LMFDB - Embedded newform 462.2.bf.a.5.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [462,2,Mod(5,462)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(462, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([15, 25, 12]))

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

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

chi := DirichletCharacter("462.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 462 = 2 \cdot 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	462.bf (of order $30$, degree $8$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.68908857338$
Analytic rank:	$0$
Dimension:	$256$
Relative dimension:	$32$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			5.17
Character	$\chi$	$=$	462.5
Dual form			462.2.bf.a.185.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.207912 - 0.978148i) q^{2} +(-1.71826 + 0.218129i) q^{3} +(-0.913545 - 0.406737i) q^{4} +(2.60800 + 2.89648i) q^{5} +(-0.143884 + 1.72606i) q^{6} +(-2.64502 - 0.0622836i) q^{7} +(-0.587785 + 0.809017i) q^{8} +(2.90484 - 0.749604i) q^{9} +O(q^{10})$	\(q+(0.207912 - 0.978148i) q^{2} +(-1.71826 + 0.218129i) q^{3} +(-0.913545 - 0.406737i) q^{4} +(2.60800 + 2.89648i) q^{5} +(-0.143884 + 1.72606i) q^{6} +(-2.64502 - 0.0622836i) q^{7} +(-0.587785 + 0.809017i) q^{8} +(2.90484 - 0.749604i) q^{9} +(3.37542 - 1.94880i) q^{10} +(-2.66075 - 1.98000i) q^{11} +(1.65843 + 0.499609i) q^{12} +(-4.64562 + 1.50945i) q^{13} +(-0.610853 + 2.57427i) q^{14} +(-5.11304 - 4.40803i) q^{15} +(0.669131 + 0.743145i) q^{16} +(-5.65019 + 1.20098i) q^{17} +(-0.129273 - 2.99721i) q^{18} +(1.34566 + 3.02240i) q^{19} +(-1.20443 - 3.70684i) q^{20} +(4.55842 - 0.469935i) q^{21} +(-2.48994 + 2.19094i) q^{22} +(-2.49481 - 1.44038i) q^{23} +(0.833498 - 1.51831i) q^{24} +(-1.06528 + 10.1355i) q^{25} +(0.510589 + 4.85793i) q^{26} +(-4.82776 + 1.92164i) q^{27} +(2.39101 + 1.13272i) q^{28} +(-0.271688 - 0.373946i) q^{29} +(-5.37477 + 4.08482i) q^{30} +(4.11773 + 3.70762i) q^{31} +(0.866025 - 0.500000i) q^{32} +(5.00376 + 2.82177i) q^{33} +5.77641i q^{34} +(-6.71782 - 7.82368i) q^{35} +(-2.95859 - 0.496707i) q^{36} +(-0.193492 - 1.84096i) q^{37} +(3.23614 - 0.687862i) q^{38} +(7.65313 - 3.60698i) q^{39} +(-3.87625 + 0.407410i) q^{40} +(6.11246 + 4.44096i) q^{41} +(0.488082 - 4.55651i) q^{42} -7.41903 q^{43} +(1.62538 + 2.89105i) q^{44} +(9.74705 + 6.45885i) q^{45} +(-1.92760 + 2.14082i) q^{46} +(0.609427 - 0.271334i) q^{47} +(-1.31184 - 1.13096i) q^{48} +(6.99224 + 0.329482i) q^{49} +(9.69250 + 3.14928i) q^{50} +(9.44652 - 3.29607i) q^{51} +(4.85793 + 0.510589i) q^{52} +(1.12647 + 1.01428i) q^{53} +(0.875903 + 5.12180i) q^{54} +(-1.20421 - 12.8707i) q^{55} +(1.60509 - 2.10326i) q^{56} +(-2.97147 - 4.89975i) q^{57} +(-0.422262 + 0.188003i) q^{58} +(-9.22518 - 4.10731i) q^{59} +(2.87808 + 6.10660i) q^{60} +(-10.1922 + 9.17711i) q^{61} +(4.48272 - 3.25689i) q^{62} +(-7.73004 + 1.80179i) q^{63} +(-0.309017 - 0.951057i) q^{64} +(-16.4879 - 9.51929i) q^{65} +(3.80045 - 4.30773i) q^{66} +(6.16351 + 10.6755i) q^{67} +(5.65019 + 1.20098i) q^{68} +(4.60092 + 1.93076i) q^{69} +(-9.04943 + 4.94438i) q^{70} +(-7.69097 - 2.49895i) q^{71} +(-1.10098 + 2.79067i) q^{72} +(0.505550 - 1.13548i) q^{73} +(-1.84096 - 0.193492i) q^{74} +(-0.380407 - 17.6477i) q^{75} -3.30843i q^{76} +(6.91441 + 5.40286i) q^{77} +(-1.93698 - 8.23582i) q^{78} +(3.54181 + 0.752835i) q^{79} +(-0.407410 + 3.87625i) q^{80} +(7.87619 - 4.35496i) q^{81} +(5.61477 - 5.05556i) q^{82} +(3.97590 - 12.2366i) q^{83} +(-4.35546 - 1.42477i) q^{84} +(-18.2143 - 13.2335i) q^{85} +(-1.54250 + 7.25691i) q^{86} +(0.548399 + 0.583274i) q^{87} +(3.16581 - 0.988776i) q^{88} +(5.34912 - 9.26495i) q^{89} +(8.34423 - 8.19118i) q^{90} +(12.3818 - 3.70318i) q^{91} +(1.69327 + 2.33058i) q^{92} +(-7.88407 - 5.47246i) q^{93} +(-0.138698 - 0.652523i) q^{94} +(-5.24485 + 11.7801i) q^{95} +(-1.37899 + 1.04804i) q^{96} +(8.70587 - 2.82871i) q^{97} +(1.77605 - 6.77094i) q^{98} +(-9.21327 - 3.75708i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 256 q - 32 q^{4} + 4 q^{7} - 12 q^{9}+O(q^{10}) $ 256 * q - 32 * q^4 + 4 * q^7 - 12 * q^9	$ 256 q - 32 q^{4} + 4 q^{7} - 12 q^{9} + 12 q^{10} + 24 q^{15} + 32 q^{16} - 8 q^{18} - 16 q^{21} - 12 q^{22} + 48 q^{25} + 6 q^{28} + 18 q^{31} - 132 q^{33} + 16 q^{36} + 4 q^{37} - 18 q^{40} - 4 q^{42} + 64 q^{43} - 48 q^{45} + 8 q^{46} + 76 q^{49} - 8 q^{51} - 88 q^{57} + 46 q^{58} - 8 q^{60} - 12 q^{63} + 64 q^{64} - 120 q^{66} - 32 q^{67} - 58 q^{70} - 12 q^{72} - 96 q^{73} - 204 q^{75} - 32 q^{78} - 4 q^{79} - 64 q^{81} + 24 q^{82} - 36 q^{84} + 232 q^{85} - 228 q^{87} - 6 q^{88} + 40 q^{91} - 2 q^{93} - 144 q^{94} + 160 q^{99}+O(q^{100}) $ 256 * q - 32 * q^4 + 4 * q^7 - 12 * q^9 + 12 * q^10 + 24 * q^15 + 32 * q^16 - 8 * q^18 - 16 * q^21 - 12 * q^22 + 48 * q^25 + 6 * q^28 + 18 * q^31 - 132 * q^33 + 16 * q^36 + 4 * q^37 - 18 * q^40 - 4 * q^42 + 64 * q^43 - 48 * q^45 + 8 * q^46 + 76 * q^49 - 8 * q^51 - 88 * q^57 + 46 * q^58 - 8 * q^60 - 12 * q^63 + 64 * q^64 - 120 * q^66 - 32 * q^67 - 58 * q^70 - 12 * q^72 - 96 * q^73 - 204 * q^75 - 32 * q^78 - 4 * q^79 - 64 * q^81 + 24 * q^82 - 36 * q^84 + 232 * q^85 - 228 * q^87 - 6 * q^88 + 40 * q^91 - 2 * q^93 - 144 * q^94 + 160 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/462\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{5}\right)$

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 $

$2$	0.207912	−	0.978148i	0.147016	−	0.691655i
$2$	0.207912	−	0.978148i	0.147016	−	0.691655i
$3$	−1.71826	+	0.218129i	−0.992038	+	0.125937i
$3$	−1.71826	+	0.218129i	−0.992038	+	0.125937i
$4$	−0.913545	−	0.406737i	−0.456773	−	0.203368i
$5$	2.60800	+	2.89648i	1.16633	+	1.29535i	0.947563	+	0.319570i	$0.103539\pi$
$5$	2.60800	+	2.89648i	1.16633	+	1.29535i	0.218772	+	0.975776i	$0.429795\pi$
$6$	−0.143884	+	1.72606i	−0.0587406	+	0.704663i
$7$	−2.64502	−	0.0622836i	−0.999723	−	0.0235410i
$7$	−2.64502	−	0.0622836i	−0.999723	−	0.0235410i
$8$	−0.587785	+	0.809017i	−0.207813	+	0.286031i
$9$	2.90484	−	0.749604i	0.968280	−	0.249868i
$10$	3.37542	−	1.94880i	1.06740	−	0.616265i
$11$	−2.66075	−	1.98000i	−0.802246	−	0.596993i
$11$	−2.66075	−	1.98000i	−0.802246	−	0.596993i
$12$	1.65843	+	0.499609i	0.478748	+	0.144225i
$13$	−4.64562	+	1.50945i	−1.28846	+	0.418647i	−0.871553	−	0.490301i	$-0.836887\pi$
$13$	−4.64562	+	1.50945i	−1.28846	+	0.418647i	−0.416910	+	0.908948i	$0.636887\pi$
$14$	−0.610853	+	2.57427i	−0.163257	+	0.688002i
$15$	−5.11304	−	4.40803i	−1.32018	−	1.13815i
$16$	0.669131	+	0.743145i	0.167283	+	0.185786i
$17$	−5.65019	+	1.20098i	−1.37037	+	0.291281i	−0.833564	−	0.552423i	$-0.813703\pi$
$17$	−5.65019	+	1.20098i	−1.37037	+	0.291281i	−0.536808	+	0.843705i	$0.680370\pi$
$18$	−0.129273	−	2.99721i	−0.0304700	−	0.706450i
$19$	1.34566	+	3.02240i	0.308716	+	0.693387i	0.999561	−	0.0296153i	$-0.00942822\pi$
$19$	1.34566	+	3.02240i	0.308716	+	0.693387i	−0.690846	+	0.723002i	$0.742762\pi$
$20$	−1.20443	−	3.70684i	−0.269318	−	0.828874i
$21$	4.55842	−	0.469935i	0.994728	−	0.102548i
$22$	−2.48994	+	2.19094i	−0.530856	+	0.467110i
$23$	−2.49481	−	1.44038i	−0.520204	−	0.300340i	0.216814	−	0.976213i	$-0.430433\pi$
$23$	−2.49481	−	1.44038i	−0.520204	−	0.300340i	−0.737018	+	0.675873i	$0.763767\pi$
$24$	0.833498	−	1.51831i	0.170137	−	0.309925i
$25$	−1.06528	+	10.1355i	−0.213056	+	2.02709i
$26$	0.510589	+	4.85793i	0.100135	+	0.952719i
$27$	−4.82776	+	1.92164i	−0.929103	+	0.369821i
$28$	2.39101	+	1.13272i	0.451859	+	0.214065i
$29$	−0.271688	−	0.373946i	−0.0504512	−	0.0694401i	0.783046	−	0.621964i	$-0.213665\pi$
$29$	−0.271688	−	0.373946i	−0.0504512	−	0.0694401i	−0.833497	+	0.552524i	$0.813665\pi$
$30$	−5.37477	+	4.08482i	−0.981293	+	0.745783i
$31$	4.11773	+	3.70762i	0.739566	+	0.665908i	0.950194	−	0.311658i	$-0.100884\pi$
$31$	4.11773	+	3.70762i	0.739566	+	0.665908i	−0.210629	+	0.977566i	$0.567551\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$	5.00376	+	2.82177i	0.871042	+	0.491208i
$34$			5.77641i			0.990647i
$35$	−6.71782	−	7.82368i	−1.13552	−	1.32244i
$36$	−2.95859	−	0.496707i	−0.493099	−	0.0827846i
$37$	−0.193492	−	1.84096i	−0.0318099	−	0.302651i	−0.998847	−	0.0480143i	$-0.984711\pi$
$37$	−0.193492	−	1.84096i	−0.0318099	−	0.302651i	0.967037	−	0.254637i	$-0.0819560\pi$
$38$	3.23614	−	0.687862i	0.524971	−	0.111586i
$39$	7.65313	−	3.60698i	1.22548	−	0.577578i
$40$	−3.87625	+	0.407410i	−0.612889	+	0.0644172i
$41$	6.11246	+	4.44096i	0.954606	+	0.693562i	0.951892	−	0.306435i	$-0.0991361\pi$
$41$	6.11246	+	4.44096i	0.954606	+	0.693562i	0.00271405	+	0.999996i	$0.499136\pi$
$42$	0.488082	−	4.55651i	0.0753127	−	0.703085i
$43$	−7.41903			−1.13139			−0.565696	−	0.824614i	$-0.691392\pi$
$43$	−7.41903			−1.13139			−0.565696	+	0.824614i	$0.691392\pi$
$44$	1.62538	+	2.89105i	0.245035	+	0.435842i
$45$	9.74705	+	6.45885i	1.45300	+	0.962828i
$46$	−1.92760	+	2.14082i	−0.284210	+	0.315647i
$47$	0.609427	−	0.271334i	0.0888940	−	0.0395782i	−0.361808	−	0.932253i	$-0.617840\pi$
$47$	0.609427	−	0.271334i	0.0888940	−	0.0395782i	0.450702	+	0.892674i	$0.351174\pi$
$48$	−1.31184	−	1.13096i	−0.189348	−	0.163240i
$49$	6.99224	+	0.329482i	0.998892	+	0.0470689i
$50$	9.69250	+	3.14928i	1.37073	+	0.445376i
$51$	9.44652	−	3.29607i	1.32278	−	0.461542i
$52$	4.85793	+	0.510589i	0.673674	+	0.0708060i
$53$	1.12647	+	1.01428i	0.154732	+	0.139322i	0.742861	−	0.669446i	$-0.233468\pi$
$53$	1.12647	+	1.01428i	0.154732	+	0.139322i	−0.588128	+	0.808768i	$0.700135\pi$
$54$	0.875903	+	5.12180i	0.119195	+	0.696988i
$55$	−1.20421	−	12.8707i	−0.162375	−	1.73548i
$56$	1.60509	−	2.10326i	0.214489	−	0.281059i
$57$	−2.97147	−	4.89975i	−0.393581	−	0.648988i
$58$	−0.422262	+	0.188003i	−0.0554457	+	0.0246860i
$59$	−9.22518	−	4.10731i	−1.20102	−	0.534727i	−0.293993	−	0.955808i	$-0.594984\pi$
$59$	−9.22518	−	4.10731i	−1.20102	−	0.534727i	−0.907023	+	0.421081i	$0.861651\pi$
$60$	2.87808	+	6.10660i	0.371559	+	0.788358i
$61$	−10.1922	+	9.17711i	−1.30498	+	1.17501i	−0.332218	+	0.943203i	$0.607797\pi$
$61$	−10.1922	+	9.17711i	−1.30498	+	1.17501i	−0.972762	+	0.231806i	$0.925536\pi$
$62$	4.48272	−	3.25689i	0.569306	−	0.413625i
$63$	−7.73004	+	1.80179i	−0.973894	+	0.227005i
$64$	−0.309017	−	0.951057i	−0.0386271	−	0.118882i
$65$	−16.4879	−	9.51929i	−2.04507	−	1.18072i
$66$	3.80045	−	4.30773i	0.467803	−	0.530245i
$67$	6.16351	+	10.6755i	0.752992	+	1.30422i	0.946366	+	0.323095i	$0.104723\pi$
$67$	6.16351	+	10.6755i	0.752992	+	1.30422i	−0.193374	+	0.981125i	$0.561943\pi$
$68$	5.65019	+	1.20098i	0.685186	+	0.145641i
$69$	4.60092	+	1.93076i	0.553886	+	0.232436i
$70$	−9.04943	+	4.94438i	−1.08161	+	0.590966i
$71$	−7.69097	−	2.49895i	−0.912750	−	0.296571i	−0.185261	−	0.982689i	$-0.559313\pi$
$71$	−7.69097	−	2.49895i	−0.912750	−	0.296571i	−0.727490	+	0.686119i	$0.759313\pi$
$72$	−1.10098	+	2.79067i	−0.129752	+	0.328884i
$73$	0.505550	−	1.13548i	0.0591702	−	0.132898i	−0.881540	−	0.472108i	$-0.843493\pi$
$73$	0.505550	−	1.13548i	0.0591702	−	0.132898i	0.940711	+	0.339210i	$0.110160\pi$
$74$	−1.84096	−	0.193492i	−0.214007	−	0.0224930i
$75$	−0.380407	−	17.6477i	−0.0439256	−	2.03779i
$76$		−	3.30843i		−	0.379503i
$77$	6.91441	+	5.40286i	0.787970	+	0.615713i
$78$	−1.93698	−	8.23582i	−0.219320	−	0.932523i
$79$	3.54181	+	0.752835i	0.398485	+	0.0847005i	0.402795	−	0.915290i	$-0.368039\pi$
$79$	3.54181	+	0.752835i	0.398485	+	0.0847005i	−0.00431050	+	0.999991i	$0.501372\pi$
$80$	−0.407410	+	3.87625i	−0.0455499	+	0.433378i
$81$	7.87619	−	4.35496i	0.875132	−	0.483884i
$82$	5.61477	−	5.05556i	0.620047	−	0.558293i
$83$	3.97590	−	12.2366i	0.436412	−	1.34314i	−0.455221	−	0.890379i	$-0.650440\pi$
$83$	3.97590	−	12.2366i	0.436412	−	1.34314i	0.891633	−	0.452760i	$-0.149560\pi$
$84$	−4.35546	−	1.42477i	−0.475220	−	0.155455i
$85$	−18.2143	−	13.2335i	−1.97562	−	1.43537i
$86$	−1.54250	+	7.25691i	−0.166332	+	0.782533i
$87$	0.548399	+	0.583274i	0.0587945	+	0.0625336i
$88$	3.16581	−	0.988776i	0.337476	−	0.105404i
$89$	5.34912	−	9.26495i	0.567006	−	0.982083i	−0.429854	−	0.902898i	$-0.641435\pi$
$89$	5.34912	−	9.26495i	0.567006	−	0.982083i	0.996860	−	0.0791843i	$-0.0252316\pi$
$90$	8.34423	−	8.19118i	0.879559	−	0.863427i
$91$	12.3818	−	3.70318i	1.29796	−	0.388199i
$92$	1.69327	+	2.33058i	0.176535	+	0.242980i
$93$	−7.88407	−	5.47246i	−0.817540	−	0.567468i
$94$	−0.138698	−	0.652523i	−0.0143056	−	0.0673026i
$95$	−5.24485	+	11.7801i	−0.538110	+	1.20862i
$96$	−1.37899	+	1.04804i	−0.140743	+	0.106965i
$97$	8.70587	−	2.82871i	0.883947	−	0.287212i	0.168352	−	0.985727i	$-0.446156\pi$
$97$	8.70587	−	2.82871i	0.883947	−	0.287212i	0.715595	+	0.698515i	$0.246156\pi$
$98$	1.77605	−	6.77094i	0.179408	−	0.683968i
$99$	−9.21327	−	3.75708i	−0.925969	−	0.377601i
$100$	5.09565	−	8.82592i	0.509565	−	0.882592i
$101$	1.48049	−	1.64425i	0.147314	−	0.163609i	−0.664972	−	0.746869i	$-0.731556\pi$
$101$	1.48049	−	1.64425i	0.147314	−	0.163609i	0.812286	+	0.583260i	$0.198223\pi$
$102$	−1.26000	−	9.92539i	−0.124759	−	0.982760i
$103$	7.83289	−	0.823270i	0.771797	−	0.0811192i	0.289560	−	0.957160i	$-0.406491\pi$
$103$	7.83289	−	0.823270i	0.771797	−	0.0811192i	0.482237	+	0.876041i	$0.339824\pi$
$104$	1.50945	−	4.64562i	0.148014	−	0.455540i
$105$	13.2495	+	11.9778i	1.29302	+	1.16891i
$106$	1.22632	−	0.890973i	0.119111	−	0.0865390i
$107$	4.69994	+	10.5562i	0.454360	+	1.02051i	0.984943	+	0.172877i	$0.0553064\pi$
$107$	4.69994	+	10.5562i	0.454360	+	1.02051i	−0.530583	+	0.847633i	$0.678027\pi$
$108$	5.19198	+	0.208118i	0.499599	+	0.0200262i
$109$	−4.68300	−	8.11119i	−0.448550	−	0.776911i	0.549742	−	0.835334i	$-0.314726\pi$
$109$	−4.68300	−	8.11119i	−0.448550	−	0.776911i	−0.998292	+	0.0584233i	$0.981393\pi$
$110$	−12.8398	−	1.49807i	−1.22423	−	0.142835i
$111$	0.734035	+	3.12103i	0.0696715	+	0.296236i
$112$	−1.72358	−	2.00731i	−0.162863	−	0.189673i
$113$	3.09358	−	4.25794i	0.291019	−	0.400554i	−0.638326	−	0.769766i	$-0.720373\pi$
$113$	3.09358	−	4.25794i	0.291019	−	0.400554i	0.929345	+	0.369213i	$0.120373\pi$
$114$	−5.41048	+	1.88782i	−0.506738	+	0.176811i
$115$	−2.33444	−	10.9827i	−0.217688	−	1.02414i
$116$	0.0961016	+	0.452122i	0.00892281	+	0.0419785i
$117$	−12.3633	+	7.86709i	−1.14299	+	0.727313i
$118$	−5.93558	+	8.16962i	−0.546414	+	0.752075i
$119$	15.0196	−	2.82471i	1.37685	−	0.258941i
$120$	6.57154	−	1.54556i	0.599897	−	0.141090i
$121$	3.15918	+	10.5366i	0.287199	+	0.957871i
$122$	6.85749	+	11.8775i	0.620848	+	1.07534i
$123$	−11.4715	−	6.29743i	−1.03435	−	0.567820i
$124$	−2.25371	−	5.06191i	−0.202389	−	0.454573i
$125$	−16.3693	+	11.8930i	−1.46412	+	1.06374i
$126$	0.155253	+	7.93574i	0.0138310	+	0.706972i
$127$	−3.21741	+	9.90215i	−0.285499	+	0.878674i	0.700750	+	0.713407i	$0.252849\pi$
$127$	−3.21741	+	9.90215i	−0.285499	+	0.878674i	−0.986249	+	0.165267i	$0.947151\pi$
$128$	−0.994522	+	0.104528i	−0.0879041	+	0.00923910i
$129$	12.7478	−	1.61830i	1.12238	−	0.142484i
$130$	−12.7393	+	14.1484i	−1.11731	+	1.24090i
$131$	−1.95180	+	3.38062i	−0.170530	+	0.295366i	−0.938605	−	0.344993i	$-0.887881\pi$
$131$	−1.95180	+	3.38062i	−0.170530	+	0.295366i	0.768075	+	0.640359i	$0.221215\pi$
$132$	−3.42344	−	4.61303i	−0.297972	−	0.401513i
$133$	−3.37105	−	8.07813i	−0.292307	−	0.700462i
$134$	11.7237	−	3.80926i	1.01277	−	0.329070i
$135$	−18.1568	−	8.97187i	−1.56269	−	0.772176i
$136$	2.34948	−	5.27702i	0.201466	−	0.452501i
$137$	−1.05320	−	4.95492i	−0.0899811	−	0.423328i	−0.999962	−	0.00867828i	$-0.997238\pi$
$137$	−1.05320	−	4.95492i	−0.0899811	−	0.423328i	0.909981	−	0.414649i	$-0.136096\pi$
$138$	2.84515	−	4.09895i	0.242195	−	0.348926i
$139$	12.3357	+	16.9787i	1.04630	+	1.44011i	0.891971	+	0.452093i	$0.149322\pi$
$139$	12.3357	+	16.9787i	1.04630	+	1.44011i	0.154332	+	0.988019i	$0.450678\pi$
$140$	2.95485	+	9.87967i	0.249730	+	0.834985i
$141$	−0.987968	+	0.599156i	−0.0832019	+	0.0504581i
$142$	−4.04338	+	7.00334i	−0.339313	+	0.587708i
$143$	15.3496	+	5.18206i	1.28359	+	0.433345i
$144$	2.50078	+	1.65713i	0.208398	+	0.138094i
$145$	0.374566	−	1.76219i	0.0311060	−	0.146342i
$146$	−1.00556	−	0.730583i	−0.0832209	−	0.0604635i
$147$	−12.0864	+	0.959072i	−0.996866	+	0.0791029i
$148$	−0.572020	+	1.76050i	−0.0470198	+	0.144712i
$149$	−2.02232	+	1.82090i	−0.165675	+	0.149174i	−0.747798	−	0.663926i	$-0.768889\pi$
$149$	−2.02232	+	1.82090i	−0.165675	+	0.149174i	0.582123	+	0.813101i	$0.302222\pi$
$150$	−17.3412	−	3.29708i	−1.41590	−	0.269205i
$151$	−0.0268402	+	0.255368i	−0.00218423	+	0.0207815i	−0.995560	−	0.0941320i	$-0.969992\pi$
$151$	−0.0268402	+	0.255368i	−0.00218423	+	0.0207815i	0.993375	+	0.114914i	$0.0366591\pi$
$152$	−3.23614	−	0.687862i	−0.262485	−	0.0557930i
$153$	−15.5126	+	7.72407i	−1.25412	+	0.624454i
$154$	6.72238	−	5.64000i	0.541705	−	0.454484i
$155$			21.5964i			1.73467i
$156$	−8.45857	+	0.182329i	−0.677228	+	0.0145980i
$157$	6.39589	+	0.672235i	0.510448	+	0.0536502i	0.356252	−	0.934390i	$-0.384055\pi$
$157$	6.39589	+	0.672235i	0.510448	+	0.0536502i	0.154196	+	0.988040i	$0.450721\pi$
$158$	1.47277	−	3.30789i	0.117167	−	0.263161i
$159$	−2.15681	−	1.49708i	−0.171046	−	0.118726i
$160$	3.70684	+	1.20443i	0.293051	+	0.0952182i
$161$	6.50910	+	3.96521i	0.512989	+	0.312503i
$162$	−2.62224	−	8.60952i	−0.206023	−	0.676428i
$163$	−4.15829	−	0.883872i	−0.325702	−	0.0692302i	0.0421588	−	0.999111i	$-0.486576\pi$
$163$	−4.15829	−	0.883872i	−0.325702	−	0.0692302i	−0.367861	+	0.929881i	$0.619910\pi$
$164$	−3.77771	−	6.54318i	−0.294989	−	0.510937i
$165$	4.87661	+	21.8525i	0.379643	+	1.70121i
$166$	−11.1425	−	6.43315i	−0.864829	−	0.499309i
$167$	−0.675334	−	2.07846i	−0.0522589	−	0.160836i	0.921521	−	0.388328i	$-0.126947\pi$
$167$	−0.675334	−	2.07846i	−0.0522589	−	0.160836i	−0.973780	+	0.227492i	$0.926947\pi$
$168$	−2.29918	+	3.96406i	−0.177386	+	0.305834i
$169$	8.78610	−	6.38348i	0.675854	−	0.491037i
$170$	−16.7313	+	15.0649i	−1.28323	+	1.15543i
$171$	6.17454	+	7.77089i	0.472179	+	0.594255i
$172$	6.77762	+	3.01759i	0.516789	+	0.230089i
$173$	7.83593	−	3.48878i	0.595755	−	0.265247i	−0.0866297	−	0.996241i	$-0.527610\pi$
$173$	7.83593	−	3.48878i	0.595755	−	0.265247i	0.682384	+	0.730993i	$0.260943\pi$
$174$	0.684547	−	0.415146i	0.0518954	−	0.0314721i
$175$	3.44896	−	26.7421i	0.260717	−	2.02152i
$176$	−0.308961	−	3.30220i	−0.0232888	−	0.248913i
$177$	16.7472	+	5.04516i	1.25880	+	0.379217i
$178$	−7.95034	−	7.15852i	−0.595903	−	0.536554i
$179$	10.3808	+	1.09107i	0.775900	+	0.0815504i	0.484197	−	0.874959i	$-0.339112\pi$
$179$	10.3808	+	1.09107i	0.775900	+	0.0815504i	0.291702	+	0.956509i	$0.405778\pi$
$180$	−6.27732	−	9.86493i	−0.467884	−	0.735289i
$181$	−18.3448	−	5.96058i	−1.36356	−	0.443047i	−0.466328	−	0.884612i	$-0.654423\pi$
$181$	−18.3448	−	5.96058i	−1.36356	−	0.443047i	−0.897229	+	0.441565i	$0.854423\pi$
$182$	−1.04795	−	12.8811i	−0.0776791	−	0.954812i
$183$	15.5111	−	17.9919i	1.14661	−	1.33000i
$184$	2.63170	−	1.17171i	0.194012	−	0.0863796i
$185$	4.82767	−	5.36167i	0.354937	−	0.394198i
$186$	−6.99206	+	6.57399i	−0.512683	+	0.482028i
$187$	17.4117	+	7.99186i	1.27327	+	0.584423i
$188$	−0.667101			−0.0486533
$189$	12.8892	−	4.78209i	0.937552	−	0.347846i
$190$	10.4322	+	7.57946i	0.756834	+	0.549872i
$191$	−3.28342	+	0.345101i	−0.237580	+	0.0249706i	−0.222570	−	0.974917i	$-0.571445\pi$
$191$	−3.28342	+	0.345101i	−0.237580	+	0.0249706i	−0.0150097	+	0.999887i	$0.504778\pi$
$192$	0.738425	+	1.56676i	0.0532912	+	0.113071i
$193$	−12.7602	+	2.71226i	−0.918498	+	0.195233i	−0.642820	−	0.766017i	$-0.722236\pi$
$193$	−12.7602	+	2.71226i	−0.918498	+	0.195233i	−0.275678	+	0.961250i	$0.588902\pi$
$194$	−0.956842	−	9.10374i	−0.0686972	−	0.653611i
$195$	30.4069	+	12.7601i	2.17749	+	0.913773i
$196$	−6.25372	−	3.14500i	−0.446694	−	0.224643i
$197$			9.64636i			0.687275i	0.939102	+	0.343637i	$0.111659\pi$
$197$			9.64636i			0.687275i	−0.939102	+	0.343637i	$0.888341\pi$
$198$	−5.59052	+	8.23080i	−0.397301	+	0.584937i
$199$	3.90969	−	2.25726i	0.277150	−	0.160013i	−0.354982	−	0.934873i	$-0.615513\pi$
$199$	3.90969	−	2.25726i	0.277150	−	0.160013i	0.632133	+	0.774860i	$0.282180\pi$
$200$	−7.57361	−	6.81931i	−0.535535	−	0.482198i
$201$	−12.9191	−	16.9989i	−0.911246	−	1.19901i
$202$	−1.30050	−	1.78999i	−0.0915032	−	0.125943i
$203$	0.695329	+	1.00602i	0.0488025	+	0.0706085i
$204$	−9.97046	−	0.831136i	−0.698072	−	0.0581912i
$205$	3.07815	+	29.2867i	0.214988	+	2.04547i
$206$	0.823270	−	7.83289i	0.0573599	−	0.545743i
$207$	−8.32673	−	2.31395i	−0.578748	−	0.160831i
$208$	−4.23027	−	2.44235i	−0.293316	−	0.169346i
$209$	2.40390	−	10.7063i	0.166281	−	0.740568i
$210$	14.4708	−	10.4697i	0.998578	−	0.722476i
$211$	−0.800497	−	2.46368i	−0.0551085	−	0.169607i	0.919714	−	0.392589i	$-0.128421\pi$
$211$	−0.800497	−	2.46368i	−0.0551085	−	0.169607i	−0.974822	+	0.222983i	$0.928421\pi$
$212$	−0.616537	−	1.38477i	−0.0423439	−	0.0951061i
$213$	13.7602	+	2.61622i	0.942832	+	0.179261i
$214$	11.3027	−	2.40247i	0.772639	−	0.164229i
$215$	−19.3489	−	21.4891i	−1.31958	−	1.46554i
$216$	1.28304	−	5.03526i	0.0873001	−	0.342606i
$217$	−10.6605	−	10.0632i	−0.723685	−	0.683133i
$218$	−8.90759	+	2.89425i	−0.603298	+	0.196023i
$219$	−0.620985	+	2.06133i	−0.0419623	+	0.139292i
$220$	−4.13487	+	12.2477i	−0.278773	+	0.825742i
$221$	24.4358	−	14.1080i	1.64373	−	0.949007i
$222$	3.20545	−	0.0690952i	0.215136	−	0.00463736i
$223$	−14.5212	+	19.9867i	−0.972409	+	1.33841i	−0.0315877	+	0.999501i	$0.510056\pi$
$223$	−14.5212	+	19.9867i	−0.972409	+	1.33841i	−0.940821	+	0.338905i	$0.889944\pi$
$224$	−2.32179	+	1.26857i	−0.155131	+	0.0847599i
$225$	4.50312	+	30.2404i	0.300208	+	2.01603i
$226$	−3.52171	−	3.91125i	−0.234260	−	0.260173i
$227$	−10.7637	−	4.79231i	−0.714413	−	0.318077i	0.0171485	−	0.999853i	$-0.494541\pi$
$227$	−10.7637	−	4.79231i	−0.714413	−	0.318077i	−0.731561	+	0.681776i	$0.761208\pi$
$228$	0.721664	+	5.68475i	0.0477934	+	0.376482i
$229$	−4.10347	+	19.3053i	−0.271165	+	1.27573i	0.605970	+	0.795487i	$0.292785\pi$
$229$	−4.10347	+	19.3053i	−0.271165	+	1.27573i	−0.877135	+	0.480243i	$0.840548\pi$
$230$	−11.2280			−0.740355
$231$	−13.0593	−	7.77529i	−0.859238	−	0.511577i
$232$	0.462223			0.0303464
$233$	3.18720	−	14.9946i	0.208801	−	0.982330i	−0.741490	−	0.670964i	$-0.765880\pi$
$233$	3.18720	−	14.9946i	0.208801	−	0.982330i	0.950290	−	0.311366i	$-0.100786\pi$
$234$	5.12471	+	13.7288i	0.335013	+	0.897478i
$235$	2.37530	+	1.05755i	0.154948	+	0.0689871i
$236$	6.75702	+	7.50443i	0.439845	+	0.488497i
$237$	−6.24996	−	0.520996i	−0.405979	−	0.0338423i
$238$	0.359776	−	15.2787i	0.0233208	−	0.990372i
$239$	4.50083	−	6.19486i	0.291135	−	0.400712i	−0.638248	−	0.769831i	$-0.720340\pi$
$239$	4.50083	−	6.19486i	0.291135	−	0.400712i	0.929382	+	0.369119i	$0.120340\pi$
$240$	−0.145484	−	6.74928i	−0.00939097	−	0.435664i
$241$	−4.92039	+	2.84079i	−0.316950	+	0.182991i	−0.650032	−	0.759906i	$-0.725245\pi$
$241$	−4.92039	+	2.84079i	−0.316950	+	0.182991i	0.333082	+	0.942898i	$0.391911\pi$
$242$	10.9632	−	0.899470i	0.704739	−	0.0578201i
$243$	−12.5834	+	9.20098i	−0.807226	+	0.590243i
$244$	13.0437	−	4.23816i	0.835039	−	0.271321i
$245$	17.2815	+	21.1122i	1.10407	+	1.34881i
$246$	−8.54487	+	9.91151i	−0.544801	+	0.631935i
$247$	−10.8136	−	12.0097i	−0.688053	−	0.764160i
$248$	−5.41986	+	1.15203i	−0.344162	+	0.0731538i
$249$	−4.16249	+	21.8929i	−0.263787	+	1.38740i
$250$	8.22975	+	18.4843i	0.520495	+	1.16905i
$251$	3.43750	+	10.5795i	0.216973	+	0.667774i	0.999008	+	0.0445392i	$0.0141820\pi$
$251$	3.43750	+	10.5795i	0.216973	+	0.667774i	−0.782035	+	0.623235i	$0.785818\pi$
$252$	7.79460	+	1.49807i	0.491014	+	0.0943697i
$253$	3.78611	+	8.77221i	0.238031	+	0.551504i
$254$	9.01683	+	5.20587i	0.565766	+	0.326645i
$255$	34.1836	+	18.7655i	2.14066	+	1.17514i
$256$	−0.104528	+	0.994522i	−0.00653303	+	0.0621576i
$257$	2.57182	+	24.4692i	0.160425	+	1.52635i	0.717897	+	0.696150i	$0.245105\pi$
$257$	2.57182	+	24.4692i	0.160425	+	1.52635i	−0.557471	+	0.830196i	$0.688228\pi$
$258$	1.06748	−	12.8057i	0.0664586	−	0.797250i
$259$	0.397129	+	4.88141i	0.0246764	+	0.303316i
$260$	11.1906	+	15.4025i	0.694011	+	0.955225i
$261$	−1.06952	−	0.882596i	−0.0662017	−	0.0546313i
$262$	2.90094	+	2.61202i	0.179221	+	0.161371i
$263$	−7.95495	+	4.59279i	−0.490523	+	0.283204i	−0.724792	−	0.688968i	$-0.758064\pi$
$263$	−7.95495	+	4.59279i	−0.490523	+	0.283204i	0.234268	+	0.972172i	$0.424731\pi$
$264$	−5.22400	+	2.38953i	−0.321515	+	0.147065i
$265$			5.90804i			0.362928i
$266$	−8.60248	+	1.61785i	−0.527452	+	0.0991967i
$267$	−7.17023	+	17.0864i	−0.438811	+	1.04567i
$268$	−1.28852	−	12.2595i	−0.0787091	−	0.748867i
$269$	−15.8624	+	3.37165i	−0.967146	+	0.205573i	−0.664300	−	0.747466i	$-0.731270\pi$
$269$	−15.8624	+	3.37165i	−0.967146	+	0.205573i	−0.302846	+	0.953040i	$0.597937\pi$
$270$	−12.5508	+	15.8947i	−0.763819	+	0.967321i
$271$	−4.76101	+	0.500402i	−0.289211	+	0.0303972i	−0.248023	−	0.968754i	$-0.579781\pi$
$271$	−4.76101	+	0.500402i	−0.289211	+	0.0303972i	−0.0411876	+	0.999151i	$0.513114\pi$
$272$	−4.67322	−	3.39529i	−0.283355	−	0.205870i
$273$	−20.4673	+	9.06385i	−1.23874	+	0.548569i
$274$	−5.06562			−0.306025
$275$	22.9027	−	24.8587i	1.38108	−	1.49904i
$276$	−3.41784	−	3.63520i	−0.205730	−	0.218813i
$277$	6.65798	−	7.39444i	0.400039	−	0.444289i	−0.509146	−	0.860680i	$-0.670039\pi$
$277$	6.65798	−	7.39444i	0.400039	−	0.444289i	0.909185	+	0.416391i	$0.136705\pi$
$278$	19.1724	−	8.53610i	1.14988	−	0.511961i
$279$	14.7406	+	7.68337i	0.882496	+	0.459991i
$280$	10.2781	−	0.836181i	0.614235	−	0.0499714i
$281$	−9.14808	−	2.97239i	−0.545729	−	0.177318i	0.0231611	−	0.999732i	$-0.492627\pi$
$281$	−9.14808	−	2.97239i	−0.545729	−	0.177318i	−0.568890	+	0.822414i	$0.692627\pi$
$282$	0.380653	+	1.09095i	0.0226676	+	0.0649651i
$283$	−4.33033	−	0.455136i	−0.257411	−	0.0270550i	−0.0250562	−	0.999686i	$-0.507976\pi$
$283$	−4.33033	−	0.455136i	−0.257411	−	0.0270550i	−0.232355	+	0.972631i	$0.574643\pi$
$284$	6.00964	+	5.41110i	0.356606	+	0.321090i
$285$	6.44244	−	21.3854i	0.381617	−	1.26676i
$286$	8.26017	−	13.9367i	0.488434	−	0.824095i
$287$	−15.8910	−	12.1271i	−0.938014	−	0.715842i
$288$	2.14086	−	2.10160i	0.126152	−	0.123838i
$289$	14.9520	−	6.65704i	0.879527	−	0.391591i
$290$	−1.64581	−	0.732761i	−0.0966451	−	0.0430292i
$291$	−14.3419	+	6.75946i	−0.840739	+	0.396246i
$292$	−0.923686	+	0.831691i	−0.0540546	+	0.0486710i
$293$	−19.1468	+	13.9110i	−1.11857	+	0.812688i	−0.983992	−	0.178215i	$-0.942968\pi$
$293$	−19.1468	+	13.9110i	−1.11857	+	0.812688i	−0.134578	+	0.990903i	$0.542968\pi$
$294$	−1.57478	+	12.0216i	−0.0918432	+	0.701117i
$295$	−12.1625	−	37.4324i	−0.708130	−	2.17940i
$296$	1.60310	+	0.925548i	0.0931781	+	0.0537964i
$297$	16.6503	+	4.44596i	0.966150	+	0.257981i
$298$	1.36065	+	2.35671i	0.0788202	+	0.136521i
$299$	13.7641	+	2.92565i	0.795999	+	0.169195i
$300$	−6.83046	+	16.2767i	−0.394357	+	0.939738i
$301$	19.6235	+	0.462084i	1.13108	+	0.0266341i
$302$	0.244207	+	0.0793476i	0.0140525	+	0.00456594i
$303$	−2.18520	+	3.14818i	−0.125537	+	0.180858i
$304$	−1.34566	+	3.02240i	−0.0771790	+	0.173347i
$305$	−53.1627	−	5.58762i	−3.04409	−	0.319946i
$306$	4.33002	+	16.7796i	0.247531	+	0.959224i
$307$			17.9052i			1.02190i	0.859610	+	0.510951i	$0.170707\pi$
$307$			17.9052i			1.02190i	−0.859610	+	0.510951i	$0.829293\pi$
$308$	−4.11909	−	7.74810i	−0.234707	−	0.441489i
$309$	−13.2794	+	3.12317i	−0.755437	+	0.177671i
$310$	21.1245	+	4.49015i	1.19979	+	0.255023i
$311$	−0.167386	+	1.59257i	−0.00949161	+	0.0903066i	−0.998242	−	0.0592674i	$-0.981124\pi$
$311$	−0.167386	+	1.59257i	−0.00949161	+	0.0903066i	0.988751	+	0.149574i	$0.0477902\pi$
$312$	−1.58029	+	8.31164i	−0.0894664	+	0.470554i
$313$	−4.73867	+	4.26672i	−0.267845	+	0.241169i	−0.792098	−	0.610394i	$-0.791011\pi$
$313$	−4.73867	+	4.26672i	−0.267845	+	0.241169i	0.524253	+	0.851563i	$0.324345\pi$
$314$	1.98733	−	6.11636i	0.112151	−	0.345166i
$315$	−25.3788	−	17.6908i	−1.42994	−	0.996766i
$316$	−2.92940	−	2.12833i	−0.164791	−	0.119728i
$317$	2.82974	−	13.3129i	0.158934	−	0.747726i	−0.824413	−	0.565989i	$-0.808495\pi$
$317$	2.82974	−	13.3129i	0.158934	−	0.747726i	0.983347	−	0.181737i	$-0.0581721\pi$
$318$	−1.91279	+	1.79842i	−0.107264	+	0.100850i
$319$	−0.0175208	+	1.53292i	−0.000980974	+	0.0858270i
$320$	1.94880	−	3.37542i	0.108941	−	0.188692i
$321$	−10.3783	−	17.1132i	−0.579263	−	0.955165i
$322$	5.23188	−	5.54245i	0.291561	−	0.308869i
$323$	−11.2331	−	15.4610i	−0.625026	−	0.860275i
$324$	−8.96658	+	0.774919i	−0.498143	+	0.0430511i
$325$	−10.3501	−	48.6935i	−0.574122	−	2.70103i
$326$	−1.72911	+	3.88365i	−0.0957668	+	0.215096i
$327$	9.81590	+	12.9156i	0.542820	+	0.714237i
$328$	−7.18563	+	2.33475i	−0.396760	+	0.128915i
$329$	−1.62884	+	0.679727i	−0.0898011	+	0.0374745i
$330$	22.3889	−	0.226651i	1.23247	−	0.0124767i
$331$	−3.44507	+	5.96704i	−0.189358	+	0.327978i	−0.945036	−	0.326965i	$-0.893974\pi$
$331$	−3.44507	+	5.96704i	−0.189358	+	0.327978i	0.755678	+	0.654943i	$0.227307\pi$
$332$	−8.60923	+	9.56152i	−0.472493	+	0.524757i
$333$	−1.94205	−	5.20264i	−0.106424	−	0.285103i
$334$	−2.17345	+	0.228439i	−0.118926	+	0.0124996i
$335$	−14.8470	+	45.6942i	−0.811176	+	2.49654i
$336$	3.39941	+	3.07312i	0.185453	+	0.167652i
$337$	26.9382	−	19.5717i	1.46742	−	1.06614i	0.486063	−	0.873924i	$-0.338432\pi$
$337$	26.9382	−	19.5717i	1.46742	−	1.06614i	0.981353	−	0.192217i	$-0.0615676\pi$
$338$	−4.41725	−	9.92130i	−0.240267	−	0.539648i
$339$	−4.38679	+	7.99106i	−0.238258	+	0.434015i
$340$	11.2571	+	19.4978i	0.610501	+	1.05742i
$341$	−3.61515	−	18.0182i	−0.195771	−	0.975738i
$342$	8.88483	−	4.42395i	0.480437	−	0.239220i
$343$	−18.4741	−	1.30699i	−0.997507	−	0.0705707i
$344$	4.36080	−	6.00212i	0.235118	−	0.323613i
$345$	6.40682	+	18.3619i	0.344931	+	0.988572i
$346$	−1.78336	−	8.39006i	−0.0958741	−	0.451052i
$347$	−1.17240	−	5.51573i	−0.0629380	−	0.296100i	0.935409	−	0.353566i	$-0.115031\pi$
$347$	−1.17240	−	5.51573i	−0.0629380	−	0.296100i	−0.998347	+	0.0574665i	$0.981698\pi$
$348$	−0.263748	−	0.755901i	−0.0141384	−	0.0405206i
$349$	4.42774	−	6.09426i	0.237011	−	0.326218i	−0.673898	−	0.738824i	$-0.735381\pi$
$349$	4.42774	−	6.09426i	0.237011	−	0.326218i	0.910910	+	0.412606i	$0.135381\pi$
$350$	−25.4407	−	8.93359i	−1.35986	−	0.477521i
$351$	19.5273	−	16.2145i	1.04229	−	0.865466i
$352$	−3.29428	−	0.384357i	−0.175586	−	0.0204863i
$353$	1.83976	+	3.18655i	0.0979203	+	0.169603i	0.910824	−	0.412796i	$-0.135448\pi$
$353$	1.83976	+	3.18655i	0.0979203	+	0.169603i	−0.812903	+	0.582399i	$0.802114\pi$
$354$	8.41684	−	15.3323i	0.447350	−	0.814901i
$355$	−12.8199	−	28.7940i	−0.680411	−	1.52823i
$356$	−8.65506	+	6.28827i	−0.458717	+	0.333278i
$357$	−25.1915	+	8.12981i	−1.33328	+	0.430275i
$358$	3.22552	−	9.92714i	0.170474	−	0.524666i
$359$	22.8429	−	2.40089i	1.20560	−	0.126714i	0.519663	−	0.854371i	$-0.326057\pi$
$359$	22.8429	−	2.40089i	1.20560	−	0.126714i	0.685941	+	0.727657i	$0.259391\pi$
$360$	−10.9545	+	4.08911i	−0.577352	+	0.215515i
$361$	5.38936	−	5.98549i	0.283650	−	0.315026i
$362$	−9.64443	+	16.7046i	−0.506900	+	0.877976i
$363$	−7.72663	−	17.4155i	−0.405543	−	0.914076i
$364$	−12.8175	−	1.65309i	−0.671821	−	0.0866453i
$365$	4.60739	−	1.49703i	0.241162	−	0.0783582i
$366$	−14.3738	−	18.9129i	−0.751330	−	0.988591i
$367$	−10.9968	+	24.6992i	−0.574027	+	1.28929i	0.360289	+	0.932841i	$0.382678\pi$
$367$	−10.9968	+	24.6992i	−0.574027	+	1.28929i	−0.934316	+	0.356445i	$0.883989\pi$
$368$	−0.598943	−	2.81781i	−0.0312221	−	0.146888i
$369$	21.0847	+	8.31836i	1.09762	+	0.433036i
$370$	−4.24077	−	5.83692i	−0.220467	−	0.303447i
$371$	−2.91636	−	2.75294i	−0.151410	−	0.142926i
$372$	4.97660	+	8.20608i	0.258025	+	0.425465i
$373$	3.17086	−	5.49209i	0.164181	−	0.284370i	−0.772183	−	0.635400i	$-0.780835\pi$
$373$	3.17086	−	5.49209i	0.164181	−	0.284370i	0.936364	+	0.351030i	$0.114169\pi$
$374$	11.4373	−	15.3696i	0.591409	−	0.794743i
$375$	25.5326	−	24.0059i	1.31850	−	1.23966i
$376$	−0.138698	+	0.652523i	−0.00715280	+	0.0336513i
$377$	1.82661	+	1.32711i	0.0940753	+	0.0683497i
$378$	−1.99778	−	13.6018i	−0.102755	−	0.699601i
$379$	−7.15945	+	22.0345i	−0.367756	+	1.13184i	0.580481	+	0.814274i	$0.302865\pi$
$379$	−7.15945	+	22.0345i	−0.367756	+	1.13184i	−0.948237	+	0.317563i	$0.897135\pi$
$380$	9.58282	−	8.62841i	0.491588	−	0.442628i
$381$	3.36840	−	17.7163i	0.172568	−	0.907633i
$382$	−0.345101	+	3.28342i	−0.0176569	+	0.167994i
$383$	−17.6276	−	3.74686i	−0.900729	−	0.191456i	−0.265801	−	0.964028i	$-0.585637\pi$
$383$	−17.6276	−	3.74686i	−0.900729	−	0.191456i	−0.634927	+	0.772572i	$0.718970\pi$
$384$	1.68605	−	0.396541i	0.0860407	−	0.0202359i
$385$	2.38352	+	34.1182i	0.121475	+	1.73882i
$386$			13.0452i			0.663986i
$387$	−21.5511	+	5.56134i	−1.09550	+	0.282699i
$388$	−9.10374	−	0.956842i	−0.462173	−	0.0485763i
$389$	−8.52355	+	19.1442i	−0.432161	+	0.970649i	0.557887	+	0.829917i	$0.311612\pi$
$389$	−8.52355	+	19.1442i	−0.432161	+	0.970649i	−0.990048	+	0.140732i	$0.955054\pi$
$390$	18.8033	−	27.0895i	0.952140	−	1.37173i
$391$	15.8260	+	5.14218i	0.800356	+	0.260051i
$392$	−4.37649	+	5.46318i	−0.221046	+	0.275932i
$393$	2.61630	−	6.23453i	0.131975	−	0.314491i
$394$	9.43556	+	2.00559i	0.475357	+	0.101040i
$395$	7.05648	+	12.2222i	0.355050	+	0.614965i
$396$	6.88860	+	7.17964i	0.346165	+	0.360790i
$397$	23.4846	+	13.5588i	1.17866	+	0.680498i	0.955703	−	0.294331i	$-0.0950969\pi$
$397$	23.4846	+	13.5588i	1.17866	+	0.680498i	0.222953	+	0.974829i	$0.428430\pi$
$398$	−1.39506	−	4.29356i	−0.0699282	−	0.215217i
$399$	7.55442	+	13.1450i	0.378194	+	0.658073i
$400$	−8.24493	+	5.99029i	−0.412247	+	0.299515i
$401$	11.3487	−	10.2184i	0.566726	−	0.510282i	−0.335215	−	0.942142i	$-0.608809\pi$
$401$	11.3487	−	10.2184i	0.566726	−	0.510282i	0.901941	+	0.431859i	$0.142142\pi$
$402$	−19.3134	+	9.10257i	−0.963267	+	0.453995i
$403$	−24.7259	−	11.0087i	−1.23168	−	0.548381i
$404$	−2.02127	+	0.899925i	−0.100562	+	0.0447730i
$405$	33.1552	+	11.4555i	1.64749	+	0.569228i
$406$	1.12860	−	0.470971i	0.0560114	−	0.0233739i
$407$	−3.13026	+	5.28144i	−0.155161	+	0.261791i
$408$	−2.88595	+	9.57978i	−0.142876	+	0.474270i
$409$	5.62646	+	5.06608i	0.278210	+	0.250502i	0.796409	−	0.604759i	$-0.206730\pi$
$409$	5.62646	+	5.06608i	0.278210	+	0.250502i	−0.518198	+	0.855260i	$0.673397\pi$
$410$	29.2867	+	3.07815i	1.44637	+	0.152019i
$411$	2.89049	+	8.28412i	0.142577	+	0.408625i
$412$	−7.49055	−	2.43383i	−0.369033	−	0.119906i
$413$	24.1449	+	11.4385i	1.18809	+	0.562851i
$414$	−3.99461	+	7.66368i	−0.196324	+	0.376649i
$415$	45.8122	−	20.3969i	2.24883	−	1.00124i
$416$	−3.26850	+	3.63003i	−0.160251	+	0.177977i
$417$	−24.8995	−	26.4830i	−1.21934	−	1.29688i
$418$	−9.97252	−	4.57733i	−0.487772	−	0.223884i
$419$	−23.7806			−1.16176			−0.580880	−	0.813989i	$-0.697291\pi$
$419$	−23.7806			−1.16176			−0.580880	+	0.813989i	$0.697291\pi$
$420$	−7.23224	−	16.3313i	−0.352897	−	0.796887i
$421$	5.48923	+	3.98816i	0.267529	+	0.194371i	0.713460	−	0.700696i	$-0.247127\pi$
$421$	5.48923	+	3.98816i	0.267529	+	0.194371i	−0.445931	+	0.895067i	$0.647127\pi$
$422$	−2.57627	+	0.270777i	−0.125411	+	0.0131812i
$423$	1.56689	−	1.24501i	0.0761850	−	0.0605345i
$424$	−1.48269	+	0.315155i	−0.0720058	+	0.0153053i
$425$	−6.15350	−	58.5467i	−0.298489	−	2.83993i
$426$	5.41996	−	12.9156i	0.262598	−	0.625760i
$427$	27.5302	−	23.6388i	1.33228	−	1.14396i
$428$		−	11.5552i		−	0.558544i
$429$	−27.5049	−	5.55595i	−1.32795	−	0.268244i
$430$	−25.0424	+	14.4582i	−1.20765	+	0.697237i
$431$	−0.308881	−	0.278118i	−0.0148783	−	0.0133965i	0.661658	−	0.749806i	$-0.269853\pi$
$431$	−0.308881	−	0.278118i	−0.0148783	−	0.0133965i	−0.676536	+	0.736409i	$0.736520\pi$
$432$	−4.65846	−	2.30190i	−0.224130	−	0.110750i
$433$	−17.0968	−	23.5317i	−0.821619	−	1.13086i	−0.989426	−	0.145041i	$-0.953668\pi$
$433$	−17.0968	−	23.5317i	−0.821619	−	1.13086i	0.167807	−	0.985820i	$-0.446332\pi$
$434$	−12.0597	+	8.33533i	−0.578886	+	0.400108i
$435$	−0.259216	+	3.10961i	−0.0124285	+	0.149094i
$436$	0.979013	+	9.31469i	0.0468862	+	0.446093i
$437$	0.996239	−	9.47858i	0.0476566	−	0.453422i
$438$	1.88718	+	1.03599i	0.0901729	+	0.0495015i
$439$	−10.8610	−	6.27060i	−0.518367	−	0.299280i	0.217899	−	0.975971i	$-0.430080\pi$
$439$	−10.8610	−	6.27060i	−0.518367	−	0.299280i	−0.736266	+	0.676692i	$0.763413\pi$
$440$	11.1204	+	6.59097i	0.530145	+	0.314212i
$441$	20.5583	−	4.28432i	0.978968	−	0.204015i
$442$	−8.71923	−	26.8350i	−0.414731	−	1.27641i
$443$	12.3327	+	27.6996i	0.585943	+	1.31605i	0.926666	+	0.375886i	$0.122662\pi$
$443$	12.3327	+	27.6996i	0.585943	+	1.31605i	−0.340723	+	0.940164i	$0.610672\pi$
$444$	0.598865	−	3.14977i	0.0284209	−	0.149481i
$445$	40.7863	−	8.66939i	1.93346	−	0.410969i
$446$	16.5308	+	18.3593i	0.782755	+	0.869338i
$447$	3.07768	−	3.56991i	0.145569	−	0.168851i
$448$	0.758120	+	2.53481i	0.0358178	+	0.119758i
$449$	−19.3479	+	6.28652i	−0.913085	+	0.296679i	−0.727627	−	0.685973i	$-0.759377\pi$
$449$	−19.3479	+	6.28652i	−0.913085	+	0.296679i	−0.185458	+	0.982652i	$0.559377\pi$
$450$	30.5159	+	1.88263i	1.43853	+	0.0887479i
$451$	−7.47062	−	23.9190i	−0.351778	−	1.12630i
$452$	−4.55799	+	2.63155i	−0.214390	+	0.123778i
$453$	−0.00958452	−	0.444643i	−0.000450320	−	0.0208911i
$454$	−6.92549	+	9.53212i	−0.325029	+	0.447365i
$455$	43.0179	+	26.2056i	2.01671	+	1.22854i
$456$	5.71057	+	0.476032i	0.267422	+	0.0222922i
$457$	14.7835	+	16.4188i	0.691545	+	0.768038i	0.982006	−	0.188848i	$-0.0604755\pi$
$457$	14.7835	+	16.4188i	0.691545	+	0.768038i	−0.290462	+	0.956887i	$0.593809\pi$
$458$	18.0303	+	8.02760i	0.842500	+	0.375105i
$459$	24.9699	−	16.6557i	1.16549	−	0.777422i
$460$	−2.33444	+	10.9827i	−0.108844	+	0.512070i
$461$	17.6440			0.821761			0.410880	−	0.911689i	$-0.365221\pi$
$461$	17.6440			0.821761			0.410880	+	0.911689i	$0.365221\pi$
$462$	−10.3206	+	11.1573i	−0.480156	+	0.519086i
$463$	−34.9377			−1.62369			−0.811845	−	0.583873i	$-0.801537\pi$
$463$	−34.9377			−1.62369			−0.811845	+	0.583873i	$0.801537\pi$
$464$	0.0961016	−	0.452122i	0.00446140	−	0.0209892i
$465$	−4.71080	−	37.1083i	−0.218458	−	1.72085i
$466$	−14.0043	−	6.23511i	−0.648736	−	0.288836i
$467$	15.7399	+	17.4809i	0.728356	+	0.808922i	0.987617	−	0.156886i	$-0.0501455\pi$
$467$	15.7399	+	17.4809i	0.728356	+	0.808922i	−0.259260	+	0.965807i	$0.583479\pi$
$468$	14.4943	−	2.15835i	0.669997	−	0.0997696i
$469$	−15.6377	−	28.6208i	−0.722081	−	1.32159i
$470$	1.52830	−	2.10352i	0.0704950	−	0.0970281i
$471$	−11.1364	+	0.240052i	−0.513140	+	0.0110610i
$472$	8.74531	−	5.04911i	0.402535	−	0.232404i
$473$	19.7402	+	14.6897i	0.907655	+	0.675433i
$474$	−1.80905	+	6.00507i	−0.0830925	+	0.275822i
$475$	−32.0670	+	10.4192i	−1.47133	+	0.478065i
$476$	−14.8700	−	3.52854i	−0.681567	−	0.161730i
$477$	4.03252	+	2.10191i	0.184636	+	0.0962398i
$478$	−5.12372	−	5.69046i	−0.234353	−	0.260276i
$479$	−2.79076	+	0.593194i	−0.127513	+	0.0271037i	−0.271226	−	0.962516i	$-0.587429\pi$
$479$	−2.79076	+	0.593194i	−0.127513	+	0.0271037i	0.143713	+	0.989619i	$0.454096\pi$
$480$	−6.63204	−	1.26095i	−0.302710	−	0.0575541i
$481$	3.67773	+	8.26031i	0.167690	+	0.376638i
$482$	1.75570	+	5.40350i	0.0799702	+	0.246123i
$483$	−12.0493	−	5.39345i	−0.548260	−	0.245410i
$484$	1.39956	−	10.9106i	0.0636161	−	0.495936i
$485$	30.8982	+	17.8391i	1.40302	+	0.810032i
$486$	6.38368	+	14.2214i	0.289570	+	0.645097i
$487$	0.465708	−	4.43092i	0.0211033	−	0.200784i	−0.978890	−	0.204387i	$-0.934480\pi$
$487$	0.465708	−	4.43092i	0.0211033	−	0.200784i	0.999994	+	0.00360250i	$0.00114671\pi$
$488$	−1.43361	−	13.6398i	−0.0648963	−	0.617447i
$489$	7.33782	+	0.611680i	0.331828	+	0.0276611i
$490$	24.2439	−	12.5143i	1.09523	−	0.565340i
$491$	−2.79419	−	3.84588i	−0.126100	−	0.173562i	0.741299	−	0.671175i	$-0.234210\pi$
$491$	−2.79419	−	3.84588i	−0.126100	−	0.173562i	−0.867399	+	0.497613i	$0.834210\pi$
$492$	7.91834	+	10.4189i	0.356986	+	0.469719i
$493$	1.98419	+	1.78657i	0.0893634	+	0.0804632i
$494$	−13.9956	+	8.08034i	−0.629690	+	0.363552i
$495$	−13.1459	−	36.4846i	−0.590866	−	1.63986i
$496$			5.54095i			0.248796i
$497$	20.1871	+	7.08878i	0.905516	+	0.317975i
$498$	20.5490	+	8.62332i	0.920824	+	0.386420i
$499$	−2.27960	−	21.6889i	−0.102049	−	0.970929i	−0.919009	−	0.394236i	$-0.871009\pi$
$499$	−2.27960	−	21.6889i	−0.102049	−	0.970929i	0.816961	−	0.576694i	$-0.195657\pi$
$500$	19.7914	−	4.20680i	0.885100	−	0.188134i
$501$	1.61377	+	3.42403i	0.0720980	+	0.152974i
$502$	11.0630	−	1.16277i	0.493768	−	0.0518971i
$503$	−2.99599	−	2.17671i	−0.133585	−	0.0970548i	0.518986	−	0.854783i	$-0.326310\pi$
$503$	−2.99599	−	2.17671i	−0.133585	−	0.0970548i	−0.652571	+	0.757728i	$0.726310\pi$
$504$	3.08592	−	7.31280i	0.137458	−	0.325738i
$505$	8.62364			0.383747
$506$	9.36770	−	1.87953i	0.416445	−	0.0835553i
$507$	−13.7044	+	12.8850i	−0.608634	+	0.572242i
$508$	6.96681	−	7.73743i	0.309102	−	0.343293i
$509$	−35.8370	+	15.9556i	−1.58845	+	0.707222i	−0.995206	−	0.0978042i	$-0.968818\pi$
$509$	−35.8370	+	15.9556i	−1.58845	+	0.707222i	−0.593240	+	0.805026i	$0.702151\pi$
$510$	25.4626	−	29.5350i	1.12750	−	1.30783i
$511$	−1.40791	+	2.97189i	−0.0622823	+	0.131469i
$512$	0.951057	+	0.309017i	0.0420312	+	0.0136568i
$513$	−12.3045	−	12.0056i	−0.543258	−	0.530059i
$514$	24.4692	+	2.57182i	1.07929	+	0.113438i
$515$	22.8128	+	20.5407i	1.00525	+	0.905133i
$516$	−12.3039	−	3.70662i	−0.541651	−	0.163175i
$517$	−2.15877	−	0.484713i	−0.0949428	−	0.0213177i
$518$	4.85731	+	0.626452i	0.213418	+	0.0275247i
$519$	−12.7032	+	7.70388i	−0.557607	+	0.338163i
$520$	17.3926	−	7.74369i	0.762716	−	0.339583i
$521$	−34.1720	−	15.2144i	−1.49710	−	0.666554i	−0.515397	−	0.856952i	$-0.672355\pi$
$521$	−34.1720	−	15.2144i	−1.49710	−	0.666554i	−0.981707	+	0.190398i	$0.939022\pi$
$522$	−1.08567	+	0.862648i	−0.0475187	+	0.0377571i
$523$	13.9899	−	12.5966i	0.611736	−	0.550809i	−0.303958	−	0.952685i	$-0.598308\pi$
$523$	13.9899	−	12.5966i	0.611736	−	0.550809i	0.915694	+	0.401876i	$0.131642\pi$
$524$	3.15808	−	2.29448i	0.137962	−	0.100235i
$525$	−0.0929813	+	46.7023i	−0.00405804	+	2.03825i
$526$	2.83850	+	8.73601i	0.123765	+	0.380908i
$527$	−27.7187	−	16.0034i	−1.20745	−	0.697119i
$528$	1.25118	+	5.60665i	0.0544507	+	0.243998i
$529$	−7.35062	−	12.7316i	−0.319592	−	0.553550i
$530$	5.77893	+	1.22835i	0.251021	+	0.0533561i
$531$	−29.8765	−	5.01586i	−1.29653	−	0.217670i
$532$	−0.206061	+	8.75087i	−0.00893388	+	0.379398i
$533$	−35.0996	−	11.4045i	−1.52033	−	0.493986i
$534$	15.2222	+	10.5660i	0.658731	+	0.457236i
$535$	−18.3185	+	41.1440i	−0.791978	+	1.77881i
$536$	−12.2595	−	1.28852i	−0.529529	−	0.0556557i
$537$	−18.0750	+	0.389616i	−0.779993	+	0.0168132i
$538$			16.2167i			0.699153i
$539$	−17.9522	−	14.7213i	−0.773257	−	0.634092i
$540$	12.9379	+	15.5813i	0.556759	+	0.670511i
$541$	−6.92289	−	1.47151i	−0.297638	−	0.0632650i	0.0566721	−	0.998393i	$-0.481951\pi$
$541$	−6.92289	−	1.47151i	−0.297638	−	0.0632650i	−0.354310	+	0.935128i	$0.615284\pi$
$542$	−0.500402	+	4.76101i	−0.0214941	+	0.204503i
$543$	32.8213	+	6.24031i	1.40850	+	0.267797i
$544$	−4.29271	+	3.86518i	−0.184049	+	0.165718i
$545$	11.2806	−	34.7182i	0.483210	−	1.48717i
$546$	4.61039	+	21.9045i	0.197307	+	0.937428i
$547$	−1.74341	−	1.26666i	−0.0745430	−	0.0541587i	0.549890	−	0.835237i	$-0.314670\pi$
$547$	−1.74341	−	1.26666i	−0.0745430	−	0.0541587i	−0.624433	+	0.781079i	$0.714670\pi$
$548$	−1.05320	+	4.95492i	−0.0449905	+	0.211664i
$549$	−22.7276	+	34.2982i	−0.969988	+	1.46381i
$550$	−19.5537	−	27.5706i	−0.833774	−	1.17562i
$551$	0.764617	−	1.32436i	0.0325738	−	0.0564194i
$552$	−4.26637	+	2.58735i	−0.181589	+	0.110125i
$553$	−9.32126	−	2.21186i	−0.396380	−	0.0940577i
$554$	−5.84858	−	8.04988i	−0.248482	−	0.342007i
$555$	−7.12566	+	10.2658i	−0.302467	+	0.435759i
$556$	−4.36340	−	20.5282i	−0.185049	−	0.870589i
$557$	7.66982	−	17.2267i	0.324981	−	0.729919i	−0.674988	−	0.737829i	$-0.735851\pi$
$557$	7.66982	−	17.2267i	0.324981	−	0.729919i	0.999969	+	0.00790981i	$0.00251780\pi$
$558$	10.5802	−	12.8210i	0.447896	−	0.542756i
$559$	34.4660	−	11.1987i	1.45776	−	0.473654i
$560$	1.31903	−	10.2274i	0.0557394	−	0.432186i
$561$	−31.6611	−	9.93411i	−1.33673	−	0.419419i
$562$	−4.80943	+	8.33018i	−0.202874	+	0.351387i
$563$	28.6217	−	31.7876i	1.20626	−	1.33969i	0.281300	−	0.959620i	$-0.409234\pi$
$563$	28.6217	−	31.7876i	1.20626	−	1.33969i	0.924959	−	0.380067i	$-0.124099\pi$
$564$	1.14625	−	0.145514i	0.0482659	−	0.00612724i
$565$	20.4011	−	2.14424i	0.858282	−	0.0902090i
$566$	−1.34552	+	4.14107i	−0.0565562	+	0.174062i
$567$	−21.1039	+	11.0284i	−0.886281	+	0.463149i
$568$	6.54233	−	4.75328i	0.274510	−	0.199443i
$569$	6.83689	+	15.3559i	0.286617	+	0.643753i	0.998271	−	0.0587774i	$-0.0187202\pi$
$569$	6.83689	+	15.3559i	0.286617	+	0.643753i	−0.711654	+	0.702530i	$0.752054\pi$
$570$	−19.5786	−	10.7479i	−0.820057	−	0.450181i
$571$	11.6958	+	20.2577i	0.489454	+	0.847760i	0.999926	−	0.0121345i	$-0.00386262\pi$
$571$	11.6958	+	20.2577i	0.489454	+	0.847760i	−0.510472	+	0.859894i	$0.670529\pi$
$572$	−11.9148	−	10.9773i	−0.498182	−	0.458983i
$573$	5.56649	−	1.30918i	0.232543	−	0.0546918i
$574$	−15.1660	+	13.0223i	−0.633018	+	0.543542i
$575$	17.2566	−	23.7516i	0.719649	−	0.990512i
$576$	−1.61056	−	2.53103i	−0.0671067	−	0.105459i
$577$	2.35633	+	11.0857i	0.0980953	+	0.461502i	0.999588	+	0.0287076i	$0.00913917\pi$
$577$	2.35633	+	11.0857i	0.0980953	+	0.461502i	−0.901493	+	0.432795i	$0.857528\pi$
$578$	−3.40288	−	16.0093i	−0.141541	−	0.665899i
$579$	21.3337	−	7.44373i	0.886598	−	0.309351i
$580$	−1.05893	+	1.45749i	−0.0439697	+	0.0605191i
$581$	−11.2785	+	32.1183i	−0.467910	+	1.33249i
$582$	3.62989	+	15.4339i	0.150464	+	0.639755i
$583$	−0.988982	−	4.92915i	−0.0409595	−	0.204145i
$584$	0.621471	+	1.07642i	0.0257167	+	0.0445426i
$585$	−55.0304	−	15.2926i	−2.27523	−	0.632272i
$586$	9.62614	+	21.6207i	0.397652	+	0.893142i
$587$	34.1222	−	24.7912i	1.40837	−	1.02324i	0.414816	−	0.909905i	$-0.363846\pi$
$587$	34.1222	−	24.7912i	1.40837	−	1.02324i	0.993557	−	0.113337i	$-0.0361539\pi$
$588$	11.4315	+	4.03981i	0.471428	+	0.166599i
$589$	−5.66486	+	17.4346i	−0.233416	+	0.718381i
$590$	−39.1432	+	4.11411i	−1.61150	+	0.169375i
$591$	−2.10415	−	16.5750i	−0.0865531	−	0.681803i
$592$	1.23862	−	1.37563i	0.0509072	−	0.0565381i
$593$	14.7398	−	25.5300i	0.605289	−	1.04839i	−0.386716	−	0.922199i	$-0.626391\pi$
$593$	14.7398	−	25.5300i	0.605289	−	1.04839i	0.992006	−	0.126193i	$-0.0402760\pi$
$594$	7.81061	−	15.3621i	0.320473	−	0.630315i
$595$	47.3530	+	36.1373i	1.94128	+	1.48148i
$596$	2.58811	−	0.840927i	0.106013	−	0.0344457i
$597$	−6.22549	+	4.73137i	−0.254792	+	0.193642i
$598$	5.72344	−	12.8551i	0.234049	−	0.525682i
$599$	−3.94281	−	18.5495i	−0.161099	−	0.757910i	−0.982306	−	0.187281i	$-0.940033\pi$
$599$	−3.94281	−	18.5495i	−0.161099	−	0.757910i	0.821208	−	0.570630i	$-0.193301\pi$
$600$	14.5009	+	10.0653i	0.591998	+	0.410915i
$601$	−25.8604	−	35.5938i	−1.05487	−	1.45190i	−0.884512	−	0.466518i	$-0.845508\pi$
$601$	−25.8604	−	35.5938i	−1.05487	−	1.45190i	−0.170356	−	0.985383i	$-0.554492\pi$
$602$	4.53194	−	19.0986i	0.184708	−	0.778400i
$603$	25.9064	+	26.3904i	1.05499	+	1.07470i
$604$	0.128387	−	0.222373i	0.00522400	−	0.00904823i
$605$	−22.2799	+	36.6300i	−0.905805	+	1.48922i
$606$	2.62505	+	2.79199i	0.106636	+	0.113417i
$607$	−7.92002	+	37.2607i	−0.321464	+	1.51237i	0.459719	+	0.888064i	$0.347950\pi$
$607$	−7.92002	+	37.2607i	−0.321464	+	1.51237i	−0.781183	+	0.624303i	$0.785383\pi$
$608$	2.67658	+	1.94465i	0.108550	+	0.0788659i
$609$	−1.41420	−	1.57693i	−0.0573061	−	0.0639003i
$610$	−16.5187	+	50.8392i	−0.668821	+	2.05842i
$611$	−2.42160	+	2.18042i	−0.0979674	+	0.0882102i
$612$	17.3131	−	0.746736i	0.699843	−	0.0301850i
$613$	−2.57561	+	24.5053i	−0.104028	+	0.989760i	0.810638	+	0.585548i	$0.199121\pi$
$613$	−2.57561	+	24.5053i	−0.104028	+	0.989760i	−0.914666	+	0.404212i	$0.867546\pi$
$614$	17.5139	+	3.72270i	0.706804	+	0.150236i
$615$	−11.6773	−	49.6507i	−0.470876	−	2.00211i
$616$	−8.43520	+	2.41815i	−0.339864	+	0.0974302i
$617$		−	15.1078i		−	0.608218i	−0.952637	−	0.304109i	$-0.901641\pi$
$617$		−	15.1078i		−	0.608218i	0.952637	−	0.304109i	$-0.0983587\pi$
$618$	0.293986	+	13.6385i	0.0118258	+	0.548622i
$619$	7.81276	+	0.821154i	0.314021	+	0.0330050i	0.260228	−	0.965547i	$-0.416202\pi$
$619$	7.81276	+	0.821154i	0.314021	+	0.0330050i	0.0537930	+	0.998552i	$0.482869\pi$
$620$	8.78405	−	19.7293i	0.352776	−	0.792348i
$621$	14.8122	+	2.15967i	0.594395	+	0.0866646i
$622$	1.52297	+	0.494844i	0.0610656	+	0.0198414i
$623$	−14.7256	+	24.1728i	−0.589968	+	0.968463i
$624$	7.80145	+	3.27384i	0.312308	+	0.131059i
$625$	−27.2962	−	5.80199i	−1.09185	−	0.232080i
$626$	3.18825	+	5.52222i	0.127428	+	0.220712i
$627$	−1.79518	+	18.9205i	−0.0716925	+	0.755613i
$628$	−5.56952	−	3.21556i	−0.222248	−	0.128315i
$629$	3.30423	+	10.1694i	0.131748	+	0.405479i
$630$	−22.5808	+	21.1461i	−0.899641	+	0.842482i
$631$	28.8426	−	20.9554i	1.14820	−	0.834219i	0.159963	−	0.987123i	$-0.448862\pi$
$631$	28.8426	−	20.9554i	1.14820	−	0.834219i	0.988241	+	0.152903i	$0.0488624\pi$
$632$	−2.69088	+	2.42288i	−0.107037	+	0.0963769i
$633$	1.91286	+	4.05863i	0.0760294	+	0.161316i
$634$	−12.4336	−	5.53581i	−0.493803	−	0.219855i
$635$	−37.0724	+	16.5057i	−1.47117	+	0.655009i
$636$	1.36143	+	2.24490i	0.0539842	+	0.0890162i
$637$	−32.9806	+	9.02381i	−1.30674	+	0.357536i
$638$	1.49578	+	0.335850i	0.0592185	+	0.0132964i
$639$	−24.2143	−	1.49386i	−0.957901	−	0.0590962i
$640$	−2.89648	−	2.60800i	−0.114494	−	0.103090i
$641$	5.13665	+	0.539883i	0.202885	+	0.0213241i	0.205426	−	0.978673i	$-0.434142\pi$
$641$	5.13665	+	0.539883i	0.202885	+	0.0213241i	−0.00254059	+	0.999997i	$0.500809\pi$
$642$	−18.8970	+	6.59352i	−0.745805	+	0.260226i
$643$	−32.5898	−	10.5891i	−1.28521	−	0.417591i	−0.414801	−	0.909912i	$-0.636149\pi$
$643$	−32.5898	−	10.5891i	−1.28521	−	0.417591i	−0.870414	+	0.492321i	$0.836149\pi$
$644$	−4.33356	−	6.26989i	−0.170766	−	0.247068i
$645$	37.9338	+	32.7033i	1.49364	+	1.28769i
$646$	−17.4587	+	7.77310i	−0.686902	+	0.305828i
$647$	29.1320	−	32.3543i	1.14530	−	1.27198i	0.188224	−	0.982126i	$-0.439727\pi$
$647$	29.1320	−	32.3543i	1.14530	−	1.27198i	0.957071	−	0.289853i	$-0.0936065\pi$
$648$	−1.10627	+	8.93175i	−0.0434584	+	0.350872i
$649$	16.4134	+	29.1944i	0.644282	+	1.14598i
$650$	−49.7813			−1.95258
$651$	20.5127	+	14.9658i	0.803954	+	0.586556i
$652$	3.43928	+	2.49879i	0.134693	+	0.0978600i
$653$	−36.4834	+	3.83456i	−1.42771	+	0.150058i	−0.786632	−	0.617422i	$-0.788177\pi$
$653$	−36.4834	+	3.83456i	−1.42771	+	0.150058i	−0.641073	+	0.767480i	$0.721511\pi$
$654$	14.6742	−	6.91608i	0.573808	−	0.270440i
$655$	−14.8822	+	3.16331i	−0.581496	+	0.123601i
$656$	0.789756	+	7.51403i	0.0308348	+	0.293373i
$657$	0.617379	−	3.67736i	0.0240862	−	0.143468i
$658$	0.326217	+	1.73457i	0.0127173	+	0.0676207i
$659$			32.2029i			1.25445i	0.778839	+	0.627224i	$0.215809\pi$
$659$			32.2029i			1.25445i	−0.778839	+	0.627224i	$0.784191\pi$
$660$	4.43321	−	21.9467i	0.172562	−	0.854276i
$661$	−38.1375	+	22.0187i	−1.48338	+	0.856428i	−0.999822	−	0.0188858i	$-0.993988\pi$
$661$	−38.1375	+	22.0187i	−1.48338	+	0.856428i	−0.483555	+	0.875314i	$0.660655\pi$
$662$	5.12038	+	4.61041i	0.199009	+	0.179189i
$663$	−38.9097	+	29.5714i	−1.51113	+	1.14846i
$664$	7.56262	+	10.4091i	0.293486	+	0.403950i
$665$	14.6064	−	30.8320i	0.566413	−	1.19561i
$666$	−5.49272	+	0.817924i	−0.212839	+	0.0316939i
$667$	0.139185	+	1.32426i	0.00538927	+	0.0512755i
$668$	−0.228439	+	2.17345i	−0.00883858	+	0.0840935i
$669$	20.5915	−	37.5098i	0.796112	−	1.45021i
$670$	41.6089	+	24.0229i	1.60749	+	0.928085i
$671$	45.2896	−	4.23740i	1.74839	−	0.163583i
$672$	3.71274	−	2.68618i	0.143222	−	0.103622i
$673$	7.78679	+	23.9653i	0.300159	+	0.923793i	0.981440	+	0.191771i	$0.0614231\pi$
$673$	7.78679	+	23.9653i	0.300159	+	0.923793i	−0.681281	+	0.732022i	$0.738577\pi$
$674$	−13.5433	−	30.4187i	−0.521668	−	1.17168i
$675$	−14.3338	−	50.9787i	−0.551710	−	1.96217i
$676$	−10.6229	+	2.25797i	−0.408573	+	0.0868449i
$677$	6.93023	+	7.69680i	0.266350	+	0.295812i	0.861453	−	0.507838i	$-0.169555\pi$
$677$	6.93023	+	7.69680i	0.266350	+	0.295812i	−0.595102	+	0.803650i	$0.702888\pi$
$678$	6.90437	+	5.95237i	0.265161	+	0.228599i
$679$	−23.2034	+	6.93975i	−0.890463	+	0.266323i
$680$	21.4122	−	6.95726i	0.821122	−	0.266799i
$681$	19.5402	+	5.88657i	0.748782	+	0.225574i
$682$	−18.3760	−	0.210032i	−0.703655	−	0.00804254i
$683$	−34.1114	+	19.6942i	−1.30524	+	0.753578i	−0.981297	−	0.192500i	$-0.938341\pi$
$683$	−34.1114	+	19.6942i	−1.30524	+	0.753578i	−0.323939	+	0.946078i	$0.605007\pi$
$684$	−2.48001	−	9.61047i	−0.0948257	−	0.367465i
$685$	11.6051	−	15.9730i	0.443408	−	0.610298i
$686$	−5.11941	+	17.7986i	−0.195460	+	0.679555i
$687$	2.83979	−	34.0666i	0.108345	−	1.29972i
$688$	−4.96430	−	5.51342i	−0.189262	−	0.210197i
$689$	−6.76415	−	3.01159i	−0.257694	−	0.114733i
$690$	19.2927	−	2.44916i	0.734461	−	0.0932379i
$691$	−3.56661	+	16.7796i	−0.135680	+	0.638325i	0.856772	+	0.515695i	$0.172466\pi$
$691$	−3.56661	+	16.7796i	−0.135680	+	0.638325i	−0.992452	+	0.122630i	$0.960867\pi$
$692$	−8.57749			−0.326067
$693$	24.1353	+	10.5114i	0.916823	+	0.399294i
$694$	−5.63895			−0.214052
$695$	−17.0068	+	80.0107i	−0.645104	+	3.03498i
$696$	−0.794219	+	0.100824i	−0.0301048	+	0.00382173i
$697$	−39.8701	−	17.7513i	−1.51019	−	0.672378i
$698$	−5.04051	−	5.59805i	−0.190786	−	0.211889i
$699$	−2.20569	+	26.4599i	−0.0834269	+	1.00080i
$700$	−14.0278	+	23.0273i	−0.530201	+	0.870352i
$701$	3.88440	−	5.34642i	0.146712	−	0.201932i	−0.729336	−	0.684156i	$-0.760171\pi$
$701$	3.88440	−	5.34642i	0.146712	−	0.201932i	0.876048	+	0.482224i	$0.160171\pi$
$702$	−11.8002	−	22.4718i	−0.445371	−	0.848142i
$703$	5.30374	−	3.06211i	0.200034	−	0.115490i
$704$	−1.06088	+	3.14238i	−0.0399833	+	0.118433i
$705$	−4.31207	−	1.29903i	−0.162402	−	0.0489243i
$706$	3.49942	−	1.13703i	0.131703	−	0.0427927i
$707$	−4.01832	+	4.25685i	−0.151124	+	0.160095i
$708$	−13.2473	−	11.4207i	−0.497862	−	0.429215i
$709$	33.3625	+	37.0529i	1.25296	+	1.39155i	0.887557	+	0.460698i	$0.152401\pi$
$709$	33.3625	+	37.0529i	1.25296	+	1.39155i	0.365400	+	0.930851i	$0.380932\pi$
$710$	−30.8302	+	6.55317i	−1.15704	+	0.245936i
$711$	10.8527	−	0.468090i	0.407009	−	0.0175547i
$712$	4.35137	+	9.77333i	0.163074	+	0.366271i
$713$	−4.93257	−	15.1809i	−0.184726	−	0.568529i
$714$	2.71454	+	26.3313i	0.101589	+	0.985424i
$715$	25.0220	+	57.9745i	0.935768	+	2.16812i
$716$	−9.03958	−	5.21901i	−0.337825	−	0.195043i
$717$	−6.38232	+	11.6262i	−0.238352	+	0.434187i
$718$	2.40089	−	22.8429i	0.0896004	−	0.852491i
$719$	4.18460	+	39.8139i	0.156059	+	1.48481i	0.739779	+	0.672850i	$0.234930\pi$
$719$	4.18460	+	39.8139i	0.156059	+	1.48481i	−0.583719	+	0.811956i	$0.698403\pi$
$720$	1.72219	+	11.5653i	0.0641823	+	0.431013i
$721$	−20.7694	+	1.68970i	−0.773493	+	0.0629278i
$722$	−4.73418	−	6.51604i	−0.176188	−	0.242502i
$723$	7.83486	−	5.95450i	0.291382	−	0.221450i
$724$	14.3344	+	12.9068i	0.532734	+	0.479676i
$725$	4.07954	−	2.35533i	0.151510	−	0.0874746i
$726$	−18.6414	+	3.93691i	−0.691846	+	0.146112i
$727$			1.30502i			0.0484006i	0.999707	+	0.0242003i	$0.00770395\pi$
$727$			1.30502i			0.0484006i	−0.999707	+	0.0242003i	$0.992296\pi$
$728$	−4.28188	+	12.1937i	−0.158697	+	0.451930i
$729$	19.6146	−	18.5545i	0.726465	−	0.687203i
$730$	−0.506387	−	4.81795i	−0.0187422	−	0.178321i
$731$	41.9189	−	8.91014i	1.55043	−	0.329553i
$732$	−21.4880	+	10.1275i	−0.794221	+	0.374322i
$733$	−10.5511	+	1.10897i	−0.389714	+	0.0409606i	−0.297359	−	0.954766i	$-0.596106\pi$
$733$	−10.5511	+	1.10897i	−0.389714	+	0.0409606i	−0.0923545	+	0.995726i	$0.529439\pi$
$734$	21.8731	+	15.8917i	0.807350	+	0.586574i
$735$	−34.2992	−	32.5067i	−1.26515	−	1.19903i
$736$	−2.88076			−0.106186
$737$	4.73797	−	40.6086i	0.174525	−	1.49584i
$738$	12.5203	−	18.8944i	0.460880	−	0.695514i
$739$	27.0037	−	29.9906i	0.993345	−	1.10322i	−0.00131282	−	0.999999i	$-0.500418\pi$
$739$	27.0037	−	29.9906i	0.993345	−	1.10322i	0.994658	−	0.103223i	$-0.0329154\pi$
$740$	−6.59108	+	2.93454i	−0.242293	+	0.107876i
$741$	21.2003	+	18.2771i	0.778811	+	0.671425i
$742$	−3.29913	+	2.28026i	−0.121115	+	0.0837110i
$743$	14.5034	+	4.71243i	0.532077	+	0.172882i	0.562719	−	0.826648i	$-0.309755\pi$
$743$	14.5034	+	4.71243i	0.532077	+	0.172882i	−0.0306425	+	0.999530i	$0.509755\pi$
$744$	9.06145	−	3.16171i	0.332209	−	0.115914i
$745$	−10.5484	−	1.10868i	−0.386464	−	0.0406190i
$746$	−4.71282	−	4.24344i	−0.172548	−	0.155363i
$747$	2.37678	−	38.5256i	0.0869618	−	1.40958i
$748$	−12.6558	−	14.3829i	−0.462741	−	0.525891i
$749$	−11.7739	−	28.2142i	−0.430211	−	1.03092i
$750$	−18.1728	−	29.9657i	−0.663577	−	1.09419i
$751$	18.9690	−	8.44555i	0.692189	−	0.308183i	−0.0303235	−	0.999540i	$-0.509654\pi$
$751$	18.9690	−	8.44555i	0.692189	−	0.308183i	0.722513	+	0.691358i	$0.242987\pi$
$752$	0.609427	+	0.271334i	0.0222235	+	0.00989454i
$753$	−8.21422	−	17.4286i	−0.299343	−	0.635133i
$754$	1.67788	−	1.51077i	0.0611050	−	0.0550192i
$755$	−0.809667	+	0.588258i	−0.0294668	+	0.0214089i
$756$	−13.7199	−	0.873852i	−0.498989	−	0.0317817i
$757$	3.97682	+	12.2394i	0.144540	+	0.444848i	0.996952	−	0.0780233i	$-0.0248608\pi$
$757$	3.97682	+	12.2394i	0.144540	+	0.444848i	−0.852412	+	0.522871i	$0.824861\pi$
$758$	20.0645	+	11.5842i	0.728775	+	0.420758i
$759$	−8.41900	−	14.2471i	−0.305590	−	0.517137i
$760$	−6.44748	−	11.1674i	−0.233875	−	0.405083i
$761$	−10.4032	−	2.21127i	−0.377116	−	0.0801584i	0.0154543	−	0.999881i	$-0.495081\pi$
$761$	−10.4032	−	2.21127i	−0.377116	−	0.0801584i	−0.392570	+	0.919722i	$0.628414\pi$
$762$	−16.6288	−	6.97821i	−0.602399	−	0.252794i
$763$	11.8814	+	21.7459i	0.430136	+	0.787255i
$764$	3.13992	+	1.02022i	0.113598	+	0.0369103i
$765$	−62.8296	−	24.7876i	−2.27161	−	0.896199i
$766$	−7.32997	+	16.4634i	−0.264843	+	0.594846i
$767$	49.0564	+	5.15604i	1.77133	+	0.186174i
$768$	−0.0373266	−	1.73165i	−0.00134691	−	0.0624855i
$769$			10.8011i			0.389496i	0.980853	+	0.194748i	$0.0623889\pi$
$769$			10.8011i			0.389496i	−0.980853	+	0.194748i	$0.937611\pi$
$770$	33.8682	+	4.76213i	1.22052	+	0.171615i
$771$	−9.75648	−	41.4835i	−0.351371	−	1.49399i
$772$	12.7602	+	2.71226i	0.459249	+	0.0976164i
$773$	−5.04775	+	48.0262i	−0.181555	+	1.72738i	0.402287	+	0.915514i	$0.368216\pi$
$773$	−5.04775	+	48.0262i	−0.181555	+	1.72738i	−0.583842	+	0.811868i	$0.698451\pi$
$774$	0.959082	+	22.2364i	0.0344735	+	0.799272i
$775$	−41.9650	+	37.7854i	−1.50743	+	1.35729i
$776$	−2.82871	+	8.70587i	−0.101545	+	0.312522i
$777$	−1.74715	−	8.30091i	−0.0626786	−	0.297794i
$778$	16.9537	+	12.3176i	0.607820	+	0.441607i
$779$	−5.19708	+	24.4504i	−0.186205	+	0.876025i
$780$	−22.5881	−	24.0246i	−0.808784	−	0.860218i
$781$	15.5158	+	21.8772i	0.555200	+	0.782828i
$782$	8.32022	−	14.4111i	0.297531	−	0.515338i
$783$	2.03024	+	1.28324i	0.0725547	+	0.0458591i
$784$	4.43387	+	5.41671i	0.158352	+	0.193454i
$785$	14.7334	+	20.2788i	0.525857	+	0.723781i
$786$	−5.55434	−	3.85536i	−0.198117	−	0.137516i
$787$	−0.722245	−	3.39790i	−0.0257453	−	0.121122i	0.963398	−	0.268074i	$-0.0863871\pi$
$787$	−0.722245	−	3.39790i	−0.0257453	−	0.121122i	−0.989144	+	0.146952i	$0.953054\pi$
$788$	3.92353	−	8.81239i	0.139770	−	0.313928i
$789$	12.6669	−	9.62682i	0.450952	−	0.342724i
$790$	13.4222	−	4.36114i	0.477541	−	0.155163i
$791$	−8.44777	+	11.0697i	−0.300368	+	0.393592i
$792$	8.45497	−	5.24534i	0.300434	−	0.186385i
$793$	33.4967	−	58.0180i	1.18950	−	2.06028i
$794$	18.1452	−	20.1523i	0.643951	−	0.715180i
$795$	−1.28871	−	10.1516i	−0.0457059	−	0.360038i
$796$	−4.48979	+	0.471896i	−0.159136	+	0.0167259i
$797$	6.80765	−	20.9518i	0.241139	−	0.742150i	−0.755108	−	0.655600i	$-0.772416\pi$
$797$	6.80765	−	20.9518i	0.241139	−	0.742150i	0.996248	−	0.0865500i	$-0.0275842\pi$
$798$	14.4284	−	4.65633i	0.510760	−	0.164832i
$799$	−3.11751	+	2.26500i	−0.110289	+	0.0801300i
$800$	4.14517	+	9.31021i	0.146554	+	0.329166i
$801$	8.59330	−	30.9229i	0.303629	−	1.09261i
$802$	−7.63557	−	13.2252i	−0.269621	−	0.466998i
$803$	−3.59340	+	2.02025i	−0.126808	+	0.0712931i
$804$	4.88816	+	20.7839i	0.172392	+	0.732992i
$805$	5.49060	+	29.1948i	0.193518	+	1.02898i
$806$	−15.9089	+	21.8967i	−0.560367	+	0.771279i
$807$	26.5202	−	9.25341i	0.933556	−	0.325736i
$808$	0.460015	+	2.16420i	0.0161833	+	0.0761363i
$809$	−7.24652	−	34.0922i	−0.254774	−	1.19862i	−0.900434	−	0.434992i	$-0.856751\pi$
$809$	−7.24652	−	34.0922i	−0.254774	−	1.19862i	0.645660	−	0.763625i	$-0.276582\pi$
$810$	18.0985	−	30.0489i	0.635917	−	1.05581i
$811$	8.35503	−	11.4997i	0.293385	−	0.403810i	−0.636725	−	0.771091i	$-0.719711\pi$
$811$	8.35503	−	11.4997i	0.293385	−	0.403810i	0.930110	+	0.367281i	$0.119711\pi$
$812$	−0.226031	−	1.20186i	−0.00793212	−	0.0421769i
$813$	8.07150	−	1.89833i	0.283080	−	0.0665774i
$814$	4.51521	+	4.15993i	0.158258	+	0.145805i
$815$	−8.28472	−	14.3496i	−0.290201	−	0.502643i
$816$	8.77042	+	4.81463i	0.307026	+	0.168546i
$817$	−9.98350	−	22.4233i	−0.349279	−	0.784493i
$818$	6.12518	−	4.45021i	0.214162	−	0.155598i
$819$	33.1911	−	20.0386i	1.15979	−	0.700204i
$820$	9.09993	−	28.0067i	0.317783	−	0.978037i
$821$	49.9003	−	5.24473i	1.74153	−	0.183042i	0.820268	−	0.571980i	$-0.193825\pi$
$821$	49.9003	−	5.24473i	1.74153	−	0.183042i	0.921264	+	0.388938i	$0.127158\pi$
$822$	8.70405	−	1.10496i	0.303589	−	0.0385398i
$823$	−25.1282	+	27.9077i	−0.875913	+	0.972800i	−0.999810	−	0.0194949i	$-0.993794\pi$
$823$	−25.1282	+	27.9077i	−0.875913	+	0.972800i	0.123897	+	0.992295i	$0.460461\pi$
$824$	−3.93802	+	6.82085i	−0.137187	+	0.237615i
$825$	−33.9304	+	47.7094i	−1.18130	+	1.66103i
$826$	16.2085	−	21.2391i	0.563968	−	0.739003i
$827$	−47.2790	+	15.3619i	−1.64405	+	0.534185i	−0.977439	−	0.211219i	$-0.932257\pi$
$827$	−47.2790	+	15.3619i	−1.64405	+	0.534185i	−0.666613	+	0.745404i	$0.732257\pi$
$828$	6.66568	+	5.50069i	0.231648	+	0.191162i
$829$	−13.8789	+	31.1726i	−0.482035	+	1.08267i	0.494865	+	0.868970i	$0.335218\pi$
$829$	−13.8789	+	31.1726i	−0.482035	+	1.08267i	−0.976900	+	0.213698i	$0.931449\pi$
$830$	−10.4263	−	49.0518i	−0.361902	−	1.70261i
$831$	−9.82721	+	14.1579i	−0.340902	+	0.491131i
$832$	2.87115	+	3.95180i	0.0995392	+	0.137004i
$833$	−39.9032	+	6.53593i	−1.38256	+	0.226457i
$834$	−31.0812	+	18.8493i	−1.07625	+	0.652697i
$835$	4.25896	−	7.37673i	0.147387	−	0.255282i
$836$	−6.55070	+	8.80291i	−0.226561	+	0.304455i
$837$	−27.0041	−	9.98669i	−0.933399	−	0.345191i
$838$	−4.94427	+	23.2610i	−0.170797	+	0.803537i
$839$	28.0779	+	20.3998i	0.969356	+	0.704278i	0.955305	−	0.295623i	$-0.0955272\pi$
$839$	28.0779	+	20.3998i	0.969356	+	0.704278i	0.0140514	+	0.999901i	$0.495527\pi$
$840$	−17.4781	+	3.67873i	−0.603052	+	0.126928i
$841$	8.89547	−	27.3774i	0.306740	−	0.944050i
$842$	5.04229	−	4.54010i	0.173769	−	0.156462i
$843$	16.3672	+	3.11188i	0.563715	+	0.107179i
$844$	−0.270777	+	2.57627i	−0.00932053	+	0.0886790i
$845$	41.4038	+	8.80065i	1.42433	+	0.302752i
$846$	−0.892029	−	1.79151i	−0.0306686	−	0.0615932i
$847$	−7.69984	−	28.0662i	−0.264570	−	0.964367i
$848$			1.51581i			0.0520533i
$849$	7.53991	−	0.162527i	0.258769	−	0.00557791i
$850$	−58.5467	−	6.15350i	−2.00813	−	0.211063i
$851$	−2.16895	+	4.87153i	−0.0743505	+	0.166994i
$852$	−11.5064	−	7.98681i	−0.394204	−	0.273624i
$853$	26.6413	+	8.65628i	0.912180	+	0.296385i	0.727255	−	0.686367i	$-0.240796\pi$
$853$	26.6413	+	8.65628i	0.912180	+	0.296385i	0.184925	+	0.982753i	$0.440796\pi$
$854$	−17.3984	−	31.8434i	−0.595361	−	1.08966i
$855$	−6.40502	+	38.1509i	−0.219047	+	1.30473i
$856$	−11.3027	−	2.40247i	−0.386319	−	0.0821147i
$857$	−5.15530	−	8.92924i	−0.176102	−	0.305017i	0.764440	−	0.644694i	$-0.223015\pi$
$857$	−5.15530	−	8.92924i	−0.176102	−	0.305017i	−0.940542	+	0.339678i	$0.889682\pi$
$858$	−11.1531	+	25.7487i	−0.380761	+	0.879046i
$859$	−10.0316	−	5.79175i	−0.342274	−	0.197612i	0.319003	−	0.947754i	$-0.396652\pi$
$859$	−10.0316	−	5.79175i	−0.342274	−	0.197612i	−0.661277	+	0.750142i	$0.729985\pi$
$860$	8.93567	+	27.5012i	0.304704	+	0.937782i
$861$	29.9501	+	17.3713i	1.02070	+	0.592012i
$862$	−0.336260	+	0.244307i	−0.0114531	+	0.00832115i
$863$	22.4784	−	20.2397i	0.765174	−	0.688966i	−0.191057	−	0.981579i	$-0.561192\pi$
$863$	22.4784	−	20.2397i	0.765174	−	0.688966i	0.956231	+	0.292613i	$0.0945248\pi$
$864$	−3.22014	+	4.07807i	−0.109551	+	0.138739i
$865$	30.5413	+	13.5979i	1.03844	+	0.462342i
$866$	−26.5721	+	11.8307i	−0.902957	+	0.402022i
$867$	−24.2393	+	14.7000i	−0.823209	+	0.499238i
$868$	5.64582	+	13.5292i	0.191632	+	0.459211i
$869$	−7.93325	−	9.01589i	−0.269117	−	0.305843i
$870$	2.98776	+	0.900076i	0.101295	+	0.0305154i
$871$	−44.7475	−	40.2908i	−1.51621	−	1.36520i
$872$	9.31469	+	0.979013i	0.315435	+	0.0331536i
$873$	23.1687	−	14.7429i	0.784143	−	0.498971i
$874$	−9.06432	−	2.94518i	−0.306605	−	0.0996221i
$875$	44.0379	−	30.4377i	1.48875	−	1.02898i
$876$	1.40572	−	1.63054i	0.0474948	−	0.0550910i
$877$	−38.9230	+	17.3296i	−1.31433	+	0.585179i	−0.939702	−	0.341994i	$-0.888898\pi$
$877$	−38.9230	+	17.3296i	−1.31433	+	0.585179i	−0.374632	+	0.927173i	$0.622231\pi$
$878$	−8.39170	+	9.31993i	−0.283206	+	0.314532i
$879$	29.8648	−	28.0792i	1.00732	−	0.947087i
$880$	8.75900	−	9.50706i	0.295266	−	0.320483i
$881$	−14.8900			−0.501657			−0.250828	−	0.968032i	$-0.580703\pi$
$881$	−14.8900			−0.501657			−0.250828	+	0.968032i	$0.580703\pi$
$882$	0.0836190	−	20.9998i	0.00281560	−	0.707101i
$883$	−9.19777	−	6.68257i	−0.309530	−	0.224886i	0.422165	−	0.906519i	$-0.361270\pi$
$883$	−9.19777	−	6.68257i	−0.309530	−	0.224886i	−0.731695	+	0.681633i	$0.761270\pi$
$884$	−28.0614	+	2.94938i	−0.943808	+	0.0991983i
$885$	29.0635	+	61.6657i	0.976959	+	2.07287i
$886$	29.6584	−	6.30410i	0.996395	−	0.211790i
$887$	3.70456	+	35.2465i	0.124387	+	1.18346i	0.861523	+	0.507719i	$0.169511\pi$
$887$	3.70456	+	35.2465i	0.124387	+	1.18346i	−0.737136	+	0.675744i	$0.763822\pi$
$888$	−2.95643	−	1.24065i	−0.0992111	−	0.0416335i
$889$	9.12684	−	25.9910i	0.306104	−	0.871710i
$890$		−	41.6975i		−	1.39770i
$891$	−29.5794	−	4.00741i	−0.990947	−	0.134253i
$892$	21.3950	−	12.3524i	0.716359	−	0.413590i
$893$	1.64016	+	1.47681i	0.0548860	+	0.0494196i
$894$	−2.85201	−	3.75265i	−0.0953856	−	0.125507i
$895$	23.9130	+	32.9134i	0.799323	+	1.10017i
$896$	2.63704	−	0.214537i	0.0880973	−	0.00716719i
$897$	−24.2885	−	2.02469i	−0.810970	−	0.0676023i
$898$	2.12649	+	20.2322i	0.0709618	+	0.675156i
$899$	0.267713	−	2.54712i	0.00892874	−	0.0849513i
$900$	8.18609	−	29.4576i	0.272870	−	0.981920i
$901$	−7.58289	−	4.37799i	−0.252623	−	0.145852i
$902$	−24.9495	+	2.33433i	−0.830728	+	0.0777247i
$903$	−33.8190	+	3.48646i	−1.12543	+	0.116022i
$904$	1.62639	+	5.00551i	0.0540929	+	0.166481i
$905$	−30.5786	−	68.6806i	−1.01647	−	2.28302i
$906$	−0.436919	−	0.0830714i	−0.0145157	−	0.00275986i
$907$	−10.4258	+	2.21607i	−0.346183	+	0.0735834i	−0.377722	−	0.925919i	$-0.623292\pi$
$907$	−10.4258	+	2.21607i	−0.346183	+	0.0735834i	0.0315391	+	0.999503i	$0.489959\pi$
$908$	7.88393	+	8.75599i	0.261637	+	0.290578i
$909$	3.06804	−	5.88605i	0.101760	−	0.195228i
$910$	34.5769	−	36.6294i	1.14621	−	1.21425i
$911$	11.6375	−	3.78126i	0.385568	−	0.125279i	−0.109818	−	0.993952i	$-0.535027\pi$
$911$	11.6375	−	3.78126i	0.385568	−	0.125279i	0.495386	+	0.868673i	$0.335027\pi$
$912$	1.65292	−	5.48681i	0.0547338	−	0.181686i
$913$	−34.8073	+	24.6862i	−1.15195	+	0.816993i
$914$	19.1337	−	11.0468i	0.632885	−	0.365396i
$915$	92.5662	−	1.99531i	3.06014	−	0.0659631i
$916$	11.6009	−	15.9672i	0.383304	−	0.527572i
$917$	5.37311	−	8.82024i	0.177436	−	0.291270i
$918$	−11.1002	−	27.8872i	−0.366362	−	0.920413i
$919$	5.33399	+	5.92400i	0.175952	+	0.195415i	0.824670	−	0.565615i	$-0.191361\pi$
$919$	5.33399	+	5.92400i	0.175952	+	0.195415i	−0.648717	+	0.761029i	$0.724694\pi$
$920$	10.2573	+	4.56686i	0.338174	+	0.150565i
$921$	−3.90563	−	30.7658i	−0.128695	−	1.01377i
$922$	3.66838	−	17.2584i	0.120812	−	0.568375i
$923$	39.5014			1.30020
$924$	8.76775	+	12.4148i	0.288438	+	0.408416i
$925$	18.8651			0.620279
$926$	−7.26395	+	34.1742i	−0.238708	+	1.12303i
$927$	22.1362	−	8.26303i	0.727047	−	0.271394i
$928$	−0.422262	−	0.188003i	−0.0138614	−	0.00617150i
$929$	31.3118	+	34.7752i	1.02731	+	1.14094i	0.989919	+	0.141638i	$0.0452367\pi$
$929$	31.3118	+	34.7752i	1.02731	+	1.14094i	0.0373870	+	0.999301i	$0.488097\pi$
$930$	−37.2768	−	3.10739i	−1.22235	−	0.101895i
$931$	8.41336	+	21.5768i	0.275737	+	0.707149i
$932$	−9.01052	+	12.4019i	−0.295149	+	0.406238i
$933$	−0.0597729	−	2.77297i	−0.00195688	−	0.0907830i
$934$	20.3715	−	11.7615i	0.666574	−	0.384847i
$935$	22.2615	+	71.2754i	0.728028	+	2.33096i
$936$	0.902345	−	14.6263i	0.0294941	−	0.478075i
$937$	−21.3539	+	6.93830i	−0.697602	+	0.226665i	−0.636285	−	0.771454i	$-0.719530\pi$
$937$	−21.3539	+	6.93830i	−0.697602	+	0.226665i	−0.0613164	+	0.998118i	$0.519530\pi$
$938$	−31.2466	+	9.34536i	−1.02024	+	0.305137i
$939$	7.21157	−	8.36497i	0.235341	−	0.272980i
$940$	−1.73980	−	1.93224i	−0.0567461	−	0.0630229i
$941$	−16.4537	+	3.49734i	−0.536375	+	0.114010i	−0.468132	−	0.883659i	$-0.655073\pi$
$941$	−16.4537	+	3.49734i	−0.536375	+	0.114010i	−0.0682432	+	0.997669i	$0.521739\pi$
$942$	−2.08059	+	10.9430i	−0.0677893	+	0.356542i
$943$	−8.85275	−	19.8836i	−0.288285	−	0.647499i
$944$	−3.12052	−	9.60397i	−0.101564	−	0.312583i
$945$	47.4663	+	24.8616i	1.54408	+	0.808749i
$946$	18.4729	−	16.2547i	0.600606	−	0.528485i
$947$	−3.09814	−	1.78871i	−0.100676	−	0.0581253i	0.448817	−	0.893624i	$-0.351846\pi$
$947$	−3.09814	−	1.78871i	−0.100676	−	0.0581253i	−0.549493	+	0.835499i	$0.685179\pi$
$948$	5.49772	+	3.01804i	0.178558	+	0.0980215i
$949$	−0.634633	+	6.03813i	−0.0206011	+	0.196006i
$950$	3.52441	+	33.5325i	0.114347	+	1.08794i
$951$	−1.95831	+	23.4923i	−0.0635026	+	0.761789i
$952$	−6.54309	+	13.8115i	−0.212063	+	0.447632i
$953$	34.0973	+	46.9310i	1.10452	+	1.52024i	0.829251	+	0.558876i	$0.188767\pi$
$953$	34.0973	+	46.9310i	1.10452	+	1.52024i	0.275270	+	0.961367i	$0.411233\pi$
$954$	2.89438	−	3.50739i	0.0937091	−	0.113556i
$955$	−9.56274	−	8.61033i	−0.309443	−	0.278624i
$956$	−6.63139	+	3.82864i	−0.214475	+	0.123827i
$957$	−0.304269	−	2.63778i	−0.00983561	−	0.0852672i
$958$			2.85311i			0.0921797i
$959$	2.47713	+	13.1715i	0.0799906	+	0.425329i
$960$	−2.61227	+	6.22494i	−0.0843107	+	0.200909i
$961$	−0.0311385	−	0.296263i	−0.00100447	−	0.00955688i
$962$	8.84444	−	1.87994i	0.285156	−	0.0606118i
$963$	21.5656	+	27.1411i	0.694941	+	0.874609i
$964$	5.65046	−	0.593887i	0.181989	−	0.0191278i
$965$	−41.1346	−	29.8860i	−1.32417	−	0.962066i
$966$	−7.78077	+	10.6646i	−0.250342	+	0.343128i
$967$	23.4142			0.752949			0.376475	−	0.926427i	$-0.377136\pi$
$967$	23.4142			0.752949			0.376475	+	0.926427i	$0.377136\pi$
$968$	−10.3812	−	3.63741i	−0.333664	−	0.116911i
$969$	22.6739	+	24.1158i	0.728390	+	0.774712i
$970$	23.8734	−	26.5141i	0.766528	−	0.851316i
$971$	18.7372	−	8.34234i	0.601305	−	0.267718i	−0.0834261	−	0.996514i	$-0.526586\pi$
$971$	18.7372	−	8.34234i	0.601305	−	0.267718i	0.684731	+	0.728796i	$0.259920\pi$
$972$	15.2379	−	3.28738i	0.488755	−	0.105443i
$973$	−31.5707	−	45.6772i	−1.01211	−	1.46434i
$974$	−4.23727	−	1.37677i	−0.135771	−	0.0441146i
$975$	28.4057	+	81.4105i	0.909709	+	2.60722i
$976$	−13.6398	−	1.43361i	−0.436601	−	0.0458886i
$977$	−23.1481	−	20.8426i	−0.740573	−	0.666815i	0.209864	−	0.977731i	$-0.432698\pi$
$977$	−23.1481	−	20.8426i	−0.740573	−	0.666815i	−0.950438	+	0.310915i	$0.899364\pi$
$978$	2.12393	−	7.05030i	0.0679159	−	0.225444i
$979$	−32.5773	+	14.0604i	−1.04117	+	0.449374i
$980$	−7.20029	−	26.3160i	−0.230005	−	0.840632i
$981$	−19.6835	−	20.0513i	−0.628447	−	0.640189i
$982$	−4.34278	+	1.93353i	−0.138584	+	0.0617014i
$983$	−20.8036	−	9.26237i	−0.663532	−	0.295424i	0.0472007	−	0.998885i	$-0.484970\pi$
$983$	−20.8036	−	9.26237i	−0.663532	−	0.295424i	−0.710733	+	0.703462i	$0.751637\pi$
$984$	11.8375	−	5.57910i	0.377366	−	0.177855i
$985$	−27.9405	+	25.1577i	−0.890259	+	0.801592i
$986$	2.16007	−	1.56938i	0.0687906	−	0.0499793i
$987$	2.65051	−	1.52325i	0.0843667	−	0.0484854i
$988$	4.99392	+	15.3697i	0.158878	+	0.488976i
$989$	18.5091	+	10.6862i	0.588554	+	0.339802i
$990$	−38.4205	+	5.27310i	−1.22108	+	0.167590i
$991$	−10.9071	−	18.8916i	−0.346474	−	0.600111i	0.639146	−	0.769085i	$-0.279288\pi$
$991$	−10.9071	−	18.8916i	−0.346474	−	0.600111i	−0.985620	+	0.168974i	$0.945955\pi$
$992$	5.41986	+	1.15203i	0.172081	+	0.0365769i
$993$	4.61795	−	11.0044i	0.146546	−	0.349214i
$994$	11.1310	−	18.2721i	0.353054	−	0.579557i
$995$	16.7346	+	5.43740i	0.530522	+	0.172377i
$996$	12.7073	−	18.3071i	0.402645	−	0.580083i
$997$	2.78040	−	6.24487i	0.0880560	−	0.197777i	−0.864149	−	0.503235i	$-0.832143\pi$
$997$	2.78040	−	6.24487i	0.0880560	−	0.197777i	0.952206	+	0.305458i	$0.0988096\pi$
$998$	−21.6889	−	2.27960i	−0.686551	−	0.0721594i
$999$	4.47180	+	8.51587i	0.141481	+	0.269430i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.bf.a.5.17	yes	256
3.2	odd	2	inner	462.2.bf.a.5.1	✓	256
7.3	odd	6	inner	462.2.bf.a.269.22	yes	256
11.9	even	5	inner	462.2.bf.a.383.7	yes	256
21.17	even	6	inner	462.2.bf.a.269.7	yes	256
33.20	odd	10	inner	462.2.bf.a.383.22	yes	256
77.31	odd	30	inner	462.2.bf.a.185.1	yes	256
231.185	even	30	inner	462.2.bf.a.185.17	yes	256

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.bf.a.5.1	✓	256	3.2	odd	2	inner
462.2.bf.a.5.17	yes	256	1.1	even	1	trivial
462.2.bf.a.185.1	yes	256	77.31	odd	30	inner
462.2.bf.a.185.17	yes	256	231.185	even	30	inner
462.2.bf.a.269.7	yes	256	21.17	even	6	inner
462.2.bf.a.269.22	yes	256	7.3	odd	6	inner
462.2.bf.a.383.7	yes	256	11.9	even	5	inner
462.2.bf.a.383.22	yes	256	33.20	odd	10	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:	\( N \)	\(=\)	\( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	462.bf (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.207912 - 0.978148i) q^{2} +(-1.71826 + 0.218129i) q^{3} +(-0.913545 - 0.406737i) q^{4} +(2.60800 + 2.89648i) q^{5} +(-0.143884 + 1.72606i) q^{6} +(-2.64502 - 0.0622836i) q^{7} +(-0.587785 + 0.809017i) q^{8} +(2.90484 - 0.749604i) q^{9} +O(q^{10})\)	\(q+(0.207912 - 0.978148i) q^{2} +(-1.71826 + 0.218129i) q^{3} +(-0.913545 - 0.406737i) q^{4} +(2.60800 + 2.89648i) q^{5} +(-0.143884 + 1.72606i) q^{6} +(-2.64502 - 0.0622836i) q^{7} +(-0.587785 + 0.809017i) q^{8} +(2.90484 - 0.749604i) q^{9} +(3.37542 - 1.94880i) q^{10} +(-2.66075 - 1.98000i) q^{11} +(1.65843 + 0.499609i) q^{12} +(-4.64562 + 1.50945i) q^{13} +(-0.610853 + 2.57427i) q^{14} +(-5.11304 - 4.40803i) q^{15} +(0.669131 + 0.743145i) q^{16} +(-5.65019 + 1.20098i) q^{17} +(-0.129273 - 2.99721i) q^{18} +(1.34566 + 3.02240i) q^{19} +(-1.20443 - 3.70684i) q^{20} +(4.55842 - 0.469935i) q^{21} +(-2.48994 + 2.19094i) q^{22} +(-2.49481 - 1.44038i) q^{23} +(0.833498 - 1.51831i) q^{24} +(-1.06528 + 10.1355i) q^{25} +(0.510589 + 4.85793i) q^{26} +(-4.82776 + 1.92164i) q^{27} +(2.39101 + 1.13272i) q^{28} +(-0.271688 - 0.373946i) q^{29} +(-5.37477 + 4.08482i) q^{30} +(4.11773 + 3.70762i) q^{31} +(0.866025 - 0.500000i) q^{32} +(5.00376 + 2.82177i) q^{33} +5.77641i q^{34} +(-6.71782 - 7.82368i) q^{35} +(-2.95859 - 0.496707i) q^{36} +(-0.193492 - 1.84096i) q^{37} +(3.23614 - 0.687862i) q^{38} +(7.65313 - 3.60698i) q^{39} +(-3.87625 + 0.407410i) q^{40} +(6.11246 + 4.44096i) q^{41} +(0.488082 - 4.55651i) q^{42} -7.41903 q^{43} +(1.62538 + 2.89105i) q^{44} +(9.74705 + 6.45885i) q^{45} +(-1.92760 + 2.14082i) q^{46} +(0.609427 - 0.271334i) q^{47} +(-1.31184 - 1.13096i) q^{48} +(6.99224 + 0.329482i) q^{49} +(9.69250 + 3.14928i) q^{50} +(9.44652 - 3.29607i) q^{51} +(4.85793 + 0.510589i) q^{52} +(1.12647 + 1.01428i) q^{53} +(0.875903 + 5.12180i) q^{54} +(-1.20421 - 12.8707i) q^{55} +(1.60509 - 2.10326i) q^{56} +(-2.97147 - 4.89975i) q^{57} +(-0.422262 + 0.188003i) q^{58} +(-9.22518 - 4.10731i) q^{59} +(2.87808 + 6.10660i) q^{60} +(-10.1922 + 9.17711i) q^{61} +(4.48272 - 3.25689i) q^{62} +(-7.73004 + 1.80179i) q^{63} +(-0.309017 - 0.951057i) q^{64} +(-16.4879 - 9.51929i) q^{65} +(3.80045 - 4.30773i) q^{66} +(6.16351 + 10.6755i) q^{67} +(5.65019 + 1.20098i) q^{68} +(4.60092 + 1.93076i) q^{69} +(-9.04943 + 4.94438i) q^{70} +(-7.69097 - 2.49895i) q^{71} +(-1.10098 + 2.79067i) q^{72} +(0.505550 - 1.13548i) q^{73} +(-1.84096 - 0.193492i) q^{74} +(-0.380407 - 17.6477i) q^{75} -3.30843i q^{76} +(6.91441 + 5.40286i) q^{77} +(-1.93698 - 8.23582i) q^{78} +(3.54181 + 0.752835i) q^{79} +(-0.407410 + 3.87625i) q^{80} +(7.87619 - 4.35496i) q^{81} +(5.61477 - 5.05556i) q^{82} +(3.97590 - 12.2366i) q^{83} +(-4.35546 - 1.42477i) q^{84} +(-18.2143 - 13.2335i) q^{85} +(-1.54250 + 7.25691i) q^{86} +(0.548399 + 0.583274i) q^{87} +(3.16581 - 0.988776i) q^{88} +(5.34912 - 9.26495i) q^{89} +(8.34423 - 8.19118i) q^{90} +(12.3818 - 3.70318i) q^{91} +(1.69327 + 2.33058i) q^{92} +(-7.88407 - 5.47246i) q^{93} +(-0.138698 - 0.652523i) q^{94} +(-5.24485 + 11.7801i) q^{95} +(-1.37899 + 1.04804i) q^{96} +(8.70587 - 2.82871i) q^{97} +(1.77605 - 6.77094i) q^{98} +(-9.21327 - 3.75708i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 256 q - 32 q^{4} + 4 q^{7} - 12 q^{9}+O(q^{10}) \) 256 * q - 32 * q^4 + 4 * q^7 - 12 * q^9	\( 256 q - 32 q^{4} + 4 q^{7} - 12 q^{9} + 12 q^{10} + 24 q^{15} + 32 q^{16} - 8 q^{18} - 16 q^{21} - 12 q^{22} + 48 q^{25} + 6 q^{28} + 18 q^{31} - 132 q^{33} + 16 q^{36} + 4 q^{37} - 18 q^{40} - 4 q^{42} + 64 q^{43} - 48 q^{45} + 8 q^{46} + 76 q^{49} - 8 q^{51} - 88 q^{57} + 46 q^{58} - 8 q^{60} - 12 q^{63} + 64 q^{64} - 120 q^{66} - 32 q^{67} - 58 q^{70} - 12 q^{72} - 96 q^{73} - 204 q^{75} - 32 q^{78} - 4 q^{79} - 64 q^{81} + 24 q^{82} - 36 q^{84} + 232 q^{85} - 228 q^{87} - 6 q^{88} + 40 q^{91} - 2 q^{93} - 144 q^{94} + 160 q^{99}+O(q^{100}) \) 256 * q - 32 * q^4 + 4 * q^7 - 12 * q^9 + 12 * q^10 + 24 * q^15 + 32 * q^16 - 8 * q^18 - 16 * q^21 - 12 * q^22 + 48 * q^25 + 6 * q^28 + 18 * q^31 - 132 * q^33 + 16 * q^36 + 4 * q^37 - 18 * q^40 - 4 * q^42 + 64 * q^43 - 48 * q^45 + 8 * q^46 + 76 * q^49 - 8 * q^51 - 88 * q^57 + 46 * q^58 - 8 * q^60 - 12 * q^63 + 64 * q^64 - 120 * q^66 - 32 * q^67 - 58 * q^70 - 12 * q^72 - 96 * q^73 - 204 * q^75 - 32 * q^78 - 4 * q^79 - 64 * q^81 + 24 * q^82 - 36 * q^84 + 232 * q^85 - 228 * q^87 - 6 * q^88 + 40 * q^91 - 2 * q^93 - 144 * q^94 + 160 * q^99

Introduction

L-functions

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