LMFDB - Embedded newform 462.2.ba.b.73.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [462,2,Mod(19,462)]

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([0, 25, 9]))

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

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

chi := DirichletCharacter("462.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 462 = 2 \cdot 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	462.ba (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:	$64$
Relative dimension:	$8$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			73.4
Character	$\chi$	$=$	462.73
Dual form			462.2.ba.b.19.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.994522 - 0.104528i) q^{2} +(-0.743145 + 0.669131i) q^{3} +(0.978148 + 0.207912i) q^{4} +(0.949965 - 2.13366i) q^{5} +(0.809017 - 0.587785i) q^{6} +(2.43658 - 1.03106i) q^{7} +(-0.951057 - 0.309017i) q^{8} +(0.104528 - 0.994522i) q^{9} +O(q^{10})$	\(q+(-0.994522 - 0.104528i) q^{2} +(-0.743145 + 0.669131i) q^{3} +(0.978148 + 0.207912i) q^{4} +(0.949965 - 2.13366i) q^{5} +(0.809017 - 0.587785i) q^{6} +(2.43658 - 1.03106i) q^{7} +(-0.951057 - 0.309017i) q^{8} +(0.104528 - 0.994522i) q^{9} +(-1.16779 + 2.02267i) q^{10} +(-2.87465 - 1.65420i) q^{11} +(-0.866025 + 0.500000i) q^{12} +(-0.634067 - 0.460677i) q^{13} +(-2.53101 + 0.770722i) q^{14} +(0.721733 + 2.22127i) q^{15} +(0.913545 + 0.406737i) q^{16} +(-0.0947974 - 0.901937i) q^{17} +(-0.207912 + 0.978148i) q^{18} +(-2.12015 + 0.450652i) q^{19} +(1.37282 - 1.88952i) q^{20} +(-1.12081 + 2.39662i) q^{21} +(2.68599 + 1.94562i) q^{22} +(-2.44656 - 4.23756i) q^{23} +(0.913545 - 0.406737i) q^{24} +(-0.304406 - 0.338077i) q^{25} +(0.582440 + 0.524431i) q^{26} +(0.587785 + 0.809017i) q^{27} +(2.59770 - 0.501938i) q^{28} +(1.72064 - 0.559071i) q^{29} +(-0.485594 - 2.28454i) q^{30} +(-1.82717 - 4.10388i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(3.24316 - 0.694207i) q^{33} +0.906905i q^{34} +(0.114731 - 6.17829i) q^{35} +(0.309017 - 0.951057i) q^{36} +(7.31548 - 8.12466i) q^{37} +(2.15564 - 0.226567i) q^{38} +(0.779456 - 0.0819242i) q^{39} +(-1.56281 + 1.73567i) q^{40} +(1.98440 - 6.10736i) q^{41} +(1.36519 - 2.26633i) q^{42} +4.13275i q^{43} +(-2.46791 - 2.21573i) q^{44} +(-2.02267 - 1.16779i) q^{45} +(1.99021 + 4.47008i) q^{46} +(-0.668111 - 3.14322i) q^{47} +(-0.951057 + 0.309017i) q^{48} +(4.87382 - 5.02453i) q^{49} +(0.267400 + 0.368044i) q^{50} +(0.673962 + 0.606838i) q^{51} +(-0.524431 - 0.582440i) q^{52} +(-1.30848 + 0.582574i) q^{53} +(-0.500000 - 0.866025i) q^{54} +(-6.26032 + 4.56209i) q^{55} +(-2.63594 + 0.227655i) q^{56} +(1.27404 - 1.75356i) q^{57} +(-1.76966 + 0.376152i) q^{58} +(0.166918 - 0.785286i) q^{59} +(0.244134 + 2.32278i) q^{60} +(7.06447 + 3.14531i) q^{61} +(1.38818 + 4.27239i) q^{62} +(-0.770722 - 2.53101i) q^{63} +(0.809017 + 0.587785i) q^{64} +(-1.58527 + 0.915255i) q^{65} +(-3.29796 + 0.351402i) q^{66} +(-7.33817 + 12.7101i) q^{67} +(0.0947974 - 0.901937i) q^{68} +(4.65362 + 1.51205i) q^{69} +(-0.759910 + 6.13246i) q^{70} +(9.60291 - 6.97692i) q^{71} +(-0.406737 + 0.913545i) q^{72} +(-11.9998 - 2.55063i) q^{73} +(-8.12466 + 7.31548i) q^{74} +(0.452435 + 0.0475529i) q^{75} -2.16752 q^{76} +(-8.70990 - 1.06664i) q^{77} -0.783750 q^{78} +(14.0497 + 1.47668i) q^{79} +(1.73567 - 1.56281i) q^{80} +(-0.978148 - 0.207912i) q^{81} +(-2.61192 + 5.86647i) q^{82} +(-13.4630 + 9.78147i) q^{83} +(-1.59461 + 2.11122i) q^{84} +(-2.01448 - 0.654544i) q^{85} +(0.431990 - 4.11011i) q^{86} +(-0.904596 + 1.56681i) q^{87} +(2.22278 + 2.46155i) q^{88} +(6.08266 - 3.51182i) q^{89} +(1.88952 + 1.37282i) q^{90} +(-2.01994 - 0.468712i) q^{91} +(-1.51205 - 4.65362i) q^{92} +(4.10388 + 1.82717i) q^{93} +(0.335896 + 3.19583i) q^{94} +(-1.05253 + 4.95178i) q^{95} +(0.978148 - 0.207912i) q^{96} +(2.55805 - 3.52085i) q^{97} +(-5.37233 + 4.48755i) q^{98} +(-1.94562 + 2.68599i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 8 q^{4} - 2 q^{5} + 16 q^{6} + 16 q^{7} - 8 q^{9}+O(q^{10}) $ 64 * q - 8 * q^4 - 2 * q^5 + 16 * q^6 + 16 * q^7 - 8 * q^9	$ 64 q - 8 q^{4} - 2 q^{5} + 16 q^{6} + 16 q^{7} - 8 q^{9} - 2 q^{10} + 4 q^{11} + 2 q^{14} - 6 q^{15} + 8 q^{16} + 30 q^{17} - 10 q^{19} - 20 q^{20} + 4 q^{21} - 2 q^{22} + 4 q^{23} + 8 q^{24} - 12 q^{26} - 20 q^{29} - 18 q^{30} + 34 q^{31} + 8 q^{33} - 2 q^{35} - 16 q^{36} - 14 q^{37} + 12 q^{38} - 18 q^{39} + 12 q^{40} + 28 q^{41} + 4 q^{42} + 6 q^{44} - 12 q^{45} + 42 q^{46} + 24 q^{47} - 44 q^{49} + 14 q^{51} - 32 q^{54} + 14 q^{55} - 4 q^{56} - 10 q^{58} - 30 q^{59} + 2 q^{60} - 28 q^{61} + 8 q^{62} + 16 q^{63} + 16 q^{64} - 12 q^{65} - 4 q^{66} + 16 q^{67} - 30 q^{68} - 30 q^{70} - 24 q^{71} - 116 q^{73} - 44 q^{74} + 12 q^{75} - 32 q^{77} - 18 q^{80} + 8 q^{81} - 28 q^{82} - 8 q^{83} - 2 q^{84} - 80 q^{85} - 18 q^{86} - 10 q^{87} - 14 q^{88} - 24 q^{89} - 4 q^{90} + 48 q^{91} + 8 q^{92} + 76 q^{93} + 6 q^{94} + 98 q^{95} - 8 q^{96} - 120 q^{97} - 40 q^{98} + 8 q^{99}+O(q^{100}) $ 64 * q - 8 * q^4 - 2 * q^5 + 16 * q^6 + 16 * q^7 - 8 * q^9 - 2 * q^10 + 4 * q^11 + 2 * q^14 - 6 * q^15 + 8 * q^16 + 30 * q^17 - 10 * q^19 - 20 * q^20 + 4 * q^21 - 2 * q^22 + 4 * q^23 + 8 * q^24 - 12 * q^26 - 20 * q^29 - 18 * q^30 + 34 * q^31 + 8 * q^33 - 2 * q^35 - 16 * q^36 - 14 * q^37 + 12 * q^38 - 18 * q^39 + 12 * q^40 + 28 * q^41 + 4 * q^42 + 6 * q^44 - 12 * q^45 + 42 * q^46 + 24 * q^47 - 44 * q^49 + 14 * q^51 - 32 * q^54 + 14 * q^55 - 4 * q^56 - 10 * q^58 - 30 * q^59 + 2 * q^60 - 28 * q^61 + 8 * q^62 + 16 * q^63 + 16 * q^64 - 12 * q^65 - 4 * q^66 + 16 * q^67 - 30 * q^68 - 30 * q^70 - 24 * q^71 - 116 * q^73 - 44 * q^74 + 12 * q^75 - 32 * q^77 - 18 * q^80 + 8 * q^81 - 28 * q^82 - 8 * q^83 - 2 * q^84 - 80 * q^85 - 18 * q^86 - 10 * q^87 - 14 * q^88 - 24 * q^89 - 4 * q^90 + 48 * q^91 + 8 * q^92 + 76 * q^93 + 6 * q^94 + 98 * q^95 - 8 * q^96 - 120 * q^97 - 40 * q^98 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$155$	$199$	$211$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{10}\right)$

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 $

$2$	−0.994522	−	0.104528i	−0.703233	−	0.0739128i
$2$	−0.994522	−	0.104528i	−0.703233	−	0.0739128i
$3$	−0.743145	+	0.669131i	−0.429055	+	0.386323i
$3$	−0.743145	+	0.669131i	−0.429055	+	0.386323i
$4$	0.978148	+	0.207912i	0.489074	+	0.103956i
$5$	0.949965	−	2.13366i	0.424837	−	0.954201i	−0.566645	−	0.823962i	$-0.691759\pi$
$5$	0.949965	−	2.13366i	0.424837	−	0.954201i	0.991483	−	0.130239i	$-0.0415743\pi$
$6$	0.809017	−	0.587785i	0.330280	−	0.239962i
$7$	2.43658	−	1.03106i	0.920940	−	0.389705i
$7$	2.43658	−	1.03106i	0.920940	−	0.389705i
$8$	−0.951057	−	0.309017i	−0.336249	−	0.109254i
$9$	0.104528	−	0.994522i	0.0348428	−	0.331507i
$10$	−1.16779	+	2.02267i	−0.369287	+	0.639625i
$11$	−2.87465	−	1.65420i	−0.866740	−	0.498760i
$11$	−2.87465	−	1.65420i	−0.866740	−	0.498760i
$12$	−0.866025	+	0.500000i	−0.250000	+	0.144338i
$13$	−0.634067	−	0.460677i	−0.175859	−	0.127769i	0.496374	−	0.868109i	$-0.334664\pi$
$13$	−0.634067	−	0.460677i	−0.175859	−	0.127769i	−0.672233	+	0.740340i	$0.734664\pi$
$14$	−2.53101	+	0.770722i	−0.676440	+	0.205984i
$15$	0.721733	+	2.22127i	0.186351	+	0.573529i
$16$	0.913545	+	0.406737i	0.228386	+	0.101684i
$17$	−0.0947974	−	0.901937i	−0.0229918	−	0.218752i	−0.999985	−	0.00548157i	$-0.998255\pi$
$17$	−0.0947974	−	0.901937i	−0.0229918	−	0.218752i	0.976993	−	0.213270i	$-0.0684115\pi$
$18$	−0.207912	+	0.978148i	−0.0490053	+	0.230552i
$19$	−2.12015	+	0.450652i	−0.486397	+	0.103387i	−0.444581	−	0.895739i	$-0.646647\pi$
$19$	−2.12015	+	0.450652i	−0.486397	+	0.103387i	−0.0418154	+	0.999125i	$0.513314\pi$
$20$	1.37282	−	1.88952i	0.306972	−	0.422510i
$21$	−1.12081	+	2.39662i	−0.244582	+	0.522985i
$22$	2.68599	+	1.94562i	0.572656	+	0.414808i
$23$	−2.44656	−	4.23756i	−0.510142	−	0.883592i	−0.999931	−	0.0117509i	$-0.996259\pi$
$23$	−2.44656	−	4.23756i	−0.510142	−	0.883592i	0.489789	−	0.871841i	$-0.337074\pi$
$24$	0.913545	−	0.406737i	0.186477	−	0.0830248i
$25$	−0.304406	−	0.338077i	−0.0608812	−	0.0676154i
$26$	0.582440	+	0.524431i	0.114226	+	0.102849i
$27$	0.587785	+	0.809017i	0.113119	+	0.155695i
$28$	2.59770	−	0.501938i	0.490920	−	0.0948574i
$29$	1.72064	−	0.559071i	0.319515	−	0.103817i	−0.144868	−	0.989451i	$-0.546276\pi$
$29$	1.72064	−	0.559071i	0.319515	−	0.103817i	0.464384	+	0.885634i	$0.346276\pi$
$30$	−0.485594	−	2.28454i	−0.0886569	−	0.417098i
$31$	−1.82717	−	4.10388i	−0.328169	−	0.737079i	0.671825	−	0.740710i	$-0.265511\pi$
$31$	−1.82717	−	4.10388i	−0.328169	−	0.737079i	−0.999993	+	0.00363111i	$0.998844\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$	3.24316	−	0.694207i	0.564561	−	0.120846i
$34$			0.906905i			0.155533i
$35$	0.114731	−	6.17829i	0.0193930	−	1.04432i
$36$	0.309017	−	0.951057i	0.0515028	−	0.158509i
$37$	7.31548	−	8.12466i	1.20266	−	1.33569i	0.275368	−	0.961339i	$-0.411200\pi$
$37$	7.31548	−	8.12466i	1.20266	−	1.33569i	0.927289	−	0.374347i	$-0.122133\pi$
$38$	2.15564	−	0.226567i	0.349692	−	0.0367541i
$39$	0.779456	−	0.0819242i	0.124813	−	0.0131184i
$40$	−1.56281	+	1.73567i	−0.247102	+	0.274434i
$41$	1.98440	−	6.10736i	0.309911	−	0.953809i	−0.667887	−	0.744262i	$-0.732801\pi$
$41$	1.98440	−	6.10736i	0.309911	−	0.953809i	0.977799	−	0.209547i	$-0.0671988\pi$
$42$	1.36519	−	2.26633i	0.210653	−	0.349703i
$43$			4.13275i			0.630239i	0.949052	+	0.315119i	$0.102045\pi$
$43$			4.13275i			0.630239i	−0.949052	+	0.315119i	$0.897955\pi$
$44$	−2.46791	−	2.21573i	−0.372051	−	0.334033i
$45$	−2.02267	−	1.16779i	−0.301522	−	0.174084i
$46$	1.99021	+	4.47008i	0.293440	+	0.659077i
$47$	−0.668111	−	3.14322i	−0.0974540	−	0.458485i	−0.999632	−	0.0271215i	$-0.991366\pi$
$47$	−0.668111	−	3.14322i	−0.0974540	−	0.458485i	0.902178	−	0.431364i	$-0.141967\pi$
$48$	−0.951057	+	0.309017i	−0.137273	+	0.0446028i
$49$	4.87382	−	5.02453i	0.696260	−	0.717790i
$50$	0.267400	+	0.368044i	0.0378160	+	0.0520493i
$51$	0.673962	+	0.606838i	0.0943736	+	0.0849743i
$52$	−0.524431	−	0.582440i	−0.0727255	−	0.0807698i
$53$	−1.30848	+	0.582574i	−0.179734	+	0.0800227i	−0.494631	−	0.869103i	$-0.664697\pi$
$53$	−1.30848	+	0.582574i	−0.179734	+	0.0800227i	0.314897	+	0.949126i	$0.398030\pi$
$54$	−0.500000	−	0.866025i	−0.0680414	−	0.117851i
$55$	−6.26032	+	4.56209i	−0.844141	+	0.615152i
$56$	−2.63594	+	0.227655i	−0.352242	+	0.0304216i
$57$	1.27404	−	1.75356i	0.168750	−	0.232265i
$58$	−1.76966	+	0.376152i	−0.232367	+	0.0493912i
$59$	0.166918	−	0.785286i	0.0217308	−	0.102236i	−0.965946	−	0.258745i	$-0.916691\pi$
$59$	0.166918	−	0.785286i	0.0217308	−	0.102236i	0.987676	+	0.156510i	$0.0500243\pi$
$60$	0.244134	+	2.32278i	0.0315176	+	0.299870i
$61$	7.06447	+	3.14531i	0.904513	+	0.402715i	0.805654	−	0.592386i	$-0.201814\pi$
$61$	7.06447	+	3.14531i	0.904513	+	0.402715i	0.0988591	+	0.995101i	$0.468481\pi$
$62$	1.38818	+	4.27239i	0.176300	+	0.542594i
$63$	−0.770722	−	2.53101i	−0.0971019	−	0.318877i
$64$	0.809017	+	0.587785i	0.101127	+	0.0734732i
$65$	−1.58527	+	0.915255i	−0.196628	+	0.113523i
$66$	−3.29796	+	0.351402i	−0.405950	+	0.0432546i
$67$	−7.33817	+	12.7101i	−0.896500	+	1.55278i	−0.0645625	+	0.997914i	$0.520565\pi$
$67$	−7.33817	+	12.7101i	−0.896500	+	1.55278i	−0.831937	+	0.554870i	$0.812768\pi$
$68$	0.0947974	−	0.901937i	0.0114959	−	0.109376i
$69$	4.65362	+	1.51205i	0.560231	+	0.182030i
$70$	−0.759910	+	6.13246i	−0.0908266	+	0.732969i
$71$	9.60291	−	6.97692i	1.13966	−	0.828008i	0.152585	−	0.988290i	$-0.451240\pi$
$71$	9.60291	−	6.97692i	1.13966	−	0.828008i	0.987071	+	0.160282i	$0.0512404\pi$
$72$	−0.406737	+	0.913545i	−0.0479344	+	0.107662i
$73$	−11.9998	−	2.55063i	−1.40447	−	0.298529i	−0.557502	−	0.830176i	$-0.688240\pi$
$73$	−11.9998	−	2.55063i	−1.40447	−	0.298529i	−0.846966	+	0.531647i	$0.821573\pi$
$74$	−8.12466	+	7.31548i	−0.944472	+	0.850407i
$75$	0.452435	+	0.0475529i	0.0522427	+	0.00549093i
$76$	−2.16752			−0.248631
$77$	−8.70990	−	1.06664i	−0.992585	−	0.121555i
$78$	−0.783750			−0.0887422
$79$	14.0497	+	1.47668i	1.58071	+	0.166139i	0.853803	−	0.520596i	$-0.174290\pi$
$79$	14.0497	+	1.47668i	1.58071	+	0.166139i	0.726907	+	0.686736i	$0.240957\pi$
$80$	1.73567	−	1.56281i	0.194054	−	0.174727i
$81$	−0.978148	−	0.207912i	−0.108683	−	0.0231013i
$82$	−2.61192	+	5.86647i	−0.288439	+	0.647844i
$83$	−13.4630	+	9.78147i	−1.47776	+	1.07366i	−0.499490	+	0.866320i	$0.666479\pi$
$83$	−13.4630	+	9.78147i	−1.47776	+	1.07366i	−0.978270	+	0.207336i	$0.933521\pi$
$84$	−1.59461	+	2.11122i	−0.173986	+	0.230352i
$85$	−2.01448	−	0.654544i	−0.218501	−	0.0709953i
$86$	0.431990	−	4.11011i	0.0465827	−	0.443205i
$87$	−0.904596	+	1.56681i	−0.0969829	+	0.167979i
$88$	2.22278	+	2.46155i	0.236949	+	0.262403i
$89$	6.08266	−	3.51182i	0.644760	−	0.372253i	−0.141685	−	0.989912i	$-0.545252\pi$
$89$	6.08266	−	3.51182i	0.644760	−	0.372253i	0.786446	+	0.617659i	$0.211919\pi$
$90$	1.88952	+	1.37282i	0.199173	+	0.144708i
$91$	−2.01994	−	0.468712i	−0.211747	−	0.0491343i
$92$	−1.51205	−	4.65362i	−0.157643	−	0.485174i
$93$	4.10388	+	1.82717i	0.425553	+	0.189468i
$94$	0.335896	+	3.19583i	0.0346450	+	0.329625i
$95$	−1.05253	+	4.95178i	−0.107988	+	0.508042i
$96$	0.978148	−	0.207912i	0.0998318	−	0.0212199i
$97$	2.55805	−	3.52085i	0.259731	−	0.357488i	−0.659159	−	0.752004i	$-0.729087\pi$
$97$	2.55805	−	3.52085i	0.259731	−	0.357488i	0.918889	+	0.394515i	$0.129087\pi$
$98$	−5.37233	+	4.48755i	−0.542687	+	0.453311i
$99$	−1.94562	+	2.68599i	−0.195542	+	0.269952i
$100$	−0.227464	−	0.393979i	−0.0227464	−	0.0393979i
$101$	−3.60259	+	1.60398i	−0.358471	+	0.159602i	−0.578067	−	0.815989i	$-0.696193\pi$
$101$	−3.60259	+	1.60398i	−0.358471	+	0.159602i	0.219596	+	0.975591i	$0.429526\pi$
$102$	−0.606838	−	0.673962i	−0.0600859	−	0.0667322i
$103$	−4.08991	−	3.68257i	−0.402991	−	0.362855i	0.442570	−	0.896734i	$-0.354067\pi$
$103$	−4.08991	−	3.68257i	−0.402991	−	0.362855i	−0.845561	+	0.533879i	$0.820734\pi$
$104$	0.460677	+	0.634067i	0.0451731	+	0.0621754i
$105$	4.04882	+	4.66814i	0.395125	+	0.455564i
$106$	1.36221	−	0.442609i	0.132310	−	0.0429900i
$107$	3.50473	+	16.4885i	0.338815	+	1.59400i	0.736474	+	0.676466i	$0.236489\pi$
$107$	3.50473	+	16.4885i	0.338815	+	1.59400i	−0.397659	+	0.917533i	$0.630177\pi$
$108$	0.406737	+	0.913545i	0.0391383	+	0.0879060i
$109$	5.05615	+	2.91917i	0.484291	+	0.279606i	0.722203	−	0.691681i	$-0.243130\pi$
$109$	5.05615	+	2.91917i	0.484291	+	0.279606i	−0.237912	+	0.971287i	$0.576463\pi$
$110$	6.70289	−	3.88272i	0.639095	−	0.370202i
$111$			10.9328i			1.03770i
$112$	2.64530	+	0.0491230i	0.249957	+	0.00464169i
$113$	−0.657944	+	2.02494i	−0.0618941	+	0.190491i	−0.977222	−	0.212218i	$-0.931931\pi$
$113$	−0.657944	+	2.02494i	−0.0618941	+	0.190491i	0.915328	+	0.402709i	$0.131931\pi$
$114$	−1.45035	+	1.61078i	−0.135838	+	0.150863i
$115$	−11.3656	+	1.19458i	−1.05985	+	0.111395i
$116$	1.79928	−	0.189112i	0.167059	−	0.0175586i
$117$	−0.524431	+	0.582440i	−0.0484837	+	0.0538466i
$118$	−0.248088	+	0.763537i	−0.0228384	+	0.0702893i
$119$	−1.16093	−	2.09990i	−0.106423	−	0.192497i
$120$		−	2.33558i		−	0.213208i
$121$	5.52725	+	9.51050i	0.502477	+	0.864591i
$122$	−6.69700	−	3.86651i	−0.606318	−	0.350058i
$123$	2.61192	+	5.86647i	0.235509	+	0.528962i
$124$	−0.933993	−	4.39409i	−0.0838751	−	0.394601i
$125$	10.0958	−	3.28033i	0.902998	−	0.293402i
$126$	0.501938	+	2.59770i	0.0447162	+	0.231422i
$127$	3.27966	+	4.51406i	0.291023	+	0.400558i	0.929346	−	0.369210i	$-0.120372\pi$
$127$	3.27966	+	4.51406i	0.291023	+	0.400558i	−0.638323	+	0.769768i	$0.720372\pi$
$128$	−0.743145	−	0.669131i	−0.0656853	−	0.0591433i
$129$	−2.76535	−	3.07123i	−0.243476	−	0.270407i
$130$	1.67225	−	0.744535i	0.146666	−	0.0653001i
$131$	6.10055	+	10.5665i	0.533008	+	0.923196i	0.999257	+	0.0385429i	$0.0122716\pi$
$131$	6.10055	+	10.5665i	0.533008	+	0.923196i	−0.466249	+	0.884653i	$0.654395\pi$
$132$	3.31662	−	0.00474682i	0.288675	−	0.000413158i
$133$	−4.70127	+	3.28406i	−0.407652	+	0.284764i
$134$	8.62653	−	11.8734i	0.745219	−	1.02571i
$135$	2.28454	−	0.485594i	0.196622	−	0.0417933i
$136$	−0.188556	+	0.887087i	−0.0161686	+	0.0760671i
$137$	0.782785	+	7.44770i	0.0668778	+	0.636300i	0.975699	+	0.219114i	$0.0703168\pi$
$137$	0.782785	+	7.44770i	0.0668778	+	0.636300i	−0.908821	+	0.417185i	$0.863017\pi$
$138$	−4.47008	−	1.99021i	−0.380518	−	0.169418i
$139$	−4.61318	−	14.1979i	−0.391285	−	1.20425i	−0.931817	−	0.362928i	$-0.881777\pi$
$139$	−4.61318	−	14.1979i	−0.391285	−	1.20425i	0.540532	−	0.841323i	$-0.318223\pi$
$140$	1.39676	−	6.01943i	0.118048	−	0.508735i
$141$	2.59973	+	1.88881i	0.218936	+	0.159067i
$142$	−10.2796	+	5.93493i	−0.862644	+	0.498048i
$143$	1.06067	+	2.37316i	0.0886977	+	0.198453i
$144$	0.500000	−	0.866025i	0.0416667	−	0.0721688i
$145$	0.441686	−	4.20236i	0.0366800	−	0.348987i
$146$	11.6674	+	3.79098i	0.965603	+	0.313744i
$147$	−0.259890	+	6.99517i	−0.0214354	+	0.576952i
$148$	8.84483	−	6.42614i	0.727040	−	0.528226i
$149$	−6.80115	+	15.2756i	−0.557172	+	1.25143i	0.387032	+	0.922066i	$0.373500\pi$
$149$	−6.80115	+	15.2756i	−0.557172	+	1.25143i	−0.944204	+	0.329362i	$0.893166\pi$
$150$	−0.444986	−	0.0945847i	−0.0363330	−	0.00772281i
$151$	−9.55629	+	8.60452i	−0.777680	+	0.700226i	−0.959065	−	0.283186i	$-0.908609\pi$
$151$	−9.55629	+	8.60452i	−0.777680	+	0.700226i	0.181385	+	0.983412i	$0.441942\pi$
$152$	2.15564	+	0.226567i	0.174846	+	0.0183770i
$153$	−0.906905			−0.0733190
$154$	8.55069	+	1.97123i	0.689034	+	0.158846i
$155$	−10.4920			−0.842740
$156$	0.779456	+	0.0819242i	0.0624065	+	0.00655918i
$157$	6.38489	−	5.74898i	0.509569	−	0.458818i	−0.373791	−	0.927513i	$-0.621942\pi$
$157$	6.38489	−	5.74898i	0.509569	−	0.458818i	0.883360	+	0.468695i	$0.155276\pi$
$158$	−13.8183	−	2.93718i	−1.09933	−	0.233669i
$159$	0.582574	−	1.30848i	0.0462011	−	0.103769i
$160$	−1.88952	+	1.37282i	−0.149380	+	0.108531i
$161$	−10.3304	−	7.80259i	−0.814150	−	0.614930i
$162$	0.951057	+	0.309017i	0.0747221	+	0.0242787i
$163$	1.46329	−	13.9223i	0.114614	−	1.09048i	−0.774431	−	0.632659i	$-0.781964\pi$
$163$	1.46329	−	13.9223i	0.114614	−	1.09048i	0.889045	−	0.457820i	$-0.151370\pi$
$164$	3.21083	−	5.56132i	0.250724	−	0.434266i
$165$	1.59969	−	7.57926i	0.124536	−	0.590045i
$166$	14.4117	−	8.32061i	1.11857	−	0.645805i
$167$	7.50815	+	5.45499i	0.580998	+	0.422120i	0.839084	−	0.544002i	$-0.183092\pi$
$167$	7.50815	+	5.45499i	0.580998	+	0.422120i	−0.258086	+	0.966122i	$0.583092\pi$
$168$	1.80655	−	1.93297i	0.139379	−	0.149132i
$169$	−3.82740	−	11.7795i	−0.294416	−	0.906118i
$170$	1.93503	+	0.861529i	0.148410	+	0.0660762i
$171$	0.226567	+	2.15564i	0.0173260	+	0.164846i
$172$	−0.859248	+	4.04244i	−0.0655170	+	0.308233i
$173$	2.34934	−	0.499367i	0.178617	−	0.0379662i	−0.117735	−	0.993045i	$-0.537563\pi$
$173$	2.34934	−	0.499367i	0.178617	−	0.0379662i	0.296352	+	0.955079i	$0.404230\pi$
$174$	1.06342	−	1.46367i	0.0806174	−	0.110960i
$175$	−1.09029	−	0.509889i	−0.0824180	−	0.0385440i
$176$	−1.95330	−	2.68041i	−0.147236	−	0.202044i
$177$	0.401415	+	0.695271i	0.0301722	+	0.0522598i
$178$	−6.41642	+	2.85678i	−0.480931	+	0.214124i
$179$	12.7261	+	14.1338i	0.951194	+	1.05641i	0.998344	+	0.0575196i	$0.0183192\pi$
$179$	12.7261	+	14.1338i	0.951194	+	1.05641i	−0.0471509	+	0.998888i	$0.515014\pi$
$180$	−1.73567	−	1.56281i	−0.129369	−	0.116485i
$181$	−8.55391	−	11.7734i	−0.635807	−	0.875113i	0.362576	−	0.931954i	$-0.381897\pi$
$181$	−8.55391	−	11.7734i	−0.635807	−	0.875113i	−0.998383	+	0.0568409i	$0.981897\pi$
$182$	1.95988	+	0.677285i	0.145276	+	0.0502037i
$183$	−7.35455	+	2.38964i	−0.543664	+	0.176647i
$184$	1.01733	+	4.78618i	0.0749989	+	0.352842i
$185$	−10.3858	−	23.3269i	−0.763578	−	1.71503i
$186$	−3.89041	−	2.24613i	−0.285259	−	0.164694i
$187$	−1.21947	+	2.74957i	−0.0891768	+	0.201068i
$188$		−	3.21344i		−	0.234364i
$189$	2.26633	+	1.36519i	0.164851	+	0.0993029i
$190$	1.56437	−	4.81464i	0.113491	−	0.349291i
$191$	−3.08238	+	3.42333i	−0.223033	+	0.247704i	−0.844268	−	0.535921i	$-0.819965\pi$
$191$	−3.08238	+	3.42333i	−0.223033	+	0.247704i	0.621235	+	0.783624i	$0.286631\pi$
$192$	−0.994522	+	0.104528i	−0.0717734	+	0.00754369i
$193$	7.36968	−	0.774585i	0.530481	−	0.0557558i	0.164498	−	0.986377i	$-0.447400\pi$
$193$	7.36968	−	0.774585i	0.530481	−	0.0557558i	0.365983	+	0.930622i	$0.380733\pi$
$194$	−2.91207	+	3.23418i	−0.209074	+	0.232200i
$195$	0.565659	−	1.74092i	0.0405076	−	0.124670i
$196$	5.81197	−	3.90140i	0.415141	−	0.278672i
$197$			12.1083i			0.862678i	0.902190	+	0.431339i	$0.141959\pi$
$197$			12.1083i			0.862678i	−0.902190	+	0.431339i	$0.858041\pi$
$198$	2.21573	−	2.46791i	0.157465	−	0.175386i
$199$	1.04016	+	0.600535i	0.0737348	+	0.0425708i	0.536414	−	0.843955i	$-0.319779\pi$
$199$	1.04016	+	0.600535i	0.0737348	+	0.0425708i	−0.462679	+	0.886526i	$0.653112\pi$
$200$	0.185036	+	0.415597i	0.0130840	+	0.0293871i
$201$	−3.05138	−	14.3556i	−0.215228	−	1.01257i
$202$	3.75052	−	1.21862i	0.263886	−	0.0857416i
$203$	3.61604	−	3.13631i	0.253797	−	0.220126i
$204$	0.533066	+	0.733702i	0.0373221	+	0.0513694i
$205$	−11.1459	−	10.0358i	−0.778463	−	0.700931i
$206$	3.68257	+	4.08991i	0.256577	+	0.284958i
$207$	−4.47008	+	1.99021i	−0.310692	+	0.138329i
$208$	−0.391875	−	0.678747i	−0.0271716	−	0.0470627i
$209$	6.84017	+	2.21169i	0.473145	+	0.152986i
$210$	−3.53869	−	5.06578i	−0.244193	−	0.349572i
$211$	9.51125	−	13.0911i	0.654781	−	0.901229i	−0.344513	−	0.938781i	$-0.611956\pi$
$211$	9.51125	−	13.0911i	0.654781	−	0.901229i	0.999295	+	0.0375521i	$0.0119560\pi$
$212$	−1.40101	+	0.297795i	−0.0962220	+	0.0204526i
$213$	−2.46788	+	11.6105i	−0.169096	+	0.795536i
$214$	−1.76202	−	16.7645i	−0.120449	−	1.14600i
$215$	8.81788	+	3.92597i	0.601374	+	0.267749i
$216$	−0.309017	−	0.951057i	−0.0210259	−	0.0647112i
$217$	−8.68339	−	8.11551i	−0.589467	−	0.550916i
$218$	−4.72332	−	3.43169i	−0.319903	−	0.232423i
$219$	10.6243	−	6.13393i	0.717922	−	0.414493i
$220$	−7.07202	+	3.16080i	−0.476796	+	0.213101i
$221$	−0.355394	+	0.615560i	−0.0239064	+	0.0414070i
$222$	1.14279	−	10.8729i	0.0766990	−	0.729742i
$223$	−12.5495	−	4.07757i	−0.840374	−	0.273054i	−0.142965	−	0.989728i	$-0.545664\pi$
$223$	−12.5495	−	4.07757i	−0.840374	−	0.273054i	−0.697409	+	0.716674i	$0.745664\pi$
$224$	−2.62567	−	0.325363i	−0.175435	−	0.0217392i
$225$	−0.368044	+	0.267400i	−0.0245363	+	0.0178266i
$226$	0.866004	−	1.94508i	0.0576057	−	0.129385i
$227$	−24.0782	−	5.11798i	−1.59813	−	0.339692i	−0.679149	−	0.734000i	$-0.737651\pi$
$227$	−24.0782	−	5.11798i	−1.59813	−	0.339692i	−0.918978	+	0.394308i	$0.870984\pi$
$228$	1.61078	−	1.45035i	0.106677	−	0.0960520i
$229$	4.80099	+	0.504605i	0.317259	+	0.0333452i	0.261820	−	0.965117i	$-0.415677\pi$
$229$	4.80099	+	0.504605i	0.317259	+	0.0333452i	0.0554391	+	0.998462i	$0.482344\pi$
$230$	11.4282			0.753556
$231$	7.18644	−	5.03539i	0.472833	−	0.331304i
$232$	−1.80919			−0.118779
$233$	−2.97581	−	0.312770i	−0.194952	−	0.0204902i	0.00654938	−	0.999979i	$-0.497915\pi$
$233$	−2.97581	−	0.312770i	−0.194952	−	0.0204902i	−0.201501	+	0.979488i	$0.564582\pi$
$234$	0.582440	−	0.524431i	0.0380753	−	0.0342831i
$235$	−7.34123	−	1.56043i	−0.478889	−	0.101791i
$236$	0.326540	−	0.733422i	0.0212560	−	0.0477417i
$237$	−11.4290	+	8.30367i	−0.742395	+	0.539381i
$238$	0.935076	+	2.20975i	0.0606120	+	0.143237i
$239$	18.1598	+	5.90046i	1.17466	+	0.381669i	0.830379	−	0.557199i	$-0.188124\pi$
$239$	18.1598	+	5.90046i	1.17466	+	0.381669i	0.344278	+	0.938868i	$0.388124\pi$
$240$	−0.244134	+	2.32278i	−0.0157588	+	0.149935i
$241$	−9.74426	+	16.8776i	−0.627683	+	1.08718i	0.360332	+	0.932824i	$0.382663\pi$
$241$	−9.74426	+	16.8776i	−0.627683	+	1.08718i	−0.988015	+	0.154355i	$0.950670\pi$
$242$	−4.50285	−	10.0362i	−0.289454	−	0.645148i
$243$	0.866025	−	0.500000i	0.0555556	−	0.0320750i
$244$	6.25615	+	4.54536i	0.400509	+	0.290987i
$245$	−6.09066	−	15.1722i	−0.389118	−	0.969316i
$246$	−1.98440	−	6.10736i	−0.126521	−	0.389391i
$247$	1.55192	+	0.690961i	0.0987466	+	0.0439648i
$248$	0.469569	+	4.46765i	0.0298177	+	0.283696i
$249$	3.45990	−	16.2776i	0.219263	−	1.03155i
$250$	−10.3834	+	2.20706i	−0.656704	+	0.139587i
$251$	−1.63773	+	2.25414i	−0.103372	+	0.142280i	−0.857569	−	0.514368i	$-0.828026\pi$
$251$	−1.63773	+	2.25414i	−0.103372	+	0.142280i	0.754197	+	0.656648i	$0.228026\pi$
$252$	−0.227655	−	2.63594i	−0.0143409	−	0.166049i
$253$	0.0232267	+	16.2286i	0.00146025	+	1.02028i
$254$	−2.78984	−	4.83215i	−0.175050	−	0.303196i
$255$	1.93503	−	0.861529i	0.121176	−	0.0539510i
$256$	0.669131	+	0.743145i	0.0418207	+	0.0464466i
$257$	8.29386	+	7.46782i	0.517357	+	0.465830i	0.885963	−	0.463756i	$-0.153498\pi$
$257$	8.29386	+	7.46782i	0.517357	+	0.465830i	−0.368607	+	0.929585i	$0.620165\pi$
$258$	2.42917	+	3.34347i	0.151234	+	0.208155i
$259$	9.44769	−	27.3391i	0.587051	−	1.69877i
$260$	−1.74092	+	0.565659i	−0.107967	+	0.0350807i
$261$	−0.376152	−	1.76966i	−0.0232832	−	0.109539i
$262$	−4.96264	−	11.1463i	−0.306593	−	0.688618i
$263$	21.3325	+	12.3163i	1.31542	+	0.759458i	0.982988	−	0.183669i	$-0.0587975\pi$
$263$	21.3325	+	12.3163i	1.31542	+	0.759458i	0.332432	+	0.943127i	$0.392131\pi$
$264$	−3.29895	−	0.341961i	−0.203036	−	0.0210462i
$265$			3.34528i			0.205499i
$266$	5.01879	−	2.77465i	0.307722	−	0.170125i
$267$	−2.17043	+	6.67989i	−0.132828	+	0.408802i
$268$	−9.82038	+	10.9066i	−0.599875	+	0.666229i
$269$	23.7871	−	2.50012i	1.45032	−	0.152435i	0.653627	−	0.756816i	$-0.273246\pi$
$269$	23.7871	−	2.50012i	1.45032	−	0.152435i	0.796695	+	0.604381i	$0.206580\pi$
$270$	−2.32278	+	0.244134i	−0.141360	+	0.0148575i
$271$	0.779533	−	0.865759i	0.0473533	−	0.0525911i	−0.719003	−	0.695007i	$-0.755401\pi$
$271$	0.779533	−	0.865759i	0.0473533	−	0.0525911i	0.766356	+	0.642416i	$0.222068\pi$
$272$	0.280249	−	0.862518i	0.0169926	−	0.0522979i
$273$	1.81474	−	1.00328i	0.109833	−	0.0607214i
$274$		−	7.48872i		−	0.452410i
$275$	0.315814	+	1.47540i	0.0190443	+	0.0889701i
$276$	4.23756	+	2.44656i	0.255071	+	0.147265i
$277$	7.85141	+	17.6346i	0.471746	+	1.05956i	0.980117	+	0.198420i	$0.0635811\pi$
$277$	7.85141	+	17.6346i	0.471746	+	1.05956i	−0.508371	+	0.861138i	$0.669752\pi$
$278$	3.10382	+	14.6023i	0.186155	+	0.875790i
$279$	−4.27239	+	1.38818i	−0.255781	+	0.0831084i
$280$	−2.01831	+	5.84045i	−0.120617	+	0.349034i
$281$	−2.84228	−	3.91207i	−0.169556	−	0.233374i	0.715780	−	0.698326i	$-0.246072\pi$
$281$	−2.84228	−	3.91207i	−0.169556	−	0.233374i	−0.885336	+	0.464952i	$0.846072\pi$
$282$	−2.38805	−	2.15021i	−0.142206	−	0.128043i
$283$	12.5905	+	13.9832i	0.748428	+	0.831213i	0.990278	−	0.139100i	$-0.0444210\pi$
$283$	12.5905	+	13.9832i	0.748428	+	0.831213i	−0.241851	+	0.970314i	$0.577754\pi$
$284$	10.8436	−	4.82790i	0.643452	−	0.286483i
$285$	−2.53121	−	4.38418i	−0.149936	−	0.259696i
$286$	−0.806798	−	2.47103i	−0.0477069	−	0.146115i
$287$	−1.46192	−	16.9271i	−0.0862944	−	0.999174i
$288$	−0.587785	+	0.809017i	−0.0346356	+	0.0476718i
$289$	15.8240	−	3.36350i	0.930824	−	0.197853i
$290$	−0.878533	+	4.13317i	−0.0515892	+	0.242708i
$291$	0.454909	+	4.32817i	0.0266673	+	0.253722i
$292$	−11.2072	−	4.98979i	−0.655855	−	0.292005i
$293$	−8.61183	−	26.5045i	−0.503108	−	1.54841i	−0.803927	−	0.594727i	$-0.797260\pi$
$293$	−8.61183	−	26.5045i	−0.503108	−	1.54841i	0.300819	−	0.953681i	$-0.402740\pi$
$294$	0.989661	−	6.92969i	0.0577182	−	0.404148i
$295$	−1.51697	−	1.10214i	−0.0883212	−	0.0641691i
$296$	−9.46809	+	5.46640i	−0.550321	+	0.317728i
$297$	−0.351402	−	3.29796i	−0.0203904	−	0.191367i
$298$	8.36063	−	14.4810i	0.484318	−	0.838864i
$299$	−0.400864	+	3.81397i	−0.0231826	+	0.220567i
$300$	0.432662	+	0.140580i	0.0249797	+	0.00811641i
$301$	4.26113	+	10.0698i	0.245607	+	0.580412i
$302$	10.4034	−	7.55848i	0.598646	−	0.434942i
$303$	1.60398	−	3.60259i	0.0921461	−	0.206964i
$304$	−2.12015	−	0.450652i	−0.121599	−	0.0258467i
$305$	13.4220	−	12.0852i	0.768542	−	0.691998i
$306$	0.901937	+	0.0947974i	0.0515603	+	0.00541921i
$307$	−18.3095			−1.04498			−0.522490	−	0.852645i	$-0.674997\pi$
$307$	−18.3095			−1.04498			−0.522490	+	0.852645i	$0.674997\pi$
$308$	−8.29780	−	2.85422i	−0.472811	−	0.162634i
$309$	5.50352			0.313084
$310$	10.4345	+	1.09672i	0.592643	+	0.0622892i
$311$	−0.243800	+	0.219518i	−0.0138246	+	0.0124477i	−0.676014	−	0.736889i	$-0.736294\pi$
$311$	−0.243800	+	0.219518i	−0.0138246	+	0.0124477i	0.662189	+	0.749337i	$0.269627\pi$
$312$	−0.766623	−	0.162951i	−0.0434015	−	0.00922527i
$313$	−12.6471	+	28.4059i	−0.714857	+	1.60560i	0.0785547	+	0.996910i	$0.474969\pi$
$313$	−12.6471	+	28.4059i	−0.714857	+	1.60560i	−0.793412	+	0.608685i	$0.791697\pi$
$314$	−6.95084	+	5.05008i	−0.392259	+	0.284993i
$315$	−6.13246	−	0.759910i	−0.345525	−	0.0428161i
$316$	13.4356	+	4.36550i	0.755813	+	0.245578i
$317$	0.363364	−	3.45718i	0.0204085	−	0.194174i	−0.979567	−	0.201116i	$-0.935543\pi$
$317$	0.363364	−	3.45718i	0.0204085	−	0.194174i	0.999976	+	0.00694200i	$0.00220973\pi$
$318$	−0.716157	+	1.24042i	−0.0401601	+	0.0695593i
$319$	−5.87107	−	1.23915i	−0.328717	−	0.0693793i
$320$	2.02267	−	1.16779i	0.113071	−	0.0652814i
$321$	−13.6375	−	9.90819i	−0.761168	−	0.553021i
$322$	9.45822	+	8.83967i	0.527086	+	0.492615i
$323$	0.607445	+	1.86952i	0.0337992	+	0.104023i
$324$	−0.913545	−	0.406737i	−0.0507525	−	0.0225965i
$325$	0.0372696	+	0.354596i	0.00206734	+	0.0196695i
$326$	−2.91055	+	13.6931i	−0.161201	+	0.758390i
$327$	−5.71076	+	1.21386i	−0.315806	+	0.0671265i
$328$	−3.77455	+	5.19523i	−0.208415	+	0.286858i
$329$	−4.86876	−	6.96983i	−0.268423	−	0.384259i
$330$	−2.38317	+	7.37053i	−0.131189	+	0.405734i
$331$	−5.73382	−	9.93126i	−0.315159	−	0.545872i	0.664312	−	0.747455i	$-0.268725\pi$
$331$	−5.73382	−	9.93126i	−0.315159	−	0.545872i	−0.979471	+	0.201584i	$0.935391\pi$
$332$	−15.2025	+	6.76860i	−0.834346	+	0.371475i
$333$	−7.31548	−	8.12466i	−0.400886	−	0.445229i
$334$	−6.89682	−	6.20992i	−0.377377	−	0.339792i
$335$	20.1479	+	27.7313i	1.10080	+	1.51512i
$336$	−1.99871	+	1.73354i	−0.109038	+	0.0945725i
$337$	19.9898	−	6.49507i	1.08891	−	0.353809i	0.291086	−	0.956697i	$-0.405983\pi$
$337$	19.9898	−	6.49507i	1.08891	−	0.353809i	0.797826	+	0.602888i	$0.205983\pi$
$338$	2.57514	+	12.1151i	0.140069	+	0.658973i
$339$	−0.866004	−	1.94508i	−0.0470349	−	0.105642i
$340$	−1.83437	−	1.05907i	−0.0994827	−	0.0574364i
$341$	−1.53618	+	14.8197i	−0.0831886	+	0.802534i
$342$		−	2.16752i		−	0.117206i
$343$	6.69484	−	17.2679i	0.361487	−	0.932377i
$344$	1.27709	−	3.93048i	0.0688561	−	0.211917i
$345$	7.64699	−	8.49284i	0.411700	−	0.457239i
$346$	−2.38867	+	0.251059i	−0.128415	+	0.0134970i
$347$	−3.41950	+	0.359404i	−0.183569	+	0.0192938i	−0.195867	−	0.980631i	$-0.562752\pi$
$347$	−3.41950	+	0.359404i	−0.183569	+	0.0192938i	0.0122981	+	0.999924i	$0.496085\pi$
$348$	−1.21059	+	1.34449i	−0.0648942	+	0.0720723i
$349$	−0.0640870	+	0.197239i	−0.00343050	+	0.0105580i	−0.952757	−	0.303733i	$-0.901767\pi$
$349$	−0.0640870	+	0.197239i	−0.00343050	+	0.0105580i	0.949327	+	0.314291i	$0.101767\pi$
$350$	1.03102	+	0.621062i	0.0551101	+	0.0331972i
$351$		−	0.783750i		−	0.0418335i
$352$	1.66242	+	2.86990i	0.0886074	+	0.152966i
$353$	26.4011	+	15.2427i	1.40519	+	0.811285i	0.994919	−	0.100680i	$-0.0321019\pi$
$353$	26.4011	+	15.2427i	1.40519	+	0.811285i	0.410268	+	0.911965i	$0.365435\pi$
$354$	−0.326540	−	0.733422i	−0.0173554	−	0.0389809i
$355$	−5.76393	−	27.1172i	−0.305918	−	1.43923i
$356$	6.67989	−	2.17043i	0.354033	−	0.115032i
$357$	2.26785	+	0.783711i	0.120027	+	0.0414784i
$358$	−11.1790	−	15.3866i	−0.590829	−	0.813206i
$359$	−3.35045	−	3.01676i	−0.176830	−	0.159219i	0.575963	−	0.817476i	$-0.304627\pi$
$359$	−3.35045	−	3.01676i	−0.176830	−	0.159219i	−0.752793	+	0.658257i	$0.771294\pi$
$360$	1.56281	+	1.73567i	0.0823672	+	0.0914780i
$361$	−13.0654	+	5.81709i	−0.687653	+	0.306163i
$362$	7.27639	+	12.6031i	0.382439	+	0.662403i
$363$	−10.4713	−	3.36923i	−0.549601	−	0.176839i
$364$	−1.87835	−	0.878438i	−0.0984522	−	0.0460427i
$365$	−16.8415	+	23.1804i	−0.881527	+	1.21332i
$366$	7.56404	−	1.60779i	0.395379	−	0.0840404i
$367$	−3.39305	+	15.9631i	−0.177116	+	0.833265i	0.796422	+	0.604741i	$0.206723\pi$
$367$	−3.39305	+	15.9631i	−0.177116	+	0.833265i	−0.973538	+	0.228524i	$0.926610\pi$
$368$	−0.511469	−	4.86631i	−0.0266622	−	0.253674i
$369$	−5.86647	−	2.61192i	−0.305396	−	0.135971i
$370$	7.89057	+	24.2847i	0.410211	+	1.26250i
$371$	−2.58755	+	2.76861i	−0.134339	+	0.143739i
$372$	3.63431	+	2.64048i	0.188430	+	0.136903i
$373$	−10.5813	+	6.10911i	−0.547878	+	0.316317i	−0.748266	−	0.663399i	$-0.769113\pi$
$373$	−10.5813	+	6.10911i	−0.547878	+	0.316317i	0.200388	+	0.979717i	$0.435780\pi$
$374$	1.50020	−	2.60704i	0.0775736	−	0.134807i
$375$	−5.30769	+	9.19318i	−0.274088	+	0.474734i
$376$	−0.335896	+	3.19583i	−0.0173225	+	0.164813i
$377$	−1.34855	−	0.438172i	−0.0694541	−	0.0225670i
$378$	−2.11122	−	1.59461i	−0.108589	−	0.0820177i
$379$	23.8407	−	17.3213i	1.22461	−	0.889734i	0.228139	−	0.973628i	$-0.426736\pi$
$379$	23.8407	−	17.3213i	1.22461	−	0.889734i	0.996475	+	0.0838944i	$0.0267358\pi$
$380$	−2.05907	+	4.62474i	−0.105628	+	0.237244i
$381$	−5.45776	−	1.16008i	−0.279609	−	0.0594328i
$382$	3.42333	−	3.08238i	0.175153	−	0.157708i
$383$	−18.4639	−	1.94063i	−0.943459	−	0.0991615i	−0.379708	−	0.925106i	$-0.623976\pi$
$383$	−18.4639	−	1.94063i	−0.943459	−	0.0991615i	−0.563751	+	0.825945i	$0.690642\pi$
$384$	1.00000			0.0510310
$385$	−10.5499	+	17.5707i	−0.537675	+	0.895484i
$386$	−7.41027			−0.377173
$387$	4.11011	+	0.431990i	0.208929	+	0.0219593i
$388$	3.23418	−	2.91207i	0.164190	−	0.147838i
$389$	6.13779	+	1.30463i	0.311198	+	0.0661472i	0.360863	−	0.932619i	$-0.382482\pi$
$389$	6.13779	+	1.30463i	0.311198	+	0.0661472i	−0.0496651	+	0.998766i	$0.515815\pi$
$390$	−0.744535	+	1.67225i	−0.0377010	+	0.0846779i
$391$	−3.59008	+	2.60835i	−0.181558	+	0.131910i
$392$	−6.18794	+	3.27252i	−0.312538	+	0.165287i
$393$	−11.6039	−	3.77035i	−0.585341	−	0.190189i
$394$	1.26566	−	12.0419i	0.0637629	−	0.606664i
$395$	16.4974	−	28.5744i	0.830075	−	1.43773i
$396$	−2.46155	+	2.22278i	−0.123698	+	0.111699i
$397$	−3.34049	+	1.92863i	−0.167654	+	0.0967953i	−0.581479	−	0.813561i	$-0.697526\pi$
$397$	−3.34049	+	1.92863i	−0.167654	+	0.0967953i	0.413825	+	0.910356i	$0.364193\pi$
$398$	−0.971686	−	0.705971i	−0.0487062	−	0.0353871i
$399$	1.29626	−	5.58629i	0.0648940	−	0.279664i
$400$	−0.140580	−	0.432662i	−0.00702902	−	0.0216331i
$401$	18.3883	+	8.18699i	0.918266	+	0.408839i	0.810769	−	0.585367i	$-0.199049\pi$
$401$	18.3883	+	8.18699i	0.918266	+	0.408839i	0.107498	+	0.994205i	$0.465716\pi$
$402$	1.53409	+	14.5959i	0.0765137	+	0.727979i
$403$	−0.732017	+	3.44387i	−0.0364644	+	0.171551i
$404$	−3.85735	+	0.819906i	−0.191911	+	0.0407918i
$405$	−1.37282	+	1.88952i	−0.0682159	+	0.0938911i
$406$	−3.92407	+	2.74115i	−0.194748	+	0.136041i
$407$	−34.4693	+	11.2543i	−1.70858	+	0.557855i
$408$	−0.453453	−	0.785403i	−0.0224493	−	0.0388832i
$409$	25.9290	−	11.5444i	1.28211	−	0.570831i	0.351274	−	0.936273i	$-0.385749\pi$
$409$	25.9290	−	11.5444i	1.28211	−	0.570831i	0.930834	+	0.365441i	$0.119082\pi$
$410$	10.0358	+	11.1459i	0.495633	+	0.550456i
$411$	−5.56520	−	5.01093i	−0.274511	−	0.247171i
$412$	−3.23489	−	4.45244i	−0.159372	−	0.219356i
$413$	−0.402971	−	2.08551i	−0.0198289	−	0.102621i
$414$	4.65362	−	1.51205i	0.228713	−	0.0743134i
$415$	8.08088	+	38.0176i	0.396675	+	1.86621i
$416$	0.318780	+	0.715991i	0.0156295	+	0.0351044i
$417$	12.9285	+	7.46429i	0.633112	+	0.365528i
$418$	−6.57152	−	2.91456i	−0.321423	−	0.142556i
$419$			31.8920i			1.55803i	0.627007	+	0.779014i	$0.284280\pi$
$419$			31.8920i			1.55803i	−0.627007	+	0.779014i	$0.715720\pi$
$420$	2.98979	+	5.40793i	0.145887	+	0.263880i
$421$	−8.60442	+	26.4817i	−0.419354	+	1.29064i	0.488944	+	0.872315i	$0.337382\pi$
$421$	−8.60442	+	26.4817i	−0.419354	+	1.29064i	−0.908298	+	0.418324i	$0.862618\pi$
$422$	−10.8275	+	12.0252i	−0.527076	+	0.585378i
$423$	−3.19583	+	0.335896i	−0.155387	+	0.0163318i
$424$	1.42447	−	0.149717i	0.0691782	−	0.00727092i
$425$	−0.276067	+	0.306604i	−0.0133912	+	0.0148725i
$426$	3.66799	−	11.2889i	0.177714	−	0.546949i
$427$	20.4561	+	0.379870i	0.989942	+	0.0183832i
$428$			16.8568i			0.814805i
$429$	−2.37618	−	1.05387i	−0.114723	−	0.0508815i
$430$	−8.35920	−	4.82618i	−0.403116	−	0.232739i
$431$	5.37055	+	12.0625i	0.258690	+	0.581028i	0.995467	−	0.0951084i	$-0.0303198\pi$
$431$	5.37055	+	12.0625i	0.258690	+	0.581028i	−0.736777	+	0.676136i	$0.763653\pi$
$432$	0.207912	+	0.978148i	0.0100032	+	0.0470611i
$433$	33.1860	−	10.7828i	1.59482	−	0.518188i	0.628999	−	0.777406i	$-0.283465\pi$
$433$	33.1860	−	10.7828i	1.59482	−	0.518188i	0.965819	+	0.259218i	$0.0834648\pi$
$434$	7.78752	+	8.97871i	0.373813	+	0.430992i
$435$	2.48369	+	3.41851i	0.119084	+	0.163905i
$436$	4.33873	+	3.90661i	0.207788	+	0.187093i
$437$	7.09674	+	7.88173i	0.339483	+	0.377034i
$438$	−11.2072	+	4.98979i	−0.535503	+	0.238421i
$439$	−11.4599	−	19.8491i	−0.546950	−	0.947346i	−0.998481	−	0.0550902i	$-0.982455\pi$
$439$	−11.4599	−	19.8491i	−0.546950	−	0.947346i	0.451531	−	0.892255i	$-0.350878\pi$
$440$	7.36368	−	2.40426i	0.351050	−	0.114619i
$441$	−4.48755	−	5.37233i	−0.213693	−	0.255825i
$442$	0.417790	−	0.575039i	0.0198722	−	0.0273518i
$443$	−27.4851	+	5.84214i	−1.30586	+	0.277569i	−0.807739	−	0.589541i	$-0.799309\pi$
$443$	−27.4851	+	5.84214i	−1.30586	+	0.277569i	−0.498118	+	0.867109i	$0.665976\pi$
$444$	−2.27306	+	10.6939i	−0.107875	+	0.507510i
$445$	−1.71471	−	16.3144i	−0.0812853	−	0.773378i
$446$	12.0545	+	5.36701i	0.570797	+	0.254135i
$447$	−5.16715	−	15.9029i	−0.244398	−	0.752179i
$448$	2.57728	+	0.598037i	0.121765	+	0.0282546i
$449$	−2.98458	−	2.16842i	−0.140851	−	0.102334i	0.515128	−	0.857113i	$-0.327744\pi$
$449$	−2.98458	−	2.16842i	−0.140851	−	0.102334i	−0.655979	+	0.754779i	$0.727744\pi$
$450$	0.393979	−	0.227464i	0.0185723	−	0.0107227i
$451$	−15.8072	+	14.2739i	−0.744334	+	0.672133i
$452$	−1.06458	+	1.84390i	−0.0500734	+	0.0867297i
$453$	1.34416	−	12.7888i	0.0631541	−	0.600871i
$454$	23.4113	+	7.60681i	1.09875	+	0.357005i
$455$	−2.91894	+	3.86460i	−0.136842	+	0.181175i
$456$	−1.75356	+	1.27404i	−0.0821179	+	0.0596622i
$457$	1.74070	−	3.90968i	0.0814266	−	0.182887i	−0.868244	−	0.496137i	$-0.834751\pi$
$457$	1.74070	−	3.90968i	0.0814266	−	0.182887i	0.949671	+	0.313250i	$0.101418\pi$
$458$	−4.72195	−	1.00368i	−0.220642	−	0.0468989i
$459$	0.673962	−	0.606838i	0.0314579	−	0.0283248i
$460$	−11.3656	−	1.19458i	−0.529926	−	0.0556974i
$461$	−39.6359			−1.84603			−0.923015	−	0.384764i	$-0.874283\pi$
$461$	−39.6359			−1.84603			−0.923015	+	0.384764i	$0.874283\pi$
$462$	−7.67341	+	4.25662i	−0.356999	+	0.198036i
$463$	5.88911			0.273690			0.136845	−	0.990592i	$-0.456304\pi$
$463$	5.88911			0.273690			0.136845	+	0.990592i	$0.456304\pi$
$464$	1.79928	+	0.189112i	0.0835295	+	0.00877931i
$465$	7.79709	−	7.02053i	0.361582	−	0.325569i
$466$	2.92681	+	0.622113i	0.135582	+	0.0288188i
$467$	−16.6933	+	37.4938i	−0.772474	+	1.73500i	−0.0998709	+	0.995000i	$0.531843\pi$
$467$	−16.6933	+	37.4938i	−0.772474	+	1.73500i	−0.672603	+	0.740004i	$0.734824\pi$
$468$	−0.634067	+	0.460677i	−0.0293098	+	0.0212948i
$469$	−4.77513	+	38.5352i	−0.220495	+	1.77939i
$470$	7.13790	+	2.31925i	0.329247	+	0.106979i
$471$	−0.898078	+	8.54464i	−0.0413813	+	0.393716i
$472$	−0.401415	+	0.695271i	−0.0184766	+	0.0320025i
$473$	6.83640	−	11.8802i	0.314338	−	0.546253i
$474$	12.2344	−	7.06352i	0.561944	−	0.324438i
$475$	0.797742	+	0.579594i	0.0366029	+	0.0265936i
$476$	−0.698972	−	2.29538i	−0.0320373	−	0.105209i
$477$	0.442609	+	1.36221i	0.0202657	+	0.0623713i
$478$	−17.4435	−	7.76635i	−0.797847	−	0.355225i
$479$	−1.74443	−	16.5972i	−0.0797052	−	0.758345i	−0.959256	−	0.282539i	$-0.908823\pi$
$479$	−1.74443	−	16.5972i	−0.0797052	−	0.758345i	0.879551	−	0.475806i	$-0.157843\pi$
$480$	0.485594	−	2.28454i	0.0221642	−	0.104275i
$481$	−8.38134	+	1.78151i	−0.382156	+	0.0812298i
$482$	11.4551	−	15.7665i	0.521764	−	0.718147i
$483$	12.8979	−	1.11394i	0.586877	−	0.0506860i
$484$	3.42912	+	10.4518i	0.155869	+	0.475084i
$485$	−5.08224	−	8.80269i	−0.230772	−	0.399710i
$486$	−0.913545	+	0.406737i	−0.0414393	+	0.0184499i
$487$	−21.7193	−	24.1217i	−0.984195	−	1.09306i	−0.995654	−	0.0931252i	$-0.970314\pi$
$487$	−21.7193	−	24.1217i	−0.984195	−	1.09306i	0.0114592	−	0.999934i	$-0.496352\pi$
$488$	−5.74676	−	5.17441i	−0.260144	−	0.234234i
$489$	8.22840	+	11.3254i	0.372101	+	0.512153i
$490$	4.47137	+	15.7257i	0.201996	+	0.710416i
$491$	24.6446	−	8.00751i	1.11219	−	0.361374i	0.305411	−	0.952221i	$-0.401206\pi$
$491$	24.6446	−	8.00751i	1.11219	−	0.361374i	0.806784	+	0.590847i	$0.201206\pi$
$492$	1.33514	+	6.28133i	0.0601926	+	0.283184i
$493$	−0.667360	−	1.49891i	−0.0300564	−	0.0675077i
$494$	−1.47120	−	0.849396i	−0.0661923	−	0.0382161i
$495$	3.88272	+	6.70289i	0.174515	+	0.301272i
$496$		−	4.49226i		−	0.201708i
$497$	16.2046	−	26.9010i	0.726875	−	1.20668i
$498$	−5.14242	+	15.8267i	−0.230437	+	0.709213i
$499$	27.0094	−	29.9969i	1.20910	−	1.34285i	0.286033	−	0.958220i	$-0.407663\pi$
$499$	27.0094	−	29.9969i	1.20910	−	1.34285i	0.923072	−	0.384627i	$-0.125670\pi$
$500$	10.5572	−	1.10961i	0.472133	−	0.0496232i
$501$	−9.22975	+	0.970085i	−0.412355	+	0.0433402i
$502$	1.86438	−	2.07060i	0.0832112	−	0.0924155i
$503$	11.5942	−	35.6831i	0.516958	−	1.59103i	−0.262733	−	0.964869i	$-0.584624\pi$
$503$	11.5942	−	35.6831i	0.516958	−	1.59103i	0.779691	−	0.626164i	$-0.215376\pi$
$504$	−0.0491230	+	2.64530i	−0.00218811	+	0.117831i
$505$			9.21042i			0.409858i
$506$	1.67325	−	16.1421i	0.0743851	−	0.717605i
$507$	10.7264	+	6.19287i	0.476374	+	0.275035i
$508$	2.26946	+	5.09730i	0.100691	+	0.226156i
$509$	−2.41239	−	11.3494i	−0.106927	−	0.503054i	−0.998719	−	0.0506067i	$-0.983884\pi$
$509$	−2.41239	−	11.3494i	−0.106927	−	0.503054i	0.891791	−	0.452447i	$-0.149449\pi$
$510$	−2.01448	+	0.654544i	−0.0892026	+	0.0289837i
$511$	−31.8683	+	6.15771i	−1.40977	+	0.272401i
$512$	−0.587785	−	0.809017i	−0.0259767	−	0.0357538i
$513$	−1.61078	−	1.45035i	−0.0711177	−	0.0640347i
$514$	−7.46782	−	8.29386i	−0.329391	−	0.365826i
$515$	−11.7426	+	5.22815i	−0.517442	+	0.230380i
$516$	−2.06638	−	3.57907i	−0.0909671	−	0.157560i
$517$	−3.27892	+	10.1408i	−0.144207	+	0.445994i
$518$	−12.2537	+	26.2018i	−0.538394	+	1.15124i
$519$	−1.41176	+	1.94312i	−0.0619692	+	0.0852933i
$520$	1.79051	−	0.380584i	0.0785190	−	0.0166897i
$521$	7.90390	−	37.1849i	0.346276	−	1.62910i	−0.368415	−	0.929661i	$-0.620099\pi$
$521$	7.90390	−	37.1849i	0.346276	−	1.62910i	0.714691	−	0.699440i	$-0.246567\pi$
$522$	0.189112	+	1.79928i	0.00827721	+	0.0787524i
$523$	16.4444	+	7.32152i	0.719064	+	0.320148i	0.733445	−	0.679749i	$-0.237911\pi$
$523$	16.4444	+	7.32152i	0.719064	+	0.320148i	−0.0143813	+	0.999897i	$0.504578\pi$
$524$	3.77035	+	11.6039i	0.164708	+	0.506920i
$525$	1.15142	−	0.350623i	0.0502523	−	0.0153024i
$526$	−19.9283	−	14.4787i	−0.868913	−	0.631303i
$527$	−3.52823	+	2.03703i	−0.153692	+	0.0887343i
$528$	3.24513	+	0.684921i	0.141226	+	0.0298074i
$529$	−0.471265	+	0.816254i	−0.0204898	+	0.0354893i
$530$	0.349677	−	3.32695i	0.0151890	−	0.144514i
$531$	−0.763537	−	0.248088i	−0.0331347	−	0.0107661i
$532$	−5.28133	+	2.23485i	−0.228975	+	0.0968929i
$533$	−4.07176	+	2.95831i	−0.176367	+	0.128138i
$534$	2.85678	−	6.41642i	0.123625	−	0.277666i
$535$	38.5101	+	8.18557i	1.66494	+	0.353893i
$536$	10.9066	−	9.82038i	0.471095	−	0.424176i
$537$	−18.9147	−	1.98801i	−0.816228	−	0.0857891i
$538$	−23.9181			−1.03118
$539$	−22.3221	+	6.38149i	−0.961481	+	0.274870i
$540$	2.33558			0.100507
$541$	−16.8252	−	1.76840i	−0.723373	−	0.0760295i	−0.264316	−	0.964436i	$-0.585146\pi$
$541$	−16.8252	−	1.76840i	−0.723373	−	0.0760295i	−0.459057	+	0.888407i	$0.651813\pi$
$542$	−0.865759	+	0.779533i	−0.0371875	+	0.0334838i
$543$	14.2348	+	3.02569i	0.610872	+	0.129845i
$544$	−0.368872	+	0.828499i	−0.0158152	+	0.0355216i
$545$	11.0317	−	8.01498i	0.472545	−	0.343324i
$546$	−1.90967	+	0.808095i	−0.0817262	+	0.0345833i
$547$	−17.6152	−	5.72353i	−0.753172	−	0.244720i	−0.0928265	−	0.995682i	$-0.529590\pi$
$547$	−17.6152	−	5.72353i	−0.753172	−	0.244720i	−0.660346	+	0.750962i	$0.729590\pi$
$548$	−0.782785	+	7.44770i	−0.0334389	+	0.318150i
$549$	3.86651	−	6.69700i	0.165019	−	0.285821i
$550$	−0.159862	−	1.50033i	−0.00681656	−	0.0639743i
$551$	−3.39608	+	1.96073i	−0.144678	+	0.0835298i
$552$	−3.95861	−	2.87610i	−0.168490	−	0.122415i
$553$	35.7556	−	10.8880i	1.52048	−	0.463006i
$554$	−5.96509	−	18.3587i	−0.253432	−	0.779984i
$555$	23.3269	+	10.3858i	0.990170	+	0.440852i
$556$	−1.56046	−	14.8468i	−0.0661783	−	0.629644i
$557$	6.92153	−	32.5632i	0.293274	−	1.37975i	−0.546794	−	0.837267i	$-0.684152\pi$
$557$	6.92153	−	32.5632i	0.293274	−	1.37975i	0.840068	−	0.542481i	$-0.182515\pi$
$558$	4.39409	−	0.933993i	0.186017	−	0.0395391i
$559$	1.90386	−	2.62044i	0.0805248	−	0.110833i
$560$	2.61775	−	5.59749i	0.110620	−	0.236537i
$561$	−0.933575	−	2.85932i	−0.0394156	−	0.120720i
$562$	2.41779	+	4.18773i	0.101988	+	0.176649i
$563$	−0.348168	+	0.155015i	−0.0146735	+	0.00653308i	−0.414060	−	0.910249i	$-0.635890\pi$
$563$	−0.348168	+	0.155015i	−0.0146735	+	0.00653308i	0.399387	+	0.916783i	$0.369223\pi$
$564$	2.15021	+	2.38805i	0.0905402	+	0.100555i
$565$	3.69551	+	3.32745i	0.155471	+	0.139987i
$566$	−11.0599	−	15.2226i	−0.464882	−	0.639855i
$567$	−2.59770	+	0.501938i	−0.109093	+	0.0210794i
$568$	−11.2889	+	3.66799i	−0.473672	+	0.153905i
$569$	1.83815	+	8.64783i	0.0770594	+	0.362536i	0.999734	−	0.0230423i	$-0.00733525\pi$
$569$	1.83815	+	8.64783i	0.0770594	+	0.362536i	−0.922675	+	0.385578i	$0.874002\pi$
$570$	2.05907	+	4.62474i	0.0862449	+	0.193709i
$571$	4.31350	+	2.49040i	0.180514	+	0.104220i	0.587534	−	0.809199i	$-0.300099\pi$
$571$	4.31350	+	2.49040i	0.180514	+	0.104220i	−0.407020	+	0.913419i	$0.633432\pi$
$572$	0.544085	+	2.54182i	0.0227493	+	0.106279i
$573$		−	4.60655i		−	0.192441i
$574$	−0.315451	+	16.9872i	−0.0131667	+	0.709031i
$575$	−0.687875	+	2.11706i	−0.0286864	+	0.0882876i
$576$	0.669131	−	0.743145i	0.0278804	−	0.0309644i
$577$	−16.2956	+	1.71273i	−0.678394	+	0.0713020i	−0.437458	−	0.899239i	$-0.644121\pi$
$577$	−16.2956	+	1.71273i	−0.678394	+	0.0713020i	−0.240936	+	0.970541i	$0.577454\pi$
$578$	−16.0889	+	1.69101i	−0.669210	+	0.0703368i
$579$	−4.95844	+	5.50691i	−0.206066	+	0.228859i
$580$	1.30575	−	4.01870i	0.0542185	−	0.166867i
$581$	−22.7184	+	37.7145i	−0.942519	+	1.56466i
$582$		−	4.35201i		−	0.180397i
$583$	4.72513	+	0.489795i	0.195695	+	0.0202852i
$584$	10.6243	+	6.13393i	0.439636	+	0.253824i
$585$	0.744535	+	1.67225i	0.0307827	+	0.0691392i
$586$	5.79418	+	27.2595i	0.239355	+	1.12608i
$587$	6.32063	−	2.05370i	0.260880	−	0.0847651i	−0.175657	−	0.984451i	$-0.556205\pi$
$587$	6.32063	−	2.05370i	0.260880	−	0.0847651i	0.436537	+	0.899686i	$0.356205\pi$
$588$	−1.70859	+	6.78828i	−0.0704610	+	0.279944i
$589$	5.72330	+	7.87744i	0.235824	+	0.324584i
$590$	1.39345	+	1.25467i	0.0573675	+	0.0516539i
$591$	−8.10201	−	8.99819i	−0.333272	−	0.370136i
$592$	9.98762	−	4.44677i	0.410489	−	0.182761i
$593$	−12.0500	−	20.8712i	−0.494834	−	0.857078i	0.505148	−	0.863033i	$-0.331438\pi$
$593$	−12.0500	−	20.8712i	−0.494834	−	0.857078i	−0.999982	+	0.00595446i	$0.998105\pi$
$594$	0.00474682	+	3.31662i	0.000194765	+	0.136083i
$595$	−5.58331	+	0.482207i	−0.228893	+	0.0197685i
$596$	−9.82851	+	13.5278i	−0.402591	+	0.554119i
$597$	−1.17482	+	0.249716i	−0.0480823	+	0.0102202i
$598$	0.797336	−	3.75117i	0.0326055	−	0.153397i
$599$	−4.02641	−	38.3088i	−0.164515	−	1.56525i	−0.695909	−	0.718130i	$-0.744999\pi$
$599$	−4.02641	−	38.3088i	−0.164515	−	1.56525i	0.531395	−	0.847124i	$-0.321668\pi$
$600$	−0.415597	−	0.185036i	−0.0169667	−	0.00755405i
$601$	2.53208	+	7.79295i	0.103286	+	0.317881i	0.989324	−	0.145731i	$-0.0465533\pi$
$601$	2.53208	+	7.79295i	0.103286	+	0.317881i	−0.886039	+	0.463612i	$0.846553\pi$
$602$	−3.18521	−	10.4600i	−0.129819	−	0.426319i
$603$	11.8734	+	8.62653i	0.483522	+	0.351300i
$604$	−11.1364	+	6.42963i	−0.453135	+	0.261618i
$605$	25.5428	−	2.75860i	1.03846	−	0.112153i
$606$	−1.97176	+	3.41520i	−0.0800975	+	0.138733i
$607$	2.11698	−	20.1417i	0.0859254	−	0.817525i	−0.863672	−	0.504054i	$-0.831841\pi$
$607$	2.11698	−	20.1417i	0.0859254	−	0.817525i	0.949598	−	0.313472i	$-0.101492\pi$
$608$	2.06143	+	0.669800i	0.0836021	+	0.0271640i
$609$	−0.588643	+	4.75034i	−0.0238530	+	0.192493i
$610$	−14.6117	+	10.6160i	−0.591612	+	0.429831i
$611$	−1.02438	+	2.30079i	−0.0414419	+	0.0930801i
$612$	−0.887087	−	0.188556i	−0.0358584	−	0.00762193i
$613$	15.2137	−	13.6985i	0.614477	−	0.553278i	−0.302029	−	0.953299i	$-0.597664\pi$
$613$	15.2137	−	13.6985i	0.614477	−	0.553278i	0.916506	+	0.400021i	$0.130997\pi$
$614$	18.2092	+	1.91387i	0.734864	+	0.0772374i
$615$	14.9983			0.604789
$616$	7.95399	+	3.70594i	0.320475	+	0.149317i
$617$	−3.82912			−0.154154			−0.0770772	−	0.997025i	$-0.524559\pi$
$617$	−3.82912			−0.154154			−0.0770772	+	0.997025i	$0.524559\pi$
$618$	−5.47337	−	0.575275i	−0.220171	−	0.0231409i
$619$	−23.3937	+	21.0637i	−0.940270	+	0.846623i	−0.988347	−	0.152220i	$-0.951358\pi$
$619$	−23.3937	+	21.0637i	−0.940270	+	0.846623i	0.0480761	+	0.998844i	$0.484691\pi$
$620$	−10.2627	−	2.18141i	−0.412162	−	0.0876077i
$621$	1.99021	−	4.47008i	0.0798643	−	0.179378i
$622$	0.265410	−	0.192832i	0.0106420	−	0.00773184i
$623$	11.2000	−	14.8284i	0.448717	−	0.594089i
$624$	0.745390	+	0.242192i	0.0298395	+	0.00969544i
$625$	2.82934	−	26.9194i	0.113174	−	1.07678i
$626$	15.5471	−	26.9283i	0.621385	−	1.07627i
$627$	−6.56315	+	2.93336i	−0.262107	+	0.117147i
$628$	7.44064	−	4.29586i	0.296914	−	0.171423i
$629$	−8.02142	−	5.82790i	−0.319835	−	0.232374i
$630$	6.01943	+	1.39676i	0.239820	+	0.0556484i
$631$	6.43517	+	19.8054i	0.256180	+	0.788441i	0.993595	+	0.113001i	$0.0360463\pi$
$631$	6.43517	+	19.8054i	0.256180	+	0.788441i	−0.737415	+	0.675440i	$0.763954\pi$
$632$	−12.9057	−	5.74599i	−0.513361	−	0.228563i
$633$	1.69143	+	16.0929i	0.0672282	+	0.639634i
$634$	−0.722747	+	3.40026i	−0.0287039	+	0.135041i
$635$	12.7470	−	2.70946i	0.505850	−	0.107522i
$636$	0.841892	−	1.15877i	0.0333832	−	0.0459480i
$637$	−5.40501	+	0.940631i	−0.214154	+	0.0372692i
$638$	5.70938	+	1.84606i	0.226036	+	0.0730862i
$639$	−5.93493	−	10.2796i	−0.234782	−	0.406654i
$640$	−2.13366	+	0.949965i	−0.0843402	+	0.0375507i
$641$	−2.59326	−	2.88010i	−0.102428	−	0.113757i	0.689751	−	0.724046i	$-0.257720\pi$
$641$	−2.59326	−	2.88010i	−0.102428	−	0.113757i	−0.792179	+	0.610289i	$0.791053\pi$
$642$	12.5271	+	11.2794i	0.494403	+	0.445163i
$643$	−21.4313	−	29.4976i	−0.845167	−	1.16327i	−0.984907	−	0.173084i	$-0.944627\pi$
$643$	−21.4313	−	29.4976i	−0.845167	−	1.16327i	0.139740	−	0.990188i	$-0.455373\pi$
$644$	−8.48241	−	9.77989i	−0.334254	−	0.385382i
$645$	−9.17995	+	2.98275i	−0.361460	+	0.117446i
$646$	−0.408699	−	1.92278i	−0.0160801	−	0.0756507i
$647$	−10.1602	−	22.8201i	−0.399438	−	0.897152i	−0.995549	−	0.0942501i	$-0.969955\pi$
$647$	−10.1602	−	22.8201i	−0.399438	−	0.897152i	0.596111	−	0.802902i	$-0.296712\pi$
$648$	0.866025	+	0.500000i	0.0340207	+	0.0196419i
$649$	−1.77885	+	1.98131i	−0.0698260	+	0.0777732i
$650$		−	0.356549i		−	0.0139850i
$651$	11.8834	+	0.220673i	0.465745	+	0.00864887i
$652$	4.32593	−	13.3138i	0.169416	−	0.521410i
$653$	−17.0732	+	18.9617i	−0.668127	+	0.742030i	−0.977967	−	0.208759i	$-0.933058\pi$
$653$	−17.0732	+	18.9617i	−0.668127	+	0.742030i	0.309841	+	0.950789i	$0.399724\pi$
$654$	5.80636	−	0.610273i	0.227046	−	0.0238635i
$655$	28.3405	−	2.97871i	1.10736	−	0.116388i
$656$	4.29693	−	4.77222i	0.167767	−	0.186324i
$657$	−3.79098	+	11.6674i	−0.147900	+	0.455190i
$658$	4.11354	+	7.44057i	0.160362	+	0.290064i
$659$		−	36.1637i		−	1.40874i	−0.709834	−	0.704369i	$-0.751230\pi$
$659$		−	36.1637i		−	1.40874i	0.709834	−	0.704369i	$-0.248770\pi$
$660$	3.14055	−	7.08104i	0.122246	−	0.275629i
$661$	35.2258	+	20.3376i	1.37012	+	0.791042i	0.990943	−	0.134280i	$-0.0428723\pi$
$661$	35.2258	+	20.3376i	1.37012	+	0.791042i	0.379181	+	0.925322i	$0.376206\pi$
$662$	4.66431	+	10.4762i	0.181283	+	0.407169i
$663$	−0.147781	−	0.695255i	−0.00573934	−	0.0270015i
$664$	15.8267	−	5.14242i	0.614197	−	0.199565i
$665$	2.54102	+	13.1506i	0.0985364	+	0.509960i
$666$	6.42614	+	8.84483i	0.249008	+	0.342730i
$667$	−6.57875	−	5.92353i	−0.254730	−	0.229360i
$668$	6.20992	+	6.89682i	0.240269	+	0.266846i
$669$	12.0545	−	5.36701i	0.466054	−	0.207500i
$670$	−17.1389	−	29.6854i	−0.662132	−	1.14685i
$671$	−15.1049	−	20.7277i	−0.583120	−	0.800184i
$672$	2.16896	−	1.51512i	0.0836695	−	0.0584472i
$673$	−24.4422	+	33.6418i	−0.942178	+	1.29680i	0.0127373	+	0.999919i	$0.495945\pi$
$673$	−24.4422	+	33.6418i	−0.942178	+	1.29680i	−0.954915	+	0.296878i	$0.904055\pi$
$674$	−20.5592	+	4.36999i	−0.791910	+	0.168326i
$675$	0.0945847	−	0.444986i	0.00364057	−	0.0171275i
$676$	−1.29466	−	12.3179i	−0.0497947	−	0.473765i
$677$	19.4997	+	8.68182i	0.749434	+	0.333669i	0.745663	−	0.666323i	$-0.232133\pi$
$677$	19.4997	+	8.68182i	0.749434	+	0.333669i	0.00377107	+	0.999993i	$0.498800\pi$
$678$	0.657944	+	2.02494i	0.0252682	+	0.0777675i
$679$	2.60267	−	11.2163i	0.0998812	−	0.430444i
$680$	1.71362	+	1.24502i	0.0657143	+	0.0477442i
$681$	21.3182	−	12.3081i	0.816915	−	0.471646i
$682$	3.07684	−	14.5780i	0.117818	−	0.558220i
$683$	23.9123	−	41.4173i	0.914979	−	1.58479i	0.108047	−	0.994146i	$-0.465540\pi$
$683$	23.9123	−	41.4173i	0.914979	−	1.58479i	0.806932	−	0.590645i	$-0.201126\pi$
$684$	−0.226567	+	2.15564i	−0.00866302	+	0.0824231i
$685$	16.6345	+	5.40486i	0.635570	+	0.206509i
$686$	−8.46315	+	16.4735i	−0.323125	+	0.628960i
$687$	−3.90548	+	2.83750i	−0.149003	+	0.108257i
$688$	−1.68094	+	3.77546i	−0.0640853	+	0.143938i
$689$	1.09804	+	0.233396i	0.0418322	+	0.00889170i
$690$	−8.49284	+	7.64699i	−0.323317	+	0.291116i
$691$	48.6342	+	5.11166i	1.85013	+	0.194457i	0.963444	−	0.267909i	$-0.0863327\pi$
$691$	48.6342	+	5.11166i	1.85013	+	0.194457i	0.886689	+	0.462366i	$0.152999\pi$
$692$	2.40182			0.0913036
$693$	−1.97123	+	8.55069i	−0.0748808	+	0.324814i
$694$	3.43834			0.130518
$695$	−34.6758	−	3.64458i	−1.31533	−	0.138247i
$696$	1.34449	−	1.21059i	0.0509628	−	0.0458871i
$697$	−5.69657	−	1.21084i	−0.215773	−	0.0458640i
$698$	0.0843530	−	0.189460i	0.00319281	−	0.00717116i
$699$	2.42074	−	1.75877i	0.0915608	−	0.0665228i
$700$	−0.960450	−	0.725430i	−0.0363016	−	0.0274187i
$701$	−30.5582	−	9.92896i	−1.15417	−	0.375012i	−0.331456	−	0.943471i	$-0.607540\pi$
$701$	−30.5582	−	9.92896i	−1.15417	−	0.375012i	−0.822712	+	0.568459i	$0.807540\pi$
$702$	−0.0819242	+	0.779456i	−0.00309203	+	0.0294187i
$703$	−11.8485	+	20.5223i	−0.446876	+	0.774012i
$704$	−1.35333	−	3.02795i	−0.0510055	−	0.114120i
$705$	6.49973	−	3.75262i	0.244794	−	0.141332i
$706$	−24.6631	−	17.9188i	−0.928210	−	0.674384i
$707$	−7.12420	+	7.62271i	−0.267933	+	0.286682i
$708$	0.248088	+	0.763537i	0.00932372	+	0.0286955i
$709$	−28.4535	−	12.6683i	−1.06859	−	0.475769i	−0.204380	−	0.978892i	$-0.565518\pi$
$709$	−28.4535	−	12.6683i	−1.06859	−	0.475769i	−0.864215	+	0.503123i	$0.832184\pi$
$710$	2.89784	+	27.5711i	0.108754	+	1.03472i
$711$	2.93718	−	13.8183i	0.110153	−	0.518228i
$712$	−6.87016	+	1.46030i	−0.257470	+	0.0547270i
$713$	−12.9202	+	17.7831i	−0.483864	+	0.665982i
$714$	−2.17351	−	1.01647i	−0.0813414	−	0.0380405i
$715$	6.07111	−	0.00868911i	0.227047	−	0.000324954i
$716$	9.50943	+	16.4708i	0.355384	+	0.615543i
$717$	−17.4435	+	7.76635i	−0.651440	+	0.290040i
$718$	3.01676	+	3.35045i	0.112585	+	0.125038i
$719$	24.5739	+	22.1265i	0.916453	+	0.825178i	0.985015	−	0.172469i	$-0.0551745\pi$
$719$	24.5739	+	22.1265i	0.916453	+	0.825178i	−0.0685622	+	0.997647i	$0.521841\pi$
$720$	−1.37282	−	1.88952i	−0.0511619	−	0.0704184i
$721$	−13.7624	−	4.75592i	−0.512537	−	0.177120i
$722$	13.6019	−	4.41952i	0.506210	−	0.164477i
$723$	−4.05189	−	19.0627i	−0.150691	−	0.708948i
$724$	−5.91915	−	13.2946i	−0.219983	−	0.494091i
$725$	−0.712783	−	0.411525i	−0.0264721	−	0.0152837i
$726$	10.0618	+	4.44532i	0.373427	+	0.164981i
$727$		−	19.6357i		−	0.728248i	−0.931351	−	0.364124i	$-0.881368\pi$
$727$		−	19.6357i		−	0.728248i	0.931351	−	0.364124i	$-0.118632\pi$
$728$	1.77624	+	1.06997i	0.0658317	+	0.0396556i
$729$	−0.309017	+	0.951057i	−0.0114451	+	0.0352243i
$730$	19.1723	−	21.2930i	0.709599	−	0.788089i
$731$	3.72748	−	0.391774i	0.137866	−	0.0144903i
$732$	−7.69067	+	0.808322i	−0.284255	+	0.0298764i
$733$	−12.2504	+	13.6055i	−0.452479	+	0.502529i	−0.925618	−	0.378459i	$-0.876454\pi$
$733$	−12.2504	+	13.6055i	−0.452479	+	0.502529i	0.473139	+	0.880988i	$0.343121\pi$
$734$	5.04306	−	15.5209i	0.186143	−	0.572888i
$735$	14.6784	+	7.19969i	0.541422	+	0.265565i
$736$			4.89311i			0.180362i
$737$	42.1197	−	24.3983i	1.55150	−	0.898721i
$738$	5.56132	+	3.21083i	0.204715	+	0.118192i
$739$	−5.98007	−	13.4315i	−0.219980	−	0.494084i	0.769519	−	0.638624i	$-0.220496\pi$
$739$	−5.98007	−	13.4315i	−0.219980	−	0.494084i	−0.989499	+	0.144541i	$0.953830\pi$
$740$	−5.30891	−	24.9764i	−0.195159	−	0.918152i
$741$	−1.61565	+	0.524956i	−0.0593523	+	0.0192847i
$742$	2.86277	−	2.48298i	0.105096	−	0.0911529i
$743$	−0.739626	−	1.01801i	−0.0271342	−	0.0373471i	0.795234	−	0.606302i	$-0.207348\pi$
$743$	−0.739626	−	1.01801i	−0.0271342	−	0.0373471i	−0.822369	+	0.568955i	$0.807348\pi$
$744$	−3.33840	−	3.00591i	−0.122392	−	0.110202i
$745$	26.1321	+	29.0226i	0.957406	+	1.06331i
$746$	11.1619	−	4.96959i	0.408666	−	0.181950i
$747$	8.32061	+	14.4117i	0.304435	+	0.527297i
$748$	−1.76449	+	2.43594i	−0.0645163	+	0.0890669i
$749$	25.5402	+	36.5618i	0.933218	+	1.33594i
$750$	6.23956	−	8.58802i	0.227837	−	0.313590i
$751$	−20.7663	+	4.41401i	−0.757772	+	0.161069i	−0.570567	−	0.821251i	$-0.693276\pi$
$751$	−20.7663	+	4.41401i	−0.757772	+	0.161069i	−0.187206	+	0.982321i	$0.559943\pi$
$752$	0.668111	−	3.14322i	0.0243635	−	0.114621i
$753$	−0.291244	−	2.77101i	−0.0106135	−	0.100981i
$754$	1.29537	+	0.576734i	0.0471744	+	0.0210034i
$755$	9.28096	+	28.5638i	0.337769	+	1.03954i
$756$	1.93297	+	1.80655i	0.0703014	+	0.0657037i
$757$	−13.9045	−	10.1022i	−0.505367	−	0.367171i	0.305696	−	0.952129i	$-0.401111\pi$
$757$	−13.9045	−	10.1022i	−0.505367	−	0.367171i	−0.811063	+	0.584958i	$0.801111\pi$
$758$	−25.5207	+	14.7344i	−0.926952	+	0.535176i
$759$	−10.8763	−	12.0447i	−0.394785	−	0.437193i
$760$	2.53121	−	4.38418i	0.0918165	−	0.159031i
$761$	−1.77685	+	16.9056i	−0.0644108	+	0.612828i	0.913936	+	0.405857i	$0.133027\pi$
$761$	−1.77685	+	16.9056i	−0.0644108	+	0.612828i	−0.978347	+	0.206970i	$0.933640\pi$
$762$	5.30660	+	1.72422i	0.192238	+	0.0624618i
$763$	15.3295	+	1.89958i	0.554967	+	0.0687693i
$764$	−3.72678	+	2.70766i	−0.134830	+	0.0979597i
$765$	−0.861529	+	1.93503i	−0.0311486	+	0.0699610i
$766$	18.1599	+	3.86000i	0.656142	+	0.139467i
$767$	−0.467600	+	0.421029i	−0.0168841	+	0.0152025i
$768$	−0.994522	−	0.104528i	−0.0358867	−	0.00377185i
$769$	20.3214			0.732809			0.366405	−	0.930456i	$-0.380589\pi$
$769$	20.3214			0.732809			0.366405	+	0.930456i	$0.380589\pi$
$770$	12.3288	−	16.3716i	0.444299	−	0.589993i
$771$	−11.1605			−0.401935
$772$	7.36968	+	0.774585i	0.265241	+	0.0278779i
$773$	−26.3429	+	23.7193i	−0.947489	+	0.853123i	−0.989284	−	0.146003i	$-0.953359\pi$
$773$	−26.3429	+	23.7193i	−0.947489	+	0.853123i	0.0417951	+	0.999126i	$0.486692\pi$
$774$	−4.04244	−	0.859248i	−0.145303	−	0.0308850i
$775$	−0.831228	+	1.86697i	−0.0298586	+	0.0670635i
$776$	−3.52085	+	2.55805i	−0.126391	+	0.0918286i
$777$	11.2724	+	26.6386i	0.404395	+	0.955656i
$778$	−5.96779	−	1.93905i	−0.213956	−	0.0695185i
$779$	−1.45494	+	13.8428i	−0.0521286	+	0.495970i
$780$	0.915255	−	1.58527i	0.0327714	−	0.0567617i
$781$	−39.1462	+	4.17109i	−1.40076	+	0.149253i
$782$	3.84306	−	2.21879i	0.137428	−	0.0793439i
$783$	1.46367	+	1.06342i	0.0523072	+	0.0380034i
$784$	6.49612	−	2.60777i	0.232004	−	0.0931347i
$785$	−6.20093	−	19.0845i	−0.221321	−	0.681155i
$786$	11.1463	+	4.96264i	0.397574	+	0.177011i
$787$	−3.75579	−	35.7340i	−0.133880	−	1.27378i	−0.830776	−	0.556607i	$-0.812103\pi$
$787$	−3.75579	−	35.7340i	−0.133880	−	1.27378i	0.696897	−	0.717172i	$-0.254564\pi$
$788$	−2.51745	+	11.8437i	−0.0896804	+	0.421913i
$789$	−24.0944	+	5.12142i	−0.857783	+	0.182327i
$790$	−19.3939	+	26.6934i	−0.690003	+	0.949708i
$791$	0.484711	+	5.61231i	0.0172343	+	0.199551i
$792$	2.68041	−	1.95330i	0.0952443	−	0.0694075i
$793$	−3.03038	−	5.24877i	−0.107612	−	0.186389i
$794$	3.52379	−	1.56889i	0.125055	−	0.0556779i
$795$	−2.23843	−	2.48603i	−0.0793889	−	0.0881703i
$796$	0.892569	+	0.803672i	0.0316363	+	0.0284854i
$797$	0.572024	+	0.787323i	0.0202621	+	0.0278884i	0.819028	−	0.573754i	$-0.194513\pi$
$797$	0.572024	+	0.787323i	0.0202621	+	0.0278884i	−0.798766	+	0.601642i	$0.794513\pi$
$798$	−1.87308	+	5.42020i	−0.0663064	+	0.191873i
$799$	−2.77165	+	0.900563i	−0.0980539	+	0.0318596i
$800$	0.0945847	+	0.444986i	0.00334408	+	0.0157326i
$801$	−2.85678	−	6.41642i	−0.100939	−	0.226713i
$802$	−17.4318	−	10.0642i	−0.615537	−	0.355380i
$803$	30.2759	+	27.1822i	1.06841	+	0.959239i
$804$		−	14.6763i		−	0.517594i
$805$	−26.4616	+	14.6294i	−0.932648	+	0.515617i
$806$	1.08799	−	3.34849i	0.0383228	−	0.117945i
$807$	−16.0043	+	17.7746i	−0.563379	+	0.625696i
$808$	3.92193	−	0.412211i	0.137973	−	0.0145015i
$809$	−32.1842	+	3.38269i	−1.13154	+	0.118929i	−0.651734	−	0.758448i	$-0.725958\pi$
$809$	−32.1842	+	3.38269i	−1.13154	+	0.118929i	−0.479802	+	0.877377i	$0.659291\pi$
$810$	1.56281	−	1.73567i	0.0549114	−	0.0609853i
$811$	2.79033	−	8.58774i	0.0979816	−	0.301556i	−0.890038	−	0.455887i	$-0.849322\pi$
$811$	2.79033	−	8.58774i	0.0979816	−	0.301556i	0.988019	+	0.154331i	$0.0493221\pi$
$812$	4.18910	−	2.31596i	0.147009	−	0.0812742i
$813$			1.16499i			0.0408581i
$814$	35.4568	−	7.58964i	1.24276	−	0.266017i
$815$	−28.3153	−	16.3479i	−0.991843	−	0.572641i
$816$	0.368872	+	0.828499i	0.0129131	+	0.0290033i
$817$	−1.86244	−	8.76207i	−0.0651584	−	0.306546i
$818$	−26.9937	+	8.77079i	−0.943813	+	0.306663i
$819$	−0.677285	+	1.95988i	−0.0236663	+	0.0684838i
$820$	−8.81577	−	12.1339i	−0.307860	−	0.423733i
$821$	−27.5751	−	24.8287i	−0.962377	−	0.866528i	0.0287310	−	0.999587i	$-0.490853\pi$
$821$	−27.5751	−	24.8287i	−0.962377	−	0.866528i	−0.991108	+	0.133059i	$0.957520\pi$
$822$	5.01093	+	5.56520i	0.174776	+	0.194109i
$823$	−26.8519	+	11.9552i	−0.935997	+	0.416733i	−0.817309	−	0.576199i	$-0.804535\pi$
$823$	−26.8519	+	11.9552i	−0.935997	+	0.416733i	−0.118687	+	0.992932i	$0.537869\pi$
$824$	2.75176	+	4.76619i	0.0958621	+	0.166038i
$825$	−1.22193	−	0.885116i	−0.0425422	−	0.0308158i
$826$	0.182768	+	2.11621i	0.00635931	+	0.0736324i
$827$	20.7072	−	28.5010i	0.720059	−	0.991076i	−0.279463	−	0.960157i	$-0.590156\pi$
$827$	20.7072	−	28.5010i	0.720059	−	0.991076i	0.999522	−	0.0309198i	$-0.00984365\pi$
$828$	−4.78618	+	1.01733i	−0.166331	+	0.0353548i
$829$	−7.11823	+	33.4886i	−0.247226	+	1.16311i	0.662878	+	0.748728i	$0.269335\pi$
$829$	−7.11823	+	33.4886i	−0.247226	+	1.16311i	−0.910104	+	0.414380i	$0.863998\pi$
$830$	−4.06270	−	38.6540i	−0.141018	−	1.34170i
$831$	−17.6346	−	7.85141i	−0.611736	−	0.272363i
$832$	−0.242192	−	0.745390i	−0.00839650	−	0.0258418i
$833$	−4.99383	−	3.91957i	−0.173026	−	0.135805i
$834$	−12.0775	−	8.77479i	−0.418208	−	0.303846i
$835$	18.7716	−	10.8378i	0.649617	−	0.375056i
$836$	6.23086	+	3.58551i	0.215499	+	0.124007i
$837$	2.24613	−	3.89041i	0.0776376	−	0.134472i
$838$	3.33363	−	31.7173i	0.115158	−	1.09566i
$839$	28.6908	+	9.32220i	0.990515	+	0.321838i	0.759069	−	0.651010i	$-0.225654\pi$
$839$	28.6908	+	9.32220i	0.990515	+	0.321838i	0.231446	+	0.972848i	$0.425654\pi$
$840$	−2.40813	−	5.69082i	−0.0830883	−	0.196352i
$841$	−20.8134	+	15.1218i	−0.717705	+	0.521443i
$842$	11.3254	−	25.4372i	0.390298	−	0.876624i
$843$	4.72991	+	1.00537i	0.162907	+	0.0346269i
$844$	12.0252	−	10.8275i	0.413925	−	0.372699i
$845$	−28.7694	−	3.02378i	−0.989697	−	0.104021i
$846$	3.21344			0.110480
$847$	23.2735	+	17.4741i	0.799686	+	0.600418i
$848$	−1.43231			−0.0491858
$849$	−18.7131	−	1.96683i	−0.642233	−	0.0675014i
$850$	0.306604	−	0.276067i	0.0105164	−	0.00946903i
$851$	−52.3264	−	11.1223i	−1.79373	−	0.381268i
$852$	−4.82790	+	10.8436i	−0.165401	+	0.371497i
$853$	−5.01388	+	3.64279i	−0.171672	+	0.124727i	−0.670303	−	0.742087i	$-0.733836\pi$
$853$	−5.01388	+	3.64279i	−0.171672	+	0.124727i	0.498632	+	0.866814i	$0.333836\pi$
$854$	−20.3044	−	2.51604i	−0.694802	−	0.0860971i
$855$	4.81464	+	1.56437i	0.164657	+	0.0535004i
$856$	1.76202	−	16.7645i	0.0602245	−	0.572998i
$857$	14.2125	−	24.6168i	0.485491	−	0.840895i	−0.514370	−	0.857568i	$-0.671974\pi$
$857$	14.2125	−	24.6168i	0.485491	−	0.840895i	0.999861	+	0.0166733i	$0.00530751\pi$
$858$	2.25301	+	1.29648i	0.0769164	+	0.0442611i
$859$	14.7524	−	8.51729i	0.503344	−	0.290606i	−0.226749	−	0.973953i	$-0.572810\pi$
$859$	14.7524	−	8.51729i	0.503344	−	0.290606i	0.730094	+	0.683347i	$0.239476\pi$
$860$	7.80893	+	5.67352i	0.266282	+	0.193465i
$861$	12.4129	+	11.6011i	0.423029	+	0.395363i
$862$	−4.08026	−	12.5577i	−0.138974	−	0.427719i
$863$	28.7222	+	12.7879i	0.977715	+	0.435307i	0.832459	−	0.554087i	$-0.186933\pi$
$863$	28.7222	+	12.7879i	0.977715	+	0.435307i	0.145256	+	0.989394i	$0.453599\pi$
$864$	−0.104528	−	0.994522i	−0.00355613	−	0.0338343i
$865$	1.16631	−	5.48706i	0.0396558	−	0.186566i
$866$	−34.1313	+	7.25484i	−1.15983	+	0.246529i
$867$	−9.50891	+	13.0879i	−0.322939	+	0.444488i
$868$	−6.80633	−	9.74354i	−0.231022	−	0.330717i
$869$	−37.9452	−	27.4859i	−1.28720	−	0.932395i
$870$	−2.11275	−	3.65940i	−0.0716291	−	0.124065i
$871$	10.5081	−	4.67852i	0.356054	−	0.158526i
$872$	−3.90661	−	4.33873i	−0.132295	−	0.146928i
$873$	−3.23418	−	2.91207i	−0.109460	−	0.0985585i
$874$	−6.23400	−	8.58036i	−0.210868	−	0.290235i
$875$	21.2170	−	18.4022i	0.717266	−	0.622108i
$876$	11.6674	−	3.79098i	0.394206	−	0.128085i
$877$	10.6047	+	49.8913i	0.358096	+	1.68471i	0.676250	+	0.736672i	$0.263604\pi$
$877$	10.6047	+	49.8913i	0.358096	+	1.68471i	−0.318154	+	0.948039i	$0.603063\pi$
$878$	9.32231	+	20.9382i	0.314613	+	0.706631i
$879$	24.1348	+	13.9342i	0.814047	+	0.469990i
$880$	−7.57465	+	1.62138i	−0.255341	+	0.0546566i
$881$			6.87275i			0.231549i	0.993276	+	0.115774i	$0.0369350\pi$
$881$			6.87275i			0.231549i	−0.993276	+	0.115774i	$0.963065\pi$
$882$	3.90140	+	5.81197i	0.131367	+	0.195699i
$883$	−13.1555	+	40.4886i	−0.442719	+	1.36255i	0.442247	+	0.896893i	$0.354182\pi$
$883$	−13.1555	+	40.4886i	−0.442719	+	1.36255i	−0.884966	+	0.465656i	$0.845818\pi$
$884$	−0.475609	+	0.528218i	−0.0159965	+	0.0177659i
$885$	1.86480	−	0.195998i	0.0626846	−	0.00658842i
$886$	27.9452	−	2.93716i	0.938838	−	0.0986758i
$887$	31.1304	−	34.5738i	1.04526	−	1.16087i	0.0585620	−	0.998284i	$-0.481348\pi$
$887$	31.1304	−	34.5738i	1.04526	−	1.16087i	0.986694	−	0.162590i	$-0.0519849\pi$
$888$	3.37842	−	10.3977i	0.113372	−	0.348925i
$889$	12.6454	+	7.61733i	0.424114	+	0.255477i
$890$			16.4043i			0.549873i
$891$	2.46791	+	2.21573i	0.0826780	+	0.0742296i
$892$	−11.4275	−	6.59764i	−0.382619	−	0.220905i
$893$	2.83300	+	6.36301i	0.0948026	+	0.212930i
$894$	3.47654	+	16.3559i	0.116273	+	0.547022i
$895$	42.2460	−	13.7265i	1.41213	−	0.458828i
$896$	−2.50065	−	0.864160i	−0.0835407	−	0.0288696i
$897$	−2.25414	−	3.10256i	−0.0752636	−	0.103591i
$898$	2.74157	+	2.46852i	0.0914873	+	0.0823756i
$899$	−5.43826	−	6.03980i	−0.181376	−	0.201439i
$900$	−0.415597	+	0.185036i	−0.0138532	+	0.00616786i
$901$	0.649486	+	1.12494i	0.0216375	+	0.0374773i
$902$	17.2127	−	12.5434i	0.573120	−	0.417650i
$903$	−9.90463	−	4.63205i	−0.329605	−	0.154145i
$904$	1.25148	−	1.72252i	0.0416237	−	0.0572901i
$905$	−33.2464	+	7.06674i	−1.10515	+	0.234906i
$906$	−2.67359	+	12.5783i	−0.0888241	+	0.417884i
$907$	0.297156	+	2.82725i	0.00986691	+	0.0938774i	0.998347	−	0.0574733i	$-0.0183044\pi$
$907$	0.297156	+	2.82725i	0.00986691	+	0.0938774i	−0.988480	+	0.151351i	$0.951638\pi$
$908$	−22.4880	−	10.0123i	−0.746289	−	0.332269i
$909$	1.21862	+	3.75052i	0.0404190	+	0.124397i
$910$	3.30691	−	3.53832i	0.109623	−	0.117294i
$911$	5.97969	+	4.34450i	0.198116	+	0.143940i	0.682421	−	0.730960i	$-0.260927\pi$
$911$	5.97969	+	4.34450i	0.198116	+	0.143940i	−0.484304	+	0.874900i	$0.660927\pi$
$912$	1.87713	−	1.08376i	0.0621579	−	0.0358869i
$913$	54.8820	−	5.84776i	1.81633	−	0.193533i
$914$	−2.13984	+	3.70631i	−0.0707796	+	0.122594i
$915$	−1.88790	+	17.9622i	−0.0624120	+	0.593811i
$916$	4.59117	+	1.49176i	0.151696	+	0.0492892i
$917$	25.7592	+	19.4560i	0.850642	+	0.642492i
$918$	−0.733702	+	0.533066i	−0.0242158	+	0.0175938i
$919$	13.4762	−	30.2681i	0.444539	−	0.998452i	−0.542805	−	0.839859i	$-0.682638\pi$
$919$	13.4762	−	30.2681i	0.444539	−	0.998452i	0.987344	−	0.158593i	$-0.0506957\pi$
$920$	11.1785	+	2.37607i	0.368545	+	0.0783366i
$921$	13.6066	−	12.2515i	0.448354	−	0.403699i
$922$	39.4188	+	4.14308i	1.29819	+	0.136445i
$923$	−9.30299			−0.306212
$924$	8.07631	−	3.43121i	0.265691	−	0.112879i
$925$	−4.97363			−0.163532
$926$	−5.85685	−	0.615579i	−0.192468	−	0.0202292i
$927$	−4.08991	+	3.68257i	−0.134330	+	0.120952i
$928$	−1.76966	−	0.376152i	−0.0580918	−	0.0123478i
$929$	−6.22057	+	13.9716i	−0.204090	+	0.458395i	−0.986372	−	0.164530i	$-0.947389\pi$
$929$	−6.22057	+	13.9716i	−0.204090	+	0.458395i	0.782282	+	0.622925i	$0.214056\pi$
$930$	−8.48823	+	6.16706i	−0.278340	+	0.202226i
$931$	−8.06893	+	12.8492i	−0.264449	+	0.421114i
$932$	−2.84575	−	0.924640i	−0.0932156	−	0.0302876i
$933$	0.0342921	−	0.326267i	0.00112267	−	0.0106815i
$934$	20.5210	−	35.5434i	0.671468	−	1.16302i
$935$	4.70818	+	5.21394i	0.153974	+	0.170514i
$936$	0.678747	−	0.391875i	0.0221855	−	0.0128088i
$937$	32.1145	+	23.3326i	1.04914	+	0.762242i	0.972048	−	0.234782i	$-0.0754377\pi$
$937$	32.1145	+	23.3326i	1.04914	+	0.762242i	0.0770881	+	0.997024i	$0.475438\pi$
$938$	8.77700	−	37.8250i	0.286579	−	1.23503i
$939$	−9.60861	−	29.5723i	−0.313565	−	0.965054i
$940$	−6.85637	−	3.05265i	−0.223630	−	0.0995666i
$941$	1.90888	+	18.1618i	0.0622277	+	0.592057i	0.980556	+	0.196238i	$0.0628725\pi$
$941$	1.90888	+	18.1618i	0.0622277	+	0.592057i	−0.918329	+	0.395819i	$0.870461\pi$
$942$	1.78632	−	8.40396i	0.0582014	−	0.273816i
$943$	−30.7352	+	6.53297i	−1.00088	+	0.212743i
$944$	0.471892	−	0.649503i	0.0153588	−	0.0211395i
$945$	5.06578	−	3.53869i	0.164790	−	0.115114i
$946$	−8.04077	+	11.1005i	−0.261428	+	0.360910i
$947$	−25.8393	−	44.7550i	−0.839664	−	1.45434i	−0.890176	−	0.455618i	$-0.849418\pi$
$947$	−25.8393	−	44.7550i	−0.839664	−	1.45434i	0.0505114	−	0.998723i	$-0.483915\pi$
$948$	−12.9057	+	5.74599i	−0.419158	+	0.186621i
$949$	6.43365	+	7.14529i	0.208845	+	0.231946i
$950$	−0.732788	−	0.659805i	−0.0237748	−	0.0214069i
$951$	2.04327	+	2.81232i	0.0662576	+	0.0911957i
$952$	0.455211	+	2.35587i	0.0147535	+	0.0763542i
$953$	18.8080	−	6.11108i	0.609250	−	0.197957i	0.0118883	−	0.999929i	$-0.496216\pi$
$953$	18.8080	−	6.11108i	0.609250	−	0.197957i	0.597362	+	0.801972i	$0.296216\pi$
$954$	−0.297795	−	1.40101i	−0.00964146	−	0.0453595i
$955$	4.37606	+	9.82880i	0.141606	+	0.318052i
$956$	16.5361	+	9.54715i	0.534817	+	0.308777i
$957$	5.19221	−	3.00764i	0.167840	−	0.0972232i
$958$			16.6886i			0.539184i
$959$	9.58636	+	17.3398i	0.309560	+	0.559931i
$960$	−0.721733	+	2.22127i	−0.0232938	+	0.0716911i
$961$	7.23973	−	8.04054i	0.233540	−	0.259372i
$962$	8.52165	−	0.895661i	0.274749	−	0.0288773i
$963$	16.7645	−	1.76202i	0.540228	−	0.0567802i
$964$	−13.0404	+	14.4828i	−0.420002	+	0.466459i
$965$	5.34824	−	16.4602i	0.172166	−	0.529873i
$966$	−12.9437	−	0.240364i	−0.416457	−	0.00773360i
$967$			25.5405i			0.821327i	0.911787	+	0.410663i	$0.134703\pi$
$967$			25.5405i			0.821327i	−0.911787	+	0.410663i	$0.865297\pi$
$968$	−2.31782	−	10.7530i	−0.0744975	−	0.345616i
$969$	−1.70238	−	0.982867i	−0.0546882	−	0.0315742i
$970$	4.13426	+	9.28571i	0.132743	+	0.298146i
$971$	3.73580	+	17.5756i	0.119888	+	0.564026i	0.996555	+	0.0829303i	$0.0264279\pi$
$971$	3.73580	+	17.5756i	0.119888	+	0.564026i	−0.876668	+	0.481096i	$0.840239\pi$
$972$	0.951057	−	0.309017i	0.0305052	−	0.00991172i
$973$	−25.8793	−	29.8378i	−0.829653	−	0.956557i
$974$	19.0789	+	26.2599i	0.611328	+	0.841420i
$975$	−0.264968	−	0.238578i	−0.00848576	−	0.00764061i
$976$	5.17441	+	5.74676i	0.165629	+	0.183949i
$977$	−3.81199	+	1.69721i	−0.121957	+	0.0542985i	−0.466808	−	0.884359i	$-0.654596\pi$
$977$	−3.81199	+	1.69721i	−0.121957	+	0.0542985i	0.344851	+	0.938657i	$0.387929\pi$
$978$	−6.99950	−	12.1235i	−0.223819	−	0.387666i
$979$	−23.2948	+	0.0333400i	−0.744504	+	0.00106555i
$980$	−2.80309	−	16.1070i	−0.0895413	−	0.514518i
$981$	3.43169	−	4.72332i	0.109565	−	0.150804i
$982$	−25.3466	+	5.38758i	−0.808842	+	0.171925i
$983$	1.71536	−	8.07012i	0.0547114	−	0.257397i	−0.942288	−	0.334803i	$-0.891330\pi$
$983$	1.71536	−	8.07012i	0.0547114	−	0.257397i	0.997000	+	0.0774057i	$0.0246637\pi$
$984$	−0.671246	−	6.38648i	−0.0213985	−	0.203593i
$985$	25.8349	+	11.5024i	0.823168	+	0.366498i
$986$	0.507025	+	1.56046i	0.0161469	+	0.0496952i
$987$	8.28192	+	1.92176i	0.263616	+	0.0611702i
$988$	1.37435	+	0.998525i	0.0437240	+	0.0317673i
$989$	17.5128	−	10.1110i	0.556874	−	0.321511i
$990$	−3.16080	−	7.07202i	−0.100457	−	0.224764i
$991$	−23.0079	+	39.8508i	−0.730869	+	1.26590i	0.225643	+	0.974210i	$0.427552\pi$
$991$	−23.0079	+	39.8508i	−0.730869	+	1.26590i	−0.956512	+	0.291692i	$0.905782\pi$
$992$	−0.469569	+	4.46765i	−0.0149088	+	0.141848i
$993$	10.9064	+	3.54369i	0.346103	+	0.112456i
$994$	−18.9277	+	25.0598i	−0.600352	+	0.794849i
$995$	2.26945	−	1.64885i	0.0719463	−	0.0522721i
$996$	6.76860	−	15.2025i	0.214471	−	0.481710i
$997$	51.0251	+	10.8457i	1.61598	+	0.343487i	0.925171	−	0.379550i	$-0.123921\pi$
$997$	51.0251	+	10.8457i	1.61598	+	0.343487i	0.690809	+	0.723037i	$0.257255\pi$
$998$	−29.9969	+	27.0094i	−0.949536	+	0.854966i
$999$	10.8729	+	1.14279i	0.344004	+	0.0361563i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.ba.b.73.4	yes	64
7.5	odd	6		462.2.ba.a.271.8	✓	64
11.8	odd	10		462.2.ba.a.283.8	yes	64
77.19	even	30	inner	462.2.ba.b.19.4	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.ba.a.271.8	✓	64	7.5	odd	6
462.2.ba.a.283.8	yes	64	11.8	odd	10
462.2.ba.b.19.4	yes	64	77.19	even	30	inner
462.2.ba.b.73.4	yes	64	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-0.994522 - 0.104528i) q^{2} +(-0.743145 + 0.669131i) q^{3} +(0.978148 + 0.207912i) q^{4} +(0.949965 - 2.13366i) q^{5} +(0.809017 - 0.587785i) q^{6} +(2.43658 - 1.03106i) q^{7} +(-0.951057 - 0.309017i) q^{8} +(0.104528 - 0.994522i) q^{9} +O(q^{10})\)	\(q+(-0.994522 - 0.104528i) q^{2} +(-0.743145 + 0.669131i) q^{3} +(0.978148 + 0.207912i) q^{4} +(0.949965 - 2.13366i) q^{5} +(0.809017 - 0.587785i) q^{6} +(2.43658 - 1.03106i) q^{7} +(-0.951057 - 0.309017i) q^{8} +(0.104528 - 0.994522i) q^{9} +(-1.16779 + 2.02267i) q^{10} +(-2.87465 - 1.65420i) q^{11} +(-0.866025 + 0.500000i) q^{12} +(-0.634067 - 0.460677i) q^{13} +(-2.53101 + 0.770722i) q^{14} +(0.721733 + 2.22127i) q^{15} +(0.913545 + 0.406737i) q^{16} +(-0.0947974 - 0.901937i) q^{17} +(-0.207912 + 0.978148i) q^{18} +(-2.12015 + 0.450652i) q^{19} +(1.37282 - 1.88952i) q^{20} +(-1.12081 + 2.39662i) q^{21} +(2.68599 + 1.94562i) q^{22} +(-2.44656 - 4.23756i) q^{23} +(0.913545 - 0.406737i) q^{24} +(-0.304406 - 0.338077i) q^{25} +(0.582440 + 0.524431i) q^{26} +(0.587785 + 0.809017i) q^{27} +(2.59770 - 0.501938i) q^{28} +(1.72064 - 0.559071i) q^{29} +(-0.485594 - 2.28454i) q^{30} +(-1.82717 - 4.10388i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(3.24316 - 0.694207i) q^{33} +0.906905i q^{34} +(0.114731 - 6.17829i) q^{35} +(0.309017 - 0.951057i) q^{36} +(7.31548 - 8.12466i) q^{37} +(2.15564 - 0.226567i) q^{38} +(0.779456 - 0.0819242i) q^{39} +(-1.56281 + 1.73567i) q^{40} +(1.98440 - 6.10736i) q^{41} +(1.36519 - 2.26633i) q^{42} +4.13275i q^{43} +(-2.46791 - 2.21573i) q^{44} +(-2.02267 - 1.16779i) q^{45} +(1.99021 + 4.47008i) q^{46} +(-0.668111 - 3.14322i) q^{47} +(-0.951057 + 0.309017i) q^{48} +(4.87382 - 5.02453i) q^{49} +(0.267400 + 0.368044i) q^{50} +(0.673962 + 0.606838i) q^{51} +(-0.524431 - 0.582440i) q^{52} +(-1.30848 + 0.582574i) q^{53} +(-0.500000 - 0.866025i) q^{54} +(-6.26032 + 4.56209i) q^{55} +(-2.63594 + 0.227655i) q^{56} +(1.27404 - 1.75356i) q^{57} +(-1.76966 + 0.376152i) q^{58} +(0.166918 - 0.785286i) q^{59} +(0.244134 + 2.32278i) q^{60} +(7.06447 + 3.14531i) q^{61} +(1.38818 + 4.27239i) q^{62} +(-0.770722 - 2.53101i) q^{63} +(0.809017 + 0.587785i) q^{64} +(-1.58527 + 0.915255i) q^{65} +(-3.29796 + 0.351402i) q^{66} +(-7.33817 + 12.7101i) q^{67} +(0.0947974 - 0.901937i) q^{68} +(4.65362 + 1.51205i) q^{69} +(-0.759910 + 6.13246i) q^{70} +(9.60291 - 6.97692i) q^{71} +(-0.406737 + 0.913545i) q^{72} +(-11.9998 - 2.55063i) q^{73} +(-8.12466 + 7.31548i) q^{74} +(0.452435 + 0.0475529i) q^{75} -2.16752 q^{76} +(-8.70990 - 1.06664i) q^{77} -0.783750 q^{78} +(14.0497 + 1.47668i) q^{79} +(1.73567 - 1.56281i) q^{80} +(-0.978148 - 0.207912i) q^{81} +(-2.61192 + 5.86647i) q^{82} +(-13.4630 + 9.78147i) q^{83} +(-1.59461 + 2.11122i) q^{84} +(-2.01448 - 0.654544i) q^{85} +(0.431990 - 4.11011i) q^{86} +(-0.904596 + 1.56681i) q^{87} +(2.22278 + 2.46155i) q^{88} +(6.08266 - 3.51182i) q^{89} +(1.88952 + 1.37282i) q^{90} +(-2.01994 - 0.468712i) q^{91} +(-1.51205 - 4.65362i) q^{92} +(4.10388 + 1.82717i) q^{93} +(0.335896 + 3.19583i) q^{94} +(-1.05253 + 4.95178i) q^{95} +(0.978148 - 0.207912i) q^{96} +(2.55805 - 3.52085i) q^{97} +(-5.37233 + 4.48755i) q^{98} +(-1.94562 + 2.68599i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 8 q^{4} - 2 q^{5} + 16 q^{6} + 16 q^{7} - 8 q^{9}+O(q^{10}) \) 64 * q - 8 * q^4 - 2 * q^5 + 16 * q^6 + 16 * q^7 - 8 * q^9	\( 64 q - 8 q^{4} - 2 q^{5} + 16 q^{6} + 16 q^{7} - 8 q^{9} - 2 q^{10} + 4 q^{11} + 2 q^{14} - 6 q^{15} + 8 q^{16} + 30 q^{17} - 10 q^{19} - 20 q^{20} + 4 q^{21} - 2 q^{22} + 4 q^{23} + 8 q^{24} - 12 q^{26} - 20 q^{29} - 18 q^{30} + 34 q^{31} + 8 q^{33} - 2 q^{35} - 16 q^{36} - 14 q^{37} + 12 q^{38} - 18 q^{39} + 12 q^{40} + 28 q^{41} + 4 q^{42} + 6 q^{44} - 12 q^{45} + 42 q^{46} + 24 q^{47} - 44 q^{49} + 14 q^{51} - 32 q^{54} + 14 q^{55} - 4 q^{56} - 10 q^{58} - 30 q^{59} + 2 q^{60} - 28 q^{61} + 8 q^{62} + 16 q^{63} + 16 q^{64} - 12 q^{65} - 4 q^{66} + 16 q^{67} - 30 q^{68} - 30 q^{70} - 24 q^{71} - 116 q^{73} - 44 q^{74} + 12 q^{75} - 32 q^{77} - 18 q^{80} + 8 q^{81} - 28 q^{82} - 8 q^{83} - 2 q^{84} - 80 q^{85} - 18 q^{86} - 10 q^{87} - 14 q^{88} - 24 q^{89} - 4 q^{90} + 48 q^{91} + 8 q^{92} + 76 q^{93} + 6 q^{94} + 98 q^{95} - 8 q^{96} - 120 q^{97} - 40 q^{98} + 8 q^{99}+O(q^{100}) \) 64 * q - 8 * q^4 - 2 * q^5 + 16 * q^6 + 16 * q^7 - 8 * q^9 - 2 * q^10 + 4 * q^11 + 2 * q^14 - 6 * q^15 + 8 * q^16 + 30 * q^17 - 10 * q^19 - 20 * q^20 + 4 * q^21 - 2 * q^22 + 4 * q^23 + 8 * q^24 - 12 * q^26 - 20 * q^29 - 18 * q^30 + 34 * q^31 + 8 * q^33 - 2 * q^35 - 16 * q^36 - 14 * q^37 + 12 * q^38 - 18 * q^39 + 12 * q^40 + 28 * q^41 + 4 * q^42 + 6 * q^44 - 12 * q^45 + 42 * q^46 + 24 * q^47 - 44 * q^49 + 14 * q^51 - 32 * q^54 + 14 * q^55 - 4 * q^56 - 10 * q^58 - 30 * q^59 + 2 * q^60 - 28 * q^61 + 8 * q^62 + 16 * q^63 + 16 * q^64 - 12 * q^65 - 4 * q^66 + 16 * q^67 - 30 * q^68 - 30 * q^70 - 24 * q^71 - 116 * q^73 - 44 * q^74 + 12 * q^75 - 32 * q^77 - 18 * q^80 + 8 * q^81 - 28 * q^82 - 8 * q^83 - 2 * q^84 - 80 * q^85 - 18 * q^86 - 10 * q^87 - 14 * q^88 - 24 * q^89 - 4 * q^90 + 48 * q^91 + 8 * q^92 + 76 * q^93 + 6 * q^94 + 98 * q^95 - 8 * q^96 - 120 * q^97 - 40 * q^98 + 8 * q^99

Introduction

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