LMFDB - Embedded newform 882.2.bb.b.151.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [882,2,Mod(25,882)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(882, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([28, 16]))

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

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

chi := DirichletCharacter("882.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 882 = 2 \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	882.bb (of order $21$, degree $12$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.04280545828$
Analytic rank:	$0$
Dimension:	$336$
Relative dimension:	$28$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			151.3
Character	$\chi$	$=$	882.151
Dual form			882.2.bb.b.625.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.900969 - 0.433884i) q^{2} +(-1.64232 + 0.550266i) q^{3} +(0.623490 - 0.781831i) q^{4} +(1.41841 + 1.31609i) q^{5} +(-1.24093 + 1.20835i) q^{6} +(2.64554 - 0.0335735i) q^{7} +(0.222521 - 0.974928i) q^{8} +(2.39442 - 1.80742i) q^{9} +O(q^{10})$	\(q+(0.900969 - 0.433884i) q^{2} +(-1.64232 + 0.550266i) q^{3} +(0.623490 - 0.781831i) q^{4} +(1.41841 + 1.31609i) q^{5} +(-1.24093 + 1.20835i) q^{6} +(2.64554 - 0.0335735i) q^{7} +(0.222521 - 0.974928i) q^{8} +(2.39442 - 1.80742i) q^{9} +(1.84897 + 0.570333i) q^{10} +(1.64632 + 1.12244i) q^{11} +(-0.593753 + 1.62710i) q^{12} +(1.72482 + 1.17596i) q^{13} +(2.36898 - 1.17810i) q^{14} +(-3.05368 - 1.38094i) q^{15} +(-0.222521 - 0.974928i) q^{16} +(-7.35401 + 1.10844i) q^{17} +(1.37308 - 2.66733i) q^{18} +(-2.17854 - 3.77334i) q^{19} +(1.91333 - 0.288388i) q^{20} +(-4.32634 + 1.51089i) q^{21} +(1.97030 + 0.296974i) q^{22} +(2.74953 + 7.00568i) q^{23} +(0.171019 + 1.72359i) q^{24} +(-0.0938620 - 1.25250i) q^{25} +(2.06424 + 0.311134i) q^{26} +(-2.93783 + 4.28593i) q^{27} +(1.62322 - 2.08930i) q^{28} +(9.29209 - 1.40056i) q^{29} +(-3.35044 + 0.0807592i) q^{30} +1.39374 q^{31} +(-0.623490 - 0.781831i) q^{32} +(-3.32143 - 0.937495i) q^{33} +(-6.14480 + 4.18945i) q^{34} +(3.79664 + 3.43415i) q^{35} +(0.0797937 - 2.99894i) q^{36} +(-1.18667 + 3.02358i) q^{37} +(-3.59999 - 2.45443i) q^{38} +(-3.47979 - 0.982194i) q^{39} +(1.59872 - 1.08999i) q^{40} +(9.56895 - 2.95163i) q^{41} +(-3.24235 + 3.23839i) q^{42} +(11.9592 + 3.68891i) q^{43} +(1.90403 - 0.587315i) q^{44} +(5.77500 + 0.587605i) q^{45} +(5.51689 + 5.11893i) q^{46} +(-4.78011 + 2.30198i) q^{47} +(0.901920 + 1.47870i) q^{48} +(6.99775 - 0.177640i) q^{49} +(-0.628006 - 1.08774i) q^{50} +(11.4677 - 5.86707i) q^{51} +(1.99481 - 0.615318i) q^{52} +(-3.49092 - 8.89471i) q^{53} +(-0.787298 + 5.13616i) q^{54} +(0.857922 + 3.75880i) q^{55} +(0.555956 - 2.58668i) q^{56} +(5.65420 + 4.99825i) q^{57} +(7.76421 - 5.29355i) q^{58} +(1.03451 + 4.53246i) q^{59} +(-2.98360 + 1.52646i) q^{60} +(-1.19835 - 1.50268i) q^{61} +(1.25572 - 0.604723i) q^{62} +(6.27384 - 4.86199i) q^{63} +(-0.900969 - 0.433884i) q^{64} +(0.898827 + 3.93802i) q^{65} +(-3.39927 + 0.596460i) q^{66} -10.3118 q^{67} +(-3.71854 + 6.44069i) q^{68} +(-8.37059 - 9.99259i) q^{69} +(4.91068 + 1.44676i) q^{70} +(-4.32524 + 5.42368i) q^{71} +(-1.22930 - 2.73657i) q^{72} +(-0.327678 + 0.223407i) q^{73} +(0.242731 + 3.23902i) q^{74} +(0.843359 + 2.00536i) q^{75} +(-4.30842 - 0.649389i) q^{76} +(4.39310 + 2.91420i) q^{77} +(-3.56134 + 0.624899i) q^{78} -8.80993 q^{79} +(0.967469 - 1.67571i) q^{80} +(2.46645 - 8.65544i) q^{81} +(7.34066 - 6.81114i) q^{82} +(-11.8694 + 8.09243i) q^{83} +(-1.51617 + 4.32449i) q^{84} +(-11.8898 - 8.10633i) q^{85} +(12.3754 - 1.86529i) q^{86} +(-14.4899 + 7.41328i) q^{87} +(1.46064 - 1.35528i) q^{88} +(0.231457 + 3.08857i) q^{89} +(5.45805 - 1.97626i) q^{90} +(4.60256 + 3.05315i) q^{91} +(7.19157 + 2.21830i) q^{92} +(-2.28897 + 0.766929i) q^{93} +(-3.30794 + 4.14803i) q^{94} +(1.87600 - 8.21931i) q^{95} +(1.45418 + 0.940931i) q^{96} +(4.51572 - 7.82146i) q^{97} +(6.22768 - 3.19626i) q^{98} +(5.97071 - 0.288004i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 336 q + 56 q^{2} + 5 q^{3} - 56 q^{4} + 2 q^{5} - 5 q^{6} + 2 q^{7} + 56 q^{8} + 5 q^{9}+O(q^{10}) $ 336 * q + 56 * q^2 + 5 * q^3 - 56 * q^4 + 2 * q^5 - 5 * q^6 + 2 * q^7 + 56 * q^8 + 5 * q^9	\( 336 q + 56 q^{2} + 5 q^{3} - 56 q^{4} + 2 q^{5} - 5 q^{6} + 2 q^{7} + 56 q^{8} + 5 q^{9} - 2 q^{10} - 2 q^{12} + 19 q^{13} - 2 q^{14} + q^{15} - 56 q^{16} + 7 q^{17} + 2 q^{18} + 38 q^{19} + 2 q^{20} + 4 q^{21} - 42 q^{23} + 2 q^{24} + 24 q^{25} + 9 q^{26} + 35 q^{27} + 2 q^{28} - 10 q^{29} - q^{30} - 88 q^{31} + 56 q^{32} + 26 q^{33} - 7 q^{34} - 2 q^{35} + 5 q^{36} + 52 q^{37} + 11 q^{38} - 60 q^{39} - 2 q^{40} + 3 q^{41} - 53 q^{42} + q^{43} + 108 q^{45} - 42 q^{46} + 3 q^{47} - 2 q^{48} + 70 q^{49} + 172 q^{50} + 13 q^{51} + 5 q^{52} - 78 q^{53} + 14 q^{54} + 23 q^{55} - 2 q^{56} - 30 q^{57} + 38 q^{58} - 28 q^{59} + q^{60} - 37 q^{61} - 24 q^{62} + 26 q^{63} - 56 q^{64} - 14 q^{65} + 2 q^{66} - 58 q^{67} - 21 q^{68} + 19 q^{69} + 44 q^{70} + 7 q^{71} + 2 q^{72} - 8 q^{73} + 4 q^{74} + q^{75} - 4 q^{76} - 13 q^{77} + 4 q^{78} + 18 q^{79} - 12 q^{80} - 87 q^{81} - 3 q^{82} + 185 q^{83} - 17 q^{84} - 159 q^{85} - q^{86} - 132 q^{87} + 47 q^{89} + 60 q^{90} + 45 q^{91} - 21 q^{92} + 53 q^{93} + 18 q^{94} + 26 q^{95} + 2 q^{96} + 111 q^{97} - 14 q^{98} - 157 q^{99}+O(q^{100}) \) 336 * q + 56 * q^2 + 5 * q^3 - 56 * q^4 + 2 * q^5 - 5 * q^6 + 2 * q^7 + 56 * q^8 + 5 * q^9 - 2 * q^10 - 2 * q^12 + 19 * q^13 - 2 * q^14 + q^15 - 56 * q^16 + 7 * q^17 + 2 * q^18 + 38 * q^19 + 2 * q^20 + 4 * q^21 - 42 * q^23 + 2 * q^24 + 24 * q^25 + 9 * q^26 + 35 * q^27 + 2 * q^28 - 10 * q^29 - q^30 - 88 * q^31 + 56 * q^32 + 26 * q^33 - 7 * q^34 - 2 * q^35 + 5 * q^36 + 52 * q^37 + 11 * q^38 - 60 * q^39 - 2 * q^40 + 3 * q^41 - 53 * q^42 + q^43 + 108 * q^45 - 42 * q^46 + 3 * q^47 - 2 * q^48 + 70 * q^49 + 172 * q^50 + 13 * q^51 + 5 * q^52 - 78 * q^53 + 14 * q^54 + 23 * q^55 - 2 * q^56 - 30 * q^57 + 38 * q^58 - 28 * q^59 + q^60 - 37 * q^61 - 24 * q^62 + 26 * q^63 - 56 * q^64 - 14 * q^65 + 2 * q^66 - 58 * q^67 - 21 * q^68 + 19 * q^69 + 44 * q^70 + 7 * q^71 + 2 * q^72 - 8 * q^73 + 4 * q^74 + q^75 - 4 * q^76 - 13 * q^77 + 4 * q^78 + 18 * q^79 - 12 * q^80 - 87 * q^81 - 3 * q^82 + 185 * q^83 - 17 * q^84 - 159 * q^85 - q^86 - 132 * q^87 + 47 * q^89 + 60 * q^90 + 45 * q^91 - 21 * q^92 + 53 * q^93 + 18 * q^94 + 26 * q^95 + 2 * q^96 + 111 * q^97 - 14 * q^98 - 157 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/882\mathbb{Z}\right)^\times$.

$n$	$199$	$785$
$\chi(n)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.900969	−	0.433884i	0.637081	−	0.306802i
$2$	0.900969	−	0.433884i	0.637081	−	0.306802i
$3$	−1.64232	+	0.550266i	−0.948193	+	0.317696i
$3$	−1.64232	+	0.550266i	−0.948193	+	0.317696i
$4$	0.623490	−	0.781831i	0.311745	−	0.390916i
$5$	1.41841	+	1.31609i	0.634332	+	0.588574i	0.930379	−	0.366599i	$-0.119478\pi$
$5$	1.41841	+	1.31609i	0.634332	+	0.588574i	−0.296047	+	0.955173i	$0.595668\pi$
$6$	−1.24093	+	1.20835i	−0.506606	+	0.493306i
$7$	2.64554	−	0.0335735i	0.999919	−	0.0126896i
$7$	2.64554	−	0.0335735i	0.999919	−	0.0126896i
$8$	0.222521	−	0.974928i	0.0786730	−	0.344689i
$9$	2.39442	−	1.80742i	0.798138	−	0.602474i
$10$	1.84897	+	0.570333i	0.584697	+	0.180355i
$11$	1.64632	+	1.12244i	0.496385	+	0.338430i	0.785497	−	0.618866i	$-0.212407\pi$
$11$	1.64632	+	1.12244i	0.496385	+	0.338430i	−0.289112	+	0.957295i	$0.593360\pi$
$12$	−0.593753	+	1.62710i	−0.171402	+	0.469704i
$13$	1.72482	+	1.17596i	0.478379	+	0.326153i	0.778388	−	0.627783i	$-0.216037\pi$
$13$	1.72482	+	1.17596i	0.478379	+	0.326153i	−0.300009	+	0.953936i	$0.596990\pi$
$14$	2.36898	−	1.17810i	0.633137	−	0.314862i
$15$	−3.05368	−	1.38094i	−0.788457	−	0.356557i
$16$	−0.222521	−	0.974928i	−0.0556302	−	0.243732i
$17$	−7.35401	+	1.10844i	−1.78361	+	0.268836i	−0.956189	−	0.292749i	$-0.905430\pi$
$17$	−7.35401	+	1.10844i	−1.78361	+	0.268836i	−0.827419	+	0.561584i	$0.810192\pi$
$18$	1.37308	−	2.66733i	0.323639	−	0.628696i
$19$	−2.17854	−	3.77334i	−0.499791	−	0.865664i	0.500208	−	0.865905i	$-0.333257\pi$
$19$	−2.17854	−	3.77334i	−0.499791	−	0.865664i	−1.00000		0.000240753i	$0.999923\pi$
$20$	1.91333	−	0.288388i	0.427833	−	0.0644854i
$21$	−4.32634	+	1.51089i	−0.944085	+	0.329703i
$22$	1.97030	+	0.296974i	0.420069	+	0.0633152i
$23$	2.74953	+	7.00568i	0.573316	+	1.46079i	0.863765	+	0.503895i	$0.168100\pi$
$23$	2.74953	+	7.00568i	0.573316	+	1.46079i	−0.290448	+	0.956891i	$0.593804\pi$
$24$	0.171019	+	1.72359i	0.0349092	+	0.351826i
$25$	−0.0938620	−	1.25250i	−0.0187724	−	0.250500i
$26$	2.06424	+	0.311134i	0.404831	+	0.0610184i
$27$	−2.93783	+	4.28593i	−0.565385	+	0.824827i
$28$	1.62322	−	2.08930i	0.306759	−	0.394840i
$29$	9.29209	−	1.40056i	1.72550	−	0.260077i	0.789923	−	0.613206i	$-0.210120\pi$
$29$	9.29209	−	1.40056i	1.72550	−	0.260077i	0.935575	+	0.353129i	$0.114882\pi$
$30$	−3.35044	+	0.0807592i	−0.611704	+	0.0147445i
$31$	1.39374			0.250324			0.125162	−	0.992136i	$-0.460055\pi$
$31$	1.39374			0.250324			0.125162	+	0.992136i	$0.460055\pi$
$32$	−0.623490	−	0.781831i	−0.110218	−	0.138210i
$33$	−3.32143	−	0.937495i	−0.578187	−	0.163197i
$34$	−6.14480	+	4.18945i	−1.05382	+	0.718485i
$35$	3.79664	+	3.43415i	0.641750	+	0.580478i
$36$	0.0797937	−	2.99894i	0.0132990	−	0.499823i
$37$	−1.18667	+	3.02358i	−0.195087	+	0.497073i	−0.994625	−	0.103542i	$-0.966982\pi$
$37$	−1.18667	+	3.02358i	−0.195087	+	0.497073i	0.799538	+	0.600615i	$0.205078\pi$
$38$	−3.59999	−	2.45443i	−0.583995	−	0.398161i
$39$	−3.47979	−	0.982194i	−0.557213	−	0.157277i
$40$	1.59872	−	1.08999i	0.252780	−	0.172343i
$41$	9.56895	−	2.95163i	1.49442	−	0.460967i	0.563476	−	0.826132i	$-0.309464\pi$
$41$	9.56895	−	2.95163i	1.49442	−	0.460967i	0.930943	+	0.365165i	$0.118987\pi$
$42$	−3.24235	+	3.23839i	−0.500305	+	0.499695i
$43$	11.9592	+	3.68891i	1.82376	+	0.562554i	0.999990	−	0.00437699i	$-0.00139324\pi$
$43$	11.9592	+	3.68891i	1.82376	+	0.562554i	0.823765	+	0.566931i	$0.191869\pi$
$44$	1.90403	−	0.587315i	0.287043	−	0.0885411i
$45$	5.77500	+	0.587605i	0.860886	+	0.0875950i
$46$	5.51689	+	5.11893i	0.813421	+	0.754745i
$47$	−4.78011	+	2.30198i	−0.697251	+	0.335778i	−0.748711	−	0.662897i	$-0.769327\pi$
$47$	−4.78011	+	2.30198i	−0.697251	+	0.335778i	0.0514599	+	0.998675i	$0.483613\pi$
$48$	0.901920	+	1.47870i	0.130181	+	0.213431i
$49$	6.99775	−	0.177640i	0.999678	−	0.0253772i
$50$	−0.628006	−	1.08774i	−0.0888135	−	0.153830i
$51$	11.4677	−	5.86707i	1.60580	−	0.821554i
$52$	1.99481	−	0.615318i	0.276631	−	0.0853293i
$53$	−3.49092	−	8.89471i	−0.479514	−	1.22178i	−0.942137	−	0.335227i	$-0.891187\pi$
$53$	−3.49092	−	8.89471i	−0.479514	−	1.22178i	0.462623	−	0.886555i	$-0.346908\pi$
$54$	−0.787298	+	5.13616i	−0.107138	+	0.698943i
$55$	0.857922	+	3.75880i	0.115682	+	0.506837i
$56$	0.555956	−	2.58668i	0.0742927	−	0.345660i
$57$	5.65420	+	4.99825i	0.748917	+	0.662035i
$58$	7.76421	−	5.29355i	1.01949	−	0.695077i
$59$	1.03451	+	4.53246i	0.134681	+	0.590077i	0.996554	+	0.0829515i	$0.0264347\pi$
$59$	1.03451	+	4.53246i	0.134681	+	0.590077i	−0.861872	+	0.507125i	$0.830708\pi$
$60$	−2.98360	+	1.52646i	−0.385181	+	0.197065i
$61$	−1.19835	−	1.50268i	−0.153432	−	0.192398i	0.699174	−	0.714951i	$-0.253551\pi$
$61$	−1.19835	−	1.50268i	−0.153432	−	0.192398i	−0.852607	+	0.522553i	$0.824980\pi$
$62$	1.25572	−	0.604723i	0.159477	−	0.0767999i
$63$	6.27384	−	4.86199i	0.790429	−	0.612554i
$64$	−0.900969	−	0.433884i	−0.112621	−	0.0542355i
$65$	0.898827	+	3.93802i	0.111486	+	0.488451i
$66$	−3.39927	+	0.596460i	−0.418421	+	0.0734192i
$67$	−10.3118			−1.25979			−0.629894	−	0.776681i	$-0.716901\pi$
$67$	−10.3118			−1.25979			−0.629894	+	0.776681i	$0.716901\pi$
$68$	−3.71854	+	6.44069i	−0.450939	+	0.781049i
$69$	−8.37059	−	9.99259i	−1.00770	−	1.20297i
$70$	4.91068	+	1.44676i	0.586939	+	0.172921i
$71$	−4.32524	+	5.42368i	−0.513312	+	0.643673i	−0.969174	−	0.246378i	$-0.920760\pi$
$71$	−4.32524	+	5.42368i	−0.513312	+	0.643673i	0.455862	+	0.890050i	$0.349331\pi$
$72$	−1.22930	−	2.73657i	−0.144874	−	0.322508i
$73$	−0.327678	+	0.223407i	−0.0383518	+	0.0261478i	−0.582344	−	0.812942i	$-0.697864\pi$
$73$	−0.327678	+	0.223407i	−0.0383518	+	0.0261478i	0.543992	+	0.839090i	$0.316912\pi$
$74$	0.242731	+	3.23902i	0.0282169	+	0.376529i
$75$	0.843359	+	2.00536i	0.0973828	+	0.231558i
$76$	−4.30842	−	0.649389i	−0.494209	−	0.0744901i
$77$	4.39310	+	2.91420i	0.500640	+	0.332104i
$78$	−3.56134	+	0.624899i	−0.403243	+	0.0707559i
$79$	−8.80993			−0.991195			−0.495597	−	0.868552i	$-0.665051\pi$
$79$	−8.80993			−0.991195			−0.495597	+	0.868552i	$0.665051\pi$
$80$	0.967469	−	1.67571i	0.108166	−	0.187350i
$81$	2.46645	−	8.65544i	0.274050	−	0.961715i
$82$	7.34066	−	6.81114i	0.810641	−	0.752165i
$83$	−11.8694	+	8.09243i	−1.30284	+	0.888260i	−0.997942	−	0.0641257i	$-0.979574\pi$
$83$	−11.8694	+	8.09243i	−1.30284	+	0.888260i	−0.304896	+	0.952386i	$0.598622\pi$
$84$	−1.51617	+	4.32449i	−0.165428	+	0.471841i
$85$	−11.8898	−	8.10633i	−1.28963	−	0.879255i
$86$	12.3754	−	1.86529i	1.33447	−	0.201139i
$87$	−14.4899	+	7.41328i	−1.55348	+	0.794787i
$88$	1.46064	−	1.35528i	0.155705	−	0.144473i
$89$	0.231457	+	3.08857i	0.0245344	+	0.327388i	0.995944	+	0.0899777i	$0.0286796\pi$
$89$	0.231457	+	3.08857i	0.0245344	+	0.327388i	−0.971409	+	0.237410i	$0.923701\pi$
$90$	5.45805	−	1.97626i	0.575329	−	0.208317i
$91$	4.60256	+	3.05315i	0.482479	+	0.320057i
$92$	7.19157	+	2.21830i	0.749773	+	0.231274i
$93$	−2.28897	+	0.766929i	−0.237355	+	0.0795269i
$94$	−3.30794	+	4.14803i	−0.341188	+	0.427836i
$95$	1.87600	−	8.21931i	0.192474	−	0.843283i
$96$	1.45418	+	0.940931i	0.148417	+	0.0960333i
$97$	4.51572	−	7.82146i	0.458502	−	0.794149i	−0.540380	−	0.841421i	$-0.681720\pi$
$97$	4.51572	−	7.82146i	0.458502	−	0.794149i	0.998882	+	0.0472724i	$0.0150529\pi$
$98$	6.22768	−	3.19626i	0.629090	−	0.322871i
$99$	5.97071	−	0.288004i	0.600079	−	0.0289455i
$100$	−1.03777	−	0.707537i	−0.103777	−	0.0707537i
$101$	0.914185	−	0.281989i	0.0909648	−	0.0280589i	−0.248939	−	0.968519i	$-0.580082\pi$
$101$	0.914185	−	0.281989i	0.0909648	−	0.0280589i	0.339903	+	0.940460i	$0.389606\pi$
$102$	7.78640	−	10.2617i	0.770968	−	1.01606i
$103$	−2.54275	−	2.35933i	−0.250545	−	0.232472i	0.544895	−	0.838504i	$-0.316570\pi$
$103$	−2.54275	−	2.35933i	−0.250545	−	0.232472i	−0.795440	+	0.606033i	$0.792760\pi$
$104$	1.53029	−	1.41990i	0.150057	−	0.139233i
$105$	−8.12499	−	3.55081i	−0.792918	−	0.346523i
$106$	−7.00448	−	6.49920i	−0.680335	−	0.631258i
$107$	−1.07855	−	14.3922i	−0.104267	−	1.39135i	−0.766593	−	0.642134i	$-0.778049\pi$
$107$	−1.07855	−	14.3922i	−0.104267	−	1.39135i	0.662325	−	0.749216i	$-0.269570\pi$
$108$	1.51917	+	4.96912i	0.146182	+	0.478154i
$109$	0.306421	−	4.08890i	0.0293498	−	0.391646i	−0.963113	−	0.269098i	$-0.913274\pi$
$109$	0.306421	−	4.08890i	0.0293498	−	0.391646i	0.992463	−	0.122548i	$-0.0391065\pi$
$110$	2.40384	+	3.01432i	0.229198	+	0.287405i
$111$	0.285113	−	5.61865i	0.0270617	−	0.533299i
$112$	−0.621419	−	2.57174i	−0.0587186	−	0.243006i
$113$	0.697532	+	9.30792i	0.0656183	+	0.875616i	0.928767	+	0.370665i	$0.120870\pi$
$113$	0.697532	+	9.30792i	0.0656183	+	0.875616i	−0.863148	+	0.504950i	$0.831511\pi$
$114$	7.26292	+	2.05001i	0.680234	+	0.192001i
$115$	−5.32017	+	13.5556i	−0.496108	+	1.26406i
$116$	4.69852	−	8.13808i	0.436247	−	0.755602i
$117$	6.25540	−	0.301736i	0.578312	−	0.0278955i
$118$	2.89862	+	3.63475i	0.266840	+	0.334606i
$119$	−19.4181	+	3.17932i	−1.78005	+	0.291447i
$120$	−2.02582	+	2.66983i	−0.184932	+	0.243721i
$121$	−2.56825	−	6.54380i	−0.233477	−	0.594891i
$122$	−1.73166	−	0.833924i	−0.156777	−	0.0754999i
$123$	−14.0911	+	10.1130i	−1.27055	+	0.911857i
$124$	0.868985	−	1.08967i	0.0780372	−	0.0978555i
$125$	7.54734	−	9.46407i	0.675055	−	0.846492i
$126$	3.54299	−	7.10262i	0.315635	−	0.632752i
$127$	−3.60032	−	4.51466i	−0.319477	−	0.400611i	0.595999	−	0.802986i	$-0.296756\pi$
$127$	−3.60032	−	4.51466i	−0.319477	−	0.400611i	−0.915475	+	0.402374i	$0.868185\pi$
$128$	−1.00000			−0.0883883
$129$	−21.6706	+	0.522350i	−1.90799	+	0.0459904i
$130$	2.51846	+	3.15805i	0.220883	+	0.276979i
$131$	17.2359	+	5.31656i	1.50590	+	0.464510i	0.934441	−	0.356117i	$-0.115900\pi$
$131$	17.2359	+	5.31656i	1.50590	+	0.464510i	0.571464	+	0.820627i	$0.306376\pi$
$132$	−2.80384	+	2.01228i	−0.244043	+	0.175146i
$133$	−5.89010	−	9.90938i	−0.510736	−	0.859252i
$134$	−9.29061	+	4.47412i	−0.802587	+	0.386505i
$135$	−9.80772	+	2.21275i	−0.844114	+	0.190443i
$136$	−0.555773	+	7.41628i	−0.0476572	+	0.635941i
$137$	4.54739	−	4.21936i	0.388510	−	0.360485i	−0.461601	−	0.887087i	$-0.652725\pi$
$137$	4.54739	−	4.21936i	0.388510	−	0.360485i	0.850111	+	0.526603i	$0.176535\pi$
$138$	−11.8773	−	5.37115i	−1.01106	−	0.457223i
$139$	−6.63504	+	2.04664i	−0.562777	+	0.173594i	−0.563074	−	0.826406i	$-0.690382\pi$
$139$	−6.63504	+	2.04664i	−0.562777	+	0.173594i	0.000297406		1.00000i	$0.499905\pi$
$140$	5.05210	−	0.827178i	0.426980	−	0.0699093i
$141$	6.58376	−	6.41091i	0.554453	−	0.539896i
$142$	−1.54366	+	6.76322i	−0.129541	+	0.567557i
$143$	1.51966	+	3.87203i	0.127080	+	0.323795i
$144$	−2.29491	−	1.93219i	−0.191243	−	0.161016i
$145$	15.0233	+	10.2427i	1.24761	+	0.850609i
$146$	−0.198295	+	0.343457i	−0.0164110	+	0.0284247i
$147$	−11.3948	+	4.14236i	−0.939825	+	0.341656i
$148$	1.62405	+	2.81294i	0.133496	+	0.231222i
$149$	−0.859855	+	11.4740i	−0.0704420	+	0.939984i	0.844281	+	0.535901i	$0.180028\pi$
$149$	−0.859855	+	11.4740i	−0.0704420	+	0.939984i	−0.914723	+	0.404082i	$0.867591\pi$
$150$	1.62993	+	1.44084i	0.133083	+	0.117644i
$151$	−19.4875	−	2.93727i	−1.58587	−	0.239032i	−0.703889	−	0.710310i	$-0.748555\pi$
$151$	−19.4875	−	2.93727i	−1.58587	−	0.239032i	−0.881985	+	0.471278i	$0.843793\pi$
$152$	−4.16351	+	1.28427i	−0.337705	+	0.104168i
$153$	−15.6051	+	15.9459i	−1.26160	+	1.28915i
$154$	5.22247	+	0.719508i	0.420838	+	0.0579796i
$155$	1.97690	+	1.83430i	0.158788	+	0.147334i
$156$	−2.93753	+	2.10822i	−0.235190	+	0.168793i
$157$	−3.31431	−	14.5210i	−0.264511	−	1.15890i	−0.916298	−	0.400496i	$-0.868838\pi$
$157$	−3.31431	−	14.5210i	−0.264511	−	1.15890i	0.651787	−	0.758402i	$-0.274019\pi$
$158$	−7.93747	+	3.82249i	−0.631471	+	0.304101i
$159$	10.6276	+	12.6870i	0.842827	+	1.00614i
$160$	0.144598	−	1.92953i	0.0114315	−	0.152543i
$161$	7.50919	+	18.4415i	0.591807	+	1.45339i
$162$	−1.53326	−	8.86843i	−0.120464	−	0.696770i
$163$	16.6915	−	15.4874i	1.30738	−	1.21307i	0.345871	−	0.938282i	$-0.387584\pi$
$163$	16.6915	−	15.4874i	1.30738	−	1.21307i	0.961506	−	0.274786i	$-0.0886069\pi$
$164$	3.65847	−	9.32162i	0.285678	−	0.727896i
$165$	−3.47732	−	5.70106i	−0.270709	−	0.443827i
$166$	−7.18280	+	12.4410i	−0.557494	+	0.965607i
$167$	−5.94882	+	15.1573i	−0.460333	+	1.17291i	0.492742	+	0.870176i	$0.335995\pi$
$167$	−5.94882	+	15.1573i	−0.460333	+	1.17291i	−0.953075	+	0.302734i	$0.902100\pi$
$168$	0.510305	+	4.55407i	0.0393709	+	0.351354i
$169$	−3.15732	−	8.04471i	−0.242871	−	0.618824i
$170$	−14.2296	−	2.14476i	−1.09136	−	0.164496i
$171$	−12.0364	−	5.09741i	−0.920443	−	0.389808i
$172$	10.3405	−	7.05005i	0.788458	−	0.537561i
$173$	4.42949	−	5.55440i	0.336768	−	0.422293i	−0.584396	−	0.811469i	$-0.698669\pi$
$173$	4.42949	−	5.55440i	0.336768	−	0.422293i	0.921164	+	0.389175i	$0.127240\pi$
$174$	−9.83844	+	12.9661i	−0.745850	+	0.982954i
$175$	−0.290366	−	3.31039i	−0.0219496	−	0.250242i
$176$	0.727961	−	1.85481i	0.0548721	−	0.139812i
$177$	−4.19305	−	6.87449i	−0.315169	−	0.516719i
$178$	1.54862	+	2.68228i	0.116074	+	0.201046i
$179$	−10.3312	+	1.55717i	−0.772189	+	0.116389i	−0.523306	−	0.852145i	$-0.675301\pi$
$179$	−10.3312	+	1.55717i	−0.772189	+	0.116389i	−0.248883	+	0.968534i	$0.580063\pi$
$180$	4.06006	−	4.14871i	0.302619	−	0.309227i
$181$	−22.7215	−	10.9421i	−1.68888	−	0.813319i	−0.995709	−	0.0925416i	$-0.970501\pi$
$181$	−22.7215	−	10.9421i	−1.68888	−	0.813319i	−0.693166	−	0.720778i	$-0.743785\pi$
$182$	5.47147	+	0.753813i	0.405572	+	0.0558764i
$183$	2.79494	+	1.80847i	0.206608	+	0.133686i
$184$	7.44186	−	1.12168i	0.548622	−	0.0826914i
$185$	−5.66248	+	2.72691i	−0.416314	+	0.200486i
$186$	−1.72953	+	1.68413i	−0.126815	+	0.123486i
$187$	−13.3512	−	6.42962i	−0.976339	−	0.470180i
$188$	−1.18059	+	5.17250i	−0.0861034	+	0.377244i
$189$	−7.62824	+	11.4372i	−0.554873	+	0.831935i
$190$	−1.87600	−	8.21931i	−0.136100	−	0.596291i
$191$	1.30630	−	5.72328i	0.0945206	−	0.414122i	−0.905425	−	0.424505i	$-0.860448\pi$
$191$	1.30630	−	5.72328i	0.0945206	−	0.414122i	0.999946	+	0.0103834i	$0.00330521\pi$
$192$	1.71843	+	0.216803i	0.124017	+	0.0156464i
$193$	−0.551824	+	2.41770i	−0.0397212	+	0.174030i	−0.990898	−	0.134618i	$-0.957019\pi$
$193$	−0.551824	+	2.41770i	−0.0397212	+	0.174030i	0.951176	+	0.308648i	$0.0998764\pi$
$194$	0.674920	−	9.00619i	0.0484565	−	0.646607i
$195$	−3.64312	−	5.97289i	−0.260889	−	0.427727i
$196$	4.22414	−	5.58181i	0.301724	−	0.398701i
$197$	−19.2897			−1.37433			−0.687167	−	0.726500i	$-0.741146\pi$
$197$	−19.2897			−1.37433			−0.687167	+	0.726500i	$0.741146\pi$
$198$	5.25447	−	2.85008i	0.373419	−	0.202546i
$199$	2.77791	+	2.57752i	0.196921	+	0.182716i	0.772470	−	0.635052i	$-0.219021\pi$
$199$	2.77791	+	2.57752i	0.196921	+	0.182716i	−0.575549	+	0.817767i	$0.695212\pi$
$200$	−1.24198	−	0.187199i	−0.0878215	−	0.0132370i
$201$	16.9353	−	5.67423i	1.19452	−	0.400229i
$202$	0.701302	−	0.650713i	0.0493434	−	0.0457840i
$203$	24.5356	−	4.01720i	1.72206	−	0.281952i
$204$	2.56293	−	12.6239i	0.179441	−	0.883846i
$205$	17.4573	+	8.40700i	1.21927	+	0.587170i
$206$	−3.31462	−	1.02242i	−0.230940	−	0.0712356i
$207$	19.2457	+	11.8050i	1.33767	+	0.820501i
$208$	0.762670	−	1.94325i	0.0528816	−	0.134740i
$209$	0.648785	−	8.65744i	0.0448774	−	0.598847i
$210$	−8.86100	+	0.326138i	−0.611467	+	0.0225056i
$211$	−0.692605	−	9.24217i	−0.0476809	−	0.636257i	−0.968938	−	0.247303i	$-0.920456\pi$
$211$	−0.692605	−	9.24217i	−0.0476809	−	0.636257i	0.921257	−	0.388954i	$-0.127163\pi$
$212$	−9.13071	−	2.81645i	−0.627100	−	0.193435i
$213$	4.11896	−	11.2874i	0.282226	−	0.773403i
$214$	−7.21630	−	12.4990i	−0.493296	−	0.854414i
$215$	12.1081	+	20.9718i	0.825762	+	1.43026i
$216$	3.52474	+	3.81788i	0.239828	+	0.259774i
$217$	3.68720	−	0.0467929i	0.250304	−	0.00317651i
$218$	−1.49803	−	3.81693i	−0.101460	−	0.258515i
$219$	0.415218	−	0.547216i	0.0280579	−	0.0369774i
$220$	3.47365	+	1.67282i	0.234194	+	0.112782i
$221$	−13.9878	−	6.73618i	−0.940923	−	0.453124i
$222$	−2.18096	−	5.18594i	−0.146377	−	0.348057i
$223$	5.81396	+	14.8137i	0.389332	+	0.992001i	0.982390	+	0.186841i	$0.0598251\pi$
$223$	5.81396	+	14.8137i	0.389332	+	0.992001i	−0.593058	+	0.805159i	$0.702080\pi$
$224$	−1.67571	−	2.04743i	−0.111963	−	0.136800i
$225$	−2.48854	−	2.82936i	−0.165903	−	0.188624i
$226$	4.66701	+	8.08350i	0.310445	+	0.537706i
$227$	−3.22163	−	5.58002i	−0.213827	−	0.370359i	0.739082	−	0.673615i	$-0.235260\pi$
$227$	−3.22163	−	5.58002i	−0.213827	−	0.370359i	−0.952909	+	0.303256i	$0.901926\pi$
$228$	7.43313	−	1.30427i	0.492271	−	0.0863774i
$229$	−14.6272	−	4.51189i	−0.966592	−	0.298154i	−0.229019	−	0.973422i	$-0.573552\pi$
$229$	−14.6272	−	4.51189i	−0.966592	−	0.298154i	−0.737573	+	0.675268i	$0.764028\pi$
$230$	1.08823	+	14.5215i	0.0717561	+	0.957518i
$231$	−8.81844	−	2.36867i	−0.580211	−	0.155847i
$232$	0.702242	−	9.37077i	0.0461045	−	0.615221i
$233$	−10.7590	+	27.4135i	−0.704846	+	1.79592i	−0.107075	+	0.994251i	$0.534149\pi$
$233$	−10.7590	+	27.4135i	−0.704846	+	1.79592i	−0.597771	+	0.801667i	$0.703947\pi$
$234$	5.50500	−	2.98597i	0.359873	−	0.195199i
$235$	−9.80978	−	3.02592i	−0.639919	−	0.197389i
$236$	4.18863	+	2.01714i	0.272656	+	0.131304i
$237$	14.4687	−	4.84780i	0.939843	−	0.314899i
$238$	−16.1156	+	11.2897i	−1.04462	+	0.731800i
$239$	−8.86208	+	8.22281i	−0.573240	+	0.531889i	−0.912646	−	0.408751i	$-0.865965\pi$
$239$	−8.86208	+	8.22281i	−0.573240	+	0.531889i	0.339406	+	0.940640i	$0.389774\pi$
$240$	−0.666808	+	3.28441i	−0.0430423	+	0.212008i
$241$	1.28183	+	0.193204i	0.0825697	+	0.0124454i	0.190197	−	0.981746i	$-0.439087\pi$
$241$	1.28183	+	0.193204i	0.0825697	+	0.0124454i	−0.107627	+	0.994191i	$0.534325\pi$
$242$	−5.15316	−	4.78143i	−0.331258	−	0.307362i
$243$	0.712100	+	15.5722i	0.0456812	+	0.998956i
$244$	−1.92200			−0.123043
$245$	10.1595	+	8.95771i	0.649064	+	0.572287i
$246$	−8.30776	+	15.2254i	−0.529684	+	0.970734i
$247$	0.679719	−	9.07022i	0.0432495	−	0.577124i
$248$	0.310137	−	1.35880i	0.0196937	−	0.0862839i
$249$	15.0404	−	19.8217i	0.953145	−	1.25615i
$250$	2.69362	−	11.8015i	0.170359	−	0.746393i
$251$	−6.37649	−	27.9372i	−0.402481	−	1.76338i	−0.617299	−	0.786729i	$-0.711773\pi$
$251$	−6.37649	−	27.9372i	−0.402481	−	1.76338i	0.214818	−	0.976654i	$-0.431084\pi$
$252$	0.110412	−	7.93649i	0.00695533	−	0.499952i
$253$	−3.33688	+	14.6198i	−0.209788	+	0.919140i
$254$	−5.20261	−	2.50545i	−0.326441	−	0.157206i
$255$	23.9875	+	6.77062i	1.50215	+	0.423993i
$256$	−0.900969	+	0.433884i	−0.0563106	+	0.0271177i
$257$	−2.25178	+	0.339401i	−0.140462	+	0.0211713i	−0.218897	−	0.975748i	$-0.570246\pi$
$257$	−2.25178	+	0.339401i	−0.140462	+	0.0211713i	0.0784348	+	0.996919i	$0.475008\pi$
$258$	−19.2979	+	9.87316i	−1.20144	+	0.614676i
$259$	−3.03786	+	8.03883i	−0.188763	+	0.499508i
$260$	3.63928	+	1.75258i	0.225698	+	0.108691i
$261$	19.7177	−	20.1482i	1.22050	−	1.24715i
$262$	17.8357	−	2.68831i	1.10190	−	0.166084i
$263$	4.54310	+	7.86889i	0.280140	+	0.485216i	0.971419	−	0.237371i	$-0.0762858\pi$
$263$	4.54310	+	7.86889i	0.280140	+	0.485216i	−0.691279	+	0.722588i	$0.742953\pi$
$264$	−1.65308	+	3.02954i	−0.101740	+	0.186455i
$265$	6.75471	−	17.2107i	0.414938	−	1.05725i
$266$	−9.60631	−	6.37243i	−0.589001	−	0.390719i
$267$	−2.07966	−	4.94506i	−0.127273	−	0.302633i
$268$	−6.42930	+	8.06209i	−0.392732	+	0.492471i
$269$	15.2946	−	10.4277i	0.932527	−	0.635786i	0.00121138	−	0.999999i	$-0.499614\pi$
$269$	15.2946	−	10.4277i	0.932527	−	0.635786i	0.931316	+	0.364213i	$0.118662\pi$
$270$	−7.87638	+	6.24903i	−0.479341	+	0.380304i
$271$	−4.69883	−	0.708234i	−0.285433	−	0.0430222i	0.00476507	−	0.999989i	$-0.498483\pi$
$271$	−4.69883	−	0.708234i	−0.285433	−	0.0430222i	−0.290198	+	0.956966i	$0.593721\pi$
$272$	2.71707	+	6.92298i	0.164746	+	0.419767i
$273$	−9.23890	−	2.48160i	−0.559164	−	0.150194i
$274$	2.26635	−	5.77455i	0.136915	−	0.348854i
$275$	1.25134	−	2.16738i	0.0754584	−	0.130698i
$276$	−13.0315	+	0.314112i	−0.784404	+	0.0189073i
$277$	4.10419	−	10.4573i	0.246597	−	0.628318i	−0.752961	−	0.658065i	$-0.771375\pi$
$277$	4.10419	−	10.4573i	0.246597	−	0.628318i	0.999557	+	0.0297472i	$0.00947023\pi$
$278$	−5.08996	+	4.72280i	−0.305276	+	0.283254i
$279$	3.33720	−	2.51908i	0.199793	−	0.150814i
$280$	4.19288	−	2.93728i	0.250573	−	0.175536i
$281$	−0.972008	+	12.9705i	−0.0579851	+	0.773758i	0.890105	+	0.455756i	$0.150631\pi$
$281$	−0.972008	+	12.9705i	−0.0579851	+	0.773758i	−0.948090	+	0.318002i	$0.896988\pi$
$282$	3.15017	−	8.63262i	0.187590	−	0.514065i
$283$	−16.9396	+	8.15770i	−1.00696	+	0.484925i	−0.863294	−	0.504701i	$-0.831603\pi$
$283$	−16.9396	+	8.15770i	−1.00696	+	0.484925i	−0.143664	+	0.989627i	$0.545888\pi$
$284$	1.54366	+	6.76322i	0.0915994	+	0.401323i
$285$	1.44181	+	14.5310i	0.0854055	+	0.860743i
$286$	3.04918	+	2.82922i	0.180302	+	0.167295i
$287$	25.2159	−	8.12992i	1.48845	−	0.479894i
$288$	−2.90599	−	0.745120i	−0.171237	−	0.0439066i
$289$	36.6081	−	11.2921i	2.15342	−	0.664241i
$290$	17.9796	+	2.70999i	1.05580	+	0.159136i
$291$	−3.11237	+	15.3302i	−0.182450	+	0.898670i
$292$	−0.0296372	+	0.395481i	−0.00173439	+	0.0231438i
$293$	−9.55513	−	16.5500i	−0.558217	−	0.966860i	−0.997645	−	0.0685823i	$-0.978152\pi$
$293$	−9.55513	−	16.5500i	−0.558217	−	0.966860i	0.439429	−	0.898277i	$-0.355181\pi$
$294$	−8.46903	+	8.67615i	−0.493924	+	0.506003i
$295$	−4.49779	+	7.79040i	−0.261871	+	0.453575i
$296$	2.68371	+	1.82972i	0.155987	+	0.106350i
$297$	−9.64733	+	3.75847i	−0.559795	+	0.218089i
$298$	4.20366	+	10.7108i	0.243512	+	0.620458i
$299$	−3.49598	+	15.3169i	−0.202178	+	0.885798i
$300$	2.09368	+	0.590954i	0.120878	+	0.0341187i
$301$	31.7623	+	9.35765i	1.83075	+	0.539366i
$302$	−18.8321	+	5.80893i	−1.08367	+	0.334267i
$303$	−1.34621	+	0.966160i	−0.0773379	+	0.0555044i
$304$	−3.19397	+	2.96357i	−0.183187	+	0.169972i
$305$	0.277917	−	3.70855i	0.0159135	−	0.212351i
$306$	−7.14109	+	21.1375i	−0.408229	+	1.20835i
$307$	11.2855	−	5.43481i	0.644097	−	0.310181i	−0.0831698	−	0.996535i	$-0.526504\pi$
$307$	11.2855	−	5.43481i	0.644097	−	0.310181i	0.727267	+	0.686354i	$0.240790\pi$
$308$	5.01746	−	1.61769i	0.285896	−	0.0921764i
$309$	5.47427	+	2.47558i	0.311420	+	0.140831i
$310$	2.57700	+	0.794898i	0.146364	+	0.0451472i
$311$	−1.70798	−	2.14175i	−0.0968509	−	0.121447i	0.731044	−	0.682330i	$-0.239033\pi$
$311$	−1.70798	−	2.14175i	−0.0968509	−	0.121447i	−0.827895	+	0.560883i	$0.810462\pi$
$312$	−1.73190	+	3.17399i	−0.0980493	+	0.179692i
$313$	−14.7227			−0.832179			−0.416089	−	0.909324i	$-0.636600\pi$
$313$	−14.7227			−0.832179			−0.416089	+	0.909324i	$0.636600\pi$
$314$	−9.28650	−	11.6449i	−0.524067	−	0.657160i
$315$	15.2977	+	1.36064i	0.861928	+	0.0766637i
$316$	−5.49290	+	6.88788i	−0.309000	+	0.387474i
$317$	1.67987	−	2.10649i	0.0943507	−	0.118312i	−0.732415	−	0.680859i	$-0.761607\pi$
$317$	1.67987	−	2.10649i	0.0943507	−	0.118312i	0.826766	+	0.562546i	$0.190178\pi$
$318$	15.0799	+	6.81943i	0.845637	+	0.382415i
$319$	16.8698	+	8.12409i	0.944530	+	0.454861i
$320$	−0.706912	−	1.80118i	−0.0395176	−	0.100689i
$321$	9.69088	+	23.0431i	0.540892	+	1.28614i
$322$	14.7670	+	13.3571i	0.822933	+	0.744362i
$323$	20.2035	+	25.3344i	1.12415	+	1.40964i
$324$	−5.22929	−	7.32493i	−0.290516	−	0.406940i
$325$	1.31100	−	2.27072i	0.0727211	−	0.125957i
$326$	8.31875	−	21.1958i	0.460733	−	1.17393i
$327$	1.74674	+	6.88389i	0.0965951	+	0.380680i
$328$	−0.748335	−	9.98584i	−0.0413199	−	0.551376i
$329$	−12.5687	+	6.25046i	−0.692934	+	0.344599i
$330$	−5.60655	−	3.62773i	−0.308631	−	0.199700i
$331$	−4.66223	−	5.84625i	−0.256259	−	0.321339i	0.637015	−	0.770852i	$-0.280169\pi$
$331$	−4.66223	−	5.84625i	−0.256259	−	0.321339i	−0.893274	+	0.449513i	$0.851598\pi$
$332$	−1.07354	+	14.3254i	−0.0589183	+	0.786210i
$333$	2.62351	+	9.38450i	0.143767	+	0.514268i
$334$	1.21682	+	16.2374i	0.0665816	+	0.888470i
$335$	−14.6264	−	13.5713i	−0.799124	−	0.741478i
$336$	2.43571	+	3.88167i	0.132879	+	0.211762i
$337$	−7.76031	+	7.20052i	−0.422731	+	0.392237i	−0.862651	−	0.505800i	$-0.831197\pi$
$337$	−7.76031	+	7.20052i	−0.422731	+	0.392237i	0.439920	+	0.898037i	$0.355007\pi$
$338$	−6.33511	−	5.87813i	−0.344585	−	0.319728i
$339$	−6.26740	−	14.9027i	−0.340398	−	0.809405i
$340$	−13.7510	+	4.24161i	−0.745751	+	0.230034i
$341$	2.29455	+	1.56440i	0.124257	+	0.0847170i
$342$	−13.0561	+	0.629774i	−0.705991	+	0.0340543i
$343$	18.5068	−	0.704893i	0.999275	−	0.0380606i
$344$	6.25759	−	10.8385i	0.337387	−	0.584371i
$345$	1.27824	−	25.1901i	0.0688182	−	1.35619i
$346$	1.58087	−	6.92623i	0.0849879	−	0.372356i
$347$	17.2732	−	21.6599i	0.927272	−	1.16276i	−0.0591033	−	0.998252i	$-0.518824\pi$
$347$	17.2732	−	21.6599i	0.927272	−	1.16276i	0.986375	−	0.164511i	$-0.0526044\pi$
$348$	−3.23836	+	15.9508i	−0.173594	+	0.855050i
$349$	12.8523	+	3.96442i	0.687969	+	0.212210i	0.618980	−	0.785407i	$-0.287546\pi$
$349$	12.8523	+	3.96442i	0.687969	+	0.212210i	0.0689896	+	0.997617i	$0.478022\pi$
$350$	−1.69793	−	2.85657i	−0.0907584	−	0.152690i
$351$	−10.1073	+	3.93768i	−0.539488	+	0.210178i
$352$	−0.148904	−	1.98698i	−0.00793659	−	0.105906i
$353$	−6.42657	+	5.96299i	−0.342052	+	0.317378i	−0.832428	−	0.554133i	$-0.813050\pi$
$353$	−6.42657	+	5.96299i	−0.342052	+	0.317378i	0.490376	+	0.871511i	$0.336859\pi$
$354$	−6.76054	−	4.37441i	−0.359318	−	0.232497i
$355$	−13.2730	+	2.00059i	−0.704460	+	0.106180i
$356$	2.55906	+	1.74473i	0.135630	+	0.0924707i
$357$	30.1412	−	15.9066i	1.59524	−	0.841864i
$358$	−8.63244	+	5.88550i	−0.456239	+	0.311058i
$359$	−13.3673	+	12.4031i	−0.705500	+	0.654608i	−0.948994	−	0.315294i	$-0.897897\pi$
$359$	−13.3673	+	12.4031i	−0.705500	+	0.654608i	0.243494	+	0.969902i	$0.421706\pi$
$360$	1.85793	−	5.49945i	0.0979215	−	0.289847i
$361$	0.00792184	−	0.0137210i	0.000416939	−	0.000722159i
$362$	−25.2190			−1.32548
$363$	7.81871	+	9.33377i	0.410376	+	0.489896i
$364$	5.25669	−	1.69482i	0.275526	−	0.0888327i
$365$	−0.758807	−	0.114372i	−0.0397178	−	0.00598649i
$366$	3.30282	+	0.416694i	0.172641	+	0.0217810i
$367$	0.682944	+	9.11326i	0.0356494	+	0.475708i	0.986247	+	0.165281i	$0.0528531\pi$
$367$	0.682944	+	9.11326i	0.0356494	+	0.475708i	−0.950597	+	0.310427i	$0.899528\pi$
$368$	6.21821	−	4.23950i	0.324147	−	0.220999i
$369$	17.5772	−	24.3626i	0.915032	−	1.26826i
$370$	−3.91856	+	4.91372i	−0.203716	+	0.255452i
$371$	−9.53398	−	23.4141i	−0.494979	−	1.21560i
$372$	−0.827540	+	2.26776i	−0.0429059	+	0.117578i
$373$	2.77890	−	4.81320i	0.143886	−	0.249218i	−0.785071	−	0.619406i	$-0.787373\pi$
$373$	2.77890	−	4.81320i	0.143886	−	0.249218i	0.928957	+	0.370188i	$0.120707\pi$
$374$	−14.8188			−0.766260
$375$	−7.18738	+	19.6961i	−0.371155	+	1.01710i
$376$	1.18059	+	5.17250i	0.0608843	+	0.266751i
$377$	17.6742	+	8.51144i	0.910267	+	0.438361i
$378$	−1.91039	+	13.6143i	−0.0982597	+	0.700246i
$379$	−3.93561	+	1.89529i	−0.202159	+	0.0973544i	−0.532224	−	0.846604i	$-0.678644\pi$
$379$	−3.93561	+	1.89529i	−0.202159	+	0.0973544i	0.330065	+	0.943958i	$0.392929\pi$
$380$	−5.25645	−	6.59137i	−0.269650	−	0.338130i
$381$	8.39713	+	5.43337i	0.430198	+	0.278360i
$382$	−1.30630	−	5.72328i	−0.0668362	−	0.292828i
$383$	0.524595	−	0.357663i	0.0268055	−	0.0182757i	−0.549843	−	0.835268i	$-0.685313\pi$
$383$	0.524595	−	0.357663i	0.0268055	−	0.0182757i	0.576649	+	0.816992i	$0.304360\pi$
$384$	1.64232	−	0.550266i	0.0838092	−	0.0280806i
$385$	2.39586	+	9.91525i	0.122104	+	0.505328i
$386$	0.551824	+	2.41770i	0.0280871	+	0.123058i
$387$	35.3026	−	12.7825i	1.79453	−	0.649770i
$388$	−3.29956	−	8.40713i	−0.167510	−	0.426807i
$389$	−28.2623	+	8.71775i	−1.43295	+	0.442008i	−0.911510	−	0.411278i	$-0.865083\pi$
$389$	−28.2623	+	8.71775i	−1.43295	+	0.442008i	−0.521444	+	0.853286i	$0.674606\pi$
$390$	−5.87387	−	3.80069i	−0.297435	−	0.192456i
$391$	−27.9854	−	48.4722i	−1.41528	−	2.45134i
$392$	1.38396	−	6.86183i	0.0699005	−	0.346575i
$393$	−31.2323	+	0.752825i	−1.57546	+	0.0379750i
$394$	−17.3794	+	8.36948i	−0.875562	+	0.421648i
$395$	−12.4961	−	11.5947i	−0.628747	−	0.583392i
$396$	3.49751	−	4.84766i	0.175756	−	0.243604i
$397$	−19.6637	+	6.06543i	−0.986890	+	0.304415i	−0.745860	−	0.666102i	$-0.767961\pi$
$397$	−19.6637	+	6.06543i	−0.986890	+	0.304415i	−0.241030	+	0.970518i	$0.577485\pi$
$398$	3.62115	+	1.11698i	0.181512	+	0.0559890i
$399$	15.1262	+	13.0332i	0.757257	+	0.652478i
$400$	−1.20021	+	0.370216i	−0.0600106	+	0.0185108i
$401$	11.9510	−	8.14808i	0.596807	−	0.406896i	−0.226895	−	0.973919i	$-0.572857\pi$
$401$	11.9510	−	8.14808i	0.596807	−	0.406896i	0.823702	+	0.567023i	$0.191905\pi$
$402$	12.7962	−	12.4602i	0.638215	−	0.621460i
$403$	2.40396	+	1.63899i	0.119750	+	0.0816439i
$404$	0.349517	−	0.890555i	0.0173891	−	0.0443068i
$405$	14.8898	−	9.03089i	0.739880	−	0.448749i
$406$	20.3628	−	14.2649i	1.01059	−	0.707958i
$407$	−5.34743	+	3.64582i	−0.265062	+	0.180716i
$408$	−3.16817	−	12.4857i	−0.156848	−	0.618135i
$409$	10.4792	+	13.1405i	0.518163	+	0.649755i	0.970218	−	0.242235i	$-0.0778804\pi$
$409$	10.4792	+	13.1405i	0.518163	+	0.649755i	−0.452055	+	0.891990i	$0.649309\pi$
$410$	19.3762			0.956920
$411$	−5.14649	+	9.43181i	−0.253858	+	0.465237i
$412$	−3.42998	+	0.516986i	−0.168983	+	0.0254701i
$413$	2.88899	+	11.9561i	0.142158	+	0.588320i
$414$	22.4618	+	2.28548i	1.10394	+	0.112325i
$415$	−27.4861	−	4.14286i	−1.34924	−	0.203365i
$416$	−0.156003	−	2.08172i	−0.00764869	−	0.102065i
$417$	9.77065	−	7.01227i	0.478471	−	0.343392i
$418$	−3.17179	−	8.08158i	−0.155137	−	0.395283i
$419$	−4.76870	−	0.718766i	−0.232966	−	0.0351140i	0.0315214	−	0.999503i	$-0.489965\pi$
$419$	−4.76870	−	0.718766i	−0.232966	−	0.0351140i	−0.264488	+	0.964389i	$0.585203\pi$
$420$	−7.84198	+	4.13848i	−0.382650	+	0.201937i
$421$	7.52050	−	1.13353i	0.366527	−	0.0552451i	0.0368033	−	0.999323i	$-0.488283\pi$
$421$	7.52050	−	1.13353i	0.366527	−	0.0552451i	0.329724	+	0.944077i	$0.393044\pi$
$422$	−4.63404	−	8.02639i	−0.225582	−	0.390719i
$423$	−7.28492	+	14.1516i	−0.354205	+	0.688073i
$424$	−9.44850	+	1.42413i	−0.458860	+	0.0691620i
$425$	2.07858	+	9.10686i	0.100826	+	0.441748i
$426$	−1.18639	−	11.9568i	−0.0574806	−	0.579308i
$427$	−3.22072	−	3.93516i	−0.155862	−	0.190436i
$428$	−11.9248	−	8.13017i	−0.576406	−	0.392987i
$429$	−4.62641	−	5.52289i	−0.223365	−	0.266647i
$430$	20.0083	+	13.6414i	0.964885	+	0.657848i
$431$	−39.0280	−	12.0386i	−1.87991	−	0.579877i	−0.993027	−	0.117891i	$-0.962387\pi$
$431$	−39.0280	−	12.0386i	−1.87991	−	0.579877i	−0.886887	−	0.461986i	$-0.847137\pi$
$432$	4.83220	+	1.91046i	0.232489	+	0.0919172i
$433$	1.84799	−	8.09657i	0.0888087	−	0.389096i	−0.910915	−	0.412594i	$-0.864623\pi$
$433$	1.84799	−	8.09657i	0.0888087	−	0.389096i	0.999724	+	0.0234973i	$0.00748010\pi$
$434$	3.30175	−	1.64198i	0.158489	−	0.0788174i
$435$	−30.3092	−	8.55496i	−1.45321	−	0.410179i
$436$	−3.00578	−	2.78896i	−0.143951	−	0.133567i
$437$	20.4449	−	25.6371i	0.978012	−	1.22639i
$438$	0.136671	−	0.673181i	0.00653038	−	0.0321658i
$439$	6.88506	−	3.31567i	0.328606	−	0.158248i	−0.262305	−	0.964985i	$-0.584483\pi$
$439$	6.88506	−	3.31567i	0.328606	−	0.158248i	0.590911	+	0.806737i	$0.298768\pi$
$440$	3.85547			0.183802
$441$	16.4344	−	13.0732i	0.782592	−	0.622535i
$442$	−15.5253			−0.738464
$443$	−28.5585	+	13.7531i	−1.35686	+	0.653428i	−0.963933	−	0.266143i	$-0.914251\pi$
$443$	−28.5585	+	13.7531i	−1.35686	+	0.653428i	−0.392923	+	0.919571i	$0.628536\pi$
$444$	−4.21508	−	3.72608i	−0.200039	−	0.176832i
$445$	−3.73655	+	4.68548i	−0.177129	+	0.222113i
$446$	11.6656	+	10.8241i	0.552384	+	0.512537i
$447$	−4.90157	−	19.3170i	−0.231837	−	0.913665i
$448$	−2.39811	−	1.11761i	−0.113300	−	0.0528020i
$449$	−2.71342	+	11.8883i	−0.128054	+	0.561043i	0.869671	+	0.493632i	$0.164331\pi$
$449$	−2.71342	+	11.8883i	−0.128054	+	0.561043i	−0.997725	+	0.0674110i	$0.978526\pi$
$450$	−3.46971	−	1.46943i	−0.163564	−	0.0692694i
$451$	19.0666	+	5.88128i	0.897813	+	0.276939i
$452$	7.71213	+	5.25804i	0.362748	+	0.247317i
$453$	33.6210	−	5.89939i	1.57965	−	0.277177i
$454$	−5.32367	−	3.62961i	−0.249852	−	0.170346i
$455$	2.51010	+	10.3880i	0.117675	+	0.486997i
$456$	6.13111	−	4.40022i	0.287116	−	0.206059i
$457$	0.00706941	+	0.0309731i	0.000330693	+	0.00144886i	0.975093	−	0.221796i	$-0.0711920\pi$
$457$	0.00706941	+	0.0309731i	0.000330693	+	0.00144886i	−0.974762	+	0.223245i	$0.928335\pi$
$458$	−15.1363	+	2.28143i	−0.707272	+	0.106604i
$459$	16.8541	−	34.7751i	0.786683	−	1.62316i
$460$	7.28110	+	12.6112i	0.339483	+	0.588002i
$461$	11.6784	−	1.76024i	0.543918	−	0.0819825i	0.128665	−	0.991688i	$-0.458931\pi$
$461$	11.6784	−	1.76024i	0.543918	−	0.0819825i	0.415254	+	0.909706i	$0.363693\pi$
$462$	−8.97287	+	1.69208i	−0.417456	+	0.0787229i
$463$	32.1148	+	4.84053i	1.49250	+	0.224958i	0.844036	−	0.536286i	$-0.180173\pi$
$463$	32.1148	+	4.84053i	1.49250	+	0.224958i	0.648465	+	0.761245i	$0.275411\pi$
$464$	−3.43313	−	8.74747i	−0.159379	−	0.406091i
$465$	−4.25605	−	1.92468i	−0.197370	−	0.0892547i
$466$	2.20074	+	29.3669i	0.101947	+	1.36039i
$467$	30.4187	+	4.58489i	1.40761	+	0.212163i	0.808497	−	0.588500i	$-0.200281\pi$
$467$	30.4187	+	4.58489i	1.40761	+	0.212163i	0.599114	+	0.800663i	$0.295519\pi$
$468$	3.66427	−	5.07879i	0.169381	−	0.234767i
$469$	−27.2803	+	0.346204i	−1.25969	+	0.0159862i
$470$	−10.1512	+	1.53005i	−0.468240	+	0.0705758i
$471$	13.4335	+	22.0243i	0.618985	+	1.01482i
$472$	4.64903			0.213989
$473$	15.5481	+	19.4966i	0.714900	+	0.896457i
$474$	10.9325	−	10.6455i	0.502145	−	0.488962i
$475$	−4.52163	+	3.08280i	−0.207467	+	0.141448i
$476$	−9.62129	+	17.1639i	−0.440991	+	0.786708i
$477$	−24.4352	−	14.9881i	−1.11881	−	0.686256i
$478$	−4.41671	+	11.2536i	−0.202016	+	0.514728i
$479$	4.65563	+	3.17415i	0.212721	+	0.145031i	0.664994	−	0.746849i	$-0.268434\pi$
$479$	4.65563	+	3.17415i	0.212721	+	0.145031i	−0.452273	+	0.891880i	$0.649387\pi$
$480$	0.824277	+	3.24847i	0.0376229	+	0.148271i
$481$	−5.60240	+	3.81965i	−0.255447	+	0.174161i
$482$	1.23871	−	0.382093i	0.0564219	−	0.0174038i
$483$	−22.4802	−	26.1547i	−1.02288	−	1.19008i
$484$	−6.71742	−	2.07205i	−0.305337	−	0.0941841i
$485$	16.6989	−	5.15093i	0.758258	−	0.233892i
$486$	7.39810	+	13.7211i	0.335585	+	0.622401i
$487$	2.60311	+	2.41534i	0.117958	+	0.109449i	0.736947	−	0.675951i	$-0.236267\pi$
$487$	2.60311	+	2.41534i	0.117958	+	0.109449i	−0.618988	+	0.785400i	$0.712457\pi$
$488$	−1.73166	+	0.833924i	−0.0783886	+	0.0377499i
$489$	−18.8905	+	34.6200i	−0.854258	+	1.56557i
$490$	13.0400	+	3.66259i	0.589086	+	0.165459i
$491$	1.20605	+	2.08894i	0.0544284	+	0.0942727i	0.891956	−	0.452123i	$-0.149333\pi$
$491$	1.20605	+	2.08894i	0.0544284	+	0.0942727i	−0.837527	+	0.546395i	$0.816000\pi$
$492$	−0.878996	+	17.3222i	−0.0396282	+	0.780945i
$493$	−66.7817	+	20.5994i	−3.00770	+	0.927751i
$494$	−3.32301	−	8.46690i	−0.149510	−	0.380944i
$495$	8.84796	+	7.44950i	0.397686	+	0.334830i
$496$	−0.310137	−	1.35880i	−0.0139256	−	0.0610119i
$497$	−11.2605	+	14.4938i	−0.505103	+	0.650135i
$498$	4.95060	−	24.3845i	0.221842	−	1.09270i
$499$	29.6599	−	20.2217i	1.32776	−	0.905250i	0.328528	−	0.944494i	$-0.393448\pi$
$499$	29.6599	−	20.2217i	1.32776	−	0.905250i	0.999230	+	0.0392448i	$0.0124952\pi$
$500$	−2.69362	−	11.8015i	−0.120462	−	0.527779i
$501$	1.42928	−	28.1666i	0.0638557	−	1.25839i
$502$	−17.8665	−	22.4039i	−0.797422	−	0.999936i
$503$	7.76605	−	3.73993i	0.346271	−	0.166755i	−0.252662	−	0.967555i	$-0.581306\pi$
$503$	7.76605	−	3.73993i	0.346271	−	0.166755i	0.598933	+	0.800799i	$0.295592\pi$
$504$	−3.34403	−	7.19843i	−0.148955	−	0.320644i
$505$	1.66781	+	0.803176i	0.0742167	+	0.0357409i
$506$	3.33688	+	14.6198i	0.148342	+	0.649930i
$507$	9.61205	+	11.4746i	0.426886	+	0.509605i
$508$	−5.77446			−0.256200
$509$	17.1417	−	29.6903i	0.759792	−	1.31600i	−0.183165	−	0.983082i	$-0.558634\pi$
$509$	17.1417	−	29.6903i	0.759792	−	1.31600i	0.942957	−	0.332916i	$-0.108032\pi$
$510$	24.5496	−	4.30766i	1.08708	−	0.190746i
$511$	−0.859385	+	0.602034i	−0.0380169	+	0.0266324i
$512$	−0.623490	+	0.781831i	−0.0275546	+	0.0345524i
$513$	22.5724	+	1.74837i	0.996598	+	0.0771923i
$514$	−1.88152	+	1.28280i	−0.0829904	+	0.0565819i
$515$	−0.501571	−	6.69300i	−0.0221018	−	0.294929i
$516$	−13.1030	+	17.2685i	−0.576829	+	0.760202i
$517$	−10.4535	−	1.57561i	−0.459743	−	0.0692950i
$518$	0.750900	+	8.56081i	0.0329927	+	0.376140i
$519$	−4.21823	+	11.5595i	−0.185160	+	0.507405i
$520$	4.03929			0.177135
$521$	1.74639	−	3.02484i	0.0765107	−	0.132520i	−0.825232	−	0.564795i	$-0.808955\pi$
$521$	1.74639	−	3.02484i	0.0765107	−	0.132520i	0.901742	+	0.432274i	$0.142289\pi$
$522$	9.02306	−	26.7081i	0.394929	−	1.16898i
$523$	4.69241	−	4.35392i	0.205185	−	0.190384i	−0.570886	−	0.821029i	$-0.693400\pi$
$523$	4.69241	−	4.35392i	0.205185	−	0.190384i	0.776071	+	0.630646i	$0.217210\pi$
$524$	14.9030	−	10.1607i	0.651042	−	0.443873i
$525$	2.29847	+	5.27693i	0.100313	+	0.230304i
$526$	7.50738	+	5.11844i	0.327337	+	0.223175i
$527$	−10.2496	+	1.54488i	−0.446480	+	0.0672960i
$528$	−0.174902	+	3.44677i	−0.00761165	+	0.150001i
$529$	−24.6595	+	22.8807i	−1.07215	+	0.994812i
$530$	−1.38167	−	18.4371i	−0.0600158	−	0.800855i
$531$	10.6691	+	8.98281i	0.463000	+	0.389821i
$532$	−11.4199	−	1.57334i	−0.495115	−	0.0682127i
$533$	19.9757	+	6.16169i	0.865245	+	0.266893i
$534$	−4.01929	−	3.55301i	−0.173932	−	0.153754i
$535$	17.4117	−	21.8336i	0.752773	−	0.943948i
$536$	−2.29459	+	10.0533i	−0.0991113	+	0.434235i
$537$	16.1102	−	8.24227i	0.695207	−	0.355680i
$538$	9.25554	−	16.0311i	0.399035	−	0.691149i
$539$	11.7199	+	7.56213i	0.504814	+	0.325724i
$540$	−4.38502	+	9.04761i	−0.188701	+	0.389347i
$541$	−9.81342	−	6.69068i	−0.421912	−	0.287655i	0.333694	−	0.942682i	$-0.391705\pi$
$541$	−9.81342	−	6.69068i	−0.421912	−	0.287655i	−0.755606	+	0.655027i	$0.772657\pi$
$542$	−4.54079	+	1.40065i	−0.195044	+	0.0601630i
$543$	43.3370	+	5.46754i	1.85977	+	0.234634i
$544$	5.45176	+	5.05849i	0.233742	+	0.216881i
$545$	5.81600	−	5.39646i	0.249130	−	0.231159i
$546$	−9.40069	+	1.77276i	−0.402313	+	0.0758672i
$547$	20.8657	+	19.3605i	0.892153	+	0.827797i	0.985820	−	0.167807i	$-0.0536685\pi$
$547$	20.8657	+	19.3605i	0.892153	+	0.827797i	−0.0936673	+	0.995604i	$0.529859\pi$
$548$	−0.463578	−	6.18602i	−0.0198031	−	0.264254i
$549$	−5.58531	−	1.43212i	−0.238375	−	0.0611213i
$550$	0.187025	−	2.49567i	0.00797477	−	0.106416i
$551$	−25.5280	−	32.0111i	−1.08753	−	1.36372i
$552$	−11.6047	+	5.93716i	−0.493928	+	0.252702i
$553$	−23.3070	+	0.295780i	−0.991115	+	0.0125779i
$554$	−0.839507	−	11.2024i	−0.0356672	−	0.475946i
$555$	7.79907	−	7.59432i	0.331052	−	0.322361i
$556$	−2.53675	+	6.46354i	−0.107582	+	0.274115i
$557$	−6.36437	+	11.0234i	−0.269667	+	0.467077i	−0.968776	−	0.247938i	$-0.920247\pi$
$557$	−6.36437	+	11.0234i	−0.269667	+	0.467077i	0.699109	+	0.715015i	$0.253580\pi$
$558$	1.91373	−	3.71757i	0.0810144	−	0.157377i
$559$	16.2894	+	20.4262i	0.688967	+	0.863938i
$560$	2.50322	−	4.46563i	0.105780	−	0.188707i
$561$	25.4650	+	3.21275i	1.07513	+	0.135642i
$562$	4.75196	+	12.1078i	0.200449	+	0.510737i
$563$	−37.6325	−	18.1228i	−1.58602	−	0.763787i	−0.587066	−	0.809539i	$-0.699717\pi$
$563$	−37.6325	−	18.1228i	−1.58602	−	0.763787i	−0.998953	+	0.0457523i	$0.985431\pi$
$564$	−0.907347	−	9.14453i	−0.0382062	−	0.385054i
$565$	−11.2607	+	14.1205i	−0.473741	+	0.594053i
$566$	−11.7226	+	14.6997i	−0.492738	+	0.617873i
$567$	6.23449	−	22.9811i	0.261824	−	0.965116i
$568$	4.32524	+	5.42368i	0.181483	+	0.227573i
$569$	18.8579			0.790562			0.395281	−	0.918560i	$-0.370647\pi$
$569$	18.8579			0.790562			0.395281	+	0.918560i	$0.370647\pi$
$570$	7.60380	+	12.4664i	0.318488	+	0.522161i
$571$	17.1447	+	21.4987i	0.717482	+	0.899694i	0.998192	−	0.0600985i	$-0.0191415\pi$
$571$	17.1447	+	21.4987i	0.717482	+	0.899694i	−0.280710	+	0.959792i	$0.590570\pi$
$572$	3.97477	+	1.22605i	0.166193	+	0.0512639i
$573$	1.00396	+	10.1183i	0.0419411	+	0.422696i
$574$	19.1913	−	18.2656i	0.801031	−	0.762391i
$575$	8.51655	−	4.10135i	0.355165	−	0.171038i
$576$	−2.94150	+	0.589533i	−0.122563	+	0.0245639i
$577$	−2.97908	+	39.7531i	−0.124021	+	1.65494i	0.494503	+	0.869176i	$0.335350\pi$
$577$	−2.97908	+	39.7531i	−0.124021	+	1.65494i	−0.618523	+	0.785766i	$0.712269\pi$
$578$	28.0833	−	26.0575i	1.16811	−	1.08385i
$579$	−0.424107	−	4.27428i	−0.0176253	−	0.177633i
$580$	17.3749	−	5.35945i	0.721454	−	0.222539i
$581$	−31.1293	+	21.8073i	−1.29146	+	0.904721i
$582$	3.84736	+	15.1624i	0.159478	+	0.628502i
$583$	4.23664	−	18.5619i	0.175464	−	0.768757i
$584$	0.144891	+	0.369175i	0.00599562	+	0.0152766i
$585$	9.26983	+	7.80469i	0.383260	+	0.322684i
$586$	−15.7896	−	10.7652i	−0.652264	−	0.444706i
$587$	8.15753	−	14.1292i	0.336697	−	0.583177i	−0.647112	−	0.762395i	$-0.724023\pi$
$587$	8.15753	−	14.1292i	0.336697	−	0.583177i	0.983809	+	0.179218i	$0.0573568\pi$
$588$	−3.86590	+	11.4915i	−0.159427	+	0.473902i
$589$	−3.03633	−	5.25907i	−0.125110	−	0.216696i
$590$	−0.672240	+	8.97043i	−0.0276757	+	0.369307i
$591$	31.6798	−	10.6145i	1.30313	−	0.436620i
$592$	3.21183	+	0.484105i	0.132005	+	0.0198966i
$593$	1.69890	−	0.524042i	0.0697656	−	0.0215198i	−0.259676	−	0.965696i	$-0.583616\pi$
$593$	1.69890	−	0.524042i	0.0697656	−	0.0215198i	0.329442	+	0.944176i	$0.393140\pi$
$594$	−7.06120	+	7.57209i	−0.289725	+	0.310687i
$595$	−31.7271	−	21.0464i	−1.30068	−	0.862820i
$596$	8.43459	+	7.82616i	0.345494	+	0.320572i
$597$	−5.98053	−	2.70452i	−0.244767	−	0.110689i
$598$	3.49598	+	15.3169i	0.142961	+	0.626354i
$599$	26.4879	−	12.7559i	1.08227	−	0.521192i	0.194225	−	0.980957i	$-0.437781\pi$
$599$	26.4879	−	12.7559i	1.08227	−	0.521192i	0.888041	+	0.459765i	$0.152066\pi$
$600$	2.14274	−	0.375981i	0.0874771	−	0.0153494i
$601$	2.02534	−	27.0263i	0.0826153	−	1.10242i	−0.789704	−	0.613488i	$-0.789766\pi$
$601$	2.02534	−	27.0263i	0.0826153	−	1.10242i	0.872319	−	0.488936i	$-0.162615\pi$
$602$	32.6770	−	5.35018i	1.33181	−	0.218057i
$603$	−24.6907	+	18.6378i	−1.00548	+	0.758989i
$604$	−14.4467	+	13.4046i	−0.587829	+	0.545426i
$605$	4.96941	−	12.6618i	0.202035	−	0.514777i
$606$	−0.793695	+	1.45458i	−0.0322417	+	0.0590883i
$607$	0.868894	−	1.50497i	0.0352673	−	0.0610848i	−0.847853	−	0.530231i	$-0.822105\pi$
$607$	0.868894	−	1.50497i	0.0352673	−	0.0610848i	0.883120	+	0.469147i	$0.155438\pi$
$608$	−1.59182	+	4.05589i	−0.0645568	+	0.164488i
$609$	−38.0847	+	20.0986i	−1.54327	+	0.814436i
$610$	−1.35868	−	3.46187i	−0.0550115	−	0.140167i
$611$	−10.9519	−	1.65073i	−0.443065	−	0.0667814i
$612$	2.73733	+	22.1427i	0.110650	+	0.895064i
$613$	−12.6006	+	8.59098i	−0.508935	+	0.346986i	−0.790406	−	0.612584i	$-0.790130\pi$
$613$	−12.6006	+	8.59098i	−0.508935	+	0.346986i	0.281470	+	0.959570i	$0.409178\pi$
$614$	7.80981	−	9.79319i	0.315178	−	0.395221i
$615$	−33.2965	−	4.20080i	−1.34265	−	0.169393i
$616$	3.81869	−	3.63448i	0.153859	−	0.146438i
$617$	−3.88669	+	9.90313i	−0.156472	+	0.398685i	−0.987515	−	0.157523i	$-0.949649\pi$
$617$	−3.88669	+	9.90313i	−0.156472	+	0.398685i	0.831043	+	0.556208i	$0.187744\pi$
$618$	6.00626	−	0.144775i	0.241607	−	0.00582371i
$619$	21.5555	+	37.3353i	0.866389	+	1.50063i	0.865661	+	0.500631i	$0.166899\pi$
$619$	21.5555	+	37.3353i	0.866389	+	1.50063i	0.000728617		1.00000i	$0.499768\pi$
$620$	2.66669	−	0.401938i	0.107097	−	0.0161422i
$621$	−38.1035	−	8.79722i	−1.52904	−	0.353020i
$622$	−2.46811	−	1.18858i	−0.0989622	−	0.0476577i
$623$	0.716022	+	8.16317i	0.0286868	+	0.327051i
$624$	−0.183242	+	3.61111i	−0.00733554	+	0.144560i
$625$	16.9509	−	2.55494i	0.678036	−	0.102197i
$626$	−13.2647	+	6.38796i	−0.530165	+	0.255314i
$627$	3.69838	+	14.5753i	0.147699	+	0.582080i
$628$	−13.4194	−	6.46243i	−0.535491	−	0.257879i
$629$	5.37530	−	23.5507i	0.214327	−	0.939030i
$630$	14.3731	−	5.41153i	0.572639	−	0.215600i
$631$	8.95585	+	39.2381i	0.356527	+	1.56205i	0.761777	+	0.647839i	$0.224327\pi$
$631$	8.95585	+	39.2381i	0.356527	+	1.56205i	−0.405250	+	0.914206i	$0.632816\pi$
$632$	−1.96039	+	8.58905i	−0.0779803	+	0.341654i
$633$	6.22312	+	14.7975i	0.247347	+	0.588146i
$634$	0.599537	−	2.62675i	0.0238107	−	0.104321i
$635$	0.834977	−	11.1420i	0.0331350	−	0.442156i
$636$	16.5453	−	0.398810i	0.656065	−	0.0158138i
$637$	12.2787	+	7.92269i	0.486502	+	0.313908i
$638$	18.7241			0.741295
$639$	−0.553541	+	20.8041i	−0.0218977	+	0.822997i
$640$	−1.41841	−	1.31609i	−0.0560676	−	0.0520231i
$641$	41.6940	+	6.28435i	1.64681	+	0.248217i	0.905933	−	0.423421i	$-0.139171\pi$
$641$	41.6940	+	6.28435i	1.64681	+	0.248217i	0.740879	+	0.671638i	$0.234409\pi$
$642$	18.7292	+	16.5564i	0.739183	+	0.653431i
$643$	−10.1351	+	9.40401i	−0.399690	+	0.370858i	−0.854254	−	0.519856i	$-0.825986\pi$
$643$	−10.1351	+	9.40401i	−0.399690	+	0.370858i	0.454564	+	0.890714i	$0.349795\pi$
$644$	19.1000	+	5.62716i	0.752647	+	0.221741i
$645$	−31.4253	−	27.7796i	−1.23737	−	1.09382i
$646$	29.1949	+	14.0595i	1.14866	+	0.553165i
$647$	3.80068	+	1.17236i	0.149420	+	0.0460900i	0.368563	−	0.929603i	$-0.379850\pi$
$647$	3.80068	+	1.17236i	0.149420	+	0.0460900i	−0.219143	+	0.975693i	$0.570326\pi$
$648$	−7.88959	−	4.33063i	−0.309932	−	0.170123i
$649$	−3.38431	+	8.62308i	−0.132846	+	0.338485i
$650$	0.195942	−	2.61467i	0.00768548	−	0.102556i
$651$	−6.02981	+	2.10579i	−0.236327	+	0.0825324i
$652$	−1.70159	−	22.7062i	−0.0666394	−	0.889242i
$653$	−23.4571	−	7.23554i	−0.917945	−	0.283149i	−0.200444	−	0.979705i	$-0.564238\pi$
$653$	−23.4571	−	7.23554i	−0.917945	−	0.283149i	−0.717502	+	0.696557i	$0.754715\pi$
$654$	4.56057	+	5.44429i	0.178332	+	0.212888i
$655$	17.4504	+	30.2251i	0.681845	+	1.18099i
$656$	−5.00692	−	8.67224i	−0.195487	−	0.338594i
$657$	−0.380806	+	1.12718i	−0.0148567	+	0.0439756i
$658$	−8.61202	+	11.0848i	−0.335731	+	0.432131i
$659$	4.03056	+	10.2697i	0.157008	+	0.400050i	0.987633	−	0.156782i	$-0.0501119\pi$
$659$	4.03056	+	10.2697i	0.157008	+	0.400050i	−0.830625	+	0.556832i	$0.812017\pi$
$660$	−6.62534	−	0.835875i	−0.257891	−	0.0325364i
$661$	41.5844	+	20.0260i	1.61745	+	0.778921i	0.999971	−	0.00766909i	$-0.00244117\pi$
$661$	41.5844	+	20.0260i	1.61745	+	0.778921i	0.617476	+	0.786590i	$0.288155\pi$
$662$	−6.73711	−	3.24442i	−0.261845	−	0.126098i
$663$	26.6791	+	3.36593i	1.03613	+	0.130722i
$664$	5.24834	+	13.3726i	0.203675	+	0.518956i
$665$	4.68709	−	21.8075i	0.181757	−	0.845658i
$666$	6.43548	+	7.31685i	0.249370	+	0.283522i
$667$	35.3607	+	61.2466i	1.36917	+	2.37148i
$668$	8.14146	+	14.1014i	0.315002	+	0.545600i
$669$	−17.6999	−	21.1296i	−0.684316	−	0.816919i
$670$	−19.0663	−	5.88116i	−0.736594	−	0.227209i
$671$	−0.286192	−	3.81897i	−0.0110483	−	0.147430i
$672$	3.87869	+	2.44045i	0.149624	+	0.0941422i
$673$	−0.277732	+	3.70607i	−0.0107058	+	0.142859i	−0.999995	−	0.00310881i	$-0.999010\pi$
$673$	−0.277732	+	3.70607i	−0.0107058	+	0.142859i	0.989289	+	0.145967i	$0.0466295\pi$
$674$	−3.86761	+	9.85451i	−0.148975	+	0.379582i
$675$	5.64388	+	3.27735i	0.217233	+	0.126145i
$676$	−8.25816	−	2.54731i	−0.317622	−	0.0979733i
$677$	9.39046	+	4.52221i	0.360905	+	0.173803i	0.605544	−	0.795812i	$-0.292955\pi$
$677$	9.39046	+	4.52221i	0.360905	+	0.173803i	−0.244640	+	0.969614i	$0.578670\pi$
$678$	−12.1128	−	10.7076i	−0.465189	−	0.411222i
$679$	11.6839	−	20.8436i	0.448388	−	0.799903i
$680$	−10.5488	+	9.78788i	−0.404529	+	0.375348i
$681$	8.36143	+	7.39142i	0.320411	+	0.283240i
$682$	2.74609	+	0.413906i	0.105153	+	0.0158493i
$683$	12.5553	+	11.6496i	0.480415	+	0.445760i	0.882827	−	0.469699i	$-0.155637\pi$
$683$	12.5553	+	11.6496i	0.480415	+	0.445760i	−0.402411	+	0.915459i	$0.631828\pi$
$684$	−11.4899	+	6.23222i	−0.439326	+	0.238295i
$685$	12.0031			0.458616
$686$	16.3682	−	8.66490i	0.624943	−	0.330828i
$687$	26.5052	−	0.638884i	1.01124	−	0.0243749i
$688$	0.935261	−	12.4802i	0.0356565	−	0.475803i
$689$	4.43864	−	19.4470i	0.169099	−	0.740870i
$690$	−9.77790	−	23.2501i	−0.372238	−	0.885115i
$691$	2.54041	−	11.1303i	0.0966417	−	0.423415i	−0.903343	−	0.428919i	$-0.858895\pi$
$691$	2.54041	−	11.1303i	0.0966417	−	0.423415i	0.999985	+	0.00550354i	$0.00175184\pi$
$692$	−1.58087	−	6.92623i	−0.0600955	−	0.263296i
$693$	15.7861	−	0.962384i	0.599664	−	0.0365579i
$694$	6.16472	−	27.0094i	0.234010	−	1.02526i
$695$	−12.1048	−	5.82935i	−0.459160	−	0.221120i
$696$	4.00311	+	15.7762i	0.151737	+	0.597996i
$697$	−67.0984	+	32.3129i	−2.54153	+	1.22394i
$698$	13.2996	−	2.00460i	0.503399	−	0.0758752i
$699$	2.58500	−	50.9420i	0.0977735	−	1.92680i
$700$	−2.76921	−	1.83698i	−0.104666	−	0.0694311i
$701$	−19.1523	−	9.22324i	−0.723371	−	0.348357i	0.0357021	−	0.999362i	$-0.488633\pi$
$701$	−19.1523	−	9.22324i	−0.723371	−	0.348357i	−0.759073	+	0.651005i	$0.774348\pi$
$702$	−7.39788	+	7.93312i	−0.279215	+	0.299416i
$703$	13.9942	−	2.10928i	0.527801	−	0.0795532i
$704$	−0.996276	−	1.72560i	−0.0375486	−	0.0650360i
$705$	17.7758	−	0.428470i	0.669477	−	0.0161371i
$706$	−3.20290	+	8.16085i	−0.120543	+	0.307138i
$707$	2.40904	−	0.776704i	0.0906014	−	0.0292110i
$708$	−7.98902	−	1.00792i	−0.300246	−	0.0378800i
$709$	−10.4485	+	13.1020i	−0.392402	+	0.492057i	−0.938313	−	0.345786i	$-0.887612\pi$
$709$	−10.4485	+	13.1020i	−0.392402	+	0.492057i	0.545911	+	0.837843i	$0.316184\pi$
$710$	−11.0906	+	7.56142i	−0.416222	+	0.283775i
$711$	−21.0946	+	15.9233i	−0.791110	+	0.597169i
$712$	3.06264	+	0.461619i	0.114777	+	0.0172999i
$713$	3.83214	+	9.76413i	0.143515	+	0.365669i
$714$	20.2547	−	27.4091i	0.758013	−	1.02576i
$715$	−2.94045	+	7.49214i	−0.109967	+	0.280190i
$716$	−5.22394	+	9.04813i	−0.195228	+	0.338144i
$717$	10.0296	−	18.3810i	0.374563	−	0.686450i
$718$	−6.66205	+	16.9746i	−0.248626	+	0.633488i
$719$	0.522413	−	0.484728i	0.0194827	−	0.0180773i	−0.670371	−	0.742026i	$-0.733865\pi$
$719$	0.522413	−	0.484728i	0.0194827	−	0.0180773i	0.689854	+	0.723948i	$0.257675\pi$
$720$	−0.712185	−	5.76096i	−0.0265416	−	0.214698i
$721$	−6.80616	−	6.15633i	−0.253475	−	0.229274i
$722$	0.00118400	−	0.0157994i	4.40639e−5	−	0.000587992i
$723$	−2.21148	+	0.388043i	−0.0822458	+	0.0144315i
$724$	−22.7215	+	10.9421i	−0.844438	+	0.406660i
$725$	−2.62637	−	11.5069i	−0.0975410	−	0.427355i
$726$	11.0942	+	5.01703i	0.411744	+	0.186199i
$727$	−6.22473	−	5.77571i	−0.230863	−	0.214209i	0.556256	−	0.831011i	$-0.312237\pi$
$727$	−6.22473	−	5.77571i	−0.230863	−	0.214209i	−0.787118	+	0.616802i	$0.788428\pi$
$728$	4.00076	−	3.80777i	0.148278	−	0.141125i
$729$	−9.73833	−	25.1826i	−0.360679	−	0.932690i
$730$	−0.733285	+	0.226189i	−0.0271401	+	0.00837161i
$731$	−92.0367	−	13.8723i	−3.40410	−	0.513086i
$732$	3.15653	−	1.05761i	0.116669	−	0.0390904i
$733$	1.91842	−	25.5996i	0.0708586	−	0.945542i	−0.842581	−	0.538569i	$-0.818965\pi$
$733$	1.91842	−	25.5996i	0.0708586	−	0.945542i	0.913440	−	0.406973i	$-0.133416\pi$
$734$	4.56941	+	7.91444i	0.168660	+	0.292127i
$735$	−21.6142	−	9.12101i	−0.797252	−	0.336433i
$736$	3.76296	−	6.51764i	0.138705	−	0.240243i
$737$	−16.9766	−	11.5744i	−0.625340	−	0.426349i
$738$	5.26599	−	29.5764i	0.193844	−	1.08872i
$739$	−2.95650	−	7.53303i	−0.108757	−	0.277107i	0.866126	−	0.499825i	$-0.166602\pi$
$739$	−2.95650	−	7.53303i	−0.108757	−	0.277107i	−0.974883	+	0.222718i	$0.928507\pi$
$740$	−1.39852	+	6.12731i	−0.0514106	+	0.225244i
$741$	3.87472	+	15.2702i	0.142341	+	0.560965i
$742$	−18.7488	−	16.9587i	−0.688290	−	0.622574i
$743$	−48.4467	+	14.9438i	−1.77734	+	0.548235i	−0.997020	−	0.0771497i	$-0.975418\pi$
$743$	−48.4467	+	14.9438i	−1.77734	+	0.548235i	−0.780316	+	0.625385i	$0.784942\pi$
$744$	0.238357	+	2.40224i	0.00873860	+	0.0880703i
$745$	−16.3204	+	15.1431i	−0.597934	+	0.554802i
$746$	0.415335	−	5.54226i	0.0152065	−	0.202917i
$747$	−13.7939	+	40.8297i	−0.504691	+	1.49388i
$748$	−13.3512	+	6.42962i	−0.488170	+	0.235090i
$749$	−3.33654	−	38.0390i	−0.121915	−	1.38992i
$750$	2.07019	+	20.8640i	0.0755926	+	0.761846i
$751$	8.11096	+	2.50190i	0.295973	+	0.0912956i	0.439186	−	0.898396i	$-0.355267\pi$
$751$	8.11096	+	2.50190i	0.295973	+	0.0912956i	−0.143212	+	0.989692i	$0.545743\pi$
$752$	3.30794	+	4.14803i	0.120628	+	0.151263i
$753$	25.8451	+	42.3731i	0.941849	+	1.54416i
$754$	19.6169			0.714404
$755$	−23.7756	−	29.8137i	−0.865283	−	1.08503i
$756$	4.18584	+	13.0950i	0.152238	+	0.476260i
$757$	−19.3357	+	24.2462i	−0.702769	+	0.881245i	−0.997227	−	0.0744197i	$-0.976290\pi$
$757$	−19.3357	+	24.2462i	−0.702769	+	0.881245i	0.294458	+	0.955665i	$0.404861\pi$
$758$	−2.72352	+	3.41519i	−0.0989229	+	0.124045i
$759$	−2.56457	−	25.8466i	−0.0930880	−	0.938171i
$760$	−7.59578	−	3.65794i	−0.275528	−	0.132687i
$761$	−6.24459	−	15.9109i	−0.226366	−	0.576771i	0.771893	−	0.635752i	$-0.219310\pi$
$761$	−6.24459	−	15.9109i	−0.226366	−	0.576771i	−0.998259	+	0.0589811i	$0.981215\pi$
$762$	9.92300	+	1.25192i	0.359472	+	0.0453522i
$763$	0.673369	−	10.8276i	0.0243776	−	0.391987i
$764$	−3.66017	−	4.58971i	−0.132420	−	0.166050i
$765$	−43.1207	+	2.07998i	−1.55903	+	0.0752017i
$766$	0.317460	−	0.549856i	0.0114703	−	0.0198671i
$767$	−3.54567	+	9.03422i	−0.128027	+	0.326207i
$768$	1.24093	−	1.20835i	0.0447781	−	0.0436025i
$769$	−1.73059	−	23.0931i	−0.0624066	−	0.832758i	−0.937318	−	0.348475i	$-0.886700\pi$
$769$	−1.73059	−	23.0931i	−0.0624066	−	0.832758i	0.874911	−	0.484283i	$-0.160919\pi$
$770$	6.46066	+	7.89381i	0.232826	+	0.284473i
$771$	3.51138	−	1.79648i	0.126459	−	0.0646987i
$772$	1.54618	+	1.93885i	0.0556482	+	0.0697806i
$773$	−2.03107	+	27.1027i	−0.0730525	+	0.974818i	0.833444	+	0.552604i	$0.186366\pi$
$773$	−2.03107	+	27.1027i	−0.0730525	+	0.974818i	−0.906496	+	0.422214i	$0.861253\pi$
$774$	26.2605	−	26.8338i	0.943913	−	0.964523i
$775$	−0.130820	−	1.74567i	−0.00469918	−	0.0627061i
$776$	−6.62051	−	6.14294i	−0.237663	−	0.220519i
$777$	0.565638	−	14.8739i	0.0202922	−	0.533599i
$778$	−21.6809	+	20.1170i	−0.777299	+	0.721228i
$779$	−31.9839	−	29.6767i	−1.14594	−	1.06328i
$780$	−6.94124	−	0.875729i	−0.248536	−	0.0313561i
$781$	−13.2085	+	4.07429i	−0.472638	+	0.145790i
$782$	−46.2453	−	31.5295i	−1.65373	−	1.12749i
$783$	−21.2959	+	43.9398i	−0.761053	+	1.57028i
$784$	−1.73033	−	6.78277i	−0.0617975	−	0.242242i
$785$	14.4099	−	24.9586i	0.514310	−	0.890811i
$786$	−27.8127	+	14.2295i	−0.992046	+	0.507548i
$787$	0.776603	−	3.40252i	0.0276829	−	0.121287i	−0.959199	−	0.282733i	$-0.908759\pi$
$787$	0.776603	−	3.40252i	0.0276829	−	0.121287i	0.986881	+	0.161447i	$0.0516160\pi$
$788$	−12.0269	+	15.0813i	−0.428441	+	0.537249i
$789$	−11.7912	−	10.4233i	−0.419778	−	0.371079i
$790$	−16.2893	−	5.02460i	−0.579549	−	0.178767i
$791$	2.15785	+	24.6010i	0.0767242	+	0.874712i
$792$	1.04783	−	5.88510i	0.0372329	−	0.209118i
$793$	−0.299838	−	4.00106i	−0.0106476	−	0.142082i
$794$	−15.0846	+	13.9965i	−0.535334	+	0.496717i
$795$	−1.62291	+	31.9823i	−0.0575587	+	1.13430i
$796$	3.74718	−	0.564797i	0.132815	−	0.0200187i
$797$	9.15586	+	6.24236i	0.324317	+	0.221116i	0.714523	−	0.699612i	$-0.246644\pi$
$797$	9.15586	+	6.24236i	0.324317	+	0.221116i	−0.390206	+	0.920728i	$0.627596\pi$
$798$	19.2831	+	5.17953i	0.682616	+	0.183353i
$799$	32.6014	−	22.2272i	1.15335	−	0.786343i
$800$	−0.920723	+	0.854306i	−0.0325525	+	0.0302043i
$801$	6.13656	+	6.97699i	0.216825	+	0.246520i
$802$	7.23220	−	12.5265i	0.255378	−	0.442327i
$803$	−0.790227			−0.0278865
$804$	6.12267	−	16.7783i	0.215930	−	0.591726i
$805$	−13.6196	+	36.0404i	−0.480028	+	1.27026i
$806$	2.87702	+	0.433641i	0.101339	+	0.0152744i
$807$	−19.3806	+	25.5416i	−0.682228	+	0.899108i
$808$	−0.0714934	−	0.954013i	−0.00251513	−	0.0335620i
$809$	31.1936	−	21.2675i	1.09671	−	0.747724i	0.126980	−	0.991905i	$-0.459472\pi$
$809$	31.1936	−	21.2675i	1.09671	−	0.747724i	0.969730	+	0.244181i	$0.0785191\pi$
$810$	9.49688	−	14.5970i	0.333687	−	0.512886i
$811$	9.09142	−	11.4003i	0.319243	−	0.400318i	−0.596154	−	0.802870i	$-0.703305\pi$
$811$	9.09142	−	11.4003i	0.319243	−	0.400318i	0.915397	+	0.402552i	$0.131877\pi$
$812$	12.1569	−	21.6874i	0.426624	−	0.761077i
$813$	8.10668	−	1.42246i	0.284314	−	0.0498878i
$814$	−3.23601	+	5.60493i	−0.113422	+	0.196453i
$815$	44.0582			1.54329
$816$	−8.27177	−	9.87462i	−0.289570	−	0.345681i
$817$	−12.1340	−	53.1625i	−0.424515	−	1.85992i
$818$	15.1429	+	7.29242i	0.529458	+	0.254973i
$819$	16.5388	−	1.00827i	0.577911	−	0.0352318i
$820$	17.4573	−	8.40700i	0.609636	−	0.293585i
$821$	1.36343	+	1.70969i	0.0475840	+	0.0596684i	0.805054	−	0.593201i	$-0.202136\pi$
$821$	1.36343	+	1.70969i	0.0475840	+	0.0596684i	−0.757470	+	0.652870i	$0.773565\pi$
$822$	−0.544520	+	10.7307i	−0.0189923	+	0.374278i
$823$	5.63009	+	24.6671i	0.196253	+	0.859839i	0.973143	+	0.230203i	$0.0739390\pi$
$823$	5.63009	+	24.6671i	0.196253	+	0.859839i	−0.776890	+	0.629636i	$0.783204\pi$
$824$	−2.86599	+	1.95400i	−0.0998416	+	0.0680708i
$825$	−0.862457	+	4.24809i	−0.0300269	+	0.147899i
$826$	7.79044	+	9.51857i	0.271064	+	0.331193i
$827$	1.38790	+	6.08077i	0.0482619	+	0.211449i	0.993309	−	0.115484i	$-0.0368419\pi$
$827$	1.38790	+	6.08077i	0.0482619	+	0.211449i	−0.945047	+	0.326933i	$0.893985\pi$
$828$	21.2290	−	7.68666i	0.737759	−	0.267130i
$829$	−12.3996	−	31.5938i	−0.430657	−	1.09730i	−0.967333	−	0.253508i	$-0.918416\pi$
$829$	−12.3996	−	31.5938i	−0.430657	−	1.09730i	0.536676	−	0.843788i	$-0.319680\pi$
$830$	−26.5616	+	8.19318i	−0.921968	+	0.284389i
$831$	−0.986086	+	19.4326i	−0.0342070	+	0.674110i
$832$	−1.04378	−	1.80788i	−0.0361865	−	0.0626768i
$833$	−51.2646	+	9.06294i	−1.77621	+	0.314012i
$834$	5.76054	−	10.5572i	0.199471	−	0.365565i
$835$	−28.3863	+	13.6701i	−0.982349	+	0.473074i
$836$	−6.36414	−	5.90506i	−0.220109	−	0.204231i
$837$	−4.09458	+	5.97348i	−0.141529	+	0.206474i
$838$	−4.60831	+	1.42148i	−0.159191	+	0.0491041i
$839$	−3.99707	−	1.23293i	−0.137994	−	0.0425656i	0.224989	−	0.974361i	$-0.427765\pi$
$839$	−3.99707	−	1.23293i	−0.137994	−	0.0425656i	−0.362983	+	0.931796i	$0.618242\pi$
$840$	−5.26976	+	7.13115i	−0.181824	+	0.246048i
$841$	56.6698	−	17.4803i	1.95413	−	0.602769i
$842$	6.28392	−	4.28430i	0.216558	−	0.147647i
$843$	−5.54090	−	21.8366i	−0.190839	−	0.752093i
$844$	−7.65765	−	5.22090i	−0.263587	−	0.179711i
$845$	6.10921	−	15.5660i	0.210163	−	0.535488i
$846$	−0.423347	+	15.9109i	−0.0145550	+	0.547029i
$847$	−7.01410	−	17.2256i	−0.241007	−	0.591880i
$848$	−7.89490	+	5.38265i	−0.271112	+	0.184841i
$849$	23.3314	−	22.7189i	0.800731	−	0.779709i
$850$	5.82406	+	7.30313i	0.199763	+	0.250495i
$851$	−24.4450			−0.837963
$852$	−6.25675	−	10.2579i	−0.214353	−	0.351431i
$853$	18.8122	−	2.83549i	0.644119	−	0.0970853i	0.181144	−	0.983457i	$-0.442020\pi$
$853$	18.8122	−	2.83549i	0.644119	−	0.0970853i	0.462975	+	0.886371i	$0.346782\pi$
$854$	−4.60917	−	2.14804i	−0.157723	−	0.0735044i
$855$	−10.3638	−	23.0712i	−0.354436	−	0.789017i
$856$	−14.2714	−	2.15107i	−0.487786	−	0.0735219i
$857$	0.470225	+	6.27472i	0.0160626	+	0.214340i	0.999460	+	0.0328729i	$0.0104657\pi$
$857$	0.470225	+	6.27472i	0.0160626	+	0.214340i	−0.983397	+	0.181467i	$0.941915\pi$
$858$	−6.56454	−	2.96862i	−0.224110	−	0.101347i
$859$	10.5411	+	26.8582i	0.359657	+	0.916391i	0.990126	+	0.140177i	$0.0447672\pi$
$859$	10.5411	+	26.8582i	0.359657	+	0.916391i	−0.630469	+	0.776214i	$0.717138\pi$
$860$	23.9456	+	3.60922i	0.816539	+	0.123073i
$861$	−36.9390	+	27.2274i	−1.25888	+	0.927906i
$862$	−40.3864	+	6.08727i	−1.37557	+	0.207333i
$863$	−6.36053	−	11.0168i	−0.216515	−	0.375015i	0.737225	−	0.675647i	$-0.236136\pi$
$863$	−6.36053	−	11.0168i	−0.216515	−	0.375015i	−0.953740	+	0.300632i	$0.902802\pi$
$864$	5.18258	−	0.375345i	0.176315	−	0.0127695i
$865$	13.5929	−	2.04881i	0.462174	−	0.0696615i
$866$	−1.84799	−	8.09657i	−0.0627972	−	0.275133i
$867$	−53.9084	+	38.6894i	−1.83083	+	1.31396i
$868$	2.26235	−	2.91195i	0.0767891	−	0.0988379i
$869$	−14.5040	−	9.88866i	−0.492014	−	0.335450i
$870$	−31.0195	+	5.44290i	−1.05166	+	0.184532i
$871$	−17.7860	−	12.1263i	−0.602656	−	0.410884i
$872$	−3.91820	−	1.20860i	−0.132687	−	0.0409285i
$873$	−3.32417	−	26.8896i	−0.112506	−	0.910076i
$874$	7.29670	−	31.9689i	0.246814	−	1.08136i
$875$	19.6490	−	25.2910i	0.664259	−	0.854990i
$876$	−0.168946	−	0.665814i	−0.00570816	−	0.0224958i
$877$	15.7001	+	14.5676i	0.530155	+	0.491912i	0.899223	−	0.437490i	$-0.144133\pi$
$877$	15.7001	+	14.5676i	0.530155	+	0.491912i	−0.369068	+	0.929402i	$0.620323\pi$
$878$	4.76461	−	5.97463i	0.160798	−	0.201634i
$879$	24.7994	+	21.9225i	0.836465	+	0.739426i
$880$	3.47365	−	1.67282i	0.117097	−	0.0563909i
$881$	−0.0989622			−0.00333412			−0.00166706	−	0.999999i	$-0.500531\pi$
$881$	−0.0989622			−0.00333412			−0.00166706	+	0.999999i	$0.500531\pi$
$882$	9.13466	−	18.9092i	0.307580	−	0.636706i
$883$	−46.0081			−1.54830			−0.774148	−	0.633005i	$-0.781821\pi$
$883$	−46.0081			−1.54830			−0.774148	+	0.633005i	$0.781821\pi$
$884$	−13.9878	+	6.73618i	−0.470461	+	0.226562i
$885$	3.10001	−	15.2693i	0.104206	−	0.513272i
$886$	−19.7631	+	24.7822i	−0.663955	+	0.832573i
$887$	−3.38429	−	3.14016i	−0.113633	−	0.105436i	0.621310	−	0.783565i	$-0.286601\pi$
$887$	−3.38429	−	3.14016i	−0.113633	−	0.105436i	−0.734943	+	0.678128i	$0.762791\pi$
$888$	−5.41434	−	1.52823i	−0.181693	−	0.0512841i
$889$	−9.67635	−	11.8228i	−0.324535	−	0.396525i
$890$	−1.33356	+	5.84270i	−0.0447010	+	0.195848i
$891$	13.7758	−	11.4812i	0.461507	−	0.384635i
$892$	15.2068	+	4.69067i	0.509161	+	0.157055i
$893$	19.0998	+	13.0220i	0.639151	+	0.435766i
$894$	−12.7975	−	15.2773i	−0.428013	−	0.510951i
$895$	−16.7032	−	11.3881i	−0.558328	−	0.380661i
$896$	−2.64554	+	0.0335735i	−0.0883812	+	0.00112161i
$897$	−2.68685	−	27.0789i	−0.0897113	−	0.904138i
$898$	2.71342	+	11.8883i	0.0905481	+	0.396717i
$899$	12.9508	−	1.95202i	0.431933	−	0.0651035i
$900$	−3.76366	+	0.181545i	−0.125455	+	0.00605148i
$901$	35.5315	+	61.5423i	1.18372	+	2.05027i
$902$	19.7302	−	2.97385i	0.656945	−	0.0990185i
$903$	−57.3130	+	2.10946i	−1.90726	+	0.0701983i
$904$	9.22977	+	1.39116i	0.306977	+	0.0462694i
$905$	−17.8276	−	45.4240i	−0.592609	−	1.50994i
$906$	27.7318	−	19.9028i	0.921329	−	0.661226i
$907$	−3.43886	−	45.8884i	−0.114185	−	1.52370i	−0.700522	−	0.713631i	$-0.747049\pi$
$907$	−3.43886	−	45.8884i	−0.114185	−	1.52370i	0.586336	−	0.810068i	$-0.300570\pi$
$908$	−6.37129	−	0.960317i	−0.211439	−	0.0318692i
$909$	1.67927	−	2.32752i	0.0556977	−	0.0771988i
$910$	6.76870	+	8.27018i	0.224380	+	0.274154i
$911$	24.1658	−	3.64241i	0.800649	−	0.120678i	0.264043	−	0.964511i	$-0.414944\pi$
$911$	24.1658	−	3.64241i	0.800649	−	0.120678i	0.536607	+	0.843833i	$0.319706\pi$
$912$	3.61476	−	6.62465i	0.119697	−	0.219364i
$913$	−28.6242			−0.947323
$914$	0.0198080	+	0.0248385i	0.000655192	+	0.000821585i
$915$	1.58426	+	6.24354i	0.0523740	+	0.206405i
$916$	−12.6474	+	8.62288i	−0.417883	+	0.284908i
$917$	45.7766	+	13.4865i	1.51168	+	0.445363i
$918$	0.0966743	−	38.6440i	0.00319073	−	1.27544i
$919$	0.865025	−	2.20405i	0.0285346	−	0.0727049i	−0.915896	−	0.401415i	$-0.868519\pi$
$919$	0.865025	−	2.20405i	0.0285346	−	0.0727049i	0.944431	+	0.328710i	$0.106614\pi$
$920$	12.0319	+	8.20318i	0.396678	+	0.270451i
$921$	−15.5438	+	15.1357i	−0.512185	+	0.498739i
$922$	9.75815	−	6.65300i	0.321368	−	0.219105i
$923$	−13.8383	+	4.26855i	−0.455494	+	0.140501i
$924$	−7.35011	+	5.41770i	−0.241801	+	0.178229i
$925$	3.89841	+	1.20250i	0.128179	+	0.0395380i
$926$	31.0346	−	9.57292i	1.01986	−	0.314586i
$927$	−10.3527	−	1.05339i	−0.340028	−	0.0345978i
$928$	−6.88852	−	6.39162i	−0.226127	−	0.209815i
$929$	−23.6023	+	11.3663i	−0.774367	+	0.372916i	−0.778960	−	0.627074i	$-0.784252\pi$
$929$	−23.6023	+	11.3663i	−0.774367	+	0.372916i	0.00459249	+	0.999989i	$0.498538\pi$
$930$	−4.66965	+	0.112558i	−0.153124	+	0.00369091i
$931$	−15.9152	−	26.0179i	−0.521599	−	0.852702i
$932$	14.7246	+	25.5038i	0.482321	+	0.835404i
$933$	3.98358	+	2.57758i	0.130417	+	0.0843862i
$934$	29.3956	−	9.06736i	0.961855	−	0.296693i
$935$	−10.4756	−	26.6913i	−0.342588	−	0.872899i
$936$	1.09779	−	6.16570i	0.0358822	−	0.201532i
$937$	1.43794	+	6.30003i	0.0469755	+	0.205813i	0.992969	−	0.118371i	$-0.0377673\pi$
$937$	1.43794	+	6.30003i	0.0469755	+	0.205813i	−0.945994	+	0.324184i	$0.894910\pi$
$938$	−24.4285	+	12.1484i	−0.797617	+	0.396659i
$939$	24.1794	−	8.10142i	0.789066	−	0.264380i
$940$	−8.48205	+	5.78297i	−0.276654	+	0.188620i
$941$	3.82478	+	16.7575i	0.124684	+	0.546278i	0.998227	+	0.0595294i	$0.0189600\pi$
$941$	3.82478	+	16.7575i	0.124684	+	0.546278i	−0.873542	+	0.486748i	$0.838183\pi$
$942$	21.6592	+	14.0146i	0.705694	+	0.456620i
$943$	46.9883	+	58.9215i	1.53015	+	1.91875i
$944$	4.18863	−	2.01714i	0.136328	−	0.0656522i
$945$	−25.8724	+	6.18319i	−0.841630	+	0.201139i
$946$	22.4676	+	10.8198i	0.730485	+	0.351783i
$947$	−4.74285	−	20.7798i	−0.154122	−	0.675253i	−0.991661	−	0.128875i	$-0.958863\pi$
$947$	−4.74285	−	20.7798i	−0.154122	−	0.675253i	0.837539	−	0.546378i	$-0.183994\pi$
$948$	5.23092	−	14.3346i	0.169893	−	0.465568i
$949$	−0.827904			−0.0268749
$950$	−2.73627	+	4.73937i	−0.0887765	+	0.153765i
$951$	−1.59975	+	4.38389i	−0.0518754	+	0.142157i
$952$	−1.22133	+	19.6387i	−0.0395835	+	0.636494i
$953$	22.4281	−	28.1239i	0.726517	−	0.911024i	−0.272170	−	0.962249i	$-0.587741\pi$
$953$	22.4281	−	28.1239i	0.726517	−	0.911024i	0.998687	+	0.0512255i	$0.0163127\pi$
$954$	−28.5184	−	2.90175i	−0.923318	−	0.0939475i
$955$	9.38523	−	6.39874i	0.303699	−	0.207058i
$956$	0.903434	+	12.0555i	0.0292191	+	0.389902i
$957$	−32.1760	−	4.05944i	−1.04010	−	0.131223i
$958$	5.57179	+	0.839812i	0.180016	+	0.0271331i
$959$	11.8886	−	11.3152i	0.383904	−	0.365386i
$960$	2.15210	+	2.56913i	0.0694589	+	0.0829182i
$961$	−29.0575			−0.937338
$962$	−3.39030	+	5.87217i	−0.109308	+	0.189326i
$963$	−28.5954	−	32.5116i	−0.921472	−	1.04767i
$964$	0.950259	−	0.881712i	0.0306058	−	0.0283980i
$965$	−3.96463	+	2.70304i	−0.127626	+	0.0870139i
$966$	−31.6021	−	13.8108i	−1.01678	−	0.444356i
$967$	4.59131	+	3.13030i	0.147647	+	0.100664i	0.634890	−	0.772602i	$-0.281045\pi$
$967$	4.59131	+	3.13030i	0.147647	+	0.100664i	−0.487244	+	0.873266i	$0.661998\pi$
$968$	−6.95122	+	1.04773i	−0.223421	+	0.0336752i
$969$	−47.1213	−	30.4899i	−1.51375	−	0.979475i
$970$	12.8103	−	11.8862i	0.411314	−	0.381643i
$971$	−2.84306	−	37.9380i	−0.0912382	−	1.21749i	−0.835458	−	0.549554i	$-0.814798\pi$
$971$	−2.84306	−	37.9380i	−0.0912382	−	1.21749i	0.744220	−	0.667935i	$-0.232821\pi$
$972$	12.6188	+	9.15236i	0.404749	+	0.293562i
$973$	−17.4845	+	5.63722i	−0.560529	+	0.180721i
$974$	3.39330	+	1.04669i	0.108728	+	0.0335383i
$975$	−0.903579	+	4.45064i	−0.0289377	+	0.142534i
$976$	−1.19835	+	1.50268i	−0.0383581	+	0.0480996i
$977$	6.25023	−	27.3841i	0.199963	−	0.876093i	−0.770995	−	0.636841i	$-0.780241\pi$
$977$	6.25023	−	27.3841i	0.199963	−	0.876093i	0.970957	−	0.239252i	$-0.0769022\pi$
$978$	−1.99869	+	39.3878i	−0.0639111	+	1.25948i
$979$	−3.08570	+	5.34459i	−0.0986194	+	0.170814i
$980$	13.3377	−	2.35795i	0.426059	−	0.0753219i
$981$	−6.65668	−	10.3444i	−0.212531	−	0.330270i
$982$	1.99297	+	1.35879i	0.0635983	+	0.0433606i
$983$	13.8636	−	4.27635i	0.442180	−	0.136394i	−0.0656675	−	0.997842i	$-0.520918\pi$
$983$	13.8636	−	4.27635i	0.442180	−	0.136394i	0.507847	+	0.861447i	$0.330441\pi$
$984$	6.72387	+	15.9881i	0.214349	+	0.509683i
$985$	−27.3607	−	25.3870i	−0.871784	−	0.808898i
$986$	−51.2305	+	47.5349i	−1.63151	+	1.51382i
$987$	17.2024	−	17.1814i	0.547557	−	0.546889i
$988$	−6.66758	−	6.18661i	−0.212124	−	0.196822i
$989$	7.03870	+	93.9249i	0.223818	+	2.98664i
$990$	11.2040	+	2.87278i	0.356085	+	0.0913031i
$991$	3.61225	−	48.2021i	0.114747	−	1.53119i	−0.581594	−	0.813479i	$-0.697571\pi$
$991$	3.61225	−	48.2021i	0.114747	−	1.53119i	0.696341	−	0.717711i	$-0.254810\pi$
$992$	−0.868985	−	1.08967i	−0.0275903	−	0.0345971i
$993$	10.8738	+	7.03593i	0.345071	+	0.223279i
$994$	−3.85675	+	17.9442i	−0.122329	+	0.569155i
$995$	0.547956	+	7.31196i	0.0173714	+	0.231805i
$996$	−6.11970	−	24.1176i	−0.193910	−	0.764197i
$997$	−10.9963	+	28.0181i	−0.348256	+	0.887341i	0.644213	+	0.764846i	$0.277185\pi$
$997$	−10.9963	+	28.0181i	−0.348256	+	0.887341i	−0.992469	+	0.122495i	$0.960910\pi$
$998$	17.9487	−	31.0881i	0.568157	−	0.984076i
$999$	−9.47260	−	13.9687i	−0.299700	−	0.441950i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	882.2.bb.b.151.3	yes	336
9.4	even	3		882.2.y.a.445.17	yes	336
49.37	even	21		882.2.y.a.331.17	✓	336
441.184	even	21	inner	882.2.bb.b.625.3	yes	336

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
882.2.y.a.331.17	✓	336	49.37	even	21
882.2.y.a.445.17	yes	336	9.4	even	3
882.2.bb.b.151.3	yes	336	1.1	even	1	trivial
882.2.bb.b.625.3	yes	336	441.184	even	21	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	882.bb (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.900969 - 0.433884i) q^{2} +(-1.64232 + 0.550266i) q^{3} +(0.623490 - 0.781831i) q^{4} +(1.41841 + 1.31609i) q^{5} +(-1.24093 + 1.20835i) q^{6} +(2.64554 - 0.0335735i) q^{7} +(0.222521 - 0.974928i) q^{8} +(2.39442 - 1.80742i) q^{9} +O(q^{10})\)	\(q+(0.900969 - 0.433884i) q^{2} +(-1.64232 + 0.550266i) q^{3} +(0.623490 - 0.781831i) q^{4} +(1.41841 + 1.31609i) q^{5} +(-1.24093 + 1.20835i) q^{6} +(2.64554 - 0.0335735i) q^{7} +(0.222521 - 0.974928i) q^{8} +(2.39442 - 1.80742i) q^{9} +(1.84897 + 0.570333i) q^{10} +(1.64632 + 1.12244i) q^{11} +(-0.593753 + 1.62710i) q^{12} +(1.72482 + 1.17596i) q^{13} +(2.36898 - 1.17810i) q^{14} +(-3.05368 - 1.38094i) q^{15} +(-0.222521 - 0.974928i) q^{16} +(-7.35401 + 1.10844i) q^{17} +(1.37308 - 2.66733i) q^{18} +(-2.17854 - 3.77334i) q^{19} +(1.91333 - 0.288388i) q^{20} +(-4.32634 + 1.51089i) q^{21} +(1.97030 + 0.296974i) q^{22} +(2.74953 + 7.00568i) q^{23} +(0.171019 + 1.72359i) q^{24} +(-0.0938620 - 1.25250i) q^{25} +(2.06424 + 0.311134i) q^{26} +(-2.93783 + 4.28593i) q^{27} +(1.62322 - 2.08930i) q^{28} +(9.29209 - 1.40056i) q^{29} +(-3.35044 + 0.0807592i) q^{30} +1.39374 q^{31} +(-0.623490 - 0.781831i) q^{32} +(-3.32143 - 0.937495i) q^{33} +(-6.14480 + 4.18945i) q^{34} +(3.79664 + 3.43415i) q^{35} +(0.0797937 - 2.99894i) q^{36} +(-1.18667 + 3.02358i) q^{37} +(-3.59999 - 2.45443i) q^{38} +(-3.47979 - 0.982194i) q^{39} +(1.59872 - 1.08999i) q^{40} +(9.56895 - 2.95163i) q^{41} +(-3.24235 + 3.23839i) q^{42} +(11.9592 + 3.68891i) q^{43} +(1.90403 - 0.587315i) q^{44} +(5.77500 + 0.587605i) q^{45} +(5.51689 + 5.11893i) q^{46} +(-4.78011 + 2.30198i) q^{47} +(0.901920 + 1.47870i) q^{48} +(6.99775 - 0.177640i) q^{49} +(-0.628006 - 1.08774i) q^{50} +(11.4677 - 5.86707i) q^{51} +(1.99481 - 0.615318i) q^{52} +(-3.49092 - 8.89471i) q^{53} +(-0.787298 + 5.13616i) q^{54} +(0.857922 + 3.75880i) q^{55} +(0.555956 - 2.58668i) q^{56} +(5.65420 + 4.99825i) q^{57} +(7.76421 - 5.29355i) q^{58} +(1.03451 + 4.53246i) q^{59} +(-2.98360 + 1.52646i) q^{60} +(-1.19835 - 1.50268i) q^{61} +(1.25572 - 0.604723i) q^{62} +(6.27384 - 4.86199i) q^{63} +(-0.900969 - 0.433884i) q^{64} +(0.898827 + 3.93802i) q^{65} +(-3.39927 + 0.596460i) q^{66} -10.3118 q^{67} +(-3.71854 + 6.44069i) q^{68} +(-8.37059 - 9.99259i) q^{69} +(4.91068 + 1.44676i) q^{70} +(-4.32524 + 5.42368i) q^{71} +(-1.22930 - 2.73657i) q^{72} +(-0.327678 + 0.223407i) q^{73} +(0.242731 + 3.23902i) q^{74} +(0.843359 + 2.00536i) q^{75} +(-4.30842 - 0.649389i) q^{76} +(4.39310 + 2.91420i) q^{77} +(-3.56134 + 0.624899i) q^{78} -8.80993 q^{79} +(0.967469 - 1.67571i) q^{80} +(2.46645 - 8.65544i) q^{81} +(7.34066 - 6.81114i) q^{82} +(-11.8694 + 8.09243i) q^{83} +(-1.51617 + 4.32449i) q^{84} +(-11.8898 - 8.10633i) q^{85} +(12.3754 - 1.86529i) q^{86} +(-14.4899 + 7.41328i) q^{87} +(1.46064 - 1.35528i) q^{88} +(0.231457 + 3.08857i) q^{89} +(5.45805 - 1.97626i) q^{90} +(4.60256 + 3.05315i) q^{91} +(7.19157 + 2.21830i) q^{92} +(-2.28897 + 0.766929i) q^{93} +(-3.30794 + 4.14803i) q^{94} +(1.87600 - 8.21931i) q^{95} +(1.45418 + 0.940931i) q^{96} +(4.51572 - 7.82146i) q^{97} +(6.22768 - 3.19626i) q^{98} +(5.97071 - 0.288004i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 336 q + 56 q^{2} + 5 q^{3} - 56 q^{4} + 2 q^{5} - 5 q^{6} + 2 q^{7} + 56 q^{8} + 5 q^{9}+O(q^{10}) \) 336 * q + 56 * q^2 + 5 * q^3 - 56 * q^4 + 2 * q^5 - 5 * q^6 + 2 * q^7 + 56 * q^8 + 5 * q^9	\( 336 q + 56 q^{2} + 5 q^{3} - 56 q^{4} + 2 q^{5} - 5 q^{6} + 2 q^{7} + 56 q^{8} + 5 q^{9} - 2 q^{10} - 2 q^{12} + 19 q^{13} - 2 q^{14} + q^{15} - 56 q^{16} + 7 q^{17} + 2 q^{18} + 38 q^{19} + 2 q^{20} + 4 q^{21} - 42 q^{23} + 2 q^{24} + 24 q^{25} + 9 q^{26} + 35 q^{27} + 2 q^{28} - 10 q^{29} - q^{30} - 88 q^{31} + 56 q^{32} + 26 q^{33} - 7 q^{34} - 2 q^{35} + 5 q^{36} + 52 q^{37} + 11 q^{38} - 60 q^{39} - 2 q^{40} + 3 q^{41} - 53 q^{42} + q^{43} + 108 q^{45} - 42 q^{46} + 3 q^{47} - 2 q^{48} + 70 q^{49} + 172 q^{50} + 13 q^{51} + 5 q^{52} - 78 q^{53} + 14 q^{54} + 23 q^{55} - 2 q^{56} - 30 q^{57} + 38 q^{58} - 28 q^{59} + q^{60} - 37 q^{61} - 24 q^{62} + 26 q^{63} - 56 q^{64} - 14 q^{65} + 2 q^{66} - 58 q^{67} - 21 q^{68} + 19 q^{69} + 44 q^{70} + 7 q^{71} + 2 q^{72} - 8 q^{73} + 4 q^{74} + q^{75} - 4 q^{76} - 13 q^{77} + 4 q^{78} + 18 q^{79} - 12 q^{80} - 87 q^{81} - 3 q^{82} + 185 q^{83} - 17 q^{84} - 159 q^{85} - q^{86} - 132 q^{87} + 47 q^{89} + 60 q^{90} + 45 q^{91} - 21 q^{92} + 53 q^{93} + 18 q^{94} + 26 q^{95} + 2 q^{96} + 111 q^{97} - 14 q^{98} - 157 q^{99}+O(q^{100}) \) 336 * q + 56 * q^2 + 5 * q^3 - 56 * q^4 + 2 * q^5 - 5 * q^6 + 2 * q^7 + 56 * q^8 + 5 * q^9 - 2 * q^10 - 2 * q^12 + 19 * q^13 - 2 * q^14 + q^15 - 56 * q^16 + 7 * q^17 + 2 * q^18 + 38 * q^19 + 2 * q^20 + 4 * q^21 - 42 * q^23 + 2 * q^24 + 24 * q^25 + 9 * q^26 + 35 * q^27 + 2 * q^28 - 10 * q^29 - q^30 - 88 * q^31 + 56 * q^32 + 26 * q^33 - 7 * q^34 - 2 * q^35 + 5 * q^36 + 52 * q^37 + 11 * q^38 - 60 * q^39 - 2 * q^40 + 3 * q^41 - 53 * q^42 + q^43 + 108 * q^45 - 42 * q^46 + 3 * q^47 - 2 * q^48 + 70 * q^49 + 172 * q^50 + 13 * q^51 + 5 * q^52 - 78 * q^53 + 14 * q^54 + 23 * q^55 - 2 * q^56 - 30 * q^57 + 38 * q^58 - 28 * q^59 + q^60 - 37 * q^61 - 24 * q^62 + 26 * q^63 - 56 * q^64 - 14 * q^65 + 2 * q^66 - 58 * q^67 - 21 * q^68 + 19 * q^69 + 44 * q^70 + 7 * q^71 + 2 * q^72 - 8 * q^73 + 4 * q^74 + q^75 - 4 * q^76 - 13 * q^77 + 4 * q^78 + 18 * q^79 - 12 * q^80 - 87 * q^81 - 3 * q^82 + 185 * q^83 - 17 * q^84 - 159 * q^85 - q^86 - 132 * q^87 + 47 * q^89 + 60 * q^90 + 45 * q^91 - 21 * q^92 + 53 * q^93 + 18 * q^94 + 26 * q^95 + 2 * q^96 + 111 * q^97 - 14 * q^98 - 157 * q^99

Introduction

L-functions

Modular forms

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