LMFDB - Embedded newform 430.2.q.a.111.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [430,2,Mod(31,430)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(430, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([0, 34]))

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

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

chi := DirichletCharacter("430.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 430 = 2 \cdot 5 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	430.q (of order $21$, degree $12$, 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:	$3.43356728692$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$3$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			111.3
Character	$\chi$	$=$	430.111
Dual form			430.2.q.a.31.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.900969 - 0.433884i) q^{2} +(0.492510 + 0.335788i) q^{3} +(0.623490 + 0.781831i) q^{4} +(-0.733052 + 0.680173i) q^{5} +(-0.298043 - 0.516226i) q^{6} +(-0.982941 + 1.70250i) q^{7} +(-0.222521 - 0.974928i) q^{8} +(-0.966210 - 2.46186i) q^{9} +O(q^{10})$	\(q+(-0.900969 - 0.433884i) q^{2} +(0.492510 + 0.335788i) q^{3} +(0.623490 + 0.781831i) q^{4} +(-0.733052 + 0.680173i) q^{5} +(-0.298043 - 0.516226i) q^{6} +(-0.982941 + 1.70250i) q^{7} +(-0.222521 - 0.974928i) q^{8} +(-0.966210 - 2.46186i) q^{9} +(0.955573 - 0.294755i) q^{10} +(-3.99493 + 5.00948i) q^{11} +(0.0445456 + 0.594420i) q^{12} +(0.766750 + 0.236511i) q^{13} +(1.62429 - 1.10742i) q^{14} +(-0.589429 + 0.0888421i) q^{15} +(-0.222521 + 0.974928i) q^{16} +(-3.05126 - 2.83115i) q^{17} +(-0.197637 + 2.63729i) q^{18} +(-0.838614 + 2.13675i) q^{19} +(-0.988831 - 0.149042i) q^{20} +(-1.05579 + 0.508441i) q^{21} +(5.77283 - 2.78005i) q^{22} +(-2.14071 - 0.322660i) q^{23} +(0.217775 - 0.554882i) q^{24} +(0.0747301 - 0.997204i) q^{25} +(-0.588199 - 0.545769i) q^{26} +(0.748721 - 3.28036i) q^{27} +(-1.94392 + 0.292999i) q^{28} +(-5.99270 + 4.08575i) q^{29} +(0.569604 + 0.175700i) q^{30} +(0.318121 + 4.24503i) q^{31} +(0.623490 - 0.781831i) q^{32} +(-3.64966 + 1.12577i) q^{33} +(1.52070 + 3.87467i) q^{34} +(-0.437450 - 1.91659i) q^{35} +(1.32234 - 2.29036i) q^{36} +(-4.21684 - 7.30378i) q^{37} +(1.68267 - 1.56129i) q^{38} +(0.298214 + 0.373949i) q^{39} +(0.826239 + 0.563320i) q^{40} +(10.2417 + 4.93216i) q^{41} +1.17184 q^{42} +(-2.07133 + 6.22170i) q^{43} -6.40736 q^{44} +(2.38277 + 1.14748i) q^{45} +(1.78872 + 1.21953i) q^{46} +(2.27396 + 2.85146i) q^{47} +(-0.436963 + 0.405442i) q^{48} +(1.56765 + 2.71526i) q^{49} +(-0.500000 + 0.866025i) q^{50} +(-0.552109 - 2.41895i) q^{51} +(0.293149 + 0.746931i) q^{52} +(-9.96419 + 3.07355i) q^{53} +(-2.09787 + 2.63064i) q^{54} +(-0.478823 - 6.38945i) q^{55} +(1.87854 + 0.579454i) q^{56} +(-1.13052 + 0.770776i) q^{57} +(7.17197 - 1.08100i) q^{58} +(-0.680983 + 2.98358i) q^{59} +(-0.436963 - 0.405442i) q^{60} +(-0.426228 + 5.68761i) q^{61} +(1.55523 - 3.96266i) q^{62} +(5.14106 + 0.774890i) q^{63} +(-0.900969 + 0.433884i) q^{64} +(-0.722935 + 0.348147i) q^{65} +(3.77669 + 0.569244i) q^{66} +(3.24862 - 8.27735i) q^{67} +(0.311057 - 4.15076i) q^{68} +(-0.945976 - 0.877738i) q^{69} +(-0.437450 + 1.91659i) q^{70} +(2.80401 - 0.422636i) q^{71} +(-2.18514 + 1.48980i) q^{72} +(10.6556 + 3.28683i) q^{73} +(0.630249 + 8.41009i) q^{74} +(0.371654 - 0.466039i) q^{75} +(-2.19345 + 0.676589i) q^{76} +(-4.60188 - 11.7254i) q^{77} +(-0.106432 - 0.466307i) q^{78} +(6.22457 - 10.7813i) q^{79} +(-0.500000 - 0.866025i) q^{80} +(-4.34581 + 4.03232i) q^{81} +(-7.08750 - 8.88744i) q^{82} +(-8.89920 - 6.06737i) q^{83} +(-1.05579 - 0.508441i) q^{84} +4.16240 q^{85} +(4.56570 - 4.70684i) q^{86} -4.32341 q^{87} +(5.77283 + 2.78005i) q^{88} +(-4.66995 - 3.18392i) q^{89} +(-1.64893 - 2.06769i) q^{90} +(-1.15633 + 1.07292i) q^{91} +(-1.08245 - 1.87485i) q^{92} +(-1.26875 + 2.19754i) q^{93} +(-0.811569 - 3.55571i) q^{94} +(-0.838614 - 2.13675i) q^{95} +(0.569604 - 0.175700i) q^{96} +(1.24320 - 1.55892i) q^{97} +(-0.234302 - 3.12654i) q^{98} +(16.1926 + 4.99475i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 6 q^{2} + 5 q^{3} - 6 q^{4} + 3 q^{5} + 5 q^{6} + q^{7} - 6 q^{8} + 12 q^{9}+O(q^{10}) $ 36 * q - 6 * q^2 + 5 * q^3 - 6 * q^4 + 3 * q^5 + 5 * q^6 + q^7 - 6 * q^8 + 12 * q^9	\( 36 q - 6 q^{2} + 5 q^{3} - 6 q^{4} + 3 q^{5} + 5 q^{6} + q^{7} - 6 q^{8} + 12 q^{9} + 3 q^{10} + 9 q^{11} - 16 q^{12} + 21 q^{13} - 6 q^{14} + 5 q^{15} - 6 q^{16} - 37 q^{17} + 19 q^{18} + 7 q^{19} + 3 q^{20} - 8 q^{21} + 16 q^{22} + 13 q^{23} + 5 q^{24} + 3 q^{25} - 21 q^{26} - 28 q^{27} - 6 q^{28} + 4 q^{29} - 2 q^{30} + 13 q^{31} - 6 q^{32} - 54 q^{33} - 23 q^{34} - 2 q^{35} - 9 q^{36} + 17 q^{37} + 28 q^{38} + 8 q^{39} + 3 q^{40} + 10 q^{41} - 50 q^{42} + 14 q^{43} - 26 q^{44} + 4 q^{45} - 8 q^{46} + 13 q^{47} - 2 q^{48} + 5 q^{49} - 18 q^{50} + 17 q^{51} - 7 q^{52} - 71 q^{53} + 7 q^{54} - 29 q^{55} + q^{56} - 70 q^{57} + 25 q^{58} + 8 q^{59} - 2 q^{60} + 25 q^{61} - 15 q^{62} + 88 q^{63} - 6 q^{64} + 7 q^{65} + 44 q^{66} + 26 q^{67} - 9 q^{68} + 78 q^{69} - 2 q^{70} - 60 q^{71} - 23 q^{72} + 7 q^{73} + 17 q^{74} - 10 q^{75} - 35 q^{76} - 5 q^{77} + 57 q^{78} + 52 q^{79} - 18 q^{80} + q^{81} - 4 q^{82} - 101 q^{83} - 8 q^{84} - 24 q^{85} + 49 q^{86} - 18 q^{87} + 16 q^{88} + 14 q^{89} - 3 q^{90} + 35 q^{91} + 6 q^{92} + 28 q^{93} - 15 q^{94} + 7 q^{95} - 2 q^{96} + 11 q^{97} + 12 q^{98} + 78 q^{99}+O(q^{100}) \) 36 * q - 6 * q^2 + 5 * q^3 - 6 * q^4 + 3 * q^5 + 5 * q^6 + q^7 - 6 * q^8 + 12 * q^9 + 3 * q^10 + 9 * q^11 - 16 * q^12 + 21 * q^13 - 6 * q^14 + 5 * q^15 - 6 * q^16 - 37 * q^17 + 19 * q^18 + 7 * q^19 + 3 * q^20 - 8 * q^21 + 16 * q^22 + 13 * q^23 + 5 * q^24 + 3 * q^25 - 21 * q^26 - 28 * q^27 - 6 * q^28 + 4 * q^29 - 2 * q^30 + 13 * q^31 - 6 * q^32 - 54 * q^33 - 23 * q^34 - 2 * q^35 - 9 * q^36 + 17 * q^37 + 28 * q^38 + 8 * q^39 + 3 * q^40 + 10 * q^41 - 50 * q^42 + 14 * q^43 - 26 * q^44 + 4 * q^45 - 8 * q^46 + 13 * q^47 - 2 * q^48 + 5 * q^49 - 18 * q^50 + 17 * q^51 - 7 * q^52 - 71 * q^53 + 7 * q^54 - 29 * q^55 + q^56 - 70 * q^57 + 25 * q^58 + 8 * q^59 - 2 * q^60 + 25 * q^61 - 15 * q^62 + 88 * q^63 - 6 * q^64 + 7 * q^65 + 44 * q^66 + 26 * q^67 - 9 * q^68 + 78 * q^69 - 2 * q^70 - 60 * q^71 - 23 * q^72 + 7 * q^73 + 17 * q^74 - 10 * q^75 - 35 * q^76 - 5 * q^77 + 57 * q^78 + 52 * q^79 - 18 * q^80 + q^81 - 4 * q^82 - 101 * q^83 - 8 * q^84 - 24 * q^85 + 49 * q^86 - 18 * q^87 + 16 * q^88 + 14 * q^89 - 3 * q^90 + 35 * q^91 + 6 * q^92 + 28 * q^93 - 15 * q^94 + 7 * q^95 - 2 * q^96 + 11 * q^97 + 12 * q^98 + 78 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/430\mathbb{Z}\right)^\times$.

$n$	$87$	$261$
$\chi(n)$	$1$	$e\left(\frac{4}{21}\right)$

Coefficient data

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

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

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

$2$	−0.900969	−	0.433884i	−0.637081	−	0.306802i
$2$	−0.900969	−	0.433884i	−0.637081	−	0.306802i
$3$	0.492510	+	0.335788i	0.284351	+	0.193867i	0.697093	−	0.716981i	$-0.254477\pi$
$3$	0.492510	+	0.335788i	0.284351	+	0.193867i	−0.412742	+	0.910848i	$0.635429\pi$
$4$	0.623490	+	0.781831i	0.311745	+	0.390916i
$5$	−0.733052	+	0.680173i	−0.327831	+	0.304182i
$5$	−0.733052	+	0.680173i	−0.327831	+	0.304182i
$6$	−0.298043	−	0.516226i	−0.121676	−	0.210749i
$7$	−0.982941	+	1.70250i	−0.371517	+	0.643486i	−0.989799	−	0.142470i	$-0.954495\pi$
$7$	−0.982941	+	1.70250i	−0.371517	+	0.643486i	0.618282	+	0.785956i	$0.287829\pi$
$8$	−0.222521	−	0.974928i	−0.0786730	−	0.344689i
$9$	−0.966210	−	2.46186i	−0.322070	−	0.820621i
$10$	0.955573	−	0.294755i	0.302179	−	0.0932098i
$11$	−3.99493	+	5.00948i	−1.20452	+	1.51041i	−0.399965	+	0.916531i	$0.630978\pi$
$11$	−3.99493	+	5.00948i	−1.20452	+	1.51041i	−0.804551	+	0.593884i	$0.797594\pi$
$12$	0.0445456	+	0.594420i	0.0128592	+	0.171594i
$13$	0.766750	+	0.236511i	0.212658	+	0.0655963i	0.399254	−	0.916840i	$-0.369269\pi$
$13$	0.766750	+	0.236511i	0.212658	+	0.0655963i	−0.186596	+	0.982437i	$0.559745\pi$
$14$	1.62429	−	1.10742i	0.434109	−	0.295971i
$15$	−0.589429	+	0.0888421i	−0.152190	+	0.0229389i
$16$	−0.222521	+	0.974928i	−0.0556302	+	0.243732i
$17$	−3.05126	−	2.83115i	−0.740038	−	0.686655i	0.217144	−	0.976139i	$-0.430326\pi$
$17$	−3.05126	−	2.83115i	−0.740038	−	0.686655i	−0.957183	+	0.289484i	$0.906516\pi$
$18$	−0.197637	+	2.63729i	−0.0465835	+	0.621614i
$19$	−0.838614	+	2.13675i	−0.192391	+	0.490205i	−0.994222	−	0.107347i	$-0.965764\pi$
$19$	−0.838614	+	2.13675i	−0.192391	+	0.490205i	0.801830	+	0.597552i	$0.203860\pi$
$20$	−0.988831	−	0.149042i	−0.221109	−	0.0333269i
$21$	−1.05579	+	0.508441i	−0.230392	+	0.110951i
$22$	5.77283	−	2.78005i	1.23077	−	0.592709i
$23$	−2.14071	−	0.322660i	−0.446369	−	0.0672793i	−0.0779882	−	0.996954i	$-0.524850\pi$
$23$	−2.14071	−	0.322660i	−0.446369	−	0.0672793i	−0.368381	+	0.929675i	$0.620088\pi$
$24$	0.217775	−	0.554882i	0.0444531	−	0.113265i
$25$	0.0747301	−	0.997204i	0.0149460	−	0.199441i
$26$	−0.588199	−	0.545769i	−0.115355	−	0.107034i
$27$	0.748721	−	3.28036i	0.144091	−	0.631305i
$28$	−1.94392	+	0.292999i	−0.367367	+	0.0553717i
$29$	−5.99270	+	4.08575i	−1.11282	+	0.758705i	−0.972847	−	0.231451i	$-0.925653\pi$
$29$	−5.99270	+	4.08575i	−1.11282	+	0.758705i	−0.139969	+	0.990156i	$0.544700\pi$
$30$	0.569604	+	0.175700i	0.103995	+	0.0320782i
$31$	0.318121	+	4.24503i	0.0571362	+	0.762429i	0.950029	+	0.312161i	$0.101053\pi$
$31$	0.318121	+	4.24503i	0.0571362	+	0.762429i	−0.892893	+	0.450269i	$0.851328\pi$
$32$	0.623490	−	0.781831i	0.110218	−	0.138210i
$33$	−3.64966	+	1.12577i	−0.635325	+	0.195972i
$34$	1.52070	+	3.87467i	0.260797	+	0.664501i
$35$	−0.437450	−	1.91659i	−0.0739425	−	0.323963i
$36$	1.32234	−	2.29036i	0.220390	−	0.381727i
$37$	−4.21684	−	7.30378i	−0.693244	−	1.20073i	−0.970769	−	0.240015i	$-0.922848\pi$
$37$	−4.21684	−	7.30378i	−0.693244	−	1.20073i	0.277525	−	0.960718i	$-0.410486\pi$
$38$	1.68267	−	1.56129i	0.272965	−	0.253274i
$39$	0.298214	+	0.373949i	0.0477525	+	0.0598798i
$40$	0.826239	+	0.563320i	0.130640	+	0.0890687i
$41$	10.2417	+	4.93216i	1.59949	+	0.770274i	0.999557	−	0.0297759i	$-0.00947937\pi$
$41$	10.2417	+	4.93216i	1.59949	+	0.770274i	0.599934	+	0.800050i	$0.295194\pi$
$42$	1.17184			0.180818
$43$	−2.07133	+	6.22170i	−0.315875	+	0.948801i
$43$	−2.07133	+	6.22170i	−0.315875	+	0.948801i
$44$	−6.40736			−0.965946
$45$	2.38277	+	1.14748i	0.355203	+	0.171057i
$46$	1.78872	+	1.21953i	0.263732	+	0.179809i
$47$	2.27396	+	2.85146i	0.331692	+	0.415928i	0.919511	−	0.393064i	$-0.128585\pi$
$47$	2.27396	+	2.85146i	0.331692	+	0.415928i	−0.587819	+	0.808992i	$0.700013\pi$
$48$	−0.436963	+	0.405442i	−0.0630701	+	0.0585205i
$49$	1.56765	+	2.71526i	0.223951	+	0.387894i
$50$	−0.500000	+	0.866025i	−0.0707107	+	0.122474i
$51$	−0.552109	−	2.41895i	−0.0773107	−	0.338720i
$52$	0.293149	+	0.746931i	0.0406524	+	0.103581i
$53$	−9.96419	+	3.07355i	−1.36869	+	0.422184i	−0.890064	−	0.455836i	$-0.849340\pi$
$53$	−9.96419	+	3.07355i	−1.36869	+	0.422184i	−0.478623	+	0.878020i	$0.658864\pi$
$54$	−2.09787	+	2.63064i	−0.285484	+	0.357985i
$55$	−0.478823	−	6.38945i	−0.0645645	−	0.861553i
$56$	1.87854	+	0.579454i	0.251031	+	0.0774328i
$57$	−1.13052	+	0.770776i	−0.149741	+	0.102092i
$58$	7.17197	−	1.08100i	0.941726	−	0.141942i
$59$	−0.680983	+	2.98358i	−0.0886564	+	0.388429i	−0.999716	−	0.0238465i	$-0.992409\pi$
$59$	−0.680983	+	2.98358i	−0.0886564	+	0.388429i	0.911059	+	0.412275i	$0.135266\pi$
$60$	−0.436963	−	0.405442i	−0.0564116	−	0.0523423i
$61$	−0.426228	+	5.68761i	−0.0545729	+	0.728224i	0.901066	+	0.433682i	$0.142786\pi$
$61$	−0.426228	+	5.68761i	−0.0545729	+	0.728224i	−0.955639	+	0.294542i	$0.904833\pi$
$62$	1.55523	−	3.96266i	0.197515	−	0.503259i
$63$	5.14106	+	0.774890i	0.647713	+	0.0976270i
$64$	−0.900969	+	0.433884i	−0.112621	+	0.0542355i
$65$	−0.722935	+	0.348147i	−0.0896691	+	0.0431824i
$66$	3.77669	+	0.569244i	0.464878	+	0.0700691i
$67$	3.24862	−	8.27735i	0.396882	−	1.01124i	−0.583144	−	0.812369i	$-0.698178\pi$
$67$	3.24862	−	8.27735i	0.396882	−	1.01124i	0.980026	−	0.198870i	$-0.0637271\pi$
$68$	0.311057	−	4.15076i	0.0377212	−	0.503354i
$69$	−0.945976	−	0.877738i	−0.113882	−	0.105667i
$70$	−0.437450	+	1.91659i	−0.0522853	+	0.229077i
$71$	2.80401	−	0.422636i	0.332774	−	0.0501576i	0.0194699	−	0.999810i	$-0.493802\pi$
$71$	2.80401	−	0.422636i	0.332774	−	0.0501576i	0.313304	+	0.949653i	$0.398564\pi$
$72$	−2.18514	+	1.48980i	−0.257521	+	0.175575i
$73$	10.6556	+	3.28683i	1.24715	+	0.384695i	0.846920	−	0.531721i	$-0.178454\pi$
$73$	10.6556	+	3.28683i	1.24715	+	0.384695i	0.400229	+	0.916415i	$0.368931\pi$
$74$	0.630249	+	8.41009i	0.0732650	+	0.977653i
$75$	0.371654	−	0.466039i	0.0429149	−	0.0538136i
$76$	−2.19345	+	0.676589i	−0.251606	+	0.0776101i
$77$	−4.60188	−	11.7254i	−0.524433	−	1.33623i
$78$	−0.106432	−	0.466307i	−0.0120510	−	0.0527989i
$79$	6.22457	−	10.7813i	0.700319	−	1.21299i	−0.268036	−	0.963409i	$-0.586375\pi$
$79$	6.22457	−	10.7813i	0.700319	−	1.21299i	0.968355	−	0.249579i	$-0.0802921\pi$
$80$	−0.500000	−	0.866025i	−0.0559017	−	0.0968246i
$81$	−4.34581	+	4.03232i	−0.482867	+	0.448036i
$82$	−7.08750	−	8.88744i	−0.782683	−	0.981454i
$83$	−8.89920	−	6.06737i	−0.976814	−	0.665980i	−0.0340424	−	0.999420i	$-0.510838\pi$
$83$	−8.89920	−	6.06737i	−0.976814	−	0.665980i	−0.942771	+	0.333440i	$0.891791\pi$
$84$	−1.05579	−	0.508441i	−0.115196	−	0.0554754i
$85$	4.16240			0.451476
$86$	4.56570	−	4.70684i	0.492332	−	0.507552i
$87$	−4.32341			−0.463518
$88$	5.77283	+	2.78005i	0.615386	+	0.296354i
$89$	−4.66995	−	3.18392i	−0.495014	−	0.337495i	0.289944	−	0.957044i	$-0.406363\pi$
$89$	−4.66995	−	3.18392i	−0.495014	−	0.337495i	−0.784958	+	0.619549i	$0.787316\pi$
$90$	−1.64893	−	2.06769i	−0.173813	−	0.217954i
$91$	−1.15633	+	1.07292i	−0.121216	+	0.112472i
$92$	−1.08245	−	1.87485i	−0.112853	−	0.195467i
$93$	−1.26875	+	2.19754i	−0.131563	+	0.227874i
$94$	−0.811569	−	3.55571i	−0.0837069	−	0.366744i
$95$	−0.838614	−	2.13675i	−0.0860400	−	0.219226i
$96$	0.569604	−	0.175700i	0.0581350	−	0.0179323i
$97$	1.24320	−	1.55892i	0.126228	−	0.158285i	−0.714702	−	0.699429i	$-0.753438\pi$
$97$	1.24320	−	1.55892i	0.126228	−	0.158285i	0.840929	+	0.541145i	$0.182009\pi$
$98$	−0.234302	−	3.12654i	−0.0236681	−	0.315828i
$99$	16.1926	+	4.99475i	1.62742	+	0.501992i
$100$	0.826239	−	0.563320i	0.0826239	−	0.0563320i
$101$	−4.31569	+	0.650486i	−0.429427	+	0.0647258i	−0.360200	−	0.932875i	$-0.617292\pi$
$101$	−4.31569	+	0.650486i	−0.429427	+	0.0647258i	−0.0692275	+	0.997601i	$0.522053\pi$
$102$	−0.552109	+	2.41895i	−0.0546669	+	0.239511i
$103$	9.65313	+	8.95680i	0.951152	+	0.882540i	0.993182	−	0.116577i	$-0.0371921\pi$
$103$	9.65313	+	8.95680i	0.951152	+	0.882540i	−0.0420301	+	0.999116i	$0.513383\pi$
$104$	0.0599633	−	0.800154i	0.00587988	−	0.0784616i
$105$	0.428120	−	1.09083i	0.0417802	−	0.106454i
$106$	10.3110	+	1.55413i	1.00149	+	0.150951i
$107$	6.29076	−	3.02947i	0.608150	−	0.292870i	−0.104351	−	0.994541i	$-0.533277\pi$
$107$	6.29076	−	3.02947i	0.608150	−	0.292870i	0.712501	+	0.701671i	$0.247562\pi$
$108$	3.03151	−	1.45990i	0.291707	−	0.140479i
$109$	14.3363	+	2.16085i	1.37317	+	0.206972i	0.793841	−	0.608125i	$-0.208078\pi$
$109$	14.3363	+	2.16085i	1.37317	+	0.206972i	0.579325	+	0.815096i	$0.303316\pi$
$110$	−2.34087	+	5.96445i	−0.223193	+	0.568688i
$111$	0.375683	−	5.01315i	0.0356583	−	0.475827i
$112$	−1.44109	−	1.33714i	−0.136171	−	0.126348i
$113$	2.41342	−	10.5739i	0.227035	−	0.994706i	−0.725008	−	0.688741i	$-0.758164\pi$
$113$	2.41342	−	10.5739i	0.227035	−	0.994706i	0.952043	−	0.305965i	$-0.0989791\pi$
$114$	1.35299	−	0.203931i	0.126719	−	0.0190999i
$115$	1.78872	−	1.21953i	0.166799	−	0.113721i
$116$	−6.93075	−	2.13785i	−0.643504	−	0.198495i
$117$	−0.158584	−	2.11615i	−0.0146611	−	0.195638i
$118$	1.90807	−	2.39265i	0.175652	−	0.220261i
$119$	7.81925	−	2.41192i	0.716790	−	0.221100i
$120$	0.217775	+	0.554882i	0.0198800	+	0.0506535i
$121$	−6.68771	−	29.3008i	−0.607974	−	2.66371i
$122$	2.85178	−	4.93943i	0.258188	−	0.447195i
$123$	3.38800	+	5.86819i	0.305486	+	0.529117i
$124$	−3.12055	+	2.89545i	−0.280234	+	0.260019i
$125$	0.623490	+	0.781831i	0.0557666	+	0.0699291i
$126$	−4.29572	−	2.92877i	−0.382693	−	0.260916i
$127$	12.3797	+	5.96173i	1.09852	+	0.529018i	0.893192	−	0.449675i	$-0.148460\pi$
$127$	12.3797	+	5.96173i	1.09852	+	0.529018i	0.205326	+	0.978694i	$0.434175\pi$
$128$	1.00000			0.0883883
$129$	−3.10932	+	2.36872i	−0.273761	+	0.208555i
$130$	0.802398			0.0703749
$131$	0.287636	+	0.138518i	0.0251309	+	0.0121024i	0.446407	−	0.894830i	$-0.352703\pi$
$131$	0.287636	+	0.138518i	0.0251309	+	0.0121024i	−0.421276	+	0.906932i	$0.638418\pi$
$132$	−3.15569	−	2.15151i	−0.274668	−	0.187265i
$133$	−2.81352	−	3.52805i	−0.243963	−	0.305920i
$134$	−6.51831	+	6.04811i	−0.563096	+	0.522477i
$135$	1.68236	+	2.91393i	0.144794	+	0.250791i
$136$	−2.08120	+	3.60475i	−0.178462	+	0.309104i
$137$	−2.03404	−	8.91170i	−0.173779	−	0.761378i	−0.984420	−	0.175833i	$-0.943738\pi$
$137$	−2.03404	−	8.91170i	−0.173779	−	0.761378i	0.810640	−	0.585544i	$-0.199119\pi$
$138$	0.471459	+	1.20126i	0.0401333	+	0.102258i
$139$	−6.31205	+	1.94701i	−0.535381	+	0.165143i	−0.550644	−	0.834740i	$-0.685618\pi$
$139$	−6.31205	+	1.94701i	−0.535381	+	0.165143i	0.0152626	+	0.999884i	$0.495142\pi$
$140$	1.22571	−	1.53699i	0.103591	−	0.129899i
$141$	0.162465	+	2.16794i	0.0136820	+	0.182574i
$142$	−2.70970	−	0.835831i	−0.227393	−	0.0701413i
$143$	−4.24790	+	2.89617i	−0.355228	+	0.242190i
$144$	2.61514	−	0.394169i	0.217928	−	0.0328474i
$145$	1.61394	−	7.07114i	0.134030	−	0.587226i
$146$	−8.17430	−	7.58464i	−0.676510	−	0.627710i
$147$	−0.139664	+	1.86369i	−0.0115193	+	0.153715i
$148$	3.08117	−	7.85069i	0.253270	−	0.645322i
$149$	2.98005	+	0.449170i	0.244135	+	0.0367974i	0.269970	−	0.962869i	$-0.412986\pi$
$149$	2.98005	+	0.449170i	0.244135	+	0.0367974i	−0.0258348	+	0.999666i	$0.508224\pi$
$150$	−0.537056	+	0.258632i	−0.0438504	+	0.0211172i
$151$	−11.3681	+	5.47457i	−0.925120	+	0.445514i	−0.834896	−	0.550407i	$-0.814472\pi$
$151$	−11.3681	+	5.47457i	−0.925120	+	0.445514i	−0.0902235	+	0.995922i	$0.528758\pi$
$152$	2.26979	+	0.342116i	0.184104	+	0.0277493i
$153$	−4.02176	+	10.2473i	−0.325140	+	0.828442i
$154$	−0.941309	+	12.5609i	−0.0758528	+	1.01219i
$155$	−3.12055	−	2.89545i	−0.250649	−	0.232568i
$156$	−0.106432	+	0.466307i	−0.00852134	+	0.0373344i
$157$	−10.4048	+	1.56827i	−0.830391	+	0.125161i	−0.550463	−	0.834860i	$-0.685549\pi$
$157$	−10.4048	+	1.56827i	−0.830391	+	0.125161i	−0.279928	+	0.960021i	$0.590311\pi$
$158$	−10.2860	+	7.01285i	−0.818307	+	0.557912i
$159$	−5.93952	−	1.83210i	−0.471035	−	0.145295i
$160$	0.0747301	+	0.997204i	0.00590793	+	0.0788359i
$161$	2.65352	−	3.32741i	0.209127	−	0.262237i
$162$	5.66499	−	1.74742i	0.445084	−	0.137290i
$163$	2.38752	+	6.08330i	0.187005	+	0.476481i	0.993373	−	0.114933i	$-0.0366653\pi$
$163$	2.38752	+	6.08330i	0.187005	+	0.476481i	−0.806368	+	0.591414i	$0.798570\pi$
$164$	2.52950	+	11.0825i	0.197521	+	0.865395i
$165$	1.90967	−	3.30765i	0.148668	−	0.257500i
$166$	5.38537	+	9.32773i	0.417985	+	0.723972i
$167$	10.4118	−	9.66071i	0.805687	−	0.747568i	−0.165417	−	0.986224i	$-0.552897\pi$
$167$	10.4118	−	9.66071i	0.805687	−	0.747568i	0.971104	+	0.238655i	$0.0767066\pi$
$168$	0.730628	+	0.916179i	0.0563692	+	0.0706847i
$169$	−10.2091	−	6.96047i	−0.785318	−	0.535421i
$170$	−3.75019	−	1.80600i	−0.287627	−	0.138514i
$171$	6.07067			0.464236
$172$	−6.15578	+	2.25974i	−0.469374	+	0.172303i
$173$	−1.91196			−0.145364			−0.0726818	−	0.997355i	$-0.523156\pi$
$173$	−1.91196			−0.145364			−0.0726818	+	0.997355i	$0.523156\pi$
$174$	3.89526	+	1.87586i	0.295299	+	0.142208i
$175$	1.62429	+	1.10742i	0.122785	+	0.0837131i
$176$	−3.99493	−	5.00948i	−0.301129	−	0.377604i
$177$	−1.33724	+	1.24078i	−0.100513	+	0.0932625i
$178$	2.82603	+	4.89483i	0.211820	+	0.366883i
$179$	−5.92576	+	10.2637i	−0.442912	+	0.767146i	−0.997904	−	0.0647093i	$-0.979388\pi$
$179$	−5.92576	+	10.2637i	−0.442912	+	0.767146i	0.554992	+	0.831856i	$0.312721\pi$
$180$	0.588497	+	2.57837i	0.0438640	+	0.192181i
$181$	4.87553	+	12.4226i	0.362395	+	0.923368i	0.989513	+	0.144444i	$0.0461392\pi$
$181$	4.87553	+	12.4226i	0.362395	+	0.923368i	−0.627118	+	0.778924i	$0.715766\pi$
$182$	1.50734	−	0.464953i	0.111731	−	0.0344646i
$183$	−2.11975	+	2.65808i	−0.156697	+	0.196491i
$184$	0.161782	+	2.15884i	0.0119268	+	0.159152i
$185$	8.05899	+	2.48587i	0.592509	+	0.182765i
$186$	2.09658	−	1.42942i	0.153729	−	0.104810i
$187$	26.3721	−	3.97496i	1.92852	−	0.290678i
$188$	−0.811569	+	3.55571i	−0.0591897	+	0.259327i
$189$	4.84888	+	4.49910i	0.352704	+	0.327261i
$190$	−0.171538	+	2.28901i	−0.0124446	+	0.166062i
$191$	−9.92847	+	25.2973i	−0.718399	+	1.83045i	−0.189233	+	0.981932i	$0.560600\pi$
$191$	−9.92847	+	25.2973i	−0.718399	+	1.83045i	−0.529166	+	0.848519i	$0.677495\pi$
$192$	−0.589429	−	0.0888421i	−0.0425384	−	0.00641163i
$193$	−6.48071	+	3.12094i	−0.466492	+	0.224651i	−0.652338	−	0.757928i	$-0.726212\pi$
$193$	−6.48071	+	3.12094i	−0.466492	+	0.224651i	0.185846	+	0.982579i	$0.440497\pi$
$194$	−1.79647	+	0.865136i	−0.128979	+	0.0621132i
$195$	−0.472957	−	0.0712867i	−0.0338691	−	0.00510495i
$196$	−1.14546	+	2.91858i	−0.0818184	+	0.208470i
$197$	−1.50253	+	20.0498i	−0.107051	+	1.42849i	0.642368	+	0.766396i	$0.277952\pi$
$197$	−1.50253	+	20.0498i	−0.107051	+	1.42849i	−0.749419	+	0.662096i	$0.769667\pi$
$198$	−12.4219	−	11.5258i	−0.882784	−	0.819104i
$199$	−3.52186	+	15.4303i	−0.249658	+	1.09382i	0.682248	+	0.731121i	$0.261003\pi$
$199$	−3.52186	+	15.4303i	−0.249658	+	1.09382i	−0.931906	+	0.362701i	$0.881855\pi$
$200$	−0.988831	+	0.149042i	−0.0699209	+	0.0105389i
$201$	4.37941	−	2.98583i	0.308900	−	0.210604i
$202$	4.17054	+	1.28644i	0.293438	+	0.0905137i
$203$	−1.06554	−	14.2186i	−0.0747862	−	0.997953i
$204$	1.54697	−	1.93984i	0.108310	−	0.135816i
$205$	−10.8624	+	3.35062i	−0.758666	+	0.234017i
$206$	−4.81096	−	12.2581i	−0.335196	−	0.854065i
$207$	1.27403	+	5.58189i	0.0885513	+	0.387968i
$208$	−0.401199	+	0.694897i	−0.0278181	+	0.0481824i
$209$	−7.35382	−	12.7372i	−0.508674	−	0.881050i
$210$	−0.859017	+	0.797051i	−0.0592778	+	0.0550018i
$211$	7.96188	+	9.98388i	0.548119	+	0.687319i	0.976312	−	0.216368i	$-0.0694212\pi$
$211$	7.96188	+	9.98388i	0.548119	+	0.687319i	−0.428193	+	0.903687i	$0.640850\pi$
$212$	−8.61557	−	5.87399i	−0.591720	−	0.403428i
$213$	1.52292	+	0.733398i	0.104349	+	0.0502516i
$214$	−6.98221			−0.477294
$215$	−2.71344	−	5.96969i	−0.185055	−	0.407130i
$216$	−3.36472			−0.228940
$217$	−7.53987	−	3.63101i	−0.511839	−	0.246489i
$218$	−11.9790	−	8.16714i	−0.811319	−	0.553148i
$219$	4.14434	+	5.19683i	0.280048	+	0.351169i
$220$	4.69693	−	4.35811i	0.316667	−	0.293824i
$221$	−1.66995	−	2.89244i	−0.112333	−	0.194567i
$222$	−2.51360	+	4.35368i	−0.168702	+	0.292200i
$223$	5.98313	+	26.2138i	0.400660	+	1.75541i	0.624736	+	0.780836i	$0.285206\pi$
$223$	5.98313	+	26.2138i	0.400660	+	1.75541i	−0.224076	+	0.974572i	$0.571936\pi$
$224$	0.718217	+	1.82999i	0.0479879	+	0.122271i
$225$	−2.52718	+	0.779533i	−0.168479	+	0.0519689i
$226$	−6.76224	+	8.47959i	−0.449818	+	0.564054i
$227$	−0.0657944	−	0.877965i	−0.00436693	−	0.0582726i	0.994595	−	0.103834i	$-0.0331112\pi$
$227$	−0.0657944	−	0.877965i	−0.00436693	−	0.0582726i	−0.998962	+	0.0455619i	$0.985492\pi$
$228$	−1.30749	−	0.403306i	−0.0865904	−	0.0267096i
$229$	−8.44297	+	5.75632i	−0.557927	+	0.380388i	−0.809205	−	0.587527i	$-0.800102\pi$
$229$	−8.44297	+	5.75632i	−0.557927	+	0.380388i	0.251278	+	0.967915i	$0.419149\pi$
$230$	−2.14071	+	0.322660i	−0.141154	+	0.0212756i
$231$	1.67077	−	7.32013i	0.109929	−	0.481629i
$232$	5.31681	+	4.93328i	0.349066	+	0.323886i
$233$	−0.406323	+	5.42200i	−0.0266191	+	0.355207i	0.967951	+	0.251139i	$0.0808051\pi$
$233$	−0.406323	+	5.42200i	−0.0266191	+	0.355207i	−0.994570	+	0.104068i	$0.966814\pi$
$234$	−0.775285	+	1.97539i	−0.0506820	+	0.129136i
$235$	−3.60642	−	0.543580i	−0.235257	−	0.0354593i
$236$	−2.75724	+	1.32782i	−0.179481	+	0.0864336i
$237$	6.68588	−	3.21975i	0.434295	−	0.209145i
$238$	−8.09139	−	1.21958i	−0.524487	−	0.0790537i
$239$	−0.0335227	+	0.0854144i	−0.00216840	+	0.00552500i	−0.931954	−	0.362577i	$-0.881897\pi$
$239$	−0.0335227	+	0.0854144i	−0.00216840	+	0.00552500i	0.929785	+	0.368102i	$0.119992\pi$
$240$	0.0445456	−	0.594420i	0.00287541	−	0.0383697i
$241$	−20.4332	−	18.9593i	−1.31622	−	1.22127i	−0.957706	−	0.287749i	$-0.907093\pi$
$241$	−20.4332	−	18.9593i	−1.31622	−	1.22127i	−0.358514	−	0.933524i	$-0.616716\pi$
$242$	−6.68771	+	29.3008i	−0.429902	+	1.88353i
$243$	−13.4758	+	2.03115i	−0.864471	+	0.130298i
$244$	−4.71250	+	3.21293i	−0.301687	+	0.205687i
$245$	−2.99602	−	0.924149i	−0.191408	−	0.0590417i
$246$	−0.506371	−	6.75705i	−0.0322850	−	0.430814i
$247$	−1.14837	+	1.44001i	−0.0730692	+	0.0916259i
$248$	4.06781	−	1.25475i	0.258306	−	0.0796768i
$249$	−2.34560	−	5.97648i	−0.148646	−	0.378744i
$250$	−0.222521	−	0.974928i	−0.0140735	−	0.0616599i
$251$	5.17618	−	8.96540i	0.326717	−	0.565891i	−0.655141	−	0.755507i	$-0.727391\pi$
$251$	5.17618	−	8.96540i	0.326717	−	0.565891i	0.981858	+	0.189615i	$0.0607241\pi$
$252$	2.59956	+	4.50258i	0.163757	+	0.283636i
$253$	10.1683	−	9.43484i	0.639278	−	0.593163i
$254$	−8.56700	−	10.7427i	−0.537541	−	0.674055i
$255$	2.05002	+	1.39768i	0.128378	+	0.0875263i
$256$	−0.900969	−	0.433884i	−0.0563106	−	0.0271177i
$257$	−24.7013			−1.54083			−0.770414	−	0.637545i	$-0.779950\pi$
$257$	−24.7013			−1.54083			−0.770414	+	0.637545i	$0.779950\pi$
$258$	3.82915	−	0.785062i	0.238393	−	0.0488758i
$259$	16.5796			1.03021
$260$	−0.722935	−	0.348147i	−0.0448346	−	0.0215912i
$261$	15.8488	+	10.8055i	0.981014	+	0.668844i
$262$	−0.199050	−	0.249601i	−0.0122974	−	0.0154204i
$263$	−1.78636	+	1.65750i	−0.110151	+	0.102206i	−0.733326	−	0.679877i	$-0.762033\pi$
$263$	−1.78636	+	1.65750i	−0.110151	+	0.102206i	0.623175	+	0.782083i	$0.285843\pi$
$264$	1.90967	+	3.30765i	0.117532	+	0.203572i
$265$	5.21373	−	9.03044i	0.320277	−	0.554736i
$266$	1.00413	+	4.39940i	0.0615674	+	0.269745i
$267$	−1.23088	−	3.13622i	−0.0753285	−	0.191934i
$268$	8.49697	−	2.62097i	0.519035	−	0.160101i
$269$	14.3987	−	18.0554i	0.877904	−	1.10086i	−0.116286	−	0.993216i	$-0.537099\pi$
$269$	14.3987	−	18.0554i	0.877904	−	1.10086i	0.994190	−	0.107641i	$-0.0343298\pi$
$270$	−0.251446	−	3.35531i	−0.0153025	−	0.204198i
$271$	−14.1128	−	4.35322i	−0.857292	−	0.264440i	−0.165210	−	0.986258i	$-0.552830\pi$
$271$	−14.1128	−	4.35322i	−0.857292	−	0.264440i	−0.692082	+	0.721819i	$0.743306\pi$
$272$	3.43914	−	2.34476i	0.208528	−	0.142172i
$273$	−0.929777	+	0.140141i	−0.0562727	+	0.00848174i
$274$	−2.03404	+	8.91170i	−0.122881	+	0.538375i
$275$	4.69693	+	4.35811i	0.283236	+	0.262804i
$276$	0.0964364	−	1.28685i	0.00580479	−	0.0774595i
$277$	−5.74668	+	14.6423i	−0.345285	+	0.879771i	0.647740	+	0.761862i	$0.275714\pi$
$277$	−5.74668	+	14.6423i	−0.345285	+	0.879771i	−0.993024	+	0.117909i	$0.962381\pi$
$278$	6.53174	+	0.984501i	0.391748	+	0.0590465i
$279$	10.1433	−	4.88476i	0.607264	−	0.292443i
$280$	−1.77120	+	0.852964i	−0.105849	+	0.0509744i
$281$	27.8661	+	4.20014i	1.66235	+	0.250559i	0.911913	−	0.410382i	$-0.134605\pi$
$281$	27.8661	+	4.20014i	1.66235	+	0.250559i	0.750437	+	0.660942i	$0.229843\pi$
$282$	0.794259	−	2.02374i	0.0472975	−	0.120512i
$283$	1.50008	−	20.0172i	0.0891707	−	1.18990i	−0.755696	−	0.654923i	$-0.772701\pi$
$283$	1.50008	−	20.0172i	0.0891707	−	1.18990i	0.844866	−	0.534977i	$-0.179680\pi$
$284$	2.07870	+	1.92875i	0.123348	+	0.114450i
$285$	0.304470	−	1.33397i	0.0180352	−	0.0790175i
$286$	5.08383	−	0.766264i	0.300613	−	0.0453102i
$287$	−18.4640	+	12.5886i	−1.08990	+	0.743080i
$288$	−2.52718	−	0.779533i	−0.148916	−	0.0459344i
$289$	0.0243313	+	0.324678i	0.00143125	+	0.0190987i
$290$	−4.52216	+	5.67061i	−0.265550	+	0.332990i
$291$	1.13575	−	0.350334i	0.0665791	−	0.0205369i
$292$	4.07394	+	10.3802i	0.238409	+	0.607457i
$293$	2.97742	+	13.0449i	0.173942	+	0.762092i	0.984350	+	0.176225i	$0.0563887\pi$
$293$	2.97742	+	13.0449i	0.173942	+	0.762092i	−0.810407	+	0.585867i	$0.800754\pi$
$294$	0.934458	−	1.61853i	0.0544987	−	0.0943945i
$295$	−1.53015	−	2.65030i	−0.0890890	−	0.154307i
$296$	−6.18232	+	5.73635i	−0.359340	+	0.333419i
$297$	13.4418	+	16.8555i	0.779973	+	0.978055i
$298$	−2.49004	−	1.69768i	−0.144244	−	0.0983440i
$299$	−1.56508	−	0.753701i	−0.0905107	−	0.0435876i
$300$	0.596087			0.0344151
$301$	−8.55648	−	9.64201i	−0.493187	−	0.555756i
$302$	12.6176			0.726061
$303$	−2.34395	−	1.12879i	−0.134656	−	0.0648470i
$304$	−1.89657	−	1.29306i	−0.108776	−	0.0741621i
$305$	−3.55611	−	4.45922i	−0.203622	−	0.255334i
$306$	8.06960	−	7.48749i	0.461308	−	0.428031i
$307$	3.91707	+	6.78457i	0.223559	+	0.387216i	0.955886	−	0.293737i	$-0.0948991\pi$
$307$	3.91707	+	6.78457i	0.223559	+	0.387216i	−0.732327	+	0.680953i	$0.761566\pi$
$308$	6.29806	−	10.9086i	0.358865	−	0.621573i
$309$	1.74668	+	7.65272i	0.0993653	+	0.435348i
$310$	1.55523	+	3.96266i	0.0883312	+	0.225064i
$311$	13.6005	−	4.19521i	0.771216	−	0.237889i	0.115918	−	0.993259i	$-0.463019\pi$
$311$	13.6005	−	4.19521i	0.771216	−	0.237889i	0.655298	+	0.755370i	$0.272543\pi$
$312$	0.298214	−	0.373949i	0.0168831	−	0.0211707i
$313$	−1.51871	−	20.2658i	−0.0858426	−	1.14549i	−0.859242	−	0.511570i	$-0.829064\pi$
$313$	−1.51871	−	20.2658i	−0.0858426	−	1.14549i	0.773399	−	0.633919i	$-0.218555\pi$
$314$	10.0548	+	3.10150i	0.567426	+	0.175028i
$315$	−4.29572	+	2.92877i	−0.242037	+	0.165018i
$316$	12.3101	−	1.85545i	0.692497	−	0.104377i
$317$	−5.53042	+	24.2303i	−0.310619	+	1.36091i	0.542877	+	0.839812i	$0.317335\pi$
$317$	−5.53042	+	24.2303i	−0.310619	+	1.36091i	−0.853496	+	0.521099i	$0.825522\pi$
$318$	4.55641	+	4.22773i	0.255511	+	0.237079i
$319$	3.47289	−	46.3425i	0.194445	−	2.59468i
$320$	0.365341	−	0.930874i	0.0204232	−	0.0520374i
$321$	4.11552	+	0.620315i	0.229706	+	0.0346226i
$322$	−3.83445	+	1.84657i	−0.213686	+	0.102906i
$323$	8.60830	−	4.14554i	0.478979	−	0.230664i
$324$	−5.86216	−	0.883579i	−0.325676	−	0.0490877i
$325$	0.293149	−	0.746931i	0.0162610	−	0.0414323i
$326$	0.488364	−	6.51677i	0.0270480	−	0.360931i
$327$	6.33518	+	5.87819i	0.350336	+	0.325064i
$328$	2.52950	−	11.0825i	0.139668	−	0.611927i
$329$	−7.08980	+	1.06861i	−0.390873	+	0.0589146i
$330$	−3.15569	+	2.15151i	−0.173715	+	0.118437i
$331$	−14.0921	−	4.34684i	−0.774573	−	0.238924i	−0.117825	−	0.993034i	$-0.537592\pi$
$331$	−14.0921	−	4.34684i	−0.774573	−	0.238924i	−0.656748	+	0.754110i	$0.728068\pi$
$332$	−0.804898	−	10.7406i	−0.0441745	−	0.589468i
$333$	−13.9065	+	17.4383i	−0.762074	+	0.955611i
$334$	−13.5723	+	4.18650i	−0.742644	+	0.229075i
$335$	3.24862	+	8.27735i	0.177491	+	0.452240i
$336$	−0.260758	−	1.14246i	−0.0142255	−	0.0623261i
$337$	7.02294	−	12.1641i	0.382564	−	0.662620i	−0.608864	−	0.793275i	$-0.708375\pi$
$337$	7.02294	−	12.1641i	0.382564	−	0.662620i	0.991428	+	0.130654i	$0.0417078\pi$
$338$	6.17808	+	10.7007i	0.336043	+	0.582044i
$339$	4.73921	−	4.39734i	0.257398	−	0.238831i
$340$	2.59522	+	3.25430i	0.140745	+	0.176489i
$341$	−22.5362	−	15.3649i	−1.22041	−	0.832058i
$342$	−5.46949	−	2.63397i	−0.295756	−	0.142429i
$343$	−19.9248			−1.07584
$344$	6.52663	+	0.634939i	0.351892	+	0.0342336i
$345$	1.29046			0.0694762
$346$	1.72262	+	0.829568i	0.0926084	+	0.0445978i
$347$	−25.5802	−	17.4403i	−1.37322	−	0.936243i	−0.999964	−	0.00851281i	$-0.997290\pi$
$347$	−25.5802	−	17.4403i	−1.37322	−	0.936243i	−0.373252	−	0.927730i	$-0.621757\pi$
$348$	−2.69560	−	3.38018i	−0.144499	−	0.181196i
$349$	1.50678	−	1.39809i	0.0806561	−	0.0748379i	−0.638815	−	0.769361i	$-0.720575\pi$
$349$	1.50678	−	1.39809i	0.0806561	−	0.0748379i	0.719471	+	0.694523i	$0.244384\pi$
$350$	−0.982941	−	1.70250i	−0.0525404	−	0.0910026i
$351$	1.34992	−	2.33813i	0.0720535	−	0.124800i
$352$	1.42577	+	6.24672i	0.0759939	+	0.332951i
$353$	8.34895	+	21.2728i	0.444370	+	1.13224i	0.961128	+	0.276104i	$0.0890434\pi$
$353$	8.34895	+	21.2728i	0.444370	+	1.13224i	−0.516758	+	0.856131i	$0.672861\pi$
$354$	1.74316	−	0.537695i	0.0926482	−	0.0285782i
$355$	−1.76802	+	2.21702i	−0.0938365	+	0.117667i
$356$	−0.422379	−	5.63626i	−0.0223860	−	0.298721i
$357$	4.66095	+	1.43771i	0.246684	+	0.0760919i
$358$	9.79219	−	6.67620i	0.517533	−	0.352848i
$359$	15.3253	−	2.30991i	0.808838	−	0.121913i	0.268412	−	0.963304i	$-0.413501\pi$
$359$	15.3253	−	2.30991i	0.808838	−	0.121913i	0.540426	+	0.841392i	$0.318263\pi$
$360$	0.588497	−	2.57837i	0.0310165	−	0.135892i
$361$	10.0655	+	9.33946i	0.529765	+	0.491551i
$362$	0.997284	−	13.3078i	0.0524161	−	0.699444i
$363$	6.54508	−	16.6766i	0.343527	−	0.875293i
$364$	−1.55980	−	0.235102i	−0.0817558	−	0.0123227i
$365$	−10.0468	+	4.83826i	−0.525871	+	0.253246i
$366$	3.06313	−	1.47513i	0.160112	−	0.0771061i
$367$	−28.4542	−	4.28878i	−1.48530	−	0.223872i	−0.644241	−	0.764822i	$-0.722827\pi$
$367$	−28.4542	−	4.28878i	−1.48530	−	0.223872i	−0.841055	+	0.540950i	$0.818065\pi$
$368$	0.790923	−	2.01524i	0.0412297	−	0.105052i
$369$	2.24663	−	29.9793i	0.116955	−	1.56066i
$370$	−6.18232	−	5.73635i	−0.321404	−	0.298219i
$371$	4.56149	−	19.9852i	0.236821	−	1.03758i
$372$	−2.50916	+	0.378195i	−0.130094	+	0.0196085i
$373$	5.32392	−	3.62979i	0.275662	−	0.187943i	−0.417596	−	0.908633i	$-0.637127\pi$
$373$	5.32392	−	3.62979i	0.275662	−	0.187943i	0.693258	+	0.720690i	$0.256175\pi$
$374$	−25.4851	−	7.86113i	−1.31781	−	0.406489i
$375$	0.0445456	+	0.594420i	0.00230033	+	0.0306957i
$376$	2.27396	−	2.85146i	0.117271	−	0.147053i
$377$	−5.56122	+	1.71541i	−0.286417	+	0.0883481i
$378$	−2.41660	−	6.15740i	−0.124296	−	0.316702i
$379$	0.186148	+	0.815567i	0.00956177	+	0.0418929i	0.979484	−	0.201523i	$-0.0645891\pi$
$379$	0.186148	+	0.815567i	0.00956177	+	0.0418929i	−0.969922	+	0.243416i	$0.921732\pi$
$380$	1.14771	−	1.98790i	0.0588765	−	0.101977i
$381$	4.09523	+	7.09315i	0.209805	+	0.363393i
$382$	19.9213	−	18.4843i	1.01926	−	0.945739i
$383$	16.7805	+	21.0420i	0.857442	+	1.07520i	0.996390	+	0.0848983i	$0.0270565\pi$
$383$	16.7805	+	21.0420i	0.857442	+	1.07520i	−0.138948	+	0.990300i	$0.544372\pi$
$384$	0.492510	+	0.335788i	0.0251333	+	0.0171356i
$385$	11.3487	+	5.46525i	0.578384	+	0.278535i
$386$	7.19304			0.366116
$387$	17.3183	−	0.912140i	0.880340	−	0.0463667i
$388$	1.99394			0.101227
$389$	−1.09819	−	0.528861i	−0.0556805	−	0.0268143i	0.405836	−	0.913946i	$-0.366980\pi$
$389$	−1.09819	−	0.528861i	−0.0556805	−	0.0268143i	−0.461517	+	0.887131i	$0.652695\pi$
$390$	0.395189	+	0.269435i	0.0200112	+	0.0136434i
$391$	5.61836	+	7.04520i	0.284132	+	0.356291i
$392$	2.29834	−	2.13255i	0.116084	−	0.107710i
$393$	0.0951510	+	0.164806i	0.00479973	+	0.00831338i
$394$	10.0530	−	17.4124i	0.506464	−	0.877222i
$395$	2.77019	+	12.1370i	0.139384	+	0.610679i
$396$	6.19086	+	15.7741i	0.311102	+	0.792676i
$397$	3.74056	−	1.15381i	0.187733	−	0.0579081i	−0.199463	−	0.979905i	$-0.563920\pi$
$397$	3.74056	−	1.15381i	0.187733	−	0.0579081i	0.387196	+	0.921997i	$0.373444\pi$
$398$	9.86802	−	12.3741i	0.494639	−	0.620258i
$399$	−0.201014	−	2.68234i	−0.0100633	−	0.134285i
$400$	0.955573	+	0.294755i	0.0477786	+	0.0147378i
$401$	−24.8884	+	16.9686i	−1.24287	+	0.847373i	−0.992674	−	0.120822i	$-0.961447\pi$
$401$	−24.8884	+	16.9686i	−1.24287	+	0.847373i	−0.250194	+	0.968196i	$0.580495\pi$
$402$	−5.24121	+	0.789986i	−0.261408	+	0.0394009i
$403$	−0.760076	+	3.33011i	−0.0378621	+	0.165885i
$404$	−3.19936	−	2.96857i	−0.159174	−	0.147692i
$405$	0.443028	−	5.91180i	0.0220142	−	0.293760i
$406$	−5.20922	+	13.2729i	−0.258529	+	0.658721i
$407$	53.4341	+	8.05389i	2.64863	+	0.399216i
$408$	−2.23544	+	1.07653i	−0.110671	+	0.0532963i
$409$	15.5410	−	7.48417i	0.768454	−	0.370068i	−0.00822340	−	0.999966i	$-0.502618\pi$
$409$	15.5410	−	7.48417i	0.768454	−	0.370068i	0.776678	+	0.629898i	$0.216903\pi$
$410$	11.2405	+	1.69423i	0.555129	+	0.0836722i
$411$	1.99065	−	5.07210i	0.0981917	−	0.250188i
$412$	−0.984077	+	13.1316i	−0.0484820	+	0.646947i
$413$	−4.41019	−	4.09206i	−0.217011	−	0.201357i
$414$	1.27403	−	5.58189i	0.0626152	−	0.274335i
$415$	10.6504	−	1.60529i	0.522809	−	0.0788008i
$416$	0.662972	−	0.452007i	0.0325049	−	0.0221615i
$417$	−3.76253	−	1.16059i	−0.184252	−	0.0568342i
$418$	1.09910	+	14.6665i	0.0537589	+	0.717363i
$419$	−17.6958	+	22.1898i	−0.864495	+	1.08404i	0.131200	+	0.991356i	$0.458117\pi$
$419$	−17.6958	+	22.1898i	−0.864495	+	1.08404i	−0.995695	+	0.0926869i	$0.970454\pi$
$420$	1.11977	−	0.345405i	0.0546394	−	0.0168540i
$421$	1.66177	+	4.23411i	0.0809895	+	0.206358i	0.965633	−	0.259911i	$-0.0836932\pi$
$421$	1.66177	+	4.23411i	0.0809895	+	0.206358i	−0.884643	+	0.466269i	$0.845598\pi$
$422$	−2.84156	−	12.4497i	−0.138325	−	0.606042i
$423$	4.82278	−	8.35330i	0.234492	−	0.406151i
$424$	5.21373	+	9.03044i	0.253201	+	0.438557i
$425$	−3.05126	+	2.83115i	−0.148008	+	0.137331i
$426$	−1.05389	−	1.32154i	−0.0510612	−	0.0640287i
$427$	−9.26422	−	6.31624i	−0.448327	−	0.305664i
$428$	6.29076	+	3.02947i	0.304075	+	0.146435i
$429$	−3.06463			−0.147962
$430$	−0.145428	+	6.55583i	−0.00701316	+	0.316150i
$431$	15.5055			0.746872			0.373436	−	0.927656i	$-0.378179\pi$
$431$	15.5055			0.746872			0.373436	+	0.927656i	$0.378179\pi$
$432$	3.03151	+	1.45990i	0.145853	+	0.0702393i
$433$	−26.8692	−	18.3191i	−1.29125	−	0.880361i	−0.294100	−	0.955775i	$-0.595020\pi$
$433$	−26.8692	−	18.3191i	−1.29125	−	0.880361i	−0.997152	+	0.0754133i	$0.975972\pi$
$434$	5.21775	+	6.54285i	0.250460	+	0.314067i
$435$	3.16928	−	2.94066i	0.151955	−	0.140994i
$436$	7.24911	+	12.5558i	0.347169	+	0.601315i
$437$	2.48467	−	4.30358i	0.118858	−	0.205868i
$438$	−1.47910	−	6.48034i	−0.0706740	−	0.309643i
$439$	−8.76578	−	22.3348i	−0.418368	−	1.06598i	−0.972365	−	0.233466i	$-0.924993\pi$
$439$	−8.76578	−	22.3348i	−0.418368	−	1.06598i	0.553997	−	0.832519i	$-0.313102\pi$
$440$	−6.12270	+	1.88860i	−0.291888	+	0.0900356i
$441$	5.16991	−	6.48286i	0.246186	−	0.308708i
$442$	0.249591	+	3.33056i	0.0118718	+	0.158419i
$443$	16.3663	+	5.04835i	0.777588	+	0.239854i	0.658049	−	0.752975i	$-0.271382\pi$
$443$	16.3663	+	5.04835i	0.777588	+	0.239854i	0.119539	+	0.992829i	$0.461858\pi$
$444$	4.15367	−	2.83192i	0.197124	−	0.134397i
$445$	5.58893	−	0.842396i	0.264941	−	0.0399334i
$446$	5.98313	−	26.2138i	0.283310	−	1.24126i
$447$	1.31688	+	1.22188i	0.0622862	+	0.0577931i
$448$	0.146911	−	1.96038i	0.00694087	−	0.0926195i
$449$	−1.25796	+	3.20523i	−0.0593668	+	0.151264i	−0.957480	−	0.288501i	$-0.906843\pi$
$449$	−1.25796	+	3.20523i	−0.0593668	+	0.151264i	0.898113	+	0.439765i	$0.144938\pi$
$450$	2.61514	+	0.394169i	0.123279	+	0.0185813i
$451$	−65.6225	+	31.6021i	−3.09004	+	1.48809i
$452$	9.77172	−	4.70581i	0.459623	−	0.221343i
$453$	−7.43718	−	1.12097i	−0.349429	−	0.0526680i
$454$	−0.321656	+	0.819566i	−0.0150961	+	0.0384642i
$455$	0.117881	−	1.57301i	0.00552633	−	0.0737438i
$456$	1.00302	+	0.930663i	0.0469705	+	0.0435823i
$457$	−7.06150	+	30.9384i	−0.330323	+	1.44724i	0.488183	+	0.872741i	$0.337660\pi$
$457$	−7.06150	+	30.9384i	−0.330323	+	1.44724i	−0.818506	+	0.574498i	$0.805197\pi$
$458$	10.1044	−	1.52300i	0.472149	−	0.0711649i
$459$	−11.5717	+	7.88948i	−0.540122	+	0.368249i
$460$	2.06871	+	0.638113i	0.0964541	+	0.0297522i
$461$	0.518945	+	6.92484i	0.0241697	+	0.322522i	0.996163	+	0.0875146i	$0.0278924\pi$
$461$	0.518945	+	6.92484i	0.0241697	+	0.322522i	−0.971994	+	0.235008i	$0.924489\pi$
$462$	−4.68140	+	5.87029i	−0.217798	+	0.273111i
$463$	−8.07744	+	2.49156i	−0.375390	+	0.115793i	−0.476708	−	0.879061i	$-0.658170\pi$
$463$	−8.07744	+	2.49156i	−0.375390	+	0.115793i	0.101318	+	0.994854i	$0.467694\pi$
$464$	−2.64981	−	6.75161i	−0.123014	−	0.313436i
$465$	−0.564647	−	2.47388i	−0.0261849	−	0.114723i
$466$	2.71860	−	4.70876i	0.125937	−	0.218129i
$467$	−0.704323	−	1.21992i	−0.0325922	−	0.0564513i	0.849269	−	0.527960i	$-0.177043\pi$
$467$	−0.704323	−	1.21992i	−0.0325922	−	0.0564513i	−0.881861	+	0.471509i	$0.843710\pi$
$468$	1.55560	−	1.44338i	0.0719076	−	0.0667205i
$469$	10.8990	+	13.6669i	0.503270	+	0.631080i
$470$	3.01342	+	2.05452i	0.138999	+	0.0947678i
$471$	−5.65106	−	2.72141i	−0.260387	−	0.125396i
$472$	3.06031			0.140862
$473$	−22.8927	−	35.2315i	−1.05261	−	1.61995i
$474$	−7.42077			−0.340847
$475$	2.06811	+	0.995949i	0.0948913	+	0.0456973i
$476$	6.76094	+	4.60953i	0.309887	+	0.211277i
$477$	17.1942	+	21.5608i	0.787266	+	0.987201i
$478$	0.0672628	−	0.0624108i	0.00307653	−	0.00285460i
$479$	−12.6608	−	21.9292i	−0.578488	−	1.00197i	−0.995653	−	0.0931393i	$-0.970310\pi$
$479$	−12.6608	−	21.9292i	−0.578488	−	1.00197i	0.417166	−	0.908831i	$-0.363024\pi$
$480$	−0.298043	+	0.516226i	−0.0136038	+	0.0235624i
$481$	−1.50584	−	6.59749i	−0.0686602	−	0.300820i
$482$	10.1836	+	25.9473i	0.463850	+	1.18187i
$483$	2.42419	−	0.747764i	0.110304	−	0.0340244i
$484$	18.7385	−	23.4974i	0.851752	−	1.06806i
$485$	0.149007	+	1.98836i	0.00676606	+	0.0902868i
$486$	13.0225	+	4.01692i	0.590714	+	0.182211i
$487$	−5.35275	+	3.64944i	−0.242556	+	0.165372i	−0.678497	−	0.734603i	$-0.737368\pi$
$487$	−5.35275	+	3.64944i	−0.242556	+	0.165372i	0.435940	+	0.899976i	$0.356416\pi$
$488$	5.63986	−	0.850072i	0.255304	−	0.0384809i
$489$	−0.866820	+	3.79779i	−0.0391990	+	0.171742i
$490$	2.29834	+	2.13255i	0.103829	+	0.0963389i
$491$	0.397626	−	5.30595i	0.0179446	−	0.239454i	−0.981018	−	0.193917i	$-0.937881\pi$
$491$	0.397626	−	5.30595i	0.0179446	−	0.239454i	0.998963	−	0.0455376i	$-0.0145001\pi$
$492$	−2.47555	+	6.30760i	−0.111606	+	0.284369i
$493$	29.8526	+	4.49956i	1.34450	+	0.202650i
$494$	1.65945	−	0.799147i	0.0746620	−	0.0359553i
$495$	−15.2673	+	7.35235i	−0.686214	+	0.330463i
$496$	−4.20938	−	0.634462i	−0.189007	−	0.0284882i
$497$	−2.03663	+	5.18925i	−0.0913554	+	0.232770i
$498$	−0.479789	+	6.40234i	−0.0214999	+	0.286896i
$499$	1.05982	+	0.983369i	0.0474440	+	0.0440216i	0.703539	−	0.710657i	$-0.251602\pi$
$499$	1.05982	+	0.983369i	0.0474440	+	0.0440216i	−0.656094	+	0.754679i	$0.727793\pi$
$500$	−0.222521	+	0.974928i	−0.00995144	+	0.0436001i
$501$	8.37185	−	1.26185i	0.374027	−	0.0563755i
$502$	−8.55352	+	5.83169i	−0.381762	+	0.260281i
$503$	−7.47120	−	2.30456i	−0.333124	−	0.102755i	0.123681	−	0.992322i	$-0.460530\pi$
$503$	−7.47120	−	2.30456i	−0.333124	−	0.102755i	−0.456805	+	0.889567i	$0.651006\pi$
$504$	−0.388531	−	5.18459i	−0.0173066	−	0.230940i
$505$	2.72118	−	3.41226i	0.121091	−	0.151843i
$506$	−13.2550	+	4.08862i	−0.589256	+	0.181761i
$507$	−2.69086	−	6.85620i	−0.119505	−	0.304495i
$508$	3.05753	+	13.3959i	0.135656	+	0.594347i
$509$	12.3345	−	21.3641i	0.546719	−	0.946945i	−0.451778	−	0.892131i	$-0.649210\pi$
$509$	12.3345	−	21.3641i	0.546719	−	0.946945i	0.998497	−	0.0548145i	$-0.0174568\pi$
$510$	−1.24058	−	2.14874i	−0.0549337	−	0.0951479i
$511$	−16.0697	+	14.9105i	−0.710882	+	0.659602i
$512$	0.623490	+	0.781831i	0.0275546	+	0.0345524i
$513$	6.38143	+	4.35079i	0.281747	+	0.192092i
$514$	22.2551	+	10.7175i	0.981632	+	0.472729i
$515$	−13.1684			−0.580270
$516$	−3.79057	−	0.954091i	−0.166871	−	0.0420015i
$517$	−23.3687			−1.02775
$518$	−14.9377	−	7.19362i	−0.656325	−	0.316070i
$519$	−0.941659	−	0.642012i	−0.0413342	−	0.0281812i
$520$	0.500287	+	0.627340i	0.0219390	+	0.0275107i
$521$	26.6341	−	24.7128i	1.16686	−	1.08269i	0.171629	−	0.985162i	$-0.445097\pi$
$521$	26.6341	−	24.7128i	1.16686	−	1.08269i	0.995233	−	0.0975280i	$-0.0310935\pi$
$522$	−9.59091	−	16.6119i	−0.419783	−	0.727085i
$523$	−5.94473	+	10.2966i	−0.259945	+	0.450238i	−0.966227	−	0.257693i	$-0.917038\pi$
$523$	−5.94473	+	10.2966i	−0.259945	+	0.450238i	0.706282	+	0.707931i	$0.250371\pi$
$524$	0.0710403	+	0.311248i	0.00310341	+	0.0135969i
$525$	0.428120	+	1.09083i	0.0186847	+	0.0476078i
$526$	2.32861	−	0.718281i	0.101532	−	0.0313186i
$527$	11.0476	−	13.8533i	0.481243	−	0.603460i
$528$	−0.285420	−	3.80867i	−0.0124213	−	0.165751i
$529$	−17.4996	−	5.39793i	−0.760854	−	0.234692i
$530$	−8.61557	+	5.87399i	−0.374236	+	0.255150i
$531$	8.00314	−	1.20628i	0.347307	−	0.0523481i
$532$	1.00413	−	4.39940i	0.0435347	−	0.190738i
$533$	6.68634	+	6.20401i	0.289617	+	0.268726i
$534$	−0.251775	+	3.35970i	−0.0108954	+	0.145388i
$535$	−2.55089	+	6.49956i	−0.110285	+	0.281000i
$536$	−8.79270	−	1.32529i	−0.379787	−	0.0572437i
$537$	−6.36493	+	3.06519i	−0.274667	+	0.132273i
$538$	−20.8067	+	10.0200i	−0.897042	+	0.431992i
$539$	−19.8647	−	2.99412i	−0.855633	−	0.128966i
$540$	−1.22927	+	3.13213i	−0.0528994	+	0.134785i
$541$	−0.00676431	+	0.0902635i	−0.000290821	+	0.00388073i	−0.997347	−	0.0727896i	$-0.976810\pi$
$541$	−0.00676431	+	0.0902635i	−0.000290821	+	0.00388073i	0.997056	+	0.0766703i	$0.0244289\pi$
$542$	10.8264	+	10.0454i	0.465034	+	0.431489i
$543$	−1.77012	+	7.75542i	−0.0759633	+	0.332817i
$544$	−4.11591	+	0.620374i	−0.176468	+	0.0265983i
$545$	−11.9790	+	8.16714i	−0.513123	+	0.349842i
$546$	0.898505	+	0.277152i	0.0384525	+	0.0118610i
$547$	1.96606	+	26.2352i	0.0840626	+	1.12174i	0.866556	+	0.499079i	$0.166328\pi$
$547$	1.96606	+	26.2352i	0.0840626	+	1.12174i	−0.782494	+	0.622658i	$0.786053\pi$
$548$	5.69924	−	7.14663i	0.243460	−	0.305289i
$549$	14.4140	−	4.44612i	0.615172	−	0.189756i
$550$	−2.34087	−	5.96445i	−0.0998151	−	0.254325i
$551$	−3.70468	−	16.2313i	−0.157825	−	0.691476i
$552$	−0.645231	+	1.11757i	−0.0274629	+	0.0475671i
$553$	12.2368	+	21.1947i	0.520360	+	0.901290i
$554$	11.5306	−	10.6989i	0.489890	−	0.454552i
$555$	3.13441	+	3.93042i	0.133048	+	0.166837i
$556$	−5.45773	−	3.72102i	−0.231460	−	0.157806i
$557$	11.4457	+	5.51195i	0.484969	+	0.233549i	0.660359	−	0.750950i	$-0.270404\pi$
$557$	11.4457	+	5.51195i	0.484969	+	0.233549i	−0.175390	+	0.984499i	$0.556119\pi$
$558$	−11.2582			−0.476598
$559$	−3.05969	+	4.28060i	−0.129411	+	0.181050i
$560$	1.96588			0.0830737
$561$	14.3233	+	6.89773i	0.604730	+	0.291222i
$562$	−23.2841	−	15.8748i	−0.982180	−	0.669639i
$563$	−1.00994	−	1.26642i	−0.0425639	−	0.0533734i	0.760094	−	0.649813i	$-0.225153\pi$
$563$	−1.00994	−	1.26642i	−0.0425639	−	0.0533734i	−0.802658	+	0.596440i	$0.796581\pi$
$564$	−1.59367	+	1.47871i	−0.0671056	+	0.0622649i
$565$	5.42290	+	9.39274i	0.228143	+	0.395155i
$566$	−10.0367	+	17.3840i	−0.421873	+	0.730705i
$567$	−2.59337	−	11.3623i	−0.108911	−	0.477171i
$568$	−1.03599	−	2.63966i	−0.0434691	−	0.110758i
$569$	−22.1977	+	6.84710i	−0.930578	+	0.287045i	−0.722741	−	0.691118i	$-0.757118\pi$
$569$	−22.1977	+	6.84710i	−0.930578	+	0.287045i	−0.207836	+	0.978164i	$0.566642\pi$
$570$	−0.853105	+	1.06976i	−0.0357326	+	0.0448073i
$571$	2.32741	+	31.0571i	0.0973989	+	1.29970i	0.805080	+	0.593166i	$0.202122\pi$
$571$	2.32741	+	31.0571i	0.0973989	+	1.29970i	−0.707681	+	0.706532i	$0.750259\pi$
$572$	−4.91284	−	1.51541i	−0.205416	−	0.0633625i
$573$	−13.3844	+	9.12533i	−0.559142	+	0.381216i
$574$	22.0975	−	3.33066i	0.922332	−	0.139019i
$575$	−0.481733	+	2.11061i	−0.0200897	+	0.0880186i
$576$	1.93869	+	1.79884i	0.0807787	+	0.0749516i
$577$	0.633166	−	8.44902i	0.0263591	−	0.351737i	−0.968394	−	0.249427i	$-0.919758\pi$
$577$	0.633166	−	8.44902i	0.0263591	−	0.351737i	0.994753	−	0.102310i	$-0.0326233\pi$
$578$	0.118951	−	0.303082i	0.00494771	−	0.0126065i
$579$	−4.23979	−	0.639045i	−0.176200	−	0.0265578i
$580$	6.53471	−	3.14695i	0.271339	−	0.130670i
$581$	19.0771	−	9.18705i	0.791452	−	0.381143i
$582$	−1.17528	−	0.177145i	−0.0487171	−	0.00734292i
$583$	24.4093	−	62.1940i	1.01093	−	2.57581i
$584$	0.833319	−	11.1199i	0.0344830	−	0.460144i
$585$	1.55560	+	1.44338i	0.0643161	+	0.0596766i
$586$	2.97742	−	13.0449i	0.122996	−	0.538880i
$587$	−17.4301	+	2.62717i	−0.719418	+	0.108435i	−0.498540	−	0.866867i	$-0.666130\pi$
$587$	−17.4301	+	2.62717i	−0.719418	+	0.108435i	−0.220878	+	0.975301i	$0.570892\pi$
$588$	−1.54417	+	1.05280i	−0.0636806	+	0.0434167i
$589$	−9.33735	−	2.88019i	−0.384739	−	0.118676i
$590$	0.228697	+	3.05175i	0.00941531	+	0.125639i
$591$	−7.47250	+	9.37022i	−0.307378	+	0.385439i
$592$	8.05899	−	2.48587i	0.331222	−	0.102169i
$593$	−2.61232	−	6.65609i	−0.107275	−	0.273333i	0.867149	−	0.498049i	$-0.165950\pi$
$593$	−2.61232	−	6.65609i	−0.107275	−	0.273333i	−0.974424	+	0.224716i	$0.927855\pi$
$594$	−4.79732	−	21.0185i	−0.196837	−	0.862398i
$595$	−4.09139	+	7.08650i	−0.167731	+	0.290518i
$596$	1.50685	+	2.60995i	0.0617231	+	0.106908i
$597$	−6.91584	+	6.41696i	−0.283047	+	0.262629i
$598$	1.08307	+	1.35812i	0.0442899	+	0.0555377i
$599$	−1.80338	−	1.22953i	−0.0736843	−	0.0502371i	0.525918	−	0.850536i	$-0.323722\pi$
$599$	−1.80338	−	1.22953i	−0.0736843	−	0.0502371i	−0.599602	+	0.800298i	$0.704674\pi$
$600$	−0.537056	−	0.258632i	−0.0219252	−	0.0105586i
$601$	45.7122			1.86464			0.932320	−	0.361635i	$-0.117781\pi$
$601$	45.7122			1.86464			0.932320	+	0.361635i	$0.117781\pi$
$602$	3.52561	+	12.3997i	0.143693	+	0.505373i
$603$	−23.5165			−0.957668
$604$	−11.3681	−	5.47457i	−0.462560	−	0.222757i
$605$	24.8320	+	16.9302i	1.00957	+	0.688310i
$606$	1.62206	+	2.03400i	0.0658917	+	0.0826256i
$607$	−26.2804	+	24.3846i	−1.06669	+	0.989742i	−0.999968	−	0.00803018i	$-0.997444\pi$
$607$	−26.2804	+	24.3846i	−1.06669	+	0.989742i	−0.0667200	+	0.997772i	$0.521253\pi$
$608$	1.14771	+	1.98790i	0.0465459	+	0.0806199i
$609$	4.24965	−	7.36062i	0.172205	−	0.298267i
$610$	1.26916	+	5.56056i	0.0513869	+	0.225141i
$611$	1.06916	+	2.72417i	0.0432536	+	0.110208i
$612$	−10.5192	+	3.24473i	−0.425212	+	0.131160i
$613$	5.67597	−	7.11744i	0.229250	−	0.287471i	−0.653880	−	0.756598i	$-0.726860\pi$
$613$	5.67597	−	7.11744i	0.229250	−	0.287471i	0.883131	+	0.469127i	$0.155431\pi$
$614$	−0.585447	−	7.81224i	−0.0236267	−	0.315276i
$615$	−6.47496	−	1.99726i	−0.261096	−	0.0805373i
$616$	−10.4074	+	7.09565i	−0.419326	+	0.285892i
$617$	−14.5400	+	2.19155i	−0.585357	+	0.0882284i	−0.435043	−	0.900410i	$-0.643267\pi$
$617$	−14.5400	+	2.19155i	−0.585357	+	0.0882284i	−0.150315	+	0.988638i	$0.548029\pi$
$618$	1.74668	−	7.65272i	0.0702619	−	0.307837i
$619$	−0.141554	−	0.131343i	−0.00568954	−	0.00527912i	0.677323	−	0.735686i	$-0.263140\pi$
$619$	−0.141554	−	0.131343i	−0.00568954	−	0.00527912i	−0.683012	+	0.730407i	$0.739331\pi$
$620$	0.318121	−	4.24503i	0.0127760	−	0.170484i
$621$	−2.66124	+	6.78072i	−0.106792	+	0.272101i
$622$	−14.0739	−	2.12130i	−0.564312	−	0.0850563i
$623$	10.0109	−	4.82100i	0.401079	−	0.193149i
$624$	−0.430932	+	0.207526i	−0.0172511	+	0.00830769i
$625$	−0.988831	−	0.149042i	−0.0395532	−	0.00596169i
$626$	−7.42468	+	18.9178i	−0.296750	+	0.756106i
$627$	0.655161	−	8.74252i	0.0261646	−	0.349142i
$628$	−7.71338	−	7.15697i	−0.307798	−	0.285594i
$629$	−7.81145	+	34.2242i	−0.311463	+	1.36461i
$630$	5.14106	−	0.774890i	0.204825	−	0.0308724i
$631$	−19.6743	+	13.4137i	−0.783221	+	0.533991i	−0.887638	−	0.460542i	$-0.847655\pi$
$631$	−19.6743	+	13.4137i	−0.783221	+	0.533991i	0.104416	+	0.994534i	$0.466703\pi$
$632$	−11.8961	−	3.66945i	−0.473200	−	0.145963i
$633$	0.568842	+	7.59067i	0.0226094	+	0.301702i
$634$	15.4959	−	19.4312i	0.615420	−	0.771713i
$635$	−13.1299	+	4.05005i	−0.521046	+	0.160721i
$636$	−2.27084	−	5.78600i	−0.0900446	−	0.229430i
$637$	0.559810	+	2.45269i	0.0221805	+	0.0971791i
$638$	−23.2362	+	40.2464i	−0.919932	+	1.59337i
$639$	−3.74973	−	6.49472i	−0.148337	−	0.256927i
$640$	−0.733052	+	0.680173i	−0.0289764	+	0.0268862i
$641$	25.2671	+	31.6839i	0.997991	+	1.25144i	0.967754	+	0.251898i	$0.0810547\pi$
$641$	25.2671	+	31.6839i	0.997991	+	1.25144i	0.0302369	+	0.999543i	$0.490374\pi$
$642$	−3.43881	−	2.34454i	−0.135719	−	0.0925317i
$643$	−4.49605	−	2.16518i	−0.177307	−	0.0853865i	0.343125	−	0.939290i	$-0.388515\pi$
$643$	−4.49605	−	2.16518i	−0.177307	−	0.0853865i	−0.520432	+	0.853903i	$0.674229\pi$
$644$	4.25592			0.167707
$645$	0.668153	−	3.85127i	0.0263085	−	0.151644i
$646$	−9.55449			−0.375916
$647$	27.2156	+	13.1064i	1.06996	+	0.515264i	0.884093	−	0.467312i	$-0.154777\pi$
$647$	27.2156	+	13.1064i	1.06996	+	0.515264i	0.185864	+	0.982576i	$0.440492\pi$
$648$	4.89825	+	3.33957i	0.192422	+	0.131191i
$649$	−12.2257	−	15.3305i	−0.479901	−	0.601777i
$650$	−0.588199	+	0.545769i	−0.0230711	+	0.0214068i
$651$	−2.49421	−	4.32010i	−0.0977559	−	0.169318i
$652$	−3.26752	+	5.65951i	−0.127966	+	0.221644i
$653$	−2.37402	−	10.4012i	−0.0929024	−	0.407032i	0.906998	−	0.421135i	$-0.138368\pi$
$653$	−2.37402	−	10.4012i	−0.0929024	−	0.407032i	−0.999901	+	0.0141026i	$0.995511\pi$
$654$	−3.15735	−	8.04479i	−0.123462	−	0.314576i
$655$	−0.305069	+	0.0941012i	−0.0119200	+	0.00367684i
$656$	−7.08750	+	8.88744i	−0.276720	+	0.346996i
$657$	−2.20386	−	29.4085i	−0.0859809	−	1.14734i
$658$	6.85134	+	2.11336i	0.267093	+	0.0823873i
$659$	19.5464	−	13.3265i	0.761421	−	0.519128i	−0.119246	−	0.992865i	$-0.538048\pi$
$659$	19.5464	−	13.3265i	0.761421	−	0.519128i	0.880666	+	0.473737i	$0.157095\pi$
$660$	3.77669	−	0.569244i	0.147007	−	0.0221578i
$661$	6.74768	−	29.5635i	0.262454	−	1.14989i	−0.656125	−	0.754652i	$-0.727806\pi$
$661$	6.74768	−	29.5635i	0.262454	−	1.14989i	0.918580	−	0.395236i	$-0.129337\pi$
$662$	10.8105	+	10.0307i	0.420163	+	0.389855i
$663$	0.148778	−	1.98531i	0.00577806	−	0.0771029i
$664$	−3.93499	+	10.0262i	−0.152707	+	0.389092i
$665$	4.46214	+	0.672559i	0.173034	+	0.0260807i
$666$	20.0955	−	9.67750i	0.778687	−	0.374996i
$667$	14.1469	−	6.81280i	0.547772	−	0.263793i
$668$	14.0447	+	2.11690i	0.543405	+	0.0819051i
$669$	−5.85552	+	14.9196i	−0.226388	+	0.576826i
$670$	0.664501	−	8.86715i	0.0256719	−	0.342568i
$671$	−26.7892	−	24.8568i	−1.03419	−	0.959585i
$672$	−0.260758	+	1.14246i	−0.0100590	+	0.0440712i
$673$	33.1655	−	4.99890i	1.27844	−	0.192693i	0.525504	−	0.850791i	$-0.323877\pi$
$673$	33.1655	−	4.99890i	1.27844	−	0.192693i	0.752933	+	0.658097i	$0.228639\pi$
$674$	−11.6053	+	7.91233i	−0.447018	+	0.304771i
$675$	−3.21523	−	0.991769i	−0.123754	−	0.0381732i
$676$	−0.923377	−	12.3216i	−0.0355145	−	0.473908i
$677$	−5.29696	+	6.64218i	−0.203579	+	0.255280i	−0.873131	−	0.487485i	$-0.837914\pi$
$677$	−5.29696	+	6.64218i	−0.203579	+	0.255280i	0.669553	+	0.742765i	$0.266486\pi$
$678$	−6.17781	+	1.90560i	−0.237257	+	0.0731842i
$679$	1.43208	+	3.64888i	0.0549581	+	0.140031i
$680$	−0.926222	−	4.05804i	−0.0355190	−	0.155619i
$681$	0.262405	−	0.454500i	0.0100554	−	0.0174165i
$682$	13.6378	+	23.6214i	0.522220	+	0.904512i
$683$	25.2752	−	23.4519i	0.967128	−	0.897364i	−0.0276304	−	0.999618i	$-0.508796\pi$
$683$	25.2752	−	23.4519i	0.967128	−	0.897364i	0.994758	+	0.102255i	$0.0326057\pi$
$684$	3.78500	+	4.74624i	0.144723	+	0.181477i
$685$	7.55255	+	5.14924i	0.288568	+	0.196742i
$686$	17.9516	+	8.64505i	0.685397	+	0.330070i
$687$	−6.09115			−0.232392
$688$	−5.60480	−	3.40386i	−0.213681	−	0.129771i
$689$	−8.36697			−0.318756
$690$	−1.16267	−	0.559911i	−0.0442620	−	0.0213154i
$691$	−20.4488	−	13.9418i	−0.777909	−	0.530370i	0.108043	−	0.994146i	$-0.465542\pi$
$691$	−20.4488	−	13.9418i	−0.777909	−	0.530370i	−0.885952	+	0.463777i	$0.846494\pi$
$692$	−1.19209	−	1.49483i	−0.0453163	−	0.0568249i
$693$	−24.4199	+	22.6584i	−0.927637	+	0.860721i
$694$	15.4799	+	26.8120i	0.587609	+	1.01777i
$695$	3.30276	−	5.72055i	0.125281	−	0.216993i
$696$	0.962049	+	4.21501i	0.0364664	+	0.159770i
$697$	−17.2865	−	44.0452i	−0.654772	−	1.66833i
$698$	−1.96417	+	0.605866i	−0.0743449	+	0.0229324i
$699$	−2.02076	+	2.53395i	−0.0764321	+	0.0958429i
$700$	0.146911	+	1.96038i	0.00555270	+	0.0740956i
$701$	34.5919	+	10.6702i	1.30652	+	0.403007i	0.868379	−	0.495901i	$-0.165162\pi$
$701$	34.5919	+	10.6702i	1.30652	+	0.403007i	0.438137	+	0.898908i	$0.355638\pi$
$702$	−2.23072	+	1.52088i	−0.0841929	+	0.0574018i
$703$	19.1427	−	2.88529i	0.721979	−	0.108821i
$704$	1.42577	−	6.24672i	0.0537358	−	0.235432i
$705$	−1.59367	−	1.47871i	−0.0600211	−	0.0556915i
$706$	1.70777	−	22.7886i	0.0642727	−	0.857660i
$707$	3.13462	−	7.98687i	0.117889	−	0.300377i
$708$	−1.80383	−	0.271884i	−0.0677923	−	0.0102180i
$709$	−23.9602	+	11.5386i	−0.899845	+	0.433343i	−0.825833	−	0.563915i	$-0.809295\pi$
$709$	−23.9602	+	11.5386i	−0.899845	+	0.433343i	−0.0740121	+	0.997257i	$0.523580\pi$
$710$	2.55486	−	1.23035i	0.0958821	−	0.0461744i
$711$	−32.5563	−	4.90707i	−1.22095	−	0.184029i
$712$	−2.06493	+	5.26135i	−0.0773865	+	0.197178i
$713$	0.688696	−	9.19002i	0.0257919	−	0.344169i
$714$	−3.57557	−	3.31765i	−0.133812	−	0.124160i
$715$	1.14404	−	5.01235i	0.0427845	−	0.187451i
$716$	−11.7191	+	1.76638i	−0.437965	+	0.0660126i
$717$	−0.0451914	+	0.0308110i	−0.00168770	+	0.00115066i
$718$	−14.8098	−	4.56823i	−0.552698	−	0.170485i
$719$	3.90655	+	52.1292i	0.145690	+	1.94409i	0.295424	+	0.955366i	$0.404539\pi$
$719$	3.90655	+	52.1292i	0.145690	+	1.94409i	−0.149735	+	0.988726i	$0.547842\pi$
$720$	−1.64893	+	2.06769i	−0.0614520	+	0.0770584i
$721$	−24.7374	+	7.63049i	−0.921271	+	0.284174i
$722$	−5.01650	−	12.7818i	−0.186695	−	0.475691i
$723$	−3.69728	−	16.1989i	−0.137503	−	0.602442i
$724$	−6.67257	+	11.5572i	−0.247984	+	0.429521i
$725$	3.62649	+	6.28127i	0.134685	+	0.233280i
$726$	−13.1326	+	12.1853i	−0.487397	+	0.452238i
$727$	−30.8162	−	38.6423i	−1.14291	−	1.43316i	−0.884139	−	0.467224i	$-0.845254\pi$
$727$	−30.8162	−	38.6423i	−1.14291	−	1.43316i	−0.258770	−	0.965939i	$-0.583317\pi$
$728$	1.30332	+	0.888592i	0.0483044	+	0.0329334i
$729$	8.70486	+	4.19204i	0.322402	+	0.155261i
$730$	11.1511			0.412719
$731$	23.9347	−	13.1198i	0.885259	−	0.485252i
$732$	−3.39982			−0.125661
$733$	−31.7896	−	15.3091i	−1.17418	−	0.565454i	−0.257968	−	0.966154i	$-0.583053\pi$
$733$	−31.7896	−	15.3091i	−1.17418	−	0.565454i	−0.916209	+	0.400700i	$0.868767\pi$
$734$	23.7755	+	16.2099i	0.877570	+	0.598317i
$735$	−1.16525	−	1.46118i	−0.0429809	−	0.0538964i
$736$	−1.58698	+	1.47250i	−0.0584967	+	0.0542770i
$737$	28.4872	+	49.3413i	1.04934	+	1.81751i
$738$	−15.0317	+	26.0356i	−0.553323	+	0.958384i
$739$	2.02070	+	8.85327i	0.0743327	+	0.325673i	0.998399	−	0.0565587i	$-0.0180128\pi$
$739$	2.02070	+	8.85327i	0.0743327	+	0.325673i	−0.924067	+	0.382232i	$0.875156\pi$
$740$	3.08117	+	7.85069i	0.113266	+	0.288597i
$741$	−1.04912	+	0.323612i	−0.0385405	+	0.0118882i
$742$	−12.7810	+	16.0269i	−0.469205	+	0.588365i
$743$	−1.21144	−	16.1655i	−0.0444434	−	0.593056i	−0.974318	−	0.225178i	$-0.927704\pi$
$743$	−1.21144	−	16.1655i	−0.0444434	−	0.593056i	0.929874	−	0.367878i	$-0.119915\pi$
$744$	2.42477	+	0.747941i	0.0888962	+	0.0274209i
$745$	−2.49004	+	1.69768i	−0.0912281	+	0.0621982i
$746$	−6.37160	+	0.960364i	−0.233281	+	0.0351614i
$747$	−6.33854	+	27.7710i	−0.231915	+	1.01609i
$748$	19.5505	+	18.1402i	0.714837	+	0.663272i
$749$	−1.02576	+	13.6878i	−0.0374805	+	0.500142i
$750$	0.217775	−	0.554882i	0.00795202	−	0.0202614i
$751$	−18.7184	−	2.82134i	−0.683043	−	0.102952i	−0.201651	−	0.979457i	$-0.564631\pi$
$751$	−18.7184	−	2.82134i	−0.683043	−	0.102952i	−0.481392	+	0.876505i	$0.659869\pi$
$752$	−3.28597	+	1.58244i	−0.119827	+	0.0577057i
$753$	5.55979	−	2.67745i	0.202610	−	0.0975719i
$754$	5.75478	+	0.867393i	0.209577	+	0.0315886i
$755$	4.60973	−	11.7454i	0.167765	−	0.427459i
$756$	−0.494313	+	6.59615i	−0.0179780	+	0.239899i
$757$	−9.88500	−	9.17194i	−0.359276	−	0.333360i	0.479795	−	0.877380i	$-0.340711\pi$
$757$	−9.88500	−	9.17194i	−0.359276	−	0.333360i	−0.839072	+	0.544021i	$0.816901\pi$
$758$	0.186148	−	0.815567i	0.00676119	−	0.0296227i
$759$	8.17611	−	1.23235i	0.296774	−	0.0447315i
$760$	−1.89657	+	1.29306i	−0.0687959	+	0.0469042i
$761$	34.7006	+	10.7037i	1.25789	+	0.388009i	0.850854	−	0.525402i	$-0.176085\pi$
$761$	34.7006	+	10.7037i	1.25789	+	0.388009i	0.407040	+	0.913410i	$0.366561\pi$
$762$	−0.612075	−	8.16757i	−0.0221731	−	0.295880i
$763$	−17.7706	+	22.2836i	−0.643338	+	0.806720i
$764$	−25.9686	+	8.01024i	−0.939509	+	0.289800i
$765$	−4.02176	−	10.2473i	−0.145407	−	0.370491i
$766$	−5.98888	−	26.2390i	−0.216387	−	0.948053i
$767$	−1.22779	+	2.12660i	−0.0443330	+	0.0767870i
$768$	−0.298043	−	0.516226i	−0.0107547	−	0.0186277i
$769$	19.4086	−	18.0086i	0.699894	−	0.649406i	−0.247718	−	0.968832i	$-0.579681\pi$
$769$	19.4086	−	18.0086i	0.699894	−	0.649406i	0.947611	+	0.319426i	$0.103490\pi$
$770$	−7.85355	−	9.84804i	−0.283022	−	0.354899i
$771$	−12.1657	−	8.29440i	−0.438135	−	0.298716i
$772$	−6.48071	−	3.12094i	−0.233246	−	0.112325i
$773$	11.7825			0.423786			0.211893	−	0.977293i	$-0.432037\pi$
$773$	11.7825			0.423786			0.211893	+	0.977293i	$0.432037\pi$
$774$	−15.9990	−	6.69233i	−0.575073	−	0.240551i
$775$	4.25693			0.152913
$776$	−1.79647	−	0.865136i	−0.0644897	−	0.0310566i
$777$	8.16562	+	5.56723i	0.292940	+	0.199723i
$778$	0.759972	+	0.952975i	0.0272463	+	0.0341658i
$779$	−19.1277	+	17.7479i	−0.685320	+	0.635884i
$780$	−0.239149	−	0.414219i	−0.00856292	−	0.0148314i
$781$	−9.08461	+	15.7350i	−0.325073	+	0.563043i
$782$	−2.00517	−	8.78522i	−0.0717047	−	0.314159i
$783$	8.91588	+	22.7173i	0.318627	+	0.811849i
$784$	−2.99602	+	0.924149i	−0.107001	+	0.0330053i
$785$	6.56054	−	8.22666i	0.234156	−	0.293622i
$786$	−0.0142213	−	0.189770i	−0.000507256	−	0.00676886i
$787$	36.9480	+	11.3969i	1.31705	+	0.406257i	0.872114	−	0.489303i	$-0.162749\pi$
$787$	36.9480	+	11.3969i	1.31705	+	0.406257i	0.444940	+	0.895560i	$0.353225\pi$
$788$	−16.6124	+	11.3261i	−0.591793	+	0.403477i
$789$	−1.43636	+	0.216497i	−0.0511359	+	0.00770750i
$790$	2.77019	−	12.1370i	0.0985591	−	0.431815i
$791$	15.6298	+	14.5023i	0.555732	+	0.515644i
$792$	1.26633	−	16.8980i	0.0449972	−	0.600446i
$793$	−1.67199	+	4.26017i	−0.0593742	+	0.151283i
$794$	−3.87075	−	0.583421i	−0.137368	−	0.0207048i
$795$	5.60012	−	2.69688i	0.198616	−	0.0956484i
$796$	−14.2597	+	6.86711i	−0.505422	+	0.243398i
$797$	−12.2554	−	1.84720i	−0.434108	−	0.0654312i	−0.0716465	−	0.997430i	$-0.522825\pi$
$797$	−12.2554	−	1.84720i	−0.434108	−	0.0654312i	−0.362461	+	0.931999i	$0.618063\pi$
$798$	−0.982718	+	2.50393i	−0.0347878	+	0.0886380i
$799$	1.13447	−	15.1385i	0.0401347	−	0.535561i
$800$	−0.733052	−	0.680173i	−0.0259173	−	0.0240477i
$801$	−3.32622	+	14.5731i	−0.117526	+	0.514916i
$802$	29.7861	−	4.48953i	1.05178	−	0.158531i
$803$	−59.0338	+	40.2486i	−2.08326	+	1.42034i
$804$	5.06493	+	1.56232i	0.178626	+	0.0550989i
$805$	0.318045	+	4.24402i	0.0112096	+	0.149582i
$806$	2.12969	−	2.67054i	0.0750150	−	0.0940658i
$807$	13.1543	−	4.05756i	0.463053	−	0.142833i
$808$	1.59451	+	4.06274i	0.0560946	+	0.142927i
$809$	0.0304643	+	0.133473i	0.00107107	+	0.00469265i	0.975461	−	0.220174i	$-0.0706625\pi$
$809$	0.0304643	+	0.133473i	0.00107107	+	0.00469265i	−0.974390	+	0.224867i	$0.927805\pi$
$810$	−2.96419	+	5.13412i	−0.104151	+	0.180395i
$811$	−9.65315	−	16.7197i	−0.338968	−	0.587109i	0.645271	−	0.763954i	$-0.276744\pi$
$811$	−9.65315	−	16.7197i	−0.338968	−	0.587109i	−0.984239	+	0.176844i	$0.943411\pi$
$812$	10.4522	−	9.69825i	0.366801	−	0.340342i
$813$	−5.48894	−	6.88291i	−0.192506	−	0.241394i
$814$	−44.6480	−	30.4405i	−1.56491	−	1.06694i
$815$	−5.88787	−	2.83545i	−0.206243	−	0.0993215i
$816$	2.48115			0.0868577
$817$	−11.5572	−	9.64353i	−0.404335	−	0.337384i
$818$	−17.2492			−0.603106
$819$	3.75863	+	1.81006i	0.131337	+	0.0632487i
$820$	−9.39224	−	6.40352i	−0.327991	−	0.223621i
$821$	24.0501	+	30.1578i	0.839353	+	1.05252i	0.997875	+	0.0651597i	$0.0207557\pi$
$821$	24.0501	+	30.1578i	0.839353	+	1.05252i	−0.158522	+	0.987355i	$0.550673\pi$
$822$	−3.99422	+	3.70610i	−0.139314	+	0.129265i
$823$	−8.87185	−	15.3665i	−0.309253	−	0.535642i	0.668946	−	0.743311i	$-0.266746\pi$
$823$	−8.87185	−	15.3665i	−0.309253	−	0.535642i	−0.978199	+	0.207669i	$0.933412\pi$
$824$	6.58421	−	11.4042i	0.229372	−	0.397284i
$825$	0.849884	+	3.72359i	0.0295892	+	0.129639i
$826$	2.19797	+	5.60033i	0.0764770	+	0.194860i
$827$	52.7551	−	16.2728i	1.83448	−	0.565861i	0.834588	−	0.550875i	$-0.185706\pi$
$827$	52.7551	−	16.2728i	1.83448	−	0.565861i	0.999888	−	0.0149854i	$-0.00477017\pi$
$828$	−3.56976	+	4.47633i	−0.124058	+	0.155563i
$829$	0.394285	+	5.26137i	0.0136941	+	0.182735i	0.999856	+	0.0169517i	$0.00539615\pi$
$829$	0.394285	+	5.26137i	0.0136941	+	0.182735i	−0.986162	+	0.165783i	$0.946985\pi$
$830$	−10.2922	−	3.17473i	−0.357248	−	0.110196i
$831$	−7.74701	+	5.28182i	−0.268741	+	0.183224i
$832$	−0.793436	+	0.119591i	−0.0275074	+	0.00414608i
$833$	2.90399	−	12.7232i	0.100617	−	0.440833i
$834$	2.88636	+	2.67815i	0.0999466	+	0.0927369i
$835$	−1.06142	+	14.1636i	−0.0367318	+	0.490152i
$836$	5.37330	−	13.6910i	0.185840	−	0.473512i
$837$	14.1634	+	2.13479i	0.489559	+	0.0737891i
$838$	25.5711	−	12.3144i	0.883340	−	0.425394i
$839$	47.7185	−	22.9800i	1.64742	−	0.793358i	0.647926	−	0.761704i	$-0.275637\pi$
$839$	47.7185	−	22.9800i	1.64742	−	0.793358i	0.999499	−	0.0316544i	$-0.0100776\pi$
$840$	−1.15875	−	0.174653i	−0.0399806	−	0.00602611i
$841$	8.62415	−	21.9740i	0.297385	−	0.757724i
$842$	0.339912	−	4.53582i	0.0117142	−	0.156315i
$843$	12.3140	+	11.4257i	0.424116	+	0.393522i
$844$	−2.84156	+	12.4497i	−0.0978106	+	0.428536i
$845$	12.2181	−	1.84159i	0.420317	−	0.0633526i
$846$	−7.96954	+	5.43354i	−0.273998	+	0.186809i
$847$	56.4583	+	17.4151i	1.93993	+	0.598389i
$848$	−0.779245	−	10.3983i	−0.0267594	−	0.357079i
$849$	7.46034	−	9.35497i	0.256038	−	0.321062i
$850$	3.97748	−	1.22689i	0.136426	−	0.0420820i
$851$	6.67039	+	16.9959i	0.228658	+	0.582611i
$852$	0.376129	+	1.64793i	0.0128860	+	0.0564572i
$853$	23.6058	−	40.8864i	0.808246	−	1.39992i	−0.105831	−	0.994384i	$-0.533750\pi$
$853$	23.6058	−	40.8864i	0.808246	−	1.39992i	0.914078	−	0.405539i	$-0.132916\pi$
$854$	5.60626	+	9.71033i	0.191842	+	0.332281i
$855$	−4.45012	+	4.12911i	−0.152191	+	0.141212i
$856$	−4.35334	−	5.45891i	−0.148794	−	0.186582i
$857$	−22.2738	−	15.1860i	−0.760859	−	0.518745i	0.119626	−	0.992819i	$-0.461831\pi$
$857$	−22.2738	−	15.1860i	−0.760859	−	0.518745i	−0.880485	+	0.474074i	$0.842783\pi$
$858$	2.76114	+	1.32969i	0.0942638	+	0.0453950i
$859$	30.3081			1.03410			0.517049	−	0.855956i	$-0.327031\pi$
$859$	30.3081			1.03410			0.517049	+	0.855956i	$0.327031\pi$
$860$	2.97549	−	5.84350i	0.101463	−	0.199262i
$861$	−13.3208			−0.453972
$862$	−13.9699	−	6.72757i	−0.475818	−	0.229142i
$863$	−8.98201	−	6.12383i	−0.305751	−	0.208458i	0.400718	−	0.916201i	$-0.368761\pi$
$863$	−8.98201	−	6.12383i	−0.305751	−	0.208458i	−0.706469	+	0.707744i	$0.749713\pi$
$864$	−2.09787	−	2.63064i	−0.0713709	−	0.0894963i
$865$	1.40156	−	1.30046i	0.0476546	−	0.0442170i
$866$	16.2600	+	28.1631i	0.552536	+	0.957021i
$867$	−0.0970396	+	0.168077i	−0.00329564	+	0.00570821i
$868$	−1.86219	−	8.15880i	−0.0632069	−	0.276928i
$869$	29.1418	+	74.2522i	0.988569	+	2.51883i
$870$	−4.13133	+	1.27435i	−0.140065	+	0.0432044i
$871$	4.44856	−	5.57832i	0.150734	−	0.189014i
$872$	−1.08345	−	14.4577i	−0.0366903	−	0.489599i
$873$	−5.03904	−	1.55434i	−0.170546	−	0.0526064i
$874$	−4.10587	+	2.79933i	−0.138883	+	0.0946889i
$875$	−1.94392	+	0.292999i	−0.0657166	+	0.00990519i
$876$	−1.47910	+	6.48034i	−0.0499740	+	0.218951i
$877$	−20.5231	−	19.0427i	−0.693016	−	0.643025i	0.252879	−	0.967498i	$-0.418623\pi$
$877$	−20.5231	−	19.0427i	−0.693016	−	0.643025i	−0.945895	+	0.324473i	$0.894813\pi$
$878$	−1.79303	+	23.9263i	−0.0605119	+	0.807475i
$879$	−2.91391	+	7.42453i	−0.0982839	+	0.250423i
$880$	6.33580	+	0.954968i	0.213580	+	0.0321920i
$881$	19.5434	−	9.41158i	0.658432	−	0.317084i	−0.0746643	−	0.997209i	$-0.523789\pi$
$881$	19.5434	−	9.41158i	0.658432	−	0.317084i	0.733097	+	0.680124i	$0.238074\pi$
$882$	−7.47073	+	3.59772i	−0.251553	+	0.121141i
$883$	33.2837	+	5.01672i	1.12009	+	0.168826i	0.682877	−	0.730533i	$-0.260729\pi$
$883$	33.2837	+	5.01672i	1.12009	+	0.168826i	0.437210	+	0.899359i	$0.355967\pi$
$884$	1.22020	−	3.10903i	0.0410399	−	0.104568i
$885$	0.136323	−	1.81911i	0.00458246	−	0.0611487i
$886$	−12.5552	−	11.6495i	−0.421799	−	0.391372i
$887$	2.16095	−	9.46772i	0.0725574	−	0.317895i	−0.925605	−	0.378491i	$-0.876443\pi$
$887$	2.16095	−	9.46772i	0.0725574	−	0.317895i	0.998162	+	0.0605962i	$0.0193002\pi$
$888$	−4.97105	+	0.749266i	−0.166818	+	0.0251437i
$889$	−22.3184	+	15.2164i	−0.748534	+	0.510342i
$890$	−5.40096	−	1.66597i	−0.181040	−	0.0558436i
$891$	−2.83864	−	37.8790i	−0.0950981	−	1.26900i
$892$	−16.7644	+	21.0219i	−0.561313	+	0.703864i
$893$	−7.99985	+	2.46763i	−0.267705	+	0.0825760i
$894$	−0.656310	−	1.67225i	−0.0219503	−	0.0559284i
$895$	−2.63721	−	11.5544i	−0.0881523	−	0.386220i
$896$	−0.982941	+	1.70250i	−0.0328377	+	0.0568767i
$897$	−0.517732	−	0.896739i	−0.0172866	−	0.0299412i
$898$	2.52408	−	2.34200i	0.0842296	−	0.0781537i
$899$	−19.2505	−	24.1394i	−0.642041	−	0.805094i
$900$	−2.18514	−	1.48980i	−0.0728379	−	0.0496601i
$901$	39.1050	+	18.8320i	1.30278	+	0.627384i
$902$	72.8355			2.42516
$903$	−0.976481	−	7.62195i	−0.0324953	−	0.253643i
$904$	−10.8458			−0.360726
$905$	−12.0236	−	5.79024i	−0.399677	−	0.192474i
$906$	6.21429	+	4.23683i	0.206456	+	0.140759i
$907$	9.27256	+	11.6274i	0.307890	+	0.386082i	0.911570	−	0.411145i	$-0.134871\pi$
$907$	9.27256	+	11.6274i	0.307890	+	0.386082i	−0.603680	+	0.797227i	$0.706299\pi$
$908$	0.645399	−	0.598842i	0.0214183	−	0.0198733i
$909$	5.77127	+	9.99614i	0.191421	+	0.331551i
$910$	−0.788710	+	1.36609i	−0.0261455	+	0.0452853i
$911$	−7.25845	−	31.8013i	−0.240483	−	1.05363i	−0.940579	−	0.339576i	$-0.889716\pi$
$911$	−7.25845	−	31.8013i	−0.240483	−	1.05363i	0.700095	−	0.714049i	$-0.253141\pi$
$912$	−0.499887	−	1.27369i	−0.0165529	−	0.0421761i
$913$	65.9460	−	20.3416i	2.18249	−	0.673210i
$914$	19.7859	−	24.8107i	0.654459	−	0.820665i
$915$	−0.254069	−	3.39031i	−0.00839925	−	0.112080i
$916$	−9.76457	−	3.01197i	−0.322631	−	0.0995183i
$917$	−0.518557	+	0.353546i	−0.0171243	+	0.0116751i
$918$	13.8489	−	2.08738i	0.457081	−	0.0688939i
$919$	−9.58748	+	42.0055i	−0.316262	+	1.38563i	0.527792	+	0.849374i	$0.323020\pi$
$919$	−9.58748	+	42.0055i	−0.316262	+	1.38563i	−0.844053	+	0.536259i	$0.819837\pi$
$920$	−1.58698	−	1.47250i	−0.0523211	−	0.0485469i
$921$	−0.348977	+	4.65677i	−0.0114992	+	0.153446i
$922$	2.53702	−	6.46423i	0.0835524	−	0.212888i
$923$	2.24993	+	0.339122i	0.0740573	+	0.0111623i
$924$	6.76482	−	3.25776i	0.222546	−	0.107173i
$925$	−7.59848	+	3.65923i	−0.249836	+	0.120315i
$926$	8.35857	+	1.25985i	0.274680	+	0.0414013i
$927$	12.7235	−	32.4189i	0.417893	−	1.06477i
$928$	−0.542016	+	7.23270i	−0.0177926	+	0.237425i
$929$	0.435851	+	0.404410i	0.0142998	+	0.0132683i	0.687290	−	0.726383i	$-0.258800\pi$
$929$	0.435851	+	0.404410i	0.0142998	+	0.0132683i	−0.672990	+	0.739651i	$0.734991\pi$
$930$	−0.564647	+	2.47388i	−0.0185155	+	0.0811217i
$931$	−7.11649	+	1.07264i	−0.233234	+	0.0351543i
$932$	−4.49243	+	3.06289i	−0.147154	+	0.100328i
$933$	8.10710	+	2.50071i	0.265415	+	0.0818696i
$934$	0.105268	+	1.40471i	0.00344448	+	0.0459634i
$935$	−16.6285	+	20.8515i	−0.543810	+	0.681916i
$936$	−2.02781	+	0.625496i	−0.0662810	+	0.0204450i
$937$	−12.2274	−	31.1549i	−0.399452	−	1.01779i	−0.979183	−	0.202979i	$-0.934938\pi$
$937$	−12.2274	−	31.1549i	−0.399452	−	1.01779i	0.579732	−	0.814808i	$-0.303157\pi$
$938$	−3.88981	−	17.0424i	−0.127007	−	0.556453i
$939$	6.05702	−	10.4911i	0.197663	−	0.342363i
$940$	−1.82358	−	3.15853i	−0.0594786	−	0.103020i
$941$	7.27375	−	6.74905i	0.237117	−	0.220013i	−0.552659	−	0.833407i	$-0.686387\pi$
$941$	7.27375	−	6.74905i	0.237117	−	0.220013i	0.789777	+	0.613395i	$0.210196\pi$
$942$	3.91065	+	4.90380i	0.127416	+	0.159775i
$943$	−20.3332	−	13.8629i	−0.662139	−	0.451439i
$944$	−2.75724	−	1.32782i	−0.0897406	−	0.0432168i
$945$	−6.61464			−0.215174
$946$	5.33920	+	41.6753i	0.173592	+	1.35498i
$947$	−41.1431			−1.33697			−0.668486	−	0.743725i	$-0.733057\pi$
$947$	−41.1431			−1.33697			−0.668486	+	0.743725i	$0.733057\pi$
$948$	6.68588	+	3.21975i	0.217147	+	0.104573i
$949$	7.39284	+	5.04035i	0.239982	+	0.163617i
$950$	−1.43118	−	1.79464i	−0.0464335	−	0.0582257i
$951$	−10.8600	+	10.0766i	−0.352161	+	0.326757i
$952$	−4.09139	−	7.08650i	−0.132603	−	0.229675i
$953$	−8.09804	+	14.0262i	−0.262321	+	0.454354i	−0.966858	−	0.255313i	$-0.917821\pi$
$953$	−8.09804	+	14.0262i	−0.262321	+	0.454354i	0.704537	+	0.709667i	$0.251155\pi$
$954$	−6.13652	−	26.8859i	−0.198677	−	0.870462i
$955$	−9.92847	−	25.2973i	−0.321278	−	0.818602i
$956$	−0.0876807	+	0.0270459i	−0.00283580	+	0.000874728i
$957$	17.2717	−	21.6580i	0.558315	−	0.700104i
$958$	1.89229	+	25.2508i	0.0611371	+	0.815817i
$959$	17.1715	+	5.29672i	0.554498	+	0.171040i
$960$	0.492510	−	0.335788i	0.0158957	−	0.0108375i
$961$	12.7347	−	1.91945i	0.410797	−	0.0619177i
$962$	−1.50584	+	6.59749i	−0.0485501	+	0.212712i
$963$	−13.5363	−	12.5599i	−0.436202	−	0.404736i
$964$	2.08304	−	27.7962i	0.0670902	−	0.895257i
$965$	2.62791	−	6.69582i	0.0845955	−	0.215546i
$966$	−2.50856	−	0.378105i	−0.0807117	−	0.0121653i
$967$	−39.3845	+	18.9666i	−1.26652	+	0.609923i	−0.941891	−	0.335919i	$-0.890953\pi$
$967$	−39.3845	+	18.9666i	−1.26652	+	0.609923i	−0.324628	+	0.945842i	$0.605239\pi$
$968$	−27.0780	+	13.0401i	−0.870320	+	0.419124i
$969$	5.63170	+	0.848842i	0.180916	+	0.0272687i
$970$	0.728466	−	1.85610i	0.0233896	−	0.0595959i
$971$	2.50571	−	33.4364i	0.0804121	−	1.07302i	−0.800371	−	0.599505i	$-0.795364\pi$
$971$	2.50571	−	33.4364i	0.0804121	−	1.07302i	0.880783	−	0.473520i	$-0.157017\pi$
$972$	−9.99002	−	9.26939i	−0.320430	−	0.297316i
$973$	2.88958	−	12.6601i	0.0926358	−	0.405864i
$974$	6.40610	−	0.965564i	0.205265	−	0.0309387i
$975$	0.395189	−	0.269435i	0.0126562	−	0.00862884i
$976$	−5.45017	−	1.68115i	−0.174456	−	0.0538124i
$977$	0.463664	+	6.18717i	0.0148339	+	0.197945i	0.999697	+	0.0246114i	$0.00783485\pi$
$977$	0.463664	+	6.18717i	0.0148339	+	0.197945i	−0.984863	+	0.173334i	$0.944546\pi$
$978$	2.42878	−	3.04559i	0.0776637	−	0.0973872i
$979$	34.6059	−	10.6745i	1.10601	−	0.341159i
$980$	−1.14546	−	2.91858i	−0.0365903	−	0.0932305i
$981$	−8.53215	−	37.3818i	−0.272411	−	1.19351i
$982$	−2.66042	+	4.60797i	−0.0848973	+	0.147046i
$983$	0.941104	+	1.63004i	0.0300165	+	0.0519902i	0.880643	−	0.473780i	$-0.157111\pi$
$983$	0.941104	+	1.63004i	0.0300165	+	0.0519902i	−0.850627	+	0.525770i	$0.823777\pi$
$984$	4.96716	−	4.60885i	0.158347	−	0.146925i
$985$	−12.5359	−	15.7196i	−0.399428	−	0.500867i
$986$	−24.9440	−	17.0065i	−0.794379	−	0.541598i
$987$	−3.85062	−	1.85436i	−0.122567	−	0.0590250i
$988$	−1.84185			−0.0585969
$989$	6.44161	−	12.6505i	0.204831	−	0.402263i
$990$	16.9454			0.538561
$991$	−14.6671	−	7.06330i	−0.465916	−	0.224373i	0.186171	−	0.982517i	$-0.440392\pi$
$991$	−14.6671	−	7.06330i	−0.465916	−	0.224373i	−0.652087	+	0.758144i	$0.726106\pi$
$992$	3.51724	+	2.39801i	0.111672	+	0.0761370i
$993$	−5.48089	−	6.87282i	−0.173931	−	0.218102i
$994$	4.08648	−	3.79170i	0.129615	−	0.120265i
$995$	−7.91354	−	13.7067i	−0.250876	−	0.434530i
$996$	3.21015	−	5.56014i	0.101717	−	0.176180i
$997$	4.86877	+	21.3315i	0.154195	+	0.675574i	0.991638	+	0.129049i	$0.0411925\pi$
$997$	4.86877	+	21.3315i	0.154195	+	0.675574i	−0.837443	+	0.546525i	$0.815950\pi$
$998$	−0.528197	−	1.34582i	−0.0167198	−	0.0426013i
$999$	−27.1162	+	8.36425i	−0.857920	+	0.264633i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	430.2.q.a.111.3	yes	36
43.31	even	21	inner	430.2.q.a.31.3	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
430.2.q.a.31.3	✓	36	43.31	even	21	inner
430.2.q.a.111.3	yes	36	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 430 = 2 \cdot 5 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	430.q (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.900969 - 0.433884i) q^{2} +(0.492510 + 0.335788i) q^{3} +(0.623490 + 0.781831i) q^{4} +(-0.733052 + 0.680173i) q^{5} +(-0.298043 - 0.516226i) q^{6} +(-0.982941 + 1.70250i) q^{7} +(-0.222521 - 0.974928i) q^{8} +(-0.966210 - 2.46186i) q^{9} +O(q^{10})\)	\(q+(-0.900969 - 0.433884i) q^{2} +(0.492510 + 0.335788i) q^{3} +(0.623490 + 0.781831i) q^{4} +(-0.733052 + 0.680173i) q^{5} +(-0.298043 - 0.516226i) q^{6} +(-0.982941 + 1.70250i) q^{7} +(-0.222521 - 0.974928i) q^{8} +(-0.966210 - 2.46186i) q^{9} +(0.955573 - 0.294755i) q^{10} +(-3.99493 + 5.00948i) q^{11} +(0.0445456 + 0.594420i) q^{12} +(0.766750 + 0.236511i) q^{13} +(1.62429 - 1.10742i) q^{14} +(-0.589429 + 0.0888421i) q^{15} +(-0.222521 + 0.974928i) q^{16} +(-3.05126 - 2.83115i) q^{17} +(-0.197637 + 2.63729i) q^{18} +(-0.838614 + 2.13675i) q^{19} +(-0.988831 - 0.149042i) q^{20} +(-1.05579 + 0.508441i) q^{21} +(5.77283 - 2.78005i) q^{22} +(-2.14071 - 0.322660i) q^{23} +(0.217775 - 0.554882i) q^{24} +(0.0747301 - 0.997204i) q^{25} +(-0.588199 - 0.545769i) q^{26} +(0.748721 - 3.28036i) q^{27} +(-1.94392 + 0.292999i) q^{28} +(-5.99270 + 4.08575i) q^{29} +(0.569604 + 0.175700i) q^{30} +(0.318121 + 4.24503i) q^{31} +(0.623490 - 0.781831i) q^{32} +(-3.64966 + 1.12577i) q^{33} +(1.52070 + 3.87467i) q^{34} +(-0.437450 - 1.91659i) q^{35} +(1.32234 - 2.29036i) q^{36} +(-4.21684 - 7.30378i) q^{37} +(1.68267 - 1.56129i) q^{38} +(0.298214 + 0.373949i) q^{39} +(0.826239 + 0.563320i) q^{40} +(10.2417 + 4.93216i) q^{41} +1.17184 q^{42} +(-2.07133 + 6.22170i) q^{43} -6.40736 q^{44} +(2.38277 + 1.14748i) q^{45} +(1.78872 + 1.21953i) q^{46} +(2.27396 + 2.85146i) q^{47} +(-0.436963 + 0.405442i) q^{48} +(1.56765 + 2.71526i) q^{49} +(-0.500000 + 0.866025i) q^{50} +(-0.552109 - 2.41895i) q^{51} +(0.293149 + 0.746931i) q^{52} +(-9.96419 + 3.07355i) q^{53} +(-2.09787 + 2.63064i) q^{54} +(-0.478823 - 6.38945i) q^{55} +(1.87854 + 0.579454i) q^{56} +(-1.13052 + 0.770776i) q^{57} +(7.17197 - 1.08100i) q^{58} +(-0.680983 + 2.98358i) q^{59} +(-0.436963 - 0.405442i) q^{60} +(-0.426228 + 5.68761i) q^{61} +(1.55523 - 3.96266i) q^{62} +(5.14106 + 0.774890i) q^{63} +(-0.900969 + 0.433884i) q^{64} +(-0.722935 + 0.348147i) q^{65} +(3.77669 + 0.569244i) q^{66} +(3.24862 - 8.27735i) q^{67} +(0.311057 - 4.15076i) q^{68} +(-0.945976 - 0.877738i) q^{69} +(-0.437450 + 1.91659i) q^{70} +(2.80401 - 0.422636i) q^{71} +(-2.18514 + 1.48980i) q^{72} +(10.6556 + 3.28683i) q^{73} +(0.630249 + 8.41009i) q^{74} +(0.371654 - 0.466039i) q^{75} +(-2.19345 + 0.676589i) q^{76} +(-4.60188 - 11.7254i) q^{77} +(-0.106432 - 0.466307i) q^{78} +(6.22457 - 10.7813i) q^{79} +(-0.500000 - 0.866025i) q^{80} +(-4.34581 + 4.03232i) q^{81} +(-7.08750 - 8.88744i) q^{82} +(-8.89920 - 6.06737i) q^{83} +(-1.05579 - 0.508441i) q^{84} +4.16240 q^{85} +(4.56570 - 4.70684i) q^{86} -4.32341 q^{87} +(5.77283 + 2.78005i) q^{88} +(-4.66995 - 3.18392i) q^{89} +(-1.64893 - 2.06769i) q^{90} +(-1.15633 + 1.07292i) q^{91} +(-1.08245 - 1.87485i) q^{92} +(-1.26875 + 2.19754i) q^{93} +(-0.811569 - 3.55571i) q^{94} +(-0.838614 - 2.13675i) q^{95} +(0.569604 - 0.175700i) q^{96} +(1.24320 - 1.55892i) q^{97} +(-0.234302 - 3.12654i) q^{98} +(16.1926 + 4.99475i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 6 q^{2} + 5 q^{3} - 6 q^{4} + 3 q^{5} + 5 q^{6} + q^{7} - 6 q^{8} + 12 q^{9}+O(q^{10}) \) 36 * q - 6 * q^2 + 5 * q^3 - 6 * q^4 + 3 * q^5 + 5 * q^6 + q^7 - 6 * q^8 + 12 * q^9	\( 36 q - 6 q^{2} + 5 q^{3} - 6 q^{4} + 3 q^{5} + 5 q^{6} + q^{7} - 6 q^{8} + 12 q^{9} + 3 q^{10} + 9 q^{11} - 16 q^{12} + 21 q^{13} - 6 q^{14} + 5 q^{15} - 6 q^{16} - 37 q^{17} + 19 q^{18} + 7 q^{19} + 3 q^{20} - 8 q^{21} + 16 q^{22} + 13 q^{23} + 5 q^{24} + 3 q^{25} - 21 q^{26} - 28 q^{27} - 6 q^{28} + 4 q^{29} - 2 q^{30} + 13 q^{31} - 6 q^{32} - 54 q^{33} - 23 q^{34} - 2 q^{35} - 9 q^{36} + 17 q^{37} + 28 q^{38} + 8 q^{39} + 3 q^{40} + 10 q^{41} - 50 q^{42} + 14 q^{43} - 26 q^{44} + 4 q^{45} - 8 q^{46} + 13 q^{47} - 2 q^{48} + 5 q^{49} - 18 q^{50} + 17 q^{51} - 7 q^{52} - 71 q^{53} + 7 q^{54} - 29 q^{55} + q^{56} - 70 q^{57} + 25 q^{58} + 8 q^{59} - 2 q^{60} + 25 q^{61} - 15 q^{62} + 88 q^{63} - 6 q^{64} + 7 q^{65} + 44 q^{66} + 26 q^{67} - 9 q^{68} + 78 q^{69} - 2 q^{70} - 60 q^{71} - 23 q^{72} + 7 q^{73} + 17 q^{74} - 10 q^{75} - 35 q^{76} - 5 q^{77} + 57 q^{78} + 52 q^{79} - 18 q^{80} + q^{81} - 4 q^{82} - 101 q^{83} - 8 q^{84} - 24 q^{85} + 49 q^{86} - 18 q^{87} + 16 q^{88} + 14 q^{89} - 3 q^{90} + 35 q^{91} + 6 q^{92} + 28 q^{93} - 15 q^{94} + 7 q^{95} - 2 q^{96} + 11 q^{97} + 12 q^{98} + 78 q^{99}+O(q^{100}) \) 36 * q - 6 * q^2 + 5 * q^3 - 6 * q^4 + 3 * q^5 + 5 * q^6 + q^7 - 6 * q^8 + 12 * q^9 + 3 * q^10 + 9 * q^11 - 16 * q^12 + 21 * q^13 - 6 * q^14 + 5 * q^15 - 6 * q^16 - 37 * q^17 + 19 * q^18 + 7 * q^19 + 3 * q^20 - 8 * q^21 + 16 * q^22 + 13 * q^23 + 5 * q^24 + 3 * q^25 - 21 * q^26 - 28 * q^27 - 6 * q^28 + 4 * q^29 - 2 * q^30 + 13 * q^31 - 6 * q^32 - 54 * q^33 - 23 * q^34 - 2 * q^35 - 9 * q^36 + 17 * q^37 + 28 * q^38 + 8 * q^39 + 3 * q^40 + 10 * q^41 - 50 * q^42 + 14 * q^43 - 26 * q^44 + 4 * q^45 - 8 * q^46 + 13 * q^47 - 2 * q^48 + 5 * q^49 - 18 * q^50 + 17 * q^51 - 7 * q^52 - 71 * q^53 + 7 * q^54 - 29 * q^55 + q^56 - 70 * q^57 + 25 * q^58 + 8 * q^59 - 2 * q^60 + 25 * q^61 - 15 * q^62 + 88 * q^63 - 6 * q^64 + 7 * q^65 + 44 * q^66 + 26 * q^67 - 9 * q^68 + 78 * q^69 - 2 * q^70 - 60 * q^71 - 23 * q^72 + 7 * q^73 + 17 * q^74 - 10 * q^75 - 35 * q^76 - 5 * q^77 + 57 * q^78 + 52 * q^79 - 18 * q^80 + q^81 - 4 * q^82 - 101 * q^83 - 8 * q^84 - 24 * q^85 + 49 * q^86 - 18 * q^87 + 16 * q^88 + 14 * q^89 - 3 * q^90 + 35 * q^91 + 6 * q^92 + 28 * q^93 - 15 * q^94 + 7 * q^95 - 2 * q^96 + 11 * q^97 + 12 * q^98 + 78 * q^99

Introduction

L-functions

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