LMFDB - Embedded newform 966.2.y.a.121.5

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			121.5
Character	$\chi$	$=$	966.121
Dual form			966.2.y.a.487.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.580057 - 0.814576i) q^{2} +(-0.235759 - 0.971812i) q^{3} +(-0.327068 + 0.945001i) q^{4} +(0.0236187 + 0.495818i) q^{5} +(-0.654861 + 0.755750i) q^{6} +(2.48735 - 0.901724i) q^{7} +(0.959493 - 0.281733i) q^{8} +(-0.888835 + 0.458227i) q^{9} +O(q^{10})$	\(q+(-0.580057 - 0.814576i) q^{2} +(-0.235759 - 0.971812i) q^{3} +(-0.327068 + 0.945001i) q^{4} +(0.0236187 + 0.495818i) q^{5} +(-0.654861 + 0.755750i) q^{6} +(2.48735 - 0.901724i) q^{7} +(0.959493 - 0.281733i) q^{8} +(-0.888835 + 0.458227i) q^{9} +(0.390181 - 0.306842i) q^{10} +(2.14770 - 3.01602i) q^{11} +(0.995472 + 0.0950560i) q^{12} +(0.594779 + 4.13678i) q^{13} +(-2.17733 - 1.50308i) q^{14} +(0.476273 - 0.139846i) q^{15} +(-0.786053 - 0.618159i) q^{16} +(6.07187 + 1.17026i) q^{17} +(0.888835 + 0.458227i) q^{18} +(-7.99991 + 1.54186i) q^{19} +(-0.476273 - 0.139846i) q^{20} +(-1.46272 - 2.20464i) q^{21} -3.70256 q^{22} +(3.05845 + 3.69403i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(4.73208 - 0.451859i) q^{25} +(3.02472 - 2.88406i) q^{26} +(0.654861 + 0.755750i) q^{27} +(0.0385981 + 2.64547i) q^{28} +(-0.964659 + 1.11328i) q^{29} +(-0.390181 - 0.306842i) q^{30} +(2.09534 + 1.99791i) q^{31} +(-0.0475819 + 0.998867i) q^{32} +(-3.43734 - 1.37610i) q^{33} +(-2.56877 - 5.62481i) q^{34} +(0.505839 + 1.21197i) q^{35} +(-0.142315 - 0.989821i) q^{36} +(6.79593 - 3.50355i) q^{37} +(5.89636 + 5.62217i) q^{38} +(3.87995 - 1.55330i) q^{39} +(0.162350 + 0.469080i) q^{40} +(4.93081 - 3.16884i) q^{41} +(-0.947389 + 2.47031i) q^{42} +(-11.9534 - 3.50983i) q^{43} +(2.14770 + 3.01602i) q^{44} +(-0.248190 - 0.429878i) q^{45} +(1.23499 - 4.63409i) q^{46} +(1.91110 - 3.31013i) q^{47} +(-0.415415 + 0.909632i) q^{48} +(5.37379 - 4.48580i) q^{49} +(-3.11295 - 3.59254i) q^{50} +(-0.294228 - 6.17661i) q^{51} +(-4.10380 - 0.790942i) q^{52} +(9.05345 - 3.62445i) q^{53} +(0.235759 - 0.971812i) q^{54} +(1.54612 + 0.993633i) q^{55} +(2.13255 - 1.56596i) q^{56} +(3.38444 + 7.41090i) q^{57} +(1.46640 + 0.140025i) q^{58} +(-0.318598 + 0.250548i) q^{59} +(-0.0236187 + 0.495818i) q^{60} +(0.236871 - 0.976394i) q^{61} +(0.412028 - 2.86572i) q^{62} +(-1.79765 + 1.94125i) q^{63} +(0.841254 - 0.540641i) q^{64} +(-2.03704 + 0.392608i) q^{65} +(0.872912 + 3.59819i) q^{66} +(0.559623 - 0.0534376i) q^{67} +(-3.09181 + 5.35517i) q^{68} +(2.86884 - 3.84314i) q^{69} +(0.693829 - 1.11506i) q^{70} +(3.78447 - 8.28684i) q^{71} +(-0.723734 + 0.690079i) q^{72} +(-3.77068 + 10.8947i) q^{73} +(-6.79593 - 3.50355i) q^{74} +(-1.55475 - 4.49216i) q^{75} +(1.15946 - 8.06421i) q^{76} +(2.62245 - 9.43852i) q^{77} +(-3.51587 - 2.25951i) q^{78} +(-8.13019 - 3.25484i) q^{79} +(0.287929 - 0.404339i) q^{80} +(0.580057 - 0.814576i) q^{81} +(-5.44141 - 2.17841i) q^{82} +(-7.51157 - 4.82739i) q^{83} +(2.56180 - 0.661203i) q^{84} +(-0.436824 + 3.03818i) q^{85} +(4.07462 + 11.7728i) q^{86} +(1.30932 + 0.675002i) q^{87} +(1.21099 - 3.49893i) q^{88} +(-0.511751 + 0.487953i) q^{89} +(-0.206204 + 0.451523i) q^{90} +(5.20966 + 9.75328i) q^{91} +(-4.49118 + 1.68204i) q^{92} +(1.44759 - 2.50730i) q^{93} +(-3.80490 + 0.363324i) q^{94} +(-0.953427 - 3.93008i) q^{95} +(0.981929 - 0.189251i) q^{96} +(7.25917 - 4.66519i) q^{97} +(-6.77113 - 1.77534i) q^{98} +(-0.526930 + 3.66488i) 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 $\left(\mathbb{Z}/966\mathbb{Z}\right)^\times$.

$n$	$323$	$829$	$925$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{9}{11}\right)$

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 $

$2$	−0.580057	−	0.814576i	−0.410162	−	0.575992i
$2$	−0.580057	−	0.814576i	−0.410162	−	0.575992i
$3$	−0.235759	−	0.971812i	−0.136115	−	0.561076i
$3$	−0.235759	−	0.971812i	−0.136115	−	0.561076i
$4$	−0.327068	+	0.945001i	−0.163534	+	0.472500i
$5$	0.0236187	+	0.495818i	0.0105626	+	0.221737i	0.997977	+	0.0635804i	$0.0202519\pi$
$5$	0.0236187	+	0.495818i	0.0105626	+	0.221737i	−0.987414	+	0.158156i	$0.949445\pi$
$6$	−0.654861	+	0.755750i	−0.267346	+	0.308533i
$7$	2.48735	−	0.901724i	0.940129	−	0.340820i
$7$	2.48735	−	0.901724i	0.940129	−	0.340820i
$8$	0.959493	−	0.281733i	0.339232	−	0.0996075i
$9$	−0.888835	+	0.458227i	−0.296278	+	0.152742i
$10$	0.390181	−	0.306842i	0.123386	−	0.0970319i
$11$	2.14770	−	3.01602i	0.647555	−	0.909364i	−0.352091	−	0.935966i	$-0.614529\pi$
$11$	2.14770	−	3.01602i	0.647555	−	0.909364i	0.999646	+	0.0266018i	$0.00846861\pi$
$12$	0.995472	+	0.0950560i	0.287368	+	0.0274403i
$13$	0.594779	+	4.13678i	0.164962	+	1.14734i	0.889110	+	0.457693i	$0.151324\pi$
$13$	0.594779	+	4.13678i	0.164962	+	1.14734i	−0.724148	+	0.689644i	$0.757767\pi$
$14$	−2.17733	−	1.50308i	−0.581915	−	0.401716i
$15$	0.476273	−	0.139846i	0.122973	−	0.0361082i
$16$	−0.786053	−	0.618159i	−0.196513	−	0.154540i
$17$	6.07187	+	1.17026i	1.47264	+	0.283829i	0.861527	−	0.507711i	$-0.169508\pi$
$17$	6.07187	+	1.17026i	1.47264	+	0.283829i	0.611117	+	0.791540i	$0.290721\pi$
$18$	0.888835	+	0.458227i	0.209501	+	0.108005i
$19$	−7.99991	+	1.54186i	−1.83530	+	0.353726i	−0.984999	−	0.172563i	$-0.944795\pi$
$19$	−7.99991	+	1.54186i	−1.83530	+	0.353726i	−0.850306	+	0.526289i	$0.823583\pi$
$20$	−0.476273	−	0.139846i	−0.106498	−	0.0312706i
$21$	−1.46272	−	2.20464i	−0.319192	−	0.481093i
$22$	−3.70256			−0.789389
$23$	3.05845	+	3.69403i	0.637732	+	0.770259i
$23$	3.05845	+	3.69403i	0.637732	+	0.770259i
$24$	−0.500000	−	0.866025i	−0.102062	−	0.176777i
$25$	4.73208	−	0.451859i	0.946416	−	0.0903718i
$26$	3.02472	−	2.88406i	0.593196	−	0.565611i
$27$	0.654861	+	0.755750i	0.126028	+	0.145444i
$28$	0.0385981	+	2.64547i	0.00729436	+	0.499947i
$29$	−0.964659	+	1.11328i	−0.179133	+	0.206730i	−0.838214	−	0.545342i	$-0.816400\pi$
$29$	−0.964659	+	1.11328i	−0.179133	+	0.206730i	0.659081	+	0.752072i	$0.270945\pi$
$30$	−0.390181	−	0.306842i	−0.0712370	−	0.0560214i
$31$	2.09534	+	1.99791i	0.376335	+	0.358835i	0.854515	−	0.519427i	$-0.173855\pi$
$31$	2.09534	+	1.99791i	0.376335	+	0.358835i	−0.478180	+	0.878262i	$0.658703\pi$
$32$	−0.0475819	+	0.998867i	−0.00841137	+	0.176576i
$33$	−3.43734	−	1.37610i	−0.598364	−	0.239549i
$34$	−2.56877	−	5.62481i	−0.440540	−	0.964647i
$35$	0.505839	+	1.21197i	0.0855024	+	0.204861i
$36$	−0.142315	−	0.989821i	−0.0237191	−	0.164970i
$37$	6.79593	−	3.50355i	1.11724	−	0.575979i	0.202204	−	0.979343i	$-0.435189\pi$
$37$	6.79593	−	3.50355i	1.11724	−	0.575979i	0.915040	+	0.403364i	$0.132159\pi$
$38$	5.89636	+	5.62217i	0.956516	+	0.912036i
$39$	3.87995	−	1.55330i	0.621289	−	0.248727i
$40$	0.162350	+	0.469080i	0.0256698	+	0.0741680i
$41$	4.93081	−	3.16884i	0.770063	−	0.494890i	−0.0956591	−	0.995414i	$-0.530496\pi$
$41$	4.93081	−	3.16884i	0.770063	−	0.494890i	0.865722	+	0.500525i	$0.166860\pi$
$42$	−0.947389	+	2.47031i	−0.146185	+	0.381178i
$43$	−11.9534	−	3.50983i	−1.82287	−	0.535244i	−0.823392	−	0.567473i	$-0.807921\pi$
$43$	−11.9534	−	3.50983i	−1.82287	−	0.535244i	−0.999481	+	0.0322293i	$0.989739\pi$
$44$	2.14770	+	3.01602i	0.323778	+	0.454682i
$45$	−0.248190	−	0.429878i	−0.0369980	−	0.0640824i
$46$	1.23499	−	4.63409i	0.182090	−	0.683259i
$47$	1.91110	−	3.31013i	0.278763	−	0.482832i	−0.692315	−	0.721596i	$-0.743409\pi$
$47$	1.91110	−	3.31013i	0.278763	−	0.482832i	0.971078	+	0.238764i	$0.0767423\pi$
$48$	−0.415415	+	0.909632i	−0.0599600	+	0.131294i
$49$	5.37379	−	4.48580i	0.767684	−	0.640828i
$50$	−3.11295	−	3.59254i	−0.440238	−	0.508061i
$51$	−0.294228	−	6.17661i	−0.0412002	−	0.864898i
$52$	−4.10380	−	0.790942i	−0.569094	−	0.109684i
$53$	9.05345	−	3.62445i	1.24359	−	0.497857i	0.345808	−	0.938305i	$-0.387605\pi$
$53$	9.05345	−	3.62445i	1.24359	−	0.497857i	0.897778	+	0.440448i	$0.145180\pi$
$54$	0.235759	−	0.971812i	0.0320827	−	0.132247i
$55$	1.54612	+	0.993633i	0.208479	+	0.133981i
$56$	2.13255	−	1.56596i	0.284974	−	0.209261i
$57$	3.38444	+	7.41090i	0.448280	+	0.981597i
$58$	1.46640	+	0.140025i	0.192548	+	0.0183861i
$59$	−0.318598	+	0.250548i	−0.0414779	+	0.0326186i	−0.638683	−	0.769470i	$-0.720520\pi$
$59$	−0.318598	+	0.250548i	−0.0414779	+	0.0326186i	0.597205	+	0.802089i	$0.296278\pi$
$60$	−0.0236187	+	0.495818i	−0.00304916	+	0.0640098i
$61$	0.236871	−	0.976394i	0.0303282	−	0.125015i	−0.954635	−	0.297778i	$-0.903754\pi$
$61$	0.236871	−	0.976394i	0.0303282	−	0.125015i	0.984963	+	0.172763i	$0.0552696\pi$
$62$	0.412028	−	2.86572i	0.0523276	−	0.363946i
$63$	−1.79765	+	1.94125i	−0.226482	+	0.244575i
$64$	0.841254	−	0.540641i	0.105157	−	0.0675801i
$65$	−2.03704	+	0.392608i	−0.252664	+	0.0486970i
$66$	0.872912	+	3.59819i	0.107448	+	0.442907i
$67$	0.559623	−	0.0534376i	0.0683689	−	0.00652844i	−0.0608155	−	0.998149i	$-0.519370\pi$
$67$	0.559623	−	0.0534376i	0.0683689	−	0.00652844i	0.129184	+	0.991621i	$0.458764\pi$
$68$	−3.09181	+	5.35517i	−0.374937	+	0.649409i
$69$	2.86884	−	3.84314i	0.345368	−	0.462660i
$70$	0.693829	−	1.11506i	0.0829285	−	0.133275i
$71$	3.78447	−	8.28684i	0.449134	−	0.983467i	−0.540696	−	0.841218i	$-0.681839\pi$
$71$	3.78447	−	8.28684i	0.449134	−	0.983467i	0.989831	−	0.142249i	$-0.0454335\pi$
$72$	−0.723734	+	0.690079i	−0.0852929	+	0.0813266i
$73$	−3.77068	+	10.8947i	−0.441324	+	1.27512i	0.476863	+	0.878978i	$0.341774\pi$
$73$	−3.77068	+	10.8947i	−0.441324	+	1.27512i	−0.918188	+	0.396146i	$0.870348\pi$
$74$	−6.79593	−	3.50355i	−0.790011	−	0.407279i
$75$	−1.55475	−	4.49216i	−0.179527	−	0.518710i
$76$	1.15946	−	8.06421i	0.132999	−	0.925028i
$77$	2.62245	−	9.43852i	0.298856	−	1.07562i
$78$	−3.51587	−	2.25951i	−0.398094	−	0.255839i
$79$	−8.13019	−	3.25484i	−0.914718	−	0.366198i	−0.133928	−	0.990991i	$-0.542759\pi$
$79$	−8.13019	−	3.25484i	−0.914718	−	0.366198i	−0.780790	+	0.624793i	$0.785183\pi$
$80$	0.287929	−	0.404339i	0.0321914	−	0.0452065i
$81$	0.580057	−	0.814576i	0.0644508	−	0.0905084i
$82$	−5.44141	−	2.17841i	−0.600903	−	0.240565i
$83$	−7.51157	−	4.82739i	−0.824502	−	0.529875i	0.0590247	−	0.998257i	$-0.481201\pi$
$83$	−7.51157	−	4.82739i	−0.824502	−	0.529875i	−0.883526	+	0.468381i	$0.844837\pi$
$84$	2.56180	−	0.661203i	0.279515	−	0.0721432i
$85$	−0.436824	+	3.03818i	−0.0473803	+	0.329537i
$86$	4.07462	+	11.7728i	0.439377	+	1.26950i
$87$	1.30932	+	0.675002i	0.140374	+	0.0723678i
$88$	1.21099	−	3.49893i	0.129092	−	0.372987i
$89$	−0.511751	+	0.487953i	−0.0542455	+	0.0517230i	−0.716717	−	0.697364i	$-0.754356\pi$
$89$	−0.511751	+	0.487953i	−0.0542455	+	0.0517230i	0.662472	+	0.749087i	$0.269508\pi$
$90$	−0.206204	+	0.451523i	−0.0217358	+	0.0475947i
$91$	5.20966	+	9.75328i	0.546120	+	1.02242i
$92$	−4.49118	+	1.68204i	−0.468238	+	0.175365i
$93$	1.44759	−	2.50730i	0.150108	−	0.259995i
$94$	−3.80490	+	0.363324i	−0.392445	+	0.0374740i
$95$	−0.953427	−	3.93008i	−0.0978196	−	0.403218i
$96$	0.981929	−	0.189251i	0.100218	−	0.0193154i
$97$	7.25917	−	4.66519i	0.737057	−	0.473678i	−0.117475	−	0.993076i	$-0.537480\pi$
$97$	7.25917	−	4.66519i	0.737057	−	0.473678i	0.854533	+	0.519398i	$0.173844\pi$
$98$	−6.77113	−	1.77534i	−0.683987	−	0.179336i
$99$	−0.526930	+	3.66488i	−0.0529584	+	0.368334i
$100$	−1.12071	+	4.61961i	−0.112071	+	0.461961i
$101$	0.677345	−	14.2192i	0.0673984	−	1.41487i	−0.671478	−	0.741024i	$-0.734340\pi$
$101$	0.677345	−	14.2192i	0.0673984	−	1.41487i	0.738876	−	0.673841i	$-0.235357\pi$
$102$	−4.86065	+	3.82246i	−0.481276	+	0.378480i
$103$	9.43595	+	0.901024i	0.929752	+	0.0887805i	0.548930	−	0.835868i	$-0.315035\pi$
$103$	9.43595	+	0.901024i	0.929752	+	0.0887805i	0.380821	+	0.924649i	$0.375641\pi$
$104$	1.73615	+	3.80164i	0.170244	+	0.372782i
$105$	1.05855	−	0.777314i	0.103304	−	0.0758580i
$106$	−8.20391	−	5.27233i	−0.796834	−	0.512094i
$107$	0.321373	−	1.32472i	0.0310683	−	0.128065i	−0.954166	−	0.299279i	$-0.903254\pi$
$107$	0.321373	−	1.32472i	0.0310683	−	0.128065i	0.985234	+	0.171214i	$0.0547689\pi$
$108$	−0.928368	+	0.371662i	−0.0893322	+	0.0357632i
$109$	−18.5190	−	3.56924i	−1.77380	−	0.341871i	−0.805677	−	0.592355i	$-0.798198\pi$
$109$	−18.5190	−	3.56924i	−1.77380	−	0.341871i	−0.968121	+	0.250484i	$0.919410\pi$
$110$	−0.0874498	−	1.83580i	−0.00833801	−	0.175036i
$111$	−5.00699	−	5.77837i	−0.475242	−	0.548459i
$112$	−2.51260	−	0.828773i	−0.237418	−	0.0783117i
$113$	−3.50612	+	7.67732i	−0.329828	+	0.722222i	−0.999797	−	0.0201672i	$-0.993580\pi$
$113$	−3.50612	+	7.67732i	−0.329828	+	0.722222i	0.669969	+	0.742389i	$0.266307\pi$
$114$	4.07357	−	7.05563i	0.381525	−	0.660820i
$115$	−1.75933	+	1.60368i	−0.164058	+	0.149544i
$116$	−0.736538	−	1.27572i	−0.0683858	−	0.118448i
$117$	−2.42424	−	3.40437i	−0.224121	−	0.314735i
$118$	0.388896	+	0.114190i	0.0358008	+	0.0105120i
$119$	16.1581	−	2.56431i	1.48121	−	0.235070i
$120$	0.417582	−	0.268363i	0.0381198	−	0.0244981i
$121$	−0.886020	−	2.55999i	−0.0805473	−	0.232726i
$122$	−0.932746	+	0.373415i	−0.0844469	+	0.0338074i
$123$	−4.24200	−	4.04474i	−0.382488	−	0.364702i
$124$	−2.57334	+	1.32665i	−0.231093	+	0.119137i
$125$	0.689017	+	4.79222i	0.0616275	+	0.428629i
$126$	2.62404	+	0.338284i	0.233768	+	0.0301368i
$127$	0.625892	+	1.37051i	0.0555389	+	0.121613i	0.935367	−	0.353679i	$-0.115070\pi$
$127$	0.625892	+	1.37051i	0.0555389	+	0.121613i	−0.879828	+	0.475292i	$0.842342\pi$
$128$	−0.928368	−	0.371662i	−0.0820569	−	0.0328506i
$129$	−0.592776	+	12.4439i	−0.0521910	+	1.09562i
$130$	1.50141	+	1.43159i	0.131682	+	0.125559i
$131$	9.21735	+	7.24861i	0.805324	+	0.633314i	0.933556	−	0.358431i	$-0.116688\pi$
$131$	9.21735	+	7.24861i	0.805324	+	0.633314i	−0.128233	+	0.991744i	$0.540930\pi$
$132$	2.42466	−	2.79821i	0.211040	−	0.243553i
$133$	−18.5082	+	11.0488i	−1.60487	+	0.958055i
$134$	−0.368142	−	0.424859i	−0.0318027	−	0.0367022i
$135$	−0.359247	+	0.342542i	−0.0309191	+	0.0294813i
$136$	6.15561	−	0.587790i	0.527839	−	0.0504026i
$137$	2.23525	+	3.87157i	0.190971	+	0.330771i	0.945572	−	0.325412i	$-0.105503\pi$
$137$	2.23525	+	3.87157i	0.190971	+	0.330771i	−0.754602	+	0.656183i	$0.772170\pi$
$138$	−4.79462	−	0.107652i	−0.408145	−	0.00916391i
$139$	7.40690			0.628245			0.314123	−	0.949382i	$-0.398290\pi$
$139$	7.40690			0.628245			0.314123	+	0.949382i	$0.398290\pi$
$140$	−1.31076	+	0.0816203i	−0.110779	+	0.00689817i
$141$	−3.66738	−	1.07684i	−0.308849	−	0.0906863i
$142$	−8.94547	+	1.72410i	−0.750687	+	0.144683i
$143$	13.7540	+	7.09069i	1.15017	+	0.592953i
$144$	0.981929	+	0.189251i	0.0818274	+	0.0157709i
$145$	−0.574766	−	0.452001i	−0.0477317	−	0.0375367i
$146$	11.0617	−	3.24802i	0.915476	−	0.268808i
$147$	−5.62627	−	4.16474i	−0.464047	−	0.343502i
$148$	1.08812	+	7.56806i	0.0894431	+	0.622090i
$149$	14.0092	+	1.33772i	1.14768	+	0.109590i	0.651513	−	0.758638i	$-0.274135\pi$
$149$	14.0092	+	1.33772i	1.14768	+	0.109590i	0.496166	+	0.868228i	$0.334741\pi$
$150$	−2.75736	+	3.87217i	−0.225138	+	0.316162i
$151$	−10.7063	+	8.41952i	−0.871265	+	0.685171i	−0.950177	−	0.311711i	$-0.899098\pi$
$151$	−10.7063	+	8.41952i	−0.871265	+	0.685171i	0.0789117	+	0.996882i	$0.474855\pi$
$152$	−7.24146	+	3.73323i	−0.587360	+	0.302805i
$153$	−5.93313	+	1.74213i	−0.479665	+	0.140842i
$154$	−9.20956	+	3.33869i	−0.742128	+	0.269039i
$155$	−0.941109	+	1.08610i	−0.0755917	+	0.0872374i
$156$	0.198860	+	4.17459i	0.0159216	+	0.334234i
$157$	−4.32576	+	12.4985i	−0.345233	+	0.997485i	0.630056	+	0.776550i	$0.283032\pi$
$157$	−4.32576	+	12.4985i	−0.345233	+	0.997485i	−0.975289	+	0.220935i	$0.929089\pi$
$158$	2.06466	+	8.51065i	0.164256	+	0.677071i
$159$	−5.65672	−	7.94375i	−0.448607	−	0.629980i
$160$	−0.496380			−0.0392423
$161$	10.9384	+	6.43046i	0.862069	+	0.506791i
$162$	−1.00000			−0.0785674
$163$	−8.01223	−	11.2516i	−0.627566	−	0.881293i	0.371319	−	0.928505i	$-0.378906\pi$
$163$	−8.01223	−	11.2516i	−0.627566	−	0.881293i	−0.998885	+	0.0472121i	$0.984966\pi$
$164$	1.38185	+	5.69605i	0.107904	+	0.444786i
$165$	0.601111	−	1.73680i	0.0467965	−	0.135210i
$166$	0.424860	+	8.91890i	0.0329755	+	0.692241i
$167$	−4.94980	+	5.71237i	−0.383027	+	0.442037i	−0.914223	−	0.405213i	$-0.867198\pi$
$167$	−4.94980	+	5.71237i	−0.383027	+	0.442037i	0.531195	+	0.847249i	$0.321743\pi$
$168$	−2.02459	−	1.70324i	−0.156200	−	0.131408i
$169$	−4.28579	+	1.25842i	−0.329676	+	0.0968017i
$170$	2.72821	−	1.40649i	0.209244	−	0.107873i
$171$	6.40408	−	5.03623i	0.489732	−	0.385130i
$172$	7.22636	−	10.1480i	0.551004	−	0.773777i
$173$	−8.05907	−	0.769547i	−0.612719	−	0.0585076i	−0.215917	−	0.976412i	$-0.569274\pi$
$173$	−8.05907	−	0.769547i	−0.612719	−	0.0585076i	−0.396802	+	0.917904i	$0.629880\pi$
$174$	−0.209640	−	1.45808i	−0.0158928	−	0.110537i
$175$	11.3629	−	5.39096i	0.858953	−	0.407518i
$176$	−3.55258	+	1.04313i	−0.267786	+	0.0786291i
$177$	0.318598	+	0.250548i	0.0239473	+	0.0188324i
$178$	0.694320	+	0.133819i	0.0520415	+	0.0100302i
$179$	8.14491	+	4.19899i	0.608779	+	0.313848i	0.734908	−	0.678166i	$-0.237225\pi$
$179$	8.14491	+	4.19899i	0.608779	+	0.313848i	−0.126129	+	0.992014i	$0.540255\pi$
$180$	0.487410	−	0.0939406i	0.0363294	−	0.00700192i
$181$	7.88250	+	2.31451i	0.585902	+	0.172036i	0.561231	−	0.827659i	$-0.310328\pi$
$181$	7.88250	+	2.31451i	0.585902	+	0.172036i	0.0246710	+	0.999696i	$0.492146\pi$
$182$	4.92289	−	9.90112i	0.364909	−	0.733920i
$183$	−1.00472			−0.0742707
$184$	3.97529	+	2.68273i	0.293062	+	0.197774i
$185$	1.89763	+	3.28680i	0.139517	+	0.241650i
$186$	−2.88208	+	0.275205i	−0.211324	+	0.0201790i
$187$	16.5701	−	15.7995i	1.21172	−	1.15537i
$188$	2.50301	+	2.88863i	0.182551	+	0.210675i
$189$	2.31034	+	1.28931i	0.168053	+	0.0937834i
$190$	−2.64831	+	3.05631i	−0.192128	+	0.221728i
$191$	−8.78589	−	6.90930i	−0.635725	−	0.499940i	0.247501	−	0.968888i	$-0.420391\pi$
$191$	−8.78589	−	6.90930i	−0.635725	−	0.499940i	−0.883226	+	0.468948i	$0.844633\pi$
$192$	−0.723734	−	0.690079i	−0.0522310	−	0.0498022i
$193$	0.888153	−	18.6446i	0.0639306	−	1.34207i	−0.707932	−	0.706280i	$-0.750372\pi$
$193$	0.888153	−	18.6446i	0.0639306	−	1.34207i	0.771863	−	0.635789i	$-0.219325\pi$
$194$	−8.01088	−	3.20707i	−0.575148	−	0.230254i
$195$	0.861792	+	1.88706i	0.0617142	+	0.135135i
$196$	2.48149	+	6.54540i	0.177249	+	0.467528i
$197$	1.32888	+	9.24255i	0.0946786	+	0.658504i	0.980795	+	0.195041i	$0.0624841\pi$
$197$	1.32888	+	9.24255i	0.0946786	+	0.658504i	−0.886116	+	0.463463i	$0.846607\pi$
$198$	3.29097	−	1.69661i	0.233879	−	0.120573i
$199$	13.9615	+	13.3123i	0.989706	+	0.943683i	0.998415	−	0.0562791i	$-0.0179237\pi$
$199$	13.9615	+	13.3123i	0.989706	+	0.943683i	−0.00870881	+	0.999962i	$0.502772\pi$
$200$	4.41310	−	1.76674i	0.312053	−	0.124927i
$201$	−0.183867	−	0.531250i	−0.0129690	−	0.0374715i
$202$	−11.9755	+	7.69621i	−0.842596	+	0.541503i
$203$	−1.39557	+	3.63896i	−0.0979501	+	0.255405i
$204$	5.93313	+	1.74213i	0.415402	+	0.121973i
$205$	1.68763	+	2.36994i	0.117869	+	0.165524i
$206$	−4.73944	−	8.20894i	−0.330212	−	0.571944i
$207$	−4.41116	−	1.88192i	−0.306597	−	0.130803i
$208$	2.08966	−	3.61940i	0.144892	−	0.250960i
$209$	−12.5311	+	27.4393i	−0.866795	+	1.89802i
$210$	−1.24720	−	0.411387i	−0.0860652	−	0.0283884i
$211$	1.38889	+	1.60286i	0.0956150	+	0.110346i	0.801540	−	0.597941i	$-0.204014\pi$
$211$	1.38889	+	1.60286i	0.0956150	+	0.110346i	−0.705925	+	0.708286i	$0.749469\pi$
$212$	0.464019	+	9.74096i	0.0318689	+	0.669012i
$213$	−8.94547	−	1.72410i	−0.612934	−	0.118133i
$214$	−1.26550	+	0.506629i	−0.0865077	+	0.0346324i
$215$	1.45791	−	6.00960i	0.0994288	−	0.409851i
$216$	0.841254	+	0.540641i	0.0572401	+	0.0367859i
$217$	7.01341	+	3.08007i	0.476101	+	0.209088i
$218$	7.83465	+	17.1555i	0.530629	+	1.16192i
$219$	11.4765	+	1.09588i	0.775512	+	0.0740524i
$220$	−1.44467	+	1.13610i	−0.0973997	+	0.0765960i
$221$	−1.22967	+	25.8140i	−0.0827168	+	1.73644i
$222$	−1.80258	+	7.43036i	−0.120982	+	0.498693i
$223$	1.92577	−	13.3940i	0.128959	−	0.896932i	−0.817918	−	0.575335i	$-0.804872\pi$
$223$	1.92577	−	13.3940i	0.128959	−	0.896932i	0.946877	−	0.321596i	$-0.104219\pi$
$224$	0.782350	+	2.52744i	0.0522729	+	0.168871i
$225$	−3.99899	+	2.56999i	−0.266599	+	0.171333i
$226$	8.28751	−	1.59729i	0.551277	−	0.106250i
$227$	0.360407	+	1.48562i	0.0239210	+	0.0986039i	0.982521	−	0.186153i	$-0.0596021\pi$
$227$	0.360407	+	1.48562i	0.0239210	+	0.0986039i	−0.958600	+	0.284757i	$0.908087\pi$
$228$	−8.11024	+	0.774434i	−0.537114	+	0.0512882i
$229$	−12.1864	+	21.1075i	−0.805302	+	1.39482i	0.110784	+	0.993844i	$0.464664\pi$
$229$	−12.1864	+	21.1075i	−0.805302	+	1.39482i	−0.916087	+	0.400980i	$0.868670\pi$
$230$	2.32683	+	0.502880i	0.153427	+	0.0331589i
$231$	−9.79073	−	0.323316i	−0.644182	−	0.0212726i
$232$	−0.611938	+	1.33996i	−0.0401757	+	0.0879724i
$233$	−6.22206	+	5.93272i	−0.407621	+	0.388666i	−0.865961	−	0.500111i	$-0.833292\pi$
$233$	−6.22206	+	5.93272i	−0.407621	+	0.388666i	0.458341	+	0.888777i	$0.348444\pi$
$234$	−1.36692	+	3.94946i	−0.0893585	+	0.258184i
$235$	1.68636	+	0.869378i	0.110006	+	0.0567120i
$236$	−0.132565	−	0.383022i	−0.00862926	−	0.0249326i
$237$	−1.24632	+	8.66837i	−0.0809574	+	0.563071i
$238$	−11.4614	−	11.6745i	−0.742935	−	0.756748i
$239$	−17.7507	−	11.4077i	−1.14820	−	0.737903i	−0.178919	−	0.983864i	$-0.557260\pi$
$239$	−17.7507	−	11.4077i	−1.14820	−	0.737903i	−0.969280	+	0.245961i	$0.920896\pi$
$240$	−0.460823	−	0.184486i	−0.0297460	−	0.0119085i
$241$	−7.01064	+	9.84507i	−0.451595	+	0.634177i	−0.976124	−	0.217216i	$-0.930302\pi$
$241$	−7.01064	+	9.84507i	−0.451595	+	0.634177i	0.524528	+	0.851393i	$0.324242\pi$
$242$	−1.57136	+	2.20667i	−0.101011	+	0.141850i
$243$	−0.928368	−	0.371662i	−0.0595548	−	0.0238422i
$244$	0.845221	+	0.543190i	0.0541097	+	0.0347742i
$245$	2.35106	+	2.55847i	0.150204	+	0.163455i
$246$	−0.834145	+	5.80161i	−0.0531831	+	0.369897i
$247$	−11.1365	−	32.1768i	−0.708599	−	2.04736i
$248$	2.57334	+	1.32665i	0.163407	+	0.0842424i
$249$	−2.92040	+	8.43793i	−0.185073	+	0.534732i
$250$	3.50396	−	3.34102i	0.221610	−	0.211304i
$251$	−7.72483	+	16.9150i	−0.487587	+	1.06767i	0.492720	+	0.870188i	$0.336003\pi$
$251$	−7.72483	+	16.9150i	−0.487587	+	1.06767i	−0.980307	+	0.197479i	$0.936725\pi$
$252$	−1.24653	−	2.33370i	−0.0785241	−	0.147009i
$253$	17.7099	−	1.29069i	1.11341	−	0.0811450i
$254$	0.753333	−	1.30481i	0.0472683	−	0.0818711i
$255$	3.05552	−	0.291767i	0.191344	−	0.0182712i
$256$	0.235759	+	0.971812i	0.0147349	+	0.0607382i
$257$	−20.9467	+	4.03715i	−1.30662	+	0.251830i	−0.794595	−	0.607140i	$-0.792317\pi$
$257$	−20.9467	+	4.03715i	−1.30662	+	0.251830i	−0.512025	+	0.858971i	$0.671104\pi$
$258$	10.4803	−	6.73531i	0.652478	−	0.419322i
$259$	13.7446	−	14.8426i	0.854048	−	0.922273i
$260$	0.295237	−	2.05342i	0.0183098	−	0.127347i
$261$	0.347291	−	1.43155i	0.0214968	−	0.0886108i
$262$	0.557951	−	11.7128i	0.0344703	−	0.723621i
$263$	20.1156	−	15.8191i	1.24038	−	0.975445i	0.240391	−	0.970676i	$-0.422724\pi$
$263$	20.1156	−	15.8191i	1.24038	−	0.975445i	0.999989	−	0.00476871i	$-0.00151793\pi$
$264$	−3.68580	−	0.351951i	−0.226845	−	0.0216611i
$265$	2.01090	+	4.40326i	0.123529	+	0.270490i
$266$	19.7359	+	8.66739i	1.21009	+	0.531432i
$267$	0.594849	+	0.382286i	0.0364041	+	0.0233955i
$268$	−0.132536	+	0.546322i	−0.00809595	+	0.0333719i
$269$	−4.30390	+	1.72302i	−0.262413	+	0.105054i	−0.499139	−	0.866522i	$-0.666350\pi$
$269$	−4.30390	+	1.72302i	−0.262413	+	0.105054i	0.236725	+	0.971577i	$0.423926\pi$
$270$	0.487410	+	0.0939406i	0.0296628	+	0.00571704i
$271$	1.19183	+	25.0196i	0.0723985	+	1.51983i	0.684477	+	0.729034i	$0.260031\pi$
$271$	1.19183	+	25.0196i	0.0723985	+	1.51983i	−0.612078	+	0.790797i	$0.709666\pi$
$272$	−4.04941	−	4.67326i	−0.245531	−	0.283358i
$273$	8.25013	−	7.36223i	0.499321	−	0.445582i
$274$	1.85712	−	4.06652i	0.112193	−	0.245667i
$275$	8.80027	−	15.2425i	0.530676	−	0.919158i
$276$	2.69346	+	3.96803i	0.162127	+	0.238847i
$277$	15.6946	+	27.1839i	0.943000	+	1.63332i	0.759707	+	0.650265i	$0.225342\pi$
$277$	15.6946	+	27.1839i	0.943000	+	1.63332i	0.183292	+	0.983058i	$0.441324\pi$
$278$	−4.29642	−	6.03348i	−0.257682	−	0.361864i
$279$	−2.77791	−	0.815668i	−0.166309	−	0.0488328i
$280$	0.826801	+	1.02037i	0.0494108	+	0.0609787i
$281$	−15.5634	+	10.0020i	−0.928433	+	0.596668i	−0.915093	−	0.403243i	$-0.867883\pi$
$281$	−15.5634	+	10.0020i	−0.928433	+	0.596668i	−0.0133404	+	0.999911i	$0.504247\pi$
$282$	1.25012	+	3.61199i	0.0744436	+	0.215091i
$283$	−24.5354	+	9.82251i	−1.45848	+	0.583888i	−0.959244	−	0.282578i	$-0.908810\pi$
$283$	−24.5354	+	9.82251i	−1.45848	+	0.583888i	−0.499237	+	0.866466i	$0.666386\pi$
$284$	6.59329	+	6.28669i	0.391240	+	0.373047i
$285$	−3.59452	+	1.85310i	−0.212921	+	0.109768i
$286$	−2.20221	−	15.3167i	−0.130219	−	0.905695i
$287$	9.40722	−	12.3282i	0.555291	−	0.727712i
$288$	−0.415415	−	0.909632i	−0.0244786	−	0.0536006i
$289$	19.7158	+	7.89302i	1.15975	+	0.464295i
$290$	−0.0347922	+	0.730377i	−0.00204307	+	0.0428892i
$291$	−6.24510	−	5.95469i	−0.366094	−	0.349070i
$292$	−9.06219	−	7.12659i	−0.530325	−	0.417052i
$293$	9.84029	−	11.3563i	0.574876	−	0.663442i	−0.391619	−	0.920127i	$-0.628085\pi$
$293$	9.84029	−	11.3563i	0.574876	−	0.663442i	0.966495	+	0.256685i	$0.0826304\pi$
$294$	−0.128943	+	6.99881i	−0.00752009	+	0.408179i
$295$	−0.131751	−	0.152049i	−0.00767086	−	0.00885264i
$296$	5.53358	−	5.27626i	0.321633	−	0.306677i
$297$	3.68580	−	0.351951i	0.213872	−	0.0204223i
$298$	−7.03646	−	12.1875i	−0.407611	−	0.706004i
$299$	−13.4623	+	14.8493i	−0.778545	+	0.858756i
$300$	4.75361			0.274450
$301$	−32.8971	+	2.04848i	−1.89616	+	0.118073i
$302$	13.0686	+	3.83728i	0.752013	+	0.220811i
$303$	−13.9781	+	2.69406i	−0.803021	+	0.154770i
$304$	7.24146	+	3.73323i	0.415326	+	0.214116i
$305$	0.489709	+	0.0943836i	0.0280406	+	0.00540439i
$306$	4.86065	+	3.82246i	0.277865	+	0.218515i
$307$	−17.7189	+	5.20275i	−1.01127	+	0.296936i	−0.745074	−	0.666982i	$-0.767586\pi$
$307$	−17.7189	+	5.20275i	−1.01127	+	0.296936i	−0.266199	+	0.963918i	$0.585768\pi$
$308$	8.06168	+	5.56526i	0.459357	+	0.317110i
$309$	−1.34898	−	9.38239i	−0.0767410	−	0.533746i
$310$	1.43061	+	0.136606i	0.0812529	+	0.00775871i
$311$	−1.11281	+	1.56273i	−0.0631018	+	0.0886140i	−0.844921	−	0.534891i	$-0.820353\pi$
$311$	−1.11281	+	1.56273i	−0.0631018	+	0.0886140i	0.781819	+	0.623505i	$0.214292\pi$
$312$	3.28517	−	2.58348i	0.185986	−	0.146261i
$313$	−4.71558	+	2.43105i	−0.266540	+	0.137411i	−0.586317	−	0.810082i	$-0.699423\pi$
$313$	−4.71558	+	2.43105i	−0.266540	+	0.137411i	0.319776	+	0.947493i	$0.396392\pi$
$314$	12.6901	−	3.72616i	0.716145	−	0.210279i
$315$	−1.00497	−	0.845457i	−0.0566234	−	0.0476361i
$316$	5.73495	−	6.61849i	0.322616	−	0.372319i
$317$	−0.839248	−	17.6180i	−0.0471368	−	0.989524i	−0.891293	−	0.453427i	$-0.850201\pi$
$317$	−0.839248	−	17.6180i	−0.0471368	−	0.989524i	0.844156	−	0.536097i	$-0.180102\pi$
$318$	−3.18957	+	9.21565i	−0.178862	+	0.516788i
$319$	1.28587	+	5.30041i	0.0719947	+	0.296766i
$320$	0.287929	+	0.404339i	0.0160957	+	0.0226033i
$321$	−1.36314			−0.0760832
$322$	−1.10681	−	12.6402i	−0.0616804	−	0.704411i
$323$	−50.3787			−2.80315
$324$	0.580057	+	0.814576i	0.0322254	+	0.0452542i
$325$	4.68379	+	19.3068i	0.259810	+	1.07095i
$326$	−4.51773	+	13.0531i	−0.250214	+	0.722946i
$327$	0.897386	+	18.8385i	0.0496256	+	1.04177i
$328$	3.83831	−	4.42965i	0.211935	−	0.244586i
$329$	1.76876	−	9.95672i	0.0975147	−	0.548932i
$330$	−1.76343	+	0.517790i	−0.0970738	+	0.0285034i
$331$	−17.8597	+	9.20731i	−0.981658	+	0.506080i	−0.872853	−	0.487983i	$-0.837733\pi$
$331$	−17.8597	+	9.20731i	−0.981658	+	0.506080i	−0.108805	+	0.994063i	$0.534702\pi$
$332$	7.01868	−	5.51955i	0.385200	−	0.302925i
$333$	−4.43505	+	6.22815i	−0.243039	+	0.341301i
$334$	7.52433	+	0.718486i	0.411713	+	0.0393138i
$335$	0.0397129	+	0.276209i	0.00216975	+	0.0150909i
$336$	−0.213045	+	2.63716i	−0.0116225	+	0.143869i
$337$	−31.7166	+	9.31284i	−1.72771	+	0.507303i	−0.986471	−	0.163934i	$-0.947582\pi$
$337$	−31.7166	+	9.31284i	−1.72771	+	0.507303i	−0.741243	+	0.671237i	$0.765763\pi$
$338$	3.51108	+	2.76115i	0.190978	+	0.150187i
$339$	8.28751	+	1.59729i	0.450116	+	0.0867527i
$340$	−2.72821	−	1.40649i	−0.147958	−	0.0762777i
$341$	10.5259	−	2.02870i	0.570009	−	0.109860i
$342$	−7.81712	−	2.29531i	−0.422701	−	0.124116i
$343$	9.32153	−	16.0034i	0.503315	−	0.864103i
$344$	−12.4580			−0.671691
$345$	1.97326	+	1.33165i	0.106237	+	0.0716939i
$346$	4.04786	+	7.01110i	0.217614	+	0.376919i
$347$	21.8740	−	2.08871i	1.17426	−	0.112128i	0.510367	−	0.859957i	$-0.329510\pi$
$347$	21.8740	−	2.08871i	1.17426	−	0.112128i	0.663892	+	0.747829i	$0.268904\pi$
$348$	−1.06611	+	1.01654i	−0.0571497	+	0.0544922i
$349$	10.6764	+	12.3212i	0.571494	+	0.659539i	0.965754	−	0.259460i	$-0.0835446\pi$
$349$	10.6764	+	12.3212i	0.571494	+	0.659539i	−0.394260	+	0.918999i	$0.628999\pi$
$350$	−10.9825	−	6.12886i	−0.587037	−	0.327601i
$351$	−2.73687	+	3.15852i	−0.146083	+	0.168589i
$352$	2.91041	+	2.28877i	0.155125	+	0.121992i
$353$	−9.53596	−	9.09252i	−0.507548	−	0.483946i	0.392491	−	0.919756i	$-0.371614\pi$
$353$	−9.53596	−	9.09252i	−0.507548	−	0.483946i	−0.900039	+	0.435810i	$0.856462\pi$
$354$	0.0192856	−	0.404855i	0.00102502	−	0.0215178i
$355$	4.19815	+	1.68069i	0.222815	+	0.0892015i
$356$	−0.293739	−	0.643199i	−0.0155681	−	0.0340895i
$357$	−6.30144	−	15.0981i	−0.333508	−	0.799074i
$358$	−1.30411	−	9.07030i	−0.0689245	−	0.479381i
$359$	−28.3919	+	14.6371i	−1.49847	+	0.772515i	−0.995764	−	0.0919431i	$-0.970692\pi$
$359$	−28.3919	+	14.6371i	−1.49847	+	0.772515i	−0.502705	+	0.864458i	$0.667662\pi$
$360$	−0.359247	−	0.342542i	−0.0189340	−	0.0180535i
$361$	43.9822	−	17.6078i	2.31485	−	0.926727i
$362$	−2.68695	−	7.76345i	−0.141223	−	0.408038i
$363$	−2.27894	+	1.46458i	−0.119613	+	0.0768707i
$364$	−10.9208	+	1.73314i	−0.572404	+	0.0908414i
$365$	−5.49083	−	1.61225i	−0.287403	−	0.0843891i
$366$	0.582792	+	0.818417i	0.0304630	+	0.0427794i
$367$	−9.42017	−	16.3162i	−0.491729	−	0.851699i	0.508226	−	0.861224i	$-0.330302\pi$
$367$	−9.42017	−	16.3162i	−0.491729	−	0.851699i	−0.999955	+	0.00952448i	$0.996968\pi$
$368$	−0.120608	−	4.79431i	−0.00628711	−	0.249921i
$369$	−2.93063	+	5.07601i	−0.152563	+	0.264246i
$370$	1.57661	−	3.45229i	0.0819640	−	0.179476i
$371$	19.2508	−	17.1790i	0.999452	−	0.891888i
$372$	1.89594	+	2.18803i	0.0983001	+	0.113444i
$373$	−1.23498	−	25.9255i	−0.0639450	−	1.34237i	−0.771733	−	0.635946i	$-0.780610\pi$
$373$	−1.23498	−	25.9255i	−0.0639450	−	1.34237i	0.707788	−	0.706424i	$-0.249693\pi$
$374$	−22.4815	−	4.33295i	−1.16249	−	0.224051i
$375$	4.49469	−	1.79940i	0.232105	−	0.0929208i
$376$	0.901119	−	3.71446i	0.0464717	−	0.191559i
$377$	−5.17914	−	3.32843i	−0.266739	−	0.171423i
$378$	−0.289891	−	2.62982i	−0.0149104	−	0.135263i
$379$	−0.245069	−	0.536627i	−0.0125884	−	0.0275647i	0.903233	−	0.429150i	$-0.141187\pi$
$379$	−0.245069	−	0.536627i	−0.0125884	−	0.0275647i	−0.915822	+	0.401585i	$0.868459\pi$
$380$	4.02577	+	0.384414i	0.206517	+	0.0197200i
$381$	1.18432	−	0.931359i	0.0606745	−	0.0477150i
$382$	−0.531834	+	11.1646i	−0.0272110	+	0.571229i
$383$	−1.31285	+	5.41166i	−0.0670837	+	0.276523i	−0.995468	−	0.0950992i	$-0.969683\pi$
$383$	−1.31285	+	5.41166i	−0.0670837	+	0.276523i	0.928384	+	0.371622i	$0.121198\pi$
$384$	−0.142315	+	0.989821i	−0.00726247	+	0.0505116i
$385$	4.74173	+	1.07733i	0.241661	+	0.0549060i
$386$	−15.7026	+	10.0915i	−0.799243	+	0.513642i
$387$	12.2329	−	2.35769i	0.621832	−	0.119848i
$388$	2.03436	+	8.38576i	0.103279	+	0.425722i
$389$	12.5448	−	1.19788i	0.636047	−	0.0607352i	0.227949	−	0.973673i	$-0.426798\pi$
$389$	12.5448	−	1.19788i	0.636047	−	0.0607352i	0.408098	+	0.912938i	$0.366192\pi$
$390$	1.03727	−	1.79660i	0.0525240	−	0.0909743i
$391$	14.2476	+	26.0088i	0.720530	+	1.31532i
$392$	3.89232	−	5.81806i	0.196592	−	0.293857i
$393$	4.87121	−	10.6665i	0.245720	−	0.538051i
$394$	6.75793	−	6.44368i	0.340460	−	0.324628i
$395$	1.42178	−	4.10797i	0.0715377	−	0.206694i
$396$	−3.29097	−	1.69661i	−0.165377	−	0.0852580i
$397$	−5.17886	−	14.9633i	−0.259919	−	0.750988i	−0.997157	−	0.0753540i	$-0.975991\pi$
$397$	−5.17886	−	14.9633i	−0.259919	−	0.750988i	0.737237	−	0.675634i	$-0.236130\pi$
$398$	2.74539	−	19.0946i	0.137614	−	0.957126i
$399$	15.1009	+	15.3816i	0.755989	+	0.770045i
$400$	−3.99899	−	2.56999i	−0.199949	−	0.128500i
$401$	−33.0260	−	13.2216i	−1.64924	−	0.660257i	−0.653893	−	0.756587i	$-0.726865\pi$
$401$	−33.0260	−	13.2216i	−1.64924	−	0.660257i	−0.995349	+	0.0963305i	$0.969289\pi$
$402$	−0.326090	+	0.457929i	−0.0162639	+	0.0228394i
$403$	−7.01864	+	9.85629i	−0.349623	+	0.490977i
$404$	13.2156	+	5.29074i	0.657503	+	0.263224i
$405$	0.417582	+	0.268363i	0.0207498	+	0.0133351i
$406$	3.77372	−	0.974002i	0.187287	−	0.0483389i
$407$	4.02884	−	28.0212i	0.199702	−	1.38896i
$408$	−2.02246	−	5.84352i	−0.100127	−	0.289297i
$409$	16.1744	+	8.33850i	0.799775	+	0.412312i	0.809120	−	0.587644i	$-0.199944\pi$
$409$	16.1744	+	8.33850i	0.799775	+	0.412312i	−0.00934513	+	0.999956i	$0.502975\pi$
$410$	0.951577	−	2.74940i	0.0469950	−	0.135783i
$411$	3.23546	−	3.08500i	0.159593	−	0.152172i
$412$	−3.93767	+	8.62229i	−0.193995	+	0.424790i
$413$	−0.566539	+	0.910488i	−0.0278775	+	0.0448022i
$414$	1.02576	+	4.68485i	0.0504133	+	0.230248i
$415$	2.21609	−	3.83839i	0.108784	−	0.188419i
$416$	−4.16040	+	0.397270i	−0.203980	+	0.0194778i
$417$	−1.74624	−	7.19811i	−0.0855139	−	0.352493i
$418$	29.6202	−	5.70882i	1.44877	−	0.279227i
$419$	24.2972	−	15.6149i	1.18700	−	0.762836i	0.210336	−	0.977629i	$-0.432544\pi$
$419$	24.2972	−	15.6149i	1.18700	−	0.762836i	0.976659	+	0.214794i	$0.0689079\pi$
$420$	0.388343	+	1.25457i	0.0189492	+	0.0612167i
$421$	3.05024	−	21.2149i	0.148660	−	1.03395i	−0.769757	−	0.638337i	$-0.779623\pi$
$421$	3.05024	−	21.2149i	0.148660	−	1.03395i	0.918417	−	0.395614i	$-0.129468\pi$
$422$	0.500019	−	2.06111i	0.0243405	−	0.100333i
$423$	−0.181868	+	3.81788i	−0.00884272	+	0.185631i
$424$	7.66559	−	6.02829i	0.372274	−	0.292760i
$425$	29.2614	+	2.79412i	1.41938	+	0.135535i
$426$	3.78447	+	8.28684i	0.183358	+	0.401499i
$427$	−0.291258	−	2.64222i	−0.0140950	−	0.127866i
$428$	1.14675	+	0.736971i	0.0554302	+	0.0356228i
$429$	3.64818	−	15.0380i	0.176136	−	0.726042i
$430$	−5.74094	+	2.29833i	−0.276853	+	0.110835i
$431$	−5.39987	−	1.04074i	−0.260102	−	0.0501306i	0.0575328	−	0.998344i	$-0.481677\pi$
$431$	−5.39987	−	1.04074i	−0.260102	−	0.0501306i	−0.317635	+	0.948213i	$0.602889\pi$
$432$	−0.0475819	−	0.998867i	−0.00228929	−	0.0480580i
$433$	1.60827	+	1.85604i	0.0772884	+	0.0891956i	0.793077	−	0.609122i	$-0.208478\pi$
$433$	1.60827	+	1.85604i	0.0772884	+	0.0891956i	−0.715788	+	0.698317i	$0.753932\pi$
$434$	−1.55923	−	7.49957i	−0.0748453	−	0.359991i
$435$	−0.303754	+	0.665128i	−0.0145639	+	0.0318904i
$436$	9.42991	−	16.3331i	0.451611	−	0.782212i
$437$	−30.1630	−	24.8362i	−1.44289	−	1.18808i
$438$	−5.76436	−	9.98417i	−0.275432	−	0.477062i
$439$	−1.86100	−	2.61341i	−0.0888208	−	0.124731i	0.767775	−	0.640720i	$-0.221364\pi$
$439$	−1.86100	−	2.61341i	−0.0888208	−	0.124731i	−0.856595	+	0.515989i	$0.827425\pi$
$440$	1.76343	+	0.517790i	0.0840683	+	0.0246847i
$441$	−2.72090	+	6.44955i	−0.129567	+	0.307121i
$442$	21.7408	−	13.9719i	1.03410	−	0.664578i
$443$	6.99637	+	20.2147i	0.332408	+	0.960429i	0.980096	+	0.198523i	$0.0636146\pi$
$443$	6.99637	+	20.2147i	0.332408	+	0.960429i	−0.647689	+	0.761905i	$0.724264\pi$
$444$	7.09819	−	2.84169i	0.336865	−	0.134860i
$445$	−0.254023	−	0.242210i	−0.0120418	−	0.0114819i
$446$	−12.0275	+	6.20062i	−0.569520	+	0.293608i
$447$	−2.00279	−	13.9297i	−0.0947285	−	0.658851i
$448$	1.60498	−	2.10334i	0.0758282	−	0.0993734i
$449$	−7.64923	−	16.7495i	−0.360989	−	0.790456i	−0.999778	−	0.0210741i	$-0.993291\pi$
$449$	−7.64923	−	16.7495i	−0.360989	−	0.790456i	0.638789	−	0.769382i	$-0.279436\pi$
$450$	4.41310	+	1.76674i	0.208035	+	0.0832848i
$451$	1.03261	−	21.6771i	0.0486237	−	1.02074i
$452$	−6.10834	−	5.82429i	−0.287312	−	0.273952i
$453$	10.7063	+	8.41952i	0.503025	+	0.395583i
$454$	1.00109	−	1.15532i	0.0469835	−	0.0542219i
$455$	−4.71281	+	2.81340i	−0.220940	+	0.131894i
$456$	5.33524	+	6.15719i	0.249845	+	0.288337i
$457$	22.9207	−	21.8549i	1.07219	−	1.02233i	0.0724971	−	0.997369i	$-0.476903\pi$
$457$	22.9207	−	21.8549i	1.07219	−	1.02233i	0.999688	−	0.0249583i	$-0.00794529\pi$
$458$	24.2625	−	2.31679i	1.13371	−	0.108256i
$459$	3.09181	+	5.35517i	0.144313	+	0.249958i
$460$	−0.940062	−	2.18708i	−0.0438306	−	0.101973i
$461$	9.90705			0.461417			0.230709	−	0.973023i	$-0.425896\pi$
$461$	9.90705			0.461417			0.230709	+	0.973023i	$0.425896\pi$
$462$	5.41581	+	8.16283i	0.251966	+	0.379769i
$463$	5.59919	+	1.64407i	0.260217	+	0.0764065i	0.409239	−	0.912427i	$-0.365794\pi$
$463$	5.59919	+	1.64407i	0.260217	+	0.0764065i	−0.149022	+	0.988834i	$0.547613\pi$
$464$	1.44645	−	0.278781i	0.0671500	−	0.0129421i
$465$	1.27736	+	0.658523i	0.0592360	+	0.0305383i
$466$	8.44180	+	1.62702i	0.391059	+	0.0753704i
$467$	−33.5905	−	26.4158i	−1.55438	−	1.22238i	−0.869754	−	0.493486i	$-0.835722\pi$
$467$	−33.5905	−	26.4158i	−1.55438	−	1.22238i	−0.684628	−	0.728893i	$-0.740035\pi$
$468$	4.01003	−	1.17745i	0.185364	−	0.0544277i
$469$	1.34379	−	0.637543i	0.0620505	−	0.0294390i
$470$	−0.270009	−	1.87796i	−0.0124546	−	0.0866236i
$471$	13.1660	+	1.25720i	0.606656	+	0.0579286i
$472$	−0.235105	+	0.330159i	−0.0108216	+	0.0151968i
$473$	−36.2579	+	28.5136i	−1.66714	+	1.31105i
$474$	7.78399	−	4.01292i	0.357530	−	0.184320i
$475$	−37.1595	+	10.9110i	−1.70500	+	0.500632i
$476$	−2.86152	+	16.1081i	−0.131157	+	0.738314i
$477$	−6.38620	+	7.37007i	−0.292404	+	0.337452i
$478$	1.00399	+	21.0764i	0.0459216	+	0.964013i
$479$	1.33911	−	3.86910i	0.0611855	−	0.176784i	−0.910265	−	0.414026i	$-0.864122\pi$
$479$	1.33911	−	3.86910i	0.0611855	−	0.176784i	0.971451	+	0.237242i	$0.0762435\pi$
$480$	0.117026	+	0.482388i	0.00534148	+	0.0220179i
$481$	18.5355	+	26.0294i	0.845145	+	1.18684i
$482$	12.0861			0.550508
$483$	3.67036	−	12.1461i	0.167007	−	0.552668i
$484$	2.70898			0.123135
$485$	2.48454	+	3.48904i	0.112817	+	0.158429i
$486$	0.235759	+	0.971812i	0.0106942	+	0.0440823i
$487$	2.75809	−	7.96898i	0.124981	−	0.361109i	−0.865101	−	0.501597i	$-0.832746\pi$
$487$	2.75809	−	7.96898i	0.124981	−	0.361109i	0.990082	+	0.140488i	$0.0448672\pi$
$488$	−0.0478063	−	1.00358i	−0.00216409	−	0.0454298i
$489$	−9.04548	+	10.4390i	−0.409051	+	0.472070i
$490$	0.720320	−	3.39918i	0.0325408	−	0.153559i
$491$	4.00580	−	1.17621i	0.180779	−	0.0530816i	−0.190090	−	0.981767i	$-0.560878\pi$
$491$	4.00580	−	1.17621i	0.180779	−	0.0530816i	0.370869	+	0.928685i	$0.379060\pi$
$492$	5.20970	−	2.68579i	0.234871	−	0.121085i
$493$	−7.16010	+	5.63077i	−0.322475	+	0.253597i
$494$	−19.7506	+	27.7359i	−0.888624	+	1.24790i
$495$	−1.82956	−	0.174702i	−0.0822325	−	0.00785225i
$496$	−0.412028	−	2.86572i	−0.0185006	−	0.128674i
$497$	1.94086	−	24.0248i	0.0870594	−	1.07766i
$498$	8.56733	−	2.51559i	0.383911	−	0.112727i
$499$	9.05614	+	7.12183i	0.405409	+	0.318817i	0.799956	−	0.600059i	$-0.204856\pi$
$499$	9.05614	+	7.12183i	0.405409	+	0.318817i	−0.394547	+	0.918876i	$0.629099\pi$
$500$	−4.75401	−	0.916259i	−0.212606	−	0.0409764i
$501$	6.71831	+	3.46353i	0.300152	+	0.154739i
$502$	18.2594	−	3.51921i	0.814958	−	0.157070i
$503$	−7.81794	−	2.29555i	−0.348585	−	0.102354i	0.102753	−	0.994707i	$-0.467235\pi$
$503$	−7.81794	−	2.29555i	−0.348585	−	0.102354i	−0.451338	+	0.892353i	$0.649053\pi$
$504$	−1.17792	+	2.36907i	−0.0524686	+	0.105527i
$505$	7.06614			0.314439
$506$	−11.3241	−	13.6774i	−0.503418	−	0.608034i
$507$	2.23336	+	3.86830i	0.0991871	+	0.171797i
$508$	−1.49984	+	0.143218i	−0.0665448	+	0.00635426i
$509$	−27.3050	+	26.0352i	−1.21027	+	1.15399i	−0.226605	+	0.973987i	$0.572763\pi$
$509$	−27.3050	+	26.0352i	−1.21027	+	1.15399i	−0.983666	+	0.180005i	$0.942389\pi$
$510$	−2.01004	−	2.31972i	−0.0890063	−	0.102719i
$511$	0.444987	+	30.4989i	0.0196851	+	1.34919i
$512$	0.654861	−	0.755750i	0.0289410	−	0.0333997i
$513$	−6.40408	−	5.03623i	−0.282747	−	0.222355i
$514$	15.4388	+	14.7209i	0.680978	+	0.649311i
$515$	−0.223879	+	4.69980i	−0.00986528	+	0.207098i
$516$	−11.5656	−	4.63018i	−0.509148	−	0.203832i
$517$	−5.87894	−	12.8731i	−0.258555	−	0.566157i
$518$	−20.0631	−	2.58648i	−0.881521	−	0.113643i
$519$	1.15214	+	8.01332i	0.0505734	+	0.351746i
$520$	−1.84392	+	0.950606i	−0.0808612	+	0.0416868i
$521$	19.9936	+	19.0639i	0.875937	+	0.835204i	0.987348	−	0.158570i	$-0.0506884\pi$
$521$	19.9936	+	19.0639i	0.875937	+	0.835204i	−0.111411	+	0.993774i	$0.535537\pi$
$522$	−1.36756	+	0.547487i	−0.0598563	+	0.0239628i
$523$	9.76487	+	28.2138i	0.426988	+	1.23370i	0.929400	+	0.369073i	$0.120325\pi$
$523$	9.76487	+	28.2138i	0.426988	+	1.23370i	−0.502412	+	0.864628i	$0.667554\pi$
$524$	−9.86464	+	6.33962i	−0.430939	+	0.276947i
$525$	−7.91790	−	9.77161i	−0.345565	−	0.426468i
$526$	−24.5540	−	7.20970i	−1.07061	−	0.314358i
$527$	10.3846	+	14.5831i	0.452360	+	0.635250i
$528$	1.85128	+	3.20651i	0.0805667	+	0.139546i
$529$	−4.29173	+	22.5960i	−0.186597	+	0.982437i
$530$	2.42035	−	4.19217i	0.105133	−	0.182096i
$531$	0.168373	−	0.368686i	0.00730678	−	0.0159996i
$532$	−4.38771	−	21.1040i	−0.190232	−	0.914974i
$533$	16.0415	+	18.5129i	0.694836	+	0.801884i
$534$	−0.0336451	−	0.706297i	−0.00145596	−	0.0305645i
$535$	0.664409	+	0.128054i	0.0287249	+	0.00553627i
$536$	0.521900	−	0.208937i	0.0225426	−	0.00902471i
$537$	2.16040	−	8.90527i	0.0932279	−	0.384291i
$538$	3.90004	+	2.50640i	0.168143	+	0.108059i
$539$	−1.98798	−	25.8416i	−0.0856285	−	1.11308i
$540$	−0.206204	−	0.451523i	−0.00887360	−	0.0194305i
$541$	−7.38037	−	0.704740i	−0.317307	−	0.0302991i	−0.0648124	−	0.997897i	$-0.520645\pi$
$541$	−7.38037	−	0.704740i	−0.317307	−	0.0302991i	−0.252495	+	0.967598i	$0.581251\pi$
$542$	19.6890	−	15.4836i	0.845716	−	0.665078i
$543$	0.390899	−	8.20597i	0.0167751	−	0.352152i
$544$	−1.45784	+	6.00931i	−0.0625045	+	0.257647i
$545$	1.33230	−	9.26635i	0.0570695	−	0.396927i
$546$	−10.7826	−	2.44985i	−0.461454	−	0.104844i
$547$	4.77894	−	3.07124i	0.204333	−	0.131317i	−0.434473	−	0.900685i	$-0.643065\pi$
$547$	4.77894	−	3.07124i	0.204333	−	0.131317i	0.638805	+	0.769368i	$0.279429\pi$
$548$	−4.38972	+	0.846049i	−0.187520	+	0.0361414i
$549$	0.236871	+	0.976394i	0.0101094	+	0.0416715i
$550$	−17.5208	+	1.67304i	−0.747091	+	0.0713385i
$551$	6.00067	−	10.3935i	0.255637	−	0.442777i
$552$	1.66990	−	4.49571i	0.0710756	−	0.191350i
$553$	−23.1576	−	0.764725i	−0.984760	−	0.0325194i
$554$	13.0396	−	28.5527i	0.553999	−	1.21309i
$555$	2.74676	−	2.61903i	0.116594	−	0.111172i
$556$	−2.42256	+	6.99953i	−0.102739	+	0.296846i
$557$	−34.1606	−	17.6110i	−1.44743	−	0.746204i	−0.457697	−	0.889108i	$-0.651325\pi$
$557$	−34.1606	−	17.6110i	−1.44743	−	0.746204i	−0.989736	+	0.142905i	$0.954356\pi$
$558$	0.946922	+	2.73595i	0.0400864	+	0.115822i
$559$	7.40977	−	51.5361i	0.313400	−	2.17974i
$560$	0.351576	−	1.26536i	0.0148568	−	0.0534714i
$561$	−19.2607	−	12.3781i	−0.813187	−	0.522603i
$562$	17.1750	+	6.87584i	0.724484	+	0.290040i
$563$	19.8928	−	27.9356i	0.838383	−	1.17734i	−0.143835	−	0.989602i	$-0.545943\pi$
$563$	19.8928	−	27.9356i	0.838383	−	1.17734i	0.982218	−	0.187743i	$-0.0601172\pi$
$564$	2.21710	−	3.11348i	0.0933566	−	0.131101i
$565$	−3.88937	−	1.55707i	−0.163627	−	0.0655063i
$566$	22.2331	+	14.2884i	0.934528	+	0.600585i
$567$	0.708280	−	2.54918i	0.0297450	−	0.107056i
$568$	1.29650	−	9.01738i	0.0544001	−	0.378361i
$569$	−15.2038	−	43.9284i	−0.637375	−	1.84157i	−0.531238	−	0.847222i	$-0.678273\pi$
$569$	−15.2038	−	43.9284i	−0.637375	−	1.84157i	−0.106136	−	0.994352i	$-0.533848\pi$
$570$	3.59452	+	1.85310i	0.150558	+	0.0776180i
$571$	12.0282	−	34.7531i	0.503363	−	1.45437i	−0.351830	−	0.936064i	$-0.614441\pi$
$571$	12.0282	−	34.7531i	0.503363	−	1.45437i	0.855193	−	0.518309i	$-0.173438\pi$
$572$	−11.1992	+	10.6784i	−0.468262	+	0.446487i
$573$	−4.64319	+	10.1672i	−0.193972	+	0.424739i
$574$	−15.4990	−	0.511818i	−0.646916	−	0.0213629i
$575$	16.1420	+	16.0985i	0.673169	+	0.671353i
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	29.7975	−	2.84532i	1.24049	−	0.118452i	0.545894	−	0.837855i	$-0.316190\pi$
$577$	29.7975	−	2.84532i	1.24049	−	0.118452i	0.694594	+	0.719402i	$0.255584\pi$
$578$	−5.00683	−	20.6384i	−0.208257	−	0.858446i
$579$	−18.3284	+	3.53252i	−0.761704	+	0.146806i
$580$	0.615129	−	0.395319i	0.0255418	−	0.0164147i
$581$	−23.0368	−	5.23404i	−0.955729	−	0.217145i
$582$	−1.22803	+	8.54117i	−0.0509037	+	0.354043i
$583$	8.51264	−	35.0896i	0.352558	−	1.45326i
$584$	−0.548559	+	11.5157i	−0.0226995	+	0.476522i
$585$	1.63069	−	1.28239i	0.0674208	−	0.0530203i
$586$	−14.9585	−	1.42836i	−0.617930	−	0.0590051i
$587$	19.4818	+	42.6592i	0.804101	+	1.76073i	0.630925	+	0.775844i	$0.282676\pi$
$587$	19.4818	+	42.6592i	0.804101	+	1.76073i	0.173176	+	0.984891i	$0.444597\pi$
$588$	5.77586	−	3.95468i	0.238192	−	0.163088i
$589$	−19.8430	−	12.7523i	−0.817618	−	0.525451i
$590$	−0.0474323	+	0.195519i	−0.00195276	+	0.00804937i
$591$	8.66872	−	3.47043i	0.356583	−	0.142754i
$592$	−7.50771	−	1.44699i	−0.308565	−	0.0594710i
$593$	0.816533	+	17.1411i	0.0335310	+	0.703903i	0.951574	+	0.307421i	$0.0994659\pi$
$593$	0.816533	+	17.1411i	0.0335310	+	0.703903i	−0.918043	+	0.396482i	$0.870231\pi$
$594$	−2.42466	−	2.79821i	−0.0994852	−	0.114812i
$595$	1.65307	+	7.95091i	0.0677691	+	0.325955i
$596$	−5.84610	+	12.8012i	−0.239466	+	0.524357i
$597$	9.64548	−	16.7065i	0.394763	−	0.683750i
$598$	19.9048	+	2.35263i	0.813967	+	0.0962063i
$599$	−4.69138	−	8.12570i	−0.191684	−	0.332007i	0.754124	−	0.656732i	$-0.228062\pi$
$599$	−4.69138	−	8.12570i	−0.191684	−	0.332007i	−0.945809	+	0.324725i	$0.894728\pi$
$600$	−2.75736	−	3.87217i	−0.112569	−	0.158081i
$601$	−10.6684	−	3.13251i	−0.435172	−	0.127778i	0.0568071	−	0.998385i	$-0.481908\pi$
$601$	−10.6684	−	3.13251i	−0.435172	−	0.127778i	−0.491979	+	0.870607i	$0.663726\pi$
$602$	20.7508	+	25.6089i	0.845740	+	1.04374i
$603$	−0.472927	+	0.303932i	−0.0192591	+	0.0123770i
$604$	−4.45477	−	12.8712i	−0.181262	−	0.523722i
$605$	1.24836	−	0.499768i	0.0507531	−	0.0203185i
$606$	10.3026	+	9.82351i	0.418515	+	0.399053i
$607$	−27.2977	+	14.0729i	−1.10798	+	0.571202i	−0.912323	−	0.409471i	$-0.865713\pi$
$607$	−27.2977	+	14.0729i	−1.10798	+	0.571202i	−0.195654	+	0.980673i	$0.562683\pi$
$608$	−1.15946	−	8.06421i	−0.0470222	−	0.327047i
$609$	3.86540	+	0.498318i	0.156634	+	0.0201929i
$610$	−0.207176	−	0.453653i	−0.00838832	−	0.0183679i
$611$	14.8300	+	5.93702i	0.599956	+	0.240186i
$612$	0.294228	−	6.17661i	0.0118935	−	0.249675i
$613$	3.07655	+	2.93348i	0.124261	+	0.118482i	0.749662	−	0.661821i	$-0.230216\pi$
$613$	3.07655	+	2.93348i	0.124261	+	0.118482i	−0.625401	+	0.780303i	$0.715065\pi$
$614$	14.5160	+	11.4155i	0.585819	+	0.460693i
$615$	1.90526	−	2.19879i	0.0768276	−	0.0886638i
$616$	−0.142912	−	9.79502i	−0.00575809	−	0.394653i
$617$	0.928236	+	1.07124i	0.0373694	+	0.0431265i	0.774127	−	0.633031i	$-0.218189\pi$
$617$	0.928236	+	1.07124i	0.0373694	+	0.0431265i	−0.736757	+	0.676157i	$0.763644\pi$
$618$	−6.86018	+	6.54117i	−0.275957	+	0.263124i
$619$	−6.42184	+	0.613212i	−0.258116	+	0.0246471i	−0.223312	−	0.974747i	$-0.571687\pi$
$619$	−6.42184	+	0.613212i	−0.258116	+	0.0246471i	−0.0348040	+	0.999394i	$0.511081\pi$
$620$	−0.718556	−	1.24458i	−0.0288579	−	0.0499834i
$621$	−0.788902	+	4.73050i	−0.0316575	+	0.189828i
$622$	1.91845			0.0769229
$623$	−0.832903	+	1.67517i	−0.0333695	+	0.0671142i
$624$	−4.01003	−	1.17745i	−0.160530	−	0.0471358i
$625$	20.9787	−	4.04332i	0.839149	−	0.161733i
$626$	4.71558	+	2.43105i	0.188472	+	0.0971642i
$627$	29.6202	+	5.70882i	1.18292	+	0.227988i
$628$	−10.3962	−	8.17569i	−0.414855	−	0.326245i
$629$	45.3640	−	13.3201i	1.80878	−	0.531106i
$630$	−0.105751	+	1.30903i	−0.00421322	+	0.0521532i
$631$	−1.52843	−	10.6305i	−0.0608460	−	0.423193i	−0.997363	−	0.0725715i	$-0.976879\pi$
$631$	−1.52843	−	10.6305i	−0.0608460	−	0.423193i	0.936517	−	0.350622i	$-0.114030\pi$
$632$	−8.71786	−	0.832455i	−0.346778	−	0.0331133i
$633$	1.23024	−	1.72763i	0.0488975	−	0.0686670i
$634$	−13.8644	+	10.9031i	−0.550624	+	0.433016i
$635$	−0.664741	+	0.342698i	−0.0263795	+	0.0135996i
$636$	9.35698	−	2.74746i	0.371028	−	0.108944i
$637$	21.7530	+	19.5621i	0.861885	+	0.775080i
$638$	3.57171	−	4.12197i	0.141405	−	0.163191i
$639$	0.433476	+	9.09979i	0.0171481	+	0.359982i
$640$	0.162350	−	0.469080i	0.00641745	−	0.0185420i
$641$	4.12155	+	16.9893i	0.162792	+	0.671036i	0.993451	+	0.114256i	$0.0364483\pi$
$641$	4.12155	+	16.9893i	0.162792	+	0.671036i	−0.830660	+	0.556780i	$0.812037\pi$
$642$	0.790700	+	1.11038i	0.0312065	+	0.0438233i
$643$	−16.5376			−0.652180			−0.326090	−	0.945339i	$-0.605731\pi$
$643$	−16.5376			−0.652180			−0.326090	+	0.945339i	$0.605731\pi$
$644$	−9.65440	+	8.23363i	−0.380437	+	0.324450i
$645$	−6.18391			−0.243491
$646$	29.2225	+	41.0373i	1.14975	+	1.61459i
$647$	−2.85425	−	11.7654i	−0.112212	−	0.462545i	−0.999997	−	0.00228683i	$-0.999272\pi$
$647$	−2.85425	−	11.7654i	−0.112212	−	0.462545i	0.887785	−	0.460258i	$-0.152243\pi$
$648$	0.327068	−	0.945001i	0.0128484	−	0.0371231i
$649$	0.0714062	+	1.49900i	0.00280294	+	0.0588409i
$650$	13.0100	−	15.0144i	0.510295	−	0.588912i
$651$	1.33977	−	7.54186i	0.0525097	−	0.295589i
$652$	13.2533	−	3.89152i	0.519040	−	0.152404i
$653$	−37.3419	+	19.2511i	−1.46130	+	0.753352i	−0.991584	−	0.129465i	$-0.958674\pi$
$653$	−37.3419	+	19.2511i	−1.46130	+	0.753352i	−0.469716	+	0.882818i	$0.655644\pi$
$654$	14.8248	−	11.6584i	0.579696	−	0.455878i
$655$	−3.37629	+	4.74133i	−0.131922	+	0.185259i
$656$	−5.83473	−	0.557149i	−0.227808	−	0.0217530i
$657$	−1.64071	−	11.4114i	−0.0640102	−	0.445200i
$658$	−9.13648	+	4.33468i	−0.356177	+	0.168983i
$659$	42.0999	−	12.3616i	1.63998	−	0.481541i	0.673693	−	0.739012i	$-0.264707\pi$
$659$	42.0999	−	12.3616i	1.63998	−	0.481541i	0.966286	+	0.257471i	$0.0828890\pi$
$660$	1.44467	+	1.13610i	0.0562337	+	0.0442227i
$661$	5.12374	+	0.987519i	0.199290	+	0.0384100i	0.287919	−	0.957655i	$-0.407036\pi$
$661$	5.12374	+	0.987519i	0.199290	+	0.0384100i	−0.0886291	+	0.996065i	$0.528249\pi$
$662$	17.8597	+	9.20731i	0.694137	+	0.357852i
$663$	25.3763	−	4.89088i	0.985533	−	0.189946i
$664$	−8.56733	−	2.51559i	−0.332477	−	0.0976240i
$665$	−5.91535	−	8.91575i	−0.229387	−	0.345738i
$666$	7.64588			0.296272
$667$	−7.06284	−	0.158579i	−0.273474	−	0.00614019i
$668$	−3.77928	−	6.54590i	−0.146225	−	0.253268i
$669$	−13.4705	+	1.28628i	−0.520800	+	0.0497304i
$670$	0.201958	−	0.192566i	0.00780231	−	0.00743948i
$671$	−2.43610	−	2.81141i	−0.0940445	−	0.108533i
$672$	2.27174	−	1.35616i	0.0876345	−	0.0523151i
$673$	−19.6783	+	22.7100i	−0.758542	+	0.875405i	−0.995367	−	0.0961478i	$-0.969348\pi$
$673$	−19.6783	+	22.7100i	−0.758542	+	0.875405i	0.236825	+	0.971552i	$0.423893\pi$
$674$	25.9835	+	20.4336i	1.00085	+	0.787074i
$675$	3.44035	+	3.28036i	0.132419	+	0.126261i
$676$	0.212535	−	4.46167i	0.00817444	−	0.171603i
$677$	−23.0763	−	9.23834i	−0.886893	−	0.355058i	−0.116925	−	0.993141i	$-0.537304\pi$
$677$	−23.0763	−	9.23834i	−0.886893	−	0.355058i	−0.769968	+	0.638082i	$0.779728\pi$
$678$	−3.50612	−	7.67732i	−0.134652	−	0.294846i
$679$	13.8494	−	18.1497i	0.531490	−	0.696522i
$680$	0.436824	+	3.03818i	0.0167515	+	0.116509i
$681$	1.35877	−	0.700495i	0.0520682	−	0.0268430i
$682$	−7.75814	−	7.39738i	−0.297075	−	0.283260i
$683$	−14.1269	+	5.65554i	−0.540549	+	0.216403i	−0.625838	−	0.779953i	$-0.715243\pi$
$683$	−14.1269	+	5.65554i	−0.540549	+	0.216403i	0.0852889	+	0.996356i	$0.472819\pi$
$684$	2.66467	+	7.69905i	0.101886	+	0.294381i
$685$	−1.86680	+	1.19972i	−0.0713269	+	0.0458390i
$686$	−18.4430	+	1.68980i	−0.704157	+	0.0645168i
$687$	23.3856	+	6.86663i	0.892216	+	0.261978i
$688$	7.22636	+	10.1480i	0.275502	+	0.386889i
$689$	20.3784	+	35.2964i	0.776354	+	1.34468i
$690$	−0.0598673	−	2.37980i	−0.00227911	−	0.0905976i
$691$	8.30976	−	14.3929i	0.316118	−	0.547533i	−0.663556	−	0.748126i	$-0.730954\pi$
$691$	8.30976	−	14.3929i	0.316118	−	0.547533i	0.979675	+	0.200593i	$0.0642870\pi$
$692$	3.36309	−	7.36413i	0.127845	−	0.279942i
$693$	1.99405	+	9.59097i	0.0757477	+	0.364331i
$694$	−14.3896	−	16.6065i	−0.546221	−	0.630373i
$695$	0.174942	+	3.67247i	0.00663591	+	0.139305i
$696$	1.44645	+	0.278781i	0.0548277	+	0.0105672i
$697$	33.6476	−	13.4705i	1.27449	−	0.510230i
$698$	3.84365	−	15.8437i	0.145484	−	0.599694i
$699$	7.23239	+	4.64798i	0.273554	+	0.175803i
$700$	1.37803	+	12.5011i	0.0520846	+	0.472499i
$701$	−8.71808	−	19.0899i	−0.329277	−	0.721017i	0.670505	−	0.741905i	$-0.266078\pi$
$701$	−8.71808	−	19.0899i	−0.329277	−	0.721017i	−0.999782	+	0.0208888i	$0.993350\pi$
$702$	4.16040	+	0.397270i	0.157024	+	0.0149940i
$703$	−48.9648	+	38.5064i	−1.84674	+	1.45230i
$704$	0.176175	−	3.69837i	0.00663985	−	0.139388i
$705$	0.447298	−	1.84379i	0.0168462	−	0.0694410i
$706$	−1.87515	+	13.0419i	−0.0705721	+	0.490840i
$707$	−11.1370	−	35.9789i	−0.418851	−	1.35313i
$708$	−0.340972	+	0.219129i	−0.0128145	+	0.00823538i
$709$	−15.5912	+	3.00495i	−0.585539	+	0.112853i	−0.473413	−	0.880841i	$-0.656978\pi$
$709$	−15.5912	+	3.00495i	−0.585539	+	0.112853i	−0.112126	+	0.993694i	$0.535766\pi$
$710$	−1.06612	−	4.39461i	−0.0400108	−	0.164927i
$711$	8.71786	−	0.832455i	0.326945	−	0.0312195i
$712$	−0.353549	+	0.612365i	−0.0132498	+	0.0229493i
$713$	−0.971818	+	13.8508i	−0.0363949	+	0.518715i
$714$	−8.64332	+	13.8907i	−0.323468	+	0.519848i
$715$	−3.19084	+	6.98696i	−0.119331	+	0.261298i
$716$	−6.63199	+	6.32359i	−0.247849	+	0.236324i
$717$	−6.90124	+	19.9398i	−0.257732	+	0.744666i
$718$	28.3919	+	14.6371i	1.05958	+	0.546250i
$719$	−11.9146	−	34.4249i	−0.444338	−	1.28383i	−0.915690	−	0.401885i	$-0.868355\pi$
$719$	−11.9146	−	34.4249i	−0.444338	−	1.28383i	0.471352	−	0.881945i	$-0.343766\pi$
$720$	−0.0706423	+	0.491328i	−0.00263268	+	0.0183107i
$721$	24.2830	−	6.26746i	0.904345	−	0.233412i
$722$	−39.8551	−	25.6133i	−1.48325	−	0.953228i
$723$	11.2204	+	4.49196i	0.417290	+	0.167058i
$724$	−4.76533	+	6.69197i	−0.177102	+	0.248705i
$725$	−4.06180	+	5.70400i	−0.150852	+	0.211841i
$726$	2.51493	+	1.00683i	0.0933377	+	0.0373668i
$727$	6.26355	+	4.02534i	0.232302	+	0.149292i	0.651614	−	0.758551i	$-0.274092\pi$
$727$	6.26355	+	4.02534i	0.232302	+	0.149292i	−0.419312	+	0.907842i	$0.637729\pi$
$728$	7.74645	+	7.89048i	0.287102	+	0.292441i
$729$	−0.142315	+	0.989821i	−0.00527092	+	0.0366601i
$730$	1.87169	+	5.40789i	0.0692743	+	0.200155i
$731$	−68.4719	−	35.2997i	−2.53252	−	1.30561i
$732$	0.328610	−	0.949457i	0.0121458	−	0.0350930i
$733$	−17.4996	+	16.6859i	−0.646364	+	0.616307i	−0.940637	−	0.339415i	$-0.889771\pi$
$733$	−17.4996	+	16.6859i	−0.646364	+	0.616307i	0.294273	+	0.955721i	$0.404923\pi$
$734$	−7.82656	+	17.1378i	−0.288884	+	0.632567i
$735$	1.93207	−	2.88797i	0.0712654	−	0.106524i
$736$	−3.83537	+	2.87922i	−0.141374	+	0.106129i
$737$	1.04073	−	1.80260i	0.0383359	−	0.0663997i
$738$	5.83473	−	0.557149i	0.214779	−	0.0205089i
$739$	5.22829	+	21.5513i	0.192326	+	0.792778i	0.983459	+	0.181133i	$0.0579766\pi$
$739$	5.22829	+	21.5513i	0.192326	+	0.792778i	−0.791133	+	0.611645i	$0.790508\pi$
$740$	−3.72668	+	0.718258i	−0.136995	+	0.0264037i
$741$	−28.6443	+	18.4085i	−1.05227	+	0.676255i
$742$	−25.1601	−	5.71646i	−0.923658	−	0.209858i
$743$	−3.53048	+	24.5550i	−0.129521	+	0.900837i	0.816642	+	0.577145i	$0.195833\pi$
$743$	−3.53048	+	24.5550i	−0.129521	+	0.900837i	−0.946163	+	0.323692i	$0.895076\pi$
$744$	0.682566	−	2.81357i	0.0250241	−	0.103151i
$745$	−0.332385	+	6.97761i	−0.0121776	+	0.255640i
$746$	−20.4019	+	16.0442i	−0.746967	+	0.587421i
$747$	8.88859	+	0.848757i	0.325216	+	0.0310544i
$748$	9.51102	+	20.8262i	0.347757	+	0.761482i
$749$	−0.395163	−	3.58482i	−0.0144389	−	0.130987i
$750$	−4.07293	−	2.61751i	−0.148722	−	0.0955780i
$751$	−6.04436	+	24.9152i	−0.220562	+	0.909168i	0.748655	+	0.662960i	$0.230700\pi$
$751$	−6.04436	+	24.9152i	−0.220562	+	0.909168i	−0.969217	+	0.246208i	$0.920815\pi$
$752$	−3.54841	+	1.42057i	−0.129397	+	0.0518029i
$753$	18.2594	+	3.51921i	0.665410	+	0.128247i
$754$	0.292936	+	6.14948i	0.0106681	+	0.223951i
$755$	−4.42742	−	5.10951i	−0.161130	−	0.185954i
$756$	−1.97404	+	1.76158i	−0.0717950	+	0.0640682i
$757$	5.51013	−	12.0655i	0.200269	−	0.438528i	−0.782676	−	0.622430i	$-0.786146\pi$
$757$	5.51013	−	12.0655i	0.200269	−	0.438528i	0.982945	+	0.183902i	$0.0588729\pi$
$758$	−0.294969	+	0.510902i	−0.0107138	+	0.0185568i
$759$	−5.42958	−	16.9064i	−0.197081	−	0.613663i
$760$	−2.02204	−	3.50227i	−0.0733470	−	0.127041i
$761$	17.6507	+	24.7870i	0.639839	+	0.898528i	0.999401	−	0.0345933i	$-0.0110136\pi$
$761$	17.6507	+	24.7870i	0.639839	+	0.898528i	−0.359563	+	0.933121i	$0.617074\pi$
$762$	−1.44564	−	0.424477i	−0.0523698	−	0.0153772i
$763$	−49.2816	+	7.82107i	−1.78411	+	0.283142i
$764$	9.40288	−	6.04286i	0.340184	−	0.218623i
$765$	−1.00391	−	2.90061i	−0.0362964	−	0.104872i
$766$	5.16974	−	2.06965i	0.186790	−	0.0747795i
$767$	−1.22596	−	1.16895i	−0.0442668	−	0.0422083i
$768$	0.888835	−	0.458227i	0.0320731	−	0.0165348i
$769$	0.327430	+	2.27732i	0.0118074	+	0.0821224i	0.994873	−	0.101131i	$-0.0322462\pi$
$769$	0.327430	+	2.27732i	0.0118074	+	0.0821224i	−0.983066	+	0.183254i	$0.941337\pi$
$770$	−1.87290	−	4.48741i	−0.0674946	−	0.161715i
$771$	8.86172	+	19.4045i	0.319147	+	0.698834i
$772$	17.3287	+	6.93736i	0.623673	+	0.249681i
$773$	1.87394	−	39.3389i	0.0674010	−	1.41492i	−0.671448	−	0.741051i	$-0.734328\pi$
$773$	1.87394	−	39.3389i	0.0674010	−	1.41492i	0.738849	−	0.673871i	$-0.235369\pi$
$774$	−9.01629	−	8.59701i	−0.324084	−	0.309013i
$775$	10.8181	+	8.50746i	0.388598	+	0.305597i
$776$	5.65079	−	6.52136i	0.202852	−	0.234103i
$777$	−17.6646	−	9.85790i	−0.633714	−	0.353650i
$778$	−8.25248	−	9.52386i	−0.295866	−	0.341447i
$779$	−34.5601	+	32.9530i	−1.23825	+	1.18066i
$780$	−2.06514	+	0.197197i	−0.0739438	+	0.00706078i
$781$	−16.8654	−	29.2117i	−0.603490	−	1.04528i
$782$	12.9218	−	26.6923i	0.462082	−	0.954516i
$783$	−1.47308			−0.0526434
$784$	−6.99702	+	0.204220i	−0.249894	+	0.00729358i
$785$	−6.29913	−	1.84959i	−0.224825	−	0.0660147i
$786$	−11.5142	+	2.21918i	−0.410698	+	0.0791556i
$787$	−9.13959	−	4.71179i	−0.325791	−	0.167957i	0.287570	−	0.957760i	$-0.407153\pi$
$787$	−9.13959	−	4.71179i	−0.325791	−	0.167957i	−0.613361	+	0.789803i	$0.710183\pi$
$788$	−9.16885	−	1.76715i	−0.326627	−	0.0629521i
$789$	−20.1156	−	15.8191i	−0.716133	−	0.563173i
$790$	−4.17097	+	1.22471i	−0.148396	+	0.0435731i
$791$	−1.79810	+	22.2577i	−0.0639332	+	0.791393i
$792$	0.526930	+	3.66488i	0.0187236	+	0.130226i
$793$	4.18002	+	0.399143i	0.148437	+	0.0141740i
$794$	−9.18473	+	12.8982i	−0.325954	+	0.457738i
$795$	3.80505	−	2.99232i	0.134951	−	0.106127i
$796$	−17.1465	+	8.83963i	−0.607741	+	0.313312i
$797$	−40.1210	+	11.7806i	−1.42116	+	0.417290i	−0.899896	−	0.436105i	$-0.856357\pi$
$797$	−40.1210	+	11.7806i	−1.42116	+	0.417290i	−0.521264	+	0.853395i	$0.674539\pi$
$798$	3.77015	−	21.2230i	0.133462	−	0.751287i
$799$	15.4777	−	17.8622i	0.547560	−	0.631918i
$800$	0.226186	+	4.74822i	0.00799687	+	0.167875i
$801$	0.231269	−	0.668208i	0.00817149	−	0.0236100i
$802$	8.38696	+	34.5715i	0.296154	+	1.22076i
$803$	24.7602	+	34.7709i	0.873769	+	1.22704i
$804$	0.562169			0.0198262
$805$	−2.92998	+	5.57535i	−0.103268	+	0.196505i
$806$	12.0999			0.426201
$807$	2.68914	+	3.77636i	0.0946620	+	0.132934i
$808$	−3.35611	−	13.8341i	−0.118068	−	0.486681i
$809$	−3.55937	+	10.2841i	−0.125141	+	0.361570i	−0.990117	−	0.140242i	$-0.955212\pi$
$809$	−3.55937	+	10.2841i	−0.125141	+	0.361570i	0.864977	+	0.501812i	$0.167333\pi$
$810$	−0.0236187	−	0.495818i	−0.000829877	−	0.0174213i
$811$	7.12455	−	8.22217i	0.250177	−	0.288719i	−0.616746	−	0.787163i	$-0.711549\pi$
$811$	7.12455	−	8.22217i	0.250177	−	0.288719i	0.866922	+	0.498443i	$0.166095\pi$
$812$	−2.98237	−	2.50901i	−0.104661	−	0.0880489i
$813$	24.0333	−	7.05682i	0.842886	−	0.247494i
$814$	−25.1624	+	12.9721i	−0.881940	+	0.454672i
$815$	5.38951	−	4.23836i	0.188786	−	0.148463i
$816$	−3.58685	+	5.03702i	−0.125565	+	0.176331i
$817$	101.038	+	9.64791i	3.53486	+	0.337538i
$818$	−2.58975	−	18.0121i	−0.0905485	−	0.629779i
$819$	−9.09974	−	6.28186i	−0.317971	−	0.219506i
$820$	−2.79156	+	0.819677i	−0.0974857	+	0.0286244i
$821$	5.21229	+	4.09899i	0.181910	+	0.143056i	0.704962	−	0.709245i	$-0.250964\pi$
$821$	5.21229	+	4.09899i	0.181910	+	0.143056i	−0.523052	+	0.852301i	$0.675207\pi$
$822$	−4.38972	−	0.846049i	−0.153109	−	0.0295094i
$823$	−31.2833	−	16.1277i	−1.09047	−	0.562175i	−0.183348	−	0.983048i	$-0.558693\pi$
$823$	−31.2833	−	16.1277i	−1.09047	−	0.562175i	−0.907120	+	0.420873i	$0.861724\pi$
$824$	9.30758	−	1.79389i	0.324245	−	0.0624931i
$825$	−16.8876	−	4.95864i	−0.587950	−	0.172638i
$826$	1.07029	−	0.0666461i	0.0372400	−	0.00231892i
$827$	−28.2629			−0.982796			−0.491398	−	0.870935i	$-0.663514\pi$
$827$	−28.2629			−0.982796			−0.491398	+	0.870935i	$0.663514\pi$
$828$	3.22117	−	3.55304i	0.111943	−	0.123477i
$829$	20.4380	+	35.3996i	0.709841	+	1.22948i	0.964916	+	0.262559i	$0.0845664\pi$
$829$	20.4380	+	35.3996i	0.709841	+	1.22948i	−0.255075	+	0.966921i	$0.582100\pi$
$830$	−4.41212	+	0.421306i	−0.153147	+	0.0146238i
$831$	22.7175	−	21.6611i	0.788061	−	0.751415i
$832$	2.73687	+	3.15852i	0.0948840	+	0.109502i
$833$	37.8785	−	20.9485i	1.31241	−	0.725821i
$834$	−4.85049	+	5.59776i	−0.167959	+	0.193835i
$835$	−2.94921	−	2.31928i	−0.102061	−	0.0802620i
$836$	−21.8316	−	20.8164i	−0.755063	−	0.719951i
$837$	−0.137758	+	2.89191i	−0.00476163	+	0.0999589i
$838$	−26.8132	−	10.7344i	−0.926248	−	0.370814i
$839$	23.3181	+	51.0595i	0.805029	+	1.76277i	0.627442	+	0.778664i	$0.284102\pi$
$839$	23.3181	+	51.0595i	0.805029	+	1.76277i	0.177588	+	0.984105i	$0.443171\pi$
$840$	0.796681	−	1.04406i	0.0274881	−	0.0360234i
$841$	3.81831	+	26.5570i	0.131666	+	0.915757i
$842$	−19.0504	+	9.82119i	−0.656522	+	0.338460i
$843$	13.3892	+	12.7666i	0.461150	+	0.439706i
$844$	−1.96897	+	0.788255i	−0.0677746	+	0.0271329i
$845$	−0.725173	−	2.09525i	−0.0249467	−	0.0720788i
$846$	3.21544	−	2.06644i	0.110549	−	0.0710457i
$847$	−4.51224	−	5.56863i	−0.155042	−	0.191340i
$848$	−9.35698	−	2.74746i	−0.321320	−	0.0943480i
$849$	15.3301	+	21.5281i	0.526127	+	0.738842i
$850$	−14.6972	−	25.4564i	−0.504111	−	0.873146i
$851$	33.7272	+	14.3889i	1.15615	+	0.493247i
$852$	4.55505	−	7.88958i	0.156054	−	0.270293i
$853$	3.83492	−	8.39729i	0.131305	−	0.287518i	−0.832548	−	0.553953i	$-0.813119\pi$
$853$	3.83492	−	8.39729i	0.131305	−	0.287518i	0.963853	+	0.266435i	$0.0858459\pi$
$854$	−1.98335	+	1.76989i	−0.0678687	+	0.0605645i
$855$	2.64831	+	3.05631i	0.0905702	+	0.104524i
$856$	−0.0648609	−	1.36160i	−0.00221690	−	0.0465385i
$857$	19.3431	+	3.72808i	0.660749	+	0.127349i	0.508592	−	0.861007i	$-0.330166\pi$
$857$	19.3431	+	3.72808i	0.660749	+	0.127349i	0.152157	+	0.988356i	$0.451378\pi$
$858$	−14.3658	+	5.75118i	−0.490439	+	0.196342i
$859$	−3.63186	+	14.9707i	−0.123917	+	0.510794i	0.875693	+	0.482869i	$0.160405\pi$
$859$	−3.63186	+	14.9707i	−0.123917	+	0.510794i	−0.999610	+	0.0279255i	$0.991110\pi$
$860$	5.20224	+	3.34327i	0.177395	+	0.114005i
$861$	−14.1986	−	6.23555i	−0.483885	−	0.212507i
$862$	2.28447	+	5.00229i	0.0778093	+	0.170379i
$863$	19.7793	+	1.88869i	0.673294	+	0.0642918i	0.426103	−	0.904675i	$-0.359886\pi$
$863$	19.7793	+	1.88869i	0.673294	+	0.0642918i	0.247192	+	0.968967i	$0.420492\pi$
$864$	−0.786053	+	0.618159i	−0.0267421	+	0.0210302i
$865$	0.191211	−	4.01401i	0.00650136	−	0.136480i
$866$	0.578999	−	2.38667i	0.0196752	−	0.0811022i
$867$	3.02235	−	21.0209i	0.102644	−	0.713908i
$868$	−5.20452	+	5.62028i	−0.176653	+	0.190765i
$869$	−27.2779	+	17.5304i	−0.925338	+	0.594679i
$870$	0.717992	−	0.138382i	0.0243422	−	0.00469157i
$871$	0.553912	+	2.28326i	0.0187686	+	0.0773652i
$872$	−18.7744	+	1.79274i	−0.635782	+	0.0607098i
$873$	−4.31450	+	7.47293i	−0.146024	+	0.252920i
$874$	−2.73472	+	38.9765i	−0.0925034	+	1.31840i
$875$	6.03508	+	11.2986i	0.204023	+	0.381963i
$876$	−4.78921	+	10.4869i	−0.161812	+	0.354320i
$877$	5.13822	−	4.89928i	0.173505	−	0.165437i	−0.598351	−	0.801234i	$-0.704177\pi$
$877$	5.13822	−	4.89928i	0.173505	−	0.165437i	0.771856	+	0.635797i	$0.219329\pi$
$878$	−1.04934	+	3.03186i	−0.0354134	+	0.102320i
$879$	−13.3561	−	6.88556i	−0.450491	−	0.232244i
$880$	−0.601111	−	1.73680i	−0.0202635	−	0.0585474i
$881$	−5.91642	+	41.1496i	−0.199329	+	1.38636i	0.606908	+	0.794772i	$0.292410\pi$
$881$	−5.91642	+	41.1496i	−0.199329	+	1.38636i	−0.806237	+	0.591593i	$0.798499\pi$
$882$	6.83193	−	1.52472i	0.230043	−	0.0513401i
$883$	8.93571	+	5.74263i	0.300711	+	0.193255i	0.682291	−	0.731081i	$-0.260984\pi$
$883$	8.93571	+	5.74263i	0.300711	+	0.193255i	−0.381580	+	0.924336i	$0.624620\pi$
$884$	−23.9921	−	9.60499i	−0.806942	−	0.323051i
$885$	−0.116701	+	0.163884i	−0.00392288	+	0.00550891i
$886$	12.4081	−	17.4247i	0.416858	−	0.585396i
$887$	−23.5365	−	9.42260i	−0.790279	−	0.316380i	−0.0588227	−	0.998268i	$-0.518735\pi$
$887$	−23.5365	−	9.42260i	−0.790279	−	0.316380i	−0.731456	+	0.681889i	$0.761159\pi$
$888$	−6.43212	−	4.13368i	−0.215848	−	0.138717i
$889$	2.79263	+	2.84456i	0.0936619	+	0.0954033i
$890$	−0.0499510	+	0.347417i	−0.00167436	+	0.0116454i
$891$	−1.21099	−	3.49893i	−0.0405697	−	0.117218i
$892$	12.0275	+	6.20062i	0.402711	+	0.207612i
$893$	−10.1849	+	29.4274i	−0.340825	+	0.984749i
$894$	−10.1851	+	9.71143i	−0.340639	+	0.324799i
$895$	−1.88956	+	4.13757i	−0.0631612	+	0.138304i
$896$	−2.64431	−	0.0873221i	−0.0883402	−	0.00291723i
$897$	17.6046	+	9.58196i	0.587799	+	0.319932i
$898$	−9.20673	+	15.9465i	−0.307233	+	0.532142i
$899$	−4.24551	+	0.405397i	−0.141596	+	0.0135208i
$900$	−1.12071	−	4.61961i	−0.0373568	−	0.153987i
$901$	59.2129	−	11.4123i	1.97267	−	0.380200i
$902$	−18.2566	+	11.7328i	−0.607880	+	0.390661i
$903$	9.74652	+	31.4868i	0.324344	+	1.04782i
$904$	−1.20114	+	8.35413i	−0.0399494	+	0.277854i
$905$	−0.961402	+	3.96295i	−0.0319581	+	0.131733i
$906$	0.648080	−	13.6049i	0.0215310	−	0.451992i
$907$	5.51089	−	4.33381i	0.182986	−	0.143902i	−0.522464	−	0.852661i	$-0.674987\pi$
$907$	5.51089	−	4.33381i	0.182986	−	0.143902i	0.705450	+	0.708759i	$0.250745\pi$
$908$	−1.52179	−	0.145313i	−0.0505023	−	0.00482238i
$909$	5.91358	+	12.9489i	0.196141	+	0.429489i
$910$	5.02543	+	2.20701i	0.166591	+	0.0731616i
$911$	14.2494	+	9.15755i	0.472105	+	0.303403i	0.754973	−	0.655755i	$-0.227650\pi$
$911$	14.2494	+	9.15755i	0.472105	+	0.303403i	−0.282869	+	0.959159i	$0.591286\pi$
$912$	1.92076	−	7.91748i	0.0636027	−	0.262174i
$913$	−30.6921	+	12.2873i	−1.01576	+	0.406649i
$914$	−31.0978	−	5.99360i	−1.02862	−	0.198251i
$915$	−0.0237301	−	0.498156i	−0.000784493	−	0.0164685i
$916$	−15.9608	−	18.4198i	−0.527361	−	0.608607i
$917$	29.4630	+	9.71829i	0.972954	+	0.320926i
$918$	2.56877	−	5.62481i	0.0847819	−	0.185646i
$919$	2.46774	−	4.27424i	0.0814031	−	0.140994i	−0.822450	−	0.568838i	$-0.807393\pi$
$919$	2.46774	−	4.27424i	0.0814031	−	0.140994i	0.903853	+	0.427843i	$0.140727\pi$
$920$	−1.23626	+	2.03438i	−0.0407581	+	0.0670717i
$921$	9.23349	+	15.9929i	0.304254	+	0.526983i
$922$	−5.74665	−	8.07005i	−0.189256	−	0.265773i
$923$	36.5318	+	10.7267i	1.20246	+	0.353074i
$924$	3.50777	−	9.14650i	0.115397	−	0.300898i
$925$	30.5758	−	19.6499i	1.00533	−	0.646084i
$926$	−1.90863	−	5.51462i	−0.0627215	−	0.181222i
$927$	−8.79988	+	3.52294i	−0.289026	+	0.115709i
$928$	−1.06611	−	1.01654i	−0.0349969	−	0.0333695i
$929$	1.80257	−	0.929287i	0.0591403	−	0.0304889i	−0.428403	−	0.903588i	$-0.640924\pi$
$929$	1.80257	−	0.929287i	0.0591403	−	0.0304889i	0.487543	+	0.873099i	$0.337893\pi$
$930$	−0.204522	−	1.42248i	−0.00670656	−	0.0466451i
$931$	−36.0734	+	44.1716i	−1.18226	+	1.44767i
$932$	−3.57139	−	7.82025i	−0.116985	−	0.256161i
$933$	1.78103	+	0.713017i	0.0583083	+	0.0233431i
$934$	−2.03332	+	42.6847i	−0.0665323	+	1.39669i
$935$	8.22505	+	7.84257i	0.268988	+	0.256479i
$936$	−3.28517	−	2.58348i	−0.107379	−	0.0844438i
$937$	26.6408	−	30.7451i	0.870317	−	1.00440i	−0.129601	−	0.991566i	$-0.541370\pi$
$937$	26.6408	−	30.7451i	0.870317	−	1.00440i	0.999918	−	0.0128327i	$-0.00408490\pi$
$938$	−1.29880	−	0.724809i	−0.0424074	−	0.0236659i
$939$	3.47426	+	4.00951i	0.113378	+	0.130845i
$940$	−1.37312	+	1.30926i	−0.0447861	+	0.0427035i
$941$	−46.3795	+	4.42871i	−1.51193	+	0.144372i	−0.817810	−	0.575489i	$-0.804812\pi$
$941$	−46.3795	+	4.42871i	−1.51193	+	0.144372i	−0.694119	+	0.719860i	$0.744206\pi$
$942$	−6.61293	−	11.4539i	−0.215461	−	0.373189i
$943$	26.7864	+	8.52282i	0.872287	+	0.277541i
$944$	0.405314			0.0131918
$945$	−0.584695	+	1.17596i	−0.0190201	+	0.0382540i
$946$	44.2581	+	12.9954i	1.43896	+	0.422516i
$947$	−4.49614	+	0.866561i	−0.146105	+	0.0281594i	−0.261779	−	0.965128i	$-0.584309\pi$
$947$	−4.49614	+	0.866561i	−0.146105	+	0.0281594i	0.115674	+	0.993287i	$0.463097\pi$
$948$	−7.78399	−	4.01292i	−0.252812	−	0.130334i
$949$	−47.3115	−	9.11855i	−1.53580	−	0.296001i
$950$	30.4425	+	23.9402i	0.987685	+	0.776724i
$951$	−16.9235	+	4.96919i	−0.548782	+	0.161137i
$952$	14.7811	−	7.01270i	0.479059	−	0.227283i
$953$	0.781667	+	5.43661i	0.0253207	+	0.176109i	0.998557	−	0.0536960i	$-0.0171002\pi$
$953$	0.781667	+	5.43661i	0.0253207	+	0.176109i	−0.973237	+	0.229805i	$0.926191\pi$
$954$	9.70784	+	0.926987i	0.314303	+	0.0300123i
$955$	3.21824	−	4.51939i	0.104140	−	0.146244i
$956$	16.5860	−	13.0434i	0.536429	−	0.421852i
$957$	4.84785	−	2.49924i	0.156709	−	0.0807889i
$958$	−3.92844	+	1.15349i	−0.126922	+	0.0372677i
$959$	9.05094	+	7.61437i	0.292270	+	0.245881i
$960$	0.325060	−	0.375139i	0.0104913	−	0.0121076i
$961$	−1.07620	−	22.5923i	−0.0347162	−	0.728783i
$962$	10.4513	−	30.1971i	0.336964	−	0.973594i
$963$	0.321373	+	1.32472i	0.0103561	+	0.0426884i
$964$	−7.01064	−	9.84507i	−0.225798	−	0.317088i
$965$	9.26531			0.298261
$966$	−12.0230	+	4.05566i	−0.386832	+	0.130489i
$967$	−16.1210			−0.518418			−0.259209	−	0.965821i	$-0.583462\pi$
$967$	−16.1210			−0.518418			−0.259209	+	0.965821i	$0.583462\pi$
$968$	−1.57136	−	2.20667i	−0.0505055	−	0.0709250i
$969$	11.8772	+	48.9586i	0.381552	+	1.57278i
$970$	1.40092	−	4.04769i	0.0449808	−	0.129963i
$971$	−2.83821	−	59.5813i	−0.0910824	−	1.91205i	−0.334934	−	0.942242i	$-0.608714\pi$
$971$	−2.83821	−	59.5813i	−0.0910824	−	1.91205i	0.243852	−	0.969813i	$-0.421589\pi$
$972$	0.654861	−	0.755750i	0.0210047	−	0.0242407i
$973$	18.4235	−	6.67898i	0.590631	−	0.214118i
$974$	−8.09119	+	2.37579i	−0.259258	+	0.0761251i
$975$	17.6584	−	9.10352i	0.565520	−	0.291546i
$976$	−0.789760	+	0.621074i	−0.0252796	+	0.0198801i
$977$	−0.971608	+	1.36443i	−0.0310845	+	0.0436521i	−0.829826	−	0.558023i	$-0.811560\pi$
$977$	−0.971608	+	1.36443i	−0.0310845	+	0.0436521i	0.798741	+	0.601675i	$0.205500\pi$
$978$	13.7503	+	1.31299i	0.439686	+	0.0419849i
$979$	0.372591	+	2.59143i	0.0119081	+	0.0828224i
$980$	−3.18672	+	1.38496i	−0.101796	+	0.0442410i
$981$	18.0959	−	5.31342i	0.577756	−	0.169645i
$982$	−3.28170	−	2.58076i	−0.104723	−	0.0823554i
$983$	7.83394	+	1.50987i	0.249864	+	0.0481573i	0.312645	−	0.949870i	$-0.398785\pi$
$983$	7.83394	+	1.50987i	0.249864	+	0.0481573i	−0.0627812	+	0.998027i	$0.519997\pi$
$984$	−5.20970	−	2.68579i	−0.166079	−	0.0856198i
$985$	−4.55124	+	0.877179i	−0.145014	+	0.0279492i
$986$	8.73995	+	2.56628i	0.278337	+	0.0817270i
$987$	−10.0931	+	0.628489i	−0.321266	+	0.0200050i
$988$	34.0495			1.08326
$989$	−23.5934	−	54.8908i	−0.750227	−	1.74543i
$990$	0.918940	+	1.59165i	0.0292058	+	0.0505860i
$991$	−31.5045	+	3.00832i	−1.00077	+	0.0955624i	−0.582562	−	0.812787i	$-0.697950\pi$
$991$	−31.5045	+	3.00832i	−1.00077	+	0.0955624i	−0.418213	+	0.908349i	$0.637343\pi$
$992$	−2.09534	+	1.99791i	−0.0665272	+	0.0634336i
$993$	13.1584	+	15.1856i	0.417568	+	0.481899i
$994$	−20.6958	+	12.3548i	−0.656432	+	0.391870i
$995$	−6.27072	+	7.23679i	−0.198795	+	0.229422i
$996$	−7.01868	−	5.51955i	−0.222395	−	0.174894i
$997$	−30.1094	−	28.7093i	−0.953575	−	0.909232i	0.0423784	−	0.999102i	$-0.486506\pi$
$997$	−30.1094	−	28.7093i	−0.953575	−	0.909232i	−0.995954	+	0.0898696i	$0.971355\pi$
$998$	0.548193	−	11.5080i	0.0173527	−	0.364279i
$999$	7.09819	+	2.84169i	0.224577	+	0.0899070i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.y.a.121.5	✓	160
7.4	even	3	inner	966.2.y.a.949.4	yes	160
23.4	even	11	inner	966.2.y.a.625.4	yes	160
161.4	even	33	inner	966.2.y.a.487.5	yes	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.y.a.121.5	✓	160	1.1	even	1	trivial
966.2.y.a.487.5	yes	160	161.4	even	33	inner
966.2.y.a.625.4	yes	160	23.4	even	11	inner
966.2.y.a.949.4	yes	160	7.4	even	3	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)

\(f(q)\)	\(=\)	\(q+(-0.580057 - 0.814576i) q^{2} +(-0.235759 - 0.971812i) q^{3} +(-0.327068 + 0.945001i) q^{4} +(0.0236187 + 0.495818i) q^{5} +(-0.654861 + 0.755750i) q^{6} +(2.48735 - 0.901724i) q^{7} +(0.959493 - 0.281733i) q^{8} +(-0.888835 + 0.458227i) q^{9} +O(q^{10})\)	\(q+(-0.580057 - 0.814576i) q^{2} +(-0.235759 - 0.971812i) q^{3} +(-0.327068 + 0.945001i) q^{4} +(0.0236187 + 0.495818i) q^{5} +(-0.654861 + 0.755750i) q^{6} +(2.48735 - 0.901724i) q^{7} +(0.959493 - 0.281733i) q^{8} +(-0.888835 + 0.458227i) q^{9} +(0.390181 - 0.306842i) q^{10} +(2.14770 - 3.01602i) q^{11} +(0.995472 + 0.0950560i) q^{12} +(0.594779 + 4.13678i) q^{13} +(-2.17733 - 1.50308i) q^{14} +(0.476273 - 0.139846i) q^{15} +(-0.786053 - 0.618159i) q^{16} +(6.07187 + 1.17026i) q^{17} +(0.888835 + 0.458227i) q^{18} +(-7.99991 + 1.54186i) q^{19} +(-0.476273 - 0.139846i) q^{20} +(-1.46272 - 2.20464i) q^{21} -3.70256 q^{22} +(3.05845 + 3.69403i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(4.73208 - 0.451859i) q^{25} +(3.02472 - 2.88406i) q^{26} +(0.654861 + 0.755750i) q^{27} +(0.0385981 + 2.64547i) q^{28} +(-0.964659 + 1.11328i) q^{29} +(-0.390181 - 0.306842i) q^{30} +(2.09534 + 1.99791i) q^{31} +(-0.0475819 + 0.998867i) q^{32} +(-3.43734 - 1.37610i) q^{33} +(-2.56877 - 5.62481i) q^{34} +(0.505839 + 1.21197i) q^{35} +(-0.142315 - 0.989821i) q^{36} +(6.79593 - 3.50355i) q^{37} +(5.89636 + 5.62217i) q^{38} +(3.87995 - 1.55330i) q^{39} +(0.162350 + 0.469080i) q^{40} +(4.93081 - 3.16884i) q^{41} +(-0.947389 + 2.47031i) q^{42} +(-11.9534 - 3.50983i) q^{43} +(2.14770 + 3.01602i) q^{44} +(-0.248190 - 0.429878i) q^{45} +(1.23499 - 4.63409i) q^{46} +(1.91110 - 3.31013i) q^{47} +(-0.415415 + 0.909632i) q^{48} +(5.37379 - 4.48580i) q^{49} +(-3.11295 - 3.59254i) q^{50} +(-0.294228 - 6.17661i) q^{51} +(-4.10380 - 0.790942i) q^{52} +(9.05345 - 3.62445i) q^{53} +(0.235759 - 0.971812i) q^{54} +(1.54612 + 0.993633i) q^{55} +(2.13255 - 1.56596i) q^{56} +(3.38444 + 7.41090i) q^{57} +(1.46640 + 0.140025i) q^{58} +(-0.318598 + 0.250548i) q^{59} +(-0.0236187 + 0.495818i) q^{60} +(0.236871 - 0.976394i) q^{61} +(0.412028 - 2.86572i) q^{62} +(-1.79765 + 1.94125i) q^{63} +(0.841254 - 0.540641i) q^{64} +(-2.03704 + 0.392608i) q^{65} +(0.872912 + 3.59819i) q^{66} +(0.559623 - 0.0534376i) q^{67} +(-3.09181 + 5.35517i) q^{68} +(2.86884 - 3.84314i) q^{69} +(0.693829 - 1.11506i) q^{70} +(3.78447 - 8.28684i) q^{71} +(-0.723734 + 0.690079i) q^{72} +(-3.77068 + 10.8947i) q^{73} +(-6.79593 - 3.50355i) q^{74} +(-1.55475 - 4.49216i) q^{75} +(1.15946 - 8.06421i) q^{76} +(2.62245 - 9.43852i) q^{77} +(-3.51587 - 2.25951i) q^{78} +(-8.13019 - 3.25484i) q^{79} +(0.287929 - 0.404339i) q^{80} +(0.580057 - 0.814576i) q^{81} +(-5.44141 - 2.17841i) q^{82} +(-7.51157 - 4.82739i) q^{83} +(2.56180 - 0.661203i) q^{84} +(-0.436824 + 3.03818i) q^{85} +(4.07462 + 11.7728i) q^{86} +(1.30932 + 0.675002i) q^{87} +(1.21099 - 3.49893i) q^{88} +(-0.511751 + 0.487953i) q^{89} +(-0.206204 + 0.451523i) q^{90} +(5.20966 + 9.75328i) q^{91} +(-4.49118 + 1.68204i) q^{92} +(1.44759 - 2.50730i) q^{93} +(-3.80490 + 0.363324i) q^{94} +(-0.953427 - 3.93008i) q^{95} +(0.981929 - 0.189251i) q^{96} +(7.25917 - 4.66519i) q^{97} +(-6.77113 - 1.77534i) q^{98} +(-0.526930 + 3.66488i) 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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