LMFDB - Embedded newform 430.2.q.a.31.3

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			31.3
Character	$\chi$	$=$	430.31
Dual form			430.2.q.a.111.3

$q$-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 $\left(\mathbb{Z}/430\mathbb{Z}\right)^\times$.

$n$	$87$	$261$
$\chi(n)$	$1$	$e\left(\frac{17}{21}\right)$

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	−0.412742	−	0.910848i	$-0.635429\pi$
$3$	0.492510	−	0.335788i	0.284351	−	0.193867i	0.697093	+	0.716981i	$0.254477\pi$
$4$	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	0.618282	−	0.785956i	$-0.287829\pi$
$7$	−0.982941	−	1.70250i	−0.371517	−	0.643486i	−0.989799	+	0.142470i	$0.954495\pi$
$8$	−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	−0.804551	−	0.593884i	$-0.797594\pi$
$11$	−3.99493	−	5.00948i	−1.20452	−	1.51041i	−0.399965	−	0.916531i	$-0.630978\pi$
$12$	0.0445456	−	0.594420i	0.0128592	−	0.171594i
$13$	0.766750	−	0.236511i	0.212658	−	0.0655963i	−0.186596	−	0.982437i	$-0.559745\pi$
$13$	0.766750	−	0.236511i	0.212658	−	0.0655963i	0.399254	+	0.916840i	$0.369269\pi$
$14$	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	−0.957183	−	0.289484i	$-0.906516\pi$
$17$	−3.05126	+	2.83115i	−0.740038	+	0.686655i	0.217144	+	0.976139i	$0.430326\pi$
$18$	−0.197637	−	2.63729i	−0.0465835	−	0.621614i
$19$	−0.838614	−	2.13675i	−0.192391	−	0.490205i	0.801830	−	0.597552i	$-0.203860\pi$
$19$	−0.838614	−	2.13675i	−0.192391	−	0.490205i	−0.994222	+	0.107347i	$0.965764\pi$
$20$	−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	−0.368381	−	0.929675i	$-0.620088\pi$
$23$	−2.14071	+	0.322660i	−0.446369	+	0.0672793i	−0.0779882	+	0.996954i	$0.524850\pi$
$24$	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	−0.139969	−	0.990156i	$-0.544700\pi$
$29$	−5.99270	−	4.08575i	−1.11282	−	0.758705i	−0.972847	+	0.231451i	$0.925653\pi$
$30$	0.569604	−	0.175700i	0.103995	−	0.0320782i
$31$	0.318121	−	4.24503i	0.0571362	−	0.762429i	−0.892893	−	0.450269i	$-0.851328\pi$
$31$	0.318121	−	4.24503i	0.0571362	−	0.762429i	0.950029	−	0.312161i	$-0.101053\pi$
$32$	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	0.277525	+	0.960718i	$0.410486\pi$
$37$	−4.21684	+	7.30378i	−0.693244	+	1.20073i	−0.970769	+	0.240015i	$0.922848\pi$
$38$	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	0.599934	−	0.800050i	$-0.295194\pi$
$41$	10.2417	−	4.93216i	1.59949	−	0.770274i	0.999557	+	0.0297759i	$0.00947937\pi$
$42$	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	−0.587819	−	0.808992i	$-0.700013\pi$
$47$	2.27396	−	2.85146i	0.331692	−	0.415928i	0.919511	+	0.393064i	$0.128585\pi$
$48$	−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	−0.478623	−	0.878020i	$-0.658864\pi$
$53$	−9.96419	−	3.07355i	−1.36869	−	0.422184i	−0.890064	+	0.455836i	$0.849340\pi$
$54$	−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	0.911059	−	0.412275i	$-0.135266\pi$
$59$	−0.680983	−	2.98358i	−0.0886564	−	0.388429i	−0.999716	+	0.0238465i	$0.992409\pi$
$60$	−0.436963	+	0.405442i	−0.0564116	+	0.0523423i
$61$	−0.426228	−	5.68761i	−0.0545729	−	0.728224i	−0.955639	−	0.294542i	$-0.904833\pi$
$61$	−0.426228	−	5.68761i	−0.0545729	−	0.728224i	0.901066	−	0.433682i	$-0.142786\pi$
$62$	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	0.980026	+	0.198870i	$0.0637271\pi$
$67$	3.24862	+	8.27735i	0.396882	+	1.01124i	−0.583144	+	0.812369i	$0.698178\pi$
$68$	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	0.313304	−	0.949653i	$-0.398564\pi$
$71$	2.80401	+	0.422636i	0.332774	+	0.0501576i	0.0194699	+	0.999810i	$0.493802\pi$
$72$	−2.18514	−	1.48980i	−0.257521	−	0.175575i
$73$	10.6556	−	3.28683i	1.24715	−	0.384695i	0.400229	−	0.916415i	$-0.368931\pi$
$73$	10.6556	−	3.28683i	1.24715	−	0.384695i	0.846920	+	0.531721i	$0.178454\pi$
$74$	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	0.968355	+	0.249579i	$0.0802921\pi$
$79$	6.22457	+	10.7813i	0.700319	+	1.21299i	−0.268036	+	0.963409i	$0.586375\pi$
$80$	−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	−0.942771	−	0.333440i	$-0.891791\pi$
$83$	−8.89920	+	6.06737i	−0.976814	+	0.665980i	−0.0340424	+	0.999420i	$0.510838\pi$
$84$	−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	−0.784958	−	0.619549i	$-0.787316\pi$
$89$	−4.66995	+	3.18392i	−0.495014	+	0.337495i	0.289944	+	0.957044i	$0.406363\pi$
$90$	−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	0.840929	−	0.541145i	$-0.182009\pi$
$97$	1.24320	+	1.55892i	0.126228	+	0.158285i	−0.714702	+	0.699429i	$0.753438\pi$
$98$	−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	−0.0692275	−	0.997601i	$-0.522053\pi$
$101$	−4.31569	−	0.650486i	−0.429427	−	0.0647258i	−0.360200	+	0.932875i	$0.617292\pi$
$102$	−0.552109	−	2.41895i	−0.0546669	−	0.239511i
$103$	9.65313	−	8.95680i	0.951152	−	0.882540i	−0.0420301	−	0.999116i	$-0.513383\pi$
$103$	9.65313	−	8.95680i	0.951152	−	0.882540i	0.993182	+	0.116577i	$0.0371921\pi$
$104$	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	0.712501	−	0.701671i	$-0.247562\pi$
$107$	6.29076	+	3.02947i	0.608150	+	0.292870i	−0.104351	+	0.994541i	$0.533277\pi$
$108$	3.03151	+	1.45990i	0.291707	+	0.140479i
$109$	14.3363	−	2.16085i	1.37317	−	0.206972i	0.579325	−	0.815096i	$-0.303316\pi$
$109$	14.3363	−	2.16085i	1.37317	−	0.206972i	0.793841	+	0.608125i	$0.208078\pi$
$110$	−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	0.952043	+	0.305965i	$0.0989791\pi$
$113$	2.41342	+	10.5739i	0.227035	+	0.994706i	−0.725008	+	0.688741i	$0.758164\pi$
$114$	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	0.205326	−	0.978694i	$-0.434175\pi$
$127$	12.3797	−	5.96173i	1.09852	−	0.529018i	0.893192	+	0.449675i	$0.148460\pi$
$128$	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	−0.421276	−	0.906932i	$-0.638418\pi$
$131$	0.287636	−	0.138518i	0.0251309	−	0.0121024i	0.446407	+	0.894830i	$0.352703\pi$
$132$	−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	0.810640	+	0.585544i	$0.199119\pi$
$137$	−2.03404	+	8.91170i	−0.173779	+	0.761378i	−0.984420	+	0.175833i	$0.943738\pi$
$138$	0.471459	−	1.20126i	0.0401333	−	0.102258i
$139$	−6.31205	−	1.94701i	−0.535381	−	0.165143i	0.0152626	−	0.999884i	$-0.495142\pi$
$139$	−6.31205	−	1.94701i	−0.535381	−	0.165143i	−0.550644	+	0.834740i	$0.685618\pi$
$140$	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	−0.0258348	−	0.999666i	$-0.508224\pi$
$149$	2.98005	−	0.449170i	0.244135	−	0.0367974i	0.269970	+	0.962869i	$0.412986\pi$
$150$	−0.537056	−	0.258632i	−0.0438504	−	0.0211172i
$151$	−11.3681	−	5.47457i	−0.925120	−	0.445514i	−0.0902235	−	0.995922i	$-0.528758\pi$
$151$	−11.3681	−	5.47457i	−0.925120	−	0.445514i	−0.834896	+	0.550407i	$0.814472\pi$
$152$	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	−0.279928	−	0.960021i	$-0.590311\pi$
$157$	−10.4048	−	1.56827i	−0.830391	−	0.125161i	−0.550463	+	0.834860i	$0.685549\pi$
$158$	−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	−0.806368	−	0.591414i	$-0.798570\pi$
$163$	2.38752	−	6.08330i	0.187005	−	0.476481i	0.993373	+	0.114933i	$0.0366653\pi$
$164$	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	0.971104	−	0.238655i	$-0.0767066\pi$
$167$	10.4118	+	9.66071i	0.805687	+	0.747568i	−0.165417	+	0.986224i	$0.552897\pi$
$168$	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	0.554992	−	0.831856i	$-0.312721\pi$
$179$	−5.92576	−	10.2637i	−0.442912	−	0.767146i	−0.997904	+	0.0647093i	$0.979388\pi$
$180$	0.588497	−	2.57837i	0.0438640	−	0.192181i
$181$	4.87553	−	12.4226i	0.362395	−	0.923368i	−0.627118	−	0.778924i	$-0.715766\pi$
$181$	4.87553	−	12.4226i	0.362395	−	0.923368i	0.989513	−	0.144444i	$-0.0461392\pi$
$182$	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	−0.529166	−	0.848519i	$-0.677495\pi$
$191$	−9.92847	−	25.2973i	−0.718399	−	1.83045i	−0.189233	−	0.981932i	$-0.560600\pi$
$192$	−0.589429	+	0.0888421i	−0.0425384	+	0.00641163i
$193$	−6.48071	−	3.12094i	−0.466492	−	0.224651i	0.185846	−	0.982579i	$-0.440497\pi$
$193$	−6.48071	−	3.12094i	−0.466492	−	0.224651i	−0.652338	+	0.757928i	$0.726212\pi$
$194$	−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	−0.749419	−	0.662096i	$-0.769667\pi$
$197$	−1.50253	−	20.0498i	−0.107051	−	1.42849i	0.642368	−	0.766396i	$-0.277952\pi$
$198$	−12.4219	+	11.5258i	−0.882784	+	0.819104i
$199$	−3.52186	−	15.4303i	−0.249658	−	1.09382i	−0.931906	−	0.362701i	$-0.881855\pi$
$199$	−3.52186	−	15.4303i	−0.249658	−	1.09382i	0.682248	−	0.731121i	$-0.261003\pi$
$200$	−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	−0.428193	−	0.903687i	$-0.640850\pi$
$211$	7.96188	−	9.98388i	0.548119	−	0.687319i	0.976312	+	0.216368i	$0.0694212\pi$
$212$	−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	−0.224076	−	0.974572i	$-0.571936\pi$
$223$	5.98313	−	26.2138i	0.400660	−	1.75541i	0.624736	−	0.780836i	$-0.285206\pi$
$224$	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	−0.998962	−	0.0455619i	$-0.985492\pi$
$227$	−0.0657944	+	0.877965i	−0.00436693	+	0.0582726i	0.994595	+	0.103834i	$0.0331112\pi$
$228$	−1.30749	+	0.403306i	−0.0865904	+	0.0267096i
$229$	−8.44297	−	5.75632i	−0.557927	−	0.380388i	0.251278	−	0.967915i	$-0.419149\pi$
$229$	−8.44297	−	5.75632i	−0.557927	−	0.380388i	−0.809205	+	0.587527i	$0.800102\pi$
$230$	−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	−0.994570	−	0.104068i	$-0.966814\pi$
$233$	−0.406323	−	5.42200i	−0.0266191	−	0.355207i	0.967951	−	0.251139i	$-0.0808051\pi$
$234$	−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	0.929785	−	0.368102i	$-0.119992\pi$
$239$	−0.0335227	−	0.0854144i	−0.00216840	−	0.00552500i	−0.931954	+	0.362577i	$0.881897\pi$
$240$	0.0445456	+	0.594420i	0.00287541	+	0.0383697i
$241$	−20.4332	+	18.9593i	−1.31622	+	1.22127i	−0.358514	+	0.933524i	$0.616716\pi$
$241$	−20.4332	+	18.9593i	−1.31622	+	1.22127i	−0.957706	+	0.287749i	$0.907093\pi$
$242$	−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	0.981858	−	0.189615i	$-0.0607241\pi$
$251$	5.17618	+	8.96540i	0.326717	+	0.565891i	−0.655141	+	0.755507i	$0.727391\pi$
$252$	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	0.623175	−	0.782083i	$-0.285843\pi$
$263$	−1.78636	−	1.65750i	−0.110151	−	0.102206i	−0.733326	+	0.679877i	$0.762033\pi$
$264$	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	0.994190	+	0.107641i	$0.0343298\pi$
$269$	14.3987	+	18.0554i	0.877904	+	1.10086i	−0.116286	+	0.993216i	$0.537099\pi$
$270$	−0.251446	+	3.35531i	−0.0153025	+	0.204198i
$271$	−14.1128	+	4.35322i	−0.857292	+	0.264440i	−0.692082	−	0.721819i	$-0.743306\pi$
$271$	−14.1128	+	4.35322i	−0.857292	+	0.264440i	−0.165210	+	0.986258i	$0.552830\pi$
$272$	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	−0.993024	−	0.117909i	$-0.962381\pi$
$277$	−5.74668	−	14.6423i	−0.345285	−	0.879771i	0.647740	−	0.761862i	$-0.275714\pi$
$278$	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	0.750437	−	0.660942i	$-0.229843\pi$
$281$	27.8661	−	4.20014i	1.66235	−	0.250559i	0.911913	+	0.410382i	$0.134605\pi$
$282$	0.794259	+	2.02374i	0.0472975	+	0.120512i
$283$	1.50008	+	20.0172i	0.0891707	+	1.18990i	0.844866	+	0.534977i	$0.179680\pi$
$283$	1.50008	+	20.0172i	0.0891707	+	1.18990i	−0.755696	+	0.654923i	$0.772701\pi$
$284$	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	−0.810407	−	0.585867i	$-0.800754\pi$
$293$	2.97742	−	13.0449i	0.173942	−	0.762092i	0.984350	−	0.176225i	$-0.0563887\pi$
$294$	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	−0.732327	−	0.680953i	$-0.761566\pi$
$307$	3.91707	−	6.78457i	0.223559	−	0.387216i	0.955886	+	0.293737i	$0.0948991\pi$
$308$	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	0.655298	−	0.755370i	$-0.272543\pi$
$311$	13.6005	+	4.19521i	0.771216	+	0.237889i	0.115918	+	0.993259i	$0.463019\pi$
$312$	0.298214	+	0.373949i	0.0168831	+	0.0211707i
$313$	−1.51871	+	20.2658i	−0.0858426	+	1.14549i	0.773399	+	0.633919i	$0.218555\pi$
$313$	−1.51871	+	20.2658i	−0.0858426	+	1.14549i	−0.859242	+	0.511570i	$0.829064\pi$
$314$	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	−0.853496	−	0.521099i	$-0.825522\pi$
$317$	−5.53042	−	24.2303i	−0.310619	−	1.36091i	0.542877	−	0.839812i	$-0.317335\pi$
$318$	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	−0.656748	−	0.754110i	$-0.728068\pi$
$331$	−14.0921	+	4.34684i	−0.774573	+	0.238924i	−0.117825	+	0.993034i	$0.537592\pi$
$332$	−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	0.991428	−	0.130654i	$-0.0417078\pi$
$337$	7.02294	+	12.1641i	0.382564	+	0.662620i	−0.608864	+	0.793275i	$0.708375\pi$
$338$	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	−0.373252	+	0.927730i	$0.621757\pi$
$347$	−25.5802	+	17.4403i	−1.37322	+	0.936243i	−0.999964	+	0.00851281i	$0.997290\pi$
$348$	−2.69560	+	3.38018i	−0.144499	+	0.181196i
$349$	1.50678	+	1.39809i	0.0806561	+	0.0748379i	0.719471	−	0.694523i	$-0.244384\pi$
$349$	1.50678	+	1.39809i	0.0806561	+	0.0748379i	−0.638815	+	0.769361i	$0.720575\pi$
$350$	−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	−0.516758	−	0.856131i	$-0.672861\pi$
$353$	8.34895	−	21.2728i	0.444370	−	1.13224i	0.961128	−	0.276104i	$-0.0890434\pi$
$354$	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	0.540426	−	0.841392i	$-0.318263\pi$
$359$	15.3253	+	2.30991i	0.808838	+	0.121913i	0.268412	+	0.963304i	$0.413501\pi$
$360$	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	−0.841055	−	0.540950i	$-0.818065\pi$
$367$	−28.4542	+	4.28878i	−1.48530	+	0.223872i	−0.644241	+	0.764822i	$0.722827\pi$
$368$	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	0.693258	−	0.720690i	$-0.256175\pi$
$373$	5.32392	+	3.62979i	0.275662	+	0.187943i	−0.417596	+	0.908633i	$0.637127\pi$
$374$	−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	−0.969922	−	0.243416i	$-0.921732\pi$
$379$	0.186148	−	0.815567i	0.00956177	−	0.0418929i	0.979484	+	0.201523i	$0.0645891\pi$
$380$	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	−0.138948	−	0.990300i	$-0.544372\pi$
$383$	16.7805	−	21.0420i	0.857442	−	1.07520i	0.996390	−	0.0848983i	$-0.0270565\pi$
$384$	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	−0.461517	−	0.887131i	$-0.652695\pi$
$389$	−1.09819	+	0.528861i	−0.0556805	+	0.0268143i	0.405836	+	0.913946i	$0.366980\pi$
$390$	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	0.387196	−	0.921997i	$-0.373444\pi$
$397$	3.74056	+	1.15381i	0.187733	+	0.0579081i	−0.199463	+	0.979905i	$0.563920\pi$
$398$	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	−0.250194	−	0.968196i	$-0.580495\pi$
$401$	−24.8884	−	16.9686i	−1.24287	−	0.847373i	−0.992674	+	0.120822i	$0.961447\pi$
$402$	−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	0.776678	−	0.629898i	$-0.216903\pi$
$409$	15.5410	+	7.48417i	0.768454	+	0.370068i	−0.00822340	+	0.999966i	$0.502618\pi$
$410$	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	−0.995695	−	0.0926869i	$-0.970454\pi$
$419$	−17.6958	−	22.1898i	−0.864495	−	1.08404i	0.131200	−	0.991356i	$-0.458117\pi$
$420$	1.11977	+	0.345405i	0.0546394	+	0.0168540i
$421$	1.66177	−	4.23411i	0.0809895	−	0.206358i	−0.884643	−	0.466269i	$-0.845598\pi$
$421$	1.66177	−	4.23411i	0.0809895	−	0.206358i	0.965633	+	0.259911i	$0.0836932\pi$
$422$	−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	−0.997152	−	0.0754133i	$-0.975972\pi$
$433$	−26.8692	+	18.3191i	−1.29125	+	0.880361i	−0.294100	+	0.955775i	$0.595020\pi$
$434$	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	0.553997	+	0.832519i	$0.313102\pi$
$439$	−8.76578	+	22.3348i	−0.418368	+	1.06598i	−0.972365	+	0.233466i	$0.924993\pi$
$440$	−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	0.119539	−	0.992829i	$-0.461858\pi$
$443$	16.3663	−	5.04835i	0.777588	−	0.239854i	0.658049	+	0.752975i	$0.271382\pi$
$444$	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	0.898113	−	0.439765i	$-0.144938\pi$
$449$	−1.25796	−	3.20523i	−0.0593668	−	0.151264i	−0.957480	+	0.288501i	$0.906843\pi$
$450$	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	−0.818506	−	0.574498i	$-0.805197\pi$
$457$	−7.06150	−	30.9384i	−0.330323	−	1.44724i	0.488183	−	0.872741i	$-0.337660\pi$
$458$	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	−0.971994	−	0.235008i	$-0.924489\pi$
$461$	0.518945	−	6.92484i	0.0241697	−	0.322522i	0.996163	−	0.0875146i	$-0.0278924\pi$
$462$	−4.68140	−	5.87029i	−0.217798	−	0.273111i
$463$	−8.07744	−	2.49156i	−0.375390	−	0.115793i	0.101318	−	0.994854i	$-0.467694\pi$
$463$	−8.07744	−	2.49156i	−0.375390	−	0.115793i	−0.476708	+	0.879061i	$0.658170\pi$
$464$	−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	−0.881861	−	0.471509i	$-0.843710\pi$
$467$	−0.704323	+	1.21992i	−0.0325922	+	0.0564513i	0.849269	+	0.527960i	$0.177043\pi$
$468$	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	0.417166	+	0.908831i	$0.363024\pi$
$479$	−12.6608	+	21.9292i	−0.578488	+	1.00197i	−0.995653	+	0.0931393i	$0.970310\pi$
$480$	−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	0.435940	−	0.899976i	$-0.356416\pi$
$487$	−5.35275	−	3.64944i	−0.242556	−	0.165372i	−0.678497	+	0.734603i	$0.737368\pi$
$488$	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	0.998963	+	0.0455376i	$0.0145001\pi$
$491$	0.397626	+	5.30595i	0.0179446	+	0.239454i	−0.981018	+	0.193917i	$0.937881\pi$
$492$	−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	−0.656094	−	0.754679i	$-0.727793\pi$
$499$	1.05982	−	0.983369i	0.0474440	−	0.0440216i	0.703539	+	0.710657i	$0.251602\pi$
$500$	−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	−0.456805	−	0.889567i	$-0.651006\pi$
$503$	−7.47120	+	2.30456i	−0.333124	+	0.102755i	0.123681	+	0.992322i	$0.460530\pi$
$504$	−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	0.998497	+	0.0548145i	$0.0174568\pi$
$509$	12.3345	+	21.3641i	0.546719	+	0.946945i	−0.451778	+	0.892131i	$0.649210\pi$
$510$	−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	0.995233	+	0.0975280i	$0.0310935\pi$
$521$	26.6341	+	24.7128i	1.16686	+	1.08269i	0.171629	+	0.985162i	$0.445097\pi$
$522$	−9.59091	+	16.6119i	−0.419783	+	0.727085i
$523$	−5.94473	−	10.2966i	−0.259945	−	0.450238i	0.706282	−	0.707931i	$-0.250371\pi$
$523$	−5.94473	−	10.2966i	−0.259945	−	0.450238i	−0.966227	+	0.257693i	$0.917038\pi$
$524$	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	0.997056	−	0.0766703i	$-0.0244289\pi$
$541$	−0.00676431	−	0.0902635i	−0.000290821	−	0.00388073i	−0.997347	+	0.0727896i	$0.976810\pi$
$542$	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	−0.782494	−	0.622658i	$-0.786053\pi$
$547$	1.96606	−	26.2352i	0.0840626	−	1.12174i	0.866556	−	0.499079i	$-0.166328\pi$
$548$	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	−0.175390	−	0.984499i	$-0.556119\pi$
$557$	11.4457	−	5.51195i	0.484969	−	0.233549i	0.660359	+	0.750950i	$0.270404\pi$
$558$	−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	−0.802658	−	0.596440i	$-0.796581\pi$
$563$	−1.00994	+	1.26642i	−0.0425639	+	0.0533734i	0.760094	+	0.649813i	$0.225153\pi$
$564$	−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	−0.207836	−	0.978164i	$-0.566642\pi$
$569$	−22.1977	−	6.84710i	−0.930578	−	0.287045i	−0.722741	+	0.691118i	$0.757118\pi$
$570$	−0.853105	−	1.06976i	−0.0357326	−	0.0448073i
$571$	2.32741	−	31.0571i	0.0973989	−	1.29970i	−0.707681	−	0.706532i	$-0.750259\pi$
$571$	2.32741	−	31.0571i	0.0973989	−	1.29970i	0.805080	−	0.593166i	$-0.202122\pi$
$572$	−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	0.994753	+	0.102310i	$0.0326233\pi$
$577$	0.633166	+	8.44902i	0.0263591	+	0.351737i	−0.968394	+	0.249427i	$0.919758\pi$
$578$	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	−0.220878	−	0.975301i	$-0.570892\pi$
$587$	−17.4301	−	2.62717i	−0.719418	−	0.108435i	−0.498540	+	0.866867i	$0.666130\pi$
$588$	−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	−0.974424	−	0.224716i	$-0.927855\pi$
$593$	−2.61232	+	6.65609i	−0.107275	+	0.273333i	0.867149	+	0.498049i	$0.165950\pi$
$594$	−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	−0.599602	−	0.800298i	$-0.704674\pi$
$599$	−1.80338	+	1.22953i	−0.0736843	+	0.0502371i	0.525918	+	0.850536i	$0.323722\pi$
$600$	−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	−0.0667200	−	0.997772i	$-0.521253\pi$
$607$	−26.2804	−	24.3846i	−1.06669	−	0.989742i	−0.999968	+	0.00803018i	$0.997444\pi$
$608$	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	0.883131	−	0.469127i	$-0.155431\pi$
$613$	5.67597	+	7.11744i	0.229250	+	0.287471i	−0.653880	+	0.756598i	$0.726860\pi$
$614$	−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	−0.150315	−	0.988638i	$-0.548029\pi$
$617$	−14.5400	−	2.19155i	−0.585357	−	0.0882284i	−0.435043	+	0.900410i	$0.643267\pi$
$618$	1.74668	+	7.65272i	0.0702619	+	0.307837i
$619$	−0.141554	+	0.131343i	−0.00568954	+	0.00527912i	−0.683012	−	0.730407i	$-0.739331\pi$
$619$	−0.141554	+	0.131343i	−0.00568954	+	0.00527912i	0.677323	+	0.735686i	$0.263140\pi$
$620$	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	0.104416	−	0.994534i	$-0.466703\pi$
$631$	−19.6743	−	13.4137i	−0.783221	−	0.533991i	−0.887638	+	0.460542i	$0.847655\pi$
$632$	−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	0.0302369	−	0.999543i	$-0.490374\pi$
$641$	25.2671	−	31.6839i	0.997991	−	1.25144i	0.967754	−	0.251898i	$-0.0810547\pi$
$642$	−3.43881	+	2.34454i	−0.135719	+	0.0925317i
$643$	−4.49605	+	2.16518i	−0.177307	+	0.0853865i	−0.520432	−	0.853903i	$-0.674229\pi$
$643$	−4.49605	+	2.16518i	−0.177307	+	0.0853865i	0.343125	+	0.939290i	$0.388515\pi$
$644$	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	0.185864	−	0.982576i	$-0.440492\pi$
$647$	27.2156	−	13.1064i	1.06996	−	0.515264i	0.884093	+	0.467312i	$0.154777\pi$
$648$	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	−0.999901	−	0.0141026i	$-0.995511\pi$
$653$	−2.37402	+	10.4012i	−0.0929024	+	0.407032i	0.906998	+	0.421135i	$0.138368\pi$
$654$	−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	0.880666	−	0.473737i	$-0.157095\pi$
$659$	19.5464	+	13.3265i	0.761421	+	0.519128i	−0.119246	+	0.992865i	$0.538048\pi$
$660$	3.77669	+	0.569244i	0.147007	+	0.0221578i
$661$	6.74768	+	29.5635i	0.262454	+	1.14989i	0.918580	+	0.395236i	$0.129337\pi$
$661$	6.74768	+	29.5635i	0.262454	+	1.14989i	−0.656125	+	0.754652i	$0.727806\pi$
$662$	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	0.752933	−	0.658097i	$-0.228639\pi$
$673$	33.1655	+	4.99890i	1.27844	+	0.192693i	0.525504	+	0.850791i	$0.323877\pi$
$674$	−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	0.669553	−	0.742765i	$-0.266486\pi$
$677$	−5.29696	−	6.64218i	−0.203579	−	0.255280i	−0.873131	+	0.487485i	$0.837914\pi$
$678$	−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	0.994758	−	0.102255i	$-0.0326057\pi$
$683$	25.2752	+	23.4519i	0.967128	+	0.897364i	−0.0276304	+	0.999618i	$0.508796\pi$
$684$	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	−0.885952	−	0.463777i	$-0.846494\pi$
$691$	−20.4488	+	13.9418i	−0.777909	+	0.530370i	0.108043	+	0.994146i	$0.465542\pi$
$692$	−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	0.438137	−	0.898908i	$-0.355638\pi$
$701$	34.5919	−	10.6702i	1.30652	−	0.403007i	0.868379	+	0.495901i	$0.165162\pi$
$702$	−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	−0.0740121	−	0.997257i	$-0.523580\pi$
$709$	−23.9602	−	11.5386i	−0.899845	−	0.433343i	−0.825833	+	0.563915i	$0.809295\pi$
$710$	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	−0.149735	−	0.988726i	$-0.547842\pi$
$719$	3.90655	−	52.1292i	0.145690	−	1.94409i	0.295424	−	0.955366i	$-0.404539\pi$
$720$	−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	−0.258770	+	0.965939i	$0.583317\pi$
$727$	−30.8162	+	38.6423i	−1.14291	+	1.43316i	−0.884139	+	0.467224i	$0.845254\pi$
$728$	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	−0.916209	−	0.400700i	$-0.868767\pi$
$733$	−31.7896	+	15.3091i	−1.17418	+	0.565454i	−0.257968	+	0.966154i	$0.583053\pi$
$734$	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	−0.924067	−	0.382232i	$-0.875156\pi$
$739$	2.02070	−	8.85327i	0.0743327	−	0.325673i	0.998399	+	0.0565587i	$0.0180128\pi$
$740$	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	0.929874	+	0.367878i	$0.119915\pi$
$743$	−1.21144	+	16.1655i	−0.0444434	+	0.593056i	−0.974318	+	0.225178i	$0.927704\pi$
$744$	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	−0.481392	−	0.876505i	$-0.659869\pi$
$751$	−18.7184	+	2.82134i	−0.683043	+	0.102952i	−0.201651	+	0.979457i	$0.564631\pi$
$752$	−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	−0.839072	−	0.544021i	$-0.816901\pi$
$757$	−9.88500	+	9.17194i	−0.359276	+	0.333360i	0.479795	+	0.877380i	$0.340711\pi$
$758$	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	0.407040	−	0.913410i	$-0.366561\pi$
$761$	34.7006	−	10.7037i	1.25789	−	0.388009i	0.850854	+	0.525402i	$0.176085\pi$
$762$	−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	0.947611	−	0.319426i	$-0.103490\pi$
$769$	19.4086	+	18.0086i	0.699894	+	0.649406i	−0.247718	+	0.968832i	$0.579681\pi$
$770$	−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	0.444940	−	0.895560i	$-0.353225\pi$
$787$	36.9480	−	11.3969i	1.31705	−	0.406257i	0.872114	+	0.489303i	$0.162749\pi$
$788$	−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	−0.362461	−	0.931999i	$-0.618063\pi$
$797$	−12.2554	+	1.84720i	−0.434108	+	0.0654312i	−0.0716465	+	0.997430i	$0.522825\pi$
$798$	−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	−0.974390	−	0.224867i	$-0.927805\pi$
$809$	0.0304643	−	0.133473i	0.00107107	−	0.00469265i	0.975461	+	0.220174i	$0.0706625\pi$
$810$	−2.96419	−	5.13412i	−0.104151	−	0.180395i
$811$	−9.65315	+	16.7197i	−0.338968	+	0.587109i	−0.984239	−	0.176844i	$-0.943411\pi$
$811$	−9.65315	+	16.7197i	−0.338968	+	0.587109i	0.645271	+	0.763954i	$0.276744\pi$
$812$	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	−0.158522	−	0.987355i	$-0.550673\pi$
$821$	24.0501	−	30.1578i	0.839353	−	1.05252i	0.997875	−	0.0651597i	$-0.0207557\pi$
$822$	−3.99422	−	3.70610i	−0.139314	−	0.129265i
$823$	−8.87185	+	15.3665i	−0.309253	+	0.535642i	−0.978199	−	0.207669i	$-0.933412\pi$
$823$	−8.87185	+	15.3665i	−0.309253	+	0.535642i	0.668946	+	0.743311i	$0.266746\pi$
$824$	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	0.999888	+	0.0149854i	$0.00477017\pi$
$827$	52.7551	+	16.2728i	1.83448	+	0.565861i	0.834588	+	0.550875i	$0.185706\pi$
$828$	−3.56976	−	4.47633i	−0.124058	−	0.155563i
$829$	0.394285	−	5.26137i	0.0136941	−	0.182735i	−0.986162	−	0.165783i	$-0.946985\pi$
$829$	0.394285	−	5.26137i	0.0136941	−	0.182735i	0.999856	−	0.0169517i	$-0.00539615\pi$
$830$	−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	0.999499	+	0.0316544i	$0.0100776\pi$
$839$	47.7185	+	22.9800i	1.64742	+	0.793358i	0.647926	+	0.761704i	$0.275637\pi$
$840$	−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	0.914078	+	0.405539i	$0.132916\pi$
$853$	23.6058	+	40.8864i	0.808246	+	1.39992i	−0.105831	+	0.994384i	$0.533750\pi$
$854$	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	−0.880485	−	0.474074i	$-0.842783\pi$
$857$	−22.2738	+	15.1860i	−0.760859	+	0.518745i	0.119626	+	0.992819i	$0.461831\pi$
$858$	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	−0.706469	−	0.707744i	$-0.749713\pi$
$863$	−8.98201	+	6.12383i	−0.305751	+	0.208458i	0.400718	+	0.916201i	$0.368761\pi$
$864$	−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	−0.945895	−	0.324473i	$-0.894813\pi$
$877$	−20.5231	+	19.0427i	−0.693016	+	0.643025i	0.252879	+	0.967498i	$0.418623\pi$
$878$	−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	0.733097	−	0.680124i	$-0.238074\pi$
$881$	19.5434	+	9.41158i	0.658432	+	0.317084i	−0.0746643	+	0.997209i	$0.523789\pi$
$882$	−7.47073	−	3.59772i	−0.251553	−	0.121141i
$883$	33.2837	−	5.01672i	1.12009	−	0.168826i	0.437210	−	0.899359i	$-0.355967\pi$
$883$	33.2837	−	5.01672i	1.12009	−	0.168826i	0.682877	+	0.730533i	$0.260729\pi$
$884$	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	0.998162	−	0.0605962i	$-0.0193002\pi$
$887$	2.16095	+	9.46772i	0.0725574	+	0.317895i	−0.925605	+	0.378491i	$0.876443\pi$
$888$	−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	−0.603680	−	0.797227i	$-0.706299\pi$
$907$	9.27256	−	11.6274i	0.307890	−	0.386082i	0.911570	+	0.411145i	$0.134871\pi$
$908$	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	0.700095	+	0.714049i	$0.253141\pi$
$911$	−7.25845	+	31.8013i	−0.240483	+	1.05363i	−0.940579	+	0.339576i	$0.889716\pi$
$912$	−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	−0.844053	−	0.536259i	$-0.819837\pi$
$919$	−9.58748	−	42.0055i	−0.316262	−	1.38563i	0.527792	−	0.849374i	$-0.323020\pi$
$920$	−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	−0.672990	−	0.739651i	$-0.734991\pi$
$929$	0.435851	−	0.404410i	0.0142998	−	0.0132683i	0.687290	+	0.726383i	$0.258800\pi$
$930$	−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	0.579732	+	0.814808i	$0.303157\pi$
$937$	−12.2274	+	31.1549i	−0.399452	+	1.01779i	−0.979183	+	0.202979i	$0.934938\pi$
$938$	−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	0.789777	−	0.613395i	$-0.210196\pi$
$941$	7.27375	+	6.74905i	0.237117	+	0.220013i	−0.552659	+	0.833407i	$0.686387\pi$
$942$	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	0.704537	−	0.709667i	$-0.251155\pi$
$953$	−8.09804	−	14.0262i	−0.262321	−	0.454354i	−0.966858	+	0.255313i	$0.917821\pi$
$954$	−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	−0.324628	−	0.945842i	$-0.605239\pi$
$967$	−39.3845	−	18.9666i	−1.26652	−	0.609923i	−0.941891	+	0.335919i	$0.890953\pi$
$968$	−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	0.880783	+	0.473520i	$0.157017\pi$
$971$	2.50571	+	33.4364i	0.0804121	+	1.07302i	−0.800371	+	0.599505i	$0.795364\pi$
$972$	−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	−0.984863	−	0.173334i	$-0.944546\pi$
$977$	0.463664	−	6.18717i	0.0148339	−	0.197945i	0.999697	−	0.0246114i	$-0.00783485\pi$
$978$	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	−0.850627	−	0.525770i	$-0.823777\pi$
$983$	0.941104	−	1.63004i	0.0300165	−	0.0519902i	0.880643	+	0.473780i	$0.157111\pi$
$984$	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	−0.652087	−	0.758144i	$-0.726106\pi$
$991$	−14.6671	+	7.06330i	−0.465916	+	0.224373i	0.186171	+	0.982517i	$0.440392\pi$
$992$	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	−0.837443	−	0.546525i	$-0.815950\pi$
$997$	4.86877	−	21.3315i	0.154195	−	0.675574i	0.991638	−	0.129049i	$-0.0411925\pi$
$998$	−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.31.3	✓	36
43.25	even	21	inner	430.2.q.a.111.3	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
430.2.q.a.31.3	✓	36	1.1	even	1	trivial
430.2.q.a.111.3	yes	36	43.25	even	21	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:	\( N \)	\(=\)	\( 430 = 2 \cdot 5 \cdot 43 \)
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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Database

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