LMFDB - Embedded newform 429.2.bn.a.4.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(4,429)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(429, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 6, 5]))

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

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

chi := DirichletCharacter("429.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.bn (of order $30$, 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:	$3.42558224671$
Analytic rank:	$0$
Dimension:	$112$
Relative dimension:	$14$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			4.6
Character	$\chi$	$=$	429.4
Dual form			429.2.bn.a.322.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.177986 - 0.399764i) q^{2} +(-0.669131 - 0.743145i) q^{3} +(1.21013 - 1.34398i) q^{4} +(0.0311778 + 0.0429126i) q^{5} +(-0.177986 + 0.399764i) q^{6} +(-0.860670 - 0.774951i) q^{7} +(-1.58502 - 0.515004i) q^{8} +(-0.104528 + 0.994522i) q^{9} +O(q^{10})$	\(q+(-0.177986 - 0.399764i) q^{2} +(-0.669131 - 0.743145i) q^{3} +(1.21013 - 1.34398i) q^{4} +(0.0311778 + 0.0429126i) q^{5} +(-0.177986 + 0.399764i) q^{6} +(-0.860670 - 0.774951i) q^{7} +(-1.58502 - 0.515004i) q^{8} +(-0.104528 + 0.994522i) q^{9} +(0.0116057 - 0.0201016i) q^{10} +(2.76016 - 1.83890i) q^{11} -1.80851 q^{12} +(-2.10385 - 2.92811i) q^{13} +(-0.156610 + 0.481996i) q^{14} +(0.0110282 - 0.0518838i) q^{15} +(-0.301850 - 2.87191i) q^{16} +(0.269984 + 0.120205i) q^{17} +(0.416179 - 0.135225i) q^{18} +(-0.314975 - 1.48184i) q^{19} +(0.0954031 + 0.0100273i) q^{20} +1.15815i q^{21} +(-1.22639 - 0.776112i) q^{22} +(-4.32080 + 7.48384i) q^{23} +(0.677863 + 1.52250i) q^{24} +(1.54422 - 4.75261i) q^{25} +(-0.796095 + 1.36221i) q^{26} +(0.809017 - 0.587785i) q^{27} +(-2.08304 + 0.218937i) q^{28} +(-4.27383 - 0.908431i) q^{29} +(-0.0227041 + 0.00482591i) q^{30} +(1.96992 - 2.71137i) q^{31} +(-3.98098 + 2.29842i) q^{32} +(-3.21347 - 0.820732i) q^{33} -0.129325i q^{34} +(0.00642133 - 0.0610949i) q^{35} +(1.21013 + 1.34398i) q^{36} +(-1.10543 + 5.20065i) q^{37} +(-0.536325 + 0.389663i) q^{38} +(-0.768257 + 3.52275i) q^{39} +(-0.0273173 - 0.0840741i) q^{40} +(6.37076 - 5.73626i) q^{41} +(0.462985 - 0.206134i) q^{42} +(-2.52214 - 4.36848i) q^{43} +(0.868694 - 5.93491i) q^{44} +(-0.0459365 + 0.0265214i) q^{45} +(3.76081 + 0.395277i) q^{46} +(2.50282 + 0.813214i) q^{47} +(-1.93227 + 2.14600i) q^{48} +(-0.591495 - 5.62770i) q^{49} +(-2.17477 + 0.228578i) q^{50} +(-0.0913251 - 0.281070i) q^{51} +(-6.48126 - 0.715846i) q^{52} +(5.00551 + 3.63672i) q^{53} +(-0.378969 - 0.218798i) q^{54} +(0.164968 + 0.0611126i) q^{55} +(0.965077 + 1.67156i) q^{56} +(-0.890463 + 1.22562i) q^{57} +(0.397526 + 1.87021i) q^{58} +(3.18835 + 2.87080i) q^{59} +(-0.0563854 - 0.0776078i) q^{60} +(-7.64149 - 3.40221i) q^{61} +(-1.43453 - 0.304918i) q^{62} +(0.860670 - 0.774951i) q^{63} +(-3.04506 - 2.21236i) q^{64} +(0.0600592 - 0.181574i) q^{65} +(0.243855 + 1.43071i) q^{66} +(9.39903 + 5.42653i) q^{67} +(0.488269 - 0.217391i) q^{68} +(8.45276 - 1.79669i) q^{69} +(-0.0255664 + 0.00830704i) q^{70} +(-0.503866 + 1.13170i) q^{71} +(0.677863 - 1.52250i) q^{72} +(11.4470 - 3.71935i) q^{73} +(2.27578 - 0.483733i) q^{74} +(-4.56516 + 2.03254i) q^{75} +(-2.37273 - 1.36990i) q^{76} +(-3.80064 - 0.556301i) q^{77} +(1.54501 - 0.319880i) q^{78} +(7.95811 + 5.78190i) q^{79} +(0.113830 - 0.102493i) q^{80} +(-0.978148 - 0.207912i) q^{81} +(-3.42706 - 1.52582i) q^{82} +(7.53731 + 10.3742i) q^{83} +(1.55653 + 1.40151i) q^{84} +(0.00325922 + 0.0153334i) q^{85} +(-1.29745 + 1.78579i) q^{86} +(2.18466 + 3.78393i) q^{87} +(-5.32194 + 1.49320i) q^{88} +(6.23579 + 3.60024i) q^{89} +(0.0187784 + 0.0136433i) q^{90} +(-0.458418 + 4.15052i) q^{91} +(4.82945 + 14.8635i) q^{92} +(-3.33307 + 0.350320i) q^{93} +(-0.120373 - 1.14528i) q^{94} +(0.0537694 - 0.0597170i) q^{95} +(4.37185 + 1.42050i) q^{96} +(11.7466 + 1.23462i) q^{97} +(-2.14447 + 1.23811i) q^{98} +(1.54031 + 2.93725i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q - 14 q^{3} - 20 q^{4} + 14 q^{9}+O(q^{10}) $ 112 * q - 14 * q^3 - 20 * q^4 + 14 * q^9	$ 112 q - 14 q^{3} - 20 q^{4} + 14 q^{9} + 21 q^{11} + 120 q^{12} - 15 q^{13} + 30 q^{14} - 6 q^{15} - 8 q^{16} - 12 q^{19} - 66 q^{20} - 17 q^{22} + 12 q^{23} + 14 q^{25} + 9 q^{26} + 28 q^{27} + 18 q^{28} - 2 q^{29} + 10 q^{30} - 30 q^{32} - 24 q^{33} + 16 q^{35} - 20 q^{36} + 38 q^{38} - 12 q^{39} - 60 q^{40} - 36 q^{41} + 12 q^{43} - 6 q^{45} + 54 q^{46} - 42 q^{48} - 40 q^{49} - 51 q^{50} - 30 q^{51} - 15 q^{52} - 22 q^{53} + 22 q^{55} - 76 q^{56} + 132 q^{58} + 72 q^{59} + 34 q^{61} + 17 q^{62} - 84 q^{64} + 28 q^{65} - 24 q^{66} - 48 q^{67} - 12 q^{68} - 7 q^{69} + 30 q^{71} + 20 q^{74} + 32 q^{75} - 48 q^{76} - 136 q^{77} - 14 q^{78} - 36 q^{79} + 18 q^{80} + 14 q^{81} - 5 q^{82} - 27 q^{84} - 66 q^{85} + 52 q^{87} + 52 q^{88} - 96 q^{89} - 20 q^{90} - 125 q^{91} - 10 q^{92} - 18 q^{93} + 22 q^{94} + 72 q^{95} - 93 q^{97} + 24 q^{98}+O(q^{100}) $ 112 * q - 14 * q^3 - 20 * q^4 + 14 * q^9 + 21 * q^11 + 120 * q^12 - 15 * q^13 + 30 * q^14 - 6 * q^15 - 8 * q^16 - 12 * q^19 - 66 * q^20 - 17 * q^22 + 12 * q^23 + 14 * q^25 + 9 * q^26 + 28 * q^27 + 18 * q^28 - 2 * q^29 + 10 * q^30 - 30 * q^32 - 24 * q^33 + 16 * q^35 - 20 * q^36 + 38 * q^38 - 12 * q^39 - 60 * q^40 - 36 * q^41 + 12 * q^43 - 6 * q^45 + 54 * q^46 - 42 * q^48 - 40 * q^49 - 51 * q^50 - 30 * q^51 - 15 * q^52 - 22 * q^53 + 22 * q^55 - 76 * q^56 + 132 * q^58 + 72 * q^59 + 34 * q^61 + 17 * q^62 - 84 * q^64 + 28 * q^65 - 24 * q^66 - 48 * q^67 - 12 * q^68 - 7 * q^69 + 30 * q^71 + 20 * q^74 + 32 * q^75 - 48 * q^76 - 136 * q^77 - 14 * q^78 - 36 * q^79 + 18 * q^80 + 14 * q^81 - 5 * q^82 - 27 * q^84 - 66 * q^85 + 52 * q^87 + 52 * q^88 - 96 * q^89 - 20 * q^90 - 125 * q^91 - 10 * q^92 - 18 * q^93 + 22 * q^94 + 72 * q^95 - 93 * q^97 + 24 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$67$	$79$	$287$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{5}\right)$	$1$

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 $

$2$	−0.177986	−	0.399764i	−0.125855	−	0.282676i	0.839618	−	0.543177i	$-0.182779\pi$
$2$	−0.177986	−	0.399764i	−0.125855	−	0.282676i	−0.965473	+	0.260501i	$0.916112\pi$
$3$	−0.669131	−	0.743145i	−0.386323	−	0.429055i
$3$	−0.669131	−	0.743145i	−0.386323	−	0.429055i
$4$	1.21013	−	1.34398i	0.605065	−	0.671992i
$5$	0.0311778	+	0.0429126i	0.0139431	+	0.0191911i	0.815932	−	0.578148i	$-0.196225\pi$
$5$	0.0311778	+	0.0429126i	0.0139431	+	0.0191911i	−0.801989	+	0.597339i	$0.796225\pi$
$6$	−0.177986	+	0.399764i	−0.0726626	+	0.163203i
$7$	−0.860670	−	0.774951i	−0.325303	−	0.292904i	0.490256	−	0.871579i	$-0.336903\pi$
$7$	−0.860670	−	0.774951i	−0.325303	−	0.292904i	−0.815558	+	0.578675i	$0.803570\pi$
$8$	−1.58502	−	0.515004i	−0.560389	−	0.182082i
$9$	−0.104528	+	0.994522i	−0.0348428	+	0.331507i
$10$	0.0116057	−	0.0201016i	0.00367004	−	0.00635669i
$11$	2.76016	−	1.83890i	0.832218	−	0.554448i
$11$	2.76016	−	1.83890i	0.832218	−	0.554448i
$12$	−1.80851			−0.522072
$13$	−2.10385	−	2.92811i	−0.583503	−	0.812111i
$13$	−2.10385	−	2.92811i	−0.583503	−	0.812111i
$14$	−0.156610	+	0.481996i	−0.0418558	+	0.128819i
$15$	0.0110282	−	0.0518838i	0.00284748	−	0.0133963i
$16$	−0.301850	−	2.87191i	−0.0754624	−	0.717977i
$17$	0.269984	+	0.120205i	0.0654808	+	0.0291539i	0.439216	−	0.898382i	$-0.355256\pi$
$17$	0.269984	+	0.120205i	0.0654808	+	0.0291539i	−0.373735	+	0.927536i	$0.621923\pi$
$18$	0.416179	−	0.135225i	0.0980942	−	0.0318728i
$19$	−0.314975	−	1.48184i	−0.0722602	−	0.339958i	0.927135	−	0.374727i	$-0.122264\pi$
$19$	−0.314975	−	1.48184i	−0.0722602	−	0.339958i	−0.999395	+	0.0347695i	$0.988930\pi$
$20$	0.0954031	+	0.0100273i	0.0213328	+	0.00224216i
$21$			1.15815i			0.252728i
$22$	−1.22639	−	0.776112i	−0.261468	−	0.165468i
$23$	−4.32080	+	7.48384i	−0.900949	+	1.56049i	−0.0746840	+	0.997207i	$0.523795\pi$
$23$	−4.32080	+	7.48384i	−0.900949	+	1.56049i	−0.826265	+	0.563282i	$0.809539\pi$
$24$	0.677863	+	1.52250i	0.138368	+	0.310780i
$25$	1.54422	−	4.75261i	0.308843	−	0.950521i
$26$	−0.796095	+	1.36221i	−0.156127	+	0.267151i
$27$	0.809017	−	0.587785i	0.155695	−	0.113119i
$28$	−2.08304	+	0.218937i	−0.393658	+	0.0413752i
$29$	−4.27383	−	0.908431i	−0.793630	−	0.168691i	−0.206781	−	0.978387i	$-0.566299\pi$
$29$	−4.27383	−	0.908431i	−0.793630	−	0.168691i	−0.586850	+	0.809696i	$0.699632\pi$
$30$	−0.0227041	+	0.00482591i	−0.00414519	+	0.000881087i
$31$	1.96992	−	2.71137i	0.353809	−	0.486976i	−0.594602	−	0.804020i	$-0.702690\pi$
$31$	1.96992	−	2.71137i	0.353809	−	0.486976i	0.948411	+	0.317044i	$0.102690\pi$
$32$	−3.98098	+	2.29842i	−0.703744	+	0.406307i
$33$	−3.21347	−	0.820732i	−0.559394	−	0.142871i
$34$		−	0.129325i		−	0.0221790i
$35$	0.00642133	−	0.0610949i	0.00108540	−	0.0103269i
$36$	1.21013	+	1.34398i	0.201688	+	0.223997i
$37$	−1.10543	+	5.20065i	−0.181732	+	0.854982i	0.788920	+	0.614495i	$0.210640\pi$
$37$	−1.10543	+	5.20065i	−0.181732	+	0.854982i	−0.970652	+	0.240487i	$0.922693\pi$
$38$	−0.536325	+	0.389663i	−0.0870035	+	0.0632117i
$39$	−0.768257	+	3.52275i	−0.123020	+	0.564092i
$40$	−0.0273173	−	0.0840741i	−0.00431925	−	0.0132933i
$41$	6.37076	−	5.73626i	0.994946	−	0.895853i	0.000383673	−	1.00000i	$-0.499878\pi$
$41$	6.37076	−	5.73626i	0.994946	−	0.895853i	0.994562	+	0.104147i	$0.0332112\pi$
$42$	0.462985	−	0.206134i	0.0714402	−	0.0318072i
$43$	−2.52214	−	4.36848i	−0.384623	−	0.666187i	0.607094	−	0.794630i	$-0.292335\pi$
$43$	−2.52214	−	4.36848i	−0.384623	−	0.666187i	−0.991717	+	0.128443i	$0.959002\pi$
$44$	0.868694	−	5.93491i	0.130961	−	0.894721i
$45$	−0.0459365	+	0.0265214i	−0.00684781	+	0.00395358i
$46$	3.76081	+	0.395277i	0.554502	+	0.0582805i
$47$	2.50282	+	0.813214i	0.365073	+	0.118619i	0.485809	−	0.874065i	$-0.338525\pi$
$47$	2.50282	+	0.813214i	0.365073	+	0.118619i	−0.120735	+	0.992685i	$0.538525\pi$
$48$	−1.93227	+	2.14600i	−0.278899	+	0.309748i
$49$	−0.591495	−	5.62770i	−0.0844993	−	0.803957i
$50$	−2.17477	+	0.228578i	−0.307559	+	0.0323257i
$51$	−0.0913251	−	0.281070i	−0.0127881	−	0.0393577i
$52$	−6.48126	−	0.715846i	−0.898789	−	0.0992699i
$53$	5.00551	+	3.63672i	0.687560	+	0.499542i	0.875857	−	0.482571i	$-0.160297\pi$
$53$	5.00551	+	3.63672i	0.687560	+	0.499542i	−0.188297	+	0.982112i	$0.560297\pi$
$54$	−0.378969	−	0.218798i	−0.0515712	−	0.0297746i
$55$	0.164968	+	0.0611126i	0.0222442	+	0.00824042i
$56$	0.965077	+	1.67156i	0.128964	+	0.223372i
$57$	−0.890463	+	1.22562i	−0.117945	+	0.162337i
$58$	0.397526	+	1.87021i	0.0521977	+	0.245571i
$59$	3.18835	+	2.87080i	0.415088	+	0.373747i	0.850050	−	0.526702i	$-0.176572\pi$
$59$	3.18835	+	2.87080i	0.415088	+	0.373747i	−0.434962	+	0.900449i	$0.643238\pi$
$60$	−0.0563854	−	0.0776078i	−0.00727932	−	0.0100191i
$61$	−7.64149	−	3.40221i	−0.978392	−	0.435608i	−0.145691	−	0.989330i	$-0.546540\pi$
$61$	−7.64149	−	3.40221i	−0.978392	−	0.435608i	−0.832702	+	0.553722i	$0.813207\pi$
$62$	−1.43453	−	0.304918i	−0.182185	−	0.0387246i
$63$	0.860670	−	0.774951i	0.108434	−	0.0976347i
$64$	−3.04506	−	2.21236i	−0.380632	−	0.276545i
$65$	0.0600592	−	0.181574i	0.00744943	−	0.0225214i
$66$	0.243855	+	1.43071i	0.0300165	+	0.176108i
$67$	9.39903	+	5.42653i	1.14827	+	0.662956i	0.948466	−	0.316879i	$-0.102635\pi$
$67$	9.39903	+	5.42653i	1.14827	+	0.662956i	0.199808	+	0.979835i	$0.435968\pi$
$68$	0.488269	−	0.217391i	0.0592113	−	0.0263626i
$69$	8.45276	−	1.79669i	1.01759	−	0.216296i
$70$	−0.0255664	+	0.00830704i	−0.00305577	+	0.000992881i
$71$	−0.503866	+	1.13170i	−0.0597979	+	0.134308i	−0.940973	−	0.338482i	$-0.890087\pi$
$71$	−0.503866	+	1.13170i	−0.0597979	+	0.134308i	0.881175	+	0.472790i	$0.156753\pi$
$72$	0.677863	−	1.52250i	0.0798869	−	0.179429i
$73$	11.4470	−	3.71935i	1.33977	−	0.435317i	0.450529	−	0.892762i	$-0.351235\pi$
$73$	11.4470	−	3.71935i	1.33977	−	0.435317i	0.889238	+	0.457445i	$0.151235\pi$
$74$	2.27578	−	0.483733i	0.264555	−	0.0562328i
$75$	−4.56516	+	2.03254i	−0.527139	+	0.234697i
$76$	−2.37273	−	1.36990i	−0.272171	−	0.157138i
$77$	−3.80064	−	0.556301i	−0.433123	−	0.0633963i
$78$	1.54501	−	0.319880i	0.174938	−	0.0362193i
$79$	7.95811	+	5.78190i	0.895357	+	0.650515i	0.937269	−	0.348606i	$-0.113345\pi$
$79$	7.95811	+	5.78190i	0.895357	+	0.650515i	−0.0419122	+	0.999121i	$0.513345\pi$
$80$	0.113830	−	0.102493i	0.0127266	−	0.0114591i
$81$	−0.978148	−	0.207912i	−0.108683	−	0.0231013i
$82$	−3.42706	−	1.52582i	−0.378455	−	0.168499i
$83$	7.53731	+	10.3742i	0.827327	+	1.13872i	0.988415	+	0.151778i	$0.0484999\pi$
$83$	7.53731	+	10.3742i	0.827327	+	1.13872i	−0.161087	+	0.986940i	$0.551500\pi$
$84$	1.55653	+	1.40151i	0.169831	+	0.152917i
$85$	0.00325922	+	0.0153334i	0.000353512	+	0.00166314i
$86$	−1.29745	+	1.78579i	−0.139908	+	0.192567i
$87$	2.18466	+	3.78393i	0.234220	+	0.405680i
$88$	−5.32194	+	1.49320i	−0.567321	+	0.159175i
$89$	6.23579	+	3.60024i	0.660993	+	0.381624i	0.792655	−	0.609670i	$-0.208698\pi$
$89$	6.23579	+	3.60024i	0.660993	+	0.381624i	−0.131663	+	0.991295i	$0.542032\pi$
$90$	0.0187784	+	0.0136433i	0.00197942	+	0.00143813i
$91$	−0.458418	+	4.15052i	−0.0480553	+	0.435092i
$92$	4.82945	+	14.8635i	0.503504	+	1.54963i
$93$	−3.33307	+	0.350320i	−0.345624	+	0.0363265i
$94$	−0.120373	−	1.14528i	−0.0124156	−	0.118126i
$95$	0.0537694	−	0.0597170i	0.00551662	−	0.00612683i
$96$	4.37185	+	1.42050i	0.446200	+	0.144979i
$97$	11.7466	+	1.23462i	1.19269	+	0.125356i	0.679995	−	0.733217i	$-0.261982\pi$
$97$	11.7466	+	1.23462i	1.19269	+	0.125356i	0.512691	+	0.858573i	$0.328649\pi$
$98$	−2.14447	+	1.23811i	−0.216624	+	0.125068i
$99$	1.54031	+	2.93725i	0.154807	+	0.295205i
$100$	−4.51873	−	7.82667i	−0.451873	−	0.782667i
$101$	13.1306	−	5.84612i	1.30654	−	0.581711i	0.368952	−	0.929449i	$-0.379717\pi$
$101$	13.1306	−	5.84612i	1.30654	−	0.581711i	0.937592	+	0.347738i	$0.113050\pi$
$102$	−0.0961070	+	0.0865351i	−0.00951601	+	0.00856825i
$103$	5.13134	+	15.7926i	0.505606	+	1.55609i	0.799750	+	0.600333i	$0.204965\pi$
$103$	5.13134	+	15.7926i	0.505606	+	1.55609i	−0.294145	+	0.955761i	$0.595035\pi$
$104$	1.82666	+	5.72460i	0.179119	+	0.561343i
$105$	−0.0496991	+	0.0361085i	−0.00485013	+	0.00352383i
$106$	0.562916	−	2.64831i	0.0546752	−	0.257227i
$107$	−13.0535	−	14.4974i	−1.26193	−	1.40152i	−0.878356	−	0.478006i	$-0.841360\pi$
$107$	−13.0535	−	14.4974i	−1.26193	−	1.40152i	−0.383574	−	0.923510i	$-0.625307\pi$
$108$	0.189041	−	1.79860i	0.0181905	−	0.173071i
$109$			3.71641i			0.355967i	0.984033	+	0.177984i	$0.0569574\pi$
$109$			3.71641i			0.355967i	−0.984033	+	0.177984i	$0.943043\pi$
$110$	−0.00493136	−	0.0768253i	−0.000470187	−	0.00732500i
$111$	4.60452	−	2.65842i	0.437041	−	0.252326i
$112$	−1.96579	+	2.70568i	−0.185750	+	0.255663i
$113$	−4.23037	+	0.899194i	−0.397960	+	0.0845890i	−0.402544	−	0.915400i	$-0.631874\pi$
$113$	−4.23037	+	0.899194i	−0.397960	+	0.0845890i	0.00458429	+	0.999989i	$0.498541\pi$
$114$	0.648448	+	0.137832i	0.0607327	+	0.0129091i
$115$	−0.455864	+	0.0479133i	−0.0425096	+	0.00446793i
$116$	−6.39280	+	4.64464i	−0.593557	+	0.431244i
$117$	3.13198	−	1.78625i	0.289552	−	0.165139i
$118$	0.580161	−	1.78555i	0.0534081	−	0.164373i
$119$	−0.139215	−	0.312681i	−0.0127618	−	0.0286634i
$120$	−0.0442003	+	0.0765572i	−0.00403492	+	0.00698869i
$121$	4.23691	−	10.1513i	0.385174	−	0.922844i
$122$			3.66034i			0.331391i
$123$	−8.52574	−	0.896092i	−0.768740	−	0.0807979i
$124$	−1.26017	−	5.92865i	−0.113167	−	0.532408i
$125$	0.504326	−	0.163865i	0.0451083	−	0.0146566i
$126$	−0.462985	−	0.206134i	−0.0412460	−	0.0183639i
$127$	−0.0356255	−	0.338954i	−0.00316125	−	0.0300773i	0.992828	−	0.119555i	$-0.0381468\pi$
$127$	−0.0356255	−	0.338954i	−0.00316125	−	0.0300773i	−0.995989	+	0.0894778i	$0.971480\pi$
$128$	−2.25392	+	10.6038i	−0.199220	+	0.937256i
$129$	−1.55877	+	4.79740i	−0.137242	+	0.422388i
$130$	−0.0832763	+	0.00830814i	−0.00730382	+	0.000728672i
$131$	−5.47162			−0.478058			−0.239029	−	0.971012i	$-0.576829\pi$
$131$	−5.47162			−0.478058			−0.239029	+	0.971012i	$0.576829\pi$
$132$	−4.99177	+	3.32566i	−0.434478	+	0.289462i
$133$	−0.877265	+	1.51947i	−0.0760685	+	0.131754i
$134$	0.496433	−	4.72324i	0.0428852	−	0.408026i
$135$	0.0504468	+	0.0163912i	0.00434177	+	0.00141073i
$136$	−0.366024	−	0.329570i	−0.0313863	−	0.0282604i
$137$	5.92119	−	13.2992i	0.505881	−	1.13623i	−0.462470	−	0.886635i	$-0.653037\pi$
$137$	5.92119	−	13.2992i	0.505881	−	1.13623i	0.968351	−	0.249592i	$-0.0802966\pi$
$138$	−2.22273	−	3.05932i	−0.189211	−	0.260427i
$139$	−0.556948	+	0.618554i	−0.0472397	+	0.0524651i	−0.766302	−	0.642481i	$-0.777905\pi$
$139$	−0.556948	+	0.618554i	−0.0472397	+	0.0524651i	0.719062	+	0.694946i	$0.244572\pi$
$140$	−0.0743400	−	0.0825629i	−0.00628287	−	0.00697784i
$141$	−1.07037	−	2.40410i	−0.0901418	−	0.202462i
$142$	0.542094			0.0454916
$143$	−11.1914	−	4.21327i	−0.935875	−	0.352331i
$144$	2.88773			0.240644
$145$	−0.0942656	−	0.211724i	−0.00782833	−	0.0175827i
$146$	−3.52427	−	3.91409i	−0.291670	−	0.323933i
$147$	−3.78641	+	4.20523i	−0.312298	+	0.346842i
$148$	5.65188	+	7.77914i	0.464582	+	0.639442i
$149$	−4.93686	+	11.0884i	−0.404443	+	0.908395i	0.590413	+	0.807101i	$0.298965\pi$
$149$	−4.93686	+	11.0884i	−0.404443	+	0.908395i	−0.994857	+	0.101294i	$0.967702\pi$
$150$	1.62507	+	1.46322i	0.132687	+	0.119471i
$151$	15.7776	+	5.12645i	1.28396	+	0.417185i	0.869974	−	0.493097i	$-0.164135\pi$
$151$	15.7776	+	5.12645i	1.28396	+	0.417185i	0.413989	+	0.910282i	$0.364135\pi$
$152$	−0.263913	+	2.51096i	−0.0214061	+	0.203666i
$153$	−0.147767	+	0.255940i	−0.0119463	+	0.0206915i
$154$	0.454073	+	1.61837i	0.0365903	+	0.130412i
$155$	0.177770			0.0142788
$156$	3.80483	+	5.29551i	0.304631	+	0.423980i
$157$	1.43077	−	4.40346i	0.114188	−	0.351434i	−0.877589	−	0.479414i	$-0.840849\pi$
$157$	1.43077	−	4.40346i	0.114188	−	0.351434i	0.991777	+	0.127980i	$0.0408493\pi$
$158$	0.894962	−	4.21046i	0.0711993	−	0.334967i
$159$	−0.646734	−	6.15326i	−0.0512893	−	0.487985i
$160$	−0.222749	−	0.0991744i	−0.0176099	−	0.00784042i
$161$	9.51840	−	3.09271i	0.750155	−	0.243740i
$162$	0.0909813	+	0.428034i	0.00714817	+	0.0336295i
$163$	−16.4610	−	1.73012i	−1.28933	−	0.135514i	−0.565068	−	0.825044i	$-0.691150\pi$
$163$	−16.4610	−	1.73012i	−1.28933	−	0.135514i	−0.724257	+	0.689531i	$0.757817\pi$
$164$		−	15.5038i		−	1.21064i
$165$	−0.0649693	−	0.163487i	−0.00505785	−	0.0127274i
$166$	2.80570	−	4.85961i	0.217765	−	0.377179i
$167$	−2.63546	−	5.91934i	−0.203938	−	0.458052i	0.782402	−	0.622773i	$-0.213994\pi$
$167$	−2.63546	−	5.91934i	−0.203938	−	0.458052i	−0.986340	+	0.164721i	$0.947327\pi$
$168$	0.596450	−	1.83569i	0.0460171	−	0.141626i
$169$	−4.14763	+	12.3206i	−0.319048	+	0.947738i
$170$	0.00554966	−	0.00403206i	0.000425639	−	0.000309245i
$171$	1.50665	−	0.158355i	0.115216	−	0.0121097i
$172$	−8.92329	−	1.89670i	−0.680394	−	0.144622i
$173$	8.47511	−	1.80144i	0.644351	−	0.136961i	0.125865	−	0.992047i	$-0.459829\pi$
$173$	8.47511	−	1.80144i	0.644351	−	0.136961i	0.518485	+	0.855086i	$0.326496\pi$
$174$	1.12384	−	1.54684i	0.0851982	−	0.117265i
$175$	−5.01210	+	2.89374i	−0.378879	+	0.218746i
$176$	−6.11429	−	7.37184i	−0.460882	−	0.555673i
$177$		−	4.29035i		−	0.322482i
$178$	0.329359	−	3.13364i	0.0246865	−	0.234876i
$179$	−4.18439	−	4.64724i	−0.312756	−	0.347351i	0.566187	−	0.824276i	$-0.308418\pi$
$179$	−4.18439	−	4.64724i	−0.312756	−	0.347351i	−0.878944	+	0.476925i	$0.841751\pi$
$180$	−0.0199447	+	0.0938323i	−0.00148659	+	0.00699385i
$181$	20.0521	−	14.5687i	1.49046	−	1.08288i	0.516463	−	0.856309i	$-0.327248\pi$
$181$	20.0521	−	14.5687i	1.49046	−	1.08288i	0.973995	−	0.226571i	$-0.0727517\pi$
$182$	1.74082	−	0.555476i	0.129038	−	0.0411746i
$183$	2.58482	+	7.95526i	0.191075	+	0.588069i
$184$	10.7028	−	9.63681i	0.789018	−	0.710435i
$185$	−0.257638	+	0.114708i	−0.0189420	+	0.00843350i
$186$	0.733287	+	1.27009i	0.0537672	+	0.0931275i
$187$	0.966242	−	0.164690i	0.0706586	−	0.0120433i
$188$	4.12168	−	2.37965i	0.300604	−	0.173554i
$189$	−1.15180	−	0.121059i	−0.0837813	−	0.00880576i
$190$	−0.0334429	−	0.0108663i	−0.00242620	−	0.000788321i
$191$	−12.4007	+	13.7723i	−0.897281	+	0.996532i	0.102717	+	0.994711i	$0.467246\pi$
$191$	−12.4007	+	13.7723i	−0.897281	+	0.996532i	−0.999998	+	0.00182104i	$0.999420\pi$
$192$	0.393434	+	3.74328i	0.0283937	+	0.270148i
$193$	−14.5947	+	1.53396i	−1.05055	+	0.110417i	−0.614033	−	0.789280i	$-0.710454\pi$
$193$	−14.5947	+	1.53396i	−1.05055	+	0.110417i	−0.436515	+	0.899697i	$0.643787\pi$
$194$	−1.59718	−	4.91561i	−0.114671	−	0.352920i
$195$	−0.175123	+	0.0768638i	−0.0125408	+	0.00550433i
$196$	−8.27933	−	6.01528i	−0.591380	−	0.429663i
$197$	−7.58113	−	4.37697i	−0.540133	−	0.311846i	0.205000	−	0.978762i	$-0.434281\pi$
$197$	−7.58113	−	4.37697i	−0.540133	−	0.311846i	−0.745133	+	0.666916i	$0.767614\pi$
$198$	0.900053	−	1.13855i	0.0639640	−	0.0809133i
$199$	4.57688	+	7.92738i	0.324446	+	0.561957i	0.981400	−	0.191973i	$-0.0614887\pi$
$199$	4.57688	+	7.92738i	0.324446	+	0.561957i	−0.656954	+	0.753931i	$0.728155\pi$
$200$	−4.89523	+	6.73770i	−0.346145	+	0.476427i
$201$	−2.25648	−	10.6159i	−0.159160	−	0.748788i
$202$	−4.67414	−	4.20861i	−0.328871	−	0.296117i
$203$	2.97437	+	4.09387i	0.208760	+	0.287333i
$204$	−0.488269	−	0.217391i	−0.0341857	−	0.0152204i
$205$	0.444784	+	0.0945418i	0.0310651	+	0.00660309i
$206$	5.40001	−	4.86220i	0.376237	−	0.338765i
$207$	−6.99120	−	5.07940i	−0.485922	−	0.353043i
$208$	−7.77421	+	6.92591i	−0.539044	+	0.480226i
$209$	−3.59433	−	3.51090i	−0.248625	−	0.242854i
$210$	0.0232806	+	0.0134411i	0.00160652	+	0.000927522i
$211$	−23.9214	+	10.6505i	−1.64681	+	0.733209i	−0.999577	−	0.0290800i	$-0.990742\pi$
$211$	−23.9214	+	10.6505i	−1.64681	+	0.733209i	−0.647237	+	0.762289i	$0.724076\pi$
$212$	10.9450	−	2.32643i	0.751706	−	0.159780i
$213$	1.17817	−	0.382811i	0.0807269	−	0.0262297i
$214$	−3.47219	+	7.79866i	−0.237354	+	0.533106i
$215$	0.108828	−	0.244431i	0.00742200	−	0.0166701i
$216$	−1.58502	+	0.515004i	−0.107847	+	0.0350416i
$217$	−3.79663	+	0.806999i	−0.257732	+	0.0547826i
$218$	1.48569	−	0.661470i	0.100623	−	0.0448004i
$219$	−10.4235	−	6.01803i	−0.704357	−	0.406661i
$220$	0.281766	−	0.147760i	0.0189967	−	0.00996195i
$221$	−0.216034	−	1.04344i	−0.0145320	−	0.0701890i
$222$	−1.88228	−	1.36756i	−0.126330	−	0.0917844i
$223$	16.7678	−	15.0978i	1.12286	−	1.01103i	0.123032	−	0.992403i	$-0.460738\pi$
$223$	16.7678	−	15.0978i	1.12286	−	1.01103i	0.999827	−	0.0186232i	$-0.00592830\pi$
$224$	5.20747	+	1.10688i	0.347939	+	0.0739567i
$225$	4.56516	+	2.03254i	0.304344	+	0.135503i
$226$	1.11241	+	1.53111i	0.0739967	+	0.101848i
$227$	−2.66452	−	2.39915i	−0.176850	−	0.159237i	0.575952	−	0.817484i	$-0.304632\pi$
$227$	−2.66452	−	2.39915i	−0.176850	−	0.159237i	−0.752802	+	0.658247i	$0.771298\pi$
$228$	0.569635	+	2.67992i	0.0377250	+	0.177482i
$229$	0.794388	−	1.09338i	0.0524946	−	0.0722527i	−0.781963	−	0.623325i	$-0.785781\pi$
$229$	0.794388	−	1.09338i	0.0524946	−	0.0722527i	0.834457	+	0.551073i	$0.185781\pi$
$230$	0.100292	+	0.173710i	0.00661303	+	0.0114541i
$231$	2.12971	+	3.19666i	0.140125	+	0.210325i
$232$	6.30626	+	3.64092i	0.414026	+	0.239038i
$233$	−1.76968	−	1.28574i	−0.115935	−	0.0842319i	0.528307	−	0.849054i	$-0.322827\pi$
$233$	−1.76968	−	1.28574i	−0.115935	−	0.0842319i	−0.644242	+	0.764822i	$0.722827\pi$
$234$	−1.27153	−	0.934123i	−0.0831225	−	0.0610656i
$235$	0.0431352	+	0.132757i	0.00281383	+	0.00866008i
$236$	7.71663	−	0.811050i	0.502310	−	0.0527949i
$237$	−1.02822	−	9.78287i	−0.0667902	−	0.635466i
$238$	−0.100220	+	0.111306i	−0.00649632	+	0.00721489i
$239$	−11.2441	−	3.65344i	−0.727323	−	0.236322i	−0.0781277	−	0.996943i	$-0.524894\pi$
$239$	−11.2441	−	3.65344i	−0.727323	−	0.236322i	−0.649195	+	0.760622i	$0.724894\pi$
$240$	−0.152334	−	0.0160110i	−0.00983313	−	0.00103350i
$241$	−7.22299	+	4.17020i	−0.465274	+	0.268626i	−0.714259	−	0.699881i	$-0.753236\pi$
$241$	−7.22299	+	4.17020i	−0.465274	+	0.268626i	0.248985	+	0.968507i	$0.419903\pi$
$242$	−4.81223	+	0.113026i	−0.309342	+	0.00726558i
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	−13.8197	+	6.15293i	−0.884716	+	0.393901i
$245$	0.223058	−	0.200842i	0.0142506	−	0.0128313i
$246$	1.15924	+	3.56778i	0.0739105	+	0.227473i
$247$	−3.67633	+	4.03985i	−0.233919	+	0.257050i
$248$	−4.51873	+	3.28305i	−0.286940	+	0.208474i
$249$	2.66610	−	12.5430i	0.168957	−	0.794882i
$250$	−0.155271	−	0.172445i	−0.00982018	−	0.0109064i
$251$	−1.48862	+	14.1633i	−0.0939610	+	0.893979i	0.841431	+	0.540365i	$0.181714\pi$
$251$	−1.48862	+	14.1633i	−0.0939610	+	0.893979i	−0.935392	+	0.353614i	$0.884953\pi$
$252$		−	2.09452i		−	0.131942i
$253$	1.83595	+	28.6021i	0.115425	+	1.79820i
$254$	−0.129161	+	0.0745710i	−0.00810427	+	0.00467900i
$255$	0.00921412	−	0.0126821i	0.000577011	−	0.000794187i
$256$	−2.72309	+	0.578811i	−0.170193	+	0.0361757i
$257$	−5.15773	−	1.09631i	−0.321731	−	0.0683859i	0.0442154	−	0.999022i	$-0.485921\pi$
$257$	−5.15773	−	1.09631i	−0.321731	−	0.0683859i	−0.365946	+	0.930636i	$0.619255\pi$
$258$	2.19527	−	0.230732i	0.136671	−	0.0143647i
$259$	4.98166	−	3.61939i	0.309546	−	0.224898i
$260$	−0.171353	−	0.300446i	−0.0106269	−	0.0186329i
$261$	1.35019	−	4.15546i	0.0835747	−	0.257217i
$262$	0.973874	+	2.18736i	0.0601661	+	0.135135i
$263$	2.04931	−	3.54951i	0.126366	−	0.218872i	−0.795900	−	0.605428i	$-0.793002\pi$
$263$	2.04931	−	3.54951i	0.126366	−	0.218872i	0.922266	+	0.386556i	$0.126335\pi$
$264$	4.67074	+	2.95583i	0.287464	+	0.181919i
$265$			0.328184i			0.0201602i
$266$	0.763569	+	0.0802544i	0.0468174	+	0.00492071i
$267$	−1.49706	−	7.04312i	−0.0916187	−	0.431032i
$268$	18.6672	−	6.06535i	1.14028	−	0.370500i
$269$	1.28855	+	0.573699i	0.0785642	+	0.0349790i	0.445643	−	0.895211i	$-0.352975\pi$
$269$	1.28855	+	0.573699i	0.0785642	+	0.0349790i	−0.367078	+	0.930190i	$0.619642\pi$
$270$	−0.00242625	−	0.0230842i	−0.000147657	−	0.00140486i
$271$	−1.58129	+	7.43939i	−0.0960566	+	0.451911i	0.903663	+	0.428244i	$0.140868\pi$
$271$	−1.58129	+	7.43939i	−0.0960566	+	0.451911i	−0.999720	+	0.0236671i	$0.992466\pi$
$272$	0.263722	−	0.811653i	0.0159905	−	0.0492137i
$273$	3.39118	−	2.43657i	0.205243	−	0.147468i
$274$	−6.37043			−0.384852
$275$	−4.47728	−	15.9576i	−0.269990	−	0.962279i
$276$	7.81421	−	13.5346i	0.470360	−	0.814687i
$277$	−0.658278	+	6.26309i	−0.0395521	+	0.376313i	0.956785	+	0.290797i	$0.0939205\pi$
$277$	−0.658278	+	6.26309i	−0.0395521	+	0.376313i	−0.996337	+	0.0855158i	$0.972746\pi$
$278$	0.346405	+	0.112554i	0.0207760	+	0.00675052i
$279$	2.49060	+	2.24255i	0.149108	+	0.134258i
$280$	−0.0416421	+	0.0935296i	−0.00248859	+	0.00558946i
$281$	4.64869	+	6.39837i	0.277317	+	0.381695i	0.924843	−	0.380349i	$-0.124196\pi$
$281$	4.64869	+	6.39837i	0.277317	+	0.381695i	−0.647526	+	0.762044i	$0.724196\pi$
$282$	−0.770561	+	0.855794i	−0.0458862	+	0.0509618i
$283$	3.79687	+	4.21685i	0.225700	+	0.250666i	0.845350	−	0.534213i	$-0.179392\pi$
$283$	3.79687	+	4.21685i	0.225700	+	0.250666i	−0.619650	+	0.784879i	$0.712725\pi$
$284$	0.911246	+	2.04669i	0.0540725	+	0.121449i
$285$	−0.0803571			−0.00475994
$286$	0.307613	+	5.22384i	0.0181895	+	0.308892i
$287$	−9.92844			−0.586058
$288$	−1.86970	−	4.19942i	−0.110173	−	0.247453i
$289$	−11.3168	−	12.5686i	−0.665693	−	0.739327i
$290$	−0.0678616	+	0.0753680i	−0.00398497	+	0.00442576i
$291$	−6.94250	−	9.55554i	−0.406977	−	0.560155i
$292$	8.85357	−	19.8854i	0.518116	−	1.16371i
$293$	−22.6948	−	20.4345i	−1.32585	−	1.19380i	−0.965327	−	0.261044i	$-0.915933\pi$
$293$	−22.6948	−	20.4345i	−1.32585	−	1.19380i	−0.360518	−	0.932752i	$-0.617400\pi$
$294$	2.35503	+	0.765195i	0.137348	+	0.0446271i
$295$	−0.0237878	+	0.226326i	−0.00138498	+	0.0131772i
$296$	4.43049	−	7.67384i	0.257517	−	0.446033i
$297$	1.15214	−	3.11008i	0.0668537	−	0.180465i
$298$	5.31142			0.307683
$299$	31.0038	−	3.09312i	1.79300	−	0.178880i
$300$	−2.79273	+	8.59514i	−0.161238	+	0.496240i
$301$	−1.21462	+	5.71436i	−0.0700098	+	0.329370i
$302$	−0.758827	−	7.21975i	−0.0436656	−	0.415450i
$303$	−13.1306	−	5.84612i	−0.754333	−	0.335851i
$304$	−4.16063	+	1.35187i	−0.238629	+	0.0775352i
$305$	−0.0922473	−	0.433990i	−0.00528207	−	0.0248502i
$306$	0.128616	+	0.0135181i	0.00735250	+	0.000772779i
$307$			12.2046i			0.696555i	0.937391	+	0.348277i	$0.113233\pi$
$307$			12.2046i			0.696555i	−0.937391	+	0.348277i	$0.886767\pi$
$308$	−5.34692	+	4.43481i	−0.304669	+	0.252696i
$309$	8.30268	−	14.3807i	0.472323	−	0.818087i
$310$	−0.0316406	−	0.0710659i	−0.00179706	−	0.00403627i
$311$	−1.23684	+	3.80662i	−0.0701350	+	0.215853i	−0.979980	−	0.199094i	$-0.936200\pi$
$311$	−1.23684	+	3.80662i	−0.0701350	+	0.215853i	0.909845	+	0.414947i	$0.136200\pi$
$312$	3.03194	−	5.18798i	0.171650	−	0.293711i
$313$	−25.9323	+	18.8409i	−1.46578	+	1.06495i	−0.483973	+	0.875083i	$0.660807\pi$
$313$	−25.9323	+	18.8409i	−1.46578	+	1.06495i	−0.981809	+	0.189870i	$0.939193\pi$
$314$	−2.01500	+	0.211785i	−0.113713	+	0.0119517i
$315$	0.0600890	+	0.0127723i	0.00338563	+	0.000719638i
$316$	17.4011	−	3.69872i	0.978890	−	0.208069i
$317$	19.6656	−	27.0673i	1.10453	−	1.52025i	0.275288	−	0.961362i	$-0.411227\pi$
$317$	19.6656	−	27.0673i	1.10453	−	1.52025i	0.829241	−	0.558891i	$-0.188773\pi$
$318$	−2.34474	+	1.35374i	−0.131487	+	0.0759138i
$319$	−13.4669	+	5.35173i	−0.754004	+	0.299639i
$320$		−	0.199648i		−	0.0111607i
$321$	−2.03916	+	19.4013i	−0.113815	+	1.08288i
$322$	−2.93050	−	3.25465i	−0.163310	−	0.181375i
$323$	0.0930859	−	0.437935i	0.00517944	−	0.0243674i
$324$	−1.46312	+	1.06302i	−0.0812842	+	0.0590564i
$325$	−17.1649	+	5.47714i	−0.952140	+	0.303817i
$326$	2.23819	+	6.88845i	0.123962	+	0.381516i
$327$	2.76183	−	2.48676i	0.152729	−	0.137518i
$328$	−13.0520	+	5.81112i	−0.720675	+	0.320865i
$329$	−1.52390	−	2.63947i	−0.0840152	−	0.145519i
$330$	−0.0537926	+	0.0550708i	−0.00296118	+	0.00303155i
$331$	28.9342	−	16.7051i	1.59036	−	0.918198i	0.597121	−	0.802151i	$-0.296311\pi$
$331$	28.9342	−	16.7051i	1.59036	−	0.918198i	0.993244	−	0.116047i	$-0.0370222\pi$
$332$	23.0639	+	2.42411i	1.26580	+	0.133041i
$333$	−5.05661	−	1.64299i	−0.277101	−	0.0900355i
$334$	−1.89726	+	2.10712i	−0.103814	+	0.115297i
$335$	0.0601747	+	0.572524i	0.00328770	+	0.0312803i
$336$	3.32609	−	0.349586i	0.181453	−	0.0190715i
$337$	8.07499	+	24.8523i	0.439873	+	1.35379i	0.888010	+	0.459825i	$0.152088\pi$
$337$	8.07499	+	24.8523i	0.439873	+	1.35379i	−0.448137	+	0.893965i	$0.647912\pi$
$338$	5.66355	−	0.534827i	0.308057	−	0.0290908i
$339$	3.49890	+	2.54210i	0.190034	+	0.138068i
$340$	0.0245520	+	0.0141751i	0.00133152	+	0.000768752i
$341$	0.451368	−	11.1063i	0.0244429	−	0.601439i
$342$	−0.331467	−	0.574118i	−0.0179237	−	0.0310448i
$343$	−8.61730	+	11.8607i	−0.465290	+	0.640417i
$344$	1.74786	+	8.22304i	0.0942384	+	0.443357i
$345$	0.340639	+	0.306713i	0.0183394	+	0.0165129i
$346$	−2.22860	−	3.06741i	−0.119811	−	0.164905i
$347$	0.422876	+	0.188277i	0.0227012	+	0.0101072i	0.418056	−	0.908421i	$-0.362712\pi$
$347$	0.422876	+	0.188277i	0.0227012	+	0.0101072i	−0.395355	+	0.918529i	$0.629378\pi$
$348$	7.72926	+	1.64291i	0.414332	+	0.0880690i
$349$	−17.9527	+	16.1647i	−0.960986	+	0.865276i	−0.990944	−	0.134276i	$-0.957129\pi$
$349$	−17.9527	+	16.1647i	−0.960986	+	0.865276i	0.0299581	+	0.999551i	$0.490463\pi$
$350$	2.04890	+	1.48861i	0.109518	+	0.0795696i
$351$	−3.42315	−	1.13228i	−0.182714	−	0.0604364i
$352$	−6.76156	+	13.6646i	−0.360392	+	0.728326i
$353$	5.08903	+	2.93815i	0.270862	+	0.156382i	0.629279	−	0.777179i	$-0.283350\pi$
$353$	5.08903	+	2.93815i	0.270862	+	0.156382i	−0.358417	+	0.933561i	$0.616684\pi$
$354$	−1.71513	+	0.763623i	−0.0911579	+	0.0405861i
$355$	−0.0642737	+	0.0136618i	−0.00341129	+	0.000725093i
$356$	12.3848	−	4.02406i	0.656392	−	0.213275i
$357$	−0.139215	+	0.312681i	−0.00736802	+	0.0165488i
$358$	−1.11303	+	2.49991i	−0.0588257	+	0.132125i
$359$	2.43979	−	0.792735i	0.128767	−	0.0418390i	−0.243925	−	0.969794i	$-0.578435\pi$
$359$	2.43979	−	0.792735i	0.128767	−	0.0418390i	0.372692	+	0.927955i	$0.378435\pi$
$360$	0.0864689	−	0.0183795i	0.00455731	−	0.000968687i
$361$	15.2607	−	6.79451i	0.803196	−	0.357606i
$362$	−9.39302	−	5.42306i	−0.493686	−	0.285030i
$363$	−10.3789	+	3.64390i	−0.544752	+	0.191255i
$364$	5.02349	+	5.63877i	0.263302	+	0.295552i
$365$	0.516499	+	0.375258i	0.0270348	+	0.0196419i
$366$	2.72016	−	2.44924i	0.142185	−	0.128024i
$367$	9.22183	+	1.96016i	0.481376	+	0.102320i	0.442207	−	0.896913i	$-0.354196\pi$
$367$	9.22183	+	1.96016i	0.481376	+	0.102320i	0.0391686	+	0.999233i	$0.487529\pi$
$368$	22.7971	+	10.1499i	1.18838	+	0.529102i
$369$	5.03891	+	6.93546i	0.262315	+	0.361046i
$370$	0.0917123	+	0.0825781i	0.00476789	+	0.00429303i
$371$	−1.48982	−	7.00904i	−0.0773475	−	0.363891i
$372$	−3.56262	+	4.90353i	−0.184713	+	0.254236i
$373$	−6.03077	−	10.4456i	−0.312262	−	0.540853i	0.666590	−	0.745425i	$-0.267753\pi$
$373$	−6.03077	−	10.4456i	−0.312262	−	0.540853i	−0.978852	+	0.204572i	$0.934420\pi$
$374$	−0.237815	−	0.356956i	−0.0122971	−	0.0184578i
$375$	−0.459236	−	0.265140i	−0.0237148	−	0.0136918i
$376$	−3.54820	−	2.57792i	−0.182985	−	0.132946i
$377$	6.33152	+	14.4254i	0.326090	+	0.742948i
$378$	0.156610	+	0.481996i	0.00805514	+	0.0247912i
$379$	12.3873	−	1.30196i	0.636295	−	0.0668773i	0.219112	−	0.975700i	$-0.429684\pi$
$379$	12.3873	−	1.30196i	0.636295	−	0.0668773i	0.417183	+	0.908823i	$0.363017\pi$
$380$	−0.0151908	−	0.144531i	−0.000779270	−	0.00741426i
$381$	−0.228054	+	0.253280i	−0.0116836	+	0.0129759i
$382$	7.71284	+	2.50605i	0.394623	+	0.128221i
$383$	−26.9167	−	2.82906i	−1.37538	−	0.144558i	−0.612179	−	0.790719i	$-0.709707\pi$
$383$	−26.9167	−	2.82906i	−1.37538	−	0.144558i	−0.763201	+	0.646161i	$0.776374\pi$
$384$	9.38835	−	5.42037i	0.479097	−	0.276607i
$385$	−0.0946234	−	0.180440i	−0.00482245	−	0.00919605i
$386$	3.21088	+	5.56140i	0.163429	+	0.283068i
$387$	4.60818	−	2.05170i	0.234247	−	0.104294i
$388$	15.8742	−	14.2932i	0.805890	−	0.725627i
$389$	5.81201	+	17.8875i	0.294680	+	0.906933i	0.983329	+	0.181837i	$0.0582044\pi$
$389$	5.81201	+	17.8875i	0.294680	+	0.906933i	−0.688648	+	0.725096i	$0.741796\pi$
$390$	0.0618969	+	0.0563272i	0.00313427	+	0.00285224i
$391$	−2.06614	+	1.50114i	−0.104489	+	0.0759158i
$392$	−1.96076	+	9.22464i	−0.0990332	+	0.465915i
$393$	3.66123	+	4.06621i	0.184685	+	0.205113i
$394$	−0.400416	+	3.80970i	−0.0201727	+	0.191930i
$395$			0.521770i			0.0262531i
$396$	5.81159	+	1.48430i	0.292044	+	0.0745890i
$397$	−1.25554	+	0.724885i	−0.0630136	+	0.0363809i	−0.531176	−	0.847262i	$-0.678250\pi$
$397$	−1.25554	+	0.724885i	−0.0630136	+	0.0363809i	0.468162	+	0.883643i	$0.344916\pi$
$398$	2.35446	−	3.24064i	0.118018	−	0.162438i
$399$	1.71619	−	0.364787i	0.0859169	−	0.0182622i
$400$	−14.1152	−	3.00027i	−0.705758	−	0.150014i
$401$	−16.0837	+	1.69047i	−0.803184	+	0.0844180i	−0.497219	−	0.867625i	$-0.665646\pi$
$401$	−16.0837	+	1.69047i	−0.803184	+	0.0844180i	−0.305964	+	0.952043i	$0.598979\pi$
$402$	−3.84223	+	2.79154i	−0.191633	+	0.139230i
$403$	−12.0836	−	0.0638371i	−0.601927	−	0.00317995i
$404$	8.03263	−	24.7219i	0.399638	−	1.22996i
$405$	−0.0215745	−	0.0484571i	−0.00107204	−	0.00240785i
$406$	1.10718	−	1.91770i	0.0549486	−	0.0951738i
$407$	6.51230	+	16.3874i	0.322803	+	0.812292i
$408$			0.492534i			0.0243841i
$409$	26.7126	+	2.80761i	1.32085	+	0.138827i	0.738580	−	0.674166i	$-0.235497\pi$
$409$	26.7126	+	2.80761i	1.32085	+	0.138827i	0.582274	+	0.812993i	$0.302163\pi$
$410$	−0.0413711	−	0.194636i	−0.00204317	−	0.00961238i
$411$	−13.8453	+	4.49860i	−0.682937	+	0.221900i
$412$	27.4346	+	12.2147i	1.35161	+	0.601774i
$413$	−0.519386	−	4.94163i	−0.0255573	−	0.243162i
$414$	−0.786224	+	3.69889i	−0.0386408	+	0.181791i
$415$	−0.210188	+	0.646891i	−0.0103177	+	0.0317546i
$416$	15.1054	+	6.82120i	0.740603	+	0.334437i
$417$	0.832346			0.0407602
$418$	−0.763790	+	2.06178i	−0.0373582	+	0.100845i
$419$	−14.5092	+	25.1306i	−0.708820	+	1.22771i	0.256476	+	0.966551i	$0.417439\pi$
$419$	−14.5092	+	25.1306i	−0.708820	+	1.22771i	−0.965295	+	0.261161i	$0.915895\pi$
$420$	−0.0116130	+	0.110491i	−0.000566658	+	0.00539139i
$421$	−1.83656	−	0.596734i	−0.0895083	−	0.0290830i	0.263921	−	0.964544i	$-0.414984\pi$
$421$	−1.83656	−	0.596734i	−0.0895083	−	0.0290830i	−0.353429	+	0.935461i	$0.614984\pi$
$422$	8.51535	+	7.66726i	0.414521	+	0.373236i
$423$	−1.07037	+	2.40410i	−0.0520434	+	0.116891i
$424$	−6.06091	−	8.34213i	−0.294344	−	0.405130i
$425$	0.988199	−	1.09751i	0.0479347	−	0.0532369i
$426$	−0.362732	−	0.402855i	−0.0175744	−	0.0195184i
$427$	3.94026	+	8.84996i	0.190682	+	0.428280i
$428$	−35.2807			−1.70536
$429$	4.35747	+	11.1361i	0.210381	+	0.537655i
$430$	−0.117085			−0.00564633
$431$	9.40305	+	21.1196i	0.452929	+	1.01729i	0.985308	+	0.170789i	$0.0546315\pi$
$431$	9.40305	+	21.1196i	0.452929	+	1.01729i	−0.532379	+	0.846506i	$0.678702\pi$
$432$	−1.93227	−	2.14600i	−0.0929662	−	0.103249i
$433$	3.77717	−	4.19498i	0.181519	−	0.201598i	−0.645517	−	0.763746i	$-0.723358\pi$
$433$	3.77717	−	4.19498i	0.181519	−	0.201598i	0.827037	+	0.562148i	$0.190025\pi$
$434$	0.998357	+	1.37412i	0.0479227	+	0.0659599i
$435$	−0.0942656	+	0.211724i	−0.00451969	+	0.0101514i
$436$	4.99479	+	4.49733i	0.239207	+	0.215383i
$437$	12.4508	+	4.04551i	0.595603	+	0.193523i
$438$	−0.550544	+	5.23808i	−0.0263060	+	0.250285i
$439$	−2.50487	+	4.33857i	−0.119551	+	0.207069i	−0.919590	−	0.392880i	$-0.871479\pi$
$439$	−2.50487	+	4.33857i	−0.119551	+	0.207069i	0.800039	+	0.599948i	$0.204812\pi$
$440$	−0.230004	−	0.181824i	−0.0109650	−	0.00866810i
$441$	5.65870			0.269462
$442$	−0.378677	+	0.272080i	−0.0180118	+	0.0129415i
$443$	−5.60834	+	17.2607i	−0.266460	+	0.820080i	0.724893	+	0.688861i	$0.241889\pi$
$443$	−5.60834	+	17.2607i	−0.266460	+	0.820080i	−0.991353	+	0.131219i	$0.958111\pi$
$444$	1.99919	−	9.40543i	0.0948771	−	0.446362i
$445$	0.0399230	+	0.379842i	0.00189253	+	0.0180062i
$446$	−9.02002	−	4.01597i	−0.427110	−	0.190162i
$447$	11.5437	−	3.75077i	0.545997	−	0.177405i
$448$	0.906317	+	4.26388i	0.0428194	+	0.201450i
$449$	11.2447	+	1.18187i	0.530671	+	0.0557758i	0.366075	−	0.930585i	$-0.380701\pi$
$449$	11.2447	+	1.18187i	0.530671	+	0.0557758i	0.164596	+	0.986361i	$0.447368\pi$
$450$		−	2.18675i		−	0.103084i
$451$	7.03589	−	27.5481i	0.331307	−	1.29719i
$452$	−3.91080	+	6.77370i	−0.183948	+	0.318608i
$453$	−6.74758	−	15.1553i	−0.317029	−	0.712059i
$454$	−0.484843	+	1.49219i	−0.0227548	+	0.0700322i
$455$	−0.192402	+	0.109732i	−0.00901994	+	0.00514432i
$456$	2.04260	−	1.48404i	0.0956535	−	0.0694963i
$457$	24.8728	−	2.61423i	1.16350	−	0.122289i	0.496970	−	0.867768i	$-0.334446\pi$
$457$	24.8728	−	2.61423i	1.16350	−	0.122289i	0.666529	+	0.745479i	$0.267779\pi$
$458$	−0.578485	−	0.122961i	−0.0270308	−	0.00574558i
$459$	0.289076	−	0.0614450i	0.0134929	−	0.00286801i
$460$	−0.487260	+	0.670656i	−0.0227186	+	0.0312695i
$461$	25.3563	−	14.6394i	1.18096	−	0.681827i	0.224722	−	0.974423i	$-0.427853\pi$
$461$	25.3563	−	14.6394i	1.18096	−	0.681827i	0.956236	+	0.292596i	$0.0945192\pi$
$462$	0.898851	−	1.42034i	0.0418183	−	0.0660804i
$463$			13.5540i			0.629907i	0.949107	+	0.314953i	$0.101989\pi$
$463$			13.5540i			0.629907i	−0.949107	+	0.314953i	$0.898011\pi$
$464$	−1.31887	+	12.5483i	−0.0612272	+	0.582538i
$465$	−0.118951	−	0.132109i	−0.00551623	−	0.00612639i
$466$	−0.199016	+	0.936298i	−0.00921925	+	0.0433731i
$467$	6.75059	−	4.90459i	0.312380	−	0.226957i	−0.420537	−	0.907275i	$-0.638158\pi$
$467$	6.75059	−	4.90459i	0.312380	−	0.226957i	0.732917	+	0.680318i	$0.238158\pi$
$468$	1.38940	−	6.37093i	0.0642251	−	0.294496i
$469$	−3.88417	−	11.9542i	−0.179354	−	0.551996i
$470$	0.0453938	−	0.0408728i	0.00209386	−	0.00188532i
$471$	−4.22978	+	1.88322i	−0.194898	+	0.0867741i
$472$	−3.57512	−	6.19229i	−0.164558	−	0.285023i
$473$	−14.9947	−	7.41972i	−0.689457	−	0.341159i
$474$	−3.72783	+	2.15226i	−0.171225	+	0.0988568i
$475$	−7.52900	−	0.791329i	−0.345454	−	0.0363087i
$476$	−0.588706	−	0.191282i	−0.0269833	−	0.00876741i
$477$	−4.14001	+	4.59795i	−0.189558	+	0.210526i
$478$	0.540789	+	5.14526i	0.0247351	+	0.235339i
$479$	−4.85939	+	0.510742i	−0.222031	+	0.0233364i	−0.214891	−	0.976638i	$-0.568940\pi$
$479$	−4.85939	+	0.510742i	−0.222031	+	0.0233364i	−0.00714037	+	0.999975i	$0.502273\pi$
$480$	0.0753474	+	0.231896i	0.00343912	+	0.0105845i
$481$	17.5537	−	7.70457i	0.800381	−	0.351298i
$482$	2.95269	+	2.14525i	0.134491	+	0.0977136i
$483$	−8.66738	−	5.00412i	−0.394380	−	0.227695i
$484$	−8.51596	−	17.9787i	−0.387089	−	0.817214i
$485$	0.313253	+	0.542569i	0.0142241	+	0.0246368i
$486$	0.257213	−	0.354023i	0.0116674	−	0.0160588i
$487$	4.42822	+	20.8331i	0.200662	+	0.944039i	0.957052	+	0.289918i	$0.0936279\pi$
$487$	4.42822	+	20.8331i	0.200662	+	0.944039i	−0.756390	+	0.654121i	$0.773039\pi$
$488$	10.3598	+	9.32797i	0.468964	+	0.422257i
$489$	9.72883	+	13.3906i	0.439953	+	0.605543i
$490$	−0.119991	−	0.0534233i	−0.00542062	−	0.00241342i
$491$	−12.7667	−	2.71364i	−0.576152	−	0.122465i	−0.0893855	−	0.995997i	$-0.528490\pi$
$491$	−12.7667	−	2.71364i	−0.576152	−	0.122465i	−0.486766	+	0.873532i	$0.661824\pi$
$492$	−11.5216	+	10.3741i	−0.519433	+	0.467700i
$493$	−1.04467	−	0.758996i	−0.0470495	−	0.0341835i
$494$	2.26932	+	0.750625i	0.102102	+	0.0337722i
$495$	−0.0780216	+	0.157676i	−0.00350681	+	0.00708700i
$496$	−8.38141	−	4.83901i	−0.376337	−	0.217278i
$497$	1.31068	−	0.583550i	0.0587918	−	0.0261758i
$498$	−5.48878	+	1.16668i	−0.245958	+	0.0522800i
$499$	−2.49500	+	0.810675i	−0.111692	+	0.0362908i	−0.364330	−	0.931270i	$-0.618702\pi$
$499$	−2.49500	+	0.810675i	−0.111692	+	0.0362908i	0.252638	+	0.967561i	$0.418702\pi$
$500$	0.390067	−	0.876105i	0.0174443	−	0.0391806i
$501$	−2.63546	+	5.91934i	−0.117744	+	0.264456i
$502$	5.92693	−	1.92578i	0.264532	−	0.0859516i
$503$	−39.1451	+	8.32055i	−1.74539	+	0.370995i	−0.966601	−	0.256286i	$-0.917501\pi$
$503$	−39.1451	+	8.32055i	−1.74539	+	0.370995i	−0.778793	+	0.627281i	$0.784168\pi$
$504$	−1.76328	+	0.785064i	−0.0785429	+	0.0349695i
$505$	0.660256	+	0.381199i	0.0293810	+	0.0169631i
$506$	11.1073	−	5.82472i	0.493780	−	0.258941i
$507$	11.9313	−	5.16180i	0.529887	−	0.229244i
$508$	−0.498661	−	0.362298i	−0.0221245	−	0.0160744i
$509$	7.53738	−	6.78669i	0.334089	−	0.300815i	−0.484963	−	0.874535i	$-0.661167\pi$
$509$	7.53738	−	6.78669i	0.334089	−	0.300815i	0.819052	+	0.573720i	$0.194500\pi$
$510$	−0.00670985	−	0.00142622i	−0.000297117	−	6.31542e-5i
$511$	−12.7344	−	5.66971i	−0.563336	−	0.250813i
$512$	13.4601	+	18.5263i	0.594859	+	0.818753i
$513$	−1.12582	−	1.01370i	−0.0497064	−	0.0447558i
$514$	0.479741	+	2.25700i	0.0211605	+	0.0995522i
$515$	−0.517719	+	0.712579i	−0.0228134	+	0.0314000i
$516$	4.56132	+	7.90044i	0.200801	+	0.347797i
$517$	8.40358	−	2.35782i	0.369589	−	0.103697i
$518$	−2.33357	−	1.34729i	−0.102531	−	0.0591964i
$519$	−7.00968	−	5.09283i	−0.307691	−	0.223551i
$520$	−0.188706	+	0.256867i	−0.00827532	+	0.0112644i
$521$	0.659077	+	2.02843i	0.0288747	+	0.0888671i	0.964455	−	0.264246i	$-0.0851231\pi$
$521$	0.659077	+	2.02843i	0.0288747	+	0.0888671i	−0.935581	+	0.353113i	$0.885123\pi$
$522$	−1.90152	+	0.199858i	−0.0832272	+	0.00874753i
$523$	1.25472	+	11.9378i	0.0548650	+	0.522005i	0.987095	+	0.160138i	$0.0511939\pi$
$523$	1.25472	+	11.9378i	0.0548650	+	0.522005i	−0.932230	+	0.361867i	$0.882139\pi$
$524$	−6.62137	+	7.35377i	−0.289256	+	0.321251i
$525$	5.50421	+	1.78843i	0.240224	+	0.0780534i
$526$	−1.78372	−	0.187476i	−0.0777737	−	0.00817434i
$527$	0.857767	−	0.495232i	0.0373649	−	0.0215726i
$528$	−1.38708	+	9.47653i	−0.0603650	+	0.412413i
$529$	−25.8386	−	44.7538i	−1.12342	−	1.94582i
$530$	0.131196	−	0.0584124i	0.00569880	−	0.00253727i
$531$	−3.18835	+	2.87080i	−0.138363	+	0.124582i
$532$	0.980537	+	3.01778i	0.0425117	+	0.130837i
$533$	−30.1995	−	6.58604i	−1.30809	−	0.285273i
$534$	−2.54913	+	1.85205i	−0.110312	+	0.0801461i
$535$	0.215141	−	1.01216i	0.00930134	−	0.0437594i
$536$	−12.1030	−	13.4417i	−0.522768	−	0.580593i
$537$	−0.653666	+	6.21922i	−0.0282078	+	0.268379i
$538$		−	0.617226i		−	0.0266105i
$539$	−11.9814	−	14.4456i	−0.516074	−	0.622217i
$540$	0.0830766	−	0.0479643i	0.00357505	−	0.00206405i
$541$	14.8907	−	20.4953i	0.640203	−	0.881163i	−0.358424	−	0.933559i	$-0.616686\pi$
$541$	14.8907	−	20.4953i	0.640203	−	0.881163i	0.998626	+	0.0523958i	$0.0166857\pi$
$542$	3.25545	−	0.691967i	0.139833	−	0.0297225i
$543$	−24.2441	−	5.15324i	−1.04041	−	0.221147i
$544$	−1.35108	+	0.142004i	−0.0579271	+	0.00608838i
$545$	−0.159481	+	0.115870i	−0.00683140	+	0.00496330i
$546$	−1.57763	−	0.921995i	−0.0675165	−	0.0394577i
$547$	9.25514	−	28.4844i	0.395721	−	1.21791i	−0.532677	−	0.846319i	$-0.678814\pi$
$547$	9.25514	−	28.4844i	0.395721	−	1.21791i	0.928398	−	0.371587i	$-0.121186\pi$
$548$	−10.7085	−	24.0517i	−0.457445	−	1.02744i
$549$	4.18233	−	7.24400i	0.178497	−	0.309166i
$550$	−5.58237	+	4.63009i	−0.238033	+	0.197428i
$551$			6.61927i			0.281990i
$552$	−14.3231	−	1.50542i	−0.609631	−	0.0640748i
$553$	−2.36861	−	11.1435i	−0.100724	−	0.473868i
$554$	2.62092	−	0.851590i	0.111352	−	0.0361806i
$555$	0.257638	+	0.114708i	0.0109361	+	0.00486908i
$556$	0.157347	+	1.49706i	0.00667301	+	0.0634895i
$557$	1.64130	−	7.72169i	0.0695440	−	0.327179i	−0.929599	−	0.368573i	$-0.879847\pi$
$557$	1.64130	−	7.72169i	0.0695440	−	0.327179i	0.999143	+	0.0413941i	$0.0131799\pi$
$558$	0.453196	−	1.39479i	0.0191853	−	0.0590464i
$559$	−7.48517	+	16.5757i	−0.316589	+	0.701079i
$560$	−0.177397			−0.00749640
$561$	−0.768930	−	0.607859i	−0.0324643	−	0.0256638i
$562$	1.73043	−	2.99720i	0.0729940	−	0.126429i
$563$	4.03089	−	38.3513i	0.169882	−	1.61632i	−0.494676	−	0.869078i	$-0.664713\pi$
$563$	4.03089	−	38.3513i	0.169882	−	1.61632i	0.664557	−	0.747237i	$-0.268620\pi$
$564$	−4.52637	−	1.47071i	−0.190594	−	0.0619279i
$565$	−0.170481	−	0.153501i	−0.00717217	−	0.00645785i
$566$	1.00995	−	2.26839i	0.0424515	−	0.0953477i
$567$	0.680741	+	0.936960i	0.0285884	+	0.0393486i
$568$	1.38147	−	1.53428i	0.0579651	−	0.0643768i
$569$	−15.6296	−	17.3584i	−0.655225	−	0.727701i	0.320366	−	0.947294i	$-0.396194\pi$
$569$	−15.6296	−	17.3584i	−0.655225	−	0.727701i	−0.975592	+	0.219592i	$0.929527\pi$
$570$	0.0143025	+	0.0321239i	0.000599065	+	0.00134552i
$571$	25.3939			1.06270			0.531351	−	0.847152i	$-0.321685\pi$
$571$	25.3939			1.06270			0.531351	+	0.847152i	$0.321685\pi$
$572$	−19.2057	+	9.94253i	−0.803029	+	0.415718i
$573$	18.5325			0.774207
$574$	1.76713	+	3.96903i	0.0737585	+	0.165664i
$575$	28.8955	+	32.0917i	1.20503	+	1.33832i
$576$	2.51854	−	2.79712i	0.104939	−	0.116547i
$577$	−19.9372	−	27.4412i	−0.829997	−	1.14239i	−0.987924	−	0.154942i	$-0.950481\pi$
$577$	−19.9372	−	27.4412i	−0.829997	−	1.14239i	0.157927	−	0.987451i	$-0.449519\pi$
$578$	−3.01022	+	6.76107i	−0.125209	+	0.281223i
$579$	10.9057	+	9.81954i	0.453226	+	0.408086i
$580$	−0.398627	−	0.129522i	−0.0165521	−	0.00537810i
$581$	1.55237	−	14.7698i	0.0644032	−	0.612756i
$582$	−2.58429	+	4.47612i	−0.107122	+	0.185541i
$583$	20.5035	+	0.833280i	0.849170	+	0.0345109i
$584$	−20.0592			−0.830054
$585$	0.174301	+	0.0787098i	0.00720646	+	0.00325425i
$586$	−4.12961	+	12.7096i	−0.170593	+	0.525030i
$587$	7.20139	−	33.8799i	0.297233	−	1.39837i	−0.535425	−	0.844583i	$-0.679848\pi$
$587$	7.20139	−	33.8799i	0.297233	−	1.39837i	0.832658	−	0.553788i	$-0.186818\pi$
$588$	1.06972	+	10.1777i	0.0441147	+	0.419723i
$589$	−4.63829	−	2.06510i	−0.191117	−	0.0850910i
$590$	0.0947108	−	0.0307734i	0.00389918	−	0.00126692i
$591$	1.82004	+	8.56264i	0.0748666	+	0.352220i
$592$	15.2695	+	1.60489i	0.627571	+	0.0659604i
$593$			39.5278i			1.62321i	0.584205	+	0.811606i	$0.301407\pi$
$593$			39.5278i			1.62321i	−0.584205	+	0.811606i	$0.698593\pi$
$594$	−1.44836	+	0.0929693i	−0.0594270	+	0.00381457i
$595$	0.00907755	−	0.0157228i	0.000372143	−	0.000644571i
$596$	8.92836	+	20.0534i	0.365720	+	0.821420i
$597$	2.82867	−	8.70574i	0.115770	−	0.356302i
$598$	−6.75477	−	11.8437i	−0.276223	−	0.484324i
$599$	1.30455	−	0.947812i	0.0533025	−	0.0387265i	−0.560815	−	0.827941i	$-0.689512\pi$
$599$	1.30455	−	0.947812i	0.0533025	−	0.0387265i	0.614117	+	0.789215i	$0.289512\pi$
$600$	8.28263	−	0.870540i	0.338137	−	0.0355396i
$601$	−4.39001	−	0.933125i	−0.179072	−	0.0380630i	0.117503	−	0.993073i	$-0.462511\pi$
$601$	−4.39001	−	0.933125i	−0.179072	−	0.0380630i	−0.296575	+	0.955010i	$0.595844\pi$
$602$	2.50058	−	0.531515i	0.101916	−	0.0216629i
$603$	−6.37927	+	8.78031i	−0.259784	+	0.357562i
$604$	25.9828	−	15.0012i	1.05723	−	0.610389i
$605$	0.567716	−	0.134678i	0.0230809	−	0.00547544i
$606$			6.28967i			0.255500i
$607$	2.10410	−	20.0192i	0.0854029	−	0.812554i	−0.865050	−	0.501686i	$-0.832713\pi$
$607$	2.10410	−	20.0192i	0.0854029	−	0.812554i	0.950453	−	0.310869i	$-0.100620\pi$
$608$	4.65980	+	5.17523i	0.188980	+	0.209883i
$609$	1.05210	−	4.94972i	0.0426331	−	0.200573i
$610$	−0.157075	+	0.114121i	−0.00635977	+	0.00462064i
$611$	−2.88437	−	9.03939i	−0.116689	−	0.365695i
$612$	0.165162	+	0.508318i	0.00667629	+	0.0205475i
$613$	−25.7530	+	23.1881i	−1.04016	+	0.936560i	−0.998042	−	0.0625529i	$-0.980076\pi$
$613$	−25.7530	+	23.1881i	−1.04016	+	0.936560i	−0.0421135	+	0.999113i	$0.513409\pi$
$614$	4.87897	−	2.17226i	0.196899	−	0.0876652i
$615$	−0.227360	−	0.393800i	−0.00916806	−	0.0158795i
$616$	5.73759	+	2.83909i	0.231174	+	0.114390i
$617$	−40.1282	+	23.1680i	−1.61550	+	0.932709i	−0.627435	+	0.778669i	$0.715895\pi$
$617$	−40.1282	+	23.1680i	−1.61550	+	0.932709i	−0.988065	+	0.154040i	$0.950772\pi$
$618$	−7.22663	−	0.759549i	−0.290698	−	0.0305536i
$619$	−40.2313	−	13.0719i	−1.61703	−	0.525406i	−0.645794	−	0.763512i	$-0.723473\pi$
$619$	−40.2313	−	13.0719i	−1.61703	−	0.525406i	−0.971239	+	0.238106i	$0.923473\pi$
$620$	0.215124	−	0.238920i	0.00863960	−	0.00959525i
$621$	0.903293	+	8.59426i	0.0362479	+	0.344876i
$622$	1.74189	−	0.183080i	0.0698434	−	0.00734084i
$623$	−2.57695	−	7.93105i	−0.103243	−	0.317751i
$624$	10.3489	+	1.14302i	0.414288	+	0.0457575i
$625$	−20.1913	−	14.6698i	−0.807652	−	0.586793i
$626$	12.1475	+	7.01338i	0.485513	+	0.280311i
$627$	−0.204031	+	5.02036i	−0.00814823	+	0.200494i
$628$	−4.18676	−	7.25169i	−0.167070	−	0.289374i
$629$	−0.923592	+	1.27121i	−0.0368260	+	0.0506867i
$630$	−0.00558911	−	0.0262947i	−0.000222676	−	0.00104761i
$631$	−8.53305	−	7.68320i	−0.339695	−	0.305863i	0.481572	−	0.876407i	$-0.340066\pi$
$631$	−8.53305	−	7.68320i	−0.339695	−	0.305863i	−0.821267	+	0.570543i	$0.806733\pi$
$632$	−9.63606	−	13.2629i	−0.383302	−	0.527570i
$633$	23.9214	+	10.6505i	0.950789	+	0.423318i
$634$	−14.3208	−	3.04397i	−0.568750	−	0.120891i
$635$	0.0134347	−	0.0120966i	0.000533139	−	0.000480041i
$636$	−9.05252	−	6.57704i	−0.358956	−	0.260797i
$637$	−15.2341	+	13.5718i	−0.603597	+	0.537734i
$638$	4.53636	+	4.43106i	0.179596	+	0.175428i
$639$	−1.07283	−	0.619400i	−0.0424406	−	0.0245031i
$640$	−0.525311	+	0.233883i	−0.0207647	+	0.00924505i
$641$	27.3412	−	5.81154i	1.07991	−	0.229542i	0.366592	−	0.930382i	$-0.380524\pi$
$641$	27.3412	−	5.81154i	1.07991	−	0.229542i	0.713319	+	0.700839i	$0.247191\pi$
$642$	8.11888	−	2.63799i	0.320427	−	0.104113i
$643$	2.62094	−	5.88672i	0.103360	−	0.232150i	−0.854461	−	0.519515i	$-0.826113\pi$
$643$	2.62094	−	5.88672i	0.103360	−	0.232150i	0.957821	+	0.287365i	$0.0927794\pi$
$644$	7.36193	−	16.5352i	0.290101	−	0.651577i
$645$	−0.254468	+	0.0826817i	−0.0100197	+	0.00325559i
$646$	−0.191639	+	0.0407340i	−0.00753992	+	0.00160266i
$647$	40.3004	−	17.9429i	1.58437	−	0.705408i	0.589616	−	0.807684i	$-0.299279\pi$
$647$	40.3004	−	17.9429i	1.58437	−	0.705408i	0.994756	+	0.102276i	$0.0326125\pi$
$648$	1.44331	+	0.833294i	0.0566985	+	0.0327349i
$649$	14.0795	+	2.06081i	0.552667	+	0.0808940i
$650$	5.24469	+	5.88707i	0.205714	+	0.230910i
$651$	3.14016	+	2.28146i	0.123073	+	0.0894174i
$652$	−22.2452	+	20.0297i	−0.871189	+	0.784422i
$653$	−19.0727	−	4.05404i	−0.746374	−	0.158647i	−0.181002	−	0.983483i	$-0.557934\pi$
$653$	−19.0727	−	4.05404i	−0.746374	−	0.158647i	−0.565372	+	0.824836i	$0.691267\pi$
$654$	−1.48569	−	0.661470i	−0.0580949	−	0.0258655i
$655$	−0.170593	−	0.234801i	−0.00666563	−	0.00917445i
$656$	−18.3970	−	16.5647i	−0.718283	−	0.646745i
$657$	2.50244	+	11.7730i	0.0976294	+	0.459310i
$658$	−0.783931	+	1.07899i	−0.0305608	+	0.0420634i
$659$	23.9691	+	41.5156i	0.933702	+	1.61722i	0.776932	+	0.629585i	$0.216775\pi$
$659$	23.9691	+	41.5156i	0.933702	+	1.61722i	0.156771	+	0.987635i	$0.449892\pi$
$660$	−0.298345	−	0.110523i	−0.0116131	−	0.00430209i
$661$	1.35017	+	0.779524i	0.0525157	+	0.0303200i	0.526028	−	0.850467i	$-0.323681\pi$
$661$	1.35017	+	0.779524i	0.0525157	+	0.0303200i	−0.473512	+	0.880787i	$0.657014\pi$
$662$	−11.8280	−	8.59354i	−0.459708	−	0.333998i
$663$	−0.630868	+	0.858739i	−0.0245009	+	0.0333507i
$664$	−6.60402	−	20.3251i	−0.256286	−	0.788767i
$665$	−0.0925555	+	0.00972797i	−0.00358915	+	0.000377235i
$666$	0.243199	+	2.31388i	0.00942376	+	0.0896611i
$667$	25.2649	−	28.0595i	0.978261	−	1.08647i
$668$	−11.1447	−	3.62115i	−0.431203	−	0.140106i
$669$	−22.4398	−	2.35851i	−0.867571	−	0.0911854i
$670$	0.218164	−	0.125957i	0.00842842	−	0.00486615i
$671$	−27.3480	+	4.66129i	−1.05576	+	0.179947i
$672$	−2.66190	−	4.61055i	−0.102685	−	0.177856i
$673$	−3.05358	+	1.35954i	−0.117707	+	0.0524065i	−0.464745	−	0.885444i	$-0.653854\pi$
$673$	−3.05358	+	1.35954i	−0.117707	+	0.0524065i	0.347038	+	0.937851i	$0.387187\pi$
$674$	8.49780	−	7.65146i	0.327323	−	0.294723i
$675$	−1.54422	−	4.75261i	−0.0594369	−	0.182928i
$676$	11.5395	+	20.4839i	0.443828	+	0.787841i
$677$	13.0258	−	9.46381i	0.500623	−	0.363724i	−0.308632	−	0.951182i	$-0.599871\pi$
$677$	13.0258	−	9.46381i	0.500623	−	0.363724i	0.809255	+	0.587458i	$0.199871\pi$
$678$	0.393484	−	1.85120i	0.0151117	−	0.0710947i
$679$	−9.15317	−	10.1656i	−0.351267	−	0.390121i
$680$	0.00273085	−	0.0259823i	0.000104723	−	0.000996377i
$681$			3.58547i			0.137395i
$682$	−4.52023	+	1.79633i	−0.173088	+	0.0687849i
$683$	−28.6278	+	16.5282i	−1.09541	+	0.632436i	−0.935012	−	0.354616i	$-0.884611\pi$
$683$	−28.6278	+	16.5282i	−1.09541	+	0.632436i	−0.160399	+	0.987052i	$0.551278\pi$
$684$	1.61041	−	2.21654i	0.0615756	−	0.0847515i
$685$	0.755313	−	0.160547i	0.0288590	−	0.00613417i
$686$	6.27524	+	1.33384i	0.239590	+	0.0509264i
$687$	−1.34409	+	0.141270i	−0.0512802	+	0.00538977i
$688$	−11.7846	+	8.56198i	−0.449282	+	0.326423i
$689$	0.117851	−	22.3078i	0.00448976	−	0.849859i
$690$	0.0619836	−	0.190766i	0.00235968	−	0.00726234i
$691$	8.12821	+	18.2562i	0.309212	+	0.694500i	0.999581	−	0.0289568i	$-0.00921854\pi$
$691$	8.12821	+	18.2562i	0.309212	+	0.694500i	−0.690369	+	0.723457i	$0.742552\pi$
$692$	7.83487	−	13.5704i	0.297837	−	0.515869i
$693$	0.950528	−	3.72167i	0.0361076	−	0.141375i
$694$		−	0.202561i		−	0.00768912i
$695$	−0.0439082	−	0.00461494i	−0.00166553	−	0.000175055i
$696$	−1.51398	−	7.12272i	−0.0573873	−	0.269986i
$697$	2.40953	−	0.782903i	0.0912674	−	0.0296546i
$698$	9.65739	+	4.29975i	0.365538	+	0.162748i
$699$	0.228650	+	2.17546i	0.00864833	+	0.0822833i
$700$	−2.17615	+	10.2380i	−0.0822507	+	0.386959i
$701$	−1.09182	+	3.36027i	−0.0412374	+	0.126916i	−0.969556	−	0.244870i	$-0.921255\pi$
$701$	−1.09182	+	3.36027i	−0.0412374	+	0.126916i	0.928318	+	0.371786i	$0.121255\pi$
$702$	0.156631	+	1.56998i	0.00591164	+	0.0592551i
$703$	8.05472			0.303790
$704$	−12.4731	−	0.506918i	−0.470099	−	0.0191052i
$705$	0.0697943	−	0.120887i	0.00262860	−	0.00455288i
$706$	0.268789	−	2.55736i	0.0101160	−	0.0962476i
$707$	−15.8316	−	5.14399i	−0.595408	−	0.193460i
$708$	−5.76616	−	5.19187i	−0.216706	−	0.195123i
$709$	4.78101	−	10.7383i	0.179554	−	0.403286i	−0.801236	−	0.598348i	$-0.795824\pi$
$709$	4.78101	−	10.7383i	0.179554	−	0.403286i	0.980791	+	0.195062i	$0.0624908\pi$
$710$	0.0169013	+	0.0232627i	0.000634296	+	0.000873033i
$711$	−6.58208	+	7.31014i	−0.246847	+	0.274152i
$712$	−8.02972	−	8.91791i	−0.300926	−	0.334213i
$713$	11.7798	+	26.4579i	0.441157	+	0.990855i
$714$	0.149777			0.00560526
$715$	−0.168123	−	0.611614i	−0.00628743	−	0.0228731i
$716$	−11.3095			−0.422655
$717$	4.80876	+	10.8007i	0.179586	+	0.403358i
$718$	−0.751156	−	0.834243i	−0.0280329	−	0.0311337i
$719$	−9.15822	+	10.1712i	−0.341544	+	0.379323i	−0.889307	−	0.457310i	$-0.848813\pi$
$719$	−9.15822	+	10.1712i	−0.341544	+	0.379323i	0.547763	+	0.836633i	$0.315480\pi$
$720$	0.0900330	+	0.123920i	0.00335533	+	0.00461822i
$721$	7.82213	−	17.5688i	0.291311	−	0.654296i
$722$	−5.43240	−	4.89136i	−0.202173	−	0.182037i
$723$	7.93218	+	2.57732i	0.295001	+	0.0958517i
$724$	4.68551	−	44.5796i	0.174136	−	1.65679i
$725$	−10.9171	+	18.9090i	−0.405452	+	0.702264i
$726$	3.30400	+	3.50055i	0.122623	+	0.129918i
$727$	5.76644			0.213865			0.106933	−	0.994266i	$-0.465897\pi$
$727$	5.76644			0.213865			0.106933	+	0.994266i	$0.465897\pi$
$728$	2.86414	−	6.34257i	0.106152	−	0.235071i
$729$	0.309017	−	0.951057i	0.0114451	−	0.0352243i
$730$	0.0580850	−	0.273268i	0.00214982	−	0.0101141i
$731$	−0.155827	−	1.48259i	−0.00576346	−	0.0548357i
$732$	13.8197	+	6.15293i	0.510791	+	0.227419i
$733$	13.3040	−	4.32272i	0.491393	−	0.159663i	−0.0528306	−	0.998603i	$-0.516824\pi$
$733$	13.3040	−	4.32272i	0.491393	−	0.159663i	0.544224	+	0.838940i	$0.316824\pi$
$734$	−0.857758	−	4.03544i	−0.0316604	−	0.148951i
$735$	−0.298509	−	0.0313746i	−0.0110107	−	0.00115727i
$736$		−	39.7240i		−	1.46425i
$737$	35.9216	−	2.30578i	1.32319	−	0.0849346i
$738$	1.87569	−	3.24879i	0.0690451	−	0.119590i
$739$	−5.50459	−	12.3635i	−0.202489	−	0.454799i	0.783546	−	0.621334i	$-0.213409\pi$
$739$	−5.50459	−	12.3635i	−0.202489	−	0.454799i	−0.986036	+	0.166535i	$0.946742\pi$
$740$	−0.157610	+	0.485074i	−0.00579386	+	0.0178317i
$741$	5.46214	+	0.0288562i	0.200657	+	0.00106006i
$742$	−2.53680	+	1.84309i	−0.0931287	+	0.0676619i
$743$	−13.3715	+	1.40540i	−0.490553	+	0.0515592i	−0.346576	−	0.938022i	$-0.612656\pi$
$743$	−13.3715	+	1.40540i	−0.490553	+	0.0515592i	−0.143977	+	0.989581i	$0.545989\pi$
$744$	5.46341	+	1.16128i	0.200298	+	0.0425747i
$745$	−0.629751	+	0.133858i	−0.0230723	+	0.00490417i
$746$	−3.10238	+	4.27006i	−0.113586	+	0.156338i
$747$	−11.1053	+	6.41162i	−0.406320	+	0.234589i
$748$	0.947937	−	1.49791i	0.0346600	−	0.0547690i
$749$			22.5933i			0.825542i
$750$	−0.0242557	+	0.230777i	−0.000885691	+	0.00842679i
$751$	17.2698	+	19.1800i	0.630183	+	0.699889i	0.970685	−	0.240355i	$-0.0772637\pi$
$751$	17.2698	+	19.1800i	0.630183	+	0.699889i	−0.340502	+	0.940244i	$0.610597\pi$
$752$	1.58000	−	7.43332i	0.0576167	−	0.271065i
$753$	11.5215	−	8.37083i	0.419865	−	0.305050i
$754$	4.63985	−	5.09864i	0.168973	−	0.185682i
$755$	0.271922	+	0.836890i	0.00989625	+	0.0304575i
$756$	−1.55653	+	1.40151i	−0.0566105	+	0.0509723i
$757$	−5.43302	+	2.41894i	−0.197466	+	0.0879177i	−0.503087	−	0.864236i	$-0.667803\pi$
$757$	−5.43302	+	2.41894i	−0.197466	+	0.0879177i	0.305621	+	0.952153i	$0.401136\pi$
$758$	−2.72525	−	4.72028i	−0.0989857	−	0.171448i
$759$	20.0270	−	20.5029i	0.726934	−	0.744208i
$760$	−0.115980	+	0.0669611i	−0.00420704	+	0.00242894i
$761$	47.4127	+	4.98328i	1.71871	+	0.180644i	0.911968	−	0.410260i	$-0.134562\pi$
$761$	47.4127	+	4.98328i	1.71871	+	0.180644i	0.806742	+	0.590904i	$0.201229\pi$
$762$	0.141843	+	0.0460874i	0.00513841	+	0.00166957i
$763$	2.88003	−	3.19860i	0.104264	−	0.115797i
$764$	3.50340	+	33.3326i	0.126749	+	1.20593i
$765$	−0.0155901	+	0.00163859i	−0.000563662	+	5.92433e-5i
$766$	3.65985	+	11.2639i	0.132236	+	0.406980i
$767$	1.69821	−	15.3756i	0.0613188	−	0.555180i
$768$	2.25224	+	1.63635i	0.0812709	+	0.0590467i
$769$	−1.57250	−	0.907885i	−0.0567059	−	0.0327392i	0.471379	−	0.881931i	$-0.343756\pi$
$769$	−1.57250	−	0.907885i	−0.0567059	−	0.0327392i	−0.528085	+	0.849192i	$0.677090\pi$
$770$	−0.0552916	+	0.0699428i	−0.00199257	+	0.00252056i
$771$	2.63648	+	4.56652i	0.0949505	+	0.164459i
$772$	−15.5998	+	21.4713i	−0.561450	+	0.772770i
$773$	4.58351	+	21.5637i	0.164857	+	0.775593i	0.980419	+	0.196923i	$0.0630948\pi$
$773$	4.58351	+	21.5637i	0.164857	+	0.775593i	−0.815562	+	0.578670i	$0.803572\pi$
$774$	−1.64039	−	1.47701i	−0.0589625	−	0.0530901i
$775$	−9.84407	−	13.5492i	−0.353609	−	0.486702i
$776$	−17.9828	−	8.00644i	−0.645543	−	0.287414i
$777$	−6.02312	−	1.28025i	−0.216078	−	0.0459288i
$778$	6.11633	−	5.50716i	0.219281	−	0.197441i
$779$	−10.5069	−	7.63368i	−0.376447	−	0.273505i
$780$	−0.108618	+	0.328378i	−0.00388914	+	0.0117578i
$781$	0.690335	+	4.05023i	0.0247021	+	0.144929i
$782$	0.967846	+	0.558786i	0.0346101	+	0.0199821i
$783$	−3.99156	+	1.77716i	−0.142647	+	0.0635105i
$784$	−15.9837	+	3.39744i	−0.570846	+	0.121337i
$785$	0.233572	−	0.0758922i	0.00833655	−	0.00270871i
$786$	0.973874	−	2.18736i	0.0347369	−	0.0780204i
$787$	14.9005	−	33.4671i	0.531146	−	1.19297i	−0.426358	−	0.904554i	$-0.640204\pi$
$787$	14.9005	−	33.4671i	0.531146	−	1.19297i	0.957504	−	0.288419i	$-0.0931296\pi$
$788$	−15.0567	+	4.89222i	−0.536373	+	0.174278i
$789$	−4.00906	+	0.852151i	−0.142726	+	0.0303374i
$790$	0.208585	−	0.0928680i	0.00742112	−	0.00330409i
$791$	4.33779	+	2.50442i	0.154234	+	0.0890471i
$792$	−0.928724	−	5.44887i	−0.0330008	−	0.193617i
$793$	6.11451	+	29.5328i	0.217133	+	1.04874i
$794$	0.513251	+	0.372899i	0.0182146	+	0.0132337i
$795$	0.243889	−	0.219598i	0.00864984	−	0.00778835i
$796$	16.1929	+	3.44191i	0.573942	+	0.121995i
$797$	−34.8547	−	15.5183i	−1.23462	−	0.549686i	−0.317481	−	0.948265i	$-0.602837\pi$
$797$	−34.8547	−	15.5183i	−1.23462	−	0.549686i	−0.917134	+	0.398579i	$0.869504\pi$
$798$	−0.451287	−	0.621143i	−0.0159754	−	0.0219882i
$799$	0.577968	+	0.520405i	0.0204470	+	0.0184106i
$800$	4.77599	+	22.4693i	0.168857	+	0.794409i
$801$	−4.23233	+	5.82530i	−0.149542	+	0.205827i
$802$	3.53847	+	6.12882i	0.124948	+	0.216416i
$803$	24.7559	−	31.3158i	0.873618	−	1.10511i
$804$	−16.9982	−	9.81393i	−0.599481	−	0.346111i
$805$	0.429479	+	0.312035i	0.0151372	+	0.0109978i
$806$	2.12520	+	4.84195i	0.0748568	+	0.170550i
$807$	−0.435866	−	1.34146i	−0.0153432	−	0.0472215i
$808$	−23.8230	+	2.50390i	−0.838092	+	0.0880870i
$809$	3.86050	+	36.7302i	0.135728	+	1.29136i	0.824282	+	0.566179i	$0.191579\pi$
$809$	3.86050	+	36.7302i	0.135728	+	1.29136i	−0.688554	+	0.725185i	$0.741754\pi$
$810$	−0.0155314	+	0.0172494i	−0.000545719	+	0.000606082i
$811$	−12.1983	−	3.96346i	−0.428339	−	0.139176i	0.0869103	−	0.996216i	$-0.472301\pi$
$811$	−12.1983	−	3.96346i	−0.428339	−	0.139176i	−0.515249	+	0.857040i	$0.672301\pi$
$812$	9.10147	+	0.956603i	0.319399	+	0.0335702i
$813$	6.58663	−	3.80280i	0.231003	−	0.133370i
$814$	5.39198	−	5.52011i	0.188989	−	0.193480i
$815$	−0.438974	−	0.760326i	−0.0153766	−	0.0266330i
$816$	−0.779640	+	0.347118i	−0.0272929	+	0.0121516i
$817$	−5.67898	+	5.11338i	−0.198682	+	0.178894i
$818$	−3.63210	−	11.1785i	−0.126993	−	0.390846i
$819$	−4.07986	−	0.889754i	−0.142562	−	0.0310905i
$820$	0.665309	−	0.483375i	0.0232336	−	0.0168802i
$821$	1.62690	−	7.65394i	0.0567790	−	0.267124i	−0.940596	−	0.339527i	$-0.889733\pi$
$821$	1.62690	−	7.65394i	0.0567790	−	0.267124i	0.997376	+	0.0724022i	$0.0230665\pi$
$822$	4.26265	+	4.73415i	0.148677	+	0.165123i
$823$	0.563039	−	5.35696i	0.0196263	−	0.186732i	−0.980316	−	0.197433i	$-0.936740\pi$
$823$	0.563039	−	5.35696i	0.0196263	−	0.186732i	0.999943	+	0.0107009i	$0.00340627\pi$
$824$		−	27.6743i		−	0.964080i
$825$	−8.86291	+	14.0050i	−0.308567	+	0.487591i
$826$	−1.88304	+	1.08717i	−0.0655194	+	0.0378276i
$827$	−12.4745	+	17.1696i	−0.433780	+	0.597046i	−0.968816	−	0.247783i	$-0.920298\pi$
$827$	−12.4745	+	17.1696i	−0.433780	+	0.597046i	0.535036	+	0.844829i	$0.320298\pi$
$828$	−15.2869	+	3.24933i	−0.531256	+	0.112922i
$829$	−38.9969	−	8.28904i	−1.35442	−	0.287890i	−0.527185	−	0.849751i	$-0.676752\pi$
$829$	−38.9969	−	8.28904i	−1.35442	−	0.287890i	−0.827232	+	0.561860i	$0.810086\pi$
$830$	0.296014	−	0.0311124i	0.0102748	−	0.00107993i
$831$	5.09486	−	3.70163i	0.176739	−	0.128408i
$832$	−0.0716935	+	13.5707i	−0.00248553	+	0.470480i
$833$	0.516781	−	1.59049i	0.0179054	−	0.0551072i
$834$	−0.148146	−	0.332742i	−0.00512989	−	0.0115219i
$835$	0.171846	−	0.297646i	0.00594698	−	0.0103005i
$836$	−9.06821	+	0.582082i	−0.313631	+	0.0201317i
$837$		−	3.35143i		−	0.115842i
$838$	12.6288	+	1.32734i	0.436253	+	0.0458521i
$839$	9.86669	+	46.4191i	0.340636	+	1.60257i	0.731315	+	0.682040i	$0.238907\pi$
$839$	9.86669	+	46.4191i	0.340636	+	1.60257i	−0.390679	+	0.920527i	$0.627760\pi$
$840$	0.0973700	−	0.0316374i	0.00335959	−	0.00109160i
$841$	−9.05244	−	4.03040i	−0.312153	−	0.138979i
$842$	0.0883296	+	0.840400i	0.00304404	+	0.0289621i
$843$	1.64434	−	7.73599i	0.0566339	−	0.266442i
$844$	−14.6339	+	45.0384i	−0.503718	+	1.55029i
$845$	−0.658023	+	0.206144i	−0.0226367	+	0.00709157i
$846$	1.15158			0.0395923
$847$	−11.5133	+	5.45351i	−0.395603	+	0.187385i
$848$	8.93340	−	15.4731i	0.306774	−	0.531349i
$849$	0.593129	−	5.64325i	0.0203561	−	0.193676i
$850$	−0.614629	−	0.199705i	−0.0210816	−	0.00684983i
$851$	−34.1445	−	30.7439i	−1.17046	−	1.05389i
$852$	0.911246	−	2.04669i	0.0312188	−	0.0701185i
$853$	−2.23457	−	3.07563i	−0.0765103	−	0.105307i	0.769047	−	0.639193i	$-0.220731\pi$
$853$	−2.23457	−	3.07563i	−0.0765103	−	0.105307i	−0.845557	+	0.533885i	$0.820731\pi$
$854$	2.83658	−	3.15035i	0.0970659	−	0.107803i
$855$	0.0537694	+	0.0597170i	0.00183887	+	0.00204228i
$856$	13.2239	+	29.7013i	0.451982	+	1.01517i
$857$	50.4239			1.72245			0.861223	−	0.508226i	$-0.169699\pi$
$857$	50.4239			1.72245			0.861223	+	0.508226i	$0.169699\pi$
$858$	3.67624	−	3.72403i	0.125505	−	0.127136i
$859$	25.3402			0.864597			0.432298	−	0.901731i	$-0.357703\pi$
$859$	25.3402			0.864597			0.432298	+	0.901731i	$0.357703\pi$
$860$	−0.196816	−	0.442056i	−0.00671138	−	0.0150740i
$861$	6.64343	+	7.37827i	0.226407	+	0.251451i
$862$	6.76924	−	7.51800i	0.230561	−	0.256064i
$863$	−9.25918	−	12.7442i	−0.315186	−	0.433816i	0.621804	−	0.783173i	$-0.286400\pi$
$863$	−9.25918	−	12.7442i	−0.315186	−	0.433816i	−0.936990	+	0.349357i	$0.886400\pi$
$864$	−1.86970	+	4.19942i	−0.0636085	+	0.142867i
$865$	0.341540	+	0.307524i	0.0116127	+	0.0104561i
$866$	−2.34929	−	0.763329i	−0.0798320	−	0.0259390i
$867$	−1.76785	+	16.8200i	−0.0600395	+	0.571237i
$868$	−3.50982	+	6.07919i	−0.119131	+	0.206341i
$869$	32.5979	+	1.32481i	1.10581	+	0.0449409i
$870$	0.101418			0.00343838
$871$	−3.88468	−	38.9380i	−0.131627	−	1.31936i
$872$	1.91397	−	5.89058i	0.0648151	−	0.199480i
$873$	−2.45571	+	11.5532i	−0.0831131	+	0.391016i
$874$	−0.598824	−	5.69743i	−0.0202555	−	0.192718i
$875$	−0.561046	−	0.249794i	−0.0189668	−	0.00844457i
$876$	−20.7020	+	6.72648i	−0.699454	+	0.227267i
$877$	2.93613	+	13.8134i	0.0991460	+	0.466445i	0.999510	+	0.0313072i	$0.00996703\pi$
$877$	2.93613	+	13.8134i	0.0991460	+	0.466445i	−0.900364	+	0.435138i	$0.856700\pi$
$878$	2.18024	+	0.229152i	0.0735794	+	0.00773351i
$879$			30.5389i			1.03005i
$880$	0.125714	−	0.492218i	0.00423783	−	0.0165927i
$881$	−17.0270	+	29.4916i	−0.573654	+	0.993597i	0.422533	+	0.906348i	$0.361141\pi$
$881$	−17.0270	+	29.4916i	−0.573654	+	0.993597i	−0.996186	+	0.0872496i	$0.972192\pi$
$882$	−1.00717	−	2.26214i	−0.0339132	−	0.0761703i
$883$	11.2919	−	34.7530i	0.380004	−	1.16953i	−0.560036	−	0.828468i	$-0.689213\pi$
$883$	11.2919	−	34.7530i	0.380004	−	1.16953i	0.940040	−	0.341064i	$-0.110787\pi$
$884$	−1.66379	−	0.972345i	−0.0559593	−	0.0327035i
$885$	0.184110	−	0.133764i	0.00618879	−	0.00449642i
$886$	7.89841	−	0.830157i	0.265352	−	0.0278897i
$887$	45.5599	+	9.68405i	1.52975	+	0.325159i	0.894472	−	0.447124i	$-0.147552\pi$
$887$	45.5599	+	9.68405i	1.52975	+	0.325159i	0.635279	+	0.772283i	$0.280885\pi$
$888$	−8.66735	+	1.84230i	−0.290857	+	0.0618236i
$889$	−0.232011	+	0.319336i	−0.00778140	+	0.0107102i
$890$	0.144741	−	0.0835664i	0.00485174	−	0.00280115i
$891$	−3.08217	+	1.22484i	−0.103256	+	0.0410338i
$892$		−	40.8061i		−	1.36629i
$893$	0.416730	−	3.96492i	0.0139453	−	0.132681i
$894$	−3.55404	−	3.94716i	−0.118865	−	0.132013i
$895$	0.0689648	−	0.324454i	0.00230524	−	0.0108453i
$896$	10.1573	−	7.37974i	0.339333	−	0.246540i
$897$	−23.0442	−	20.9706i	−0.769425	−	0.700189i
$898$	−1.52894	−	4.70559i	−0.0510213	−	0.157028i
$899$	−10.8822	+	9.79838i	−0.362942	+	0.326794i
$900$	8.25613	−	3.67587i	0.275204	−	0.122529i
$901$	0.914258	+	1.58354i	0.0304584	+	0.0527554i
$902$	−12.2650	+	2.09050i	−0.408381	+	0.0696059i
$903$	5.05934	−	2.92101i	0.168364	−	0.0972051i
$904$	7.16832	+	0.753421i	0.238415	+	0.0250584i
$905$	1.25036	+	0.406266i	0.0415633	+	0.0135047i
$906$	−4.85757	+	5.39488i	−0.161382	+	0.179233i
$907$	3.61182	+	34.3641i	0.119928	+	1.14104i	0.874568	+	0.484903i	$0.161145\pi$
$907$	3.61182	+	34.3641i	0.119928	+	1.14104i	−0.754640	+	0.656139i	$0.772188\pi$
$908$	−6.44883	+	0.677799i	−0.214012	+	0.0224936i
$909$	4.44157	+	13.6698i	0.147318	+	0.453397i
$910$	0.0781119	+	0.0573845i	0.00258938	+	0.00190228i
$911$	20.1153	+	14.6146i	0.666450	+	0.484204i	0.868835	−	0.495102i	$-0.164869\pi$
$911$	20.1153	+	14.6146i	0.666450	+	0.484204i	−0.202385	+	0.979306i	$0.564869\pi$
$912$	3.78864	+	2.18738i	0.125455	+	0.0724312i
$913$	39.8813	+	14.7741i	1.31988	+	0.488952i
$914$	−5.47209	−	9.47794i	−0.181001	−	0.313502i
$915$	−0.260792	+	0.358949i	−0.00862151	+	0.0118665i
$916$	−0.508176	−	2.39078i	−0.0167906	−	0.0789935i
$917$	4.70926	+	4.24024i	0.155514	+	0.140025i
$918$	−0.0760151	−	0.104626i	−0.00250887	−	0.00345317i
$919$	19.8202	+	8.82452i	0.653808	+	0.291094i	0.706707	−	0.707506i	$-0.250180\pi$
$919$	19.8202	+	8.82452i	0.653808	+	0.291094i	−0.0528997	+	0.998600i	$0.516846\pi$
$920$	0.747230	+	0.158829i	0.0246354	+	0.00523642i
$921$	9.06981	−	8.16649i	0.298860	−	0.269095i
$922$	−10.3654	−	7.53089i	−0.341366	−	0.248017i
$923$	4.37380	−	0.905557i	0.143965	−	0.0298068i
$924$	6.87349	+	1.00607i	0.226121	+	0.0330974i
$925$	23.0096	+	13.2846i	0.756552	+	0.436795i
$926$	5.41839	−	2.41242i	0.178059	−	0.0792772i
$927$	−16.2425	+	3.45245i	−0.533473	+	0.113393i
$928$	19.1020	−	6.20661i	0.627053	−	0.203742i
$929$	−4.83487	+	10.8593i	−0.158627	+	0.356282i	−0.975322	−	0.220788i	$-0.929137\pi$
$929$	−4.83487	+	10.8593i	−0.158627	+	0.356282i	0.816695	+	0.577069i	$0.195804\pi$
$930$	−0.0316406	+	0.0710659i	−0.00103754	+	0.00233034i
$931$	−8.15305	+	2.64909i	−0.267205	+	0.0868203i
$932$	−3.86956	+	0.822500i	−0.126752	+	0.0269419i
$933$	3.65648	−	1.62797i	0.119708	−	0.0532973i
$934$	−3.16219	−	1.82569i	−0.103470	−	0.0597384i
$935$	0.0371926	+	0.0363293i	0.00121633	+	0.00118809i
$936$	−5.88418	+	1.21827i	−0.192330	+	0.0398203i
$937$	−19.1647	−	13.9240i	−0.626084	−	0.454877i	0.228957	−	0.973437i	$-0.426468\pi$
$937$	−19.1647	−	13.9240i	−0.626084	−	0.454877i	−0.855041	+	0.518560i	$0.826468\pi$
$938$	−4.08755	+	3.68044i	−0.133463	+	0.120171i
$939$	31.3537	+	6.66443i	1.02319	+	0.217485i
$940$	0.230622	+	0.102680i	0.00752206	+	0.00334904i
$941$	18.7555	+	25.8147i	0.611410	+	0.841534i	0.996693	−	0.0812647i	$-0.0258959\pi$
$941$	18.7555	+	25.8147i	0.611410	+	0.841534i	−0.385282	+	0.922799i	$0.625896\pi$
$942$	1.50569	+	1.35573i	0.0490579	+	0.0441719i
$943$	15.4025	+	72.4630i	0.501574	+	2.35972i
$944$	7.28228	−	10.0232i	0.237018	−	0.326227i
$945$	−0.0307157	−	0.0532012i	−0.000999182	−	0.00173063i
$946$	−0.297285	+	7.31494i	−0.00966557	+	0.237829i
$947$	−27.0359	−	15.6092i	−0.878550	−	0.507231i	−0.00837004	−	0.999965i	$-0.502664\pi$
$947$	−27.0359	−	15.6092i	−0.878550	−	0.507231i	−0.870180	+	0.492734i	$0.835998\pi$
$948$	−14.3923	−	10.4566i	−0.467441	−	0.339615i
$949$	−34.9734	−	25.6930i	−1.13528	−	0.834031i
$950$	1.02371	+	3.15067i	0.0332137	+	0.102221i
$951$	−33.2738	+	3.49722i	−1.07898	+	0.113405i
$952$	0.0596258	+	0.567302i	0.00193248	+	0.0183864i
$953$	−34.0557	+	37.8226i	−1.10317	+	1.22520i	−0.130886	+	0.991397i	$0.541782\pi$
$953$	−34.0557	+	37.8226i	−1.10317	+	1.22520i	−0.972285	+	0.233798i	$0.924884\pi$
$954$	2.57496	+	0.836656i	0.0833674	+	0.0270877i
$955$	−0.977633	−	0.102753i	−0.0316355	−	0.00332502i
$956$	−18.5170	+	10.6908i	−0.598884	+	0.345766i
$957$	12.9883	+	6.42689i	0.419851	+	0.207752i
$958$	1.06908	+	1.85170i	0.0345404	+	0.0598258i
$959$	−15.4024	+	6.85760i	−0.497370	+	0.221443i
$960$	−0.148367	+	0.133591i	−0.00478853	+	0.00431162i
$961$	6.10862	+	18.8004i	0.197052	+	0.606464i
$962$	−6.20433	−	5.64604i	−0.200036	−	0.182036i
$963$	15.7824	−	11.4666i	0.508582	−	0.369507i
$964$	−3.13607	+	14.7541i	−0.101006	+	0.475196i
$965$	−0.520857	−	0.578470i	−0.0167670	−	0.0186216i
$966$	−0.457789	+	4.35557i	−0.0147291	+	0.140138i
$967$			51.9013i			1.66903i	0.550982	+	0.834517i	$0.314253\pi$
$967$			51.9013i			1.66903i	−0.550982	+	0.834517i	$0.685747\pi$
$968$	−11.9435	+	13.9080i	−0.383880	+	0.447019i
$969$	−0.387736	+	0.223859i	−0.0124559	+	0.00719140i
$970$	0.161145	−	0.221797i	0.00517405	−	0.00712147i
$971$	−4.40402	+	0.936103i	−0.141332	+	0.0300410i	−0.278034	−	0.960571i	$-0.589683\pi$
$971$	−4.40402	+	0.936103i	−0.141332	+	0.0300410i	0.136703	+	0.990612i	$0.456350\pi$
$972$	1.76899	+	0.376010i	0.0567404	+	0.0120605i
$973$	0.958698	−	0.100763i	0.0307344	−	0.00323032i
$974$	7.54017	−	5.47825i	0.241603	−	0.175535i
$975$	15.5559	+	9.09111i	0.498187	+	0.291149i
$976$	−7.46425	+	22.9726i	−0.238925	+	0.735335i
$977$	10.4598	+	23.4930i	0.334638	+	0.751609i	0.999987	+	0.00507653i	$0.00161592\pi$
$977$	10.4598	+	23.4930i	0.334638	+	0.751609i	−0.665349	+	0.746532i	$0.731717\pi$
$978$	3.62147	−	6.27258i	0.115802	−	0.200575i
$979$	23.8322	−	1.52977i	0.761681	−	0.0488917i
$980$		−	0.542831i		−	0.0173401i
$981$	−3.69605	−	0.388470i	−0.118006	−	0.0124029i
$982$	1.18748	+	5.58665i	0.0378940	+	0.178277i
$983$	38.7078	−	12.5769i	1.23459	−	0.401142i	0.382213	−	0.924074i	$-0.375162\pi$
$983$	38.7078	−	12.5769i	1.23459	−	0.401142i	0.852374	+	0.522933i	$0.175162\pi$
$984$	13.0520	+	5.81112i	0.416082	+	0.185252i
$985$	−0.0485361	−	0.461790i	−0.00154649	−	0.0147139i
$986$	−0.117483	+	0.552712i	−0.00374141	+	0.0176019i
$987$	−0.941821	+	2.89863i	−0.0299785	+	0.0922643i
$988$	0.980666	+	9.82967i	0.0311991	+	0.312724i
$989$	43.5907			1.38610
$990$	0.0769199	+	0.00312608i	0.00244467	+	9.93535e-5i
$991$	−6.53017	+	11.3106i	−0.207438	+	0.359293i	−0.950907	−	0.309478i	$-0.899846\pi$
$991$	−6.53017	+	11.3106i	−0.207438	+	0.359293i	0.743469	+	0.668770i	$0.233179\pi$
$992$	−1.61036	+	15.3216i	−0.0511291	+	0.486461i
$993$	−31.7751	−	10.3243i	−1.00835	−	0.327633i
$994$	−0.466565	−	0.420097i	−0.0147985	−	0.0133247i
$995$	−0.197488	+	0.443564i	−0.00626078	+	0.0140619i
$996$	−13.6313	−	18.7619i	−0.431924	−	0.594493i
$997$	22.1003	−	24.5448i	0.699922	−	0.777342i	−0.283442	−	0.958989i	$-0.591476\pi$
$997$	22.1003	−	24.5448i	0.699922	−	0.777342i	0.983364	+	0.181647i	$0.0581429\pi$
$998$	0.768155	+	0.853122i	0.0243155	+	0.0270051i
$999$	2.16255	+	4.85717i	0.0684201	+	0.153674i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.bn.a.4.6	✓	112
11.3	even	5	inner	429.2.bn.a.355.6	yes	112
13.10	even	6	inner	429.2.bn.a.400.6	yes	112
143.36	even	30	inner	429.2.bn.a.322.6	yes	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.bn.a.4.6	✓	112	1.1	even	1	trivial
429.2.bn.a.322.6	yes	112	143.36	even	30	inner
429.2.bn.a.355.6	yes	112	11.3	even	5	inner
429.2.bn.a.400.6	yes	112	13.10	even	6	inner

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.bn (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.177986 - 0.399764i) q^{2} +(-0.669131 - 0.743145i) q^{3} +(1.21013 - 1.34398i) q^{4} +(0.0311778 + 0.0429126i) q^{5} +(-0.177986 + 0.399764i) q^{6} +(-0.860670 - 0.774951i) q^{7} +(-1.58502 - 0.515004i) q^{8} +(-0.104528 + 0.994522i) q^{9} +O(q^{10})\)	\(q+(-0.177986 - 0.399764i) q^{2} +(-0.669131 - 0.743145i) q^{3} +(1.21013 - 1.34398i) q^{4} +(0.0311778 + 0.0429126i) q^{5} +(-0.177986 + 0.399764i) q^{6} +(-0.860670 - 0.774951i) q^{7} +(-1.58502 - 0.515004i) q^{8} +(-0.104528 + 0.994522i) q^{9} +(0.0116057 - 0.0201016i) q^{10} +(2.76016 - 1.83890i) q^{11} -1.80851 q^{12} +(-2.10385 - 2.92811i) q^{13} +(-0.156610 + 0.481996i) q^{14} +(0.0110282 - 0.0518838i) q^{15} +(-0.301850 - 2.87191i) q^{16} +(0.269984 + 0.120205i) q^{17} +(0.416179 - 0.135225i) q^{18} +(-0.314975 - 1.48184i) q^{19} +(0.0954031 + 0.0100273i) q^{20} +1.15815i q^{21} +(-1.22639 - 0.776112i) q^{22} +(-4.32080 + 7.48384i) q^{23} +(0.677863 + 1.52250i) q^{24} +(1.54422 - 4.75261i) q^{25} +(-0.796095 + 1.36221i) q^{26} +(0.809017 - 0.587785i) q^{27} +(-2.08304 + 0.218937i) q^{28} +(-4.27383 - 0.908431i) q^{29} +(-0.0227041 + 0.00482591i) q^{30} +(1.96992 - 2.71137i) q^{31} +(-3.98098 + 2.29842i) q^{32} +(-3.21347 - 0.820732i) q^{33} -0.129325i q^{34} +(0.00642133 - 0.0610949i) q^{35} +(1.21013 + 1.34398i) q^{36} +(-1.10543 + 5.20065i) q^{37} +(-0.536325 + 0.389663i) q^{38} +(-0.768257 + 3.52275i) q^{39} +(-0.0273173 - 0.0840741i) q^{40} +(6.37076 - 5.73626i) q^{41} +(0.462985 - 0.206134i) q^{42} +(-2.52214 - 4.36848i) q^{43} +(0.868694 - 5.93491i) q^{44} +(-0.0459365 + 0.0265214i) q^{45} +(3.76081 + 0.395277i) q^{46} +(2.50282 + 0.813214i) q^{47} +(-1.93227 + 2.14600i) q^{48} +(-0.591495 - 5.62770i) q^{49} +(-2.17477 + 0.228578i) q^{50} +(-0.0913251 - 0.281070i) q^{51} +(-6.48126 - 0.715846i) q^{52} +(5.00551 + 3.63672i) q^{53} +(-0.378969 - 0.218798i) q^{54} +(0.164968 + 0.0611126i) q^{55} +(0.965077 + 1.67156i) q^{56} +(-0.890463 + 1.22562i) q^{57} +(0.397526 + 1.87021i) q^{58} +(3.18835 + 2.87080i) q^{59} +(-0.0563854 - 0.0776078i) q^{60} +(-7.64149 - 3.40221i) q^{61} +(-1.43453 - 0.304918i) q^{62} +(0.860670 - 0.774951i) q^{63} +(-3.04506 - 2.21236i) q^{64} +(0.0600592 - 0.181574i) q^{65} +(0.243855 + 1.43071i) q^{66} +(9.39903 + 5.42653i) q^{67} +(0.488269 - 0.217391i) q^{68} +(8.45276 - 1.79669i) q^{69} +(-0.0255664 + 0.00830704i) q^{70} +(-0.503866 + 1.13170i) q^{71} +(0.677863 - 1.52250i) q^{72} +(11.4470 - 3.71935i) q^{73} +(2.27578 - 0.483733i) q^{74} +(-4.56516 + 2.03254i) q^{75} +(-2.37273 - 1.36990i) q^{76} +(-3.80064 - 0.556301i) q^{77} +(1.54501 - 0.319880i) q^{78} +(7.95811 + 5.78190i) q^{79} +(0.113830 - 0.102493i) q^{80} +(-0.978148 - 0.207912i) q^{81} +(-3.42706 - 1.52582i) q^{82} +(7.53731 + 10.3742i) q^{83} +(1.55653 + 1.40151i) q^{84} +(0.00325922 + 0.0153334i) q^{85} +(-1.29745 + 1.78579i) q^{86} +(2.18466 + 3.78393i) q^{87} +(-5.32194 + 1.49320i) q^{88} +(6.23579 + 3.60024i) q^{89} +(0.0187784 + 0.0136433i) q^{90} +(-0.458418 + 4.15052i) q^{91} +(4.82945 + 14.8635i) q^{92} +(-3.33307 + 0.350320i) q^{93} +(-0.120373 - 1.14528i) q^{94} +(0.0537694 - 0.0597170i) q^{95} +(4.37185 + 1.42050i) q^{96} +(11.7466 + 1.23462i) q^{97} +(-2.14447 + 1.23811i) q^{98} +(1.54031 + 2.93725i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q - 14 q^{3} - 20 q^{4} + 14 q^{9}+O(q^{10}) \) 112 * q - 14 * q^3 - 20 * q^4 + 14 * q^9	\( 112 q - 14 q^{3} - 20 q^{4} + 14 q^{9} + 21 q^{11} + 120 q^{12} - 15 q^{13} + 30 q^{14} - 6 q^{15} - 8 q^{16} - 12 q^{19} - 66 q^{20} - 17 q^{22} + 12 q^{23} + 14 q^{25} + 9 q^{26} + 28 q^{27} + 18 q^{28} - 2 q^{29} + 10 q^{30} - 30 q^{32} - 24 q^{33} + 16 q^{35} - 20 q^{36} + 38 q^{38} - 12 q^{39} - 60 q^{40} - 36 q^{41} + 12 q^{43} - 6 q^{45} + 54 q^{46} - 42 q^{48} - 40 q^{49} - 51 q^{50} - 30 q^{51} - 15 q^{52} - 22 q^{53} + 22 q^{55} - 76 q^{56} + 132 q^{58} + 72 q^{59} + 34 q^{61} + 17 q^{62} - 84 q^{64} + 28 q^{65} - 24 q^{66} - 48 q^{67} - 12 q^{68} - 7 q^{69} + 30 q^{71} + 20 q^{74} + 32 q^{75} - 48 q^{76} - 136 q^{77} - 14 q^{78} - 36 q^{79} + 18 q^{80} + 14 q^{81} - 5 q^{82} - 27 q^{84} - 66 q^{85} + 52 q^{87} + 52 q^{88} - 96 q^{89} - 20 q^{90} - 125 q^{91} - 10 q^{92} - 18 q^{93} + 22 q^{94} + 72 q^{95} - 93 q^{97} + 24 q^{98}+O(q^{100}) \) 112 * q - 14 * q^3 - 20 * q^4 + 14 * q^9 + 21 * q^11 + 120 * q^12 - 15 * q^13 + 30 * q^14 - 6 * q^15 - 8 * q^16 - 12 * q^19 - 66 * q^20 - 17 * q^22 + 12 * q^23 + 14 * q^25 + 9 * q^26 + 28 * q^27 + 18 * q^28 - 2 * q^29 + 10 * q^30 - 30 * q^32 - 24 * q^33 + 16 * q^35 - 20 * q^36 + 38 * q^38 - 12 * q^39 - 60 * q^40 - 36 * q^41 + 12 * q^43 - 6 * q^45 + 54 * q^46 - 42 * q^48 - 40 * q^49 - 51 * q^50 - 30 * q^51 - 15 * q^52 - 22 * q^53 + 22 * q^55 - 76 * q^56 + 132 * q^58 + 72 * q^59 + 34 * q^61 + 17 * q^62 - 84 * q^64 + 28 * q^65 - 24 * q^66 - 48 * q^67 - 12 * q^68 - 7 * q^69 + 30 * q^71 + 20 * q^74 + 32 * q^75 - 48 * q^76 - 136 * q^77 - 14 * q^78 - 36 * q^79 + 18 * q^80 + 14 * q^81 - 5 * q^82 - 27 * q^84 - 66 * q^85 + 52 * q^87 + 52 * q^88 - 96 * q^89 - 20 * q^90 - 125 * q^91 - 10 * q^92 - 18 * q^93 + 22 * q^94 + 72 * q^95 - 93 * q^97 + 24 * q^98

Introduction

L-functions

Modular forms

Varieties

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