LMFDB - Embedded newform 966.2.y.b.163.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(25,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([0, 44, 6]))

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

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

chi := DirichletCharacter("966.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.y (of order $33$, degree $20$, 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:	$7.71354883526$
Analytic rank:	$0$
Dimension:	$160$
Relative dimension:	$8$ over $\Q(\zeta_{33})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{33}]$

Embedding invariants

Embedding label			163.6
Character	$\chi$	$=$	966.163
Dual form			966.2.y.b.403.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.888835 - 0.458227i) q^{2} +(-0.786053 + 0.618159i) q^{3} +(0.580057 - 0.814576i) q^{4} +(0.468732 - 0.446935i) q^{5} +(-0.415415 + 0.909632i) q^{6} +(2.25050 + 1.39113i) q^{7} +(0.142315 - 0.989821i) q^{8} +(0.235759 - 0.971812i) q^{9} +O(q^{10})$	\(q+(0.888835 - 0.458227i) q^{2} +(-0.786053 + 0.618159i) q^{3} +(0.580057 - 0.814576i) q^{4} +(0.468732 - 0.446935i) q^{5} +(-0.415415 + 0.909632i) q^{6} +(2.25050 + 1.39113i) q^{7} +(0.142315 - 0.989821i) q^{8} +(0.235759 - 0.971812i) q^{9} +(0.211828 - 0.612037i) q^{10} +(5.34177 + 2.75387i) q^{11} +(0.0475819 + 0.998867i) q^{12} +(-1.24237 - 1.43377i) q^{13} +(2.63778 + 0.205249i) q^{14} +(-0.0921714 + 0.641066i) q^{15} +(-0.327068 - 0.945001i) q^{16} +(-3.72113 + 0.355325i) q^{17} +(-0.235759 - 0.971812i) q^{18} +(-1.41754 - 0.135359i) q^{19} +(-0.0921714 - 0.641066i) q^{20} +(-2.62895 + 0.297663i) q^{21} +6.00985 q^{22} +(-1.05148 + 4.67915i) q^{23} +(0.500000 + 0.866025i) q^{24} +(-0.217951 + 4.57535i) q^{25} +(-1.76126 - 0.705101i) q^{26} +(0.415415 + 0.909632i) q^{27} +(2.43860 - 1.02627i) q^{28} +(3.91380 - 8.57003i) q^{29} +(0.211828 + 0.612037i) q^{30} +(7.18233 - 2.87537i) q^{31} +(-0.723734 - 0.690079i) q^{32} +(-5.90125 + 1.13737i) q^{33} +(-3.14465 + 2.02095i) q^{34} +(1.67663 - 0.353759i) q^{35} +(-0.654861 - 0.755750i) q^{36} +(0.899378 - 3.70729i) q^{37} +(-1.32199 + 0.529244i) q^{38} +(1.86287 + 0.359039i) q^{39} +(-0.375679 - 0.527567i) q^{40} +(4.99156 + 1.46566i) q^{41} +(-2.20031 + 1.46923i) q^{42} +(1.36411 + 9.48758i) q^{43} +(5.34177 - 2.75387i) q^{44} +(-0.323829 - 0.560888i) q^{45} +(1.20952 + 4.64080i) q^{46} +(1.62496 - 2.81451i) q^{47} +(0.841254 + 0.540641i) q^{48} +(3.12950 + 6.26149i) q^{49} +(1.90282 + 4.16660i) q^{50} +(2.70536 - 2.57955i) q^{51} +(-1.88856 + 0.180336i) q^{52} +(9.04378 + 1.74305i) q^{53} +(0.786053 + 0.618159i) q^{54} +(3.73466 - 1.09660i) q^{55} +(1.69725 - 2.02961i) q^{56} +(1.19794 - 0.769867i) q^{57} +(-0.448290 - 9.41076i) q^{58} +(4.48148 - 12.9484i) q^{59} +(0.468732 + 0.446935i) q^{60} +(-1.83765 - 1.44514i) q^{61} +(5.06634 - 5.84686i) q^{62} +(1.88249 - 1.85909i) q^{63} +(-0.959493 - 0.281733i) q^{64} +(-1.22314 - 0.116796i) q^{65} +(-4.72406 + 3.71504i) q^{66} +(-0.269278 + 5.65284i) q^{67} +(-1.86903 + 3.23725i) q^{68} +(-2.06594 - 4.32804i) q^{69} +(1.32814 - 1.08271i) q^{70} +(-8.71620 - 5.60156i) q^{71} +(-0.928368 - 0.371662i) q^{72} +(-5.41226 + 7.60046i) q^{73} +(-0.899378 - 3.70729i) q^{74} +(-2.65697 - 3.73120i) q^{75} +(-0.932515 + 1.07618i) q^{76} +(8.19065 + 13.6287i) q^{77} +(1.82031 - 0.534490i) q^{78} +(-5.49831 + 1.05971i) q^{79} +(-0.575662 - 0.296774i) q^{80} +(-0.888835 - 0.458227i) q^{81} +(5.10828 - 0.984540i) q^{82} +(-5.08882 + 1.49421i) q^{83} +(-1.28247 + 2.31414i) q^{84} +(-1.58541 + 1.82966i) q^{85} +(5.55993 + 7.80783i) q^{86} +(2.22119 + 9.15585i) q^{87} +(3.48606 - 4.89548i) q^{88} +(-13.4056 - 5.36680i) q^{89} +(-0.544845 - 0.350150i) q^{90} +(-0.801389 - 4.95501i) q^{91} +(3.20160 + 3.57068i) q^{92} +(-3.86825 + 6.70001i) q^{93} +(0.154637 - 3.24624i) q^{94} +(-0.724944 + 0.570102i) q^{95} +(0.995472 + 0.0950560i) q^{96} +(-8.55220 - 2.51115i) q^{97} +(5.65079 + 4.13141i) q^{98} +(3.93562 - 4.54194i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q - 8 q^{2} + 8 q^{3} + 8 q^{4} + 6 q^{5} + 16 q^{6} - 10 q^{7} + 16 q^{8} + 8 q^{9}+O(q^{10}) $ 160 * q - 8 * q^2 + 8 * q^3 + 8 * q^4 + 6 * q^5 + 16 * q^6 - 10 * q^7 + 16 * q^8 + 8 * q^9	\( 160 q - 8 q^{2} + 8 q^{3} + 8 q^{4} + 6 q^{5} + 16 q^{6} - 10 q^{7} + 16 q^{8} + 8 q^{9} - 6 q^{10} + 8 q^{11} + 8 q^{12} + 4 q^{13} - 13 q^{14} + 10 q^{15} + 8 q^{16} + 9 q^{17} - 8 q^{18} - 8 q^{19} + 10 q^{20} - 3 q^{21} - 28 q^{22} + 22 q^{23} + 80 q^{24} + 46 q^{25} + 2 q^{26} - 16 q^{27} - 14 q^{28} + 62 q^{29} - 6 q^{30} + 7 q^{31} - 8 q^{32} - 14 q^{33} - 4 q^{34} + 24 q^{35} - 16 q^{36} + 15 q^{37} + 19 q^{38} - 2 q^{39} + 5 q^{40} - 14 q^{41} + 10 q^{42} - 56 q^{43} + 8 q^{44} - 16 q^{45} + 66 q^{47} - 16 q^{48} + 42 q^{49} + 4 q^{50} + 9 q^{51} - 2 q^{52} + 12 q^{53} - 8 q^{54} - 14 q^{55} + 10 q^{56} - 6 q^{57} - 13 q^{58} + 62 q^{59} + 6 q^{60} + 16 q^{61} - 8 q^{62} + 2 q^{63} - 16 q^{64} + 70 q^{65} - 8 q^{66} - 14 q^{67} - 46 q^{68} + 22 q^{69} + 24 q^{70} - 108 q^{71} - 8 q^{72} + 40 q^{73} - 15 q^{74} + 2 q^{75} + 16 q^{76} + 29 q^{77} + 18 q^{78} + 22 q^{79} + 6 q^{80} + 8 q^{81} - 7 q^{82} - 18 q^{83} - 9 q^{84} + 26 q^{85} - 6 q^{86} + 2 q^{87} + 3 q^{88} + 112 q^{89} + 12 q^{90} + 18 q^{91} - 66 q^{92} - 26 q^{93} + 23 q^{95} - 8 q^{96} + 8 q^{97} + 9 q^{98} + 28 q^{99}+O(q^{100}) \) 160 * q - 8 * q^2 + 8 * q^3 + 8 * q^4 + 6 * q^5 + 16 * q^6 - 10 * q^7 + 16 * q^8 + 8 * q^9 - 6 * q^10 + 8 * q^11 + 8 * q^12 + 4 * q^13 - 13 * q^14 + 10 * q^15 + 8 * q^16 + 9 * q^17 - 8 * q^18 - 8 * q^19 + 10 * q^20 - 3 * q^21 - 28 * q^22 + 22 * q^23 + 80 * q^24 + 46 * q^25 + 2 * q^26 - 16 * q^27 - 14 * q^28 + 62 * q^29 - 6 * q^30 + 7 * q^31 - 8 * q^32 - 14 * q^33 - 4 * q^34 + 24 * q^35 - 16 * q^36 + 15 * q^37 + 19 * q^38 - 2 * q^39 + 5 * q^40 - 14 * q^41 + 10 * q^42 - 56 * q^43 + 8 * q^44 - 16 * q^45 + 66 * q^47 - 16 * q^48 + 42 * q^49 + 4 * q^50 + 9 * q^51 - 2 * q^52 + 12 * q^53 - 8 * q^54 - 14 * q^55 + 10 * q^56 - 6 * q^57 - 13 * q^58 + 62 * q^59 + 6 * q^60 + 16 * q^61 - 8 * q^62 + 2 * q^63 - 16 * q^64 + 70 * q^65 - 8 * q^66 - 14 * q^67 - 46 * q^68 + 22 * q^69 + 24 * q^70 - 108 * q^71 - 8 * q^72 + 40 * q^73 - 15 * q^74 + 2 * q^75 + 16 * q^76 + 29 * q^77 + 18 * q^78 + 22 * q^79 + 6 * q^80 + 8 * q^81 - 7 * q^82 - 18 * q^83 - 9 * q^84 + 26 * q^85 - 6 * q^86 + 2 * q^87 + 3 * q^88 + 112 * q^89 + 12 * q^90 + 18 * q^91 - 66 * q^92 - 26 * q^93 + 23 * q^95 - 8 * q^96 + 8 * q^97 + 9 * q^98 + 28 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/966\mathbb{Z}\right)^\times$.

$n$	$323$	$829$	$925$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{11}\right)$

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 $

$2$	0.888835	−	0.458227i	0.628502	−	0.324015i
$2$	0.888835	−	0.458227i	0.628502	−	0.324015i
$3$	−0.786053	+	0.618159i	−0.453828	+	0.356894i
$3$	−0.786053	+	0.618159i	−0.453828	+	0.356894i
$4$	0.580057	−	0.814576i	0.290028	−	0.407288i
$5$	0.468732	−	0.446935i	0.209623	−	0.199876i	−0.577992	−	0.816042i	$-0.696164\pi$
$5$	0.468732	−	0.446935i	0.209623	−	0.199876i	0.787616	+	0.616167i	$0.211315\pi$
$6$	−0.415415	+	0.909632i	−0.169592	+	0.371356i
$7$	2.25050	+	1.39113i	0.850609	+	0.525799i
$7$	2.25050	+	1.39113i	0.850609	+	0.525799i
$8$	0.142315	−	0.989821i	0.0503159	−	0.349955i
$9$	0.235759	−	0.971812i	0.0785863	−	0.323937i
$10$	0.211828	−	0.612037i	0.0669860	−	0.193543i
$11$	5.34177	+	2.75387i	1.61060	+	0.830324i	0.999240	+	0.0389749i	$0.0124092\pi$
$11$	5.34177	+	2.75387i	1.61060	+	0.830324i	0.611364	+	0.791349i	$0.290621\pi$
$12$	0.0475819	+	0.998867i	0.0137357	+	0.288348i
$13$	−1.24237	−	1.43377i	−0.344572	−	0.397657i	0.556840	−	0.830620i	$-0.312014\pi$
$13$	−1.24237	−	1.43377i	−0.344572	−	0.397657i	−0.901412	+	0.432963i	$0.857468\pi$
$14$	2.63778	+	0.205249i	0.704976	+	0.0548550i
$15$	−0.0921714	+	0.641066i	−0.0237985	+	0.165523i
$16$	−0.327068	−	0.945001i	−0.0817670	−	0.236250i
$17$	−3.72113	+	0.355325i	−0.902506	+	0.0861789i	−0.535982	−	0.844229i	$-0.680058\pi$
$17$	−3.72113	+	0.355325i	−0.902506	+	0.0861789i	−0.366524	+	0.930408i	$0.619452\pi$
$18$	−0.235759	−	0.971812i	−0.0555689	−	0.229058i
$19$	−1.41754	−	0.135359i	−0.325206	−	0.0310534i	−0.0688238	−	0.997629i	$-0.521925\pi$
$19$	−1.41754	−	0.135359i	−0.325206	−	0.0310534i	−0.256383	+	0.966575i	$0.582531\pi$
$20$	−0.0921714	−	0.641066i	−0.0206101	−	0.143347i
$21$	−2.62895	+	0.297663i	−0.573685	+	0.0649554i
$22$	6.00985			1.28130
$23$	−1.05148	+	4.67915i	−0.219248	+	0.975669i
$23$	−1.05148	+	4.67915i	−0.219248	+	0.975669i
$24$	0.500000	+	0.866025i	0.102062	+	0.176777i
$25$	−0.217951	+	4.57535i	−0.0435902	+	0.915070i
$26$	−1.76126	−	0.705101i	−0.345411	−	0.138282i
$27$	0.415415	+	0.909632i	0.0799467	+	0.175059i
$28$	2.43860	−	1.02627i	0.460852	−	0.193946i
$29$	3.91380	−	8.57003i	0.726775	−	1.59142i	−0.0773841	−	0.997001i	$-0.524657\pi$
$29$	3.91380	−	8.57003i	0.726775	−	1.59142i	0.804159	−	0.594414i	$-0.202616\pi$
$30$	0.211828	+	0.612037i	0.0386744	+	0.111742i
$31$	7.18233	−	2.87537i	1.28998	−	0.516432i	0.377676	−	0.925938i	$-0.376723\pi$
$31$	7.18233	−	2.87537i	1.28998	−	0.516432i	0.912307	+	0.409506i	$0.134299\pi$
$32$	−0.723734	−	0.690079i	−0.127939	−	0.121990i
$33$	−5.90125	+	1.13737i	−1.02728	+	0.197991i
$34$	−3.14465	+	2.02095i	−0.539303	+	0.346589i
$35$	1.67663	−	0.353759i	0.283402	−	0.0597963i
$36$	−0.654861	−	0.755750i	−0.109143	−	0.125958i
$37$	0.899378	−	3.70729i	0.147857	−	0.609474i	−0.848868	−	0.528605i	$-0.822715\pi$
$37$	0.899378	−	3.70729i	0.147857	−	0.609474i	0.996725	−	0.0808691i	$-0.0257696\pi$
$38$	−1.32199	+	0.529244i	−0.214455	+	0.0858546i
$39$	1.86287	+	0.359039i	0.298298	+	0.0574922i
$40$	−0.375679	−	0.527567i	−0.0594000	−	0.0834156i
$41$	4.99156	+	1.46566i	0.779551	+	0.228897i	0.647215	−	0.762308i	$-0.275934\pi$
$41$	4.99156	+	1.46566i	0.779551	+	0.228897i	0.132337	+	0.991205i	$0.457752\pi$
$42$	−2.20031	+	1.46923i	−0.339515	+	0.226707i
$43$	1.36411	+	9.48758i	0.208025	+	1.44684i	0.779592	+	0.626287i	$0.215426\pi$
$43$	1.36411	+	9.48758i	0.208025	+	1.44684i	−0.571568	+	0.820555i	$0.693665\pi$
$44$	5.34177	−	2.75387i	0.805302	−	0.415162i
$45$	−0.323829	−	0.560888i	−0.0482736	−	0.0836123i
$46$	1.20952	+	4.64080i	0.178334	+	0.684249i
$47$	1.62496	−	2.81451i	0.237025	−	0.410539i	−0.722834	−	0.691021i	$-0.757161\pi$
$47$	1.62496	−	2.81451i	0.237025	−	0.410539i	0.959859	+	0.280482i	$0.0904944\pi$
$48$	0.841254	+	0.540641i	0.121424	+	0.0780348i
$49$	3.12950	+	6.26149i	0.447072	+	0.894498i
$50$	1.90282	+	4.16660i	0.269100	+	0.589247i
$51$	2.70536	−	2.57955i	0.378826	−	0.361210i
$52$	−1.88856	+	0.180336i	−0.261897	+	0.0250081i
$53$	9.04378	+	1.74305i	1.24226	+	0.239426i	0.767707	−	0.640801i	$-0.221398\pi$
$53$	9.04378	+	1.74305i	1.24226	+	0.239426i	0.474552	+	0.880227i	$0.342610\pi$
$54$	0.786053	+	0.618159i	0.106968	+	0.0841208i
$55$	3.73466	−	1.09660i	0.503582	−	0.147865i
$56$	1.69725	−	2.02961i	0.226805	−	0.271219i
$57$	1.19794	−	0.769867i	0.158671	−	0.101971i
$58$	−0.448290	−	9.41076i	−0.0588633	−	1.23569i
$59$	4.48148	−	12.9484i	0.583440	−	1.68574i	−0.135596	−	0.990764i	$-0.543295\pi$
$59$	4.48148	−	12.9484i	0.583440	−	1.68574i	0.719035	−	0.694974i	$-0.244584\pi$
$60$	0.468732	+	0.446935i	0.0605131	+	0.0576991i
$61$	−1.83765	−	1.44514i	−0.235287	−	0.185032i	0.493553	−	0.869716i	$-0.335698\pi$
$61$	−1.83765	−	1.44514i	−0.235287	−	0.185032i	−0.728840	+	0.684684i	$0.759940\pi$
$62$	5.06634	−	5.84686i	0.643425	−	0.742552i
$63$	1.88249	−	1.85909i	0.237172	−	0.234223i
$64$	−0.959493	−	0.281733i	−0.119937	−	0.0352166i
$65$	−1.22314	−	0.116796i	−0.151712	−	0.0144868i
$66$	−4.72406	+	3.71504i	−0.581492	+	0.457290i
$67$	−0.269278	+	5.65284i	−0.0328975	+	0.690604i	0.920836	+	0.389950i	$0.127508\pi$
$67$	−0.269278	+	5.65284i	−0.0328975	+	0.690604i	−0.953733	+	0.300653i	$0.902795\pi$
$68$	−1.86903	+	3.23725i	−0.226653	+	0.392574i
$69$	−2.06594	−	4.32804i	−0.248710	−	0.521034i
$70$	1.32814	−	1.08271i	0.158744	−	0.129409i
$71$	−8.71620	−	5.60156i	−1.03442	−	0.664783i	−0.0908218	−	0.995867i	$-0.528949\pi$
$71$	−8.71620	−	5.60156i	−1.03442	−	0.664783i	−0.943601	+	0.331084i	$0.892586\pi$
$72$	−0.928368	−	0.371662i	−0.109409	−	0.0438008i
$73$	−5.41226	+	7.60046i	−0.633458	+	0.889567i	−0.999152	−	0.0411681i	$-0.986892\pi$
$73$	−5.41226	+	7.60046i	−0.633458	+	0.889567i	0.365695	+	0.930735i	$0.380831\pi$
$74$	−0.899378	−	3.70729i	−0.104551	−	0.430963i
$75$	−2.65697	−	3.73120i	−0.306801	−	0.430842i
$76$	−0.932515	+	1.07618i	−0.106967	+	0.123446i
$77$	8.19065	+	13.6287i	0.933411	+	1.55313i
$78$	1.82031	−	0.534490i	0.206109	−	0.0605191i
$79$	−5.49831	+	1.05971i	−0.618608	+	0.119227i	−0.488921	−	0.872328i	$-0.662609\pi$
$79$	−5.49831	+	1.05971i	−0.618608	+	0.119227i	−0.129687	+	0.991555i	$0.541397\pi$
$80$	−0.575662	−	0.296774i	−0.0643609	−	0.0331804i
$81$	−0.888835	−	0.458227i	−0.0987595	−	0.0509141i
$82$	5.10828	−	0.984540i	0.564115	−	0.108724i
$83$	−5.08882	+	1.49421i	−0.558571	+	0.164011i	−0.548819	−	0.835941i	$-0.684922\pi$
$83$	−5.08882	+	1.49421i	−0.558571	+	0.164011i	−0.00975191	+	0.999952i	$0.503104\pi$
$84$	−1.28247	+	2.31414i	−0.139929	+	0.252494i
$85$	−1.58541	+	1.82966i	−0.171961	+	0.198454i
$86$	5.55993	+	7.80783i	0.599542	+	0.841940i
$87$	2.22119	+	9.15585i	0.238136	+	0.981611i
$88$	3.48606	−	4.89548i	0.371615	−	0.521860i
$89$	−13.4056	−	5.36680i	−1.42099	−	0.568880i	−0.471275	−	0.881986i	$-0.656206\pi$
$89$	−13.4056	−	5.36680i	−1.42099	−	0.568880i	−0.949718	+	0.313106i	$0.898630\pi$
$90$	−0.544845	−	0.350150i	−0.0574317	−	0.0369091i
$91$	−0.801389	−	4.95501i	−0.0840084	−	0.519426i
$92$	3.20160	+	3.57068i	0.333790	+	0.372269i
$93$	−3.86825	+	6.70001i	−0.401119	+	0.694759i
$94$	0.154637	−	3.24624i	0.0159496	−	0.334824i
$95$	−0.724944	+	0.570102i	−0.0743777	+	0.0584913i
$96$	0.995472	+	0.0950560i	0.101600	+	0.00970162i
$97$	−8.55220	−	2.51115i	−0.868344	−	0.254969i	−0.182933	−	0.983125i	$-0.558559\pi$
$97$	−8.55220	−	2.51115i	−0.868344	−	0.254969i	−0.685411	+	0.728157i	$0.740377\pi$
$98$	5.65079	+	4.13141i	0.570816	+	0.417335i
$99$	3.93562	−	4.54194i	0.395544	−	0.456483i
$100$	3.60055	+	2.83150i	0.360055	+	0.283150i
$101$	−1.37557	−	1.31160i	−0.136874	−	0.130509i	0.618550	−	0.785746i	$-0.287721\pi$
$101$	−1.37557	−	1.31160i	−0.136874	−	0.130509i	−0.755424	+	0.655236i	$0.772569\pi$
$102$	1.22260	−	3.53247i	0.121055	−	0.349766i
$103$	−0.553558	−	11.6206i	−0.0545437	−	1.14501i	−0.845790	−	0.533516i	$-0.820871\pi$
$103$	−0.553558	−	11.6206i	−0.0545437	−	1.14501i	0.791246	−	0.611497i	$-0.209432\pi$
$104$	−1.59599	+	1.02568i	−0.156499	+	0.100576i
$105$	−1.09924	+	1.31450i	−0.107275	+	0.128282i
$106$	8.83715	−	2.59482i	0.858339	−	0.252031i
$107$	−1.24115	−	0.976051i	−0.119987	−	0.0943585i	0.556363	−	0.830940i	$-0.312197\pi$
$107$	−1.24115	−	0.976051i	−0.119987	−	0.0943585i	−0.676349	+	0.736581i	$0.736439\pi$
$108$	0.981929	+	0.189251i	0.0944861	+	0.0182107i
$109$	−15.5962	+	1.48925i	−1.49384	+	0.142645i	−0.809761	−	0.586760i	$-0.800403\pi$
$109$	−15.5962	+	1.48925i	−1.49384	+	0.142645i	−0.684082	+	0.729405i	$0.739797\pi$
$110$	2.81701	−	2.68602i	0.268592	−	0.256102i
$111$	1.58473	+	3.47008i	0.150416	+	0.329366i
$112$	0.578555	−	2.58172i	0.0546683	−	0.243950i
$113$	5.64068	+	3.62505i	0.530631	+	0.341016i	0.778365	−	0.627812i	$-0.216049\pi$
$113$	5.64068	+	3.62505i	0.530631	+	0.341016i	−0.247734	+	0.968828i	$0.579686\pi$
$114$	0.711995	−	1.23321i	0.0666844	−	0.115501i
$115$	1.59841	+	2.66321i	0.149053	+	0.248345i
$116$	−4.71072	−	8.15920i	−0.437379	−	0.757562i
$117$	−1.68626	+	0.869326i	−0.155895	+	0.0803692i
$118$	−1.95000	−	13.5625i	−0.179512	−	1.24853i
$119$	−8.86871	−	4.37692i	−0.812993	−	0.401232i
$120$	0.621423	+	0.182466i	0.0567279	+	0.0166568i
$121$	14.5701	+	20.4608i	1.32455	+	1.86007i
$122$	−2.29557	−	0.442435i	−0.207831	−	0.0400562i
$123$	−4.82964	+	1.93350i	−0.435474	+	0.174338i
$124$	1.82395	−	7.51843i	0.163796	−	0.675175i
$125$	4.06335	+	4.68936i	0.363437	+	0.419429i
$126$	0.821343	−	2.51503i	0.0731710	−	0.224057i
$127$	6.00687	−	3.86038i	0.533024	−	0.342554i	−0.246281	−	0.969198i	$-0.579209\pi$
$127$	6.00687	−	3.86038i	0.533024	−	0.342554i	0.779305	+	0.626645i	$0.215572\pi$
$128$	−0.981929	+	0.189251i	−0.0867911	+	0.0167276i
$129$	−6.93709	−	6.61451i	−0.610777	−	0.582375i
$130$	−1.14069	+	0.456664i	−0.100045	+	0.0400521i
$131$	2.45892	+	7.10458i	0.214837	+	0.620730i	0.999999	+	0.00143989i	$0.000458332\pi$
$131$	2.45892	+	7.10458i	0.214837	+	0.620730i	−0.785162	+	0.619290i	$0.787420\pi$
$132$	−2.49658	+	5.46675i	−0.217300	+	0.475820i
$133$	−3.00188	−	2.27661i	−0.260296	−	0.197407i
$134$	2.35094	+	5.14783i	0.203090	+	0.444705i
$135$	0.601265	+	0.240710i	0.0517487	+	0.0207170i
$136$	−0.177864	+	3.73382i	−0.0152517	+	0.320173i
$137$	−5.03508	−	8.72101i	−0.430176	−	0.745086i	0.566713	−	0.823916i	$-0.308215\pi$
$137$	−5.03508	−	8.72101i	−0.430176	−	0.745086i	−0.996888	+	0.0788297i	$0.974882\pi$
$138$	−3.81950	−	2.90024i	−0.325138	−	0.246885i
$139$	−6.55432			−0.555931			−0.277965	−	0.960591i	$-0.589660\pi$
$139$	−6.55432			−0.555931			−0.277965	+	0.960591i	$0.589660\pi$
$140$	0.684376	−	1.57094i	0.0578403	−	0.132769i
$141$	0.462512	+	3.21684i	0.0389505	+	0.270907i
$142$	−10.3141	−	0.984873i	−0.865536	−	0.0826487i
$143$	−2.68803	−	11.0802i	−0.224785	−	0.926575i
$144$	−0.995472	+	0.0950560i	−0.0829560	+	0.00792134i
$145$	−1.99572	−	5.76627i	−0.165736	−	0.478863i
$146$	−1.32788	+	9.23560i	−0.109896	+	0.764344i
$147$	−6.33055	−	2.98733i	−0.522135	−	0.246391i
$148$	−2.49818	−	2.88305i	−0.205349	−	0.236985i
$149$	0.415335	+	8.71896i	0.0340256	+	0.714285i	0.949850	+	0.312706i	$0.101235\pi$
$149$	0.415335	+	8.71896i	0.0340256	+	0.714285i	−0.915824	+	0.401579i	$0.868461\pi$
$150$	−4.07135	−	2.09892i	−0.332424	−	0.171376i
$151$	0.300958	−	0.869560i	0.0244916	−	0.0707638i	−0.932092	−	0.362221i	$-0.882019\pi$
$151$	0.300958	−	0.869560i	0.0244916	−	0.0707638i	0.956584	+	0.291457i	$0.0941399\pi$
$152$	−0.335718	+	1.38385i	−0.0272304	+	0.112245i
$153$	−0.531981	+	3.70001i	−0.0430081	+	0.299128i
$154$	13.5252	+	8.36050i	1.08989	+	0.673708i
$155$	2.08148	−	4.55781i	0.167189	−	0.366092i
$156$	1.37303	−	1.30919i	0.109931	−	0.104819i
$157$	−7.82429	+	10.9877i	−0.624446	+	0.876912i	−0.998729	−	0.0504026i	$-0.983950\pi$
$157$	−7.82429	+	10.9877i	−0.624446	+	0.876912i	0.374283	+	0.927315i	$0.377889\pi$
$158$	−4.40150	+	3.46138i	−0.350165	+	0.275373i
$159$	−8.18637	+	4.22037i	−0.649222	+	0.334697i
$160$	−0.647658			−0.0512019
$161$	−8.87566	+	9.06768i	−0.699500	+	0.714633i
$162$	−1.00000			−0.0785674
$163$	−5.90912	+	3.04637i	−0.462838	+	0.238610i	−0.673842	−	0.738876i	$-0.735357\pi$
$163$	−5.90912	+	3.04637i	−0.462838	+	0.238610i	0.211004	+	0.977485i	$0.432327\pi$
$164$	4.08928	−	3.21584i	0.319319	−	0.251115i
$165$	−2.25777	+	3.17060i	−0.175767	+	0.246831i
$166$	−3.83844	+	3.65994i	−0.297921	+	0.284067i
$167$	9.45305	−	20.6993i	0.731499	−	1.60176i	−0.0655534	−	0.997849i	$-0.520881\pi$
$167$	9.45305	−	20.6993i	0.731499	−	1.60176i	0.797052	−	0.603910i	$-0.206391\pi$
$168$	−0.0795057	+	2.64456i	−0.00613400	+	0.204032i
$169$	1.33787	−	9.30512i	0.102913	−	0.715779i
$170$	−0.570768	+	2.35274i	−0.0437759	+	0.180447i
$171$	−0.465741	+	1.34567i	−0.0356161	+	0.102906i
$172$	8.51961	+	4.39217i	0.649614	+	0.334900i
$173$	0.787490	+	16.5315i	0.0598718	+	1.25686i	0.806344	+	0.591447i	$0.201443\pi$
$173$	0.787490	+	16.5315i	0.0598718	+	1.25686i	−0.746472	+	0.665416i	$0.768254\pi$
$174$	6.16972	+	7.12024i	0.467726	+	0.539784i
$175$	−6.85542	+	9.99363i	−0.518221	+	0.755447i
$176$	0.855291	−	5.94868i	0.0644700	−	0.448399i
$177$	4.48148	+	12.9484i	0.336849	+	0.973261i
$178$	−14.3746	+	1.37261i	−1.07742	+	0.102881i
$179$	−5.80688	−	23.9363i	−0.434027	−	1.78908i	−0.596769	−	0.802413i	$-0.703549\pi$
$179$	−5.80688	−	23.9363i	−0.434027	−	1.78908i	0.162742	−	0.986669i	$-0.447966\pi$
$180$	−0.644726	−	0.0615638i	−0.0480550	−	0.00458870i
$181$	1.44001	+	10.0155i	0.107035	+	0.744448i	0.970685	+	0.240355i	$0.0772639\pi$
$181$	1.44001	+	10.0155i	0.107035	+	0.744448i	−0.863650	+	0.504093i	$0.831827\pi$
$182$	−2.98282	−	4.03697i	−0.221101	−	0.299240i
$183$	2.33782			0.172817
$184$	4.48188	+	1.70668i	0.330408	+	0.125818i
$185$	−1.23535	−	2.13969i	−0.0908247	−	0.157313i
$186$	−0.368118	+	7.72775i	−0.0269917	+	0.566626i
$187$	−20.8559	−	8.34946i	−1.52514	−	0.610573i
$188$	−1.35007	−	2.95623i	−0.0984637	−	0.215605i
$189$	−0.330527	+	2.62502i	−0.0240423	+	0.190942i
$190$	−0.383120	+	0.838916i	−0.0277945	+	0.0608614i
$191$	−3.89497	−	11.2538i	−0.281830	−	0.814296i	−0.993709	−	0.111993i	$-0.964277\pi$
$191$	−3.89497	−	11.2538i	−0.281830	−	0.814296i	0.711879	−	0.702303i	$-0.247845\pi$
$192$	0.928368	−	0.371662i	0.0669992	−	0.0268224i
$193$	−9.67112	−	9.22139i	−0.696142	−	0.663770i	0.256959	−	0.966422i	$-0.417280\pi$
$193$	−9.67112	−	9.22139i	−0.696142	−	0.663770i	−0.953101	+	0.302652i	$0.902128\pi$
$194$	−8.75217	+	1.68684i	−0.628369	+	0.121108i
$195$	1.03365	−	0.664289i	0.0740215	−	0.0475707i
$196$	6.91575	+	1.08280i	0.493982	+	0.0773429i
$197$	−11.5244	−	13.2999i	−0.821083	−	0.947580i	0.178254	−	0.983984i	$-0.442955\pi$
$197$	−11.5244	−	13.2999i	−0.821083	−	0.947580i	−0.999337	+	0.0364043i	$0.988410\pi$
$198$	1.41688	−	5.84044i	0.100693	−	0.415062i
$199$	−18.9736	+	7.59587i	−1.34500	+	0.538457i	−0.928721	−	0.370780i	$-0.879091\pi$
$199$	−18.9736	+	7.59587i	−1.34500	+	0.538457i	−0.416280	+	0.909237i	$0.636666\pi$
$200$	4.49776	+	0.866873i	0.318040	+	0.0612972i
$201$	−3.28268	−	4.60988i	−0.231543	−	0.325156i
$202$	−1.82366	−	0.535476i	−0.128312	−	0.0376759i
$203$	20.7301	−	13.8422i	1.45497	−	0.971535i
$204$	−0.531981	−	3.70001i	−0.0372461	−	0.259052i
$205$	2.99476	−	1.54391i	0.209163	−	0.107831i
$206$	−5.81689	−	10.0752i	−0.405282	−	0.701969i
$207$	4.29935	+	2.12499i	0.298826	+	0.147697i
$208$	−0.948577	+	1.64298i	−0.0657720	+	0.113920i
$209$	−7.19942	−	4.62679i	−0.497994	−	0.320042i
$210$	−0.374706	+	1.67207i	−0.0258571	+	0.115384i
$211$	−3.90346	−	8.54739i	−0.268726	−	0.588427i	0.726375	−	0.687299i	$-0.241204\pi$
$211$	−3.90346	−	8.54739i	−0.268726	−	0.588427i	−0.995100	+	0.0988721i	$0.968477\pi$
$212$	6.66575	−	6.35578i	0.457806	−	0.436517i
$213$	10.3141	−	0.984873i	0.706708	−	0.0674824i
$214$	−1.55043	−	0.298821i	−0.105985	−	0.0204270i
$215$	4.87974	+	3.83747i	0.332795	+	0.261713i
$216$	0.959493	−	0.281733i	0.0652852	−	0.0191695i
$217$	20.1638	+	3.52055i	1.36881	+	0.238990i
$218$	−13.1800	+	8.47029i	−0.892664	+	0.573680i
$219$	−0.443967	−	9.32001i	−0.0300005	−	0.629788i
$220$	1.27306	−	3.67826i	0.0858295	−	0.247988i
$221$	5.13248	+	4.89381i	0.345248	+	0.329193i
$222$	2.99865	+	2.35817i	0.201256	+	0.158270i
$223$	−14.8841	+	17.1772i	−0.996713	+	1.15027i	−0.00807260	+	0.999967i	$0.502570\pi$
$223$	−14.8841	+	17.1772i	−0.996713	+	1.15027i	−0.988640	+	0.150301i	$0.951976\pi$
$224$	−0.668772	−	2.55983i	−0.0446842	−	0.171036i
$225$	4.39499	+	1.29049i	0.293000	+	0.0860325i
$226$	6.67473	+	0.637360i	0.443997	+	0.0423965i
$227$	−6.52390	+	5.13045i	−0.433007	+	0.340520i	−0.810752	−	0.585389i	$-0.800942\pi$
$227$	−6.52390	+	5.13045i	−0.433007	+	0.340520i	0.377746	+	0.925909i	$0.376699\pi$
$228$	0.0677562	−	1.42238i	0.00448726	−	0.0941992i
$229$	−5.60462	+	9.70748i	−0.370363	+	0.641488i	−0.989621	−	0.143699i	$-0.954100\pi$
$229$	−5.60462	+	9.70748i	−0.370363	+	0.641488i	0.619258	+	0.785188i	$0.287434\pi$
$230$	2.64108	+	1.63472i	0.174148	+	0.107790i
$231$	−14.8630	−	5.64976i	−0.977913	−	0.371727i
$232$	−7.92581	−	5.09361i	−0.520355	−	0.334412i
$233$	20.8850	+	8.36108i	1.36822	+	0.547753i	0.935356	−	0.353707i	$-0.115079\pi$
$233$	20.8850	+	8.36108i	1.36822	+	0.547753i	0.432864	+	0.901459i	$0.357503\pi$
$234$	−1.10046	+	1.54538i	−0.0719391	+	0.101024i
$235$	−0.496234	−	2.04551i	−0.0323708	−	0.133434i
$236$	−7.94794	−	11.1613i	−0.517367	−	0.726540i
$237$	3.66689	−	4.23182i	0.238190	−	0.274886i
$238$	−9.88844	+	0.173511i	−0.640973	+	0.0112470i
$239$	19.3816	−	5.69095i	1.25369	−	0.368117i	0.413548	−	0.910482i	$-0.364289\pi$
$239$	19.3816	−	5.69095i	1.25369	−	0.368117i	0.840143	+	0.542366i	$0.182471\pi$
$240$	0.635954	−	0.122570i	0.0410507	−	0.00791187i
$241$	0.789601	+	0.407068i	0.0508627	+	0.0262215i	0.483470	−	0.875361i	$-0.339376\pi$
$241$	0.789601	+	0.407068i	0.0508627	+	0.0262215i	−0.432608	+	0.901582i	$0.642406\pi$
$242$	22.3261	+	11.5099i	1.43517	+	0.739884i
$243$	0.981929	−	0.189251i	0.0629908	−	0.0121405i
$244$	−2.24312	+	0.658640i	−0.143601	+	0.0421651i
$245$	4.26538	+	1.53628i	0.272505	+	0.0981491i
$246$	−3.40678	+	3.93163i	−0.217208	+	0.250672i
$247$	1.56704	+	2.20060i	0.0997084	+	0.140021i
$248$	−1.82395	−	7.51843i	−0.115821	−	0.477421i
$249$	3.07642	−	4.32023i	0.194960	−	0.273784i
$250$	5.76044	+	2.30613i	0.364322	+	0.145853i
$251$	10.9744	+	7.05280i	0.692696	+	0.445169i	0.839043	−	0.544064i	$-0.183115\pi$
$251$	10.9744	+	7.05280i	0.692696	+	0.445169i	−0.146347	+	0.989233i	$0.546752\pi$
$252$	−0.422417	−	2.61181i	−0.0266097	−	0.164529i
$253$	−18.5025	+	22.0993i	−1.16324	+	1.38937i
$254$	3.57019	−	6.18375i	0.224014	−	0.388003i
$255$	0.115195	−	2.41824i	0.00721379	−	0.151436i
$256$	−0.786053	+	0.618159i	−0.0491283	+	0.0386349i
$257$	−15.5644	−	1.48622i	−0.970879	−	0.0927077i	−0.402452	−	0.915441i	$-0.631842\pi$
$257$	−15.5644	−	1.48622i	−0.970879	−	0.0927077i	−0.568427	+	0.822733i	$0.692448\pi$
$258$	−9.19688	−	2.70045i	−0.572573	−	0.168122i
$259$	7.18138	−	7.09210i	0.446229	−	0.440681i
$260$	−0.804632	+	0.928595i	−0.0499012	+	0.0575890i
$261$	−7.40574	−	5.82394i	−0.458404	−	0.360493i
$262$	5.44108	+	5.18806i	0.336151	+	0.320519i
$263$	3.36791	−	9.73092i	0.207674	−	0.600034i	−0.792275	−	0.610164i	$-0.791103\pi$
$263$	3.36791	−	9.73092i	0.207674	−	0.600034i	0.999949	+	0.0101301i	$0.00322456\pi$
$264$	0.285960	+	6.00305i	0.0175996	+	0.369462i
$265$	5.01814	−	3.22496i	0.308262	−	0.198108i
$266$	−3.71138	−	0.647995i	−0.227559	−	0.0397311i
$267$	13.8551	−	4.06822i	0.847916	−	0.248971i
$268$	4.44847	+	3.49831i	0.271733	+	0.213693i
$269$	1.40278	+	0.270364i	0.0855292	+	0.0164844i	0.231836	−	0.972755i	$-0.425527\pi$
$269$	1.40278	+	0.270364i	0.0855292	+	0.0164844i	−0.146307	+	0.989239i	$0.546739\pi$
$270$	0.644726	−	0.0615638i	0.0392367	−	0.00374665i
$271$	2.92798	−	2.79182i	0.177862	−	0.169591i	−0.595918	−	0.803045i	$-0.703212\pi$
$271$	2.92798	−	2.79182i	0.177862	−	0.169591i	0.773781	+	0.633454i	$0.218363\pi$
$272$	1.55284	+	3.40025i	0.0941550	+	0.206171i
$273$	3.69292	+	3.39951i	0.223506	+	0.205748i
$274$	−8.47155	−	5.44433i	−0.511785	−	0.328904i
$275$	−13.7642	+	23.8403i	−0.830011	+	1.43762i
$276$	−4.72388	−	0.827642i	−0.284344	−	0.0498182i
$277$	−1.96255	−	3.39923i	−0.117918	−	0.204240i	0.801024	−	0.598632i	$-0.204289\pi$
$277$	−1.96255	−	3.39923i	−0.117918	−	0.204240i	−0.918942	+	0.394392i	$0.870955\pi$
$278$	−5.82572	+	3.00337i	−0.349403	+	0.180130i
$279$	−1.10102	−	7.65776i	−0.0659163	−	0.458458i
$280$	−0.111550	−	1.70991i	−0.00666636	−	0.102187i
$281$	−5.17247	−	1.51878i	−0.308564	−	0.0906026i	0.123785	−	0.992309i	$-0.460497\pi$
$281$	−5.17247	−	1.51878i	−0.308564	−	0.0906026i	−0.432349	+	0.901707i	$0.642315\pi$
$282$	1.88514	+	2.64731i	0.112258	+	0.157645i
$283$	−1.97958	−	0.381533i	−0.117674	−	0.0226798i	0.130074	−	0.991504i	$-0.458478\pi$
$283$	−1.97958	−	0.381533i	−0.117674	−	0.0226798i	−0.247748	+	0.968824i	$0.579691\pi$
$284$	−9.61879	+	3.85078i	−0.570770	+	0.228502i
$285$	0.217431	−	0.896262i	0.0128795	−	0.0530900i
$286$	−7.46647	−	8.61677i	−0.441502	−	0.509520i
$287$	9.19459	+	10.2424i	0.542740	+	0.604589i
$288$	−0.841254	+	0.540641i	−0.0495713	+	0.0318576i
$289$	−2.97224	+	0.572853i	−0.174838	+	0.0336972i
$290$	−4.41613	−	4.21077i	−0.259324	−	0.247265i
$291$	8.27477	−	3.31272i	0.485076	−	0.194195i
$292$	3.05173	+	8.81740i	0.178589	+	0.515999i
$293$	7.65983	−	16.7727i	0.447492	−	0.979870i	−0.542670	−	0.839946i	$-0.682587\pi$
$293$	7.65983	−	16.7727i	0.447492	−	0.979870i	0.990162	−	0.139925i	$-0.0446860\pi$
$294$	−6.99569	+	0.245580i	−0.407997	+	0.0143225i
$295$	−3.68648	−	8.07227i	−0.214635	−	0.469985i
$296$	−3.54156	−	1.41783i	−0.205849	−	0.0824094i
$297$	−0.285960	+	6.00305i	−0.0165931	+	0.348332i
$298$	4.36442	+	7.55940i	0.252824	+	0.437905i
$299$	8.01516	−	4.30566i	0.463528	−	0.249003i
$300$	−4.58054			−0.264458
$301$	−10.1286	+	23.2495i	−0.583800	+	1.34008i
$302$	−0.130954	−	0.910802i	−0.00753553	−	0.0524108i
$303$	1.89205	+	0.180669i	0.108695	+	0.0103791i
$304$	0.335718	+	1.38385i	0.0192548	+	0.0793692i
$305$	−1.50725	+	0.143925i	−0.0863050	+	0.00824113i
$306$	1.22260	+	3.53247i	0.0698913	+	0.201938i
$307$	−3.48784	+	24.2585i	−0.199062	+	1.38450i	0.607953	+	0.793973i	$0.291991\pi$
$307$	−3.48784	+	24.2585i	−0.199062	+	1.38450i	−0.807015	+	0.590531i	$0.798918\pi$
$308$	15.8527	+	1.23351i	0.903289	+	0.0702860i
$309$	7.61851	+	8.79223i	0.433402	+	0.500173i
$310$	−0.238415	−	5.00494i	−0.0135410	−	0.284261i
$311$	−25.5947	−	13.1950i	−1.45134	−	0.748218i	−0.461069	−	0.887364i	$-0.652534\pi$
$311$	−25.5947	−	13.1950i	−1.45134	−	0.748218i	−0.990272	+	0.139146i	$0.955564\pi$
$312$	0.620498	−	1.79281i	0.0351288	−	0.101498i
$313$	2.13023	−	8.78091i	0.120407	−	0.496326i	−0.879388	−	0.476106i	$-0.842048\pi$
$313$	2.13023	−	8.78091i	0.120407	−	0.496326i	0.999796	−	0.0202207i	$-0.00643688\pi$
$314$	−1.91966	+	13.3515i	−0.108333	+	0.753471i
$315$	0.0514925	−	1.71277i	0.00290128	−	0.0965036i
$316$	−2.32612	+	5.09349i	−0.130854	+	0.286531i
$317$	−7.38114	+	7.03790i	−0.414566	+	0.395288i	−0.868453	−	0.495771i	$-0.834885\pi$
$317$	−7.38114	+	7.03790i	−0.414566	+	0.395288i	0.453887	+	0.891059i	$0.350037\pi$
$318$	−5.34245	+	7.50243i	−0.299590	+	0.420715i
$319$	44.5074	−	35.0010i	2.49194	−	1.95968i
$320$	−0.575662	+	0.296774i	−0.0321805	+	0.0165902i
$321$	1.57897			0.0881292
$322$	−3.73395	+	12.1267i	−0.208085	+	0.675796i
$323$	5.32295			0.296177
$324$	−0.888835	+	0.458227i	−0.0493797	+	0.0254570i
$325$	6.83079	−	5.37179i	0.378904	−	0.297973i
$326$	−3.85631	+	5.41543i	−0.213581	+	0.299933i
$327$	11.3388	−	10.8116i	0.627039	−	0.597880i
$328$	2.16111	−	4.73217i	0.119327	−	0.261291i
$329$	7.57233	−	4.07353i	0.417476	−	0.224581i
$330$	−0.553936	+	3.85271i	−0.0304932	+	0.212085i
$331$	−5.81506	+	23.9700i	−0.319624	+	1.31751i	0.554652	+	0.832082i	$0.312851\pi$
$331$	−5.81506	+	23.9700i	−0.319624	+	1.31751i	−0.874277	+	0.485428i	$0.838664\pi$
$332$	−1.73466	+	5.01196i	−0.0952017	+	0.275067i
$333$	−3.39075	−	1.74805i	−0.185812	−	0.0957927i
$334$	−1.08276	−	22.7299i	−0.0592459	−	1.24372i
$335$	2.40023	+	2.77002i	0.131139	+	0.151342i
$336$	1.14114	+	2.38701i	0.0622542	+	0.130222i
$337$	0.923545	−	6.42340i	0.0503087	−	0.349905i	−0.949083	−	0.315027i	$-0.897987\pi$
$337$	0.923545	−	6.42340i	0.0503087	−	0.349905i	0.999392	−	0.0348782i	$-0.0111043\pi$
$338$	−3.07470	−	8.88377i	−0.167242	−	0.483213i
$339$	−6.67473	+	0.637360i	−0.362522	+	0.0346166i
$340$	0.570768	+	2.35274i	0.0309542	+	0.127595i
$341$	46.2847	+	4.41966i	2.50646	+	0.239338i
$342$	0.202655	+	1.40950i	0.0109583	+	0.0762168i
$343$	−1.66761	+	18.4450i	−0.0900425	+	0.995938i
$344$	9.58514			0.516796
$345$	−2.90272	−	1.10535i	−0.156277	−	0.0595100i
$346$	8.27510	+	14.3329i	0.444872	+	0.770541i
$347$	−1.24953	+	26.2310i	−0.0670786	+	1.40815i	0.674989	+	0.737827i	$0.264148\pi$
$347$	−1.24953	+	26.2310i	−0.0670786	+	1.40815i	−0.742068	+	0.670325i	$0.766155\pi$
$348$	8.74655	+	3.50159i	0.468864	+	0.187705i
$349$	11.6170	+	25.4376i	0.621842	+	1.36164i	0.914172	+	0.405327i	$0.132842\pi$
$349$	11.6170	+	25.4376i	0.621842	+	1.36164i	−0.292329	+	0.956318i	$0.594430\pi$
$350$	−1.51399	+	12.0240i	−0.0809262	+	0.642711i
$351$	0.788106	−	1.72571i	0.0420660	−	0.0921117i
$352$	−1.96563	−	5.67932i	−0.104768	−	0.302709i
$353$	−14.6435	+	5.86237i	−0.779395	+	0.312023i	−0.727030	−	0.686605i	$-0.759100\pi$
$353$	−14.6435	+	5.86237i	−0.779395	+	0.312023i	−0.0523645	+	0.998628i	$0.516676\pi$
$354$	9.91660	+	9.45546i	0.527061	+	0.502552i
$355$	−6.58910	+	1.26995i	−0.349713	+	0.0674017i
$356$	−12.1477	+	7.80685i	−0.643826	+	0.413762i
$357$	9.67691	−	2.04178i	0.512156	−	0.108062i
$358$	−16.1296	−	18.6146i	−0.852476	−	0.983810i
$359$	−4.73751	+	19.5283i	−0.250036	+	1.03066i	0.698906	+	0.715213i	$0.253671\pi$
$359$	−4.73751	+	19.5283i	−0.250036	+	1.03066i	−0.948942	+	0.315450i	$0.897845\pi$
$360$	−0.601265	+	0.240710i	−0.0316895	+	0.0126865i
$361$	−16.6655	−	3.21202i	−0.877134	−	0.169054i
$362$	5.86931	+	8.24230i	0.308484	+	0.433205i
$363$	−24.1009	−	7.07665i	−1.26497	−	0.371428i
$364$	−4.50108	−	2.22140i	−0.235921	−	0.116433i
$365$	0.860012	+	5.98151i	0.0450151	+	0.313087i
$366$	2.07794	−	1.07125i	0.108615	−	0.0559952i
$367$	4.37069	+	7.57026i	0.228148	+	0.395164i	0.957259	−	0.289231i	$-0.0933996\pi$
$367$	4.37069	+	7.57026i	0.228148	+	0.395164i	−0.729111	+	0.684395i	$0.760066\pi$
$368$	4.76570	−	0.536753i	0.248429	−	0.0279802i
$369$	2.60115	−	4.50532i	0.135410	−	0.234537i
$370$	−2.07848	−	1.33576i	−0.108055	−	0.0694429i
$371$	17.9282	+	16.5038i	0.930787	+	0.856836i
$372$	3.21386	+	7.03738i	0.166631	+	0.364871i
$373$	24.3569	−	23.2243i	1.26115	−	1.20251i	0.291897	−	0.956450i	$-0.405714\pi$
$373$	24.3569	−	23.2243i	1.26115	−	1.20251i	0.969255	−	0.246057i	$-0.0791349\pi$
$374$	−22.3634	+	2.13545i	−1.15639	+	0.110421i
$375$	−6.09278	−	1.17429i	−0.314630	−	0.0606400i
$376$	−2.55461	−	2.00897i	−0.131744	−	0.103605i
$377$	−17.1499	+	5.03566i	−0.883264	+	0.259350i
$378$	0.909072	+	2.48467i	0.0467576	+	0.127798i
$379$	28.7992	−	18.5081i	1.47932	−	0.950698i	0.482101	−	0.876116i	$-0.339874\pi$
$379$	28.7992	−	18.5081i	1.47932	−	0.950698i	0.997215	−	0.0745826i	$-0.0237624\pi$
$380$	0.0438828	+	0.921214i	0.00225114	+	0.0472573i
$381$	−2.33539	+	6.74767i	−0.119646	+	0.345693i
$382$	−8.61878	−	8.21799i	−0.440975	−	0.420469i
$383$	8.15535	+	6.41344i	0.416719	+	0.327711i	0.804406	−	0.594080i	$-0.202484\pi$
$383$	8.15535	+	6.41344i	0.416719	+	0.327711i	−0.387687	+	0.921791i	$0.626726\pi$
$384$	0.654861	−	0.755750i	0.0334182	−	0.0385667i
$385$	9.93037	+	2.72752i	0.506099	+	0.139007i
$386$	−12.8215	−	3.76474i	−0.652598	−	0.191620i
$387$	9.54174	+	0.911126i	0.485034	+	0.0463151i
$388$	−7.00628	+	5.50980i	−0.355690	+	0.279718i
$389$	0.428709	−	8.99971i	0.0217364	−	0.456303i	−0.961594	−	0.274476i	$-0.911496\pi$
$389$	0.428709	−	8.99971i	0.0217364	−	0.456303i	0.983330	−	0.181828i	$-0.0582013\pi$
$390$	0.614354	−	1.06409i	0.0311090	−	0.0538824i
$391$	2.25006	−	17.7853i	0.113790	−	0.899442i
$392$	6.64313	−	2.20655i	0.335529	−	0.111447i
$393$	−6.32460	−	4.06457i	−0.319034	−	0.205031i
$394$	−16.3377	−	6.54063i	−0.823082	−	0.329512i
$395$	−2.10361	+	2.95411i	−0.105844	+	0.148637i
$396$	−1.41688	−	5.84044i	−0.0712007	−	0.293493i
$397$	−20.5447	−	28.8510i	−1.03111	−	1.44799i	−0.888872	−	0.458155i	$-0.848510\pi$
$397$	−20.5447	−	28.8510i	−1.03111	−	1.44799i	−0.142235	−	0.989833i	$-0.545429\pi$
$398$	−13.3838	+	15.4457i	−0.670867	+	0.774222i
$399$	3.76694	−	0.0660979i	0.188583	−	0.00330903i
$400$	4.39499	−	1.29049i	0.219750	−	0.0645243i
$401$	−7.05676	+	1.36008i	−0.352398	+	0.0679191i	−0.362378	−	0.932031i	$-0.618035\pi$
$401$	−7.05676	+	1.36008i	−0.352398	+	0.0679191i	0.00998047	+	0.999950i	$0.496823\pi$
$402$	−5.03014	−	2.59322i	−0.250880	−	0.129338i
$403$	−13.0457	−	6.72555i	−0.649855	−	0.335023i
$404$	−1.86631	+	0.359701i	−0.0928522	+	0.0178958i
$405$	−0.621423	+	0.182466i	−0.0308788	+	0.00906683i
$406$	12.0827	−	21.8025i	0.599656	−	1.08204i
$407$	15.0137	−	17.3267i	0.744200	−	0.858853i
$408$	−2.16828	−	3.04493i	−0.107346	−	0.150746i
$409$	−8.67889	−	35.7749i	−0.429143	−	1.76895i	−0.617212	−	0.786797i	$-0.711738\pi$
$409$	−8.67889	−	35.7749i	−0.429143	−	1.76895i	0.188069	−	0.982156i	$-0.439777\pi$
$410$	1.95439	−	2.74456i	0.0965204	−	0.135544i
$411$	9.34881	+	3.74270i	0.461143	+	0.184614i
$412$	−9.78697	−	6.28970i	−0.482169	−	0.309871i
$413$	28.0985	−	22.9060i	1.38264	−	1.12713i
$414$	4.79514	−	0.0813141i	0.235668	−	0.00399637i
$415$	−1.71748	+	2.97476i	−0.0843077	+	0.146025i
$416$	−0.0902702	+	1.89500i	−0.00442586	+	0.0929103i
$417$	5.15205	−	4.05161i	0.252297	−	0.198408i
$418$	−8.51922	−	0.813487i	−0.416689	−	0.0397889i
$419$	36.7803	+	10.7997i	1.79683	+	0.527598i	0.997328	−	0.0730598i	$-0.0232764\pi$
$419$	36.7803	+	10.7997i	1.79683	+	0.527598i	0.799506	+	0.600658i	$0.205095\pi$
$420$	0.433136	+	1.65790i	0.0211349	+	0.0808971i
$421$	−2.08293	+	2.40383i	−0.101516	+	0.117155i	−0.804234	−	0.594313i	$-0.797424\pi$
$421$	−2.08293	+	2.40383i	−0.101516	+	0.117155i	0.702718	+	0.711468i	$0.251969\pi$
$422$	−7.38618	−	5.80856i	−0.359554	−	0.282756i
$423$	−2.35208	−	2.24270i	−0.114362	−	0.109044i
$424$	3.01237	−	8.70367i	0.146294	−	0.422688i
$425$	−0.814712	−	17.1029i	−0.0395193	−	0.829613i
$426$	8.71620	−	5.60156i	0.422301	−	0.271397i
$427$	−2.12525	−	5.80871i	−0.102848	−	0.281103i
$428$	−1.51501	+	0.444846i	−0.0732306	+	0.0215024i
$429$	8.96227	+	7.04801i	0.432703	+	0.340281i
$430$	6.09571	+	1.17485i	0.293961	+	0.0566564i
$431$	−36.2035	+	3.45701i	−1.74386	+	0.166518i	−0.917795	−	0.397055i	$-0.870032\pi$
$431$	−36.2035	+	3.45701i	−1.74386	+	0.166518i	−0.826066	+	0.563574i	$0.809426\pi$
$432$	0.723734	−	0.690079i	0.0348207	−	0.0332014i
$433$	13.3918	+	29.3239i	0.643568	+	1.40922i	0.897072	+	0.441883i	$0.145690\pi$
$433$	13.3918	+	29.3239i	0.643568	+	1.40922i	−0.253504	+	0.967334i	$0.581583\pi$
$434$	19.5355	−	6.11042i	0.937736	−	0.293310i
$435$	5.13322	+	3.29892i	0.246119	+	0.158171i
$436$	−7.83356	+	13.5681i	−0.375160	+	0.649795i
$437$	2.12387	−	6.49056i	0.101599	−	0.310486i
$438$	−4.66529	−	8.08052i	−0.222916	−	0.386102i
$439$	18.0352	−	9.29779i	0.860773	−	0.443759i	0.0294615	−	0.999566i	$-0.490621\pi$
$439$	18.0352	−	9.29779i	0.860773	−	0.443759i	0.831312	+	0.555807i	$0.187590\pi$
$440$	−0.553936	−	3.85271i	−0.0264079	−	0.183671i
$441$	6.82279	−	1.56509i	0.324895	−	0.0745279i
$442$	6.80440	+	1.99795i	0.323652	+	0.0950329i
$443$	−11.7391	−	16.4852i	−0.557740	−	0.783237i	0.435391	−	0.900241i	$-0.356610\pi$
$443$	−11.7391	−	16.4852i	−0.557740	−	0.783237i	−0.993131	+	0.117005i	$0.962671\pi$
$444$	3.74588	+	0.721960i	0.177772	+	0.0342627i
$445$	−8.68226	+	3.47585i	−0.411579	+	0.164771i
$446$	−5.35848	+	22.0880i	−0.253731	+	1.04590i
$447$	−5.71618	−	6.59682i	−0.270366	−	0.312019i
$448$	−1.76741	−	1.96882i	−0.0835024	−	0.0930180i
$449$	15.4828	−	9.95020i	0.730679	−	0.469579i	−0.121658	−	0.992572i	$-0.538821\pi$
$449$	15.4828	−	9.95020i	0.730679	−	0.469579i	0.852337	+	0.522993i	$0.175185\pi$
$450$	4.49776	−	0.866873i	0.212027	−	0.0408648i
$451$	22.6276	+	21.5753i	1.06549	+	1.01594i
$452$	6.22480	−	2.49203i	0.292790	−	0.117215i
$453$	0.300958	+	0.869560i	0.0141402	+	0.0408555i
$454$	−3.44777	+	7.54956i	−0.161812	+	0.354318i
$455$	−2.59021	−	1.96440i	−0.121431	−	0.0920927i
$456$	−0.591547	−	1.29531i	−0.0277017	−	0.0606583i
$457$	9.63297	+	3.85646i	0.450611	+	0.180398i	0.585857	−	0.810415i	$-0.300758\pi$
$457$	9.63297	+	3.85646i	0.450611	+	0.180398i	−0.135245	+	0.990812i	$0.543182\pi$
$458$	−0.533357	+	11.1965i	−0.0249221	+	0.523180i
$459$	−1.86903	−	3.23725i	−0.0872387	−	0.151102i
$460$	3.09656	+	0.242782i	0.144378	+	0.0113198i
$461$	29.0887			1.35480			0.677399	−	0.735616i	$-0.263107\pi$
$461$	29.0887			1.35480			0.677399	+	0.735616i	$0.263107\pi$
$462$	−15.7996	+	1.78891i	−0.735065	+	0.0832277i
$463$	−1.86771	−	12.9902i	−0.0868001	−	0.603708i	−0.986072	−	0.166318i	$-0.946812\pi$
$463$	−1.86771	−	12.9902i	−0.0868001	−	0.603708i	0.899272	−	0.437390i	$-0.144097\pi$
$464$	−9.37877	−	0.895564i	−0.435398	−	0.0415755i
$465$	1.18130	+	4.86937i	0.0547813	+	0.225812i
$466$	22.3946	−	2.13842i	1.03741	−	0.0990605i
$467$	−9.73014	−	28.1134i	−0.450257	−	1.30093i	−0.910636	−	0.413210i	$-0.864407\pi$
$467$	−9.73014	−	28.1134i	−0.450257	−	1.30093i	0.460378	−	0.887723i	$-0.347714\pi$
$468$	−0.269993	+	1.87784i	−0.0124804	+	0.0868033i
$469$	−8.46985	+	12.3471i	−0.391101	+	0.570136i
$470$	−1.37838	−	1.59073i	−0.0635797	−	0.0733749i
$471$	−0.641824	−	13.4736i	−0.0295737	−	0.620829i
$472$	−12.1788	−	6.27862i	−0.560576	−	0.288997i
$473$	−18.8408	+	54.4371i	−0.866303	+	2.50302i
$474$	1.32013	−	5.44166i	0.0606357	−	0.249944i
$475$	0.928269	−	6.45625i	0.0425919	−	0.296233i
$476$	−8.70969	+	4.68537i	−0.399208	+	0.214754i
$477$	3.82607	−	8.37791i	0.175183	−	0.383598i
$478$	14.6193	−	13.9395i	0.668671	−	0.637577i
$479$	10.9773	−	15.4154i	0.501565	−	0.704350i	−0.483729	−	0.875218i	$-0.660718\pi$
$479$	10.9773	−	15.4154i	0.501565	−	0.704350i	0.985294	+	0.170868i	$0.0546572\pi$
$480$	0.509094	−	0.400356i	0.0232368	−	0.0182737i
$481$	−6.43277	+	3.31632i	−0.293309	+	0.151211i
$482$	0.888355			0.0404635
$483$	1.37147	−	12.6142i	0.0624041	−	0.573968i
$484$	25.1183			1.14174
$485$	−5.13101	+	2.64522i	−0.232987	+	0.120113i
$486$	0.786053	−	0.618159i	0.0356561	−	0.0280403i
$487$	1.28524	−	1.80486i	0.0582397	−	0.0817862i	−0.784429	−	0.620219i	$-0.787044\pi$
$487$	1.28524	−	1.80486i	0.0582397	−	0.0817862i	0.842669	+	0.538432i	$0.180983\pi$
$488$	−1.69196	+	1.61328i	−0.0765914	+	0.0730297i
$489$	2.76175	−	6.04738i	0.124891	−	0.273472i
$490$	4.49518	−	0.589013i	0.203072	−	0.0266089i
$491$	1.83535	−	12.7651i	0.0828282	−	0.576083i	−0.905570	−	0.424197i	$-0.860556\pi$
$491$	1.83535	−	12.7651i	0.0828282	−	0.576083i	0.988398	−	0.151886i	$-0.0485346\pi$
$492$	−1.22649	+	5.05565i	−0.0552943	+	0.227926i
$493$	−11.5186	+	33.2809i	−0.518773	+	1.49890i
$494$	2.40121	+	1.23791i	0.108036	+	0.0556963i
$495$	−0.185205	−	3.88792i	−0.00832432	−	0.174749i
$496$	−5.06634	−	5.84686i	−0.227485	−	0.262532i
$497$	−11.8233	−	24.7317i	−0.530348	−	1.10937i
$498$	0.754789	−	5.24967i	0.0338229	−	0.235244i
$499$	0.574759	+	1.66066i	0.0257297	+	0.0743412i	0.957134	−	0.289644i	$-0.0935370\pi$
$499$	0.574759	+	1.66066i	0.0257297	+	0.0743412i	−0.931405	+	0.363985i	$0.881416\pi$
$500$	6.17682	−	0.589815i	0.276236	−	0.0263773i
$501$	5.36485	+	22.1142i	0.239684	+	0.987991i
$502$	12.9862	+	1.24003i	0.579602	+	0.0553453i
$503$	−2.55060	−	17.7398i	−0.113726	−	0.790979i	−0.964241	−	0.265029i	$-0.914619\pi$
$503$	−2.55060	−	17.7398i	−0.113726	−	0.790979i	0.850515	−	0.525951i	$-0.176290\pi$
$504$	−1.57226	−	2.12791i	−0.0700341	−	0.0947846i
$505$	−1.23097			−0.0547776
$506$	−6.31921	+	28.1210i	−0.280923	+	1.25013i
$507$	4.70040	+	8.14134i	0.208752	+	0.361570i
$508$	0.339753	−	7.13230i	0.0150741	−	0.316444i
$509$	−38.0404	−	15.2291i	−1.68611	−	0.675018i	−0.687426	−	0.726254i	$-0.741260\pi$
$509$	−38.0404	−	15.2291i	−1.68611	−	0.675018i	−0.998687	+	0.0512363i	$0.983684\pi$
$510$	−1.00571	−	2.20220i	−0.0445337	−	0.0975152i
$511$	−22.7536	+	9.57567i	−1.00656	+	0.423603i
$512$	−0.415415	+	0.909632i	−0.0183589	+	0.0402004i
$513$	−0.465741	−	1.34567i	−0.0205630	−	0.0594129i
$514$	−14.5152	+	5.81101i	−0.640238	+	0.256313i
$515$	−5.45313	−	5.19955i	−0.240294	−	0.229120i
$516$	−9.41193	+	1.81400i	−0.414337	+	0.0798569i
$517$	16.4310	−	10.5596i	0.722634	−	0.464408i
$518$	3.13328	−	9.59440i	0.137668	−	0.421554i
$519$	−10.8381	−	12.5078i	−0.475739	−	0.549032i
$520$	−0.289679	+	1.19407i	−0.0127032	+	0.0523635i
$521$	2.76613	−	1.10739i	0.121186	−	0.0485158i	−0.310277	−	0.950646i	$-0.600422\pi$
$521$	2.76613	−	1.10739i	0.121186	−	0.0485158i	0.431463	+	0.902131i	$0.357997\pi$
$522$	−9.25117	−	1.78302i	−0.404913	−	0.0780406i
$523$	11.5358	+	16.1998i	0.504426	+	0.708367i	0.985758	−	0.168171i	$-0.0537862\pi$
$523$	11.5358	+	16.1998i	0.504426	+	0.708367i	−0.481332	+	0.876538i	$0.659847\pi$
$524$	7.21353	+	2.11808i	0.315125	+	0.0925290i
$525$	−0.788931	−	12.0933i	−0.0344318	−	0.527793i
$526$	−1.46545	−	10.1925i	−0.0638968	−	0.444412i
$527$	−25.7047	+	13.2517i	−1.11971	+	0.577252i
$528$	3.00493	+	5.20469i	0.130773	+	0.226505i
$529$	−20.7888	−	9.84001i	−0.903861	−	0.427827i
$530$	2.98254	−	5.16591i	0.129553	−	0.224393i
$531$	−11.5269	−	7.40786i	−0.500223	−	0.321474i
$532$	−3.59573	+	1.12469i	−0.155895	+	0.0487615i
$533$	−4.09996	−	8.97766i	−0.177589	−	0.388866i
$534$	10.4507	−	9.96473i	0.452247	−	0.431216i
$535$	−1.01800	+	0.0972071i	−0.0440119	+	0.00420263i
$536$	5.55698	+	1.07102i	0.240025	+	0.0462610i
$537$	19.3609	+	15.2256i	0.835486	+	0.657034i
$538$	1.37073	−	0.402483i	0.0590964	−	0.0173523i
$539$	−0.526263	+	42.0657i	−0.0226677	+	1.81190i
$540$	0.544845	−	0.350150i	0.0234464	−	0.0150681i
$541$	0.241470	+	5.06909i	0.0103816	+	0.217937i	0.998097	+	0.0616706i	$0.0196428\pi$
$541$	0.241470	+	5.06909i	0.0103816	+	0.217937i	−0.987715	+	0.156267i	$0.950054\pi$
$542$	1.32321	−	3.82315i	0.0568365	−	0.164218i
$543$	−7.32311	−	6.98257i	−0.314265	−	0.299651i
$544$	2.93831	+	2.31071i	0.125979	+	0.0990710i
$545$	−6.64483	+	7.66855i	−0.284633	+	0.328484i
$546$	4.84014	+	1.32942i	0.207139	+	0.0568938i
$547$	6.14081	+	1.80311i	0.262562	+	0.0770952i	0.410364	−	0.911922i	$-0.365402\pi$
$547$	6.14081	+	1.80311i	0.262562	+	0.0770952i	−0.147802	+	0.989017i	$0.547220\pi$
$548$	−10.0246	−	0.957229i	−0.428228	−	0.0408908i
$549$	−1.83765	+	1.44514i	−0.0784290	+	0.0616772i
$550$	−1.30985	+	27.4972i	−0.0558523	+	1.17248i
$551$	−6.70801	+	11.6186i	−0.285771	+	0.494970i
$552$	−4.57800	+	1.42897i	−0.194852	+	0.0608209i
$553$	−13.8481	−	5.26399i	−0.588883	−	0.223848i
$554$	−3.30200	−	2.12207i	−0.140289	−	0.0901580i
$555$	2.29372	+	0.918266i	0.0973629	+	0.0389782i
$556$	−3.80188	+	5.33900i	−0.161236	+	0.226424i
$557$	1.12523	+	4.63827i	0.0476776	+	0.196530i	0.990670	−	0.136286i	$-0.0435165\pi$
$557$	1.12523	+	4.63827i	0.0476776	+	0.196530i	−0.942992	+	0.332815i	$0.892001\pi$
$558$	−4.48761	−	6.30197i	−0.189976	−	0.266784i
$559$	11.9083	−	13.7429i	0.503668	−	0.581264i
$560$	−0.882674	−	1.46871i	−0.0372998	−	0.0620644i
$561$	21.5552	−	6.32917i	0.910060	−	0.267218i
$562$	−5.29342	+	1.02022i	−0.223290	+	0.0430355i
$563$	−3.39777	−	1.75167i	−0.143199	−	0.0738242i	0.385138	−	0.922859i	$-0.374154\pi$
$563$	−3.39777	−	1.75167i	−0.143199	−	0.0738242i	−0.528337	+	0.849035i	$0.677184\pi$
$564$	2.88864	+	1.48920i	0.121634	+	0.0627066i
$565$	4.26413	−	0.821844i	0.179393	−	0.0345752i
$566$	−1.93435	+	0.567977i	−0.0813069	+	0.0238739i
$567$	−1.36287	−	2.26773i	−0.0572352	−	0.0952356i
$568$	−6.78499	+	7.83030i	−0.284692	+	0.328552i
$569$	12.3463	+	17.3380i	0.517585	+	0.726846i	0.987804	−	0.155704i	$-0.0497646\pi$
$569$	12.3463	+	17.3380i	0.517585	+	0.726846i	−0.470219	+	0.882550i	$0.655825\pi$
$570$	−0.217431	−	0.896262i	−0.00910717	−	0.0375403i
$571$	0.700979	−	0.984387i	0.0293350	−	0.0411953i	−0.799648	−	0.600469i	$-0.794981\pi$
$571$	0.700979	−	0.984387i	0.0293350	−	0.0411953i	0.828983	+	0.559274i	$0.188920\pi$
$572$	−10.5849	−	4.23755i	−0.442577	−	0.177181i
$573$	10.0183	+	6.43836i	0.418520	+	0.268966i
$574$	12.8658	+	4.89059i	0.537009	+	0.204129i
$575$	−21.1796	−	5.83069i	−0.883249	−	0.243157i
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	−0.561964	+	11.7971i	−0.0233949	+	0.491119i	0.956516	+	0.291681i	$0.0942145\pi$
$577$	−0.561964	+	11.7971i	−0.0233949	+	0.491119i	−0.979911	+	0.199438i	$0.936088\pi$
$578$	−2.37934	+	1.87113i	−0.0989674	+	0.0778288i
$579$	13.3023	+	1.27022i	0.552825	+	0.0527884i
$580$	−5.85470	−	1.71909i	−0.243103	−	0.0713815i
$581$	−13.5310	−	3.71650i	−0.561362	−	0.154186i
$582$	5.83693	−	6.73618i	0.241949	−	0.279224i
$583$	43.5097	+	34.2164i	1.80199	+	1.41710i
$584$	6.75286	+	6.43883i	0.279435	+	0.266441i
$585$	−0.401871	+	1.16113i	−0.0166153	+	0.0480068i
$586$	−0.877362	−	18.4181i	−0.0362435	−	0.760844i
$587$	34.6517	−	22.2693i	1.43023	−	0.919152i	0.430365	−	0.902655i	$-0.358385\pi$
$587$	34.6517	−	22.2693i	1.43023	−	0.919152i	0.999864	−	0.0164969i	$-0.00525135\pi$
$588$	−6.10549	+	3.42389i	−0.251786	+	0.141199i
$589$	−10.5705	+	3.10377i	−0.435548	+	0.127888i
$590$	−6.97560	−	5.48567i	−0.287181	−	0.225842i
$591$	17.2803	+	3.33050i	0.710816	+	0.136999i
$592$	−3.79755	+	0.362622i	−0.156078	+	0.0149037i
$593$	19.8196	−	18.8980i	0.813895	−	0.776047i	−0.163707	−	0.986509i	$-0.552345\pi$
$593$	19.8196	−	18.8980i	0.813895	−	0.776047i	0.977602	+	0.210462i	$0.0674968\pi$
$594$	2.49658	+	5.46675i	0.102436	+	0.224304i
$595$	−6.11325	+	1.91213i	−0.250619	+	0.0783898i
$596$	7.34317	+	4.71917i	0.300788	+	0.193305i
$597$	10.2188	−	17.6994i	0.418227	−	0.724390i
$598$	5.15119	−	7.49978i	0.210648	−	0.306689i
$599$	4.75860	+	8.24214i	0.194431	+	0.336765i	0.946714	−	0.322076i	$-0.104381\pi$
$599$	4.75860	+	8.24214i	0.194431	+	0.336765i	−0.752283	+	0.658840i	$0.771047\pi$
$600$	−4.07135	+	2.09892i	−0.166212	+	0.0856882i
$601$	−2.44129	−	16.9795i	−0.0995822	−	0.692609i	−0.977056	−	0.212984i	$-0.931682\pi$
$601$	−2.44129	−	16.9795i	−0.0995822	−	0.692609i	0.877474	−	0.479625i	$-0.159227\pi$
$602$	1.65090	+	25.3061i	0.0672857	+	1.03140i
$603$	5.43001	+	1.59439i	0.221127	+	0.0649287i
$604$	−0.533750	−	0.749547i	−0.0217180	−	0.0304986i
$605$	15.9741	+	3.07876i	0.649440	+	0.125169i
$606$	1.76451	−	0.706401i	0.0716781	−	0.0286956i
$607$	2.11085	−	8.70102i	0.0856766	−	0.353164i	−0.912796	−	0.408416i	$-0.866081\pi$
$607$	2.11085	−	8.70102i	0.0856766	−	0.353164i	0.998472	+	0.0552525i	$0.0175964\pi$
$608$	0.932515	+	1.07618i	0.0378185	+	0.0436449i
$609$	−7.73822	+	23.6952i	−0.313569	+	0.960179i
$610$	−1.27375	+	0.818588i	−0.0515726	+	0.0331437i
$611$	−6.05418	+	1.16685i	−0.244926	+	0.0472056i
$612$	2.70536	+	2.57955i	0.109358	+	0.104272i
$613$	8.99268	−	3.60013i	0.363211	−	0.145408i	−0.182877	−	0.983136i	$-0.558541\pi$
$613$	8.99268	−	3.60013i	0.363211	−	0.145408i	0.546087	+	0.837728i	$0.316117\pi$
$614$	8.01575	+	23.1600i	0.323490	+	0.934662i
$615$	−1.39966	+	3.06483i	−0.0564398	+	0.123586i
$616$	14.6556	−	6.16772i	0.590492	−	0.248504i
$617$	7.16443	+	15.6879i	0.288429	+	0.631571i	0.997274	−	0.0737934i	$-0.0235105\pi$
$617$	7.16443	+	15.6879i	0.288429	+	0.631571i	−0.708845	+	0.705365i	$0.750783\pi$
$618$	10.8004	+	4.32384i	0.434457	+	0.173930i
$619$	−0.163477	+	3.43181i	−0.00657071	+	0.137936i	0.993198	+	0.116436i	$0.0371471\pi$
$619$	−0.163477	+	3.43181i	−0.00657071	+	0.137936i	−0.999769	+	0.0214997i	$0.993156\pi$
$620$	−2.50531	−	4.33932i	−0.100616	−	0.174271i
$621$	−4.69310	+	0.987331i	−0.188328	+	0.0396202i
$622$	−28.7957			−1.15460
$623$	−22.7034	−	30.7270i	−0.909594	−	1.23105i
$624$	−0.269993	−	1.87784i	−0.0108084	−	0.0751739i
$625$	−18.7985	−	1.79504i	−0.751941	−	0.0718017i
$626$	−2.13023	−	8.78091i	−0.0851409	−	0.350956i
$627$	8.51922	−	0.813487i	0.340225	−	0.0324875i
$628$	4.41176	+	12.7470i	0.176049	+	0.508659i
$629$	−2.02941	+	14.1149i	−0.0809179	+	0.562796i
$630$	−0.739068	−	1.54596i	−0.0294452	−	0.0615927i
$631$	16.2131	+	18.7109i	0.645432	+	0.744868i	0.980325	−	0.197388i	$-0.0632459\pi$
$631$	16.2131	+	18.7109i	0.645432	+	0.744868i	−0.334894	+	0.942256i	$0.608700\pi$
$632$	0.266435	+	5.59316i	0.0105982	+	0.222484i
$633$	8.35198	+	4.30574i	0.331961	+	0.171138i
$634$	−3.33566	+	9.63777i	−0.132476	+	0.382765i
$635$	1.09027	−	4.49417i	0.0432662	−	0.178346i
$636$	−1.31075	+	9.11648i	−0.0519747	+	0.361492i
$637$	5.08955	−	12.2661i	0.201655	−	0.486000i
$638$	23.5214	−	51.5046i	0.931220	−	2.03909i
$639$	−7.49859	+	7.14989i	−0.296640	+	0.282845i
$640$	−0.375679	+	0.527567i	−0.0148500	+	0.0208539i
$641$	−13.7450	+	10.8092i	−0.542896	+	0.426938i	−0.851578	−	0.524227i	$-0.824354\pi$
$641$	−13.7450	+	10.8092i	−0.542896	+	0.426938i	0.308683	+	0.951165i	$0.400112\pi$
$642$	1.40344	−	0.723524i	0.0553894	−	0.0285552i
$643$	15.4345			0.608676			0.304338	−	0.952564i	$-0.401565\pi$
$643$	15.4345			0.608676			0.304338	+	0.952564i	$0.401565\pi$
$644$	2.23792	+	12.4897i	0.0881866	+	0.492162i
$645$	−6.20790			−0.244436
$646$	4.73123	−	2.43912i	0.186148	−	0.0959658i
$647$	−3.12862	+	2.46037i	−0.122999	+	0.0967272i	−0.677763	−	0.735280i	$-0.737051\pi$
$647$	−3.12862	+	2.46037i	−0.122999	+	0.0967272i	0.554765	+	0.832007i	$0.312808\pi$
$648$	−0.580057	+	0.814576i	−0.0227868	+	0.0319996i
$649$	59.5973	−	56.8259i	2.33940	−	2.23061i
$650$	3.60995	−	7.90469i	0.141594	−	0.310047i
$651$	−18.0261	+	9.69713i	−0.706499	+	0.380060i
$652$	−0.946132	+	6.58050i	−0.0370534	+	0.257712i
$653$	−0.356180	+	1.46820i	−0.0139384	+	0.0574549i	−0.978356	−	0.206928i	$-0.933653\pi$
$653$	−0.356180	+	1.46820i	−0.0139384	+	0.0574549i	0.964418	+	0.264383i	$0.0851684\pi$
$654$	5.12421	−	14.8054i	0.200373	−	0.578939i
$655$	4.32786	+	2.23117i	0.169104	+	0.0871790i
$656$	−0.247535	−	5.19640i	−0.00966462	−	0.202885i
$657$	6.11023	+	7.05158i	0.238383	+	0.275108i
$658$	4.86396	−	7.09054i	0.189617	−	0.276418i
$659$	−0.695573	+	4.83782i	−0.0270957	+	0.188455i	−0.998874	−	0.0474412i	$-0.984893\pi$
$659$	−0.695573	+	4.83782i	−0.0270957	+	0.188455i	0.971778	+	0.235896i	$0.0758024\pi$
$660$	1.27306	+	3.67826i	0.0495537	+	0.143176i
$661$	30.2796	−	2.89135i	1.17774	−	0.112461i	0.512230	−	0.858848i	$-0.328820\pi$
$661$	30.2796	−	2.89135i	1.17774	−	0.112461i	0.665511	+	0.746388i	$0.268214\pi$
$662$	5.81506	+	23.9700i	0.226009	+	0.931620i
$663$	−7.05955	−	0.674106i	−0.274170	−	0.0261801i
$664$	0.754789	+	5.24967i	0.0292915	+	0.203727i
$665$	−2.42458	+	0.274522i	−0.0940210	+	0.0106455i
$666$	−3.81482			−0.147821
$667$	35.9852	+	27.3244i	1.39335	+	1.05801i
$668$	−11.3778	−	19.7070i	−0.440222	−	0.762486i
$669$	1.08147	−	22.7029i	0.0418121	−	0.877745i
$670$	3.40271	+	1.36224i	0.131458	+	0.0526278i
$671$	−5.83656	−	12.7803i	−0.225318	−	0.493377i
$672$	2.10807	+	1.59876i	0.0813207	+	0.0616734i
$673$	−0.143087	+	0.313318i	−0.00551561	+	0.0120775i	−0.912370	−	0.409367i	$-0.865750\pi$
$673$	−0.143087	+	0.313318i	−0.00551561	+	0.0120775i	0.906854	+	0.421445i	$0.138477\pi$
$674$	−2.12249	−	6.13254i	−0.0817553	−	0.236216i
$675$	−4.25243	+	1.70241i	−0.163676	+	0.0655260i
$676$	−6.80368	−	6.48730i	−0.261680	−	0.249512i
$677$	−10.7518	+	2.07224i	−0.413226	+	0.0796427i	−0.391627	−	0.920124i	$-0.628088\pi$
$677$	−10.7518	+	2.07224i	−0.413226	+	0.0796427i	−0.0215985	+	0.999767i	$0.506876\pi$
$678$	−5.64068	+	3.62505i	−0.216629	+	0.139219i
$679$	−15.7534	−	17.5486i	−0.604559	−	0.673453i
$680$	1.58541	+	1.82966i	0.0607975	+	0.0701641i
$681$	1.95670	−	8.06562i	0.0749808	−	0.309075i
$682$	43.1647	−	17.2805i	1.65286	−	0.661706i
$683$	−8.34708	−	1.60877i	−0.319392	−	0.0615578i	0.0270356	−	0.999634i	$-0.491393\pi$
$683$	−8.34708	−	1.60877i	−0.319392	−	0.0615578i	−0.346428	+	0.938077i	$0.612605\pi$
$684$	0.825995	+	1.15995i	0.0315827	+	0.0443517i
$685$	−6.25783	−	1.83746i	−0.239099	−	0.0702059i
$686$	6.96977	+	17.1587i	0.266107	+	0.655124i
$687$	−1.59524	−	11.0951i	−0.0608622	−	0.423306i
$688$	8.51961	−	4.39217i	0.324807	−	0.167450i
$689$	−8.73661	−	15.1322i	−0.332838	−	0.576493i
$690$	−3.08654	+	0.347633i	−0.117503	+	0.0132341i
$691$	6.55042	−	11.3457i	0.249190	−	0.431609i	−0.714111	−	0.700032i	$-0.753169\pi$
$691$	6.55042	−	11.3457i	0.249190	−	0.431609i	0.963301	+	0.268423i	$0.0865024\pi$
$692$	13.9229	+	8.94771i	0.529270	+	0.340141i
$693$	15.1756	−	4.74668i	0.576471	−	0.180312i
$694$	10.9091	+	23.8876i	0.414104	+	0.906760i
$695$	−3.07222	+	2.92936i	−0.116536	+	0.111117i
$696$	9.37877	−	0.895564i	0.355501	−	0.0339463i
$697$	−19.0950	−	3.68027i	−0.723276	−	0.139400i
$698$	21.9818	+	17.2867i	0.832022	+	0.654310i
$699$	−21.5852	+	6.33798i	−0.816426	+	0.239724i
$700$	4.16404	+	11.3811i	0.157386	+	0.430166i
$701$	−8.44634	+	5.42813i	−0.319014	+	0.205018i	−0.690341	−	0.723484i	$-0.742539\pi$
$701$	−8.44634	+	5.42813i	−0.319014	+	0.205018i	0.371327	+	0.928502i	$0.378903\pi$
$702$	−0.0902702	−	1.89500i	−0.00340703	−	0.0715223i
$703$	−1.77672	+	5.13350i	−0.0670103	+	0.193613i
$704$	−4.34954	−	4.14727i	−0.163929	−	0.156306i
$705$	1.65451	+	1.30112i	0.0623126	+	0.0490032i
$706$	−10.3294	+	11.9207i	−0.388751	+	0.448642i
$707$	−1.27110	−	4.86535i	−0.0478048	−	0.182980i
$708$	13.1470	+	3.86030i	0.494093	+	0.145079i
$709$	39.4038	+	3.76260i	1.47984	+	0.141308i	0.803510	−	0.595291i	$-0.202963\pi$
$709$	39.4038	+	3.76260i	1.47984	+	0.141308i	0.676330	+	0.736599i	$0.263569\pi$
$710$	−5.27471	+	4.14807i	−0.197956	+	0.155674i
$711$	−0.266435	+	5.59316i	−0.00999209	+	0.209760i
$712$	−7.21999	+	12.5054i	−0.270581	+	0.468660i
$713$	5.90223	+	36.6305i	0.221040	+	1.37182i
$714$	7.66558	−	6.24902i	0.286877	−	0.233864i
$715$	−6.21211	−	3.99228i	−0.232320	−	0.149303i
$716$	−22.8662	−	9.15426i	−0.854552	−	0.342111i
$717$	−11.7170	+	16.4543i	−0.437581	+	0.614497i
$718$	4.73751	+	19.5283i	0.176802	+	0.728789i
$719$	19.2302	+	27.0050i	0.717164	+	1.00712i	0.998866	+	0.0476137i	$0.0151616\pi$
$719$	19.2302	+	27.0050i	0.717164	+	1.00712i	−0.281702	+	0.959502i	$0.590899\pi$
$720$	−0.424126	+	0.489467i	−0.0158062	+	0.0182414i
$721$	14.9200	−	26.9223i	0.555651	−	1.00264i
$722$	−16.2848	+	4.78164i	−0.606056	+	0.177954i
$723$	−0.872301	+	0.168122i	−0.0324412	+	0.00625254i
$724$	8.99369	+	4.63657i	0.334248	+	0.172317i
$725$	38.3579	+	19.7749i	1.42458	+	0.734420i
$726$	−24.6644	+	4.75368i	−0.915382	+	0.176425i
$727$	25.1998	−	7.39934i	0.934611	−	0.274426i	0.221245	−	0.975218i	$-0.428988\pi$
$727$	25.1998	−	7.39934i	0.934611	−	0.274426i	0.713366	+	0.700792i	$0.247170\pi$
$728$	−5.01862	+	0.0880609i	−0.186003	+	0.00326375i
$729$	−0.654861	+	0.755750i	−0.0242541	+	0.0279907i
$730$	3.50530	+	4.92250i	0.129737	+	0.182190i
$731$	−8.44719	−	34.8198i	−0.312431	−	1.28786i
$732$	1.35607	−	1.90433i	0.0501217	−	0.0703861i
$733$	31.9362	+	12.7853i	1.17959	+	0.472237i	0.876817	−	0.480825i	$-0.159663\pi$
$733$	31.9362	+	12.7853i	1.17959	+	0.472237i	0.302775	+	0.953062i	$0.402087\pi$
$734$	7.35372	+	4.72595i	0.271431	+	0.174438i
$735$	−4.30248	+	1.42909i	−0.158699	+	0.0527127i
$736$	3.98997	−	2.66086i	0.147072	−	0.0980804i
$737$	−17.0056	+	29.4546i	−0.626410	+	1.08497i
$738$	0.247535	−	5.19640i	0.00911189	−	0.191282i
$739$	26.0658	−	20.4984i	0.958846	−	0.754045i	−0.0104491	−	0.999945i	$-0.503326\pi$
$739$	26.0658	−	20.4984i	0.958846	−	0.754045i	0.969295	+	0.245901i	$0.0790837\pi$
$740$	−2.45951	−	0.234855i	−0.0904135	−	0.00863344i
$741$	−2.59210	−	0.761108i	−0.0952231	−	0.0279600i
$742$	23.4977	+	6.45399i	0.862629	+	0.236934i
$743$	−15.0119	+	17.3246i	−0.550732	+	0.635579i	−0.961054	−	0.276362i	$-0.910871\pi$
$743$	−15.0119	+	17.3246i	−0.550732	+	0.635579i	0.410321	+	0.911941i	$0.365416\pi$
$744$	6.08131	+	4.78239i	0.222951	+	0.175331i
$745$	4.09149	+	3.90123i	0.149901	+	0.142930i
$746$	11.0073	−	31.8035i	0.403006	−	1.16441i
$747$	0.252358	+	5.29765i	0.00923330	+	0.193831i
$748$	−18.8989	+	12.1456i	−0.691012	+	0.444087i
$749$	−1.43539	−	3.92321i	−0.0524481	−	0.143351i
$750$	−5.95357	+	1.74813i	−0.217394	+	0.0638325i
$751$	−39.7019	−	31.2219i	−1.44874	−	1.13930i	−0.964407	−	0.264423i	$-0.914819\pi$
$751$	−39.7019	−	31.2219i	−1.44874	−	1.13930i	−0.484337	−	0.874882i	$-0.660939\pi$
$752$	−3.19119	−	0.615052i	−0.116371	−	0.0224286i
$753$	−12.9862	+	1.24003i	−0.473243	+	0.0451892i
$754$	−12.9360	+	12.3344i	−0.471100	+	0.449192i
$755$	−0.247568	−	0.542099i	−0.00900994	−	0.0197290i
$756$	1.94656	+	1.79190i	0.0707956	+	0.0651709i
$757$	−18.4896	−	11.8825i	−0.672016	−	0.431878i	0.159636	−	0.987176i	$-0.448968\pi$
$757$	−18.4896	−	11.8825i	−0.672016	−	0.431878i	−0.831652	+	0.555298i	$0.812604\pi$
$758$	17.1168	−	29.6472i	0.621712	−	1.07684i
$759$	0.883088	−	28.8087i	0.0320541	−	1.04569i
$760$	0.461129	+	0.798699i	0.0167269	+	0.0289719i
$761$	−38.1493	+	19.6673i	−1.38291	+	0.712940i	−0.979380	−	0.202026i	$-0.935247\pi$
$761$	−38.1493	+	19.6673i	−1.38291	+	0.712940i	−0.403531	+	0.914966i	$0.632217\pi$
$762$	1.01618	+	7.06770i	0.0368124	+	0.256036i
$763$	−37.1710	−	18.3448i	−1.34568	−	0.664126i
$764$	−11.4264	−	3.35509i	−0.413392	−	0.121383i
$765$	1.40431	+	1.97207i	0.0507728	+	0.0713005i
$766$	10.1876	+	1.96349i	0.368092	+	0.0709439i
$767$	−24.1327	+	9.66129i	−0.871382	+	0.348849i
$768$	0.235759	−	0.971812i	0.00850722	−	0.0350672i
$769$	−23.6978	−	27.3487i	−0.854565	−	0.986220i	0.145430	−	0.989369i	$-0.453543\pi$
$769$	−23.6978	−	27.3487i	−0.854565	−	0.986220i	−0.999995	+	0.00314819i	$0.998998\pi$
$770$	10.0763	−	2.12604i	0.363124	−	0.0766172i
$771$	13.1531	−	8.45301i	0.473699	−	0.304428i
$772$	−13.1213	+	2.52893i	−0.472247	+	0.0910181i
$773$	39.7533	+	37.9047i	1.42983	+	1.36334i	0.822323	+	0.569021i	$0.192678\pi$
$773$	39.7533	+	37.9047i	1.42983	+	1.36334i	0.607504	+	0.794316i	$0.292171\pi$
$774$	8.89854	−	3.56244i	0.319851	−	0.128049i
$775$	11.5904	+	33.4883i	0.416341	+	1.20294i
$776$	−3.70270	+	8.10777i	−0.132919	+	0.291052i
$777$	−1.26090	+	10.0140i	−0.0452345	+	0.359250i
$778$	−3.74285	−	8.19571i	−0.134188	−	0.293830i
$779$	−6.87736	−	2.75328i	−0.246407	−	0.0986465i
$780$	0.0584642	−	1.22732i	0.00209336	−	0.0439449i
$781$	−31.1340	−	53.9256i	−1.11406	−	1.92961i
$782$	−6.14977	−	16.8393i	−0.219915	−	0.602171i
$783$	9.42143			0.336694
$784$	4.89355	−	5.00531i	0.174770	−	0.178761i
$785$	1.24328	+	8.64723i	0.0443747	+	0.308633i
$786$	−7.48403	−	0.714638i	−0.266946	−	0.0254903i
$787$	6.81665	+	28.0986i	0.242987	+	1.00161i	0.954328	+	0.298760i	$0.0965730\pi$
$787$	6.81665	+	28.0986i	0.242987	+	1.00161i	−0.711341	+	0.702847i	$0.751912\pi$
$788$	−17.5186	+	1.67283i	−0.624075	+	0.0595920i
$789$	3.36791	+	9.73092i	0.119901	+	0.346430i
$790$	−0.516114	+	3.58965i	−0.0183625	+	0.127714i
$791$	7.65144	+	16.0051i	0.272054	+	0.569076i
$792$	−3.93562	−	4.54194i	−0.139846	−	0.161391i
$793$	0.211035	+	4.43018i	0.00749409	+	0.157320i
$794$	−31.4811	−	16.2296i	−1.11722	−	0.575968i
$795$	−1.95099	+	5.63700i	−0.0691943	+	0.199924i
$796$	−4.81834	+	19.8615i	−0.170781	+	0.703970i
$797$	−4.16459	+	28.9654i	−0.147517	+	1.02601i	0.772749	+	0.634712i	$0.218881\pi$
$797$	−4.16459	+	28.9654i	−0.147517	+	1.02601i	−0.920266	+	0.391294i	$0.872028\pi$
$798$	3.31791	−	1.78486i	0.117453	−	0.0631835i
$799$	−5.04662	+	11.0506i	−0.178537	+	0.390941i
$800$	3.31509	−	3.16093i	0.117206	−	0.111756i
$801$	−8.37602	+	11.7625i	−0.295952	+	0.415606i
$802$	−5.64908	+	4.44248i	−0.199476	+	0.156870i
$803$	−49.8418	+	25.6952i	−1.75888	+	0.906765i
$804$	−5.65925			−0.199586
$805$	−0.107642	+	8.21716i	−0.00379388	+	0.289617i
$806$	−14.6773			−0.516987
$807$	−1.26979	+	0.654622i	−0.0446987	+	0.0230438i
$808$	−1.49401	+	1.17491i	−0.0525592	+	0.0413330i
$809$	−23.0893	+	32.4244i	−0.811777	+	1.13998i	0.176043	+	0.984383i	$0.443670\pi$
$809$	−23.0893	+	32.4244i	−0.811777	+	1.13998i	−0.987820	+	0.155599i	$0.950269\pi$
$810$	−0.468732	+	0.446935i	−0.0164696	+	0.0157037i
$811$	−6.74221	+	14.7634i	−0.236751	+	0.518412i	−0.990294	−	0.138986i	$-0.955616\pi$
$811$	−6.74221	+	14.7634i	−0.236751	+	0.518412i	0.753543	+	0.657398i	$0.228343\pi$
$812$	0.749058	−	24.9155i	0.0262868	−	0.874363i
$813$	−0.575757	+	4.00448i	−0.0201927	+	0.140443i
$814$	5.40513	−	22.2802i	0.189450	−	0.780922i
$815$	−1.40827	+	4.06893i	−0.0493295	+	0.142528i
$816$	−3.32252	−	1.71288i	−0.116311	−	0.0599627i
$817$	−0.649453	−	13.6337i	−0.0227215	−	0.476982i
$818$	−24.1071	−	27.8211i	−0.842885	−	0.972741i
$819$	−5.00427	−	0.389388i	−0.174863	−	0.0136063i
$820$	0.479502	−	3.33501i	0.0167450	−	0.116464i
$821$	17.2869	+	49.9473i	0.603318	+	1.74317i	0.666849	+	0.745193i	$0.267642\pi$
$821$	17.2869	+	49.9473i	0.603318	+	1.74317i	−0.0635315	+	0.997980i	$0.520236\pi$
$822$	10.0246	−	0.957229i	0.349646	−	0.0333872i
$823$	0.847482	+	3.49337i	0.0295414	+	0.121771i	0.984673	−	0.174410i	$-0.0558019\pi$
$823$	0.847482	+	3.49337i	0.0295414	+	0.121771i	−0.955132	+	0.296181i	$0.904287\pi$
$824$	−11.5811	−	1.10586i	−0.403447	−	0.0385245i
$825$	−3.91769	−	27.2482i	−0.136397	−	0.948659i
$826$	14.4788	−	33.2352i	0.503782	−	1.15640i
$827$	−20.2557			−0.704361			−0.352180	−	0.935932i	$-0.614560\pi$
$827$	−20.2557			−0.704361			−0.352180	+	0.935932i	$0.614560\pi$
$828$	4.22483	−	2.26954i	0.146823	−	0.0788718i
$829$	2.82187	+	4.88763i	0.0980077	+	0.169754i	0.910860	−	0.412716i	$-0.135420\pi$
$829$	2.82187	+	4.88763i	0.0980077	+	0.169754i	−0.812852	+	0.582470i	$0.802086\pi$
$830$	−0.163442	+	3.43107i	−0.00567315	+	0.119094i
$831$	3.64393	+	1.45881i	0.126407	+	0.0506056i
$832$	0.788106	+	1.72571i	0.0273227	+	0.0598283i
$833$	−13.8701	−	22.1878i	−0.480572	−	0.768762i
$834$	2.72276	−	5.96202i	0.0942816	−	0.206448i
$835$	−4.82029	−	13.9273i	−0.166813	−	0.481975i
$836$	−7.94495	+	3.18068i	−0.274782	+	0.110006i
$837$	5.59917	+	5.33880i	0.193536	+	0.184536i
$838$	37.6403	−	7.25457i	1.30026	−	0.250605i
$839$	−27.8472	+	17.8963i	−0.961393	+	0.617850i	−0.924383	−	0.381465i	$-0.875420\pi$
$839$	−27.8472	+	17.8963i	−0.961393	+	0.617850i	−0.0370098	+	0.999315i	$0.511783\pi$
$840$	1.14468	+	1.27512i	0.0394952	+	0.0439959i
$841$	−39.1367	−	45.1661i	−1.34954	−	1.55745i
$842$	−0.749883	+	3.09106i	−0.0258427	+	0.106525i
$843$	5.00468	−	2.00357i	0.172370	−	0.0690067i
$844$	−9.22673	−	1.77831i	−0.317597	−	0.0612119i
$845$	−3.53168	−	4.95955i	−0.121494	−	0.170614i
$846$	−3.11828	−	0.915608i	−0.107209	−	0.0314793i
$847$	4.32626	+	66.3159i	0.148652	+	2.27864i
$848$	−1.31075	−	9.11648i	−0.0450114	−	0.313061i
$849$	1.79191	−	0.923791i	0.0614980	−	0.0317044i
$850$	−8.56115	−	14.8284i	−0.293645	−	0.508608i
$851$	16.4013	+	8.10644i	0.562228	+	0.277885i
$852$	5.18049	−	8.97286i	0.177481	−	0.307405i
$853$	7.76145	+	4.98798i	0.265747	+	0.170785i	0.666728	−	0.745301i	$-0.267694\pi$
$853$	7.76145	+	4.98798i	0.265747	+	0.170785i	−0.400981	+	0.916086i	$0.631331\pi$
$854$	−4.55070	−	4.18914i	−0.155722	−	0.143350i
$855$	0.383120	+	0.838916i	0.0131024	+	0.0286903i
$856$	−1.14275	+	1.08961i	−0.0390584	+	0.0372421i
$857$	−34.3883	+	3.28369i	−1.17468	+	0.112169i	−0.664089	−	0.747654i	$-0.731180\pi$
$857$	−34.3883	+	3.28369i	−1.17468	+	0.112169i	−0.510593	+	0.859822i	$0.670574\pi$
$858$	11.1956	+	2.15777i	0.382211	+	0.0736650i
$859$	8.33926	+	6.55807i	0.284532	+	0.223758i	0.750216	−	0.661193i	$-0.229949\pi$
$859$	8.33926	+	6.55807i	0.284532	+	0.223758i	−0.465684	+	0.884951i	$0.654192\pi$
$860$	5.95643	−	1.74897i	0.203113	−	0.0596393i
$861$	−13.5589	−	2.36734i	−0.462085	−	0.0806786i
$862$	−30.5948	+	19.6621i	−1.04206	+	0.669694i
$863$	−1.83320	−	38.4835i	−0.0624027	−	1.30999i	−0.785333	−	0.619073i	$-0.787508\pi$
$863$	−1.83320	−	38.4835i	−0.0624027	−	1.30999i	0.722930	−	0.690921i	$-0.242795\pi$
$864$	0.327068	−	0.945001i	0.0111271	−	0.0321496i
$865$	7.75761	+	7.39687i	0.263767	+	0.251501i
$866$	25.3401	+	19.9277i	0.861091	+	0.677170i
$867$	1.98223	−	2.28761i	0.0673199	−	0.0776913i
$868$	14.5639	−	14.3829i	0.494332	−	0.488186i
$869$	−32.2890	−	9.48091i	−1.09533	−	0.321618i
$870$	6.07424	+	0.580019i	0.205936	+	0.0196645i
$871$	8.43943	−	6.63684i	0.285959	−	0.224881i
$872$	−0.745472	+	15.6494i	−0.0252449	+	0.529955i
$873$	−4.45662	+	7.71910i	−0.150834	+	0.261252i
$874$	−1.08637	−	6.74225i	−0.0367470	−	0.228060i
$875$	2.62106	+	16.2061i	0.0886080	+	0.547865i
$876$	−7.84938	−	5.04449i	−0.265206	−	0.170438i
$877$	−46.8701	−	18.7639i	−1.58269	−	0.633613i	−0.597008	−	0.802235i	$-0.703644\pi$
$877$	−46.8701	−	18.7639i	−1.58269	−	0.633613i	−0.985681	+	0.168622i	$0.946068\pi$
$878$	11.7698	−	16.5284i	0.397213	−	0.557807i
$879$	4.34715	+	17.9192i	0.146626	+	0.604400i
$880$	−2.25777	−	3.17060i	−0.0761095	−	0.106881i
$881$	−4.21620	+	4.86576i	−0.142048	+	0.163932i	−0.822315	−	0.569032i	$-0.807318\pi$
$881$	−4.21620	+	4.86576i	−0.142048	+	0.163932i	0.680268	+	0.732964i	$0.261863\pi$
$882$	5.34718	−	4.51749i	0.180049	−	0.152112i
$883$	24.7768	−	7.27513i	0.833806	−	0.244827i	0.163155	−	0.986600i	$-0.447833\pi$
$883$	24.7768	−	7.27513i	0.833806	−	0.244827i	0.670651	+	0.741773i	$0.266015\pi$
$884$	6.96351	−	1.34211i	0.234208	−	0.0451399i
$885$	7.88771	+	4.06640i	0.265143	+	0.136690i
$886$	−17.9881	−	9.27350i	−0.604321	−	0.311549i
$887$	2.77372	−	0.534590i	0.0931323	−	0.0179498i	−0.142472	−	0.989799i	$-0.545505\pi$
$887$	2.77372	−	0.534590i	0.0931323	−	0.0179498i	0.235604	+	0.971849i	$0.424293\pi$
$888$	3.66029	−	1.07476i	0.122831	−	0.0360666i
$889$	18.8888	−	0.331438i	0.633509	−	0.0111161i
$890$	−6.12437	+	7.06790i	−0.205289	+	0.236917i
$891$	−3.48606	−	4.89548i	−0.116787	−	0.164005i
$892$	5.35848	+	22.0880i	0.179415	+	0.739560i
$893$	−2.68442	+	3.76974i	−0.0898307	+	0.126149i
$894$	−8.10358	−	3.24419i	−0.271024	−	0.108502i
$895$	−13.4198	−	8.62441i	−0.448576	−	0.288282i
$896$	−2.47310	−	0.940083i	−0.0826206	−	0.0314060i
$897$	−3.63876	+	8.33912i	−0.121495	+	0.278435i
$898$	9.20223	−	15.9387i	0.307082	−	0.531882i
$899$	3.46820	−	72.8064i	0.115671	−	2.42823i
$900$	3.60055	−	2.83150i	0.120018	−	0.0943834i
$901$	−34.2724	−	3.27262i	−1.14178	−	0.109027i
$902$	29.9986	+	8.80837i	0.998843	+	0.293287i
$903$	−6.41028	−	24.5364i	−0.213321	−	0.816519i
$904$	4.39090	−	5.06737i	0.146039	−	0.168538i
$905$	5.15127	+	4.05100i	0.171234	+	0.134660i
$906$	0.665957	+	0.634989i	0.0221249	+	0.0210961i
$907$	−9.27811	+	26.8074i	−0.308075	+	0.890124i	0.679597	+	0.733585i	$0.262155\pi$
$907$	−9.27811	+	26.8074i	−0.308075	+	0.890124i	−0.987672	+	0.156538i	$0.949967\pi$
$908$	0.394910	+	8.29017i	0.0131055	+	0.275119i
$909$	−1.59893	+	1.02757i	−0.0530332	+	0.0340824i
$910$	−3.20241	−	0.559131i	−0.106159	−	0.0185350i
$911$	−1.92178	+	0.564287i	−0.0636715	+	0.0186957i	−0.313413	−	0.949617i	$-0.601472\pi$
$911$	−1.92178	+	0.564287i	−0.0636715	+	0.0186957i	0.249742	+	0.968313i	$0.419654\pi$
$912$	−1.11933	−	0.880252i	−0.0370648	−	0.0291481i
$913$	−31.2982	−	6.03223i	−1.03582	−	0.199638i
$914$	10.3293	−	0.986325i	0.341662	−	0.0326247i
$915$	1.09581	−	1.04485i	0.0362264	−	0.0345418i
$916$	4.65648	+	10.1963i	0.153855	+	0.336894i
$917$	−4.34961	+	19.4095i	−0.143637	+	0.640960i
$918$	−3.14465	−	2.02095i	−0.103789	−	0.0667011i
$919$	12.5881	−	21.8033i	0.415244	−	0.719223i	−0.580210	−	0.814467i	$-0.697030\pi$
$919$	12.5881	−	21.8033i	0.415244	−	0.719223i	0.995454	+	0.0952437i	$0.0303630\pi$
$920$	2.86358	−	1.20313i	0.0944094	−	0.0396661i
$921$	−12.2540	−	21.2245i	−0.403782	−	0.699370i
$922$	25.8551	−	13.3292i	0.851493	−	0.438975i
$923$	2.79739	+	19.4563i	0.0920772	+	0.640411i
$924$	−13.2235	+	8.82985i	−0.435023	+	0.290481i
$925$	16.7661	+	4.92298i	0.551267	+	0.161866i
$926$	−7.61256	−	10.6904i	−0.250164	−	0.351307i
$927$	−11.4236	−	2.20171i	−0.375199	−	0.0723136i
$928$	−8.74655	+	3.50159i	−0.287120	+	0.114945i
$929$	12.5346	−	51.6683i	0.411246	−	1.69518i	−0.269780	−	0.962922i	$-0.586951\pi$
$929$	12.5346	−	51.6683i	0.411246	−	1.69518i	0.681026	−	0.732259i	$-0.261534\pi$
$930$	3.28125	+	3.78677i	0.107597	+	0.124173i
$931$	−3.58865	−	9.29953i	−0.117613	−	0.304780i
$932$	18.9252	−	12.1625i	0.619916	−	0.398396i
$933$	28.2754	−	5.44963i	0.925694	−	0.178413i
$934$	−21.5308	−	20.5296i	−0.704509	−	0.671748i
$935$	−13.5075	+	5.40759i	−0.441743	+	0.176847i
$936$	0.620498	+	1.79281i	0.0202816	+	0.0585999i
$937$	−18.7421	+	41.0395i	−0.612279	+	1.34070i	0.308726	+	0.951151i	$0.400097\pi$
$937$	−18.7421	+	41.0395i	−0.612279	+	1.34070i	−0.921004	+	0.389552i	$0.872630\pi$
$938$	−1.87053	+	14.8557i	−0.0610750	+	0.485054i
$939$	3.75353	+	8.21908i	0.122492	+	0.268220i
$940$	−1.95406	−	0.782289i	−0.0637345	−	0.0255155i
$941$	−0.387979	+	8.14468i	−0.0126478	+	0.265509i	0.983682	+	0.179914i	$0.0575821\pi$
$941$	−0.387979	+	8.14468i	−0.0126478	+	0.265509i	−0.996330	+	0.0855947i	$0.972721\pi$
$942$	−6.74442	−	11.6817i	−0.219745	−	0.380609i
$943$	−12.1065	+	21.8152i	−0.394243	+	0.710399i
$944$	−13.7020			−0.445962
$945$	1.01829	+	1.37816i	0.0331249	+	0.0448315i
$946$	8.19809	+	57.0190i	0.266543	+	1.85385i
$947$	20.2106	+	1.92988i	0.656755	+	0.0627125i	0.418113	−	0.908395i	$-0.362692\pi$
$947$	20.2106	+	1.92988i	0.656755	+	0.0627125i	0.238642	+	0.971108i	$0.423298\pi$
$948$	−1.32013	−	5.44166i	−0.0428759	−	0.176737i
$949$	17.6214	−	1.68264i	0.572014	−	0.0546207i
$950$	−2.13335	−	6.16390i	−0.0692149	−	0.199983i
$951$	1.45142	−	10.0949i	0.0470657	−	0.327349i
$952$	−5.59452	+	8.15553i	−0.181319	+	0.264322i
$953$	−16.9519	−	19.5636i	−0.549126	−	0.633726i	0.411553	−	0.911386i	$-0.364987\pi$
$953$	−16.9519	−	19.5636i	−0.549126	−	0.633726i	−0.960679	+	0.277660i	$0.910441\pi$
$954$	−0.438240	−	9.19979i	−0.0141885	−	0.297854i
$955$	−6.85542	−	3.53421i	−0.221836	−	0.114364i
$956$	6.60671	−	19.0888i	0.213676	−	0.617377i
$957$	−13.3490	+	55.0253i	−0.431512	+	1.77872i
$958$	2.69324	−	18.7319i	0.0870146	−	0.605200i
$959$	0.800635	−	26.6311i	0.0258538	−	0.859963i
$960$	0.269047	−	0.589131i	0.00868345	−	0.0190141i
$961$	20.8823	−	19.9112i	0.673623	−	0.642298i
$962$	−4.19805	+	5.89533i	−0.135350	+	0.190073i
$963$	−1.24115	+	0.976051i	−0.0399955	+	0.0314528i
$964$	0.789601	−	0.407068i	0.0254313	−	0.0131108i
$965$	−8.65453			−0.278599
$966$	−4.56117	−	11.8404i	−0.146753	−	0.380960i
$967$	16.5009			0.530632			0.265316	−	0.964162i	$-0.414524\pi$
$967$	16.5009			0.530632			0.265316	+	0.964162i	$0.414524\pi$
$968$	22.3261	−	11.5099i	0.717587	−	0.369942i
$969$	−4.18412	+	3.29043i	−0.134413	+	0.105704i
$970$	−3.34852	+	4.70233i	−0.107514	+	0.150983i
$971$	−2.47998	+	2.36466i	−0.0795864	+	0.0758855i	−0.728828	−	0.684696i	$-0.759935\pi$
$971$	−2.47998	+	2.36466i	−0.0795864	+	0.0758855i	0.649242	+	0.760582i	$0.275086\pi$
$972$	0.415415	−	0.909632i	0.0133244	−	0.0291765i
$973$	−14.7505	−	9.11793i	−0.472880	−	0.292307i
$974$	0.315329	−	2.19316i	0.0101038	−	0.0702733i
$975$	−2.04874	+	8.44503i	−0.0656123	+	0.270457i
$976$	−0.764626	+	2.20924i	−0.0244751	+	0.0707161i
$977$	8.71252	+	4.49161i	0.278738	+	0.143699i	0.591928	−	0.805991i	$-0.298367\pi$
$977$	8.71252	+	4.49161i	0.278738	+	0.143699i	−0.313189	+	0.949691i	$0.601397\pi$
$978$	−0.316332	−	6.64063i	−0.0101152	−	0.212344i
$979$	−56.8303	−	65.5856i	−1.81630	−	2.09613i
$980$	3.72558	−	2.58335i	0.119009	−	0.0825220i
$981$	−2.22966	+	15.5077i	−0.0711877	+	0.495121i
$982$	−4.21800	−	12.1871i	−0.134602	−	0.388907i
$983$	16.4477	−	1.57056i	0.524599	−	0.0500931i	0.170603	−	0.985340i	$-0.445429\pi$
$983$	16.4477	−	1.57056i	0.524599	−	0.0500931i	0.353996	+	0.935247i	$0.384822\pi$
$984$	1.22649	+	5.05565i	0.0390990	+	0.161168i
$985$	−11.3461	−	1.08342i	−0.361516	−	0.0345206i
$986$	5.01202	+	34.8594i	0.159615	+	1.11015i
$987$	−3.43417	+	7.88292i	−0.109311	+	0.250916i
$988$	2.70153			0.0859470
$989$	−45.8281	−	3.59310i	−1.45725	−	0.114254i
$990$	−1.94617	−	3.37086i	−0.0618532	−	0.107133i
$991$	−0.281881	+	5.91741i	−0.00895424	+	0.187973i	0.989959	+	0.141357i	$0.0451466\pi$
$991$	−0.281881	+	5.91741i	−0.00895424	+	0.187973i	−0.998913	+	0.0466155i	$0.985156\pi$
$992$	−7.18233	−	2.87537i	−0.228039	−	0.0912931i
$993$	−10.2463	−	22.4363i	−0.325157	−	0.711995i
$994$	−21.8417	−	16.5647i	−0.692777	−	0.525400i
$995$	−5.49866	+	12.0404i	−0.174319	+	0.381706i
$996$	−1.73466	−	5.01196i	−0.0549647	−	0.158810i
$997$	49.6205	−	19.8650i	1.57150	−	0.629132i	0.587806	−	0.809002i	$-0.299992\pi$
$997$	49.6205	−	19.8650i	1.57150	−	0.629132i	0.983690	+	0.179870i	$0.0575677\pi$
$998$	1.27182	+	1.21268i	0.0402589	+	0.0383867i
$999$	3.74588	−	0.721960i	0.118514	−	0.0228418i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.y.b.163.6	yes	160
7.4	even	3	inner	966.2.y.b.25.6	✓	160
23.12	even	11	inner	966.2.y.b.541.6	yes	160
161.81	even	33	inner	966.2.y.b.403.6	yes	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.y.b.25.6	✓	160	7.4	even	3	inner
966.2.y.b.163.6	yes	160	1.1	even	1	trivial
966.2.y.b.403.6	yes	160	161.81	even	33	inner
966.2.y.b.541.6	yes	160	23.12	even	11	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:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.y (of order \(33\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.888835 - 0.458227i) q^{2} +(-0.786053 + 0.618159i) q^{3} +(0.580057 - 0.814576i) q^{4} +(0.468732 - 0.446935i) q^{5} +(-0.415415 + 0.909632i) q^{6} +(2.25050 + 1.39113i) q^{7} +(0.142315 - 0.989821i) q^{8} +(0.235759 - 0.971812i) q^{9} +O(q^{10})\)	\(q+(0.888835 - 0.458227i) q^{2} +(-0.786053 + 0.618159i) q^{3} +(0.580057 - 0.814576i) q^{4} +(0.468732 - 0.446935i) q^{5} +(-0.415415 + 0.909632i) q^{6} +(2.25050 + 1.39113i) q^{7} +(0.142315 - 0.989821i) q^{8} +(0.235759 - 0.971812i) q^{9} +(0.211828 - 0.612037i) q^{10} +(5.34177 + 2.75387i) q^{11} +(0.0475819 + 0.998867i) q^{12} +(-1.24237 - 1.43377i) q^{13} +(2.63778 + 0.205249i) q^{14} +(-0.0921714 + 0.641066i) q^{15} +(-0.327068 - 0.945001i) q^{16} +(-3.72113 + 0.355325i) q^{17} +(-0.235759 - 0.971812i) q^{18} +(-1.41754 - 0.135359i) q^{19} +(-0.0921714 - 0.641066i) q^{20} +(-2.62895 + 0.297663i) q^{21} +6.00985 q^{22} +(-1.05148 + 4.67915i) q^{23} +(0.500000 + 0.866025i) q^{24} +(-0.217951 + 4.57535i) q^{25} +(-1.76126 - 0.705101i) q^{26} +(0.415415 + 0.909632i) q^{27} +(2.43860 - 1.02627i) q^{28} +(3.91380 - 8.57003i) q^{29} +(0.211828 + 0.612037i) q^{30} +(7.18233 - 2.87537i) q^{31} +(-0.723734 - 0.690079i) q^{32} +(-5.90125 + 1.13737i) q^{33} +(-3.14465 + 2.02095i) q^{34} +(1.67663 - 0.353759i) q^{35} +(-0.654861 - 0.755750i) q^{36} +(0.899378 - 3.70729i) q^{37} +(-1.32199 + 0.529244i) q^{38} +(1.86287 + 0.359039i) q^{39} +(-0.375679 - 0.527567i) q^{40} +(4.99156 + 1.46566i) q^{41} +(-2.20031 + 1.46923i) q^{42} +(1.36411 + 9.48758i) q^{43} +(5.34177 - 2.75387i) q^{44} +(-0.323829 - 0.560888i) q^{45} +(1.20952 + 4.64080i) q^{46} +(1.62496 - 2.81451i) q^{47} +(0.841254 + 0.540641i) q^{48} +(3.12950 + 6.26149i) q^{49} +(1.90282 + 4.16660i) q^{50} +(2.70536 - 2.57955i) q^{51} +(-1.88856 + 0.180336i) q^{52} +(9.04378 + 1.74305i) q^{53} +(0.786053 + 0.618159i) q^{54} +(3.73466 - 1.09660i) q^{55} +(1.69725 - 2.02961i) q^{56} +(1.19794 - 0.769867i) q^{57} +(-0.448290 - 9.41076i) q^{58} +(4.48148 - 12.9484i) q^{59} +(0.468732 + 0.446935i) q^{60} +(-1.83765 - 1.44514i) q^{61} +(5.06634 - 5.84686i) q^{62} +(1.88249 - 1.85909i) q^{63} +(-0.959493 - 0.281733i) q^{64} +(-1.22314 - 0.116796i) q^{65} +(-4.72406 + 3.71504i) q^{66} +(-0.269278 + 5.65284i) q^{67} +(-1.86903 + 3.23725i) q^{68} +(-2.06594 - 4.32804i) q^{69} +(1.32814 - 1.08271i) q^{70} +(-8.71620 - 5.60156i) q^{71} +(-0.928368 - 0.371662i) q^{72} +(-5.41226 + 7.60046i) q^{73} +(-0.899378 - 3.70729i) q^{74} +(-2.65697 - 3.73120i) q^{75} +(-0.932515 + 1.07618i) q^{76} +(8.19065 + 13.6287i) q^{77} +(1.82031 - 0.534490i) q^{78} +(-5.49831 + 1.05971i) q^{79} +(-0.575662 - 0.296774i) q^{80} +(-0.888835 - 0.458227i) q^{81} +(5.10828 - 0.984540i) q^{82} +(-5.08882 + 1.49421i) q^{83} +(-1.28247 + 2.31414i) q^{84} +(-1.58541 + 1.82966i) q^{85} +(5.55993 + 7.80783i) q^{86} +(2.22119 + 9.15585i) q^{87} +(3.48606 - 4.89548i) q^{88} +(-13.4056 - 5.36680i) q^{89} +(-0.544845 - 0.350150i) q^{90} +(-0.801389 - 4.95501i) q^{91} +(3.20160 + 3.57068i) q^{92} +(-3.86825 + 6.70001i) q^{93} +(0.154637 - 3.24624i) q^{94} +(-0.724944 + 0.570102i) q^{95} +(0.995472 + 0.0950560i) q^{96} +(-8.55220 - 2.51115i) q^{97} +(5.65079 + 4.13141i) q^{98} +(3.93562 - 4.54194i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q - 8 q^{2} + 8 q^{3} + 8 q^{4} + 6 q^{5} + 16 q^{6} - 10 q^{7} + 16 q^{8} + 8 q^{9}+O(q^{10}) \) 160 * q - 8 * q^2 + 8 * q^3 + 8 * q^4 + 6 * q^5 + 16 * q^6 - 10 * q^7 + 16 * q^8 + 8 * q^9	\( 160 q - 8 q^{2} + 8 q^{3} + 8 q^{4} + 6 q^{5} + 16 q^{6} - 10 q^{7} + 16 q^{8} + 8 q^{9} - 6 q^{10} + 8 q^{11} + 8 q^{12} + 4 q^{13} - 13 q^{14} + 10 q^{15} + 8 q^{16} + 9 q^{17} - 8 q^{18} - 8 q^{19} + 10 q^{20} - 3 q^{21} - 28 q^{22} + 22 q^{23} + 80 q^{24} + 46 q^{25} + 2 q^{26} - 16 q^{27} - 14 q^{28} + 62 q^{29} - 6 q^{30} + 7 q^{31} - 8 q^{32} - 14 q^{33} - 4 q^{34} + 24 q^{35} - 16 q^{36} + 15 q^{37} + 19 q^{38} - 2 q^{39} + 5 q^{40} - 14 q^{41} + 10 q^{42} - 56 q^{43} + 8 q^{44} - 16 q^{45} + 66 q^{47} - 16 q^{48} + 42 q^{49} + 4 q^{50} + 9 q^{51} - 2 q^{52} + 12 q^{53} - 8 q^{54} - 14 q^{55} + 10 q^{56} - 6 q^{57} - 13 q^{58} + 62 q^{59} + 6 q^{60} + 16 q^{61} - 8 q^{62} + 2 q^{63} - 16 q^{64} + 70 q^{65} - 8 q^{66} - 14 q^{67} - 46 q^{68} + 22 q^{69} + 24 q^{70} - 108 q^{71} - 8 q^{72} + 40 q^{73} - 15 q^{74} + 2 q^{75} + 16 q^{76} + 29 q^{77} + 18 q^{78} + 22 q^{79} + 6 q^{80} + 8 q^{81} - 7 q^{82} - 18 q^{83} - 9 q^{84} + 26 q^{85} - 6 q^{86} + 2 q^{87} + 3 q^{88} + 112 q^{89} + 12 q^{90} + 18 q^{91} - 66 q^{92} - 26 q^{93} + 23 q^{95} - 8 q^{96} + 8 q^{97} + 9 q^{98} + 28 q^{99}+O(q^{100}) \) 160 * q - 8 * q^2 + 8 * q^3 + 8 * q^4 + 6 * q^5 + 16 * q^6 - 10 * q^7 + 16 * q^8 + 8 * q^9 - 6 * q^10 + 8 * q^11 + 8 * q^12 + 4 * q^13 - 13 * q^14 + 10 * q^15 + 8 * q^16 + 9 * q^17 - 8 * q^18 - 8 * q^19 + 10 * q^20 - 3 * q^21 - 28 * q^22 + 22 * q^23 + 80 * q^24 + 46 * q^25 + 2 * q^26 - 16 * q^27 - 14 * q^28 + 62 * q^29 - 6 * q^30 + 7 * q^31 - 8 * q^32 - 14 * q^33 - 4 * q^34 + 24 * q^35 - 16 * q^36 + 15 * q^37 + 19 * q^38 - 2 * q^39 + 5 * q^40 - 14 * q^41 + 10 * q^42 - 56 * q^43 + 8 * q^44 - 16 * q^45 + 66 * q^47 - 16 * q^48 + 42 * q^49 + 4 * q^50 + 9 * q^51 - 2 * q^52 + 12 * q^53 - 8 * q^54 - 14 * q^55 + 10 * q^56 - 6 * q^57 - 13 * q^58 + 62 * q^59 + 6 * q^60 + 16 * q^61 - 8 * q^62 + 2 * q^63 - 16 * q^64 + 70 * q^65 - 8 * q^66 - 14 * q^67 - 46 * q^68 + 22 * q^69 + 24 * q^70 - 108 * q^71 - 8 * q^72 + 40 * q^73 - 15 * q^74 + 2 * q^75 + 16 * q^76 + 29 * q^77 + 18 * q^78 + 22 * q^79 + 6 * q^80 + 8 * q^81 - 7 * q^82 - 18 * q^83 - 9 * q^84 + 26 * q^85 - 6 * q^86 + 2 * q^87 + 3 * q^88 + 112 * q^89 + 12 * q^90 + 18 * q^91 - 66 * q^92 - 26 * q^93 + 23 * q^95 - 8 * q^96 + 8 * q^97 + 9 * q^98 + 28 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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