LMFDB - Embedded newform 804.2.e.b.535.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [804,2,Mod(535,804)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(804, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 1]))

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

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

chi := DirichletCharacter("804.535");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 804 = 2^{2} \cdot 3 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	804.e (of order $2$, degree $1$, 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:	$6.41997232251$
Analytic rank:	$0$
Dimension:	$34$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			535.12
Character	$\chi$	$=$	804.535
Dual form			804.2.e.b.535.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707921 + 1.22427i) q^{2} +1.00000 q^{3} +(-0.997695 - 1.73338i) q^{4} +3.14565i q^{5} +(-0.707921 + 1.22427i) q^{6} +1.38193 q^{7} +(2.82842 + 0.00564312i) q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+(-0.707921 + 1.22427i) q^{2} +1.00000 q^{3} +(-0.997695 - 1.73338i) q^{4} +3.14565i q^{5} +(-0.707921 + 1.22427i) q^{6} +1.38193 q^{7} +(2.82842 + 0.00564312i) q^{8} +1.00000 q^{9} +(-3.85114 - 2.22687i) q^{10} +2.19154 q^{11} +(-0.997695 - 1.73338i) q^{12} +1.11168i q^{13} +(-0.978299 + 1.69186i) q^{14} +3.14565i q^{15} +(-2.00921 + 3.45877i) q^{16} +0.639776 q^{17} +(-0.707921 + 1.22427i) q^{18} -2.14755i q^{19} +(5.45260 - 3.13840i) q^{20} +1.38193 q^{21} +(-1.55144 + 2.68304i) q^{22} +5.50995i q^{23} +(2.82842 + 0.00564312i) q^{24} -4.89510 q^{25} +(-1.36100 - 0.786978i) q^{26} +1.00000 q^{27} +(-1.37875 - 2.39541i) q^{28} +6.70206 q^{29} +(-3.85114 - 2.22687i) q^{30} +4.75833 q^{31} +(-2.81212 - 4.90836i) q^{32} +2.19154 q^{33} +(-0.452911 + 0.783262i) q^{34} +4.34707i q^{35} +(-0.997695 - 1.73338i) q^{36} -10.7663 q^{37} +(2.62919 + 1.52030i) q^{38} +1.11168i q^{39} +(-0.0177513 + 8.89722i) q^{40} +2.53783i q^{41} +(-0.978299 + 1.69186i) q^{42} -5.51787 q^{43} +(-2.18649 - 3.79877i) q^{44} +3.14565i q^{45} +(-6.74569 - 3.90061i) q^{46} -2.88421i q^{47} +(-2.00921 + 3.45877i) q^{48} -5.09026 q^{49} +(3.46535 - 5.99295i) q^{50} +0.639776 q^{51} +(1.92696 - 1.10911i) q^{52} +0.00678779i q^{53} +(-0.707921 + 1.22427i) q^{54} +6.89381i q^{55} +(3.90869 + 0.00779841i) q^{56} -2.14755i q^{57} +(-4.74453 + 8.20516i) q^{58} +0.119485i q^{59} +(5.45260 - 3.13840i) q^{60} +10.3863i q^{61} +(-3.36852 + 5.82550i) q^{62} +1.38193 q^{63} +(7.99994 + 0.0319223i) q^{64} -3.49694 q^{65} +(-1.55144 + 2.68304i) q^{66} +(8.18434 + 0.128944i) q^{67} +(-0.638302 - 1.10897i) q^{68} +5.50995i q^{69} +(-5.32201 - 3.07738i) q^{70} +5.27216i q^{71} +(2.82842 + 0.00564312i) q^{72} +2.16400 q^{73} +(7.62168 - 13.1809i) q^{74} -4.89510 q^{75} +(-3.72252 + 2.14260i) q^{76} +3.02855 q^{77} +(-1.36100 - 0.786978i) q^{78} +1.72829 q^{79} +(-10.8801 - 6.32026i) q^{80} +1.00000 q^{81} +(-3.10700 - 1.79658i) q^{82} +6.31463i q^{83} +(-1.37875 - 2.39541i) q^{84} +2.01251i q^{85} +(3.90622 - 6.75539i) q^{86} +6.70206 q^{87} +(6.19859 + 0.0123671i) q^{88} -13.2000 q^{89} +(-3.85114 - 2.22687i) q^{90} +1.53626i q^{91} +(9.55084 - 5.49725i) q^{92} +4.75833 q^{93} +(3.53106 + 2.04179i) q^{94} +6.75544 q^{95} +(-2.81212 - 4.90836i) q^{96} -5.12276i q^{97} +(3.60351 - 6.23188i) q^{98} +2.19154 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q + 34 q^{3} + 2 q^{4} + 4 q^{7} - 6 q^{8} + 34 q^{9}+O(q^{10}) $ 34 * q + 34 * q^3 + 2 * q^4 + 4 * q^7 - 6 * q^8 + 34 * q^9	$ 34 q + 34 q^{3} + 2 q^{4} + 4 q^{7} - 6 q^{8} + 34 q^{9} - 6 q^{10} + 2 q^{12} - 4 q^{14} + 2 q^{16} - 12 q^{20} + 4 q^{21} - 8 q^{22} - 6 q^{24} - 34 q^{25} + 10 q^{26} + 34 q^{27} - 8 q^{28} - 16 q^{29} - 6 q^{30} - 4 q^{31} + 2 q^{36} + 12 q^{37} + 26 q^{38} - 18 q^{40} - 4 q^{42} - 4 q^{43} + 26 q^{44} - 4 q^{46} + 2 q^{48} + 46 q^{49} - 18 q^{50} + 32 q^{52} + 14 q^{56} + 4 q^{58} - 12 q^{60} - 2 q^{62} + 4 q^{63} + 26 q^{64} - 8 q^{66} - 18 q^{67} - 34 q^{68} + 56 q^{70} - 6 q^{72} + 12 q^{73} + 22 q^{74} - 34 q^{75} - 32 q^{76} - 8 q^{77} + 10 q^{78} - 12 q^{79} - 2 q^{80} + 34 q^{81} + 26 q^{82} - 8 q^{84} + 6 q^{86} - 16 q^{87} - 28 q^{88} - 6 q^{90} - 46 q^{92} - 4 q^{93} + 32 q^{94} - 40 q^{95} - 40 q^{98}+O(q^{100}) $ 34 * q + 34 * q^3 + 2 * q^4 + 4 * q^7 - 6 * q^8 + 34 * q^9 - 6 * q^10 + 2 * q^12 - 4 * q^14 + 2 * q^16 - 12 * q^20 + 4 * q^21 - 8 * q^22 - 6 * q^24 - 34 * q^25 + 10 * q^26 + 34 * q^27 - 8 * q^28 - 16 * q^29 - 6 * q^30 - 4 * q^31 + 2 * q^36 + 12 * q^37 + 26 * q^38 - 18 * q^40 - 4 * q^42 - 4 * q^43 + 26 * q^44 - 4 * q^46 + 2 * q^48 + 46 * q^49 - 18 * q^50 + 32 * q^52 + 14 * q^56 + 4 * q^58 - 12 * q^60 - 2 * q^62 + 4 * q^63 + 26 * q^64 - 8 * q^66 - 18 * q^67 - 34 * q^68 + 56 * q^70 - 6 * q^72 + 12 * q^73 + 22 * q^74 - 34 * q^75 - 32 * q^76 - 8 * q^77 + 10 * q^78 - 12 * q^79 - 2 * q^80 + 34 * q^81 + 26 * q^82 - 8 * q^84 + 6 * q^86 - 16 * q^87 - 28 * q^88 - 6 * q^90 - 46 * q^92 - 4 * q^93 + 32 * q^94 - 40 * q^95 - 40 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/804\mathbb{Z}\right)^\times$.

$n$	$269$	$337$	$403$
$\chi(n)$	$1$	$-1$	$-1$

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 $

$2$	−0.707921	+	1.22427i	−0.500576	+	0.865693i
$2$	−0.707921	+	1.22427i	−0.500576	+	0.865693i
$3$	1.00000			0.577350
$3$	1.00000			0.577350
$4$	−0.997695	−	1.73338i	−0.498848	−	0.866690i
$5$			3.14565i			1.40678i	0.710806	+	0.703388i	$0.248330\pi$
$5$			3.14565i			1.40678i	−0.710806	+	0.703388i	$0.751670\pi$
$6$	−0.707921	+	1.22427i	−0.289008	+	0.499808i
$7$	1.38193			0.522321			0.261161	−	0.965295i	$-0.415895\pi$
$7$	1.38193			0.522321			0.261161	+	0.965295i	$0.415895\pi$
$8$	2.82842	+	0.00564312i	0.999998	+	0.00199515i
$9$	1.00000			0.333333
$10$	−3.85114	−	2.22687i	−1.21784	−	0.704198i
$11$	2.19154			0.660773			0.330387	−	0.943846i	$-0.392821\pi$
$11$	2.19154			0.660773			0.330387	+	0.943846i	$0.392821\pi$
$12$	−0.997695	−	1.73338i	−0.288010	−	0.500384i
$13$			1.11168i			0.308323i	0.988046	+	0.154162i	$0.0492676\pi$
$13$			1.11168i			0.308323i	−0.988046	+	0.154162i	$0.950732\pi$
$14$	−0.978299	+	1.69186i	−0.261461	+	0.452170i
$15$			3.14565i			0.812203i
$16$	−2.00921	+	3.45877i	−0.502302	+	0.864692i
$17$	0.639776			0.155169			0.0775843	−	0.996986i	$-0.475279\pi$
$17$	0.639776			0.155169			0.0775843	+	0.996986i	$0.475279\pi$
$18$	−0.707921	+	1.22427i	−0.166859	+	0.288564i
$19$		−	2.14755i		−	0.492682i	−0.969183	−	0.246341i	$-0.920772\pi$
$19$		−	2.14755i		−	0.492682i	0.969183	−	0.246341i	$-0.0792283\pi$
$20$	5.45260	−	3.13840i	1.21924	−	0.701767i
$21$	1.38193			0.301562
$22$	−1.55144	+	2.68304i	−0.330767	+	0.572027i
$23$			5.50995i			1.14890i	0.818538	+	0.574452i	$0.194785\pi$
$23$			5.50995i			1.14890i	−0.818538	+	0.574452i	$0.805215\pi$
$24$	2.82842	+	0.00564312i	0.577349	+	0.00115190i
$25$	−4.89510			−0.979020
$26$	−1.36100	−	0.786978i	−0.266913	−	0.154339i
$27$	1.00000			0.192450
$28$	−1.37875	−	2.39541i	−0.260559	−	0.452690i
$29$	6.70206			1.24454			0.622271	−	0.782802i	$-0.286210\pi$
$29$	6.70206			1.24454			0.622271	+	0.782802i	$0.286210\pi$
$30$	−3.85114	−	2.22687i	−0.703118	−	0.406569i
$31$	4.75833			0.854620			0.427310	−	0.904105i	$-0.359461\pi$
$31$	4.75833			0.854620			0.427310	+	0.904105i	$0.359461\pi$
$32$	−2.81212	−	4.90836i	−0.497117	−	0.867683i
$33$	2.19154			0.381498
$34$	−0.452911	+	0.783262i	−0.0776736	+	0.134328i
$35$			4.34707i			0.734789i
$36$	−0.997695	−	1.73338i	−0.166283	−	0.288897i
$37$	−10.7663			−1.76997			−0.884983	−	0.465624i	$-0.845830\pi$
$37$	−10.7663			−1.76997			−0.884983	+	0.465624i	$0.845830\pi$
$38$	2.62919	+	1.52030i	0.426511	+	0.246625i
$39$			1.11168i			0.178011i
$40$	−0.0177513	+	8.89722i	−0.00280672	+	1.40677i
$41$			2.53783i			0.396342i	0.980167	+	0.198171i	$0.0635002\pi$
$41$			2.53783i			0.396342i	−0.980167	+	0.198171i	$0.936500\pi$
$42$	−0.978299	+	1.69186i	−0.150955	+	0.261060i
$43$	−5.51787			−0.841467			−0.420734	−	0.907184i	$-0.638227\pi$
$43$	−5.51787			−0.841467			−0.420734	+	0.907184i	$0.638227\pi$
$44$	−2.18649	−	3.79877i	−0.329625	−	0.572685i
$45$			3.14565i			0.468926i
$46$	−6.74569	−	3.90061i	−0.994598	−	0.575114i
$47$		−	2.88421i		−	0.420705i	−0.977626	−	0.210353i	$-0.932539\pi$
$47$		−	2.88421i		−	0.420705i	0.977626	−	0.210353i	$-0.0674612\pi$
$48$	−2.00921	+	3.45877i	−0.290004	+	0.499230i
$49$	−5.09026			−0.727181
$50$	3.46535	−	5.99295i	0.490074	−	0.847531i
$51$	0.639776			0.0895866
$52$	1.92696	−	1.10911i	0.267221	−	0.153806i
$53$			0.00678779i			0.000932375i	1.00000		0.000466188i	$0.000148392\pi$
$53$			0.00678779i			0.000932375i	−1.00000		0.000466188i	$0.999852\pi$
$54$	−0.707921	+	1.22427i	−0.0963359	+	0.166603i
$55$			6.89381i			0.929560i
$56$	3.90869	+	0.00779841i	0.522320	+	0.00104211i
$57$		−	2.14755i		−	0.284450i
$58$	−4.74453	+	8.20516i	−0.622987	+	1.07739i
$59$			0.119485i			0.0155556i	0.999970	+	0.00777779i	$0.00247577\pi$
$59$			0.119485i			0.0155556i	−0.999970	+	0.00777779i	$0.997524\pi$
$60$	5.45260	−	3.13840i	0.703928	−	0.405165i
$61$			10.3863i			1.32983i	0.746917	+	0.664917i	$0.231533\pi$
$61$			10.3863i			1.32983i	−0.746917	+	0.664917i	$0.768467\pi$
$62$	−3.36852	+	5.82550i	−0.427802	+	0.739839i
$63$	1.38193			0.174107
$64$	7.99994	+	0.0319223i	0.999992	+	0.00399028i
$65$	−3.49694			−0.433742
$66$	−1.55144	+	2.68304i	−0.190969	+	0.330260i
$67$	8.18434	+	0.128944i	0.999876	+	0.0157530i
$67$	8.18434	+	0.128944i	0.999876	+	0.0157530i
$68$	−0.638302	−	1.10897i	−0.0774055	−	0.134483i
$69$			5.50995i			0.663320i
$70$	−5.32201	−	3.07738i	−0.636102	−	0.367818i
$71$			5.27216i			0.625690i	0.949804	+	0.312845i	$0.101282\pi$
$71$			5.27216i			0.625690i	−0.949804	+	0.312845i	$0.898718\pi$
$72$	2.82842	+	0.00564312i	0.333333	+	0.000665048i
$73$	2.16400			0.253277			0.126639	−	0.991949i	$-0.459581\pi$
$73$	2.16400			0.253277			0.126639	+	0.991949i	$0.459581\pi$
$74$	7.62168	−	13.1809i	0.886002	−	1.53225i
$75$	−4.89510			−0.565238
$76$	−3.72252	+	2.14260i	−0.427002	+	0.245773i
$77$	3.02855			0.345136
$78$	−1.36100	−	0.786978i	−0.154102	−	0.0891078i
$79$	1.72829			0.194447			0.0972237	−	0.995263i	$-0.469004\pi$
$79$	1.72829			0.194447			0.0972237	+	0.995263i	$0.469004\pi$
$80$	−10.8801	−	6.32026i	−1.21643	−	0.706627i
$81$	1.00000			0.111111
$82$	−3.10700	−	1.79658i	−0.343111	−	0.198399i
$83$			6.31463i			0.693121i	0.938028	+	0.346561i	$0.112650\pi$
$83$			6.31463i			0.693121i	−0.938028	+	0.346561i	$0.887350\pi$
$84$	−1.37875	−	2.39541i	−0.150434	−	0.261361i
$85$			2.01251i			0.218287i
$86$	3.90622	−	6.75539i	0.421218	−	0.728452i
$87$	6.70206			0.718536
$88$	6.19859	+	0.0123671i	0.660772	+	0.00131834i
$89$	−13.2000			−1.39919			−0.699597	−	0.714537i	$-0.746637\pi$
$89$	−13.2000			−1.39919			−0.699597	+	0.714537i	$0.746637\pi$
$90$	−3.85114	−	2.22687i	−0.405945	−	0.234733i
$91$			1.53626i			0.161044i
$92$	9.55084	−	5.49725i	0.995744	−	0.573128i
$93$	4.75833			0.493415
$94$	3.53106	+	2.04179i	0.364201	+	0.210595i
$95$	6.75544			0.693093
$96$	−2.81212	−	4.90836i	−0.287011	−	0.500957i
$97$		−	5.12276i		−	0.520138i	−0.965590	−	0.260069i	$-0.916255\pi$
$97$		−	5.12276i		−	0.520138i	0.965590	−	0.260069i	$-0.0837453\pi$
$98$	3.60351	−	6.23188i	0.364009	−	0.629515i
$99$	2.19154			0.220258
$100$	4.88382	+	8.48507i	0.488382	+	0.848507i
$101$			6.31707i			0.628572i	0.949328	+	0.314286i	$0.101765\pi$
$101$			6.31707i			0.628572i	−0.949328	+	0.314286i	$0.898235\pi$
$102$	−0.452911	+	0.783262i	−0.0448449	+	0.0775545i
$103$		−	18.2109i		−	1.79437i	−0.441652	−	0.897186i	$-0.645607\pi$
$103$		−	18.2109i		−	1.79437i	0.441652	−	0.897186i	$-0.354393\pi$
$104$	−0.00627332	+	3.14429i	−0.000615150	+	0.308323i
$105$			4.34707i			0.424231i
$106$	−0.00831012	−	0.00480522i	−0.000807150	−	0.000466724i
$107$		−	16.8450i		−	1.62846i	−0.580540	−	0.814232i	$-0.697158\pi$
$107$		−	16.8450i		−	1.62846i	0.580540	−	0.814232i	$-0.302842\pi$
$108$	−0.997695	−	1.73338i	−0.0960033	−	0.166795i
$109$			12.4899i			1.19632i	0.801378	+	0.598158i	$0.204100\pi$
$109$			12.4899i			1.19632i	−0.801378	+	0.598158i	$0.795900\pi$
$110$	−8.43991	−	4.88027i	−0.804714	−	0.465316i
$111$	−10.7663			−1.02189
$112$	−2.77659	+	4.77978i	−0.262363	+	0.451647i
$113$		−	6.63902i		−	0.624547i	−0.949992	−	0.312273i	$-0.898910\pi$
$113$		−	6.63902i		−	0.624547i	0.949992	−	0.312273i	$-0.101090\pi$
$114$	2.62919	+	1.52030i	0.246246	+	0.142389i
$115$	−17.3324			−1.61625
$116$	−6.68661	−	11.6172i	−0.620836	−	1.07863i
$117$			1.11168i			0.102774i
$118$	−0.146282	−	0.0845857i	−0.0134664	−	0.00778675i
$119$	0.884127			0.0810478
$120$	−0.0177513	+	8.89722i	−0.00162046	+	0.812201i
$121$	−6.19716			−0.563379
$122$	−12.7157	−	7.35271i	−1.15123	−	0.665683i
$123$			2.53783i			0.228828i
$124$	−4.74736	−	8.24798i	−0.426325	−	0.740691i
$125$			0.329971i			0.0295135i
$126$	−0.978299	+	1.69186i	−0.0871538	+	0.150723i
$127$		−	10.8899i		−	0.966319i	−0.875532	−	0.483159i	$-0.839489\pi$
$127$		−	10.8899i		−	0.966319i	0.875532	−	0.483159i	$-0.160511\pi$
$128$	−5.70241	+	9.77152i	−0.504026	+	0.863688i
$129$	−5.51787			−0.485821
$130$	2.47556	−	4.28121i	0.217121	−	0.375487i
$131$		−	6.00800i		−	0.524922i	−0.964943	−	0.262461i	$-0.915466\pi$
$131$		−	6.00800i		−	0.524922i	0.964943	−	0.262461i	$-0.0845340\pi$
$132$	−2.18649	−	3.79877i	−0.190309	−	0.330640i
$133$		−	2.96777i		−	0.257338i
$134$	−5.95173	+	9.92859i	−0.514151	+	0.857700i
$135$			3.14565i			0.270734i
$136$	1.80956	+	0.00361034i	0.155168	+	0.000309584i
$137$		−	11.6091i		−	0.991834i	−0.868370	−	0.495917i	$-0.834832\pi$
$137$		−	11.6091i		−	0.991834i	0.868370	−	0.495917i	$-0.165168\pi$
$138$	−6.74569	−	3.90061i	−0.574232	−	0.332042i
$139$	10.4089			0.882871			0.441436	−	0.897293i	$-0.354469\pi$
$139$	10.4089			0.882871			0.441436	+	0.897293i	$0.354469\pi$
$140$	7.53512	−	4.33705i	0.636834	−	0.366548i
$141$		−	2.88421i		−	0.242894i
$142$	−6.45457	−	3.73227i	−0.541656	−	0.313205i
$143$			2.43628i			0.203732i
$144$	−2.00921	+	3.45877i	−0.167434	+	0.288231i
$145$			21.0823i			1.75079i
$146$	−1.53194	+	2.64933i	−0.126784	+	0.219260i
$147$	−5.09026			−0.419838
$148$	10.7415	+	18.6620i	0.882943	+	1.53401i
$149$	18.0368			1.47763			0.738815	−	0.673908i	$-0.235386\pi$
$149$	18.0368			1.47763			0.738815	+	0.673908i	$0.235386\pi$
$150$	3.46535	−	5.99295i	0.282944	−	0.489322i
$151$		−	22.5460i		−	1.83476i	−0.398008	−	0.917382i	$-0.630298\pi$
$151$		−	22.5460i		−	1.83476i	0.398008	−	0.917382i	$-0.369702\pi$
$152$	0.0121189	−	6.07418i	0.000982972	−	0.492681i
$153$	0.639776			0.0517228
$154$	−2.14398	+	3.70778i	−0.172767	+	0.298782i
$155$			14.9680i			1.20226i
$156$	1.92696	−	1.10911i	0.154280	−	0.0888001i
$157$	15.4129			1.23008			0.615040	−	0.788496i	$-0.289140\pi$
$157$	15.4129			1.23008			0.615040	+	0.788496i	$0.289140\pi$
$158$	−1.22349	+	2.11590i	−0.0973357	+	0.168332i
$159$			0.00678779i			0.000538307i
$160$	15.4400	−	8.84594i	1.22064	−	0.699333i
$161$			7.61438i			0.600097i
$162$	−0.707921	+	1.22427i	−0.0556195	+	0.0961881i
$163$		−	4.46026i		−	0.349354i	−0.984626	−	0.174677i	$-0.944112\pi$
$163$		−	4.46026i		−	0.349354i	0.984626	−	0.174677i	$-0.0558882\pi$
$164$	4.39902	−	2.53198i	0.343506	−	0.197714i
$165$			6.89381i			0.536682i
$166$	−7.73084	−	4.47026i	−0.600030	−	0.346960i
$167$		−	3.92760i		−	0.303927i	−0.988386	−	0.151964i	$-0.951440\pi$
$167$		−	3.92760i		−	0.303927i	0.988386	−	0.151964i	$-0.0485596\pi$
$168$	3.90869	+	0.00779841i	0.301562	+	0.000601660i
$169$	11.7642			0.904937
$170$	−2.46387	−	1.42470i	−0.188970	−	0.109269i
$171$		−	2.14755i		−	0.164227i
$172$	5.50515	+	9.56456i	0.419764	+	0.729291i
$173$	14.8244			1.12708			0.563540	−	0.826089i	$-0.309439\pi$
$173$	14.8244			1.12708			0.563540	+	0.826089i	$0.309439\pi$
$174$	−4.74453	+	8.20516i	−0.359682	+	0.622032i
$175$	−6.76470			−0.511363
$176$	−4.40325	+	7.58002i	−0.331908	+	0.571366i
$177$			0.119485i			0.00898102i
$178$	9.34454	−	16.1604i	0.700403	−	1.21127i
$179$	7.74057			0.578558			0.289279	−	0.957245i	$-0.406585\pi$
$179$	7.74057			0.578558			0.289279	+	0.957245i	$0.406585\pi$
$180$	5.45260	−	3.13840i	0.406413	−	0.233922i
$181$	6.47986			0.481645			0.240822	−	0.970569i	$-0.422583\pi$
$181$	6.47986			0.481645			0.240822	+	0.970569i	$0.422583\pi$
$182$	−1.88080	−	1.08755i	−0.139414	−	0.0806146i
$183$			10.3863i			0.767780i
$184$	−0.0310933	+	15.5845i	−0.00229223	+	1.14890i
$185$		−	33.8669i		−	2.48995i
$186$	−3.36852	+	5.82550i	−0.246992	+	0.427146i
$187$	1.40209			0.102531
$188$	−4.99943	+	2.87756i	−0.364621	+	0.209868i
$189$	1.38193			0.100521
$190$	−4.78232	+	8.27051i	−0.346946	+	0.600006i
$191$	4.35527			0.315136			0.157568	−	0.987508i	$-0.449635\pi$
$191$	4.35527			0.315136			0.157568	+	0.987508i	$0.449635\pi$
$192$	7.99994	+	0.0319223i	0.577346	+	0.00230379i
$193$	−9.69919			−0.698163			−0.349082	−	0.937092i	$-0.613506\pi$
$193$	−9.69919			−0.698163			−0.349082	+	0.937092i	$0.613506\pi$
$194$	6.27167	+	3.62651i	0.450279	+	0.260368i
$195$	−3.49694			−0.250421
$196$	5.07853	+	8.82336i	0.362752	+	0.630240i
$197$		−	9.45364i		−	0.673544i	−0.941586	−	0.336772i	$-0.890665\pi$
$197$		−	9.45364i		−	0.673544i	0.941586	−	0.336772i	$-0.109335\pi$
$198$	−1.55144	+	2.68304i	−0.110256	+	0.190676i
$199$		−	14.4262i		−	1.02265i	−0.859389	−	0.511323i	$-0.829156\pi$
$199$		−	14.4262i		−	1.02265i	0.859389	−	0.511323i	$-0.170844\pi$
$200$	−13.8454	−	0.0276237i	−0.979019	−	0.00195329i
$201$	8.18434	+	0.128944i	0.577279	+	0.00909499i
$202$	−7.73383	−	4.47199i	−0.544150	−	0.314648i
$203$	9.26179			0.650050
$204$	−0.638302	−	1.10897i	−0.0446901	−	0.0776438i
$205$	−7.98312			−0.557565
$206$	22.2951	+	12.8919i	1.55338	+	0.898220i
$207$			5.50995i			0.382968i
$208$	−3.84503	−	2.23359i	−0.266605	−	0.154871i
$209$		−	4.70644i		−	0.325551i
$210$	−5.32201	−	3.07738i	−0.367253	−	0.212360i
$211$			0.971455i			0.0668777i	0.999441	+	0.0334388i	$0.0106459\pi$
$211$			0.971455i			0.0668777i	−0.999441	+	0.0334388i	$0.989354\pi$
$212$	0.0117658	−	0.00677215i	0.000808080	−	0.000465113i
$213$			5.27216i			0.361243i
$214$	20.6229	+	11.9249i	1.40975	+	0.815170i
$215$		−	17.3573i		−	1.18376i
$216$	2.82842	+	0.00564312i	0.192450	+	0.000383966i
$217$	6.57568			0.446386
$218$	−15.2911	−	8.84187i	−1.03564	−	0.598847i
$219$	2.16400			0.146230
$220$	11.9496	−	6.87792i	0.805640	−	0.463709i
$221$			0.711223i			0.0478421i
$222$	7.62168	−	13.1809i	0.511533	−	0.884643i
$223$			1.40727i			0.0942379i	0.998889	+	0.0471189i	$0.0150040\pi$
$223$			1.40727i			0.0942379i	−0.998889	+	0.0471189i	$0.984996\pi$
$224$	−3.88616	−	6.78302i	−0.259655	−	0.453209i
$225$	−4.89510			−0.326340
$226$	8.12798	+	4.69990i	0.540665	+	0.312633i
$227$			1.05501i			0.0700238i	0.999387	+	0.0350119i	$0.0111469\pi$
$227$			1.05501i			0.0700238i	−0.999387	+	0.0350119i	$0.988853\pi$
$228$	−3.72252	+	2.14260i	−0.246530	+	0.141897i
$229$		−	19.5924i		−	1.29470i	−0.762193	−	0.647350i	$-0.775877\pi$
$229$		−	19.5924i		−	1.29470i	0.762193	−	0.647350i	$-0.224123\pi$
$230$	12.2700	−	21.2196i	0.809057	−	1.39918i
$231$	3.02855			0.199264
$232$	18.9562	+	0.0378205i	1.24454	+	0.00248304i
$233$			7.76027i			0.508392i	0.967153	+	0.254196i	$0.0818109\pi$
$233$			7.76027i			0.508392i	−0.967153	+	0.254196i	$0.918189\pi$
$234$	−1.36100	−	0.786978i	−0.0889711	−	0.0514464i
$235$	9.07271			0.591838
$236$	0.207112	−	0.119209i	0.0134819	−	0.00775986i
$237$	1.72829			0.112264
$238$	−0.625892	+	1.08241i	−0.0405706	+	0.0701625i
$239$	12.9701			0.838968			0.419484	−	0.907763i	$-0.362211\pi$
$239$	12.9701			0.838968			0.419484	+	0.907763i	$0.362211\pi$
$240$	−10.8801	−	6.32026i	−0.702306	−	0.407971i
$241$	−11.1159			−0.716040			−0.358020	−	0.933714i	$-0.616548\pi$
$241$	−11.1159			−0.716040			−0.358020	+	0.933714i	$0.616548\pi$
$242$	4.38710	−	7.58703i	0.282014	−	0.487713i
$243$	1.00000			0.0641500
$244$	18.0035	−	10.3624i	1.15255	−	0.663385i
$245$		−	16.0122i		−	1.02298i
$246$	−3.10700	−	1.79658i	−0.198095	−	0.114546i
$247$	2.38738			0.151905
$248$	13.4585	+	0.0268518i	0.854619	+	0.00170509i
$249$			6.31463i			0.400174i
$250$	−0.403975	−	0.233593i	−0.0255496	−	0.0147737i
$251$	16.3410			1.03143			0.515716	−	0.856760i	$-0.327526\pi$
$251$	16.3410			1.03143			0.515716	+	0.856760i	$0.327526\pi$
$252$	−1.37875	−	2.39541i	−0.0868529	−	0.150897i
$253$			12.0753i			0.759166i
$254$	13.3322	+	7.70916i	0.836535	+	0.483716i
$255$			2.01251i			0.126028i
$256$	−7.92617	−	13.8988i	−0.495385	−	0.868673i
$257$	20.2146			1.26095			0.630476	−	0.776209i	$-0.282860\pi$
$257$	20.2146			1.26095			0.630476	+	0.776209i	$0.282860\pi$
$258$	3.90622	−	6.75539i	0.243190	−	0.420572i
$259$	−14.8783			−0.924490
$260$	3.48888	+	6.06152i	0.216371	+	0.375920i
$261$	6.70206			0.414847
$262$	7.35544	+	4.25319i	0.454421	+	0.262763i
$263$			27.8557i			1.71765i	0.512266	+	0.858827i	$0.328806\pi$
$263$			27.8557i			1.71765i	−0.512266	+	0.858827i	$0.671194\pi$
$264$	6.19859	+	0.0123671i	0.381497	+	0.000761143i
$265$	−0.0213520			−0.00131164
$266$	3.63336	+	2.10095i	0.222776	+	0.128817i
$267$	−13.2000			−0.807825
$268$	−7.94197	−	14.3152i	−0.485133	−	0.874440i
$269$	−10.6172			−0.647340			−0.323670	−	0.946170i	$-0.604917\pi$
$269$	−10.6172			−0.647340			−0.323670	+	0.946170i	$0.604917\pi$
$270$	−3.85114	−	2.22687i	−0.234373	−	0.135523i
$271$	−5.63033			−0.342018			−0.171009	−	0.985269i	$-0.554703\pi$
$271$	−5.63033			−0.342018			−0.171009	+	0.985269i	$0.554703\pi$
$272$	−1.28544	+	2.21284i	−0.0779415	+	0.134173i
$273$			1.53626i			0.0929786i
$274$	14.2127	+	8.21834i	0.858623	+	0.496488i
$275$	−10.7278			−0.646911
$276$	9.55084	−	5.49725i	0.574893	−	0.330896i
$277$	−14.7953			−0.888962			−0.444481	−	0.895788i	$-0.646612\pi$
$277$	−14.7953			−0.888962			−0.444481	+	0.895788i	$0.646612\pi$
$278$	−7.36868	+	12.7433i	−0.441944	+	0.764295i
$279$	4.75833			0.284873
$280$	−0.0245311	+	12.2953i	−0.00146601	+	0.734788i
$281$			12.3188i			0.734881i	0.930047	+	0.367440i	$0.119766\pi$
$281$			12.3188i			0.734881i	−0.930047	+	0.367440i	$0.880234\pi$
$282$	3.53106	+	2.04179i	0.210272	+	0.121587i
$283$			7.50228i			0.445964i	0.974823	+	0.222982i	$0.0715792\pi$
$283$			7.50228i			0.445964i	−0.974823	+	0.222982i	$0.928421\pi$
$284$	9.13866	−	5.26001i	0.542279	−	0.312124i
$285$	6.75544			0.400158
$286$	−2.98267	−	1.72469i	−0.176369	−	0.101983i
$287$			3.50711i			0.207018i
$288$	−2.81212	−	4.90836i	−0.165706	−	0.289228i
$289$	−16.5907			−0.975923
$290$	−25.8105	−	14.9246i	−1.51565	−	0.876404i
$291$		−	5.12276i		−	0.300302i
$292$	−2.15901	−	3.75104i	−0.126347	−	0.219513i
$293$	−6.01579			−0.351446			−0.175723	−	0.984440i	$-0.556226\pi$
$293$	−6.01579			−0.351446			−0.175723	+	0.984440i	$0.556226\pi$
$294$	3.60351	−	6.23188i	0.210161	−	0.363451i
$295$	−0.375857			−0.0218832
$296$	−30.4516	−	0.0607554i	−1.76996	−	0.00353134i
$297$	2.19154			0.127166
$298$	−12.7686	+	22.0820i	−0.739666	+	1.27917i
$299$	−6.12528			−0.354234
$300$	4.88382	+	8.48507i	0.281968	+	0.489886i
$301$	−7.62532			−0.439516
$302$	27.6024	+	15.9608i	1.58834	+	0.918438i
$303$			6.31707i			0.362906i
$304$	7.42788	+	4.31487i	0.426018	+	0.247475i
$305$	−32.6718			−1.87078
$306$	−0.452911	+	0.783262i	−0.0258912	+	0.0447761i
$307$		−	12.3473i		−	0.704698i	−0.935869	−	0.352349i	$-0.885383\pi$
$307$		−	12.3473i		−	0.704698i	0.935869	−	0.352349i	$-0.114617\pi$
$308$	−3.02158	−	5.24963i	−0.172170	−	0.299126i
$309$		−	18.2109i		−	1.03598i
$310$	−18.3250	−	10.5962i	−1.04079	−	0.601822i
$311$	−18.7816			−1.06501			−0.532503	−	0.846428i	$-0.678748\pi$
$311$	−18.7816			−1.06501			−0.532503	+	0.846428i	$0.678748\pi$
$312$	−0.00627332	+	3.14429i	−0.000355157	+	0.178010i
$313$		−	34.2048i		−	1.93337i	−0.255965	−	0.966686i	$-0.582393\pi$
$313$		−	34.2048i		−	1.93337i	0.255965	−	0.966686i	$-0.417607\pi$
$314$	−10.9111	+	18.8696i	−0.615749	+	1.06487i
$315$			4.34707i			0.244930i
$316$	−1.72430	−	2.99578i	−0.0969997	−	0.168526i
$317$	−17.1962			−0.965837			−0.482919	−	0.875665i	$-0.660423\pi$
$317$	−17.1962			−0.965837			−0.482919	+	0.875665i	$0.660423\pi$
$318$	−0.00831012	−	0.00480522i	−0.000466008	−	0.000269463i
$319$	14.6878			0.822360
$320$	−0.100416	+	25.1650i	−0.00561344	+	1.40677i
$321$		−	16.8450i		−	0.940194i
$322$	−9.32209	−	5.39038i	−0.519500	−	0.300394i
$323$		−	1.37395i		−	0.0764487i
$324$	−0.997695	−	1.73338i	−0.0554275	−	0.0962989i
$325$		−	5.44176i		−	0.301855i
$326$	5.46058	+	3.15751i	0.302434	+	0.174878i
$327$			12.4899i			0.690693i
$328$	−0.0143213	+	7.17805i	−0.000790761	+	0.396342i
$329$		−	3.98578i		−	0.219743i
$330$	−8.43991	−	4.88027i	−0.464602	−	0.268650i
$331$	−30.2833			−1.66452			−0.832260	−	0.554385i	$-0.812953\pi$
$331$	−30.2833			−1.66452			−0.832260	+	0.554385i	$0.812953\pi$
$332$	10.9457	−	6.30008i	0.600721	−	0.345762i
$333$	−10.7663			−0.589988
$334$	4.80846	+	2.78043i	0.263107	+	0.152139i
$335$	−0.405612	+	25.7450i	−0.0221609	+	1.40660i
$336$	−2.77659	+	4.77978i	−0.151475	+	0.260759i
$337$		−	27.7390i		−	1.51104i	−0.655127	−	0.755519i	$-0.727385\pi$
$337$		−	27.7390i		−	1.51104i	0.655127	−	0.755519i	$-0.272615\pi$
$338$	−8.32811	+	14.4026i	−0.452989	+	0.783397i
$339$		−	6.63902i		−	0.360582i
$340$	3.48844	−	2.00787i	0.189187	−	0.108892i
$341$	10.4280			0.564710
$342$	2.62919	+	1.52030i	0.142170	+	0.0822082i
$343$	−16.7079			−0.902143
$344$	−15.6069	−	0.0311380i	−0.841466	−	0.00167885i
$345$	−17.3324			−0.933144
$346$	−10.4945	+	18.1492i	−0.564189	+	0.975705i
$347$	−13.7586			−0.738598			−0.369299	−	0.929311i	$-0.620402\pi$
$347$	−13.7586			−0.738598			−0.369299	+	0.929311i	$0.620402\pi$
$348$	−6.68661	−	11.6172i	−0.358440	−	0.622748i
$349$	27.9839			1.49795			0.748973	−	0.662600i	$-0.230547\pi$
$349$	27.9839			1.49795			0.748973	+	0.662600i	$0.230547\pi$
$350$	4.78887	−	8.28185i	0.255976	−	0.442683i
$351$			1.11168i			0.0593368i
$352$	−6.16287	−	10.7568i	−0.328482	−	0.573342i
$353$			12.7760i			0.680000i	0.940425	+	0.340000i	$0.110427\pi$
$353$			12.7760i			0.680000i	−0.940425	+	0.340000i	$0.889573\pi$
$354$	−0.146282	−	0.0845857i	−0.00777480	−	0.00449568i
$355$	−16.5844			−0.880207
$356$	13.1696	+	22.8806i	0.697985	+	1.21267i
$357$	0.884127			0.0467930
$358$	−5.47972	+	9.47659i	−0.289612	+	0.500853i
$359$			15.8329i			0.835626i	0.908533	+	0.417813i	$0.137203\pi$
$359$			15.8329i			0.835626i	−0.908533	+	0.417813i	$0.862797\pi$
$360$	−0.0177513	+	8.89722i	−0.000935575	+	0.468925i
$361$	14.3880			0.757265
$362$	−4.58723	+	7.93313i	−0.241100	+	0.416956i
$363$	−6.19716			−0.325267
$364$	2.66292	−	1.53272i	0.139575	−	0.0803363i
$365$			6.80719i			0.356305i
$366$	−12.7157	−	7.35271i	−0.664662	−	0.384332i
$367$	10.9260			0.570331			0.285166	−	0.958478i	$-0.407951\pi$
$367$	10.9260			0.570331			0.285166	+	0.958478i	$0.407951\pi$
$368$	−19.0577	−	11.0706i	−0.993449	−	0.577097i
$369$			2.53783i			0.132114i
$370$	41.4624	+	23.9751i	2.15553	+	1.24641i
$371$			0.00938027i			0.000486999i
$372$	−4.74736	−	8.24798i	−0.246139	−	0.427638i
$373$		−	14.1215i		−	0.731184i	−0.930775	−	0.365592i	$-0.880867\pi$
$373$		−	14.1215i		−	0.731184i	0.930775	−	0.365592i	$-0.119133\pi$
$374$	−0.992572	+	1.71655i	−0.0513247	+	0.0887605i
$375$			0.329971i			0.0170396i
$376$	0.0162760	−	8.15776i	0.000839368	−	0.420704i
$377$			7.45051i			0.383721i
$378$	−0.978299	+	1.69186i	−0.0503183	+	0.0870201i
$379$	14.1951			0.729152			0.364576	−	0.931174i	$-0.381214\pi$
$379$	14.1951			0.729152			0.364576	+	0.931174i	$0.381214\pi$
$380$	−6.73987	−	11.7097i	−0.345748	−	0.600697i
$381$		−	10.8899i		−	0.557904i
$382$	−3.08319	+	5.33205i	−0.157750	+	0.272811i
$383$	−13.5159			−0.690628			−0.345314	−	0.938487i	$-0.612228\pi$
$383$	−13.5159			−0.690628			−0.345314	+	0.938487i	$0.612228\pi$
$384$	−5.70241	+	9.77152i	−0.291000	+	0.498651i
$385$			9.52677i			0.485529i
$386$	6.86626	−	11.8745i	0.349484	−	0.604395i
$387$	−5.51787			−0.280489
$388$	−8.87969	+	5.11096i	−0.450798	+	0.259469i
$389$	13.3769			0.678235			0.339118	−	0.940744i	$-0.389872\pi$
$389$	13.3769			0.678235			0.339118	+	0.940744i	$0.389872\pi$
$390$	2.47556	−	4.28121i	0.125355	−	0.216788i
$391$			3.52514i			0.178274i
$392$	−14.3974	−	0.0287250i	−0.727179	−	0.00145083i
$393$		−	6.00800i		−	0.303064i
$394$	11.5739	+	6.69243i	0.583082	+	0.337160i
$395$			5.43658i			0.273544i
$396$	−2.18649	−	3.79877i	−0.109875	−	0.190895i
$397$	−12.0757			−0.606064			−0.303032	−	0.952980i	$-0.597999\pi$
$397$	−12.0757			−0.606064			−0.303032	+	0.952980i	$0.597999\pi$
$398$	17.6616	+	10.2126i	0.885297	+	0.511912i
$399$		−	2.96777i		−	0.148574i
$400$	9.83528	−	16.9310i	0.491764	−	0.846551i
$401$			28.7633i			1.43637i	0.695853	+	0.718184i	$0.255027\pi$
$401$			28.7633i			1.43637i	−0.695853	+	0.718184i	$0.744973\pi$
$402$	−5.95173	+	9.92859i	−0.296845	+	0.495193i
$403$			5.28971i			0.263499i
$404$	10.9499	−	6.30251i	0.544777	−	0.313562i
$405$			3.14565i			0.156309i
$406$	−6.55662	+	11.3390i	−0.325399	+	0.562744i
$407$	−23.5947			−1.16955
$408$	1.80956	+	0.00361034i	0.0895864	+	0.000178738i
$409$		−	17.2602i		−	0.853460i	−0.904379	−	0.426730i	$-0.859665\pi$
$409$		−	17.2602i		−	0.853460i	0.904379	−	0.426730i	$-0.140335\pi$
$410$	5.65142	−	9.77353i	0.279104	−	0.482680i
$411$		−	11.6091i		−	0.572636i
$412$	−31.5664	+	18.1689i	−1.55516	+	0.895119i
$413$			0.165120i			0.00812501i
$414$	−6.74569	−	3.90061i	−0.331533	−	0.191705i
$415$	−19.8636			−0.975067
$416$	5.45650	−	3.12617i	0.267527	−	0.153273i
$417$	10.4089			0.509726
$418$	5.76197	+	3.33179i	0.281827	+	0.162963i
$419$			7.97231i			0.389473i	0.980856	+	0.194737i	$0.0623852\pi$
$419$			7.97231i			0.389473i	−0.980856	+	0.194737i	$0.937615\pi$
$420$	7.53512	−	4.33705i	0.367676	−	0.211626i
$421$	21.6191			1.05365			0.526825	−	0.849974i	$-0.323382\pi$
$421$	21.6191			1.05365			0.526825	+	0.849974i	$0.323382\pi$
$422$	−1.18933	−	0.687713i	−0.0578955	−	0.0334774i
$423$		−	2.88421i		−	0.140235i
$424$	−3.83043e−5		0.0191987i	−1.86022e−6		0.000932373i
$425$	−3.13177			−0.151913
$426$	−6.45457	−	3.73227i	−0.312725	−	0.180829i
$427$			14.3532i			0.694600i
$428$	−29.1987	+	16.8061i	−1.41137	+	0.812355i
$429$			2.43628i			0.117625i
$430$	21.2501	+	12.2876i	1.02477	+	0.592560i
$431$		−	0.433829i		−	0.0208968i	−0.999945	−	0.0104484i	$-0.996674\pi$
$431$		−	0.433829i		−	0.0208968i	0.999945	−	0.0104484i	$-0.00332589\pi$
$432$	−2.00921	+	3.45877i	−0.0966681	+	0.166410i
$433$			28.9747i			1.39244i	0.717831	+	0.696218i	$0.245135\pi$
$433$			28.9747i			1.39244i	−0.717831	+	0.696218i	$0.754865\pi$
$434$	−4.65506	+	8.05044i	−0.223450	+	0.386433i
$435$			21.0823i			1.01082i
$436$	21.6497	−	12.4611i	1.03683	−	0.596779i
$437$	11.8329			0.566044
$438$	−1.53194	+	2.64933i	−0.0731991	+	0.126590i
$439$		−	14.7047i		−	0.701817i	−0.936410	−	0.350909i	$-0.885873\pi$
$439$		−	14.7047i		−	0.701817i	0.936410	−	0.350909i	$-0.114127\pi$
$440$	−0.0389026	+	19.4986i	−0.00185461	+	0.929559i
$441$	−5.09026			−0.242394
$442$	−0.870733	−	0.503490i	−0.0414165	−	0.0239486i
$443$	−31.2739			−1.48587			−0.742935	−	0.669364i	$-0.766567\pi$
$443$	−31.2739			−1.48587			−0.742935	+	0.669364i	$0.766567\pi$
$444$	10.7415	+	18.6620i	0.509767	+	0.885661i
$445$		−	41.5225i		−	1.96835i
$446$	−1.72289	−	0.996237i	−0.0815810	−	0.0471732i
$447$	18.0368			0.853110
$448$	11.0554	+	0.0441144i	0.522317	+	0.00208421i
$449$	−19.0234			−0.897770			−0.448885	−	0.893590i	$-0.648179\pi$
$449$	−19.0234			−0.897770			−0.448885	+	0.893590i	$0.648179\pi$
$450$	3.46535	−	5.99295i	0.163358	−	0.282510i
$451$			5.56175i			0.261893i
$452$	−11.5079	+	6.62372i	−0.541288	+	0.311554i
$453$		−	22.5460i		−	1.05930i
$454$	−1.29163	−	0.746867i	−0.0606191	−	0.0350522i
$455$	−4.83253			−0.226553
$456$	0.0121189	−	6.07418i	0.000567519	−	0.284449i
$457$	−33.5199			−1.56800			−0.783998	−	0.620764i	$-0.786823\pi$
$457$	−33.5199			−1.56800			−0.783998	+	0.620764i	$0.786823\pi$
$458$	23.9864	+	13.8698i	1.12081	+	0.648096i
$459$	0.639776			0.0298622
$460$	17.2924	+	30.0436i	0.806264	+	1.40079i
$461$	11.4031			0.531093			0.265547	−	0.964098i	$-0.414448\pi$
$461$	11.4031			0.531093			0.265547	+	0.964098i	$0.414448\pi$
$462$	−2.14398	+	3.70778i	−0.0997469	+	0.172502i
$463$	38.3973			1.78447			0.892236	−	0.451569i	$-0.149135\pi$
$463$	38.3973			1.78447			0.892236	+	0.451569i	$0.149135\pi$
$464$	−13.4658	+	23.1809i	−0.625136	+	1.07615i
$465$			14.9680i			0.694125i
$466$	−9.50071	−	5.49366i	−0.440112	−	0.254489i
$467$		−	12.4776i		−	0.577394i	−0.957420	−	0.288697i	$-0.906778\pi$
$467$		−	12.4776i		−	0.577394i	0.957420	−	0.288697i	$-0.0932220\pi$
$468$	1.92696	−	1.10911i	0.0890735	−	0.0512688i
$469$	11.3102	+	0.178192i	0.522256	+	0.00822812i
$470$	−6.42276	+	11.1075i	−0.296260	+	0.512350i
$471$	15.4129			0.710187
$472$	−0.000674267		0.337953i	−3.10356e−5		0.0155555i
$473$	−12.0926			−0.556019
$474$	−1.22349	+	2.11590i	−0.0561968	+	0.0971864i
$475$			10.5125i			0.482346i
$476$	−0.882089	−	1.53253i	−0.0404305	−	0.0702433i
$477$			0.00678779i			0.000310792i
$478$	−9.18183	+	15.8790i	−0.419967	+	0.726288i
$479$		−	5.48777i		−	0.250743i	−0.992110	−	0.125371i	$-0.959988\pi$
$479$		−	5.48777i		−	0.250743i	0.992110	−	0.125371i	$-0.0400122\pi$
$480$	15.4400	−	8.84594i	0.704735	−	0.403760i
$481$		−	11.9686i		−	0.545721i
$482$	7.86920	−	13.6089i	0.358432	−	0.619871i
$483$			7.61438i			0.346466i
$484$	6.18288	+	10.7420i	0.281040	+	0.488274i
$485$	16.1144			0.731718
$486$	−0.707921	+	1.22427i	−0.0321120	+	0.0555342i
$487$	−30.2314			−1.36992			−0.684958	−	0.728583i	$-0.740179\pi$
$487$	−30.2314			−1.36992			−0.684958	+	0.728583i	$0.740179\pi$
$488$	−0.0586114	+	29.3769i	−0.00265321	+	1.32983i
$489$		−	4.46026i		−	0.201700i
$490$	19.6033	+	11.3354i	0.885587	+	0.512079i
$491$		−	26.7584i		−	1.20759i	−0.797140	−	0.603795i	$-0.793655\pi$
$491$		−	26.7584i		−	1.20759i	0.797140	−	0.603795i	$-0.206345\pi$
$492$	4.39902	−	2.53198i	0.198323	−	0.114151i
$493$	4.28782			0.193114
$494$	−1.69008	+	2.92281i	−0.0760401	+	0.131503i
$495$			6.89381i			0.309853i
$496$	−9.56047	+	16.4579i	−0.429278	+	0.738984i
$497$			7.28577i			0.326811i
$498$	−7.73084	−	4.47026i	−0.346427	−	0.200317i
$499$	28.4951			1.27561			0.637807	−	0.770196i	$-0.279842\pi$
$499$	28.4951			1.27561			0.637807	+	0.770196i	$0.279842\pi$
$500$	0.571964	−	0.329210i	0.0255790	−	0.0147227i
$501$		−	3.92760i		−	0.175472i
$502$	−11.5681	+	20.0058i	−0.516310	+	0.892903i
$503$	−38.6829			−1.72478			−0.862392	−	0.506241i	$-0.831035\pi$
$503$	−38.6829			−1.72478			−0.862392	+	0.506241i	$0.831035\pi$
$504$	3.90869	+	0.00779841i	0.174107	+	0.000347369i
$505$	−19.8713			−0.884261
$506$	−14.7834	−	8.54834i	−0.657204	−	0.380020i
$507$	11.7642			0.522465
$508$	−18.8763	+	10.8648i	−0.837499	+	0.482046i
$509$	26.3881			1.16963			0.584816	−	0.811166i	$-0.301167\pi$
$509$	26.3881			1.16963			0.584816	+	0.811166i	$0.301167\pi$
$510$	−2.46387	−	1.42470i	−0.109102	−	0.0630867i
$511$	2.99050			0.132292
$512$	22.6270	+	0.135434i	0.999982	+	0.00598540i
$513$		−	2.14755i		−	0.0948166i
$514$	−14.3103	+	24.7482i	−0.631202	+	1.09160i
$515$	57.2851			2.52428
$516$	5.50515	+	9.56456i	0.242351	+	0.421056i
$517$		−	6.32085i		−	0.277991i
$518$	10.5326	−	18.2151i	0.462777	−	0.800324i
$519$	14.8244			0.650720
$520$	−9.89082	−	0.0197337i	−0.433741	−	0.000865378i
$521$			8.86494i			0.388380i	0.980964	+	0.194190i	$0.0622078\pi$
$521$			8.86494i			0.388380i	−0.980964	+	0.194190i	$0.937792\pi$
$522$	−4.74453	+	8.20516i	−0.207662	+	0.359130i
$523$			3.50424i			0.153230i	0.997061	+	0.0766148i	$0.0244112\pi$
$523$			3.50424i			0.153230i	−0.997061	+	0.0766148i	$0.975589\pi$
$524$	−10.4141	+	5.99416i	−0.454944	+	0.261856i
$525$	−6.76470			−0.295236
$526$	−34.1030	−	19.7196i	−1.48696	−	0.859816i
$527$	3.04426			0.132610
$528$	−4.40325	+	7.58002i	−0.191627	+	0.329878i
$529$	−7.35958			−0.319982
$530$	0.0151155	−	0.0261407i	0.000656577	−	0.00113548i
$531$			0.119485i			0.00518519i
$532$	−5.14427	+	2.96093i	−0.223032	+	0.128372i
$533$	−2.82124			−0.122202
$534$	9.34454	−	16.1604i	0.404378	−	0.699329i
$535$	52.9883			2.29089
$536$	23.1480	+	0.410893i	0.999842	+	0.0177479i
$537$	7.74057			0.334030
$538$	7.51612	−	12.9983i	0.324043	−	0.560398i
$539$	−11.1555			−0.480502
$540$	5.45260	−	3.13840i	0.234643	−	0.135055i
$541$			30.5009i			1.31134i	0.755049	+	0.655669i	$0.227613\pi$
$541$			30.5009i			1.31134i	−0.755049	+	0.655669i	$0.772387\pi$
$542$	3.98583	−	6.89307i	0.171206	−	0.296083i
$543$	6.47986			0.278078
$544$	−1.79913	−	3.14025i	−0.0771370	−	0.134637i
$545$	−39.2889			−1.68295
$546$	−1.88080	−	1.08755i	−0.0804909	−	0.0465429i
$547$	−24.1720			−1.03352			−0.516760	−	0.856130i	$-0.672862\pi$
$547$	−24.1720			−1.03352			−0.516760	+	0.856130i	$0.672862\pi$
$548$	−20.1230	+	11.5824i	−0.859612	+	0.494774i
$549$			10.3863i			0.443278i
$550$	7.59444	−	13.1338i	0.323828	−	0.560026i
$551$		−	14.3930i		−	0.613163i
$552$	−0.0310933	+	15.5845i	−0.00132342	+	0.663319i
$553$	2.38837			0.101564
$554$	10.4739	−	18.1135i	0.444993	−	0.769568i
$555$		−	33.8669i		−	1.43757i
$556$	−10.3849	−	18.0426i	−0.440418	−	0.765175i
$557$	25.5094			1.08087			0.540435	−	0.841386i	$-0.318260\pi$
$557$	25.5094			1.08087			0.540435	+	0.841386i	$0.318260\pi$
$558$	−3.36852	+	5.82550i	−0.142601	+	0.246613i
$559$		−	6.13408i		−	0.259444i
$560$	−15.0355	−	8.73417i	−0.635366	−	0.369086i
$561$	1.40209			0.0591964
$562$	−15.0816	−	8.72077i	−0.636181	−	0.367864i
$563$	−27.1023			−1.14222			−0.571112	−	0.820872i	$-0.693488\pi$
$563$	−27.1023			−1.14222			−0.571112	+	0.820872i	$0.693488\pi$
$564$	−4.99943	+	2.87756i	−0.210514	+	0.121167i
$565$	20.8840			0.878597
$566$	−9.18485	−	5.31103i	−0.386068	−	0.223239i
$567$	1.38193			0.0580357
$568$	−0.0297515	+	14.9119i	−0.00124834	+	0.625689i
$569$	−26.4581			−1.10918			−0.554590	−	0.832123i	$-0.687125\pi$
$569$	−26.4581			−1.10918			−0.554590	+	0.832123i	$0.687125\pi$
$570$	−4.78232	+	8.27051i	−0.200309	+	0.346413i
$571$		−	11.9001i		−	0.498002i	−0.968503	−	0.249001i	$-0.919898\pi$
$571$		−	11.9001i		−	0.498002i	0.968503	−	0.249001i	$-0.0801022\pi$
$572$	4.22299	−	2.43066i	0.176572	−	0.101631i
$573$	4.35527			0.181944
$574$	−4.29366	−	2.48276i	−0.179214	−	0.103628i
$575$		−	26.9718i		−	1.12480i
$576$	7.99994	+	0.0319223i	0.333331	+	0.00133009i
$577$			41.8269i			1.74128i	0.491924	+	0.870638i	$0.336294\pi$
$577$			41.8269i			1.74128i	−0.491924	+	0.870638i	$0.663706\pi$
$578$	11.7449	−	20.3116i	0.488523	−	0.844849i
$579$	−9.69919			−0.403085
$580$	36.5437	−	21.0337i	1.51739	−	0.873378i
$581$			8.72639i			0.362032i
$582$	6.27167	+	3.62651i	0.259969	+	0.150324i
$583$			0.0148757i			0.000616089i
$584$	6.12071	+	0.0122117i	0.253277	+	0.000505325i
$585$	−3.49694			−0.144581
$586$	4.25870	−	7.36498i	0.175925	−	0.304244i
$587$	5.82667			0.240492			0.120246	−	0.992744i	$-0.461632\pi$
$587$	5.82667			0.240492			0.120246	+	0.992744i	$0.461632\pi$
$588$	5.07853	+	8.82336i	0.209435	+	0.363869i
$589$		−	10.2187i		−	0.421056i
$590$	0.266077	−	0.460152i	0.0109542	−	0.0189441i
$591$		−	9.45364i		−	0.388871i
$592$	21.6317	−	37.2381i	0.889057	−	1.53048i
$593$		−	36.1548i		−	1.48470i	−0.670013	−	0.742349i	$-0.733711\pi$
$593$		−	36.1548i		−	1.48470i	0.670013	−	0.742349i	$-0.266289\pi$
$594$	−1.55144	+	2.68304i	−0.0636562	+	0.110087i
$595$			2.78115i			0.114016i
$596$	−17.9952	−	31.2646i	−0.737112	−	1.28065i
$597$		−	14.4262i		−	0.590425i
$598$	4.33621	−	7.49902i	0.177321	−	0.306658i
$599$	7.36156			0.300785			0.150393	−	0.988626i	$-0.451946\pi$
$599$	7.36156			0.300785			0.150393	+	0.988626i	$0.451946\pi$
$600$	−13.8454	−	0.0276237i	−0.565237	−	0.00112773i
$601$	−7.88351			−0.321575			−0.160788	−	0.986989i	$-0.551403\pi$
$601$	−7.88351			−0.321575			−0.160788	+	0.986989i	$0.551403\pi$
$602$	5.39813	−	9.33548i	0.220011	−	0.380486i
$603$	8.18434	+	0.128944i	0.333292	+	0.00525100i
$604$	−39.0807	+	22.4940i	−1.59017	+	0.915268i
$605$		−	19.4941i		−	0.792548i
$606$	−7.73383	−	4.47199i	−0.314165	−	0.181662i
$607$		−	31.0113i		−	1.25871i	−0.777118	−	0.629355i	$-0.783319\pi$
$607$		−	31.0113i		−	1.25871i	0.777118	−	0.629355i	$-0.216681\pi$
$608$	−10.5409	+	6.03917i	−0.427492	+	0.244921i
$609$	9.26179			0.375307
$610$	23.1290	−	39.9992i	0.936467	−	1.61952i
$611$	3.20630			0.129713
$612$	−0.638302	−	1.10897i	−0.0258018	−	0.0448277i
$613$	−26.0434			−1.05188			−0.525941	−	0.850521i	$-0.676287\pi$
$613$	−26.0434			−1.05188			−0.525941	+	0.850521i	$0.676287\pi$
$614$	15.1165	+	8.74092i	0.610052	+	0.352755i
$615$	−7.98312			−0.321910
$616$	8.56603	+	0.0170905i	0.345135	+	0.000688596i
$617$	24.7270			0.995472			0.497736	−	0.867329i	$-0.334165\pi$
$617$	24.7270			0.995472			0.497736	+	0.867329i	$0.334165\pi$
$618$	22.2951	+	12.8919i	0.896842	+	0.518587i
$619$			21.3340i			0.857487i	0.903426	+	0.428743i	$0.141044\pi$
$619$			21.3340i			0.857487i	−0.903426	+	0.428743i	$0.858956\pi$
$620$	25.9453	−	14.9335i	1.04199	−	0.599745i
$621$			5.50995i			0.221107i
$622$	13.2959	−	22.9938i	0.533116	−	0.921968i
$623$	−18.2415			−0.730829
$624$	−3.84503	−	2.23359i	−0.153924	−	0.0894150i
$625$	−25.5135			−1.02054
$626$	41.8761	+	24.2143i	1.67371	+	0.967799i
$627$		−	4.70644i		−	0.187957i
$628$	−15.3773	−	26.7163i	−0.613623	−	1.06610i
$629$	−6.88801			−0.274643
$630$	−5.32201	−	3.07738i	−0.212034	−	0.122606i
$631$	34.0951			1.35731			0.678653	−	0.734459i	$-0.262564\pi$
$631$	34.0951			1.35731			0.678653	+	0.734459i	$0.262564\pi$
$632$	4.88832	+	0.00975293i	0.194447	+	0.000387951i
$633$			0.971455i			0.0386119i
$634$	12.1736	−	21.0529i	0.483475	−	0.836118i
$635$	34.2557			1.35939
$636$	0.0117658	−	0.00677215i	0.000466545	−	0.000268533i
$637$		−	5.65872i		−	0.224207i
$638$	−10.3978	+	17.9819i	−0.411653	+	0.711911i
$639$			5.27216i			0.208563i
$640$	−30.7378	−	17.9378i	−1.21502	−	0.709052i
$641$			27.8415i			1.09967i	0.835273	+	0.549836i	$0.185310\pi$
$641$			27.8415i			1.09967i	−0.835273	+	0.549836i	$0.814690\pi$
$642$	20.6229	+	11.9249i	0.813919	+	0.470638i
$643$			4.70790i			0.185662i	0.995682	+	0.0928308i	$0.0295916\pi$
$643$			4.70790i			0.185662i	−0.995682	+	0.0928308i	$0.970408\pi$
$644$	13.1986	−	7.59683i	0.520098	−	0.299357i
$645$		−	17.3573i		−	0.683442i
$646$	1.68209	+	0.972649i	0.0661811	+	0.0382684i
$647$	−40.9256			−1.60895			−0.804475	−	0.593986i	$-0.797553\pi$
$647$	−40.9256			−1.60895			−0.804475	+	0.593986i	$0.797553\pi$
$648$	2.82842	+	0.00564312i	0.111111	+	0.000221683i
$649$			0.261855i			0.0102787i
$650$	6.66221	+	3.85234i	0.261313	+	0.151101i
$651$	6.57568			0.257721
$652$	−7.73132	+	4.44998i	−0.302782	+	0.174275i
$653$		−	1.64074i		−	0.0642071i	−0.999485	−	0.0321036i	$-0.989779\pi$
$653$		−	1.64074i		−	0.0642071i	0.999485	−	0.0321036i	$-0.0102206\pi$
$654$	−15.2911	−	8.84187i	−0.597928	−	0.345744i
$655$	18.8991			0.738448
$656$	−8.77777	−	5.09903i	−0.342714	−	0.199084i
$657$	2.16400			0.0844258
$658$	4.87969	+	2.82162i	0.190230	+	0.109998i
$659$			1.17743i			0.0458661i	0.999737	+	0.0229331i	$0.00730046\pi$
$659$			1.17743i			0.0458661i	−0.999737	+	0.0229331i	$0.992700\pi$
$660$	11.9496	−	6.87792i	0.465137	−	0.267723i
$661$		−	6.28049i		−	0.244283i	−0.992513	−	0.122141i	$-0.961024\pi$
$661$		−	6.28049i		−	0.244283i	0.992513	−	0.122141i	$-0.0389762\pi$
$662$	21.4382	−	37.0751i	0.833219	−	1.44096i
$663$			0.711223i			0.0276216i
$664$	−0.0356343	+	17.8604i	−0.00138288	+	0.693120i
$665$	9.33555			0.362017
$666$	7.62168	−	13.1809i	0.295334	−	0.510749i
$667$			36.9280i			1.42986i
$668$	−6.80803	+	3.91855i	−0.263410	+	0.151613i
$669$			1.40727i			0.0544083i
$670$	−31.2319	−	18.7220i	−1.20659	−	0.723296i
$671$			22.7620i			0.878719i
$672$	−3.88616	−	6.78302i	−0.149912	−	0.261660i
$673$		−	15.5875i		−	0.600853i	−0.953805	−	0.300426i	$-0.902871\pi$
$673$		−	15.5875i		−	0.600853i	0.953805	−	0.300426i	$-0.0971289\pi$
$674$	33.9601	+	19.6370i	1.30809	+	0.756389i
$675$	−4.89510			−0.188413
$676$	−11.7371	−	20.3918i	−0.451426	−	0.784299i
$677$		−	4.46472i		−	0.171593i	−0.996313	−	0.0857967i	$-0.972656\pi$
$677$		−	4.46472i		−	0.171593i	0.996313	−	0.0857967i	$-0.0273435\pi$
$678$	8.12798	+	4.69990i	0.312153	+	0.180499i
$679$		−	7.07931i		−	0.271679i
$680$	−0.0113568	+	5.69223i	−0.000435515	+	0.218287i
$681$			1.05501i			0.0404282i
$682$	−7.38223	+	12.7668i	−0.282680	+	0.488866i
$683$	−10.6789			−0.408616			−0.204308	−	0.978907i	$-0.565494\pi$
$683$	−10.6789			−0.408616			−0.204308	+	0.978907i	$0.565494\pi$
$684$	−3.72252	+	2.14260i	−0.142334	+	0.0819244i
$685$	36.5182			1.39529
$686$	11.8279	−	20.4551i	0.451591	−	0.780979i
$687$		−	19.5924i		−	0.747495i
$688$	11.0865	−	19.0850i	0.422671	−	0.727610i
$689$	−0.00754582			−0.000287473
$690$	12.2700	−	21.2196i	0.467109	−	0.807816i
$691$		−	36.5726i		−	1.39129i	−0.718387	−	0.695643i	$-0.755119\pi$
$691$		−	36.5726i		−	1.39129i	0.718387	−	0.695643i	$-0.244881\pi$
$692$	−14.7903	−	25.6963i	−0.562241	−	0.976829i
$693$	3.02855			0.115045
$694$	9.73997	−	16.8442i	0.369724	−	0.639399i
$695$			32.7427i			1.24200i
$696$	18.9562	+	0.0378205i	0.718535	+	0.00143358i
$697$			1.62364i			0.0614999i
$698$	−19.8104	+	34.2600i	−0.749836	+	1.29676i
$699$			7.76027i			0.293521i
$700$	6.74911	+	11.7258i	0.255092	+	0.443193i
$701$			52.7118i			1.99090i	0.0952943	+	0.995449i	$0.469621\pi$
$701$			52.7118i			1.99090i	−0.0952943	+	0.995449i	$0.530379\pi$
$702$	−1.36100	−	0.786978i	−0.0513675	−	0.0297026i
$703$			23.1211i			0.872029i
$704$	17.5322	+	0.0699588i	0.660768	+	0.00263667i
$705$	9.07271			0.341698
$706$	−15.6414	−	9.04443i	−0.588671	−	0.340392i
$707$			8.72976i			0.328317i
$708$	0.207112	−	0.119209i	0.00778376	−	0.00448016i
$709$	−30.2718			−1.13688			−0.568441	−	0.822724i	$-0.692453\pi$
$709$	−30.2718			−1.13688			−0.568441	+	0.822724i	$0.692453\pi$
$710$	11.7404	−	20.3038i	0.440610	−	0.761988i
$711$	1.72829			0.0648158
$712$	−37.3351	−	0.0744891i	−1.39919	−	0.00279160i
$713$			26.2181i			0.981877i
$714$	−0.625892	+	1.08241i	−0.0234234	+	0.0405083i
$715$	−7.66367			−0.286605
$716$	−7.72273	−	13.4174i	−0.288612	−	0.501430i
$717$	12.9701			0.484378
$718$	−19.3838	−	11.2084i	−0.723395	−	0.418294i
$719$		−	31.4605i		−	1.17328i	−0.809849	−	0.586639i	$-0.800451\pi$
$719$		−	31.4605i		−	1.17328i	0.809849	−	0.586639i	$-0.199549\pi$
$720$	−10.8801	−	6.32026i	−0.405476	−	0.235542i
$721$		−	25.1662i		−	0.937239i
$722$	−10.1856	+	17.6149i	−0.379068	+	0.655559i
$723$	−11.1159			−0.413406
$724$	−6.46493	−	11.2321i	−0.240267	−	0.417436i
$725$	−32.8073			−1.21843
$726$	4.38710	−	7.58703i	0.162821	−	0.281581i
$727$	12.3523			0.458120			0.229060	−	0.973412i	$-0.426435\pi$
$727$	12.3523			0.458120			0.229060	+	0.973412i	$0.426435\pi$
$728$	−0.00866930	+	4.34519i	−0.000321306	+	0.161043i
$729$	1.00000			0.0370370
$730$	−8.33387	−	4.81895i	−0.308450	−	0.178357i
$731$	−3.53020			−0.130569
$732$	18.0035	−	10.3624i	0.665427	−	0.383005i
$733$			34.5045i			1.27445i	0.770677	+	0.637226i	$0.219918\pi$
$733$			34.5045i			1.27445i	−0.770677	+	0.637226i	$0.780082\pi$
$734$	−7.73473	+	13.3764i	−0.285494	+	0.493732i
$735$		−	16.0122i		−	0.590618i
$736$	27.0448	−	15.4947i	0.996885	−	0.571141i
$737$	17.9363	+	0.282585i	0.660691	+	0.0104092i
$738$	−3.10700	−	1.79658i	−0.114370	−	0.0661331i
$739$	−10.6844			−0.393032			−0.196516	−	0.980501i	$-0.562963\pi$
$739$	−10.6844			−0.393032			−0.196516	+	0.980501i	$0.562963\pi$
$740$	−58.7042	+	33.7889i	−2.15801	+	1.24210i
$741$	2.38738			0.0877025
$742$	−0.0114840	−	0.00664049i	−0.000421592	−	0.000243780i
$743$			34.7212i			1.27380i	0.770947	+	0.636899i	$0.219783\pi$
$743$			34.7212i			1.27380i	−0.770947	+	0.636899i	$0.780217\pi$
$744$	13.4585	+	0.0268518i	0.493414	+	0.000984435i
$745$			56.7374i			2.07870i
$746$	17.2886	+	9.99691i	0.632981	+	0.366013i
$747$			6.31463i			0.231040i
$748$	−1.39886	−	2.43036i	−0.0511475	−	0.0888628i
$749$		−	23.2786i		−	0.850581i
$750$	−0.403975	−	0.233593i	−0.0147511	−	0.00852962i
$751$			42.8498i			1.56361i	0.623522	+	0.781806i	$0.285701\pi$
$751$			42.8498i			1.56361i	−0.623522	+	0.781806i	$0.714299\pi$
$752$	9.97582	+	5.79498i	0.363781	+	0.211321i
$753$	16.3410			0.595497
$754$	−9.12147	−	5.27438i	−0.332184	−	0.192081i
$755$	70.9216			2.58110
$756$	−1.37875	−	2.39541i	−0.0501445	−	0.0871203i
$757$		−	28.2434i		−	1.02652i	−0.858232	−	0.513262i	$-0.828437\pi$
$757$		−	28.2434i		−	1.02652i	0.858232	−	0.513262i	$-0.171563\pi$
$758$	−10.0490	+	17.3787i	−0.364996	+	0.631222i
$759$			12.0753i			0.438304i
$760$	19.1072	+	0.0381218i	0.693092	+	0.00138282i
$761$	49.9893			1.81211			0.906056	−	0.423158i	$-0.139079\pi$
$761$	49.9893			1.81211			0.906056	+	0.423158i	$0.139079\pi$
$762$	13.3322	+	7.70916i	0.482974	+	0.279273i
$763$			17.2602i			0.624861i
$764$	−4.34523	−	7.54934i	−0.157205	−	0.273125i
$765$			2.01251i			0.0727625i
$766$	9.56816	−	16.5471i	0.345712	−	0.597872i
$767$	−0.132828			−0.00479615
$768$	−7.92617	−	13.8988i	−0.286011	−	0.501529i
$769$			14.2597i			0.514219i	0.966382	+	0.257110i	$0.0827702\pi$
$769$			14.2597i			0.514219i	−0.966382	+	0.257110i	$0.917230\pi$
$770$	−11.6634	−	6.74420i	−0.420319	−	0.243044i
$771$	20.2146			0.728011
$772$	9.67684	+	16.8124i	0.348277	+	0.605091i
$773$	−7.05027			−0.253580			−0.126790	−	0.991930i	$-0.540468\pi$
$773$	−7.05027			−0.253580			−0.126790	+	0.991930i	$0.540468\pi$
$774$	3.90622	−	6.75539i	0.140406	−	0.242817i
$775$	−23.2925			−0.836691
$776$	0.0289084	−	14.4893i	0.00103775	−	0.520137i
$777$	−14.8783			−0.533755
$778$	−9.46979	+	16.3770i	−0.339508	+	0.587143i
$779$	5.45012			0.195271
$780$	3.48888	+	6.06152i	0.124922	+	0.217037i
$781$			11.5541i			0.413440i
$782$	−4.31573	−	2.49552i	−0.154330	−	0.0892396i
$783$	6.70206			0.239512
$784$	10.2274	−	17.6060i	0.365264	−	0.628787i
$785$			48.4835i			1.73045i
$786$	7.35544	+	4.25319i	0.262360	+	0.151706i
$787$	35.9660			1.28205			0.641024	−	0.767521i	$-0.278510\pi$
$787$	35.9660			1.28205			0.641024	+	0.767521i	$0.278510\pi$
$788$	−16.3868	+	9.43186i	−0.583754	+	0.335996i
$789$			27.8557i			0.991688i
$790$	−6.65587	−	3.84867i	−0.236805	−	0.136930i
$791$		−	9.17467i		−	0.326214i
$792$	6.19859	+	0.0123671i	0.220257	+	0.000439446i
$793$	−11.5462			−0.410019
$794$	8.54867	−	14.7840i	0.303381	−	0.524665i
$795$	−0.0213520			−0.000757278
$796$	−25.0061	+	14.3930i	−0.886317	+	0.510145i
$797$	38.0086			1.34633			0.673166	−	0.739491i	$-0.264934\pi$
$797$	38.0086			1.34633			0.673166	+	0.739491i	$0.264934\pi$
$798$	3.63336	+	2.10095i	0.128620	+	0.0743727i
$799$		−	1.84525i		−	0.0652802i
$800$	13.7656	+	24.0269i	0.486688	+	0.849480i
$801$	−13.2000			−0.466398
$802$	−35.2141	−	20.3621i	−1.24345	−	0.719012i
$803$	4.74249			0.167359
$804$	−7.94197	−	14.3152i	−0.280092	−	0.504858i
$805$	−23.9522			−0.844203
$806$	−6.47606	−	3.74470i	−0.228109	−	0.131901i
$807$	−10.6172			−0.373742
$808$	−0.0356480	+	17.8673i	−0.00125409	+	0.628571i
$809$			7.19050i			0.252804i	0.991979	+	0.126402i	$0.0403430\pi$
$809$			7.19050i			0.252804i	−0.991979	+	0.126402i	$0.959657\pi$
$810$	−3.85114	−	2.22687i	−0.135315	−	0.0782443i
$811$	−32.8682			−1.15416			−0.577079	−	0.816689i	$-0.695807\pi$
$811$	−32.8682			−1.15416			−0.577079	+	0.816689i	$0.695807\pi$
$812$	−9.24044	−	16.0542i	−0.324276	−	0.563392i
$813$	−5.63033			−0.197464
$814$	16.7032	−	28.8864i	0.585446	−	1.01247i
$815$	14.0304			0.491464
$816$	−1.28544	+	2.21284i	−0.0449995	+	0.0774648i
$817$			11.8499i			0.414576i
$818$	21.1312	+	12.2188i	0.738834	+	0.427222i
$819$			1.53626i			0.0536812i
$820$	7.96472	+	13.8378i	0.278140	+	0.483236i
$821$	−19.4101			−0.677418			−0.338709	−	0.940891i	$-0.609990\pi$
$821$	−19.4101			−0.677418			−0.338709	+	0.940891i	$0.609990\pi$
$822$	14.2127	+	8.21834i	0.495726	+	0.286648i
$823$		−	42.2307i		−	1.47207i	−0.676944	−	0.736034i	$-0.736696\pi$
$823$		−	42.2307i		−	1.47207i	0.676944	−	0.736034i	$-0.263304\pi$
$824$	0.102766	−	51.5081i	0.00358003	−	1.79437i
$825$	−10.7278			−0.373494
$826$	−0.202152	−	0.116892i	−0.00703376	−	0.00406718i
$827$		−	13.9836i		−	0.486258i	−0.969994	−	0.243129i	$-0.921826\pi$
$827$		−	13.9836i		−	0.486258i	0.969994	−	0.243129i	$-0.0781738\pi$
$828$	9.55084	−	5.49725i	0.331915	−	0.191043i
$829$	30.0609			1.04406			0.522030	−	0.852927i	$-0.325175\pi$
$829$	30.0609			1.04406			0.522030	+	0.852927i	$0.325175\pi$
$830$	14.0619	−	24.3185i	0.488095	−	0.844108i
$831$	−14.7953			−0.513243
$832$	−0.0354872	+	8.89333i	−0.00123030	+	0.308321i
$833$	−3.25663			−0.112836
$834$	−7.36868	+	12.7433i	−0.255156	+	0.441266i
$835$	12.3549			0.427557
$836$	−8.15804	+	4.69559i	−0.282152	+	0.162400i
$837$	4.75833			0.164472
$838$	−9.76030	−	5.64377i	−0.337164	−	0.194961i
$839$		−	47.3646i		−	1.63521i	−0.575781	−	0.817604i	$-0.695302\pi$
$839$		−	47.3646i		−	1.63521i	0.575781	−	0.817604i	$-0.304698\pi$
$840$	−0.0245311	+	12.2953i	−0.000846402	+	0.424230i
$841$	15.9176			0.548883
$842$	−15.3046	+	26.4677i	−0.527431	+	0.912137i
$843$			12.3188i			0.424284i
$844$	1.68390	−	0.969216i	0.0579622	−	0.0333618i
$845$			37.0060i			1.27304i
$846$	3.53106	+	2.04179i	0.121400	+	0.0701983i
$847$	−8.56406			−0.294265
$848$	−0.0234774	−	0.0136381i	−0.000806217	−	0.000468334i
$849$			7.50228i			0.257478i
$850$	2.21705	−	3.83415i	0.0760441	−	0.131510i
$851$		−	59.3217i		−	2.03352i
$852$	9.13866	−	5.26001i	0.313085	−	0.180205i
$853$	13.1189			0.449183			0.224592	−	0.974453i	$-0.427895\pi$
$853$	13.1189			0.449183			0.224592	+	0.974453i	$0.427895\pi$
$854$	−17.5723	−	10.1609i	−0.601311	−	0.347700i
$855$	6.75544			0.231031
$856$	0.0950582	−	47.6447i	0.00324902	−	1.62846i
$857$		−	45.5182i		−	1.55487i	−0.628961	−	0.777436i	$-0.716520\pi$
$857$		−	45.5182i		−	1.55487i	0.628961	−	0.777436i	$-0.283480\pi$
$858$	−2.98267	−	1.72469i	−0.101827	−	0.0588800i
$859$		−	30.6691i		−	1.04642i	−0.852205	−	0.523208i	$-0.824735\pi$
$859$		−	30.6691i		−	1.04642i	0.852205	−	0.523208i	$-0.175265\pi$
$860$	−30.0867	+	17.3173i	−1.02595	+	0.590514i
$861$			3.50711i			0.119522i
$862$	0.531125	+	0.307116i	0.0180902	+	0.0104604i
$863$		−	25.2201i		−	0.858502i	−0.903185	−	0.429251i	$-0.858778\pi$
$863$		−	25.2201i		−	0.858502i	0.903185	−	0.429251i	$-0.141222\pi$
$864$	−2.81212	−	4.90836i	−0.0956703	−	0.166986i
$865$			46.6324i			1.58555i
$866$	−35.4730	−	20.5118i	−1.20542	−	0.697019i
$867$	−16.5907			−0.563449
$868$	−6.56053	−	11.3981i	−0.222679	−	0.386878i
$869$	3.78760			0.128486
$870$	−25.8105	−	14.9246i	−0.875059	−	0.505992i
$871$	−0.143344	+	9.09833i	−0.00485701	+	0.308285i
$872$	−0.0704821	+	35.3267i	−0.00238682	+	1.19631i
$873$		−	5.12276i		−	0.173379i
$874$	−8.37676	+	14.4867i	−0.283348	+	0.490020i
$875$			0.455997i			0.0154155i
$876$	−2.15901	−	3.75104i	−0.0729463	−	0.126736i
$877$	48.9065			1.65145			0.825727	−	0.564069i	$-0.190765\pi$
$877$	48.9065			1.65145			0.825727	+	0.564069i	$0.190765\pi$
$878$	18.0026	+	10.4098i	0.607558	+	0.351313i
$879$	−6.01579			−0.202908
$880$	−23.8441	−	13.8511i	−0.803784	−	0.466920i
$881$	−30.6112			−1.03132			−0.515658	−	0.856794i	$-0.672453\pi$
$881$	−30.6112			−1.03132			−0.515658	+	0.856794i	$0.672453\pi$
$882$	3.60351	−	6.23188i	0.121336	−	0.209838i
$883$	0.660511			0.0222280			0.0111140	−	0.999938i	$-0.496462\pi$
$883$	0.660511			0.0222280			0.0111140	+	0.999938i	$0.496462\pi$
$884$	1.23282	−	0.709584i	0.0414642	−	0.0238659i
$885$	−0.375857			−0.0126343
$886$	22.1395	−	38.2879i	0.743790	−	1.28631i
$887$			43.0586i			1.44577i	0.690971	+	0.722883i	$0.257183\pi$
$887$			43.0586i			1.44577i	−0.690971	+	0.722883i	$0.742817\pi$
$888$	−30.4516	−	0.0607554i	−1.02189	−	0.00203882i
$889$		−	15.0490i		−	0.504729i
$890$	50.8349	+	29.3946i	1.70399	+	0.985311i
$891$	2.19154			0.0734193
$892$	2.43934	−	1.40403i	0.0816750	−	0.0470103i
$893$	−6.19398			−0.207274
$894$	−12.7686	+	22.0820i	−0.427046	+	0.738531i
$895$			24.3491i			0.813901i
$896$	−7.88034	+	13.5036i	−0.263264	+	0.451123i
$897$	−6.12528			−0.204517
$898$	13.4671	−	23.2899i	0.449402	−	0.777193i
$899$	31.8906			1.06361
$900$	4.88382	+	8.48507i	0.162794	+	0.282836i
$901$			0.00434267i			0.000144675i
$902$	−6.80911	−	3.93728i	−0.226718	−	0.131097i
$903$	−7.62532			−0.253755
$904$	0.0374648	−	18.7779i	0.00124606	−	0.624545i
$905$			20.3834i			0.677566i
$906$	27.6024	+	15.9608i	0.917029	+	0.530261i
$907$			20.5458i			0.682211i	0.940025	+	0.341106i	$0.110801\pi$
$907$			20.5458i			0.682211i	−0.940025	+	0.341106i	$0.889199\pi$
$908$	1.82874	−	1.05258i	0.0606889	−	0.0349312i
$909$			6.31707i			0.209524i
$910$	3.42105	−	5.91634i	0.113407	−	0.196125i
$911$		−	14.9460i		−	0.495184i	−0.968864	−	0.247592i	$-0.920361\pi$
$911$		−	14.9460i		−	0.495184i	0.968864	−	0.247592i	$-0.0796393\pi$
$912$	7.42788	+	4.31487i	0.245962	+	0.142880i
$913$			13.8388i			0.457996i
$914$	23.7295	−	41.0376i	0.784901	−	1.35740i
$915$	−32.6718			−1.08010
$916$	−33.9610	+	19.5472i	−1.12210	+	0.645858i
$917$		−	8.30265i		−	0.274178i
$918$	−0.452911	+	0.783262i	−0.0149483	+	0.0258515i
$919$	−58.4298			−1.92742			−0.963711	−	0.266948i	$-0.913985\pi$
$919$	−58.4298			−1.92742			−0.963711	+	0.266948i	$0.913985\pi$
$920$	−49.0233	−	0.0978087i	−1.61625	−	0.00322466i
$921$		−	12.3473i		−	0.406858i
$922$	−8.07246	+	13.9605i	−0.265852	+	0.459763i
$923$	−5.86093			−0.192915
$924$	−3.02158	−	5.24963i	−0.0994025	−	0.172700i
$925$	52.7020			1.73283
$926$	−27.1822	+	47.0088i	−0.893264	+	1.54481i
$927$		−	18.2109i		−	0.598124i
$928$	−18.8470	−	32.8961i	−0.618683	−	1.07987i
$929$		−	8.57190i		−	0.281235i	−0.990064	−	0.140618i	$-0.955091\pi$
$929$		−	8.57190i		−	0.281235i	0.990064	−	0.140618i	$-0.0449088\pi$
$930$	−18.3250	−	10.5962i	−0.600899	−	0.347462i
$931$			10.9316i			0.358269i
$932$	13.4515	−	7.74239i	0.440619	−	0.253610i
$933$	−18.7816			−0.614881
$934$	15.2760	+	8.83315i	0.499846	+	0.289030i
$935$			4.41049i			0.144239i
$936$	−0.00627332	+	3.14429i	−0.000205050	+	0.102774i
$937$		−	37.0400i		−	1.21004i	−0.796209	−	0.605022i	$-0.793164\pi$
$937$		−	37.0400i		−	1.21004i	0.796209	−	0.605022i	$-0.206836\pi$
$938$	−8.22488	+	13.7206i	−0.268552	+	0.447995i
$939$		−	34.2048i		−	1.11623i
$940$	−9.05180	−	15.7264i	−0.295237	−	0.512940i
$941$		−	2.35672i		−	0.0768268i	−0.999262	−	0.0384134i	$-0.987770\pi$
$941$		−	2.35672i		−	0.0768268i	0.999262	−	0.0384134i	$-0.0122304\pi$
$942$	−10.9111	+	18.8696i	−0.355503	+	0.614804i
$943$	−13.9833			−0.455360
$944$	−0.413270	−	0.240070i	−0.0134508	−	0.00781360i
$945$			4.34707i			0.141410i
$946$	8.56062	−	14.8047i	0.278330	−	0.481342i
$947$			57.8744i			1.88066i	0.340259	+	0.940332i	$0.389485\pi$
$947$			57.8744i			1.88066i	−0.340259	+	0.940332i	$0.610515\pi$
$948$	−1.72430	−	2.99578i	−0.0560028	−	0.0972983i
$949$			2.40567i			0.0780913i
$950$	−12.8702	−	7.44200i	−0.417563	−	0.241451i
$951$	−17.1962			−0.557627
$952$	2.50068	+	0.00498924i	0.0810476	+	0.000161702i
$953$	−3.54818			−0.114937			−0.0574684	−	0.998347i	$-0.518303\pi$
$953$	−3.54818			−0.114937			−0.0574684	+	0.998347i	$0.518303\pi$
$954$	−0.00831012	−	0.00480522i	−0.000269050	−	0.000155575i
$955$			13.7002i			0.443327i
$956$	−12.9402	−	22.4822i	−0.418517	−	0.727125i
$957$	14.6878			0.474790
$958$	6.71854	+	3.88491i	0.217066	+	0.125516i
$959$		−	16.0430i		−	0.518056i
$960$	−0.100416	+	25.1650i	−0.00324092	+	0.812196i
$961$	−8.35834			−0.269624
$962$	14.6529	+	8.47283i	0.472427	+	0.273175i
$963$		−	16.8450i		−	0.542821i
$964$	11.0903	+	19.2681i	0.357195	+	0.620584i
$965$		−	30.5102i		−	0.982160i
$966$	−9.32209	−	5.39038i	−0.299933	−	0.173433i
$967$			17.9433i			0.577016i	0.957477	+	0.288508i	$0.0931592\pi$
$967$			17.9433i			0.577016i	−0.957477	+	0.288508i	$0.906841\pi$
$968$	−17.5282	−	0.0349714i	−0.563377	−	0.00112402i
$969$		−	1.37395i		−	0.0441377i
$970$	−11.4077	+	19.7285i	−0.366280	+	0.633443i
$971$		−	51.3581i		−	1.64816i	−0.566474	−	0.824080i	$-0.691693\pi$
$971$		−	51.3581i		−	1.64816i	0.566474	−	0.824080i	$-0.308307\pi$
$972$	−0.997695	−	1.73338i	−0.0320011	−	0.0555982i
$973$	14.3844			0.461142
$974$	21.4014	−	37.0115i	0.685746	−	1.18593i
$975$		−	5.44176i		−	0.174276i
$976$	−35.9239	−	20.8683i	−1.14990	−	0.667978i
$977$	−8.39664			−0.268632			−0.134316	−	0.990939i	$-0.542884\pi$
$977$	−8.39664			−0.268632			−0.134316	+	0.990939i	$0.542884\pi$
$978$	5.46058	+	3.15751i	0.174610	+	0.100966i
$979$	−28.9282			−0.924551
$980$	−27.7552	+	15.9753i	−0.886607	+	0.510312i
$981$			12.4899i			0.398772i
$982$	32.7596	+	18.9428i	1.04540	+	0.604490i
$983$	49.0943			1.56586			0.782932	−	0.622107i	$-0.213723\pi$
$983$	49.0943			1.56586			0.782932	+	0.622107i	$0.213723\pi$
$984$	−0.0143213	+	7.17805i	−0.000456546	+	0.228828i
$985$	29.7378			0.947526
$986$	−3.03544	+	5.24947i	−0.0966680	+	0.167177i
$987$		−	3.98578i		−	0.126869i
$988$	−2.38188	−	4.13823i	−0.0757776	−	0.131655i
$989$		−	30.4032i		−	0.966766i
$990$	−8.43991	−	4.88027i	−0.268238	−	0.155105i
$991$	50.3560			1.59961			0.799805	−	0.600260i	$-0.204936\pi$
$991$	50.3560			1.59961			0.799805	+	0.600260i	$0.204936\pi$
$992$	−13.3810	−	23.3556i	−0.424847	−	0.741540i
$993$	−30.2833			−0.961011
$994$	−8.91978	−	5.15775i	−0.282918	−	0.163594i
$995$	45.3797			1.43863
$996$	10.9457	−	6.30008i	0.346826	−	0.199626i
$997$	−9.29175			−0.294273			−0.147136	−	0.989116i	$-0.547006\pi$
$997$	−9.29175			−0.294273			−0.147136	+	0.989116i	$0.547006\pi$
$998$	−20.1723	+	34.8858i	−0.638541	+	1.10429i
$999$	−10.7663			−0.340630

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.e.b.535.12	yes	34
4.3	odd	2		804.2.e.a.535.24	yes	34
67.66	odd	2		804.2.e.a.535.23	✓	34
268.267	even	2	inner	804.2.e.b.535.11	yes	34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.e.a.535.23	✓	34	67.66	odd	2
804.2.e.a.535.24	yes	34	4.3	odd	2
804.2.e.b.535.11	yes	34	268.267	even	2	inner
804.2.e.b.535.12	yes	34	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:	\( N \)	\(=\)	\( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	804.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707921 + 1.22427i) q^{2} +1.00000 q^{3} +(-0.997695 - 1.73338i) q^{4} +3.14565i q^{5} +(-0.707921 + 1.22427i) q^{6} +1.38193 q^{7} +(2.82842 + 0.00564312i) q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+(-0.707921 + 1.22427i) q^{2} +1.00000 q^{3} +(-0.997695 - 1.73338i) q^{4} +3.14565i q^{5} +(-0.707921 + 1.22427i) q^{6} +1.38193 q^{7} +(2.82842 + 0.00564312i) q^{8} +1.00000 q^{9} +(-3.85114 - 2.22687i) q^{10} +2.19154 q^{11} +(-0.997695 - 1.73338i) q^{12} +1.11168i q^{13} +(-0.978299 + 1.69186i) q^{14} +3.14565i q^{15} +(-2.00921 + 3.45877i) q^{16} +0.639776 q^{17} +(-0.707921 + 1.22427i) q^{18} -2.14755i q^{19} +(5.45260 - 3.13840i) q^{20} +1.38193 q^{21} +(-1.55144 + 2.68304i) q^{22} +5.50995i q^{23} +(2.82842 + 0.00564312i) q^{24} -4.89510 q^{25} +(-1.36100 - 0.786978i) q^{26} +1.00000 q^{27} +(-1.37875 - 2.39541i) q^{28} +6.70206 q^{29} +(-3.85114 - 2.22687i) q^{30} +4.75833 q^{31} +(-2.81212 - 4.90836i) q^{32} +2.19154 q^{33} +(-0.452911 + 0.783262i) q^{34} +4.34707i q^{35} +(-0.997695 - 1.73338i) q^{36} -10.7663 q^{37} +(2.62919 + 1.52030i) q^{38} +1.11168i q^{39} +(-0.0177513 + 8.89722i) q^{40} +2.53783i q^{41} +(-0.978299 + 1.69186i) q^{42} -5.51787 q^{43} +(-2.18649 - 3.79877i) q^{44} +3.14565i q^{45} +(-6.74569 - 3.90061i) q^{46} -2.88421i q^{47} +(-2.00921 + 3.45877i) q^{48} -5.09026 q^{49} +(3.46535 - 5.99295i) q^{50} +0.639776 q^{51} +(1.92696 - 1.10911i) q^{52} +0.00678779i q^{53} +(-0.707921 + 1.22427i) q^{54} +6.89381i q^{55} +(3.90869 + 0.00779841i) q^{56} -2.14755i q^{57} +(-4.74453 + 8.20516i) q^{58} +0.119485i q^{59} +(5.45260 - 3.13840i) q^{60} +10.3863i q^{61} +(-3.36852 + 5.82550i) q^{62} +1.38193 q^{63} +(7.99994 + 0.0319223i) q^{64} -3.49694 q^{65} +(-1.55144 + 2.68304i) q^{66} +(8.18434 + 0.128944i) q^{67} +(-0.638302 - 1.10897i) q^{68} +5.50995i q^{69} +(-5.32201 - 3.07738i) q^{70} +5.27216i q^{71} +(2.82842 + 0.00564312i) q^{72} +2.16400 q^{73} +(7.62168 - 13.1809i) q^{74} -4.89510 q^{75} +(-3.72252 + 2.14260i) q^{76} +3.02855 q^{77} +(-1.36100 - 0.786978i) q^{78} +1.72829 q^{79} +(-10.8801 - 6.32026i) q^{80} +1.00000 q^{81} +(-3.10700 - 1.79658i) q^{82} +6.31463i q^{83} +(-1.37875 - 2.39541i) q^{84} +2.01251i q^{85} +(3.90622 - 6.75539i) q^{86} +6.70206 q^{87} +(6.19859 + 0.0123671i) q^{88} -13.2000 q^{89} +(-3.85114 - 2.22687i) q^{90} +1.53626i q^{91} +(9.55084 - 5.49725i) q^{92} +4.75833 q^{93} +(3.53106 + 2.04179i) q^{94} +6.75544 q^{95} +(-2.81212 - 4.90836i) q^{96} -5.12276i q^{97} +(3.60351 - 6.23188i) q^{98} +2.19154 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q + 34 q^{3} + 2 q^{4} + 4 q^{7} - 6 q^{8} + 34 q^{9}+O(q^{10}) \) 34 * q + 34 * q^3 + 2 * q^4 + 4 * q^7 - 6 * q^8 + 34 * q^9	\( 34 q + 34 q^{3} + 2 q^{4} + 4 q^{7} - 6 q^{8} + 34 q^{9} - 6 q^{10} + 2 q^{12} - 4 q^{14} + 2 q^{16} - 12 q^{20} + 4 q^{21} - 8 q^{22} - 6 q^{24} - 34 q^{25} + 10 q^{26} + 34 q^{27} - 8 q^{28} - 16 q^{29} - 6 q^{30} - 4 q^{31} + 2 q^{36} + 12 q^{37} + 26 q^{38} - 18 q^{40} - 4 q^{42} - 4 q^{43} + 26 q^{44} - 4 q^{46} + 2 q^{48} + 46 q^{49} - 18 q^{50} + 32 q^{52} + 14 q^{56} + 4 q^{58} - 12 q^{60} - 2 q^{62} + 4 q^{63} + 26 q^{64} - 8 q^{66} - 18 q^{67} - 34 q^{68} + 56 q^{70} - 6 q^{72} + 12 q^{73} + 22 q^{74} - 34 q^{75} - 32 q^{76} - 8 q^{77} + 10 q^{78} - 12 q^{79} - 2 q^{80} + 34 q^{81} + 26 q^{82} - 8 q^{84} + 6 q^{86} - 16 q^{87} - 28 q^{88} - 6 q^{90} - 46 q^{92} - 4 q^{93} + 32 q^{94} - 40 q^{95} - 40 q^{98}+O(q^{100}) \) 34 * q + 34 * q^3 + 2 * q^4 + 4 * q^7 - 6 * q^8 + 34 * q^9 - 6 * q^10 + 2 * q^12 - 4 * q^14 + 2 * q^16 - 12 * q^20 + 4 * q^21 - 8 * q^22 - 6 * q^24 - 34 * q^25 + 10 * q^26 + 34 * q^27 - 8 * q^28 - 16 * q^29 - 6 * q^30 - 4 * q^31 + 2 * q^36 + 12 * q^37 + 26 * q^38 - 18 * q^40 - 4 * q^42 - 4 * q^43 + 26 * q^44 - 4 * q^46 + 2 * q^48 + 46 * q^49 - 18 * q^50 + 32 * q^52 + 14 * q^56 + 4 * q^58 - 12 * q^60 - 2 * q^62 + 4 * q^63 + 26 * q^64 - 8 * q^66 - 18 * q^67 - 34 * q^68 + 56 * q^70 - 6 * q^72 + 12 * q^73 + 22 * q^74 - 34 * q^75 - 32 * q^76 - 8 * q^77 + 10 * q^78 - 12 * q^79 - 2 * q^80 + 34 * q^81 + 26 * q^82 - 8 * q^84 + 6 * q^86 - 16 * q^87 - 28 * q^88 - 6 * q^90 - 46 * q^92 - 4 * q^93 + 32 * q^94 - 40 * q^95 - 40 * q^98

Introduction

L-functions

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