LMFDB - Embedded newform 429.2.n.a.235.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(157,429)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(429, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 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("429.157");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.n (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:	$3.42558224671$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$3$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} + 9 x^{10} - 15 x^{9} + 29 x^{8} - 26 x^{7} + 43 x^{6} + 24 x^{5} + 16 x^{4} + \cdots + 1 $ x^12 - 3x^11 + 9x^10 - 15x^9 + 29x^8 - 26x^7 + 43x^6 + 24x^5 + 16x^4 - 17x^3 + 14x^2 - 5*x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			235.1
Root			$-0.689843 + 0.501200i$ of defining polynomial
Character	$\chi$	$=$	429.235
Dual form			429.2.n.a.157.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.689843 - 0.501200i) q^{2} +(0.309017 - 0.951057i) q^{3} +(-0.393353 - 1.21061i) q^{4} +(-0.139763 + 0.101543i) q^{5} +(-0.689843 + 0.501200i) q^{6} +(-0.572513 - 1.76202i) q^{7} +(-0.862402 + 2.65420i) q^{8} +(-0.809017 - 0.587785i) q^{9} +O(q^{10})$	\(q+(-0.689843 - 0.501200i) q^{2} +(0.309017 - 0.951057i) q^{3} +(-0.393353 - 1.21061i) q^{4} +(-0.139763 + 0.101543i) q^{5} +(-0.689843 + 0.501200i) q^{6} +(-0.572513 - 1.76202i) q^{7} +(-0.862402 + 2.65420i) q^{8} +(-0.809017 - 0.587785i) q^{9} +0.147308 q^{10} +(-3.17617 - 0.954941i) q^{11} -1.27292 q^{12} +(-0.809017 - 0.587785i) q^{13} +(-0.488178 + 1.50246i) q^{14} +(0.0533846 + 0.164301i) q^{15} +(-0.134416 + 0.0976586i) q^{16} +(0.443630 - 0.322316i) q^{17} +(0.263496 + 0.810959i) q^{18} +(0.849874 - 2.61564i) q^{19} +(0.177906 + 0.129256i) q^{20} -1.85269 q^{21} +(1.71244 + 2.25066i) q^{22} -1.38605 q^{23} +(2.25780 + 1.64039i) q^{24} +(-1.53586 + 4.72690i) q^{25} +(0.263496 + 0.810959i) q^{26} +(-0.809017 + 0.587785i) q^{27} +(-1.90792 + 1.38619i) q^{28} +(1.91938 + 5.90726i) q^{29} +(0.0455206 - 0.140098i) q^{30} +(-6.83549 - 4.96627i) q^{31} +5.72325 q^{32} +(-1.88970 + 2.72563i) q^{33} -0.467579 q^{34} +(0.258937 + 0.188129i) q^{35} +(-0.393353 + 1.21061i) q^{36} +(-3.34770 - 10.3032i) q^{37} +(-1.89724 + 1.37843i) q^{38} +(-0.809017 + 0.587785i) q^{39} +(-0.148985 - 0.458529i) q^{40} +(-1.05513 + 3.24734i) q^{41} +(1.27807 + 0.928569i) q^{42} +1.27402 q^{43} +(0.0932905 + 4.22075i) q^{44} +0.172756 q^{45} +(0.956157 + 0.694689i) q^{46} +(-2.04899 + 6.30614i) q^{47} +(0.0513422 + 0.158015i) q^{48} +(2.88619 - 2.09694i) q^{49} +(3.42862 - 2.49104i) q^{50} +(-0.169451 - 0.521518i) q^{51} +(-0.393353 + 1.21061i) q^{52} +(-2.87900 - 2.09172i) q^{53} +0.852692 q^{54} +(0.540878 - 0.189055i) q^{55} +5.17048 q^{56} +(-2.22500 - 1.61656i) q^{57} +(1.63664 - 5.03707i) q^{58} +(-4.02419 - 12.3852i) q^{59} +(0.177906 - 0.129256i) q^{60} +(2.04752 - 1.48761i) q^{61} +(2.22632 + 6.85189i) q^{62} +(-0.572513 + 1.76202i) q^{63} +(-3.67931 - 2.67318i) q^{64} +0.172756 q^{65} +(2.66968 - 0.933140i) q^{66} -0.221791 q^{67} +(-0.564703 - 0.410281i) q^{68} +(-0.428313 + 1.31821i) q^{69} +(-0.0843357 - 0.259558i) q^{70} +(5.52891 - 4.01699i) q^{71} +(2.25780 - 1.64039i) q^{72} +(-3.19997 - 9.84851i) q^{73} +(-2.85456 + 8.78542i) q^{74} +(4.02094 + 2.92138i) q^{75} -3.50084 q^{76} +(0.135782 + 6.14318i) q^{77} +0.852692 q^{78} +(2.20161 + 1.59956i) q^{79} +(0.00886967 - 0.0272980i) q^{80} +(0.309017 + 0.951057i) q^{81} +(2.35544 - 1.71133i) q^{82} +(8.18023 - 5.94329i) q^{83} +(0.728761 + 2.24290i) q^{84} +(-0.0292738 + 0.0900954i) q^{85} +(-0.878870 - 0.638537i) q^{86} +6.21126 q^{87} +(5.27374 - 7.60666i) q^{88} -7.26923 q^{89} +(-0.119174 - 0.0865853i) q^{90} +(-0.572513 + 1.76202i) q^{91} +(0.545207 + 1.67797i) q^{92} +(-6.83549 + 4.96627i) q^{93} +(4.57412 - 3.32329i) q^{94} +(0.146821 + 0.451868i) q^{95} +(1.76858 - 5.44314i) q^{96} +(12.5534 + 9.12059i) q^{97} -3.04201 q^{98} +(2.00828 + 2.63947i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 3 q^{2} - 3 q^{3} - 3 q^{4} + 8 q^{5} + 3 q^{6} + 5 q^{7} - q^{8} - 3 q^{9}+O(q^{10}) $ 12 * q + 3 * q^2 - 3 * q^3 - 3 * q^4 + 8 * q^5 + 3 * q^6 + 5 * q^7 - q^8 - 3 * q^9	\( 12 q + 3 q^{2} - 3 q^{3} - 3 q^{4} + 8 q^{5} + 3 q^{6} + 5 q^{7} - q^{8} - 3 q^{9} + 14 q^{10} - 6 q^{11} + 2 q^{12} - 3 q^{13} + 11 q^{14} - 2 q^{15} - 5 q^{16} - 14 q^{17} - 2 q^{18} - 2 q^{19} - 9 q^{20} - 10 q^{21} + 21 q^{22} - 6 q^{23} + 4 q^{24} + 19 q^{25} - 2 q^{26} - 3 q^{27} - 12 q^{28} - 12 q^{29} - q^{30} - 12 q^{31} + 26 q^{32} + 9 q^{33} - 24 q^{34} - 2 q^{35} - 3 q^{36} + 4 q^{37} - 13 q^{38} - 3 q^{39} + 4 q^{40} - 10 q^{41} + q^{42} + 28 q^{43} - 12 q^{45} - 5 q^{46} + 28 q^{47} + 10 q^{48} + 20 q^{49} - q^{50} + 11 q^{51} - 3 q^{52} - 29 q^{53} - 2 q^{54} + 4 q^{55} + 12 q^{56} + 8 q^{57} + 22 q^{58} - 11 q^{59} - 9 q^{60} - 18 q^{61} + 40 q^{62} + 5 q^{63} + 11 q^{64} - 12 q^{65} + 16 q^{66} - 72 q^{67} - 35 q^{68} + 4 q^{69} - 6 q^{70} + 10 q^{71} + 4 q^{72} - 11 q^{73} - 15 q^{74} - 11 q^{75} + 4 q^{76} + 20 q^{77} - 2 q^{78} - 7 q^{79} - 27 q^{80} - 3 q^{81} - 10 q^{82} + 16 q^{83} + 8 q^{84} - 26 q^{85} - 35 q^{86} + 28 q^{87} + 25 q^{88} - 62 q^{89} - 6 q^{90} + 5 q^{91} - 34 q^{92} - 12 q^{93} - q^{94} + 15 q^{95} + q^{96} + 54 q^{97} + 50 q^{98} - 6 q^{99}+O(q^{100}) \) 12 * q + 3 * q^2 - 3 * q^3 - 3 * q^4 + 8 * q^5 + 3 * q^6 + 5 * q^7 - q^8 - 3 * q^9 + 14 * q^10 - 6 * q^11 + 2 * q^12 - 3 * q^13 + 11 * q^14 - 2 * q^15 - 5 * q^16 - 14 * q^17 - 2 * q^18 - 2 * q^19 - 9 * q^20 - 10 * q^21 + 21 * q^22 - 6 * q^23 + 4 * q^24 + 19 * q^25 - 2 * q^26 - 3 * q^27 - 12 * q^28 - 12 * q^29 - q^30 - 12 * q^31 + 26 * q^32 + 9 * q^33 - 24 * q^34 - 2 * q^35 - 3 * q^36 + 4 * q^37 - 13 * q^38 - 3 * q^39 + 4 * q^40 - 10 * q^41 + q^42 + 28 * q^43 - 12 * q^45 - 5 * q^46 + 28 * q^47 + 10 * q^48 + 20 * q^49 - q^50 + 11 * q^51 - 3 * q^52 - 29 * q^53 - 2 * q^54 + 4 * q^55 + 12 * q^56 + 8 * q^57 + 22 * q^58 - 11 * q^59 - 9 * q^60 - 18 * q^61 + 40 * q^62 + 5 * q^63 + 11 * q^64 - 12 * q^65 + 16 * q^66 - 72 * q^67 - 35 * q^68 + 4 * q^69 - 6 * q^70 + 10 * q^71 + 4 * q^72 - 11 * q^73 - 15 * q^74 - 11 * q^75 + 4 * q^76 + 20 * q^77 - 2 * q^78 - 7 * q^79 - 27 * q^80 - 3 * q^81 - 10 * q^82 + 16 * q^83 + 8 * q^84 - 26 * q^85 - 35 * q^86 + 28 * q^87 + 25 * q^88 - 62 * q^89 - 6 * q^90 + 5 * q^91 - 34 * q^92 - 12 * q^93 - q^94 + 15 * q^95 + q^96 + 54 * q^97 + 50 * q^98 - 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/429\mathbb{Z}\right)^\times$.

$n$	$67$	$79$	$287$
$\chi(n)$	$1$	$e\left(\frac{1}{5}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.689843	−	0.501200i	−0.487792	−	0.354402i	0.316542	−	0.948578i	$-0.397478\pi$
$2$	−0.689843	−	0.501200i	−0.487792	−	0.354402i	−0.804335	+	0.594177i	$0.797478\pi$
$3$	0.309017	−	0.951057i	0.178411	−	0.549093i
$3$	0.309017	−	0.951057i	0.178411	−	0.549093i
$4$	−0.393353	−	1.21061i	−0.196676	−	0.605307i
$5$	−0.139763	+	0.101543i	−0.0625037	+	0.0454116i	−0.618598	−	0.785707i	$-0.712299\pi$
$5$	−0.139763	+	0.101543i	−0.0625037	+	0.0454116i	0.556095	+	0.831119i	$0.312299\pi$
$6$	−0.689843	+	0.501200i	−0.281627	+	0.204614i
$7$	−0.572513	−	1.76202i	−0.216390	−	0.665979i	−0.999052	−	0.0435325i	$-0.986139\pi$
$7$	−0.572513	−	1.76202i	−0.216390	−	0.665979i	0.782662	−	0.622447i	$-0.213861\pi$
$8$	−0.862402	+	2.65420i	−0.304905	+	0.938401i
$9$	−0.809017	−	0.587785i	−0.269672	−	0.195928i
$10$	0.147308			0.0465828
$11$	−3.17617	−	0.954941i	−0.957653	−	0.287926i
$11$	−3.17617	−	0.954941i	−0.957653	−	0.287926i
$12$	−1.27292			−0.367459
$13$	−0.809017	−	0.587785i	−0.224381	−	0.163022i
$13$	−0.809017	−	0.587785i	−0.224381	−	0.163022i
$14$	−0.488178	+	1.50246i	−0.130471	+	0.401548i
$15$	0.0533846	+	0.164301i	0.0137838	+	0.0424223i
$16$	−0.134416	+	0.0976586i	−0.0336039	+	0.0244147i
$17$	0.443630	−	0.322316i	0.107596	−	0.0781731i	−0.532686	−	0.846313i	$-0.678817\pi$
$17$	0.443630	−	0.322316i	0.107596	−	0.0781731i	0.640282	+	0.768140i	$0.278817\pi$
$18$	0.263496	+	0.810959i	0.0621067	+	0.191145i
$19$	0.849874	−	2.61564i	0.194975	−	0.600070i	−0.805002	−	0.593272i	$-0.797836\pi$
$19$	0.849874	−	2.61564i	0.194975	−	0.600070i	0.999977	−	0.00679835i	$-0.00216400\pi$
$20$	0.177906	+	0.129256i	0.0397810	+	0.0289026i
$21$	−1.85269			−0.404291
$22$	1.71244	+	2.25066i	0.365094	+	0.479842i
$23$	−1.38605			−0.289012			−0.144506	−	0.989504i	$-0.546159\pi$
$23$	−1.38605			−0.289012			−0.144506	+	0.989504i	$0.546159\pi$
$24$	2.25780	+	1.64039i	0.460871	+	0.334842i
$25$	−1.53586	+	4.72690i	−0.307172	+	0.945380i
$26$	0.263496	+	0.810959i	0.0516759	+	0.159042i
$27$	−0.809017	+	0.587785i	−0.155695	+	0.113119i
$28$	−1.90792	+	1.38619i	−0.360563	+	0.261965i
$29$	1.91938	+	5.90726i	0.356421	+	1.09695i	0.955181	+	0.296022i	$0.0956601\pi$
$29$	1.91938	+	5.90726i	0.356421	+	1.09695i	−0.598760	+	0.800928i	$0.704340\pi$
$30$	0.0455206	−	0.140098i	0.00831089	−	0.0255783i
$31$	−6.83549	−	4.96627i	−1.22769	−	0.891969i	−0.230975	−	0.972960i	$-0.574192\pi$
$31$	−6.83549	−	4.96627i	−1.22769	−	0.891969i	−0.996715	+	0.0809906i	$0.974192\pi$
$32$	5.72325			1.01174
$33$	−1.88970	+	2.72563i	−0.328954	+	0.474471i
$34$	−0.467579			−0.0801892
$35$	0.258937	+	0.188129i	0.0437684	+	0.0317996i
$36$	−0.393353	+	1.21061i	−0.0655588	+	0.201769i
$37$	−3.34770	−	10.3032i	−0.550358	−	1.69383i	−0.707897	−	0.706315i	$-0.750356\pi$
$37$	−3.34770	−	10.3032i	−0.550358	−	1.69383i	0.157539	−	0.987513i	$-0.449644\pi$
$38$	−1.89724	+	1.37843i	−0.307773	+	0.223610i
$39$	−0.809017	+	0.587785i	−0.129546	+	0.0941210i
$40$	−0.148985	−	0.458529i	−0.0235566	−	0.0724998i
$41$	−1.05513	+	3.24734i	−0.164783	+	0.507150i	−0.999020	−	0.0442558i	$-0.985908\pi$
$41$	−1.05513	+	3.24734i	−0.164783	+	0.507150i	0.834237	+	0.551406i	$0.185908\pi$
$42$	1.27807	+	0.928569i	0.197210	+	0.143281i
$43$	1.27402			0.194286			0.0971428	−	0.995270i	$-0.469030\pi$
$43$	1.27402			0.194286			0.0971428	+	0.995270i	$0.469030\pi$
$44$	0.0932905	+	4.22075i	0.0140641	+	0.636303i
$45$	0.172756			0.0257530
$46$	0.956157	+	0.694689i	0.140978	+	0.102426i
$47$	−2.04899	+	6.30614i	−0.298876	+	0.919846i	0.683016	+	0.730404i	$0.260668\pi$
$47$	−2.04899	+	6.30614i	−0.298876	+	0.919846i	−0.981892	+	0.189442i	$0.939332\pi$
$48$	0.0513422	+	0.158015i	0.00741061	+	0.0228075i
$49$	2.88619	−	2.09694i	0.412313	−	0.299563i
$50$	3.42862	−	2.49104i	0.484881	−	0.352286i
$51$	−0.169451	−	0.521518i	−0.0237279	−	0.0730271i
$52$	−0.393353	+	1.21061i	−0.0545482	+	0.167882i
$53$	−2.87900	−	2.09172i	−0.395461	−	0.287319i	0.372228	−	0.928141i	$-0.378594\pi$
$53$	−2.87900	−	2.09172i	−0.395461	−	0.287319i	−0.767690	+	0.640822i	$0.778594\pi$
$54$	0.852692			0.116037
$55$	0.540878	−	0.189055i	0.0729320	−	0.0254921i
$56$	5.17048			0.690934
$57$	−2.22500	−	1.61656i	−0.294708	−	0.214118i
$58$	1.63664	−	5.03707i	0.214902	−	0.661400i
$59$	−4.02419	−	12.3852i	−0.523904	−	1.61241i	−0.766472	−	0.642277i	$-0.777990\pi$
$59$	−4.02419	−	12.3852i	−0.523904	−	1.61241i	0.242568	−	0.970134i	$-0.422010\pi$
$60$	0.177906	−	0.129256i	0.0229676	−	0.0166869i
$61$	2.04752	−	1.48761i	0.262158	−	0.190469i	−0.448940	−	0.893562i	$-0.648198\pi$
$61$	2.04752	−	1.48761i	0.262158	−	0.190469i	0.711098	+	0.703093i	$0.248198\pi$
$62$	2.22632	+	6.85189i	0.282742	+	0.870191i
$63$	−0.572513	+	1.76202i	−0.0721299	+	0.221993i
$64$	−3.67931	−	2.67318i	−0.459914	−	0.334147i
$65$	0.172756			0.0214278
$66$	2.66968	−	0.933140i	0.328615	−	0.114862i
$67$	−0.221791			−0.0270961			−0.0135480	−	0.999908i	$-0.504313\pi$
$67$	−0.221791			−0.0270961			−0.0135480	+	0.999908i	$0.504313\pi$
$68$	−0.564703	−	0.410281i	−0.0684803	−	0.0497539i
$69$	−0.428313	+	1.31821i	−0.0515629	+	0.158694i
$70$	−0.0843357	−	0.259558i	−0.0100800	−	0.0310232i
$71$	5.52891	−	4.01699i	0.656161	−	0.476729i	−0.209204	−	0.977872i	$-0.567087\pi$
$71$	5.52891	−	4.01699i	0.656161	−	0.476729i	0.865364	+	0.501143i	$0.167087\pi$
$72$	2.25780	−	1.64039i	0.266084	−	0.193321i
$73$	−3.19997	−	9.84851i	−0.374529	−	1.15268i	−0.943796	−	0.330528i	$-0.892773\pi$
$73$	−3.19997	−	9.84851i	−0.374529	−	1.15268i	0.569267	−	0.822152i	$-0.307227\pi$
$74$	−2.85456	+	8.78542i	−0.331835	+	1.02128i
$75$	4.02094	+	2.92138i	0.464298	+	0.337332i
$76$	−3.50084			−0.401574
$77$	0.135782	+	6.14318i	0.0154738	+	0.700081i
$78$	0.852692			0.0965484
$79$	2.20161	+	1.59956i	0.247701	+	0.179965i	0.704707	−	0.709498i	$-0.251078\pi$
$79$	2.20161	+	1.59956i	0.247701	+	0.179965i	−0.457007	+	0.889463i	$0.651078\pi$
$80$	0.00886967	−	0.0272980i	0.000991660	−	0.00305201i
$81$	0.309017	+	0.951057i	0.0343352	+	0.105673i
$82$	2.35544	−	1.71133i	0.260115	−	0.188984i
$83$	8.18023	−	5.94329i	0.897897	−	0.652361i	−0.0400277	−	0.999199i	$-0.512745\pi$
$83$	8.18023	−	5.94329i	0.897897	−	0.652361i	0.937925	+	0.346838i	$0.112745\pi$
$84$	0.728761	+	2.24290i	0.0795144	+	0.244720i
$85$	−0.0292738	+	0.0900954i	−0.00317519	+	0.00977222i
$86$	−0.878870	−	0.638537i	−0.0947710	−	0.0688552i
$87$	6.21126			0.665917
$88$	5.27374	−	7.60666i	0.562183	−	0.810872i
$89$	−7.26923			−0.770536			−0.385268	−	0.922805i	$-0.625891\pi$
$89$	−7.26923			−0.770536			−0.385268	+	0.922805i	$0.625891\pi$
$90$	−0.119174	−	0.0865853i	−0.0125621	−	0.00912689i
$91$	−0.572513	+	1.76202i	−0.0600157	+	0.184709i
$92$	0.545207	+	1.67797i	0.0568417	+	0.174941i
$93$	−6.83549	+	4.96627i	−0.708807	+	0.514979i
$94$	4.57412	−	3.32329i	0.471784	−	0.342771i
$95$	0.146821	+	0.451868i	0.0150635	+	0.0463607i
$96$	1.76858	−	5.44314i	0.180505	−	0.555538i
$97$	12.5534	+	9.12059i	1.27461	+	0.926056i	0.999376	−	0.0353227i	$-0.0112459\pi$
$97$	12.5534	+	9.12059i	1.27461	+	0.926056i	0.275230	+	0.961378i	$0.411246\pi$
$98$	−3.04201			−0.307289
$99$	2.00828	+	2.63947i	0.201840	+	0.265277i
$100$	6.32659			0.632659
$101$	4.75558	+	3.45513i	0.473198	+	0.343799i	0.798686	−	0.601748i	$-0.205529\pi$
$101$	4.75558	+	3.45513i	0.473198	+	0.343799i	−0.325488	+	0.945546i	$0.605529\pi$
$102$	−0.144490	+	0.444694i	−0.0143066	+	0.0440313i
$103$	−5.78241	−	17.7964i	−0.569758	−	1.75353i	−0.653373	−	0.757036i	$-0.726647\pi$
$103$	−5.78241	−	17.7964i	−0.569758	−	1.75353i	0.0836150	−	0.996498i	$-0.473353\pi$
$104$	2.25780	−	1.64039i	0.221395	−	0.160853i
$105$	0.258937	−	0.188129i	0.0252697	−	0.0183595i
$106$	0.937689	+	2.88591i	0.0910764	+	0.280304i
$107$	1.46054	−	4.49509i	0.141196	−	0.434556i	−0.855306	−	0.518123i	$-0.826631\pi$
$107$	1.46054	−	4.49509i	0.141196	−	0.434556i	0.996502	+	0.0835663i	$0.0266310\pi$
$108$	1.02981	+	0.748201i	0.0990936	+	0.0719957i
$109$	12.2494			1.17328			0.586640	−	0.809848i	$-0.300451\pi$
$109$	12.2494			1.17328			0.586640	+	0.809848i	$0.300451\pi$
$110$	−0.467875	−	0.140670i	−0.0446101	−	0.0134124i
$111$	−10.8334			−1.02826
$112$	0.249031	+	0.180931i	0.0235312	+	0.0170964i
$113$	5.56955	−	17.1413i	0.523939	−	1.61252i	−0.242464	−	0.970160i	$-0.577956\pi$
$113$	5.56955	−	17.1413i	0.523939	−	1.61252i	0.766404	−	0.642359i	$-0.222044\pi$
$114$	0.724681	+	2.23034i	0.0678726	+	0.208890i
$115$	0.193718	−	0.140744i	0.0180643	−	0.0131245i
$116$	6.39642	−	4.64727i	0.593893	−	0.431488i
$117$	0.309017	+	0.951057i	0.0285686	+	0.0879252i
$118$	−3.43139	+	10.5607i	−0.315885	+	0.972195i
$119$	−0.821909	−	0.597152i	−0.0753443	−	0.0547408i
$120$	−0.482126			−0.0440119
$121$	9.17617	+	6.06612i	0.834198	+	0.551466i
$122$	−2.15805			−0.195381
$123$	2.76236	+	2.00697i	0.249073	+	0.180962i
$124$	−3.32349	+	10.2286i	−0.298458	+	0.918559i
$125$	−0.532252	−	1.63810i	−0.0476061	−	0.146516i
$126$	1.27807	−	0.928569i	0.113859	−	0.0827235i
$127$	9.84465	−	7.15256i	0.873571	−	0.634687i	−0.0579716	−	0.998318i	$-0.518463\pi$
$127$	9.84465	−	7.15256i	0.873571	−	0.634687i	0.931543	+	0.363632i	$0.118463\pi$
$128$	−2.33881	−	7.19813i	−0.206724	−	0.636231i
$129$	0.393692	−	1.21166i	0.0346627	−	0.106681i
$130$	−0.119174	−	0.0865853i	−0.0104523	−	0.00759404i
$131$	−4.67113			−0.408118			−0.204059	−	0.978959i	$-0.565414\pi$
$131$	−4.67113			−0.408118			−0.204059	+	0.978959i	$0.565414\pi$
$132$	4.04300	+	1.21556i	0.351898	+	0.105801i
$133$	−5.09537			−0.441825
$134$	0.153001	+	0.111162i	0.0132173	+	0.00960290i
$135$	0.0533846	−	0.164301i	0.00459461	−	0.0141408i
$136$	0.472903	+	1.45545i	0.0405511	+	0.124804i
$137$	−10.2725	+	7.46339i	−0.877637	+	0.637640i	−0.932625	−	0.360847i	$-0.882488\pi$
$137$	−10.2725	+	7.46339i	−0.877637	+	0.637640i	0.0549884	+	0.998487i	$0.482488\pi$
$138$	0.956157	−	0.694689i	0.0813935	−	0.0591358i
$139$	2.62280	+	8.07216i	0.222463	+	0.684672i	0.998539	+	0.0540322i	$0.0172074\pi$
$139$	2.62280	+	8.07216i	0.222463	+	0.684672i	−0.776076	+	0.630640i	$0.782793\pi$
$140$	0.125898	−	0.387474i	0.0106403	−	0.0327475i
$141$	5.36433	+	3.89741i	0.451758	+	0.328221i
$142$	−5.82739			−0.489024
$143$	2.00828	+	2.63947i	0.167941	+	0.220724i
$144$	0.166147			0.0138456
$145$	−0.868101	−	0.630713i	−0.0720919	−	0.0523778i
$146$	−2.72859	+	8.39775i	−0.225820	+	0.695002i
$147$	−1.10243	−	3.39292i	−0.0909267	−	0.279844i
$148$	−11.1563	+	8.10555i	−0.917044	+	0.666272i
$149$	10.4677	−	7.60522i	0.857547	−	0.623044i	−0.0696698	−	0.997570i	$-0.522195\pi$
$149$	10.4677	−	7.60522i	0.857547	−	0.623044i	0.927216	+	0.374526i	$0.122195\pi$
$150$	−1.30962	−	4.03059i	−0.106930	−	0.329096i
$151$	1.93126	−	5.94382i	0.157164	−	0.483701i	−0.841210	−	0.540709i	$-0.818156\pi$
$151$	1.93126	−	5.94382i	0.157164	−	0.483701i	0.998374	+	0.0570079i	$0.0181560\pi$
$152$	6.20951	+	4.51147i	0.503658	+	0.365929i
$153$	−0.548356			−0.0443320
$154$	2.98530	−	4.30588i	0.240562	−	0.346978i
$155$	1.45964			0.117241
$156$	1.02981	+	0.748201i	0.0824508	+	0.0599040i
$157$	−1.19106	+	3.66571i	−0.0950571	+	0.292556i	−0.987269	−	0.159062i	$-0.949153\pi$
$157$	−1.19106	+	3.66571i	−0.0950571	+	0.292556i	0.892211	+	0.451618i	$0.149153\pi$
$158$	−0.717064	−	2.20689i	−0.0570465	−	0.175571i
$159$	−2.87900	+	2.09172i	−0.228320	+	0.165884i
$160$	−0.799897	+	0.581159i	−0.0632374	+	0.0459446i
$161$	0.793533	+	2.44224i	0.0625391	+	0.192476i
$162$	0.263496	−	0.810959i	0.0207022	−	0.0637149i
$163$	−7.06734	−	5.13472i	−0.553557	−	0.402183i	0.275538	−	0.961290i	$-0.411144\pi$
$163$	−7.06734	−	5.13472i	−0.553557	−	0.402183i	−0.829095	+	0.559107i	$0.811144\pi$
$164$	4.34632			0.339391
$165$	−0.0126611	−	0.572827i	−0.000985665	−	0.0445945i
$166$	−8.62185			−0.669185
$167$	−11.3332	−	8.23408i	−0.876993	−	0.637172i	0.0554615	−	0.998461i	$-0.482337\pi$
$167$	−11.3332	−	8.23408i	−0.876993	−	0.637172i	−0.932454	+	0.361288i	$0.882337\pi$
$168$	1.59776	−	4.91741i	0.123270	−	0.379387i
$169$	0.309017	+	0.951057i	0.0237705	+	0.0731582i
$170$	0.0653501	−	0.0474796i	0.00501212	−	0.00364152i
$171$	−2.22500	+	1.61656i	−0.170150	+	0.123621i
$172$	−0.501137	−	1.54234i	−0.0382114	−	0.117603i
$173$	−1.01135	+	3.11262i	−0.0768916	+	0.236648i	−0.982113	−	0.188292i	$-0.939705\pi$
$173$	−1.01135	+	3.11262i	−0.0768916	+	0.236648i	0.905221	+	0.424940i	$0.139705\pi$
$174$	−4.28479	−	3.11308i	−0.324829	−	0.236002i
$175$	9.20817			0.696072
$176$	0.520186	−	0.181822i	0.0392105	−	0.0137053i
$177$	−13.0225			−0.978834
$178$	5.01462	+	3.64334i	0.375862	+	0.273080i
$179$	−5.68153	+	17.4860i	−0.424657	+	1.30696i	0.478664	+	0.877998i	$0.341121\pi$
$179$	−5.68153	+	17.4860i	−0.424657	+	1.30696i	−0.903322	+	0.428963i	$0.858879\pi$
$180$	−0.0679541	−	0.209141i	−0.00506500	−	0.0155885i
$181$	−9.07745	+	6.59516i	−0.674722	+	0.490214i	−0.871602	−	0.490213i	$-0.836919\pi$
$181$	−9.07745	+	6.59516i	−0.674722	+	0.490214i	0.196881	+	0.980427i	$0.436919\pi$
$182$	1.27807	−	0.928569i	0.0947365	−	0.0688301i
$183$	−0.782082	−	2.40700i	−0.0578132	−	0.177931i
$184$	1.19533	−	3.67885i	0.0881211	−	0.271209i
$185$	1.51410	+	1.10006i	0.111319	+	0.0808779i
$186$	7.20451			0.528260
$187$	−1.71684	+	0.600091i	−0.125548	+	0.0438830i
$188$	8.44029			0.615571
$189$	1.49886	+	1.08899i	0.109026	+	0.0792120i
$190$	0.125193	−	0.385305i	0.00908246	−	0.0279529i
$191$	−5.93571	−	18.2682i	−0.429493	−	1.32184i	−0.898626	−	0.438716i	$-0.855434\pi$
$191$	−5.93571	−	18.2682i	−0.429493	−	1.32184i	0.469133	−	0.883127i	$-0.344566\pi$
$192$	−3.67931	+	2.67318i	−0.265531	+	0.192920i
$193$	−16.3832	+	11.9031i	−1.17929	+	0.856804i	−0.992091	−	0.125518i	$-0.959941\pi$
$193$	−16.3832	+	11.9031i	−1.17929	+	0.856804i	−0.187198	+	0.982322i	$0.559941\pi$
$194$	−4.08864	−	12.5835i	−0.293547	−	0.903446i
$195$	0.0533846	−	0.164301i	0.00382295	−	0.0117658i
$196$	−3.67388	−	2.66923i	−0.262420	−	0.190659i
$197$	−14.8916			−1.06098			−0.530491	−	0.847690i	$-0.677993\pi$
$197$	−14.8916			−1.06098			−0.530491	+	0.847690i	$0.677993\pi$
$198$	−0.0624928	−	2.82737i	−0.00444117	−	0.200932i
$199$	1.67683			0.118868			0.0594338	−	0.998232i	$-0.481070\pi$
$199$	1.67683			0.118868			0.0594338	+	0.998232i	$0.481070\pi$
$200$	−11.2216	−	8.15297i	−0.793487	−	0.576502i
$201$	−0.0685371	+	0.210936i	−0.00483424	+	0.0148783i
$202$	−1.54889	−	4.76699i	−0.108980	−	0.335405i
$203$	9.30980	−	6.76397i	0.653420	−	0.474737i
$204$	−0.564703	+	0.410281i	−0.0395371	+	0.0287254i
$205$	−0.182279	−	0.560998i	−0.0127309	−	0.0391818i
$206$	−4.93062	+	15.1749i	−0.343532	+	1.05728i
$207$	1.12134	+	0.814700i	0.0779384	+	0.0566256i
$208$	0.166147			0.0115202
$209$	−5.19714	+	7.49616i	−0.359493	+	0.518521i
$210$	−0.272916			−0.0188330
$211$	15.3012	+	11.1170i	1.05338	+	0.765323i	0.972852	−	0.231430i	$-0.0743404\pi$
$211$	15.3012	+	11.1170i	1.05338	+	0.765323i	0.0805247	+	0.996753i	$0.474340\pi$
$212$	−1.39980	+	4.30814i	−0.0961387	+	0.295885i
$213$	−2.11185	−	6.49962i	−0.144702	−	0.445347i
$214$	−3.26048	+	2.36888i	−0.222882	+	0.161933i
$215$	−0.178060	+	0.129368i	−0.0121436	+	0.00882282i
$216$	−0.862402	−	2.65420i	−0.0586790	−	0.180595i
$217$	−4.83724	+	14.8875i	−0.328373	+	1.01063i
$218$	−8.45015	−	6.13940i	−0.572317	−	0.415812i
$219$	−10.3553			−0.699749
$220$	−0.441628	−	0.580430i	−0.0297746	−	0.0391326i
$221$	−0.548356			−0.0368864
$222$	7.47332	+	5.42969i	0.501577	+	0.364417i
$223$	−2.15272	+	6.62539i	−0.144157	+	0.443669i	−0.996902	−	0.0786589i	$-0.974936\pi$
$223$	−2.15272	+	6.62539i	−0.144157	+	0.443669i	0.852745	+	0.522328i	$0.174936\pi$
$224$	−3.27664	−	10.0845i	−0.218930	−	0.673796i
$225$	4.02094	−	2.92138i	0.268063	−	0.194759i
$226$	−12.4333	+	9.03335i	−0.827054	+	0.600890i
$227$	2.85962	+	8.80100i	0.189800	+	0.584143i	0.999998	−	0.00201267i	$-0.000640653\pi$
$227$	2.85962	+	8.80100i	0.189800	+	0.584143i	−0.810198	+	0.586156i	$0.800641\pi$
$228$	−1.08182	+	3.32950i	−0.0716452	+	0.220501i
$229$	7.93611	+	5.76592i	0.524433	+	0.381023i	0.818271	−	0.574832i	$-0.194933\pi$
$229$	7.93611	+	5.76592i	0.524433	+	0.381023i	−0.293838	+	0.955855i	$0.594933\pi$
$230$	−0.204176			−0.0134630
$231$	5.88447	+	1.76921i	0.387170	+	0.116406i
$232$	−17.3343			−1.13805
$233$	−19.8909	−	14.4516i	−1.30310	−	0.946757i	−0.303118	−	0.952953i	$-0.598028\pi$
$233$	−19.8909	−	14.4516i	−1.30310	−	0.946757i	−0.999981	+	0.00619617i	$0.998028\pi$
$234$	0.263496	−	0.810959i	0.0172253	−	0.0530140i
$235$	−0.353976	−	1.08942i	−0.0230908	−	0.0710662i
$236$	−13.4107	+	9.74348i	−0.872965	+	0.634247i
$237$	2.20161	−	1.59956i	0.143010	−	0.103903i
$238$	0.267695	+	0.823882i	0.0173521	+	0.0534043i
$239$	−7.60820	+	23.4156i	−0.492133	+	1.51463i	0.329243	+	0.944245i	$0.393206\pi$
$239$	−7.60820	+	23.4156i	−0.492133	+	1.51463i	−0.821377	+	0.570386i	$0.806794\pi$
$240$	−0.0232211	−	0.0168711i	−0.00149892	−	0.00108903i
$241$	7.03658			0.453266			0.226633	−	0.973980i	$-0.427228\pi$
$241$	7.03658			0.453266			0.226633	+	0.973980i	$0.427228\pi$
$242$	−3.28978	−	8.78377i	−0.211475	−	0.564642i
$243$	1.00000			0.0641500
$244$	−2.60632	−	1.89360i	−0.166852	−	0.121225i
$245$	−0.190451	+	0.586148i	−0.0121675	+	0.0374476i
$246$	−0.899698	−	2.76899i	−0.0573626	−	0.176544i
$247$	−2.22500	+	1.61656i	−0.141573	+	0.102859i
$248$	19.0764	−	13.8598i	1.21135	−	0.880100i
$249$	−3.12457	−	9.61644i	−0.198012	−	0.609417i
$250$	−0.453847	+	1.39680i	−0.0287038	+	0.0883413i
$251$	17.3405	+	12.5986i	1.09452	+	0.795218i	0.980157	−	0.198220i	$-0.0635162\pi$
$251$	17.3405	+	12.5986i	1.09452	+	0.795218i	0.114366	+	0.993439i	$0.463516\pi$
$252$	2.35832			0.148560
$253$	4.40234	+	1.32360i	0.276773	+	0.0832138i
$254$	−10.3761			−0.651056
$255$	0.0766397	+	0.0556820i	0.00479936	+	0.00348694i
$256$	−4.80503	+	14.7884i	−0.300315	+	0.924273i
$257$	0.632139	+	1.94552i	0.0394318	+	0.121358i	0.968835	−	0.247708i	$-0.0796774\pi$
$257$	0.632139	+	1.94552i	0.0394318	+	0.121358i	−0.929403	+	0.369067i	$0.879677\pi$
$258$	−0.878870	+	0.638537i	−0.0547161	+	0.0397535i
$259$	−16.2377	+	11.7974i	−1.00896	+	0.733054i
$260$	−0.0679541	−	0.209141i	−0.00421433	−	0.0129704i
$261$	1.91938	−	5.90726i	0.118807	−	0.365650i
$262$	3.22234	+	2.34117i	0.199077	+	0.144638i
$263$	8.13734			0.501770			0.250885	−	0.968017i	$-0.419278\pi$
$263$	8.13734			0.501770			0.250885	+	0.968017i	$0.419278\pi$
$264$	−5.60469	−	7.36621i	−0.344945	−	0.453359i
$265$	0.614777			0.0377654
$266$	3.51500	+	2.55380i	0.215519	+	0.156583i
$267$	−2.24631	+	6.91344i	−0.137472	+	0.423096i
$268$	0.0872420	+	0.268503i	0.00532915	+	0.0164015i
$269$	−4.17675	+	3.03459i	−0.254661	+	0.185022i	−0.707790	−	0.706423i	$-0.750308\pi$
$269$	−4.17675	+	3.03459i	−0.254661	+	0.185022i	0.453129	+	0.891445i	$0.350308\pi$
$270$	−0.119174	+	0.0865853i	−0.00725273	+	0.00526941i
$271$	0.376481	+	1.15869i	0.0228696	+	0.0703854i	0.961840	−	0.273613i	$-0.0882186\pi$
$271$	0.376481	+	1.15869i	0.0228696	+	0.0703854i	−0.938970	+	0.343998i	$0.888219\pi$
$272$	−0.0281538	+	0.0866485i	−0.00170708	+	0.00525384i
$273$	1.49886	+	1.08899i	0.0907151	+	0.0659084i
$274$	10.8270			0.654085
$275$	9.39208	−	13.5468i	0.566364	−	0.816903i
$276$	1.76433			0.106200
$277$	6.06454	+	4.40615i	0.364383	+	0.264740i	0.754878	−	0.655865i	$-0.227696\pi$
$277$	6.06454	+	4.40615i	0.364383	+	0.264740i	−0.390495	+	0.920605i	$0.627696\pi$
$278$	2.23644	−	6.88307i	0.134133	−	0.412819i
$279$	2.61092	+	8.03560i	0.156312	+	0.481079i
$280$	−0.722639	+	0.525028i	−0.0431859	+	0.0313764i
$281$	−16.8404	+	12.2353i	−1.00462	+	0.729896i	−0.963073	−	0.269241i	$-0.913227\pi$
$281$	−16.8404	+	12.2353i	−1.00462	+	0.729896i	−0.0415424	+	0.999137i	$0.513227\pi$
$282$	−1.74716	−	5.37720i	−0.104042	−	0.320208i
$283$	9.12621	−	28.0876i	0.542497	−	1.66963i	−0.184372	−	0.982857i	$-0.559025\pi$
$283$	9.12621	−	28.0876i	0.542497	−	1.66963i	0.726868	−	0.686777i	$-0.240975\pi$
$284$	−7.03783	−	5.11329i	−0.417619	−	0.303418i
$285$	0.475123			0.0281438
$286$	−0.0624928	−	2.82737i	−0.00369528	−	0.167186i
$287$	6.32594			0.373409
$288$	−4.63021	−	3.36404i	−0.272838	−	0.198228i
$289$	−5.16037	+	15.8820i	−0.303551	+	0.934234i
$290$	0.282740	+	0.870185i	0.0166031	+	0.0510990i
$291$	12.5534	−	9.12059i	0.735894	−	0.534658i
$292$	−10.6640	+	7.74787i	−0.624065	+	0.453410i
$293$	−3.43627	−	10.5758i	−0.200749	−	0.617843i	−0.999861	−	0.0166604i	$-0.994697\pi$
$293$	−3.43627	−	10.5758i	−0.200749	−	0.617843i	0.799112	−	0.601182i	$-0.205303\pi$
$294$	−0.940032	+	2.89312i	−0.0548238	+	0.168730i
$295$	1.82006	+	1.32235i	0.105968	+	0.0769904i
$296$	30.2337			1.75730
$297$	3.13088	−	1.09435i	0.181672	−	0.0635003i
$298$	−11.0328			−0.639113
$299$	1.12134	+	0.814700i	0.0648487	+	0.0471153i
$300$	1.95502	−	6.01694i	0.112873	−	0.347388i
$301$	−0.729391	−	2.24483i	−0.0420414	−	0.129390i
$302$	−4.31131	+	3.13235i	−0.248088	+	0.180246i
$303$	4.75558	−	3.45513i	0.273201	−	0.198492i
$304$	0.141204	+	0.434581i	0.00809860	+	0.0249249i
$305$	−0.135109	+	0.415824i	−0.00773634	+	0.0238100i
$306$	0.378280	+	0.274836i	0.0216248	+	0.0157113i
$307$	20.7554			1.18457			0.592286	−	0.805728i	$-0.298226\pi$
$307$	20.7554			1.18457			0.592286	+	0.805728i	$0.298226\pi$
$308$	7.38362	−	2.58082i	0.420721	−	0.147056i
$309$	−18.7123			−1.06450
$310$	−1.00692	−	0.731571i	−0.0571892	−	0.0415504i
$311$	4.58242	−	14.1032i	0.259845	−	0.799721i	−0.732991	−	0.680238i	$-0.761876\pi$
$311$	4.58242	−	14.1032i	0.259845	−	0.799721i	0.992836	−	0.119483i	$-0.0381236\pi$
$312$	−0.862402	−	2.65420i	−0.0488239	−	0.150264i
$313$	1.39488	−	1.01344i	0.0788433	−	0.0572830i	−0.547665	−	0.836697i	$-0.684483\pi$
$313$	1.39488	−	1.01344i	0.0788433	−	0.0572830i	0.626509	+	0.779414i	$0.284483\pi$
$314$	2.65890	−	1.93180i	0.150050	−	0.109018i
$315$	−0.0989052	−	0.304399i	−0.00557267	−	0.0171509i
$316$	1.07045	−	3.29450i	0.0602173	−	0.185330i
$317$	−10.0338	−	7.28998i	−0.563554	−	0.409446i	0.269204	−	0.963083i	$-0.413239\pi$
$317$	−10.0338	−	7.28998i	−0.563554	−	0.409446i	−0.832758	+	0.553637i	$0.813239\pi$
$318$	3.03443			0.170162
$319$	−0.455216	−	20.5954i	−0.0254872	−	1.15312i
$320$	0.785674			0.0439205
$321$	−3.82375	−	2.77812i	−0.213421	−	0.155059i
$322$	0.676639	−	2.08248i	0.0377076	−	0.116052i
$323$	−0.466034	−	1.43431i	−0.0259308	−	0.0798069i
$324$	1.02981	−	0.748201i	0.0572117	−	0.0415667i
$325$	4.02094	−	2.92138i	0.223042	−	0.162049i
$326$	2.30183	+	7.08430i	0.127487	+	0.392363i
$327$	3.78527	−	11.6499i	0.209326	−	0.644239i
$328$	−7.70916	−	5.60103i	−0.425667	−	0.309265i
$329$	12.2846			0.677272
$330$	−0.278367	+	0.401506i	−0.0153236	+	0.0221022i
$331$	4.57442			0.251433			0.125716	−	0.992066i	$-0.459877\pi$
$331$	4.57442			0.251433			0.125716	+	0.992066i	$0.459877\pi$
$332$	−10.4128	−	7.56531i	−0.571474	−	0.415200i
$333$	−3.34770	+	10.3032i	−0.183453	+	0.564609i
$334$	3.69123	+	11.3604i	0.201975	+	0.621616i
$335$	0.0309981	−	0.0225214i	0.00169361	−	0.00123048i
$336$	0.249031	−	0.180931i	0.0135857	−	0.00987062i
$337$	9.25340	+	28.4790i	0.504065	+	1.55135i	0.802337	+	0.596871i	$0.203590\pi$
$337$	9.25340	+	28.4790i	0.504065	+	1.55135i	−0.298272	+	0.954481i	$0.596410\pi$
$338$	0.263496	−	0.810959i	0.0143323	−	0.0441103i
$339$	−14.5813	−	10.5939i	−0.791946	−	0.575383i
$340$	0.120586			0.00653968
$341$	16.9682	+	22.3012i	0.918880	+	1.20768i
$342$	2.34512			0.126809
$343$	−15.8392	−	11.5079i	−0.855239	−	0.621367i
$344$	−1.09871	+	3.38149i	−0.0592386	+	0.182318i
$345$	−0.0739937	−	0.227729i	−0.00398369	−	0.0122605i
$346$	2.25772	−	1.64033i	0.121376	−	0.0881846i
$347$	24.2843	−	17.6436i	1.30365	−	0.947156i	0.303664	−	0.952779i	$-0.401790\pi$
$347$	24.2843	−	17.6436i	1.30365	−	0.947156i	0.999984	+	0.00562321i	$0.00178993\pi$
$348$	−2.44321	−	7.51944i	−0.130970	−	0.403084i
$349$	−2.39633	+	7.37515i	−0.128273	+	0.394783i	−0.994483	−	0.104897i	$-0.966549\pi$
$349$	−2.39633	+	7.37515i	−0.128273	+	0.394783i	0.866210	+	0.499679i	$0.166549\pi$
$350$	−6.35219	−	4.61513i	−0.339539	−	0.246689i
$351$	1.00000			0.0533761
$352$	−18.1781	−	5.46537i	−0.968893	−	0.291305i
$353$	14.6203			0.778161			0.389081	−	0.921204i	$-0.372793\pi$
$353$	14.6203			0.778161			0.389081	+	0.921204i	$0.372793\pi$
$354$	8.98350	+	6.52690i	0.477468	+	0.346901i
$355$	−0.364836	+	1.12285i	−0.0193635	+	0.0595946i
$356$	2.85937	+	8.80023i	0.151546	+	0.466411i
$357$	−0.821909	+	0.597152i	−0.0435000	+	0.0316046i
$358$	12.6833	−	9.21497i	0.670334	−	0.487026i
$359$	3.36805	+	10.3658i	0.177759	+	0.547085i	0.999749	−	0.0224170i	$-0.00713614\pi$
$359$	3.36805	+	10.3658i	0.177759	+	0.547085i	−0.821990	+	0.569502i	$0.807136\pi$
$360$	−0.148985	+	0.458529i	−0.00785220	+	0.0241666i
$361$	9.25201	+	6.72198i	0.486948	+	0.353788i
$362$	9.56751			0.502857
$363$	8.60482	−	6.85253i	0.451636	−	0.359664i
$364$	2.35832			0.123610
$365$	1.44729	+	1.05152i	0.0757545	+	0.0550389i
$366$	−0.666875	+	2.05243i	−0.0348581	+	0.107282i
$367$	−2.42547	−	7.46483i	−0.126609	−	0.389661i	0.867582	−	0.497294i	$-0.165673\pi$
$367$	−2.42547	−	7.46483i	−0.126609	−	0.389661i	−0.994191	+	0.107633i	$0.965673\pi$
$368$	0.186307	−	0.135360i	0.00971192	−	0.00705612i
$369$	2.76236	−	2.00697i	0.143803	−	0.104479i
$370$	−0.493142	−	1.51773i	−0.0256372	−	0.0789032i
$371$	−2.03737	+	6.27038i	−0.105775	+	0.325542i
$372$	8.70100	+	6.32165i	0.451126	+	0.327762i
$373$	12.0843			0.625700			0.312850	−	0.949802i	$-0.398716\pi$
$373$	12.0843			0.625700			0.312850	+	0.949802i	$0.398716\pi$
$374$	1.48511	+	0.446511i	0.0767934	+	0.0230885i
$375$	−1.72240			−0.0889446
$376$	−14.9707	−	10.8769i	−0.772055	−	0.560931i
$377$	1.91938	−	5.90726i	0.0988533	−	0.304239i
$378$	−0.488178	−	1.50246i	−0.0251092	−	0.0772780i
$379$	14.7876	−	10.7438i	0.759589	−	0.551874i	−0.139195	−	0.990265i	$-0.544452\pi$
$379$	14.7876	−	10.7438i	0.759589	−	0.551874i	0.898784	+	0.438391i	$0.144452\pi$
$380$	0.489286	−	0.355487i	0.0250999	−	0.0182361i
$381$	−3.76032	−	11.5731i	−0.192647	−	0.592907i
$382$	−5.06133	+	15.5772i	−0.258960	+	0.796998i
$383$	6.73611	+	4.89407i	0.344199	+	0.250075i	0.746432	−	0.665462i	$-0.231766\pi$
$383$	6.73611	+	4.89407i	0.344199	+	0.250075i	−0.402232	+	0.915538i	$0.631766\pi$
$384$	−7.56856			−0.386232
$385$	−0.642777	−	0.844800i	−0.0327590	−	0.0430550i
$386$	17.2677			0.878901
$387$	−1.03070	−	0.748848i	−0.0523934	−	0.0380661i
$388$	6.10360	−	18.7850i	0.309864	−	0.953662i
$389$	−1.53220	−	4.71562i	−0.0776855	−	0.239091i	0.904671	−	0.426112i	$-0.140117\pi$
$389$	−1.53220	−	4.71562i	−0.0776855	−	0.239091i	−0.982356	+	0.187020i	$0.940117\pi$
$390$	−0.119174	+	0.0865853i	−0.00603463	+	0.00438442i
$391$	−0.614893	+	0.446746i	−0.0310965	+	0.0225929i
$392$	3.07664	+	9.46894i	0.155394	+	0.478254i
$393$	−1.44346	+	4.44251i	−0.0728128	+	0.224095i
$394$	10.2729	+	7.46367i	0.517539	+	0.376014i
$395$	−0.470128			−0.0236547
$396$	2.40542	−	3.46950i	0.120877	−	0.174349i
$397$	−20.5073			−1.02923			−0.514617	−	0.857420i	$-0.672066\pi$
$397$	−20.5073			−1.02923			−0.514617	+	0.857420i	$0.672066\pi$
$398$	−1.15675	−	0.840429i	−0.0579827	−	0.0421269i
$399$	−1.57456	+	4.84598i	−0.0788264	+	0.242603i
$400$	−0.255179	−	0.785359i	−0.0127589	−	0.0392680i
$401$	20.4299	−	14.8432i	1.02022	−	0.741233i	0.0538918	−	0.998547i	$-0.482837\pi$
$401$	20.4299	−	14.8432i	1.02022	−	0.741233i	0.966328	+	0.257314i	$0.0828374\pi$
$402$	0.153001	−	0.111162i	0.00763098	−	0.00554423i
$403$	2.61092	+	8.03560i	0.130059	+	0.400282i
$404$	2.31221	−	7.11626i	0.115037	−	0.354047i
$405$	−0.139763	−	0.101543i	−0.00694486	−	0.00504574i
$406$	−9.81240			−0.486981
$407$	0.793966	+	35.9215i	0.0393554	+	1.78056i
$408$	1.53035			0.0757635
$409$	23.4876	+	17.0648i	1.16139	+	0.843798i	0.989953	−	0.141397i	$-0.0451594\pi$
$409$	23.4876	+	17.0648i	1.16139	+	0.843798i	0.171436	+	0.985195i	$0.445159\pi$
$410$	−0.155428	+	0.478359i	−0.00767605	+	0.0236245i
$411$	3.92374	+	12.0760i	0.193544	+	0.595666i
$412$	−19.2701	+	14.0005i	−0.949370	+	0.689757i
$413$	−19.5190	+	14.1814i	−0.960465	+	0.697819i
$414$	−0.365219	−	1.12403i	−0.0179496	−	0.0552430i
$415$	−0.539789	+	1.66130i	−0.0264972	+	0.0815499i
$416$	−4.63021	−	3.36404i	−0.227015	−	0.164936i
$417$	8.48757			0.415638
$418$	7.34228	−	2.56637i	0.359123	−	0.125525i
$419$	25.8631			1.26349			0.631747	−	0.775175i	$-0.282338\pi$
$419$	25.8631			1.26349			0.631747	+	0.775175i	$0.282338\pi$
$420$	−0.329605	−	0.239472i	−0.0160831	−	0.0116850i
$421$	−7.97425	+	24.5422i	−0.388641	+	1.19611i	0.545163	+	0.838330i	$0.316468\pi$
$421$	−7.97425	+	24.5422i	−0.388641	+	1.19611i	−0.933804	+	0.357784i	$0.883532\pi$
$422$	−4.98358	−	15.3379i	−0.242597	−	0.746637i
$423$	5.36433	−	3.89741i	0.260823	−	0.189499i
$424$	8.03469	−	5.83754i	0.390199	−	0.283496i
$425$	0.842200	+	2.59202i	0.0408527	+	0.125732i
$426$	−1.80076	+	5.54218i	−0.0872472	+	0.268519i
$427$	−3.79342	−	2.75608i	−0.183576	−	0.133376i
$428$	−6.01633			−0.290810
$429$	3.13088	−	1.09435i	0.151160	−	0.0528355i
$430$	0.187672			0.00905037
$431$	−21.3139	−	15.4855i	−1.02666	−	0.745909i	−0.0590189	−	0.998257i	$-0.518797\pi$
$431$	−21.3139	−	15.4855i	−1.02666	−	0.745909i	−0.967637	+	0.252348i	$0.918797\pi$
$432$	0.0513422	−	0.158015i	0.00247020	−	0.00760250i
$433$	−7.99197	−	24.5968i	−0.384070	−	1.18204i	−0.937153	−	0.348919i	$-0.886549\pi$
$433$	−7.99197	−	24.5968i	−0.384070	−	1.18204i	0.553083	−	0.833126i	$-0.313451\pi$
$434$	10.7985	−	7.84560i	0.518347	−	0.376601i
$435$	−0.868101	+	0.630713i	−0.0416223	+	0.0302404i
$436$	−4.81833	−	14.8293i	−0.230756	−	0.710195i
$437$	−1.17797	+	3.62542i	−0.0563499	+	0.173427i
$438$	7.14355	+	5.19009i	0.341332	+	0.247992i
$439$	12.2665			0.585446			0.292723	−	0.956197i	$-0.405439\pi$
$439$	12.2665			0.585446			0.292723	+	0.956197i	$0.405439\pi$
$440$	0.0353345	+	1.59864i	0.00168450	+	0.0762122i
$441$	−3.56753			−0.169882
$442$	0.378280	+	0.274836i	0.0179929	+	0.0130726i
$443$	5.30807	−	16.3365i	0.252194	−	0.776173i	−0.742176	−	0.670205i	$-0.766206\pi$
$443$	5.30807	−	16.3365i	0.252194	−	0.776173i	0.994370	−	0.105968i	$-0.0337940\pi$
$444$	4.26134	+	13.1150i	0.202234	+	0.622413i
$445$	1.01597	−	0.738142i	0.0481614	−	0.0349913i
$446$	4.80568	−	3.49153i	0.227556	−	0.165329i
$447$	−3.99830	−	12.3055i	−0.189113	−	0.582031i
$448$	−2.60372	+	8.01343i	−0.123014	+	0.378599i
$449$	−0.761028	−	0.552919i	−0.0359151	−	0.0260939i	0.569683	−	0.821865i	$-0.307066\pi$
$449$	−0.761028	−	0.552919i	−0.0359151	−	0.0260939i	−0.605598	+	0.795771i	$0.707066\pi$
$450$	−4.23801			−0.199782
$451$	6.45229	−	9.30655i	0.303826	−	0.438228i
$452$	−22.9423			−1.07912
$453$	−5.05611	−	3.67348i	−0.237557	−	0.172595i
$454$	2.43838	−	7.50455i	0.114439	−	0.352206i
$455$	−0.0989052	−	0.304399i	−0.00463675	−	0.0142704i
$456$	6.20951	−	4.51147i	0.290787	−	0.211269i
$457$	4.30155	−	3.12526i	0.201218	−	0.146193i	−0.482613	−	0.875834i	$-0.660312\pi$
$457$	4.30155	−	3.12526i	0.201218	−	0.146193i	0.683831	+	0.729640i	$0.260312\pi$
$458$	−2.58479	−	7.95516i	−0.120779	−	0.371720i
$459$	−0.169451	+	0.521518i	−0.00790932	+	0.0243424i
$460$	−0.246587	−	0.179156i	−0.0114972	−	0.00835318i
$461$	−40.3418			−1.87890			−0.939452	−	0.342681i	$-0.888665\pi$
$461$	−40.3418			−1.87890			−0.939452	+	0.342681i	$0.888665\pi$
$462$	−3.17263	−	4.16978i	−0.147604	−	0.193996i
$463$	−5.79684			−0.269402			−0.134701	−	0.990886i	$-0.543007\pi$
$463$	−5.79684			−0.269402			−0.134701	+	0.990886i	$0.543007\pi$
$464$	−0.834890	−	0.606583i	−0.0387588	−	0.0281599i
$465$	0.451053	−	1.38820i	0.0209171	−	0.0643762i
$466$	6.47847	+	19.9387i	0.300109	+	0.923641i
$467$	−22.6129	+	16.4292i	−1.04640	+	0.760254i	−0.971525	−	0.236939i	$-0.923856\pi$
$467$	−22.6129	+	16.4292i	−1.04640	+	0.760254i	−0.0748753	+	0.997193i	$0.523856\pi$
$468$	1.02981	−	0.748201i	0.0476030	−	0.0345856i
$469$	0.126978	+	0.390799i	0.00586331	+	0.0180454i
$470$	−0.301832	+	0.928944i	−0.0139225	+	0.0428490i
$471$	3.11824	+	2.26553i	0.143681	+	0.104390i
$472$	36.3432			1.67283
$473$	−4.04650	−	1.21661i	−0.186058	−	0.0559398i
$474$	−2.32047			−0.106583
$475$	11.0586	+	8.03454i	0.507403	+	0.368650i
$476$	−0.399621	+	1.22991i	−0.0183166	+	0.0563727i
$477$	1.09968	+	3.38447i	0.0503509	+	0.154964i
$478$	16.9844	−	12.3399i	0.776847	−	0.564412i
$479$	−4.96379	+	3.60641i	−0.226801	+	0.164781i	−0.695383	−	0.718639i	$-0.744765\pi$
$479$	−4.96379	+	3.60641i	−0.226801	+	0.164781i	0.468582	+	0.883420i	$0.344765\pi$
$480$	0.305533	+	0.940335i	0.0139456	+	0.0429202i
$481$	−3.34770	+	10.3032i	−0.152642	+	0.469783i
$482$	−4.85413	−	3.52673i	−0.221100	−	0.160638i
$483$	2.56793			0.116845
$484$	3.73427	−	13.4949i	0.169739	−	0.613406i
$485$	−2.68063			−0.121721
$486$	−0.689843	−	0.501200i	−0.0312919	−	0.0227349i
$487$	2.01422	−	6.19913i	0.0912730	−	0.280910i	−0.894991	−	0.446083i	$-0.852818\pi$
$487$	2.01422	−	6.19913i	0.0912730	−	0.280910i	0.986264	+	0.165174i	$0.0528185\pi$
$488$	2.18263	+	6.71743i	0.0988028	+	0.304084i
$489$	−7.06734	+	5.13472i	−0.319596	+	0.232200i
$490$	0.425159	−	0.308896i	0.0192067	−	0.0139545i
$491$	0.538750	+	1.65810i	0.0243134	+	0.0748291i	0.962477	−	0.271363i	$-0.0874745\pi$
$491$	0.538750	+	1.65810i	0.0243134	+	0.0748291i	−0.938164	+	0.346192i	$0.887474\pi$
$492$	1.34309	−	4.13360i	0.0605510	−	0.186357i
$493$	2.75550	+	2.00199i	0.124101	+	0.0901649i
$494$	2.34512			0.105512
$495$	−0.548703	−	0.164972i	−0.0246624	−	0.00741494i
$496$	1.40380			0.0630323
$497$	−10.2434	−	7.44224i	−0.459478	−	0.333830i
$498$	−2.66430	+	8.19987i	−0.119390	+	0.367445i
$499$	4.54218	+	13.9794i	0.203336	+	0.625804i	0.999778	+	0.0210883i	$0.00671311\pi$
$499$	4.54218	+	13.9794i	0.203336	+	0.625804i	−0.796442	+	0.604715i	$0.793287\pi$
$500$	−1.77375	+	1.28871i	−0.0793245	+	0.0576327i
$501$	−11.3332	+	8.23408i	−0.506332	+	0.367872i
$502$	−5.64780	−	17.3821i	−0.252074	−	0.775803i
$503$	0.479902	−	1.47699i	0.0213978	−	0.0658556i	−0.939787	−	0.341760i	$-0.888977\pi$
$503$	0.479902	−	1.47699i	0.0213978	−	0.0658556i	0.961185	+	0.275904i	$0.0889772\pi$
$504$	−4.18300	−	3.03913i	−0.186326	−	0.135374i
$505$	−1.01550			−0.0451891
$506$	−2.37353	−	3.11953i	−0.105516	−	0.138680i
$507$	1.00000			0.0444116
$508$	−12.5314	−	9.10460i	−0.555991	−	0.403951i
$509$	7.79862	−	24.0017i	0.345668	−	1.06386i	−0.615558	−	0.788092i	$-0.711069\pi$
$509$	7.79862	−	24.0017i	0.345668	−	1.06386i	0.961225	−	0.275764i	$-0.0889308\pi$
$510$	−0.0249615	−	0.0768236i	−0.00110531	−	0.00340181i
$511$	−15.5212	+	11.2768i	−0.686617	+	0.498857i
$512$	−1.51955	+	1.10401i	−0.0671551	+	0.0487910i
$513$	0.849874	+	2.61564i	0.0375229	+	0.115484i
$514$	0.539020	−	1.65893i	0.0237752	−	0.0731724i
$515$	2.61528	+	1.90011i	0.115243	+	0.0837288i
$516$	−1.62171			−0.0713920
$517$	12.5300	−	18.0728i	0.551067	−	0.794839i
$518$	17.1143			0.751960
$519$	2.64775	+	1.92370i	0.116223	+	0.0844412i
$520$	−0.148985	+	0.458529i	−0.00653343	+	0.0201078i
$521$	5.94754	+	18.3046i	0.260566	+	0.801941i	0.992682	+	0.120760i	$0.0385332\pi$
$521$	5.94754	+	18.3046i	0.260566	+	0.801941i	−0.732115	+	0.681181i	$0.761467\pi$
$522$	−4.28479	+	3.11308i	−0.187540	+	0.136256i
$523$	4.89972	−	3.55985i	0.214250	−	0.155662i	−0.475485	−	0.879724i	$-0.657727\pi$
$523$	4.89972	−	3.55985i	0.214250	−	0.155662i	0.689734	+	0.724062i	$0.257727\pi$
$524$	1.83740	+	5.65494i	0.0802672	+	0.247037i
$525$	2.84548	−	8.75749i	0.124187	−	0.382208i
$526$	−5.61348	−	4.07843i	−0.244759	−	0.177828i
$527$	−4.63313			−0.201822
$528$	−0.0121767	−	0.550912i	−0.000529923	−	0.0239754i
$529$	−21.0789			−0.916472
$530$	−0.424099	−	0.308126i	−0.0184217	−	0.0133841i
$531$	−4.02419	+	12.3852i	−0.174635	+	0.537471i
$532$	2.00428	+	6.16853i	0.0868964	+	0.267440i
$533$	2.76236	−	2.00697i	0.119651	−	0.0869315i
$534$	5.01462	−	3.64334i	0.217004	−	0.157663i
$535$	0.252318	+	0.776554i	0.0109086	+	0.0335733i
$536$	0.191273	−	0.588677i	0.00826173	−	0.0254270i
$537$	14.8744	+	10.8069i	0.641879	+	0.466353i
$538$	4.40223			0.189794
$539$	−11.1695	+	3.90411i	−0.481105	+	0.168162i
$540$	−0.219904			−0.00946316
$541$	26.9164	+	19.5559i	1.15723	+	0.840775i	0.989425	−	0.145046i	$-0.0463330\pi$
$541$	26.9164	+	19.5559i	1.15723	+	0.840775i	0.167802	+	0.985821i	$0.446333\pi$
$542$	0.321022	−	0.988005i	0.0137891	−	0.0424385i
$543$	3.46728	+	10.6712i	0.148795	+	0.457944i
$544$	2.53900	−	1.84469i	0.108859	−	0.0790906i
$545$	−1.71201	+	1.24385i	−0.0733343	+	0.0532805i
$546$	−0.488178	−	1.50246i	−0.0208921	−	0.0642992i
$547$	−1.22152	+	3.75946i	−0.0522286	+	0.160743i	−0.973769	−	0.227540i	$-0.926932\pi$
$547$	−1.22152	+	3.75946i	−0.0522286	+	0.160743i	0.921540	+	0.388283i	$0.126932\pi$
$548$	13.0760	+	9.50027i	0.558579	+	0.405831i
$549$	−2.53087			−0.108015
$550$	−13.2687	+	4.63785i	−0.565780	+	0.197759i
$551$	17.0825			0.727740
$552$	−3.12942	−	2.27366i	−0.133197	−	0.0967733i
$553$	1.55800	−	4.79504i	0.0662531	−	0.203906i
$554$	−1.97522	−	6.07910i	−0.0839190	−	0.258276i
$555$	1.51410	−	1.10006i	0.0642700	−	0.0466949i
$556$	8.74059	−	6.35041i	0.370684	−	0.269317i
$557$	5.23602	+	16.1148i	0.221857	+	0.682806i	0.998595	+	0.0529825i	$0.0168728\pi$
$557$	5.23602	+	16.1148i	0.221857	+	0.682806i	−0.776738	+	0.629823i	$0.783127\pi$
$558$	2.22632	−	6.85189i	0.0942474	−	0.290064i
$559$	−1.03070	−	0.748848i	−0.0435940	−	0.0316729i
$560$	−0.0531776			−0.00224716
$561$	0.0401884	+	1.81825i	0.00169676	+	0.0767665i
$562$	17.7496			0.748720
$563$	−10.2414	−	7.44078i	−0.431622	−	0.313592i	0.350675	−	0.936497i	$-0.385952\pi$
$563$	−10.2414	−	7.44078i	−0.431622	−	0.313592i	−0.782297	+	0.622906i	$0.785952\pi$
$564$	2.60819	−	8.02719i	0.109825	−	0.338006i
$565$	0.962174	+	2.96127i	0.0404790	+	0.124581i
$566$	−20.3731	+	14.8020i	−0.856347	+	0.622172i
$567$	1.49886	−	1.08899i	0.0629462	−	0.0457331i
$568$	5.89374	+	18.1391i	0.247296	+	0.761099i
$569$	−10.9926	+	33.8318i	−0.460834	+	1.41830i	0.403313	+	0.915062i	$0.367859\pi$
$569$	−10.9926	+	33.8318i	−0.460834	+	1.41830i	−0.864147	+	0.503240i	$0.832141\pi$
$570$	−0.327760	−	0.238131i	−0.0137283	−	0.00997423i
$571$	−46.3864			−1.94121			−0.970606	−	0.240674i	$-0.922632\pi$
$571$	−46.3864			−1.94121			−0.970606	+	0.240674i	$0.922632\pi$
$572$	2.40542	−	3.46950i	0.100576	−	0.145067i
$573$	−19.2084			−0.802441
$574$	−4.36390	−	3.17056i	−0.182146	−	0.132337i
$575$	2.12878	−	6.55172i	0.0887764	−	0.273226i
$576$	1.40537	+	4.32529i	0.0585572	+	0.180220i
$577$	27.0680	−	19.6661i	1.12686	−	0.818709i	0.141623	−	0.989921i	$-0.454768\pi$
$577$	27.0680	−	19.6661i	1.12686	−	0.818709i	0.985234	+	0.171211i	$0.0547681\pi$
$578$	11.5199	−	8.36969i	0.479164	−	0.348133i
$579$	6.25783	+	19.2596i	0.260067	+	0.800403i
$580$	−0.422080	+	1.29903i	−0.0175259	+	0.0539392i
$581$	−15.1555	−	11.0111i	−0.628754	−	0.456817i
$582$	−13.2311			−0.548448
$583$	7.14674	+	9.39294i	0.295988	+	0.389016i
$584$	28.8996			1.19587
$585$	−0.139763	−	0.101543i	−0.00577847	−	0.00419831i
$586$	−2.93008	+	9.01787i	−0.121041	+	0.372525i
$587$	9.23585	+	28.4250i	0.381204	+	1.17323i	0.939197	+	0.343380i	$0.111572\pi$
$587$	9.23585	+	28.4250i	0.381204	+	1.17323i	−0.557993	+	0.829846i	$0.688428\pi$
$588$	−3.67388	+	2.66923i	−0.151508	+	0.110077i
$589$	−18.7993	+	13.6585i	−0.774612	+	0.562789i
$590$	−0.592794	−	1.82443i	−0.0244049	−	0.0751107i
$591$	−4.60176	+	14.1628i	−0.189291	+	0.582578i
$592$	1.45617	+	1.05797i	0.0598484	+	0.0434824i
$593$	−23.8386			−0.978935			−0.489468	−	0.872022i	$-0.662809\pi$
$593$	−23.8386			−0.978935			−0.489468	+	0.872022i	$0.662809\pi$
$594$	−2.70830	−	0.814271i	−0.111123	−	0.0334099i
$595$	0.175509			0.00719517
$596$	−13.3245	−	9.68081i	−0.545792	−	0.396541i
$597$	0.518170	−	1.59476i	0.0212073	−	0.0652694i
$598$	−0.365219	−	1.12403i	−0.0149349	−	0.0459650i
$599$	7.61027	−	5.52918i	0.310947	−	0.225916i	−0.421356	−	0.906895i	$-0.638446\pi$
$599$	7.61027	−	5.52918i	0.310947	−	0.225916i	0.732303	+	0.680979i	$0.238446\pi$
$600$	−11.2216	+	8.15297i	−0.458120	+	0.332844i
$601$	−0.616132	−	1.89626i	−0.0251326	−	0.0773500i	0.937704	−	0.347436i	$-0.112948\pi$
$601$	−0.616132	−	1.89626i	−0.0251326	−	0.0773500i	−0.962836	+	0.270086i	$0.912948\pi$
$602$	−0.621946	+	1.91415i	−0.0253486	+	0.0780151i
$603$	0.179433	+	0.130365i	0.00730706	+	0.00530889i
$604$	−7.95534			−0.323698
$605$	−1.89846	+	0.0839637i	−0.0771834	+	0.00341361i
$606$	−5.01231			−0.203611
$607$	−35.0770	−	25.4849i	−1.42373	−	1.03440i	−0.991142	−	0.132810i	$-0.957600\pi$
$607$	−35.0770	−	25.4849i	−1.42373	−	1.03440i	−0.432589	−	0.901591i	$-0.642400\pi$
$608$	4.86405	−	14.9700i	0.197263	−	0.607113i
$609$	−3.55603	−	10.9443i	−0.144098	−	0.443487i
$610$	0.301615	−	0.219136i	0.0122120	−	0.00887256i
$611$	5.36433	−	3.89741i	0.217017	−	0.157672i
$612$	0.215697	+	0.663848i	0.00871905	+	0.0268345i
$613$	13.9982	−	43.0821i	0.565383	−	1.74007i	−0.101430	−	0.994843i	$-0.532342\pi$
$613$	13.9982	−	43.0821i	0.565383	−	1.74007i	0.666812	−	0.745226i	$-0.267658\pi$
$614$	−14.3179	−	10.4026i	−0.577825	−	0.419814i
$615$	−0.589869			−0.0237858
$616$	−16.4223	−	4.93750i	−0.661675	−	0.198938i
$617$	−0.834176			−0.0335827			−0.0167913	−	0.999859i	$-0.505345\pi$
$617$	−0.834176			−0.0335827			−0.0167913	+	0.999859i	$0.505345\pi$
$618$	12.9085	+	9.37859i	0.519257	+	0.377262i
$619$	14.9306	−	45.9515i	0.600110	−	1.84695i	0.0726700	−	0.997356i	$-0.476848\pi$
$619$	14.9306	−	45.9515i	0.600110	−	1.84695i	0.527440	−	0.849592i	$-0.323152\pi$
$620$	−0.574153	−	1.76706i	−0.0230585	−	0.0709668i
$621$	1.12134	−	0.814700i	0.0449978	−	0.0326928i
$622$	−10.2297	+	7.43230i	−0.410173	+	0.298008i
$623$	4.16173	+	12.8085i	0.166736	+	0.513161i
$624$	0.0513422	−	0.158015i	0.00205533	−	0.00632566i
$625$	−19.8640	−	14.4320i	−0.794559	−	0.577281i
$626$	−1.47018			−0.0587604
$627$	5.52327	+	7.25921i	0.220578	+	0.289905i
$628$	4.90627			0.195782
$629$	−4.80601	−	3.49177i	−0.191628	−	0.139226i
$630$	−0.0843357	+	0.259558i	−0.00336001	+	0.0103411i
$631$	−10.2044	−	31.4058i	−0.406229	−	1.25024i	−0.919865	−	0.392236i	$-0.871702\pi$
$631$	−10.2044	−	31.4058i	−0.406229	−	1.25024i	0.513636	−	0.858008i	$-0.328298\pi$
$632$	−6.14423	+	4.46405i	−0.244405	+	0.177570i
$633$	15.3012	−	11.1170i	0.608167	−	0.441859i
$634$	3.26800	+	10.0579i	0.129789	+	0.399449i
$635$	−0.649618	+	1.99932i	−0.0257793	+	0.0793406i
$636$	3.66473	+	2.66258i	0.145316	+	0.105578i
$637$	−3.56753			−0.141351
$638$	−10.0084	+	14.4357i	−0.396235	+	0.571516i
$639$	−6.83411			−0.270353
$640$	1.05780	+	0.768538i	0.0418133	+	0.0303791i
$641$	−3.06457	+	9.43179i	−0.121043	+	0.372533i	−0.993159	−	0.116766i	$-0.962747\pi$
$641$	−3.06457	+	9.43179i	−0.121043	+	0.372533i	0.872116	+	0.489299i	$0.162747\pi$
$642$	1.24539	+	3.83293i	0.0491517	+	0.151274i
$643$	0.489273	−	0.355478i	0.0192950	−	0.0140187i	−0.578096	−	0.815969i	$-0.696204\pi$
$643$	0.489273	−	0.355478i	0.0192950	−	0.0140187i	0.597391	+	0.801950i	$0.296204\pi$
$644$	2.64448	−	1.92132i	0.104207	−	0.0757108i
$645$	0.0680128	+	0.209322i	0.00267800	+	0.00824204i
$646$	−0.397384	+	1.22302i	−0.0156348	+	0.0481191i
$647$	−22.5571	−	16.3887i	−0.886812	−	0.644307i	0.0482326	−	0.998836i	$-0.484641\pi$
$647$	−22.5571	−	16.3887i	−0.886812	−	0.644307i	−0.935045	+	0.354529i	$0.884641\pi$
$648$	−2.79079			−0.109633
$649$	0.954407	+	43.1803i	0.0374637	+	1.69498i
$650$	−4.23801			−0.166229
$651$	12.6641	+	9.20098i	0.496344	+	0.360615i
$652$	−3.43622	+	10.5756i	−0.134573	+	0.414172i
$653$	−1.89710	−	5.83868i	−0.0742394	−	0.228485i	0.907050	−	0.421022i	$-0.138329\pi$
$653$	−1.89710	−	5.83868i	−0.0742394	−	0.228485i	−0.981290	+	0.192537i	$0.938329\pi$
$654$	−8.45015	+	6.13940i	−0.330427	+	0.240069i
$655$	0.652849	−	0.474323i	0.0255089	−	0.0185333i
$656$	−0.175306	−	0.539536i	−0.00684454	−	0.0210653i
$657$	−3.19997	+	9.84851i	−0.124843	+	0.384227i
$658$	−8.47444	−	6.15704i	−0.330368	−	0.240026i
$659$	7.12501			0.277551			0.138776	−	0.990324i	$-0.455683\pi$
$659$	7.12501			0.277551			0.138776	+	0.990324i	$0.455683\pi$
$660$	−0.688493	+	0.240651i	−0.0267995	+	0.00936732i
$661$	2.04570			0.0795687			0.0397843	−	0.999208i	$-0.487333\pi$
$661$	2.04570			0.0795687			0.0397843	+	0.999208i	$0.487333\pi$
$662$	−3.15563	−	2.29270i	−0.122647	−	0.0891082i
$663$	−0.169451	+	0.521518i	−0.00658095	+	0.0202541i
$664$	8.72002	+	26.8375i	0.338403	+	1.04150i
$665$	0.712142	−	0.517401i	0.0276157	−	0.0200640i
$666$	7.47332	−	5.42969i	0.289585	−	0.210396i
$667$	−2.66036	−	8.18776i	−0.103010	−	0.317031i
$668$	−5.51034	+	16.9591i	−0.213202	+	0.656167i
$669$	5.63589	+	4.09471i	0.217896	+	0.158311i
$670$	−0.0326715			−0.00126221
$671$	−7.92385	+	2.76964i	−0.305897	+	0.106921i
$672$	−10.6034			−0.409036
$673$	−34.1284	−	24.7957i	−1.31555	−	0.955804i	−0.999976	−	0.00690374i	$-0.997802\pi$
$673$	−34.1284	−	24.7957i	−1.31555	−	0.955804i	−0.315575	−	0.948900i	$-0.602198\pi$
$674$	7.89030	−	24.2839i	0.303923	−	0.935379i
$675$	−1.53586	−	4.72690i	−0.0591154	−	0.181938i
$676$	1.02981	−	0.748201i	0.0396081	−	0.0287770i
$677$	−9.10079	+	6.61211i	−0.349772	+	0.254124i	−0.748773	−	0.662826i	$-0.769357\pi$
$677$	−9.10079	+	6.61211i	−0.349772	+	0.254124i	0.399002	+	0.916950i	$0.369357\pi$
$678$	4.74911	+	14.6163i	0.182389	+	0.561335i
$679$	8.88362	−	27.3410i	0.340922	−	1.04925i
$680$	−0.213885	−	0.155397i	−0.00820213	−	0.00595919i
$681$	9.25392			0.354611
$682$	−0.528010	−	23.8888i	−0.0202185	−	0.914750i
$683$	17.1656			0.656823			0.328412	−	0.944535i	$-0.393487\pi$
$683$	17.1656			0.656823			0.328412	+	0.944535i	$0.393487\pi$
$684$	2.83224	+	2.05774i	0.108293	+	0.0786797i
$685$	0.677849	−	2.08621i	0.0258993	−	0.0797098i
$686$	5.15883	+	15.8773i	0.196965	+	0.606196i
$687$	7.93611	−	5.76592i	0.302781	−	0.219984i
$688$	−0.171248	+	0.124419i	−0.00652875	+	0.00474342i
$689$	1.09968	+	3.38447i	0.0418945	+	0.128938i
$690$	−0.0630939	+	0.194183i	−0.00240194	+	0.00739242i
$691$	16.0049	+	11.6282i	0.608855	+	0.442359i	0.849011	−	0.528376i	$-0.177199\pi$
$691$	16.0049	+	11.6282i	0.608855	+	0.442359i	−0.240156	+	0.970734i	$0.577199\pi$
$692$	4.16600			0.158368
$693$	3.50102	−	5.04975i	0.132993	−	0.191824i
$694$	−25.5953			−0.971583
$695$	−1.18625	−	0.861857i	−0.0449968	−	0.0326921i
$696$	−5.35660	+	16.4859i	−0.203041	+	0.624897i
$697$	0.578585	+	1.78070i	0.0219155	+	0.0674489i
$698$	5.34952	−	3.88665i	0.202482	−	0.147112i
$699$	−19.8909	+	14.4516i	−0.752345	+	0.546610i
$700$	−3.62206	−	11.1475i	−0.136901	−	0.421338i
$701$	6.46511	−	19.8976i	0.244184	−	0.751521i	−0.751586	−	0.659636i	$-0.770711\pi$
$701$	6.46511	−	19.8976i	0.244184	−	0.751521i	0.995770	−	0.0918854i	$-0.0292893\pi$
$702$	−0.689843	−	0.501200i	−0.0260364	−	0.0189166i
$703$	−29.7945			−1.12372
$704$	9.13341	+	12.0040i	0.344228	+	0.452418i
$705$	−1.14549			−0.0431416
$706$	−10.0857	−	7.32770i	−0.379581	−	0.275782i
$707$	3.36536	−	10.3575i	0.126567	−	0.389534i
$708$	5.12245	+	15.7653i	0.192513	+	0.592496i
$709$	6.07072	−	4.41064i	0.227991	−	0.165645i	−0.467926	−	0.883768i	$-0.654998\pi$
$709$	6.07072	−	4.41064i	0.227991	−	0.165645i	0.695916	+	0.718123i	$0.254998\pi$
$710$	0.814451	−	0.591733i	0.0305658	−	0.0222074i
$711$	−0.840941	−	2.58815i	−0.0315377	−	0.0970632i
$712$	6.26899	−	19.2940i	0.234940	−	0.723072i
$713$	9.47433	+	6.88351i	0.354817	+	0.257789i
$714$	0.866280			0.0324197
$715$	−0.548703	−	0.164972i	−0.0205203	−	0.00616960i
$716$	23.4036			0.874634
$717$	19.9185	+	14.4717i	0.743871	+	0.540454i
$718$	2.87191	−	8.83882i	0.107179	−	0.329862i
$719$	−3.97587	−	12.2365i	−0.148275	−	0.456343i	0.849143	−	0.528163i	$-0.177119\pi$
$719$	−3.97587	−	12.2365i	−0.148275	−	0.456343i	−0.997418	+	0.0718203i	$0.977119\pi$
$720$	−0.0232211	+	0.0168711i	−0.000865400	+	0.000628750i
$721$	−28.0471	+	20.3774i	−1.04453	+	0.758894i
$722$	−3.01338	−	9.27422i	−0.112146	−	0.345151i
$723$	2.17442	−	6.69218i	0.0808676	−	0.248885i
$724$	11.5548	+	8.39508i	0.429432	+	0.312001i
$725$	−30.8709			−1.14652
$726$	−9.37045	+	0.414429i	−0.347770	+	0.0153809i
$727$	5.61078			0.208092			0.104046	−	0.994572i	$-0.466821\pi$
$727$	5.61078			0.208092			0.104046	+	0.994572i	$0.466821\pi$
$728$	−4.18300	−	3.03913i	−0.155032	−	0.112638i
$729$	0.309017	−	0.951057i	0.0114451	−	0.0352243i
$730$	−0.471381	−	1.45076i	−0.0174466	−	0.0536951i
$731$	0.565191	−	0.410635i	0.0209043	−	0.0151879i
$732$	−2.60632	+	1.89360i	−0.0963322	+	0.0699895i
$733$	−4.58181	−	14.1014i	−0.169233	−	0.520846i	0.830090	−	0.557629i	$-0.188289\pi$
$733$	−4.58181	−	14.1014i	−0.169233	−	0.520846i	−0.999323	+	0.0367834i	$0.988289\pi$
$734$	−2.06818	+	6.36521i	−0.0763379	+	0.234944i
$735$	0.498607	+	0.362259i	0.0183914	+	0.0133621i
$736$	−7.93272			−0.292404
$737$	0.704447	+	0.211797i	0.0259486	+	0.00780165i
$738$	−2.91148			−0.107173
$739$	28.7651	+	20.8991i	1.05814	+	0.768786i	0.973744	−	0.227647i	$-0.0731031\pi$
$739$	28.7651	+	20.8991i	1.05814	+	0.768786i	0.0843987	+	0.996432i	$0.473103\pi$
$740$	0.736172	−	2.26570i	0.0270622	−	0.0832889i
$741$	0.849874	+	2.61564i	0.0312209	+	0.0960881i
$742$	4.54818	−	3.30444i	0.166969	−	0.121310i
$743$	−25.4830	+	18.5145i	−0.934882	+	0.679232i	−0.947183	−	0.320693i	$-0.896084\pi$
$743$	−25.4830	+	18.5145i	−0.934882	+	0.679232i	0.0123011	+	0.999924i	$0.496084\pi$
$744$	−7.28654	−	22.4257i	−0.267138	−	0.822165i
$745$	−0.690731	+	2.12585i	−0.0253064	+	0.0778852i
$746$	−8.33625	−	6.05664i	−0.305212	−	0.221749i
$747$	−10.1113			−0.369954
$748$	1.40180	+	1.84238i	0.0512550	+	0.0673642i
$749$	−8.75659			−0.319959
$750$	1.18819	+	0.863269i	0.0433865	+	0.0315221i
$751$	−7.15116	+	22.0090i	−0.260950	+	0.803120i	0.731649	+	0.681681i	$0.238751\pi$
$751$	−7.15116	+	22.0090i	−0.260950	+	0.803120i	−0.992599	+	0.121439i	$0.961249\pi$
$752$	−0.340433	−	1.04775i	−0.0124143	−	0.0382074i
$753$	17.3405	−	12.5986i	0.631924	−	0.459119i
$754$	−4.28479	+	3.11308i	−0.156043	+	0.113372i
$755$	0.333638	+	1.02683i	0.0121423	+	0.0373702i
$756$	0.728761	−	2.24290i	0.0265048	−	0.0815734i
$757$	32.0521	+	23.2872i	1.16496	+	0.846389i	0.990396	−	0.138257i	$-0.0441501\pi$
$757$	32.0521	+	23.2872i	1.16496	+	0.846389i	0.174559	+	0.984647i	$0.444150\pi$
$758$	−15.5859			−0.566107
$759$	2.61921	−	3.77786i	0.0950714	−	0.137128i
$760$	−1.32597			−0.0480979
$761$	31.8139	+	23.1141i	1.15325	+	0.837886i	0.988910	−	0.148517i	$-0.0474501\pi$
$761$	31.8139	+	23.1141i	1.15325	+	0.837886i	0.164341	+	0.986404i	$0.447450\pi$
$762$	−3.20640	+	9.86827i	−0.116155	+	0.357490i
$763$	−7.01294	−	21.5836i	−0.253886	−	0.781379i
$764$	−19.7810	+	14.3717i	−0.715650	+	0.519950i
$765$	0.0766397	−	0.0556820i	0.00277091	−	0.00201319i
$766$	−2.19395	−	6.75228i	−0.0792706	−	0.243970i
$767$	−4.02419	+	12.3852i	−0.145305	+	0.447203i
$768$	12.5797	+	9.13972i	0.453932	+	0.329801i
$769$	−26.1930			−0.944542			−0.472271	−	0.881453i	$-0.656566\pi$
$769$	−26.1930			−0.944542			−0.472271	+	0.881453i	$0.656566\pi$
$770$	0.0200017	+	0.904939i	0.000720811	+	0.0326117i
$771$	2.04565			0.0736721
$772$	20.8545	+	15.1516i	0.750568	+	0.545320i
$773$	13.1535	−	40.4822i	0.473097	−	1.45604i	−0.375410	−	0.926859i	$-0.622498\pi$
$773$	13.1535	−	40.4822i	0.473097	−	1.45604i	0.848507	−	0.529185i	$-0.177502\pi$
$774$	0.335699	+	1.03317i	0.0120664	+	0.0371367i
$775$	33.9734	−	24.6832i	1.22036	−	0.886645i
$776$	−35.0339	+	25.4537i	−1.25765	+	0.913733i
$777$	6.20225	+	19.0886i	0.222505	+	0.684799i
$778$	−1.30649	+	4.02097i	−0.0468400	+	0.144159i
$779$	7.59717	+	5.51967i	0.272197	+	0.197763i
$780$	−0.219904			−0.00787382
$781$	−21.3968	+	7.47887i	−0.765636	+	0.267615i
$782$	0.648089			0.0231756
$783$	−5.02501	−	3.65089i	−0.179579	−	0.130472i
$784$	−0.183165	+	0.563724i	−0.00654160	+	0.0201330i
$785$	−0.205763	−	0.633274i	−0.00734400	−	0.0226025i
$786$	3.22234	−	2.34117i	0.114937	−	0.0835067i
$787$	28.9874	−	21.0605i	1.03329	−	0.750727i	0.0643236	−	0.997929i	$-0.479511\pi$
$787$	28.9874	−	21.0605i	1.03329	−	0.750727i	0.968964	+	0.247202i	$0.0795110\pi$
$788$	5.85765	+	18.0280i	0.208670	+	0.642221i
$789$	2.51458	−	7.73907i	0.0895213	−	0.275518i
$790$	0.324314	+	0.235628i	0.0115386	+	0.00838327i
$791$	−33.3919			−1.18728
$792$	−8.73763	+	3.05409i	−0.310478	+	0.108522i
$793$	−2.53087			−0.0898738
$794$	14.1468	+	10.2783i	0.502052	+	0.364762i
$795$	0.189976	−	0.584688i	0.00673777	−	0.0207367i
$796$	−0.659587	−	2.03000i	−0.0233785	−	0.0719515i
$797$	21.2971	−	15.4732i	0.754382	−	0.548090i	−0.142800	−	0.989752i	$-0.545611\pi$
$797$	21.2971	−	15.4732i	0.754382	−	0.548090i	0.897182	+	0.441661i	$0.145611\pi$
$798$	3.51500	−	2.55380i	0.124430	−	0.0904035i
$799$	1.12358	+	3.45801i	0.0397493	+	0.122336i
$800$	−8.79013	+	27.0532i	−0.310778	+	0.956476i
$801$	5.88093	+	4.27274i	0.207792	+	0.150970i
$802$	−21.5328			−0.760350
$803$	0.758931	+	34.3364i	0.0267821	+	1.21170i
$804$	0.282321			0.00995670
$805$	−0.358900	−	0.260756i	−0.0126496	−	0.00919044i
$806$	2.22632	−	6.85189i	0.0784186	−	0.241348i
$807$	1.59538	+	4.91006i	0.0561599	+	0.172842i
$808$	−13.2718	+	9.64255i	−0.466901	+	0.339224i
$809$	−7.47966	+	5.43429i	−0.262971	+	0.191059i	−0.711456	−	0.702731i	$-0.751964\pi$
$809$	−7.47966	+	5.43429i	−0.262971	+	0.191059i	0.448485	+	0.893790i	$0.351964\pi$
$810$	0.0455206	+	0.140098i	0.00159943	+	0.00492254i
$811$	0.108868	−	0.335060i	0.00382286	−	0.0117655i	−0.949127	−	0.314894i	$-0.898031\pi$
$811$	0.108868	−	0.335060i	0.00382286	−	0.0117655i	0.952950	+	0.303128i	$0.0980311\pi$
$812$	−11.8506	−	8.60996i	−0.415874	−	0.302150i
$813$	1.21832			0.0427283
$814$	17.4561	−	25.1781i	0.611837	−	0.882492i
$815$	1.50915			0.0528631
$816$	0.0737076	+	0.0535517i	0.00258028	+	0.00187469i
$817$	1.08275	−	3.33237i	0.0378807	−	0.116585i
$818$	−7.64991	−	23.5440i	−0.267473	−	0.823197i
$819$	1.49886	−	1.08899i	0.0523744	−	0.0380522i
$820$	−0.607453	+	0.441340i	−0.0212132	+	0.0154123i
$821$	−4.16149	−	12.8078i	−0.145237	−	0.446994i	0.851804	−	0.523860i	$-0.175509\pi$
$821$	−4.16149	−	12.8078i	−0.145237	−	0.446994i	−0.997041	+	0.0768662i	$0.975509\pi$
$822$	3.34574	−	10.2971i	0.116696	−	0.359154i
$823$	−37.0080	−	26.8879i	−1.29002	−	0.937252i	−0.290211	−	0.956963i	$-0.593726\pi$
$823$	−37.0080	−	26.8879i	−1.29002	−	0.937252i	−0.999806	+	0.0197106i	$0.993726\pi$
$824$	52.2220			1.81924
$825$	−9.98146	−	13.1186i	−0.347510	−	0.456731i
$826$	20.5727			0.715816
$827$	−1.39247	−	1.01169i	−0.0484208	−	0.0351798i	0.563312	−	0.826245i	$-0.309527\pi$
$827$	−1.39247	−	1.01169i	−0.0484208	−	0.0351798i	−0.611732	+	0.791065i	$0.709527\pi$
$828$	0.545207	−	1.67797i	0.0189472	−	0.0583136i
$829$	−3.58704	−	11.0398i	−0.124583	−	0.383427i	0.869242	−	0.494387i	$-0.164607\pi$
$829$	−3.58704	−	11.0398i	−0.124583	−	0.383427i	−0.993825	+	0.110960i	$0.964607\pi$
$830$	1.20501	−	0.875492i	0.0418266	−	0.0303888i
$831$	6.06454	−	4.40615i	0.210377	−	0.152848i
$832$	1.40537	+	4.32529i	0.0487225	+	0.149952i
$833$	0.604523	−	1.86053i	0.0209455	−	0.0644636i
$834$	−5.85509	−	4.25397i	−0.202745	−	0.147303i
$835$	2.42008			0.0837503
$836$	11.1193	+	3.34310i	0.384568	+	0.115623i
$837$	8.44913			0.292045
$838$	−17.8414	−	12.9626i	−0.616322	−	0.447784i
$839$	6.68508	−	20.5746i	0.230795	−	0.710313i	−0.766857	−	0.641818i	$-0.778180\pi$
$839$	6.68508	−	20.5746i	0.230795	−	0.710313i	0.997651	−	0.0684948i	$-0.0218197\pi$
$840$	0.276024	+	0.849513i	0.00952372	+	0.0293110i
$841$	−7.75015	+	5.63082i	−0.267247	+	0.194166i
$842$	17.8015	−	12.9336i	0.613481	−	0.445720i
$843$	6.43247	+	19.7971i	0.221546	+	0.681848i
$844$	7.43959	−	22.8967i	0.256081	−	0.788137i
$845$	−0.139763	−	0.101543i	−0.00480798	−	0.00349320i
$846$	−5.65392			−0.194386
$847$	5.43511	−	19.6415i	0.186753	−	0.674890i
$848$	0.591257			0.0203038
$849$	−23.8927	−	17.3591i	−0.819996	−	0.595762i
$850$	0.718137	−	2.21020i	0.0246319	−	0.0758092i
$851$	4.64008	+	14.2807i	0.159060	+	0.489536i
$852$	−7.03783	+	5.11329i	−0.241112	+	0.175178i
$853$	4.86655	−	3.53576i	0.166628	−	0.121062i	−0.501346	−	0.865247i	$-0.667162\pi$
$853$	4.86655	−	3.53576i	0.166628	−	0.121062i	0.667974	+	0.744185i	$0.267162\pi$
$854$	1.23551	+	3.80252i	0.0422784	+	0.130120i
$855$	0.146821	−	0.451868i	0.00502117	−	0.0154536i
$856$	10.6713	+	7.75314i	0.364737	+	0.264997i
$857$	35.8965			1.22620			0.613101	−	0.790005i	$-0.289922\pi$
$857$	35.8965			1.22620			0.613101	+	0.790005i	$0.289922\pi$
$858$	−2.70830	−	0.814271i	−0.0924598	−	0.0277988i
$859$	17.3215			0.591002			0.295501	−	0.955342i	$-0.404513\pi$
$859$	17.3215			0.591002			0.295501	+	0.955342i	$0.404513\pi$
$860$	0.226655	+	0.164675i	0.00772887	+	0.00561536i
$861$	1.95482	−	6.01633i	0.0666202	−	0.205036i
$862$	6.94193	+	21.3651i	0.236443	+	0.727697i
$863$	11.6154	−	8.43911i	0.395394	−	0.287271i	−0.372268	−	0.928125i	$-0.621420\pi$
$863$	11.6154	−	8.43911i	0.395394	−	0.287271i	0.767662	+	0.640855i	$0.221420\pi$
$864$	−4.63021	+	3.36404i	−0.157523	+	0.114447i
$865$	−0.174717	−	0.537724i	−0.00594056	−	0.0182832i
$866$	−6.81469	+	20.9735i	−0.231573	+	0.712707i
$867$	13.5100	+	9.81561i	0.458824	+	0.333355i
$868$	19.9258			0.676324
$869$	−5.46521	−	7.18290i	−0.185395	−	0.243663i
$870$	0.914966			0.0310203
$871$	0.179433	+	0.130365i	0.00607984	+	0.00441726i
$872$	−10.5639	+	32.5123i	−0.357739	+	1.10101i
$873$	−4.79498	−	14.7574i	−0.162285	−	0.499463i
$874$	2.62967	−	1.91057i	0.0889500	−	0.0646259i
$875$	−2.58164	+	1.87567i	−0.0872755	+	0.0634093i
$876$	4.07330	+	12.5363i	0.137624	+	0.423563i
$877$	9.93832	−	30.5870i	0.335593	−	1.03285i	−0.630836	−	0.775916i	$-0.717288\pi$
$877$	9.93832	−	30.5870i	0.335593	−	1.03285i	0.966429	−	0.256934i	$-0.0827121\pi$
$878$	−8.46192	−	6.14795i	−0.285576	−	0.207483i
$879$	−11.1200			−0.375069
$880$	−0.0542397	+	0.0782334i	−0.00182842	+	0.00263725i
$881$	0.467184			0.0157398			0.00786992	−	0.999969i	$-0.497495\pi$
$881$	0.467184			0.0157398			0.00786992	+	0.999969i	$0.497495\pi$
$882$	2.46103	+	1.78805i	0.0828674	+	0.0602067i
$883$	−11.7068	+	36.0297i	−0.393964	+	1.21250i	0.535802	+	0.844344i	$0.320009\pi$
$883$	−11.7068	+	36.0297i	−0.393964	+	1.21250i	−0.929766	+	0.368152i	$0.879991\pi$
$884$	0.215697	+	0.663848i	0.00725469	+	0.0223276i
$885$	1.82006	−	1.32235i	0.0611808	−	0.0444504i
$886$	−11.8496	+	8.60924i	−0.398095	+	0.289233i
$887$	17.0017	+	52.3257i	0.570860	+	1.75693i	0.649862	+	0.760052i	$0.274827\pi$
$887$	17.0017	+	52.3257i	0.570860	+	1.75693i	−0.0790020	+	0.996874i	$0.525173\pi$
$888$	9.34272	−	28.7539i	0.313521	−	0.964919i
$889$	−18.2391	−	13.2515i	−0.611720	−	0.444441i
$890$	−1.07081			−0.0358937
$891$	−0.0732888	−	3.31581i	−0.00245527	−	0.111084i
$892$	8.86757			0.296908
$893$	14.7532	+	10.7189i	0.493699	+	0.358693i
$894$	−3.40932	+	10.4928i	−0.114025	+	0.350932i
$895$	−0.981519	−	3.02080i	−0.0328086	−	0.100974i
$896$	−11.3442	+	8.24205i	−0.378984	+	0.275348i
$897$	1.12134	−	0.814700i	0.0374404	−	0.0272020i
$898$	0.247866	+	0.762854i	0.00827141	+	0.0254568i
$899$	16.2171	−	49.9112i	0.540871	−	1.66463i
$900$	−5.11832	−	3.71868i	−0.170611	−	0.123956i
$901$	−1.95140			−0.0650107
$902$	−9.11550	+	3.18617i	−0.303513	+	0.106088i
$903$	−2.36036			−0.0785478
$904$	40.6933	+	29.5654i	1.35344	+	0.983331i
$905$	0.598993	−	1.84351i	0.0199112	−	0.0612804i
$906$	1.64677	+	5.06825i	0.0547104	+	0.168381i
$907$	22.7898	−	16.5577i	0.756722	−	0.549790i	−0.141181	−	0.989984i	$-0.545090\pi$
$907$	22.7898	−	16.5577i	0.756722	−	0.549790i	0.897903	+	0.440193i	$0.145090\pi$
$908$	9.52979	−	6.92380i	0.316257	−	0.229774i
$909$	−1.81647	−	5.59052i	−0.0602485	−	0.185426i
$910$	−0.0843357	+	0.259558i	−0.00279570	+	0.00860428i
$911$	−30.8279	−	22.3978i	−1.02137	−	0.742072i	−0.0548102	−	0.998497i	$-0.517455\pi$
$911$	−30.8279	−	22.3978i	−1.02137	−	0.742072i	−0.966564	+	0.256425i	$0.917455\pi$
$912$	0.456946			0.0151310
$913$	−31.6573	+	11.0653i	−1.04771	+	0.366207i
$914$	−4.53377			−0.149964
$915$	0.353721	+	0.256993i	0.0116937	+	0.00849594i
$916$	3.85862	−	11.8756i	0.127492	−	0.392381i
$917$	2.67428	+	8.23060i	0.0883126	+	0.271798i
$918$	0.378280	−	0.274836i	0.0124851	−	0.00907095i
$919$	−34.4445	+	25.0254i	−1.13622	+	0.825512i	−0.986588	−	0.163230i	$-0.947809\pi$
$919$	−34.4445	+	25.0254i	−1.13622	+	0.825512i	−0.149632	+	0.988742i	$0.547809\pi$
$920$	0.206501	+	0.635544i	0.00680813	+	0.0209533i
$921$	6.41376	−	19.7395i	0.211341	−	0.650440i
$922$	27.8295	+	20.2193i	0.916515	+	0.665887i
$923$	−6.83411			−0.224947
$924$	−0.172839	−	7.81976i	−0.00568597	−	0.257251i
$925$	53.8436			1.77037
$926$	3.99891	+	2.90538i	0.131412	+	0.0954766i
$927$	−5.78241	+	17.7964i	−0.189919	+	0.584511i
$928$	10.9851	+	33.8087i	0.360604	+	1.10983i
$929$	15.6391	−	11.3625i	0.513102	−	0.372790i	−0.300897	−	0.953657i	$-0.597286\pi$
$929$	15.6391	−	11.3625i	0.513102	−	0.372790i	0.813999	+	0.580866i	$0.197286\pi$
$930$	−1.00692	+	0.731571i	−0.0330182	+	0.0239891i
$931$	−3.03195	−	9.33139i	−0.0993683	−	0.305824i
$932$	−9.67119	+	29.7649i	−0.316790	+	0.974980i
$933$	−11.9969	−	8.71628i	−0.392762	−	0.285358i
$934$	23.8337			0.779861
$935$	0.179014	−	0.258204i	0.00585440	−	0.00844417i
$936$	−2.79079			−0.0912198
$937$	44.3795	+	32.2436i	1.44982	+	1.05335i	0.985874	+	0.167488i	$0.0535656\pi$
$937$	44.3795	+	32.2436i	1.44982	+	1.05335i	0.463943	+	0.885865i	$0.346434\pi$
$938$	0.108273	−	0.333231i	0.00353525	−	0.0108804i
$939$	−0.532797	−	1.63978i	−0.0173872	−	0.0535122i
$940$	−1.17964	+	0.857056i	−0.0384755	+	0.0279541i
$941$	13.1670	−	9.56640i	0.429233	−	0.311856i	−0.352109	−	0.935959i	$-0.614535\pi$
$941$	13.1670	−	9.56640i	0.429233	−	0.311856i	0.781342	+	0.624103i	$0.214535\pi$
$942$	−1.01561	−	3.12572i	−0.0330903	−	0.101842i
$943$	1.46246	−	4.50098i	0.0476242	−	0.146572i
$944$	1.75043	+	1.27176i	0.0569717	+	0.0413924i
$945$	−0.320064			−0.0104117
$946$	2.18168	+	2.86737i	0.0709325	+	0.0932263i
$947$	22.3602			0.726608			0.363304	−	0.931671i	$-0.381649\pi$
$947$	22.3602			0.726608			0.363304	+	0.931671i	$0.381649\pi$
$948$	−2.80247	−	2.03611i	−0.0910199	−	0.0661298i
$949$	−3.19997	+	9.84851i	−0.103876	+	0.319696i
$950$	−3.60178	−	11.0851i	−0.116857	−	0.359649i
$951$	−10.0338	+	7.28998i	−0.325368	+	0.236394i
$952$	2.29378	−	1.66653i	0.0743417	−	0.0540124i
$953$	−1.16474	−	3.58470i	−0.0377296	−	0.116120i	0.930418	−	0.366501i	$-0.119444\pi$
$953$	−1.16474	−	3.58470i	−0.0377296	−	0.116120i	−0.968147	+	0.250381i	$0.919444\pi$
$954$	0.937689	−	2.88591i	0.0303588	−	0.0934348i
$955$	2.68461	+	1.95048i	0.0868719	+	0.0631162i
$956$	31.3400			1.01361
$957$	−19.7280	−	5.93139i	−0.637717	−	0.191734i
$958$	5.23176			0.169031
$959$	19.0317	+	13.8274i	0.614567	+	0.446509i
$960$	0.242787	−	0.747220i	0.00783590	−	0.0241164i
$961$	12.4805	+	38.4111i	0.402597	+	1.23907i
$962$	7.47332	−	5.42969i	0.240950	−	0.175060i
$963$	−3.82375	+	2.77812i	−0.123219	+	0.0895236i
$964$	−2.76786	−	8.51859i	−0.0891467	−	0.274365i
$965$	1.08108	−	3.32722i	0.0348011	−	0.107107i
$966$	−1.77146	−	1.28704i	−0.0569959	−	0.0414100i
$967$	−27.9890			−0.900064			−0.450032	−	0.893012i	$-0.648588\pi$
$967$	−27.9890			−0.900064			−0.450032	+	0.893012i	$0.648588\pi$
$968$	−24.0142	+	19.1240i	−0.771847	+	0.614667i
$969$	−1.50812			−0.0484477
$970$	1.84922	+	1.34353i	0.0593747	+	0.0431383i
$971$	1.27345	−	3.91927i	0.0408669	−	0.125775i	−0.928542	−	0.371228i	$-0.878937\pi$
$971$	1.27345	−	3.91927i	0.0408669	−	0.125775i	0.969408	+	0.245453i	$0.0789367\pi$
$972$	−0.393353	−	1.21061i	−0.0126168	−	0.0388305i
$973$	12.7217	−	9.24284i	0.407838	−	0.296312i
$974$	−4.49650	+	3.26690i	−0.144077	+	0.104678i
$975$	−1.53586	−	4.72690i	−0.0491870	−	0.151382i
$976$	−0.129940	+	0.399915i	−0.00415929	+	0.0128010i
$977$	4.47089	+	3.24829i	0.143036	+	0.103922i	0.657002	−	0.753889i	$-0.271824\pi$
$977$	4.47089	+	3.24829i	0.143036	+	0.103922i	−0.513966	+	0.857811i	$0.671824\pi$
$978$	7.44888			0.238189
$979$	23.0883	+	6.94168i	0.737906	+	0.221857i
$980$	0.784514			0.0250604
$981$	−9.90997	−	7.20001i	−0.316401	−	0.229879i
$982$	0.459388	−	1.41385i	0.0146597	−	0.0451178i
$983$	17.5414	+	53.9870i	0.559485	+	1.72192i	0.683794	+	0.729675i	$0.260329\pi$
$983$	17.5414	+	53.9870i	0.559485	+	1.72192i	−0.124309	+	0.992244i	$0.539671\pi$
$984$	−7.70916	+	5.60103i	−0.245759	+	0.178554i
$985$	2.08129	−	1.51214i	0.0663154	−	0.0481809i
$986$	−0.897464	−	2.76211i	−0.0285811	−	0.0879635i
$987$	3.79615	−	11.6833i	0.120833	−	0.371885i
$988$	2.83224	+	2.05774i	0.0901055	+	0.0654655i
$989$	−1.76585			−0.0561508
$990$	0.295835	+	0.388815i	0.00940226	+	0.0123573i
$991$	−36.9761			−1.17459			−0.587293	−	0.809375i	$-0.699806\pi$
$991$	−36.9761			−1.17459			−0.587293	+	0.809375i	$0.699806\pi$
$992$	−39.1212	−	28.4232i	−1.24210	−	0.902439i
$993$	1.41357	−	4.35053i	0.0448584	−	0.138060i
$994$	3.33626	+	10.2679i	0.105820	+	0.325680i
$995$	−0.234359	+	0.170272i	−0.00742967	+	0.00539797i
$996$	−10.4128	+	7.56531i	−0.329941	+	0.239716i
$997$	−16.1240	−	49.6247i	−0.510654	−	1.57163i	−0.791053	−	0.611747i	$-0.790467\pi$
$997$	−16.1240	−	49.6247i	−0.510654	−	1.57163i	0.280400	−	0.959883i	$-0.409533\pi$
$998$	3.87308	−	11.9201i	0.122600	−	0.377325i
$999$	8.76439	+	6.36770i	0.277293	+	0.201465i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.n.a.235.1	yes	12
11.3	even	5	inner	429.2.n.a.157.1	✓	12
11.5	even	5		4719.2.a.bg.1.5		6
11.6	odd	10		4719.2.a.bh.1.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.n.a.157.1	✓	12	11.3	even	5	inner
429.2.n.a.235.1	yes	12	1.1	even	1	trivial
4719.2.a.bg.1.5		6	11.5	even	5
4719.2.a.bh.1.2		6	11.6	odd	10

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:	\( N \)	\(=\)	\( 429 = 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	429.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.689843 - 0.501200i) q^{2} +(0.309017 - 0.951057i) q^{3} +(-0.393353 - 1.21061i) q^{4} +(-0.139763 + 0.101543i) q^{5} +(-0.689843 + 0.501200i) q^{6} +(-0.572513 - 1.76202i) q^{7} +(-0.862402 + 2.65420i) q^{8} +(-0.809017 - 0.587785i) q^{9} +O(q^{10})\)	\(q+(-0.689843 - 0.501200i) q^{2} +(0.309017 - 0.951057i) q^{3} +(-0.393353 - 1.21061i) q^{4} +(-0.139763 + 0.101543i) q^{5} +(-0.689843 + 0.501200i) q^{6} +(-0.572513 - 1.76202i) q^{7} +(-0.862402 + 2.65420i) q^{8} +(-0.809017 - 0.587785i) q^{9} +0.147308 q^{10} +(-3.17617 - 0.954941i) q^{11} -1.27292 q^{12} +(-0.809017 - 0.587785i) q^{13} +(-0.488178 + 1.50246i) q^{14} +(0.0533846 + 0.164301i) q^{15} +(-0.134416 + 0.0976586i) q^{16} +(0.443630 - 0.322316i) q^{17} +(0.263496 + 0.810959i) q^{18} +(0.849874 - 2.61564i) q^{19} +(0.177906 + 0.129256i) q^{20} -1.85269 q^{21} +(1.71244 + 2.25066i) q^{22} -1.38605 q^{23} +(2.25780 + 1.64039i) q^{24} +(-1.53586 + 4.72690i) q^{25} +(0.263496 + 0.810959i) q^{26} +(-0.809017 + 0.587785i) q^{27} +(-1.90792 + 1.38619i) q^{28} +(1.91938 + 5.90726i) q^{29} +(0.0455206 - 0.140098i) q^{30} +(-6.83549 - 4.96627i) q^{31} +5.72325 q^{32} +(-1.88970 + 2.72563i) q^{33} -0.467579 q^{34} +(0.258937 + 0.188129i) q^{35} +(-0.393353 + 1.21061i) q^{36} +(-3.34770 - 10.3032i) q^{37} +(-1.89724 + 1.37843i) q^{38} +(-0.809017 + 0.587785i) q^{39} +(-0.148985 - 0.458529i) q^{40} +(-1.05513 + 3.24734i) q^{41} +(1.27807 + 0.928569i) q^{42} +1.27402 q^{43} +(0.0932905 + 4.22075i) q^{44} +0.172756 q^{45} +(0.956157 + 0.694689i) q^{46} +(-2.04899 + 6.30614i) q^{47} +(0.0513422 + 0.158015i) q^{48} +(2.88619 - 2.09694i) q^{49} +(3.42862 - 2.49104i) q^{50} +(-0.169451 - 0.521518i) q^{51} +(-0.393353 + 1.21061i) q^{52} +(-2.87900 - 2.09172i) q^{53} +0.852692 q^{54} +(0.540878 - 0.189055i) q^{55} +5.17048 q^{56} +(-2.22500 - 1.61656i) q^{57} +(1.63664 - 5.03707i) q^{58} +(-4.02419 - 12.3852i) q^{59} +(0.177906 - 0.129256i) q^{60} +(2.04752 - 1.48761i) q^{61} +(2.22632 + 6.85189i) q^{62} +(-0.572513 + 1.76202i) q^{63} +(-3.67931 - 2.67318i) q^{64} +0.172756 q^{65} +(2.66968 - 0.933140i) q^{66} -0.221791 q^{67} +(-0.564703 - 0.410281i) q^{68} +(-0.428313 + 1.31821i) q^{69} +(-0.0843357 - 0.259558i) q^{70} +(5.52891 - 4.01699i) q^{71} +(2.25780 - 1.64039i) q^{72} +(-3.19997 - 9.84851i) q^{73} +(-2.85456 + 8.78542i) q^{74} +(4.02094 + 2.92138i) q^{75} -3.50084 q^{76} +(0.135782 + 6.14318i) q^{77} +0.852692 q^{78} +(2.20161 + 1.59956i) q^{79} +(0.00886967 - 0.0272980i) q^{80} +(0.309017 + 0.951057i) q^{81} +(2.35544 - 1.71133i) q^{82} +(8.18023 - 5.94329i) q^{83} +(0.728761 + 2.24290i) q^{84} +(-0.0292738 + 0.0900954i) q^{85} +(-0.878870 - 0.638537i) q^{86} +6.21126 q^{87} +(5.27374 - 7.60666i) q^{88} -7.26923 q^{89} +(-0.119174 - 0.0865853i) q^{90} +(-0.572513 + 1.76202i) q^{91} +(0.545207 + 1.67797i) q^{92} +(-6.83549 + 4.96627i) q^{93} +(4.57412 - 3.32329i) q^{94} +(0.146821 + 0.451868i) q^{95} +(1.76858 - 5.44314i) q^{96} +(12.5534 + 9.12059i) q^{97} -3.04201 q^{98} +(2.00828 + 2.63947i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 3 q^{2} - 3 q^{3} - 3 q^{4} + 8 q^{5} + 3 q^{6} + 5 q^{7} - q^{8} - 3 q^{9}+O(q^{10}) \) 12 * q + 3 * q^2 - 3 * q^3 - 3 * q^4 + 8 * q^5 + 3 * q^6 + 5 * q^7 - q^8 - 3 * q^9	\( 12 q + 3 q^{2} - 3 q^{3} - 3 q^{4} + 8 q^{5} + 3 q^{6} + 5 q^{7} - q^{8} - 3 q^{9} + 14 q^{10} - 6 q^{11} + 2 q^{12} - 3 q^{13} + 11 q^{14} - 2 q^{15} - 5 q^{16} - 14 q^{17} - 2 q^{18} - 2 q^{19} - 9 q^{20} - 10 q^{21} + 21 q^{22} - 6 q^{23} + 4 q^{24} + 19 q^{25} - 2 q^{26} - 3 q^{27} - 12 q^{28} - 12 q^{29} - q^{30} - 12 q^{31} + 26 q^{32} + 9 q^{33} - 24 q^{34} - 2 q^{35} - 3 q^{36} + 4 q^{37} - 13 q^{38} - 3 q^{39} + 4 q^{40} - 10 q^{41} + q^{42} + 28 q^{43} - 12 q^{45} - 5 q^{46} + 28 q^{47} + 10 q^{48} + 20 q^{49} - q^{50} + 11 q^{51} - 3 q^{52} - 29 q^{53} - 2 q^{54} + 4 q^{55} + 12 q^{56} + 8 q^{57} + 22 q^{58} - 11 q^{59} - 9 q^{60} - 18 q^{61} + 40 q^{62} + 5 q^{63} + 11 q^{64} - 12 q^{65} + 16 q^{66} - 72 q^{67} - 35 q^{68} + 4 q^{69} - 6 q^{70} + 10 q^{71} + 4 q^{72} - 11 q^{73} - 15 q^{74} - 11 q^{75} + 4 q^{76} + 20 q^{77} - 2 q^{78} - 7 q^{79} - 27 q^{80} - 3 q^{81} - 10 q^{82} + 16 q^{83} + 8 q^{84} - 26 q^{85} - 35 q^{86} + 28 q^{87} + 25 q^{88} - 62 q^{89} - 6 q^{90} + 5 q^{91} - 34 q^{92} - 12 q^{93} - q^{94} + 15 q^{95} + q^{96} + 54 q^{97} + 50 q^{98} - 6 q^{99}+O(q^{100}) \) 12 * q + 3 * q^2 - 3 * q^3 - 3 * q^4 + 8 * q^5 + 3 * q^6 + 5 * q^7 - q^8 - 3 * q^9 + 14 * q^10 - 6 * q^11 + 2 * q^12 - 3 * q^13 + 11 * q^14 - 2 * q^15 - 5 * q^16 - 14 * q^17 - 2 * q^18 - 2 * q^19 - 9 * q^20 - 10 * q^21 + 21 * q^22 - 6 * q^23 + 4 * q^24 + 19 * q^25 - 2 * q^26 - 3 * q^27 - 12 * q^28 - 12 * q^29 - q^30 - 12 * q^31 + 26 * q^32 + 9 * q^33 - 24 * q^34 - 2 * q^35 - 3 * q^36 + 4 * q^37 - 13 * q^38 - 3 * q^39 + 4 * q^40 - 10 * q^41 + q^42 + 28 * q^43 - 12 * q^45 - 5 * q^46 + 28 * q^47 + 10 * q^48 + 20 * q^49 - q^50 + 11 * q^51 - 3 * q^52 - 29 * q^53 - 2 * q^54 + 4 * q^55 + 12 * q^56 + 8 * q^57 + 22 * q^58 - 11 * q^59 - 9 * q^60 - 18 * q^61 + 40 * q^62 + 5 * q^63 + 11 * q^64 - 12 * q^65 + 16 * q^66 - 72 * q^67 - 35 * q^68 + 4 * q^69 - 6 * q^70 + 10 * q^71 + 4 * q^72 - 11 * q^73 - 15 * q^74 - 11 * q^75 + 4 * q^76 + 20 * q^77 - 2 * q^78 - 7 * q^79 - 27 * q^80 - 3 * q^81 - 10 * q^82 + 16 * q^83 + 8 * q^84 - 26 * q^85 - 35 * q^86 + 28 * q^87 + 25 * q^88 - 62 * q^89 - 6 * q^90 + 5 * q^91 - 34 * q^92 - 12 * q^93 - q^94 + 15 * q^95 + q^96 + 54 * q^97 + 50 * q^98 - 6 * q^99

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