0.0461883	+	0.998933i	$0.514707\pi$
$762$	−7.63705	+	23.5044i	−0.276661	+	0.851475i
$763$	6.53792	+	11.6370i	0.236689	+	0.421287i
$764$	9.19883	−	6.68334i	0.332802	−	0.241795i
$765$	−1.97080	−	18.7509i	−0.0712545	−	0.677941i
$766$	−16.0465	+	17.8214i	−0.579783	+	0.643914i
$767$	12.5458	−	2.66670i	0.453004	−	0.0962890i
$768$	10.0315	−	4.46631i	0.361981	−	0.161164i
$769$	−38.7769			−1.39833			−0.699165	−	0.714960i	$-0.746445\pi$
$769$	−38.7769			−1.39833			−0.699165	+	0.714960i	$0.746445\pi$
$770$	−20.0315	+	53.7763i	−0.721884	+	1.93796i
$771$	−10.0049			−0.360319
$772$	9.56316	−	4.25779i	0.344186	−	0.153241i
$773$	−13.6281	+	2.89674i	−0.490169	+	0.104189i	−0.446364	−	0.894852i	$-0.647281\pi$
$773$	−13.6281	+	2.89674i	−0.490169	+	0.104189i	−0.0438049	+	0.999040i	$0.513948\pi$
$774$	−4.03937	+	4.48617i	−0.145192	+	0.161252i
$775$	5.93726	+	56.4893i	0.213273	+	2.02915i
$776$	7.18950	−	5.22348i	0.258088	−	0.187512i
$777$	8.43749	+	0.0989226i	0.302693	+	0.00354883i
$778$	2.82858	−	8.70547i	0.101409	−	0.312106i
$779$	48.2488	−	21.4818i	1.72869	−	0.769664i
$780$	1.95782	+	3.39105i	0.0701014	+	0.121419i
$781$	13.2776	+	3.25109i	0.475109	+	0.116333i
$782$	3.54722	−	6.14397i	0.126848	−	0.219708i
$783$	−2.23409	−	1.62316i	−0.0798400	−	0.0580072i
$784$	2.68982	+	33.0234i	0.0960649	+	1.17941i
$785$	10.6299	+	32.7156i	0.379398	+	1.16767i
$786$	1.77639	+	16.9012i	0.0633617	+	0.602846i
$787$	24.4386	+	10.8807i	0.871140	+	0.387857i	0.793099	−	0.609093i	$-0.208467\pi$
$787$	24.4386	+	10.8807i	0.871140	+	0.387857i	0.0780419	+	0.996950i	$0.475133\pi$
$788$	−4.92060	+	5.46488i	−0.175289	+	0.194678i
$789$	−4.46873	−	4.96303i	−0.159091	−	0.176688i
$790$	6.86281	+	4.98613i	0.244168	+	0.177398i
$791$	13.0442	−	38.6002i	0.463799	−	1.37247i
$792$	5.48194	−	5.72482i	0.194792	−	0.203423i
$793$	7.37555	−	12.7748i	0.261914	−	0.453648i
$794$	−3.46449	+	32.9624i	−0.122950	+	1.16979i
$795$	39.3862	−	8.37180i	1.39688	−	0.296917i
$796$	−6.24741	−	1.32793i	−0.221433	−	0.0470671i
$797$	11.9802	−	8.70412i	0.424360	−	0.308316i	−0.355029	−	0.934855i	$-0.615529\pi$
$797$	11.9802	−	8.70412i	0.424360	−	0.308316i	0.779390	+	0.626539i	$0.215529\pi$
$798$	20.5266	+	4.61523i	0.726635	+	0.163377i
$799$	8.41129	+	25.8873i	0.297570	+	0.915827i
$800$	21.9112	+	24.3348i	0.774676	+	0.860365i
$801$	−1.63042	+	15.5124i	−0.0576081	+	0.548104i
$802$	−0.251827	−	0.436177i	−0.00889231	−	0.0154019i
$803$	−15.6204	−	0.479558i	−0.551231	−	0.0169232i
$804$	0.892383			0.0314719
$805$	−9.88566	−	4.54098i	−0.348424	−	0.160049i
$806$	4.41705	−	13.5943i	0.155584	−	0.478838i
$807$	−26.9769	−	5.73412i	−0.949632	−	0.201851i
$808$	−25.0609	−	11.1578i	−0.881640	−	0.392531i
$809$	−3.75781	−	1.67309i	−0.132118	−	0.0588226i	0.339613	−	0.940565i	$-0.389704\pi$
$809$	−3.75781	−	1.67309i	−0.132118	−	0.0588226i	−0.471731	+	0.881743i	$0.656371\pi$
$810$	−6.39683	−	1.35969i	−0.224762	−	0.0477746i
$811$	8.54601	−	26.3019i	0.300091	−	0.923585i	−0.681373	−	0.731936i	$-0.738617\pi$
$811$	8.54601	−	26.3019i	0.300091	−	0.923585i	0.981464	−	0.191648i	$-0.0613832\pi$
$812$	−3.21021	−	1.47461i	−0.112656	−	0.0517487i
$813$	4.33643			0.152085
$814$	−13.1789	−	10.2073i	−0.461922	−	0.357767i
$815$	−5.34423	−	9.25648i	−0.187200	−	0.324241i
$816$	−2.24789	+	21.3873i	−0.0786920	+	0.748705i
$817$	−12.9337	−	14.3643i	−0.452493	−	0.502545i
$818$	4.77093	+	14.6834i	0.166812	+	0.513393i
$819$	5.03737	+	1.13261i	0.176020	+	0.0395765i
$820$	−16.9906	+	12.3444i	−0.593339	+	0.431086i
$821$	−22.0625	−	4.68954i	−0.769988	−	0.163666i	−0.193864	−	0.981028i	$-0.562102\pi$
$821$	−22.0625	−	4.68954i	−0.769988	−	0.163666i	−0.576124	+	0.817362i	$0.695435\pi$
$822$	−24.0130	+	5.10413i	−0.837551	+	0.178027i
$823$	−4.73887	+	45.0873i	−0.165187	+	1.57164i	0.526962	+	0.849889i	$0.323331\pi$
$823$	−4.73887	+	45.0873i	−0.165187	+	1.57164i	−0.692148	+	0.721756i	$0.743335\pi$
$824$	−7.13562	+	12.3593i	−0.248581	+	0.430555i
$825$	36.5043	+	17.6142i	1.27092	+	0.613249i
$826$	−8.77327	+	25.9617i	−0.305261	+	0.903323i
$827$	22.1062	+	16.0611i	0.768708	+	0.558499i	0.901569	−	0.432636i	$-0.142416\pi$
$827$	22.1062	+	16.0611i	0.768708	+	0.558499i	−0.132861	+	0.991135i	$0.542416\pi$
$828$	−0.320573	−	0.356032i	−0.0111407	−	0.0123730i
$829$	−14.6719	+	16.2948i	−0.509576	+	0.565942i	−0.941950	−	0.335753i	$-0.891009\pi$
$829$	−14.6719	+	16.2948i	−0.509576	+	0.565942i	0.432374	+	0.901694i	$0.357676\pi$
$830$	−8.14057	−	3.62441i	−0.282563	−	0.125805i
$831$	0.799494	+	7.60667i	0.0277341	+	0.263873i
$832$	3.16223	+	9.73234i	0.109631	+	0.337408i
$833$	−28.7430	−	13.6134i	−0.995887	−	0.471677i
$834$	22.8758	+	16.6202i	0.792124	+	0.575512i
$835$	−27.9924	+	48.4842i	−0.968717	+	1.67787i
$836$	−5.22749	−	6.17681i	−0.180797	−	0.213630i
$837$	2.32393	+	4.02516i	0.0803267	+	0.139130i
$838$	35.2426	−	15.6910i	1.21744	−	0.542037i
$839$	6.51321	−	20.0456i	0.224861	−	0.692051i	−0.773445	−	0.633864i	$-0.781468\pi$
$839$	6.51321	−	20.0456i	0.224861	−	0.692051i	0.998306	−	0.0581871i	$-0.0185320\pi$
$840$	26.2371	+	0.307609i	0.905267	+	0.0106135i
$841$	17.2921	−	12.5634i	0.596278	−	0.433221i
$842$	−1.17022	−	11.1339i	−0.0403284	−	0.383699i
$843$	−7.85416	+	8.72293i	−0.270512	+	0.300434i
$844$	5.74632	−	1.22142i	0.197796	−	0.0420429i
$845$	34.8461	−	15.5145i	1.19874	−	0.533714i
$846$	9.44131			0.324599
$847$	5.14808	−	28.6443i	0.176890	−	0.984231i
$848$	−45.9274			−1.57715
$849$	−6.91015	+	3.07660i	−0.237156	+	0.105589i
$850$	−85.5893	+	18.1926i	−2.93569	+	0.624000i
$851$	2.11450	−	2.34839i	0.0724842	−	0.0805018i
$852$	0.208312	+	1.98196i	0.00713665	+	0.0679007i
$853$	−6.49921	+	4.72195i	−0.222529	+	0.161677i	−0.693464	−	0.720491i	$-0.743916\pi$
$853$	−6.49921	+	4.72195i	−0.222529	+	0.161677i	0.470935	+	0.882168i	$0.343916\pi$
$854$	15.4374	+	27.4773i	0.528256	+	0.940253i
$855$	6.47072	−	19.9148i	0.221294	−	0.681073i
$856$	−8.33694	+	3.71185i	−0.284951	+	0.126868i
$857$	1.46402	+	2.53576i	0.0500099	+	0.0866198i	0.889947	−	0.456064i	$-0.150741\pi$
$857$	1.46402	+	2.53576i	0.0500099	+	0.0866198i	−0.839937	+	0.542684i	$0.817408\pi$
$858$	−6.58922	−	7.78584i	−0.224952	−	0.265804i
$859$	−12.8540	+	22.2638i	−0.438572	+	0.759629i	−0.997580	−	0.0695333i	$-0.977849\pi$
$859$	−12.8540	+	22.2638i	−0.438572	+	0.759629i	0.559007	+	0.829163i	$0.311182\pi$
$860$	6.21822	+	4.51780i	0.212039	+	0.154056i
$861$	−3.21732	+	27.5049i	−0.109646	+	0.937366i
$862$	3.73793	+	11.5042i	0.127314	+	0.391834i
$863$	−0.163461	−	1.55523i	−0.00556427	−	0.0529405i	0.991387	−	0.130962i	$-0.0418065\pi$
$863$	−0.163461	−	1.55523i	−0.00556427	−	0.0529405i	−0.996952	+	0.0780212i	$0.975140\pi$
$864$	2.44785	+	1.08985i	0.0832776	+	0.0370776i
$865$	−1.40970	+	1.56563i	−0.0479311	+	0.0532329i
$866$	−3.63948	−	4.04205i	−0.123675	−	0.137355i
$867$	−2.94691	−	2.14106i	−0.100082	−	0.0727141i
$868$	3.92648	+	4.46497i	0.133273	+	0.151551i
$869$	−3.87462	−	1.86960i	−0.131437	−	0.0634219i
$870$	−9.02972	+	15.6399i	−0.306136	+	0.530243i
$871$	−0.376476	+	3.58193i	−0.0127564	+	0.121369i
$872$	−11.7933	+	2.50675i	−0.399372	+	0.0848891i
$873$	3.63726	+	0.773124i	0.123103	+	0.0261663i
$874$	6.37438	−	4.63126i	0.215617	−	0.156655i
$875$	23.6131	+	75.6812i	0.798267	+	2.55849i
$876$	−0.704036	−	2.16680i	−0.0237872	−	0.0732094i
$877$	36.3060	+	40.3219i	1.22597	+	1.36157i	0.910965	+	0.412483i	$0.135338\pi$
$877$	36.3060	+	40.3219i	1.22597	+	1.36157i	0.315001	+	0.949091i	$0.397995\pi$
$878$	5.19072	−	49.3864i	0.175178	−	1.66671i
$879$	−7.59156	−	13.1490i	−0.256057	−	0.443504i
$880$	−51.5037	−	39.8906i	−1.73619	−	1.34471i
$881$	44.2360			1.49035			0.745174	−	0.666870i	$-0.232366\pi$
$881$	44.2360			1.49035			0.745174	+	0.666870i	$0.232366\pi$
$882$	−7.57164	+	8.02264i	−0.254950	+	0.270136i
$883$	11.4908	−	35.3652i	0.386698	−	1.19013i	−0.548543	−	0.836122i	$-0.684817\pi$
$883$	11.4908	−	35.3652i	0.386698	−	1.19013i	0.935241	−	0.354011i	$-0.115183\pi$
$884$	4.19337	+	0.891329i	0.141038	+	0.0299786i
$885$	24.9166	+	11.0936i	0.837561	+	0.372906i
$886$	14.0520	+	6.25636i	0.472087	+	0.210187i
$887$	13.0342	+	2.77051i	0.437646	+	0.0930245i	0.421465	−	0.906845i	$-0.361516\pi$
$887$	13.0342	+	2.77051i	0.437646	+	0.0930245i	0.0161806	+	0.999869i	$0.494849\pi$
$888$	−2.35531	+	7.24889i	−0.0790389	+	0.243257i
$889$	33.8509	−	23.9929i	1.13532	−	0.804695i
$890$	102.006			3.41925
$891$	3.31506	+	0.101775i	0.111059	+	0.00340959i
$892$	2.34960	+	4.06963i	0.0786705	+	0.136261i
$893$	−3.15993	+	30.0647i	−0.105743	+	1.00608i
$894$	−4.10415	−	4.55813i	−0.137263	−	0.152447i
$895$	19.7445	+	60.7672i	0.659985	+	2.03122i
$896$	−35.1647	−	7.90647i	−1.17477	−	0.264137i
$897$	1.56432	−	1.13654i	0.0522310	−	0.0379480i
$898$	25.6628	+	5.45479i	0.856378	+	0.182029i
$899$	12.5545	−	2.66855i	0.418717	−	0.0890011i
$900$	−0.617656	+	5.87661i	−0.0205885	+	0.195887i
$901$	22.0427	−	38.1791i	0.734349	−	1.27193i
$902$	37.8364	−	39.5127i	1.25982	−	1.31563i
$903$	9.93741	−	1.99079i	0.330696	−	0.0662494i
$904$	29.7749	+	21.6327i	0.990299	+	0.719494i
$905$	65.0266	+	72.2193i	2.16156	+	2.40065i
$906$	−1.71265	+	1.90209i	−0.0568990	+	0.0631927i
$907$	1.36948	+	0.609732i	0.0454728	+	0.0202458i	0.429347	−	0.903140i	$-0.358744\pi$
$907$	1.36948	+	0.609732i	0.0454728	+	0.0202458i	−0.383874	+	0.923385i	$0.625410\pi$
$908$	0.989991	+	9.41914i	0.0328540	+	0.312585i
$909$	−3.54714	−	10.9170i	−0.117651	−	0.362093i
$910$	3.92289	−	33.5369i	0.130043	−	1.11174i
$911$	−16.7328	−	12.1571i	−0.554384	−	0.402784i	0.275015	−	0.961440i	$-0.411317\pi$
$911$	−16.7328	−	12.1571i	−0.554384	−	0.402784i	−0.829399	+	0.558656i	$0.811317\pi$
$912$	−11.9419	+	20.6840i	−0.395435	+	0.684914i
$913$	4.38952	+	1.07480i	0.145272	+	0.0355706i
$914$	−10.0407	−	17.3909i	−0.332115	−	0.575241i
$915$	28.6561	−	12.7585i	0.947342	−	0.421784i
$916$	−0.486097	+	1.49605i	−0.0160611	+	0.0494310i
$917$	14.5543	−	24.5397i	0.480624	−	0.810374i
$918$	−5.79260	+	4.20857i	−0.191184	+	0.138903i
$919$	−1.22941	−	11.6970i	−0.0405544	−	0.385849i	−0.995907	−	0.0903817i	$-0.971191\pi$
$919$	−1.22941	−	11.6970i	−0.0405544	−	0.385849i	0.955353	−	0.295467i	$-0.0954754\pi$
$920$	6.57523	−	7.30253i	0.216779	−	0.240757i
$921$	11.6254	−	2.47106i	0.383071	−	0.0814242i
$922$	−7.50921	+	3.34332i	−0.247303	+	0.110106i
$923$	−8.04323			−0.264746
$924$	4.18381	−	0.705372i	0.137637	−	0.0232050i
$925$	−38.9757			−1.28151
$926$	15.3399	−	6.82976i	0.504100	−	0.224440i
$927$	−5.84111	+	1.24157i	−0.191847	+	0.0407784i
$928$	4.95119	−	5.49886i	0.162531	−	0.180509i
$929$	−2.94637	−	28.0329i	−0.0966673	−	0.919728i	−0.930149	−	0.367182i	$-0.880323\pi$
$929$	−2.94637	−	28.0329i	−0.0966673	−	0.919728i	0.833482	−	0.552547i	$-0.186344\pi$
$930$	24.5907	−	17.8662i	0.806360	−	0.585855i
$931$	−23.0129	−	26.7961i	−0.754219	−	0.878206i
$932$	4.25832	−	13.1058i	0.139486	−	0.429294i
$933$	−16.1845	+	7.20583i	−0.529858	+	0.235908i
$934$	−23.3929	−	40.5177i	−0.765440	−	1.32578i
$935$	57.8797	−	23.6692i	1.89287	−	0.774067i
$936$	−2.33187	+	4.03892i	−0.0762196	+	0.132016i
$937$	21.6468	+	15.7273i	0.707170	+	0.513789i	0.882259	−	0.470763i	$-0.156021\pi$
$937$	21.6468	+	15.7273i	0.707170	+	0.513789i	−0.175090	+	0.984553i	$0.556021\pi$
$938$	−6.17211	−	4.59581i	−0.201527	−	0.150059i
$939$	4.02687	+	12.3934i	0.131412	+	0.404444i
$940$	−1.25653	−	11.9551i	−0.0409835	−	0.389932i
$941$	−15.7183	−	6.99822i	−0.512401	−	0.228136i	0.134214	−	0.990952i	$-0.457149\pi$
$941$	−15.7183	−	6.99822i	−0.512401	−	0.228136i	−0.646615	+	0.762817i	$0.723816\pi$
$942$	8.74110	−	9.70798i	0.284800	−	0.316303i
$943$	6.93947	+	7.70706i	0.225980	+	0.250976i
$944$	−25.1680	−	18.2856i	−0.819148	−	0.595146i
$945$	7.25044	+	8.24479i	0.235857	+	0.268203i
$946$	−18.0321	−	8.70095i	−0.586275	−	0.282892i
$947$	−19.2943	+	33.4187i	−0.626980	+	1.08596i	0.361174	+	0.932498i	$0.382376\pi$
$947$	−19.2943	+	33.4187i	−0.626980	+	1.08596i	−0.988154	+	0.153463i	$0.950957\pi$
$948$	0.0655589	−	0.623752i	0.00212926	−	0.0202585i
$949$	8.99431	−	1.91180i	0.291968	−	0.0620597i
$950$	−95.0564	−	20.2049i	−3.08404	−	0.655532i
$951$	13.2505	−	9.62705i	0.429677	−	0.312178i
$952$	19.4716	−	21.1221i	0.631078	−	0.684570i
$953$	−6.61448	−	20.3573i	−0.214264	−	0.659437i	−0.999205	−	0.0398663i	$-0.987307\pi$
$953$	−6.61448	−	20.3573i	−0.214264	−	0.659437i	0.784941	−	0.619571i	$-0.212693\pi$
$954$	−10.2319	−	11.3637i	−0.331271	−	0.367914i
$955$	−10.2005	+	97.0516i	−0.330082	+	3.14052i
$956$	−0.394219	−	0.682807i	−0.0127500	−	0.0220836i
$957$	3.09620	−	8.61962i	0.100086	−	0.278633i
$958$	34.8016			1.12439
$959$	37.4529	+	17.2040i	1.20942	+	0.555547i
$960$	−6.72443	+	20.6957i	−0.217030	+	0.667950i
$961$	9.19210	+	1.95384i	0.296519	+	0.0630271i
$962$	8.96029	+	3.98938i	0.288891	+	0.128623i
$963$	−3.48848	−	1.55317i	−0.112415	−	0.0500502i
$964$	−2.58242	−	0.548911i	−0.0831743	−	0.0176792i
$965$	−27.7630	+	85.4458i	−0.893724	+	2.75060i
$966$	0.383640	+	4.11344i	0.0123434	+	0.132348i
$967$	−54.9040			−1.76559			−0.882796	−	0.469756i	$-0.844342\pi$
$967$	−54.9040			−1.76559			−0.882796	+	0.469756i	$0.844342\pi$
$968$	23.3145	+	12.1455i	0.749355	+	0.390372i
$969$	−11.4629	−	19.8544i	−0.368243	−	0.637815i
$970$	2.54194	−	24.1849i	0.0816167	−	0.776531i
$971$	35.0096	+	38.8821i	1.12351	+	1.24779i	0.965515	+	0.260347i	$0.0838369\pi$
$971$	35.0096	+	38.8821i	1.12351	+	1.24779i	0.157997	+	0.987440i	$0.449496\pi$
$972$	0.149415	+	0.459853i	0.00479250	+	0.0147498i
$973$	−14.1392	−	45.3171i	−0.453283	−	1.45280i
$974$	−41.3533	+	30.0450i	−1.32505	+	0.962703i
$975$	−23.3275	−	4.95841i	−0.747077	−	0.158796i
$976$	−34.9965	+	7.43873i	−1.12021	+	0.238108i
$977$	−6.44842	+	61.3526i	−0.206303	+	1.96284i	0.0577332	+	0.998332i	$0.481613\pi$
$977$	−6.44842	+	61.3526i	−0.206303	+	1.96284i	−0.264036	+	0.964513i	$0.585054\pi$
$978$	−2.02952	+	3.51523i	−0.0648968	+	0.112405i
$979$	−50.9080	+	9.19789i	−1.62703	+	0.293966i
$980$	11.1664	+	8.51989i	0.356697	+	0.272158i
$981$	−4.08149	−	2.96537i	−0.130312	−	0.0946771i
$982$	5.62476	+	6.24693i	0.179493	+	0.199348i
$983$	6.94838	−	7.71695i	0.221619	−	0.246133i	−0.622075	−	0.782958i	$-0.713710\pi$
$983$	6.94838	−	7.71695i	0.221619	−	0.246133i	0.843693	+	0.536825i	$0.180377\pi$
$984$	−22.8514	−	10.1741i	−0.728477	−	0.324339i
$985$	−6.59714	−	62.7676i	−0.210202	−	1.99994i
$986$	6.11001	+	18.8047i	0.194582	+	0.598863i
$987$	−12.7134	−	9.46648i	−0.404670	−	0.301321i
$988$	3.85193	+	2.79859i	0.122546	+	0.0890351i
$989$	1.89776	−	3.28702i	0.0603453	−	0.104521i
$990$	−1.60420	−	21.6304i	−0.0509849	−	0.687461i
$991$	−21.8063	−	37.7696i	−0.692699	−	1.19979i	−0.970950	−	0.239282i	$-0.923088\pi$
$991$	−21.8063	−	37.7696i	−0.692699	−	1.19979i	0.278251	−	0.960508i	$-0.410245\pi$
$992$	−11.3773	+	5.06548i	−0.361228	+	0.160829i
$993$	−1.01888	+	3.13580i	−0.0323332	+	0.0995115i
$994$	8.76638	−	14.7809i	0.278053	−	0.468821i
$995$	44.3472	−	32.2201i	1.40590	−	1.02145i
$996$	0.0688671	+	0.655227i	0.00218214	+	0.0207617i
$997$	18.4452	−	20.4855i	0.584165	−	0.648781i	−0.376524	−	0.926407i	$-0.622881\pi$
$997$	18.4452	−	20.4855i	0.584165	−	0.648781i	0.960689	+	0.277626i	$0.0895475\pi$
$998$	−57.5443	+	12.2314i	−1.82153	+	0.387179i
$999$	−2.91356	+	1.29720i	−0.0921811	+	0.0410416i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	231.2.y.b.37.2	yes	64
3.2	odd	2		693.2.by.c.37.7		64
7.4	even	3	inner	231.2.y.b.4.7	✓	64
11.3	even	5	inner	231.2.y.b.58.7	yes	64
21.11	odd	6		693.2.by.c.235.2		64
33.14	odd	10		693.2.by.c.289.2		64
77.25	even	15	inner	231.2.y.b.25.2	yes	64
231.179	odd	30		693.2.by.c.487.7		64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.y.b.4.7	✓	64	7.4	even	3	inner
231.2.y.b.25.2	yes	64	77.25	even	15	inner
231.2.y.b.37.2	yes	64	1.1	even	1	trivial
231.2.y.b.58.7	yes	64	11.3	even	5	inner
693.2.by.c.37.7		64	3.2	odd	2
693.2.by.c.235.2		64	21.11	odd	6
693.2.by.c.289.2		64	33.14	odd	10
693.2.by.c.487.7		64	231.179	odd	30

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:	\( N \)	\(=\)	\( 231 = 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	231.y (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.43967 + 0.640984i) q^{2} +(-0.978148 + 0.207912i) q^{3} +(0.323537 - 0.359324i) q^{4} +(0.433772 + 4.12706i) q^{5} +(1.27494 - 0.926302i) q^{6} +(-2.64557 - 0.0310171i) q^{7} +(0.738505 - 2.27288i) q^{8} +(0.913545 - 0.406737i) q^{9} +O(q^{10})\)	\(q+(-1.43967 + 0.640984i) q^{2} +(-0.978148 + 0.207912i) q^{3} +(0.323537 - 0.359324i) q^{4} +(0.433772 + 4.12706i) q^{5} +(1.27494 - 0.926302i) q^{6} +(-2.64557 - 0.0310171i) q^{7} +(0.738505 - 2.27288i) q^{8} +(0.913545 - 0.406737i) q^{9} +(-3.26987 - 5.66358i) q^{10} +(2.14258 + 2.53167i) q^{11} +(-0.241759 + 0.418739i) q^{12} +(-1.57878 - 1.14705i) q^{13} +(3.82864 - 1.65111i) q^{14} +(-1.28236 - 3.94669i) q^{15} +(0.494759 + 4.70732i) q^{16} +(-4.15061 - 1.84797i) q^{17} +(-1.05450 + 1.17114i) q^{18} +(-3.37641 - 3.74988i) q^{19} +(1.62329 + 1.17939i) q^{20} +(2.59421 - 0.519706i) q^{21} +(-4.70737 - 2.27142i) q^{22} +(0.495419 - 0.858091i) q^{23} +(-0.249807 + 2.37676i) q^{24} +(-11.9537 + 2.54085i) q^{25} +(3.00817 + 0.639406i) q^{26} +(-0.809017 + 0.587785i) q^{27} +(-0.867085 + 0.940582i) q^{28} +(0.853348 + 2.62634i) q^{29} +(4.37594 + 4.85997i) q^{30} +(0.485833 - 4.62239i) q^{31} +(-1.33975 - 2.32052i) q^{32} +(-2.62212 - 2.03088i) q^{33} +7.16004 q^{34} +(-1.01956 - 10.9319i) q^{35} +(0.149415 - 0.459853i) q^{36} +(3.11960 + 0.663091i) q^{37} +(7.26453 + 3.23438i) q^{38} +(1.78277 + 0.793738i) q^{39} +(9.70067 + 2.06194i) q^{40} +(-3.23441 + 9.95449i) q^{41} +(-3.40169 + 2.41105i) q^{42} +3.83062 q^{43} +(1.60289 + 0.0492102i) q^{44} +(2.07490 + 3.59383i) q^{45} +(-0.163219 + 1.55293i) q^{46} +(-4.00875 - 4.45217i) q^{47} +(-1.46265 - 4.50159i) q^{48} +(6.99808 + 0.164116i) q^{49} +(15.5808 - 11.3201i) q^{50} +(4.44413 + 0.944628i) q^{51} +(-0.922957 + 0.196181i) q^{52} +(-1.01426 + 9.65000i) q^{53} +(0.787959 - 1.36479i) q^{54} +(-9.51898 + 9.94071i) q^{55} +(-2.02426 + 5.99016i) q^{56} +(4.08227 + 2.96594i) q^{57} +(-2.91198 - 3.23408i) q^{58} +(-4.39787 + 4.88433i) q^{59} +(-1.83303 - 0.816118i) q^{60} +(0.790124 + 7.51753i) q^{61} +(2.26344 + 6.96614i) q^{62} +(-2.42946 + 1.04771i) q^{63} +(-4.24233 - 3.08223i) q^{64} +(4.04912 - 7.01328i) q^{65} +(5.07676 + 1.24307i) q^{66} +(-0.922802 - 1.59834i) q^{67} +(-2.00690 + 0.893529i) q^{68} +(-0.306186 + 0.942343i) q^{69} +(8.47500 + 15.0848i) q^{70} +(3.33445 - 2.42262i) q^{71} +(-0.249807 - 2.37676i) q^{72} +(-3.15290 + 3.50165i) q^{73} +(-4.91623 + 1.04498i) q^{74} +(11.1642 - 4.97064i) q^{75} -2.43982 q^{76} +(-5.58981 - 6.76417i) q^{77} -3.07537 q^{78} +(-1.18499 + 0.527591i) q^{79} +(-19.2128 + 4.08380i) q^{80} +(0.669131 - 0.743145i) q^{81} +(-1.72417 - 16.4044i) q^{82} +(1.10236 - 0.800908i) q^{83} +(0.652579 - 1.10031i) q^{84} +(5.82627 - 17.9314i) q^{85} +(-5.51483 + 2.45536i) q^{86} +(-1.38075 - 2.39152i) q^{87} +(7.33650 - 3.00017i) q^{88} +(-7.79893 + 13.5081i) q^{89} +(-5.29076 - 3.84396i) q^{90} +(4.14119 + 3.08357i) q^{91} +(-0.148047 - 0.455640i) q^{92} +(0.485833 + 4.62239i) q^{93} +(8.62506 + 3.84013i) q^{94} +(14.0114 - 15.5612i) q^{95} +(1.79294 + 1.99126i) q^{96} +(3.00835 + 2.18569i) q^{97} +(-10.1801 + 4.24938i) q^{98} +(2.98706 + 1.44133i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 4 q^{2} + 8 q^{3} + 10 q^{4} - 4 q^{5} - 8 q^{6} - q^{7} + 8 q^{8} + 8 q^{9}+O(q^{10}) \) 64 * q + 4 * q^2 + 8 * q^3 + 10 * q^4 - 4 * q^5 - 8 * q^6 - q^7 + 8 * q^8 + 8 * q^9	\( 64 q + 4 q^{2} + 8 q^{3} + 10 q^{4} - 4 q^{5} - 8 q^{6} - q^{7} + 8 q^{8} + 8 q^{9} - 14 q^{10} + 11 q^{11} - 30 q^{12} - 8 q^{13} + 6 q^{14} - 12 q^{15} - 4 q^{17} - q^{18} - 2 q^{19} + 24 q^{20} - 2 q^{21} - 14 q^{22} + 16 q^{24} - 10 q^{25} + 4 q^{26} - 16 q^{27} + 29 q^{28} - 58 q^{29} + 11 q^{30} - 19 q^{31} - 64 q^{32} + 6 q^{33} - 88 q^{34} + 17 q^{35} - 20 q^{36} - 20 q^{37} + 29 q^{38} + 4 q^{39} + 51 q^{40} - 68 q^{41} - 11 q^{42} + 92 q^{43} - 21 q^{44} - 4 q^{45} - 5 q^{46} - 26 q^{47} - 10 q^{48} + 37 q^{49} - 10 q^{50} + 6 q^{51} - 14 q^{52} - 3 q^{53} - 6 q^{54} - 32 q^{55} + 24 q^{56} - 36 q^{57} + 52 q^{58} + 7 q^{59} - 12 q^{60} - 21 q^{61} + 92 q^{62} - 7 q^{63} - 72 q^{64} - 66 q^{65} - 23 q^{66} - 4 q^{67} - 17 q^{68} + 40 q^{69} - q^{70} + 58 q^{71} + 16 q^{72} - 3 q^{73} - 28 q^{74} + 20 q^{75} + 168 q^{76} - 34 q^{77} + 132 q^{78} + 9 q^{79} - 5 q^{80} + 8 q^{81} - 42 q^{82} + 60 q^{83} - 39 q^{84} + 110 q^{85} + 13 q^{86} - 46 q^{87} + 92 q^{88} - 10 q^{89} + 8 q^{90} + 10 q^{91} + 110 q^{92} - 19 q^{93} - 46 q^{94} + 43 q^{95} - 4 q^{96} + 64 q^{97} - 88 q^{98} + 28 q^{99}+O(q^{100}) \) 64 * q + 4 * q^2 + 8 * q^3 + 10 * q^4 - 4 * q^5 - 8 * q^6 - q^7 + 8 * q^8 + 8 * q^9 - 14 * q^10 + 11 * q^11 - 30 * q^12 - 8 * q^13 + 6 * q^14 - 12 * q^15 - 4 * q^17 - q^18 - 2 * q^19 + 24 * q^20 - 2 * q^21 - 14 * q^22 + 16 * q^24 - 10 * q^25 + 4 * q^26 - 16 * q^27 + 29 * q^28 - 58 * q^29 + 11 * q^30 - 19 * q^31 - 64 * q^32 + 6 * q^33 - 88 * q^34 + 17 * q^35 - 20 * q^36 - 20 * q^37 + 29 * q^38 + 4 * q^39 + 51 * q^40 - 68 * q^41 - 11 * q^42 + 92 * q^43 - 21 * q^44 - 4 * q^45 - 5 * q^46 - 26 * q^47 - 10 * q^48 + 37 * q^49 - 10 * q^50 + 6 * q^51 - 14 * q^52 - 3 * q^53 - 6 * q^54 - 32 * q^55 + 24 * q^56 - 36 * q^57 + 52 * q^58 + 7 * q^59 - 12 * q^60 - 21 * q^61 + 92 * q^62 - 7 * q^63 - 72 * q^64 - 66 * q^65 - 23 * q^66 - 4 * q^67 - 17 * q^68 + 40 * q^69 - q^70 + 58 * q^71 + 16 * q^72 - 3 * q^73 - 28 * q^74 + 20 * q^75 + 168 * q^76 - 34 * q^77 + 132 * q^78 + 9 * q^79 - 5 * q^80 + 8 * q^81 - 42 * q^82 + 60 * q^83 - 39 * q^84 + 110 * q^85 + 13 * q^86 - 46 * q^87 + 92 * q^88 - 10 * q^89 + 8 * q^90 + 10 * q^91 + 110 * q^92 - 19 * q^93 - 46 * q^94 + 43 * q^95 - 4 * q^96 + 64 * q^97 - 88 * q^98 + 28 * q^99

Introduction

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