LMFDB - Embedded newform 966.2.y.a.25.1

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			25.1
Character	$\chi$	$=$	966.25
Dual form			966.2.y.a.541.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0475819 + 0.998867i) q^{2} +(-0.928368 - 0.371662i) q^{3} +(-0.995472 - 0.0950560i) q^{4} +(-0.740155 - 3.05096i) q^{5} +(0.415415 - 0.909632i) q^{6} +(0.385204 - 2.61756i) q^{7} +(0.142315 - 0.989821i) q^{8} +(0.723734 + 0.690079i) q^{9} +O(q^{10})$	\(q+(-0.0475819 + 0.998867i) q^{2} +(-0.928368 - 0.371662i) q^{3} +(-0.995472 - 0.0950560i) q^{4} +(-0.740155 - 3.05096i) q^{5} +(0.415415 - 0.909632i) q^{6} +(0.385204 - 2.61756i) q^{7} +(0.142315 - 0.989821i) q^{8} +(0.723734 + 0.690079i) q^{9} +(3.08272 - 0.594146i) q^{10} +(-0.102640 - 2.15469i) q^{11} +(0.888835 + 0.458227i) q^{12} +(-0.489466 - 0.564874i) q^{13} +(2.59627 + 0.509316i) q^{14} +(-0.446791 + 3.10750i) q^{15} +(0.981929 + 0.189251i) q^{16} +(-0.946382 - 1.32901i) q^{17} +(-0.723734 + 0.690079i) q^{18} +(-2.69214 + 3.78059i) q^{19} +(0.446791 + 3.10750i) q^{20} +(-1.33046 + 2.28689i) q^{21} +2.15713 q^{22} +(-2.57762 + 4.04424i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(-4.31635 + 2.22523i) q^{25} +(0.587524 - 0.462034i) q^{26} +(-0.415415 - 0.909632i) q^{27} +(-0.632274 + 2.56909i) q^{28} +(0.164279 - 0.359722i) q^{29} +(-3.08272 - 0.594146i) q^{30} +(-1.86611 - 1.46752i) q^{31} +(-0.235759 + 0.971812i) q^{32} +(-0.705528 + 2.03849i) q^{33} +(1.37253 - 0.882073i) q^{34} +(-8.27118 + 0.762159i) q^{35} +(-0.654861 - 0.755750i) q^{36} +(5.45116 + 5.19767i) q^{37} +(-3.64821 - 2.86898i) q^{38} +(0.244462 + 0.706327i) q^{39} +(-3.12524 + 0.298424i) q^{40} +(-7.30136 - 2.14387i) q^{41} +(-2.22100 - 1.43777i) q^{42} +(0.272585 + 1.89587i) q^{43} +(-0.102640 + 2.15469i) q^{44} +(1.56973 - 2.71885i) q^{45} +(-3.91701 - 2.76713i) q^{46} +(-3.22145 - 5.57971i) q^{47} +(-0.841254 - 0.540641i) q^{48} +(-6.70324 - 2.01659i) q^{49} +(-2.01733 - 4.41734i) q^{50} +(0.384648 + 1.58554i) q^{51} +(0.433555 + 0.608843i) q^{52} +(-0.930128 - 2.68743i) q^{53} +(0.928368 - 0.371662i) q^{54} +(-6.49789 + 1.90795i) q^{55} +(-2.53610 - 0.753800i) q^{56} +(3.90440 - 2.50921i) q^{57} +(0.351498 + 0.181210i) q^{58} +(9.53303 - 1.83734i) q^{59} +(0.740155 - 3.05096i) q^{60} +(-5.84014 + 2.33804i) q^{61} +(1.55465 - 1.79417i) q^{62} +(2.08511 - 1.62860i) q^{63} +(-0.959493 - 0.281733i) q^{64} +(-1.36113 + 1.91144i) q^{65} +(-2.00261 - 0.801724i) q^{66} +(-9.85157 + 5.07884i) q^{67} +(0.815766 + 1.41295i) q^{68} +(3.89607 - 2.79654i) q^{69} +(-0.367737 - 8.29808i) q^{70} +(-0.279477 - 0.179609i) q^{71} +(0.786053 - 0.618159i) q^{72} +(7.62906 + 0.728487i) q^{73} +(-5.45116 + 5.19767i) q^{74} +(4.83419 - 0.461610i) q^{75} +(3.03932 - 3.50756i) q^{76} +(-5.67956 - 0.561325i) q^{77} +(-0.717159 + 0.210577i) q^{78} +(0.205206 - 0.592905i) q^{79} +(-0.149381 - 3.13590i) q^{80} +(0.0475819 + 0.998867i) q^{81} +(2.48886 - 7.19108i) q^{82} +(-5.82846 + 1.71139i) q^{83} +(1.54182 - 2.15007i) q^{84} +(-3.35428 + 3.87104i) q^{85} +(-1.90670 + 0.182067i) q^{86} +(-0.286207 + 0.272898i) q^{87} +(-2.14736 - 0.205048i) q^{88} +(10.2206 - 8.03754i) q^{89} +(2.64108 + 1.69732i) q^{90} +(-1.66714 + 1.06362i) q^{91} +(2.95038 - 3.78091i) q^{92} +(1.18701 + 2.05596i) q^{93} +(5.72668 - 2.95231i) q^{94} +(13.5270 + 5.41540i) q^{95} +(0.580057 - 0.814576i) q^{96} +(-10.7845 - 3.16660i) q^{97} +(2.33326 - 6.59969i) q^{98} +(1.41262 - 1.63025i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q - 8 q^{2} - 8 q^{3} + 8 q^{4} + 2 q^{5} - 16 q^{6} - 2 q^{7} + 16 q^{8} + 8 q^{9}+O(q^{10}) $ 160 * q - 8 * q^2 - 8 * q^3 + 8 * q^4 + 2 * q^5 - 16 * q^6 - 2 * q^7 + 16 * q^8 + 8 * q^9	\( 160 q - 8 q^{2} - 8 q^{3} + 8 q^{4} + 2 q^{5} - 16 q^{6} - 2 q^{7} + 16 q^{8} + 8 q^{9} - 2 q^{10} + 4 q^{11} - 8 q^{12} + 4 q^{13} - 9 q^{14} - 18 q^{15} + 8 q^{16} + 9 q^{17} - 8 q^{18} + 18 q^{20} + 7 q^{21} + 52 q^{22} + 22 q^{23} - 80 q^{24} + 42 q^{25} + 2 q^{26} + 16 q^{27} - 18 q^{28} - 54 q^{29} + 2 q^{30} - 15 q^{31} - 8 q^{32} + 18 q^{33} + 84 q^{34} + 82 q^{35} - 16 q^{36} + 3 q^{37} + 11 q^{38} + 2 q^{39} - 13 q^{40} + 22 q^{41} - 2 q^{42} - 96 q^{43} + 4 q^{44} - 20 q^{45} - 26 q^{47} + 16 q^{48} - 2 q^{49} - 4 q^{50} + 13 q^{51} - 2 q^{52} + 16 q^{53} + 8 q^{54} - 34 q^{55} + 2 q^{56} - 22 q^{57} - 5 q^{58} - 6 q^{59} - 2 q^{60} + 40 q^{61} - 8 q^{62} - 2 q^{63} - 16 q^{64} - 82 q^{65} + 4 q^{66} + 10 q^{67} - 46 q^{68} - 22 q^{69} + 100 q^{70} + 92 q^{71} - 8 q^{72} + 68 q^{73} - 3 q^{74} + 2 q^{75} - 7 q^{77} - 18 q^{78} - 78 q^{79} + 2 q^{80} + 8 q^{81} + 55 q^{82} - 42 q^{83} - 9 q^{84} + 50 q^{85} + 40 q^{86} + 6 q^{87} + 7 q^{88} - 80 q^{89} + 4 q^{90} - 62 q^{91} + 66 q^{92} + 26 q^{93} + 4 q^{94} - 17 q^{95} + 8 q^{96} - 8 q^{97} - 3 q^{98} + 36 q^{99}+O(q^{100}) \) 160 * q - 8 * q^2 - 8 * q^3 + 8 * q^4 + 2 * q^5 - 16 * q^6 - 2 * q^7 + 16 * q^8 + 8 * q^9 - 2 * q^10 + 4 * q^11 - 8 * q^12 + 4 * q^13 - 9 * q^14 - 18 * q^15 + 8 * q^16 + 9 * q^17 - 8 * q^18 + 18 * q^20 + 7 * q^21 + 52 * q^22 + 22 * q^23 - 80 * q^24 + 42 * q^25 + 2 * q^26 + 16 * q^27 - 18 * q^28 - 54 * q^29 + 2 * q^30 - 15 * q^31 - 8 * q^32 + 18 * q^33 + 84 * q^34 + 82 * q^35 - 16 * q^36 + 3 * q^37 + 11 * q^38 + 2 * q^39 - 13 * q^40 + 22 * q^41 - 2 * q^42 - 96 * q^43 + 4 * q^44 - 20 * q^45 - 26 * q^47 + 16 * q^48 - 2 * q^49 - 4 * q^50 + 13 * q^51 - 2 * q^52 + 16 * q^53 + 8 * q^54 - 34 * q^55 + 2 * q^56 - 22 * q^57 - 5 * q^58 - 6 * q^59 - 2 * q^60 + 40 * q^61 - 8 * q^62 - 2 * q^63 - 16 * q^64 - 82 * q^65 + 4 * q^66 + 10 * q^67 - 46 * q^68 - 22 * q^69 + 100 * q^70 + 92 * q^71 - 8 * q^72 + 68 * q^73 - 3 * q^74 + 2 * q^75 - 7 * q^77 - 18 * q^78 - 78 * q^79 + 2 * q^80 + 8 * q^81 + 55 * q^82 - 42 * q^83 - 9 * q^84 + 50 * q^85 + 40 * q^86 + 6 * q^87 + 7 * q^88 - 80 * q^89 + 4 * q^90 - 62 * q^91 + 66 * q^92 + 26 * q^93 + 4 * q^94 - 17 * q^95 + 8 * q^96 - 8 * q^97 - 3 * q^98 + 36 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$323$	$829$	$925$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{11}\right)$

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 $

$2$	−0.0475819	+	0.998867i	−0.0336455	+	0.706306i
$2$	−0.0475819	+	0.998867i	−0.0336455	+	0.706306i
$3$	−0.928368	−	0.371662i	−0.535993	−	0.214579i
$3$	−0.928368	−	0.371662i	−0.535993	−	0.214579i
$4$	−0.995472	−	0.0950560i	−0.497736	−	0.0475280i
$5$	−0.740155	−	3.05096i	−0.331007	−	1.36443i	−0.857602	−	0.514314i	$-0.828047\pi$
$5$	−0.740155	−	3.05096i	−0.331007	−	1.36443i	0.526595	−	0.850117i	$-0.323469\pi$
$6$	0.415415	−	0.909632i	0.169592	−	0.371356i
$7$	0.385204	−	2.61756i	0.145593	−	0.989345i
$7$	0.385204	−	2.61756i	0.145593	−	0.989345i
$8$	0.142315	−	0.989821i	0.0503159	−	0.349955i
$9$	0.723734	+	0.690079i	0.241245	+	0.230026i
$10$	3.08272	−	0.594146i	0.974842	−	0.187885i
$11$	−0.102640	−	2.15469i	−0.0309472	−	0.649662i	−0.960048	−	0.279836i	$-0.909720\pi$
$11$	−0.102640	−	2.15469i	−0.0309472	−	0.649662i	0.929101	−	0.369827i	$-0.120583\pi$
$12$	0.888835	+	0.458227i	0.256585	+	0.132279i
$13$	−0.489466	−	0.564874i	−0.135753	−	0.156668i	0.683802	−	0.729667i	$-0.260325\pi$
$13$	−0.489466	−	0.564874i	−0.135753	−	0.156668i	−0.819556	+	0.573000i	$0.805780\pi$
$14$	2.59627	+	0.509316i	0.693881	+	0.136120i
$15$	−0.446791	+	3.10750i	−0.115361	+	0.802353i
$16$	0.981929	+	0.189251i	0.245482	+	0.0473128i
$17$	−0.946382	−	1.32901i	−0.229531	−	0.322332i	0.683708	−	0.729756i	$-0.260366\pi$
$17$	−0.946382	−	1.32901i	−0.229531	−	0.322332i	−0.913239	+	0.407424i	$0.866427\pi$
$18$	−0.723734	+	0.690079i	−0.170586	+	0.162653i
$19$	−2.69214	+	3.78059i	−0.617620	+	0.867326i	−0.998354	−	0.0573585i	$-0.981732\pi$
$19$	−2.69214	+	3.78059i	−0.617620	+	0.867326i	0.380733	+	0.924685i	$0.375672\pi$
$20$	0.446791	+	3.10750i	0.0999055	+	0.694858i
$21$	−1.33046	+	2.28689i	−0.290330	+	0.499041i
$22$	2.15713			0.459902
$23$	−2.57762	+	4.04424i	−0.537471	+	0.843282i
$23$	−2.57762	+	4.04424i	−0.537471	+	0.843282i
$24$	−0.500000	+	0.866025i	−0.102062	+	0.176777i
$25$	−4.31635	+	2.22523i	−0.863270	+	0.445046i
$26$	0.587524	−	0.462034i	0.115223	−	0.0906123i
$27$	−0.415415	−	0.909632i	−0.0799467	−	0.175059i
$28$	−0.632274	+	2.56909i	−0.119489	+	0.485513i
$29$	0.164279	−	0.359722i	0.0305059	−	0.0667986i	−0.893766	−	0.448534i	$-0.851946\pi$
$29$	0.164279	−	0.359722i	0.0305059	−	0.0667986i	0.924272	+	0.381736i	$0.124673\pi$
$30$	−3.08272	−	0.594146i	−0.562825	−	0.108476i
$31$	−1.86611	−	1.46752i	−0.335163	−	0.263575i	0.436366	−	0.899769i	$-0.356265\pi$
$31$	−1.86611	−	1.46752i	−0.335163	−	0.263575i	−0.771529	+	0.636194i	$0.780508\pi$
$32$	−0.235759	+	0.971812i	−0.0416767	+	0.171794i
$33$	−0.705528	+	2.03849i	−0.122817	+	0.354855i
$34$	1.37253	−	0.882073i	0.235387	−	0.151274i
$35$	−8.27118	+	0.762159i	−1.39808	+	0.128828i
$36$	−0.654861	−	0.755750i	−0.109143	−	0.125958i
$37$	5.45116	+	5.19767i	0.896165	+	0.854492i	0.989996	−	0.141096i	$-0.0450627\pi$
$37$	5.45116	+	5.19767i	0.896165	+	0.854492i	−0.0938305	+	0.995588i	$0.529911\pi$
$38$	−3.64821	−	2.86898i	−0.591818	−	0.465411i
$39$	0.244462	+	0.706327i	0.0391453	+	0.113103i
$40$	−3.12524	+	0.298424i	−0.494144	+	0.0471850i
$41$	−7.30136	−	2.14387i	−1.14028	−	0.334817i	−0.343540	−	0.939138i	$-0.611626\pi$
$41$	−7.30136	−	2.14387i	−1.14028	−	0.334817i	−0.796741	+	0.604321i	$0.793444\pi$
$42$	−2.22100	−	1.43777i	−0.342707	−	0.221852i
$43$	0.272585	+	1.89587i	0.0415689	+	0.289118i	0.999993	+	0.00377005i	$0.00120005\pi$
$43$	0.272585	+	1.89587i	0.0415689	+	0.289118i	−0.958424	+	0.285348i	$0.907891\pi$
$44$	−0.102640	+	2.15469i	−0.0154736	+	0.324831i
$45$	1.56973	−	2.71885i	0.234001	−	0.405302i
$46$	−3.91701	−	2.76713i	−0.577532	−	0.407992i
$47$	−3.22145	−	5.57971i	−0.469897	−	0.813885i	0.529511	−	0.848303i	$-0.322375\pi$
$47$	−3.22145	−	5.57971i	−0.469897	−	0.813885i	−0.999408	+	0.0344183i	$0.989042\pi$
$48$	−0.841254	−	0.540641i	−0.121424	−	0.0780348i
$49$	−6.70324	−	2.01659i	−0.957605	−	0.288084i
$50$	−2.01733	−	4.41734i	−0.285294	−	0.624706i
$51$	0.384648	+	1.58554i	0.0538615	+	0.222020i
$52$	0.433555	+	0.608843i	0.0601233	+	0.0844313i
$53$	−0.930128	−	2.68743i	−0.127763	−	0.369147i	0.862919	−	0.505342i	$-0.168634\pi$
$53$	−0.930128	−	2.68743i	−0.127763	−	0.369147i	−0.990682	+	0.136195i	$0.956513\pi$
$54$	0.928368	−	0.371662i	0.126335	−	0.0505769i
$55$	−6.49789	+	1.90795i	−0.876175	+	0.257268i
$56$	−2.53610	−	0.753800i	−0.338900	−	0.100731i
$57$	3.90440	−	2.50921i	0.517151	−	0.332353i
$58$	0.351498	+	0.181210i	0.0461539	+	0.0237940i
$59$	9.53303	−	1.83734i	1.24109	−	0.239201i	0.473879	−	0.880590i	$-0.342854\pi$
$59$	9.53303	−	1.83734i	1.24109	−	0.239201i	0.767216	+	0.641389i	$0.221641\pi$
$60$	0.740155	−	3.05096i	0.0955536	−	0.393877i
$61$	−5.84014	+	2.33804i	−0.747754	+	0.299355i	−0.714067	−	0.700077i	$-0.753149\pi$
$61$	−5.84014	+	2.33804i	−0.747754	+	0.299355i	−0.0336864	+	0.999432i	$0.510725\pi$
$62$	1.55465	−	1.79417i	0.197441	−	0.227859i
$63$	2.08511	−	1.62860i	0.262699	−	0.205184i
$64$	−0.959493	−	0.281733i	−0.119937	−	0.0352166i
$65$	−1.36113	+	1.91144i	−0.168827	+	0.237084i
$66$	−2.00261	−	0.801724i	−0.246504	−	0.0986854i
$67$	−9.85157	+	5.07884i	−1.20356	+	0.620479i	−0.939009	−	0.343893i	$-0.888254\pi$
$67$	−9.85157	+	5.07884i	−1.20356	+	0.620479i	−0.264552	+	0.964371i	$0.585224\pi$
$68$	0.815766	+	1.41295i	0.0989262	+	0.171345i
$69$	3.89607	−	2.79654i	0.469032	−	0.336663i
$70$	−0.367737	−	8.29808i	−0.0439530	−	0.991810i
$71$	−0.279477	−	0.179609i	−0.0331678	−	0.0213156i	0.523952	−	0.851748i	$-0.324457\pi$
$71$	−0.279477	−	0.179609i	−0.0331678	−	0.0213156i	−0.557120	+	0.830432i	$0.688094\pi$
$72$	0.786053	−	0.618159i	0.0926372	−	0.0728507i
$73$	7.62906	+	0.728487i	0.892914	+	0.0852629i	0.531417	−	0.847110i	$-0.321660\pi$
$73$	7.62906	+	0.728487i	0.892914	+	0.0852629i	0.361497	+	0.932373i	$0.382266\pi$
$74$	−5.45116	+	5.19767i	−0.633685	+	0.604217i
$75$	4.83419	−	0.461610i	0.558205	−	0.0533021i
$76$	3.03932	−	3.50756i	0.348634	−	0.402345i
$77$	−5.67956	−	0.561325i	−0.647246	−	0.0639690i
$78$	−0.717159	+	0.210577i	−0.0812023	+	0.0238431i
$79$	0.205206	−	0.592905i	0.0230875	−	0.0667070i	−0.932868	−	0.360218i	$-0.882702\pi$
$79$	0.205206	−	0.592905i	0.0230875	−	0.0667070i	0.955956	+	0.293511i	$0.0948236\pi$
$80$	−0.149381	−	3.13590i	−0.0167013	−	0.350604i
$81$	0.0475819	+	0.998867i	0.00528688	+	0.110985i
$82$	2.48886	−	7.19108i	0.274848	−	0.794122i
$83$	−5.82846	+	1.71139i	−0.639757	+	0.187850i	−0.585493	−	0.810677i	$-0.699099\pi$
$83$	−5.82846	+	1.71139i	−0.639757	+	0.187850i	−0.0542633	+	0.998527i	$0.517281\pi$
$84$	1.54182	−	2.15007i	0.168226	−	0.234592i
$85$	−3.35428	+	3.87104i	−0.363823	+	0.419874i
$86$	−1.90670	+	0.182067i	−0.205604	+	0.0196328i
$87$	−0.286207	+	0.272898i	−0.0306846	+	0.0292577i
$88$	−2.14736	−	0.205048i	−0.228910	−	0.0218582i
$89$	10.2206	−	8.03754i	1.08338	−	0.851977i	0.0937444	−	0.995596i	$-0.470116\pi$
$89$	10.2206	−	8.03754i	1.08338	−	0.851977i	0.989633	+	0.143619i	$0.0458739\pi$
$90$	2.64108	+	1.69732i	0.278394	+	0.178913i
$91$	−1.66714	+	1.06362i	−0.174763	+	0.111497i
$92$	2.95038	−	3.78091i	0.307598	−	0.394187i
$93$	1.18701	+	2.05596i	0.123087	+	0.213193i
$94$	5.72668	−	2.95231i	0.590662	−	0.304507i
$95$	13.5270	+	5.41540i	1.38784	+	0.555609i
$96$	0.580057	−	0.814576i	0.0592018	−	0.0831373i
$97$	−10.7845	−	3.16660i	−1.09500	−	0.321520i	−0.316133	−	0.948715i	$-0.602385\pi$
$97$	−10.7845	−	3.16660i	−1.09500	−	0.321520i	−0.778862	+	0.627195i	$0.784203\pi$
$98$	2.33326	−	6.59969i	0.235694	−	0.666669i
$99$	1.41262	−	1.63025i	0.141974	−	0.163846i
$100$	4.50833	−	1.80486i	0.450833	−	0.180486i
$101$	4.18507	−	17.2511i	0.416430	−	1.71655i	−0.247619	−	0.968857i	$-0.579648\pi$
$101$	4.18507	−	17.2511i	0.416430	−	1.71655i	0.664049	−	0.747689i	$-0.268837\pi$
$102$	−1.60205	+	0.308770i	−0.158626	+	0.0305727i
$103$	1.47181	+	0.758770i	0.145022	+	0.0747638i	0.529210	−	0.848491i	$-0.322488\pi$
$103$	1.47181	+	0.758770i	0.145022	+	0.0747638i	−0.384188	+	0.923255i	$0.625519\pi$
$104$	−0.628783	+	0.404094i	−0.0616572	+	0.0396247i
$105$	7.96196	+	2.36652i	0.777008	+	0.230949i
$106$	2.72864	−	0.801202i	0.265029	−	0.0778196i
$107$	−12.4565	+	4.98684i	−1.20422	+	0.482096i	−0.885002	−	0.465586i	$-0.845843\pi$
$107$	−12.4565	+	4.98684i	−1.20422	+	0.482096i	−0.319215	+	0.947682i	$0.603419\pi$
$108$	0.327068	+	0.945001i	0.0314721	+	0.0909327i
$109$	8.45260	+	11.8700i	0.809613	+	1.13694i	0.988223	+	0.153022i	$0.0489005\pi$
$109$	8.45260	+	11.8700i	0.809613	+	1.13694i	−0.178610	+	0.983920i	$0.557160\pi$
$110$	−1.59661	−	6.58131i	−0.152231	−	0.627504i
$111$	−3.12890	−	6.85134i	−0.296982	−	0.650301i
$112$	0.873619	−	2.49736i	0.0825492	−	0.235978i
$113$	−12.2148	−	7.84998i	−1.14907	−	0.738464i	−0.179618	−	0.983736i	$-0.557486\pi$
$113$	−12.2148	−	7.84998i	−1.14907	−	0.738464i	−0.969454	+	0.245272i	$0.921123\pi$
$114$	2.32059	+	4.01937i	0.217343	+	0.376449i
$115$	14.2466	+	4.87086i	1.32851	+	0.454210i
$116$	−0.197729	+	0.342477i	−0.0183587	+	0.0317982i
$117$	0.0355644	−	0.746589i	0.00328793	−	0.0690222i
$118$	1.38166	+	9.60966i	0.127192	+	0.884641i
$119$	−3.84330	+	1.96527i	−0.352315	+	0.180156i
$120$	3.01229	+	0.884487i	0.274983	+	0.0807422i
$121$	6.31805	−	0.603301i	0.574369	−	0.0548455i
$122$	−2.05751	−	5.94478i	−0.186278	−	0.538215i
$123$	5.98155	+	4.70395i	0.539338	+	0.424140i
$124$	1.71816	+	1.63826i	0.154295	+	0.147120i
$125$	−0.295673	−	0.341224i	−0.0264458	−	0.0305200i
$126$	1.52754	+	2.16024i	0.136084	+	0.192449i
$127$	−11.5034	+	7.39277i	−1.02076	+	0.656002i	−0.940156	−	0.340744i	$-0.889321\pi$
$127$	−11.5034	+	7.39277i	−1.02076	+	0.656002i	−0.0806031	+	0.996746i	$0.525685\pi$
$128$	0.327068	−	0.945001i	0.0289090	−	0.0835271i
$129$	0.451565	−	1.86138i	0.0397581	−	0.163885i
$130$	−1.84451	−	1.45054i	−0.161774	−	0.127220i
$131$	5.71731	+	1.10192i	0.499523	+	0.0962752i	0.432788	−	0.901496i	$-0.357530\pi$
$131$	5.71731	+	1.10192i	0.499523	+	0.0962752i	0.0667349	+	0.997771i	$0.478742\pi$
$132$	0.896104	−	1.96219i	0.0779958	−	0.170787i
$133$	8.85889	+	8.50315i	0.768163	+	0.737316i
$134$	−4.60433	−	10.0821i	−0.397753	−	0.870959i
$135$	−2.46778	+	1.94068i	−0.212393	+	0.167027i
$136$	−1.45016	+	0.747611i	−0.124351	+	0.0641072i
$137$	2.53707	−	4.39433i	0.216756	−	0.375433i	−0.737058	−	0.675829i	$-0.763786\pi$
$137$	2.53707	−	4.39433i	0.216756	−	0.375433i	0.953814	+	0.300396i	$0.0971189\pi$
$138$	2.60799	+	4.02472i	0.222007	+	0.342607i
$139$	−12.2236			−1.03679			−0.518397	−	0.855140i	$-0.673471\pi$
$139$	−12.2236			−1.03679			−0.518397	+	0.855140i	$0.673471\pi$
$140$	8.30617	+	0.0275178i	0.702000	+	0.00232567i
$141$	0.916920	+	6.37732i	0.0772186	+	0.537067i
$142$	0.192703	−	0.270614i	0.0161713	−	0.0227094i
$143$	−1.16689	+	1.11262i	−0.0975800	+	0.0930423i
$144$	0.580057	+	0.814576i	0.0483381	+	0.0678813i
$145$	−1.21909	−	0.234960i	−0.101240	−	0.0195124i
$146$	−1.09067	+	7.58575i	−0.0902642	+	0.627802i
$147$	5.47358	+	4.36348i	0.451453	+	0.359893i
$148$	−4.93241	−	5.69230i	−0.405441	−	0.467904i
$149$	7.31358	+	3.77041i	0.599152	+	0.308884i	0.730991	−	0.682387i	$-0.239058\pi$
$149$	7.31358	+	3.77041i	0.599152	+	0.308884i	−0.131839	+	0.991271i	$0.542088\pi$
$150$	0.231067	+	4.85068i	0.0188665	+	0.396057i
$151$	9.96886	−	1.92134i	0.811254	−	0.156356i	0.233278	−	0.972410i	$-0.425055\pi$
$151$	9.96886	−	1.92134i	0.811254	−	0.156356i	0.577976	+	0.816054i	$0.303843\pi$
$152$	3.35898	+	3.20278i	0.272449	+	0.259779i
$153$	0.232191	−	1.61493i	0.0187716	−	0.130559i
$154$	0.830934	−	5.64641i	0.0669586	−	0.455001i
$155$	−3.09615	+	6.77961i	−0.248688	+	0.544552i
$156$	−0.176215	−	0.726366i	−0.0141085	−	0.0581558i
$157$	−0.0784610	−	0.00749212i	−0.00626187	−	0.000597936i	0.0919246	−	0.995766i	$-0.470698\pi$
$157$	−0.0784610	−	0.00749212i	−0.00626187	−	0.000597936i	−0.0981865	+	0.995168i	$0.531304\pi$
$158$	0.582469	+	0.233185i	0.0463388	+	0.0185512i
$159$	−0.135315	+	2.84062i	−0.0107312	+	0.225276i
$160$	3.13946			0.248196
$161$	9.59313	+	8.30493i	0.756044	+	0.654520i
$162$	−1.00000			−0.0785674
$163$	−0.350963	+	7.36762i	−0.0274895	+	0.577076i	0.942541	+	0.334092i	$0.108430\pi$
$163$	−0.350963	+	7.36762i	−0.0274895	+	0.577076i	−0.970030	+	0.242985i	$0.921874\pi$
$164$	7.06451	+	2.82820i	0.551646	+	0.220846i
$165$	6.74155	+	0.643740i	0.524829	+	0.0501151i
$166$	−1.43212	−	5.90329i	−0.111154	−	0.458184i
$167$	1.28289	−	2.80914i	0.0992730	−	0.217377i	−0.853479	−	0.521128i	$-0.825512\pi$
$167$	1.28289	−	2.80914i	0.0992730	−	0.217377i	0.952752	+	0.303750i	$0.0982388\pi$
$168$	2.07427	+	1.64238i	0.160034	+	0.126712i
$169$	1.77059	−	12.3147i	0.136199	−	0.947285i
$170$	−3.70706	−	3.53467i	−0.284318	−	0.271097i
$171$	−4.55730	+	0.878348i	−0.348506	+	0.0671689i
$172$	−0.0911369	−	1.91320i	−0.00694912	−	0.145880i
$173$	−15.1227	−	7.79628i	−1.14976	−	0.592740i	−0.225398	−	0.974267i	$-0.572368\pi$
$173$	−15.1227	−	7.79628i	−1.14976	−	0.592740i	−0.924358	+	0.381527i	$0.875398\pi$
$174$	−0.258970	−	0.298868i	−0.0196325	−	0.0226571i
$175$	4.16201	+	12.1555i	0.314618	+	0.918867i
$176$	0.306992	−	2.13517i	0.0231404	−	0.160945i
$177$	−9.53303	−	1.83734i	−0.716546	−	0.138103i
$178$	7.54212	+	10.5914i	0.565306	+	0.793861i
$179$	−4.10350	+	3.91268i	−0.306710	+	0.292447i	−0.827764	−	0.561076i	$-0.810387\pi$
$179$	−4.10350	+	3.91268i	−0.306710	+	0.292447i	0.521054	+	0.853524i	$0.325539\pi$
$180$	−1.82106	+	2.55733i	−0.135734	+	0.190612i
$181$	3.32637	+	23.1354i	0.247247	+	1.71964i	0.613985	+	0.789318i	$0.289566\pi$
$181$	3.32637	+	23.1354i	0.247247	+	1.71964i	−0.366738	+	0.930324i	$0.619525\pi$
$182$	−0.983085	−	1.71586i	−0.0728711	−	0.127188i
$183$	6.29076			0.465027
$184$	3.63624	+	3.12694i	0.268067	+	0.230521i
$185$	11.8232	−	20.4784i	0.869258	−	1.50560i
$186$	−2.11011	+	1.08784i	−0.154721	+	0.0797643i
$187$	−2.76646	+	2.17557i	−0.202303	+	0.159093i
$188$	2.67648	+	5.86067i	0.195202	+	0.427433i
$189$	−2.54104	+	0.736980i	−0.184833	+	0.0536074i
$190$	−6.05291	+	13.2540i	−0.439124	+	0.961548i
$191$	−23.5563	−	4.54010i	−1.70447	−	0.328510i	−0.758235	−	0.651981i	$-0.773938\pi$
$191$	−23.5563	−	4.54010i	−1.70447	−	0.328510i	−0.946238	+	0.323471i	$0.895150\pi$
$192$	0.786053	+	0.618159i	0.0567285	+	0.0446118i
$193$	1.42919	−	5.89119i	0.102875	−	0.424057i	−0.896962	−	0.442108i	$-0.854231\pi$
$193$	1.42919	−	5.89119i	0.102875	−	0.424057i	0.999837	+	0.0180505i	$0.00574598\pi$
$194$	3.67616	−	10.6216i	0.263933	−	0.762584i
$195$	1.97404	−	1.26864i	0.141364	−	0.0908489i
$196$	6.48120	+	2.64464i	0.462943	+	0.188903i
$197$	4.06503	+	4.69129i	0.289621	+	0.334241i	0.881851	−	0.471529i	$-0.156298\pi$
$197$	4.06503	+	4.69129i	0.289621	+	0.334241i	−0.592229	+	0.805769i	$0.701752\pi$
$198$	1.56119	+	1.48859i	0.110949	+	0.105789i
$199$	1.45059	+	1.14076i	0.102830	+	0.0808662i	0.668250	−	0.743937i	$-0.267044\pi$
$199$	1.45059	+	1.14076i	0.102830	+	0.0808662i	−0.565420	+	0.824803i	$0.691286\pi$
$200$	1.58830	+	4.58910i	0.112310	+	0.324498i
$201$	11.0335	−	1.05357i	0.778243	−	0.0743132i
$202$	17.0324	+	5.00117i	1.19840	+	0.351881i
$203$	−0.878312	−	0.568577i	−0.0616454	−	0.0399063i
$204$	−0.232191	−	1.61493i	−0.0162566	−	0.113067i
$205$	−1.13673	+	23.8630i	−0.0793929	+	1.66666i
$206$	−0.827942	+	1.43404i	−0.0576854	+	0.0999141i
$207$	−4.65636	+	1.14819i	−0.323639	+	0.0798048i
$208$	−0.373718	−	0.647298i	−0.0259127	−	0.0448820i
$209$	8.42230	+	5.41269i	0.582583	+	0.374403i
$210$	−2.74269	+	7.84034i	−0.189263	+	0.541035i
$211$	−4.11581	−	9.01237i	−0.283344	−	0.620437i	0.713427	−	0.700729i	$-0.247142\pi$
$211$	−4.11581	−	9.01237i	−0.283344	−	0.620437i	−0.996771	+	0.0802923i	$0.974415\pi$
$212$	0.670460	+	2.76367i	0.0460474	+	0.189810i
$213$	0.192703	+	0.270614i	0.0132038	+	0.0185422i
$214$	−4.38849	−	12.6797i	−0.299991	−	0.866766i
$215$	5.58248	−	2.23489i	0.380722	−	0.152418i
$216$	−0.959493	+	0.281733i	−0.0652852	+	0.0191695i
$217$	−4.56016	+	4.31935i	−0.309564	+	0.293217i
$218$	−12.2588	+	7.87823i	−0.830269	+	0.533581i
$219$	−6.81182	−	3.51174i	−0.460300	−	0.237301i
$220$	6.64983	−	1.28165i	0.448331	−	0.0864088i
$221$	−0.287500	+	1.18509i	−0.0193393	+	0.0797178i
$222$	6.99246	−	2.79936i	0.469303	−	0.187881i
$223$	11.7105	−	13.5147i	0.784194	−	0.905008i	−0.213211	−	0.977006i	$-0.568392\pi$
$223$	11.7105	−	13.5147i	0.784194	−	0.905008i	0.997405	+	0.0719979i	$0.0229375\pi$
$224$	2.45296	+	0.991458i	0.163895	+	0.0662446i
$225$	−4.65947	−	1.36815i	−0.310632	−	0.0912097i
$226$	8.42230	−	11.8275i	0.560243	−	0.786751i
$227$	−12.8923	−	5.16129i	−0.855690	−	0.342567i	−0.0980043	−	0.995186i	$-0.531246\pi$
$227$	−12.8923	−	5.16129i	−0.855690	−	0.342567i	−0.757686	+	0.652619i	$0.773670\pi$
$228$	−4.12524	+	2.12671i	−0.273201	+	0.140845i
$229$	0.950968	+	1.64712i	0.0628417	+	0.108845i	0.895735	−	0.444589i	$-0.146650\pi$
$229$	0.950968	+	1.64712i	0.0628417	+	0.108845i	−0.832893	+	0.553434i	$0.813317\pi$
$230$	−5.54322	+	13.9987i	−0.365509	+	0.923050i
$231$	5.06409	+	2.63199i	0.333193	+	0.173173i
$232$	−0.332681	−	0.213801i	−0.0218416	−	0.0140367i
$233$	20.9847	−	16.5026i	1.37476	−	1.08112i	0.387520	−	0.921862i	$-0.373332\pi$
$233$	20.9847	−	16.5026i	1.37476	−	1.08112i	0.987237	−	0.159259i	$-0.0509104\pi$
$234$	0.744051	+	0.0710482i	0.0486401	+	0.00464457i
$235$	−14.6391	+	13.9584i	−0.954950	+	0.910543i
$236$	−9.66451	+	0.922849i	−0.629106	+	0.0600724i
$237$	−0.410867	+	0.474166i	−0.0266887	+	0.0308004i
$238$	−1.78017	−	3.93246i	−0.115392	−	0.254904i
$239$	−3.52663	+	1.03551i	−0.228118	+	0.0669816i	−0.393794	−	0.919199i	$-0.628838\pi$
$239$	−3.52663	+	1.03551i	−0.228118	+	0.0669816i	0.165676	+	0.986180i	$0.447020\pi$
$240$	−1.02682	+	2.96679i	−0.0662807	+	0.191505i
$241$	−0.452848	−	9.50644i	−0.0291705	−	0.612364i	−0.965368	−	0.260891i	$-0.915984\pi$
$241$	−0.452848	−	9.50644i	−0.0291705	−	0.612364i	0.936198	−	0.351473i	$-0.114319\pi$
$242$	0.301993	+	6.33960i	0.0194128	+	0.407525i
$243$	0.327068	−	0.945001i	0.0209814	−	0.0606218i
$244$	6.03594	−	1.77231i	0.386412	−	0.113461i
$245$	−1.19109	+	21.9439i	−0.0760960	+	1.40194i
$246$	−4.98323	+	5.75096i	−0.317719	+	0.366668i
$247$	3.45327	−	0.329747i	0.219726	−	0.0209813i
$248$	−1.71816	+	1.63826i	−0.109103	+	0.104030i
$249$	6.04702	+	0.577420i	0.383214	+	0.0365925i
$250$	0.354907	−	0.279102i	0.0224463	−	0.0176519i
$251$	6.50414	+	4.17996i	0.410538	+	0.263837i	0.729569	−	0.683908i	$-0.239721\pi$
$251$	6.50414	+	4.17996i	0.410538	+	0.263837i	−0.319031	+	0.947744i	$0.603357\pi$
$252$	−2.23047	+	1.42302i	−0.140507	+	0.0896418i
$253$	8.97863	+	5.13886i	0.564482	+	0.323078i
$254$	−6.83704	−	11.8421i	−0.428994	−	0.743040i
$255$	4.55273	−	2.34709i	0.285103	−	0.146981i
$256$	0.928368	+	0.371662i	0.0580230	+	0.0232289i
$257$	15.0822	−	21.1800i	0.940802	−	1.32117i	−0.00621254	−	0.999981i	$-0.501978\pi$
$257$	15.0822	−	21.1800i	0.940802	−	1.32117i	0.947015	−	0.321191i	$-0.104083\pi$
$258$	1.83778	+	0.539622i	0.114415	+	0.0335954i
$259$	15.7050	−	12.2666i	0.975863	−	0.762208i
$260$	1.53666	−	1.77340i	0.0952994	−	0.109981i
$261$	0.367131	−	0.146977i	0.0227248	−	0.00909765i
$262$	−1.37271	+	5.65840i	−0.0848065	+	0.349577i
$263$	3.78812	−	0.730099i	0.233585	−	0.0450199i	−0.0711152	−	0.997468i	$-0.522656\pi$
$263$	3.78812	−	0.730099i	0.233585	−	0.0450199i	0.304700	+	0.952448i	$0.401444\pi$
$264$	1.91733	+	0.988454i	0.118004	+	0.0608351i
$265$	−7.51080	+	4.82690i	−0.461385	+	0.296514i
$266$	−8.91504	+	8.44426i	−0.546616	+	0.517751i
$267$	−12.4757	+	3.66319i	−0.763500	+	0.224184i
$268$	10.2897	−	4.11939i	0.628546	−	0.251632i
$269$	0.914624	+	2.64263i	0.0557656	+	0.161124i	0.969443	−	0.245315i	$-0.0788914\pi$
$269$	0.914624	+	2.64263i	0.0557656	+	0.161124i	−0.913678	+	0.406439i	$0.866770\pi$
$270$	−1.82106	−	2.55733i	−0.110826	−	0.155634i
$271$	2.30931	+	9.51910i	0.140281	+	0.578244i	0.997947	+	0.0640385i	$0.0203980\pi$
$271$	2.30931	+	9.51910i	0.140281	+	0.578244i	−0.857667	+	0.514206i	$0.828087\pi$
$272$	−0.677763	−	1.48409i	−0.0410954	−	0.0899864i
$273$	1.94302	−	0.367815i	0.117597	−	0.0222612i
$274$	4.26864	+	2.74329i	0.257878	+	0.165728i
$275$	5.23771	+	9.07198i	0.315846	+	0.547061i
$276$	−4.14426	+	2.41353i	−0.249455	+	0.145277i
$277$	14.6475	−	25.3703i	0.880086	−	1.52435i	0.0288411	−	0.999584i	$-0.490818\pi$
$277$	14.6475	−	25.3703i	0.880086	−	1.52435i	0.851245	−	0.524769i	$-0.175848\pi$
$278$	0.581623	−	12.2098i	0.0348834	−	0.732293i
$279$	−0.337859	−	2.34986i	−0.0202271	−	0.140682i
$280$	−0.422710	+	8.29546i	−0.0252618	+	0.495748i
$281$	−18.6276	−	5.46954i	−1.11123	−	0.326286i	−0.325923	−	0.945396i	$-0.605675\pi$
$281$	−18.6276	−	5.46954i	−1.11123	−	0.326286i	−0.785304	+	0.619111i	$0.787493\pi$
$282$	−6.41372	+	0.612436i	−0.381932	+	0.0364701i
$283$	4.38010	+	12.6555i	0.260370	+	0.752289i	0.997100	+	0.0761023i	$0.0242476\pi$
$283$	4.38010	+	12.6555i	0.260370	+	0.752289i	−0.736730	+	0.676187i	$0.763631\pi$
$284$	0.261138	+	0.205361i	0.0154957	+	0.0121860i
$285$	−10.5454	−	10.0550i	−0.624653	−	0.595605i
$286$	−1.05584	−	1.21851i	−0.0624332	−	0.0720518i
$287$	−8.42423	+	18.2859i	−0.497266	+	1.07938i
$288$	−0.841254	+	0.540641i	−0.0495713	+	0.0318576i
$289$	4.68953	−	13.5495i	0.275855	−	0.797030i
$290$	0.292701	−	1.20653i	0.0171880	−	0.0708498i
$291$	8.83503	+	6.94795i	0.517919	+	0.407296i
$292$	−7.52527	−	1.45038i	−0.440383	−	0.0848769i
$293$	4.32512	−	9.47070i	0.252676	−	0.553284i	−0.740206	−	0.672380i	$-0.765272\pi$
$293$	4.32512	−	9.47070i	0.252676	−	0.553284i	0.992883	+	0.119096i	$0.0379995\pi$
$294$	−4.61898	+	5.25976i	−0.269384	+	0.306755i
$295$	−12.6616	−	27.7250i	−0.737185	−	1.61421i
$296$	5.92055	−	4.65597i	0.344125	−	0.270623i
$297$	−1.91733	+	0.988454i	−0.111255	+	0.0573559i
$298$	−4.11414	+	7.12589i	−0.238325	+	0.412792i
$299$	3.54614	−	0.523486i	0.205079	−	0.0302740i
$300$	−4.85618			−0.280372
$301$	5.06756	+	0.0167885i	0.292089	+	0.000967671i
$302$	1.44483	+	10.0490i	0.0831404	+	0.578254i
$303$	−10.2969	+	14.4599i	−0.591539	+	0.830700i
$304$	−3.35898	+	3.20278i	−0.192650	+	0.183692i
$305$	11.4559	+	16.0875i	0.655962	+	0.921169i
$306$	1.60205	+	0.308770i	0.0915830	+	0.0176512i
$307$	3.09218	−	21.5066i	0.176480	−	1.22744i	−0.688350	−	0.725379i	$-0.741665\pi$
$307$	3.09218	−	21.5066i	0.176480	−	1.22744i	0.864830	−	0.502065i	$-0.167426\pi$
$308$	5.60048	+	1.09866i	0.319117	+	0.0626020i
$309$	−1.08437	−	1.25143i	−0.0616878	−	0.0711915i
$310$	−6.62461	−	3.41523i	−0.376253	−	0.193972i
$311$	1.59185	+	33.4170i	0.0902655	+	1.89491i	0.361468	+	0.932385i	$0.382276\pi$
$311$	1.59185	+	33.4170i	0.0902655	+	1.89491i	−0.271202	+	0.962522i	$0.587421\pi$
$312$	0.733928	−	0.141453i	0.0415505	−	0.00800820i
$313$	−6.37189	−	6.07558i	−0.360160	−	0.343412i	0.488296	−	0.872678i	$-0.337619\pi$
$313$	−6.37189	−	6.07558i	−0.360160	−	0.343412i	−0.848456	+	0.529266i	$0.822467\pi$
$314$	0.0112170	−	0.0780156i	0.000633009	−	0.00440268i
$315$	−6.51208	−	5.15617i	−0.366914	−	0.290517i
$316$	−0.260636	+	0.570714i	−0.0146619	+	0.0321052i
$317$	−1.59790	−	6.58661i	−0.0897467	−	0.369941i	0.909173	−	0.416420i	$-0.136715\pi$
$317$	−1.59790	−	6.58661i	−0.0897467	−	0.369941i	−0.998919	+	0.0464785i	$0.985200\pi$
$318$	−2.83096	−	0.270324i	−0.158752	−	0.0151590i
$319$	−0.791949	−	0.317049i	−0.0443406	−	0.0177513i
$320$	−0.149381	+	3.13590i	−0.00835067	+	0.175302i
$321$	13.4177			0.748901
$322$	−8.75199	+	9.18710i	−0.487729	+	0.511977i
$323$	7.57223			0.421330
$324$	0.0475819	−	0.998867i	0.00264344	−	0.0554926i
$325$	3.36968	+	1.34902i	0.186916	+	0.0748300i
$326$	−7.34257	−	0.701131i	−0.406668	−	0.0388320i
$327$	−3.43549	−	14.1613i	−0.189983	−	0.783120i
$328$	−3.16114	+	6.92194i	−0.174545	+	0.382200i
$329$	−15.8461	+	6.28301i	−0.873626	+	0.346394i
$330$	−0.963786	+	6.70328i	−0.0530547	+	0.369004i
$331$	−12.8527	−	12.2550i	−0.706449	−	0.673598i	0.249084	−	0.968482i	$-0.419870\pi$
$331$	−12.8527	−	12.2550i	−0.706449	−	0.673598i	−0.955533	+	0.294884i	$0.904719\pi$
$332$	5.96475	−	1.14961i	0.327358	−	0.0630931i
$333$	0.358387	+	7.52346i	0.0196395	+	0.412283i
$334$	2.74491	+	1.41510i	0.150195	+	0.0774308i
$335$	22.7870	+	26.2976i	1.24499	+	1.43679i
$336$	−1.73921	+	1.99377i	−0.0948819	+	0.108769i
$337$	3.77737	−	26.2722i	0.205767	−	1.43114i	−0.581008	−	0.813898i	$-0.697341\pi$
$337$	3.77737	−	26.2722i	0.205767	−	1.43114i	0.786774	−	0.617241i	$-0.211750\pi$
$338$	12.2165	+	2.35454i	0.664490	+	0.128070i
$339$	8.42230	+	11.8275i	0.457436	+	0.642379i
$340$	3.70706	−	3.53467i	0.201043	−	0.191694i
$341$	−2.97051	+	4.17150i	−0.160862	+	0.225900i
$342$	−0.660508	−	4.59393i	−0.0357162	−	0.248411i
$343$	−7.86065	+	16.7693i	−0.424435	+	0.905458i
$344$	1.91537			0.103270
$345$	−11.4158	−	9.81689i	−0.614607	−	0.528524i
$346$	8.50702	−	14.7346i	0.457340	−	0.792136i
$347$	−11.9587	+	6.16513i	−0.641975	+	0.330961i	−0.748290	−	0.663371i	$-0.769125\pi$
$347$	−11.9587	+	6.16513i	−0.641975	+	0.330961i	0.106315	+	0.994332i	$0.466095\pi$
$348$	0.310851	−	0.244456i	0.0166634	−	0.0131042i
$349$	8.16002	+	17.8679i	0.436796	+	0.956449i	0.992175	+	0.124852i	$0.0398457\pi$
$349$	8.16002	+	17.8679i	0.436796	+	0.956449i	−0.555380	+	0.831597i	$0.687427\pi$
$350$	−12.3397	+	3.57891i	−0.659587	+	0.191301i
$351$	−0.310496	+	0.679891i	−0.0165730	+	0.0362899i
$352$	2.11815	+	0.408239i	0.112898	+	0.0217592i
$353$	−27.2704	−	21.4457i	−1.45146	−	1.14144i	−0.963216	−	0.268729i	$-0.913396\pi$
$353$	−27.2704	−	21.4457i	−1.45146	−	1.14144i	−0.488240	−	0.872709i	$-0.662361\pi$
$354$	2.28886	−	9.43481i	0.121652	−	0.501454i
$355$	−0.341123	+	0.985610i	−0.0181049	+	0.0523108i
$356$	−10.9383	+	7.02962i	−0.579729	+	0.372569i
$357$	4.29842	−	0.396084i	0.227496	−	0.0209630i
$358$	−3.71300	−	4.28503i	−0.196238	−	0.226471i
$359$	20.6487	+	19.6885i	1.08980	+	1.03912i	0.999064	+	0.0432452i	$0.0137697\pi$
$359$	20.6487	+	19.6885i	1.08980	+	1.03912i	0.0907336	+	0.995875i	$0.471079\pi$
$360$	−2.46778	−	1.94068i	−0.130063	−	0.102283i
$361$	−0.830914	−	2.40077i	−0.0437323	−	0.126356i
$362$	−23.2675	+	2.22178i	−1.22291	+	0.116774i
$363$	−6.08970	−	1.78810i	−0.319626	−	0.0938508i
$364$	1.76069	−	0.900328i	0.0922852	−	0.0471900i
$365$	−3.42410	−	23.8151i	−0.179226	−	1.24654i
$366$	−0.299327	+	6.28364i	−0.0156461	+	0.328451i
$367$	−1.52960	+	2.64934i	−0.0798443	+	0.138294i	−0.903183	−	0.429256i	$-0.858776\pi$
$367$	−1.52960	+	2.64934i	−0.0798443	+	0.138294i	0.823338	+	0.567551i	$0.192109\pi$
$368$	−3.29642	+	3.48334i	−0.171838	+	0.181581i
$369$	−3.80480	−	6.59011i	−0.198070	−	0.343067i
$370$	19.8926	+	12.7842i	1.03417	+	0.664618i
$371$	−7.39279	+	1.39946i	−0.383815	+	0.0726563i
$372$	−0.986204	−	2.15949i	−0.0511323	−	0.111964i
$373$	−0.347746	−	1.43343i	−0.0180056	−	0.0742201i	0.962100	−	0.272697i	$-0.0879157\pi$
$373$	−0.347746	−	1.43343i	−0.0180056	−	0.0742201i	−0.980106	+	0.198477i	$0.936401\pi$
$374$	−2.04147	−	2.86684i	−0.105562	−	0.148241i
$375$	0.147673	+	0.426672i	0.00762579	+	0.0220333i
$376$	−5.98138	+	2.39458i	−0.308466	+	0.123491i
$377$	−0.283607	+	0.0832744i	−0.0146065	+	0.00428885i
$378$	−0.615238	−	2.57322i	−0.0316444	−	0.132352i
$379$	18.8358	−	12.1050i	0.967528	−	0.621793i	0.0414565	−	0.999140i	$-0.486800\pi$
$379$	18.8358	−	12.1050i	0.967528	−	0.621793i	0.926072	+	0.377348i	$0.123164\pi$
$380$	−12.9510	−	6.67671i	−0.664373	−	0.342508i
$381$	13.4270	−	2.58784i	0.687885	−	0.132579i
$382$	5.65581	−	23.3136i	0.289377	−	1.19283i
$383$	27.5177	−	11.0164i	1.40609	−	0.562914i	0.460322	−	0.887752i	$-0.347734\pi$
$383$	27.5177	−	11.0164i	1.40609	−	0.562914i	0.945770	+	0.324838i	$0.105310\pi$
$384$	−0.654861	+	0.755750i	−0.0334182	+	0.0385667i
$385$	2.49117	+	17.7436i	0.126962	+	0.904296i
$386$	5.81652	+	1.70788i	0.296053	+	0.0869290i
$387$	−1.11102	+	1.56021i	−0.0564765	+	0.0793101i
$388$	10.4346	+	4.17739i	0.529737	+	0.212075i
$389$	20.8953	−	10.7723i	1.05943	−	0.546177i	0.161758	−	0.986831i	$-0.448284\pi$
$389$	20.8953	−	10.7723i	1.05943	−	0.546177i	0.897677	+	0.440654i	$0.145253\pi$
$390$	1.17327	+	2.03216i	0.0594108	+	0.102903i
$391$	7.81424	−	0.401716i	0.395183	−	0.0203156i
$392$	−2.95003	+	6.34802i	−0.148999	+	0.320623i
$393$	−4.89822	−	3.14790i	−0.247083	−	0.158790i
$394$	−4.87940	+	3.83720i	−0.245821	+	0.193316i
$395$	−1.96081	−	0.187235i	−0.0986592	−	0.00942081i
$396$	−1.56119	+	1.48859i	−0.0784527	+	0.0748045i
$397$	−22.9598	+	2.19239i	−1.15232	+	0.110033i	−0.653676	−	0.756775i	$-0.726774\pi$
$397$	−22.9598	+	2.19239i	−1.15232	+	0.110033i	−0.498642	+	0.866808i	$0.666168\pi$
$398$	−1.20849	+	1.39467i	−0.0605760	+	0.0699084i
$399$	−5.06401	−	11.1866i	−0.253518	−	0.560029i
$400$	−4.65947	+	1.36815i	−0.232974	+	0.0684073i
$401$	−8.19259	+	23.6709i	−0.409119	+	1.18207i	0.532804	+	0.846239i	$0.321138\pi$
$401$	−8.19259	+	23.6709i	−0.409119	+	1.18207i	−0.941922	+	0.335831i	$0.890983\pi$
$402$	0.527383	+	11.0711i	0.0263035	+	0.552178i
$403$	0.0844307	+	1.77242i	0.00420579	+	0.0882904i
$404$	−5.80593	+	16.7751i	−0.288856	+	0.834595i
$405$	3.01229	−	0.884487i	0.149682	−	0.0439505i
$406$	0.609725	−	0.850263i	0.0302601	−	0.0421979i
$407$	10.6398	−	12.2790i	0.527397	−	0.608649i
$408$	1.62414	−	0.155087i	0.0804071	−	0.00767795i
$409$	12.4418	−	11.8632i	0.615206	−	0.586598i	−0.317044	−	0.948411i	$-0.602690\pi$
$409$	12.4418	−	11.8632i	0.615206	−	0.586598i	0.932251	+	0.361813i	$0.117842\pi$
$410$	−23.7818	−	2.27089i	−1.17450	−	0.112151i
$411$	−3.98854	+	3.13662i	−0.196740	+	0.154718i
$412$	−1.39302	−	0.895238i	−0.0686290	−	0.0441052i
$413$	−1.13719	−	25.6610i	−0.0559576	−	1.26270i
$414$	−0.925332	−	4.70572i	−0.0454776	−	0.231273i
$415$	9.53535	+	16.5157i	0.468072	+	0.810724i
$416$	0.664347	−	0.342495i	0.0325723	−	0.0167922i
$417$	11.3480	+	4.54306i	0.555715	+	0.222475i
$418$	−5.80730	+	8.15522i	−0.284045	+	0.398885i
$419$	7.05887	+	2.07267i	0.344848	+	0.101257i	0.449570	−	0.893245i	$-0.351577\pi$
$419$	7.05887	+	2.07267i	0.344848	+	0.101257i	−0.104722	+	0.994502i	$0.533395\pi$
$420$	−7.70096	−	3.11264i	−0.375768	−	0.151881i
$421$	11.0730	−	12.7789i	0.539663	−	0.622804i	−0.418780	−	0.908088i	$-0.637542\pi$
$421$	11.0730	−	12.7789i	0.539663	−	0.622804i	0.958443	+	0.285283i	$0.0920877\pi$
$422$	9.19800	−	3.68232i	0.447752	−	0.179253i
$423$	1.51897	−	6.26128i	0.0738549	−	0.304434i
$424$	−2.79245	+	0.538200i	−0.135613	+	0.0261373i
$425$	7.04226	+	3.63054i	0.341600	+	0.176107i
$426$	−0.279477	+	0.179609i	−0.0135407	+	0.00870207i
$427$	3.87032	+	16.1875i	0.187298	+	0.783370i
$428$	12.8741	−	3.78019i	0.622295	−	0.182722i
$429$	1.49682	−	0.599237i	0.0722672	−	0.0289314i
$430$	1.96673	+	5.68249i	0.0948442	+	0.274034i
$431$	−9.67501	−	13.5867i	−0.466029	−	0.654446i	0.512947	−	0.858420i	$-0.328554\pi$
$431$	−9.67501	−	13.5867i	−0.466029	−	0.654446i	−0.978976	+	0.203974i	$0.934614\pi$
$432$	−0.235759	−	0.971812i	−0.0113430	−	0.0467563i
$433$	−12.4795	−	27.3264i	−0.599728	−	1.31322i	−0.929382	−	0.369119i	$-0.879659\pi$
$433$	−12.4795	−	27.3264i	−0.599728	−	1.31322i	0.329654	−	0.944102i	$-0.393068\pi$
$434$	−4.09748	−	4.76052i	−0.196685	−	0.228512i
$435$	1.04444	+	0.671219i	0.0500769	+	0.0321825i
$436$	−7.28601	−	12.6197i	−0.348937	−	0.604376i
$437$	−8.35027	−	20.6326i	−0.399448	−	0.986991i
$438$	3.83188	−	6.63701i	0.183094	−	0.317129i
$439$	1.38168	−	29.0051i	0.0659442	−	1.38434i	−0.687193	−	0.726475i	$-0.741157\pi$
$439$	1.38168	−	29.0051i	0.0659442	−	1.38434i	0.753137	−	0.657864i	$-0.228540\pi$
$440$	0.963786	+	6.70328i	0.0459467	+	0.319566i
$441$	−3.45976	−	6.08523i	−0.164750	−	0.289773i
$442$	−1.17007	−	0.343563i	−0.0556545	−	0.0163416i
$443$	7.81840	−	0.746567i	0.371464	−	0.0354705i	0.0923449	−	0.995727i	$-0.470564\pi$
$443$	7.81840	−	0.746567i	0.371464	−	0.0354705i	0.279119	+	0.960257i	$0.409958\pi$
$444$	2.46347	+	7.11774i	0.116911	+	0.337793i
$445$	−32.0870	−	25.2335i	−1.52107	−	1.19618i
$446$	12.9421	+	12.3403i	0.612828	+	0.584330i
$447$	−5.38837	−	6.21851i	−0.254861	−	0.294126i
$448$	−1.10705	+	2.40301i	−0.0523033	+	0.113531i
$449$	4.31132	−	2.77072i	0.203464	−	0.130758i	−0.434941	−	0.900459i	$-0.643231\pi$
$449$	4.31132	−	2.77072i	0.203464	−	0.130758i	0.638405	+	0.769701i	$0.279594\pi$
$450$	1.58830	−	4.58910i	0.0748733	−	0.216332i
$451$	−3.86996	+	15.9522i	−0.182229	+	0.751159i
$452$	11.4133	+	8.97553i	0.536837	+	0.422173i
$453$	−9.96886	−	1.92134i	−0.468378	−	0.0902724i
$454$	5.76888	−	12.6321i	0.270747	−	0.592853i
$455$	4.47899	+	4.29912i	0.209978	+	0.201546i
$456$	−1.92801	−	4.22176i	−0.0902875	−	0.197702i
$457$	−19.5162	+	15.3477i	−0.912928	+	0.717935i	−0.959716	−	0.280970i	$-0.909344\pi$
$457$	−19.5162	+	15.3477i	−0.912928	+	0.717935i	0.0467884	+	0.998905i	$0.485101\pi$
$458$	−1.69051	+	0.871517i	−0.0789922	+	0.0407233i
$459$	−0.815766	+	1.41295i	−0.0380767	+	0.0659508i
$460$	−13.7191	−	6.20303i	−0.639658	−	0.289218i
$461$	−25.5167			−1.18843			−0.594215	−	0.804306i	$-0.702537\pi$
$461$	−25.5167			−1.18843			−0.594215	+	0.804306i	$0.702537\pi$
$462$	−2.86997	+	4.93312i	−0.133523	+	0.229510i
$463$	−3.09719	−	21.5415i	−0.143939	−	1.00112i	−0.925894	−	0.377782i	$-0.876687\pi$
$463$	−3.09719	−	21.5415i	−0.143939	−	1.00112i	0.781956	−	0.623334i	$-0.214222\pi$
$464$	0.229388	−	0.322131i	0.0106491	−	0.0149546i
$465$	5.39409	−	5.14325i	0.250145	−	0.238513i
$466$	15.4854	+	21.7462i	0.717347	+	1.00737i
$467$	−20.1659	−	3.88667i	−0.933169	−	0.179853i	−0.300063	−	0.953919i	$-0.597008\pi$
$467$	−20.1659	−	3.88667i	−0.933169	−	0.179853i	−0.633105	+	0.774066i	$0.718220\pi$
$468$	−0.106371	+	0.739828i	−0.00491701	+	0.0341985i
$469$	9.49930	+	27.7435i	0.438637	+	1.28107i
$470$	−13.2460	−	15.2867i	−0.610992	−	0.705123i
$471$	0.0700561	+	0.0361164i	0.00322802	+	0.00166416i
$472$	−0.461948	−	9.69748i	−0.0212629	−	0.446363i
$473$	4.05703	−	0.781929i	0.186543	−	0.0359531i
$474$	−0.454079	−	0.432964i	−0.0208566	−	0.0198867i
$475$	3.20755	−	22.3090i	0.147172	−	1.02361i
$476$	4.01271	−	1.59104i	0.183922	−	0.0729254i
$477$	1.18137	−	2.58685i	0.0540914	−	0.118444i
$478$	−0.866534	−	3.57190i	−0.0396344	−	0.163375i
$479$	−11.0820	−	1.05820i	−0.506349	−	0.0483504i	−0.161244	−	0.986915i	$-0.551551\pi$
$479$	−11.0820	−	1.05820i	−0.506349	−	0.0483504i	−0.345105	+	0.938564i	$0.612157\pi$
$480$	−2.91457	−	1.16682i	−0.133031	−	0.0532577i
$481$	0.267871	−	5.62330i	0.0122139	−	0.256401i
$482$	9.51722			0.433498
$483$	−5.81932	−	11.2754i	−0.264788	−	0.513050i
$484$	−6.34679			−0.288491
$485$	−1.67901	+	35.2467i	−0.0762398	+	1.60047i
$486$	0.928368	+	0.371662i	0.0421116	+	0.0168590i
$487$	−16.4662	−	1.57233i	−0.746155	−	0.0712492i	−0.284949	−	0.958543i	$-0.591977\pi$
$487$	−16.4662	−	1.57233i	−0.746155	−	0.0712492i	−0.461205	+	0.887293i	$0.652583\pi$
$488$	1.48310	+	6.11344i	0.0671370	+	0.276742i
$489$	3.06409	−	6.70942i	0.138563	−	0.303410i
$490$	−21.8624	−	2.23387i	−0.987641	−	0.100916i
$491$	−1.47608	+	10.2663i	−0.0666144	+	0.463313i	0.929024	+	0.370019i	$0.120649\pi$
$491$	−1.47608	+	10.2663i	−0.0666144	+	0.463313i	−0.995639	+	0.0932942i	$0.970260\pi$
$492$	−5.50733	−	5.25123i	−0.248290	−	0.236744i
$493$	−0.633544	+	0.122106i	−0.0285334	+	0.00549936i
$494$	0.165061	+	3.46505i	0.00742643	+	0.155900i
$495$	−6.01938	−	3.10321i	−0.270551	−	0.139479i
$496$	−1.55465	−	1.79417i	−0.0698060	−	0.0805604i
$497$	−0.577792	+	0.662361i	−0.0259175	+	0.0297109i
$498$	−0.864495	+	6.01269i	−0.0387389	+	0.269435i
$499$	−23.0887	−	4.44999i	−1.03359	−	0.199209i	−0.355878	−	0.934533i	$-0.615818\pi$
$499$	−23.0887	−	4.44999i	−1.03359	−	0.199209i	−0.677716	+	0.735324i	$0.737030\pi$
$500$	0.261898	+	0.367785i	0.0117125	+	0.0164478i
$501$	−2.23504	+	2.13111i	−0.0998544	+	0.0952110i
$502$	−4.48471	+	6.29789i	−0.200162	+	0.281088i
$503$	−0.490382	−	3.41068i	−0.0218651	−	0.152075i	0.975964	−	0.217932i	$-0.0699310\pi$
$503$	−0.490382	−	3.41068i	−0.0218651	−	0.152075i	−0.997829	+	0.0658568i	$0.979022\pi$
$504$	−1.31528	−	2.29566i	−0.0585871	−	0.102257i
$505$	−55.7299			−2.47995
$506$	−5.56026	+	8.72395i	−0.247184	+	0.387827i
$507$	−6.22067	+	10.7745i	−0.276270	+	0.478513i
$508$	12.1540	−	6.26583i	0.539247	−	0.278001i
$509$	31.3042	−	24.6179i	1.38753	−	1.09117i	0.403151	−	0.915134i	$-0.367915\pi$
$509$	31.3042	−	24.6179i	1.38753	−	1.09117i	0.984384	−	0.176036i	$-0.0563274\pi$
$510$	2.12781	+	4.65925i	0.0942209	+	0.206315i
$511$	4.84560	−	19.6889i	0.214357	−	0.870986i
$512$	−0.415415	+	0.909632i	−0.0183589	+	0.0402004i
$513$	4.55730	+	0.878348i	0.201210	+	0.0387800i
$514$	20.4384	+	16.0729i	0.901497	+	0.708945i
$515$	1.22561	−	5.05203i	0.0540068	−	0.222619i
$516$	−0.626456	+	1.81003i	−0.0275782	+	0.0796819i
$517$	−11.6919	+	7.51392i	−0.514208	+	0.330462i
$518$	11.5054	+	16.2709i	0.505519	+	0.714902i
$519$	11.1418	+	12.8583i	0.489072	+	0.564419i
$520$	1.69827	+	1.61930i	0.0744741	+	0.0710109i
$521$	−15.2423	−	11.9867i	−0.667776	−	0.525145i	0.225733	−	0.974189i	$-0.427522\pi$
$521$	−15.2423	−	11.9867i	−0.667776	−	0.525145i	−0.893510	+	0.449044i	$0.851765\pi$
$522$	0.129342	+	0.373709i	0.00566114	+	0.0163568i
$523$	30.6986	−	2.93136i	1.34236	−	0.128180i	0.600978	−	0.799266i	$-0.294778\pi$
$523$	30.6986	−	2.93136i	1.34236	−	0.128180i	0.741380	+	0.671086i	$0.234172\pi$
$524$	−5.58667	−	1.64040i	−0.244055	−	0.0716610i
$525$	0.653858	−	12.8316i	0.0285367	−	0.560017i
$526$	0.549027	+	3.81856i	0.0239387	+	0.166497i
$527$	−0.184299	+	3.86891i	−0.00802818	+	0.168532i
$528$	−1.07856	+	1.86813i	−0.0469385	+	0.0812999i
$529$	−9.71173	−	20.8490i	−0.422249	−	0.906480i
$530$	−4.46405	−	7.73196i	−0.193906	−	0.335855i
$531$	8.16729	+	5.24880i	0.354430	+	0.227778i
$532$	−8.01050	−	9.30673i	−0.347299	−	0.403498i
$533$	2.36275	+	5.17370i	0.102342	+	0.224098i
$534$	−3.06543	−	12.6359i	−0.132654	−	0.546807i
$535$	24.4344	+	34.3133i	1.05639	+	1.48349i
$536$	3.62512	+	10.4741i	0.156581	+	0.452412i
$537$	5.26376	−	2.10729i	0.227148	−	0.0909363i
$538$	−2.68316	+	0.787847i	−0.115679	+	0.0339665i
$539$	−3.65709	+	14.6504i	−0.157522	+	0.631035i
$540$	2.64108	−	1.69732i	0.113654	−	0.0730409i
$541$	−22.0165	−	11.3503i	−0.946562	−	0.487987i	−0.0854166	−	0.996345i	$-0.527222\pi$
$541$	−22.0165	−	11.3503i	−0.946562	−	0.487987i	−0.861145	+	0.508359i	$0.830252\pi$
$542$	−9.61820	+	1.85376i	−0.413137	+	0.0796256i
$543$	5.51047	−	22.7145i	0.236477	−	0.974771i
$544$	1.51466	−	0.606379i	0.0649406	−	0.0259983i
$545$	29.9587	−	34.5742i	1.28329	−	1.48100i
$546$	0.274945	+	1.95832i	0.0117666	+	0.0838084i
$547$	−24.7396	−	7.26422i	−1.05779	−	0.310595i	−0.293830	−	0.955858i	$-0.594930\pi$
$547$	−24.7396	−	7.26422i	−1.05779	−	0.310595i	−0.763961	+	0.645262i	$0.776748\pi$
$548$	−2.94329	+	4.13327i	−0.125731	+	0.176565i
$549$	−5.84014	−	2.33804i	−0.249251	−	0.0997851i
$550$	−9.31092	+	4.80011i	−0.397019	+	0.204678i
$551$	0.917696	+	1.58950i	0.0390952	+	0.0677148i
$552$	−2.21360	−	4.25441i	−0.0942172	−	0.181080i
$553$	−1.47292	−	0.765529i	−0.0626348	−	0.0325536i
$554$	24.6446	+	15.8381i	1.04705	+	0.672897i
$555$	−18.5873	+	14.6172i	−0.788987	+	0.620466i
$556$	12.1683	+	1.16193i	0.516049	+	0.0492767i
$557$	−2.91815	+	2.78245i	−0.123646	+	0.117896i	−0.749380	−	0.662141i	$-0.769648\pi$
$557$	−2.91815	+	2.78245i	−0.123646	+	0.117896i	0.625734	+	0.780037i	$0.284800\pi$
$558$	2.36327	−	0.225665i	0.100045	−	0.00955317i
$559$	0.937508	−	1.08194i	0.0396524	−	0.0457613i
$560$	−8.26595	−	0.816945i	−0.349300	−	0.0345222i
$561$	3.37687	−	0.991537i	0.142571	−	0.0418627i
$562$	6.34968	−	18.3462i	0.267845	−	0.773888i
$563$	−1.48320	−	31.1361i	−0.0625093	−	1.31223i	−0.784413	−	0.620238i	$-0.787036\pi$
$563$	−1.48320	−	31.1361i	−0.0625093	−	1.31223i	0.721904	−	0.691993i	$-0.243267\pi$
$564$	−0.306565	−	6.43560i	−0.0129087	−	0.270988i
$565$	−14.9091	+	43.0771i	−0.627232	+	1.81227i
$566$	−12.8495	+	3.77297i	−0.540106	+	0.158590i
$567$	2.63292	+	0.260219i	0.110572	+	0.0109282i
$568$	−0.217554	+	0.251071i	−0.00912837	+	0.0105347i
$569$	25.6931	−	2.45340i	1.07711	−	0.102852i	0.458612	−	0.888637i	$-0.348347\pi$
$569$	25.6931	−	2.45340i	1.07711	−	0.102852i	0.618500	+	0.785785i	$0.287741\pi$
$570$	10.5454	−	10.0550i	0.441696	−	0.421157i
$571$	−1.28117	−	0.122337i	−0.0536151	−	0.00511963i	0.0682140	−	0.997671i	$-0.478270\pi$
$571$	−1.28117	−	0.122337i	−0.0536151	−	0.00511963i	−0.121829	+	0.992551i	$0.538876\pi$
$572$	1.26737	−	0.996667i	0.0529912	−	0.0416727i
$573$	20.1815	+	12.9699i	0.843095	+	0.541824i
$574$	−17.8644	−	9.28476i	−0.745644	−	0.387539i
$575$	2.12654	−	23.1921i	0.0886830	−	0.967179i
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	25.8703	−	13.3371i	1.07699	−	0.555229i	0.173941	−	0.984756i	$-0.444350\pi$
$577$	25.8703	−	13.3371i	1.07699	−	0.555229i	0.903054	+	0.429527i	$0.141320\pi$
$578$	13.3110	+	5.32893i	0.553666	+	0.221654i
$579$	−3.51635	+	4.93802i	−0.146134	+	0.205217i
$580$	1.19123	+	0.349778i	0.0494633	+	0.0145237i
$581$	2.23452	+	15.9156i	0.0927036	+	0.660289i
$582$	−7.36046	+	8.49443i	−0.305101	+	0.352105i
$583$	−5.69510	+	2.27997i	−0.235867	+	0.0944268i
$584$	1.80680	−	7.44773i	0.0747659	−	0.308189i
$585$	−2.30414	+	0.444086i	−0.0952643	+	0.0183607i
$586$	9.25418	+	4.77086i	0.382286	+	0.197082i
$587$	−14.0537	+	9.03175i	−0.580057	+	0.372780i	−0.797524	−	0.603288i	$-0.793857\pi$
$587$	−14.0537	+	9.03175i	−0.580057	+	0.372780i	0.217466	+	0.976068i	$0.430221\pi$
$588$	−5.03402	−	4.86401i	−0.207600	−	0.200589i
$589$	10.5719	−	3.10420i	0.435609	−	0.127906i
$590$	28.2960	−	11.3280i	1.16493	−	0.466367i
$591$	−2.03026	−	5.86606i	−0.0835139	−	0.241298i
$592$	4.36899	+	6.13538i	0.179564	+	0.252163i
$593$	4.34455	+	17.9085i	0.178409	+	0.735414i	0.988765	+	0.149476i	$0.0477586\pi$
$593$	4.34455	+	17.9085i	0.178409	+	0.735414i	−0.810356	+	0.585938i	$0.800726\pi$
$594$	−0.896104	−	1.96219i	−0.0367676	−	0.0805098i
$595$	8.84061	+	10.2712i	0.362430	+	0.421077i
$596$	−6.92206	−	4.44854i	−0.283539	−	0.182219i
$597$	−0.922706	−	1.59817i	−0.0377638	−	0.0654089i
$598$	0.354161	+	3.56704i	0.0144827	+	0.145867i
$599$	−3.58055	+	6.20170i	−0.146297	+	0.253395i	−0.929856	−	0.367923i	$-0.880069\pi$
$599$	−3.58055	+	6.20170i	−0.146297	+	0.253395i	0.783559	+	0.621318i	$0.213402\pi$
$600$	0.231067	−	4.85068i	0.00943325	−	0.198028i
$601$	−2.97313	−	20.6786i	−0.121277	−	0.843498i	−0.956113	−	0.292999i	$-0.905347\pi$
$601$	−2.97313	−	20.6786i	−0.121277	−	0.843498i	0.834836	−	0.550499i	$-0.185562\pi$
$602$	−0.257894	+	5.06102i	−0.0105110	+	0.206272i
$603$	−10.6347	−	3.12263i	−0.433079	−	0.127164i
$604$	−10.1064	+	0.965040i	−0.411222	+	0.0392669i
$605$	−6.51698	−	18.8296i	−0.264953	−	0.765532i
$606$	−13.9536	−	10.9732i	−0.566826	−	0.445757i
$607$	−22.1948	−	21.1627i	−0.900861	−	0.858969i	0.0897103	−	0.995968i	$-0.471406\pi$
$607$	−22.1948	−	21.1627i	−0.900861	−	0.858969i	−0.990571	+	0.136999i	$0.956254\pi$
$608$	−3.03932	−	3.50756i	−0.123261	−	0.142251i
$609$	0.604078	+	0.854284i	0.0244785	+	0.0346174i
$610$	−16.6144	+	10.6774i	−0.672697	+	0.432316i
$611$	−1.57504	+	4.55079i	−0.0637195	+	0.184105i
$612$	−0.384648	+	1.58554i	−0.0155485	+	0.0640917i
$613$	1.41400	+	1.11198i	0.0571110	+	0.0449126i	0.646306	−	0.763078i	$-0.276313\pi$
$613$	1.41400	+	1.11198i	0.0571110	+	0.0449126i	−0.589195	+	0.807991i	$0.700555\pi$
$614$	21.3351	+	4.11200i	0.861013	+	0.165947i
$615$	9.92427	−	21.7311i	0.400185	−	0.876284i
$616$	−1.36390	+	5.54186i	−0.0549530	+	0.223288i
$617$	1.92914	+	4.22424i	0.0776644	+	0.170061i	0.944481	−	0.328565i	$-0.106565\pi$
$617$	1.92914	+	4.22424i	0.0776644	+	0.170061i	−0.866817	+	0.498627i	$0.833838\pi$
$618$	1.30161	−	1.02360i	0.0523585	−	0.0411752i
$619$	−27.5465	+	14.2012i	−1.10719	+	0.570794i	−0.912090	−	0.409990i	$-0.865532\pi$
$619$	−27.5465	+	14.2012i	−1.10719	+	0.570794i	−0.195096	+	0.980784i	$0.562502\pi$
$620$	3.72657	−	6.45461i	0.149663	−	0.259223i
$621$	4.74955	+	0.664650i	0.190593	+	0.0266715i
$622$	−33.4549			−1.34142
$623$	−17.1017	−	29.8490i	−0.685167	−	1.19588i
$624$	0.106371	+	0.739828i	0.00425825	+	0.0296168i
$625$	−14.9065	+	20.9333i	−0.596261	+	0.837332i
$626$	6.37189	−	6.07558i	0.254672	−	0.242829i
$627$	−5.80730	−	8.15522i	−0.231921	−	0.325688i
$628$	0.0773935	+	0.0149164i	0.00308834	+	0.000595228i
$629$	1.74886	−	12.1636i	0.0697318	−	0.484995i
$630$	5.46018	−	6.25937i	0.217539	−	0.249379i
$631$	12.9580	+	14.9543i	0.515850	+	0.595322i	0.952587	−	0.304267i	$-0.0984114\pi$
$631$	12.9580	+	14.9543i	0.515850	+	0.595322i	−0.436737	+	0.899589i	$0.643866\pi$
$632$	−0.557666	−	0.287497i	−0.0221828	−	0.0114360i
$633$	0.471428	+	9.89649i	0.0187376	+	0.393350i
$634$	6.65518	−	1.28268i	0.264311	−	0.0509418i
$635$	31.0693	+	29.6245i	1.23295	+	1.17561i
$636$	0.404720	−	2.81489i	0.0160482	−	0.111618i
$637$	2.14189	+	4.77353i	0.0848648	+	0.189134i
$638$	0.354372	−	0.775966i	0.0140297	−	0.0307208i
$639$	−0.0783225	−	0.322850i	−0.00309839	−	0.0127717i
$640$	−3.12524	−	0.298424i	−0.123536	−	0.0117963i
$641$	28.6887	+	11.4852i	1.13314	+	0.453639i	0.860992	−	0.508618i	$-0.169843\pi$
$641$	28.6887	+	11.4852i	1.13314	+	0.453639i	0.272143	+	0.962257i	$0.412268\pi$
$642$	−0.638438	+	13.4025i	−0.0251971	+	0.528953i
$643$	17.6817			0.697297			0.348649	−	0.937254i	$-0.386641\pi$
$643$	17.6817			0.697297			0.348649	+	0.937254i	$0.386641\pi$
$644$	−8.76025	−	9.17921i	−0.345202	−	0.361712i
$645$	−6.01322			−0.236770
$646$	−0.360301	+	7.56365i	−0.0141759	+	0.297588i
$647$	2.01716	+	0.807550i	0.0793028	+	0.0317481i	0.410975	−	0.911647i	$-0.365188\pi$
$647$	2.01716	+	0.807550i	0.0793028	+	0.0317481i	−0.331672	+	0.943395i	$0.607613\pi$
$648$	0.995472	+	0.0950560i	0.0391058	+	0.00373415i
$649$	−4.93737	−	20.3521i	−0.193809	−	0.798890i
$650$	−1.50783	+	3.30168i	−0.0591418	+	0.129502i
$651$	5.83885	−	2.31511i	0.228842	−	0.0907362i
$652$	1.04971	−	7.30090i	0.0411098	−	0.285925i
$653$	17.1563	+	16.3585i	0.671377	+	0.640156i	0.947047	−	0.321096i	$-0.104051\pi$
$653$	17.1563	+	16.3585i	0.671377	+	0.640156i	−0.275670	+	0.961252i	$0.588900\pi$
$654$	14.3087	−	2.75777i	0.559514	−	0.107837i
$655$	−0.869777	−	18.2589i	−0.0339850	−	0.713433i
$656$	−6.76369	−	3.48692i	−0.264078	−	0.136141i
$657$	5.01870	+	5.79188i	0.195798	+	0.225963i
$658$	−5.52190	−	16.1272i	−0.215266	−	0.628702i
$659$	3.34666	−	23.2766i	0.130368	−	0.906726i	−0.814707	−	0.579872i	$-0.803102\pi$
$659$	3.34666	−	23.2766i	0.130368	−	0.906726i	0.945075	−	0.326854i	$-0.105988\pi$
$660$	−6.64983	−	1.28165i	−0.258844	−	0.0498881i
$661$	−8.19761	−	11.5119i	−0.318850	−	0.447762i	0.623781	−	0.781599i	$-0.285596\pi$
$661$	−8.19761	−	11.5119i	−0.318850	−	0.447762i	−0.942631	+	0.333837i	$0.891656\pi$
$662$	12.8527	−	12.2550i	0.499535	−	0.476306i
$663$	0.707359	−	0.993347i	0.0274716	−	0.0385784i
$664$	0.864495	+	6.01269i	0.0335489	+	0.233338i
$665$	19.3858	−	33.3218i	0.751749	−	1.29216i
$666$	−7.53200			−0.291859
$667$	1.03135	+	1.59161i	0.0399340	+	0.0616274i
$668$	−1.54411	+	2.67447i	−0.0597432	+	0.103478i
$669$	−15.8946	+	8.19421i	−0.614519	+	0.316807i
$670$	−27.3521	+	21.5099i	−1.05670	+	0.831001i
$671$	5.63718	+	12.3437i	0.217621	+	0.476523i
$672$	−1.90876	−	1.83211i	−0.0736321	−	0.0706752i
$673$	−14.0650	+	30.7981i	−0.542167	+	1.18718i	0.418178	+	0.908365i	$0.362669\pi$
$673$	−14.0650	+	30.7981i	−0.542167	+	1.18718i	−0.960345	+	0.278815i	$0.910058\pi$
$674$	26.0627	+	5.02318i	1.00390	+	0.193486i
$675$	3.81722	+	3.00189i	0.146925	+	0.115543i
$676$	−2.93316	+	12.0906i	−0.112814	+	0.465025i
$677$	−12.6013	+	36.4091i	−0.484308	+	1.39931i	0.393068	+	0.919510i	$0.371414\pi$
$677$	−12.6013	+	36.4091i	−0.484308	+	1.39931i	−0.877375	+	0.479805i	$0.840707\pi$
$678$	−12.2148	+	7.84998i	−0.469107	+	0.301477i
$679$	−12.4430	+	27.0092i	−0.477518	+	1.03652i
$680$	3.35428	+	3.87104i	0.128631	+	0.148448i
$681$	10.0505	+	9.58315i	0.385137	+	0.367227i
$682$	−4.02544	−	3.16564i	−0.154142	−	0.121219i
$683$	−2.96931	−	8.57927i	−0.113618	−	0.328277i	0.873828	−	0.486235i	$-0.161630\pi$
$683$	−2.96931	−	8.57927i	−0.113618	−	0.328277i	−0.987446	+	0.157958i	$0.949509\pi$
$684$	4.62016	−	0.441172i	0.176656	−	0.0168686i
$685$	−15.2847	−	4.48801i	−0.584000	−	0.171478i
$686$	−16.3763	−	8.64966i	−0.625250	−	0.330245i
$687$	−0.270674	−	1.88258i	−0.0103268	−	0.0718248i
$688$	−0.0911369	+	1.91320i	−0.00347456	+	0.0729400i
$689$	−1.06279	+	1.84081i	−0.0404892	+	0.0701293i
$690$	10.3490	−	10.9358i	0.393978	−	0.416318i
$691$	16.5658	+	28.6929i	0.630194	+	1.09153i	0.987512	+	0.157545i	$0.0503580\pi$
$691$	16.5658	+	28.6929i	0.630194	+	1.09153i	−0.357318	+	0.933983i	$0.616309\pi$
$692$	14.3131	+	9.19848i	0.544103	+	0.349674i
$693$	−3.72313	−	4.32559i	−0.141430	−	0.164316i
$694$	−5.58913	−	12.2385i	−0.212160	−	0.464566i
$695$	9.04737	+	37.2938i	0.343186	+	1.41463i
$696$	0.229388	+	0.322131i	0.00869495	+	0.0122103i
$697$	4.06065	+	11.7325i	0.153808	+	0.444400i
$698$	−18.2360	+	7.30058i	−0.690242	+	0.276331i
$699$	−25.6150	+	7.52123i	−0.968847	+	0.284479i
$700$	−2.98771	−	12.4960i	−0.112925	−	0.472306i
$701$	−8.45071	+	5.43094i	−0.319179	+	0.205124i	−0.690413	−	0.723415i	$-0.742571\pi$
$701$	−8.45071	+	5.43094i	−0.319179	+	0.205124i	0.371234	+	0.928539i	$0.378935\pi$
$702$	−0.664347	−	0.342495i	−0.0250742	−	0.0129266i
$703$	−34.3256	+	6.61571i	−1.29461	+	0.249516i
$704$	−0.508563	+	2.09632i	−0.0191672	+	0.0790082i
$705$	18.7783	−	7.51769i	0.707231	−	0.283133i
$706$	22.7190	−	26.2191i	0.855039	−	0.986768i
$707$	−43.5436	−	17.5998i	−1.63763	−	0.661910i
$708$	9.31521	+	2.73519i	0.350087	+	0.102795i
$709$	−2.30462	+	3.23639i	−0.0865520	+	0.121545i	−0.855582	−	0.517668i	$-0.826800\pi$
$709$	−2.30462	+	3.23639i	−0.0865520	+	0.121545i	0.769030	+	0.639213i	$0.220740\pi$
$710$	−0.968263	−	0.387634i	−0.0363382	−	0.0145476i
$711$	0.557666	−	0.287497i	0.0209141	−	0.0107820i
$712$	−6.50119	−	11.2604i	−0.243642	−	0.422001i
$713$	10.7451	−	3.76426i	0.402408	−	0.140973i
$714$	0.191108	+	4.31240i	0.00715204	+	0.161387i
$715$	4.25825	+	2.73661i	0.159250	+	0.102343i
$716$	4.45684	−	3.50490i	0.166560	−	0.130984i
$717$	3.65887	+	0.349379i	0.136643	+	0.0130478i
$718$	−20.6487	+	19.6885i	−0.770604	+	0.734769i
$719$	−3.17144	+	0.302836i	−0.118275	+	0.0112939i	−0.154025	−	0.988067i	$-0.549224\pi$
$719$	−3.17144	+	0.302836i	−0.118275	+	0.0112939i	0.0357508	+	0.999361i	$0.488618\pi$
$720$	2.05591	−	2.37264i	0.0766191	−	0.0884232i
$721$	2.55307	−	3.56026i	0.0950813	−	0.132591i
$722$	2.43758	−	0.715739i	0.0907175	−	0.0266371i
$723$	−3.11278	+	8.99378i	−0.115765	+	0.334482i
$724$	−1.11215	−	23.3469i	−0.0413326	−	0.867679i
$725$	0.0913772	+	1.91824i	0.00339366	+	0.0712418i
$726$	2.07583	−	5.99772i	0.0770414	−	0.222596i
$727$	−30.1640	+	8.85695i	−1.11872	+	0.328486i	−0.788265	−	0.615336i	$-0.789021\pi$
$727$	−30.1640	+	8.85695i	−1.11872	+	0.328486i	−0.330455	+	0.943822i	$0.607202\pi$
$728$	0.815531	+	1.80153i	0.0302256	+	0.0667693i
$729$	−0.654861	+	0.755750i	−0.0242541	+	0.0279907i
$730$	23.9511	−	2.28705i	0.886470	−	0.0846476i
$731$	2.26166	−	2.15649i	0.0836505	−	0.0797606i
$732$	−6.26228	−	0.597975i	−0.231460	−	0.0221018i
$733$	−25.6219	+	20.1493i	−0.946367	+	0.744231i	−0.966793	−	0.255560i	$-0.917740\pi$
$733$	−25.6219	+	20.1493i	−0.946367	+	0.744231i	0.0204263	+	0.999791i	$0.493498\pi$
$734$	−2.57356	−	1.65392i	−0.0949917	−	0.0610475i
$735$	9.26149	−	19.9293i	0.341615	−	0.735104i
$736$	−3.32254	−	3.45843i	−0.122470	−	0.127479i
$737$	11.9545	+	20.7058i	0.440349	+	0.762706i
$738$	6.76369	−	3.48692i	0.248975	−	0.128355i
$739$	46.5207	+	18.6241i	1.71129	+	0.685098i	0.999844	−	0.0176425i	$-0.00561608\pi$
$739$	46.5207	+	18.6241i	1.71129	+	0.685098i	0.711447	+	0.702740i	$0.248040\pi$
$740$	−13.7162	+	19.2618i	−0.504219	+	0.708076i
$741$	−3.32846	−	0.977324i	−0.122274	−	0.0359029i
$742$	−1.04611	−	7.45101i	−0.0384039	−	0.273535i
$743$	−24.9721	+	28.8193i	−0.916136	+	1.05728i	0.0820236	+	0.996630i	$0.473862\pi$
$743$	−24.9721	+	28.8193i	−0.916136	+	1.05728i	−0.998159	+	0.0606466i	$0.980684\pi$
$744$	2.20397	−	0.882335i	0.0808013	−	0.0323480i
$745$	6.09019	−	25.1041i	0.223127	−	0.919744i
$746$	1.44835	−	0.279147i	0.0530279	−	0.0102203i
$747$	−5.39925	−	2.78351i	−0.197548	−	0.101843i
$748$	2.96073	−	1.90275i	0.108255	−	0.0695713i
$749$	8.25505	+	34.5266i	0.301633	+	1.26158i
$750$	−0.433216	+	0.127204i	−0.0158188	+	0.00464482i
$751$	−36.6664	+	14.6790i	−1.33798	+	0.535645i	−0.926678	−	0.375856i	$-0.877349\pi$
$751$	−36.6664	+	14.6790i	−1.33798	+	0.535645i	−0.411298	+	0.911501i	$0.634925\pi$
$752$	−2.10727	−	6.08854i	−0.0768441	−	0.222026i
$753$	−4.48471	−	6.29789i	−0.163432	−	0.229508i
$754$	−0.0696855	−	0.287248i	−0.00253780	−	0.0104609i
$755$	−13.2404	−	28.9925i	−0.481868	−	1.05514i
$756$	2.59958	−	0.492102i	0.0945459	−	0.0178976i
$757$	25.9831	+	16.6983i	0.944373	+	0.606912i	0.919632	−	0.392782i	$-0.128487\pi$
$757$	25.9831	+	16.6983i	0.944373	+	0.606912i	0.0247416	+	0.999694i	$0.492124\pi$
$758$	11.1951	+	19.3904i	0.406623	+	0.704291i
$759$	−6.42555	−	8.10778i	−0.233233	−	0.294294i
$760$	7.28538	−	12.6186i	0.264269	−	0.457726i
$761$	−0.0824675	+	1.73121i	−0.00298944	+	0.0627561i	−0.999869	−	0.0161804i	$-0.994849\pi$
$761$	−0.0824675	+	1.73121i	−0.00298944	+	0.0627561i	0.996880	+	0.0789365i	$0.0251524\pi$
$762$	1.94603	+	13.5349i	0.0704970	+	0.490318i
$763$	34.3265	−	17.5528i	1.24270	−	0.635455i
$764$	23.0181	+	6.75871i	0.832764	+	0.244522i
$765$	−5.09893	+	0.486889i	−0.184352	+	0.0176035i
$766$	9.69462	+	28.0108i	0.350281	+	1.01207i
$767$	−5.70396	−	4.48564i	−0.205958	−	0.161967i
$768$	−0.723734	−	0.690079i	−0.0261155	−	0.0249011i
$769$	17.0093	+	19.6298i	0.613371	+	0.707868i	0.974434	−	0.224673i	$-0.0721314\pi$
$769$	17.0093	+	19.6298i	0.613371	+	0.707868i	−0.361063	+	0.932542i	$0.617586\pi$
$770$	−17.8420	+	1.64408i	−0.642981	+	0.0592484i
$771$	−21.8736	+	14.0573i	−0.787760	+	0.506263i
$772$	−1.98271	+	5.72866i	−0.0713593	+	0.206179i
$773$	−8.33121	+	34.3417i	−0.299653	+	1.23519i	0.600504	+	0.799621i	$0.294966\pi$
$773$	−8.33121	+	34.3417i	−0.299653	+	1.23519i	−0.900157	+	0.435565i	$0.856549\pi$
$774$	−1.50558	−	1.18400i	−0.0541170	−	0.0425581i
$775$	11.3203	+	2.18182i	0.406639	+	0.0783732i
$776$	−4.66916	+	10.2240i	−0.167613	+	0.367021i
$777$	−19.1391	+	5.55093i	−0.686610	+	0.199139i
$778$	9.76584	+	21.3842i	0.350122	+	0.766661i
$779$	27.7614	−	21.8318i	0.994656	−	0.782206i
$780$	−2.08569	+	1.07525i	−0.0746796	+	0.0385000i
$781$	−0.358315	+	0.620620i	−0.0128215	+	0.0222075i
$782$	0.0294446	+	7.82450i	0.00105294	+	0.279804i
$783$	−0.395458			−0.0141325
$784$	−6.20046	−	3.24874i	−0.221445	−	0.116026i
$785$	0.0352151	+	0.244927i	0.00125688	+	0.00874181i
$786$	3.37740	−	4.74289i	0.120468	−	0.169173i
$787$	24.6093	−	23.4649i	0.877225	−	0.836433i	−0.110299	−	0.993898i	$-0.535181\pi$
$787$	24.6093	−	23.4649i	0.877225	−	0.836433i	0.987524	+	0.157466i	$0.0503324\pi$
$788$	−3.60069	−	5.05646i	−0.128269	−	0.180129i
$789$	−3.78812	−	0.730099i	−0.134860	−	0.0259922i
$790$	0.280322	−	1.94968i	0.00997341	−	0.0693666i
$791$	−25.2530	+	28.9492i	−0.897893	+	1.02931i
$792$	−1.41262	−	1.63025i	−0.0501952	−	0.0579284i
$793$	4.17925	+	2.15455i	0.148410	+	0.0765104i
$794$	−1.09744	−	23.0381i	−0.0389467	−	0.817591i
$795$	8.76676	−	1.68965i	0.310925	−	0.0599259i
$796$	−1.33559	−	1.27348i	−0.0473386	−	0.0451373i
$797$	−4.64343	+	32.2958i	−0.164479	+	1.14397i	0.725583	+	0.688135i	$0.241570\pi$
$797$	−4.64343	+	32.2958i	−0.164479	+	1.14397i	−0.890062	+	0.455840i	$0.849339\pi$
$798$	11.4148	−	4.52600i	0.404081	−	0.160219i
$799$	−4.36676	+	9.56187i	−0.154485	+	0.338275i
$800$	−1.14489	−	4.71930i	−0.0404779	−	0.166852i
$801$	12.9435	+	1.23595i	0.457336	+	0.0436703i
$802$	−23.2543	−	9.30962i	−0.821138	−	0.328734i
$803$	0.786611	−	16.5130i	0.0277589	−	0.582731i
$804$	−11.0837			−0.390891
$805$	18.2376	−	35.4152i	0.642792	−	1.24822i
$806$	−1.77443			−0.0625016
$807$	0.133060	−	2.79327i	0.00468392	−	0.0983277i
$808$	−16.4799	−	6.59755i	−0.579760	−	0.232101i
$809$	−0.384701	−	0.0367345i	−0.0135254	−	0.00129152i	0.0882912	−	0.996095i	$-0.471859\pi$
$809$	−0.384701	−	0.0367345i	−0.0135254	−	0.00129152i	−0.101817	+	0.994803i	$0.532465\pi$
$810$	0.740155	+	3.05096i	0.0260064	+	0.107200i
$811$	−4.61650	+	10.1087i	−0.162107	+	0.354965i	−0.973203	−	0.229948i	$-0.926144\pi$
$811$	−4.61650	+	10.1087i	−0.162107	+	0.354965i	0.811096	+	0.584914i	$0.198872\pi$
$812$	0.820288	+	0.649491i	0.0287865	+	0.0227927i
$813$	1.39400	−	9.69551i	0.0488899	−	0.340036i
$814$	11.7589	+	11.2121i	0.412148	+	0.392982i
$815$	22.7381	−	4.38240i	0.796480	−	0.153509i
$816$	0.0776314	+	1.62968i	0.00271764	+	0.0570504i
$817$	−7.90136	−	4.07343i	−0.276433	−	0.142511i
$818$	11.2578	+	12.9922i	0.393619	+	0.454260i
$819$	−1.94054	−	0.380681i	−0.0678080	−	0.0133021i
$820$	3.39990	−	23.6469i	0.118730	−	0.825784i
$821$	23.3040	+	4.49147i	0.813314	+	0.156753i	0.578916	−	0.815387i	$-0.303476\pi$
$821$	23.3040	+	4.49147i	0.813314	+	0.156753i	0.234398	+	0.972141i	$0.424688\pi$
$822$	−2.94329	−	4.13327i	−0.102659	−	0.144164i
$823$	33.5991	−	32.0366i	1.17119	−	1.11673i	0.180084	−	0.983651i	$-0.442363\pi$
$823$	33.5991	−	32.0366i	1.17119	−	1.11673i	0.991106	−	0.133076i	$-0.0424855\pi$
$824$	0.960506	−	1.34884i	0.0334608	−	0.0469892i
$825$	−1.49081	−	10.3688i	−0.0519032	−	0.360995i
$826$	25.6861	+	0.0850961i	0.893733	+	0.00296087i
$827$	−23.2092			−0.807064			−0.403532	−	0.914965i	$-0.632218\pi$
$827$	−23.2092			−0.807064			−0.403532	+	0.914965i	$0.632218\pi$
$828$	4.74441	−	0.700377i	0.164880	−	0.0243398i
$829$	−1.66633	+	2.88616i	−0.0578740	+	0.100241i	−0.893511	−	0.449042i	$-0.851765\pi$
$829$	−1.66633	+	2.88616i	−0.0578740	+	0.100241i	0.835637	+	0.549282i	$0.185099\pi$
$830$	−16.9507	+	8.73870i	−0.588368	+	0.303325i
$831$	−23.0275	+	18.1090i	−0.798815	+	0.628195i
$832$	0.310496	+	0.679891i	0.0107645	+	0.0235710i
$833$	3.66376	+	10.8171i	0.126942	+	0.374791i
$834$	−5.07787	+	11.1190i	−0.175832	+	0.385019i
$835$	−9.52010	−	1.83485i	−0.329457	−	0.0634975i
$836$	−7.86966	−	6.18877i	−0.272178	−	0.214043i
$837$	−0.559697	+	2.30710i	−0.0193460	+	0.0797451i
$838$	−2.40620	+	6.95225i	−0.0831207	+	0.240161i
$839$	−4.51920	+	2.90431i	−0.156020	+	0.100268i	−0.616321	−	0.787495i	$-0.711378\pi$
$839$	−4.51920	+	2.90431i	−0.156020	+	0.100268i	0.460301	+	0.887763i	$0.347741\pi$
$840$	3.47554	−	7.54413i	0.119918	−	0.260297i
$841$	18.8885	+	21.7985i	0.651329	+	0.751674i
$842$	12.2375	+	11.6685i	0.421733	+	0.402122i
$843$	15.2604	+	12.0009i	0.525596	+	0.413333i
$844$	3.24049	+	9.36279i	0.111542	+	0.322281i
$845$	−38.8822	+	3.71280i	−1.33759	+	0.127724i
$846$	6.18192	+	1.81517i	0.212539	+	0.0624070i
$847$	0.854560	−	16.7703i	0.0293630	−	0.576233i
$848$	−0.404720	−	2.81489i	−0.0138982	−	0.0966638i
$849$	0.637218	−	13.3768i	0.0218693	−	0.459092i
$850$	−3.96151	+	6.86154i	−0.135879	+	0.235349i
$851$	−35.0717	+	8.64817i	−1.20224	+	0.296455i
$852$	−0.166107	−	0.287706i	−0.00569074	−	0.00985665i
$853$	15.3107	+	9.83957i	0.524228	+	0.336901i	0.775842	−	0.630927i	$-0.217325\pi$
$853$	15.3107	+	9.83957i	0.524228	+	0.336901i	−0.251615	+	0.967827i	$0.580962\pi$
$854$	−16.3534	+	3.09570i	−0.559601	+	0.105933i
$855$	6.05291	+	13.2540i	0.207005	+	0.453278i
$856$	3.16333	+	13.0394i	0.108120	+	0.445679i
$857$	16.4025	+	23.0341i	0.560299	+	0.786830i	0.993423	−	0.114505i	$-0.0365281\pi$
$857$	16.4025	+	23.0341i	0.560299	+	0.786830i	−0.433124	+	0.901334i	$0.642589\pi$
$858$	0.527337	+	1.52364i	0.0180030	+	0.0520162i
$859$	49.4186	−	19.7842i	1.68614	−	0.675030i	0.687454	−	0.726228i	$-0.258728\pi$
$859$	49.4186	−	19.7842i	1.68614	−	0.675030i	0.998688	+	0.0511987i	$0.0163042\pi$
$860$	−5.76964	+	1.69412i	−0.196743	+	0.0577690i
$861$	14.6170	−	13.8451i	0.498145	−	0.471840i
$862$	14.0316	−	9.01757i	0.477919	−	0.307140i
$863$	−39.5792	−	20.4045i	−1.34729	−	0.694577i	−0.374711	−	0.927142i	$-0.622258\pi$
$863$	−39.5792	−	20.4045i	−1.34729	−	0.694577i	−0.972581	+	0.232564i	$0.925288\pi$
$864$	0.981929	−	0.189251i	0.0334059	−	0.00643846i
$865$	−12.5930	+	51.9091i	−0.428175	+	1.76496i
$866$	27.8892	−	11.1652i	0.947714	−	0.379407i
$867$	−9.38946	+	10.8360i	−0.318883	+	0.368010i
$868$	4.95009	−	3.86632i	0.168017	−	0.131232i
$869$	−1.29859	−	0.381299i	−0.0440515	−	0.0129347i
$870$	−0.720155	+	1.01132i	−0.0244155	+	0.0342868i
$871$	7.69091	+	3.07898i	0.260597	+	0.104327i
$872$	12.9521	−	6.67729i	0.438615	−	0.226122i
$873$	−5.61987	−	9.73390i	−0.190204	−	0.329443i
$874$	21.0066	−	7.35907i	0.710557	−	0.248924i
$875$	−1.00707	+	0.642500i	−0.0340452	+	0.0217205i
$876$	6.44717	+	4.14334i	0.217830	+	0.139991i
$877$	−17.3912	+	13.6766i	−0.587258	+	0.461825i	−0.867040	−	0.498239i	$-0.833980\pi$
$877$	−17.3912	+	13.6766i	−0.587258	+	0.461825i	0.279782	+	0.960064i	$0.409738\pi$
$878$	28.9065	+	2.76024i	0.975548	+	0.0931535i
$879$	−7.53521	+	7.18481i	−0.254156	+	0.242338i
$880$	−6.74155	+	0.643740i	−0.227258	+	0.0217005i
$881$	−33.0221	+	38.1096i	−1.11254	+	1.28394i	−0.157487	+	0.987521i	$0.550339\pi$
$881$	−33.0221	+	38.1096i	−1.11254	+	1.28394i	−0.955057	+	0.296423i	$0.904206\pi$
$882$	6.24296	−	3.16629i	0.210212	−	0.106615i
$883$	−10.5434	+	3.09582i	−0.354813	+	0.104183i	−0.454281	−	0.890858i	$-0.650104\pi$
$883$	−10.5434	+	3.09582i	−0.354813	+	0.104183i	0.0994684	+	0.995041i	$0.468286\pi$
$884$	0.398848	−	1.15240i	0.0134147	−	0.0387593i
$885$	1.45026	+	30.4448i	0.0487501	+	1.02339i
$886$	0.373707	+	7.84507i	0.0125549	+	0.263560i
$887$	1.58736	−	4.58639i	0.0532985	−	0.153996i	−0.915209	−	0.402978i	$-0.867975\pi$
$887$	1.58736	−	4.58639i	0.0532985	−	0.153996i	0.968508	+	0.248983i	$0.0800962\pi$
$888$	−7.22690	+	2.12201i	−0.242519	+	0.0712099i
$889$	14.9199	+	32.9585i	0.500396	+	1.10539i
$890$	26.7317	−	30.8500i	0.896048	−	1.03409i
$891$	2.14736	−	0.205048i	0.0719393	−	0.00686937i
$892$	−12.9421	+	12.3403i	−0.433335	+	0.413184i
$893$	29.7672	+	2.84242i	0.996122	+	0.0951181i
$894$	6.46786	−	5.08638i	0.216318	−	0.170114i
$895$	14.9747	+	9.62363i	0.500548	+	0.321682i
$896$	−2.34761	−	1.22014i	−0.0784281	−	0.0407619i
$897$	−3.48669	−	0.831981i	−0.116417	−	0.0277790i
$898$	2.56244	+	4.43828i	0.0855097	+	0.148107i
$899$	−0.834463	+	0.430195i	−0.0278309	+	0.0143478i
$900$	4.50833	+	1.80486i	0.150278	+	0.0601620i
$901$	−2.69136	+	3.77948i	−0.0896621	+	0.125913i
$902$	−15.7500	−	4.62461i	−0.524417	−	0.153983i
$903$	−4.69832	−	1.89901i	−0.156350	−	0.0631950i
$904$	−9.50843	+	10.9733i	−0.316246	+	0.364967i
$905$	68.1232	−	27.2724i	2.26449	−	0.906566i
$906$	2.39350	−	9.86614i	0.0795187	−	0.327781i
$907$	58.1069	−	11.1992i	1.92941	−	0.371863i	0.929413	−	0.369041i	$-0.120314\pi$
$907$	58.1069	−	11.1992i	1.92941	−	0.371863i	0.999996	−	0.00282239i	$-0.000898396\pi$
$908$	12.3433	+	6.36341i	0.409626	+	0.211177i
$909$	14.9335	−	9.59717i	0.495312	−	0.318318i
$910$	−4.50737	+	4.26935i	−0.149418	+	0.141528i
$911$	56.5624	−	16.6082i	1.87400	−	0.550255i	0.876352	−	0.481671i	$-0.159970\pi$
$911$	56.5624	−	16.6082i	1.87400	−	0.550255i	0.997645	−	0.0685844i	$-0.0218483\pi$
$912$	4.30872	−	1.72495i	0.142676	−	0.0571188i
$913$	4.28575	+	12.3828i	0.141837	+	0.409812i
$914$	−14.4017	−	20.2243i	−0.476365	−	0.668962i
$915$	−4.65614	−	19.1929i	−0.153927	−	0.634497i
$916$	−0.790093	−	1.73006i	−0.0261054	−	0.0571628i
$917$	5.08667	−	14.5409i	0.167977	−	0.480184i
$918$	−1.37253	−	0.882073i	−0.0453003	−	0.0291127i
$919$	−13.3742	−	23.1648i	−0.441175	−	0.764137i	0.556602	−	0.830779i	$-0.312105\pi$
$919$	−13.3742	−	23.1648i	−0.441175	−	0.764137i	−0.997777	+	0.0666418i	$0.978772\pi$
$920$	6.84879	−	13.4084i	0.225798	−	0.442063i
$921$	−10.8639	+	18.8167i	−0.357976	+	0.620033i
$922$	1.21413	−	25.4878i	0.0399853	−	0.839395i
$923$	0.0353380	+	0.245781i	0.00116317	+	0.00808999i
$924$	−4.79098	−	3.10145i	−0.157612	−	0.102030i
$925$	−35.0951	−	10.3049i	−1.15392	−	0.338822i
$926$	21.6644	−	2.06870i	0.711937	−	0.0679818i
$927$	0.541586	+	1.56481i	0.0177880	+	0.0513951i
$928$	0.310851	+	0.244456i	0.0102042	+	0.00802467i
$929$	38.1383	+	36.3648i	1.25128	+	1.19309i	0.972543	+	0.232722i	$0.0747632\pi$
$929$	38.1383	+	36.3648i	1.25128	+	1.19309i	0.278734	+	0.960368i	$0.410085\pi$
$930$	4.88077	+	5.63271i	0.160047	+	0.184704i
$931$	25.6700	−	19.9132i	0.841299	−	0.652630i
$932$	−22.4584	+	14.4331i	−0.735649	+	0.472773i
$933$	10.9420	−	31.6149i	0.358226	−	1.03503i
$934$	4.84180	−	19.9582i	0.158428	−	0.653051i
$935$	8.68517	+	6.83009i	0.284035	+	0.223368i
$936$	−0.733928	−	0.141453i	−0.0239892	−	0.00462354i
$937$	14.0772	−	30.8247i	0.459881	−	1.00700i	−0.527633	−	0.849472i	$-0.676920\pi$
$937$	14.0772	−	30.8247i	0.459881	−	1.00700i	0.987515	−	0.157527i	$-0.0503523\pi$
$938$	−28.1640	+	8.16846i	−0.919588	+	0.266710i
$939$	3.65739	+	8.00857i	0.119354	+	0.261350i
$940$	15.8996	−	12.5036i	0.518589	−	0.407823i
$941$	−25.8646	+	13.3341i	−0.843162	+	0.434680i	−0.824985	−	0.565155i	$-0.808817\pi$
$941$	−25.8646	+	13.3341i	−0.843162	+	0.434680i	−0.0181770	+	0.999835i	$0.505786\pi$
$942$	−0.0394089	+	0.0682583i	−0.00128401	+	0.00222398i
$943$	27.4905	−	24.0024i	0.895213	−	0.781624i
$944$	9.70847			0.315984
$945$	4.12926	+	7.20712i	0.134325	+	0.234448i
$946$	0.588002	+	4.08964i	0.0191176	+	0.132966i
$947$	−14.2724	+	20.0428i	−0.463791	+	0.651303i	−0.978545	−	0.206035i	$-0.933944\pi$
$947$	−14.2724	+	20.0428i	−0.463791	+	0.651303i	0.514754	+	0.857338i	$0.327883\pi$
$948$	0.454079	−	0.432964i	0.0147478	−	0.0140620i
$949$	−3.32266	−	4.66603i	−0.107858	−	0.151466i
$950$	22.1311	+	4.26542i	0.718027	+	0.138388i
$951$	−0.964562	+	6.70868i	−0.0312781	+	0.217544i
$952$	1.39831	+	4.08387i	0.0453195	+	0.132359i
$953$	4.38672	+	5.06255i	0.142100	+	0.163992i	0.822338	−	0.568999i	$-0.192669\pi$
$953$	4.38672	+	5.06255i	0.142100	+	0.163992i	−0.680238	+	0.732991i	$0.738124\pi$
$954$	2.52770	+	1.30312i	0.0818374	+	0.0421901i
$955$	3.58363	+	75.2297i	0.115964	+	2.43438i
$956$	3.60909	−	0.695595i	0.116726	−	0.0224971i
$957$	0.617385	+	0.588675i	0.0199572	+	0.0190292i
$958$	1.58430	−	11.0191i	0.0511866	−	0.356010i
$959$	−10.5251	−	8.33364i	−0.339874	−	0.269107i
$960$	1.30418	−	2.85575i	0.0420921	−	0.0921689i
$961$	−5.97979	−	24.6490i	−0.192897	−	0.795131i
$962$	5.60419	+	0.535135i	0.180686	+	0.0172534i
$963$	−12.4565	−	4.98684i	−0.401406	−	0.160699i
$964$	−0.452848	+	9.50644i	−0.0145852	+	0.306182i
$965$	−19.0316			−0.612649
$966$	11.5396	−	5.27622i	0.371279	−	0.169760i
$967$	18.9645			0.609859			0.304929	−	0.952375i	$-0.401367\pi$
$967$	18.9645			0.609859			0.304929	+	0.952375i	$0.401367\pi$
$968$	0.301993	−	6.33960i	0.00970641	−	0.203763i
$969$	−7.02981	−	2.81431i	−0.225830	−	0.0904087i
$970$	−35.1269	−	3.35421i	−1.12786	−	0.107697i
$971$	−8.28281	−	34.1422i	−0.265808	−	1.09568i	−0.935582	−	0.353110i	$-0.885124\pi$
$971$	−8.28281	−	34.1422i	−0.265808	−	1.09568i	0.669774	−	0.742565i	$-0.266391\pi$
$972$	−0.415415	+	0.909632i	−0.0133244	+	0.0291765i
$973$	−4.70858	+	31.9960i	−0.150950	+	1.02575i
$974$	2.35404	−	16.3727i	0.0754285	−	0.524616i
$975$	−2.62693	−	2.50477i	−0.0841289	−	0.0802168i
$976$	−6.17708	+	1.19053i	−0.197724	+	0.0381081i
$977$	−1.95780	−	41.0992i	−0.0626355	−	1.31488i	−0.783321	−	0.621618i	$-0.786476\pi$
$977$	−1.95780	−	41.0992i	−0.0626355	−	1.31488i	0.720685	−	0.693262i	$-0.243827\pi$
$978$	6.55603	+	3.37987i	0.209639	+	0.108076i
$979$	−18.3674	−	21.1971i	−0.587025	−	0.677463i
$980$	3.27160	−	21.7313i	0.104507	−	0.694181i
$981$	−2.07382	+	14.4237i	−0.0662118	+	0.460513i
$982$	−10.1845	−	1.96290i	−0.324999	−	0.0626385i
$983$	−19.1238	−	26.8556i	−0.609954	−	0.856561i	0.387922	−	0.921692i	$-0.373193\pi$
$983$	−19.1238	−	26.8556i	−0.609954	−	0.856561i	−0.997877	+	0.0651309i	$0.979254\pi$
$984$	5.50733	−	5.25123i	0.175567	−	0.167403i
$985$	11.3042	−	15.8745i	0.360182	−	0.505804i
$986$	−0.0918220	−	0.638636i	−0.00292421	−	0.0203383i
$987$	17.0462	+	0.0564729i	0.542587	+	0.00179755i
$988$	−3.46898			−0.110363
$989$	−8.36999	−	3.78444i	−0.266150	−	0.120338i
$990$	3.38611	−	5.86491i	0.107618	−	0.186399i
$991$	55.8152	−	28.7747i	1.77303	−	0.914059i	0.853416	−	0.521230i	$-0.174527\pi$
$991$	55.8152	−	28.7747i	1.77303	−	0.914059i	0.919612	−	0.392829i	$-0.128504\pi$
$992$	1.86611	−	1.46752i	0.0592490	−	0.0465939i
$993$	7.37731	+	16.1541i	0.234112	+	0.512633i
$994$	−0.634118	−	0.608654i	−0.0201130	−	0.0193053i
$995$	2.40674	−	5.27003i	0.0762989	−	0.167071i
$996$	−5.96475	−	1.14961i	−0.189000	−	0.0364268i
$997$	−35.7082	−	28.0813i	−1.13089	−	0.889343i	−0.136042	−	0.990703i	$-0.543438\pi$
$997$	−35.7082	−	28.0813i	−1.13089	−	0.889343i	−0.994850	+	0.101360i	$0.967681\pi$
$998$	5.54356	−	22.8508i	0.175478	−	0.723331i
$999$	2.46347	−	7.11774i	0.0779409	−	0.225195i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.y.a.25.1	✓	160
7.2	even	3	inner	966.2.y.a.163.1	yes	160
23.12	even	11	inner	966.2.y.a.403.1	yes	160
161.58	even	33	inner	966.2.y.a.541.1	yes	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.y.a.25.1	✓	160	1.1	even	1	trivial
966.2.y.a.163.1	yes	160	7.2	even	3	inner
966.2.y.a.403.1	yes	160	23.12	even	11	inner
966.2.y.a.541.1	yes	160	161.58	even	33	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)

\(f(q)\)	\(=\)	\(q+(-0.0475819 + 0.998867i) q^{2} +(-0.928368 - 0.371662i) q^{3} +(-0.995472 - 0.0950560i) q^{4} +(-0.740155 - 3.05096i) q^{5} +(0.415415 - 0.909632i) q^{6} +(0.385204 - 2.61756i) q^{7} +(0.142315 - 0.989821i) q^{8} +(0.723734 + 0.690079i) q^{9} +O(q^{10})\)	\(q+(-0.0475819 + 0.998867i) q^{2} +(-0.928368 - 0.371662i) q^{3} +(-0.995472 - 0.0950560i) q^{4} +(-0.740155 - 3.05096i) q^{5} +(0.415415 - 0.909632i) q^{6} +(0.385204 - 2.61756i) q^{7} +(0.142315 - 0.989821i) q^{8} +(0.723734 + 0.690079i) q^{9} +(3.08272 - 0.594146i) q^{10} +(-0.102640 - 2.15469i) q^{11} +(0.888835 + 0.458227i) q^{12} +(-0.489466 - 0.564874i) q^{13} +(2.59627 + 0.509316i) q^{14} +(-0.446791 + 3.10750i) q^{15} +(0.981929 + 0.189251i) q^{16} +(-0.946382 - 1.32901i) q^{17} +(-0.723734 + 0.690079i) q^{18} +(-2.69214 + 3.78059i) q^{19} +(0.446791 + 3.10750i) q^{20} +(-1.33046 + 2.28689i) q^{21} +2.15713 q^{22} +(-2.57762 + 4.04424i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(-4.31635 + 2.22523i) q^{25} +(0.587524 - 0.462034i) q^{26} +(-0.415415 - 0.909632i) q^{27} +(-0.632274 + 2.56909i) q^{28} +(0.164279 - 0.359722i) q^{29} +(-3.08272 - 0.594146i) q^{30} +(-1.86611 - 1.46752i) q^{31} +(-0.235759 + 0.971812i) q^{32} +(-0.705528 + 2.03849i) q^{33} +(1.37253 - 0.882073i) q^{34} +(-8.27118 + 0.762159i) q^{35} +(-0.654861 - 0.755750i) q^{36} +(5.45116 + 5.19767i) q^{37} +(-3.64821 - 2.86898i) q^{38} +(0.244462 + 0.706327i) q^{39} +(-3.12524 + 0.298424i) q^{40} +(-7.30136 - 2.14387i) q^{41} +(-2.22100 - 1.43777i) q^{42} +(0.272585 + 1.89587i) q^{43} +(-0.102640 + 2.15469i) q^{44} +(1.56973 - 2.71885i) q^{45} +(-3.91701 - 2.76713i) q^{46} +(-3.22145 - 5.57971i) q^{47} +(-0.841254 - 0.540641i) q^{48} +(-6.70324 - 2.01659i) q^{49} +(-2.01733 - 4.41734i) q^{50} +(0.384648 + 1.58554i) q^{51} +(0.433555 + 0.608843i) q^{52} +(-0.930128 - 2.68743i) q^{53} +(0.928368 - 0.371662i) q^{54} +(-6.49789 + 1.90795i) q^{55} +(-2.53610 - 0.753800i) q^{56} +(3.90440 - 2.50921i) q^{57} +(0.351498 + 0.181210i) q^{58} +(9.53303 - 1.83734i) q^{59} +(0.740155 - 3.05096i) q^{60} +(-5.84014 + 2.33804i) q^{61} +(1.55465 - 1.79417i) q^{62} +(2.08511 - 1.62860i) q^{63} +(-0.959493 - 0.281733i) q^{64} +(-1.36113 + 1.91144i) q^{65} +(-2.00261 - 0.801724i) q^{66} +(-9.85157 + 5.07884i) q^{67} +(0.815766 + 1.41295i) q^{68} +(3.89607 - 2.79654i) q^{69} +(-0.367737 - 8.29808i) q^{70} +(-0.279477 - 0.179609i) q^{71} +(0.786053 - 0.618159i) q^{72} +(7.62906 + 0.728487i) q^{73} +(-5.45116 + 5.19767i) q^{74} +(4.83419 - 0.461610i) q^{75} +(3.03932 - 3.50756i) q^{76} +(-5.67956 - 0.561325i) q^{77} +(-0.717159 + 0.210577i) q^{78} +(0.205206 - 0.592905i) q^{79} +(-0.149381 - 3.13590i) q^{80} +(0.0475819 + 0.998867i) q^{81} +(2.48886 - 7.19108i) q^{82} +(-5.82846 + 1.71139i) q^{83} +(1.54182 - 2.15007i) q^{84} +(-3.35428 + 3.87104i) q^{85} +(-1.90670 + 0.182067i) q^{86} +(-0.286207 + 0.272898i) q^{87} +(-2.14736 - 0.205048i) q^{88} +(10.2206 - 8.03754i) q^{89} +(2.64108 + 1.69732i) q^{90} +(-1.66714 + 1.06362i) q^{91} +(2.95038 - 3.78091i) q^{92} +(1.18701 + 2.05596i) q^{93} +(5.72668 - 2.95231i) q^{94} +(13.5270 + 5.41540i) q^{95} +(0.580057 - 0.814576i) q^{96} +(-10.7845 - 3.16660i) q^{97} +(2.33326 - 6.59969i) q^{98} +(1.41262 - 1.63025i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q - 8 q^{2} - 8 q^{3} + 8 q^{4} + 2 q^{5} - 16 q^{6} - 2 q^{7} + 16 q^{8} + 8 q^{9}+O(q^{10}) \) 160 * q - 8 * q^2 - 8 * q^3 + 8 * q^4 + 2 * q^5 - 16 * q^6 - 2 * q^7 + 16 * q^8 + 8 * q^9	\( 160 q - 8 q^{2} - 8 q^{3} + 8 q^{4} + 2 q^{5} - 16 q^{6} - 2 q^{7} + 16 q^{8} + 8 q^{9} - 2 q^{10} + 4 q^{11} - 8 q^{12} + 4 q^{13} - 9 q^{14} - 18 q^{15} + 8 q^{16} + 9 q^{17} - 8 q^{18} + 18 q^{20} + 7 q^{21} + 52 q^{22} + 22 q^{23} - 80 q^{24} + 42 q^{25} + 2 q^{26} + 16 q^{27} - 18 q^{28} - 54 q^{29} + 2 q^{30} - 15 q^{31} - 8 q^{32} + 18 q^{33} + 84 q^{34} + 82 q^{35} - 16 q^{36} + 3 q^{37} + 11 q^{38} + 2 q^{39} - 13 q^{40} + 22 q^{41} - 2 q^{42} - 96 q^{43} + 4 q^{44} - 20 q^{45} - 26 q^{47} + 16 q^{48} - 2 q^{49} - 4 q^{50} + 13 q^{51} - 2 q^{52} + 16 q^{53} + 8 q^{54} - 34 q^{55} + 2 q^{56} - 22 q^{57} - 5 q^{58} - 6 q^{59} - 2 q^{60} + 40 q^{61} - 8 q^{62} - 2 q^{63} - 16 q^{64} - 82 q^{65} + 4 q^{66} + 10 q^{67} - 46 q^{68} - 22 q^{69} + 100 q^{70} + 92 q^{71} - 8 q^{72} + 68 q^{73} - 3 q^{74} + 2 q^{75} - 7 q^{77} - 18 q^{78} - 78 q^{79} + 2 q^{80} + 8 q^{81} + 55 q^{82} - 42 q^{83} - 9 q^{84} + 50 q^{85} + 40 q^{86} + 6 q^{87} + 7 q^{88} - 80 q^{89} + 4 q^{90} - 62 q^{91} + 66 q^{92} + 26 q^{93} + 4 q^{94} - 17 q^{95} + 8 q^{96} - 8 q^{97} - 3 q^{98} + 36 q^{99}+O(q^{100}) \) 160 * q - 8 * q^2 - 8 * q^3 + 8 * q^4 + 2 * q^5 - 16 * q^6 - 2 * q^7 + 16 * q^8 + 8 * q^9 - 2 * q^10 + 4 * q^11 - 8 * q^12 + 4 * q^13 - 9 * q^14 - 18 * q^15 + 8 * q^16 + 9 * q^17 - 8 * q^18 + 18 * q^20 + 7 * q^21 + 52 * q^22 + 22 * q^23 - 80 * q^24 + 42 * q^25 + 2 * q^26 + 16 * q^27 - 18 * q^28 - 54 * q^29 + 2 * q^30 - 15 * q^31 - 8 * q^32 + 18 * q^33 + 84 * q^34 + 82 * q^35 - 16 * q^36 + 3 * q^37 + 11 * q^38 + 2 * q^39 - 13 * q^40 + 22 * q^41 - 2 * q^42 - 96 * q^43 + 4 * q^44 - 20 * q^45 - 26 * q^47 + 16 * q^48 - 2 * q^49 - 4 * q^50 + 13 * q^51 - 2 * q^52 + 16 * q^53 + 8 * q^54 - 34 * q^55 + 2 * q^56 - 22 * q^57 - 5 * q^58 - 6 * q^59 - 2 * q^60 + 40 * q^61 - 8 * q^62 - 2 * q^63 - 16 * q^64 - 82 * q^65 + 4 * q^66 + 10 * q^67 - 46 * q^68 - 22 * q^69 + 100 * q^70 + 92 * q^71 - 8 * q^72 + 68 * q^73 - 3 * q^74 + 2 * q^75 - 7 * q^77 - 18 * q^78 - 78 * q^79 + 2 * q^80 + 8 * q^81 + 55 * q^82 - 42 * q^83 - 9 * q^84 + 50 * q^85 + 40 * q^86 + 6 * q^87 + 7 * q^88 - 80 * q^89 + 4 * q^90 - 62 * q^91 + 66 * q^92 + 26 * q^93 + 4 * q^94 - 17 * q^95 + 8 * q^96 - 8 * q^97 - 3 * q^98 + 36 * q^99

Introduction

L-functions

Modular forms

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Database

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