LMFDB - Embedded newform 80.2.l.a.21.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [80,2,Mod(21,80)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(80, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("80.21");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 80 = 2^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	80.l (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.638803216170$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} + 4 x^{14} + 7 x^{12} - 8 x^{11} - 28 x^{10} + 28 x^{9} + 17 x^{8} + 56 x^{7} + \cdots + 256 $ x^16 - 4x^15 + 4x^14 + 7x^12 - 8x^11 - 28x^10 + 28x^9 + 17x^8 + 56x^7 - 112x^6 - 64x^5 + 112x^4 + 256x^2 - 512*x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{5} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			21.8
Root			$1.38652 - 0.278517i$ of defining polynomial
Character	$\chi$	$=$	80.21
Dual form			80.2.l.a.61.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.40727 - 0.139945i) q^{2} +(-2.32624 + 2.32624i) q^{3} +(1.96083 - 0.393883i) q^{4} +(0.707107 + 0.707107i) q^{5} +(-2.94811 + 3.59920i) q^{6} -0.982011i q^{7} +(2.70430 - 0.828709i) q^{8} -7.82281i q^{9} +O(q^{10})$	\(q+(1.40727 - 0.139945i) q^{2} +(-2.32624 + 2.32624i) q^{3} +(1.96083 - 0.393883i) q^{4} +(0.707107 + 0.707107i) q^{5} +(-2.94811 + 3.59920i) q^{6} -0.982011i q^{7} +(2.70430 - 0.828709i) q^{8} -7.82281i q^{9} +(1.09405 + 0.896135i) q^{10} +(-1.62645 - 1.62645i) q^{11} +(-3.64510 + 5.47764i) q^{12} +(-0.690562 + 0.690562i) q^{13} +(-0.137428 - 1.38196i) q^{14} -3.28980 q^{15} +(3.68971 - 1.54467i) q^{16} -2.19577 q^{17} +(-1.09477 - 11.0088i) q^{18} +(1.92659 - 1.92659i) q^{19} +(1.66503 + 1.10800i) q^{20} +(2.28440 + 2.28440i) q^{21} +(-2.51647 - 2.06124i) q^{22} +2.01442i q^{23} +(-4.36308 + 8.21864i) q^{24} +1.00000i q^{25} +(-0.875168 + 1.06845i) q^{26} +(11.2190 + 11.2190i) q^{27} +(-0.386797 - 1.92556i) q^{28} +(-5.27182 + 5.27182i) q^{29} +(-4.62965 + 0.460393i) q^{30} +0.435286 q^{31} +(4.97626 - 2.69014i) q^{32} +7.56703 q^{33} +(-3.09004 + 0.307288i) q^{34} +(0.694387 - 0.694387i) q^{35} +(-3.08127 - 15.3392i) q^{36} +(-5.79805 - 5.79805i) q^{37} +(2.44162 - 2.98086i) q^{38} -3.21283i q^{39} +(2.49822 + 1.32624i) q^{40} +3.93139i q^{41} +(3.53446 + 2.89508i) q^{42} +(-0.507592 - 0.507592i) q^{43} +(-3.82982 - 2.54856i) q^{44} +(5.53157 - 5.53157i) q^{45} +(0.281909 + 2.83484i) q^{46} -9.21960 q^{47} +(-4.98988 + 12.1765i) q^{48} +6.03565 q^{49} +(0.139945 + 1.40727i) q^{50} +(5.10789 - 5.10789i) q^{51} +(-1.08208 + 1.62608i) q^{52} +(6.29357 + 6.29357i) q^{53} +(17.3583 + 14.2182i) q^{54} -2.30015i q^{55} +(-0.813802 - 2.65565i) q^{56} +8.96345i q^{57} +(-6.68111 + 8.15665i) q^{58} +(-5.67778 - 5.67778i) q^{59} +(-6.45075 + 1.29580i) q^{60} +(-3.60301 + 3.60301i) q^{61} +(0.612566 - 0.0609163i) q^{62} -7.68209 q^{63} +(6.62648 - 4.48216i) q^{64} -0.976603 q^{65} +(10.6489 - 1.05897i) q^{66} +(4.53563 - 4.53563i) q^{67} +(-4.30553 + 0.864875i) q^{68} +(-4.68603 - 4.68603i) q^{69} +(0.880015 - 1.07437i) q^{70} +10.3984i q^{71} +(-6.48284 - 21.1552i) q^{72} -9.24439i q^{73} +(-8.97085 - 7.34803i) q^{74} +(-2.32624 - 2.32624i) q^{75} +(3.01887 - 4.53658i) q^{76} +(-1.59719 + 1.59719i) q^{77} +(-0.449621 - 4.52133i) q^{78} +15.4493 q^{79} +(3.70127 + 1.51677i) q^{80} -28.7280 q^{81} +(0.550180 + 5.53253i) q^{82} +(-0.683244 + 0.683244i) q^{83} +(5.37910 + 3.57953i) q^{84} +(-1.55264 - 1.55264i) q^{85} +(-0.785356 - 0.643285i) q^{86} -24.5271i q^{87} +(-5.74626 - 3.05055i) q^{88} +5.44401i q^{89} +(7.01030 - 8.55854i) q^{90} +(0.678140 + 0.678140i) q^{91} +(0.793445 + 3.94994i) q^{92} +(-1.01258 + 1.01258i) q^{93} +(-12.9745 + 1.29024i) q^{94} +2.72461 q^{95} +(-5.31808 + 17.8339i) q^{96} +5.54540 q^{97} +(8.49381 - 0.844662i) q^{98} +(-12.7234 + 12.7234i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{4} - 12 q^{6}+O(q^{10}) $ 16 * q - 4 * q^4 - 12 * q^6	$ 16 q - 4 q^{4} - 12 q^{6} + 4 q^{10} - 8 q^{11} - 12 q^{12} + 4 q^{14} - 8 q^{15} + 16 q^{16} - 8 q^{19} + 8 q^{20} - 20 q^{22} + 8 q^{24} - 16 q^{26} + 24 q^{27} - 4 q^{28} - 16 q^{29} + 16 q^{34} - 4 q^{36} - 16 q^{37} + 20 q^{38} + 60 q^{42} + 8 q^{43} + 40 q^{44} - 4 q^{46} - 40 q^{47} - 40 q^{48} - 16 q^{49} - 4 q^{50} - 32 q^{51} + 56 q^{52} + 16 q^{53} + 32 q^{54} + 16 q^{56} - 12 q^{58} - 8 q^{59} - 28 q^{60} + 16 q^{61} - 8 q^{62} + 40 q^{63} - 16 q^{64} + 40 q^{67} - 48 q^{68} + 16 q^{69} - 8 q^{70} - 40 q^{72} - 72 q^{74} + 16 q^{77} - 16 q^{78} + 16 q^{79} + 16 q^{80} - 16 q^{81} - 76 q^{82} + 40 q^{83} - 64 q^{84} - 16 q^{85} + 28 q^{86} + 36 q^{90} + 32 q^{91} - 52 q^{92} - 48 q^{93} - 36 q^{94} + 32 q^{95} + 8 q^{96} + 60 q^{98} - 8 q^{99}+O(q^{100}) $ 16 * q - 4 * q^4 - 12 * q^6 + 4 * q^10 - 8 * q^11 - 12 * q^12 + 4 * q^14 - 8 * q^15 + 16 * q^16 - 8 * q^19 + 8 * q^20 - 20 * q^22 + 8 * q^24 - 16 * q^26 + 24 * q^27 - 4 * q^28 - 16 * q^29 + 16 * q^34 - 4 * q^36 - 16 * q^37 + 20 * q^38 + 60 * q^42 + 8 * q^43 + 40 * q^44 - 4 * q^46 - 40 * q^47 - 40 * q^48 - 16 * q^49 - 4 * q^50 - 32 * q^51 + 56 * q^52 + 16 * q^53 + 32 * q^54 + 16 * q^56 - 12 * q^58 - 8 * q^59 - 28 * q^60 + 16 * q^61 - 8 * q^62 + 40 * q^63 - 16 * q^64 + 40 * q^67 - 48 * q^68 + 16 * q^69 - 8 * q^70 - 40 * q^72 - 72 * q^74 + 16 * q^77 - 16 * q^78 + 16 * q^79 + 16 * q^80 - 16 * q^81 - 76 * q^82 + 40 * q^83 - 64 * q^84 - 16 * q^85 + 28 * q^86 + 36 * q^90 + 32 * q^91 - 52 * q^92 - 48 * q^93 - 36 * q^94 + 32 * q^95 + 8 * q^96 + 60 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/80\mathbb{Z}\right)^\times$.

$n$	$17$	$21$	$31$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$1$

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 $

$2$	1.40727	−	0.139945i	0.995092	−	0.0989564i
$2$	1.40727	−	0.139945i	0.995092	−	0.0989564i
$3$	−2.32624	+	2.32624i	−1.34306	+	1.34306i	−0.450058	+	0.893000i	$0.648597\pi$
$3$	−2.32624	+	2.32624i	−1.34306	+	1.34306i	−0.893000	+	0.450058i	$0.851403\pi$
$4$	1.96083	−	0.393883i	0.980415	−	0.196941i
$5$	0.707107	+	0.707107i	0.316228	+	0.316228i
$5$	0.707107	+	0.707107i	0.316228	+	0.316228i
$6$	−2.94811	+	3.59920i	−1.20356	+	1.46937i
$7$		−	0.982011i		−	0.371165i	−0.982629	−	0.185583i	$-0.940583\pi$
$7$		−	0.982011i		−	0.371165i	0.982629	−	0.185583i	$-0.0594172\pi$
$8$	2.70430	−	0.828709i	0.956115	−	0.292993i
$9$		−	7.82281i		−	2.60760i
$10$	1.09405	+	0.896135i	0.345968	+	0.283383i
$11$	−1.62645	−	1.62645i	−0.490393	−	0.490393i	0.418037	−	0.908430i	$-0.362718\pi$
$11$	−1.62645	−	1.62645i	−0.490393	−	0.490393i	−0.908430	+	0.418037i	$0.862718\pi$
$12$	−3.64510	+	5.47764i	−1.05225	+	1.58126i
$13$	−0.690562	+	0.690562i	−0.191528	+	0.191528i	−0.796356	−	0.604828i	$-0.793242\pi$
$13$	−0.690562	+	0.690562i	−0.191528	+	0.191528i	0.604828	+	0.796356i	$0.293242\pi$
$14$	−0.137428	−	1.38196i	−0.0367292	−	0.369344i
$15$	−3.28980			−0.849424
$16$	3.68971	−	1.54467i	0.922428	−	0.386169i
$17$	−2.19577			−0.532552			−0.266276	−	0.963897i	$-0.585793\pi$
$17$	−2.19577			−0.532552			−0.266276	+	0.963897i	$0.585793\pi$
$18$	−1.09477	−	11.0088i	−0.258039	−	2.59481i
$19$	1.92659	−	1.92659i	0.441991	−	0.441991i	−0.450690	−	0.892681i	$-0.648822\pi$
$19$	1.92659	−	1.92659i	0.441991	−	0.441991i	0.892681	+	0.450690i	$0.148822\pi$
$20$	1.66503	+	1.10800i	0.372313	+	0.247756i
$21$	2.28440	+	2.28440i	0.498496	+	0.498496i
$22$	−2.51647	−	2.06124i	−0.536513	−	0.439458i
$23$			2.01442i			0.420035i	0.977698	+	0.210018i	$0.0673522\pi$
$23$			2.01442i			0.420035i	−0.977698	+	0.210018i	$0.932648\pi$
$24$	−4.36308	+	8.21864i	−0.890610	+	1.67762i
$25$			1.00000i			0.200000i
$26$	−0.875168	+	1.06845i	−0.171635	+	0.209540i
$27$	11.2190	+	11.2190i	2.15911	+	2.15911i
$28$	−0.386797	−	1.92556i	−0.0730978	−	0.363896i
$29$	−5.27182	+	5.27182i	−0.978952	+	0.978952i	−0.999783	−	0.0208314i	$-0.993369\pi$
$29$	−5.27182	+	5.27182i	−0.978952	+	0.978952i	0.0208314	+	0.999783i	$0.493369\pi$
$30$	−4.62965	+	0.460393i	−0.845255	+	0.0840559i
$31$	0.435286			0.0781797			0.0390898	−	0.999236i	$-0.487554\pi$
$31$	0.435286			0.0781797			0.0390898	+	0.999236i	$0.487554\pi$
$32$	4.97626	−	2.69014i	0.879687	−	0.475553i
$33$	7.56703			1.31725
$34$	−3.09004	+	0.307288i	−0.529938	+	0.0526994i
$35$	0.694387	−	0.694387i	0.117373	−	0.117373i
$36$	−3.08127	−	15.3392i	−0.513545	−	2.55654i
$37$	−5.79805	−	5.79805i	−0.953194	−	0.953194i	0.0457583	−	0.998953i	$-0.485430\pi$
$37$	−5.79805	−	5.79805i	−0.953194	−	0.953194i	−0.998953	+	0.0457583i	$0.985430\pi$
$38$	2.44162	−	2.98086i	0.396084	−	0.483559i
$39$		−	3.21283i		−	0.514465i
$40$	2.49822	+	1.32624i	0.395003	+	0.209697i
$41$			3.93139i			0.613980i	0.951713	+	0.306990i	$0.0993218\pi$
$41$			3.93139i			0.613980i	−0.951713	+	0.306990i	$0.900678\pi$
$42$	3.53446	+	2.89508i	0.545379	+	0.446720i
$43$	−0.507592	−	0.507592i	−0.0774071	−	0.0774071i	0.667343	−	0.744750i	$-0.267431\pi$
$43$	−0.507592	−	0.507592i	−0.0774071	−	0.0774071i	−0.744750	+	0.667343i	$0.767431\pi$
$44$	−3.82982	−	2.54856i	−0.577367	−	0.384210i
$45$	5.53157	−	5.53157i	0.824597	−	0.824597i
$46$	0.281909	+	2.83484i	0.0415652	+	0.417974i
$47$	−9.21960			−1.34482			−0.672409	−	0.740180i	$-0.734740\pi$
$47$	−9.21960			−1.34482			−0.672409	+	0.740180i	$0.734740\pi$
$48$	−4.98988	+	12.1765i	−0.720227	+	1.75752i
$49$	6.03565			0.862236
$50$	0.139945	+	1.40727i	0.0197913	+	0.199018i
$51$	5.10789	−	5.10789i	0.715248	−	0.715248i
$52$	−1.08208	+	1.62608i	−0.150057	+	0.225496i
$53$	6.29357	+	6.29357i	0.864488	+	0.864488i	0.991856	−	0.127367i	$-0.0406527\pi$
$53$	6.29357	+	6.29357i	0.864488	+	0.864488i	−0.127367	+	0.991856i	$0.540653\pi$
$54$	17.3583	+	14.2182i	2.36216	+	1.93485i
$55$		−	2.30015i		−	0.310152i
$56$	−0.813802	−	2.65565i	−0.108749	−	0.354877i
$57$			8.96345i			1.18724i
$58$	−6.68111	+	8.15665i	−0.877273	+	1.07102i
$59$	−5.67778	−	5.67778i	−0.739183	−	0.739183i	0.233237	−	0.972420i	$-0.425068\pi$
$59$	−5.67778	−	5.67778i	−0.739183	−	0.739183i	−0.972420	+	0.233237i	$0.925068\pi$
$60$	−6.45075	+	1.29580i	−0.832788	+	0.167287i
$61$	−3.60301	+	3.60301i	−0.461318	+	0.461318i	−0.899087	−	0.437770i	$-0.855769\pi$
$61$	−3.60301	+	3.60301i	−0.461318	+	0.461318i	0.437770	+	0.899087i	$0.355769\pi$
$62$	0.612566	−	0.0609163i	0.0777959	−	0.00773637i
$63$	−7.68209			−0.967852
$64$	6.62648	−	4.48216i	0.828310	−	0.560270i
$65$	−0.976603			−0.121133
$66$	10.6489	−	1.05897i	1.31079	−	0.130350i
$67$	4.53563	−	4.53563i	0.554116	−	0.554116i	−0.373510	−	0.927626i	$-0.621846\pi$
$67$	4.53563	−	4.53563i	0.554116	−	0.554116i	0.927626	+	0.373510i	$0.121846\pi$
$68$	−4.30553	+	0.864875i	−0.522122	+	0.104882i
$69$	−4.68603	−	4.68603i	−0.564132	−	0.564132i
$70$	0.880015	−	1.07437i	0.105182	−	0.128411i
$71$			10.3984i			1.23407i	0.786937	+	0.617033i	$0.211665\pi$
$71$			10.3984i			1.23407i	−0.786937	+	0.617033i	$0.788335\pi$
$72$	−6.48284	−	21.1552i	−0.764010	−	2.49317i
$73$		−	9.24439i		−	1.08197i	−0.841031	−	0.540987i	$-0.818051\pi$
$73$		−	9.24439i		−	1.08197i	0.841031	−	0.540987i	$-0.181949\pi$
$74$	−8.97085	−	7.34803i	−1.04284	−	0.854191i
$75$	−2.32624	−	2.32624i	−0.268611	−	0.268611i
$76$	3.01887	−	4.53658i	0.346288	−	0.520381i
$77$	−1.59719	+	1.59719i	−0.182017	+	0.182017i
$78$	−0.449621	−	4.52133i	−0.0509096	−	0.511940i
$79$	15.4493			1.73818			0.869091	−	0.494653i	$-0.164705\pi$
$79$	15.4493			1.73818			0.869091	+	0.494653i	$0.164705\pi$
$80$	3.70127	+	1.51677i	0.413815	+	0.169580i
$81$	−28.7280			−3.19200
$82$	0.550180	+	5.53253i	0.0607572	+	0.610966i
$83$	−0.683244	+	0.683244i	−0.0749957	+	0.0749957i	−0.743610	−	0.668614i	$-0.766888\pi$
$83$	−0.683244	+	0.683244i	−0.0749957	+	0.0749957i	0.668614	+	0.743610i	$0.266888\pi$
$84$	5.37910	+	3.57953i	0.586908	+	0.390559i
$85$	−1.55264	−	1.55264i	−0.168408	−	0.168408i
$86$	−0.785356	−	0.643285i	−0.0846871	−	0.0693672i
$87$		−	24.5271i		−	2.62958i
$88$	−5.74626	−	3.05055i	−0.612553	−	0.325190i
$89$			5.44401i			0.577064i	0.957470	+	0.288532i	$0.0931672\pi$
$89$			5.44401i			0.577064i	−0.957470	+	0.288532i	$0.906833\pi$
$90$	7.01030	−	8.55854i	0.738951	−	0.902149i
$91$	0.678140	+	0.678140i	0.0710884	+	0.0710884i
$92$	0.793445	+	3.94994i	0.0827223	+	0.411809i
$93$	−1.01258	+	1.01258i	−0.105000	+	0.105000i
$94$	−12.9745	+	1.29024i	−1.33822	+	0.133078i
$95$	2.72461			0.279540
$96$	−5.31808	+	17.8339i	−0.542775	+	1.82016i
$97$	5.54540			0.563050			0.281525	−	0.959554i	$-0.409160\pi$
$97$	5.54540			0.563050			0.281525	+	0.959554i	$0.409160\pi$
$98$	8.49381	−	0.844662i	0.858004	−	0.0853238i
$99$	−12.7234	+	12.7234i	−1.27875	+	1.27875i
$100$	0.393883	+	1.96083i	0.0393883	+	0.196083i
$101$	−0.291294	−	0.291294i	−0.0289848	−	0.0289848i	0.692466	−	0.721451i	$-0.256524\pi$
$101$	−0.291294	−	0.291294i	−0.0289848	−	0.0289848i	−0.721451	+	0.692466i	$0.756524\pi$
$102$	6.47337	−	7.90302i	0.640959	−	0.782516i
$103$			4.50219i			0.443614i	0.975091	+	0.221807i	$0.0711955\pi$
$103$			4.50219i			0.443614i	−0.975091	+	0.221807i	$0.928805\pi$
$104$	−1.29521	+	2.43976i	−0.127006	+	0.239239i
$105$			3.23062i			0.315277i
$106$	9.73752	+	7.97601i	0.945792	+	0.774698i
$107$	−6.49890	−	6.49890i	−0.628272	−	0.628272i	0.319361	−	0.947633i	$-0.396532\pi$
$107$	−6.49890	−	6.49890i	−0.628272	−	0.628272i	−0.947633	+	0.319361i	$0.896532\pi$
$108$	26.4176	+	17.5796i	2.54204	+	1.69160i
$109$	−2.51950	+	2.51950i	−0.241324	+	0.241324i	−0.817398	−	0.576074i	$-0.804584\pi$
$109$	−2.51950	+	2.51950i	−0.241324	+	0.241324i	0.576074	+	0.817398i	$0.304584\pi$
$110$	−0.321895	−	3.23693i	−0.0306915	−	0.308629i
$111$	26.9754			2.56039
$112$	−1.51689	−	3.62334i	−0.143332	−	0.342373i
$113$	5.38101			0.506203			0.253102	−	0.967440i	$-0.418549\pi$
$113$	5.38101			0.506203			0.253102	+	0.967440i	$0.418549\pi$
$114$	1.25439	+	12.6140i	0.117485	+	1.18141i
$115$	−1.42441	+	1.42441i	−0.132827	+	0.132827i
$116$	−8.26066	+	12.4136i	−0.766983	+	1.15258i
$117$	5.40214	+	5.40214i	0.499428	+	0.499428i
$118$	−8.78476	−	7.19560i	−0.808702	−	0.662408i
$119$			2.15627i			0.197665i
$120$	−8.89662	+	2.72629i	−0.812147	+	0.248875i
$121$		−	5.70933i		−	0.519030i
$122$	−4.56619	+	5.57464i	−0.413403	+	0.504704i
$123$	−9.14536	−	9.14536i	−0.824610	−	0.824610i
$124$	0.853522	−	0.171452i	0.0766485	−	0.0153968i
$125$	−0.707107	+	0.707107i	−0.0632456	+	0.0632456i
$126$	−10.8108	+	1.07507i	−0.963102	+	0.0957751i
$127$	4.86578			0.431768			0.215884	−	0.976419i	$-0.430737\pi$
$127$	4.86578			0.431768			0.215884	+	0.976419i	$0.430737\pi$
$128$	8.69801	−	7.23496i	0.768802	−	0.639486i
$129$	2.36157			0.207924
$130$	−1.37435	+	0.136671i	−0.120538	+	0.0119868i
$131$	8.00581	−	8.00581i	0.699471	−	0.699471i	−0.264825	−	0.964296i	$-0.585314\pi$
$131$	8.00581	−	8.00581i	0.699471	−	0.699471i	0.964296	+	0.264825i	$0.0853143\pi$
$132$	14.8377	−	2.98052i	1.29145	−	0.259421i
$133$	−1.89194	−	1.89194i	−0.164052	−	0.164052i
$134$	5.74813	−	7.01761i	0.496563	−	0.606229i
$135$			15.8661i			1.36554i
$136$	−5.93802	+	1.81965i	−0.509181	+	0.156034i
$137$		−	13.5567i		−	1.15822i	−0.815248	−	0.579112i	$-0.803399\pi$
$137$		−	13.5567i		−	1.15822i	0.815248	−	0.579112i	$-0.196601\pi$
$138$	−7.25031	−	5.93873i	−0.617187	−	0.505538i
$139$	8.22645	+	8.22645i	0.697758	+	0.697758i	0.963927	−	0.266168i	$-0.0857577\pi$
$139$	8.22645	+	8.22645i	0.697758	+	0.697758i	−0.266168	+	0.963927i	$0.585758\pi$
$140$	1.08807	−	1.63508i	0.0919585	−	0.138190i
$141$	21.4470	−	21.4470i	1.80617	−	1.80617i
$142$	1.45521	+	14.6334i	0.122119	+	1.22801i
$143$	2.24633			0.187847
$144$	−12.0837	−	28.8639i	−1.00697	−	2.40533i
$145$	−7.45547			−0.619143
$146$	−1.29371	−	13.0094i	−0.107068	−	1.07666i
$147$	−14.0404	+	14.0404i	−1.15803	+	1.15803i
$148$	−13.6528	−	9.08525i	−1.12225	−	0.746803i
$149$	12.6363	+	12.6363i	1.03521	+	1.03521i	0.999357	+	0.0358519i	$0.0114144\pi$
$149$	12.6363	+	12.6363i	1.03521	+	1.03521i	0.0358519	+	0.999357i	$0.488586\pi$
$150$	−3.59920	−	2.94811i	−0.293874	−	0.240712i
$151$			15.1562i			1.23339i	0.787201	+	0.616696i	$0.211529\pi$
$151$			15.1562i			1.23339i	−0.787201	+	0.616696i	$0.788471\pi$
$152$	3.61350	−	6.80667i	0.293094	−	0.552094i
$153$			17.1771i			1.38869i
$154$	−2.02416	+	2.47120i	−0.163112	+	0.199135i
$155$	0.307794	+	0.307794i	0.0247226	+	0.0247226i
$156$	−1.26548	−	6.29982i	−0.101319	−	0.504389i
$157$	−1.75816	+	1.75816i	−0.140316	+	0.140316i	−0.773776	−	0.633460i	$-0.781634\pi$
$157$	−1.75816	+	1.75816i	−0.140316	+	0.140316i	0.633460	+	0.773776i	$0.281634\pi$
$158$	21.7414	−	2.16206i	1.72965	−	0.172004i
$159$	−29.2807			−2.32211
$160$	5.42096	+	1.61653i	0.428565	+	0.127798i
$161$	1.97818			0.155903
$162$	−40.4281	+	4.02035i	−3.17633	+	0.315868i
$163$	−13.9102	+	13.9102i	−1.08953	+	1.08953i	−0.0939562	+	0.995576i	$0.529951\pi$
$163$	−13.9102	+	13.9102i	−1.08953	+	1.08953i	−0.995576	+	0.0939562i	$0.970049\pi$
$164$	1.54851	+	7.70879i	0.120918	+	0.601955i
$165$	5.35070	+	5.35070i	0.416551	+	0.416551i
$166$	−0.865893	+	1.05713i	−0.0672063	+	0.0820490i
$167$			18.8620i			1.45958i	0.683669	+	0.729792i	$0.260383\pi$
$167$			18.8620i			1.45958i	−0.683669	+	0.729792i	$0.739617\pi$
$168$	8.07079	+	4.28459i	0.622675	+	0.330564i
$169$			12.0462i			0.926634i
$170$	−2.40228	−	1.96771i	−0.184246	−	0.150916i
$171$	−15.0714	−	15.0714i	−1.15254	−	1.15254i
$172$	−1.19523	−	0.795370i	−0.0911357	−	0.0606464i
$173$	16.0724	−	16.0724i	1.22196	−	1.22196i	0.255031	−	0.966933i	$-0.417914\pi$
$173$	16.0724	−	16.0724i	1.22196	−	1.22196i	0.966933	−	0.255031i	$-0.0820856\pi$
$174$	−3.43245	−	34.5162i	−0.260213	−	2.61667i
$175$	0.982011			0.0742331
$176$	−8.51346	−	3.48879i	−0.641726	−	0.262978i
$177$	26.4158			1.98553
$178$	0.761865	+	7.66121i	0.0571042	+	0.574232i
$179$	16.4341	−	16.4341i	1.22834	−	1.22834i	0.263749	−	0.964591i	$-0.415041\pi$
$179$	16.4341	−	16.4341i	1.22834	−	1.22834i	0.964591	−	0.263749i	$-0.0849591\pi$
$180$	8.66767	−	13.0252i	0.646050	−	0.970845i
$181$	−15.4539	−	15.4539i	−1.14868	−	1.14868i	−0.986812	−	0.161870i	$-0.948247\pi$
$181$	−15.4539	−	15.4539i	−1.14868	−	1.14868i	−0.161870	−	0.986812i	$-0.551753\pi$
$182$	1.04923	+	0.859425i	0.0777741	+	0.0637048i
$183$		−	16.7629i		−	1.23915i
$184$	1.66937	+	5.44760i	0.123067	+	0.401602i
$185$		−	8.19969i		−	0.602853i
$186$	−1.28327	+	1.56668i	−0.0940940	+	0.114875i
$187$	3.57130	+	3.57130i	0.261160	+	0.261160i
$188$	−18.0781	+	3.63144i	−1.31848	+	0.264850i
$189$	11.0172	−	11.0172i	0.801385	−	0.801385i
$190$	3.83427	−	0.381297i	0.278168	−	0.0276622i
$191$	−14.7872			−1.06997			−0.534983	−	0.844863i	$-0.679682\pi$
$191$	−14.7872			−1.06997			−0.534983	+	0.844863i	$0.679682\pi$
$192$	−4.98822	+	25.8414i	−0.359994	+	1.86494i
$193$	−11.2912			−0.812758			−0.406379	−	0.913705i	$-0.633209\pi$
$193$	−11.2912			−0.812758			−0.406379	+	0.913705i	$0.633209\pi$
$194$	7.80388	−	0.776053i	0.560286	−	0.0557173i
$195$	2.27182	−	2.27182i	0.162688	−	0.162688i
$196$	11.8349	−	2.37734i	0.845350	−	0.169810i
$197$	−10.6152	−	10.6152i	−0.756302	−	0.756302i	0.219345	−	0.975647i	$-0.429608\pi$
$197$	−10.6152	−	10.6152i	−0.756302	−	0.756302i	−0.975647	+	0.219345i	$0.929608\pi$
$198$	−16.1247	+	19.6859i	−1.14593	+	1.39901i
$199$		−	4.68789i		−	0.332316i	−0.986099	−	0.166158i	$-0.946864\pi$
$199$		−	4.68789i		−	0.332316i	0.986099	−	0.166158i	$-0.0531361\pi$
$200$	0.828709	+	2.70430i	0.0585986	+	0.191223i
$201$			21.1020i			1.48842i
$202$	−0.450695	−	0.369165i	−0.0317108	−	0.0259743i
$203$	5.17698	+	5.17698i	0.363353	+	0.363353i
$204$	8.00380	−	12.0276i	0.560378	−	0.842102i
$205$	−2.77991	+	2.77991i	−0.194157	+	0.194157i
$206$	0.630061	+	6.33581i	0.0438984	+	0.441437i
$207$	15.7584			1.09529
$208$	−1.48128	+	3.61467i	−0.102709	+	0.250632i
$209$	−6.26701			−0.433498
$210$	0.452111	+	4.54637i	0.0311986	+	0.313729i
$211$	−2.63215	+	2.63215i	−0.181205	+	0.181205i	−0.791881	−	0.610676i	$-0.790898\pi$
$211$	−2.63215	+	2.63215i	−0.181205	+	0.181205i	0.610676	+	0.791881i	$0.290898\pi$
$212$	14.8195	+	9.86169i	1.01781	+	0.677304i
$213$	−24.1893	−	24.1893i	−1.65742	−	1.65742i
$214$	−10.0552	−	8.23623i	−0.687360	−	0.563017i
$215$		−	0.717844i		−	0.0489565i
$216$	39.6370	+	21.0423i	2.69695	+	1.43175i
$217$		−	0.427456i		−	0.0290176i
$218$	−3.19303	+	3.89821i	−0.216259	+	0.264020i
$219$	21.5047	+	21.5047i	1.45315	+	1.45315i
$220$	−0.905987	−	4.51020i	−0.0610816	−	0.304077i
$221$	1.51632	−	1.51632i	0.101998	−	0.101998i
$222$	37.9617	−	3.77508i	2.54782	−	0.253367i
$223$	3.45644			0.231461			0.115730	−	0.993281i	$-0.463079\pi$
$223$	3.45644			0.231461			0.115730	+	0.993281i	$0.463079\pi$
$224$	−2.64174	−	4.88674i	−0.176509	−	0.326509i
$225$	7.82281			0.521521
$226$	7.57255	−	0.753048i	0.503719	−	0.0500920i
$227$	−4.74550	+	4.74550i	−0.314970	+	0.314970i	−0.846831	−	0.531862i	$-0.821493\pi$
$227$	−4.74550	+	4.74550i	−0.314970	+	0.314970i	0.531862	+	0.846831i	$0.321493\pi$
$228$	3.53055	+	17.5758i	0.233816	+	1.16399i
$229$	−13.3576	−	13.3576i	−0.882697	−	0.882697i	0.111111	−	0.993808i	$-0.464559\pi$
$229$	−13.3576	−	13.3576i	−0.882697	−	0.882697i	−0.993808	+	0.111111i	$0.964559\pi$
$230$	−1.80519	+	2.20387i	−0.119031	+	0.145319i
$231$		−	7.43091i		−	0.488918i
$232$	−9.88777	+	18.6254i	−0.649164	+	1.22282i
$233$		−	4.82691i		−	0.316222i	−0.987421	−	0.158111i	$-0.949460\pi$
$233$		−	4.82691i		−	0.316222i	0.987421	−	0.158111i	$-0.0505403\pi$
$234$	8.35829	+	6.84628i	0.546399	+	0.447555i
$235$	−6.51924	−	6.51924i	−0.425269	−	0.425269i
$236$	−13.3695	−	8.89678i	−0.870282	−	0.579131i
$237$	−35.9388	+	35.9388i	−2.33448	+	2.33448i
$238$	0.301760	+	3.03446i	0.0195602	+	0.196695i
$239$	−8.82497			−0.570840			−0.285420	−	0.958403i	$-0.592133\pi$
$239$	−8.82497			−0.570840			−0.285420	+	0.958403i	$0.592133\pi$
$240$	−12.1384	+	5.08168i	−0.783533	+	0.328021i
$241$	−3.74147			−0.241009			−0.120504	−	0.992713i	$-0.538451\pi$
$241$	−3.74147			−0.241009			−0.120504	+	0.992713i	$0.538451\pi$
$242$	−0.798995	−	8.03458i	−0.0513613	−	0.516483i
$243$	33.1712	−	33.1712i	2.12793	−	2.12793i
$244$	−5.64572	+	8.48405i	−0.361430	+	0.543135i
$245$	4.26785	+	4.26785i	0.272663	+	0.272663i
$246$	−14.1499	−	11.5902i	−0.902163	−	0.738962i
$247$			2.66087i			0.169307i
$248$	1.17714	−	0.360725i	0.0747487	−	0.0229061i
$249$		−	3.17878i		−	0.201447i
$250$	−0.896135	+	1.09405i	−0.0566766	+	0.0691937i
$251$	−5.99322	−	5.99322i	−0.378289	−	0.378289i	0.492196	−	0.870484i	$-0.336194\pi$
$251$	−5.99322	−	5.99322i	−0.378289	−	0.378289i	−0.870484	+	0.492196i	$0.836194\pi$
$252$	−15.0633	+	3.02584i	−0.948897	+	0.190610i
$253$	3.27635	−	3.27635i	0.205982	−	0.205982i
$254$	6.84748	−	0.680944i	0.429649	−	0.0427262i
$255$	7.22365			0.452362
$256$	11.2280	−	11.3988i	0.701748	−	0.712426i
$257$	−14.7662			−0.921091			−0.460545	−	0.887636i	$-0.652346\pi$
$257$	−14.7662			−0.921091			−0.460545	+	0.887636i	$0.652346\pi$
$258$	3.32337	−	0.330490i	0.206904	−	0.0205754i
$259$	−5.69375	+	5.69375i	−0.353793	+	0.353793i
$260$	−1.91495	+	0.384667i	−0.118760	+	0.0238560i
$261$	41.2404	+	41.2404i	2.55272	+	2.55272i
$262$	10.1460	−	12.3867i	0.626821	−	0.765255i
$263$		−	6.79486i		−	0.418989i	−0.977810	−	0.209494i	$-0.932818\pi$
$263$		−	6.79486i		−	0.418989i	0.977810	−	0.209494i	$-0.0671818\pi$
$264$	20.4635	−	6.27087i	1.25944	−	0.385945i
$265$			8.90045i			0.546750i
$266$	−2.92724	−	2.39770i	−0.179480	−	0.147013i
$267$	−12.6641	−	12.6641i	−0.775030	−	0.775030i
$268$	7.10710	−	10.6801i	0.434135	−	0.652392i
$269$	−6.03990	+	6.03990i	−0.368259	+	0.368259i	−0.866842	−	0.498583i	$-0.833854\pi$
$269$	−6.03990	+	6.03990i	−0.368259	+	0.368259i	0.498583	+	0.866842i	$0.333854\pi$
$270$	2.22039	+	22.3279i	0.135129	+	1.35884i
$271$	−24.6221			−1.49568			−0.747842	−	0.663877i	$-0.768910\pi$
$271$	−24.6221			−1.49568			−0.747842	+	0.663877i	$0.768910\pi$
$272$	−8.10175	+	3.39175i	−0.491241	+	0.205655i
$273$	−3.15504			−0.190952
$274$	−1.89719	−	19.0779i	−0.114614	−	1.15254i
$275$	1.62645	−	1.62645i	0.0980785	−	0.0980785i
$276$	−11.0343	−	7.34276i	−0.664184	−	0.441982i
$277$	9.98018	+	9.98018i	0.599651	+	0.599651i	0.940220	−	0.340569i	$-0.110620\pi$
$277$	9.98018	+	9.98018i	0.599651	+	0.599651i	−0.340569	+	0.940220i	$0.610620\pi$
$278$	12.7281	+	10.4256i	0.763381	+	0.625286i
$279$		−	3.40516i		−	0.203862i
$280$	1.30239	−	2.45327i	0.0778324	−	0.146611i
$281$		−	14.4611i		−	0.862675i	−0.902191	−	0.431337i	$-0.858042\pi$
$281$		−	14.4611i		−	0.862675i	0.902191	−	0.431337i	$-0.141958\pi$
$282$	27.1804	−	33.1832i	1.61857	−	1.97603i
$283$	20.0783	+	20.0783i	1.19353	+	1.19353i	0.976069	+	0.217462i	$0.0697777\pi$
$283$	20.0783	+	20.0783i	1.19353	+	1.19353i	0.217462	+	0.976069i	$0.430222\pi$
$284$	4.09576	+	20.3895i	0.243039	+	1.20990i
$285$	−6.33812	+	6.33812i	−0.375438	+	0.375438i
$286$	3.16120	−	0.314363i	0.186925	−	0.0185887i
$287$	3.86067			0.227888
$288$	−21.0444	−	38.9284i	−1.24006	−	2.29388i
$289$	−12.1786			−0.716388
$290$	−10.4919	+	1.04336i	−0.616104	+	0.0612682i
$291$	−12.8999	+	12.8999i	−0.756208	+	0.756208i
$292$	−3.64121	−	18.1267i	−0.213085	−	1.06078i
$293$	15.4038	+	15.4038i	0.899899	+	0.899899i	0.995427	−	0.0955279i	$-0.0304539\pi$
$293$	15.4038	+	15.4038i	0.899899	+	0.899899i	−0.0955279	+	0.995427i	$0.530454\pi$
$294$	−17.7938	+	21.7236i	−1.03775	+	1.26694i
$295$		−	8.02959i		−	0.467501i
$296$	−20.4846	−	10.8748i	−1.19064	−	0.632084i
$297$		−	36.4944i		−	2.11762i
$298$	19.5512	+	16.0144i	1.13257	+	0.927687i
$299$	−1.39108	−	1.39108i	−0.0804484	−	0.0804484i
$300$	−5.47764	−	3.64510i	−0.316251	−	0.210450i
$301$	−0.498461	+	0.498461i	−0.0287308	+	0.0287308i
$302$	2.12104	+	21.3289i	0.122052	+	1.22734i
$303$	1.35524			0.0778566
$304$	4.13262	−	10.0845i	0.237022	−	0.578388i
$305$	−5.09542			−0.291763
$306$	2.40385	+	24.1728i	0.137419	+	1.38187i
$307$	9.12398	−	9.12398i	0.520733	−	0.520733i	−0.397060	−	0.917793i	$-0.629969\pi$
$307$	9.12398	−	9.12398i	0.520733	−	0.520733i	0.917793	+	0.397060i	$0.129969\pi$
$308$	−2.50271	+	3.76092i	−0.142605	+	0.214299i
$309$	−10.4732	−	10.4732i	−0.595799	−	0.595799i
$310$	0.476224	+	0.390075i	0.0270477	+	0.0221548i
$311$		−	0.642911i		−	0.0364561i	−0.999834	−	0.0182281i	$-0.994198\pi$
$311$		−	0.642911i		−	0.0364561i	0.999834	−	0.0182281i	$-0.00580249\pi$
$312$	−2.66250	−	8.68846i	−0.150735	−	0.491887i
$313$		−	21.3775i		−	1.20833i	−0.796860	−	0.604164i	$-0.793507\pi$
$313$		−	21.3775i		−	1.20833i	0.796860	−	0.604164i	$-0.206493\pi$
$314$	−2.22816	+	2.72025i	−0.125742	+	0.153513i
$315$	−5.43206	−	5.43206i	−0.306062	−	0.306062i
$316$	30.2935	−	6.08521i	1.70414	−	0.342320i
$317$	8.66200	−	8.66200i	0.486507	−	0.486507i	−0.420695	−	0.907202i	$-0.638214\pi$
$317$	8.66200	−	8.66200i	0.486507	−	0.486507i	0.907202	+	0.420695i	$0.138214\pi$
$318$	−41.2060	+	4.09771i	−2.31072	+	0.229788i
$319$	17.1487			0.960141
$320$	7.85499	+	1.51627i	0.439108	+	0.0847618i
$321$	30.2360			1.68761
$322$	2.78384	−	0.276838i	0.155137	−	0.0154276i
$323$	−4.23035	+	4.23035i	−0.235383	+	0.235383i
$324$	−56.3307	+	11.3155i	−3.12948	+	0.628636i
$325$	−0.690562	−	0.690562i	−0.0383055	−	0.0383055i
$326$	−17.6288	+	21.5221i	−0.976369	+	1.19200i
$327$		−	11.7219i		−	0.648224i
$328$	3.25798	+	10.6317i	0.179892	+	0.587035i
$329$			9.05375i			0.499150i
$330$	8.27869	+	6.78108i	0.455727	+	0.373286i
$331$	−8.43941	−	8.43941i	−0.463872	−	0.463872i	0.436050	−	0.899922i	$-0.356377\pi$
$331$	−8.43941	−	8.43941i	−0.463872	−	0.463872i	−0.899922	+	0.436050i	$0.856377\pi$
$332$	−1.07061	+	1.60884i	−0.0587572	+	0.0882967i
$333$	−45.3571	+	45.3571i	−2.48555	+	2.48555i
$334$	2.63965	+	26.5440i	0.144435	+	1.45242i
$335$	6.41435			0.350454
$336$	11.9574	+	4.90012i	0.652330	+	0.267323i
$337$	30.7047			1.67259			0.836295	−	0.548280i	$-0.184717\pi$
$337$	30.7047			1.67259			0.836295	+	0.548280i	$0.184717\pi$
$338$	1.68582	+	16.9523i	0.0916964	+	0.922086i
$339$	−12.5175	+	12.5175i	−0.679860	+	0.679860i
$340$	−3.65603	−	2.43291i	−0.198276	−	0.131943i
$341$	−0.707970	−	0.707970i	−0.0383387	−	0.0383387i
$342$	−23.3187	−	19.1004i	−1.26093	−	1.03283i
$343$		−	12.8012i		−	0.691197i
$344$	−1.79333	−	0.952035i	−0.0966898	−	0.0513303i
$345$		−	6.62705i		−	0.356788i
$346$	20.3690	−	24.8675i	1.09504	−	1.33689i
$347$	13.6418	+	13.6418i	0.732329	+	0.732329i	0.971081	−	0.238752i	$-0.0767383\pi$
$347$	13.6418	+	13.6418i	0.732329	+	0.732329i	−0.238752	+	0.971081i	$0.576738\pi$
$348$	−9.66078	−	48.0934i	−0.517872	−	2.57808i
$349$	9.97321	−	9.97321i	0.533854	−	0.533854i	−0.387863	−	0.921717i	$-0.626787\pi$
$349$	9.97321	−	9.97321i	0.533854	−	0.533854i	0.921717	+	0.387863i	$0.126787\pi$
$350$	1.38196	−	0.137428i	0.0738687	−	0.00734583i
$351$	−15.4949			−0.827056
$352$	−12.4690	−	3.71826i	−0.664600	−	0.198184i
$353$	−26.7843			−1.42559			−0.712793	−	0.701374i	$-0.752570\pi$
$353$	−26.7843			−1.42559			−0.712793	+	0.701374i	$0.752570\pi$
$354$	37.1742	−	3.69677i	1.97579	−	0.196481i
$355$	−7.35280	+	7.35280i	−0.390246	+	0.390246i
$356$	2.14430	+	10.6748i	0.113648	+	0.565763i
$357$	−5.01601	−	5.01601i	−0.265475	−	0.265475i
$358$	20.8273	−	25.4271i	1.10076	−	1.34386i
$359$		−	19.1190i		−	1.00906i	−0.863393	−	0.504532i	$-0.831665\pi$
$359$		−	19.1190i		−	1.00906i	0.863393	−	0.504532i	$-0.168335\pi$
$360$	10.3750	−	19.5431i	0.546808	−	1.03001i
$361$			11.5765i			0.609288i
$362$	−23.9106	−	19.5852i	−1.25671	−	1.02937i
$363$	13.2813	+	13.2813i	0.697087	+	0.697087i
$364$	1.59683	+	1.06261i	0.0836964	+	0.0556959i
$365$	6.53677	−	6.53677i	0.342150	−	0.342150i
$366$	−2.34590	−	23.5900i	−0.122622	−	1.23307i
$367$	4.24385			0.221527			0.110764	−	0.993847i	$-0.464670\pi$
$367$	4.24385			0.221527			0.110764	+	0.993847i	$0.464670\pi$
$368$	3.11162	+	7.43263i	0.162204	+	0.387453i
$369$	30.7545			1.60102
$370$	−1.14751	−	11.5392i	−0.0596561	−	0.599894i
$371$	6.18035	−	6.18035i	0.320868	−	0.320868i
$372$	−1.58666	+	2.38434i	−0.0822646	+	0.123622i
$373$	23.9514	+	23.9514i	1.24016	+	1.24016i	0.959935	+	0.280221i	$0.0904078\pi$
$373$	23.9514	+	23.9514i	1.24016	+	1.24016i	0.280221	+	0.959935i	$0.409592\pi$
$374$	5.52558	+	4.52601i	0.285721	+	0.234034i
$375$		−	3.28980i		−	0.169885i
$376$	−24.9326	+	7.64037i	−1.28580	+	0.394022i
$377$		−	7.28104i		−	0.374992i
$378$	13.9624	−	17.0460i	0.718149	−	0.876754i
$379$	−7.45685	−	7.45685i	−0.383033	−	0.383033i	0.489161	−	0.872194i	$-0.337303\pi$
$379$	−7.45685	−	7.45685i	−0.383033	−	0.383033i	−0.872194	+	0.489161i	$0.837303\pi$
$380$	5.34251	−	1.07318i	0.274065	−	0.0550529i
$381$	−11.3190	+	11.3190i	−0.579890	+	0.579890i
$382$	−20.8097	+	2.06941i	−1.06472	+	0.105880i
$383$	5.19667			0.265538			0.132769	−	0.991147i	$-0.457613\pi$
$383$	5.19667			0.265538			0.132769	+	0.991147i	$0.457613\pi$
$384$	−3.40340	+	37.0640i	−0.173679	+	1.89141i
$385$	−2.25877			−0.115117
$386$	−15.8898	+	1.58015i	−0.808768	+	0.0804275i
$387$	−3.97080	+	3.97080i	−0.201847	+	0.201847i
$388$	10.8736	−	2.18424i	0.552022	−	0.110888i
$389$	10.3846	+	10.3846i	0.526522	+	0.526522i	0.919534	−	0.393011i	$-0.128567\pi$
$389$	10.3846	+	10.3846i	0.526522	+	0.526522i	−0.393011	+	0.919534i	$0.628567\pi$
$390$	2.87913	−	3.51499i	0.145791	−	0.177989i
$391$		−	4.42320i		−	0.223691i
$392$	16.3222	−	5.00180i	0.824397	−	0.252629i
$393$			37.2469i			1.87886i
$394$	−16.4240	−	13.4529i	−0.827431	−	0.677749i
$395$	10.9243	+	10.9243i	0.549661	+	0.549661i
$396$	−19.9369	+	29.9600i	−1.00187	+	1.50554i
$397$	9.93104	−	9.93104i	0.498425	−	0.498425i	−0.412523	−	0.910947i	$-0.635352\pi$
$397$	9.93104	−	9.93104i	0.498425	−	0.498425i	0.910947	+	0.412523i	$0.135352\pi$
$398$	−0.656048	−	6.59714i	−0.0328847	−	0.330684i
$399$	8.80221			0.440662
$400$	1.54467	+	3.68971i	0.0772337	+	0.184486i
$401$	9.51392			0.475102			0.237551	−	0.971375i	$-0.423655\pi$
$401$	9.51392			0.475102			0.237551	+	0.971375i	$0.423655\pi$
$402$	2.95312	+	29.6962i	0.147288	+	1.48111i
$403$	−0.300592	+	0.300592i	−0.0149736	+	0.0149736i
$404$	−0.685914	−	0.456442i	−0.0341255	−	0.0227089i
$405$	−20.3138	−	20.3138i	−1.00940	−	1.00940i
$406$	8.00992	+	6.56093i	0.397525	+	0.325613i
$407$			18.8605i			0.934879i
$408$	9.58031	−	18.0462i	0.474296	−	0.893421i
$409$			4.81799i			0.238234i	0.992880	+	0.119117i	$0.0380064\pi$
$409$			4.81799i			0.238234i	−0.992880	+	0.119117i	$0.961994\pi$
$410$	−3.52306	+	4.30113i	−0.173991	+	0.212418i
$411$	31.5361	+	31.5361i	1.55556	+	1.55556i
$412$	1.77333	+	8.82803i	0.0873659	+	0.434926i
$413$	−5.57564	+	5.57564i	−0.274359	+	0.274359i
$414$	22.1764	−	2.20532i	1.08991	−	0.108386i
$415$	−0.966253			−0.0474315
$416$	−1.57871	+	5.29413i	−0.0774027	+	0.259566i
$417$	−38.2734			−1.87426
$418$	−8.81939	+	0.877039i	−0.431370	+	0.0428974i
$419$	21.4380	−	21.4380i	1.04731	−	1.04731i	0.0484914	−	0.998824i	$-0.484559\pi$
$419$	21.4380	−	21.4380i	1.04731	−	1.04731i	0.998824	−	0.0484914i	$-0.0154413\pi$
$420$	1.27249	+	6.33471i	0.0620910	+	0.309102i
$421$	−4.80145	−	4.80145i	−0.234008	−	0.234008i	0.580355	−	0.814363i	$-0.302914\pi$
$421$	−4.80145	−	4.80145i	−0.234008	−	0.234008i	−0.814363	+	0.580355i	$0.802914\pi$
$422$	−3.33579	+	4.07251i	−0.162384	+	0.198246i
$423$			72.1232i			3.50675i
$424$	22.2352	+	11.8042i	1.07984	+	0.573261i
$425$		−	2.19577i		−	0.106510i
$426$	−37.4261	−	30.6557i	−1.81330	−	1.48527i
$427$	3.53819	+	3.53819i	0.171225	+	0.171225i
$428$	−15.3030	−	10.1834i	−0.739700	−	0.492235i
$429$	−5.22551	+	5.22551i	−0.252290	+	0.252290i
$430$	−0.100459	−	1.01020i	−0.00484456	−	0.0487162i
$431$	13.2369			0.637597			0.318799	−	0.947822i	$-0.396721\pi$
$431$	13.2369			0.637597			0.318799	+	0.947822i	$0.396721\pi$
$432$	58.7248	+	24.0653i	2.82540	+	1.15784i
$433$	−1.50709			−0.0724259			−0.0362129	−	0.999344i	$-0.511529\pi$
$433$	−1.50709			−0.0724259			−0.0362129	+	0.999344i	$0.511529\pi$
$434$	−0.0598204	−	0.601546i	−0.00287147	−	0.0288751i
$435$	17.3432	−	17.3432i	0.831545	−	0.831545i
$436$	−3.94792	+	5.93270i	−0.189071	+	0.284125i
$437$	3.88097	+	3.88097i	0.185652	+	0.185652i
$438$	33.2725	+	27.2535i	1.58982	+	1.30222i
$439$		−	10.3092i		−	0.492033i	−0.969266	−	0.246016i	$-0.920878\pi$
$439$		−	10.3092i		−	0.492033i	0.969266	−	0.246016i	$-0.0791217\pi$
$440$	−1.90615	−	6.22028i	−0.0908722	−	0.296540i
$441$		−	47.2158i		−	2.24837i
$442$	1.92167	−	2.34607i	0.0914044	−	0.111591i
$443$	−14.2651	−	14.2651i	−0.677755	−	0.677755i	0.281736	−	0.959492i	$-0.409090\pi$
$443$	−14.2651	−	14.2651i	−0.677755	−	0.677755i	−0.959492	+	0.281736i	$0.909090\pi$
$444$	52.8941	−	10.6251i	2.51024	−	0.504246i
$445$	−3.84950	+	3.84950i	−0.182484	+	0.182484i
$446$	4.86416	−	0.483713i	0.230324	−	0.0229045i
$447$	−58.7904			−2.78069
$448$	−4.40153	−	6.50728i	−0.207953	−	0.307440i
$449$	−19.5711			−0.923618			−0.461809	−	0.886979i	$-0.652799\pi$
$449$	−19.5711			−0.923618			−0.461809	+	0.886979i	$0.652799\pi$
$450$	11.0088	−	1.09477i	0.518961	−	0.0516078i
$451$	6.39420	−	6.39420i	0.301091	−	0.301091i
$452$	10.5513	−	2.11949i	0.496289	−	0.0996923i
$453$	−35.2569	−	35.2569i	−1.65652	−	1.65652i
$454$	−6.01410	+	7.34232i	−0.282256	+	0.344592i
$455$			0.959035i			0.0449602i
$456$	7.42810	+	24.2399i	0.347852	+	1.13514i
$457$			39.0185i			1.82521i	0.408845	+	0.912604i	$0.365932\pi$
$457$			39.0185i			1.82521i	−0.408845	+	0.912604i	$0.634068\pi$
$458$	−20.6672	−	16.9285i	−0.965713	−	0.791016i
$459$	−24.6344	−	24.6344i	−1.14984	−	1.14984i
$460$	−2.23198	+	3.35408i	−0.104066	+	0.156385i
$461$	19.6941	−	19.6941i	0.917245	−	0.917245i	−0.0795833	−	0.996828i	$-0.525359\pi$
$461$	19.6941	−	19.6941i	0.917245	−	0.917245i	0.996828	+	0.0795833i	$0.0253590\pi$
$462$	−1.03992	−	10.4573i	−0.0483815	−	0.486518i
$463$	−14.9979			−0.697009			−0.348505	−	0.937307i	$-0.613310\pi$
$463$	−14.9979			−0.697009			−0.348505	+	0.937307i	$0.613310\pi$
$464$	−11.3082	+	27.5947i	−0.524972	+	1.28105i
$465$	−1.43201			−0.0664077
$466$	−0.675505	−	6.79278i	−0.0312921	−	0.314670i
$467$	4.88870	−	4.88870i	0.226222	−	0.226222i	−0.584890	−	0.811112i	$-0.698862\pi$
$467$	4.88870	−	4.88870i	0.226222	−	0.226222i	0.811112	+	0.584890i	$0.198862\pi$
$468$	12.7205	+	8.46488i	0.588005	+	0.391289i
$469$	−4.45404	−	4.45404i	−0.205669	−	0.205669i
$470$	−10.0867	−	8.26201i	−0.465264	−	0.381098i
$471$		−	8.17980i		−	0.376905i
$472$	−20.0596	−	10.6492i	−0.923320	−	0.490168i
$473$			1.65114i			0.0759197i
$474$	−45.5462	+	55.6052i	−2.09201	+	2.55403i
$475$	1.92659	+	1.92659i	0.0883982	+	0.0883982i
$476$	0.849317	+	4.22808i	0.0389284	+	0.193794i
$477$	49.2334	−	49.2334i	2.25424	−	2.25424i
$478$	−12.4191	+	1.23501i	−0.568038	+	0.0564883i
$479$	−27.3381			−1.24911			−0.624555	−	0.780981i	$-0.714720\pi$
$479$	−27.3381			−1.24911			−0.624555	+	0.780981i	$0.714720\pi$
$480$	−16.3709	+	8.85002i	−0.747227	+	0.403946i
$481$	8.00784			0.365126
$482$	−5.26526	+	0.523601i	−0.239826	+	0.0238494i
$483$	−4.60173	+	4.60173i	−0.209386	+	0.209386i
$484$	−2.24881	−	11.1950i	−0.102218	−	0.508865i
$485$	3.92119	+	3.92119i	0.178052	+	0.178052i
$486$	42.0387	−	51.3230i	1.90691	−	2.32806i
$487$		−	35.4769i		−	1.60761i	−0.594892	−	0.803806i	$-0.702805\pi$
$487$		−	35.4769i		−	1.60761i	0.594892	−	0.803806i	$-0.297195\pi$
$488$	−6.75777	+	12.7295i	−0.305910	+	0.576235i
$489$		−	64.7171i		−	2.92661i
$490$	6.60330	+	5.40876i	0.298307	+	0.244343i
$491$	3.55614	+	3.55614i	0.160486	+	0.160486i	0.782782	−	0.622296i	$-0.213800\pi$
$491$	3.55614	+	3.55614i	0.160486	+	0.160486i	−0.622296	+	0.782782i	$0.713800\pi$
$492$	−21.5347	−	14.3303i	−0.970860	−	0.646060i
$493$	11.5757	−	11.5757i	0.521343	−	0.521343i
$494$	0.372376	+	3.74456i	0.0167540	+	0.168476i
$495$	−17.9936			−0.808753
$496$	1.60608	−	0.672375i	0.0721151	−	0.0301905i
$497$	10.2114			0.458042
$498$	−0.444856	−	4.47341i	−0.0199345	−	0.200458i
$499$	−17.6521	+	17.6521i	−0.790218	+	0.790218i	−0.981529	−	0.191312i	$-0.938726\pi$
$499$	−17.6521	+	17.6521i	−0.790218	+	0.790218i	0.191312	+	0.981529i	$0.438726\pi$
$500$	−1.10800	+	1.66503i	−0.0495512	+	0.0744626i
$501$	−43.8776	−	43.8776i	−1.96031	−	1.96031i
$502$	−9.27281	−	7.59537i	−0.413866	−	0.338998i
$503$		−	31.8567i		−	1.42042i	−0.703990	−	0.710210i	$-0.748600\pi$
$503$		−	31.8567i		−	1.42042i	0.703990	−	0.710210i	$-0.251400\pi$
$504$	−20.7747	+	6.36622i	−0.925378	+	0.283574i
$505$		−	0.411952i		−	0.0183316i
$506$	4.15220	−	5.06923i	0.184588	−	0.225355i
$507$	−28.0225	−	28.0225i	−1.24452	−	1.24452i
$508$	9.54097	−	1.91655i	0.423312	−	0.0850330i
$509$	−5.61054	+	5.61054i	−0.248683	+	0.248683i	−0.820430	−	0.571747i	$-0.806266\pi$
$509$	−5.61054	+	5.61054i	−0.248683	+	0.248683i	0.571747	+	0.820430i	$0.306266\pi$
$510$	10.1656	−	1.01092i	0.450142	−	0.0447641i
$511$	−9.07810			−0.401591
$512$	14.2056	−	17.6125i	0.627804	−	0.778371i
$513$	43.2291			1.90861
$514$	−20.7801	+	2.06646i	−0.916570	+	0.0911478i
$515$	−3.18353	+	3.18353i	−0.140283	+	0.140283i
$516$	4.63063	−	0.930180i	0.203852	−	0.0409489i
$517$	14.9952	+	14.9952i	0.659489	+	0.659489i
$518$	−7.21585	+	8.80948i	−0.317046	+	0.387066i
$519$			74.7767i			3.28233i
$520$	−2.64103	+	0.809320i	−0.115817	+	0.0354910i
$521$			33.1977i			1.45442i	0.686417	+	0.727208i	$0.259182\pi$
$521$			33.1977i			1.45442i	−0.686417	+	0.727208i	$0.740818\pi$
$522$	63.8079	+	52.2651i	2.79280	+	2.28758i
$523$	−2.60707	−	2.60707i	−0.113999	−	0.113999i	0.647806	−	0.761805i	$-0.275687\pi$
$523$	−2.60707	−	2.60707i	−0.113999	−	0.113999i	−0.761805	+	0.647806i	$0.775687\pi$
$524$	12.5447	−	18.8514i	0.548017	−	0.823527i
$525$	−2.28440	+	2.28440i	−0.0996992	+	0.0996992i
$526$	−0.950909	−	9.56221i	−0.0414616	−	0.416932i
$527$	−0.955787			−0.0416347
$528$	27.9202	−	11.6886i	1.21507	−	0.508681i
$529$	18.9421			0.823570
$530$	1.24558	+	12.5254i	0.0541044	+	0.544067i
$531$	−44.4162	+	44.4162i	−1.92750	+	1.92750i
$532$	−4.45497	−	2.96457i	−0.193147	−	0.128530i
$533$	−2.71487	−	2.71487i	−0.117594	−	0.117594i
$534$	−19.5941	−	16.0496i	−0.847921	−	0.694532i
$535$		−	9.19083i		−	0.397354i
$536$	8.50699	−	16.0244i	0.367446	−	0.692150i
$537$			76.4593i			3.29946i
$538$	−7.65452	+	9.34504i	−0.330010	+	0.402893i
$539$	−9.81668	−	9.81668i	−0.422834	−	0.422834i
$540$	6.24939	+	31.1108i	0.268931	+	1.33879i
$541$	−22.6839	+	22.6839i	−0.975257	+	0.975257i	−0.999701	−	0.0244439i	$-0.992218\pi$
$541$	−22.6839	+	22.6839i	−0.975257	+	0.975257i	0.0244439	+	0.999701i	$0.492218\pi$
$542$	−34.6499	+	3.44574i	−1.48834	+	0.148007i
$543$	71.8992			3.08549
$544$	−10.9267	+	5.90691i	−0.468479	+	0.253257i
$545$	−3.56311			−0.152627
$546$	−4.44000	+	0.441533i	−0.190014	+	0.0188959i
$547$	−3.02284	+	3.02284i	−0.129248	+	0.129248i	−0.768771	−	0.639524i	$-0.779132\pi$
$547$	−3.02284	+	3.02284i	−0.129248	+	0.129248i	0.639524	+	0.768771i	$0.279132\pi$
$548$	−5.33974	−	26.5823i	−0.228102	−	1.13554i
$549$	28.1857	+	28.1857i	1.20293	+	1.20293i
$550$	2.06124	−	2.51647i	0.0878916	−	0.107303i
$551$			20.3133i			0.865375i
$552$	−16.5558	−	8.78907i	−0.704661	−	0.374088i
$553$		−	15.1714i		−	0.645153i
$554$	15.4415	+	12.6481i	0.656047	+	0.537368i
$555$	19.0745	+	19.0745i	0.809666	+	0.809666i
$556$	19.3709	+	12.8904i	0.821510	+	0.546675i
$557$	9.27495	−	9.27495i	0.392992	−	0.392992i	−0.482760	−	0.875753i	$-0.660366\pi$
$557$	9.27495	−	9.27495i	0.392992	−	0.392992i	0.875753	+	0.482760i	$0.160366\pi$
$558$	−0.476537	−	4.79199i	−0.0201734	−	0.202861i
$559$	0.701048			0.0296512
$560$	1.48949	−	3.63469i	0.0629423	−	0.153594i
$561$	−16.6154			−0.701504
$562$	−2.02376	−	20.3507i	−0.0853672	−	0.858441i
$563$	−20.3025	+	20.3025i	−0.855649	+	0.855649i	−0.990822	−	0.135173i	$-0.956841\pi$
$563$	−20.3025	+	20.3025i	−0.855649	+	0.855649i	0.135173	+	0.990822i	$0.456841\pi$
$564$	33.6064	−	50.5016i	1.41508	−	2.12650i
$565$	3.80495	+	3.80495i	0.160076	+	0.160076i
$566$	31.0655	+	25.4458i	1.30578	+	1.06956i
$567$			28.2112i			1.18476i
$568$	8.61727	+	28.1205i	0.361573	+	1.17991i
$569$		−	14.3362i		−	0.601005i	−0.953781	−	0.300503i	$-0.902846\pi$
$569$		−	14.3362i		−	0.601005i	0.953781	−	0.300503i	$-0.0971544\pi$
$570$	−8.03247	+	9.80645i	−0.336443	+	0.410747i
$571$	8.54368	+	8.54368i	0.357542	+	0.357542i	0.862906	−	0.505364i	$-0.168642\pi$
$571$	8.54368	+	8.54368i	0.357542	+	0.357542i	−0.505364	+	0.862906i	$0.668642\pi$
$572$	4.40467	−	0.884790i	0.184168	−	0.0369949i
$573$	34.3987	−	34.3987i	1.43703	−	1.43703i
$574$	5.43301	−	0.540283i	0.226769	−	0.0225510i
$575$	−2.01442			−0.0840071
$576$	−35.0631	−	51.8377i	−1.46096	−	2.15991i
$577$	−8.68179			−0.361428			−0.180714	−	0.983536i	$-0.557841\pi$
$577$	−8.68179			−0.361428			−0.180714	+	0.983536i	$0.557841\pi$
$578$	−17.1386	+	1.70434i	−0.712872	+	0.0708912i
$579$	26.2661	−	26.2661i	1.09158	−	1.09158i
$580$	−14.6189	+	2.93658i	−0.607018	+	0.121935i
$581$	0.670953	+	0.670953i	0.0278358	+	0.0278358i
$582$	−16.3484	+	19.9590i	−0.677665	+	0.827328i
$583$		−	20.4723i		−	0.847877i
$584$	−7.66092	−	24.9996i	−0.317011	−	1.03449i
$585$			7.63978i			0.315866i
$586$	23.8330	+	19.5216i	0.984533	+	0.806431i
$587$	21.9042	+	21.9042i	0.904082	+	0.904082i	0.995786	−	0.0917043i	$-0.0292315\pi$
$587$	21.9042	+	21.9042i	0.904082	+	0.904082i	−0.0917043	+	0.995786i	$0.529231\pi$
$588$	−22.0006	+	33.0611i	−0.907288	+	1.36342i
$589$	0.838619	−	0.838619i	0.0345547	−	0.0345547i
$590$	−1.12370	−	11.2998i	−0.0462622	−	0.465206i
$591$	49.3871			2.03151
$592$	−30.3493	−	12.4371i	−1.24735	−	0.511160i
$593$	−17.5142			−0.719222			−0.359611	−	0.933102i	$-0.617091\pi$
$593$	−17.5142			−0.719222			−0.359611	+	0.933102i	$0.617091\pi$
$594$	−5.10722	−	51.3575i	−0.209552	−	2.10722i
$595$	−1.52471	+	1.52471i	−0.0625071	+	0.0625071i
$596$	29.7549	+	19.8005i	1.21881	+	0.811059i
$597$	10.9052	+	10.9052i	0.446319	+	0.446319i
$598$	−2.15231	−	1.76296i	−0.0880144	−	0.0720926i
$599$		−	19.0276i		−	0.777447i	−0.921354	−	0.388724i	$-0.872916\pi$
$599$		−	19.0276i		−	0.777447i	0.921354	−	0.388724i	$-0.127084\pi$
$600$	−8.21864	−	4.36308i	−0.335525	−	0.178122i
$601$			5.52545i			0.225388i	0.993630	+	0.112694i	$0.0359479\pi$
$601$			5.52545i			0.225388i	−0.993630	+	0.112694i	$0.964052\pi$
$602$	−0.631713	+	0.771228i	−0.0257467	+	0.0314329i
$603$	−35.4814	−	35.4814i	−1.44491	−	1.44491i
$604$	5.96975	+	29.7187i	0.242906	+	1.20924i
$605$	4.03711	−	4.03711i	0.164132	−	0.164132i
$606$	1.90719	−	0.189660i	0.0774744	−	0.00770440i
$607$	−12.1064			−0.491384			−0.245692	−	0.969348i	$-0.579015\pi$
$607$	−12.1064			−0.491384			−0.245692	+	0.969348i	$0.579015\pi$
$608$	4.40443	−	14.7700i	0.178623	−	0.599004i
$609$	−24.0858			−0.976007
$610$	−7.17064	+	0.713081i	−0.290331	+	0.0288718i
$611$	6.36671	−	6.36671i	0.257570	−	0.257570i
$612$	6.76576	+	33.6814i	0.273490	+	1.36149i
$613$	17.8073	+	17.8073i	0.719230	+	0.719230i	0.968448	−	0.249218i	$-0.0801734\pi$
$613$	17.8073	+	17.8073i	0.719230	+	0.719230i	−0.249218	+	0.968448i	$0.580173\pi$
$614$	11.5631	−	14.1168i	0.466647	−	0.569707i
$615$		−	12.9335i		−	0.521529i
$616$	−2.99568	+	5.64289i	−0.120699	+	0.227358i
$617$		−	1.10944i		−	0.0446642i	−0.999751	−	0.0223321i	$-0.992891\pi$
$617$		−	1.10944i		−	0.0446642i	0.999751	−	0.0223321i	$-0.00710912\pi$
$618$	−16.2043	−	13.2730i	−0.651833	−	0.533917i
$619$	−31.8702	−	31.8702i	−1.28097	−	1.28097i	−0.940115	−	0.340859i	$-0.889282\pi$
$619$	−31.8702	−	31.8702i	−1.28097	−	1.28097i	−0.340859	−	0.940115i	$-0.610718\pi$
$620$	0.724766	+	0.482297i	0.0291073	+	0.0193695i
$621$	−22.5998	+	22.5998i	−0.906901	+	0.906901i
$622$	−0.0899724	−	0.904750i	−0.00360756	−	0.0362772i
$623$	5.34608			0.214186
$624$	−4.96278	−	11.8544i	−0.198670	−	0.474557i
$625$	−1.00000			−0.0400000
$626$	−2.99168	−	30.0840i	−0.119572	−	1.20240i
$627$	14.5786	−	14.5786i	0.582213	−	0.582213i
$628$	−2.75494	+	4.13996i	−0.109934	+	0.165202i
$629$	12.7312	+	12.7312i	0.507626	+	0.507626i
$630$	−8.40458	−	6.88419i	−0.334846	−	0.274273i
$631$			6.80064i			0.270729i	0.990796	+	0.135365i	$0.0432206\pi$
$631$			6.80064i			0.270729i	−0.990796	+	0.135365i	$0.956779\pi$
$632$	41.7795	−	12.8030i	1.66190	−	0.509275i
$633$		−	12.2460i		−	0.486736i
$634$	10.9776	−	13.4020i	0.435976	−	0.532262i
$635$	3.44063	+	3.44063i	0.136537	+	0.136537i
$636$	−57.4146	+	11.5332i	−2.27664	+	0.457320i
$637$	−4.16800	+	4.16800i	−0.165142	+	0.165142i
$638$	24.1328	−	2.39988i	0.955429	−	0.0950121i
$639$	81.3449			3.21796
$640$	11.2663	+	1.03453i	0.445340	+	0.0408933i
$641$	14.2566			0.563100			0.281550	−	0.959547i	$-0.409151\pi$
$641$	14.2566			0.563100			0.281550	+	0.959547i	$0.409151\pi$
$642$	42.5503	−	4.23139i	1.67933	−	0.167000i
$643$	14.4137	−	14.4137i	0.568422	−	0.568422i	−0.363264	−	0.931686i	$-0.618338\pi$
$643$	14.4137	−	14.4137i	0.568422	−	0.568422i	0.931686	+	0.363264i	$0.118338\pi$
$644$	3.87888	−	0.779172i	0.152849	−	0.0307037i
$645$	1.66988	+	1.66988i	0.0657514	+	0.0657514i
$646$	−5.36124	+	6.54528i	−0.210935	+	0.257520i
$647$			20.5723i			0.808782i	0.914586	+	0.404391i	$0.132517\pi$
$647$			20.5723i			0.808782i	−0.914586	+	0.404391i	$0.867483\pi$
$648$	−77.6891	+	23.8071i	−3.05192	+	0.935233i
$649$			18.4692i			0.724980i
$650$	−1.06845	−	0.875168i	−0.0419081	−	0.0343269i
$651$	0.994365	+	0.994365i	0.0389723	+	0.0389723i
$652$	−21.7966	+	32.7546i	−0.853620	+	1.28277i
$653$	−9.79946	+	9.79946i	−0.383482	+	0.383482i	−0.872355	−	0.488873i	$-0.837408\pi$
$653$	−9.79946	+	9.79946i	−0.383482	+	0.383482i	0.488873	+	0.872355i	$0.337408\pi$
$654$	−1.64043	−	16.4960i	−0.0641459	−	0.645043i
$655$	11.3219			0.442384
$656$	6.07271	+	14.5057i	0.237100	+	0.566352i
$657$	−72.3172			−2.82136
$658$	1.26703	+	12.7411i	0.0493940	+	0.496700i
$659$	−8.70669	+	8.70669i	−0.339165	+	0.339165i	−0.856053	−	0.516888i	$-0.827090\pi$
$659$	−8.70669	+	8.70669i	−0.339165	+	0.339165i	0.516888	+	0.856053i	$0.327090\pi$
$660$	12.5994	+	8.38426i	0.490429	+	0.326357i
$661$	19.7899	+	19.7899i	0.769737	+	0.769737i	0.978060	−	0.208323i	$-0.0668006\pi$
$661$	19.7899	+	19.7899i	0.769737	+	0.769737i	−0.208323	+	0.978060i	$0.566801\pi$
$662$	−13.0576	−	10.6955i	−0.507498	−	0.415692i
$663$			7.05464i			0.273979i
$664$	−1.28149	+	2.41391i	−0.0497313	+	0.0936778i
$665$		−	2.67560i		−	0.103755i
$666$	−57.4823	+	70.1773i	−2.22739	+	2.71932i
$667$	−10.6196	−	10.6196i	−0.411194	−	0.411194i
$668$	7.42941	+	36.9852i	0.287453	+	1.43100i
$669$	−8.04053	+	8.04053i	−0.310865	+	0.310865i
$670$	9.02674	−	0.897659i	0.348733	−	0.0346796i
$671$	11.7202			0.452454
$672$	17.5131	+	5.22242i	0.675582	+	0.201459i
$673$	−14.0829			−0.542857			−0.271429	−	0.962459i	$-0.587496\pi$
$673$	−14.0829			−0.542857			−0.271429	+	0.962459i	$0.587496\pi$
$674$	43.2098	−	4.29698i	1.66438	−	0.165513i
$675$	−11.2190	+	11.2190i	−0.431821	+	0.431821i
$676$	4.74481	+	23.6206i	0.182493	+	0.908487i
$677$	−29.8166	−	29.8166i	−1.14594	−	1.14594i	−0.987343	−	0.158601i	$-0.949302\pi$
$677$	−29.8166	−	29.8166i	−1.14594	−	1.14594i	−0.158601	−	0.987343i	$-0.550698\pi$
$678$	−15.8638	+	19.3674i	−0.609247	+	0.743799i
$679$		−	5.44564i		−	0.208984i
$680$	−5.48550	−	2.91212i	−0.210359	−	0.111675i
$681$		−	22.0784i		−	0.846045i
$682$	−1.09538	−	0.897229i	−0.0419444	−	0.0343567i
$683$	−12.0646	−	12.0646i	−0.461641	−	0.461641i	0.437552	−	0.899193i	$-0.355845\pi$
$683$	−12.0646	−	12.0646i	−0.461641	−	0.461641i	−0.899193	+	0.437552i	$0.855845\pi$
$684$	−35.4888	−	23.6161i	−1.35695	−	0.902983i
$685$	9.58601	−	9.58601i	0.366263	−	0.366263i
$686$	−1.79146	−	18.0147i	−0.0683984	−	0.687805i
$687$	62.1462			2.37102
$688$	−2.65693	−	1.08880i	−0.101295	−	0.0415103i
$689$	−8.69221			−0.331147
$690$	−0.927425	−	9.32606i	−0.0353065	−	0.355037i
$691$	2.58867	−	2.58867i	0.0984776	−	0.0984776i	−0.656152	−	0.754629i	$-0.727817\pi$
$691$	2.58867	−	2.58867i	0.0984776	−	0.0984776i	0.754629	+	0.656152i	$0.227817\pi$
$692$	25.1847	−	37.8459i	0.957377	−	1.43869i
$693$	12.4945	+	12.4945i	0.474628	+	0.474628i
$694$	21.1068	+	17.2886i	0.801203	+	0.656266i
$695$			11.6340i			0.441301i
$696$	−20.3258	−	66.3285i	−0.770447	−	2.51418i
$697$		−	8.63242i		−	0.326976i
$698$	12.6393	−	15.4307i	0.478405	−	0.584062i
$699$	11.2286	+	11.2286i	0.424704	+	0.424704i
$700$	1.92556	−	0.386797i	0.0727792	−	0.0146196i
$701$	−26.9943	+	26.9943i	−1.01956	+	1.01956i	−0.0197572	+	0.999805i	$0.506289\pi$
$701$	−26.9943	+	26.9943i	−1.01956	+	1.01956i	−0.999805	+	0.0197572i	$0.993711\pi$
$702$	−21.8055	+	2.16844i	−0.822997	+	0.0818425i
$703$	−22.3410			−0.842606
$704$	−18.0676	−	3.48763i	−0.680949	−	0.131445i
$705$	30.3307			1.14232
$706$	−37.6929	+	3.74835i	−1.41859	+	0.141071i
$707$	−0.286054	+	0.286054i	−0.0107582	+	0.0107582i
$708$	51.7969	−	10.4047i	1.94665	−	0.391033i
$709$	−35.0639	−	35.0639i	−1.31685	−	1.31685i	−0.916254	−	0.400598i	$-0.868802\pi$
$709$	−35.0639	−	35.0639i	−1.31685	−	1.31685i	−0.400598	−	0.916254i	$-0.631198\pi$
$710$	−9.31840	+	11.3764i	−0.349713	+	0.426948i
$711$		−	120.857i		−	4.53249i
$712$	4.51151	+	14.7223i	0.169076	+	0.551740i
$713$			0.876848i			0.0328382i
$714$	−7.76085	−	6.35692i	−0.290443	−	0.237902i
$715$	1.58839	+	1.58839i	0.0594026	+	0.0594026i
$716$	25.7513	−	38.6975i	0.962373	−	1.44619i
$717$	20.5290	−	20.5290i	0.766671	−	0.766671i
$718$	−2.67562	−	26.9057i	−0.0998534	−	1.00411i
$719$	−0.436840			−0.0162914			−0.00814568	−	0.999967i	$-0.502593\pi$
$719$	−0.436840			−0.0162914			−0.00814568	+	0.999967i	$0.502593\pi$
$720$	11.8654	−	28.9544i	0.442198	−	1.07907i
$721$	4.42120			0.164654
$722$	1.62007	+	16.2913i	0.0602929	+	0.606298i
$723$	8.70356	−	8.70356i	0.323689	−	0.323689i
$724$	−36.3896	−	24.2155i	−1.35241	−	0.899963i
$725$	−5.27182	−	5.27182i	−0.195790	−	0.195790i
$726$	20.5491	+	16.8317i	0.762647	+	0.624684i
$727$			38.8072i			1.43928i	0.694348	+	0.719640i	$0.255693\pi$
$727$			38.8072i			1.43928i	−0.694348	+	0.719640i	$0.744307\pi$
$728$	2.39588	+	1.27191i	0.0887970	+	0.0471402i
$729$			68.1444i			2.52387i
$730$	8.28423	−	10.1138i	0.306613	−	0.374329i
$731$	1.11455	+	1.11455i	0.0412233	+	0.0412233i
$732$	−6.60263	−	32.8693i	−0.244040	−	1.21488i
$733$	−24.3059	+	24.3059i	−0.897758	+	0.897758i	−0.995238	−	0.0974793i	$-0.968922\pi$
$733$	−24.3059	+	24.3059i	−0.897758	+	0.897758i	0.0974793	+	0.995238i	$0.468922\pi$
$734$	5.97226	−	0.593908i	0.220440	−	0.0219215i
$735$	−19.8561			−0.732404
$736$	5.41906	+	10.0243i	0.199749	+	0.369500i
$737$	−14.7539			−0.543469
$738$	43.2800	−	4.30395i	1.59316	−	0.158431i
$739$	−27.0262	+	27.0262i	−0.994174	+	0.994174i	−0.999983	−	0.00580951i	$-0.998151\pi$
$739$	−27.0262	+	27.0262i	−0.994174	+	0.994174i	0.00580951	+	0.999983i	$0.498151\pi$
$740$	−3.22971	−	16.0782i	−0.118727	−	0.591046i
$741$	−6.18982	−	6.18982i	−0.227389	−	0.227389i
$742$	7.83253	−	9.56235i	0.287541	−	0.351045i
$743$			12.1663i			0.446337i	0.974780	+	0.223169i	$0.0716401\pi$
$743$			12.1663i			0.446337i	−0.974780	+	0.223169i	$0.928360\pi$
$744$	−1.89919	+	3.57746i	−0.0696276	+	0.131156i
$745$			17.8705i			0.654724i
$746$	37.0580	+	30.3543i	1.35679	+	1.11135i
$747$	5.34489	+	5.34489i	0.195559	+	0.195559i
$748$	8.40940	+	5.59605i	0.307478	+	0.204612i
$749$	−6.38199	+	6.38199i	−0.233193	+	0.233193i
$750$	−0.460393	−	4.62965i	−0.0168112	−	0.169051i
$751$	−40.8606			−1.49102			−0.745512	−	0.666492i	$-0.767795\pi$
$751$	−40.8606			−1.49102			−0.745512	+	0.666492i	$0.767795\pi$
$752$	−34.0177	+	14.2413i	−1.24050	+	0.519326i
$753$	27.8834			1.01613
$754$	−1.01895	−	10.2464i	−0.0371079	−	0.373152i
$755$	−10.7170	+	10.7170i	−0.390033	+	0.390033i
$756$	17.2634	−	25.9424i	0.627864	−	0.943516i
$757$	−0.00399171	−	0.00399171i	−0.000145081	−	0.000145081i	0.707034	−	0.707179i	$-0.250033\pi$
$757$	−0.00399171	−	0.00399171i	−0.000145081	−	0.000145081i	−0.707179	+	0.707034i	$0.750033\pi$
$758$	−11.5374	−	9.45026i	−0.419056	−	0.343249i
$759$			15.2432i			0.553292i
$760$	7.36818	−	2.25791i	0.267272	−	0.0819031i
$761$			0.751325i			0.0272355i	0.999907	+	0.0136178i	$0.00433480\pi$
$761$			0.751325i			0.0272355i	−0.999907	+	0.0136178i	$0.995665\pi$
$762$	−14.3449	+	17.5129i	−0.519660	+	0.634427i
$763$	2.47418	+	2.47418i	0.0895712	+	0.0895712i
$764$	−28.9953	+	5.82443i	−1.04901	+	0.210721i
$765$	−12.1460	+	12.1460i	−0.439141	+	0.439141i
$766$	7.31313	−	0.727250i	0.264234	−	0.0262766i
$767$	7.84172			0.283148
$768$	0.397428	+	52.6354i	0.0143410	+	1.89932i

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:	\( N \)	\(=\)	\( 80 = 2^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	80.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.40727 - 0.139945i) q^{2} +(-2.32624 + 2.32624i) q^{3} +(1.96083 - 0.393883i) q^{4} +(0.707107 + 0.707107i) q^{5} +(-2.94811 + 3.59920i) q^{6} -0.982011i q^{7} +(2.70430 - 0.828709i) q^{8} -7.82281i q^{9} +O(q^{10})\)	\(q+(1.40727 - 0.139945i) q^{2} +(-2.32624 + 2.32624i) q^{3} +(1.96083 - 0.393883i) q^{4} +(0.707107 + 0.707107i) q^{5} +(-2.94811 + 3.59920i) q^{6} -0.982011i q^{7} +(2.70430 - 0.828709i) q^{8} -7.82281i q^{9} +(1.09405 + 0.896135i) q^{10} +(-1.62645 - 1.62645i) q^{11} +(-3.64510 + 5.47764i) q^{12} +(-0.690562 + 0.690562i) q^{13} +(-0.137428 - 1.38196i) q^{14} -3.28980 q^{15} +(3.68971 - 1.54467i) q^{16} -2.19577 q^{17} +(-1.09477 - 11.0088i) q^{18} +(1.92659 - 1.92659i) q^{19} +(1.66503 + 1.10800i) q^{20} +(2.28440 + 2.28440i) q^{21} +(-2.51647 - 2.06124i) q^{22} +2.01442i q^{23} +(-4.36308 + 8.21864i) q^{24} +1.00000i q^{25} +(-0.875168 + 1.06845i) q^{26} +(11.2190 + 11.2190i) q^{27} +(-0.386797 - 1.92556i) q^{28} +(-5.27182 + 5.27182i) q^{29} +(-4.62965 + 0.460393i) q^{30} +0.435286 q^{31} +(4.97626 - 2.69014i) q^{32} +7.56703 q^{33} +(-3.09004 + 0.307288i) q^{34} +(0.694387 - 0.694387i) q^{35} +(-3.08127 - 15.3392i) q^{36} +(-5.79805 - 5.79805i) q^{37} +(2.44162 - 2.98086i) q^{38} -3.21283i q^{39} +(2.49822 + 1.32624i) q^{40} +3.93139i q^{41} +(3.53446 + 2.89508i) q^{42} +(-0.507592 - 0.507592i) q^{43} +(-3.82982 - 2.54856i) q^{44} +(5.53157 - 5.53157i) q^{45} +(0.281909 + 2.83484i) q^{46} -9.21960 q^{47} +(-4.98988 + 12.1765i) q^{48} +6.03565 q^{49} +(0.139945 + 1.40727i) q^{50} +(5.10789 - 5.10789i) q^{51} +(-1.08208 + 1.62608i) q^{52} +(6.29357 + 6.29357i) q^{53} +(17.3583 + 14.2182i) q^{54} -2.30015i q^{55} +(-0.813802 - 2.65565i) q^{56} +8.96345i q^{57} +(-6.68111 + 8.15665i) q^{58} +(-5.67778 - 5.67778i) q^{59} +(-6.45075 + 1.29580i) q^{60} +(-3.60301 + 3.60301i) q^{61} +(0.612566 - 0.0609163i) q^{62} -7.68209 q^{63} +(6.62648 - 4.48216i) q^{64} -0.976603 q^{65} +(10.6489 - 1.05897i) q^{66} +(4.53563 - 4.53563i) q^{67} +(-4.30553 + 0.864875i) q^{68} +(-4.68603 - 4.68603i) q^{69} +(0.880015 - 1.07437i) q^{70} +10.3984i q^{71} +(-6.48284 - 21.1552i) q^{72} -9.24439i q^{73} +(-8.97085 - 7.34803i) q^{74} +(-2.32624 - 2.32624i) q^{75} +(3.01887 - 4.53658i) q^{76} +(-1.59719 + 1.59719i) q^{77} +(-0.449621 - 4.52133i) q^{78} +15.4493 q^{79} +(3.70127 + 1.51677i) q^{80} -28.7280 q^{81} +(0.550180 + 5.53253i) q^{82} +(-0.683244 + 0.683244i) q^{83} +(5.37910 + 3.57953i) q^{84} +(-1.55264 - 1.55264i) q^{85} +(-0.785356 - 0.643285i) q^{86} -24.5271i q^{87} +(-5.74626 - 3.05055i) q^{88} +5.44401i q^{89} +(7.01030 - 8.55854i) q^{90} +(0.678140 + 0.678140i) q^{91} +(0.793445 + 3.94994i) q^{92} +(-1.01258 + 1.01258i) q^{93} +(-12.9745 + 1.29024i) q^{94} +2.72461 q^{95} +(-5.31808 + 17.8339i) q^{96} +5.54540 q^{97} +(8.49381 - 0.844662i) q^{98} +(-12.7234 + 12.7234i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{4} - 12 q^{6}+O(q^{10}) \) 16 * q - 4 * q^4 - 12 * q^6	\( 16 q - 4 q^{4} - 12 q^{6} + 4 q^{10} - 8 q^{11} - 12 q^{12} + 4 q^{14} - 8 q^{15} + 16 q^{16} - 8 q^{19} + 8 q^{20} - 20 q^{22} + 8 q^{24} - 16 q^{26} + 24 q^{27} - 4 q^{28} - 16 q^{29} + 16 q^{34} - 4 q^{36} - 16 q^{37} + 20 q^{38} + 60 q^{42} + 8 q^{43} + 40 q^{44} - 4 q^{46} - 40 q^{47} - 40 q^{48} - 16 q^{49} - 4 q^{50} - 32 q^{51} + 56 q^{52} + 16 q^{53} + 32 q^{54} + 16 q^{56} - 12 q^{58} - 8 q^{59} - 28 q^{60} + 16 q^{61} - 8 q^{62} + 40 q^{63} - 16 q^{64} + 40 q^{67} - 48 q^{68} + 16 q^{69} - 8 q^{70} - 40 q^{72} - 72 q^{74} + 16 q^{77} - 16 q^{78} + 16 q^{79} + 16 q^{80} - 16 q^{81} - 76 q^{82} + 40 q^{83} - 64 q^{84} - 16 q^{85} + 28 q^{86} + 36 q^{90} + 32 q^{91} - 52 q^{92} - 48 q^{93} - 36 q^{94} + 32 q^{95} + 8 q^{96} + 60 q^{98} - 8 q^{99}+O(q^{100}) \) 16 * q - 4 * q^4 - 12 * q^6 + 4 * q^10 - 8 * q^11 - 12 * q^12 + 4 * q^14 - 8 * q^15 + 16 * q^16 - 8 * q^19 + 8 * q^20 - 20 * q^22 + 8 * q^24 - 16 * q^26 + 24 * q^27 - 4 * q^28 - 16 * q^29 + 16 * q^34 - 4 * q^36 - 16 * q^37 + 20 * q^38 + 60 * q^42 + 8 * q^43 + 40 * q^44 - 4 * q^46 - 40 * q^47 - 40 * q^48 - 16 * q^49 - 4 * q^50 - 32 * q^51 + 56 * q^52 + 16 * q^53 + 32 * q^54 + 16 * q^56 - 12 * q^58 - 8 * q^59 - 28 * q^60 + 16 * q^61 - 8 * q^62 + 40 * q^63 - 16 * q^64 + 40 * q^67 - 48 * q^68 + 16 * q^69 - 8 * q^70 - 40 * q^72 - 72 * q^74 + 16 * q^77 - 16 * q^78 + 16 * q^79 + 16 * q^80 - 16 * q^81 - 76 * q^82 + 40 * q^83 - 64 * q^84 - 16 * q^85 + 28 * q^86 + 36 * q^90 + 32 * q^91 - 52 * q^92 - 48 * q^93 - 36 * q^94 + 32 * q^95 + 8 * q^96 + 60 * q^98 - 8 * q^99

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