LMFDB - Embedded newform 429.2.bv.a.20.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(20,429)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(429, base_ring=CyclotomicField(60))

chi = DirichletCharacter(H, H._module([30, 36, 55]))

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

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

chi := DirichletCharacter("429.20");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.bv (of order $60$, degree $16$, 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:	$832$
Relative dimension:	$52$ over $\Q(\zeta_{60})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			20.14
Character	$\chi$	$=$	429.20
Dual form			429.2.bv.a.236.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.40019 - 0.0733811i) q^{2} +(-0.460922 - 1.66960i) q^{3} +(-0.0338826 - 0.00356121i) q^{4} +(2.36606 + 1.20557i) q^{5} +(0.522864 + 2.37158i) q^{6} +(0.593855 + 0.733350i) q^{7} +(2.81689 + 0.446151i) q^{8} +(-2.57510 + 1.53911i) q^{9} +O(q^{10})$	\(q+(-1.40019 - 0.0733811i) q^{2} +(-0.460922 - 1.66960i) q^{3} +(-0.0338826 - 0.00356121i) q^{4} +(2.36606 + 1.20557i) q^{5} +(0.522864 + 2.37158i) q^{6} +(0.593855 + 0.733350i) q^{7} +(2.81689 + 0.446151i) q^{8} +(-2.57510 + 1.53911i) q^{9} +(-3.22448 - 1.86166i) q^{10} +(-1.30863 + 3.04754i) q^{11} +(0.00967147 + 0.0582117i) q^{12} +(-3.60440 - 0.0910566i) q^{13} +(-0.777699 - 1.07041i) q^{14} +(0.922243 - 4.50604i) q^{15} +(-3.84481 - 0.817239i) q^{16} +(-2.48390 + 2.75865i) q^{17} +(3.71859 - 1.96609i) q^{18} +(1.47061 + 3.83106i) q^{19} +(-0.0758751 - 0.0492739i) q^{20} +(0.950678 - 1.32952i) q^{21} +(2.05596 - 4.17112i) q^{22} +(-2.03565 + 3.52585i) q^{23} +(-0.553474 - 4.90871i) q^{24} +(1.20593 + 1.65982i) q^{25} +(5.04018 + 0.391992i) q^{26} +(3.75661 + 3.58997i) q^{27} +(-0.0175098 - 0.0269627i) q^{28} +(1.93074 + 4.33651i) q^{29} +(-1.62198 + 6.24166i) q^{30} +(8.25938 - 4.20836i) q^{31} +(-0.186138 - 0.0498754i) q^{32} +(5.69133 + 0.780198i) q^{33} +(3.68038 - 3.68038i) q^{34} +(0.520994 + 2.45109i) q^{35} +(0.0927323 - 0.0429785i) q^{36} +(-2.01199 + 5.24141i) q^{37} +(-1.77801 - 5.47214i) q^{38} +(1.50932 + 6.05986i) q^{39} +(6.12707 + 4.45158i) q^{40} +(4.93705 + 3.99794i) q^{41} +(-1.42870 + 1.79182i) q^{42} +(1.89680 - 1.09512i) q^{43} +(0.0551926 - 0.0985984i) q^{44} +(-7.94835 + 0.537162i) q^{45} +(3.10904 - 4.78750i) q^{46} +(2.39864 + 0.379907i) q^{47} +(0.407698 + 6.79596i) q^{48} +(1.27024 - 5.97603i) q^{49} +(-1.56674 - 2.41256i) q^{50} +(5.75072 + 2.87559i) q^{51} +(0.121802 + 0.0159213i) q^{52} +(-8.29755 - 2.69604i) q^{53} +(-4.99655 - 5.30232i) q^{54} +(-6.77031 + 5.63303i) q^{55} +(1.34564 + 2.33072i) q^{56} +(5.71849 - 4.22114i) q^{57} +(-2.38519 - 6.21364i) q^{58} +(-2.35522 + 1.90722i) q^{59} +(-0.0472950 + 0.149392i) q^{60} +(0.102899 - 0.114281i) q^{61} +(-11.8736 + 5.28645i) q^{62} +(-2.65794 - 0.974444i) q^{63} +(7.73361 + 2.51280i) q^{64} +(-8.41846 - 4.56080i) q^{65} +(-7.91173 - 1.51007i) q^{66} +(4.93505 - 1.32234i) q^{67} +(0.0939852 - 0.0846246i) q^{68} +(6.82503 + 1.77357i) q^{69} +(-0.549630 - 3.47023i) q^{70} +(-0.0305430 - 0.582795i) q^{71} +(-7.94045 + 3.18661i) q^{72} +(-2.55827 + 0.405190i) q^{73} +(3.20180 - 7.19135i) q^{74} +(2.21539 - 2.77846i) q^{75} +(-0.0361848 - 0.135043i) q^{76} +(-3.01205 + 0.850116i) q^{77} +(-1.66866 - 8.59575i) q^{78} +(-5.01906 + 15.4471i) q^{79} +(-8.11181 - 6.56882i) q^{80} +(4.26230 - 7.92672i) q^{81} +(-6.61946 - 5.96019i) q^{82} +(1.95822 + 0.997763i) q^{83} +(-0.0369461 + 0.0416619i) q^{84} +(-9.20281 + 3.53263i) q^{85} +(-2.73625 + 1.39419i) q^{86} +(6.35030 - 5.22234i) q^{87} +(-5.04592 + 8.00074i) q^{88} +(-9.09008 + 2.43568i) q^{89} +(11.1687 - 0.168872i) q^{90} +(-2.07372 - 2.69736i) q^{91} +(0.0815295 - 0.112216i) q^{92} +(-10.8332 - 11.8501i) q^{93} +(-3.33069 - 0.707959i) q^{94} +(-1.13906 + 10.8374i) q^{95} +(0.00252313 + 0.333763i) q^{96} +(-6.84478 - 4.44505i) q^{97} +(-2.21712 + 8.27439i) q^{98} +(-1.32065 - 9.86184i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 832 q - 6 q^{3} - 36 q^{4} - 4 q^{6} - 24 q^{7} - 6 q^{9}+O(q^{10}) $ 832 * q - 6 * q^3 - 36 * q^4 - 4 * q^6 - 24 * q^7 - 6 * q^9	$ 832 q - 6 q^{3} - 36 q^{4} - 4 q^{6} - 24 q^{7} - 6 q^{9} - 96 q^{10} - 40 q^{13} + 12 q^{15} - 68 q^{16} - 20 q^{18} - 32 q^{19} - 84 q^{21} - 24 q^{22} - 72 q^{24} - 114 q^{30} - 8 q^{31} + 14 q^{33} - 24 q^{34} + 78 q^{36} - 24 q^{37} - 72 q^{39} - 112 q^{40} + 2 q^{42} - 96 q^{43} + 4 q^{45} - 16 q^{46} + 14 q^{48} - 36 q^{49} + 8 q^{52} + 32 q^{54} - 24 q^{55} - 12 q^{57} + 112 q^{58} - 120 q^{60} + 12 q^{61} + 28 q^{63} - 300 q^{66} - 32 q^{67} - 18 q^{69} - 140 q^{70} + 204 q^{72} - 24 q^{73} + 66 q^{75} + 176 q^{76} - 28 q^{78} - 224 q^{79} - 58 q^{81} - 264 q^{82} + 20 q^{84} - 168 q^{85} + 72 q^{87} - 120 q^{88} - 146 q^{93} - 4 q^{94} - 10 q^{96} - 88 q^{97} + 40 q^{99}+O(q^{100}) $ 832 * q - 6 * q^3 - 36 * q^4 - 4 * q^6 - 24 * q^7 - 6 * q^9 - 96 * q^10 - 40 * q^13 + 12 * q^15 - 68 * q^16 - 20 * q^18 - 32 * q^19 - 84 * q^21 - 24 * q^22 - 72 * q^24 - 114 * q^30 - 8 * q^31 + 14 * q^33 - 24 * q^34 + 78 * q^36 - 24 * q^37 - 72 * q^39 - 112 * q^40 + 2 * q^42 - 96 * q^43 + 4 * q^45 - 16 * q^46 + 14 * q^48 - 36 * q^49 + 8 * q^52 + 32 * q^54 - 24 * q^55 - 12 * q^57 + 112 * q^58 - 120 * q^60 + 12 * q^61 + 28 * q^63 - 300 * q^66 - 32 * q^67 - 18 * q^69 - 140 * q^70 + 204 * q^72 - 24 * q^73 + 66 * q^75 + 176 * q^76 - 28 * q^78 - 224 * q^79 - 58 * q^81 - 264 * q^82 + 20 * q^84 - 168 * q^85 + 72 * q^87 - 120 * q^88 - 146 * q^93 - 4 * q^94 - 10 * q^96 - 88 * q^97 + 40 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$67$	$79$	$287$
$\chi(n)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{3}{5}\right)$	$-1$

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 $

$2$	−1.40019	−	0.0733811i	−0.990087	−	0.0518883i	−0.449591	−	0.893235i	$-0.648430\pi$
$2$	−1.40019	−	0.0733811i	−0.990087	−	0.0518883i	−0.540496	+	0.841346i	$0.681764\pi$
$3$	−0.460922	−	1.66960i	−0.266114	−	0.963942i
$3$	−0.460922	−	1.66960i	−0.266114	−	0.963942i
$4$	−0.0338826	−	0.00356121i	−0.0169413	−	0.00178060i
$5$	2.36606	+	1.20557i	1.05814	+	0.539147i	0.894359	−	0.447351i	$-0.147632\pi$
$5$	2.36606	+	1.20557i	1.05814	+	0.539147i	0.163777	+	0.986497i	$0.447632\pi$
$6$	0.522864	+	2.37158i	0.213458	+	0.968195i
$7$	0.593855	+	0.733350i	0.224456	+	0.277180i	0.876917	−	0.480642i	$-0.159596\pi$
$7$	0.593855	+	0.733350i	0.224456	+	0.277180i	−0.652460	+	0.757823i	$0.726263\pi$
$8$	2.81689	+	0.446151i	0.995921	+	0.157738i
$9$	−2.57510	+	1.53911i	−0.858367	+	0.513036i
$10$	−3.22448	−	1.86166i	−1.01967	−	0.588707i
$11$	−1.30863	+	3.04754i	−0.394566	+	0.918868i
$11$	−1.30863	+	3.04754i	−0.394566	+	0.918868i
$12$	0.00967147	+	0.0582117i	0.00279191	+	0.0168043i
$13$	−3.60440	−	0.0910566i	−0.999681	−	0.0252546i
$13$	−3.60440	−	0.0910566i	−0.999681	−	0.0252546i
$14$	−0.777699	−	1.07041i	−0.207849	−	0.286079i
$15$	0.922243	−	4.50604i	0.238122	−	1.16346i
$16$	−3.84481	−	0.817239i	−0.961201	−	0.204310i
$17$	−2.48390	+	2.75865i	−0.602434	+	0.669071i	−0.964806	−	0.262963i	$-0.915300\pi$
$17$	−2.48390	+	2.75865i	−0.602434	+	0.669071i	0.362372	+	0.932034i	$0.381967\pi$
$18$	3.71859	−	1.96609i	0.876479	−	0.463411i
$19$	1.47061	+	3.83106i	0.337380	+	0.878905i	0.992373	+	0.123270i	$0.0393382\pi$
$19$	1.47061	+	3.83106i	0.337380	+	0.878905i	−0.654993	+	0.755635i	$0.727328\pi$
$20$	−0.0758751	−	0.0492739i	−0.0169662	−	0.0110180i
$21$	0.950678	−	1.32952i	0.207455	−	0.290124i
$22$	2.05596	−	4.17112i	0.438333	−	0.889286i
$23$	−2.03565	+	3.52585i	−0.424463	+	0.735191i	−0.996370	−	0.0851270i	$-0.972870\pi$
$23$	−2.03565	+	3.52585i	−0.424463	+	0.735191i	0.571907	+	0.820318i	$0.306204\pi$
$24$	−0.553474	−	4.90871i	−0.112977	−	1.00199i
$25$	1.20593	+	1.65982i	0.241186	+	0.331964i
$26$	5.04018	+	0.391992i	0.988461	+	0.0768759i
$27$	3.75661	+	3.58997i	0.722960	+	0.690890i
$28$	−0.0175098	−	0.0269627i	−0.00330903	−	0.00509547i
$29$	1.93074	+	4.33651i	0.358529	+	0.805269i	0.999295	+	0.0375333i	$0.0119500\pi$
$29$	1.93074	+	4.33651i	0.358529	+	0.805269i	−0.640766	+	0.767736i	$0.721383\pi$
$30$	−1.62198	+	6.24166i	−0.296131	+	1.13957i
$31$	8.25938	−	4.20836i	1.48343	−	0.755845i	0.490155	−	0.871635i	$-0.336940\pi$
$31$	8.25938	−	4.20836i	1.48343	−	0.755845i	0.993274	+	0.115791i	$0.0369402\pi$
$32$	−0.186138	−	0.0498754i	−0.0329048	−	0.00881681i
$33$	5.69133	+	0.780198i	0.990734	+	0.135815i
$34$	3.68038	−	3.68038i	0.631180	−	0.631180i
$35$	0.520994	+	2.45109i	0.0880641	+	0.414309i
$36$	0.0927323	−	0.0429785i	0.0154554	−	0.00716309i
$37$	−2.01199	+	5.24141i	−0.330769	+	0.861682i	0.662836	+	0.748765i	$0.269353\pi$
$37$	−2.01199	+	5.24141i	−0.330769	+	0.861682i	−0.993604	+	0.112917i	$0.963980\pi$
$38$	−1.77801	−	5.47214i	−0.288431	−	0.887699i
$39$	1.50932	+	6.05986i	0.241685	+	0.970355i
$40$	6.12707	+	4.45158i	0.968775	+	0.703856i
$41$	4.93705	+	3.99794i	0.771038	+	0.624374i	0.931947	−	0.362595i	$-0.118109\pi$
$41$	4.93705	+	3.99794i	0.771038	+	0.624374i	−0.160909	+	0.986969i	$0.551443\pi$
$42$	−1.42870	+	1.79182i	−0.220452	+	0.276484i
$43$	1.89680	−	1.09512i	0.289259	−	0.167004i	−0.348349	−	0.937365i	$-0.613257\pi$
$43$	1.89680	−	1.09512i	0.289259	−	0.167004i	0.637608	+	0.770361i	$0.279924\pi$
$44$	0.0551926	−	0.0985984i	0.00832060	−	0.0148643i
$45$	−7.94835	+	0.537162i	−1.18487	+	0.0800753i
$46$	3.10904	−	4.78750i	0.458403	−	0.705879i
$47$	2.39864	+	0.379907i	0.349878	+	0.0554152i	0.328900	−	0.944365i	$-0.393322\pi$
$47$	2.39864	+	0.379907i	0.349878	+	0.0554152i	0.0209777	+	0.999780i	$0.493322\pi$
$48$	0.407698	+	6.79596i	0.0588461	+	0.980912i
$49$	1.27024	−	5.97603i	0.181463	−	0.853718i
$50$	−1.56674	−	2.41256i	−0.221570	−	0.341188i
$51$	5.75072	+	2.87559i	0.805261	+	0.402663i
$52$	0.121802	+	0.0159213i	0.0168909	+	0.00220788i
$53$	−8.29755	−	2.69604i	−1.13976	−	0.370329i	−0.322480	−	0.946576i	$-0.604517\pi$
$53$	−8.29755	−	2.69604i	−1.13976	−	0.370329i	−0.817276	+	0.576247i	$0.804517\pi$
$54$	−4.99655	−	5.30232i	−0.679944	−	0.721555i
$55$	−6.77031	+	5.63303i	−0.912908	+	0.759558i
$56$	1.34564	+	2.33072i	0.179819	+	0.311455i
$57$	5.71849	−	4.22114i	0.757432	−	0.559103i
$58$	−2.38519	−	6.21364i	−0.313191	−	0.815890i
$59$	−2.35522	+	1.90722i	−0.306624	+	0.248299i	−0.770265	−	0.637724i	$-0.779876\pi$
$59$	−2.35522	+	1.90722i	−0.306624	+	0.248299i	0.463641	+	0.886023i	$0.346543\pi$
$60$	−0.0472950	+	0.149392i	−0.00610575	+	0.0192865i
$61$	0.102899	−	0.114281i	0.0131749	−	0.0146322i	−0.736521	−	0.676414i	$-0.763533\pi$
$61$	0.102899	−	0.114281i	0.0131749	−	0.0146322i	0.749696	+	0.661782i	$0.230200\pi$
$62$	−11.8736	+	5.28645i	−1.50794	+	0.671380i
$63$	−2.65794	−	0.974444i	−0.334869	−	0.122768i
$64$	7.73361	+	2.51280i	0.966701	+	0.314100i
$65$	−8.41846	−	4.56080i	−1.04418	−	0.565698i
$66$	−7.91173	−	1.51007i	−0.973866	−	0.185876i
$67$	4.93505	−	1.32234i	0.602912	−	0.161550i	0.0555643	−	0.998455i	$-0.482304\pi$
$67$	4.93505	−	1.32234i	0.602912	−	0.161550i	0.547348	+	0.836905i	$0.315638\pi$
$68$	0.0939852	−	0.0846246i	0.0113974	−	0.0102622i
$69$	6.82503	+	1.77357i	0.821637	+	0.213513i
$70$	−0.549630	−	3.47023i	−0.0656934	−	0.414772i
$71$	−0.0305430	−	0.582795i	−0.00362479	−	0.0691650i	0.996218	−	0.0868871i	$-0.0276919\pi$
$71$	−0.0305430	−	0.582795i	−0.00362479	−	0.0691650i	−0.999843	+	0.0177221i	$0.994359\pi$
$72$	−7.94045	+	3.18661i	−0.935791	+	0.375546i
$73$	−2.55827	+	0.405190i	−0.299423	+	0.0474239i	−0.304338	−	0.952564i	$-0.598435\pi$
$73$	−2.55827	+	0.405190i	−0.299423	+	0.0474239i	0.00491540	+	0.999988i	$0.498435\pi$
$74$	3.20180	−	7.19135i	0.372201	−	0.835978i
$75$	2.21539	−	2.77846i	0.255811	−	0.320829i
$76$	−0.0361848	−	0.135043i	−0.00415068	−	0.0154905i
$77$	−3.01205	+	0.850116i	−0.343255	+	0.0968798i
$78$	−1.66866	−	8.59575i	−0.188939	−	0.973277i
$79$	−5.01906	+	15.4471i	−0.564688	+	1.73793i	0.104189	+	0.994558i	$0.466775\pi$
$79$	−5.01906	+	15.4471i	−0.564688	+	1.73793i	−0.668877	+	0.743373i	$0.733225\pi$
$80$	−8.11181	−	6.56882i	−0.906928	−	0.734416i
$81$	4.26230	−	7.92672i	0.473589	−	0.880746i
$82$	−6.61946	−	5.96019i	−0.730997	−	0.658193i
$83$	1.95822	+	0.997763i	0.214943	+	0.109519i	0.558147	−	0.829742i	$-0.311512\pi$
$83$	1.95822	+	0.997763i	0.214943	+	0.109519i	−0.343205	+	0.939261i	$0.611512\pi$
$84$	−0.0369461	+	0.0416619i	−0.00403115	+	0.00454569i
$85$	−9.20281	+	3.53263i	−0.998185	+	0.383167i
$86$	−2.73625	+	1.39419i	−0.295057	+	0.150339i
$87$	6.35030	−	5.22234i	0.680823	−	0.559894i
$88$	−5.04592	+	8.00074i	−0.537897	+	0.852881i
$89$	−9.09008	+	2.43568i	−0.963547	+	0.258182i	−0.706101	−	0.708111i	$-0.749547\pi$
$89$	−9.09008	+	2.43568i	−0.963547	+	0.258182i	−0.257446	+	0.966293i	$0.582881\pi$
$90$	11.1687	−	0.168872i	1.17728	−	0.0178007i
$91$	−2.07372	−	2.69736i	−0.217385	−	0.282760i
$92$	0.0815295	−	0.112216i	0.00850004	−	0.0116993i
$93$	−10.8332	−	11.8501i	−1.12335	−	1.22880i
$94$	−3.33069	−	0.707959i	−0.343534	−	0.0730204i
$95$	−1.13906	+	10.8374i	−0.116865	+	1.11190i
$96$	0.00252313	+	0.333763i	0.000257516	+	0.0340646i
$97$	−6.84478	−	4.44505i	−0.694982	−	0.451327i	0.148198	−	0.988958i	$-0.452653\pi$
$97$	−6.84478	−	4.44505i	−0.694982	−	0.451327i	−0.843180	+	0.537631i	$0.819319\pi$
$98$	−2.21712	+	8.27439i	−0.223963	+	0.835839i
$99$	−1.32065	−	9.86184i	−0.132730	−	0.991152i
$100$	−0.0349491	−	0.0605336i	−0.00349491	−	0.00605336i
$101$	6.71366	+	7.45628i	0.668034	+	0.741927i	0.977951	−	0.208836i	$-0.0669676\pi$
$101$	6.71366	+	7.45628i	0.668034	+	0.741927i	−0.309916	+	0.950764i	$0.600301\pi$
$102$	−7.84111	−	4.44838i	−0.776386	−	0.440455i
$103$	11.3157	−	15.5747i	1.11496	−	1.53462i	0.301071	−	0.953602i	$-0.402656\pi$
$103$	11.3157	−	15.5747i	1.11496	−	1.53462i	0.813893	−	0.581015i	$-0.197344\pi$
$104$	−10.1126	−	1.86461i	−0.991619	−	0.182840i
$105$	3.85219	−	1.99961i	0.375935	−	0.195142i
$106$	11.4203	+	4.38386i	1.10924	+	0.425798i
$107$	15.7644	−	1.65690i	1.52400	−	0.160179i	0.694829	−	0.719175i	$-0.255480\pi$
$107$	15.7644	−	1.65690i	1.52400	−	0.160179i	0.829170	+	0.558996i	$0.188813\pi$
$108$	−0.114499	−	0.135016i	−0.0110177	−	0.0129919i
$109$	−0.965219	−	0.965219i	−0.0924512	−	0.0924512i	0.659369	−	0.751820i	$-0.270824\pi$
$109$	−0.965219	−	0.965219i	−0.0924512	−	0.0924512i	−0.751820	+	0.659369i	$0.770824\pi$
$110$	9.89311	−	7.39053i	0.943271	−	0.704659i
$111$	9.67840	+	0.943326i	0.918634	+	0.0895366i
$112$	−1.68394	−	3.30491i	−0.159117	−	0.312285i
$113$	5.45703	−	12.2567i	0.513354	−	1.15301i	−0.451988	−	0.892024i	$-0.649285\pi$
$113$	5.45703	−	12.2567i	0.513354	−	1.15301i	0.965342	−	0.260988i	$-0.0840482\pi$
$114$	−8.31675	+	5.49079i	−0.778935	+	0.514259i
$115$	−9.06714	+	5.88827i	−0.845515	+	0.549084i
$116$	−0.0499753	−	0.153808i	−0.00464009	−	0.0142807i
$117$	9.42185	−	5.31308i	0.871050	−	0.491195i
$118$	3.43773	−	2.49765i	0.316468	−	0.229928i
$119$	−3.49813	−	0.183329i	−0.320673	−	0.0168058i
$120$	4.60823	−	12.2816i	0.420672	−	1.12115i
$121$	−7.57500	−	7.97618i	−0.688636	−	0.725107i
$122$	−0.152465	+	0.152465i	−0.0138035	+	0.0138035i
$123$	4.39936	−	10.0856i	0.396677	−	0.909390i
$124$	−0.294836	+	0.113177i	−0.0264771	+	0.0101636i
$125$	−1.22478	−	7.73294i	−0.109547	−	0.691655i
$126$	3.65013	+	1.55945i	0.325180	+	0.138927i
$127$	−1.79369	+	8.43865i	−0.159164	+	0.748810i	0.824074	+	0.566483i	$0.191696\pi$
$127$	−1.79369	+	8.43865i	−0.159164	+	0.748810i	−0.983238	+	0.182327i	$0.941637\pi$
$128$	−10.2844	−	3.94779i	−0.909017	−	0.348939i
$129$	−2.70268	−	2.66212i	−0.237958	−	0.234387i
$130$	11.4528	+	7.00377i	1.00448	+	0.614271i
$131$			5.59729i			0.489038i	0.969645	+	0.244519i	$0.0786300\pi$
$131$			5.59729i			0.489038i	−0.969645	+	0.244519i	$0.921370\pi$
$132$	−0.190059	−	0.0467032i	−0.0165425	−	0.00406499i
$133$	−1.93618	+	3.35356i	−0.167888	+	0.290791i
$134$	−7.00706	+	1.48940i	−0.605318	+	0.128664i
$135$	4.56041	+	13.0229i	0.392498	+	1.12084i
$136$	−8.22765	+	6.66262i	−0.705515	+	0.571315i
$137$	−14.5172	+	0.760814i	−1.24029	+	0.0650008i	−0.661166	−	0.750240i	$-0.729938\pi$
$137$	−14.5172	+	0.760814i	−1.24029	+	0.0650008i	−0.579122	+	0.815241i	$0.696605\pi$
$138$	−9.42622	−	2.98418i	−0.802413	−	0.254030i
$139$	1.23990	−	11.7968i	0.105167	−	1.00059i	−0.806938	−	0.590636i	$-0.798877\pi$
$139$	1.23990	−	11.7968i	0.105167	−	1.00059i	0.912105	−	0.409957i	$-0.134456\pi$
$140$	−0.00892383	−	0.0849046i	−0.000754202	−	0.00717575i
$141$	−0.471295	−	4.17987i	−0.0396902	−	0.352008i
$142$			0.818268i			0.0686675i
$143$	4.99431	−	10.8654i	0.417645	−	0.908610i
$144$	11.1586	−	3.81310i	0.929882	−	0.317758i
$145$	−0.659714	+	12.5881i	−0.0547862	+	1.04538i
$146$	3.61181	−	0.379617i	0.298916	−	0.0314173i
$147$	−10.5630	+	0.633689i	−0.871224	+	0.0522658i
$148$	0.0868372	−	0.170428i	0.00713797	−	0.0140091i
$149$	−0.323298	−	6.16889i	−0.0264856	−	0.505375i	−0.979374	−	0.202055i	$-0.935238\pi$
$149$	−0.323298	−	6.16889i	−0.0264856	−	0.505375i	0.952889	−	0.303321i	$-0.0980953\pi$
$150$	−3.30586	+	3.72782i	−0.269922	+	0.304375i
$151$	−3.64318	+	23.0021i	−0.296478	+	1.87189i	0.167258	+	0.985913i	$0.446509\pi$
$151$	−3.64318	+	23.0021i	−0.296478	+	1.87189i	−0.463736	+	0.885973i	$0.653491\pi$
$152$	2.43330	+	11.4478i	0.197367	+	0.928538i
$153$	2.15044	−	10.9268i	0.173852	−	0.883379i
$154$	4.27984	−	0.969301i	0.344879	−	0.0781085i
$155$	24.6157			1.97718
$156$	−0.0295593	−	0.210699i	−0.00236664	−	0.0168694i
$157$	−2.02346	+	1.47013i	−0.161489	+	0.117329i	−0.665595	−	0.746313i	$-0.731822\pi$
$157$	−2.02346	+	1.47013i	−0.161489	+	0.117329i	0.504106	+	0.863642i	$0.331822\pi$
$158$	8.16118	−	21.2606i	0.649269	−	1.69140i
$159$	−0.676769	+	15.0962i	−0.0536713	+	1.19721i
$160$	−0.380285	−	0.342410i	−0.0300642	−	0.0270699i
$161$	−3.79457	+	0.601001i	−0.299054	+	0.0473655i
$162$	−6.54972	+	10.7862i	−0.514594	+	0.847442i
$163$	−4.11205	+	6.33200i	−0.322080	+	0.495960i	−0.962211	−	0.272306i	$-0.912214\pi$
$163$	−4.11205	+	6.33200i	−0.322080	+	0.495960i	0.640130	+	0.768266i	$0.278880\pi$
$164$	−0.153043	−	0.153043i	−0.0119506	−	0.0119506i
$165$	12.5255	+	8.70730i	0.975107	+	0.677862i
$166$	−2.66867	−	1.54076i	−0.207129	−	0.119586i
$167$	−0.750929	+	14.3286i	−0.0581086	+	1.10878i	0.801556	+	0.597920i	$0.204006\pi$
$167$	−0.750929	+	14.3286i	−0.0581086	+	1.10878i	−0.859664	+	0.510859i	$0.829327\pi$
$168$	3.27112	−	3.32095i	0.252372	−	0.256217i
$169$	12.9834	+	0.656409i	0.998724	+	0.0504930i
$170$	13.1450	−	4.27105i	1.00817	−	0.327575i
$171$	−9.68337	−	7.60195i	−0.740506	−	0.581335i
$172$	−0.0681684	+	0.0303505i	−0.00519779	+	0.00231421i
$173$	−2.72462	−	1.21308i	−0.207149	−	0.0922286i	0.300540	−	0.953769i	$-0.402833\pi$
$173$	−2.72462	−	1.21308i	−0.207149	−	0.0922286i	−0.507688	+	0.861541i	$0.669500\pi$
$174$	−9.27487	+	6.84631i	−0.703126	+	0.519017i
$175$	−0.501081	+	1.87006i	−0.0378782	+	0.141363i
$176$	7.52198	−	10.6477i	0.566991	−	0.802603i
$177$	4.26987	+	3.05319i	0.320943	+	0.229492i
$178$	12.9066	−	2.74339i	0.967392	−	0.205625i
$179$	1.71131	+	16.2820i	0.127909	+	1.21697i	0.850604	+	0.525806i	$0.176236\pi$
$179$	1.71131	+	16.2820i	0.127909	+	1.21697i	−0.722695	+	0.691167i	$0.757097\pi$
$180$	0.271224	+	0.0101053i	0.0202158	+	0.000753203i
$181$	−11.8738	+	3.85802i	−0.882570	+	0.286764i	−0.715024	−	0.699100i	$-0.753584\pi$
$181$	−11.8738	+	3.85802i	−0.882570	+	0.286764i	−0.167546	+	0.985864i	$0.553584\pi$
$182$	2.70567	+	3.92901i	0.200558	+	0.291237i
$183$	−0.238231	−	0.119125i	−0.0176106	−	0.00880599i
$184$	−7.30727	+	9.02373i	−0.538699	+	0.665238i
$185$	−11.0794	+	9.97591i	−0.814571	+	0.733443i
$186$	14.2990	+	17.3874i	1.04845	+	1.27491i
$187$	−5.15660	−	11.1798i	−0.377088	−	0.817550i
$188$	−0.0799193	−	0.0214143i	−0.00582871	−	0.00156180i
$189$	−0.401824	+	4.88683i	−0.0292284	+	0.355465i
$190$	2.39017	−	15.0909i	0.173401	−	1.09481i
$191$	5.09244	+	0.535237i	0.368476	+	0.0387284i	0.286957	−	0.957943i	$-0.407356\pi$
$191$	5.09244	+	0.535237i	0.368476	+	0.0387284i	0.0815190	+	0.996672i	$0.474023\pi$
$192$	0.630772	−	14.0702i	0.0455221	−	1.01543i
$193$	13.7041	−	8.89955i	0.986443	−	0.640604i	0.0527237	−	0.998609i	$-0.483210\pi$
$193$	13.7041	−	8.89955i	0.986443	−	0.640604i	0.933719	+	0.358005i	$0.116543\pi$
$194$	9.25784	+	6.72622i	0.664674	+	0.482914i
$195$	−3.73444	+	16.1576i	−0.267429	+	1.15707i
$196$	−0.0643210	+	0.197960i	−0.00459436	+	0.0141400i
$197$	−5.94735	−	22.1958i	−0.423731	−	1.58139i	−0.766678	−	0.642031i	$-0.778092\pi$
$197$	−5.94735	−	22.1958i	−0.423731	−	1.58139i	0.342947	−	0.939355i	$-0.388575\pi$
$198$	1.12549	+	13.9054i	0.0799850	+	0.988214i
$199$	−3.53036	+	2.03826i	−0.250261	+	0.144488i	−0.619884	−	0.784694i	$-0.712820\pi$
$199$	−3.53036	+	2.03826i	−0.250261	+	0.144488i	0.369623	+	0.929182i	$0.379487\pi$
$200$	2.65644	+	5.21355i	0.187838	+	0.368654i
$201$	−4.48245	−	7.63004i	−0.316168	−	0.538181i
$202$	−8.85329	−	10.9329i	−0.622915	−	0.769236i
$203$	−2.03360	+	3.99116i	−0.142731	+	0.280125i
$204$	−0.184609	−	0.117912i	−0.0129252	−	0.00825549i
$205$	6.86157	+	15.4113i	0.479233	+	1.07637i
$206$	−16.9870	+	20.9772i	−1.18354	+	1.46155i
$207$	−0.184655	−	12.2125i	−0.0128344	−	0.848829i
$208$	13.7838	+	3.29575i	0.955735	+	0.228519i
$209$	−13.5998	−	0.531694i	−0.940716	−	0.0367781i
$210$	−5.54054	+	2.51717i	−0.382334	+	0.173701i
$211$	−10.9567	−	12.1687i	−0.754292	−	0.837726i	0.236709	−	0.971581i	$-0.423931\pi$
$211$	−10.9567	−	12.1687i	−0.754292	−	0.837726i	−0.991001	+	0.133854i	$0.957265\pi$
$212$	0.271542	+	0.120898i	0.0186496	+	0.00830332i
$213$	−0.958954	+	0.319618i	−0.0657065	+	0.0218998i
$214$	−22.1948	+	1.16318i	−1.51720	+	0.0795133i
$215$	5.80818	−	0.304394i	0.396115	−	0.0207595i
$216$	8.98028	+	11.7886i	0.611031	+	0.802110i
$217$	7.99108	+	3.55786i	0.542470	+	0.241523i
$218$	1.28067	+	1.42232i	0.0867377	+	0.0963319i
$219$	1.85567	+	4.08452i	0.125394	+	0.276006i
$220$	0.249456	−	0.166751i	0.0168183	−	0.0112424i
$221$	9.20417	−	9.71711i	0.619139	−	0.653643i
$222$	−13.4824	−	2.03105i	−0.904882	−	0.136315i
$223$	17.7422	−	21.9098i	1.18811	−	1.46719i	0.337552	−	0.941307i	$-0.390401\pi$
$223$	17.7422	−	21.9098i	1.18811	−	1.46719i	0.850556	−	0.525885i	$-0.176266\pi$
$224$	−0.0739626	−	0.166123i	−0.00494184	−	0.0110995i
$225$	−5.66003	−	2.41815i	−0.377335	−	0.161210i
$226$	−8.54031	+	16.7613i	−0.568093	+	1.11495i
$227$	2.98473	+	3.68584i	0.198104	+	0.244638i	0.866511	−	0.499158i	$-0.166357\pi$
$227$	2.98473	+	3.68584i	0.198104	+	0.244638i	−0.668408	+	0.743795i	$0.733024\pi$
$228$	−0.208790	+	0.122659i	−0.0138274	+	0.00812326i
$229$	9.27386	+	18.2010i	0.612834	+	1.20275i	0.963865	+	0.266390i	$0.0858311\pi$
$229$	9.27386	+	18.2010i	0.612834	+	1.20275i	−0.351031	+	0.936364i	$0.614169\pi$
$230$	13.1279	−	7.57937i	0.865625	−	0.499769i
$231$	2.80767	+	4.63707i	0.184731	+	0.305097i
$232$	3.50393	+	13.0769i	0.230045	+	0.858538i
$233$	−7.56414	+	23.2800i	−0.495543	+	1.52513i	0.320565	+	0.947227i	$0.396127\pi$
$233$	−7.56414	+	23.2800i	−0.495543	+	1.52513i	−0.816108	+	0.577899i	$0.803873\pi$
$234$	−13.5823	+	6.74796i	−0.887903	+	0.441128i
$235$	5.21733	+	3.79061i	0.340341	+	0.247272i
$236$	0.0865932	−	0.0562343i	0.00563674	−	0.00366054i
$237$	28.1038	+	1.25990i	1.82553	+	0.0818394i
$238$	4.88462	+	0.513394i	0.316623	+	0.0332784i
$239$	0.863598	−	5.45254i	0.0558615	−	0.352696i	−0.943887	−	0.330269i	$-0.892861\pi$
$239$	0.863598	−	5.45254i	0.0558615	−	0.352696i	0.999748	−	0.0224271i	$-0.00713935\pi$
$240$	−7.22836	+	16.5712i	−0.466588	+	1.06966i
$241$	5.89014	+	1.57826i	0.379417	+	0.101665i	0.443487	−	0.896281i	$-0.353741\pi$
$241$	5.89014	+	1.57826i	0.379417	+	0.101665i	−0.0640697	+	0.997945i	$0.520408\pi$
$242$	10.0212	+	11.7241i	0.644185	+	0.753652i
$243$	−15.1990	−	3.46271i	−0.975016	−	0.222133i
$244$	−0.00389347	+	0.00350569i	−0.000249254	+	0.000224429i
$245$	10.2100	−	12.6083i	0.652292	−	0.805514i
$246$	−6.90005	+	13.7990i	−0.439931	+	0.879792i
$247$	−4.95181	−	13.9426i	−0.315076	−	0.887145i
$248$	25.1433	−	8.16956i	1.59660	−	0.518768i
$249$	0.763274	−	3.72933i	0.0483705	−	0.236337i
$250$	1.14748	+	10.9175i	0.0725727	+	0.690483i
$251$	14.0232	−	2.98071i	0.885133	−	0.188141i	0.257154	−	0.966371i	$-0.417215\pi$
$251$	14.0232	−	2.98071i	0.885133	−	0.188141i	0.627980	+	0.778230i	$0.283882\pi$
$252$	0.0865879	+	0.0424822i	0.00545452	+	0.00267613i
$253$	−8.08127	−	10.8178i	−0.508065	−	0.680106i
$254$	3.13076	−	11.6841i	0.196441	−	0.733128i
$255$	10.1398	+	13.7367i	0.634981	+	0.860226i
$256$	−0.746754	−	0.332476i	−0.0466721	−	0.0207798i
$257$	−19.1876	+	8.54287i	−1.19689	+	0.532890i	−0.905759	−	0.423794i	$-0.860698\pi$
$257$	−19.1876	+	8.54287i	−1.19689	+	0.532890i	−0.291131	+	0.956683i	$0.594032\pi$
$258$	3.58893	+	3.92582i	0.223437	+	0.244411i
$259$	−5.03862	+	1.63715i	−0.313085	+	0.101727i
$260$	0.268998	+	0.184512i	0.0166825	+	0.0114429i
$261$	−11.6462	−	8.19533i	−0.720881	−	0.507278i
$262$	0.410735	−	7.83730i	0.0253753	−	0.484190i
$263$	−21.4207	−	12.3672i	−1.32086	−	0.762597i	−0.336992	−	0.941508i	$-0.609409\pi$
$263$	−21.4207	−	12.3672i	−1.32086	−	0.762597i	−0.983865	+	0.178911i	$0.942743\pi$
$264$	15.6838	+	4.73693i	0.965269	+	0.291538i
$265$	−16.3823	−	16.3823i	−1.00635	−	1.00635i
$266$	2.95712	−	4.55356i	0.181313	−	0.279197i
$267$	8.25642	+	14.0541i	0.505285	+	0.860097i
$268$	−0.171922	+	0.0272297i	−0.0105018	+	0.00166332i
$269$	19.4243	+	17.4897i	1.18432	+	1.06637i	0.996451	+	0.0841716i	$0.0268244\pi$
$269$	19.4243	+	17.4897i	1.18432	+	1.06637i	0.187868	+	0.982194i	$0.439842\pi$
$270$	−5.42983	−	18.5693i	−0.330449	−	1.13009i
$271$	8.79051	−	22.9001i	0.533985	−	1.39108i	−0.355741	−	0.934585i	$-0.615771\pi$
$271$	8.79051	−	22.9001i	0.533985	−	1.39108i	0.889726	−	0.456495i	$-0.150895\pi$
$272$	11.8046	−	8.57654i	0.715758	−	0.520029i
$273$	−3.54768	+	4.70554i	−0.214716	+	0.284792i
$274$	20.3827			1.23137
$275$	−6.63647	+	1.50303i	−0.400194	+	0.0906364i
$276$	−0.224934	−	0.0843987i	−0.0135394	−	0.00508020i
$277$	−1.95015	−	9.17475i	−0.117173	−	0.551257i	−0.997097	−	0.0761421i	$-0.975740\pi$
$277$	−1.95015	−	9.17475i	−0.117173	−	0.551257i	0.879924	−	0.475115i	$-0.157594\pi$
$278$	−2.60176	+	16.4269i	−0.156043	+	0.985218i
$279$	−14.7916	+	23.5490i	−0.885551	+	1.40984i
$280$	0.374028	+	7.13688i	0.0223525	+	0.426510i
$281$	−8.71830	+	17.1106i	−0.520090	+	1.02073i	0.470310	+	0.882501i	$0.344142\pi$
$281$	−8.71830	+	17.1106i	−0.520090	+	1.02073i	−0.990400	+	0.138233i	$0.955858\pi$
$282$	0.353181	+	5.88721i	0.0210316	+	0.350578i
$283$	16.2865	−	1.71178i	0.968131	−	0.101755i	0.392755	−	0.919643i	$-0.371522\pi$
$283$	16.2865	−	1.71178i	0.968131	−	0.101755i	0.575377	+	0.817889i	$0.304855\pi$
$284$	−0.00104058	+	0.0198554i	−6.17469e−5	+	0.00117820i
$285$	18.6192	−	3.09345i	1.10290	−	0.183240i
$286$	−7.79033	+	14.8472i	−0.460652	+	0.877933i
$287$			5.99479i			0.353861i
$288$	0.556087	−	0.158051i	0.0327677	−	0.00931327i
$289$	0.336591	+	3.20245i	0.0197995	+	0.188379i
$290$	1.84746	−	17.5774i	0.108486	−	1.03218i
$291$	−4.26653	+	13.4768i	−0.250108	+	0.790026i
$292$	0.0881239	−	0.00461838i	0.00515706	−	0.000270270i
$293$	10.7241	−	8.68424i	0.626511	−	0.507339i	−0.262675	−	0.964884i	$-0.584605\pi$
$293$	10.7241	−	8.68424i	0.626511	−	0.507339i	0.889186	+	0.457546i	$0.151271\pi$
$294$	14.8368	−	0.112161i	0.865300	−	0.00654137i
$295$	−7.87190	+	1.67322i	−0.458319	+	0.0974188i
$296$	−8.00601	+	13.8668i	−0.465340	+	0.805992i
$297$	−15.8566	+	6.75049i	−0.920092	+	0.391703i
$298$			8.66138i			0.501740i
$299$	7.65836	−	12.5232i	0.442894	−	0.724237i
$300$	−0.0849578	+	0.0862521i	−0.00490504	+	0.00497977i
$301$	1.92953	+	0.740676i	0.111216	+	0.0426919i
$302$	6.78908	−	31.9401i	0.390668	−	1.83795i
$303$	9.35450	−	14.6459i	0.537402	−	0.841383i
$304$	−2.52330	−	15.9315i	−0.144721	−	0.913735i
$305$	0.381239	−	0.146344i	0.0218297	−	0.00837963i
$306$	−3.81285	+	15.1418i	−0.217966	+	0.865601i
$307$	−5.94523	+	5.94523i	−0.339312	+	0.339312i	−0.856108	−	0.516796i	$-0.827124\pi$
$307$	−5.94523	+	5.94523i	−0.339312	+	0.339312i	0.516796	+	0.856108i	$0.327124\pi$
$308$	0.105084	−	0.0180776i	0.00598769	−	0.00103007i
$309$	−31.2190	−	11.7139i	−1.77599	−	0.666378i
$310$	−34.4668	−	1.80633i	−1.95758	−	0.102592i
$311$	10.7232	−	7.79086i	0.608057	−	0.441779i	−0.240673	−	0.970606i	$-0.577368\pi$
$311$	10.7232	−	7.79086i	0.608057	−	0.441779i	0.848729	+	0.528827i	$0.177368\pi$
$312$	1.54797	+	17.7434i	0.0876366	+	1.00452i
$313$	−3.06049	−	9.41922i	−0.172989	−	0.532406i	0.826547	−	0.562868i	$-0.190302\pi$
$313$	−3.06049	−	9.41922i	−0.172989	−	0.532406i	−0.999536	+	0.0304621i	$0.990302\pi$
$314$	2.94111	−	1.90998i	0.165977	−	0.107786i
$315$	−5.11410	−	5.50993i	−0.288147	−	0.310449i
$316$	0.225069	−	0.505513i	0.0126611	−	0.0284373i
$317$	−10.1124	−	19.8468i	−0.567972	−	1.11471i	−0.979147	−	0.203151i	$-0.934882\pi$
$317$	−10.1124	−	19.8468i	−0.567972	−	1.11471i	0.411176	−	0.911556i	$-0.365118\pi$
$318$	2.05539	−	21.0880i	0.115260	−	1.18256i
$319$	−15.7423	+	0.209133i	−0.881399	+	0.0117092i
$320$	15.2688	+	15.2688i	0.853554	+	0.853554i
$321$	−10.0325	−	25.5564i	−0.559960	−	1.42642i
$322$	5.35724	−	0.563068i	0.298547	−	0.0313786i
$323$	−14.2214	−	5.45908i	−0.791299	−	0.303751i
$324$	−0.172646	+	0.253399i	−0.00959147	+	0.0140777i
$325$	−4.19551	−	6.09246i	−0.232725	−	0.337949i
$326$	6.22232	−	8.56429i	0.344622	−	0.474332i
$327$	−1.16664	+	2.05642i	−0.0645151	+	0.113720i
$328$	12.1234	+	13.4644i	0.669405	+	0.743449i
$329$	1.14584	+	1.98465i	0.0631722	+	0.109417i
$330$	−16.8991	−	13.1110i	−0.930268	−	0.721739i
$331$	5.21775	−	19.4729i	0.286793	−	1.07033i	−0.660726	−	0.750627i	$-0.729751\pi$
$331$	5.21775	−	19.4729i	0.286793	−	1.07033i	0.947519	−	0.319700i	$-0.103582\pi$
$332$	−0.0627964	−	0.0407805i	−0.00344640	−	0.00223812i
$333$	−2.88602	−	16.5938i	−0.158153	−	0.909336i
$334$	2.10289	−	20.0077i	0.115065	−	1.09477i
$335$	13.2708	+	2.82080i	0.725062	+	0.154117i
$336$	−4.74170	+	4.33480i	−0.258681	+	0.236483i
$337$	8.69817	−	11.9720i	0.473819	−	0.652156i	−0.503483	−	0.864005i	$-0.667948\pi$
$337$	8.69817	−	11.9720i	0.473819	−	0.652156i	0.977302	+	0.211849i	$0.0679484\pi$
$338$	−18.1311	−	1.87184i	−0.986204	−	0.101815i
$339$	−22.9790	−	3.46165i	−1.24805	−	0.188011i
$340$	0.324396	−	0.0869216i	0.0175928	−	0.00471398i
$341$	2.01672	+	30.6780i	0.109211	+	1.66131i
$342$	13.0008	+	11.3548i	0.703001	+	0.613996i
$343$	11.0224	−	5.61620i	0.595155	−	0.303246i
$344$	5.83166	−	2.23856i	0.314422	−	0.120695i
$345$	14.0103	+	12.4244i	0.754288	+	0.668909i
$346$	3.72598	+	1.89848i	0.200310	+	0.102063i
$347$	−17.1919	−	15.4797i	−0.922911	−	0.830993i	0.0630431	−	0.998011i	$-0.479919\pi$
$347$	−17.1919	−	15.4797i	−0.922911	−	0.830993i	−0.985954	+	0.167018i	$0.946586\pi$
$348$	−0.233763	+	0.154332i	−0.0125310	+	0.00827306i
$349$	−1.51138	−	1.22389i	−0.0809024	−	0.0655135i	0.588016	−	0.808849i	$-0.299909\pi$
$349$	−1.51138	−	1.22389i	−0.0809024	−	0.0655135i	−0.668919	+	0.743336i	$0.733243\pi$
$350$	0.838838	−	2.58168i	0.0448378	−	0.137997i
$351$	−13.2134	−	13.2818i	−0.705281	−	0.708928i
$352$	0.395582	−	0.501993i	0.0210846	−	0.0267563i
$353$	−6.38885	−	23.8435i	−0.340044	−	1.26906i	−0.898296	−	0.439390i	$-0.855195\pi$
$353$	−6.38885	−	23.8435i	−0.340044	−	1.26906i	0.558252	−	0.829671i	$-0.311472\pi$
$354$	−5.75460	−	4.58839i	−0.305853	−	0.243870i
$355$	0.630333	−	1.41575i	0.0334546	−	0.0751403i
$356$	0.316670	−	0.0501556i	0.0167835	−	0.00265824i
$357$	1.30628	+	5.92497i	0.0691357	+	0.313583i
$358$	−1.20137	−	22.9235i	−0.0634945	−	1.21155i
$359$	−1.60327	−	10.1227i	−0.0846174	−	0.534253i	−0.993188	−	0.116522i	$-0.962825\pi$
$359$	−1.60327	−	10.1227i	−0.0846174	−	0.534253i	0.908571	−	0.417731i	$-0.137175\pi$
$360$	−22.6293	−	2.03304i	−1.19267	−	0.107151i
$361$	1.60542	−	1.44553i	0.0844957	−	0.0760803i
$362$	16.9087	−	4.53067i	0.888701	−	0.238127i
$363$	−9.82551	+	16.3236i	−0.515706	+	0.856766i
$364$	0.0606571	+	0.0987787i	0.00317930	+	0.00517741i
$365$	−6.54152	−	2.12547i	−0.342399	−	0.111252i
$366$	0.324829	+	0.184280i	0.0169791	+	0.00963248i
$367$	−10.4782	+	4.66518i	−0.546955	+	0.243520i	−0.661562	−	0.749891i	$-0.730106\pi$
$367$	−10.4782	+	4.66518i	−0.546955	+	0.243520i	0.114606	+	0.993411i	$0.463439\pi$
$368$	10.7082	−	11.8926i	0.558201	−	0.619945i
$369$	−18.8667	−	2.69646i	−0.982160	−	0.140372i
$370$	16.2453	−	13.1552i	0.844554	−	0.683906i
$371$	−2.95040	−	7.68606i	−0.153177	−	0.399041i
$372$	0.324857	+	0.440092i	0.0168430	+	0.0228177i
$373$	14.4561	+	25.0387i	0.748508	+	1.29645i	0.948538	+	0.316664i	$0.102563\pi$
$373$	14.4561	+	25.0387i	0.748508	+	1.29645i	−0.200030	+	0.979790i	$0.564104\pi$
$374$	6.39986	+	16.0323i	0.330929	+	0.829012i
$375$	−12.3464	+	5.60916i	−0.637563	+	0.289656i
$376$	6.58721	+	2.14031i	0.339709	+	0.110378i
$377$	−6.56428	−	15.8063i	−0.338078	−	0.814067i
$378$	0.921233	−	6.81303i	0.0473831	−	0.350425i
$379$	7.46837	+	11.5003i	0.383624	+	0.590729i	0.976750	−	0.214380i	$-0.0687731\pi$
$379$	7.46837	+	11.5003i	0.383624	+	0.590729i	−0.593126	+	0.805110i	$0.702106\pi$
$380$	0.0771888	−	0.363145i	0.00395970	−	0.0186289i
$381$	14.9159	−	0.894823i	0.764164	−	0.0458431i
$382$	−7.09114	−	1.12313i	−0.362814	−	0.0574641i
$383$	3.76428	−	5.79648i	0.192345	−	0.296186i	−0.729319	−	0.684174i	$-0.760163\pi$
$383$	3.76428	−	5.79648i	0.192345	−	0.296186i	0.921665	+	0.387988i	$0.126830\pi$
$384$	−1.85093	+	18.9903i	−0.0944551	+	0.969097i
$385$	−8.15157	−	1.61980i	−0.415442	−	0.0825528i
$386$	−19.8415	+	11.4555i	−1.00990	+	0.583069i
$387$	−3.19894	+	5.73941i	−0.162611	+	0.291751i
$388$	0.216089	+	0.174986i	0.0109703	+	0.00888355i
$389$	6.18974	+	4.49711i	0.313832	+	0.228012i	0.733539	−	0.679647i	$-0.237867\pi$
$389$	6.18974	+	4.49711i	0.313832	+	0.228012i	−0.419707	+	0.907660i	$0.637867\pi$
$390$	6.41460	−	22.3498i	0.324816	−	1.13172i
$391$	−4.67024	−	14.3735i	−0.236184	−	0.726900i
$392$	6.24435	−	16.2671i	0.315387	−	0.821612i
$393$	9.34521	−	2.57992i	0.471404	−	0.130140i
$394$	6.69870	+	31.5149i	0.337475	+	1.58770i
$395$	−30.4979	+	30.4979i	−1.53452	+	1.53452i
$396$	0.00962690	+	0.338848i	0.000483770	+	0.0170278i
$397$	21.1313	+	5.66212i	1.06055	+	0.284174i	0.746605	−	0.665268i	$-0.231683\pi$
$397$	21.1313	+	5.66212i	1.06055	+	0.284174i	0.313945	+	0.949441i	$0.398349\pi$
$398$	5.09277	−	2.59489i	0.255277	−	0.130070i
$399$	6.49153	+	1.68691i	0.324983	+	0.0844510i
$400$	−3.28009	−	7.36721i	−0.164005	−	0.368361i
$401$	−16.6708	−	25.6707i	−0.832498	−	1.28193i	−0.957109	−	0.289729i	$-0.906435\pi$
$401$	−16.6708	−	25.6707i	−0.832498	−	1.28193i	0.124611	−	0.992206i	$-0.460232\pi$
$402$	5.71640	+	11.0125i	0.285108	+	0.549252i
$403$	−30.1533	+	14.4166i	−1.50204	+	0.718140i
$404$	−0.200923	−	0.276547i	−0.00999630	−	0.0137587i
$405$	19.6411	−	13.6166i	0.975972	−	0.676615i
$406$	3.14031	−	5.43918i	0.155851	−	0.269942i
$407$	−13.3405	−	12.9907i	−0.661262	−	0.643923i
$408$	14.9162	+	10.6659i	0.738461	+	0.528041i
$409$	27.0060	+	17.5379i	1.33536	+	0.867195i	0.997264	−	0.0739157i	$-0.0235496\pi$
$409$	27.0060	+	17.5379i	1.33536	+	0.867195i	0.338099	+	0.941111i	$0.390216\pi$
$410$	−8.47664	−	22.0824i	−0.418631	−	1.09057i
$411$	7.96155	+	23.8872i	0.392714	+	1.17827i
$412$	−0.438869	+	0.487413i	−0.0216215	+	0.0240131i
$413$	−2.79732	−	0.594590i	−0.137647	−	0.0292578i
$414$	−0.637615	+	17.1135i	−0.0313370	+	0.841081i
$415$	3.43040	+	4.72154i	0.168392	+	0.231771i
$416$	0.666373	+	0.196720i	0.0326716	+	0.00964499i
$417$	−20.2674	+	3.36729i	−0.992500	+	0.164897i
$418$	19.0033	+	1.74244i	0.929483	+	0.0852256i
$419$	17.9087	+	10.3396i	0.874898	+	0.505122i	0.868973	−	0.494860i	$-0.164781\pi$
$419$	17.9087	+	10.3396i	0.874898	+	0.505122i	0.00592508	+	0.999982i	$0.498114\pi$
$420$	−0.137643	+	0.0540336i	−0.00671630	+	0.00263657i
$421$	32.2347	+	5.10547i	1.57102	+	0.248825i	0.880344	−	0.474336i	$-0.157312\pi$
$421$	32.2347	+	5.10547i	1.57102	+	0.248825i	0.690679	+	0.723162i	$0.257312\pi$
$422$	14.4486	+	17.8425i	0.703347	+	0.868561i
$423$	−6.76146	+	2.71347i	−0.328753	+	0.131933i
$424$	−22.1704	−	11.2964i	−1.07669	−	0.548602i
$425$	−7.57427	−	0.796087i	−0.367406	−	0.0386159i
$426$	1.36618	−	0.377158i	0.0661915	−	0.0182734i
$427$	0.144915	+	0.00759468i	0.00701293	+	0.000367532i
$428$	−0.540039			−0.0261038
$429$	−20.4428	−	3.33038i	−0.986988	−	0.160792i
$430$	−8.15492			−0.393265
$431$	−28.7636	−	1.50744i	−1.38549	−	0.0726106i	−0.655051	−	0.755585i	$-0.727353\pi$
$431$	−28.7636	−	1.50744i	−1.38549	−	0.0726106i	−0.730442	+	0.682974i	$0.760686\pi$
$432$	−11.5096	−	16.8728i	−0.553754	−	0.811792i
$433$	3.96420	+	0.416654i	0.190507	+	0.0200231i	0.199302	−	0.979938i	$-0.436133\pi$
$433$	3.96420	+	0.416654i	0.190507	+	0.0200231i	−0.00879432	+	0.999961i	$0.502799\pi$
$434$	−10.9280	−	5.56809i	−0.524560	−	0.267277i
$435$	21.3211	−	4.70067i	1.02227	−	0.225380i
$436$	0.0292668	+	0.0361415i	0.00140163	+	0.00173086i
$437$	−16.5014	−	2.61356i	−0.789369	−	0.125024i
$438$	−2.29857	−	5.85529i	−0.109830	−	0.279777i
$439$	9.40865	+	5.43209i	0.449050	+	0.259259i	0.707429	−	0.706784i	$-0.249855\pi$
$439$	9.40865	+	5.43209i	0.449050	+	0.259259i	−0.258379	+	0.966044i	$0.583188\pi$
$440$	−21.5844	+	12.8470i	−1.02900	+	0.612459i
$441$	5.92674	+	17.3439i	0.282226	+	0.825901i
$442$	−13.6007	+	12.9304i	−0.646918	+	0.615038i
$443$	19.3216	+	26.5939i	0.917997	+	1.26351i	0.964361	+	0.264590i	$0.0852366\pi$
$443$	19.3216	+	26.5939i	0.917997	+	1.26351i	−0.0463640	+	0.998925i	$0.514763\pi$
$444$	−0.324570	−	0.0664292i	−0.0154034	−	0.00315259i
$445$	−24.4441	−	5.19575i	−1.15876	−	0.246302i
$446$	−26.4504	+	29.3761i	−1.25246	+	1.39100i
$447$	−10.1505	+	3.38316i	−0.480104	+	0.160018i
$448$	2.74988	+	7.16368i	0.129920	+	0.338452i
$449$	7.81828	+	5.07725i	0.368967	+	0.239610i	0.715783	−	0.698323i	$-0.246070\pi$
$449$	7.81828	+	5.07725i	0.368967	+	0.239610i	−0.346815	+	0.937934i	$0.612737\pi$
$450$	7.74770	+	3.80122i	0.365230	+	0.179191i
$451$	−18.6446	+	9.81404i	−0.877942	+	0.462125i
$452$	−0.228547	+	0.395855i	−0.0107499	+	0.0186194i
$453$	40.0835	−	4.51955i	1.88329	−	0.212347i
$454$	−3.90873	−	5.37991i	−0.183446	−	0.252492i
$455$	−1.65469	−	8.88214i	−0.0775729	−	0.416401i
$456$	17.9916	−	9.33917i	0.842534	−	0.437347i
$457$	−1.20102	−	1.84941i	−0.0561814	−	0.0865118i	0.809464	−	0.587170i	$-0.199758\pi$
$457$	−1.20102	−	1.84941i	−0.0561814	−	0.0865118i	−0.865645	+	0.500658i	$0.833091\pi$
$458$	−11.6496	−	26.1654i	−0.544350	−	1.22263i
$459$	−19.2345	+	1.44604i	−0.897790	+	0.0674955i
$460$	0.328188	−	0.167220i	0.0153018	−	0.00779668i
$461$	21.6408	+	5.79862i	1.00791	+	0.270069i	0.724756	−	0.689005i	$-0.241952\pi$
$461$	21.6408	+	5.79862i	1.00791	+	0.270069i	0.283154	+	0.959074i	$0.408619\pi$
$462$	−3.59101	−	6.69883i	−0.167069	−	0.311658i
$463$	11.2553	−	11.2553i	0.523077	−	0.523077i	−0.395423	−	0.918499i	$-0.629402\pi$
$463$	11.2553	−	11.2553i	0.523077	−	0.523077i	0.918499	+	0.395423i	$0.129402\pi$
$464$	−3.87935	−	18.2509i	−0.180094	−	0.847277i
$465$	−11.3459	−	41.0983i	−0.526154	−	1.90589i
$466$	12.2996	−	32.0415i	0.569767	−	1.48429i
$467$	−2.08865	−	6.42820i	−0.0966512	−	0.297462i	0.891029	−	0.453946i	$-0.149984\pi$
$467$	−2.08865	−	6.42820i	−0.0966512	−	0.297462i	−0.987680	+	0.156484i	$0.949984\pi$
$468$	−0.338158	+	0.146468i	−0.0156314	+	0.00677048i
$469$	3.90044	+	2.83384i	0.180106	+	0.130855i
$470$	−7.02712	−	5.69045i	−0.324137	−	0.262481i
$471$	3.38717	+	2.70074i	0.156073	+	0.124444i
$472$	−7.48532	+	4.32165i	−0.344540	+	0.198920i
$473$	0.855213	+	7.21366i	0.0393227	+	0.331685i
$474$	−39.2583	−	3.82639i	−1.80319	−	0.175752i
$475$	−4.58542	+	7.06092i	−0.210393	+	0.323977i
$476$	0.117873	+	0.0186693i	0.00540270	+	0.000855704i
$477$	25.5165	−	5.82825i	1.16832	−	0.266857i
$478$	−1.60932	+	7.57125i	−0.0736086	+	0.346301i
$479$	5.11021	+	7.86904i	0.233492	+	0.359545i	0.935922	−	0.352207i	$-0.114569\pi$
$479$	5.11021	+	7.86904i	0.233492	+	0.359545i	−0.702431	+	0.711752i	$0.747902\pi$
$480$	−0.396405	+	0.792746i	−0.0180933	+	0.0361838i
$481$	7.72928	−	18.7089i	0.352425	−	0.853054i
$482$	−8.13153	−	2.64209i	−0.370381	−	0.120344i
$483$	2.75243	+	6.05838i	0.125240	+	0.275666i
$484$	0.228256	+	0.297230i	0.0103753	+	0.0135105i
$485$	−10.8364	−	18.7691i	−0.492054	−	0.852262i
$486$	21.0275	+	5.96379i	0.953825	+	0.270523i
$487$	12.5336	+	32.6512i	0.567953	+	1.47957i	0.853443	+	0.521186i	$0.174510\pi$
$487$	12.5336	+	32.6512i	0.567953	+	1.47957i	−0.285490	+	0.958382i	$0.592156\pi$
$488$	0.340842	−	0.276008i	0.0154292	−	0.0124943i
$489$	12.4672	+	3.94690i	0.563787	+	0.178485i
$490$	−15.2212	+	16.9048i	−0.687623	+	0.763683i
$491$	−2.57776	+	1.14769i	−0.116332	+	0.0517946i	−0.464078	−	0.885795i	$-0.653614\pi$
$491$	−2.57776	+	1.14769i	−0.116332	+	0.0517946i	0.347745	+	0.937589i	$0.386947\pi$
$492$	−0.184979	+	0.326060i	−0.00833949	+	0.0146999i
$493$	−16.7587	−	5.44522i	−0.754772	−	0.245240i
$494$	5.91038	+	19.8857i	0.265920	+	0.894700i
$495$	8.76440	−	24.9259i	0.393930	−	1.12033i
$496$	−35.1950	+	9.43046i	−1.58030	+	0.423440i
$497$	0.409255	−	0.368495i	0.0183576	−	0.0165292i
$498$	−1.34240	+	5.16578i	−0.0601542	+	0.231484i
$499$	−1.56109	−	9.85631i	−0.0698838	−	0.441229i	−0.997676	−	0.0681325i	$-0.978296\pi$
$499$	−1.56109	−	9.85631i	−0.0698838	−	0.441229i	0.927792	−	0.373097i	$-0.121704\pi$
$500$	0.0139601	+	0.266374i	0.000624313	+	0.0119126i
$501$	24.2691	−	5.35061i	1.08426	−	0.239048i
$502$	−19.8539	+	3.14454i	−0.886122	+	0.140348i
$503$	12.7197	−	28.5690i	0.567145	−	1.27383i	−0.371336	−	0.928499i	$-0.621100\pi$
$503$	12.7197	−	28.5690i	0.567145	−	1.27383i	0.938481	−	0.345331i	$-0.112233\pi$
$504$	−7.05238	−	3.93075i	−0.314138	−	0.175089i
$505$	6.89589	+	25.7358i	0.306863	+	1.14523i
$506$	10.5215	+	15.7400i	0.467739	+	0.699727i
$507$	−4.88841	−	21.9796i	−0.217102	−	0.976149i
$508$	0.0908268	−	0.279536i	0.00402979	−	0.0124024i
$509$	1.49978	+	1.21450i	0.0664768	+	0.0538318i	0.661983	−	0.749519i	$-0.269715\pi$
$509$	1.49978	+	1.21450i	0.0664768	+	0.0538318i	−0.595506	+	0.803351i	$0.703048\pi$
$510$	−13.1897	−	19.9781i	−0.584051	−	0.884647i
$511$	−1.81639	−	1.63548i	−0.0803523	−	0.0723496i
$512$	20.6519	+	10.5227i	0.912695	+	0.465041i
$513$	−8.22890	+	19.6712i	−0.363315	+	0.868506i
$514$	27.4933	−	10.5537i	1.21268	−	0.465503i
$515$	45.5499	−	23.2088i	2.00717	−	1.02270i
$516$	0.0820935	+	0.0998245i	0.00361396	+	0.00439453i
$517$	−4.29671	+	6.81279i	−0.188969	+	0.299626i
$518$	7.17518	−	1.92258i	0.315259	−	0.0844735i
$519$	−0.769513	+	5.10814i	−0.0337779	+	0.224223i
$520$	−21.6791	−	16.6032i	−0.950690	−	0.728098i
$521$	−21.4697	+	29.5505i	−0.940604	+	1.29463i	0.0149731	+	0.999888i	$0.495234\pi$
$521$	−21.4697	+	29.5505i	−0.940604	+	1.29463i	−0.955577	+	0.294742i	$0.904766\pi$
$522$	15.7056	+	12.3297i	0.687414	+	0.539655i
$523$	14.3177	+	3.04331i	0.626067	+	0.133075i	0.510011	−	0.860168i	$-0.329641\pi$
$523$	14.3177	+	3.04331i	0.626067	+	0.133075i	0.116056	+	0.993243i	$0.462975\pi$
$524$	0.0199331	−	0.189651i	0.000870782	−	0.00828494i
$525$	3.35320	−	0.0253491i	0.146346	−	0.00110632i
$526$	29.0856	+	18.8884i	1.26819	+	0.823575i
$527$	−8.90607	+	33.2379i	−0.387954	+	1.44787i
$528$	−21.2445	−	7.65089i	−0.924547	−	0.332962i
$529$	3.21224	+	5.56376i	0.139663	+	0.241903i
$530$	21.7362	+	24.1405i	0.944161	+	1.04860i
$531$	3.12952	−	8.53623i	0.135810	−	0.370441i
$532$	0.0775456	−	0.106732i	0.00336203	−	0.00462744i
$533$	−17.4311	−	14.8597i	−0.755024	−	0.643647i
$534$	−10.5293	−	20.2843i	−0.455647	−	0.877790i
$535$	39.2970	+	15.0847i	1.69896	+	0.652169i
$536$	14.4914	−	1.52311i	0.625935	−	0.0657884i
$537$	26.3956	−	10.3619i	1.13905	−	0.447150i
$538$	−25.9144	−	25.9144i	−1.11725	−	1.11725i
$539$	16.5499	+	11.6915i	0.712855	+	0.503589i
$540$	−0.108141	−	0.457492i	−0.00465366	−	0.0196873i
$541$	−13.6251	−	26.7408i	−0.585788	−	1.14967i	−0.973669	−	0.227965i	$-0.926793\pi$
$541$	−13.6251	−	26.7408i	−0.585788	−	1.14967i	0.387881	−	0.921710i	$-0.373207\pi$
$542$	−13.9889	+	31.4195i	−0.600873	+	1.34958i
$543$	11.9142	+	18.0461i	0.511288	+	0.774434i
$544$	0.599936	−	0.389603i	0.0257220	−	0.0167041i
$545$	−1.12013	−	3.44741i	−0.0479811	−	0.147671i
$546$	5.31275	−	6.32834i	0.227365	−	0.270828i
$547$	−1.46119	+	1.06161i	−0.0624758	+	0.0453913i	−0.618585	−	0.785718i	$-0.712294\pi$
$547$	−1.46119	+	1.06161i	−0.0624758	+	0.0453913i	0.556109	+	0.831109i	$0.312294\pi$
$548$	0.494590	+	0.0259204i	0.0211279	+	0.00110726i
$549$	−0.0890848	+	0.452658i	−0.00380205	+	0.0193190i
$550$	9.40265	−	1.61755i	0.400930	−	0.0689725i
$551$	−13.7741	+	13.7741i	−0.586795	+	0.586795i
$552$	18.4341	+	8.04096i	0.784606	+	0.342246i
$553$	−14.3087	+	5.49260i	−0.608468	+	0.233569i
$554$	2.05734	+	12.9895i	0.0874081	+	0.551873i
$555$	21.7625	+	13.9000i	0.923765	+	0.590020i
$556$	−0.0840218	+	0.395292i	−0.00356332	+	0.0167641i
$557$	37.9755	+	14.5774i	1.60907	+	0.617665i	0.986333	−	0.164763i	$-0.0526860\pi$
$557$	37.9755	+	14.5774i	1.60907	+	0.617665i	0.622740	+	0.782429i	$0.286019\pi$
$558$	22.4392	−	31.8878i	0.949927	−	1.34992i
$559$	−6.93654	+	3.77452i	−0.293384	+	0.159645i
$560$		−	9.84973i		−	0.416227i
$561$	−16.2890	+	13.7625i	−0.687722	+	0.581052i
$562$	13.4629	−	23.3184i	0.567899	−	0.983629i
$563$	−11.3670	+	2.41613i	−0.479062	+	0.101828i	−0.441113	−	0.897452i	$-0.645416\pi$
$563$	−11.3670	+	2.41613i	−0.479062	+	0.101828i	−0.0379498	+	0.999280i	$0.512083\pi$
$564$	0.00108332	+	0.143303i	4.56161e−5	+	0.00603416i
$565$	27.6879	−	22.4213i	1.16484	−	0.943269i
$566$	−22.9299	+	1.20170i	−0.963815	+	0.0505114i
$567$	8.34425	−	1.58157i	0.350425	−	0.0664195i
$568$	0.173979	−	1.65530i	0.00729998	−	0.0694547i
$569$	−1.45155	−	13.8105i	−0.0608520	−	0.578968i	−0.981884	−	0.189482i	$-0.939319\pi$
$569$	−1.45155	−	13.8105i	−0.0608520	−	0.578968i	0.921032	−	0.389486i	$-0.127347\pi$
$570$	−26.2975	+	2.96513i	−1.10148	+	0.124196i
$571$			10.1105i			0.423110i	0.977366	+	0.211555i	$0.0678527\pi$
$571$			10.1105i			0.423110i	−0.977366	+	0.211555i	$0.932147\pi$
$572$	−0.207914	+	0.350362i	−0.00869333	+	0.0146494i
$573$	−1.45359	−	8.74903i	−0.0607246	−	0.365496i
$574$	0.439904	−	8.39387i	0.0183612	−	0.350353i
$575$	−8.30713	+	0.873114i	−0.346431	+	0.0364114i
$576$	−23.7823	+	5.43213i	−0.990929	+	0.226339i
$577$	−6.64938	+	13.0502i	−0.276817	+	0.543285i	−0.986998	−	0.160735i	$-0.948613\pi$
$577$	−6.64938	+	13.0502i	−0.276817	+	0.543285i	0.710180	+	0.704020i	$0.248613\pi$
$578$	−0.236294	−	4.50875i	−0.00982852	−	0.187539i
$579$	−21.1752	−	18.7783i	−0.880010	−	0.780400i
$580$	0.0671816	−	0.424168i	0.00278956	−	0.0176126i
$581$	0.431190	+	2.02859i	0.0178888	+	0.0841600i
$582$	6.96292	−	18.5571i	0.288622	−	0.769217i
$583$	19.0747	−	21.7590i	0.789992	−	0.901166i
$584$	−7.38714			−0.305682
$585$	28.6980	−	1.21240i	1.18651	−	0.0501264i
$586$	−15.6532	+	11.3727i	−0.646626	+	0.469801i
$587$	−8.93825	+	23.2849i	−0.368921	+	0.961072i	0.615950	+	0.787785i	$0.288772\pi$
$587$	−8.93825	+	23.2849i	−0.368921	+	0.961072i	−0.984871	+	0.173287i	$0.944561\pi$
$588$	0.360160	+	0.0161461i	0.0148527	+	0.000665854i
$589$	28.2688	+	25.4533i	1.16480	+	1.04879i
$590$	11.1450	−	1.76519i	0.458831	−	0.0726717i
$591$	−34.3168	+	20.1602i	−1.41160	+	0.829280i
$592$	12.0192	−	18.5079i	0.493985	−	0.760671i
$593$	−32.3781	−	32.3781i	−1.32961	−	1.32961i	−0.905708	−	0.423901i	$-0.860660\pi$
$593$	−32.3781	−	32.3781i	−1.32961	−	1.32961i	−0.423901	−	0.905708i	$-0.639340\pi$
$594$	22.6977	−	8.28842i	0.931296	−	0.340078i
$595$	−8.05579	−	4.65101i	−0.330255	−	0.190673i
$596$	−0.0110145	+	0.210170i	−0.000451172	+	0.00860888i
$597$	5.03029	+	4.95480i	0.205876	+	0.202787i
$598$	−11.6422	+	16.9730i	−0.476084	+	0.694077i
$599$	35.7884	−	11.6283i	1.46227	−	0.475121i	0.533509	−	0.845794i	$-0.320873\pi$
$599$	35.7884	−	11.6283i	1.46227	−	0.475121i	0.928763	+	0.370673i	$0.120873\pi$
$600$	7.48011	−	6.83822i	0.305374	−	0.279169i
$601$	−12.3780	+	5.51106i	−0.504911	+	0.224801i	−0.643353	−	0.765570i	$-0.722457\pi$
$601$	−12.3780	+	5.51106i	−0.504911	+	0.224801i	0.138442	+	0.990371i	$0.455791\pi$
$602$	−2.64736	−	1.17868i	−0.107898	−	0.0480395i
$603$	−10.6730	+	11.0007i	−0.434639	+	0.447985i
$604$	0.205356	−	0.766398i	0.00835581	−	0.0311843i
$605$	−8.30708	−	28.0043i	−0.337731	−	1.13854i
$606$	−14.1728	+	19.8206i	−0.575733	+	0.805158i
$607$	−39.0491	+	8.30015i	−1.58496	+	0.336893i	−0.914351	−	0.404922i	$-0.867299\pi$
$607$	−39.0491	+	8.30015i	−1.58496	+	0.336893i	−0.670605	+	0.741815i	$0.733965\pi$
$608$	−0.0826593	−	0.786451i	−0.00335228	−	0.0318948i
$609$	7.60096	+	1.55567i	0.308007	+	0.0630391i
$610$	−0.544548	+	0.176934i	−0.0220481	+	0.00716386i
$611$	−8.61107	−	1.58775i	−0.348367	−	0.0642335i
$612$	−0.111775	+	0.362570i	−0.00451824	+	0.0146560i
$613$	−14.8135	+	18.2931i	−0.598312	+	0.738853i	−0.982881	−	0.184243i	$-0.941017\pi$
$613$	−14.8135	+	18.2931i	−0.598312	+	0.738853i	0.384569	+	0.923096i	$0.374350\pi$
$614$	8.76074	−	7.88821i	0.353555	−	0.318342i
$615$	22.5681	−	18.5595i	0.910032	−	0.748391i
$616$	−8.86389	+	1.05085i	−0.357136	+	0.0423401i
$617$	15.7660	+	4.22448i	0.634714	+	0.170071i	0.561808	−	0.827268i	$-0.310106\pi$
$617$	15.7660	+	4.22448i	0.634714	+	0.170071i	0.0729063	+	0.997339i	$0.476773\pi$
$618$	42.8531	+	18.6926i	1.72381	+	0.751926i
$619$	1.24320	−	7.84924i	0.0499683	−	0.315488i	−0.950026	−	0.312170i	$-0.898944\pi$
$619$	1.24320	−	7.84924i	0.0499683	−	0.315488i	0.999994	−	0.00331734i	$-0.00105595\pi$
$620$	−0.834044	−	0.0876616i	−0.0334960	−	0.00352057i
$621$	−20.3049	+	5.93732i	−0.814806	+	0.238256i
$622$	−15.5863	+	10.1218i	−0.624952	+	0.405849i
$623$	−7.18440	−	5.21977i	−0.287837	−	0.209126i
$624$	−0.850689	−	24.5325i	−0.0340548	−	0.982085i
$625$	9.59466	−	29.5293i	0.383787	−	1.18117i
$626$	3.59409	+	13.4133i	0.143649	+	0.536105i
$627$	5.38072	+	22.9512i	0.214885	+	0.916583i
$628$	0.0737954	−	0.0426058i	0.00294476	−	0.00170016i
$629$	−9.46164	−	18.5695i	−0.377260	−	0.740415i
$630$	6.75641	+	8.09025i	0.269182	+	0.322323i
$631$	−5.47382	−	6.75961i	−0.217909	−	0.269096i	0.656455	−	0.754365i	$-0.272055\pi$
$631$	−5.47382	−	6.75961i	−0.217909	−	0.269096i	−0.874365	+	0.485269i	$0.838722\pi$
$632$	−21.0299	+	41.2734i	−0.836523	+	1.64177i
$633$	−15.2666	+	23.9021i	−0.606792	+	0.950024i
$634$	12.7030	+	28.5314i	0.504501	+	1.13313i
$635$	−14.4174	+	17.8040i	−0.572136	+	0.706529i
$636$	0.0766915	−	0.509089i	0.00304101	−	0.0201867i
$637$	−5.12262	+	21.4243i	−0.202966	+	0.848863i
$638$	22.0576	+	0.862360i	0.873270	+	0.0341412i
$639$	0.975635	+	1.45375i	0.0385955	+	0.0575093i
$640$	−19.5741	−	21.7392i	−0.773734	−	0.859318i
$641$	16.2613	+	7.24000i	0.642283	+	0.285963i	0.701918	−	0.712257i	$-0.252327\pi$
$641$	16.2613	+	7.24000i	0.642283	+	0.285963i	−0.0596352	+	0.998220i	$0.518994\pi$
$642$	12.1721	+	36.5202i	0.480395	+	1.44134i
$643$	23.6354	−	1.23868i	0.932090	−	0.0488488i	0.419758	−	0.907636i	$-0.362115\pi$
$643$	23.6354	−	1.23868i	0.932090	−	0.0488488i	0.512332	+	0.858787i	$0.328782\pi$
$644$	0.130710	−	0.00685023i	0.00515070	−	0.000269937i
$645$	−3.18533	−	9.55701i	−0.125422	−	0.376307i
$646$	19.5121	+	8.68736i	0.767694	+	0.341800i
$647$	30.0149	+	33.3350i	1.18001	+	1.31053i	0.940561	+	0.339624i	$0.110300\pi$
$647$	30.0149	+	33.3350i	1.18001	+	1.31053i	0.239448	+	0.970909i	$0.423034\pi$
$648$	15.5429	−	20.4271i	0.610584	−	0.802450i
$649$	−2.73023	−	9.67348i	−0.107171	−	0.379717i
$650$	5.42747	+	8.83850i	0.212883	+	0.346675i
$651$	2.25692	−	14.9818i	0.0884557	−	0.587182i
$652$	0.161877	−	0.199901i	0.00633957	−	0.00782872i
$653$	9.95592	+	22.3614i	0.389605	+	0.875068i	0.996756	+	0.0804814i	$0.0256458\pi$
$653$	9.95592	+	22.3614i	0.389605	+	0.875068i	−0.607151	+	0.794587i	$0.707688\pi$
$654$	1.78442	−	2.79378i	0.0697763	−	0.109245i
$655$	−6.74792	+	13.2435i	−0.263663	+	0.517468i
$656$	−15.7147	−	19.4061i	−0.613557	−	0.757680i
$657$	5.96418	−	4.98086i	0.232685	−	0.194322i
$658$	−1.45876	−	2.86298i	−0.0568685	−	0.111611i
$659$	30.4138	−	17.5594i	1.18475	−	0.684018i	0.227644	−	0.973744i	$-0.426898\pi$
$659$	30.4138	−	17.5594i	1.18475	−	0.684018i	0.957110	+	0.289726i	$0.0935643\pi$
$660$	−0.393387	−	0.339632i	−0.0153126	−	0.0132202i
$661$	−1.31579	−	4.91061i	−0.0511784	−	0.191000i	0.935604	−	0.353051i	$-0.114856\pi$
$661$	−1.31579	−	4.91061i	−0.0511784	−	0.191000i	−0.986782	+	0.162051i	$0.948189\pi$
$662$	−8.73480	+	26.8830i	−0.339488	+	1.04484i
$663$	−20.4660	−	10.8884i	−0.794835	−	0.422871i
$664$	5.07094	+	3.68425i	0.196791	+	0.142977i
$665$	−8.62408	+	5.60054i	−0.334427	+	0.217180i
$666$	2.82331	+	23.4464i	0.109401	+	0.908528i
$667$	−19.2202	−	2.02012i	−0.744209	−	0.0782195i
$668$	0.0764705	−	0.482816i	0.00295873	−	0.0186807i
$669$	−44.7584	−	19.5236i	−1.73046	−	0.754828i
$670$	−18.3747	−	4.92349i	−0.709877	−	0.190211i
$671$	0.213619	+	0.463140i	0.00824668	+	0.0178793i
$672$	−0.243267	+	0.200057i	−0.00938422	+	0.00771738i
$673$	−19.4731	+	17.5337i	−0.750633	+	0.675873i	−0.952841	−	0.303470i	$-0.901855\pi$
$673$	−19.4731	+	17.5337i	−0.750633	+	0.675873i	0.202208	+	0.979343i	$0.435188\pi$
$674$	−13.0576	+	16.1249i	−0.502962	+	0.621106i
$675$	−1.42850	+	10.5645i	−0.0549829	+	0.406629i
$676$	−0.437575	−	0.0684775i	−0.0168298	−	0.00263375i
$677$	17.8880	−	5.81218i	0.687494	−	0.223380i	0.0556204	−	0.998452i	$-0.482286\pi$
$677$	17.8880	−	5.81218i	0.687494	−	0.223380i	0.631873	+	0.775072i	$0.282286\pi$
$678$	31.9210	+	6.53321i	1.22592	+	0.250906i
$679$	−0.805029	−	7.65934i	−0.0308942	−	0.293938i
$680$	−27.4994	+	5.84517i	−1.05455	+	0.224152i
$681$	4.77813	−	6.68218i	0.183098	−	0.256062i
$682$	−0.572615	−	43.1031i	−0.0219266	−	1.65050i
$683$	8.36348	−	31.2129i	0.320020	−	1.19433i	−0.599205	−	0.800596i	$-0.704516\pi$
$683$	8.36348	−	31.2129i	0.320020	−	1.19433i	0.919224	−	0.393734i	$-0.128817\pi$
$684$	0.301026	+	0.292058i	0.0115100	+	0.0111671i
$685$	−35.2658	−	15.7014i	−1.34744	−	0.599918i
$686$	−15.8457	+	7.05494i	−0.604990	+	0.269359i
$687$	26.1137	−	23.8728i	0.996302	−	0.910805i
$688$	−8.18779	+	2.66037i	−0.312157	+	0.101426i
$689$	29.6622	+	10.4731i	1.13004	+	0.398995i
$690$	−18.7054	−	18.4247i	−0.712102	−	0.701417i
$691$	1.06492	−	20.3198i	0.0405113	−	0.773002i	−0.900547	−	0.434758i	$-0.856834\pi$
$691$	1.06492	−	20.3198i	0.0405113	−	0.773002i	0.941058	−	0.338244i	$-0.109833\pi$
$692$	0.0879972	+	0.0508052i	0.00334515	+	0.00193132i
$693$	6.44791	−	6.82500i	0.244936	−	0.259260i
$694$	22.9361	+	22.9361i	0.870643	+	0.870643i
$695$	17.1556	−	26.4172i	0.650747	−	1.00206i
$696$	20.2180	−	11.8776i	0.766363	−	0.450218i
$697$	−23.2921	+	3.68910i	−0.882250	+	0.139735i
$698$	2.02642	+	1.82460i	0.0767011	+	0.0690620i
$699$	42.3547	+	1.89878i	1.60200	+	0.0718184i
$700$	0.0236376	−	0.0615781i	0.000893418	−	0.00232743i
$701$	−30.0349	+	21.8216i	−1.13440	+	0.824191i	−0.986329	−	0.164786i	$-0.947307\pi$
$701$	−30.0349	+	21.8216i	−1.13440	+	0.824191i	−0.148072	+	0.988977i	$0.547307\pi$
$702$	17.5268	+	19.5667i	0.661505	+	0.738496i
$703$	−23.0390			−0.868932
$704$	−17.7783	+	20.2802i	−0.670043	+	0.764337i
$705$	3.92401	−	10.4580i	0.147787	−	0.393871i
$706$	7.19597	+	33.8544i	0.270824	+	1.27413i
$707$	−1.48112	+	9.35142i	−0.0557032	+	0.351696i
$708$	−0.133801	−	0.118656i	−0.00502856	−	0.00445937i
$709$	−1.35741	−	25.9009i	−0.0509786	−	0.972729i	−0.897676	−	0.440655i	$-0.854746\pi$
$709$	−1.35741	−	25.9009i	−0.0509786	−	0.972729i	0.846698	−	0.532074i	$-0.178587\pi$
$710$	−0.986478	+	1.93607i	−0.0370219	+	0.0726595i
$711$	−10.8501	−	47.5026i	−0.406911	−	1.78149i
$712$	−26.6924	+	2.80549i	−1.00034	+	0.105140i
$713$	−1.97515	+	37.6881i	−0.0739700	+	1.41143i
$714$	−1.39427	−	8.39197i	−0.0521792	−	0.314062i
$715$	24.9158	−	19.6872i	0.931800	−	0.736260i
$716$		−	0.557771i		−	0.0208449i
$717$	−9.50160	+	1.07134i	−0.354844	+	0.0400099i
$718$	1.50208	+	14.2913i	0.0560571	+	0.533348i
$719$	−0.162080	+	1.54209i	−0.00604456	+	0.0575102i	−0.997128	−	0.0757297i	$-0.975871\pi$
$719$	−0.162080	+	1.54209i	−0.00604456	+	0.0575102i	0.991084	+	0.133240i	$0.0425381\pi$
$720$	30.9989	+	4.43042i	1.15526	+	0.165112i
$721$	18.1415	−	0.950758i	0.675626	−	0.0354081i
$722$	−2.35397	+	1.90621i	−0.0876058	+	0.0709418i
$723$	−0.0798421	−	10.5616i	−0.00296936	−	0.392790i
$724$	0.416054	−	0.0884349i	0.0154625	−	0.00328666i
$725$	−4.86948	+	8.43419i	−0.180848	+	0.313238i
$726$	14.9555	−	22.1352i	0.555050	−	0.821514i
$727$			4.09525i			0.151885i	0.997112	+	0.0759423i	$0.0241965\pi$
$727$			4.09525i			0.151885i	−0.997112	+	0.0759423i	$0.975804\pi$
$728$	−4.63800	−	8.52336i	−0.171896	−	0.315897i
$729$	1.22422	+	26.9722i	0.0453415	+	0.998972i
$730$	9.00343	+	3.45609i	0.333232	+	0.127916i
$731$	−1.69041	+	7.95276i	−0.0625221	+	0.294144i
$732$	0.00764768	+	0.00488467i	0.000282666	+	0.000180542i
$733$	−3.15540	−	19.9224i	−0.116547	−	0.735852i	−0.974875	−	0.222751i	$-0.928496\pi$
$733$	−3.15540	−	19.9224i	−0.116547	−	0.735852i	0.858328	−	0.513101i	$-0.171504\pi$
$734$	15.0138	−	5.76326i	0.554169	−	0.212726i
$735$	−25.7567	−	11.2351i	−0.950052	−	0.414413i
$736$	0.554765	−	0.554765i	0.0204489	−	0.0204489i
$737$	−2.42824	+	16.7702i	−0.0894454	+	0.617738i
$738$	26.2192	+	5.16003i	0.965140	+	0.189943i
$739$	−4.49992	−	0.235831i	−0.165532	−	0.00867519i	−0.0306103	−	0.999531i	$-0.509745\pi$
$739$	−4.49992	−	0.235831i	−0.165532	−	0.00867519i	−0.134922	+	0.990856i	$0.543078\pi$
$740$	0.410924	−	0.298554i	0.0151059	−	0.0109751i
$741$	−20.9961	+	14.6940i	−0.771310	+	0.539796i
$742$	3.56713	+	10.9785i	0.130953	+	0.403033i
$743$	3.51729	−	2.28416i	0.129037	−	0.0837976i	−0.478507	−	0.878084i	$-0.658822\pi$
$743$	3.51729	−	2.28416i	0.129037	−	0.0837976i	0.607543	+	0.794286i	$0.292155\pi$
$744$	−25.2290	−	38.2137i	−0.924940	−	1.40098i
$745$	6.67208	−	14.9857i	0.244446	−	0.549035i
$746$	−18.4040	−	36.1198i	−0.673818	−	1.32244i
$747$	−6.57828	+	0.444570i	−0.240687	+	0.0162660i
$748$	0.134905	+	0.397166i	0.00493263	+	0.0145218i
$749$	10.5768	+	10.5768i	0.386470	+	0.386470i
$750$	17.6989	−	6.94794i	0.646273	−	0.253703i
$751$	−5.25527	+	0.552351i	−0.191767	+	0.0201556i	−0.199925	−	0.979811i	$-0.564070\pi$
$751$	−5.25527	+	0.552351i	−0.191767	+	0.0201556i	0.00815783	+	0.999967i	$0.497403\pi$
$752$	−8.91183	−	3.42093i	−0.324981	−	0.124749i
$753$	−11.4402	−	22.0391i	−0.416903	−	0.803150i
$754$	8.03139	+	22.6136i	0.292486	+	0.823540i
$755$	−36.3506	+	50.0324i	−1.32294	+	1.82086i
$756$	0.0310179	−	0.164148i	0.00112811	−	0.00597000i
$757$	14.2026	+	15.7736i	0.516204	+	0.573302i	0.943737	−	0.330697i	$-0.107284\pi$
$757$	14.2026	+	15.7736i	0.516204	+	0.573302i	−0.427533	+	0.904000i	$0.640617\pi$
$758$	−9.61327	−	16.6507i	−0.349170	−	0.604779i
$759$	−14.3364	+	18.4786i	−0.520380	+	0.670731i
$760$	−8.04375	+	30.0197i	−0.291777	+	1.08893i
$761$	7.99821	+	5.19410i	0.289935	+	0.188286i	0.681408	−	0.731904i	$-0.261368\pi$
$761$	7.99821	+	5.19410i	0.289935	+	0.188286i	−0.391474	+	0.920189i	$0.628035\pi$
$762$	−20.9508	+	0.158381i	−0.758968	+	0.00573754i
$763$	0.134643	−	1.28104i	0.00487441	−	0.0463769i
$764$	−0.170639	−	0.0362705i	−0.00617351	−	0.00131222i
$765$	18.2611	−	23.2610i	0.660230	−	0.841003i
$766$	−5.69607	+	7.83997i	−0.205807	+	0.283270i
$767$	8.66284	−	6.65994i	0.312797	−	0.240476i
$768$	−0.210906	+	1.40002i	−0.00761040	+	0.0505190i
$769$	−22.2385	+	5.95879i	−0.801941	+	0.214879i	−0.636436	−	0.771330i	$-0.719592\pi$
$769$	−22.2385	+	5.95879i	−0.801941	+	0.214879i	−0.165505	+	0.986209i	$0.552925\pi$
$770$	11.2949	+	2.86621i	0.407041	+	0.103291i
$771$	23.1071	+	28.0979i	0.832183	+	1.01192i
$772$	−0.496024	+	0.252737i	−0.0178523	+	0.00909620i
$773$	−23.8567	+	9.15773i	−0.858066	+	0.329381i	−0.747317	−	0.664468i	$-0.768658\pi$
$773$	−23.8567	+	9.15773i	−0.858066	+	0.329381i	−0.110749	+	0.993848i	$0.535325\pi$
$774$	4.90031	−	7.80155i	0.176138	−	0.280421i
$775$	16.9453	+	8.63409i	0.608695	+	0.310145i
$776$	−17.2978	−	15.5750i	−0.620956	−	0.559111i
$777$	5.05578	+	7.65786i	0.181375	+	0.274724i
$778$	−8.33684	−	6.75104i	−0.298890	−	0.242036i
$779$	−8.05591	+	24.7935i	−0.288633	+	0.888321i
$780$	0.184073	−	0.534163i	0.00659088	−	0.0191261i
$781$	1.81606	+	0.669580i	0.0649837	+	0.0239594i
$782$	5.48450	+	20.4684i	0.196125	+	0.731950i
$783$	−8.31491	+	23.2219i	−0.297151	+	0.829881i
$784$	−9.76768	+	21.9386i	−0.348846	+	0.783520i
$785$	−6.55996	+	1.03900i	−0.234135	+	0.0370834i
$786$	−13.2744	+	2.92662i	−0.473484	+	0.104389i
$787$	1.48127	+	28.2642i	0.0528014	+	1.00751i	0.888660	+	0.458566i	$0.151637\pi$
$787$	1.48127	+	28.2642i	0.0528014	+	1.00751i	−0.835859	+	0.548944i	$0.815030\pi$
$788$	0.122468	+	0.773232i	0.00436274	+	0.0275453i
$789$	−10.7750	+	41.4643i	−0.383601	+	1.47617i
$790$	44.9410	−	40.4650i	1.59893	−	1.43968i
$791$	12.2291	−	3.27678i	0.434818	−	0.116509i
$792$	0.679761	−	28.3689i	0.0241542	−	1.00805i
$793$	−0.381295	+	0.402545i	−0.0135402	+	0.0142948i
$794$	−29.1725	−	9.47871i	−1.03529	−	0.336387i
$795$	−19.8008	+	34.9027i	−0.702262	+	1.23787i
$796$	0.126877	−	0.0564891i	0.00449702	−	0.00200220i
$797$	6.12947	−	6.80746i	0.217117	−	0.241133i	−0.624741	−	0.780832i	$-0.714795\pi$
$797$	6.12947	−	6.80746i	0.217117	−	0.241133i	0.841858	+	0.539699i	$0.181462\pi$
$798$	−8.96561	−	2.83836i	−0.317379	−	0.100477i
$799$	−7.00601	+	5.67336i	−0.247855	+	0.200709i
$800$	−0.141684	−	0.369101i	−0.00500930	−	0.0130497i
$801$	19.6591	−	20.2627i	0.694620	−	0.715948i
$802$	21.4586	+	37.1673i	0.757728	+	1.31242i
$803$	2.11299	−	8.32668i	0.0745657	−	0.293842i
$804$	0.124705	+	0.274489i	0.00439801	+	0.00968047i
$805$	−9.70273	−	3.15261i	−0.341976	−	0.111115i
$806$	43.2784	−	17.9733i	1.52442	−	0.633083i
$807$	20.2477	−	40.4921i	0.712751	−	1.42539i
$808$	15.5850	+	23.9988i	0.548279	+	0.844276i
$809$	0.943813	−	4.44029i	0.0331827	−	0.156112i	−0.958437	−	0.285305i	$-0.907905\pi$
$809$	0.943813	−	4.44029i	0.0331827	−	0.156112i	0.991620	+	0.129192i	$0.0412385\pi$
$810$	−28.5005	+	17.6246i	−1.00141	+	0.619266i
$811$	16.0318	+	2.53918i	0.562952	+	0.0891628i	0.431423	−	0.902150i	$-0.358012\pi$
$811$	16.0318	+	2.53918i	0.562952	+	0.0891628i	0.131528	+	0.991312i	$0.458012\pi$
$812$	0.0831171	−	0.127989i	0.00291684	−	0.00449154i
$813$	−42.2856	−	4.12146i	−1.48302	−	0.144546i
$814$	17.7260	+	19.1684i	0.621295	+	0.671852i
$815$	−17.3630	+	10.0245i	−0.608200	+	0.351145i
$816$	−19.7603	−	15.7558i	−0.691750	−	0.551563i
$817$	6.98490	+	5.65626i	0.244371	+	0.197887i
$818$	−36.5268	−	26.5383i	−1.27713	−	0.927888i
$819$	9.49156	+	3.75431i	0.331662	+	0.131186i
$820$	−0.177605	−	0.546612i	−0.00620224	−	0.0190885i
$821$	6.94311	−	18.0874i	0.242316	−	0.631255i	−0.757450	−	0.652894i	$-0.773555\pi$
$821$	6.94311	−	18.0874i	0.242316	−	0.631255i	0.999766	+	0.0216383i	$0.00688822\pi$
$822$	−9.39486	−	34.0309i	−0.327683	−	1.18697i
$823$	−7.51403	−	35.3507i	−0.261922	−	1.23225i	−0.890674	−	0.454642i	$-0.849767\pi$
$823$	−7.51403	−	35.3507i	−0.261922	−	1.23225i	0.628752	−	0.777606i	$-0.283566\pi$
$824$	38.8236	−	38.8236i	1.35248	−	1.35248i
$825$	5.56836	+	10.3874i	0.193865	+	0.361644i
$826$	3.87317	+	1.03781i	0.134765	+	0.0361101i
$827$	11.4947	−	5.85682i	0.399708	−	0.203661i	−0.242569	−	0.970134i	$-0.577990\pi$
$827$	11.4947	−	5.85682i	0.399708	−	0.203661i	0.642277	+	0.766473i	$0.277990\pi$
$828$	−0.0372347	+	0.414450i	−0.00129400	+	0.0144031i
$829$	−9.20572	−	20.6764i	−0.319728	−	0.718120i	0.680161	−	0.733063i	$-0.261910\pi$
$829$	−9.20572	−	20.6764i	−0.319728	−	0.718120i	−0.999888	+	0.0149429i	$0.995243\pi$
$830$	−4.45676	−	6.86280i	−0.154696	−	0.238211i
$831$	−14.4193	+	7.48481i	−0.500198	+	0.259645i
$832$	−27.6462	−	9.76134i	−0.958460	−	0.338414i
$833$	13.3306	+	18.3480i	0.461878	+	0.635721i
$834$	28.6254	−	3.22762i	0.991218	−	0.111763i
$835$	−19.0508	+	32.9970i	−0.659282	+	1.14191i
$836$	0.458903	+	0.0664468i	0.0158715	+	0.00229811i
$837$	46.1352	+	13.8418i	1.59466	+	0.478441i
$838$	−24.3170	−	15.7916i	−0.840015	−	0.545512i
$839$	0.00802873	+	0.0209156i	0.000277183	+	0.000722085i	0.933719	−	0.358007i	$-0.116544\pi$
$839$	0.00802873	+	0.0209156i	0.000277183	+	0.000722085i	−0.933442	+	0.358729i	$0.883210\pi$
$840$	11.7433	−	3.91402i	0.405183	−	0.135047i
$841$	4.32724	−	4.80589i	0.149215	−	0.165720i
$842$	−44.7602	−	9.51407i	−1.54254	−	0.327877i
$843$	32.5863	+	6.66937i	1.12233	+	0.229705i
$844$	0.327907	+	0.451326i	0.0112870	+	0.0155353i
$845$	29.9282	+	17.2055i	1.02956	+	0.591888i
$846$	9.66648	−	3.30322i	0.332340	−	0.113567i
$847$	1.35088	−	10.2918i	0.0464168	−	0.353631i
$848$	29.6992	+	17.1468i	1.01987	+	0.588824i
$849$	−10.3648	−	26.4029i	−0.355718	−	0.906144i
$850$	10.5470	+	1.67049i	0.361760	+	0.0572972i
$851$	−14.3847	−	17.7637i	−0.493102	−	0.608930i
$852$	0.0336301	−	0.00741445i	0.00115215	−	0.000254015i
$853$	23.3649	+	11.9050i	0.800000	+	0.407620i	0.805671	−	0.592364i	$-0.201805\pi$
$853$	23.3649	+	11.9050i	0.800000	+	0.407620i	−0.00567088	+	0.999984i	$0.501805\pi$
$854$	−0.202352	−	0.0212681i	−0.00692434	−	0.000727778i
$855$	−13.7468	−	29.6607i	−0.470130	−	1.01437i
$856$	45.1457	+	2.36599i	1.54305	+	0.0808678i
$857$	−29.2468			−0.999051			−0.499525	−	0.866299i	$-0.666492\pi$
$857$	−29.2468			−0.999051			−0.499525	+	0.866299i	$0.666492\pi$
$858$	28.3795	+	6.16330i	0.968861	+	0.210412i
$859$	2.18053			0.0743988			0.0371994	−	0.999308i	$-0.488156\pi$
$859$	2.18053			0.0743988			0.0371994	+	0.999308i	$0.488156\pi$
$860$	−0.197880	−	0.0103705i	−0.00674767	−	0.000353630i
$861$	10.0089	−	2.76313i	0.341102	−	0.0941672i
$862$	40.1640	+	4.22141i	1.36799	+	0.143782i
$863$	18.8551	+	9.60713i	0.641834	+	0.327031i	0.744438	−	0.667692i	$-0.232718\pi$
$863$	18.8551	+	9.60713i	0.641834	+	0.327031i	−0.102604	+	0.994722i	$0.532718\pi$
$864$	−0.520195	−	0.855591i	−0.0176974	−	0.0291078i
$865$	−4.98417	−	6.15493i	−0.169467	−	0.209274i
$866$	−5.52007	−	0.874294i	−0.187580	−	0.0297097i
$867$	5.19165	−	2.03805i	0.176318	−	0.0692158i
$868$	−0.258089	−	0.149008i	−0.00876010	−	0.00505764i
$869$	−40.5075	−	35.5102i	−1.37412	−	1.20460i
$870$	−30.1986	+	5.01729i	−1.02383	+	0.170102i
$871$	−17.9083	+	4.31688i	−0.606800	+	0.146272i
$872$	−2.28828	−	3.14955i	−0.0774910	−	0.106657i
$873$	24.4674	+	0.911609i	0.828097	+	0.0308533i
$874$	22.9134	+	4.87039i	0.775057	+	0.164743i
$875$	4.94361	−	5.49044i	0.167125	−	0.185611i
$876$	−0.0483291	−	0.145003i	−0.00163289	−	0.00489918i
$877$	−9.52846	−	24.8225i	−0.321753	−	0.838196i	−0.995100	−	0.0988693i	$-0.968477\pi$
$877$	−9.52846	−	24.8225i	−0.321753	−	0.838196i	0.673347	−	0.739326i	$-0.264856\pi$
$878$	−12.7753	−	8.29640i	−0.431147	−	0.279990i
$879$	−19.4422	−	13.9022i	−0.655768	−	0.468911i
$880$	30.6341	−	16.1249i	1.03267	−	0.543572i
$881$	9.32755	−	16.1558i	0.314253	−	0.544303i	−0.665025	−	0.746821i	$-0.731579\pi$
$881$	9.32755	−	16.1558i	0.314253	−	0.544303i	0.979278	+	0.202518i	$0.0649126\pi$
$882$	−7.02587	−	24.7198i	−0.236574	−	0.832358i
$883$	33.7564	+	46.4617i	1.13599	+	1.56356i	0.776152	+	0.630546i	$0.217169\pi$
$883$	33.7564	+	46.4617i	1.13599	+	1.56356i	0.359841	+	0.933014i	$0.382831\pi$
$884$	−0.346466	+	0.296463i	−0.0116529	+	0.00997114i
$885$	6.42194	+	12.3717i	0.215871	+	0.415869i
$886$	−25.1025	−	38.6545i	−0.843336	−	1.29862i
$887$	−18.8747	−	42.3933i	−0.633751	−	1.42343i	−0.889613	−	0.456715i	$-0.849026\pi$
$887$	−18.8747	−	42.3933i	−0.633751	−	1.42343i	0.255862	−	0.966713i	$-0.417641\pi$
$888$	26.8421	+	6.97528i	0.900763	+	0.234075i
$889$	−7.25368	+	3.69594i	−0.243281	+	0.123958i
$890$	33.8452	+	9.06879i	1.13449	+	0.303987i
$891$	18.5792	+	23.3626i	0.622428	+	0.782677i
$892$	−0.679179	+	0.679179i	−0.0227406	+	0.0227406i
$893$	2.07201	+	9.74803i	0.0693371	+	0.326205i
$894$	14.4610	−	3.99222i	0.483648	−	0.133520i
$895$	−15.5800	+	40.5873i	−0.520782	+	1.35668i
$896$	−3.21230	−	9.88645i	−0.107316	−	0.330283i
$897$	−24.4386	−	7.01413i	−0.815983	−	0.234195i
$898$	−10.5745	−	7.68285i	−0.352877	−	0.256380i
$899$	34.1963	+	27.6916i	1.14051	+	0.923567i
$900$	0.183165	+	0.102090i	0.00610550	+	0.00340299i
$901$	28.0477	−	16.1933i	0.934405	−	0.539479i
$902$	26.8263	−	12.3734i	0.893218	−	0.411989i
$903$	0.347268	−	3.56293i	0.0115564	−	0.118567i
$904$	20.8402	−	32.0911i	0.693134	−	1.06733i
$905$	−32.7452	−	5.18633i	−1.08849	−	0.172399i
$906$	−56.4563	+	3.38688i	−1.87564	+	0.112522i
$907$	−7.01550	+	33.0053i	−0.232946	+	1.09592i	0.693780	+	0.720187i	$0.255944\pi$
$907$	−7.01550	+	33.0053i	−0.232946	+	1.09592i	−0.926726	+	0.375738i	$0.877389\pi$
$908$	−0.0880045	−	0.135515i	−0.00292053	−	0.00449722i
$909$	−28.7644	−	8.86763i	−0.954054	−	0.294121i
$910$	1.66510	+	12.5581i	0.0551976	+	0.416299i
$911$	−30.1177	−	9.78584i	−0.997845	−	0.324219i	−0.235841	−	0.971792i	$-0.575784\pi$
$911$	−30.1177	−	9.78584i	−0.997845	−	0.324219i	−0.762004	+	0.647572i	$0.775784\pi$
$912$	−25.4361	+	11.5561i	−0.842275	+	0.382660i
$913$	−5.60330	+	4.66206i	−0.185442	+	0.154292i
$914$	1.54595	+	2.67767i	0.0511355	+	0.0885694i
$915$	−0.420057	−	0.569062i	−0.0138866	−	0.0188126i
$916$	−0.249405	−	0.649723i	−0.00824058	−	0.0214674i
$917$	−4.10477	+	3.32398i	−0.135552	+	0.109768i
$918$	27.0382	−	0.613292i	0.892393	−	0.0202416i
$919$	7.83822	−	8.70522i	0.258559	−	0.287159i	−0.599863	−	0.800103i	$-0.704778\pi$
$919$	7.83822	−	8.70522i	0.258559	−	0.287159i	0.858422	+	0.512944i	$0.171445\pi$
$920$	−28.1682	+	12.5413i	−0.928678	+	0.413474i
$921$	12.6664	+	7.18584i	0.417372	+	0.236781i
$922$	−29.8758	−	9.70723i	−0.983906	−	0.319690i
$923$	0.0570219	+	2.10341i	0.00187690	+	0.0692345i
$924$	−0.0786177	−	0.167115i	−0.00258633	−	0.00549767i
$925$	−11.1261	+	2.98123i	−0.365824	+	0.0980222i
$926$	−16.5855	+	14.9337i	−0.545033	+	0.490750i
$927$	−5.16788	+	57.5223i	−0.169735	+	1.88928i
$928$	−0.143098	−	0.903483i	−0.00469741	−	0.0296583i
$929$	2.01815	+	38.5086i	0.0662134	+	1.26343i	0.806540	+	0.591179i	$0.201338\pi$
$929$	2.01815	+	38.5086i	0.0662134	+	1.26343i	−0.740327	+	0.672247i	$0.765329\pi$
$930$	12.8707	+	58.3781i	0.422045	+	1.91429i
$931$	24.7625	−	3.92200i	0.811559	−	0.128538i
$932$	0.339198	−	0.761851i	0.0111108	−	0.0249553i
$933$	−17.9501	−	14.3124i	−0.587661	−	0.468568i
$934$	2.45281	+	9.15400i	0.0802583	+	0.299528i
$935$	1.27721	−	32.6688i	0.0417693	−	1.06838i
$936$	28.9107	−	10.7628i	0.944977	−	0.351793i
$937$	15.2732	−	47.0062i	0.498955	−	1.53563i	−0.311747	−	0.950165i	$-0.600914\pi$
$937$	15.2732	−	47.0062i	0.498955	−	1.53563i	0.810701	−	0.585460i	$-0.199086\pi$
$938$	−5.25343	−	4.25415i	−0.171531	−	0.138903i
$939$	−14.3156	+	9.45131i	−0.467174	+	0.308432i
$940$	−0.163278	−	0.147016i	−0.00532553	−	0.00479513i
$941$	7.48038	+	3.81144i	0.243853	+	0.124250i	0.571646	−	0.820500i	$-0.306305\pi$
$941$	7.48038	+	3.81144i	0.243853	+	0.124250i	−0.327793	+	0.944750i	$0.606305\pi$
$942$	−4.54452	−	4.03012i	−0.148068	−	0.131308i
$943$	−24.1463	+	9.26889i	−0.786311	+	0.301837i
$944$	10.6140	−	5.40812i	0.345457	−	0.176019i
$945$	−6.84215	+	11.0781i	−0.222575	+	0.360371i
$946$	−0.668118	−	10.1633i	−0.0217224	−	0.330437i
$947$	3.86099	−	1.03455i	0.125465	−	0.0336184i	−0.195540	−	0.980696i	$-0.562646\pi$
$947$	3.86099	−	1.03455i	0.125465	−	0.0336184i	0.321005	+	0.947077i	$0.395979\pi$
$948$	−0.947742	−	0.142772i	−0.0307812	−	0.00463702i
$949$	9.25793	−	1.22752i	0.300525	−	0.0398470i
$950$	6.93862	−	9.55019i	0.225118	−	0.309849i
$951$	−28.4751	+	26.0315i	−0.923368	+	0.844130i
$952$	−9.77206	−	2.07712i	−0.316714	−	0.0673197i
$953$	−1.45902	+	13.8816i	−0.0472623	+	0.449671i	0.945143	+	0.326658i	$0.105922\pi$
$953$	−1.45902	+	13.8816i	−0.0472623	+	0.449671i	−0.992405	+	0.123013i	$0.960744\pi$
$954$	−36.1558	+	6.28825i	−1.17059	+	0.203590i
$955$	11.4038	+	7.40570i	0.369017	+	0.239643i
$956$	−0.0486786	+	0.181671i	−0.00157438	+	0.00587566i
$957$	7.60514	+	26.1869i	0.245839	+	0.846501i
$958$	−6.57785	−	11.3932i	−0.212521	−	0.368097i
$959$	−9.17906	−	10.1944i	−0.296407	−	0.329194i
$960$	18.4550	−	32.5305i	0.595634	−	1.04992i
$961$	32.2857	−	44.4374i	1.04147	−	1.43347i
$962$	−12.1954	+	25.6290i	−0.393195	+	0.826311i
$963$	−38.0447	+	28.5298i	−1.22597	+	0.919359i
$964$	−0.193953	−	0.0744515i	−0.00624680	−	0.00239792i
$965$	43.1538	−	4.53565i	1.38917	−	0.146008i
$966$	−3.40937	−	8.68489i	−0.109695	−	0.279432i
$967$	−3.39095	−	3.39095i	−0.109046	−	0.109046i	0.650479	−	0.759524i	$-0.274568\pi$
$967$	−3.39095	−	3.39095i	−0.109046	−	0.109046i	−0.759524	+	0.650479i	$0.774568\pi$
$968$	−17.7793	−	25.8476i	−0.571450	−	0.830774i
$969$	−2.55951	+	26.2602i	−0.0822232	+	0.843599i
$970$	13.7957	+	27.0756i	0.442954	+	0.869346i
$971$	−13.1672	+	29.5740i	−0.422555	+	0.949075i	0.569350	+	0.822095i	$0.307195\pi$
$971$	−13.1672	+	29.5740i	−0.422555	+	0.949075i	−0.991905	+	0.126980i	$0.959472\pi$
$972$	0.502651	+	0.171453i	0.0161225	+	0.00549935i
$973$	9.38752	−	6.09633i	0.300950	−	0.195439i
$974$	−15.1535	−	46.6378i	−0.485551	−	1.49437i
$975$	−8.23814	+	9.81296i	−0.263832	+	0.314266i
$976$	−0.489022	+	0.355295i	−0.0156532	+	0.0113727i
$977$	20.5479	+	1.07687i	0.657385	+	0.0344521i	0.378113	−	0.925760i	$-0.376573\pi$
$977$	20.5479	+	1.07687i	0.657385	+	0.0344521i	0.279273	+	0.960212i	$0.409907\pi$
$978$	−17.1669	−	6.44129i	−0.548937	−	0.205970i
$979$	4.47268	−	30.8898i	0.142948	−	0.987241i
$980$	−0.390842	+	0.390842i	−0.0124850	+	0.0124850i
$981$	3.97111	+	0.999961i	0.126788	+	0.0319263i
$982$	3.69358	−	1.41783i	0.117867	−	0.0452448i
$983$	−7.93777	−	50.1171i	−0.253176	−	1.59849i	−0.706879	−	0.707335i	$-0.749897\pi$
$983$	−7.93777	−	50.1171i	−0.253176	−	1.59849i	0.453703	−	0.891153i	$-0.350103\pi$
$984$	16.8922	−	26.4473i	0.538504	−	0.843109i
$985$	12.6868	−	59.6866i	0.404235	−	1.90177i
$986$	23.0658	+	8.85414i	0.734566	+	0.281973i
$987$	2.78543	−	2.82786i	0.0886611	−	0.0900118i
$988$	0.118128	+	0.490046i	0.00375815	+	0.0155904i
$989$			8.91711i			0.283548i
$990$	−14.1010	+	34.2579i	−0.448158	+	1.08879i
$991$	30.9849	−	53.6674i	0.984268	−	1.70480i	0.339122	−	0.940742i	$-0.389870\pi$
$991$	30.9849	−	53.6674i	0.984268	−	1.70480i	0.645146	−	0.764059i	$-0.276797\pi$
$992$	−1.74727	+	0.371395i	−0.0554760	+	0.0117918i
$993$	−34.9168	+	0.263959i	−1.10805	+	0.00837650i
$994$	−0.600077	+	0.485933i	−0.0190333	+	0.0154128i
$995$	−10.8103	+	0.566545i	−0.342710	+	0.0179607i
$996$	−0.0391426	+	0.123641i	−0.00124028	+	0.00391772i
$997$	−3.18648	+	30.3174i	−0.100917	+	0.960161i	0.820516	+	0.571623i	$0.193686\pi$
$997$	−3.18648	+	30.3174i	−0.100917	+	0.960161i	−0.921433	+	0.388537i	$0.872980\pi$
$998$	1.46256	+	13.9153i	0.0462965	+	0.440482i
$999$	−26.3748	+	12.4669i	−0.834460	+	0.394437i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.bv.a.20.14	✓	832
3.2	odd	2	inner	429.2.bv.a.20.39	yes	832
11.5	even	5	inner	429.2.bv.a.137.39	yes	832
13.2	odd	12	inner	429.2.bv.a.119.14	yes	832
33.5	odd	10	inner	429.2.bv.a.137.14	yes	832
39.2	even	12	inner	429.2.bv.a.119.39	yes	832
143.93	odd	60	inner	429.2.bv.a.236.39	yes	832
429.236	even	60	inner	429.2.bv.a.236.14	yes	832

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.bv.a.20.14	✓	832	1.1	even	1	trivial
429.2.bv.a.20.39	yes	832	3.2	odd	2	inner
429.2.bv.a.119.14	yes	832	13.2	odd	12	inner
429.2.bv.a.119.39	yes	832	39.2	even	12	inner
429.2.bv.a.137.14	yes	832	33.5	odd	10	inner
429.2.bv.a.137.39	yes	832	11.5	even	5	inner
429.2.bv.a.236.14	yes	832	429.236	even	60	inner
429.2.bv.a.236.39	yes	832	143.93	odd	60	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.bv (of order \(60\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.40019 - 0.0733811i) q^{2} +(-0.460922 - 1.66960i) q^{3} +(-0.0338826 - 0.00356121i) q^{4} +(2.36606 + 1.20557i) q^{5} +(0.522864 + 2.37158i) q^{6} +(0.593855 + 0.733350i) q^{7} +(2.81689 + 0.446151i) q^{8} +(-2.57510 + 1.53911i) q^{9} +O(q^{10})\)	\(q+(-1.40019 - 0.0733811i) q^{2} +(-0.460922 - 1.66960i) q^{3} +(-0.0338826 - 0.00356121i) q^{4} +(2.36606 + 1.20557i) q^{5} +(0.522864 + 2.37158i) q^{6} +(0.593855 + 0.733350i) q^{7} +(2.81689 + 0.446151i) q^{8} +(-2.57510 + 1.53911i) q^{9} +(-3.22448 - 1.86166i) q^{10} +(-1.30863 + 3.04754i) q^{11} +(0.00967147 + 0.0582117i) q^{12} +(-3.60440 - 0.0910566i) q^{13} +(-0.777699 - 1.07041i) q^{14} +(0.922243 - 4.50604i) q^{15} +(-3.84481 - 0.817239i) q^{16} +(-2.48390 + 2.75865i) q^{17} +(3.71859 - 1.96609i) q^{18} +(1.47061 + 3.83106i) q^{19} +(-0.0758751 - 0.0492739i) q^{20} +(0.950678 - 1.32952i) q^{21} +(2.05596 - 4.17112i) q^{22} +(-2.03565 + 3.52585i) q^{23} +(-0.553474 - 4.90871i) q^{24} +(1.20593 + 1.65982i) q^{25} +(5.04018 + 0.391992i) q^{26} +(3.75661 + 3.58997i) q^{27} +(-0.0175098 - 0.0269627i) q^{28} +(1.93074 + 4.33651i) q^{29} +(-1.62198 + 6.24166i) q^{30} +(8.25938 - 4.20836i) q^{31} +(-0.186138 - 0.0498754i) q^{32} +(5.69133 + 0.780198i) q^{33} +(3.68038 - 3.68038i) q^{34} +(0.520994 + 2.45109i) q^{35} +(0.0927323 - 0.0429785i) q^{36} +(-2.01199 + 5.24141i) q^{37} +(-1.77801 - 5.47214i) q^{38} +(1.50932 + 6.05986i) q^{39} +(6.12707 + 4.45158i) q^{40} +(4.93705 + 3.99794i) q^{41} +(-1.42870 + 1.79182i) q^{42} +(1.89680 - 1.09512i) q^{43} +(0.0551926 - 0.0985984i) q^{44} +(-7.94835 + 0.537162i) q^{45} +(3.10904 - 4.78750i) q^{46} +(2.39864 + 0.379907i) q^{47} +(0.407698 + 6.79596i) q^{48} +(1.27024 - 5.97603i) q^{49} +(-1.56674 - 2.41256i) q^{50} +(5.75072 + 2.87559i) q^{51} +(0.121802 + 0.0159213i) q^{52} +(-8.29755 - 2.69604i) q^{53} +(-4.99655 - 5.30232i) q^{54} +(-6.77031 + 5.63303i) q^{55} +(1.34564 + 2.33072i) q^{56} +(5.71849 - 4.22114i) q^{57} +(-2.38519 - 6.21364i) q^{58} +(-2.35522 + 1.90722i) q^{59} +(-0.0472950 + 0.149392i) q^{60} +(0.102899 - 0.114281i) q^{61} +(-11.8736 + 5.28645i) q^{62} +(-2.65794 - 0.974444i) q^{63} +(7.73361 + 2.51280i) q^{64} +(-8.41846 - 4.56080i) q^{65} +(-7.91173 - 1.51007i) q^{66} +(4.93505 - 1.32234i) q^{67} +(0.0939852 - 0.0846246i) q^{68} +(6.82503 + 1.77357i) q^{69} +(-0.549630 - 3.47023i) q^{70} +(-0.0305430 - 0.582795i) q^{71} +(-7.94045 + 3.18661i) q^{72} +(-2.55827 + 0.405190i) q^{73} +(3.20180 - 7.19135i) q^{74} +(2.21539 - 2.77846i) q^{75} +(-0.0361848 - 0.135043i) q^{76} +(-3.01205 + 0.850116i) q^{77} +(-1.66866 - 8.59575i) q^{78} +(-5.01906 + 15.4471i) q^{79} +(-8.11181 - 6.56882i) q^{80} +(4.26230 - 7.92672i) q^{81} +(-6.61946 - 5.96019i) q^{82} +(1.95822 + 0.997763i) q^{83} +(-0.0369461 + 0.0416619i) q^{84} +(-9.20281 + 3.53263i) q^{85} +(-2.73625 + 1.39419i) q^{86} +(6.35030 - 5.22234i) q^{87} +(-5.04592 + 8.00074i) q^{88} +(-9.09008 + 2.43568i) q^{89} +(11.1687 - 0.168872i) q^{90} +(-2.07372 - 2.69736i) q^{91} +(0.0815295 - 0.112216i) q^{92} +(-10.8332 - 11.8501i) q^{93} +(-3.33069 - 0.707959i) q^{94} +(-1.13906 + 10.8374i) q^{95} +(0.00252313 + 0.333763i) q^{96} +(-6.84478 - 4.44505i) q^{97} +(-2.21712 + 8.27439i) q^{98} +(-1.32065 - 9.86184i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 832 q - 6 q^{3} - 36 q^{4} - 4 q^{6} - 24 q^{7} - 6 q^{9}+O(q^{10}) \) 832 * q - 6 * q^3 - 36 * q^4 - 4 * q^6 - 24 * q^7 - 6 * q^9	\( 832 q - 6 q^{3} - 36 q^{4} - 4 q^{6} - 24 q^{7} - 6 q^{9} - 96 q^{10} - 40 q^{13} + 12 q^{15} - 68 q^{16} - 20 q^{18} - 32 q^{19} - 84 q^{21} - 24 q^{22} - 72 q^{24} - 114 q^{30} - 8 q^{31} + 14 q^{33} - 24 q^{34} + 78 q^{36} - 24 q^{37} - 72 q^{39} - 112 q^{40} + 2 q^{42} - 96 q^{43} + 4 q^{45} - 16 q^{46} + 14 q^{48} - 36 q^{49} + 8 q^{52} + 32 q^{54} - 24 q^{55} - 12 q^{57} + 112 q^{58} - 120 q^{60} + 12 q^{61} + 28 q^{63} - 300 q^{66} - 32 q^{67} - 18 q^{69} - 140 q^{70} + 204 q^{72} - 24 q^{73} + 66 q^{75} + 176 q^{76} - 28 q^{78} - 224 q^{79} - 58 q^{81} - 264 q^{82} + 20 q^{84} - 168 q^{85} + 72 q^{87} - 120 q^{88} - 146 q^{93} - 4 q^{94} - 10 q^{96} - 88 q^{97} + 40 q^{99}+O(q^{100}) \) 832 * q - 6 * q^3 - 36 * q^4 - 4 * q^6 - 24 * q^7 - 6 * q^9 - 96 * q^10 - 40 * q^13 + 12 * q^15 - 68 * q^16 - 20 * q^18 - 32 * q^19 - 84 * q^21 - 24 * q^22 - 72 * q^24 - 114 * q^30 - 8 * q^31 + 14 * q^33 - 24 * q^34 + 78 * q^36 - 24 * q^37 - 72 * q^39 - 112 * q^40 + 2 * q^42 - 96 * q^43 + 4 * q^45 - 16 * q^46 + 14 * q^48 - 36 * q^49 + 8 * q^52 + 32 * q^54 - 24 * q^55 - 12 * q^57 + 112 * q^58 - 120 * q^60 + 12 * q^61 + 28 * q^63 - 300 * q^66 - 32 * q^67 - 18 * q^69 - 140 * q^70 + 204 * q^72 - 24 * q^73 + 66 * q^75 + 176 * q^76 - 28 * q^78 - 224 * q^79 - 58 * q^81 - 264 * q^82 + 20 * q^84 - 168 * q^85 + 72 * q^87 - 120 * q^88 - 146 * q^93 - 4 * q^94 - 10 * q^96 - 88 * q^97 + 40 * q^99

Introduction

L-functions

Modular forms

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