LMFDB - Embedded newform 966.2.y.b.25.3

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			25.3
Character	$\chi$	$=$	966.25
Dual form			966.2.y.b.541.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0475819 + 0.998867i) q^{2} +(0.928368 + 0.371662i) q^{3} +(-0.995472 - 0.0950560i) q^{4} +(-0.365274 - 1.50568i) q^{5} +(-0.415415 + 0.909632i) q^{6} +(0.990231 + 2.45346i) q^{7} +(0.142315 - 0.989821i) q^{8} +(0.723734 + 0.690079i) q^{9} +O(q^{10})$	\(q+(-0.0475819 + 0.998867i) q^{2} +(0.928368 + 0.371662i) q^{3} +(-0.995472 - 0.0950560i) q^{4} +(-0.365274 - 1.50568i) q^{5} +(-0.415415 + 0.909632i) q^{6} +(0.990231 + 2.45346i) q^{7} +(0.142315 - 0.989821i) q^{8} +(0.723734 + 0.690079i) q^{9} +(1.52136 - 0.293217i) q^{10} +(-0.199993 - 4.19837i) q^{11} +(-0.888835 - 0.458227i) q^{12} +(0.816388 + 0.942162i) q^{13} +(-2.49779 + 0.872369i) q^{14} +(0.220496 - 1.53358i) q^{15} +(0.981929 + 0.189251i) q^{16} +(4.64851 + 6.52792i) q^{17} +(-0.723734 + 0.690079i) q^{18} +(-0.719057 + 1.00977i) q^{19} +(0.220496 + 1.53358i) q^{20} +(0.00744112 + 2.64574i) q^{21} +4.20313 q^{22} +(1.62126 - 4.51348i) q^{23} +(0.500000 - 0.866025i) q^{24} +(2.31053 - 1.19116i) q^{25} +(-0.979941 + 0.770634i) q^{26} +(0.415415 + 0.909632i) q^{27} +(-0.752531 - 2.53647i) q^{28} +(-1.46004 + 3.19704i) q^{29} +(1.52136 + 0.293217i) q^{30} +(8.06598 + 6.34316i) q^{31} +(-0.235759 + 0.971812i) q^{32} +(1.37471 - 3.97196i) q^{33} +(-6.74171 + 4.33264i) q^{34} +(3.33241 - 2.38715i) q^{35} +(-0.654861 - 0.755750i) q^{36} +(-0.453486 - 0.432398i) q^{37} +(-0.974417 - 0.766290i) q^{38} +(0.407742 + 1.17809i) q^{39} +(-1.54234 + 0.147276i) q^{40} +(-1.68649 - 0.495197i) q^{41} +(-2.64310 - 0.118457i) q^{42} +(0.277224 + 1.92814i) q^{43} +(-0.199993 + 4.19837i) q^{44} +(0.774677 - 1.34178i) q^{45} +(4.43123 + 1.83419i) q^{46} +(-2.08057 - 3.60366i) q^{47} +(0.841254 + 0.540641i) q^{48} +(-5.03889 + 4.85897i) q^{49} +(1.07987 + 2.36459i) q^{50} +(1.88935 + 7.78799i) q^{51} +(-0.723134 - 1.01550i) q^{52} +(1.03085 + 2.97846i) q^{53} +(-0.928368 + 0.371662i) q^{54} +(-6.24835 + 1.83468i) q^{55} +(2.56941 - 0.630988i) q^{56} +(-1.04285 + 0.670196i) q^{57} +(-3.12394 - 1.61050i) q^{58} +(12.1832 - 2.34812i) q^{59} +(-0.365274 + 1.50568i) q^{60} +(8.67919 - 3.47462i) q^{61} +(-6.71977 + 7.75503i) q^{62} +(-0.976414 + 2.45899i) q^{63} +(-0.959493 - 0.281733i) q^{64} +(1.12039 - 1.57337i) q^{65} +(3.90205 + 1.56215i) q^{66} +(-10.1435 + 5.22936i) q^{67} +(-4.00694 - 6.94023i) q^{68} +(3.18262 - 3.58761i) q^{69} +(2.22589 + 3.44223i) q^{70} +(6.45242 + 4.14672i) q^{71} +(0.786053 - 0.618159i) q^{72} +(-14.1804 - 1.35407i) q^{73} +(0.453486 - 0.432398i) q^{74} +(2.58773 - 0.247098i) q^{75} +(0.811787 - 0.936852i) q^{76} +(10.1025 - 4.64803i) q^{77} +(-1.19616 + 0.351225i) q^{78} +(-2.47020 + 7.13718i) q^{79} +(-0.0737213 - 1.54760i) q^{80} +(0.0475819 + 0.998867i) q^{81} +(0.574882 - 1.66101i) q^{82} +(13.8521 - 4.06733i) q^{83} +(0.244086 - 2.63447i) q^{84} +(8.13098 - 9.38365i) q^{85} +(-1.93915 + 0.185166i) q^{86} +(-2.54367 + 2.42538i) q^{87} +(-4.18410 - 0.399533i) q^{88} +(-0.735385 + 0.578313i) q^{89} +(1.30340 + 0.837644i) q^{90} +(-1.50314 + 2.93593i) q^{91} +(-2.04296 + 4.33893i) q^{92} +(5.13069 + 8.88661i) q^{93} +(3.69857 - 1.90675i) q^{94} +(1.78305 + 0.713826i) q^{95} +(-0.580057 + 0.814576i) q^{96} +(-14.9196 - 4.38079i) q^{97} +(-4.61371 - 5.26438i) q^{98} +(2.75246 - 3.17651i) 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 $\left(\mathbb{Z}/966\mathbb{Z}\right)^\times$.

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

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
$5$	−0.365274	−	1.50568i	−0.163356	−	0.673361i	−0.993305	−	0.115522i	$-0.963146\pi$
$5$	−0.365274	−	1.50568i	−0.163356	−	0.673361i	0.829949	−	0.557839i	$-0.188369\pi$
$6$	−0.415415	+	0.909632i	−0.169592	+	0.371356i
$7$	0.990231	+	2.45346i	0.374272	+	0.927319i
$7$	0.990231	+	2.45346i	0.374272	+	0.927319i
$8$	0.142315	−	0.989821i	0.0503159	−	0.349955i
$9$	0.723734	+	0.690079i	0.241245	+	0.230026i
$10$	1.52136	−	0.293217i	0.481095	−	0.0927234i
$11$	−0.199993	−	4.19837i	−0.0603002	−	1.26586i	−0.802897	−	0.596117i	$-0.796709\pi$
$11$	−0.199993	−	4.19837i	−0.0603002	−	1.26586i	0.742597	−	0.669738i	$-0.233594\pi$
$12$	−0.888835	−	0.458227i	−0.256585	−	0.132279i
$13$	0.816388	+	0.942162i	0.226425	+	0.261309i	0.857583	−	0.514346i	$-0.171965\pi$
$13$	0.816388	+	0.942162i	0.226425	+	0.261309i	−0.631157	+	0.775655i	$0.717420\pi$
$14$	−2.49779	+	0.872369i	−0.667563	+	0.233150i
$15$	0.220496	−	1.53358i	0.0569319	−	0.395970i
$16$	0.981929	+	0.189251i	0.245482	+	0.0473128i
$17$	4.64851	+	6.52792i	1.12743	+	1.58325i	0.755707	+	0.654909i	$0.227293\pi$
$17$	4.64851	+	6.52792i	1.12743	+	1.58325i	0.371722	+	0.928344i	$0.378767\pi$
$18$	−0.723734	+	0.690079i	−0.170586	+	0.162653i
$19$	−0.719057	+	1.00977i	−0.164963	+	0.231658i	−0.888780	−	0.458334i	$-0.848447\pi$
$19$	−0.719057	+	1.00977i	−0.164963	+	0.231658i	0.723817	+	0.689992i	$0.242386\pi$
$20$	0.220496	+	1.53358i	0.0493044	+	0.342920i
$21$	0.00744112	+	2.64574i	0.00162379	+	0.577348i
$22$	4.20313			0.896110
$23$	1.62126	−	4.51348i	0.338057	−	0.941126i
$23$	1.62126	−	4.51348i	0.338057	−	0.941126i
$24$	0.500000	−	0.866025i	0.102062	−	0.176777i
$25$	2.31053	−	1.19116i	0.462106	−	0.238232i
$26$	−0.979941	+	0.770634i	−0.192182	+	0.151134i
$27$	0.415415	+	0.909632i	0.0799467	+	0.175059i
$28$	−0.752531	−	2.53647i	−0.142215	−	0.479348i
$29$	−1.46004	+	3.19704i	−0.271122	+	0.593675i	−0.995397	−	0.0958366i	$-0.969447\pi$
$29$	−1.46004	+	3.19704i	−0.271122	+	0.593675i	0.724275	+	0.689511i	$0.242175\pi$
$30$	1.52136	+	0.293217i	0.277760	+	0.0535339i
$31$	8.06598	+	6.34316i	1.44869	+	1.13926i	0.964429	+	0.264343i	$0.0851551\pi$
$31$	8.06598	+	6.34316i	1.44869	+	1.13926i	0.484264	+	0.874922i	$0.339087\pi$
$32$	−0.235759	+	0.971812i	−0.0416767	+	0.171794i
$33$	1.37471	−	3.97196i	0.239306	−	0.691430i
$34$	−6.74171	+	4.33264i	−1.15619	+	0.743041i
$35$	3.33241	−	2.38715i	0.563281	−	0.403503i
$36$	−0.654861	−	0.755750i	−0.109143	−	0.125958i
$37$	−0.453486	−	0.432398i	−0.0745527	−	0.0710858i	0.651887	−	0.758316i	$-0.273978\pi$
$37$	−0.453486	−	0.432398i	−0.0745527	−	0.0710858i	−0.726439	+	0.687231i	$0.758826\pi$
$38$	−0.974417	−	0.766290i	−0.158071	−	0.124309i
$39$	0.407742	+	1.17809i	0.0652910	+	0.188646i
$40$	−1.54234	+	0.147276i	−0.243865	+	0.0232863i
$41$	−1.68649	−	0.495197i	−0.263385	−	0.0773368i	0.147374	−	0.989081i	$-0.452918\pi$
$41$	−1.68649	−	0.495197i	−0.263385	−	0.0773368i	−0.410759	+	0.911744i	$0.634736\pi$
$42$	−2.64310	−	0.118457i	−0.407839	−	0.0182783i
$43$	0.277224	+	1.92814i	0.0422763	+	0.294038i	0.999980	+	0.00628293i	$0.00199993\pi$
$43$	0.277224	+	1.92814i	0.0422763	+	0.294038i	−0.957704	+	0.287755i	$0.907091\pi$
$44$	−0.199993	+	4.19837i	−0.0301501	+	0.632928i
$45$	0.774677	−	1.34178i	0.115482	−	0.200021i
$46$	4.43123	+	1.83419i	0.653349	+	0.270436i
$47$	−2.08057	−	3.60366i	−0.303483	−	0.525648i	0.673440	−	0.739242i	$-0.264816\pi$
$47$	−2.08057	−	3.60366i	−0.303483	−	0.525648i	−0.976922	+	0.213595i	$0.931483\pi$
$48$	0.841254	+	0.540641i	0.121424	+	0.0780348i
$49$	−5.03889	+	4.85897i	−0.719841	+	0.694139i
$50$	1.07987	+	2.36459i	0.152717	+	0.334403i
$51$	1.88935	+	7.78799i	0.264561	+	1.09054i
$52$	−0.723134	−	1.01550i	−0.100281	−	0.140824i
$53$	1.03085	+	2.97846i	0.141599	+	0.409123i	0.993394	−	0.114752i	$-0.0366073\pi$
$53$	1.03085	+	2.97846i	0.141599	+	0.409123i	−0.851795	+	0.523875i	$0.824486\pi$
$54$	−0.928368	+	0.371662i	−0.126335	+	0.0505769i
$55$	−6.24835	+	1.83468i	−0.842527	+	0.247388i
$56$	2.56941	−	0.630988i	0.343351	−	0.0843194i
$57$	−1.04285	+	0.670196i	−0.138128	+	0.0887696i
$58$	−3.12394	−	1.61050i	−0.410194	−	0.211470i
$59$	12.1832	−	2.34812i	1.58612	−	0.305700i	0.681467	−	0.731849i	$-0.261342\pi$
$59$	12.1832	−	2.34812i	1.58612	−	0.305700i	0.904653	+	0.426149i	$0.140130\pi$
$60$	−0.365274	+	1.50568i	−0.0471567	+	0.194383i
$61$	8.67919	−	3.47462i	1.11126	−	0.444880i	0.257881	−	0.966177i	$-0.416976\pi$
$61$	8.67919	−	3.47462i	1.11126	−	0.444880i	0.853375	+	0.521297i	$0.174552\pi$
$62$	−6.71977	+	7.75503i	−0.853411	+	0.984889i
$63$	−0.976414	+	2.45899i	−0.123017	+	0.309803i
$64$	−0.959493	−	0.281733i	−0.119937	−	0.0352166i
$65$	1.12039	−	1.57337i	0.138967	−	0.195152i
$66$	3.90205	+	1.56215i	0.480309	+	0.192287i
$67$	−10.1435	+	5.22936i	−1.23923	+	0.638868i	−0.948148	−	0.317829i	$-0.897046\pi$
$67$	−10.1435	+	5.22936i	−1.23923	+	0.638868i	−0.291084	+	0.956698i	$0.594016\pi$
$68$	−4.00694	−	6.94023i	−0.485913	−	0.841627i
$69$	3.18262	−	3.58761i	0.383142	−	0.431897i
$70$	2.22589	+	3.44223i	0.266045	+	0.411425i
$71$	6.45242	+	4.14672i	0.765761	+	0.492125i	0.864280	−	0.503010i	$-0.167774\pi$
$71$	6.45242	+	4.14672i	0.765761	+	0.492125i	−0.0985191	+	0.995135i	$0.531411\pi$
$72$	0.786053	−	0.618159i	0.0926372	−	0.0728507i
$73$	−14.1804	−	1.35407i	−1.65970	−	0.158482i	−0.777345	−	0.629074i	$-0.783434\pi$
$73$	−14.1804	−	1.35407i	−1.65970	−	0.158482i	−0.882351	+	0.470592i	$0.844040\pi$
$74$	0.453486	−	0.432398i	0.0527167	−	0.0502653i
$75$	2.58773	−	0.247098i	0.298805	−	0.0285324i
$76$	0.811787	−	0.936852i	0.0931183	−	0.107464i
$77$	10.1025	−	4.64803i	1.15128	−	0.529692i
$78$	−1.19616	+	0.351225i	−0.135439	+	0.0397684i
$79$	−2.47020	+	7.13718i	−0.277920	+	0.802996i	0.716508	+	0.697578i	$0.245739\pi$
$79$	−2.47020	+	7.13718i	−0.277920	+	0.802996i	−0.994428	+	0.105418i	$0.966382\pi$
$80$	−0.0737213	−	1.54760i	−0.00824229	−	0.173027i
$81$	0.0475819	+	0.998867i	0.00528688	+	0.110985i
$82$	0.574882	−	1.66101i	0.0634851	−	0.183428i
$83$	13.8521	−	4.06733i	1.52046	−	0.446448i	0.588347	−	0.808609i	$-0.299779\pi$
$83$	13.8521	−	4.06733i	1.52046	−	0.446448i	0.932116	+	0.362161i	$0.117961\pi$
$84$	0.244086	−	2.63447i	0.0266320	−	0.287444i
$85$	8.13098	−	9.38365i	0.881929	−	1.01780i
$86$	−1.93915	+	0.185166i	−0.209103	+	0.0199670i
$87$	−2.54367	+	2.42538i	−0.272710	+	0.260029i
$88$	−4.18410	−	0.399533i	−0.446026	−	0.0425904i
$89$	−0.735385	+	0.578313i	−0.0779507	+	0.0613011i	−0.656374	−	0.754436i	$-0.727911\pi$
$89$	−0.735385	+	0.578313i	−0.0779507	+	0.0613011i	0.578423	+	0.815737i	$0.303668\pi$
$90$	1.30340	+	0.837644i	0.137390	+	0.0882955i
$91$	−1.50314	+	2.93593i	−0.157572	+	0.307769i
$92$	−2.04296	+	4.33893i	−0.212993	+	0.452365i
$93$	5.13069	+	8.88661i	0.532027	+	0.921498i
$94$	3.69857	−	1.90675i	0.381479	−	0.196666i
$95$	1.78305	+	0.713826i	0.182937	+	0.0732370i
$96$	−0.580057	+	0.814576i	−0.0592018	+	0.0831373i
$97$	−14.9196	−	4.38079i	−1.51486	−	0.444802i	−0.584480	−	0.811408i	$-0.698701\pi$
$97$	−14.9196	−	4.38079i	−1.51486	−	0.444802i	−0.930376	+	0.366607i	$0.880519\pi$
$98$	−4.61371	−	5.26438i	−0.466055	−	0.531783i
$99$	2.75246	−	3.17651i	0.276633	−	0.319252i
$100$	−2.41329	+	0.966137i	−0.241329	+	0.0966137i
$101$	3.92508	−	16.1794i	0.390560	−	1.60991i	−0.349205	−	0.937046i	$-0.613548\pi$
$101$	3.92508	−	16.1794i	0.390560	−	1.60991i	0.739766	−	0.672865i	$-0.234936\pi$
$102$	−7.86907	+	1.51664i	−0.779154	+	0.150170i
$103$	−1.91407	−	0.986773i	−0.188599	−	0.0972297i	0.361341	−	0.932434i	$-0.382319\pi$
$103$	−1.91407	−	0.986773i	−0.188599	−	0.0972297i	−0.549940	+	0.835204i	$0.685349\pi$
$104$	1.04876	−	0.673995i	0.102839	−	0.0660907i
$105$	3.98092	−	0.977625i	0.388498	−	0.0954064i
$106$	−3.02413	+	0.887966i	−0.293730	+	0.0862469i
$107$	−9.01095	+	3.60744i	−0.871122	+	0.348744i	−0.763779	−	0.645478i	$-0.776658\pi$
$107$	−9.01095	+	3.60744i	−0.871122	+	0.348744i	−0.107342	+	0.994222i	$0.534234\pi$
$108$	−0.327068	−	0.945001i	−0.0314721	−	0.0909327i
$109$	−0.341962	−	0.480218i	−0.0327540	−	0.0459966i	0.797874	−	0.602824i	$-0.205958\pi$
$109$	−0.341962	−	0.480218i	−0.0327540	−	0.0459966i	−0.830628	+	0.556827i	$0.812018\pi$
$110$	−1.53529	−	6.32857i	−0.146385	−	0.603406i
$111$	−0.260296	−	0.569968i	−0.0247062	−	0.0540990i
$112$	0.508016	+	2.59652i	0.0480030	+	0.245348i
$113$	−10.9533	−	7.03927i	−1.03040	−	0.662199i	−0.0878069	−	0.996138i	$-0.527986\pi$
$113$	−10.9533	−	7.03927i	−1.03040	−	0.662199i	−0.942595	+	0.333939i	$0.891622\pi$
$114$	−0.619816	−	1.07355i	−0.0580511	−	0.100547i
$115$	−7.38807	−	0.792447i	−0.688941	−	0.0738961i
$116$	1.75732	−	3.04377i	0.163163	−	0.282607i
$117$	−0.0593185	+	1.24525i	−0.00548399	+	0.115123i
$118$	1.76576	+	12.2811i	0.162552	+	1.13057i
$119$	−11.4129	+	17.8691i	−1.04622	+	1.63805i
$120$	−1.48659	−	0.436504i	−0.135707	−	0.0398471i
$121$	−6.63612	+	0.633672i	−0.603283	+	0.0576066i
$122$	3.05772	+	8.83469i	0.276833	+	0.799855i
$123$	−1.38163	−	1.08653i	−0.124578	−	0.0979690i
$124$	−7.42650	−	7.08116i	−0.666920	−	0.635907i
$125$	−7.71054	−	8.89844i	−0.689652	−	0.795900i
$126$	−2.40974	−	1.09231i	−0.214677	−	0.0973109i
$127$	−12.0380	+	7.73632i	−1.06820	+	0.686488i	−0.951801	−	0.306716i	$-0.900770\pi$
$127$	−12.0380	+	7.73632i	−1.06820	+	0.686488i	−0.116394	+	0.993203i	$0.537134\pi$
$128$	0.327068	−	0.945001i	0.0289090	−	0.0835271i
$129$	−0.459250	+	1.89306i	−0.0404347	+	0.166674i
$130$	1.51828	+	1.19399i	0.133162	+	0.104719i
$131$	−12.5229	−	2.41360i	−1.09413	−	0.210877i	−0.389909	−	0.920853i	$-0.627494\pi$
$131$	−12.5229	−	2.41360i	−1.09413	−	0.210877i	−0.704226	+	0.709976i	$0.748706\pi$
$132$	−1.74604	+	3.82330i	−0.151974	+	0.332776i
$133$	−3.18947	−	0.764265i	−0.276562	−	0.0662702i
$134$	−4.74079	−	10.3809i	−0.409542	−	0.896772i
$135$	1.21787	−	0.957747i	0.104818	−	0.0824298i
$136$	7.12303	−	3.67218i	0.610795	−	0.314887i
$137$	2.58213	−	4.47239i	0.220607	−	0.382102i	−0.734386	−	0.678732i	$-0.762530\pi$
$137$	2.58213	−	4.47239i	0.220607	−	0.382102i	0.954992	+	0.296631i	$0.0958630\pi$
$138$	3.43211	+	3.34972i	0.292161	+	0.285147i
$139$	10.9167			0.925941			0.462971	−	0.886374i	$-0.346784\pi$
$139$	10.9167			0.925941			0.462971	+	0.886374i	$0.346784\pi$
$140$	−3.54424	+	2.05958i	−0.299543	+	0.174066i
$141$	−0.592193	−	4.11879i	−0.0498716	−	0.346865i
$142$	−4.44904	+	6.24780i	−0.373355	+	0.524304i
$143$	3.79227	−	3.61593i	0.317126	−	0.302379i
$144$	0.580057	+	0.814576i	0.0483381	+	0.0678813i
$145$	5.34703	+	1.03056i	0.444047	+	0.0855830i
$146$	2.02727	−	14.1000i	0.167778	−	1.16692i
$147$	−6.48384	+	2.63815i	−0.534778	+	0.217591i
$148$	0.410331	+	0.473547i	0.0337290	+	0.0389253i
$149$	7.39623	+	3.81302i	0.605923	+	0.312375i	0.733748	−	0.679422i	$-0.237769\pi$
$149$	7.39623	+	3.81302i	0.605923	+	0.312375i	−0.127825	+	0.991797i	$0.540800\pi$
$150$	0.123689	+	2.59656i	0.0100992	+	0.212008i
$151$	18.1144	−	3.49126i	1.47413	−	0.284115i	0.612020	−	0.790842i	$-0.290357\pi$
$151$	18.1144	−	3.49126i	1.47413	−	0.284115i	0.862106	+	0.506727i	$0.169145\pi$
$152$	0.897164	+	0.855444i	0.0727696	+	0.0693857i
$153$	−1.14050	+	7.93232i	−0.0922036	+	0.641290i
$154$	4.16207	+	10.3122i	0.335389	+	0.830980i
$155$	6.60448	−	14.4618i	0.530484	−	1.16160i
$156$	−0.293911	−	1.21152i	−0.0235317	−	0.0969991i
$157$	−3.04763	−	0.291013i	−0.243227	−	0.0232254i	−0.0272695	−	0.999628i	$-0.508681\pi$
$157$	−3.04763	−	0.291013i	−0.243227	−	0.0232254i	−0.215958	+	0.976403i	$0.569287\pi$
$158$	−7.01156	−	2.80701i	−0.557810	−	0.223313i
$159$	−0.149969	+	3.14824i	−0.0118933	+	0.249671i
$160$	1.54935			0.122487
$161$	12.6790	−	0.491689i	0.999249	−	0.0387505i
$162$	−1.00000			−0.0785674
$163$	−0.316609	+	6.64644i	−0.0247987	+	0.520590i	0.951957	+	0.306233i	$0.0990686\pi$
$163$	−0.316609	+	6.64644i	−0.0247987	+	0.520590i	−0.976755	+	0.214357i	$0.931234\pi$
$164$	1.63178	+	0.653266i	0.127420	+	0.0510115i
$165$	−6.48265	−	0.619018i	−0.504674	−	0.0481905i
$166$	3.40362	+	14.0299i	0.264172	+	1.08893i
$167$	2.35888	−	5.16523i	0.182536	−	0.399698i	−0.796139	−	0.605114i	$-0.793128\pi$
$167$	2.35888	−	5.16523i	0.182536	−	0.399698i	0.978675	+	0.205416i	$0.0658548\pi$
$168$	2.61987	+	0.369163i	0.202127	+	0.0284815i
$169$	1.62891	−	11.3293i	0.125301	−	0.871488i
$170$	8.98614	+	8.56827i	0.689205	+	0.657156i
$171$	−1.21723	+	0.234602i	−0.0930840	+	0.0179405i
$172$	−0.0926879	−	1.94576i	−0.00706739	−	0.148363i
$173$	−13.9957	−	7.21529i	−1.06407	−	0.548568i	−0.164967	−	0.986299i	$-0.552752\pi$
$173$	−13.9957	−	7.21529i	−1.06407	−	0.548568i	−0.899106	+	0.437731i	$0.855782\pi$
$174$	−2.30160	−	2.65619i	−0.174484	−	0.201365i
$175$	5.21041	+	4.48925i	0.393870	+	0.339356i
$176$	0.598168	−	4.16035i	0.0450886	−	0.313598i
$177$	12.1832	+	2.34812i	0.915747	+	0.176496i
$178$	−0.542667	−	0.762070i	−0.0406746	−	0.0571195i
$179$	8.14803	−	7.76914i	0.609013	−	0.580692i	−0.321519	−	0.946903i	$-0.604194\pi$
$179$	8.14803	−	7.76914i	0.609013	−	0.580692i	0.930532	+	0.366211i	$0.119345\pi$
$180$	−0.898714	+	1.26207i	−0.0669862	+	0.0940689i
$181$	−1.40792	−	9.79231i	−0.104650	−	0.727857i	−0.972815	−	0.231582i	$-0.925610\pi$
$181$	−1.40792	−	9.79231i	−0.104650	−	0.727857i	0.868165	−	0.496275i	$-0.165299\pi$
$182$	−2.86108	−	1.64114i	−0.212078	−	0.121649i
$183$	9.34887			0.691088
$184$	−4.23681	−	2.24710i	−0.312342	−	0.165658i
$185$	−0.485407	+	0.840749i	−0.0356878	+	0.0618131i
$186$	−9.12067	+	4.70203i	−0.668760	+	0.344770i
$187$	26.4770	−	20.8217i	1.93619	−	1.52263i
$188$	1.72860	+	3.78511i	0.126071	+	0.276058i
$189$	−1.82038	+	1.91995i	−0.132414	+	0.139656i
$190$	−0.797859	+	1.74707i	−0.0578828	+	0.126746i
$191$	−12.0161	−	2.31591i	−0.869453	−	0.167573i	−0.265033	−	0.964239i	$-0.585383\pi$
$191$	−12.0161	−	2.31591i	−0.869453	−	0.167573i	−0.604420	+	0.796666i	$0.706595\pi$
$192$	−0.786053	−	0.618159i	−0.0567285	−	0.0446118i
$193$	−4.12521	+	17.0043i	−0.296939	+	1.22400i	0.606430	+	0.795137i	$0.292601\pi$
$193$	−4.12521	+	17.0043i	−0.296939	+	1.22400i	−0.903369	+	0.428863i	$0.858914\pi$
$194$	5.08573	−	14.6943i	0.365134	−	1.05499i
$195$	1.62490	−	1.04426i	0.116361	−	0.0747808i
$196$	5.47794	−	4.35799i	0.391282	−	0.311285i
$197$	−7.42715	−	8.57139i	−0.529163	−	0.610686i	0.426738	−	0.904375i	$-0.359662\pi$
$197$	−7.42715	−	8.57139i	−0.529163	−	0.610686i	−0.955901	+	0.293689i	$0.905117\pi$
$198$	3.04195	+	2.90049i	0.216182	+	0.206129i
$199$	−1.73350	−	1.36324i	−0.122885	−	0.0966375i	0.554825	−	0.831967i	$-0.312785\pi$
$199$	−1.73350	−	1.36324i	−0.122885	−	0.0966375i	−0.677710	+	0.735329i	$0.737027\pi$
$200$	−0.850213	−	2.45653i	−0.0601192	−	0.173703i
$201$	−11.3605	+	1.08480i	−0.801308	+	0.0765157i
$202$	15.9743	+	4.69048i	1.12395	+	0.330021i
$203$	−9.28956	−	0.416334i	−0.651999	−	0.0292209i
$204$	−1.14050	−	7.93232i	−0.0798506	−	0.555373i
$205$	−0.129579	+	2.72019i	−0.00905017	+	0.189986i
$206$	1.07673	−	1.86495i	0.0750194	−	0.129937i
$207$	4.28802	−	2.14776i	0.298038	−	0.149280i
$208$	0.623330	+	1.07964i	0.0432201	+	0.0748595i
$209$	4.38321	+	2.81692i	0.303193	+	0.194850i
$210$	0.787098	+	4.02293i	0.0543149	+	0.277609i
$211$	−3.74956	−	8.21040i	−0.258131	−	0.565227i	0.735550	−	0.677470i	$-0.236924\pi$
$211$	−3.74956	−	8.21040i	−0.258131	−	0.565227i	−0.993681	+	0.112243i	$0.964196\pi$
$212$	−0.743066	−	3.06296i	−0.0510340	−	0.210365i
$213$	4.44904	+	6.24780i	0.304843	+	0.428092i
$214$	−3.17460	−	9.17239i	−0.217011	−	0.627012i
$215$	2.80190	−	1.12171i	0.191088	−	0.0765000i
$216$	0.959493	−	0.281733i	0.0652852	−	0.0191695i
$217$	−7.57547	+	26.0707i	−0.514257	+	1.76980i
$218$	0.495946	−	0.318725i	0.0335897	−	0.0215868i
$219$	−12.6614	−	6.52741i	−0.855579	−	0.441082i
$220$	6.39446	−	1.23243i	0.431114	−	0.0830904i
$221$	−2.35537	+	9.70897i	−0.158439	+	0.653096i
$222$	0.581708	−	0.232881i	0.0390417	−	0.0156299i
$223$	16.9951	−	19.6134i	1.13808	−	1.31341i	0.195016	−	0.980800i	$-0.437524\pi$
$223$	16.9951	−	19.6134i	1.13808	−	1.31341i	0.943063	−	0.332613i	$-0.107930\pi$
$224$	−2.61775	+	0.383894i	−0.174906	+	0.0256500i
$225$	2.49420	+	0.732364i	0.166280	+	0.0488243i
$226$	7.55248	−	10.6060i	0.502383	−	0.705499i
$227$	13.6119	+	5.44940i	0.903456	+	0.361689i	0.776425	−	0.630210i	$-0.217031\pi$
$227$	13.6119	+	5.44940i	0.903456	+	0.361689i	0.127031	+	0.991899i	$0.459455\pi$
$228$	1.10183	−	0.568033i	0.0729704	−	0.0376189i
$229$	−3.47186	−	6.01343i	−0.229427	−	0.397379i	0.728212	−	0.685352i	$-0.240352\pi$
$229$	−3.47186	−	6.01343i	−0.229427	−	0.397379i	−0.957638	+	0.287974i	$0.907018\pi$
$230$	1.14309	−	7.34199i	0.0753730	−	0.484117i
$231$	11.1063	−	0.560370i	0.730741	−	0.0368697i
$232$	2.95671	+	1.90016i	0.194117	+	0.124752i
$233$	3.28248	−	2.58137i	0.215043	−	0.169111i	−0.504827	−	0.863220i	$-0.668444\pi$
$233$	3.28248	−	2.58137i	0.215043	−	0.169111i	0.719870	+	0.694109i	$0.244201\pi$
$234$	−1.24101	−	0.118503i	−0.0811277	−	0.00774675i
$235$	−4.66598	+	4.44900i	−0.304375	+	0.290221i
$236$	−12.3513	+	1.17940i	−0.803998	+	0.0767725i
$237$	−4.94588	+	5.70785i	−0.321270	+	0.370765i
$238$	−17.3058	−	12.2502i	−1.12177	−	0.794061i
$239$	15.3496	−	4.50704i	0.992882	−	0.291536i	0.255350	−	0.966849i	$-0.417809\pi$
$239$	15.3496	−	4.50704i	0.992882	−	0.291536i	0.737532	+	0.675312i	$0.235991\pi$
$240$	0.506744	−	1.46414i	0.0327102	−	0.0945099i
$241$	−0.288935	−	6.06550i	−0.0186120	−	0.390713i	−0.988883	−	0.148694i	$-0.952493\pi$
$241$	−0.288935	−	6.06550i	−0.0186120	−	0.390713i	0.970271	−	0.242020i	$-0.0778099\pi$
$242$	−0.317195	−	6.65875i	−0.0203901	−	0.428041i
$243$	−0.327068	+	0.945001i	−0.0209814	+	0.0606218i
$244$	−8.97017	+	2.63388i	−0.574256	+	0.168617i
$245$	9.15664	+	5.81210i	0.584996	+	0.371321i
$246$	1.15104	−	1.32837i	0.0733876	−	0.0846938i
$247$	−1.53840	+	0.146900i	−0.0978862	+	0.00934700i
$248$	7.42650	−	7.08116i	0.471583	−	0.449654i
$249$	14.3715	+	1.37231i	0.910756	+	0.0869667i
$250$	9.25524	−	7.27840i	0.585353	−	0.460327i
$251$	−15.4645	−	9.93842i	−0.976110	−	0.627308i	−0.0476984	−	0.998862i	$-0.515189\pi$
$251$	−15.4645	−	9.93842i	−0.976110	−	0.627308i	−0.928411	+	0.371554i	$0.878825\pi$
$252$	1.20573	−	2.35504i	0.0759541	−	0.148353i
$253$	−19.2735	−	5.90400i	−1.21171	−	0.371181i
$254$	−7.15477	−	12.3924i	−0.448930	−	0.777570i
$255$	11.0361	−	5.68950i	0.691107	−	0.356290i
$256$	0.928368	+	0.371662i	0.0580230	+	0.0232289i
$257$	−12.9633	+	18.2044i	−0.808629	+	1.13556i	0.179774	+	0.983708i	$0.442463\pi$
$257$	−12.9633	+	18.2044i	−0.808629	+	1.13556i	−0.988403	+	0.151853i	$0.951476\pi$
$258$	−1.86906	−	0.548805i	−0.116363	−	0.0341671i
$259$	0.611814	−	1.54078i	0.0380163	−	0.0957396i
$260$	−1.26488	+	1.45974i	−0.0784442	+	0.0905295i
$261$	−3.26289	+	1.30626i	−0.201968	+	0.0808556i
$262$	3.00673	−	12.3939i	0.185756	−	0.765699i
$263$	−4.29335	+	0.827475i	−0.264739	+	0.0510243i	−0.319893	−	0.947454i	$-0.603647\pi$
$263$	−4.29335	+	0.827475i	−0.264739	+	0.0510243i	0.0551542	+	0.998478i	$0.482435\pi$
$264$	−3.73589	−	1.92599i	−0.229928	−	0.118536i
$265$	4.10806	−	2.64009i	0.252356	−	0.162180i
$266$	0.915161	−	3.14949i	0.0561121	−	0.193108i
$267$	−0.897645	+	0.263572i	−0.0549350	+	0.0161304i
$268$	10.5947	−	4.24148i	0.647174	−	0.259090i
$269$	2.05340	+	5.93291i	0.125198	+	0.361736i	0.990130	−	0.140153i	$-0.0447596\pi$
$269$	2.05340	+	5.93291i	0.125198	+	0.361736i	−0.864932	+	0.501890i	$0.832638\pi$
$270$	0.898714	+	1.26207i	0.0546940	+	0.0768069i
$271$	−3.07374	−	12.6701i	−0.186716	−	0.769655i	−0.985729	−	0.168341i	$-0.946159\pi$
$271$	−3.07374	−	12.6701i	−0.186716	−	0.769655i	0.799013	−	0.601314i	$-0.205356\pi$
$272$	3.32909	+	7.28969i	0.201856	+	0.442002i
$273$	−2.48664	+	2.16696i	−0.150498	+	0.131151i
$274$	4.34446	+	2.79201i	0.262458	+	0.168672i
$275$	−5.46302	−	9.46223i	−0.329432	−	0.570594i
$276$	−3.50923	+	3.26884i	−0.211231	+	0.196761i
$277$	−4.03879	+	6.99539i	−0.242667	+	0.420312i	−0.961473	−	0.274899i	$-0.911356\pi$
$277$	−4.03879	+	6.99539i	−0.242667	+	0.420312i	0.718806	+	0.695211i	$0.244689\pi$
$278$	−0.519437	+	10.9043i	−0.0311538	+	0.653998i
$279$	1.46035	+	10.1569i	0.0874286	+	0.608079i
$280$	−1.88861	−	3.63822i	−0.112866	−	0.217425i
$281$	−10.4594	−	3.07115i	−0.623955	−	0.183210i	−0.0455533	−	0.998962i	$-0.514505\pi$
$281$	−10.4594	−	3.07115i	−0.623955	−	0.183210i	−0.578401	+	0.815752i	$0.696323\pi$
$282$	4.14230	−	0.395542i	0.246671	−	0.0235542i
$283$	−5.26772	−	15.2201i	−0.313133	−	0.904739i	−0.986258	−	0.165210i	$-0.947170\pi$
$283$	−5.26772	−	15.2201i	−0.313133	−	0.904739i	0.673125	−	0.739529i	$-0.264952\pi$
$284$	−6.02903	−	4.74128i	−0.357757	−	0.281343i
$285$	1.39003	+	1.32539i	0.0823380	+	0.0785091i
$286$	3.43139	+	3.96003i	0.202902	+	0.234162i
$287$	−0.455067	−	4.62808i	−0.0268617	−	0.273187i
$288$	−0.841254	+	0.540641i	−0.0495713	+	0.0318576i
$289$	−15.4449	+	44.6252i	−0.908526	+	2.62501i
$290$	−1.28381	+	5.29194i	−0.0753879	+	0.310753i
$291$	−12.2227	−	9.61204i	−0.716507	−	0.563468i
$292$	13.9875	+	2.69587i	0.818558	+	0.157764i
$293$	−0.323294	+	0.707915i	−0.0188870	+	0.0413568i	−0.918840	−	0.394629i	$-0.870873\pi$
$293$	−0.323294	+	0.707915i	−0.0188870	+	0.0413568i	0.899953	+	0.435986i	$0.143600\pi$
$294$	−2.32665	−	6.60202i	−0.135693	−	0.385038i
$295$	−7.98574	−	17.4863i	−0.464948	−	1.01809i
$296$	−0.492535	+	0.387334i	−0.0286280	+	0.0225133i
$297$	3.73589	−	1.92599i	0.216778	−	0.111757i
$298$	−4.16063	+	7.20643i	−0.241019	+	0.417457i
$299$	5.57601	−	2.15726i	0.322469	−	0.124758i
$300$	−2.59950			−0.150082
$301$	−4.45609	+	2.58946i	−0.256844	+	0.149254i
$302$	2.62539	+	18.2600i	0.151074	+	1.05074i
$303$	9.65720	−	13.5616i	0.554791	−	0.779096i
$304$	−0.897164	+	0.855444i	−0.0514559	+	0.0490631i
$305$	−8.40196	−	11.7989i	−0.481095	−	0.675603i
$306$	−7.86907	−	1.51664i	−0.449845	−	0.0867004i
$307$	−2.62051	+	18.2260i	−0.149560	+	1.04022i	0.767380	+	0.641192i	$0.221560\pi$
$307$	−2.62051	+	18.2260i	−0.149560	+	1.04022i	−0.916941	+	0.399023i	$0.869349\pi$
$308$	−10.4986	+	3.66668i	−0.598210	+	0.208928i
$309$	−1.41022	−	1.62748i	−0.0802245	−	0.0925840i
$310$	14.1312	+	7.28511i	0.802595	+	0.413767i
$311$	1.62116	+	34.0322i	0.0919273	+	1.92979i	0.304250	+	0.952592i	$0.401594\pi$
$311$	1.62116	+	34.0322i	0.0919273	+	1.92979i	−0.212323	+	0.977200i	$0.568103\pi$
$312$	1.22413	−	0.235932i	0.0693028	−	0.0133570i
$313$	−18.2209	−	17.3736i	−1.02991	−	0.982014i	−0.0300604	−	0.999548i	$-0.509570\pi$
$313$	−18.2209	−	17.3736i	−1.02991	−	0.982014i	−0.999846	+	0.0175340i	$0.994418\pi$
$314$	0.435695	−	3.03033i	0.0245877	−	0.171011i
$315$	4.05911	+	0.571964i	0.228705	+	0.0322265i
$316$	3.13745	−	6.87006i	0.176495	−	0.386471i
$317$	−5.83978	−	24.0719i	−0.327995	−	1.35201i	−0.862162	−	0.506633i	$-0.830890\pi$
$317$	−5.83978	−	24.0719i	−0.327995	−	1.35201i	0.534167	−	0.845379i	$-0.320625\pi$
$318$	−3.13753	−	0.299598i	−0.175944	−	0.0168006i
$319$	13.7143	+	5.49039i	0.767855	+	0.307403i
$320$	−0.0737213	+	1.54760i	−0.00412114	+	0.0865134i
$321$	−9.70623			−0.541749
$322$	−0.112161	+	12.6881i	−0.00625051	+	0.707079i
$323$	−9.93428			−0.552758
$324$	0.0475819	−	0.998867i	0.00264344	−	0.0554926i
$325$	3.00855	+	1.20444i	0.166885	+	0.0668105i
$326$	−6.62385	−	0.632501i	−0.366861	−	0.0350310i
$327$	−0.138987	−	0.572914i	−0.00768602	−	0.0316822i
$328$	−0.730169	+	1.59885i	−0.0403168	+	0.0882815i
$329$	6.78117	−	8.67305i	0.373858	−	0.478160i
$330$	0.926774	−	6.44585i	0.0510172	−	0.354833i
$331$	10.2429	+	9.76657i	0.563000	+	0.536819i	0.917240	−	0.398335i	$-0.130412\pi$
$331$	10.2429	+	9.76657i	0.563000	+	0.536819i	−0.354240	+	0.935155i	$0.615260\pi$
$332$	−14.1760	+	2.73219i	−0.778008	+	0.149949i
$333$	−0.0298145	−	0.625883i	−0.00163382	−	0.0342982i
$334$	5.04714	+	2.60198i	0.276167	+	0.142374i
$335$	11.5789	+	13.3628i	0.632624	+	0.730087i
$336$	−0.493403	+	2.59934i	−0.0269173	+	0.141805i
$337$	1.64498	−	11.4411i	0.0896078	−	0.623236i	−0.894686	−	0.446696i	$-0.852601\pi$
$337$	1.64498	−	11.4411i	0.0896078	−	0.623236i	0.984294	−	0.176540i	$-0.0564904\pi$
$338$	11.2390	+	2.16614i	0.611321	+	0.117822i
$339$	−7.55248	−	10.6060i	−0.410194	−	0.576037i
$340$	−8.98614	+	8.56827i	−0.487342	+	0.464679i
$341$	25.0178	−	35.1326i	1.35479	−	1.90253i
$342$	−0.176418	−	1.22701i	−0.00953960	−	0.0663494i
$343$	−16.9109	−	7.55118i	−0.913105	−	0.407725i
$344$	1.94797			0.105027
$345$	−6.56432	−	3.48155i	−0.353411	−	0.187440i
$346$	7.87305	−	13.6365i	0.423258	−	0.733104i
$347$	25.6416	−	13.2191i	1.37651	−	0.709641i	0.398301	−	0.917255i	$-0.369600\pi$
$347$	25.6416	−	13.2191i	1.37651	−	0.709641i	0.978211	+	0.207614i	$0.0665697\pi$
$348$	2.76270	−	2.17261i	0.148096	−	0.116464i
$349$	6.35210	+	13.9092i	0.340020	+	0.744540i	0.999977	−	0.00676327i	$-0.00215283\pi$
$349$	6.35210	+	13.9092i	0.340020	+	0.744540i	−0.659957	+	0.751303i	$0.729426\pi$
$350$	−4.73209	+	4.99091i	−0.252941	+	0.266775i
$351$	−0.517881	+	1.13400i	−0.0276424	+	0.0605285i
$352$	4.12717	+	0.795448i	0.219979	+	0.0423975i
$353$	−10.6274	−	8.35749i	−0.565640	−	0.444824i	0.293941	−	0.955824i	$-0.405033\pi$
$353$	−10.6274	−	8.35749i	−0.565640	−	0.444824i	−0.859581	+	0.510999i	$0.829275\pi$
$354$	−2.92516	+	12.0577i	−0.155471	+	0.640859i
$355$	3.88673	−	11.2300i	0.206286	−	0.596025i
$356$	0.787028	−	0.505792i	0.0417124	−	0.0268069i
$357$	−17.2366	+	12.3473i	−0.912257	+	0.653490i
$358$	7.37264	+	8.50848i	0.389656	+	0.449687i
$359$	−23.1198	−	22.0447i	−1.22022	−	1.16348i	−0.981310	−	0.192434i	$-0.938362\pi$
$359$	−23.1198	−	22.0447i	−1.22022	−	1.16348i	−0.238909	−	0.971042i	$-0.576790\pi$
$360$	−1.21787	−	0.957747i	−0.0641876	−	0.0504777i
$361$	5.71169	+	16.5028i	0.300615	+	0.868571i
$362$	9.84821	−	0.940390i	0.517610	−	0.0494258i
$363$	−6.39627	−	1.87811i	−0.335717	−	0.0985754i
$364$	1.77541	−	2.77975i	0.0930569	−	0.145699i
$365$	3.14096	+	21.8458i	0.164405	+	1.14346i
$366$	−0.444837	+	9.33828i	−0.0232520	+	0.488120i
$367$	7.23926	−	12.5388i	0.377886	−	0.654518i	−0.612868	−	0.790185i	$-0.709984\pi$
$367$	7.23926	−	12.5388i	0.377886	−	0.654518i	0.990754	+	0.135667i	$0.0433177\pi$
$368$	2.44615	−	4.12509i	0.127514	−	0.215035i
$369$	−0.878842	−	1.52220i	−0.0457507	−	0.0792426i
$370$	−0.816701	−	0.524862i	−0.0424582	−	0.0272863i
$371$	−6.28673	+	5.47852i	−0.326391	+	0.284430i
$372$	−4.26273	−	9.33407i	−0.221012	−	0.483949i
$373$	−2.58062	−	10.6374i	−0.133619	−	0.550786i	−0.998784	−	0.0492984i	$-0.984301\pi$
$373$	−2.58062	−	10.6374i	−0.133619	−	0.550786i	0.865165	−	0.501488i	$-0.167214\pi$
$374$	19.5383	+	27.4377i	1.01030	+	1.41877i
$375$	−3.85100	−	11.1267i	−0.198865	−	0.574583i
$376$	−3.86307	+	1.54654i	−0.199223	+	0.0797568i
$377$	−4.20408	+	1.23443i	−0.216521	+	0.0635764i
$378$	−1.83116	−	1.90968i	−0.0941845	−	0.0982232i
$379$	−9.33401	+	5.99860i	−0.479456	+	0.308128i	−0.757953	−	0.652310i	$-0.773800\pi$
$379$	−9.33401	+	5.99860i	−0.479456	+	0.308128i	0.278497	+	0.960437i	$0.410164\pi$
$380$	−1.70712	−	0.880084i	−0.0875736	−	0.0451473i
$381$	−14.0509	+	2.70810i	−0.719852	+	0.138740i
$382$	2.88503	−	11.8923i	0.147611	−	0.608462i
$383$	−17.3008	+	6.92620i	−0.884030	+	0.353912i	−0.768847	−	0.639432i	$-0.779169\pi$
$383$	−17.3008	+	6.92620i	−0.884030	+	0.353912i	−0.115182	+	0.993344i	$0.536745\pi$
$384$	0.654861	−	0.755750i	0.0334182	−	0.0385667i
$385$	−10.6886	−	13.5133i	−0.544742	−	0.688701i
$386$	−16.7888	−	4.92964i	−0.854528	−	0.250912i
$387$	−1.12993	+	1.58677i	−0.0574376	+	0.0806599i
$388$	14.4356	+	5.77915i	0.732858	+	0.293392i
$389$	−17.2134	+	8.87413i	−0.872755	+	0.449936i	−0.835578	−	0.549372i	$-0.814867\pi$
$389$	−17.2134	+	8.87413i	−0.872755	+	0.449936i	−0.0371771	+	0.999309i	$0.511837\pi$
$390$	0.965759	+	1.67274i	0.0489031	+	0.0847027i
$391$	37.0001	−	10.3975i	1.87118	−	0.525823i
$392$	4.09241	+	5.67910i	0.206698	+	0.286838i
$393$	−10.7289	−	6.89502i	−0.541199	−	0.347808i
$394$	8.91508	−	7.01090i	0.449135	−	0.353204i
$395$	11.6486	+	1.11231i	0.586106	+	0.0559663i
$396$	−3.04195	+	2.90049i	−0.152864	+	0.145755i
$397$	25.0107	−	2.38824i	1.25525	−	0.119862i	0.553843	−	0.832621i	$-0.313161\pi$
$397$	25.0107	−	2.38824i	1.25525	−	0.119862i	0.701409	+	0.712759i	$0.252555\pi$
$398$	1.44418	−	1.66667i	0.0723901	−	0.0835427i
$399$	−2.67695	−	1.89493i	−0.134015	−	0.0948649i
$400$	2.49420	−	0.732364i	0.124710	−	0.0366182i
$401$	−9.56797	+	27.6448i	−0.477802	+	1.38052i	0.406521	+	0.913642i	$0.366742\pi$
$401$	−9.56797	+	27.6448i	−0.477802	+	1.38052i	−0.884323	+	0.466876i	$0.845379\pi$
$402$	−0.543013	−	11.3993i	−0.0270830	−	0.568543i
$403$	0.608689	+	12.7779i	0.0303209	+	0.636515i
$404$	−5.44526	+	15.7330i	−0.270912	+	0.782748i
$405$	1.48659	−	0.436504i	0.0738695	−	0.0216900i
$406$	0.857877	−	9.25923i	0.0425757	−	0.459528i
$407$	−1.72467	+	1.99038i	−0.0854889	+	0.0986594i
$408$	7.97760	−	0.761769i	0.394950	−	0.0377132i
$409$	15.1178	−	14.4148i	0.747527	−	0.712765i	−0.217168	−	0.976134i	$-0.569682\pi$
$409$	15.1178	−	14.4148i	0.747527	−	0.712765i	0.964695	+	0.263369i	$0.0848336\pi$
$410$	−2.71095	−	0.258864i	−0.133884	−	0.0127844i
$411$	4.05939	−	3.19234i	0.200235	−	0.157466i
$412$	1.81161	+	1.16425i	0.0892515	+	0.0573585i
$413$	17.8252	+	27.5658i	0.877121	+	1.35642i
$414$	1.94129	+	4.38536i	0.0954094	+	0.215529i
$415$	−11.1839	−	19.3711i	−0.548997	−	0.950890i
$416$	−1.10808	+	0.571252i	−0.0543279	+	0.0280080i
$417$	10.1347	+	4.05732i	0.496299	+	0.198688i
$418$	−3.02229	+	4.24422i	−0.147825	+	0.207591i
$419$	8.33195	+	2.44648i	0.407042	+	0.119518i	0.478843	−	0.877901i	$-0.341056\pi$
$419$	8.33195	+	2.44648i	0.407042	+	0.119518i	−0.0718007	+	0.997419i	$0.522875\pi$
$420$	−4.05583	+	0.594787i	−0.197904	+	0.0290226i
$421$	−14.3434	+	16.5531i	−0.699053	+	0.806750i	−0.988624	−	0.150406i	$-0.951942\pi$
$421$	−14.3434	+	16.5531i	−0.699053	+	0.806750i	0.289571	+	0.957156i	$0.406487\pi$
$422$	8.37951	−	3.35465i	0.407908	−	0.163302i
$423$	0.981027	−	4.04385i	0.0476992	−	0.196619i
$424$	3.09485	−	0.596483i	0.150299	−	0.0289678i
$425$	18.5163	+	9.54582i	0.898173	+	0.463040i
$426$	−6.45242	+	4.14672i	−0.312621	+	0.200909i
$427$	17.1192	+	17.8533i	0.828458	+	0.863983i
$428$	9.31306	−	2.73456i	0.450164	−	0.132180i
$429$	4.86453	−	1.94746i	0.234862	−	0.0940244i
$430$	0.987120	+	2.85210i	0.0476032	+	0.137540i
$431$	20.8915	+	29.3381i	1.00631	+	1.41317i	0.908464	+	0.417963i	$0.137256\pi$
$431$	20.8915	+	29.3381i	1.00631	+	1.41317i	0.0978464	+	0.995202i	$0.468805\pi$
$432$	0.235759	+	0.971812i	0.0113430	+	0.0467563i
$433$	−3.08831	−	6.76245i	−0.148415	−	0.324982i	0.820794	−	0.571225i	$-0.193531\pi$
$433$	−3.08831	−	6.76245i	−0.148415	−	0.324982i	−0.969208	+	0.246242i	$0.920804\pi$
$434$	−25.6807	−	8.80739i	−1.23271	−	0.422768i
$435$	4.58099	+	2.94402i	0.219642	+	0.141155i
$436$	0.294766	+	0.510549i	0.0141167	+	0.0244509i
$437$	3.39182	+	4.88256i	0.162253	+	0.233565i
$438$	7.12248	−	12.3365i	0.340325	−	0.589460i
$439$	−1.93007	+	40.5172i	−0.0921173	+	1.93378i	0.204661	+	0.978833i	$0.434391\pi$
$439$	−1.93007	+	40.5172i	−0.0921173	+	1.93378i	−0.296779	+	0.954946i	$0.595912\pi$
$440$	0.926774	+	6.44585i	0.0441822	+	0.307294i
$441$	−6.99989	+	0.0393746i	−0.333328	+	0.00187498i
$442$	−9.58590	−	2.81467i	−0.455955	−	0.133880i
$443$	−39.8658	+	3.80673i	−1.89408	+	0.180863i	−0.976330	−	0.216288i	$-0.930605\pi$
$443$	−39.8658	+	3.80673i	−1.89408	+	0.180863i	−0.917753	+	0.397151i	$0.869999\pi$
$444$	0.204938	+	0.592130i	0.00972594	+	0.0281013i
$445$	1.13937	+	0.896012i	0.0540114	+	0.0424751i
$446$	18.7826	+	17.9091i	0.889380	+	0.848022i
$447$	5.44927	+	6.28879i	0.257742	+	0.297450i
$448$	−0.258901	−	2.63305i	−0.0122319	−	0.124400i
$449$	−32.8150	+	21.0889i	−1.54863	+	0.995247i	−0.562980	+	0.826470i	$0.690345\pi$
$449$	−32.8150	+	21.0889i	−1.54863	+	0.995247i	−0.985654	+	0.168777i	$0.946018\pi$
$450$	−0.850213	+	2.45653i	−0.0400794	+	0.115802i
$451$	−1.74173	+	7.17953i	−0.0820151	+	0.338071i
$452$	10.2346	+	8.04858i	0.481395	+	0.378573i
$453$	18.1144	+	3.49126i	0.851087	+	0.164034i
$454$	−6.09091	+	13.3372i	−0.285860	+	0.625947i
$455$	4.96963	+	1.19083i	0.232980	+	0.0558270i
$456$	0.514962	+	1.12761i	0.0241153	+	0.0528052i
$457$	−11.7071	+	9.20660i	−0.547637	+	0.430666i	−0.853260	−	0.521486i	$-0.825378\pi$
$457$	−11.7071	+	9.20660i	−0.547637	+	0.430666i	0.305623	+	0.952153i	$0.401135\pi$
$458$	6.17182	−	3.18179i	0.288390	−	0.148675i
$459$	−4.00694	+	6.94023i	−0.187028	+	0.323942i
$460$	7.27929	+	1.49114i	0.339398	+	0.0695247i
$461$	4.78084			0.222666			0.111333	−	0.993783i	$-0.464488\pi$
$461$	4.78084			0.222666			0.111333	+	0.993783i	$0.464488\pi$
$462$	0.0312760	+	11.1204i	0.00145509	+	0.517367i
$463$	1.67355	+	11.6398i	0.0777763	+	0.540946i	0.991039	+	0.133574i	$0.0426455\pi$
$463$	1.67355	+	11.6398i	0.0777763	+	0.540946i	−0.913263	+	0.407372i	$0.866445\pi$
$464$	−2.03870	+	2.86295i	−0.0946441	+	0.132909i
$465$	11.5063	−	10.9712i	0.533591	−	0.508778i
$466$	2.42226	+	3.40159i	0.112209	+	0.157576i
$467$	−4.30182	−	0.829107i	−0.199064	−	0.0383665i	0.0887443	−	0.996054i	$-0.471715\pi$
$467$	−4.30182	−	0.829107i	−0.199064	−	0.0383665i	−0.287809	+	0.957688i	$0.592927\pi$
$468$	0.177418	−	1.23397i	0.00820116	−	0.0570403i
$469$	−22.8745	−	19.7085i	−1.05624	−	0.910053i
$470$	−4.22195	−	4.87239i	−0.194744	−	0.224746i
$471$	−2.72116	−	1.40286i	−0.125384	−	0.0646402i
$472$	−0.590370	−	12.3934i	−0.0271740	−	0.570452i
$473$	8.03959	−	1.54950i	0.369661	−	0.0712463i
$474$	−5.46605	−	5.21187i	−0.251064	−	0.239389i
$475$	−0.458599	+	3.18963i	−0.0210420	+	0.146350i
$476$	13.0597	−	16.7033i	0.598593	−	0.765594i
$477$	−1.30931	+	2.86698i	−0.0599491	+	0.131270i
$478$	3.77158	+	15.5467i	0.172508	+	0.711087i
$479$	11.0834	+	1.05833i	0.506412	+	0.0483565i	0.345136	−	0.938553i	$-0.387833\pi$
$479$	11.0834	+	1.05833i	0.506412	+	0.0483565i	0.161276	+	0.986909i	$0.448439\pi$
$480$	1.43837	+	0.575837i	0.0656524	+	0.0262832i
$481$	0.0371685	−	0.780263i	0.00169474	−	0.0355769i
$482$	6.07238			0.276589
$483$	11.9536	+	4.25586i	0.543906	+	0.193648i
$484$	6.66630			0.303014
$485$	−1.14633	+	24.0643i	−0.0520520	+	1.09271i
$486$	−0.928368	−	0.371662i	−0.0421116	−	0.0168590i
$487$	10.5581	+	1.00817i	0.478432	+	0.0456847i	0.331487	−	0.943460i	$-0.392450\pi$
$487$	10.5581	+	1.00817i	0.478432	+	0.0456847i	0.146945	+	0.989145i	$0.453056\pi$
$488$	−2.20408	−	9.08534i	−0.0997740	−	0.411274i
$489$	−2.76416	+	6.05267i	−0.125000	+	0.273711i
$490$	−6.24120	+	8.86972i	−0.281949	+	0.400693i
$491$	4.40577	−	30.6428i	0.198830	−	1.38289i	−0.608858	−	0.793279i	$-0.708372\pi$
$491$	4.40577	−	30.6428i	0.198830	−	1.38289i	0.807688	−	0.589611i	$-0.200719\pi$
$492$	1.27210	+	1.21294i	0.0573505	+	0.0546836i
$493$	−27.6570	+	5.33045i	−1.24561	+	0.240071i
$494$	−0.0735331	−	1.54365i	−0.00330841	−	0.0694521i
$495$	−5.78822	−	2.98403i	−0.260161	−	0.134122i
$496$	6.71977	+	7.75503i	0.301727	+	0.348211i
$497$	−3.78441	+	19.9369i	−0.169754	+	0.894294i
$498$	−2.05458	+	14.2899i	−0.0920679	+	0.640347i
$499$	−18.5747	−	3.57999i	−0.831520	−	0.160262i	−0.244310	−	0.969697i	$-0.578561\pi$
$499$	−18.5747	−	3.57999i	−0.831520	−	0.160262i	−0.587210	+	0.809435i	$0.699774\pi$
$500$	6.82978	+	9.59108i	0.305437	+	0.428926i
$501$	4.10964	−	3.91853i	0.183605	−	0.175067i
$502$	10.6630	−	14.9741i	0.475913	−	0.668326i
$503$	−0.545971	−	3.79732i	−0.0243437	−	0.169314i	0.974023	−	0.226450i	$-0.0727121\pi$
$503$	−0.545971	−	3.79732i	−0.0243437	−	0.169314i	−0.998366	+	0.0571364i	$0.981803\pi$
$504$	2.29500	+	1.31643i	0.102227	+	0.0586383i
$505$	−25.7947			−1.14785
$506$	6.81438	−	18.9707i	0.302936	−	0.843352i
$507$	5.72292	−	9.91239i	0.254164	−	0.440225i
$508$	12.7188	−	6.55701i	0.564307	−	0.290920i
$509$	3.21599	−	2.52908i	0.142546	−	0.112100i	−0.544339	−	0.838865i	$-0.683220\pi$
$509$	3.21599	−	2.52908i	0.142546	−	0.112100i	0.686886	+	0.726765i	$0.258977\pi$
$510$	5.15794	+	11.2943i	0.228397	+	0.500121i
$511$	−10.7198	−	36.1319i	−0.474215	−	1.59838i
$512$	−0.415415	+	0.909632i	−0.0183589	+	0.0402004i
$513$	−1.21723	−	0.234602i	−0.0537421	−	0.0103579i
$514$	−17.5670	−	13.8148i	−0.774847	−	0.609346i
$515$	−0.786604	+	3.24243i	−0.0346619	+	0.142878i
$516$	0.637117	−	1.84083i	0.0280475	−	0.0810380i
$517$	−14.7134	+	9.45572i	−0.647094	+	0.415862i
$518$	1.50993	+	0.684434i	0.0663423	+	0.0300723i
$519$	−10.3115	−	11.9001i	−0.452625	−	0.522357i
$520$	−1.39791	−	1.33290i	−0.0613022	−	0.0584515i
$521$	3.98015	+	3.13002i	0.174373	+	0.137129i	0.701531	−	0.712638i	$-0.252500\pi$
$521$	3.98015	+	3.13002i	0.174373	+	0.137129i	−0.527158	+	0.849767i	$0.676742\pi$
$522$	−1.14953	−	3.32134i	−0.0503135	−	0.145371i
$523$	1.80419	−	0.172279i	0.0788917	−	0.00753325i	−0.0555355	−	0.998457i	$-0.517687\pi$
$523$	1.80419	−	0.172279i	0.0788917	−	0.00753325i	0.134427	+	0.990923i	$0.457081\pi$
$524$	12.2368	+	3.59305i	0.534568	+	0.156963i
$525$	3.16869	+	6.10420i	0.138293	+	0.266409i
$526$	−0.622252	−	4.32786i	−0.0271315	−	0.188704i
$527$	−3.91283	+	82.1403i	−0.170445	+	3.57809i
$528$	2.10156	−	3.64002i	0.0914589	−	0.158411i
$529$	−17.7430	−	14.6351i	−0.771435	−	0.636308i
$530$	2.44163	+	4.22903i	0.106058	+	0.183697i
$531$	10.4378	+	6.70797i	0.452962	+	0.291101i
$532$	3.10238	+	1.06398i	0.134505	+	0.0461295i
$533$	−0.910272	−	1.99322i	−0.0394283	−	0.0863358i
$534$	−0.220562	−	0.909170i	−0.00954466	−	0.0393436i
$535$	8.72312	+	12.2499i	0.377133	+	0.529610i
$536$	3.73256	+	10.7845i	0.161222	+	0.465820i
$537$	10.4519	−	4.18430i	0.451031	−	0.180566i
$538$	−6.02390	+	1.76878i	−0.259709	+	0.0762573i
$539$	21.4075	+	20.1833i	0.922087	+	0.869358i
$540$	−1.30340	+	0.837644i	−0.0560894	+	0.0360465i
$541$	10.2460	+	5.28219i	0.440511	+	0.227099i	0.664190	−	0.747564i	$-0.268777\pi$
$541$	10.2460	+	5.28219i	0.440511	+	0.227099i	−0.223679	+	0.974663i	$0.571807\pi$
$542$	12.8020	−	2.46739i	0.549894	−	0.105983i
$543$	2.33236	−	9.61414i	0.100091	−	0.412582i
$544$	−7.43984	+	2.97846i	−0.318980	+	0.127700i
$545$	−0.598146	+	0.690297i	−0.0256217	+	0.0295691i
$546$	−2.04619	−	2.58693i	−0.0875688	−	0.110711i
$547$	20.0256	+	5.88006i	0.856235	+	0.251413i	0.680250	−	0.732980i	$-0.261871\pi$
$547$	20.0256	+	5.88006i	0.856235	+	0.251413i	0.175984	+	0.984393i	$0.443689\pi$
$548$	−2.99557	+	4.20669i	−0.127964	+	0.179701i
$549$	8.67919	+	3.47462i	0.370419	+	0.148293i
$550$	9.71145	−	5.00660i	0.414098	−	0.213482i
$551$	−2.17844	−	3.77316i	−0.0928045	−	0.160742i
$552$	−3.09816	−	3.66080i	−0.131866	−	0.155814i
$553$	−19.9568	+	1.00692i	−0.848651	+	0.0428188i
$554$	−6.79530	−	4.36707i	−0.288704	−	0.185539i
$555$	−0.763111	+	0.600117i	−0.0323923	+	0.0254736i
$556$	−10.8673	−	1.03770i	−0.460874	−	0.0440082i
$557$	20.1196	−	19.1840i	0.852495	−	0.812852i	−0.131451	−	0.991323i	$-0.541963\pi$
$557$	20.1196	−	19.1840i	0.852495	−	0.812852i	0.983945	+	0.178471i	$0.0571150\pi$
$558$	−10.2149	+	0.975405i	−0.432431	+	0.0412922i
$559$	−1.59030	+	1.83530i	−0.0672624	+	0.0776249i
$560$	3.72397	−	1.71335i	0.157366	−	0.0724024i
$561$	32.3190	−	9.48971i	1.36451	−	0.400656i
$562$	3.56535	−	10.3014i	0.150395	−	0.434539i
$563$	2.00762	+	42.1451i	0.0846109	+	1.77620i	0.499484	+	0.866323i	$0.333523\pi$
$563$	2.00762	+	42.1451i	0.0846109	+	1.77620i	−0.414873	+	0.909879i	$0.636174\pi$
$564$	0.197995	+	4.15643i	0.00833711	+	0.175017i
$565$	−6.59793	+	19.0635i	−0.277577	+	0.802006i
$566$	15.4535	−	4.53755i	0.649558	−	0.190727i
$567$	−2.40356	+	1.10585i	−0.100940	+	0.0464413i
$568$	5.02279	−	5.79660i	0.210751	−	0.243220i
$569$	−31.1012	+	2.96981i	−1.30383	+	0.124501i	−0.723752	−	0.690060i	$-0.757584\pi$
$569$	−31.1012	+	2.96981i	−1.30383	+	0.124501i	−0.580078	+	0.814561i	$0.696978\pi$
$570$	−1.39003	+	1.32539i	−0.0582218	+	0.0555143i
$571$	−15.5986	−	1.48949i	−0.652782	−	0.0623332i	−0.236590	−	0.971610i	$-0.576030\pi$
$571$	−15.5986	−	1.48949i	−0.652782	−	0.0623332i	−0.416193	+	0.909276i	$0.636636\pi$
$572$	−4.11882	+	3.23907i	−0.172216	+	0.135432i
$573$	−10.2946	−	6.61594i	−0.430063	−	0.276385i
$574$	4.64449	−	0.234338i	0.193857	−	0.00978109i
$575$	−1.63030	−	12.3597i	−0.0679883	−	0.515435i
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	−28.9275	+	14.9132i	−1.20427	+	0.620843i	−0.939194	−	0.343386i	$-0.888426\pi$
$577$	−28.9275	+	14.9132i	−1.20427	+	0.620843i	−0.265072	+	0.964229i	$0.585396\pi$
$578$	−43.8398	−	17.5508i	−1.82349	−	0.730017i
$579$	−10.1496	+	14.2531i	−0.421803	+	0.592339i
$580$	−5.22486	−	1.53416i	−0.216950	−	0.0637024i
$581$	23.6958	+	29.9578i	0.983066	+	1.24286i
$582$	10.1827	−	11.7515i	0.422088	−	0.487115i
$583$	12.2985	−	4.92358i	0.509352	−	0.203914i
$584$	−3.35837	+	13.8434i	−0.138971	+	0.572844i
$585$	1.89661	−	0.365542i	0.0784153	−	0.0151133i
$586$	−0.691730	−	0.356612i	−0.0285751	−	0.0147315i
$587$	−16.7295	+	10.7514i	−0.690499	+	0.443757i	−0.838263	−	0.545266i	$-0.816429\pi$
$587$	−16.7295	+	10.7514i	−0.690499	+	0.443757i	0.147764	+	0.989023i	$0.452792\pi$
$588$	6.70525	−	2.00988i	0.276520	−	0.0828859i
$589$	−12.2051	+	3.58373i	−0.502901	+	0.147665i
$590$	17.8465	−	7.14466i	0.734729	−	0.294141i
$591$	−3.70947	−	10.7178i	−0.152587	−	0.440871i
$592$	−0.363459	−	0.510407i	−0.0149381	−	0.0209776i
$593$	3.99945	+	16.4860i	0.164238	+	0.676998i	0.993072	+	0.117504i	$0.0374893\pi$
$593$	3.99945	+	16.4860i	0.164238	+	0.676998i	−0.828835	+	0.559494i	$0.810996\pi$
$594$	1.74604	+	3.82330i	0.0716410	+	0.156872i
$595$	31.0739	+	10.6570i	1.27391	+	0.436895i
$596$	−7.00029	−	4.49881i	−0.286743	−	0.184279i
$597$	−1.10266	−	1.90986i	−0.0451289	−	0.0781656i
$598$	1.88950	+	5.67234i	0.0772673	+	0.231959i
$599$	1.94119	−	3.36224i	0.0793148	−	0.137377i	−0.823640	−	0.567113i	$-0.808060\pi$
$599$	1.94119	−	3.36224i	0.0793148	−	0.137377i	0.902955	+	0.429736i	$0.141393\pi$
$600$	0.123689	−	2.59656i	0.00504959	−	0.106004i
$601$	3.38151	+	23.5189i	0.137935	+	0.959356i	0.934794	+	0.355191i	$0.115584\pi$
$601$	3.38151	+	23.5189i	0.137935	+	0.959356i	−0.796859	+	0.604165i	$0.793507\pi$
$602$	−2.37450	−	4.57425i	−0.0967773	−	0.186432i
$603$	−10.9499	−	3.21518i	−0.445915	−	0.130932i
$604$	−18.3642	+	1.75357i	−0.747229	+	0.0713517i
$605$	3.37811	+	9.76041i	0.137340	+	0.396817i
$606$	13.0868	+	10.2915i	0.531614	+	0.418065i
$607$	7.59731	+	7.24402i	0.308365	+	0.294026i	0.828420	−	0.560107i	$-0.189240\pi$
$607$	7.59731	+	7.24402i	0.308365	+	0.294026i	−0.520055	+	0.854133i	$0.674089\pi$
$608$	−0.811787	−	0.936852i	−0.0329223	−	0.0379944i
$609$	−8.46939	−	3.83909i	−0.343197	−	0.155568i
$610$	12.1853	−	7.83103i	0.493369	−	0.317069i
$611$	1.69668	−	4.90222i	0.0686401	−	0.198323i
$612$	1.88935	−	7.78799i	0.0763723	−	0.314811i
$613$	29.8235	+	23.4535i	1.20456	+	0.947277i	0.999505	−	0.0314727i	$-0.0100197\pi$
$613$	29.8235	+	23.4535i	1.20456	+	0.947277i	0.205057	+	0.978750i	$0.434262\pi$
$614$	−18.0807	−	3.48477i	−0.729678	−	0.140634i
$615$	−1.13129	+	2.47718i	−0.0456180	+	0.0998895i
$616$	−3.16299	−	10.6611i	−0.127440	−	0.429549i
$617$	−11.1388	−	24.3907i	−0.448433	−	0.981931i	−0.989973	−	0.141256i	$-0.954886\pi$
$617$	−11.1388	−	24.3907i	−0.448433	−	0.981931i	0.541540	−	0.840675i	$-0.317841\pi$
$618$	1.69274	−	1.33118i	0.0680918	−	0.0535480i
$619$	38.9736	−	20.0923i	1.56648	−	0.807578i	0.566617	−	0.823981i	$-0.308252\pi$
$619$	38.9736	−	20.0923i	1.56648	−	0.807578i	0.999865	+	0.0164034i	$0.00522160\pi$
$620$	−7.94925	+	13.7685i	−0.319250	+	0.552956i
$621$	4.77910	−	0.400214i	0.191779	−	0.0160600i
$622$	−34.0708			−1.36612
$623$	−2.14707	−	1.23157i	−0.0860204	−	0.0493419i
$624$	0.177418	+	1.23397i	0.00710241	+	0.0493984i
$625$	−3.04245	+	4.27253i	−0.121698	+	0.170901i
$626$	18.2209	−	17.3736i	0.728254	−	0.694389i
$627$	3.02229	+	4.24422i	0.120699	+	0.169498i
$628$	3.00616	+	0.579391i	0.119959	+	0.0231202i
$629$	0.714626	−	4.97033i	0.0284940	−	0.198180i
$630$	−0.764456	+	4.02729i	−0.0304567	+	0.160451i
$631$	9.17381	+	10.5871i	0.365204	+	0.421467i	0.908376	−	0.418154i	$-0.137323\pi$
$631$	9.17381	+	10.5871i	0.365204	+	0.421467i	−0.543173	+	0.839621i	$0.682777\pi$
$632$	6.71299	+	3.46079i	0.267028	+	0.137663i
$633$	−0.429477	−	9.01584i	−0.0170702	−	0.358348i
$634$	24.3225	−	4.68778i	0.965970	−	0.186175i
$635$	16.0456	+	15.2994i	0.636750	+	0.607139i
$636$	0.448549	−	3.11972i	0.0177861	−	0.123705i
$637$	−8.69163	−	0.780640i	−0.344375	−	0.0309301i
$638$	−6.13673	+	13.4376i	−0.242955	+	0.531998i
$639$	1.80827	+	7.45380i	0.0715342	+	0.294868i
$640$	−1.54234	−	0.147276i	−0.0609663	−	0.00582158i
$641$	−25.9910	−	10.4052i	−1.02658	−	0.410982i	−0.203605	−	0.979053i	$-0.565266\pi$
$641$	−25.9910	−	10.4052i	−1.02658	−	0.410982i	−0.822980	+	0.568071i	$0.807690\pi$
$642$	0.461841	−	9.69524i	0.0182274	−	0.382640i
$643$	−26.8815			−1.06010			−0.530052	−	0.847965i	$-0.677828\pi$
$643$	−26.8815			−1.06010			−0.530052	+	0.847965i	$0.677828\pi$
$644$	−12.6684	−	0.715758i	−0.499204	−	0.0282048i
$645$	3.01809			0.118837
$646$	0.472692	−	9.92303i	0.0185978	−	0.390416i
$647$	−14.6429	−	5.86214i	−0.575673	−	0.230465i	0.0655111	−	0.997852i	$-0.479132\pi$
$647$	−14.6429	−	5.86214i	−0.575673	−	0.230465i	−0.641184	+	0.767387i	$0.721556\pi$
$648$	0.995472	+	0.0950560i	0.0391058	+	0.00373415i
$649$	−12.2948	−	50.6800i	−0.482615	−	1.98937i
$650$	−1.34623	+	2.94784i	−0.0528036	+	0.115624i
$651$	−16.7223	+	21.3877i	−0.655400	+	0.838250i
$652$	0.946960	−	6.58625i	0.0370858	−	0.257938i
$653$	−23.2186	−	22.1389i	−0.908613	−	0.866360i	0.0828751	−	0.996560i	$-0.473590\pi$
$653$	−23.2186	−	22.1389i	−0.908613	−	0.866360i	−0.991488	+	0.130199i	$0.958438\pi$
$654$	0.578878	−	0.111570i	0.0226359	−	0.00436272i
$655$	0.940198	+	19.7372i	0.0367366	+	0.771195i
$656$	−1.56229	−	0.805418i	−0.0609973	−	0.0314463i
$657$	−9.32846	−	10.7656i	−0.363938	−	0.420007i
$658$	8.34056	+	7.18617i	0.325149	+	0.280146i
$659$	0.577726	−	4.01817i	0.0225050	−	0.156526i	−0.975470	−	0.220132i	$-0.929351\pi$
$659$	0.577726	−	4.01817i	0.0225050	−	0.156526i	0.997975	+	0.0636064i	$0.0202602\pi$
$660$	6.39446	+	1.23243i	0.248904	+	0.0479723i
$661$	−22.4189	−	31.4829i	−0.871992	−	1.22454i	−0.973265	−	0.229683i	$-0.926231\pi$
$661$	−22.4189	−	31.4829i	−0.871992	−	1.22454i	0.101273	−	0.994859i	$-0.467708\pi$
$662$	−10.2429	+	9.76657i	−0.398101	+	0.379589i
$663$	−5.79511	+	8.13810i	−0.225063	+	0.316057i
$664$	−2.05458	−	14.2899i	−0.0797332	−	0.554556i
$665$	0.0142916	+	5.08149i	0.000554206	+	0.197052i
$666$	0.626592			0.0242800
$667$	12.0627	+	11.7731i	0.467068	+	0.455856i
$668$	−2.83919	+	4.91762i	−0.109852	+	0.190268i
$669$	23.0673	−	11.8920i	0.891834	−	0.459773i
$670$	−13.8986	+	10.9300i	−0.536950	+	0.422262i
$671$	−16.3235	−	35.7435i	−0.630163	−	1.37986i
$672$	−2.57292	−	0.616526i	−0.0992524	−	0.0237830i
$673$	−12.6894	+	27.7860i	−0.489141	+	1.07107i	0.490706	+	0.871325i	$0.336739\pi$
$673$	−12.6894	+	27.7860i	−0.489141	+	1.07107i	−0.979848	+	0.199745i	$0.935988\pi$
$674$	11.3499	+	2.18751i	0.437180	+	0.0842596i
$675$	2.04335	+	1.60690i	0.0786484	+	0.0618498i
$676$	−2.69846	+	11.1232i	−0.103787	+	0.427815i
$677$	1.19352	−	3.44846i	0.0458708	−	0.132535i	−0.919739	−	0.392530i	$-0.871600\pi$
$677$	1.19352	−	3.44846i	0.0458708	−	0.132535i	0.965610	+	0.259995i	$0.0837210\pi$
$678$	10.9533	−	7.03927i	0.420660	−	0.270342i
$679$	−4.02577	−	40.9426i	−0.154495	−	1.57123i
$680$	−8.13098	−	9.38365i	−0.311809	−	0.359847i
$681$	10.6115	+	10.1181i	0.406635	+	0.387726i
$682$	33.9024	+	26.6611i	1.29819	+	1.02091i
$683$	−6.17612	−	17.8447i	−0.236323	−	0.682809i	−0.999336	−	0.0364271i	$-0.988402\pi$
$683$	−6.17612	−	17.8447i	−0.236323	−	0.682809i	0.763014	−	0.646382i	$-0.223719\pi$
$684$	1.23402	−	0.117835i	0.0471839	−	0.00450552i
$685$	−7.67717	−	2.25422i	−0.293330	−	0.0861294i
$686$	8.34728	−	16.5325i	0.318701	−	0.631213i
$687$	−0.988193	−	6.87304i	−0.0377019	−	0.262223i
$688$	−0.0926879	+	1.94576i	−0.00353369	+	0.0741814i
$689$	−1.96461	+	3.40281i	−0.0748458	+	0.129637i
$690$	3.78995	−	6.39123i	0.144281	−	0.243310i
$691$	8.49422	+	14.7124i	0.323135	+	0.559687i	0.981133	−	0.193333i	$-0.0619297\pi$
$691$	8.49422	+	14.7124i	0.323135	+	0.559687i	−0.657998	+	0.753020i	$0.728596\pi$
$692$	13.2465	+	8.51299i	0.503555	+	0.323615i
$693$	10.5190	+	3.60757i	0.399584	+	0.137040i
$694$	11.9841	+	26.2415i	0.454910	+	0.996114i
$695$	−3.98758	−	16.4370i	−0.151258	−	0.623493i
$696$	2.03870	+	2.86295i	0.0772766	+	0.108520i
$697$	−4.60704	−	13.3112i	−0.174504	−	0.504197i
$698$	−14.1956	+	5.68308i	−0.537313	+	0.215108i
$699$	4.00675	−	1.17649i	0.151549	−	0.0444989i
$700$	−4.76009	−	4.96421i	−0.179914	−	0.187629i
$701$	−16.9630	+	10.9015i	−0.640684	+	0.411742i	−0.820251	−	0.572003i	$-0.806166\pi$
$701$	−16.9630	+	10.9015i	−0.640684	+	0.411742i	0.179568	+	0.983746i	$0.442530\pi$
$702$	−1.10808	−	0.571252i	−0.0418216	−	0.0215605i
$703$	0.762708	−	0.147000i	0.0287661	−	0.00554420i
$704$	−0.990925	+	4.08465i	−0.0373469	+	0.153946i
$705$	−5.98527	+	2.39614i	−0.225418	+	0.0902439i
$706$	8.85369	−	10.2177i	0.333213	−	0.384548i
$707$	43.5822	−	6.39133i	1.63908	−	0.240371i
$708$	−11.9048	−	3.49558i	−0.447412	−	0.131372i
$709$	18.8130	−	26.4192i	0.706538	−	0.992193i	−0.292813	−	0.956170i	$-0.594591\pi$
$709$	18.8130	−	26.4192i	0.706538	−	0.992193i	0.999351	−	0.0360237i	$-0.0114692\pi$
$710$	11.0323	+	4.41667i	0.414035	+	0.165755i
$711$	−6.71299	+	3.46079i	−0.251757	+	0.129790i
$712$	0.467771	+	0.810203i	0.0175304	+	0.0303636i
$713$	41.7068	−	26.1217i	1.56193	−	0.978266i
$714$	−11.5132	−	17.8046i	−0.430871	−	0.666320i
$715$	−6.82965	−	4.38915i	−0.255414	−	0.164145i
$716$	−8.84964	+	6.95944i	−0.330727	+	0.260086i
$717$	15.9252	+	1.52067i	0.594736	+	0.0567904i
$718$	23.1198	−	22.0447i	0.862825	−	0.822702i
$719$	14.7650	−	1.40989i	0.550642	−	0.0525799i	0.183973	−	0.982931i	$-0.441104\pi$
$719$	14.7650	−	1.40989i	0.550642	−	0.0525799i	0.366669	+	0.930351i	$0.380498\pi$
$720$	1.01461	−	1.17092i	0.0378123	−	0.0436378i
$721$	0.525630	−	5.67323i	0.0195755	−	0.211282i
$722$	−16.7559	+	4.91998i	−0.623591	+	0.183103i
$723$	1.98608	−	5.73840i	0.0738631	−	0.213414i
$724$	0.470728	+	9.88180i	0.0174945	+	0.367254i
$725$	0.434724	+	9.12598i	0.0161452	+	0.338930i
$726$	2.18033	−	6.29966i	0.0809198	−	0.233802i
$727$	0.291636	−	0.0856320i	0.0108162	−	0.00317592i	−0.276320	−	0.961066i	$-0.589115\pi$
$727$	0.291636	−	0.0856320i	0.0108162	−	0.00317592i	0.287136	+	0.957890i	$0.407297\pi$
$728$	2.69213	+	1.90567i	0.0997769	+	0.0706287i
$729$	−0.654861	+	0.755750i	−0.0242541	+	0.0279907i
$730$	−21.9705	+	2.09793i	−0.813166	+	0.0776480i
$731$	−11.2981	+	10.7727i	−0.417874	+	0.398442i
$732$	−9.30654	−	0.888666i	−0.343979	−	0.0328461i
$733$	9.71032	−	7.63628i	0.358659	−	0.282052i	−0.422528	−	0.906350i	$-0.638857\pi$
$733$	9.71032	−	7.63628i	0.358659	−	0.282052i	0.781187	+	0.624297i	$0.214615\pi$
$734$	12.1801	+	7.82768i	0.449576	+	0.288925i
$735$	6.34059	+	8.79894i	0.233876	+	0.324554i
$736$	4.00403	+	2.63966i	0.147590	+	0.0972990i
$737$	23.9834	+	41.5405i	0.883441	+	1.53017i
$738$	1.56229	−	0.805418i	0.0575088	−	0.0296478i
$739$	−18.3662	−	7.35272i	−0.675612	−	0.270474i	0.00837865	−	0.999965i	$-0.497333\pi$
$739$	−18.3662	−	7.35272i	−0.675612	−	0.270474i	−0.683991	+	0.729491i	$0.739757\pi$
$740$	0.563127	−	0.790802i	0.0207010	−	0.0290704i
$741$	−1.48280	−	0.435389i	−0.0544720	−	0.0159944i
$742$	−5.17318	−	6.54029i	−0.189913	−	0.240102i
$743$	5.86652	−	6.77032i	0.215222	−	0.248379i	−0.637865	−	0.770148i	$-0.720182\pi$
$743$	5.86652	−	6.77032i	0.215222	−	0.248379i	0.853087	+	0.521769i	$0.174728\pi$
$744$	9.52633	−	3.81377i	0.349252	−	0.139819i
$745$	3.03954	−	12.5292i	0.111360	−	0.459033i
$746$	10.7482	−	2.07154i	0.393519	−	0.0758446i
$747$	12.8320	+	6.61535i	0.469498	+	0.242043i
$748$	−28.3363	+	18.2106i	−1.03608	+	0.665847i
$749$	−17.7736	−	18.5358i	−0.649434	−	0.677282i
$750$	11.2974	−	3.31721i	0.412522	−	0.121127i
$751$	0.495608	−	0.198412i	0.0180850	−	0.00724014i	−0.362602	−	0.931944i	$-0.618112\pi$
$751$	0.495608	−	0.198412i	0.0180850	−	0.00724014i	0.380687	+	0.924704i	$0.375687\pi$
$752$	−1.36098	−	3.93229i	−0.0496297	−	0.143396i
$753$	−10.6630	−	14.9741i	−0.388581	−	0.545686i
$754$	−1.03299	−	4.25806i	−0.0376194	−	0.155069i
$755$	−11.8734	−	25.9992i	−0.432118	−	0.946207i
$756$	1.99464	−	1.73822i	0.0725445	−	0.0632183i
$757$	23.9331	+	15.3808i	0.869862	+	0.559026i	0.897710	−	0.440586i	$-0.145229\pi$
$757$	23.9331	+	15.3808i	0.869862	+	0.559026i	−0.0278487	+	0.999612i	$0.508866\pi$
$758$	−5.54768	−	9.60886i	−0.201501	−	0.349010i
$759$	−15.6986	−	12.6443i	−0.569823	−	0.458960i
$760$	0.960315	−	1.66331i	0.0348343	−	0.0603348i
$761$	1.96907	−	41.3358i	0.0713786	−	1.49842i	−0.624931	−	0.780680i	$-0.714873\pi$
$761$	1.96907	−	41.3358i	0.0713786	−	1.49842i	0.696310	−	0.717742i	$-0.254824\pi$
$762$	−2.03646	−	14.1639i	−0.0737732	−	0.513104i
$763$	0.839573	−	1.31452i	0.0303946	−	0.0475887i
$764$	11.7415	+	3.44762i	0.424794	+	0.124731i
$765$	12.3601	−	1.18025i	0.446882	−	0.0426720i
$766$	−6.09515	−	17.6108i	−0.220227	−	0.636303i
$767$	12.1586	+	9.56159i	0.439020	+	0.345249i
$768$	0.723734	+	0.690079i	0.0261155	+	0.0249011i
$769$	−5.66686	−	6.53990i	−0.204352	−	0.235835i	0.644318	−	0.764758i	$-0.277141\pi$
$769$	−5.66686	−	6.53990i	−0.204352	−	0.235835i	−0.848670	+	0.528923i	$0.822596\pi$
$770$	14.0066	−	10.0335i	0.504762	−	0.361583i
$771$	−18.8006	+	12.0824i	−0.677088	+	0.435138i
$772$	5.72290	−	16.5352i	0.205972	−	0.595116i
$773$	6.57424	−	27.0994i	0.236459	−	0.974697i	−0.722550	−	0.691319i	$-0.757030\pi$
$773$	6.57424	−	27.0994i	0.236459	−	0.974697i	0.959008	−	0.283378i	$-0.0914550\pi$
$774$	−1.53120	−	1.20415i	−0.0550380	−	0.0432824i
$775$	26.1924	+	5.04817i	0.940859	+	0.181336i
$776$	−6.45948	+	14.1443i	−0.231882	+	0.507750i
$777$	1.14064	−	1.20302i	0.0409202	−	0.0431583i
$778$	−8.04503	−	17.6162i	−0.288428	−	0.631570i
$779$	1.71272	−	1.34690i	0.0613645	−	0.0482576i
$780$	−1.71680	+	0.885073i	−0.0614714	+	0.0316907i
$781$	16.1190	−	27.9190i	0.576784	−	0.999019i
$782$	8.62517	+	37.4529i	0.308436	+	1.33931i
$783$	−3.51465			−0.125603
$784$	−5.86739	+	3.81755i	−0.209550	+	0.136341i
$785$	0.675047	+	4.69505i	0.0240934	+	0.167574i
$786$	7.39771	−	10.3886i	0.263867	−	0.370550i
$787$	5.78101	−	5.51218i	0.206071	−	0.196488i	−0.580014	−	0.814606i	$-0.696953\pi$
$787$	5.78101	−	5.51218i	0.206071	−	0.196488i	0.786085	+	0.618118i	$0.212105\pi$
$788$	6.57876	+	9.23857i	0.234359	+	0.329111i
$789$	−4.29335	−	0.827475i	−0.152847	−	0.0294589i
$790$	−1.66531	+	11.5825i	−0.0592492	+	0.412087i
$791$	6.42423	−	33.8440i	0.228419	−	1.20335i
$792$	−2.75246	−	3.17651i	−0.0978046	−	0.112872i
$793$	10.3592	+	5.34056i	0.367868	+	0.189649i
$794$	1.19547	+	25.0960i	0.0424257	+	0.890625i
$795$	4.79502	−	0.924164i	0.170062	−	0.0327767i
$796$	1.59607	+	1.52185i	0.0565711	+	0.0539404i
$797$	2.87105	−	19.9686i	0.101698	−	0.707323i	−0.873635	−	0.486582i	$-0.838243\pi$
$797$	2.87105	−	19.9686i	0.101698	−	0.707323i	0.975333	−	0.220741i	$-0.0708474\pi$
$798$	2.02015	−	2.58376i	0.0715127	−	0.0914640i
$799$	13.8528	−	30.3335i	0.490078	−	1.07312i
$800$	0.612855	+	2.52622i	0.0216677	+	0.0893155i
$801$	−0.931305	−	0.0889289i	−0.0329061	−	0.00314215i
$802$	−27.1583	−	10.8725i	−0.958992	−	0.383922i
$803$	−2.84889	+	59.8056i	−0.100535	+	2.11049i
$804$	11.4122			0.402477
$805$	−5.37165	−	18.9110i	−0.189326	−	0.666525i
$806$	−12.7924			−0.450594
$807$	−0.298729	+	6.27110i	−0.0105158	+	0.220753i
$808$	−15.4561	−	6.18770i	−0.543745	−	0.217682i
$809$	24.8170	+	2.36973i	0.872518	+	0.0833154i	0.521701	−	0.853129i	$-0.325298\pi$
$809$	24.8170	+	2.36973i	0.872518	+	0.0833154i	0.350817	+	0.936444i	$0.385904\pi$
$810$	0.365274	+	1.50568i	0.0128344	+	0.0529042i
$811$	−9.36648	+	20.5097i	−0.328902	+	0.720194i	−0.999771	−	0.0213811i	$-0.993194\pi$
$811$	−9.36648	+	20.5097i	−0.328902	+	0.720194i	0.670870	+	0.741575i	$0.265921\pi$
$812$	9.20792	+	1.29748i	0.323135	+	0.0455325i
$813$	1.85545	−	12.9049i	0.0650734	−	0.452596i
$814$	−1.90606	−	1.81743i	−0.0668074	−	0.0637008i
$815$	10.1231	−	1.95106i	0.354596	−	0.0683427i
$816$	0.381316	+	8.00481i	0.0133487	+	0.280224i
$817$	−2.14633	−	1.10651i	−0.0750904	−	0.0387118i
$818$	13.6791	+	15.7866i	0.478279	+	0.551964i
$819$	−3.11390	+	1.08755i	−0.108808	+	0.0380020i
$820$	0.387563	−	2.69556i	0.0135343	−	0.0941330i
$821$	37.8984	+	7.30432i	1.32266	+	0.254923i	0.801224	−	0.598365i	$-0.204183\pi$
$821$	37.8984	+	7.30432i	1.32266	+	0.254923i	0.521440	+	0.853288i	$0.325395\pi$
$822$	2.99557	+	4.20669i	0.104482	+	0.146725i
$823$	34.5973	−	32.9884i	1.20598	−	1.14990i	0.221365	−	0.975191i	$-0.428949\pi$
$823$	34.5973	−	32.9884i	1.20598	−	1.14990i	0.984619	−	0.174713i	$-0.0558997\pi$
$824$	−1.24913	+	1.75416i	−0.0435155	+	0.0611090i
$825$	−1.55494	−	10.8148i	−0.0541360	−	0.376524i
$826$	−28.3827	+	16.4934i	−0.987562	+	0.573878i
$827$	−10.9865			−0.382039			−0.191019	−	0.981586i	$-0.561179\pi$
$827$	−10.9865			−0.382039			−0.191019	+	0.981586i	$0.561179\pi$
$828$	−4.47276	+	1.73043i	−0.155439	+	0.0601367i
$829$	5.88892	−	10.1999i	0.204531	−	0.354257i	−0.745453	−	0.666559i	$-0.767767\pi$
$829$	5.88892	−	10.1999i	0.204531	−	0.354257i	0.949983	+	0.312301i	$0.101100\pi$
$830$	19.8813	−	10.2495i	0.690090	−	0.355766i
$831$	−6.34941	+	4.99323i	−0.220259	+	0.173213i
$832$	−0.517881	−	1.13400i	−0.0179543	−	0.0393144i
$833$	−55.1423	−	10.3065i	−1.91057	−	0.357098i
$834$	−4.53496	+	9.93017i	−0.157033	+	0.343854i
$835$	−8.63883	−	1.66500i	−0.298959	−	0.0576196i
$836$	−4.09560	−	3.22082i	−0.141649	−	0.111394i
$837$	−2.41921	+	9.97212i	−0.0836201	+	0.344687i
$838$	−2.84016	+	8.20610i	−0.0981117	+	0.283475i
$839$	45.6352	−	29.3280i	1.57550	−	1.01251i	0.598024	−	0.801478i	$-0.295953\pi$
$839$	45.6352	−	29.3280i	1.57550	−	1.01251i	0.977478	−	0.211036i	$-0.0676838\pi$
$840$	−0.401130	−	4.07953i	−0.0138403	−	0.140757i
$841$	10.9016	+	12.5812i	0.375918	+	0.433833i
$842$	−15.8519	−	15.1147i	−0.546292	−	0.520889i
$843$	−8.56873	−	6.73852i	−0.295123	−	0.232087i
$844$	2.95214	+	8.52964i	0.101617	+	0.293602i
$845$	−17.6534	+	1.68569i	−0.607294	+	0.0579896i
$846$	3.99259	+	1.17233i	0.137268	+	0.0403055i
$847$	−8.12597	−	15.6539i	−0.279212	−	0.537875i
$848$	0.448549	+	3.11972i	0.0154032	+	0.107132i
$849$	0.766349	−	16.0876i	0.0263010	−	0.552126i
$850$	−10.4161	+	18.0411i	−0.357268	+	0.618806i
$851$	−2.68684	+	1.34577i	−0.0921037	+	0.0461324i
$852$	−3.83500	−	6.64242i	−0.131385	−	0.227566i
$853$	11.3490	+	7.29357i	0.388583	+	0.249727i	0.720316	−	0.693646i	$-0.243997\pi$
$853$	11.3490	+	7.29357i	0.388583	+	0.249727i	−0.331733	+	0.943373i	$0.607633\pi$
$854$	−18.6477	+	16.2503i	−0.638110	+	0.556075i
$855$	0.797859	+	1.74707i	0.0272862	+	0.0597484i
$856$	2.28833	+	9.43263i	0.0782135	+	0.322401i
$857$	12.8683	+	18.0710i	0.439573	+	0.617293i	0.973624	−	0.228159i	$-0.0732705\pi$
$857$	12.8683	+	18.0710i	0.439573	+	0.617293i	−0.534051	+	0.845452i	$0.679331\pi$
$858$	1.71379	+	4.95168i	0.0585080	+	0.169048i
$859$	48.3898	−	19.3724i	1.65104	−	0.660976i	0.655489	−	0.755205i	$-0.272463\pi$
$859$	48.3898	−	19.3724i	1.65104	−	0.660976i	0.995551	+	0.0942285i	$0.0300384\pi$
$860$	−2.89584	+	0.850294i	−0.0987472	+	0.0289948i
$861$	1.29761	−	4.46569i	0.0442226	−	0.152190i
$862$	−30.2989	+	19.4719i	−1.03198	+	0.663216i
$863$	−4.09187	−	2.10951i	−0.139289	−	0.0718084i	0.387173	−	0.922007i	$-0.373452\pi$
$863$	−4.09187	−	2.10951i	−0.139289	−	0.0718084i	−0.526462	+	0.850199i	$0.676482\pi$
$864$	−0.981929	+	0.189251i	−0.0334059	+	0.00643846i
$865$	−5.75165	+	23.7086i	−0.195562	+	0.806117i
$866$	6.90173	−	2.76304i	0.234530	−	0.0938918i
$867$	−30.9241	+	35.6883i	−1.05024	+	1.21204i
$868$	10.0194	−	25.2326i	0.340079	−	0.856449i
$869$	30.4586	+	8.94344i	1.03324	+	0.303385i
$870$	−3.15866	+	4.43572i	−0.107089	+	0.150385i
$871$	−13.2080	−	5.28768i	−0.447536	−	0.179166i
$872$	−0.523997	+	0.270139i	−0.0177448	+	0.00914806i
$873$	−7.77473	−	13.4662i	−0.263135	−	0.455763i
$874$	−5.03842	+	3.15565i	−0.170427	+	0.106742i
$875$	14.1967	−	27.7290i	0.479936	−	0.937410i
$876$	11.9836	+	7.70140i	0.404889	+	0.260206i
$877$	4.78098	−	3.75980i	0.161442	−	0.126960i	−0.534170	−	0.845377i	$-0.679376\pi$
$877$	4.78098	−	3.75980i	0.161442	−	0.126960i	0.695612	+	0.718418i	$0.255133\pi$
$878$	−40.3794	−	3.85577i	−1.36274	−	0.130126i
$879$	−0.563241	+	0.537049i	−0.0189977	+	0.0181142i
$880$	−6.48265	+	0.619018i	−0.218530	+	0.0208671i
$881$	−33.6376	+	38.8199i	−1.13328	+	1.30788i	−0.187797	+	0.982208i	$0.560135\pi$
$881$	−33.6376	+	38.8199i	−1.13328	+	1.30788i	−0.945484	+	0.325668i	$0.894411\pi$
$882$	0.293738	−	6.99383i	0.00989068	−	0.235495i
$883$	−9.19554	+	2.70006i	−0.309455	+	0.0908641i	−0.432773	−	0.901503i	$-0.642465\pi$
$883$	−9.19554	+	2.70006i	−0.309455	+	0.0908641i	0.123318	+	0.992367i	$0.460647\pi$
$884$	3.26760	−	9.44112i	0.109901	−	0.317539i
$885$	−0.914692	−	19.2017i	−0.0307470	−	0.645460i
$886$	−1.90552	−	40.0018i	−0.0640172	−	1.34389i
$887$	0.0429389	−	0.124064i	0.00144175	−	0.00416565i	−0.944278	−	0.329150i	$-0.893238\pi$
$887$	0.0429389	−	0.124064i	0.00144175	−	0.00416565i	0.945719	+	0.324984i	$0.105359\pi$
$888$	−0.601211	+	0.176531i	−0.0201753	+	0.00592401i
$889$	−30.9011	−	21.8738i	−1.03639	−	0.733625i
$890$	−0.949211	+	1.09545i	−0.0318176	+	0.0367195i
$891$	4.18410	−	0.399533i	0.140173	−	0.0133849i
$892$	−18.7826	+	17.9091i	−0.628887	+	0.599642i
$893$	5.13493	+	0.490327i	0.171834	+	0.0164082i
$894$	−6.54096	+	5.14386i	−0.218762	+	0.172037i
$895$	−14.6741	−	9.43047i	−0.490501	−	0.315226i
$896$	2.64239	−	0.133322i	0.0882761	−	0.00445398i
$897$	5.97836	+	0.0696640i	0.199612	+	0.00232601i
$898$	−19.5036	−	33.7813i	−0.650844	−	1.12730i
$899$	−32.0559	+	16.5260i	−1.06913	+	0.551172i
$900$	−2.41329	−	0.966137i	−0.0804431	−	0.0322046i
$901$	−14.6512	+	20.5747i	−0.488102	+	0.685444i
$902$	−7.08852	−	2.08138i	−0.236022	−	0.0693023i
$903$	−5.09929	+	0.747812i	−0.169694	+	0.0248856i
$904$	−8.52644	+	9.84004i	−0.283585	+	0.327275i
$905$	−14.2298	+	5.69676i	−0.473015	+	0.189367i
$906$	−4.34922	+	17.9277i	−0.144493	+	0.595609i
$907$	−22.5653	+	4.34910i	−0.749267	+	0.144409i	−0.549569	−	0.835448i	$-0.685208\pi$
$907$	−22.5653	+	4.34910i	−0.749267	+	0.144409i	−0.199698	+	0.979858i	$0.563996\pi$
$908$	−13.0323	−	6.71862i	−0.432492	−	0.222965i
$909$	14.0058	−	9.00097i	0.464542	−	0.298543i
$910$	−1.42595	+	4.90734i	−0.0472697	+	0.162677i
$911$	0.689366	−	0.202416i	0.0228397	−	0.00670635i	−0.270293	−	0.962778i	$-0.587120\pi$
$911$	0.689366	−	0.202416i	0.0228397	−	0.00670635i	0.293132	+	0.956072i	$0.405302\pi$
$912$	−1.15084	+	0.460725i	−0.0381080	+	0.0152561i
$913$	−19.8465	−	57.3427i	−0.656823	−	1.89777i
$914$	−8.63912	−	12.1319i	−0.285757	−	0.401289i
$915$	−3.41490	−	14.0764i	−0.112893	−	0.465352i
$916$	2.88452	+	6.31622i	0.0953073	+	0.208694i
$917$	−6.47894	−	33.1145i	−0.213954	−	1.09354i
$918$	−6.74171	−	4.33264i	−0.222510	−	0.142998i
$919$	−7.55865	−	13.0920i	−0.249337	−	0.431864i	0.714005	−	0.700140i	$-0.246879\pi$
$919$	−7.55865	−	13.0920i	−0.249337	−	0.431864i	−0.963342	+	0.268276i	$0.913546\pi$
$920$	−1.83581	+	7.20009i	−0.0605250	+	0.237380i
$921$	−9.20673	+	15.9465i	−0.303372	+	0.525456i
$922$	−0.227482	+	4.77543i	−0.00749171	+	0.157270i
$923$	1.36080	+	9.46456i	0.0447912	+	0.311530i
$924$	−11.1093	−	0.497889i	−0.365469	−	0.0163793i
$925$	−1.56285	−	0.458894i	−0.0513861	−	0.0150883i
$926$	−11.7062	+	1.11781i	−0.384690	+	0.0367334i
$927$	−0.704328	−	2.03502i	−0.0231332	−	0.0668389i
$928$	−2.76270	−	2.17261i	−0.0906901	−	0.0713194i
$929$	0.661060	+	0.630319i	0.0216887	+	0.0206801i	0.700846	−	0.713313i	$-0.252806\pi$
$929$	0.661060	+	0.630319i	0.0216887	+	0.0206801i	−0.679157	+	0.733993i	$0.737655\pi$
$930$	10.4113	+	12.0153i	0.341400	+	0.393997i
$931$	−1.28322	−	8.58202i	−0.0420559	−	0.281264i
$932$	−3.51300	+	2.25767i	−0.115072	+	0.0739523i
$933$	−11.1435	+	32.1970i	−0.364821	+	1.05408i
$934$	1.03286	−	4.25749i	0.0337961	−	0.139309i
$935$	−41.0222	−	32.2602i	−1.34157	−	1.05502i
$936$	1.22413	+	0.235932i	0.0400120	+	0.00771167i
$937$	8.95973	−	19.6191i	0.292702	−	0.640927i	−0.704962	−	0.709245i	$-0.749036\pi$
$937$	8.95973	−	19.6191i	0.292702	−	0.640927i	0.997664	+	0.0683179i	$0.0217632\pi$
$938$	20.7746	−	21.9108i	0.678313	−	0.715413i
$939$	−10.4586	−	22.9011i	−0.341303	−	0.747350i
$940$	5.06775	−	3.98533i	0.165292	−	0.129987i
$941$	−16.6342	+	8.57555i	−0.542261	+	0.279555i	−0.707518	−	0.706696i	$-0.750185\pi$
$941$	−16.6342	+	8.57555i	−0.542261	+	0.279555i	0.165257	+	0.986251i	$0.447155\pi$
$942$	1.53074	−	2.65133i	0.0498744	−	0.0863849i
$943$	−4.96930	+	6.80908i	−0.161823	+	0.221734i
$944$	12.4074			0.403828
$945$	3.55577	+	2.03961i	0.115669	+	0.0663485i
$946$	1.16521	+	8.10422i	0.0378843	+	0.263491i
$947$	−19.7080	+	27.6761i	−0.640425	+	0.899351i	−0.999422	−	0.0339873i	$-0.989179\pi$
$947$	−19.7080	+	27.6761i	−0.640425	+	0.899351i	0.358997	+	0.933339i	$0.383119\pi$
$948$	5.46605	−	5.21187i	0.177529	−	0.169274i
$949$	−10.3010	−	14.4657i	−0.334385	−	0.469578i
$950$	−3.16419	−	0.609848i	−0.102660	−	0.0197861i
$951$	3.52516	−	24.5180i	0.114311	−	0.795051i
$952$	16.0630	+	13.8397i	0.520604	+	0.448548i
$953$	0.351980	+	0.406206i	0.0114017	+	0.0131583i	0.761422	−	0.648257i	$-0.224502\pi$
$953$	0.351980	+	0.406206i	0.0114017	+	0.0131583i	−0.750020	+	0.661415i	$0.769956\pi$
$954$	−2.80144	−	1.44424i	−0.0906998	−	0.0467590i
$955$	0.902143	+	18.9383i	0.0291927	+	0.612830i
$956$	−15.7085	+	3.02757i	−0.508049	+	0.0979185i
$957$	10.6914	+	10.1942i	0.345603	+	0.329532i
$958$	−1.58450	+	11.0205i	−0.0511929	+	0.356055i
$959$	13.5297	+	1.90646i	0.436897	+	0.0615627i
$960$	−0.643625	+	1.40934i	−0.0207729	+	0.0454863i
$961$	17.5159	+	72.2014i	0.565028	+	2.32908i
$962$	0.777610	+	0.0742528i	0.0250712	+	0.00239401i
$963$	−9.01095	−	3.60744i	−0.290374	−	0.116248i
$964$	−0.288935	+	6.06550i	−0.00930599	+	0.195357i
$965$	27.1100			0.872700
$966$	−4.81981	+	11.7375i	−0.155075	+	0.377649i
$967$	−14.1523			−0.455109			−0.227554	−	0.973765i	$-0.573073\pi$
$967$	−14.1523			−0.455109			−0.227554	+	0.973765i	$0.573073\pi$
$968$	−0.317195	+	6.65875i	−0.0101950	+	0.214020i
$969$	−9.22266	−	3.69220i	−0.296275	−	0.118610i
$970$	−23.9825	−	2.29005i	−0.770033	−	0.0735292i
$971$	5.81294	+	23.9613i	0.186546	+	0.768953i	0.985795	+	0.167953i	$0.0537157\pi$
$971$	5.81294	+	23.9613i	0.186546	+	0.768953i	−0.799249	+	0.601000i	$0.794769\pi$
$972$	0.415415	−	0.909632i	0.0133244	−	0.0291765i
$973$	10.8100	+	26.7836i	0.346554	+	0.858643i
$974$	−1.50941	+	10.4981i	−0.0483645	+	0.336382i
$975$	2.34540	+	2.23633i	0.0751129	+	0.0716200i
$976$	9.17992	−	1.76928i	0.293842	−	0.0566334i
$977$	0.574293	+	12.0559i	0.0183733	+	0.385702i	0.989260	+	0.146164i	$0.0466929\pi$
$977$	0.574293	+	12.0559i	0.0183733	+	0.385702i	−0.970887	+	0.239538i	$0.923004\pi$
$978$	−5.91429	−	3.04903i	−0.189118	−	0.0974972i
$979$	2.57504	+	2.97176i	0.0822988	+	0.0949779i
$980$	−8.56270	−	6.65617i	−0.273525	−	0.212624i
$981$	0.0838991	−	0.583531i	0.00267869	−	0.0186307i
$982$	30.3984	+	5.85882i	0.970054	+	0.186962i
$983$	−8.79069	−	12.3448i	−0.280380	−	0.393738i	0.650238	−	0.759730i	$-0.274669\pi$
$983$	−8.79069	−	12.3448i	−0.280380	−	0.393738i	−0.930618	+	0.365992i	$0.880730\pi$
$984$	−1.27210	+	1.21294i	−0.0405530	+	0.0386672i
$985$	−10.1928	+	14.3138i	−0.324771	+	0.456076i
$986$	−4.00844	−	27.8793i	−0.127655	−	0.887858i
$987$	9.51886	−	5.53147i	0.302989	−	0.176069i
$988$	1.54540			0.0491657
$989$	9.15207	+	1.87477i	0.291019	+	0.0596143i
$990$	3.25607	−	5.63968i	0.103485	−	0.179241i
$991$	7.76880	−	4.00509i	0.246784	−	0.127226i	−0.330397	−	0.943842i	$-0.607183\pi$
$991$	7.76880	−	4.00509i	0.246784	−	0.127226i	0.577182	+	0.816616i	$0.304152\pi$
$992$	−8.06598	+	6.34316i	−0.256095	+	0.201395i
$993$	5.87930	+	12.8739i	0.186574	+	0.408540i
$994$	−19.7343	−	4.72876i	−0.625933	−	0.149987i
$995$	−1.41940	+	3.10805i	−0.0449980	+	0.0985319i
$996$	−14.1760	−	2.73219i	−0.449183	−	0.0865729i
$997$	−15.6834	−	12.3336i	−0.496698	−	0.390608i	0.338146	−	0.941094i	$-0.390200\pi$
$997$	−15.6834	−	12.3336i	−0.496698	−	0.390608i	−0.834845	+	0.550486i	$0.814443\pi$
$998$	4.45976	−	18.3834i	0.141171	−	0.581915i
$999$	0.204938	−	0.592130i	0.00648396	−	0.0187342i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.y.b.25.3	✓	160
7.2	even	3	inner	966.2.y.b.163.3	yes	160
23.12	even	11	inner	966.2.y.b.403.3	yes	160
161.58	even	33	inner	966.2.y.b.541.3	yes	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.y.b.25.3	✓	160	1.1	even	1	trivial
966.2.y.b.163.3	yes	160	7.2	even	3	inner
966.2.y.b.403.3	yes	160	23.12	even	11	inner
966.2.y.b.541.3	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)

\(f(q)\)	\(=\)	\(q+(-0.0475819 + 0.998867i) q^{2} +(0.928368 + 0.371662i) q^{3} +(-0.995472 - 0.0950560i) q^{4} +(-0.365274 - 1.50568i) q^{5} +(-0.415415 + 0.909632i) q^{6} +(0.990231 + 2.45346i) q^{7} +(0.142315 - 0.989821i) q^{8} +(0.723734 + 0.690079i) q^{9} +O(q^{10})\)	\(q+(-0.0475819 + 0.998867i) q^{2} +(0.928368 + 0.371662i) q^{3} +(-0.995472 - 0.0950560i) q^{4} +(-0.365274 - 1.50568i) q^{5} +(-0.415415 + 0.909632i) q^{6} +(0.990231 + 2.45346i) q^{7} +(0.142315 - 0.989821i) q^{8} +(0.723734 + 0.690079i) q^{9} +(1.52136 - 0.293217i) q^{10} +(-0.199993 - 4.19837i) q^{11} +(-0.888835 - 0.458227i) q^{12} +(0.816388 + 0.942162i) q^{13} +(-2.49779 + 0.872369i) q^{14} +(0.220496 - 1.53358i) q^{15} +(0.981929 + 0.189251i) q^{16} +(4.64851 + 6.52792i) q^{17} +(-0.723734 + 0.690079i) q^{18} +(-0.719057 + 1.00977i) q^{19} +(0.220496 + 1.53358i) q^{20} +(0.00744112 + 2.64574i) q^{21} +4.20313 q^{22} +(1.62126 - 4.51348i) q^{23} +(0.500000 - 0.866025i) q^{24} +(2.31053 - 1.19116i) q^{25} +(-0.979941 + 0.770634i) q^{26} +(0.415415 + 0.909632i) q^{27} +(-0.752531 - 2.53647i) q^{28} +(-1.46004 + 3.19704i) q^{29} +(1.52136 + 0.293217i) q^{30} +(8.06598 + 6.34316i) q^{31} +(-0.235759 + 0.971812i) q^{32} +(1.37471 - 3.97196i) q^{33} +(-6.74171 + 4.33264i) q^{34} +(3.33241 - 2.38715i) q^{35} +(-0.654861 - 0.755750i) q^{36} +(-0.453486 - 0.432398i) q^{37} +(-0.974417 - 0.766290i) q^{38} +(0.407742 + 1.17809i) q^{39} +(-1.54234 + 0.147276i) q^{40} +(-1.68649 - 0.495197i) q^{41} +(-2.64310 - 0.118457i) q^{42} +(0.277224 + 1.92814i) q^{43} +(-0.199993 + 4.19837i) q^{44} +(0.774677 - 1.34178i) q^{45} +(4.43123 + 1.83419i) q^{46} +(-2.08057 - 3.60366i) q^{47} +(0.841254 + 0.540641i) q^{48} +(-5.03889 + 4.85897i) q^{49} +(1.07987 + 2.36459i) q^{50} +(1.88935 + 7.78799i) q^{51} +(-0.723134 - 1.01550i) q^{52} +(1.03085 + 2.97846i) q^{53} +(-0.928368 + 0.371662i) q^{54} +(-6.24835 + 1.83468i) q^{55} +(2.56941 - 0.630988i) q^{56} +(-1.04285 + 0.670196i) q^{57} +(-3.12394 - 1.61050i) q^{58} +(12.1832 - 2.34812i) q^{59} +(-0.365274 + 1.50568i) q^{60} +(8.67919 - 3.47462i) q^{61} +(-6.71977 + 7.75503i) q^{62} +(-0.976414 + 2.45899i) q^{63} +(-0.959493 - 0.281733i) q^{64} +(1.12039 - 1.57337i) q^{65} +(3.90205 + 1.56215i) q^{66} +(-10.1435 + 5.22936i) q^{67} +(-4.00694 - 6.94023i) q^{68} +(3.18262 - 3.58761i) q^{69} +(2.22589 + 3.44223i) q^{70} +(6.45242 + 4.14672i) q^{71} +(0.786053 - 0.618159i) q^{72} +(-14.1804 - 1.35407i) q^{73} +(0.453486 - 0.432398i) q^{74} +(2.58773 - 0.247098i) q^{75} +(0.811787 - 0.936852i) q^{76} +(10.1025 - 4.64803i) q^{77} +(-1.19616 + 0.351225i) q^{78} +(-2.47020 + 7.13718i) q^{79} +(-0.0737213 - 1.54760i) q^{80} +(0.0475819 + 0.998867i) q^{81} +(0.574882 - 1.66101i) q^{82} +(13.8521 - 4.06733i) q^{83} +(0.244086 - 2.63447i) q^{84} +(8.13098 - 9.38365i) q^{85} +(-1.93915 + 0.185166i) q^{86} +(-2.54367 + 2.42538i) q^{87} +(-4.18410 - 0.399533i) q^{88} +(-0.735385 + 0.578313i) q^{89} +(1.30340 + 0.837644i) q^{90} +(-1.50314 + 2.93593i) q^{91} +(-2.04296 + 4.33893i) q^{92} +(5.13069 + 8.88661i) q^{93} +(3.69857 - 1.90675i) q^{94} +(1.78305 + 0.713826i) q^{95} +(-0.580057 + 0.814576i) q^{96} +(-14.9196 - 4.38079i) q^{97} +(-4.61371 - 5.26438i) q^{98} +(2.75246 - 3.17651i) 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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Representations

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Database

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