LMFDB - Embedded newform 98.2.g.a.93.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [98,2,Mod(9,98)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(98, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([2]))

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

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

chi := DirichletCharacter("98.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 98 = 2 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	98.g (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:	$0.782533939809$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$2$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			93.1
Character	$\chi$	$=$	98.93
Dual form			98.2.g.a.39.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.988831 - 0.149042i) q^{2} +(-1.46985 - 1.00212i) q^{3} +(0.955573 - 0.294755i) q^{4} +(0.169008 - 2.25526i) q^{5} +(-1.60279 - 0.771862i) q^{6} +(2.40601 + 1.10050i) q^{7} +(0.900969 - 0.433884i) q^{8} +(0.0601727 + 0.153317i) q^{9} +O(q^{10})$	\(q+(0.988831 - 0.149042i) q^{2} +(-1.46985 - 1.00212i) q^{3} +(0.955573 - 0.294755i) q^{4} +(0.169008 - 2.25526i) q^{5} +(-1.60279 - 0.771862i) q^{6} +(2.40601 + 1.10050i) q^{7} +(0.900969 - 0.433884i) q^{8} +(0.0601727 + 0.153317i) q^{9} +(-0.169008 - 2.25526i) q^{10} +(-2.21901 + 5.65396i) q^{11} +(-1.69993 - 0.524358i) q^{12} +(0.113866 + 0.142784i) q^{13} +(2.54316 + 0.729608i) q^{14} +(-2.50847 + 3.14552i) q^{15} +(0.826239 - 0.563320i) q^{16} +(-3.61347 + 3.35281i) q^{17} +(0.0823514 + 0.142637i) q^{18} +(1.31263 - 2.27355i) q^{19} +(-0.503250 - 2.20488i) q^{20} +(-2.43364 - 4.02869i) q^{21} +(-1.35155 + 5.92153i) q^{22} +(3.05939 + 2.83870i) q^{23} +(-1.75909 - 0.265140i) q^{24} +(-0.113477 - 0.0171038i) q^{25} +(0.133875 + 0.124218i) q^{26} +(-1.12237 + 4.91742i) q^{27} +(2.62350 + 0.342420i) q^{28} +(-2.05900 - 9.02107i) q^{29} +(-2.01163 + 3.48425i) q^{30} +(0.668329 + 1.15758i) q^{31} +(0.733052 - 0.680173i) q^{32} +(8.92758 - 6.08672i) q^{33} +(-3.07340 + 3.85392i) q^{34} +(2.88854 - 5.24019i) q^{35} +(0.102691 + 0.128770i) q^{36} +(2.71766 + 0.838288i) q^{37} +(0.959119 - 2.44379i) q^{38} +(-0.0242788 - 0.323978i) q^{39} +(-0.826249 - 2.10525i) q^{40} +(-0.529812 + 0.255144i) q^{41} +(-3.00690 - 3.62098i) q^{42} +(-7.91285 - 3.81063i) q^{43} +(-0.453897 + 6.05683i) q^{44} +(0.355940 - 0.109793i) q^{45} +(3.44831 + 2.35102i) q^{46} +(-8.72992 + 1.31582i) q^{47} -1.77896 q^{48} +(4.57781 + 5.29562i) q^{49} -0.114758 q^{50} +(8.67118 - 1.30697i) q^{51} +(0.150894 + 0.102878i) q^{52} +(0.187258 - 0.0577613i) q^{53} +(-0.376930 + 5.02978i) q^{54} +(12.3761 + 5.96002i) q^{55} +(2.64523 - 0.0524170i) q^{56} +(-4.20775 + 2.02635i) q^{57} +(-3.38053 - 8.61344i) q^{58} +(-0.873665 - 11.6583i) q^{59} +(-1.46987 + 3.74516i) q^{60} +(-0.523978 - 0.161626i) q^{61} +(0.833393 + 1.04504i) q^{62} +(-0.0239491 + 0.435104i) q^{63} +(0.623490 - 0.781831i) q^{64} +(0.341259 - 0.232666i) q^{65} +(7.92069 - 7.34932i) q^{66} +(-3.83993 - 6.65096i) q^{67} +(-2.46468 + 4.26894i) q^{68} +(-1.65211 - 7.23835i) q^{69} +(2.07527 - 5.61218i) q^{70} +(1.01113 - 4.43005i) q^{71} +(0.120736 + 0.112026i) q^{72} +(7.77715 + 1.17222i) q^{73} +(2.81225 + 0.423878i) q^{74} +(0.149653 + 0.138858i) q^{75} +(0.584177 - 2.55945i) q^{76} +(-11.5611 + 11.1615i) q^{77} +(-0.0722941 - 0.316741i) q^{78} +(0.263203 - 0.455881i) q^{79} +(-1.13079 - 1.95859i) q^{80} +(6.93979 - 6.43918i) q^{81} +(-0.485868 + 0.331259i) q^{82} +(-11.1180 + 13.9415i) q^{83} +(-3.51299 - 3.13238i) q^{84} +(6.95075 + 8.71597i) q^{85} +(-8.39241 - 2.58872i) q^{86} +(-6.01382 + 15.3230i) q^{87} +(0.453897 + 6.05683i) q^{88} +(1.42282 + 3.62529i) q^{89} +(0.335601 - 0.161617i) q^{90} +(0.116831 + 0.468849i) q^{91} +(3.76019 + 1.81081i) q^{92} +(0.177698 - 2.37121i) q^{93} +(-8.43630 + 2.60225i) q^{94} +(-4.90560 - 3.34458i) q^{95} +(-1.75909 + 0.265140i) q^{96} -4.21519 q^{97} +(5.31595 + 4.55419i) q^{98} -1.00037 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 2 q^{2} + 7 q^{3} + 2 q^{4} - 7 q^{6} + 4 q^{8} - 33 q^{9}+O(q^{10}) $ 24 * q - 2 * q^2 + 7 * q^3 + 2 * q^4 - 7 * q^6 + 4 * q^8 - 33 * q^9	$ 24 q - 2 q^{2} + 7 q^{3} + 2 q^{4} - 7 q^{6} + 4 q^{8} - 33 q^{9} - 7 q^{11} + 14 q^{13} - 7 q^{15} + 2 q^{16} - 7 q^{17} + 5 q^{18} - 7 q^{20} + 7 q^{21} - 7 q^{22} - 21 q^{23} + 4 q^{25} - 7 q^{26} - 35 q^{27} - 14 q^{28} - 11 q^{29} + 28 q^{31} - 2 q^{32} + 14 q^{33} + 7 q^{34} + 21 q^{35} + 3 q^{36} - 24 q^{37} - 7 q^{38} - 40 q^{39} + 14 q^{40} + 28 q^{41} - 21 q^{42} + 10 q^{43} + 21 q^{44} + 7 q^{45} + 42 q^{46} - 70 q^{47} - 14 q^{48} + 84 q^{49} + 8 q^{50} + 60 q^{51} - 7 q^{52} + 26 q^{53} + 63 q^{54} + 56 q^{55} + 21 q^{56} - 33 q^{57} - 30 q^{58} - 7 q^{59} + 14 q^{60} + 14 q^{61} + 28 q^{62} - 14 q^{63} - 4 q^{64} - 21 q^{66} - 36 q^{67} - 14 q^{68} - 35 q^{69} + 14 q^{70} - 2 q^{72} - 7 q^{73} - 11 q^{74} - 28 q^{75} - 91 q^{77} - 24 q^{78} - 26 q^{79} + 55 q^{81} + 14 q^{82} - 7 q^{83} - 21 q^{84} + 49 q^{85} - 16 q^{86} + 35 q^{87} - 21 q^{88} - 56 q^{89} - 21 q^{90} + 7 q^{91} + 21 q^{92} + 72 q^{93} - 35 q^{94} - 14 q^{95} - 126 q^{97} - 56 q^{98} - 14 q^{99}+O(q^{100}) $ 24 * q - 2 * q^2 + 7 * q^3 + 2 * q^4 - 7 * q^6 + 4 * q^8 - 33 * q^9 - 7 * q^11 + 14 * q^13 - 7 * q^15 + 2 * q^16 - 7 * q^17 + 5 * q^18 - 7 * q^20 + 7 * q^21 - 7 * q^22 - 21 * q^23 + 4 * q^25 - 7 * q^26 - 35 * q^27 - 14 * q^28 - 11 * q^29 + 28 * q^31 - 2 * q^32 + 14 * q^33 + 7 * q^34 + 21 * q^35 + 3 * q^36 - 24 * q^37 - 7 * q^38 - 40 * q^39 + 14 * q^40 + 28 * q^41 - 21 * q^42 + 10 * q^43 + 21 * q^44 + 7 * q^45 + 42 * q^46 - 70 * q^47 - 14 * q^48 + 84 * q^49 + 8 * q^50 + 60 * q^51 - 7 * q^52 + 26 * q^53 + 63 * q^54 + 56 * q^55 + 21 * q^56 - 33 * q^57 - 30 * q^58 - 7 * q^59 + 14 * q^60 + 14 * q^61 + 28 * q^62 - 14 * q^63 - 4 * q^64 - 21 * q^66 - 36 * q^67 - 14 * q^68 - 35 * q^69 + 14 * q^70 - 2 * q^72 - 7 * q^73 - 11 * q^74 - 28 * q^75 - 91 * q^77 - 24 * q^78 - 26 * q^79 + 55 * q^81 + 14 * q^82 - 7 * q^83 - 21 * q^84 + 49 * q^85 - 16 * q^86 + 35 * q^87 - 21 * q^88 - 56 * q^89 - 21 * q^90 + 7 * q^91 + 21 * q^92 + 72 * q^93 - 35 * q^94 - 14 * q^95 - 126 * q^97 - 56 * q^98 - 14 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/98\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{4}{21}\right)$

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 $

$2$	0.988831	−	0.149042i	0.699209	−	0.105389i
$2$	0.988831	−	0.149042i	0.699209	−	0.105389i
$3$	−1.46985	−	1.00212i	−0.848616	−	0.578577i	0.0590568	−	0.998255i	$-0.481191\pi$
$3$	−1.46985	−	1.00212i	−0.848616	−	0.578577i	−0.907673	+	0.419678i	$0.862143\pi$
$4$	0.955573	−	0.294755i	0.477786	−	0.147378i
$5$	0.169008	−	2.25526i	0.0755828	−	1.00858i	−0.822503	−	0.568761i	$-0.807423\pi$
$5$	0.169008	−	2.25526i	0.0755828	−	1.00858i	0.898085	−	0.439821i	$-0.144958\pi$
$6$	−1.60279	−	0.771862i	−0.654336	−	0.315111i
$7$	2.40601	+	1.10050i	0.909388	+	0.415949i
$7$	2.40601	+	1.10050i	0.909388	+	0.415949i
$8$	0.900969	−	0.433884i	0.318541	−	0.153401i
$9$	0.0601727	+	0.153317i	0.0200576	+	0.0511058i
$10$	−0.169008	−	2.25526i	−0.0534451	−	0.713176i
$11$	−2.21901	+	5.65396i	−0.669058	+	1.70473i	0.0396341	+	0.999214i	$0.487381\pi$
$11$	−2.21901	+	5.65396i	−0.669058	+	1.70473i	−0.708692	+	0.705518i	$0.750714\pi$
$12$	−1.69993	−	0.524358i	−0.490727	−	0.151369i
$13$	0.113866	+	0.142784i	0.0315808	+	0.0396011i	0.797371	−	0.603489i	$-0.206223\pi$
$13$	0.113866	+	0.142784i	0.0315808	+	0.0396011i	−0.765790	+	0.643090i	$0.777652\pi$
$14$	2.54316	+	0.729608i	0.679689	+	0.194996i
$15$	−2.50847	+	3.14552i	−0.647683	+	0.812169i
$16$	0.826239	−	0.563320i	0.206560	−	0.140830i
$17$	−3.61347	+	3.35281i	−0.876395	+	0.813176i	−0.983469	−	0.181075i	$-0.942042\pi$
$17$	−3.61347	+	3.35281i	−0.876395	+	0.813176i	0.107074	+	0.994251i	$0.465852\pi$
$18$	0.0823514	+	0.142637i	0.0194104	+	0.0336198i
$19$	1.31263	−	2.27355i	0.301139	−	0.521588i	−0.675255	−	0.737584i	$-0.735966\pi$
$19$	1.31263	−	2.27355i	0.301139	−	0.521588i	0.976394	+	0.215996i	$0.0692998\pi$
$20$	−0.503250	−	2.20488i	−0.112530	−	0.493026i
$21$	−2.43364	−	4.02869i	−0.531063	−	0.879132i
$22$	−1.35155	+	5.92153i	−0.288152	+	1.26248i
$23$	3.05939	+	2.83870i	0.637927	+	0.591910i	0.931373	−	0.364066i	$-0.118612\pi$
$23$	3.05939	+	2.83870i	0.637927	+	0.591910i	−0.293446	+	0.955976i	$0.594802\pi$
$24$	−1.75909	−	0.265140i	−0.359073	−	0.0541216i
$25$	−0.113477	−	0.0171038i	−0.0226953	−	0.00342077i
$26$	0.133875	+	0.124218i	0.0262551	+	0.0243612i
$27$	−1.12237	+	4.91742i	−0.216000	+	0.946358i
$28$	2.62350	+	0.342420i	0.495795	+	0.0647113i
$29$	−2.05900	−	9.02107i	−0.382347	−	1.67517i	−0.690107	−	0.723707i	$-0.742437\pi$
$29$	−2.05900	−	9.02107i	−0.382347	−	1.67517i	0.307760	−	0.951464i	$-0.400421\pi$
$30$	−2.01163	+	3.48425i	−0.367272	+	0.636135i
$31$	0.668329	+	1.15758i	0.120035	+	0.207907i	0.919781	−	0.392431i	$-0.128366\pi$
$31$	0.668329	+	1.15758i	0.120035	+	0.207907i	−0.799746	+	0.600339i	$0.795033\pi$
$32$	0.733052	−	0.680173i	0.129586	−	0.120239i
$33$	8.92758	−	6.08672i	1.55409	−	1.05956i
$34$	−3.07340	+	3.85392i	−0.527084	+	0.660942i
$35$	2.88854	−	5.24019i	0.488253	−	0.885754i
$36$	0.102691	+	0.128770i	0.0171151	+	0.0214616i
$37$	2.71766	+	0.838288i	0.446781	+	0.137814i	0.509978	−	0.860187i	$-0.329654\pi$
$37$	2.71766	+	0.838288i	0.446781	+	0.137814i	−0.0631972	+	0.998001i	$0.520130\pi$
$38$	0.959119	−	2.44379i	0.155590	−	0.396436i
$39$	−0.0242788	−	0.323978i	−0.00388772	−	0.0518781i
$40$	−0.826249	−	2.10525i	−0.130641	−	0.332869i
$41$	−0.529812	+	0.255144i	−0.0827428	+	0.0398468i	−0.474797	−	0.880095i	$-0.657479\pi$
$41$	−0.529812	+	0.255144i	−0.0827428	+	0.0398468i	0.392055	+	0.919942i	$0.371764\pi$
$42$	−3.00690	−	3.62098i	−0.463975	−	0.558729i
$43$	−7.91285	−	3.81063i	−1.20670	−	0.581115i	−0.281120	−	0.959673i	$-0.590706\pi$
$43$	−7.91285	−	3.81063i	−1.20670	−	0.581115i	−0.925578	+	0.378558i	$0.876420\pi$
$44$	−0.453897	+	6.05683i	−0.0684275	+	0.913102i
$45$	0.355940	−	0.109793i	0.0530605	−	0.0163670i
$46$	3.44831	+	2.35102i	0.508425	+	0.346638i
$47$	−8.72992	+	1.31582i	−1.27339	+	0.191933i	−0.750730	−	0.660609i	$-0.770298\pi$
$47$	−8.72992	+	1.31582i	−1.27339	+	0.191933i	−0.522659	+	0.852542i	$0.675060\pi$
$48$	−1.77896			−0.256771
$49$	4.57781	+	5.29562i	0.653973	+	0.756518i
$50$	−0.114758			−0.0162293
$51$	8.67118	−	1.30697i	1.21421	−	0.183012i
$52$	0.150894	+	0.102878i	0.0209252	+	0.0142666i
$53$	0.187258	−	0.0577613i	0.0257218	−	0.00793413i	−0.281868	−	0.959453i	$-0.590954\pi$
$53$	0.187258	−	0.0577613i	0.0257218	−	0.00793413i	0.307589	+	0.951519i	$0.400478\pi$
$54$	−0.376930	+	5.02978i	−0.0512937	+	0.684466i
$55$	12.3761	+	5.96002i	1.66879	+	0.803649i
$56$	2.64523	−	0.0524170i	0.353484	−	0.00700452i
$57$	−4.20775	+	2.02635i	−0.557330	+	0.268396i
$58$	−3.38053	−	8.61344i	−0.443885	−	1.13100i
$59$	−0.873665	−	11.6583i	−0.113742	−	1.51778i	−0.703790	−	0.710408i	$-0.748511\pi$
$59$	−0.873665	−	11.6583i	−0.113742	−	1.51778i	0.590049	−	0.807368i	$-0.299109\pi$
$60$	−1.46987	+	3.74516i	−0.189759	+	0.483497i
$61$	−0.523978	−	0.161626i	−0.0670885	−	0.0206941i	0.261029	−	0.965331i	$-0.415938\pi$
$61$	−0.523978	−	0.161626i	−0.0670885	−	0.0206941i	−0.328118	+	0.944637i	$0.606414\pi$
$62$	0.833393	+	1.04504i	0.105841	+	0.132720i
$63$	−0.0239491	+	0.435104i	−0.00301730	+	0.0548180i
$64$	0.623490	−	0.781831i	0.0779362	−	0.0977289i
$65$	0.341259	−	0.232666i	0.0423279	−	0.0288587i
$66$	7.92069	−	7.34932i	0.974969	−	0.904639i
$67$	−3.83993	−	6.65096i	−0.469123	−	0.812544i	0.530254	−	0.847839i	$-0.322096\pi$
$67$	−3.83993	−	6.65096i	−0.469123	−	0.812544i	−0.999377	+	0.0352944i	$0.988763\pi$
$68$	−2.46468	+	4.26894i	−0.298886	+	0.517685i
$69$	−1.65211	−	7.23835i	−0.198890	−	0.871395i
$70$	2.07527	−	5.61218i	0.248042	−	0.670784i
$71$	1.01113	−	4.43005i	0.119999	−	0.525750i	−0.878820	−	0.477154i	$-0.841668\pi$
$71$	1.01113	−	4.43005i	0.119999	−	0.525750i	0.998819	−	0.0485956i	$-0.0154746\pi$
$72$	0.120736	+	0.112026i	0.0142288	+	0.0132024i
$73$	7.77715	+	1.17222i	0.910246	+	0.137198i	0.587440	−	0.809268i	$-0.300136\pi$
$73$	7.77715	+	1.17222i	0.910246	+	0.137198i	0.322806	+	0.946465i	$0.395374\pi$
$74$	2.81225	+	0.423878i	0.326917	+	0.0492748i
$75$	0.149653	+	0.138858i	0.0172804	+	0.0160339i
$76$	0.584177	−	2.55945i	0.0670098	−	0.293589i
$77$	−11.5611	+	11.1615i	−1.31751	+	1.27197i
$78$	−0.0722941	−	0.316741i	−0.00818570	−	0.0358639i
$79$	0.263203	−	0.455881i	0.0296127	−	0.0512906i	−0.850839	−	0.525426i	$-0.823906\pi$
$79$	0.263203	−	0.455881i	0.0296127	−	0.0512906i	0.880452	+	0.474135i	$0.157239\pi$
$80$	−1.13079	−	1.95859i	−0.126426	−	0.218977i
$81$	6.93979	−	6.43918i	0.771088	−	0.715465i
$82$	−0.485868	+	0.331259i	−0.0536551	+	0.0365814i
$83$	−11.1180	+	13.9415i	−1.22035	+	1.53028i	−0.449476	+	0.893293i	$0.648389\pi$
$83$	−11.1180	+	13.9415i	−1.22035	+	1.53028i	−0.770878	+	0.636983i	$0.780182\pi$
$84$	−3.51299	−	3.13238i	−0.383299	−	0.341770i
$85$	6.95075	+	8.71597i	0.753915	+	0.945379i
$86$	−8.39241	−	2.58872i	−0.904977	−	0.279148i
$87$	−6.01382	+	15.3230i	−0.644750	+	1.64280i
$88$	0.453897	+	6.05683i	0.0483856	+	0.645661i
$89$	1.42282	+	3.62529i	0.150819	+	0.384280i	0.986238	−	0.165334i	$-0.0528701\pi$
$89$	1.42282	+	3.62529i	0.150819	+	0.384280i	−0.835419	+	0.549614i	$0.814775\pi$
$90$	0.335601	−	0.161617i	0.0353755	−	0.0170359i
$91$	0.116831	+	0.468849i	0.0122472	+	0.0491488i
$92$	3.76019	+	1.81081i	0.392027	+	0.188790i
$93$	0.177698	−	2.37121i	0.0184264	−	0.245883i
$94$	−8.43630	+	2.60225i	−0.870138	+	0.268402i
$95$	−4.90560	−	3.34458i	−0.503304	−	0.343147i
$96$	−1.75909	+	0.265140i	−0.179537	+	0.0270608i
$97$	−4.21519			−0.427988			−0.213994	−	0.976835i	$-0.568647\pi$
$97$	−4.21519			−0.427988			−0.213994	+	0.976835i	$0.568647\pi$
$98$	5.31595	+	4.55419i	0.536992	+	0.460043i
$99$	−1.00037			−0.100541
$100$	−0.113477	+	0.0171038i	−0.0113477	+	0.00171038i
$101$	−0.872265	−	0.594700i	−0.0867937	−	0.0591749i	0.519146	−	0.854686i	$-0.326250\pi$
$101$	−0.872265	−	0.594700i	−0.0867937	−	0.0591749i	−0.605939	+	0.795511i	$0.707203\pi$
$102$	8.37954	−	2.58474i	0.829698	−	0.255928i
$103$	−0.472419	+	6.30399i	−0.0465488	+	0.621151i	0.924332	+	0.381589i	$0.124623\pi$
$103$	−0.472419	+	6.30399i	−0.0465488	+	0.621151i	−0.970881	+	0.239562i	$0.922996\pi$
$104$	0.164541	+	0.0792390i	0.0161346	+	0.00777002i
$105$	−9.49704	+	4.80760i	−0.926816	+	0.469174i
$106$	0.176557	−	0.0850255i	0.0171488	−	0.00825840i
$107$	0.0340972	+	0.0868783i	0.00329630	+	0.00839884i	0.932512	−	0.361138i	$-0.117612\pi$
$107$	0.0340972	+	0.0868783i	0.00329630	+	0.00839884i	−0.929216	+	0.369537i	$0.879516\pi$
$108$	0.376930	+	5.02978i	0.0362701	+	0.483991i
$109$	−6.13600	+	15.6343i	−0.587722	+	1.49749i	0.259227	+	0.965817i	$0.416532\pi$
$109$	−6.13600	+	15.6343i	−0.587722	+	1.49749i	−0.846949	+	0.531675i	$0.821563\pi$
$110$	13.1262	+	4.04889i	1.25153	+	0.386046i
$111$	−3.15448	−	3.95559i	−0.299410	−	0.375448i
$112$	2.60787	−	0.446083i	0.246421	−	0.0421509i
$113$	6.28669	−	7.88326i	0.591402	−	0.741594i	−0.392609	−	0.919706i	$-0.628427\pi$
$113$	6.28669	−	7.88326i	0.591402	−	0.741594i	0.984010	+	0.178111i	$0.0569987\pi$
$114$	−3.85874	+	2.63085i	−0.361404	+	0.246401i
$115$	6.91907	−	6.41996i	0.645207	−	0.598664i
$116$	−4.62653	−	8.01339i	−0.429563	−	0.744025i
$117$	−0.0150396	+	0.0260494i	−0.00139041	+	0.00240826i
$118$	−2.60148	−	11.3978i	−0.239486	−	1.04926i
$119$	−12.3838	+	4.09030i	−1.13522	+	0.374957i
$120$	−0.895261	+	3.92240i	−0.0817258	+	0.358064i
$121$	−18.9796	−	17.6105i	−1.72542	−	1.60096i
$122$	−0.542215	−	0.0817257i	−0.0490898	−	0.00739910i
$123$	1.03443	+	0.155915i	0.0932713	+	0.0140584i
$124$	0.979840	+	0.909158i	0.0879922	+	0.0816448i
$125$	2.45850	−	10.7714i	0.219895	−	0.963421i
$126$	0.0411673	+	0.433814i	0.00366747	+	0.0386472i
$127$	1.90411	+	8.34245i	0.168963	+	0.740273i	0.986414	+	0.164276i	$0.0525288\pi$
$127$	1.90411	+	8.34245i	0.168963	+	0.740273i	−0.817452	+	0.575997i	$0.804614\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	7.81195	+	13.5307i	0.687804	+	1.19131i
$130$	0.302770	−	0.280930i	0.0265547	−	0.0246391i
$131$	15.3114	−	10.4391i	1.33776	−	0.912073i	0.338185	−	0.941079i	$-0.390187\pi$
$131$	15.3114	−	10.4391i	1.33776	−	0.912073i	0.999579	+	0.0290069i	$0.00923449\pi$
$132$	6.73686	−	8.44776i	0.586368	−	0.735283i
$133$	5.66025	−	4.02564i	0.490806	−	0.349068i
$134$	−4.78832	−	6.00436i	−0.413648	−	0.518698i
$135$	10.9004	+	3.36232i	0.938155	+	0.289382i
$136$	−1.80089	+	4.58860i	−0.154425	+	0.393470i
$137$	−0.113219	−	1.51080i	−0.00967295	−	0.129077i	0.990277	−	0.139112i	$-0.0444247\pi$
$137$	−0.113219	−	1.51080i	−0.00967295	−	0.129077i	−0.999950	+	0.0100351i	$0.996806\pi$
$138$	−2.71247	−	6.91127i	−0.230901	−	0.588326i
$139$	18.7040	−	9.00739i	1.58646	−	0.763997i	0.587480	−	0.809239i	$-0.300120\pi$
$139$	18.7040	−	9.00739i	1.58646	−	0.763997i	0.998976	+	0.0452418i	$0.0144058\pi$
$140$	1.21564	−	5.85880i	0.102740	−	0.495159i
$141$	14.1503	+	6.81441i	1.19167	+	0.573877i
$142$	0.339572	−	4.53127i	0.0284962	−	0.380256i
$143$	−1.05996	+	0.326956i	−0.0886386	+	0.0273414i
$144$	0.136084	+	0.0927804i	0.0113403	+	0.00773170i
$145$	−20.6929	+	3.11895i	−1.71845	+	0.259014i
$146$	7.86499			0.650912
$147$	−1.42181	−	12.3713i	−0.117269	−	1.02037i
$148$	2.84401			0.233776
$149$	−4.33550	+	0.653471i	−0.355178	+	0.0535345i	−0.324208	−	0.945986i	$-0.605098\pi$
$149$	−4.33550	+	0.653471i	−0.355178	+	0.0535345i	−0.0309700	+	0.999520i	$0.509860\pi$
$150$	0.168677	+	0.115002i	0.0137724	+	0.00938989i
$151$	12.1837	−	3.75816i	0.991492	−	0.305835i	0.243760	−	0.969836i	$-0.421619\pi$
$151$	12.1837	−	3.75816i	0.991492	−	0.305835i	0.747732	+	0.664001i	$0.231143\pi$
$152$	0.196187	−	2.61793i	0.0159128	−	0.212342i
$153$	−0.731477	−	0.352261i	−0.0591364	−	0.0284786i
$154$	−9.76848	+	12.7599i	−0.787167	+	1.02822i
$155$	2.72360	−	1.31161i	0.218764	−	0.105351i
$156$	−0.118694	−	0.302429i	−0.00950316	−	0.0242137i
$157$	0.564354	+	7.53079i	0.0450404	+	0.601022i	0.973366	+	0.229255i	$0.0736290\pi$
$157$	0.564354	+	7.53079i	0.0450404	+	0.601022i	−0.928326	+	0.371767i	$0.878752\pi$
$158$	0.192318	−	0.490018i	0.0153000	−	0.0389837i
$159$	−0.333124	−	0.102755i	−0.0264185	−	0.00814901i
$160$	−1.41007	−	1.76818i	−0.111476	−	0.139787i
$161$	4.23696	+	10.1968i	0.333919	+	0.803621i
$162$	5.90257	−	7.40158i	0.463749	−	0.581523i
$163$	−1.23172	+	0.839774i	−0.0964760	+	0.0657762i	−0.610597	−	0.791941i	$-0.709071\pi$
$163$	−1.23172	+	0.839774i	−0.0964760	+	0.0657762i	0.514121	+	0.857718i	$0.328118\pi$
$164$	−0.431069	+	0.399974i	−0.0336609	+	0.0312327i
$165$	−12.2183	−	21.1627i	−0.951193	−	1.64752i
$166$	−8.91591	+	15.4428i	−0.692008	+	1.19859i
$167$	−0.557147	−	2.44102i	−0.0431133	−	0.188892i	0.948786	−	0.315920i	$-0.102313\pi$
$167$	−0.557147	−	2.44102i	−0.0431133	−	0.188892i	−0.991899	+	0.127028i	$0.959456\pi$
$168$	−3.94061	−	2.57381i	−0.304025	−	0.198574i
$169$	2.88535	−	12.6415i	0.221950	−	0.972427i
$170$	8.17216	+	7.58266i	0.626776	+	0.581563i
$171$	0.427560	+	0.0644443i	0.0326963	+	0.00492818i
$172$	−8.68450	−	1.30898i	−0.662187	−	0.0998086i
$173$	16.3996	+	15.2166i	1.24684	+	1.15690i	0.981234	+	0.192819i	$0.0617631\pi$
$173$	16.3996	+	15.2166i	1.24684	+	1.15690i	0.265608	+	0.964081i	$0.414427\pi$
$174$	−3.66288	+	16.0481i	−0.277682	+	1.21661i
$175$	−0.254204	−	0.166033i	−0.0192160	−	0.0125509i
$176$	1.35155	+	5.92153i	0.101877	+	0.446352i
$177$	−10.3989	+	18.0114i	−0.781627	+	1.35382i
$178$	1.94725	+	3.37274i	0.145953	+	0.252797i
$179$	0.535212	−	0.496604i	0.0400036	−	0.0371179i	−0.659918	−	0.751338i	$-0.729409\pi$
$179$	0.535212	−	0.496604i	0.0400036	−	0.0371179i	0.699921	+	0.714220i	$0.253218\pi$
$180$	0.307765	−	0.209831i	0.0229394	−	0.0156398i
$181$	8.38691	−	10.5168i	0.623394	−	0.781711i	−0.365424	−	0.930841i	$-0.619076\pi$
$181$	8.38691	−	10.5168i	0.623394	−	0.781711i	0.988818	+	0.149130i	$0.0476473\pi$
$182$	0.185404	+	0.446200i	0.0137431	+	0.0330745i
$183$	0.608198	+	0.762656i	0.0449593	+	0.0563772i
$184$	3.98808	+	1.23016i	0.294005	+	0.0906887i
$185$	2.34986	−	5.98735i	0.172765	−	0.440199i
$186$	−0.177698	−	2.37121i	−0.0130294	−	0.173866i
$187$	−10.9383	−	27.8703i	−0.799888	−	2.03808i
$188$	−7.95423	+	3.83055i	−0.580122	+	0.279372i
$189$	−8.11205	+	10.5962i	−0.590065	+	0.770762i
$190$	−5.34929	−	2.57608i	−0.388078	−	0.186889i
$191$	−0.384938	+	5.13664i	−0.0278531	+	0.371674i	0.965808	+	0.259258i	$0.0834781\pi$
$191$	−0.384938	+	5.13664i	−0.0278531	+	0.371674i	−0.993661	+	0.112416i	$0.964141\pi$
$192$	−1.69993	+	0.524358i	−0.122682	+	0.0378423i
$193$	−16.2726	−	11.0945i	−1.17133	−	0.798599i	−0.188312	−	0.982109i	$-0.560301\pi$
$193$	−16.2726	−	11.0945i	−1.17133	−	0.798599i	−0.983018	+	0.183510i	$0.941254\pi$
$194$	−4.16811	+	0.628241i	−0.299253	+	0.0451051i
$195$	−0.734758			−0.0526171
$196$	5.93535	+	3.71102i	0.423953	+	0.265073i
$197$	20.1088			1.43270			0.716348	−	0.697743i	$-0.245812\pi$
$197$	20.1088			1.43270			0.716348	+	0.697743i	$0.245812\pi$
$198$	−0.989201	+	0.149098i	−0.0702995	+	0.0105959i
$199$	−14.5537	−	9.92254i	−1.03168	−	0.703390i	−0.0757964	−	0.997123i	$-0.524150\pi$
$199$	−14.5537	−	9.92254i	−1.03168	−	0.703390i	−0.955887	+	0.293733i	$0.905102\pi$
$200$	−0.109660	+	0.0338256i	−0.00775413	+	0.00239183i
$201$	−1.02098	+	13.6240i	−0.0720141	+	0.960962i
$202$	−0.951158	−	0.458054i	−0.0669233	−	0.0322286i
$203$	4.97368	−	23.9708i	0.349084	−	1.68242i
$204$	7.90071	−	3.80478i	0.553160	−	0.266388i
$205$	0.485874	+	1.23799i	0.0339349	+	0.0864647i
$206$	0.472419	+	6.30399i	0.0329150	+	0.439220i
$207$	−0.251131	+	0.639871i	−0.0174548	+	0.0444741i
$208$	0.174514	+	0.0538303i	0.0121003	+	0.00373246i
$209$	9.94180	+	12.4666i	0.687689	+	0.862334i
$210$	−8.67443	+	6.16937i	−0.598593	+	0.425727i
$211$	−10.9154	+	13.6875i	−0.751450	+	0.942289i	−0.999651	−	0.0264196i	$-0.991589\pi$
$211$	−10.9154	+	13.6875i	−0.751450	+	0.942289i	0.248200	+	0.968709i	$0.420161\pi$
$212$	0.161913	−	0.110390i	0.0111202	−	0.00758164i
$213$	−5.92566	+	5.49821i	−0.406020	+	0.376731i
$214$	0.0466649	+	0.0808260i	0.00318995	+	0.00552515i
$215$	−9.93129	+	17.2015i	−0.677308	+	1.17313i
$216$	1.12237	+	4.91742i	0.0763676	+	0.334588i
$217$	0.334096	+	3.52065i	0.0226799	+	0.238997i
$218$	−3.73730	+	16.3742i	−0.253122	+	1.10900i
$219$	−10.2565	−	9.51665i	−0.693071	−	0.643076i
$220$	13.5830	+	2.04731i	0.915767	+	0.138030i
$221$	−0.890179	−	0.134173i	−0.0598799	−	0.00902545i
$222$	−3.70879	−	3.44126i	−0.248918	−	0.230962i
$223$	0.0525690	−	0.230320i	0.00352028	−	0.0154233i	−0.973137	−	0.230226i	$-0.926054\pi$
$223$	0.0525690	−	0.230320i	0.00352028	−	0.0154233i	0.976658	+	0.214802i	$0.0689107\pi$
$224$	2.51226	−	0.829784i	0.167858	−	0.0554423i
$225$	−0.00420587	−	0.0184271i	−0.000280392	−	0.00122848i
$226$	5.04153	−	8.73219i	0.335358	−	0.580857i
$227$	7.67581	+	13.2949i	0.509461	+	0.882413i	0.999940	+	0.0109598i	$0.00348869\pi$
$227$	7.67581	+	13.2949i	0.509461	+	0.882413i	−0.490478	+	0.871453i	$0.663178\pi$
$228$	−3.42354	+	3.17658i	−0.226729	+	0.210374i
$229$	−17.4134	+	11.8723i	−1.15071	+	0.784541i	−0.979649	−	0.200719i	$-0.935672\pi$
$229$	−17.4134	+	11.8723i	−1.15071	+	0.784541i	−0.171062	+	0.985260i	$0.554720\pi$
$230$	5.88494	−	7.37949i	0.388042	−	0.486589i
$231$	28.1783	−	4.81996i	1.85400	−	0.317130i
$232$	−5.76919	−	7.23434i	−0.378766	−	0.474958i
$233$	−4.73312	−	1.45997i	−0.310077	−	0.0956460i	0.135811	−	0.990735i	$-0.456636\pi$
$233$	−4.73312	−	1.45997i	−0.310077	−	0.0956460i	−0.445888	+	0.895089i	$0.647112\pi$
$234$	−0.0109892	+	0.0280000i	−0.000718385	+	0.00183041i
$235$	1.49209	+	19.9106i	0.0973335	+	1.29883i
$236$	−4.27118	−	10.8828i	−0.278030	−	0.708410i
$237$	−0.843718	+	0.406313i	−0.0548053	+	0.0263929i
$238$	−11.6359	+	5.89032i	−0.754242	+	0.381813i
$239$	−10.5775	−	5.09386i	−0.684202	−	0.329494i	0.0592885	−	0.998241i	$-0.481117\pi$
$239$	−10.5775	−	5.09386i	−0.684202	−	0.329494i	−0.743490	+	0.668747i	$0.766831\pi$
$240$	−0.300659	+	4.01202i	−0.0194075	+	0.258975i
$241$	8.73373	−	2.69400i	0.562589	−	0.173536i	−0.000400347	−	1.00000i	$-0.500127\pi$
$241$	8.73373	−	2.69400i	0.562589	−	0.173536i	0.562989	+	0.826464i	$0.309651\pi$
$242$	−21.3924	−	14.5851i	−1.37515	−	0.937563i
$243$	−1.69064	+	0.254824i	−0.108455	+	0.0163469i
$244$	−0.548339			−0.0351038
$245$	12.7167	−	9.42915i	0.812440	−	0.602406i
$246$	1.04611			0.0666978
$247$	0.474091	−	0.0714577i	0.0301657	−	0.00454674i
$248$	1.10440	+	0.752966i	0.0701294	+	0.0478134i
$249$	30.3128	−	9.35025i	1.92099	−	0.592548i
$250$	0.825646	−	11.0175i	0.0522185	−	0.696807i
$251$	−20.8555	−	10.0435i	−1.31639	−	0.633938i	−0.361907	−	0.932214i	$-0.617874\pi$
$251$	−20.8555	−	10.0435i	−1.31639	−	0.633938i	−0.954480	+	0.298276i	$0.903588\pi$
$252$	0.105364	+	0.422833i	0.00663731	+	0.0266360i
$253$	−22.8387	+	10.9986i	−1.43586	+	0.691473i
$254$	3.12622	+	7.96548i	0.196157	+	0.499799i
$255$	−1.48205	−	19.7766i	−0.0928099	−	1.23846i
$256$	0.365341	−	0.930874i	0.0228338	−	0.0581796i
$257$	16.7440	+	5.16483i	1.04446	+	0.322173i	0.769074	−	0.639160i	$-0.220718\pi$
$257$	16.7440	+	5.16483i	1.04446	+	0.322173i	0.275387	+	0.961334i	$0.411194\pi$
$258$	9.74134	+	12.2153i	0.606469	+	0.760489i
$259$	5.61620	+	5.00771i	0.348974	+	0.311164i
$260$	0.257518	−	0.322917i	0.0159706	−	0.0200265i
$261$	1.25919	−	0.858503i	0.0779421	−	0.0531400i
$262$	13.5845	−	12.6046i	0.839255	−	0.778715i
$263$	8.96724	+	15.5317i	0.552944	+	0.957726i	0.998060	+	0.0622539i	$0.0198288\pi$
$263$	8.96724	+	15.5317i	0.552944	+	0.957726i	−0.445117	+	0.895473i	$0.646838\pi$
$264$	5.40254	−	9.35748i	0.332503	−	0.575913i
$265$	−0.0986187	−	0.432077i	−0.00605810	−	0.0265423i
$266$	4.99704	−	4.82430i	0.306388	−	0.295797i
$267$	1.54166	−	6.75447i	0.0943482	−	0.413367i
$268$	−5.62974	−	5.22364i	−0.343891	−	0.319084i
$269$	15.4429	+	2.32764i	0.941571	+	0.141919i	0.601852	−	0.798608i	$-0.294430\pi$
$269$	15.4429	+	2.32764i	0.941571	+	0.141919i	0.339719	+	0.940527i	$0.389668\pi$
$270$	11.2798	+	1.70015i	0.686464	+	0.103468i
$271$	1.98330	+	1.84023i	0.120477	+	0.111786i	0.738111	−	0.674679i	$-0.235718\pi$
$271$	1.98330	+	1.84023i	0.120477	+	0.111786i	−0.617634	+	0.786466i	$0.711909\pi$
$272$	−1.09688	+	4.80576i	−0.0665084	+	0.291392i
$273$	0.298122	−	0.806215i	0.0180432	−	0.0487944i
$274$	−0.337128	−	1.47705i	−0.0203666	−	0.0892321i
$275$	0.348511	−	0.603638i	0.0210160	−	0.0364008i
$276$	−3.71225	−	6.42980i	−0.223451	−	0.387029i
$277$	−17.9814	+	16.6843i	−1.08040	+	1.00246i	−0.0804140	+	0.996762i	$0.525624\pi$
$277$	−17.9814	+	16.6843i	−1.08040	+	1.00246i	−0.999984	+	0.00570111i	$0.998185\pi$
$278$	17.1526	−	11.6945i	1.02875	−	0.701388i
$279$	−0.137262	+	0.172121i	−0.00821767	+	0.0103046i
$280$	0.328852	−	5.97454i	0.0196527	−	0.357047i
$281$	−0.854883	−	1.07199i	−0.0509980	−	0.0639495i	0.755678	−	0.654943i	$-0.227307\pi$
$281$	−0.854883	−	1.07199i	−0.0509980	−	0.0639495i	−0.806676	+	0.590993i	$0.798736\pi$
$282$	15.0079	+	4.62931i	0.893704	+	0.275671i
$283$	2.01624	−	5.13731i	0.119853	−	0.305381i	−0.858339	−	0.513083i	$-0.828503\pi$
$283$	2.01624	−	5.13731i	0.119853	−	0.305381i	0.978192	+	0.207702i	$0.0665985\pi$
$284$	−0.339572	−	4.53127i	−0.0201499	−	0.268881i
$285$	3.85879	+	9.83204i	0.228575	+	0.582400i
$286$	−0.999395	+	0.481283i	−0.0590955	+	0.0284589i
$287$	−1.55552	+	0.0308237i	−0.0918195	+	0.00181946i
$288$	0.148392	+	0.0714619i	0.00874409	+	0.00421093i
$289$	0.545418	−	7.27810i	0.0320834	−	0.428123i
$290$	−19.9969	+	6.16822i	−1.17426	+	0.362210i
$291$	6.19568	+	4.22414i	0.363197	+	0.247624i
$292$	7.77715	−	1.17222i	0.455123	−	0.0685988i
$293$	−13.8951			−0.811762			−0.405881	−	0.913926i	$-0.633035\pi$
$293$	−13.8951			−0.811762			−0.405881	+	0.913926i	$0.633035\pi$
$294$	−3.24977	−	12.0212i	−0.189531	−	0.701091i
$295$	−26.4400			−1.53940
$296$	2.81225	−	0.423878i	0.163459	−	0.0246374i
$297$	−25.3123	−	17.2577i	−1.46877	−	1.00139i
$298$	−4.18968	+	1.29235i	−0.242702	+	0.0748636i
$299$	−0.0569589	+	0.760064i	−0.00329402	+	0.0439556i
$300$	0.183933	+	0.0885777i	0.0106194	+	0.00511403i
$301$	−14.8448	−	17.8765i	−0.855642	−	1.03038i
$302$	11.4874	−	5.53206i	0.661028	−	0.318335i
$303$	0.686133	+	1.74824i	0.0394173	+	0.100434i
$304$	−0.196187	−	2.61793i	−0.0112521	−	0.150149i
$305$	−0.453065	+	1.15439i	−0.0259424	+	0.0661002i
$306$	−0.775808	−	0.239305i	−0.0443500	−	0.0136802i
$307$	−7.46525	−	9.36113i	−0.426065	−	0.534268i	0.521746	−	0.853101i	$-0.325281\pi$
$307$	−7.46525	−	9.36113i	−0.426065	−	0.534268i	−0.947811	+	0.318832i	$0.896709\pi$
$308$	−7.75761	+	14.0733i	−0.442031	+	0.801902i
$309$	7.01176	−	8.79248i	0.398885	−	0.500186i
$310$	2.49769	−	1.70290i	0.141859	−	0.0967180i
$311$	−4.34797	+	4.03433i	−0.246551	+	0.228766i	−0.793761	−	0.608229i	$-0.791880\pi$
$311$	−4.34797	+	4.03433i	−0.246551	+	0.228766i	0.547211	+	0.836995i	$0.315690\pi$
$312$	−0.162443	−	0.281360i	−0.00919655	−	0.0159289i
$313$	8.11969	−	14.0637i	0.458952	−	0.794928i	−0.539954	−	0.841695i	$-0.681558\pi$
$313$	8.11969	−	14.0637i	0.458952	−	0.794928i	0.998906	+	0.0467665i	$0.0148917\pi$
$314$	1.68046	+	7.36256i	0.0948337	+	0.415493i
$315$	0.977225	+	0.127548i	0.0550604	+	0.00718650i
$316$	0.117136	−	0.513208i	0.00658944	−	0.0288702i
$317$	20.8926	+	19.3855i	1.17345	+	1.08880i	0.994478	+	0.104944i	$0.0334665\pi$
$317$	20.8926	+	19.3855i	1.17345	+	1.08880i	0.178968	+	0.983855i	$0.442724\pi$
$318$	−0.344718	−	0.0519579i	−0.0193308	−	0.00291365i
$319$	55.5737	+	8.37639i	3.11153	+	0.468988i
$320$	−1.65786	−	1.53827i	−0.0926771	−	0.0859918i
$321$	0.0369452	−	0.161867i	0.00206208	−	0.00903455i
$322$	5.70939	+	9.45143i	0.318172	+	0.526708i
$323$	2.87962	+	12.6164i	0.160226	+	0.701996i
$324$	4.73349	−	8.19865i	0.262972	−	0.455480i
$325$	−0.0104790	−	0.0181502i	−0.000581271	−	0.00100679i
$326$	−1.09280	+	1.01397i	−0.0605248	+	0.0561588i
$327$	24.6865	−	16.8309i	1.36516	−	0.930753i
$328$	−0.366642	+	0.459754i	−0.0202444	+	0.0253857i
$329$	−22.4524	−	6.44136i	−1.23784	−	0.355124i
$330$	−15.2360	−	19.1053i	−0.838712	−	1.05171i
$331$	−12.4316	−	3.83464i	−0.683303	−	0.210771i	−0.0663795	−	0.997794i	$-0.521145\pi$
$331$	−12.4316	−	3.83464i	−0.683303	−	0.210771i	−0.616923	+	0.787024i	$0.711621\pi$
$332$	−6.51469	+	16.5992i	−0.357540	+	0.910998i
$333$	0.0350048	+	0.467107i	0.00191825	+	0.0255973i
$334$	−0.914739	−	2.33072i	−0.0500523	−	0.127531i
$335$	−15.6486	+	7.53598i	−0.854976	+	0.411735i
$336$	−4.28021	−	1.95774i	−0.233504	−	0.106804i
$337$	12.5418	+	6.03984i	0.683198	+	0.329011i	0.743088	−	0.669194i	$-0.233361\pi$
$337$	12.5418	+	6.03984i	0.683198	+	0.329011i	−0.0598896	+	0.998205i	$0.519075\pi$
$338$	0.968999	−	12.9304i	0.0527066	−	0.703320i
$339$	−17.1405	+	5.28714i	−0.930943	+	0.287158i
$340$	9.21102	+	6.27997i	0.499538	+	0.340579i
$341$	−8.02794	+	1.21002i	−0.434737	+	0.0655261i
$342$	0.432389			0.0233809
$343$	5.18646	+	17.7792i	0.280043	+	0.959988i
$344$	−8.78260			−0.473526
$345$	−16.6036	+	2.50259i	−0.893906	+	0.134735i
$346$	18.4844	+	12.6025i	0.993728	+	0.677512i
$347$	−4.94649	+	1.52579i	−0.265541	+	0.0819086i	−0.424667	−	0.905350i	$-0.639609\pi$
$347$	−4.94649	+	1.52579i	−0.265541	+	0.0819086i	0.159125	+	0.987258i	$0.449133\pi$
$348$	−1.23012	+	16.4148i	−0.0659414	+	0.879927i
$349$	−0.0965100	−	0.0464768i	−0.00516606	−	0.00248784i	0.431299	−	0.902209i	$-0.358055\pi$
$349$	−0.0965100	−	0.0464768i	−0.00516606	−	0.00248784i	−0.436465	+	0.899721i	$0.643770\pi$
$350$	−0.276110	−	0.126291i	−0.0147587	−	0.00675055i
$351$	−0.829928	+	0.399672i	−0.0442983	+	0.0213329i
$352$	2.21901	+	5.65396i	0.118274	+	0.301357i
$353$	−1.40771	−	18.7846i	−0.0749250	−	0.999805i	−0.900314	−	0.435241i	$-0.856663\pi$
$353$	−1.40771	−	18.7846i	−0.0749250	−	0.999805i	0.825389	−	0.564564i	$-0.190956\pi$
$354$	−7.59827	+	19.3601i	−0.403843	+	1.02898i
$355$	−9.82002	−	3.02907i	−0.521192	−	0.160767i
$356$	2.42818	+	3.04484i	0.128693	+	0.161376i
$357$	22.3013	+	6.39802i	1.18031	+	0.338619i
$358$	0.455219	−	0.570827i	0.0240591	−	0.0301691i
$359$	14.1202	−	9.62700i	0.745236	−	0.508094i	−0.130164	−	0.991492i	$-0.541550\pi$
$359$	14.1202	−	9.62700i	0.745236	−	0.508094i	0.875400	+	0.483399i	$0.160598\pi$
$360$	0.273054	−	0.253357i	0.0143912	−	0.0133531i
$361$	6.05398	+	10.4858i	0.318631	+	0.551884i
$362$	6.72578	−	11.6494i	0.353499	−	0.612278i
$363$	10.2492	+	44.9047i	0.537944	+	2.35689i
$364$	0.249836	+	0.413583i	0.0130950	+	0.0216776i
$365$	3.95806	−	17.3414i	0.207174	−	0.907689i
$366$	0.715073	+	0.663491i	0.0373775	+	0.0346812i
$367$	−16.6492	−	2.50946i	−0.869079	−	0.130993i	−0.300660	−	0.953731i	$-0.597207\pi$
$367$	−16.6492	−	2.50946i	−0.869079	−	0.130993i	−0.568420	+	0.822739i	$0.692445\pi$
$368$	4.12689	+	0.622028i	0.215129	+	0.0324255i
$369$	−0.0709983	−	0.0658768i	−0.00369602	−	0.00342941i
$370$	1.43125	−	6.27071i	0.0744071	−	0.325999i
$371$	0.514111	+	0.0671019i	0.0266913	+	0.00348376i
$372$	−0.529124	−	2.31824i	−0.0274338	−	0.120195i
$373$	7.23774	−	12.5361i	0.374756	−	0.649097i	−0.615534	−	0.788110i	$-0.711060\pi$
$373$	7.23774	−	12.5361i	0.374756	−	0.649097i	0.990291	+	0.139013i	$0.0443931\pi$
$374$	−14.9700	−	25.9288i	−0.774080	−	1.34075i
$375$	−14.4079	+	13.3685i	−0.744019	+	0.690349i
$376$	−7.29447	+	4.97329i	−0.376184	+	0.256478i
$377$	1.05361	−	1.32119i	0.0542638	−	0.0680446i
$378$	−6.44216	+	11.6869i	−0.331349	+	0.601110i
$379$	15.1855	+	19.0420i	0.780028	+	0.978124i	0.999997	+	0.00261698i	$0.000833011\pi$
$379$	15.1855	+	19.0420i	0.780028	+	0.978124i	−0.219969	+	0.975507i	$0.570596\pi$
$380$	−5.67349	−	1.75004i	−0.291044	−	0.0897751i
$381$	5.56143	−	14.1703i	0.284921	−	0.725966i
$382$	0.384938	+	5.13664i	0.0196951	+	0.262814i
$383$	−9.51831	−	24.2523i	−0.486363	−	1.23923i	−0.937877	−	0.346968i	$-0.887211\pi$
$383$	−9.51831	−	24.2523i	−0.486363	−	1.23923i	0.451514	−	0.892264i	$-0.350884\pi$
$384$	−1.60279	+	0.771862i	−0.0817920	+	0.0393889i
$385$	23.2181	+	27.9598i	1.18330	+	1.42496i
$386$	−17.7444	−	8.54526i	−0.903167	−	0.434942i
$387$	0.108098	−	1.44247i	0.00549495	−	0.0733250i
$388$	−4.02792	+	1.24245i	−0.204487	+	0.0630758i
$389$	−9.27453	−	6.32326i	−0.470237	−	0.320602i	0.304912	−	0.952381i	$-0.401373\pi$
$389$	−9.27453	−	6.32326i	−0.470237	−	0.320602i	−0.775149	+	0.631778i	$0.782325\pi$
$390$	−0.726552	+	0.109510i	−0.0367904	+	0.00554526i
$391$	−20.5727			−1.04040
$392$	6.42215	+	2.78495i	0.324368	+	0.140661i
$393$	−32.9668			−1.66295
$394$	19.8843	−	2.99707i	1.00175	−	0.150990i
$395$	−0.983646	−	0.670639i	−0.0494926	−	0.0337435i
$396$	−0.955931	+	0.294866i	−0.0480373	+	0.0148176i
$397$	0.195838	−	2.61328i	0.00982883	−	0.131157i	−0.990131	−	0.140147i	$-0.955243\pi$
$397$	0.195838	−	2.61328i	0.00982883	−	0.131157i	0.999960	+	0.00899000i	$0.00286164\pi$
$398$	−15.8700	−	7.64260i	−0.795492	−	0.383089i
$399$	−12.3539	+	0.244801i	−0.618469	+	0.0122554i
$400$	−0.103394	+	0.0497918i	−0.00516969	+	0.00248959i
$401$	−2.76386	−	7.04219i	−0.138020	−	0.351670i	0.845106	−	0.534599i	$-0.179537\pi$
$401$	−2.76386	−	7.04219i	−0.138020	−	0.351670i	−0.983126	+	0.182929i	$0.941442\pi$
$402$	1.02098	+	13.6240i	0.0509217	+	0.679503i
$403$	−0.0891835	+	0.227236i	−0.00444254	+	0.0113194i
$404$	−1.00880	−	0.311175i	−0.0501899	−	0.0154815i
$405$	−13.3491	−	16.7393i	−0.663324	−	0.831782i
$406$	1.34547	−	24.4443i	0.0667746	−	1.21315i
$407$	−10.7702	+	13.5054i	−0.533858	+	0.669436i
$408$	7.24539	−	4.93982i	0.358700	−	0.244558i
$409$	24.4370	−	22.6742i	1.20833	−	1.12117i	0.218966	−	0.975733i	$-0.429732\pi$
$409$	24.4370	−	22.6742i	1.20833	−	1.12117i	0.989368	−	0.145437i	$-0.0464587\pi$
$410$	0.664959	+	1.15174i	0.0328400	+	0.0568805i
$411$	−1.34760	+	2.33411i	−0.0664721	+	0.115133i
$412$	1.40670	+	6.16317i	0.0693033	+	0.303638i
$413$	10.7278	−	29.0114i	0.527882	−	1.42756i
$414$	−0.152958	+	0.670153i	−0.00751748	+	0.0329362i
$415$	29.5626	+	27.4301i	1.45117	+	1.34649i
$416$	0.180587	+	0.0272192i	0.00885403	+	0.00133453i
$417$	−36.5186	−	5.50429i	−1.78832	−	0.269546i
$418$	11.6888	+	10.8456i	0.571718	+	0.530477i
$419$	−3.14488	+	13.7786i	−0.153637	+	0.673129i	0.838173	+	0.545405i	$0.183624\pi$
$419$	−3.14488	+	13.7786i	−0.153637	+	0.673129i	−0.991810	+	0.127724i	$0.959233\pi$
$420$	−7.65805	+	7.39332i	−0.373675	+	0.360757i
$421$	1.33212	+	5.83640i	0.0649236	+	0.284449i	0.996960	−	0.0779160i	$-0.0248266\pi$
$421$	1.33212	+	5.83640i	0.0649236	+	0.284449i	−0.932036	+	0.362365i	$0.881969\pi$
$422$	−8.75351	+	15.1615i	−0.426114	+	0.738051i
$423$	−0.727041	−	1.25927i	−0.0353500	−	0.0612279i
$424$	0.143652	−	0.133289i	0.00697634	−	0.00647309i
$425$	0.467390	−	0.318661i	0.0226718	−	0.0154573i
$426$	−5.04001	+	6.31998i	−0.244189	+	0.306204i
$427$	−1.08283	−	0.965510i	−0.0524018	−	0.0467243i
$428$	0.0581902	+	0.0729682i	0.00281273	+	0.00352705i
$429$	1.88563	+	0.581641i	0.0910393	+	0.0280819i
$430$	−7.25661	+	18.4895i	−0.349945	+	0.891645i
$431$	1.27227	+	16.9772i	0.0612829	+	0.817763i	0.940164	+	0.340722i	$0.110672\pi$
$431$	1.27227	+	16.9772i	0.0612829	+	0.817763i	−0.878881	+	0.477041i	$0.841709\pi$
$432$	1.84274	+	4.69522i	0.0886588	+	0.225899i
$433$	5.40870	−	2.60469i	0.259926	−	0.125174i	−0.299383	−	0.954133i	$-0.596781\pi$
$433$	5.40870	−	2.60469i	0.259926	−	0.125174i	0.559309	+	0.828959i	$0.311067\pi$
$434$	0.855090	+	3.43153i	0.0410456	+	0.164719i
$435$	33.5409	+	16.1524i	1.60816	+	0.774450i
$436$	−1.25511	+	16.7483i	−0.0601089	+	0.802098i
$437$	10.4698	−	3.22950i	0.500838	−	0.154488i
$438$	−11.5603	−	7.88170i	−0.552374	−	0.376602i
$439$	5.41860	−	0.816722i	0.258615	−	0.0389800i	−0.0184547	−	0.999830i	$-0.505875\pi$
$439$	5.41860	−	0.816722i	0.258615	−	0.0389800i	0.277070	+	0.960850i	$0.410637\pi$
$440$	13.7364			0.654859
$441$	−0.536453	+	1.02051i	−0.0255454	+	0.0485957i
$442$	−0.900234			−0.0428198
$443$	0.0234358	−	0.00353238i	0.00111347	−	0.000167828i	−0.148486	−	0.988915i	$-0.547440\pi$
$443$	0.0234358	−	0.00353238i	0.00111347	−	0.000167828i	0.149599	+	0.988747i	$0.452202\pi$
$444$	−4.18026	−	2.85006i	−0.198387	−	0.135258i
$445$	8.41644	−	2.59613i	0.398977	−	0.123068i
$446$	0.0176544	−	0.235582i	0.000835962	−	0.0111551i
$447$	7.02738	+	3.38421i	0.332384	+	0.160068i
$448$	2.36053	−	1.19495i	0.111525	−	0.0564560i
$449$	−3.30210	+	1.59021i	−0.155836	+	0.0750465i	−0.510176	−	0.860070i	$-0.670420\pi$
$449$	−3.30210	+	1.59021i	−0.155836	+	0.0750465i	0.354340	+	0.935117i	$0.384705\pi$
$450$	−0.00690532	−	0.0175945i	−0.000325520	−	0.000829411i
$451$	−0.266913	−	3.56171i	−0.0125684	−	0.167714i
$452$	3.68376	−	9.38606i	0.173269	−	0.441483i
$453$	−21.6742	−	6.68562i	−1.01835	−	0.314118i
$454$	9.57158	+	12.0024i	0.449216	+	0.563300i
$455$	1.07712	−	0.184244i	0.0504963	−	0.00863750i
$456$	−2.91185	+	3.65135i	−0.136360	+	0.170990i
$457$	−10.8018	+	7.36454i	−0.505287	+	0.344499i	−0.788982	−	0.614416i	$-0.789392\pi$
$457$	−10.8018	+	7.36454i	−0.505287	+	0.344499i	0.283696	+	0.958914i	$0.408439\pi$
$458$	−15.4494	+	14.3350i	−0.721905	+	0.669830i
$459$	−12.4315	−	21.5321i	−0.580254	−	1.00503i
$460$	4.71936	−	8.17417i	0.220041	−	0.381123i
$461$	3.52878	+	15.4606i	0.164351	+	0.720071i	0.988188	+	0.153244i	$0.0489720\pi$
$461$	3.52878	+	15.4606i	0.164351	+	0.720071i	−0.823837	+	0.566827i	$0.808171\pi$
$462$	27.1452	−	8.96589i	1.26291	−	0.417131i
$463$	5.24397	−	22.9754i	0.243708	−	1.06776i	−0.693903	−	0.720069i	$-0.744110\pi$
$463$	5.24397	−	22.9754i	0.243708	−	1.06776i	0.937611	−	0.347686i	$-0.113033\pi$
$464$	−6.78298	−	6.29368i	−0.314892	−	0.292177i
$465$	−5.31767	−	0.801510i	−0.246601	−	0.0371691i
$466$	−4.89785	−	0.738232i	−0.226888	−	0.0341979i
$467$	4.19491	+	3.89231i	0.194117	+	0.180115i	0.771243	−	0.636541i	$-0.219635\pi$
$467$	4.19491	+	3.89231i	0.194117	+	0.180115i	−0.577126	+	0.816655i	$0.695826\pi$
$468$	−0.00669326	+	0.0293251i	−0.000309396	+	0.00135555i
$469$	−1.91957	−	20.2281i	−0.0886377	−	0.934049i
$470$	4.44295	+	19.4658i	0.204938	+	0.897893i
$471$	6.71727	−	11.6347i	0.309516	−	0.536097i
$472$	−5.84547	−	10.1247i	−0.269060	−	0.466025i
$473$	39.1038	−	36.2831i	1.79800	−	1.66830i
$474$	−0.773736	+	0.527524i	−0.0355389	+	0.0242300i
$475$	−0.187840	+	0.235544i	−0.00861868	+	0.0108075i
$476$	−10.6280	+	7.55877i	−0.487134	+	0.346456i
$477$	0.0201236	+	0.0252342i	0.000921397	+	0.00115540i
$478$	−11.2186	−	3.46047i	−0.513125	−	0.158278i
$479$	1.78955	−	4.55971i	0.0817667	−	0.208338i	−0.884144	−	0.467215i	$-0.845257\pi$
$479$	1.78955	−	4.55971i	0.0817667	−	0.208338i	0.965910	+	0.258877i	$0.0833525\pi$
$480$	0.300659	+	4.01202i	0.0137232	+	0.183123i
$481$	0.189756	+	0.483490i	0.00865213	+	0.0220453i
$482$	8.23466	−	3.96560i	0.375078	−	0.180628i
$483$	3.99079	−	19.2337i	0.181587	−	0.875164i
$484$	−23.3272	−	11.2338i	−1.06033	−	0.510627i
$485$	−0.712402	+	9.50634i	−0.0323485	+	0.431661i
$486$	−1.63378	+	0.503955i	−0.0741099	+	0.0228599i
$487$	−13.6896	−	9.33341i	−0.620335	−	0.422937i	0.211954	−	0.977280i	$-0.432017\pi$
$487$	−13.6896	−	9.33341i	−0.620335	−	0.422937i	−0.832289	+	0.554343i	$0.812970\pi$
$488$	−0.542215	+	0.0817257i	−0.0245449	+	0.00369955i
$489$	2.65200			0.119928
$490$	11.1693	−	11.2192i	0.504578	−	0.506830i
$491$	−2.09618			−0.0945994			−0.0472997	−	0.998881i	$-0.515062\pi$
$491$	−2.09618			−0.0945994			−0.0472997	+	0.998881i	$0.515062\pi$
$492$	1.03443	−	0.155915i	0.0466357	−	0.00702920i
$493$	37.6861	+	25.6939i	1.69730	+	1.15720i
$494$	0.458145	−	0.141319i	0.0206129	−	0.00635825i
$495$	−0.169072	+	2.25610i	−0.00759920	+	0.101404i
$496$	1.20429	+	0.579954i	0.0540741	+	0.0260407i
$497$	7.30805	−	9.54601i	0.327811	−	0.428197i
$498$	28.5806	−	13.7637i	1.28073	−	0.616766i
$499$	−0.677599	−	1.72649i	−0.0303335	−	0.0772885i	0.914905	−	0.403670i	$-0.132266\pi$
$499$	−0.677599	−	1.72649i	−0.0303335	−	0.0772885i	−0.945238	+	0.326382i	$0.894170\pi$
$500$	−0.825646	−	11.0175i	−0.0369240	−	0.492717i
$501$	−1.62728	+	4.14625i	−0.0727017	+	0.185241i
$502$	−22.1194	−	6.82295i	−0.987239	−	0.304523i
$503$	−13.7170	−	17.2006i	−0.611612	−	0.766937i	0.375526	−	0.926812i	$-0.377462\pi$
$503$	−13.7170	−	17.2006i	−0.611612	−	0.766937i	−0.987137	+	0.159875i	$0.948891\pi$
$504$	0.167207	+	0.402406i	0.00744800	+	0.0179246i
$505$	−1.48862	+	1.86668i	−0.0662429	+	0.0830660i
$506$	−20.9444	+	14.2796i	−0.931092	+	0.634808i
$507$	−16.9094	+	15.6897i	−0.750974	+	0.696802i
$508$	4.27850	+	7.41058i	0.189828	+	0.328791i
$509$	−1.80058	+	3.11869i	−0.0798091	+	0.138233i	−0.903167	−	0.429288i	$-0.858764\pi$
$509$	−1.80058	+	3.11869i	−0.0798091	+	0.138233i	0.823358	+	0.567522i	$0.192098\pi$
$510$	−4.41306	−	19.3349i	−0.195414	−	0.856163i
$511$	17.4219	+	11.3791i	0.770700	+	0.503382i
$512$	0.222521	−	0.974928i	0.00983413	−	0.0430861i
$513$	9.70675	+	9.00654i	0.428563	+	0.397649i
$514$	17.3267	+	2.61158i	0.764249	+	0.115192i
$515$	14.1373	+	2.13085i	0.622963	+	0.0938966i
$516$	11.4531	+	10.6269i	0.504196	+	0.467825i
$517$	11.9322	−	52.2784i	0.524778	−	2.29920i
$518$	6.29983	+	4.11473i	0.276799	+	0.180791i
$519$	−8.85599	−	38.8006i	−0.388735	−	1.70316i
$520$	0.206513	−	0.357692i	0.00905621	−	0.0156858i
$521$	10.6475	+	18.4421i	0.466477	+	0.807962i	0.999267	−	0.0382857i	$-0.0121897\pi$
$521$	10.6475	+	18.4421i	0.466477	+	0.807962i	−0.532790	+	0.846248i	$0.678856\pi$
$522$	1.11718	−	1.03659i	0.0488974	−	0.0453702i
$523$	3.90591	−	2.66300i	0.170794	−	0.116445i	−0.474906	−	0.880036i	$-0.657518\pi$
$523$	3.90591	−	2.66300i	0.170794	−	0.116445i	0.645700	+	0.763591i	$0.276566\pi$
$524$	11.5542	−	14.4885i	0.504747	−	0.632932i
$525$	0.207255	+	0.498786i	0.00904534	+	0.0217688i
$526$	11.1820	+	14.0217i	0.487557	+	0.611377i
$527$	−6.29613	−	1.94210i	−0.274264	−	0.0845992i
$528$	3.94754	−	10.0582i	0.171795	−	0.437726i
$529$	−0.417135	−	5.56628i	−0.0181363	−	0.242012i
$530$	−0.161915	−	0.412552i	−0.00703313	−	0.0179201i
$531$	1.73484	−	0.835457i	0.0752858	−	0.0362557i
$532$	4.22221	−	5.51519i	0.183056	−	0.239114i
$533$	−0.0967582	−	0.0465963i	−0.00419106	−	0.00201831i
$534$	0.517743	−	6.90880i	0.0224049	−	0.298973i
$535$	0.201696	−	0.0622149i	0.00872007	−	0.00268978i
$536$	−6.34540	−	4.32622i	−0.274080	−	0.186864i
$537$	−1.28434	+	0.193583i	−0.0554233	+	0.00835372i
$538$	15.6173			0.673312
$539$	−40.0995	+	14.1317i	−1.72721	+	0.608695i
$540$	11.4072			0.490886
$541$	−25.5565	+	3.85202i	−1.09876	+	0.165611i	−0.673302	−	0.739367i	$-0.735125\pi$
$541$	−25.5565	+	3.85202i	−1.09876	+	0.165611i	−0.425457	+	0.904979i	$0.639887\pi$
$542$	2.23542	+	1.52409i	0.0960196	+	0.0654651i
$543$	−22.8667	+	7.05343i	−0.981302	+	0.302692i
$544$	−0.368371	+	4.91557i	−0.0157938	+	0.210753i
$545$	34.2223	+	16.4806i	1.46592	+	0.705951i
$546$	0.174632	−	0.841643i	0.00747356	−	0.0360190i
$547$	6.23455	−	3.00240i	0.266570	−	0.128373i	−0.295825	−	0.955242i	$-0.595594\pi$
$547$	6.23455	−	3.00240i	0.266570	−	0.128373i	0.562395	+	0.826869i	$0.309880\pi$
$548$	−0.553506	−	1.41031i	−0.0236446	−	0.0602455i
$549$	−0.00674910	−	0.0900605i	−0.000288045	−	0.00384369i
$550$	0.254651	−	0.648839i	0.0108583	−	0.0276666i
$551$	−23.2126	−	7.16013i	−0.988889	−	0.305032i
$552$	−4.62910	−	5.80470i	−0.197027	−	0.247065i
$553$	1.13497	−	0.807202i	0.0482637	−	0.0343257i
$554$	−15.2939	+	19.1779i	−0.649776	+	0.814793i
$555$	−9.45401	+	6.44564i	−0.401300	+	0.273602i
$556$	15.2181	−	14.1203i	0.645391	−	0.598835i
$557$	9.03756	+	15.6535i	0.382934	+	0.663260i	0.991480	−	0.130258i	$-0.0415805\pi$
$557$	9.03756	+	15.6535i	0.382934	+	0.663260i	−0.608547	+	0.793518i	$0.708247\pi$
$558$	−0.110076	+	0.190657i	−0.00465987	+	0.00807114i
$559$	−0.356911	−	1.56373i	−0.0150957	−	0.0661386i
$560$	−0.565280	−	5.95683i	−0.0238874	−	0.251722i
$561$	−11.8519	+	51.9267i	−0.500389	+	2.19235i
$562$	−1.00511	−	0.932602i	−0.0423978	−	0.0393394i
$563$	7.93953	+	1.19669i	0.334611	+	0.0504345i	0.314199	−	0.949357i	$-0.398264\pi$
$563$	7.93953	+	1.19669i	0.334611	+	0.0504345i	0.0204121	+	0.999792i	$0.493502\pi$
$564$	15.5302	+	2.34080i	0.653939	+	0.0985654i
$565$	−16.7163	−	15.5104i	−0.703259	−	0.652529i
$566$	1.22805	−	5.38043i	0.0516187	−	0.226156i
$567$	23.7835	−	7.85555i	0.998815	−	0.329902i
$568$	−1.01113	−	4.43005i	−0.0424260	−	0.185881i
$569$	0.620152	−	1.07413i	0.0259981	−	0.0450300i	−0.852734	−	0.522346i	$-0.825057\pi$
$569$	0.620152	−	1.07413i	0.0259981	−	0.0450300i	0.878732	+	0.477316i	$0.158390\pi$
$570$	5.28108	+	9.14710i	0.221200	+	0.383130i
$571$	−26.5053	+	24.5933i	−1.10921	+	1.02920i	−0.109833	+	0.993950i	$0.535032\pi$
$571$	−26.5053	+	24.5933i	−1.10921	+	1.02920i	−0.999379	+	0.0352482i	$0.988778\pi$
$572$	−0.916501	+	0.624860i	−0.0383208	+	0.0261267i
$573$	5.71336	−	7.16432i	0.238679	−	0.299294i
$574$	−1.53355	+	0.262318i	−0.0640093	+	0.0109489i
$575$	−0.298617	−	0.374454i	−0.0124532	−	0.0156158i
$576$	0.157386	+	0.0485470i	0.00655773	+	0.00202279i
$577$	−9.95918	+	25.3756i	−0.414606	+	1.05640i	0.559203	+	0.829031i	$0.311107\pi$
$577$	−9.95918	+	25.3756i	−0.414606	+	1.05640i	−0.973809	+	0.227368i	$0.926988\pi$
$578$	−0.545418	−	7.27810i	−0.0226864	−	0.302729i
$579$	12.8002	+	32.6144i	0.531958	+	1.35541i
$580$	−18.8542	+	9.07970i	−0.782878	+	0.377014i
$581$	−42.0925	+	21.3081i	−1.74629	+	0.884009i
$582$	6.75606	+	3.25355i	0.280048	+	0.134864i
$583$	−0.0889473	+	1.18692i	−0.00368382	+	0.0491572i
$584$	7.51558	−	2.31825i	0.310997	−	0.0959298i
$585$	0.0562063	+	0.0383208i	0.00232384	+	0.00158437i
$586$	−13.7399	+	2.07096i	−0.567591	+	0.0855506i
$587$	33.2205			1.37116			0.685578	−	0.727999i	$-0.259549\pi$
$587$	33.2205			1.37116			0.685578	+	0.727999i	$0.259549\pi$
$588$	−5.00514	−	11.4026i	−0.206409	−	0.470235i
$589$	3.50909			0.144589
$590$	−26.1447	+	3.94068i	−1.07636	+	0.162235i
$591$	−29.5569	−	20.1516i	−1.21581	−	0.828925i
$592$	2.71766	−	0.838288i	0.111695	−	0.0344534i
$593$	−2.27379	+	30.3417i	−0.0933735	+	1.24598i	0.731964	+	0.681343i	$0.238604\pi$
$593$	−2.27379	+	30.3417i	−0.0933735	+	1.24598i	−0.825338	+	0.564640i	$0.809015\pi$
$594$	−27.6017	−	13.2923i	−1.13251	−	0.545390i
$595$	7.13171	+	28.6200i	0.292372	+	1.17331i
$596$	−3.95027	+	1.90235i	−0.161809	+	0.0779233i
$597$	11.4481	+	29.1692i	0.468539	+	1.19382i
$598$	0.0569589	+	0.760064i	0.00232922	+	0.0310813i
$599$	11.8667	−	30.2358i	0.484859	−	1.23540i	−0.453969	−	0.891017i	$-0.649992\pi$
$599$	11.8667	−	30.2358i	0.484859	−	1.23540i	0.938829	−	0.344384i	$-0.111912\pi$
$600$	0.195081	+	0.0601745i	0.00796414	+	0.00245661i
$601$	3.32133	+	4.16482i	0.135480	+	0.169887i	0.844943	−	0.534856i	$-0.179634\pi$
$601$	3.32133	+	4.16482i	0.135480	+	0.169887i	−0.709463	+	0.704742i	$0.751063\pi$
$602$	−17.3434	−	15.4643i	−0.706864	−	0.630278i
$603$	0.788650	−	0.988935i	0.0321163	−	0.0402726i
$604$	10.5346	−	7.18239i	0.428648	−	0.292247i
$605$	−42.9240	+	39.8277i	−1.74511	+	1.61922i
$606$	0.939030	+	1.62645i	0.0381455	+	0.0660699i
$607$	1.74006	−	3.01388i	0.0706270	−	0.122330i	−0.828549	−	0.559916i	$-0.810833\pi$
$607$	1.74006	−	3.01388i	0.0706270	−	0.122330i	0.899176	+	0.437587i	$0.144167\pi$
$608$	−0.584177	−	2.55945i	−0.0236915	−	0.103799i
$609$	−31.3322	+	30.2491i	−1.26965	+	1.22576i
$610$	−0.275952	+	1.20902i	−0.0111729	+	0.0489519i
$611$	−1.18192	−	1.09666i	−0.0478154	−	0.0443662i
$612$	−0.802810	−	0.121004i	−0.0324517	−	0.00489130i
$613$	−35.2979	−	5.32030i	−1.42567	−	0.214885i	−0.609540	−	0.792755i	$-0.708646\pi$
$613$	−35.2979	−	5.32030i	−1.42567	−	0.214885i	−0.816129	+	0.577870i	$0.803884\pi$
$614$	−8.77708	−	8.14394i	−0.354214	−	0.328663i
$615$	0.526456	−	2.30656i	0.0212288	−	0.0930093i
$616$	−5.57344	+	15.0723i	−0.224560	+	0.607282i
$617$	−6.75193	−	29.5821i	−0.271822	−	1.19093i	−0.907860	−	0.419273i	$-0.862285\pi$
$617$	−6.75193	−	29.5821i	−0.271822	−	1.19093i	0.636038	−	0.771658i	$-0.280572\pi$
$618$	5.62300	−	9.73932i	0.226190	−	0.391773i
$619$	17.4022	+	30.1415i	0.699453	+	1.21149i	0.968656	+	0.248405i	$0.0799063\pi$
$619$	17.4022	+	30.1415i	0.699453	+	1.21149i	−0.269203	+	0.963083i	$0.586760\pi$
$620$	2.21599	−	2.05614i	0.0889962	−	0.0825764i
$621$	−17.3929	+	11.8583i	−0.697952	+	0.475855i
$622$	−3.69812	+	4.63730i	−0.148281	+	0.185939i
$623$	−0.566292	+	10.2883i	−0.0226880	+	0.412193i
$624$	−0.202564	−	0.254007i	−0.00810903	−	0.0101684i
$625$	−24.4250	−	7.53413i	−0.977001	−	0.301365i
$626$	5.93291	−	15.1168i	0.237127	−	0.604189i
$627$	−2.11981	−	28.2869i	−0.0846572	−	1.12967i
$628$	2.75902	+	7.02987i	0.110097	+	0.280522i
$629$	−12.6308	+	6.08268i	−0.503623	+	0.242532i
$630$	0.985320	−	0.0195248i	0.0392561	−	0.000777885i
$631$	8.35839	+	4.02519i	0.332742	+	0.160240i	0.592793	−	0.805355i	$-0.298025\pi$
$631$	8.35839	+	4.02519i	0.332742	+	0.160240i	−0.260051	+	0.965595i	$0.583739\pi$
$632$	0.0393384	−	0.524934i	0.00156480	−	0.0208808i
$633$	29.7607	−	9.17995i	1.18288	−	0.364870i
$634$	23.5485	+	16.0551i	0.935232	+	0.637630i
$635$	19.1362	−	2.88432i	0.759397	−	0.114461i
$636$	−0.348612			−0.0138234
$637$	−0.234871	+	1.25663i	−0.00930592	+	0.0497895i
$638$	56.2014			2.22504
$639$	0.740046	−	0.111544i	0.0292758	−	0.00441261i
$640$	−1.86861	−	1.27400i	−0.0738632	−	0.0503591i
$641$	0.0556417	−	0.0171632i	0.00219772	−	0.000677906i	−0.293656	−	0.955911i	$-0.594872\pi$
$641$	0.0556417	−	0.0171632i	0.00219772	−	0.000677906i	0.295854	+	0.955233i	$0.404396\pi$
$642$	0.0124074	−	0.165566i	0.000489683	−	0.00653436i
$643$	−6.73317	−	3.24253i	−0.265530	−	0.127873i	0.296382	−	0.955070i	$-0.404220\pi$
$643$	−6.73317	−	3.24253i	−0.265530	−	0.127873i	−0.561912	+	0.827197i	$0.689934\pi$
$644$	7.05429	+	8.49493i	0.277978	+	0.334747i
$645$	31.8355	−	15.3312i	1.25352	−	0.603664i
$646$	4.72783	+	12.0463i	0.186014	+	0.473956i
$647$	1.23987	+	16.5449i	0.0487444	+	0.650448i	0.967052	+	0.254580i	$0.0819372\pi$
$647$	1.23987	+	16.5449i	0.0487444	+	0.650448i	−0.918307	+	0.395868i	$0.870444\pi$
$648$	3.45868	−	8.81256i	0.135870	−	0.346190i
$649$	67.8539	+	20.9302i	2.66350	+	0.821581i
$650$	−0.0130671	−	0.0163856i	−0.000512534	−	0.000642697i
$651$	3.03706	−	5.50962i	0.119032	−	0.215939i
$652$	−0.929473	+	1.16552i	−0.0364010	+	0.0456454i
$653$	16.6049	−	11.3210i	0.649798	−	0.443025i	−0.193041	−	0.981191i	$-0.561835\pi$
$653$	16.6049	−	11.3210i	0.649798	−	0.443025i	0.842839	+	0.538166i	$0.180883\pi$
$654$	21.9022	−	20.3223i	0.856444	−	0.794664i
$655$	−20.9552	−	36.2955i	−0.818788	−	1.41818i
$656$	−0.294024	+	0.509264i	−0.0114797	+	0.0198834i
$657$	0.288251	+	1.26291i	0.0112457	+	0.0492708i
$658$	−23.1616	−	3.02306i	−0.902934	−	0.117851i
$659$	2.52843	−	11.0778i	0.0984935	−	0.431528i	−0.901506	−	0.432767i	$-0.857537\pi$
$659$	2.52843	−	11.0778i	0.0984935	−	0.431528i	0.999999	+	0.00123890i	$0.000394354\pi$
$660$	−17.9133	−	16.6211i	−0.697274	−	0.646976i
$661$	−46.1436	−	6.95503i	−1.79478	−	0.270519i	−0.834792	−	0.550566i	$-0.814412\pi$
$661$	−46.1436	−	6.95503i	−1.79478	−	0.270519i	−0.959986	+	0.280047i	$0.909650\pi$
$662$	−12.8643	−	1.93898i	−0.499984	−	0.0753605i
$663$	1.17397	+	1.08928i	0.0455932	+	0.0423043i
$664$	−3.96795	+	17.3847i	−0.153986	+	0.674658i
$665$	−8.12224	−	13.4457i	−0.314967	−	0.521402i
$666$	0.104233	+	0.456673i	0.00403893	+	0.0176957i
$667$	19.3088	−	33.4439i	0.747641	−	1.29495i
$668$	−1.25190	−	2.16835i	−0.0484374	−	0.0838960i
$669$	−0.308077	+	0.285854i	−0.0119110	+	0.0110518i
$670$	−14.3507	+	9.78411i	−0.554414	+	0.377993i
$671$	2.07654	−	2.60390i	0.0801640	−	0.100522i
$672$	−4.52419	−	1.29794i	−0.174524	−	0.0500693i
$673$	−2.87359	−	3.60337i	−0.110769	−	0.138900i	0.723356	−	0.690475i	$-0.242598\pi$
$673$	−2.87359	−	3.60337i	−0.110769	−	0.138900i	−0.834125	+	0.551575i	$0.814027\pi$
$674$	13.3020	+	4.10311i	0.512372	+	0.158046i
$675$	0.211470	−	0.538816i	0.00813947	−	0.0207390i
$676$	−0.968999	−	12.9304i	−0.0372692	−	0.497323i
$677$	−6.84788	−	17.4481i	−0.263186	−	0.670586i	0.736799	−	0.676112i	$-0.236336\pi$
$677$	−6.84788	−	17.4481i	−0.263186	−	0.670586i	−0.999985	+	0.00552579i	$0.998241\pi$
$678$	−16.1610	+	7.78274i	−0.620660	+	0.298894i
$679$	−10.1418	−	4.63880i	−0.389207	−	0.178021i
$680$	10.0441	+	4.83700i	0.385175	+	0.185490i
$681$	2.04087	−	27.2336i	0.0782065	−	1.04359i
$682$	−7.75793	+	2.39300i	−0.297066	+	0.0916328i
$683$	30.7765	+	20.9831i	1.17763	+	0.802896i	0.983998	−	0.178178i	$-0.0570203\pi$
$683$	30.7765	+	20.9831i	1.17763	+	0.802896i	0.193634	+	0.981074i	$0.437973\pi$
$684$	0.427560	−	0.0644443i	0.0163482	−	0.00246409i
$685$	−3.42639			−0.130916
$686$	7.77839	+	16.8076i	0.296980	+	0.641719i
$687$	37.4925			1.43043
$688$	−8.68450	+	1.30898i	−0.331094	+	0.0499043i
$689$	0.0295697	+	0.0201603i	0.00112652	+	0.000768045i
$690$	−16.0451	+	4.94927i	−0.610828	+	0.188415i
$691$	0.863414	−	11.5215i	0.0328458	−	0.438297i	−0.956403	−	0.292052i	$-0.905662\pi$
$691$	0.863414	−	11.5215i	0.0328458	−	0.438297i	0.989248	−	0.146245i	$-0.0467189\pi$
$692$	20.1562	+	9.70674i	0.766225	+	0.368995i
$693$	−2.40692	−	1.10091i	−0.0914312	−	0.0418201i
$694$	−4.66383	+	2.24598i	−0.177037	+	0.0852563i
$695$	−17.1529	−	43.7048i	−0.650645	−	1.65782i
$696$	1.23012	+	16.4148i	0.0466276	+	0.622202i
$697$	1.05901	−	2.69832i	0.0401129	−	0.102206i
$698$	−0.102359	−	0.0315736i	−0.00387435	−	0.00119508i
$699$	5.49388	+	6.88911i	0.207798	+	0.260570i
$700$	−0.291849	−	0.0837286i	−0.0110309	−	0.00316464i
$701$	18.7262	−	23.4820i	0.707280	−	0.886901i	−0.290264	−	0.956947i	$-0.593743\pi$
$701$	18.7262	−	23.4820i	0.707280	−	0.886901i	0.997544	+	0.0700455i	$0.0223144\pi$
$702$	−0.761090	+	0.518903i	−0.0287255	+	0.0195847i
$703$	5.47319	−	5.07837i	0.206425	−	0.191535i
$704$	3.03691	+	5.26008i	0.114458	+	0.198247i
$705$	17.7598	−	30.7608i	0.668872	−	1.15852i
$706$	−4.19169	−	18.3650i	−0.157756	−	0.691176i
$707$	−1.44422	−	2.39078i	−0.0543154	−	0.0899147i
$708$	−4.62793	+	20.2763i	−0.173928	+	0.762030i
$709$	−16.2984	−	15.1227i	−0.612100	−	0.567946i	0.312007	−	0.950080i	$-0.398999\pi$
$709$	−16.2984	−	15.1227i	−0.612100	−	0.567946i	−0.924107	+	0.382134i	$0.875189\pi$
$710$	−10.1618	−	1.53164i	−0.381365	−	0.0574816i
$711$	0.0857322	+	0.0129220i	0.00321521	+	0.000484615i
$712$	2.85487	+	2.64893i	0.106991	+	0.0992730i
$713$	−1.24134	+	5.43868i	−0.0464886	+	0.203680i
$714$	23.0058	+	3.00272i	0.860970	+	0.112374i
$715$	0.558227	+	2.44575i	0.0208765	+	0.0914659i
$716$	0.365057	−	0.632298i	0.0136428	−	0.0236301i
$717$	10.4426	+	18.0872i	0.389987	+	0.675478i
$718$	12.5277	−	11.6240i	0.467529	−	0.433803i
$719$	−36.6510	+	24.9882i	−1.36685	+	0.931904i	−0.366854	+	0.930279i	$0.619565\pi$
$719$	−36.6510	+	24.9882i	−1.36685	+	0.931904i	−0.999999	+	0.00162567i	$0.999483\pi$
$720$	0.232243	−	0.291224i	0.00865519	−	0.0108533i
$721$	−8.07417	+	14.6476i	−0.300698	+	0.545505i
$722$	7.54919	+	9.46638i	0.280952	+	0.352302i
$723$	−15.5370	−	4.79252i	−0.577826	−	0.178236i
$724$	4.91440	−	12.5217i	0.182642	−	0.465365i
$725$	0.0793534	+	1.05890i	0.00294711	+	0.0393265i
$726$	16.8274	+	42.8756i	0.624525	+	1.59126i
$727$	30.4457	−	14.6619i	1.12917	−	0.543778i	0.226454	−	0.974022i	$-0.427287\pi$
$727$	30.4457	−	14.6619i	1.12917	−	0.543778i	0.902713	+	0.430244i	$0.141572\pi$
$728$	0.308687	+	0.371728i	0.0114407	+	0.0137771i
$729$	−22.8480	−	11.0030i	−0.846223	−	0.407519i
$730$	1.32925	−	17.7376i	0.0491977	−	0.656498i
$731$	41.3691	−	12.7607i	1.53009	−	0.471971i
$732$	0.805975	+	0.549504i	0.0297897	+	0.0203103i
$733$	38.9677	−	5.87344i	1.43931	−	0.216941i	0.617439	−	0.786619i	$-0.288170\pi$
$733$	38.9677	−	5.87344i	1.43931	−	0.216941i	0.821868	+	0.569678i	$0.192932\pi$
$734$	−16.8372			−0.621473
$735$	−28.1408	+	1.11569i	−1.03799	+	0.0411530i
$736$	4.17350			0.153837
$737$	46.1251	−	6.95224i	1.69904	−	0.256089i
$738$	−0.0800237	−	0.0545593i	−0.00294571	−	0.00200835i
$739$	−15.6412	+	4.82468i	−0.575372	+	0.177479i	−0.568766	−	0.822499i	$-0.692579\pi$
$739$	−15.6412	+	4.82468i	−0.575372	+	0.177479i	−0.00660596	+	0.999978i	$0.502103\pi$
$740$	0.480662	−	6.41399i	0.0176695	−	0.235783i
$741$	−0.768450	−	0.370066i	−0.0282297	−	0.0135947i
$742$	0.518370	−	0.0102718i	0.0190299	−	0.000377091i
$743$	−37.3880	+	18.0051i	−1.37163	+	0.660543i	−0.967198	−	0.254025i	$-0.918246\pi$
$743$	−37.3880	+	18.0051i	−1.37163	+	0.660543i	−0.404433	+	0.914567i	$0.632531\pi$
$744$	−0.868731	−	2.21349i	−0.0318492	−	0.0811505i
$745$	0.741012	+	9.88812i	0.0271486	+	0.362273i
$746$	5.28849	−	13.4749i	0.193625	−	0.493349i
$747$	−2.80647	−	0.865681i	−0.102683	−	0.0316736i
$748$	−18.6673	−	23.4080i	−0.682543	−	0.855882i
$749$	−0.0135709	+	0.246554i	−0.000495870	+	0.00900889i
$750$	−12.2545	+	15.3666i	−0.447470	+	0.561109i
$751$	−19.1574	+	13.0613i	−0.699063	+	0.476613i	−0.859962	−	0.510358i	$-0.829513\pi$
$751$	−19.1574	+	13.0613i	−0.699063	+	0.476613i	0.160899	+	0.986971i	$0.448561\pi$
$752$	−6.47177	+	6.00492i	−0.236001	+	0.218977i
$753$	20.5896	+	35.6622i	0.750325	+	1.29960i
$754$	0.844931	−	1.46346i	0.0307706	−	0.0532962i
$755$	−6.41649	−	28.1125i	−0.233520	−	1.02312i
$756$	−4.62836	+	12.5165i	−0.168332	+	0.455222i
$757$	−0.258636	+	1.13316i	−0.00940029	+	0.0411853i	−0.979411	−	0.201879i	$-0.935295\pi$
$757$	−0.258636	+	1.13316i	−0.00940029	+	0.0411853i	0.970010	+	0.243064i	$0.0781525\pi$
$758$	17.8540	+	16.5661i	0.648486	+	0.601707i
$759$	44.5914	+	6.72106i	1.61856	+	0.243959i
$760$	−5.87095	−	0.884904i	−0.212962	−	0.0320988i
$761$	9.24811	+	8.58099i	0.335244	+	0.311061i	0.829774	−	0.558100i	$-0.188469\pi$
$761$	9.24811	+	8.58099i	0.335244	+	0.311061i	−0.494530	+	0.869161i	$0.664660\pi$
$762$	3.38734	−	14.8409i	0.122710	−	0.537629i
$763$	−31.9688	+	30.8636i	−1.15735	+	1.11734i
$764$	1.14622	+	5.02190i	0.0414686	+	0.181686i
$765$	−0.918065	+	1.59013i	−0.0331927	+	0.0574914i
$766$	−13.0266	−	22.5627i	−0.470671	−	0.815225i
$767$	1.56513	−	1.45223i	0.0565135	−	0.0524369i
$768$	−1.46985	+	1.00212i	−0.0530385	+	0.0361611i
$769$	−27.9138	+	35.0028i	−1.00660	+	1.26223i	−0.0418320	+	0.999125i	$0.513319\pi$
$769$	−27.9138	+	35.0028i	−1.00660	+	1.26223i	−0.964766	+	0.263109i	$0.915252\pi$
$770$	27.1260	+	24.1870i	0.977552	+	0.871639i
$771$	−19.4353	−	24.3711i	−0.699944	−	0.877702i
$772$	−18.8198	−	5.80515i	−0.677341	−	0.208932i
$773$	3.96908	−	10.1130i	0.142758	−	0.363741i	−0.841555	−	0.540171i	$-0.818360\pi$
$773$	3.96908	−	10.1130i	0.142758	−	0.363741i	0.984313	+	0.176430i	$0.0564549\pi$
$774$	−0.108098	−	1.44247i	−0.00388552	−	0.0518486i
$775$	−0.0560406	−	0.142789i	−0.00201304	−	0.00512914i
$776$	−3.79775	+	1.82890i	−0.136331	+	0.0656537i
$777$	−3.23660	−	12.9887i	−0.116113	−	0.465967i
$778$	−10.1134	−	4.87034i	−0.362582	−	0.174610i
$779$	−0.115367	+	1.53947i	−0.00413345	+	0.0551571i
$780$	−0.702115	+	0.216574i	−0.0251398	+	0.00775459i
$781$	22.8036	+	15.5472i	0.815976	+	0.556323i
$782$	−20.3429	+	3.06619i	−0.727460	+	0.109647i
$783$	46.6714			1.66790
$784$	6.76550	+	1.79668i	0.241625	+	0.0641670i
$785$	17.0793			0.609585
$786$	−32.5985	+	4.91344i	−1.16275	+	0.175257i
$787$	−3.92784	−	2.67796i	−0.140013	−	0.0954589i	0.491288	−	0.870997i	$-0.336526\pi$
$787$	−3.92784	−	2.67796i	−0.140013	−	0.0954589i	−0.631301	+	0.775538i	$0.717479\pi$
$788$	19.2155	−	5.92719i	0.684523	−	0.211147i
$789$	2.38424	−	31.8155i	0.0848813	−	1.13266i
$790$	−1.07261	−	0.516543i	−0.0381619	−	0.0183778i
$791$	23.8014	−	12.0487i	0.846279	−	0.428404i
$792$	−0.901306	+	0.434046i	−0.0320265	+	0.0154232i
$793$	−0.0365859	−	0.0932193i	−0.00129920	−	0.00331031i
$794$	−0.195838	−	2.61328i	−0.00695003	−	0.0927418i
$795$	−0.288040	+	0.733915i	−0.0102157	+	0.0260293i
$796$	−16.8318	−	5.19193i	−0.596588	−	0.184023i
$797$	−1.88011	−	2.35759i	−0.0665970	−	0.0835100i	0.747417	−	0.664355i	$-0.231294\pi$
$797$	−1.88011	−	2.35759i	−0.0665970	−	0.0835100i	−0.814014	+	0.580845i	$0.802722\pi$
$798$	−12.1794	+	2.08332i	−0.431147	+	0.0737487i
$799$	27.1336	−	34.0245i	0.959918	−	1.20370i
$800$	−0.0948178	+	0.0646457i	−0.00335232	+	0.00228557i
$801$	−0.470205	+	0.436287i	−0.0166139	+	0.0154154i
$802$	−3.78257	−	6.55160i	−0.133567	−	0.231345i
$803$	−23.8853	+	41.3705i	−0.842893	+	1.45993i
$804$	3.04012	+	13.3196i	0.107217	+	0.469748i
$805$	23.7125	−	7.83210i	0.835757	−	0.276045i
$806$	−0.0543196	+	0.237990i	−0.00191333	+	0.00838283i
$807$	−20.3661	−	18.8970i	−0.716922	−	0.665206i
$808$	−1.04391	−	0.157345i	−0.0367248	−	0.00553537i
$809$	−44.2483	−	6.66936i	−1.55569	−	0.234482i	−0.685822	−	0.727769i	$-0.740557\pi$
$809$	−44.2483	−	6.66936i	−1.55569	−	0.234482i	−0.869867	+	0.493287i	$0.835795\pi$
$810$	−15.6949	−	14.5627i	−0.551463	−	0.511683i
$811$	−2.43410	+	10.6645i	−0.0854728	+	0.374481i	−0.999515	−	0.0311381i	$-0.990087\pi$
$811$	−2.43410	+	10.6645i	−0.0854728	+	0.374481i	0.914042	+	0.405619i	$0.132944\pi$
$812$	−2.31279	−	24.3718i	−0.0811632	−	0.855283i
$813$	−1.07100	−	4.69238i	−0.0375618	−	0.164569i
$814$	−8.63701	+	14.9597i	−0.302727	+	0.524338i
$815$	1.68574	+	2.91978i	0.0590488	+	0.102276i
$816$	6.42822	−	5.96452i	0.225033	−	0.208800i
$817$	−19.0503	+	12.9883i	−0.666487	+	0.454403i
$818$	20.7847	−	26.0631i	0.726719	−	0.911276i
$819$	−0.0648528	+	0.0461241i	−0.00226614	+	0.00161171i
$820$	0.829190	+	1.03977i	0.0289566	+	0.0363104i
$821$	44.1349	+	13.6138i	1.54032	+	0.475125i	0.944643	−	0.328100i	$-0.106408\pi$
$821$	44.1349	+	13.6138i	1.54032	+	0.475125i	0.595675	+	0.803226i	$0.296885\pi$
$822$	−0.984666	+	2.50889i	−0.0343442	+	0.0875075i
$823$	−3.01450	−	40.2257i	−0.105079	−	1.40218i	−0.761686	−	0.647947i	$-0.775628\pi$
$823$	−3.01450	−	40.2257i	−0.105079	−	1.40218i	0.656607	−	0.754233i	$-0.271991\pi$
$824$	2.30956	+	5.88467i	0.0804575	+	0.205002i
$825$	−1.11718	+	0.538005i	−0.0388951	+	0.0187309i
$826$	6.28408	−	30.2863i	0.218651	−	1.05379i
$827$	16.7327	+	8.05803i	0.581852	+	0.280205i	0.701567	−	0.712603i	$-0.252484\pi$
$827$	16.7327	+	8.05803i	0.581852	+	0.280205i	−0.119715	+	0.992808i	$0.538198\pi$
$828$	−0.0513685	+	0.685465i	−0.00178518	+	0.0238216i
$829$	−5.70053	+	1.75838i	−0.197988	+	0.0610711i	−0.392163	−	0.919896i	$-0.628273\pi$
$829$	−5.70053	+	1.75838i	−0.197988	+	0.0610711i	0.194175	+	0.980967i	$0.437797\pi$
$830$	33.3207	+	22.7176i	1.15658	+	0.788541i
$831$	43.1497	−	6.50376i	1.49684	−	0.225613i
$832$	0.182627			0.00633146
$833$	−34.2970	−	3.78704i	−1.18832	−	0.131213i
$834$	−36.9311			−1.27882
$835$	−5.59929	+	0.843958i	−0.193772	+	0.0292064i
$836$	13.1747	+	8.98237i	0.455657	+	0.310662i
$837$	−6.44242	+	1.98722i	−0.222683	+	0.0686885i
$838$	−1.05616	+	14.0934i	−0.0364843	+	0.486849i
$839$	6.95715	+	3.35038i	0.240187	+	0.115668i	0.550106	−	0.835095i	$-0.314587\pi$
$839$	6.95715	+	3.35038i	0.240187	+	0.115668i	−0.309918	+	0.950763i	$0.600302\pi$
$840$	−6.47060	+	8.45211i	−0.223257	+	0.291626i
$841$	−51.0122	+	24.5662i	−1.75904	+	0.847110i
$842$	2.18711	+	5.57267i	0.0753729	+	0.192047i
$843$	0.182280	+	2.43236i	0.00627806	+	0.0837749i
$844$	−6.39603	+	16.2968i	−0.220161	+	0.560960i
$845$	−28.0223	−	8.64374i	−0.963997	−	0.297354i
$846$	−0.906606	−	1.13685i	−0.0311698	−	0.0390856i
$847$	−26.2849	−	63.2582i	−0.903161	−	2.17358i
$848$	0.122181	−	0.153211i	0.00419573	−	0.00526127i
$849$	−8.11179	+	5.53052i	−0.278396	+	0.189807i
$850$	0.414676	−	0.384763i	0.0142233	−	0.0131973i
$851$	5.93475	+	10.2793i	0.203440	+	0.352369i
$852$	−4.04178	+	7.00056i	−0.138469	+	0.239835i
$853$	9.09979	+	39.8688i	0.311571	+	1.36508i	0.851934	+	0.523649i	$0.175430\pi$
$853$	9.09979	+	39.8688i	0.311571	+	1.36508i	−0.540363	+	0.841432i	$0.681713\pi$
$854$	−1.21464	−	0.793339i	−0.0415640	−	0.0271475i
$855$	0.217600	−	0.953367i	0.00744175	−	0.0326044i
$856$	0.0684156	+	0.0634804i	0.00233840	+	0.00216971i
$857$	−51.2944	−	7.73139i	−1.75218	−	0.264099i	−0.806980	−	0.590579i	$-0.798900\pi$
$857$	−51.2944	−	7.73139i	−1.75218	−	0.264099i	−0.945204	+	0.326479i	$0.894138\pi$
$858$	1.95126	+	0.294106i	0.0666150	+	0.0100406i
$859$	3.85661	+	3.57841i	0.131586	+	0.122094i	0.743221	−	0.669047i	$-0.233297\pi$
$859$	3.85661	+	3.57841i	0.131586	+	0.122094i	−0.611635	+	0.791140i	$0.709488\pi$
$860$	−4.41984	+	19.3646i	−0.150715	+	0.660327i
$861$	2.31727	+	1.51352i	0.0789723	+	0.0515806i
$862$	3.78838	+	16.5980i	0.129033	+	0.565329i
$863$	−17.8385	+	30.8972i	−0.607229	+	1.05175i	0.384466	+	0.923139i	$0.374386\pi$
$863$	−17.8385	+	30.8972i	−0.607229	+	1.05175i	−0.991695	+	0.128612i	$0.958948\pi$
$864$	2.52194	+	4.36813i	0.0857982	+	0.148607i
$865$	37.0892	−	34.4137i	1.26107	−	1.17010i
$866$	4.96008	−	3.38173i	0.168550	−	0.114916i
$867$	−8.09524	+	10.1511i	−0.274929	+	0.344750i
$868$	1.35698	+	3.26576i	0.0460590	+	0.110847i
$869$	1.99348	+	2.49975i	0.0676242	+	0.0847980i
$870$	35.5737	+	10.9730i	1.20606	+	0.372020i
$871$	0.512410	−	1.30560i	0.0173624	−	0.0442386i
$872$	1.25511	+	16.7483i	0.0425034	+	0.567169i
$873$	−0.253639	−	0.646262i	−0.00858439	−	0.0218727i
$874$	9.87152	−	4.75388i	0.333909	−	0.160802i
$875$	17.7690	−	23.2105i	0.600703	−	0.784659i
$876$	−12.6059	−	6.07069i	−0.425915	−	0.205110i
$877$	−4.24787	+	56.6839i	−0.143440	+	1.91408i	0.208444	+	0.978034i	$0.433160\pi$
$877$	−4.24787	+	56.6839i	−0.143440	+	1.91408i	−0.351884	+	0.936044i	$0.614459\pi$
$878$	5.23635	−	1.61520i	0.176718	−	0.0545103i
$879$	20.4237	+	13.9246i	0.688875	+	0.469667i
$880$	13.5830	−	2.04731i	0.457883	−	0.0690148i
$881$	−13.6699			−0.460551			−0.230276	−	0.973125i	$-0.573963\pi$
$881$	−13.6699			−0.460551			−0.230276	+	0.973125i	$0.573963\pi$
$882$	−0.378362	+	1.08907i	−0.0127401	+	0.0366708i
$883$	−47.5163			−1.59905			−0.799525	−	0.600632i	$-0.794916\pi$
$883$	−47.5163			−1.59905			−0.799525	+	0.600632i	$0.794916\pi$
$884$	−0.890179	+	0.134173i	−0.0299400	+	0.00451272i
$885$	38.8628	+	26.4962i	1.30636	+	0.890661i
$886$	0.0226476	−	0.00698585i	0.000760860	−	0.000234694i
$887$	1.29532	−	17.2848i	0.0434926	−	0.580368i	−0.932302	−	0.361680i	$-0.882203\pi$
$887$	1.29532	−	17.2848i	0.0434926	−	0.580368i	0.975795	−	0.218688i	$-0.0701776\pi$
$888$	−4.55835	−	2.19519i	−0.152968	−	0.0736656i
$889$	−4.59953	+	22.1675i	−0.154263	+	0.743475i
$890$	7.93550	−	3.82154i	0.265999	−	0.128098i
$891$	21.0074	+	53.5259i	0.703773	+	1.79319i
$892$	−0.0176544	−	0.235582i	−0.000591115	−	0.00788788i
$893$	−8.46761	+	21.5751i	−0.283358	+	0.721983i
$894$	7.45328	+	2.29903i	0.249275	+	0.0768911i
$895$	−1.02952	−	1.29097i	−0.0344129	−	0.0431524i
$896$	2.15607	−	1.53342i	0.0720291	−	0.0512280i
$897$	0.845399	−	1.06010i	0.0282271	−	0.0353956i
$898$	−3.02821	+	2.06460i	−0.101053	+	0.0688966i
$899$	9.06652	−	8.41250i	0.302385	−	0.280573i
$900$	−0.00945051	−	0.0163688i	−0.000315017	−	0.000545626i
$901$	−0.482987	+	0.836558i	−0.0160906	+	0.0278698i
$902$	−0.794776	−	3.48214i	−0.0264632	−	0.115943i
$903$	3.90518	+	41.1521i	0.129956	+	1.36946i
$904$	2.24369	−	9.83026i	0.0746241	−	0.326950i
$905$	−22.3008	−	20.6921i	−0.741302	−	0.687828i
$906$	−22.4286	−	3.38057i	−0.745141	−	0.112312i
$907$	−22.7350	−	3.42676i	−0.754904	−	0.113784i	−0.239695	−	0.970848i	$-0.577048\pi$
$907$	−22.7350	−	3.42676i	−0.754904	−	0.113784i	−0.515209	+	0.857065i	$0.672286\pi$
$908$	11.2535	+	10.4418i	0.373462	+	0.346522i
$909$	0.0386914	−	0.169518i	0.00128331	−	0.00562257i
$910$	1.03763	−	0.342723i	0.0343971	−	0.0113612i
$911$	0.384543	+	1.68479i	0.0127405	+	0.0558197i	0.980899	−	0.194520i	$-0.0623149\pi$
$911$	0.384543	+	1.68479i	0.0127405	+	0.0558197i	−0.968158	+	0.250340i	$0.919458\pi$
$912$	−2.33513	+	4.04456i	−0.0773238	+	0.133929i
$913$	−54.1536	−	93.7967i	−1.79222	−	3.10422i
$914$	−9.58352	+	8.89221i	−0.316995	+	0.294128i
$915$	1.82278	−	1.24275i	0.0602592	−	0.0410840i
$916$	−13.1404	+	16.4775i	−0.434170	+	0.544432i
$917$	48.3277	−	8.26657i	1.59592	−	0.272986i
$918$	−15.5019	−	19.4387i	−0.511638	−	0.641574i
$919$	24.4649	+	7.54642i	0.807022	+	0.248933i	0.670698	−	0.741731i	$-0.265995\pi$
$919$	24.4649	+	7.54642i	0.807022	+	0.248933i	0.136325	+	0.990664i	$0.456471\pi$
$920$	3.44835	−	8.78626i	0.113689	−	0.289674i
$921$	1.59176	+	21.2405i	0.0524502	+	0.699900i
$922$	5.79364	+	14.7620i	0.190803	+	0.486159i
$923$	0.747672	−	0.360060i	0.0246099	−	0.0118515i
$924$	25.5057	−	12.9115i	0.839076	−	0.424758i
$925$	−0.294053	−	0.141609i	−0.00966841	−	0.00465606i
$926$	1.76110	−	23.5003i	0.0578735	−	0.772268i
$927$	−0.994939	+	0.306898i	−0.0326781	+	0.0100798i
$928$	−7.64524	−	5.21244i	−0.250967	−	0.171107i
$929$	21.9420	−	3.30723i	0.719895	−	0.108507i	0.221130	−	0.975244i	$-0.429025\pi$
$929$	21.9420	−	3.30723i	0.719895	−	0.108507i	0.498764	+	0.866738i	$0.333787\pi$
$930$	−5.37773			−0.176343
$931$	18.0489	−	3.45667i	0.591528	−	0.113288i
$932$	−4.95317			−0.162247
$933$	10.4338	−	1.57264i	0.341586	−	0.0514858i
$934$	4.72818	+	3.22362i	0.154711	+	0.105480i
$935$	−64.7035	+	19.9584i	−2.11603	+	0.652709i
$936$	−0.00224782	+	0.0299951i	−7.34724e−5	+	0.000980421i
$937$	19.0839	+	9.19033i	0.623444	+	0.300235i	0.718809	−	0.695208i	$-0.244688\pi$
$937$	19.0839	+	9.19033i	0.623444	+	0.300235i	−0.0953650	+	0.995442i	$0.530402\pi$
$938$	−4.91298	−	19.7161i	−0.160415	−	0.643754i
$939$	−26.0283	+	12.5346i	−0.849401	+	0.409050i
$940$	7.29456	+	18.5862i	0.237922	+	0.606216i
$941$	3.08277	+	41.1367i	0.100495	+	1.34102i	0.788376	+	0.615194i	$0.210922\pi$
$941$	3.08277	+	41.1367i	0.100495	+	1.34102i	−0.687881	+	0.725824i	$0.741459\pi$
$942$	4.90819	−	12.5059i	0.159917	−	0.407463i
$943$	−2.34518	−	0.723393i	−0.0763696	−	0.0235569i
$944$	−7.28918	−	9.14035i	−0.237243	−	0.297493i
$945$	22.5262	+	20.0856i	0.732778	+	0.653385i
$946$	33.2594	−	41.7059i	1.08136	−	1.35598i
$947$	−0.851466	+	0.580520i	−0.0276689	+	0.0188644i	−0.577076	−	0.816691i	$-0.695806\pi$
$947$	−0.851466	+	0.580520i	−0.0276689	+	0.0188644i	0.549407	+	0.835555i	$0.314854\pi$
$948$	−0.686471	+	0.636952i	−0.0222955	+	0.0206872i
$949$	0.718181	+	1.24393i	0.0233131	+	0.0403796i
$950$	−0.150636	+	0.260909i	−0.00488727	+	0.00846500i
$951$	−11.2822	−	49.4307i	−0.365852	−	1.60290i
$952$	−9.38272	+	9.05837i	−0.304096	+	0.293583i
$953$	0.627459	−	2.74908i	0.0203254	−	0.0890513i	−0.963748	−	0.266814i	$-0.914029\pi$
$953$	0.627459	−	2.74908i	0.0203254	−	0.0890513i	0.984073	+	0.177763i	$0.0568861\pi$
$954$	0.0236598	+	0.0219531i	0.000766015	+	0.000710758i
$955$	11.5194	+	1.73627i	0.372759	+	0.0561844i
$956$	−11.6090	−	1.74978i	−0.375462	−	0.0565919i
$957$	−73.2907	−	68.0038i	−2.36915	−	2.19825i
$958$	1.08998	−	4.77550i	0.0352155	−	0.154289i
$959$	1.39023	−	3.75961i	0.0448928	−	0.121404i
$960$	0.895261	+	3.92240i	0.0288944	+	0.126595i
$961$	14.6067	−	25.2995i	0.471183	−	0.816113i
$962$	0.259697	+	0.449809i	0.00837297	+	0.0145024i
$963$	−0.0112682	+	0.0104554i	−0.000363114	+	0.000336920i
$964$	7.55164	−	5.14862i	0.243222	−	0.165826i
$965$	−27.7712	+	34.8239i	−0.893985	+	1.12102i
$966$	1.07958	−	19.6137i	0.0347350	−	0.631060i
$967$	21.2034	+	26.5882i	0.681854	+	0.855018i	0.995524	−	0.0945140i	$-0.0301297\pi$
$967$	21.2034	+	26.5882i	0.681854	+	0.855018i	−0.313669	+	0.949532i	$0.601558\pi$
$968$	−24.7410	−	7.63158i	−0.795205	−	0.245288i
$969$	8.41063	−	21.4299i	0.270188	−	0.688429i
$970$	0.712402	+	9.50634i	0.0228738	+	0.305230i
$971$	−10.2900	−	26.2186i	−0.330223	−	0.841394i	−0.995497	−	0.0947948i	$-0.969780\pi$
$971$	−10.2900	−	26.2186i	−0.330223	−	0.841394i	0.665274	−	0.746599i	$-0.268315\pi$
$972$	−1.54042	+	0.741829i	−0.0494091	+	0.0237942i
$973$	54.9148	−	1.08817i	1.76049	−	0.0348852i
$974$	−14.9278	−	7.18883i	−0.478317	−	0.230345i
$975$	−0.00278620	+	0.0371792i	−8.92297e−5	+	0.00119069i
$976$	−0.523978	+	0.161626i	−0.0167721	+	0.00517352i
$977$	8.84889	+	6.03307i	0.283101	+	0.193015i	0.696542	−	0.717516i	$-0.254721\pi$
$977$	8.84889	+	6.03307i	0.283101	+	0.193015i	−0.413441	+	0.910531i	$0.635673\pi$
$978$	2.62238	−	0.395260i	0.0838545	−	0.0126390i
$979$	−23.6545			−0.756001
$980$	9.37244	−	12.7586i	0.299391	−	0.407557i
$981$	−2.76623			−0.0883188
$982$	−2.07277	+	0.312420i	−0.0661447	+	0.00996971i
$983$	17.5083	+	11.9370i	0.558430	+	0.380731i	0.809394	−	0.587265i	$-0.199795\pi$
$983$	17.5083	+	11.9370i	0.558430	+	0.380731i	−0.250965	+	0.967996i	$0.580748\pi$
$984$	0.999638	−	0.308347i	0.0318673	−	0.00982975i
$985$	3.39856	−	45.3507i	0.108287	−	1.44499i
$986$	41.0947	+	19.7901i	1.30872	+	0.630246i
$987$	26.5465	+	31.9679i	0.844984	+	1.01755i
$988$	0.431966	−	0.208024i	0.0137427	−	0.00661812i
$989$	−13.3913	−	34.1204i	−0.425818	−	1.08497i
$990$	0.169072	+	2.25610i	0.00537345	+	0.0717037i
$991$	12.5925	−	32.0852i	0.400015	−	1.01922i	−0.578981	−	0.815341i	$-0.696550\pi$
$991$	12.5925	−	32.0852i	0.400015	−	1.01922i	0.978996	−	0.203880i	$-0.0653551\pi$
$992$	1.27727	+	0.393987i	0.0405535	+	0.0125091i
$993$	14.4298	+	18.0943i	0.457915	+	0.574207i
$994$	5.80366	−	10.5286i	0.184081	−	0.333947i
$995$	−24.8376	+	31.1454i	−0.787405	+	0.987374i
$996$	26.2100	−	17.8697i	0.830497	−	0.566223i
$997$	−19.6692	+	18.2504i	−0.622930	+	0.577995i	−0.927189	−	0.374595i	$-0.877782\pi$
$997$	−19.6692	+	18.2504i	−0.622930	+	0.577995i	0.304259	+	0.952590i	$0.401591\pi$
$998$	−0.927351	−	1.60622i	−0.0293548	−	0.0508440i
$999$	−7.17244	+	12.4230i	−0.226926	+	0.393047i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	98.2.g.a.93.1	yes	24
3.2	odd	2		882.2.z.d.289.1		24
4.3	odd	2		784.2.bg.a.289.2		24
7.2	even	3		686.2.e.f.393.3		24
7.3	odd	6		686.2.g.c.557.2		24
7.4	even	3		686.2.g.a.557.1		24
7.5	odd	6		686.2.e.e.393.2		24
7.6	odd	2		686.2.g.b.79.2		24
49.6	odd	14		686.2.g.c.569.2		24
49.10	odd	42		686.2.g.b.165.2		24
49.16	even	21		686.2.e.f.295.3		24
49.23	even	21		4802.2.a.i.1.4		12
49.26	odd	42		4802.2.a.k.1.9		12
49.33	odd	42		686.2.e.e.295.2		24
49.39	even	21	inner	98.2.g.a.39.1	✓	24
49.43	even	7		686.2.g.a.569.1		24
147.137	odd	42		882.2.z.d.235.1		24
196.39	odd	42		784.2.bg.a.529.2		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
98.2.g.a.39.1	✓	24	49.39	even	21	inner
98.2.g.a.93.1	yes	24	1.1	even	1	trivial
686.2.e.e.295.2		24	49.33	odd	42
686.2.e.e.393.2		24	7.5	odd	6
686.2.e.f.295.3		24	49.16	even	21
686.2.e.f.393.3		24	7.2	even	3
686.2.g.a.557.1		24	7.4	even	3
686.2.g.a.569.1		24	49.43	even	7
686.2.g.b.79.2		24	7.6	odd	2
686.2.g.b.165.2		24	49.10	odd	42
686.2.g.c.557.2		24	7.3	odd	6
686.2.g.c.569.2		24	49.6	odd	14
784.2.bg.a.289.2		24	4.3	odd	2
784.2.bg.a.529.2		24	196.39	odd	42
882.2.z.d.235.1		24	147.137	odd	42
882.2.z.d.289.1		24	3.2	odd	2
4802.2.a.i.1.4		12	49.23	even	21
4802.2.a.k.1.9		12	49.26	odd	42

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:	\( N \)	\(=\)	\( 98 = 2 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	98.g (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.988831 - 0.149042i) q^{2} +(-1.46985 - 1.00212i) q^{3} +(0.955573 - 0.294755i) q^{4} +(0.169008 - 2.25526i) q^{5} +(-1.60279 - 0.771862i) q^{6} +(2.40601 + 1.10050i) q^{7} +(0.900969 - 0.433884i) q^{8} +(0.0601727 + 0.153317i) q^{9} +O(q^{10})\)	\(q+(0.988831 - 0.149042i) q^{2} +(-1.46985 - 1.00212i) q^{3} +(0.955573 - 0.294755i) q^{4} +(0.169008 - 2.25526i) q^{5} +(-1.60279 - 0.771862i) q^{6} +(2.40601 + 1.10050i) q^{7} +(0.900969 - 0.433884i) q^{8} +(0.0601727 + 0.153317i) q^{9} +(-0.169008 - 2.25526i) q^{10} +(-2.21901 + 5.65396i) q^{11} +(-1.69993 - 0.524358i) q^{12} +(0.113866 + 0.142784i) q^{13} +(2.54316 + 0.729608i) q^{14} +(-2.50847 + 3.14552i) q^{15} +(0.826239 - 0.563320i) q^{16} +(-3.61347 + 3.35281i) q^{17} +(0.0823514 + 0.142637i) q^{18} +(1.31263 - 2.27355i) q^{19} +(-0.503250 - 2.20488i) q^{20} +(-2.43364 - 4.02869i) q^{21} +(-1.35155 + 5.92153i) q^{22} +(3.05939 + 2.83870i) q^{23} +(-1.75909 - 0.265140i) q^{24} +(-0.113477 - 0.0171038i) q^{25} +(0.133875 + 0.124218i) q^{26} +(-1.12237 + 4.91742i) q^{27} +(2.62350 + 0.342420i) q^{28} +(-2.05900 - 9.02107i) q^{29} +(-2.01163 + 3.48425i) q^{30} +(0.668329 + 1.15758i) q^{31} +(0.733052 - 0.680173i) q^{32} +(8.92758 - 6.08672i) q^{33} +(-3.07340 + 3.85392i) q^{34} +(2.88854 - 5.24019i) q^{35} +(0.102691 + 0.128770i) q^{36} +(2.71766 + 0.838288i) q^{37} +(0.959119 - 2.44379i) q^{38} +(-0.0242788 - 0.323978i) q^{39} +(-0.826249 - 2.10525i) q^{40} +(-0.529812 + 0.255144i) q^{41} +(-3.00690 - 3.62098i) q^{42} +(-7.91285 - 3.81063i) q^{43} +(-0.453897 + 6.05683i) q^{44} +(0.355940 - 0.109793i) q^{45} +(3.44831 + 2.35102i) q^{46} +(-8.72992 + 1.31582i) q^{47} -1.77896 q^{48} +(4.57781 + 5.29562i) q^{49} -0.114758 q^{50} +(8.67118 - 1.30697i) q^{51} +(0.150894 + 0.102878i) q^{52} +(0.187258 - 0.0577613i) q^{53} +(-0.376930 + 5.02978i) q^{54} +(12.3761 + 5.96002i) q^{55} +(2.64523 - 0.0524170i) q^{56} +(-4.20775 + 2.02635i) q^{57} +(-3.38053 - 8.61344i) q^{58} +(-0.873665 - 11.6583i) q^{59} +(-1.46987 + 3.74516i) q^{60} +(-0.523978 - 0.161626i) q^{61} +(0.833393 + 1.04504i) q^{62} +(-0.0239491 + 0.435104i) q^{63} +(0.623490 - 0.781831i) q^{64} +(0.341259 - 0.232666i) q^{65} +(7.92069 - 7.34932i) q^{66} +(-3.83993 - 6.65096i) q^{67} +(-2.46468 + 4.26894i) q^{68} +(-1.65211 - 7.23835i) q^{69} +(2.07527 - 5.61218i) q^{70} +(1.01113 - 4.43005i) q^{71} +(0.120736 + 0.112026i) q^{72} +(7.77715 + 1.17222i) q^{73} +(2.81225 + 0.423878i) q^{74} +(0.149653 + 0.138858i) q^{75} +(0.584177 - 2.55945i) q^{76} +(-11.5611 + 11.1615i) q^{77} +(-0.0722941 - 0.316741i) q^{78} +(0.263203 - 0.455881i) q^{79} +(-1.13079 - 1.95859i) q^{80} +(6.93979 - 6.43918i) q^{81} +(-0.485868 + 0.331259i) q^{82} +(-11.1180 + 13.9415i) q^{83} +(-3.51299 - 3.13238i) q^{84} +(6.95075 + 8.71597i) q^{85} +(-8.39241 - 2.58872i) q^{86} +(-6.01382 + 15.3230i) q^{87} +(0.453897 + 6.05683i) q^{88} +(1.42282 + 3.62529i) q^{89} +(0.335601 - 0.161617i) q^{90} +(0.116831 + 0.468849i) q^{91} +(3.76019 + 1.81081i) q^{92} +(0.177698 - 2.37121i) q^{93} +(-8.43630 + 2.60225i) q^{94} +(-4.90560 - 3.34458i) q^{95} +(-1.75909 + 0.265140i) q^{96} -4.21519 q^{97} +(5.31595 + 4.55419i) q^{98} -1.00037 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 2 q^{2} + 7 q^{3} + 2 q^{4} - 7 q^{6} + 4 q^{8} - 33 q^{9}+O(q^{10}) \) 24 * q - 2 * q^2 + 7 * q^3 + 2 * q^4 - 7 * q^6 + 4 * q^8 - 33 * q^9	\( 24 q - 2 q^{2} + 7 q^{3} + 2 q^{4} - 7 q^{6} + 4 q^{8} - 33 q^{9} - 7 q^{11} + 14 q^{13} - 7 q^{15} + 2 q^{16} - 7 q^{17} + 5 q^{18} - 7 q^{20} + 7 q^{21} - 7 q^{22} - 21 q^{23} + 4 q^{25} - 7 q^{26} - 35 q^{27} - 14 q^{28} - 11 q^{29} + 28 q^{31} - 2 q^{32} + 14 q^{33} + 7 q^{34} + 21 q^{35} + 3 q^{36} - 24 q^{37} - 7 q^{38} - 40 q^{39} + 14 q^{40} + 28 q^{41} - 21 q^{42} + 10 q^{43} + 21 q^{44} + 7 q^{45} + 42 q^{46} - 70 q^{47} - 14 q^{48} + 84 q^{49} + 8 q^{50} + 60 q^{51} - 7 q^{52} + 26 q^{53} + 63 q^{54} + 56 q^{55} + 21 q^{56} - 33 q^{57} - 30 q^{58} - 7 q^{59} + 14 q^{60} + 14 q^{61} + 28 q^{62} - 14 q^{63} - 4 q^{64} - 21 q^{66} - 36 q^{67} - 14 q^{68} - 35 q^{69} + 14 q^{70} - 2 q^{72} - 7 q^{73} - 11 q^{74} - 28 q^{75} - 91 q^{77} - 24 q^{78} - 26 q^{79} + 55 q^{81} + 14 q^{82} - 7 q^{83} - 21 q^{84} + 49 q^{85} - 16 q^{86} + 35 q^{87} - 21 q^{88} - 56 q^{89} - 21 q^{90} + 7 q^{91} + 21 q^{92} + 72 q^{93} - 35 q^{94} - 14 q^{95} - 126 q^{97} - 56 q^{98} - 14 q^{99}+O(q^{100}) \) 24 * q - 2 * q^2 + 7 * q^3 + 2 * q^4 - 7 * q^6 + 4 * q^8 - 33 * q^9 - 7 * q^11 + 14 * q^13 - 7 * q^15 + 2 * q^16 - 7 * q^17 + 5 * q^18 - 7 * q^20 + 7 * q^21 - 7 * q^22 - 21 * q^23 + 4 * q^25 - 7 * q^26 - 35 * q^27 - 14 * q^28 - 11 * q^29 + 28 * q^31 - 2 * q^32 + 14 * q^33 + 7 * q^34 + 21 * q^35 + 3 * q^36 - 24 * q^37 - 7 * q^38 - 40 * q^39 + 14 * q^40 + 28 * q^41 - 21 * q^42 + 10 * q^43 + 21 * q^44 + 7 * q^45 + 42 * q^46 - 70 * q^47 - 14 * q^48 + 84 * q^49 + 8 * q^50 + 60 * q^51 - 7 * q^52 + 26 * q^53 + 63 * q^54 + 56 * q^55 + 21 * q^56 - 33 * q^57 - 30 * q^58 - 7 * q^59 + 14 * q^60 + 14 * q^61 + 28 * q^62 - 14 * q^63 - 4 * q^64 - 21 * q^66 - 36 * q^67 - 14 * q^68 - 35 * q^69 + 14 * q^70 - 2 * q^72 - 7 * q^73 - 11 * q^74 - 28 * q^75 - 91 * q^77 - 24 * q^78 - 26 * q^79 + 55 * q^81 + 14 * q^82 - 7 * q^83 - 21 * q^84 + 49 * q^85 - 16 * q^86 + 35 * q^87 - 21 * q^88 - 56 * q^89 - 21 * q^90 + 7 * q^91 + 21 * q^92 + 72 * q^93 - 35 * q^94 - 14 * q^95 - 126 * q^97 - 56 * q^98 - 14 * q^99

Introduction

L-functions

Modular forms

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