LMFDB - Embedded newform 966.2.y.d.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.d.541.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0475819 - 0.998867i) q^{2} +(0.928368 + 0.371662i) q^{3} +(-0.995472 - 0.0950560i) q^{4} +(-0.363961 - 1.50027i) q^{5} +(0.415415 - 0.909632i) q^{6} +(-0.661406 + 2.56175i) q^{7} +(-0.142315 + 0.989821i) q^{8} +(0.723734 + 0.690079i) q^{9} +O(q^{10})$	\(q+(0.0475819 - 0.998867i) q^{2} +(0.928368 + 0.371662i) q^{3} +(-0.995472 - 0.0950560i) q^{4} +(-0.363961 - 1.50027i) q^{5} +(0.415415 - 0.909632i) q^{6} +(-0.661406 + 2.56175i) q^{7} +(-0.142315 + 0.989821i) q^{8} +(0.723734 + 0.690079i) q^{9} +(-1.51589 + 0.292163i) q^{10} +(-0.00791688 - 0.166196i) q^{11} +(-0.888835 - 0.458227i) q^{12} +(-4.11286 - 4.74649i) q^{13} +(2.52737 + 0.782550i) q^{14} +(0.219703 - 1.52807i) q^{15} +(0.981929 + 0.189251i) q^{16} +(-3.57017 - 5.01360i) q^{17} +(0.723734 - 0.690079i) q^{18} +(0.775548 - 1.08911i) q^{19} +(0.219703 + 1.52807i) q^{20} +(-1.56613 + 2.13242i) q^{21} -0.166384 q^{22} +(1.08147 - 4.67230i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(2.32584 - 1.19906i) q^{25} +(-4.93681 + 3.88235i) q^{26} +(0.415415 + 0.909632i) q^{27} +(0.901921 - 2.48728i) q^{28} +(4.31355 - 9.44535i) q^{29} +(-1.51589 - 0.292163i) q^{30} +(-3.04842 - 2.39731i) q^{31} +(0.235759 - 0.971812i) q^{32} +(0.0544189 - 0.157233i) q^{33} +(-5.17780 + 3.32757i) q^{34} +(4.08403 + 0.0599106i) q^{35} +(-0.654861 - 0.755750i) q^{36} +(-4.52038 - 4.31017i) q^{37} +(-1.05097 - 0.826492i) q^{38} +(-2.05415 - 5.93509i) q^{39} +(1.53679 - 0.146746i) q^{40} +(5.43129 + 1.59477i) q^{41} +(2.05549 + 1.66582i) q^{42} +(1.30751 + 9.09392i) q^{43} +(-0.00791688 + 0.166196i) q^{44} +(0.771892 - 1.33696i) q^{45} +(-4.61555 - 1.30256i) q^{46} +(2.69119 + 4.66128i) q^{47} +(0.841254 + 0.540641i) q^{48} +(-6.12508 - 3.38871i) q^{49} +(-1.08703 - 2.38026i) q^{50} +(-1.45106 - 5.98136i) q^{51} +(3.64305 + 5.11595i) q^{52} +(0.988027 + 2.85472i) q^{53} +(0.928368 - 0.371662i) q^{54} +(-0.246456 + 0.0723662i) q^{55} +(-2.44154 - 1.01925i) q^{56} +(1.12477 - 0.722848i) q^{57} +(-9.22940 - 4.75809i) q^{58} +(-9.28085 + 1.78874i) q^{59} +(-0.363961 + 1.50027i) q^{60} +(2.73959 - 1.09676i) q^{61} +(-2.53964 + 2.93090i) q^{62} +(-2.24649 + 1.39760i) q^{63} +(-0.959493 - 0.281733i) q^{64} +(-5.62408 + 7.89792i) q^{65} +(-0.154466 - 0.0618388i) q^{66} +(-7.54567 + 3.89007i) q^{67} +(3.07743 + 5.33026i) q^{68} +(2.74052 - 3.93568i) q^{69} +(0.254169 - 4.07655i) q^{70} +(11.7576 + 7.55616i) q^{71} +(-0.786053 + 0.618159i) q^{72} +(-13.8729 - 1.32470i) q^{73} +(-4.52038 + 4.31017i) q^{74} +(2.60488 - 0.248736i) q^{75} +(-0.875563 + 1.01045i) q^{76} +(0.430988 + 0.0896418i) q^{77} +(-6.02610 + 1.76942i) q^{78} +(2.65122 - 7.66020i) q^{79} +(-0.0734562 - 1.54203i) q^{80} +(0.0475819 + 0.998867i) q^{81} +(1.85139 - 5.34925i) q^{82} +(7.94535 - 2.33296i) q^{83} +(1.76174 - 1.97390i) q^{84} +(-6.22233 + 7.18096i) q^{85} +(9.14583 - 0.873321i) q^{86} +(7.51504 - 7.16558i) q^{87} +(0.165631 + 0.0158158i) q^{88} +(-3.86146 + 3.03669i) q^{89} +(-1.29871 - 0.834632i) q^{90} +(14.8796 - 7.39674i) q^{91} +(-1.52070 + 4.54835i) q^{92} +(-1.93907 - 3.35857i) q^{93} +(4.78405 - 2.46635i) q^{94} +(-1.91622 - 0.767138i) q^{95} +(0.580057 - 0.814576i) q^{96} +(2.57283 + 0.755451i) q^{97} +(-3.67631 + 5.95691i) q^{98} +(0.108958 - 0.125745i) 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} + 6 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 + 6 * q^7 - 16 * q^8 + 8 * q^9	\( 160 q + 8 q^{2} + 8 q^{3} + 8 q^{4} - 2 q^{5} - 16 q^{6} + 6 q^{7} - 16 q^{8} + 8 q^{9} - 2 q^{10} - 4 q^{11} + 8 q^{12} - 4 q^{13} + 5 q^{14} + 26 q^{15} + 8 q^{16} - 13 q^{17} + 8 q^{18} + 4 q^{19} + 26 q^{20} + 11 q^{21} - 124 q^{22} + 26 q^{23} - 80 q^{24} + 14 q^{25} + 2 q^{26} - 16 q^{27} - 22 q^{28} + 54 q^{29} - 2 q^{30} + 15 q^{31} + 8 q^{32} - 4 q^{33} + 4 q^{34} - 2 q^{35} - 16 q^{36} + 7 q^{37} - 7 q^{38} + 2 q^{39} + 9 q^{40} - 30 q^{41} + 6 q^{42} + 36 q^{43} - 4 q^{44} + 20 q^{45} + 4 q^{46} - 6 q^{47} - 16 q^{48} + 14 q^{49} - 28 q^{50} + 9 q^{51} + 2 q^{52} - 24 q^{53} + 8 q^{54} - 14 q^{55} + 6 q^{56} - 30 q^{57} - 5 q^{58} + 4 q^{59} - 2 q^{60} + 32 q^{61} - 8 q^{62} - 6 q^{63} - 16 q^{64} + 38 q^{65} - 4 q^{66} + 6 q^{67} + 42 q^{68} - 30 q^{69} - 8 q^{70} - 180 q^{71} + 8 q^{72} - 32 q^{73} + 7 q^{74} + 14 q^{75} - 8 q^{76} + 61 q^{77} + 18 q^{78} - 66 q^{79} - 2 q^{80} + 8 q^{81} - 7 q^{82} + 130 q^{83} + 5 q^{84} - 70 q^{85} - 40 q^{86} + 6 q^{87} - 15 q^{88} - 4 q^{89} + 4 q^{90} - 6 q^{91} + 58 q^{92} - 18 q^{93} + 16 q^{94} + 19 q^{95} + 8 q^{96} + 40 q^{97} + 43 q^{98} + 8 q^{99}+O(q^{100}) \) 160 * q + 8 * q^2 + 8 * q^3 + 8 * q^4 - 2 * q^5 - 16 * q^6 + 6 * q^7 - 16 * q^8 + 8 * q^9 - 2 * q^10 - 4 * q^11 + 8 * q^12 - 4 * q^13 + 5 * q^14 + 26 * q^15 + 8 * q^16 - 13 * q^17 + 8 * q^18 + 4 * q^19 + 26 * q^20 + 11 * q^21 - 124 * q^22 + 26 * q^23 - 80 * q^24 + 14 * q^25 + 2 * q^26 - 16 * q^27 - 22 * q^28 + 54 * q^29 - 2 * q^30 + 15 * q^31 + 8 * q^32 - 4 * q^33 + 4 * q^34 - 2 * q^35 - 16 * q^36 + 7 * q^37 - 7 * q^38 + 2 * q^39 + 9 * q^40 - 30 * q^41 + 6 * q^42 + 36 * q^43 - 4 * q^44 + 20 * q^45 + 4 * q^46 - 6 * q^47 - 16 * q^48 + 14 * q^49 - 28 * q^50 + 9 * q^51 + 2 * q^52 - 24 * q^53 + 8 * q^54 - 14 * q^55 + 6 * q^56 - 30 * q^57 - 5 * q^58 + 4 * q^59 - 2 * q^60 + 32 * q^61 - 8 * q^62 - 6 * q^63 - 16 * q^64 + 38 * q^65 - 4 * q^66 + 6 * q^67 + 42 * q^68 - 30 * q^69 - 8 * q^70 - 180 * q^71 + 8 * q^72 - 32 * q^73 + 7 * q^74 + 14 * q^75 - 8 * q^76 + 61 * q^77 + 18 * q^78 - 66 * q^79 - 2 * q^80 + 8 * q^81 - 7 * q^82 + 130 * q^83 + 5 * q^84 - 70 * q^85 - 40 * q^86 + 6 * q^87 - 15 * q^88 - 4 * q^89 + 4 * q^90 - 6 * q^91 + 58 * q^92 - 18 * q^93 + 16 * q^94 + 19 * q^95 + 8 * q^96 + 40 * q^97 + 43 * q^98 + 8 * 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
$5$	−0.363961	−	1.50027i	−0.162768	−	0.670940i	−0.993457	−	0.114203i	$-0.963569\pi$
$5$	−0.363961	−	1.50027i	−0.162768	−	0.670940i	0.830689	−	0.556736i	$-0.187947\pi$
$6$	0.415415	−	0.909632i	0.169592	−	0.371356i
$7$	−0.661406	+	2.56175i	−0.249988	+	0.968249i
$7$	−0.661406	+	2.56175i	−0.249988	+	0.968249i
$8$	−0.142315	+	0.989821i	−0.0503159	+	0.349955i
$9$	0.723734	+	0.690079i	0.241245	+	0.230026i
$10$	−1.51589	+	0.292163i	−0.479365	+	0.0923900i
$11$	−0.00791688	−	0.166196i	−0.00238703	−	0.0501099i	0.997360	−	0.0726219i	$-0.0231366\pi$
$11$	−0.00791688	−	0.166196i	−0.00238703	−	0.0501099i	−0.999747	+	0.0225120i	$0.992834\pi$
$12$	−0.888835	−	0.458227i	−0.256585	−	0.132279i
$13$	−4.11286	−	4.74649i	−1.14070	−	1.31644i	−0.941705	−	0.336440i	$-0.890777\pi$
$13$	−4.11286	−	4.74649i	−1.14070	−	1.31644i	−0.198997	−	0.980000i	$-0.563768\pi$
$14$	2.52737	+	0.782550i	0.675469	+	0.209145i
$15$	0.219703	−	1.52807i	0.0567271	−	0.394546i
$16$	0.981929	+	0.189251i	0.245482	+	0.0473128i
$17$	−3.57017	−	5.01360i	−0.865893	−	1.21598i	−0.975057	−	0.221953i	$-0.928757\pi$
$17$	−3.57017	−	5.01360i	−0.865893	−	1.21598i	0.109165	−	0.994024i	$-0.465182\pi$
$18$	0.723734	−	0.690079i	0.170586	−	0.162653i
$19$	0.775548	−	1.08911i	0.177923	−	0.249858i	−0.715977	−	0.698123i	$-0.754019\pi$
$19$	0.775548	−	1.08911i	0.177923	−	0.249858i	0.893900	+	0.448265i	$0.147958\pi$
$20$	0.219703	+	1.52807i	0.0491271	+	0.341687i
$21$	−1.56613	+	2.13242i	−0.341758	+	0.465333i
$22$	−0.166384			−0.0354732
$23$	1.08147	−	4.67230i	0.225501	−	0.974243i
$23$	1.08147	−	4.67230i	0.225501	−	0.974243i
$24$	−0.500000	+	0.866025i	−0.102062	+	0.176777i
$25$	2.32584	−	1.19906i	0.465169	−	0.239811i
$26$	−4.93681	+	3.88235i	−0.968189	+	0.761392i
$27$	0.415415	+	0.909632i	0.0799467	+	0.175059i
$28$	0.901921	−	2.48728i	0.170447	−	0.470051i
$29$	4.31355	−	9.44535i	0.801006	−	1.75396i	0.158969	−	0.987284i	$-0.449183\pi$
$29$	4.31355	−	9.44535i	0.801006	−	1.75396i	0.642037	−	0.766674i	$-0.278090\pi$
$30$	−1.51589	−	0.292163i	−0.276762	−	0.0533414i
$31$	−3.04842	−	2.39731i	−0.547513	−	0.430569i	0.305703	−	0.952127i	$-0.401109\pi$
$31$	−3.04842	−	2.39731i	−0.547513	−	0.430569i	−0.853216	+	0.521558i	$0.825351\pi$
$32$	0.235759	−	0.971812i	0.0416767	−	0.171794i
$33$	0.0544189	−	0.157233i	0.00947312	−	0.0273708i
$34$	−5.17780	+	3.32757i	−0.887985	+	0.570673i
$35$	4.08403	+	0.0599106i	0.690327	+	0.0101267i
$36$	−0.654861	−	0.755750i	−0.109143	−	0.125958i
$37$	−4.52038	−	4.31017i	−0.743146	−	0.708588i	0.220614	−	0.975361i	$-0.429194\pi$
$37$	−4.52038	−	4.31017i	−0.743146	−	0.708588i	−0.963759	+	0.266773i	$0.914042\pi$
$38$	−1.05097	−	0.826492i	−0.170490	−	0.134075i
$39$	−2.05415	−	5.93509i	−0.328928	−	0.950374i
$40$	1.53679	−	0.146746i	0.242988	−	0.0232026i
$41$	5.43129	+	1.59477i	0.848225	+	0.249061i	0.676828	−	0.736141i	$-0.263354\pi$
$41$	5.43129	+	1.59477i	0.848225	+	0.249061i	0.171396	+	0.985202i	$0.445172\pi$
$42$	2.05549	+	1.66582i	0.317169	+	0.257042i
$43$	1.30751	+	9.09392i	0.199393	+	1.38681i	0.806051	+	0.591846i	$0.201601\pi$
$43$	1.30751	+	9.09392i	0.199393	+	1.38681i	−0.606658	+	0.794963i	$0.707490\pi$
$44$	−0.00791688	+	0.166196i	−0.00119351	+	0.0250549i
$45$	0.771892	−	1.33696i	0.115067	−	0.199302i
$46$	−4.61555	−	1.30256i	−0.680526	−	0.192052i
$47$	2.69119	+	4.66128i	0.392551	+	0.679918i	0.992785	−	0.119906i	$-0.0382594\pi$
$47$	2.69119	+	4.66128i	0.392551	+	0.679918i	−0.600235	+	0.799824i	$0.704926\pi$
$48$	0.841254	+	0.540641i	0.121424	+	0.0780348i
$49$	−6.12508	−	3.38871i	−0.875012	−	0.484101i
$50$	−1.08703	−	2.38026i	−0.153729	−	0.336620i
$51$	−1.45106	−	5.98136i	−0.203189	−	0.837558i
$52$	3.64305	+	5.11595i	0.505201	+	0.709455i
$53$	0.988027	+	2.85472i	0.135716	+	0.392126i	0.992296	−	0.123888i	$-0.0395365\pi$
$53$	0.988027	+	2.85472i	0.135716	+	0.392126i	−0.856580	+	0.516014i	$0.827415\pi$
$54$	0.928368	−	0.371662i	0.126335	−	0.0505769i
$55$	−0.246456	+	0.0723662i	−0.0332322	+	0.00975785i
$56$	−2.44154	−	1.01925i	−0.326265	−	0.136203i
$57$	1.12477	−	0.722848i	0.148980	−	0.0957436i
$58$	−9.22940	−	4.75809i	−1.21188	−	0.624768i
$59$	−9.28085	+	1.78874i	−1.20826	+	0.232874i	−0.753325	−	0.657649i	$-0.771551\pi$
$59$	−9.28085	+	1.78874i	−1.20826	+	0.232874i	−0.454939	+	0.890522i	$0.650339\pi$
$60$	−0.363961	+	1.50027i	−0.0469871	+	0.193684i
$61$	2.73959	−	1.09676i	0.350768	−	0.140426i	−0.189586	−	0.981864i	$-0.560715\pi$
$61$	2.73959	−	1.09676i	0.350768	−	0.140426i	0.540354	+	0.841438i	$0.318290\pi$
$62$	−2.53964	+	2.93090i	−0.322535	+	0.372225i
$63$	−2.24649	+	1.39760i	−0.283031	+	0.176081i
$64$	−0.959493	−	0.281733i	−0.119937	−	0.0352166i
$65$	−5.62408	+	7.89792i	−0.697582	+	0.979617i
$66$	−0.154466	−	0.0618388i	−0.0190134	−	0.00761182i
$67$	−7.54567	+	3.89007i	−0.921851	+	0.475247i	−0.852725	−	0.522361i	$-0.825051\pi$
$67$	−7.54567	+	3.89007i	−0.921851	+	0.475247i	−0.0691262	+	0.997608i	$0.522021\pi$
$68$	3.07743	+	5.33026i	0.373193	+	0.646389i
$69$	2.74052	−	3.93568i	0.329920	−	0.473800i
$70$	0.254169	−	4.07655i	0.0303790	−	0.487241i
$71$	11.7576	+	7.55616i	1.39537	+	0.896751i	0.999765	−	0.0216692i	$-0.00689807\pi$
$71$	11.7576	+	7.55616i	1.39537	+	0.896751i	0.395606	+	0.918420i	$0.370534\pi$
$72$	−0.786053	+	0.618159i	−0.0926372	+	0.0728507i
$73$	−13.8729	−	1.32470i	−1.62370	−	0.155045i	−0.756843	−	0.653597i	$-0.773259\pi$
$73$	−13.8729	−	1.32470i	−1.62370	−	0.155045i	−0.866860	+	0.498552i	$0.833865\pi$
$74$	−4.52038	+	4.31017i	−0.525483	+	0.501047i
$75$	2.60488	−	0.248736i	0.300786	−	0.0287216i
$76$	−0.875563	+	1.01045i	−0.100434	+	0.115907i
$77$	0.430988	+	0.0896418i	0.0491156	+	0.0102156i
$78$	−6.02610	+	1.76942i	−0.682322	+	0.200348i
$79$	2.65122	−	7.66020i	0.298286	−	0.861840i	−0.691889	−	0.722004i	$-0.743221\pi$
$79$	2.65122	−	7.66020i	0.298286	−	0.861840i	0.990175	−	0.139836i	$-0.0446575\pi$
$80$	−0.0734562	−	1.54203i	−0.00821265	−	0.172405i
$81$	0.0475819	+	0.998867i	0.00528688	+	0.110985i
$82$	1.85139	−	5.34925i	0.204452	−	0.590726i
$83$	7.94535	−	2.33296i	0.872115	−	0.256076i	0.185100	−	0.982720i	$-0.440739\pi$
$83$	7.94535	−	2.33296i	0.872115	−	0.256076i	0.687015	+	0.726644i	$0.258921\pi$
$84$	1.76174	−	1.97390i	0.192222	−	0.215370i
$85$	−6.22233	+	7.18096i	−0.674907	+	0.778884i
$86$	9.14583	−	0.873321i	0.986220	−	0.0941726i
$87$	7.51504	−	7.16558i	0.805697	−	0.768230i
$88$	0.165631	+	0.0158158i	0.0176563	+	0.00168597i
$89$	−3.86146	+	3.03669i	−0.409314	+	0.321888i	−0.801497	−	0.597999i	$-0.795963\pi$
$89$	−3.86146	+	3.03669i	−0.409314	+	0.321888i	0.392182	+	0.919887i	$0.371720\pi$
$90$	−1.29871	−	0.834632i	−0.136896	−	0.0879780i
$91$	14.8796	−	7.39674i	1.55980	−	0.775389i
$92$	−1.52070	+	4.54835i	−0.158544	+	0.474198i
$93$	−1.93907	−	3.35857i	−0.201072	−	0.348267i
$94$	4.78405	−	2.46635i	0.493437	−	0.254385i
$95$	−1.91622	−	0.767138i	−0.196600	−	0.0787067i
$96$	0.580057	−	0.814576i	0.0592018	−	0.0831373i
$97$	2.57283	+	0.755451i	0.261231	+	0.0767045i	0.409726	−	0.912209i	$-0.365624\pi$
$97$	2.57283	+	0.755451i	0.261231	+	0.0767045i	−0.148494	+	0.988913i	$0.547443\pi$
$98$	−3.67631	+	5.95691i	−0.371364	+	0.601738i
$99$	0.108958	−	0.125745i	0.0109507	−	0.0126378i
$100$	−2.42929	+	0.972541i	−0.242929	+	0.0972541i
$101$	2.12441	−	8.75692i	0.211386	−	0.871346i	−0.762988	−	0.646413i	$-0.776268\pi$
$101$	2.12441	−	8.75692i	0.211386	−	0.871346i	0.974374	−	0.224933i	$-0.0722165\pi$
$102$	−6.04363	+	1.16481i	−0.598409	+	0.115334i
$103$	4.97541	+	2.56500i	0.490242	+	0.252737i	0.685578	−	0.727999i	$-0.259549\pi$
$103$	4.97541	+	2.56500i	0.490242	+	0.252737i	−0.195336	+	0.980736i	$0.562580\pi$
$104$	5.28350	−	3.39550i	0.518090	−	0.332956i
$105$	3.76921	+	1.57350i	0.367838	+	0.153558i
$106$	2.89850	−	0.851075i	0.281527	−	0.0826637i
$107$	−9.60537	+	3.84541i	−0.928586	+	0.371750i	−0.786137	−	0.618052i	$-0.787922\pi$
$107$	−9.60537	+	3.84541i	−0.928586	+	0.371750i	−0.142449	+	0.989802i	$0.545498\pi$
$108$	−0.327068	−	0.945001i	−0.0314721	−	0.0909327i
$109$	0.528923	+	0.742768i	0.0506616	+	0.0711443i	0.839130	−	0.543931i	$-0.183065\pi$
$109$	0.528923	+	0.742768i	0.0506616	+	0.0711443i	−0.788468	+	0.615076i	$0.789125\pi$
$110$	0.0605573	+	0.249621i	0.00577391	+	0.0238004i
$111$	−2.59465	−	5.68148i	−0.246273	−	0.539262i
$112$	−1.13427	+	2.39028i	−0.107178	+	0.225860i
$113$	3.29120	+	2.11512i	0.309610	+	0.198974i	0.686213	−	0.727400i	$-0.259272\pi$
$113$	3.29120	+	2.11512i	0.309610	+	0.198974i	−0.376604	+	0.926375i	$0.622908\pi$
$114$	−0.668511	−	1.15789i	−0.0626118	−	0.108447i
$115$	−7.40331	+	0.0780481i	−0.690363	+	0.00727802i
$116$	−5.19185	+	8.99255i	−0.482051	+	0.834937i
$117$	0.298839	−	6.27340i	0.0276276	−	0.579976i
$118$	1.34511	+	9.35545i	0.123827	+	0.861239i
$119$	15.2049	−	5.82984i	1.39383	−	0.534420i
$120$	1.48125	+	0.434934i	0.135219	+	0.0397039i
$121$	10.9226	−	1.04298i	0.992967	−	0.0948168i
$122$	−0.965168	−	2.78867i	−0.0873822	−	0.252474i
$123$	4.44952	+	3.49914i	0.401199	+	0.315507i
$124$	2.80674	+	2.67622i	0.252053	+	0.240332i
$125$	−7.70024	−	8.88655i	−0.688730	−	0.794837i
$126$	1.28912	+	2.31045i	0.114844	+	0.205831i
$127$	−0.331179	+	0.212836i	−0.0293873	+	0.0188861i	−0.555252	−	0.831682i	$-0.687378\pi$
$127$	−0.331179	+	0.212836i	−0.0293873	+	0.0188861i	0.525865	+	0.850568i	$0.323742\pi$
$128$	−0.327068	+	0.945001i	−0.0289090	+	0.0835271i
$129$	−2.16602	+	8.92845i	−0.190707	+	0.786106i
$130$	7.62137	+	5.99351i	0.668439	+	0.525666i
$131$	−7.09375	−	1.36721i	−0.619784	−	0.119454i	−0.130313	−	0.991473i	$-0.541598\pi$
$131$	−7.09375	−	1.36721i	−0.619784	−	0.119454i	−0.489471	+	0.872019i	$0.662810\pi$
$132$	−0.0691185	+	0.151348i	−0.00601599	+	0.0131732i
$133$	2.27706	+	2.70710i	0.197446	+	0.234735i
$134$	3.52662	+	7.72222i	0.304654	+	0.667099i
$135$	1.21350	−	0.954304i	0.104441	−	0.0821334i
$136$	5.47066	−	2.82032i	0.469105	−	0.241840i
$137$	−5.01350	+	8.68364i	−0.428332	+	0.741893i	−0.996725	−	0.0808641i	$-0.974232\pi$
$137$	−5.01350	+	8.68364i	−0.428332	+	0.741893i	0.568393	+	0.822757i	$0.307565\pi$
$138$	−3.80082	−	2.92468i	−0.323547	−	0.248965i
$139$	7.57948			0.642883			0.321442	−	0.946929i	$-0.395833\pi$
$139$	7.57948			0.642883			0.321442	+	0.946929i	$0.395833\pi$
$140$	−4.05984	−	0.447851i	−0.343119	−	0.0378503i
$141$	0.765993	+	5.32760i	0.0645083	+	0.448665i
$142$	8.10705	−	11.3848i	0.680328	−	0.955388i
$143$	−0.756286	+	0.721117i	−0.0632438	+	0.0603028i
$144$	0.580057	+	0.814576i	0.0483381	+	0.0678813i
$145$	−15.7405	−	3.03373i	−1.30718	−	0.251938i
$146$	−1.98330	+	13.7942i	−0.164139	+	1.14161i
$147$	−4.42688	−	5.42243i	−0.365123	−	0.447235i
$148$	4.09020	+	4.72034i	0.336213	+	0.388010i
$149$	16.7748	+	8.64799i	1.37424	+	0.708471i	0.977790	−	0.209585i	$-0.0672112\pi$
$149$	16.7748	+	8.64799i	1.37424	+	0.708471i	0.396451	+	0.918056i	$0.370242\pi$
$150$	−0.124509	−	2.61377i	−0.0101661	−	0.213413i
$151$	−14.5613	+	2.80647i	−1.18499	+	0.228387i	−0.743409	−	0.668837i	$-0.766793\pi$
$151$	−14.5613	+	2.80647i	−1.18499	+	0.228387i	−0.441576	+	0.897224i	$0.645580\pi$
$152$	0.967648	+	0.922650i	0.0784866	+	0.0748368i
$153$	0.875928	−	6.09221i	0.0708145	−	0.492526i
$154$	0.110048	−	0.426234i	0.00886788	−	0.0343469i
$155$	−2.48709	+	5.44597i	−0.199768	+	0.437431i
$156$	1.48069	+	6.10347i	0.118550	+	0.488669i
$157$	−10.0253	−	0.957298i	−0.800104	−	0.0764007i	−0.313010	−	0.949750i	$-0.601337\pi$
$157$	−10.0253	−	0.957298i	−0.800104	−	0.0764007i	−0.487094	+	0.873349i	$0.661943\pi$
$158$	−7.52537	−	3.01270i	−0.598686	−	0.239678i
$159$	−0.143738	+	3.01744i	−0.0113992	+	0.239299i
$160$	−1.54378			−0.122047
$161$	11.2540	+	5.86073i	0.886937	+	0.461890i
$162$	1.00000			0.0785674
$163$	0.648572	−	13.6152i	0.0508001	−	1.06642i	−0.819242	−	0.573448i	$-0.805606\pi$
$163$	0.648572	−	13.6152i	0.0508001	−	1.06642i	0.870042	−	0.492977i	$-0.164091\pi$
$164$	−5.25510	−	2.10383i	−0.410354	−	0.164281i
$165$	−0.255698	−	0.0244162i	−0.0199061	−	0.00190080i
$166$	−1.95227	−	8.04735i	−0.151525	−	0.624596i
$167$	−3.49984	+	7.66357i	−0.270825	+	0.593025i	−0.995361	−	0.0962126i	$-0.969327\pi$
$167$	−3.49984	+	7.66357i	−0.270825	+	0.593025i	0.724535	+	0.689238i	$0.242054\pi$
$168$	−1.88783	−	1.85367i	−0.145650	−	0.143014i
$169$	−3.76349	+	26.1756i	−0.289499	+	2.01351i
$170$	6.87675	+	6.55697i	0.527423	+	0.502897i
$171$	1.31286	−	0.253033i	0.100397	−	0.0193499i
$172$	−0.437156	−	9.17702i	−0.0333328	−	0.699742i
$173$	18.7800	+	9.68176i	1.42782	+	0.736091i	0.986881	−	0.161448i	$-0.0516165\pi$
$173$	18.7800	+	9.68176i	1.42782	+	0.736091i	0.440935	+	0.897539i	$0.354647\pi$
$174$	−6.79988	−	7.84748i	−0.515498	−	0.594916i
$175$	1.53335	+	6.75129i	0.115910	+	0.510349i
$176$	0.0236789	−	0.164691i	0.00178487	−	0.0124140i
$177$	−9.28085	−	1.78874i	−0.697592	−	0.134450i
$178$	2.84951	+	4.00158i	0.213580	+	0.299931i
$179$	5.47497	−	5.22037i	0.409218	−	0.390189i	−0.457318	−	0.889303i	$-0.651190\pi$
$179$	5.47497	−	5.22037i	0.409218	−	0.390189i	0.866536	+	0.499114i	$0.166341\pi$
$180$	−0.895482	+	1.25753i	−0.0667453	+	0.0937307i
$181$	−2.59098	−	18.0206i	−0.192586	−	1.33946i	−0.825132	−	0.564940i	$-0.808899\pi$
$181$	−2.59098	−	18.0206i	−0.192586	−	1.33946i	0.632546	−	0.774523i	$-0.282010\pi$
$182$	−6.68036	−	15.2147i	−0.495182	−	1.12779i
$183$	2.95097			0.218142
$184$	4.47084	+	1.73540i	0.329595	+	0.127935i
$185$	−4.82117	+	8.35051i	−0.354459	+	0.613941i
$186$	−3.44703	+	1.77707i	−0.252748	+	0.130301i
$187$	−0.804974	+	0.633039i	−0.0588655	+	0.0462924i
$188$	−2.23592	−	4.89599i	−0.163071	−	0.357077i
$189$	−2.60500	+	0.462552i	−0.189486	+	0.0336457i
$190$	−0.857446	+	1.87755i	−0.0622057	+	0.136211i
$191$	−4.16888	−	0.803486i	−0.301650	−	0.0581382i	0.0361806	−	0.999345i	$-0.488481\pi$
$191$	−4.16888	−	0.803486i	−0.301650	−	0.0581382i	−0.337830	+	0.941207i	$0.609693\pi$
$192$	−0.786053	−	0.618159i	−0.0567285	−	0.0446118i
$193$	−2.26722	+	9.34562i	−0.163198	+	0.672712i	0.830148	+	0.557543i	$0.188256\pi$
$193$	−2.26722	+	9.34562i	−0.163198	+	0.672712i	−0.993346	+	0.115169i	$0.963259\pi$
$194$	0.877016	−	2.53397i	0.0629661	−	0.181929i
$195$	−8.15658	+	5.24192i	−0.584105	+	0.375381i
$196$	5.77523	+	3.95559i	0.412517	+	0.282542i
$197$	−0.903934	−	1.04320i	−0.0644026	−	0.0743246i	0.722634	−	0.691231i	$-0.242931\pi$
$197$	−0.903934	−	1.04320i	−0.0644026	−	0.0743246i	−0.787037	+	0.616906i	$0.788386\pi$
$198$	−0.120418	−	0.114818i	−0.00855773	−	0.00815978i
$199$	16.2722	+	12.7966i	1.15351	+	0.907128i	0.996754	−	0.0805093i	$-0.0256547\pi$
$199$	16.2722	+	12.7966i	1.15351	+	0.907128i	0.156754	+	0.987638i	$0.449897\pi$
$200$	0.855849	+	2.47281i	0.0605177	+	0.174854i
$201$	−8.45095	+	0.806968i	−0.596084	+	0.0569191i
$202$	−8.64592	−	2.53867i	−0.608325	−	0.178620i
$203$	21.3436	+	17.2974i	1.49803	+	1.21404i
$204$	0.875928	+	6.09221i	0.0613272	+	0.426540i
$205$	0.415805	−	8.72881i	0.0290411	−	0.609647i
$206$	2.79884	−	4.84773i	0.195004	−	0.337757i
$207$	4.00695	−	2.63521i	0.278502	−	0.183160i
$208$	−3.14025	−	5.43908i	−0.217737	−	0.377132i
$209$	−0.187145	−	0.120271i	−0.0129451	−	0.00831929i
$210$	1.75106	−	3.69007i	0.120835	−	0.254639i
$211$	−10.5311	−	23.0599i	−0.724990	−	1.58751i	−0.806776	−	0.590858i	$-0.798789\pi$
$211$	−10.5311	−	23.0599i	−0.724990	−	1.58751i	0.0817854	−	0.996650i	$-0.473938\pi$
$212$	−0.712195	−	2.93571i	−0.0489138	−	0.201625i
$213$	8.10705	+	11.3848i	0.555486	+	0.780071i
$214$	3.38401	+	9.77746i	0.231326	+	0.668374i
$215$	13.1674	−	5.27144i	0.898010	−	0.359509i
$216$	−0.959493	+	0.281733i	−0.0652852	+	0.0191695i
$217$	8.15753	−	6.22369i	0.553769	−	0.422492i
$218$	0.767094	−	0.492982i	0.0519542	−	0.0333889i
$219$	−12.3868	−	6.38586i	−0.837024	−	0.431516i
$220$	0.252219	−	0.0486113i	0.0170046	−	0.00327737i
$221$	−9.11341	+	37.5660i	−0.613034	+	2.52696i
$222$	−5.79850	+	2.32137i	−0.389170	+	0.155800i
$223$	−5.98067	+	6.90206i	−0.400495	+	0.462196i	−0.919797	−	0.392395i	$-0.871647\pi$
$223$	−5.98067	+	6.90206i	−0.400495	+	0.462196i	0.519302	+	0.854591i	$0.326192\pi$
$224$	2.33360	+	1.24672i	0.155920	+	0.0832998i
$225$	2.51074	+	0.737219i	0.167382	+	0.0491479i
$226$	2.26933	−	3.18683i	0.150954	−	0.211985i
$227$	11.5340	+	4.61752i	0.765540	+	0.306476i	0.721372	−	0.692548i	$-0.243512\pi$
$227$	11.5340	+	4.61752i	0.765540	+	0.306476i	0.0441682	+	0.999024i	$0.485936\pi$
$228$	−1.18839	+	0.612659i	−0.0787032	+	0.0405743i
$229$	1.63100	+	2.82498i	0.107780	+	0.186680i	0.914870	−	0.403747i	$-0.132293\pi$
$229$	1.63100	+	2.82498i	0.107780	+	0.186680i	−0.807091	+	0.590427i	$0.798959\pi$
$230$	−0.274304	+	7.39864i	−0.0180871	+	0.487852i
$231$	0.366798	+	0.243402i	0.0241336	+	0.0160147i
$232$	8.73533	+	5.61385i	0.573502	+	0.368568i
$233$	18.5867	−	14.6168i	1.21766	−	0.957576i	0.217827	−	0.975987i	$-0.430103\pi$
$233$	18.5867	−	14.6168i	1.21766	−	0.957576i	0.999830	+	0.0184112i	$0.00586080\pi$
$234$	−6.25207	−	0.597000i	−0.408711	−	0.0390271i
$235$	6.01368	−	5.73403i	0.392289	−	0.374047i
$236$	9.40886	−	0.898437i	0.612465	−	0.0584833i
$237$	5.30832	−	6.12612i	0.344812	−	0.397934i
$238$	−5.09976	−	15.4651i	−0.330568	−	1.00245i
$239$	11.0116	−	3.23330i	0.712283	−	0.209145i	0.0945351	−	0.995522i	$-0.469864\pi$
$239$	11.0116	−	3.23330i	0.712283	−	0.209145i	0.617748	+	0.786376i	$0.288045\pi$
$240$	0.504922	−	1.45888i	0.0325926	−	0.0941701i
$241$	−0.479575	−	10.0675i	−0.0308921	−	0.648506i	−0.960219	−	0.279248i	$-0.909915\pi$
$241$	−0.479575	−	10.0675i	−0.0308921	−	0.648506i	0.929327	−	0.369258i	$-0.120388\pi$
$242$	−0.522084	−	10.9599i	−0.0335608	−	0.704528i
$243$	−0.327068	+	0.945001i	−0.0209814	+	0.0606218i
$244$	−2.83143	+	0.831384i	−0.181264	+	0.0532239i
$245$	−2.85468	+	10.4226i	−0.182379	+	0.665876i
$246$	3.70689	−	4.27798i	0.236343	−	0.272754i
$247$	−8.35915	+	0.798202i	−0.531880	+	0.0507884i
$248$	2.80674	−	2.67622i	0.178228	−	0.169940i
$249$	8.24328	+	0.787138i	0.522397	+	0.0498828i
$250$	−9.24287	+	7.26868i	−0.584571	+	0.459711i
$251$	−22.2700	−	14.3120i	−1.40567	−	0.903368i	−0.405725	−	0.913995i	$-0.632981\pi$
$251$	−22.2700	−	14.3120i	−1.40567	−	0.903368i	−0.999944	+	0.0106266i	$0.996617\pi$
$252$	2.36917	−	1.17773i	0.149244	−	0.0741900i
$253$	−0.785079	−	0.142745i	−0.0493575	−	0.00897430i
$254$	0.196836	+	0.340931i	0.0123506	+	0.0213919i
$255$	−8.44551	+	4.35396i	−0.528878	+	0.272656i
$256$	0.928368	+	0.371662i	0.0580230	+	0.0232289i
$257$	4.30476	−	6.04519i	0.268524	−	0.377089i	−0.658193	−	0.752849i	$-0.728679\pi$
$257$	4.30476	−	6.04519i	0.268524	−	0.377089i	0.926717	+	0.375760i	$0.122618\pi$
$258$	8.81528	+	2.58840i	0.548815	+	0.161147i
$259$	14.0314	−	8.72929i	0.871867	−	0.542411i
$260$	6.34936	−	7.32756i	0.393771	−	0.454436i
$261$	9.63990	−	3.85923i	0.596695	−	0.238881i
$262$	−1.70319	+	7.02067i	−0.105224	+	0.433738i
$263$	16.5318	−	3.18625i	1.01940	−	0.196472i	0.347940	−	0.937517i	$-0.386881\pi$
$263$	16.5318	−	3.18625i	1.01940	−	0.196472i	0.671456	+	0.741045i	$0.265669\pi$
$264$	0.147888	+	0.0762416i	0.00910189	+	0.00469235i
$265$	3.92323	−	2.52131i	0.241002	−	0.154883i
$266$	2.81238	−	2.14567i	0.172438	−	0.131560i
$267$	−4.71348	+	1.38400i	−0.288460	+	0.0846996i
$268$	7.88128	−	3.15519i	0.481426	−	0.192734i
$269$	−1.34083	−	3.87408i	−0.0817520	−	0.236207i	0.896716	−	0.442607i	$-0.145946\pi$
$269$	−1.34083	−	3.87408i	−0.0817520	−	0.236207i	−0.978468	+	0.206400i	$0.933825\pi$
$270$	−0.895482	−	1.25753i	−0.0544973	−	0.0765308i
$271$	3.08134	+	12.7015i	0.187178	+	0.771558i	0.985549	+	0.169392i	$0.0541804\pi$
$271$	3.08134	+	12.7015i	0.187178	+	0.771558i	−0.798371	+	0.602166i	$0.794304\pi$
$272$	−2.55682	−	5.59866i	−0.155030	−	0.339468i
$273$	16.5628	−	1.33672i	1.00243	−	0.0809018i
$274$	8.43525	+	5.42101i	0.509592	+	0.327495i
$275$	−0.217691	−	0.377053i	−0.0131273	−	0.0227371i
$276$	−3.10222	+	3.65735i	−0.186732	+	0.220147i
$277$	11.3006	−	19.5731i	0.678985	−	1.17604i	−0.296302	−	0.955094i	$-0.595753\pi$
$277$	11.3006	−	19.5731i	0.678985	−	1.17604i	0.975287	−	0.220942i	$-0.0709132\pi$
$278$	0.360646	−	7.57090i	0.0216301	−	0.454072i
$279$	−0.551917	−	3.83866i	−0.0330424	−	0.229815i
$280$	−0.640518	+	4.03393i	−0.0382783	+	0.241074i
$281$	29.9202	+	8.78537i	1.78489	+	0.524091i	0.995912	−	0.0903296i	$-0.0287921\pi$
$281$	29.9202	+	8.78537i	1.78489	+	0.524091i	0.788979	+	0.614421i	$0.210610\pi$
$282$	5.35801	−	0.511628i	0.319065	−	0.0304670i
$283$	3.97300	+	11.4792i	0.236170	+	0.682369i	0.999345	+	0.0361773i	$0.0115181\pi$
$283$	3.97300	+	11.4792i	0.236170	+	0.682369i	−0.763175	+	0.646192i	$0.776361\pi$
$284$	−10.9861	−	8.63957i	−0.651906	−	0.512664i
$285$	−1.49384	−	1.42437i	−0.0884874	−	0.0843725i
$286$	0.684315	+	0.789741i	0.0404644	+	0.0466984i
$287$	−7.67768	+	12.8588i	−0.453199	+	0.759030i
$288$	0.841254	−	0.540641i	0.0495713	−	0.0318576i
$289$	−6.82992	+	19.7338i	−0.401760	+	1.16081i
$290$	−3.77926	+	15.5783i	−0.221926	+	0.914791i
$291$	2.10776	+	1.65756i	0.123559	+	0.0971680i
$292$	13.6842	+	2.63741i	0.800806	+	0.154343i
$293$	6.75475	−	14.7908i	0.394617	−	0.864090i	−0.603171	−	0.797612i	$-0.706096\pi$
$293$	6.75475	−	14.7908i	0.394617	−	0.864090i	0.997788	−	0.0664782i	$-0.0211763\pi$
$294$	−5.62693	+	4.16385i	−0.328169	+	0.242841i
$295$	6.06145	+	13.2727i	0.352911	+	0.772768i
$296$	4.90962	−	3.86097i	0.285366	−	0.224414i
$297$	0.147888	−	0.0762416i	0.00858134	−	0.00442399i
$298$	9.43637	−	16.3443i	0.546634	−	0.946798i
$299$	−26.6250	+	14.0834i	−1.53976	+	0.814462i
$300$	−2.61673			−0.151077
$301$	−24.1611	−	2.66527i	−1.39262	−	0.153624i
$302$	2.11043	+	14.6784i	0.121442	+	0.844646i
$303$	5.22685	−	7.34008i	0.300275	−	0.421677i
$304$	0.967648	−	0.922650i	0.0554984	−	0.0529176i
$305$	−2.64254	−	3.71093i	−0.151311	−	0.212487i
$306$	−6.04363	−	1.16481i	−0.345491	−	0.0665880i
$307$	4.33090	−	30.1221i	0.247177	−	1.71916i	−0.367197	−	0.930143i	$-0.619683\pi$
$307$	4.33090	−	30.1221i	0.247177	−	1.71916i	0.614375	−	0.789014i	$-0.289408\pi$
$308$	−0.420515	−	0.130204i	−0.0239611	−	0.00741906i
$309$	3.66570	+	4.23044i	0.208534	+	0.240661i
$310$	5.32146	+	2.74340i	0.302239	+	0.155815i
$311$	−1.00555	−	21.1090i	−0.0570193	−	1.19698i	−0.828225	−	0.560396i	$-0.810649\pi$
$311$	−1.00555	−	21.1090i	−0.0570193	−	1.19698i	0.771206	−	0.636586i	$-0.219654\pi$
$312$	6.16701	−	1.18859i	0.349138	−	0.0672909i
$313$	−0.686207	−	0.654298i	−0.0387867	−	0.0369831i	0.670438	−	0.741966i	$-0.266106\pi$
$313$	−0.686207	−	0.654298i	−0.0387867	−	0.0369831i	−0.709225	+	0.704983i	$0.750955\pi$
$314$	−1.43323	+	9.96837i	−0.0808821	+	0.562548i
$315$	2.91441	+	2.86166i	0.164208	+	0.161236i
$316$	−3.36736	+	7.37350i	−0.189429	+	0.414792i
$317$	−5.24962	−	21.6392i	−0.294848	−	1.21538i	−0.905798	−	0.423710i	$-0.860727\pi$
$317$	−5.24962	−	21.6392i	−0.294848	−	1.21538i	0.610950	−	0.791669i	$-0.290788\pi$
$318$	3.00718	+	0.287151i	0.168634	+	0.0161026i
$319$	−1.60393	−	0.642115i	−0.0898027	−	0.0359516i
$320$	−0.0734562	+	1.54203i	−0.00410632	+	0.0862024i
$321$	−10.3465			−0.577486
$322$	6.38958	−	10.9624i	0.356077	−	0.610908i
$323$	−8.22918			−0.457884
$324$	0.0475819	−	0.998867i	0.00264344	−	0.0554926i
$325$	−15.2572	−	6.10806i	−0.846316	−	0.338814i
$326$	−13.5689	−	1.29567i	−0.751513	−	0.0717608i
$327$	0.214976	+	0.886143i	0.0118882	+	0.0490038i
$328$	−2.35149	+	5.14905i	−0.129839	+	0.284308i
$329$	−13.7210	+	3.81115i	−0.756463	+	0.210116i
$330$	−0.0365552	+	0.254247i	−0.00201230	+	0.0139958i
$331$	11.7595	+	11.2127i	0.646362	+	0.616305i	0.940636	−	0.339416i	$-0.110230\pi$
$331$	11.7595	+	11.2127i	0.646362	+	0.616305i	−0.294275	+	0.955721i	$0.595078\pi$
$332$	−8.13113	+	1.56715i	−0.446254	+	0.0860084i
$333$	−0.297192	−	6.23884i	−0.0162860	−	0.341886i
$334$	7.48836	+	3.86052i	0.409745	+	0.211238i
$335$	8.58246	+	9.90469i	0.468910	+	0.541151i
$336$	−1.94139	+	1.79749i	−0.105912	+	0.0980614i
$337$	−4.43069	+	30.8161i	−0.241355	+	1.67866i	0.403984	+	0.914766i	$0.367625\pi$
$337$	−4.43069	+	30.8161i	−0.241355	+	1.67866i	−0.645340	+	0.763896i	$0.723284\pi$
$338$	25.9669	+	5.00471i	1.41241	+	0.272220i
$339$	2.26933	+	3.18683i	0.123253	+	0.173085i
$340$	6.87675	−	6.55697i	0.372944	−	0.355602i
$341$	−0.374288	+	0.525614i	−0.0202688	+	0.0284636i
$342$	−0.190278	−	1.32341i	−0.0102891	−	0.0715619i
$343$	12.7322	−	13.4496i	0.687473	−	0.726210i
$344$	−9.18743			−0.495353
$345$	−6.90201	−	2.67908i	−0.371592	−	0.144237i
$346$	10.5644	−	18.2980i	0.567945	−	0.983709i
$347$	11.3162	−	5.83388i	0.607483	−	0.313179i	−0.126899	−	0.991916i	$-0.540502\pi$
$347$	11.3162	−	5.83388i	0.607483	−	0.313179i	0.734382	+	0.678736i	$0.237472\pi$
$348$	−8.16214	+	6.41878i	−0.437537	+	0.344083i
$349$	−0.813685	−	1.78172i	−0.0435556	−	0.0953734i	0.886603	−	0.462530i	$-0.153058\pi$
$349$	−0.813685	−	1.78172i	−0.0435556	−	0.0953734i	−0.930159	+	0.367157i	$0.880331\pi$
$350$	6.81660	−	1.21037i	0.364363	−	0.0646972i
$351$	2.60902	−	5.71295i	0.139259	−	0.304935i
$352$	−0.163377	−	0.0314884i	−0.00870805	−	0.00167834i
$353$	−21.3018	−	16.7519i	−1.13378	−	0.891615i	−0.138665	−	0.990339i	$-0.544281\pi$
$353$	−21.3018	−	16.7519i	−1.13378	−	0.891615i	−0.995115	+	0.0987247i	$0.968524\pi$
$354$	−2.22831	+	9.18523i	−0.118433	+	0.488189i
$355$	7.05694	−	20.3897i	0.374544	−	1.08217i
$356$	4.13264	−	2.65588i	0.219029	−	0.140762i
$357$	16.2825	+	0.238855i	0.861760	+	0.0126416i
$358$	−4.95395	−	5.71716i	−0.261824	−	0.302161i
$359$	3.09868	+	2.95459i	0.163542	+	0.155937i	0.767431	−	0.641131i	$-0.221535\pi$
$359$	3.09868	+	2.95459i	0.163542	+	0.155937i	−0.603889	+	0.797068i	$0.706383\pi$
$360$	1.21350	+	0.954304i	0.0639568	+	0.0502962i
$361$	5.62962	+	16.2657i	0.296296	+	0.856090i
$362$	−18.1235	+	1.73059i	−0.952550	+	0.0909575i
$363$	10.5279	+	3.09126i	0.552569	+	0.162249i
$364$	−15.5153	+	5.94885i	−0.813223	+	0.311805i
$365$	3.06179	+	21.2952i	0.160261	+	1.11464i
$366$	0.140413	−	2.94763i	0.00733949	−	0.154075i
$367$	6.26934	−	10.8588i	0.327257	−	0.566826i	−0.654709	−	0.755881i	$-0.727209\pi$
$367$	6.26934	−	10.8588i	0.327257	−	0.566826i	0.981967	+	0.189055i	$0.0605424\pi$
$368$	1.94616	−	4.38320i	0.101451	−	0.228490i
$369$	2.83029	+	4.90221i	0.147339	+	0.255199i
$370$	8.11165	+	5.21304i	0.421704	+	0.271013i
$371$	−7.96655	+	0.642947i	−0.413602	+	0.0333802i
$372$	1.61104	+	3.52768i	0.0835284	+	0.182902i
$373$	8.42900	+	34.7448i	0.436437	+	1.79902i	0.586052	+	0.810273i	$0.300681\pi$
$373$	8.42900	+	34.7448i	0.436437	+	1.79902i	−0.149615	+	0.988744i	$0.547803\pi$
$374$	0.594019	+	0.834184i	0.0307160	+	0.0431346i
$375$	−3.84586	−	11.1119i	−0.198599	−	0.573815i
$376$	−4.99683	+	2.00043i	−0.257692	+	0.103164i
$377$	−62.5733	+	18.3732i	−3.22269	+	0.946267i
$378$	0.338077	+	2.62406i	0.0173888	+	0.134967i
$379$	12.2413	−	7.86703i	0.628795	−	0.404102i	−0.187068	−	0.982347i	$-0.559898\pi$
$379$	12.2413	−	7.86703i	0.628795	−	0.404102i	0.815863	+	0.578245i	$0.196262\pi$
$380$	1.83462	+	0.945812i	0.0941140	+	0.0485191i
$381$	−0.386558	+	0.0745030i	−0.0198040	+	0.00381691i
$382$	−1.00094	+	4.12593i	−0.0512125	+	0.211101i
$383$	19.5303	−	7.81877i	0.997954	−	0.399520i	0.185562	−	0.982633i	$-0.440589\pi$
$383$	19.5303	−	7.81877i	0.997954	−	0.399520i	0.812392	+	0.583112i	$0.198165\pi$
$384$	−0.654861	+	0.755750i	−0.0334182	+	0.0385667i
$385$	−0.0223759	−	0.679222i	−0.00114038	−	0.0346164i
$386$	9.22715	+	2.70934i	0.469650	+	0.137902i
$387$	−5.32923	+	7.48386i	−0.270900	+	0.380426i
$388$	−2.48937	−	0.996594i	−0.126379	−	0.0505944i
$389$	−23.8969	+	12.3197i	−1.21162	+	0.624633i	−0.941115	−	0.338086i	$-0.890221\pi$
$389$	−23.8969	+	12.3197i	−1.21162	+	0.624633i	−0.270504	+	0.962719i	$0.587190\pi$
$390$	4.84787	+	8.39676i	0.245482	+	0.425187i
$391$	−27.2861	+	11.2589i	−1.37992	+	0.569386i
$392$	4.22591	−	5.58048i	0.213441	−	0.281857i
$393$	−6.07747	−	3.90576i	−0.306568	−	0.197019i
$394$	−1.08502	+	0.853273i	−0.0546627	+	0.0429873i
$395$	−12.4573	−	1.18953i	−0.626794	−	0.0598515i
$396$	−0.120418	+	0.114818i	−0.00605123	+	0.00576983i
$397$	−6.18117	+	0.590230i	−0.310224	+	0.0296228i	−0.249007	−	0.968502i	$-0.580104\pi$
$397$	−6.18117	+	0.590230i	−0.310224	+	0.0296228i	−0.0612169	+	0.998124i	$0.519498\pi$
$398$	13.5564	−	15.6449i	0.679520	−	0.784208i
$399$	1.10782	+	3.35948i	0.0554604	+	0.168184i
$400$	2.51074	−	0.737219i	0.125537	−	0.0368609i
$401$	−2.64763	+	7.64984i	−0.132217	+	0.382015i	−0.991604	−	0.129310i	$-0.958724\pi$
$401$	−2.64763	+	7.64984i	−0.132217	+	0.382015i	0.859388	+	0.511325i	$0.170845\pi$
$402$	0.403942	+	8.47978i	0.0201468	+	0.422933i
$403$	1.15894	+	24.3291i	0.0577308	+	1.21192i
$404$	−2.94719	+	8.51533i	−0.146628	+	0.423654i
$405$	1.48125	−	0.434934i	0.0736039	−	0.0216120i
$406$	18.2934	−	20.4964i	0.907886	−	1.01722i
$407$	−0.680545	+	0.785391i	−0.0337334	+	0.0389304i
$408$	6.12699	−	0.585056i	0.303331	−	0.0289646i
$409$	−23.4283	+	22.3388i	−1.15845	+	1.10458i	−0.165484	+	0.986213i	$0.552919\pi$
$409$	−23.4283	+	22.3388i	−1.15845	+	1.10458i	−0.992970	+	0.118370i	$0.962233\pi$
$410$	−8.69914	−	0.830667i	−0.429620	−	0.0410237i
$411$	−7.88175	+	6.19828i	−0.388778	+	0.305739i
$412$	−4.70906	−	3.02633i	−0.231999	−	0.149097i
$413$	1.55612	−	24.9583i	0.0765717	−	1.22812i
$414$	−2.44157	−	4.12780i	−0.119996	−	0.202870i
$415$	−6.39186	−	11.0710i	−0.313764	−	0.543456i
$416$	−5.58234	+	2.87790i	−0.273697	+	0.141100i
$417$	7.03655	+	2.81701i	0.344581	+	0.137950i
$418$	−0.129039	+	0.181210i	−0.00631150	+	0.00886327i
$419$	3.80660	+	1.11772i	0.185964	+	0.0546041i	0.373389	−	0.927675i	$-0.378196\pi$
$419$	3.80660	+	1.11772i	0.185964	+	0.0546041i	−0.187424	+	0.982279i	$0.560014\pi$
$420$	−3.60258	−	1.92466i	−0.175788	−	0.0939138i
$421$	−2.51328	+	2.90048i	−0.122490	+	0.141361i	−0.813682	−	0.581310i	$-0.802540\pi$
$421$	−2.51328	+	2.90048i	−0.122490	+	0.141361i	0.691192	+	0.722671i	$0.257086\pi$
$422$	−23.5349	+	9.42193i	−1.14566	+	0.458653i
$423$	−1.26895	+	5.23066i	−0.0616982	+	0.254324i
$424$	−2.96627	+	0.571702i	−0.144055	+	0.0277643i
$425$	−14.3152	−	7.38002i	−0.694391	−	0.357984i
$426$	11.7576	−	7.55616i	0.569658	−	0.366097i
$427$	0.997654	+	7.74353i	0.0482798	+	0.374736i
$428$	9.92741	−	2.91495i	0.479859	−	0.140899i
$429$	−0.970124	+	0.388379i	−0.0468380	+	0.0187511i
$430$	−4.63894	−	13.4033i	−0.223709	−	0.646366i
$431$	−18.5492	−	26.0487i	−0.893483	−	1.25472i	−0.966311	−	0.257377i	$-0.917142\pi$
$431$	−18.5492	−	26.0487i	−0.893483	−	1.25472i	0.0728281	−	0.997345i	$-0.476798\pi$
$432$	0.235759	+	0.971812i	0.0113430	+	0.0467563i
$433$	12.0359	+	26.3550i	0.578409	+	1.26654i	0.942198	+	0.335057i	$0.108756\pi$
$433$	12.0359	+	26.3550i	0.578409	+	1.26654i	−0.363789	+	0.931481i	$0.618517\pi$
$434$	−5.82849	−	8.44443i	−0.279776	−	0.405346i
$435$	−13.4855	−	8.66658i	−0.646578	−	0.415530i
$436$	−0.455923	−	0.789682i	−0.0218348	−	0.0378189i
$437$	−4.24990	−	4.80143i	−0.203300	−	0.229683i
$438$	−6.96801	+	12.0689i	−0.332944	+	0.576677i
$439$	1.45179	−	30.4767i	0.0692899	−	1.45457i	−0.650037	−	0.759903i	$-0.725247\pi$
$439$	1.45179	−	30.4767i	0.0692899	−	1.45457i	0.719327	−	0.694672i	$-0.244450\pi$
$440$	−0.0365552	−	0.254247i	−0.00174270	−	0.0121207i
$441$	−2.09445	−	6.67932i	−0.0997360	−	0.318063i
$442$	37.0898	+	10.8906i	1.76418	+	0.518011i
$443$	−3.41904	+	0.326479i	−0.162443	+	0.0155115i	−0.175961	−	0.984397i	$-0.556303\pi$
$443$	−3.41904	+	0.326479i	−0.162443	+	0.0155115i	0.0135174	+	0.999909i	$0.495697\pi$
$444$	2.04284	+	5.90239i	0.0969488	+	0.280115i
$445$	5.96127	+	4.68799i	0.282591	+	0.222232i
$446$	6.60967	+	6.30230i	0.312977	+	0.298423i
$447$	12.3590	+	14.2631i	0.584561	+	0.674620i
$448$	1.35634	−	2.27164i	0.0640811	−	0.107325i
$449$	24.0517	−	15.4571i	1.13507	−	0.729465i	0.168458	−	0.985709i	$-0.446121\pi$
$449$	24.0517	−	15.4571i	1.13507	−	0.729465i	0.966612	+	0.256244i	$0.0824850\pi$
$450$	0.855849	−	2.47281i	0.0403451	−	0.116570i
$451$	0.222045	−	0.915282i	0.0104557	−	0.0430990i
$452$	−3.07524	−	2.41839i	−0.144647	−	0.113752i
$453$	−14.5613	−	2.80647i	−0.684152	−	0.131859i
$454$	5.16111	−	11.3012i	0.242223	−	0.530394i
$455$	−16.5127	−	19.6312i	−0.774126	−	0.920325i
$456$	0.555419	+	1.21620i	0.0260099	+	0.0569537i
$457$	−29.9608	+	23.5615i	−1.40151	+	1.10216i	−0.420696	+	0.907201i	$0.638214\pi$
$457$	−29.9608	+	23.5615i	−1.40151	+	1.10216i	−0.980812	+	0.194957i	$0.937543\pi$
$458$	2.89938	−	1.49474i	0.135479	−	0.0698445i
$459$	3.07743	−	5.33026i	0.143642	−	0.248795i
$460$	7.37721	+	0.626035i	0.343964	+	0.0291890i
$461$	18.2036			0.847824			0.423912	−	0.905703i	$-0.360657\pi$
$461$	18.2036			0.847824			0.423912	+	0.905703i	$0.360657\pi$
$462$	0.260580	−	0.354801i	0.0121233	−	0.0165069i
$463$	−1.30841	−	9.10018i	−0.0608069	−	0.422921i	−0.997373	−	0.0724312i	$-0.976924\pi$
$463$	−1.30841	−	9.10018i	−0.0608069	−	0.422921i	0.936567	−	0.350490i	$-0.113985\pi$
$464$	6.02314	−	8.45832i	0.279617	−	0.392667i
$465$	−4.33300	+	4.13151i	−0.200938	+	0.191594i
$466$	−13.7158	−	19.2612i	−0.635373	−	0.892257i
$467$	−31.7888	−	6.12679i	−1.47101	−	0.283514i	−0.610122	−	0.792307i	$-0.708880\pi$
$467$	−31.7888	−	6.12679i	−1.47101	−	0.283514i	−0.860889	+	0.508793i	$0.830092\pi$
$468$	−0.893810	+	6.21658i	−0.0413164	+	0.287362i
$469$	−4.97460	−	21.9030i	−0.229706	−	1.01139i
$470$	−5.44139	−	6.27970i	−0.250993	−	0.289661i
$471$	−8.95135	−	4.61474i	−0.412456	−	0.212636i
$472$	−0.449728	−	9.44095i	−0.0207004	−	0.434555i
$473$	1.50102	−	0.289298i	0.0690169	−	0.0133019i
$474$	−5.86660	−	5.59380i	−0.269462	−	0.256932i
$475$	0.497907	−	3.46302i	0.0228455	−	0.158894i
$476$	−15.6902	+	4.35812i	−0.719160	+	0.199754i
$477$	−1.25491	+	2.74787i	−0.0574584	+	0.125816i
$478$	−2.70569	−	11.1530i	−0.123755	−	0.510126i
$479$	6.05320	+	0.578010i	0.276578	+	0.0264100i	0.232423	−	0.972615i	$-0.425335\pi$
$479$	6.05320	+	0.578010i	0.276578	+	0.0264100i	0.0441544	+	0.999025i	$0.485941\pi$
$480$	−1.43320	−	0.573766i	−0.0654163	−	0.0261887i
$481$	−1.86652	+	39.1831i	−0.0851060	+	1.78659i
$482$	−10.0789			−0.459083
$483$	8.26961	+	9.62359i	0.376280	+	0.437889i
$484$	−10.9723			−0.498742
$485$	0.196969	−	4.13489i	0.00894390	−	0.187756i
$486$	0.928368	+	0.371662i	0.0421116	+	0.0168590i
$487$	−17.4536	−	1.66662i	−0.790899	−	0.0755217i	−0.308216	−	0.951317i	$-0.599732\pi$
$487$	−17.4536	−	1.66662i	−0.790899	−	0.0755217i	−0.482684	+	0.875795i	$0.660338\pi$
$488$	0.695717	+	2.86779i	0.0314936	+	0.129819i
$489$	5.66237	−	12.3989i	0.256061	−	0.560696i
$490$	10.2750	+	3.34737i	0.464176	+	0.151219i
$491$	−0.364026	+	2.53185i	−0.0164282	+	0.114261i	−0.996385	−	0.0849471i	$-0.972928\pi$
$491$	−0.364026	+	2.53185i	−0.0164282	+	0.114261i	0.979957	+	0.199208i	$0.0638370\pi$
$492$	−4.09675	−	3.90625i	−0.184696	−	0.176107i
$493$	−62.7553	+	12.0951i	−2.82636	+	0.544735i
$494$	0.399554	+	8.38766i	0.0179768	+	0.377379i
$495$	−0.228307	−	0.117701i	−0.0102617	−	0.00529025i
$496$	−2.53964	−	2.93090i	−0.114033	−	0.131601i
$497$	−27.1335	+	25.1223i	−1.21710	+	1.12689i
$498$	1.17848	−	8.19649i	0.0528088	−	0.367293i
$499$	−29.1514	−	5.61847i	−1.30500	−	0.251517i	−0.511074	−	0.859537i	$-0.670752\pi$
$499$	−29.1514	−	5.61847i	−1.30500	−	0.251517i	−0.793922	+	0.608019i	$0.791964\pi$
$500$	6.82065	+	9.57826i	0.305029	+	0.428353i
$501$	−6.09740	+	5.81386i	−0.272412	+	0.259744i
$502$	−15.3555	+	21.5638i	−0.685349	+	0.962438i
$503$	−0.341667	−	2.37635i	−0.0152342	−	0.105956i	0.980786	−	0.195089i	$-0.0624995\pi$
$503$	−0.341667	−	2.37635i	−0.0152342	−	0.105956i	−0.996020	+	0.0891328i	$0.971590\pi$
$504$	−1.06367	−	2.42252i	−0.0473794	−	0.107908i
$505$	−13.9109			−0.619028
$506$	−0.179939	+	0.777398i	−0.00799926	+	0.0345595i
$507$	−13.2224	+	22.9019i	−0.587227	+	1.01711i
$508$	0.349910	−	0.180391i	0.0155248	−	0.00800357i
$509$	11.7526	−	9.24238i	0.520927	−	0.409661i	−0.322773	−	0.946476i	$-0.604615\pi$
$509$	11.7526	−	9.24238i	0.520927	−	0.409661i	0.843700	+	0.536815i	$0.180373\pi$
$510$	3.94718	+	8.64311i	0.174784	+	0.382723i
$511$	12.5692	−	34.6627i	0.556028	−	1.53339i
$512$	0.415415	−	0.909632i	0.0183589	−	0.0402004i
$513$	1.31286	+	0.253033i	0.0579642	+	0.0111717i
$514$	−5.83351	−	4.58753i	−0.257305	−	0.202347i
$515$	2.03733	−	8.39801i	0.0897757	−	0.370060i
$516$	3.00491	−	8.68213i	0.132284	−	0.382209i
$517$	0.753379	−	0.484167i	0.0331336	−	0.0212937i
$518$	−8.05176	−	14.4308i	−0.353774	−	0.634054i
$519$	13.8364	+	15.9681i	0.607350	+	0.700920i
$520$	−7.01714	−	6.69083i	−0.307722	−	0.293412i
$521$	7.55450	+	5.94092i	0.330969	+	0.260277i	0.769789	−	0.638298i	$-0.220361\pi$
$521$	7.55450	+	5.94092i	0.330969	+	0.260277i	−0.438821	+	0.898575i	$0.644604\pi$
$522$	−3.39618	−	9.81261i	−0.148647	−	0.429486i
$523$	4.56869	−	0.436257i	0.199775	−	0.0190762i	0.00531117	−	0.999986i	$-0.498309\pi$
$523$	4.56869	−	0.436257i	0.199775	−	0.0190762i	0.194464	+	0.980910i	$0.437703\pi$
$524$	6.93167	+	2.03532i	0.302811	+	0.0889135i
$525$	−1.08569	+	6.83757i	−0.0473833	+	0.298416i
$526$	−2.39602	−	16.6647i	−0.104472	−	0.726615i
$527$	−1.13575	+	23.8424i	−0.0494741	+	1.03859i
$528$	0.0831921	−	0.144093i	0.00362047	−	0.00627084i
$529$	−20.6609	−	10.1059i	−0.898298	−	0.439386i
$530$	−2.33178	−	4.03876i	−0.101286	−	0.175432i
$531$	−7.95124	−	5.10995i	−0.345054	−	0.221753i
$532$	−2.00942	−	2.91129i	−0.0871195	−	0.126220i
$533$	−14.7686	−	32.3386i	−0.639697	−	1.40074i
$534$	1.15816	+	4.77400i	0.0501185	+	0.206591i
$535$	9.26512	+	13.0110i	0.400566	+	0.562516i
$536$	−2.77661	−	8.02248i	−0.119931	−	0.346519i
$537$	7.02300	−	2.81159i	0.303065	−	0.121329i
$538$	−3.93349	+	1.15498i	−0.169585	+	0.0497946i
$539$	−0.514697	+	1.04479i	−0.0221696	+	0.0450023i
$540$	−1.29871	+	0.834632i	−0.0558877	+	0.0359169i
$541$	0.152942	+	0.0788470i	0.00657548	+	0.00338990i	0.461511	−	0.887134i	$-0.347307\pi$
$541$	0.152942	+	0.0788470i	0.00657548	+	0.00338990i	−0.454936	+	0.890524i	$0.650338\pi$
$542$	12.8337	−	2.47349i	0.551254	−	0.106245i
$543$	4.29221	−	17.6927i	0.184197	−	0.759269i
$544$	−5.71397	+	2.28753i	−0.244985	+	0.0980770i
$545$	0.921843	−	1.06386i	0.0394874	−	0.0455709i
$546$	−0.547112	−	16.6077i	−0.0234142	−	0.710742i
$547$	35.2481	+	10.3498i	1.50710	+	0.442524i	0.927952	−	0.372699i	$-0.121568\pi$
$547$	35.2481	+	10.3498i	1.50710	+	0.442524i	0.579146	+	0.815224i	$0.303386\pi$
$548$	5.81623	−	8.16775i	0.248457	−	0.348909i
$549$	2.73959	+	1.09676i	0.116923	+	0.0468088i
$550$	−0.386984	+	0.199504i	−0.0165010	+	0.00850688i
$551$	−6.94162	−	12.0232i	−0.295723	−	0.512207i
$552$	3.50560	+	3.27273i	0.149208	+	0.139297i
$553$	17.8699	+	11.8583i	0.759908	+	0.504264i
$554$	−19.0133	−	12.2191i	−0.807797	−	0.519139i
$555$	−7.57939	+	5.96050i	−0.321727	+	0.253009i
$556$	−7.54516	−	0.720476i	−0.319986	−	0.0305550i
$557$	14.8346	−	14.1447i	0.628560	−	0.599331i	−0.307338	−	0.951600i	$-0.599438\pi$
$557$	14.8346	−	14.1447i	0.628560	−	0.599331i	0.935899	+	0.352269i	$0.114590\pi$
$558$	−3.86058	+	0.368640i	−0.163431	+	0.0156058i
$559$	37.7866	−	43.6081i	1.59820	−	1.84442i
$560$	3.99889	+	0.831735i	0.168984	+	0.0351472i
$561$	−0.982589	+	0.288514i	−0.0414849	+	0.0121811i
$562$	10.1991	−	29.4683i	0.430222	−	1.24305i
$563$	0.332721	+	6.98468i	0.0140225	+	0.294369i	0.994975	+	0.100122i	$0.0319233\pi$
$563$	0.332721	+	6.98468i	0.0140225	+	0.294369i	−0.980953	+	0.194247i	$0.937774\pi$
$564$	−0.256104	−	5.37629i	−0.0107839	−	0.226383i
$565$	1.97538	−	5.70749i	0.0831050	−	0.240116i
$566$	11.6553	−	3.42229i	0.489907	−	0.143850i
$567$	−2.59032	−	0.538764i	−0.108783	−	0.0226260i
$568$	−9.15253	+	10.5626i	−0.384032	+	0.443196i
$569$	14.6527	−	1.39916i	0.614272	−	0.0586558i	0.216717	−	0.976234i	$-0.430465\pi$
$569$	14.6527	−	1.39916i	0.614272	−	0.0586558i	0.397554	+	0.917579i	$0.369859\pi$
$570$	−1.49384	+	1.42437i	−0.0625700	+	0.0596604i
$571$	35.0780	+	3.34954i	1.46797	+	0.140174i	0.798199	−	0.602394i	$-0.205786\pi$
$571$	35.0780	+	3.34954i	1.46797	+	0.140174i	0.669770	+	0.742568i	$0.266393\pi$
$572$	0.821408	−	0.645962i	0.0343448	−	0.0270090i
$573$	−3.57163	−	2.29535i	−0.149207	−	0.0958895i
$574$	12.4789	+	8.28083i	0.520859	+	0.345635i
$575$	−3.08703	−	12.1638i	−0.128738	−	0.507265i
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	7.68078	−	3.95972i	0.319755	−	0.164845i	−0.290875	−	0.956761i	$-0.593946\pi$
$577$	7.68078	−	3.95972i	0.319755	−	0.164845i	0.610630	+	0.791916i	$0.290916\pi$
$578$	19.3864	+	7.76116i	0.806369	+	0.322822i
$579$	−5.57823	+	7.83353i	−0.231823	+	0.325550i
$580$	15.3809	+	4.51623i	0.638655	+	0.187526i
$581$	0.721361	+	21.8970i	0.0299271	+	0.908440i
$582$	1.75598	−	2.02650i	0.0727875	−	0.0840013i
$583$	0.466620	−	0.186806i	0.0193254	−	0.00773673i
$584$	3.28554	−	13.5432i	0.135957	−	0.560421i
$585$	−9.52053	+	1.83493i	−0.393626	+	0.0758651i
$586$	−14.4527	−	7.45087i	−0.597035	−	0.307793i
$587$	−8.59451	+	5.52336i	−0.354734	+	0.227973i	−0.705855	−	0.708357i	$-0.749437\pi$
$587$	−8.59451	+	5.52336i	−0.354734	+	0.227973i	0.351121	+	0.936330i	$0.385801\pi$
$588$	3.89140	+	5.81868i	0.160478	+	0.239958i
$589$	−4.97512	+	1.46083i	−0.204996	+	0.0601923i
$590$	13.5461	−	5.42304i	0.557684	−	0.223263i
$591$	−0.451467	−	1.30443i	−0.0185709	−	0.0536570i
$592$	−3.62298	−	5.08777i	−0.148904	−	0.209106i
$593$	−2.94864	−	12.1545i	−0.121086	−	0.499124i	−0.999764	−	0.0217095i	$-0.993089\pi$
$593$	−2.94864	−	12.1545i	−0.121086	−	0.499124i	0.878678	−	0.477415i	$-0.158426\pi$
$594$	−0.0691185	−	0.151348i	−0.00283597	−	0.00620990i
$595$	−14.2803	−	20.6896i	−0.585435	−	0.848190i
$596$	−15.8768	−	10.2034i	−0.650337	−	0.417946i
$597$	10.3506	+	17.9277i	0.423621	+	0.733734i
$598$	12.8005	+	27.2649i	0.523453	+	1.11495i
$599$	7.14165	−	12.3697i	0.291800	−	0.505412i	−0.682436	−	0.730946i	$-0.739079\pi$
$599$	7.14165	−	12.3697i	0.291800	−	0.505412i	0.974235	+	0.225534i	$0.0724126\pi$
$600$	−0.124509	+	2.61377i	−0.00508307	+	0.106707i
$601$	−3.09291	−	21.5117i	−0.126163	−	0.877480i	−0.950354	−	0.311169i	$-0.899279\pi$
$601$	−3.09291	−	21.5117i	−0.126163	−	0.877480i	0.824192	−	0.566311i	$-0.191630\pi$
$602$	−3.81188	+	24.0069i	−0.155361	+	0.978449i
$603$	−8.14551	−	2.39174i	−0.331711	−	0.0973991i
$604$	14.7622	−	1.40962i	0.600665	−	0.0573565i
$605$	−5.54016	−	16.0073i	−0.225240	−	0.650787i
$606$	−7.08307	−	5.57018i	−0.287730	−	0.226273i
$607$	9.63187	+	9.18397i	0.390946	+	0.372766i	0.859905	−	0.510454i	$-0.170523\pi$
$607$	9.63187	+	9.18397i	0.390946	+	0.372766i	−0.468960	+	0.883220i	$0.655371\pi$
$608$	−0.875563	−	1.01045i	−0.0355088	−	0.0409793i
$609$	13.3859	+	23.9910i	0.542424	+	0.972164i
$610$	−3.83246	+	2.46297i	−0.155172	+	0.0997229i
$611$	11.0562	−	31.9449i	0.447288	−	1.29235i
$612$	−1.45106	+	5.98136i	−0.0586557	+	0.241782i
$613$	−0.296761	−	0.233375i	−0.0119861	−	0.00942594i	0.612148	−	0.790743i	$-0.290306\pi$
$613$	−0.296761	−	0.233375i	−0.0119861	−	0.00942594i	−0.624134	+	0.781317i	$0.714548\pi$
$614$	−29.8819	−	5.75926i	−1.20593	−	0.232425i
$615$	3.63019	−	7.94901i	0.146383	−	0.320535i
$616$	−0.150065	+	0.413843i	−0.00604630	+	0.0166742i
$617$	−19.1248	−	41.8774i	−0.769934	−	1.68592i	−0.726798	−	0.686852i	$-0.758992\pi$
$617$	−19.1248	−	41.8774i	−0.769934	−	1.68592i	−0.0431365	−	0.999069i	$-0.513735\pi$
$618$	4.40007	−	3.46025i	0.176997	−	0.139192i
$619$	−38.9246	+	20.0670i	−1.56451	+	0.806562i	−0.999824	−	0.0187435i	$-0.994033\pi$
$619$	−38.9246	+	20.0670i	−1.56451	+	0.806562i	−0.564687	+	0.825305i	$0.691003\pi$
$620$	2.99350	−	5.18490i	0.120222	−	0.208231i
$621$	4.69934	−	0.957209i	0.188578	−	0.0384115i
$622$	−21.1329			−0.847354
$623$	−5.22523	−	11.9006i	−0.209344	−	0.476787i
$624$	−0.893810	−	6.21658i	−0.0357810	−	0.248862i
$625$	−2.94034	+	4.12912i	−0.117613	+	0.165165i
$626$	−0.686207	+	0.654298i	−0.0274264	+	0.0261510i
$627$	−0.129039	−	0.181210i	−0.00515332	−	0.00723683i
$628$	9.88888	+	1.90593i	0.394609	+	0.0760547i
$629$	−5.47097	+	38.0514i	−0.218142	+	1.51721i
$630$	2.99709	−	2.77494i	0.119407	−	0.110556i
$631$	25.5534	+	29.4902i	1.01727	+	1.17399i	0.984654	+	0.174520i	$0.0558372\pi$
$631$	25.5534	+	29.4902i	1.01727	+	1.17399i	0.0326124	+	0.999468i	$0.489617\pi$
$632$	7.20492	+	3.71439i	0.286596	+	0.147751i
$633$	−1.20624	−	25.3221i	−0.0479437	−	1.00646i
$634$	−21.8645	+	4.21404i	−0.868350	+	0.167361i
$635$	0.439846	+	0.419392i	0.0174548	+	0.0166431i
$636$	0.429913	−	2.99011i	0.0170472	−	0.118566i
$637$	9.10713	+	43.0099i	0.360838	+	1.70412i
$638$	−0.717706	+	1.57156i	−0.0284143	+	0.0622185i
$639$	3.29504	+	13.5823i	0.130350	+	0.537309i
$640$	1.53679	+	0.146746i	0.0607471	+	0.00580064i
$641$	7.57456	+	3.03240i	0.299177	+	0.119772i	0.516395	−	0.856351i	$-0.327274\pi$
$641$	7.57456	+	3.03240i	0.299177	+	0.119772i	−0.217217	+	0.976123i	$0.569698\pi$
$642$	−0.492307	+	10.3348i	−0.0194298	+	0.407882i
$643$	38.1424			1.50419			0.752094	−	0.659056i	$-0.229044\pi$
$643$	38.1424			1.50419			0.752094	+	0.659056i	$0.229044\pi$
$644$	−10.6459	−	6.90395i	−0.419508	−	0.272054i
$645$	14.1834			0.558471
$646$	−0.391560	+	8.21985i	−0.0154057	+	0.323406i
$647$	−33.4661	−	13.3978i	−1.31569	−	0.526723i	−0.395598	−	0.918424i	$-0.629462\pi$
$647$	−33.4661	−	13.3978i	−1.31569	−	0.526723i	−0.920092	+	0.391701i	$0.871887\pi$
$648$	−0.995472	−	0.0950560i	−0.0391058	−	0.00373415i
$649$	0.370756	+	1.52828i	0.0145534	+	0.0599901i
$650$	−6.82710	+	14.9493i	−0.267781	+	0.586359i
$651$	9.88630	−	2.74603i	0.387475	−	0.107625i
$652$	−1.93984	+	13.4919i	−0.0759701	+	0.528383i
$653$	5.76657	+	5.49841i	0.225663	+	0.215170i	0.794473	−	0.607300i	$-0.207747\pi$
$653$	5.76657	+	5.49841i	0.225663	+	0.215170i	−0.568809	+	0.822469i	$0.692596\pi$
$654$	0.895368	−	0.172568i	0.0350117	−	0.00674795i
$655$	0.530670	+	11.1401i	0.0207350	+	0.435281i
$656$	5.03132	+	2.59383i	0.196440	+	0.101272i
$657$	−9.12615	−	10.5321i	−0.356045	−	0.410898i
$658$	3.15396	+	13.8868i	0.122954	+	0.541363i
$659$	−2.50161	+	17.3991i	−0.0974488	+	0.677771i	0.881277	+	0.472600i	$0.156684\pi$
$659$	−2.50161	+	17.3991i	−0.0974488	+	0.677771i	−0.978726	+	0.205172i	$0.934225\pi$
$660$	0.252219	+	0.0486113i	0.00981762	+	0.00189219i
$661$	17.1394	+	24.0689i	0.666646	+	0.936174i	0.999978	−	0.00663607i	$-0.00211234\pi$
$661$	17.1394	+	24.0689i	0.666646	+	0.936174i	−0.333332	+	0.942810i	$0.608173\pi$
$662$	11.7595	−	11.2127i	0.457047	−	0.435793i
$663$	−22.4225	+	31.4880i	−0.870817	+	1.22289i
$664$	1.17848	+	8.19649i	0.0457338	+	0.318085i
$665$	3.23261	−	4.40147i	0.125355	−	0.170682i
$666$	−6.24591			−0.242024
$667$	−39.4666	−	30.3690i	−1.52815	−	1.17589i
$668$	4.21246	−	7.29619i	0.162985	−	0.282298i
$669$	−8.11749	+	4.18486i	−0.313840	+	0.161796i
$670$	10.3018	−	8.10146i	0.397995	−	0.312987i
$671$	−0.203967	−	0.446624i	−0.00787404	−	0.0172417i
$672$	1.70308	+	2.02472i	0.0656979	+	0.0781054i
$673$	−14.9983	+	32.8418i	−0.578143	+	1.26596i	0.364204	+	0.931319i	$0.381341\pi$
$673$	−14.9983	+	32.8418i	−0.578143	+	1.26596i	−0.942347	+	0.334638i	$0.891386\pi$
$674$	30.5704	+	5.89196i	1.17753	+	0.226950i
$675$	2.05689	+	1.61756i	0.0791698	+	0.0622598i
$676$	6.23460	−	25.6994i	0.239792	−	0.988437i
$677$	−9.64557	+	27.8690i	−0.370709	+	1.07109i	0.593244	+	0.805023i	$0.297847\pi$
$677$	−9.64557	+	27.8690i	−0.370709	+	1.07109i	−0.963953	+	0.266072i	$0.914274\pi$
$678$	3.29120	−	2.11512i	0.126398	−	0.0812308i
$679$	−3.63696	+	6.09128i	−0.139574	+	0.233762i
$680$	−6.22233	−	7.18096i	−0.238616	−	0.275377i
$681$	8.99165	+	8.57352i	0.344561	+	0.328538i
$682$	0.507209	+	0.398874i	0.0194220	+	0.0152737i
$683$	8.17896	+	23.6316i	0.312959	+	0.904236i	0.986308	+	0.164912i	$0.0527339\pi$
$683$	8.17896	+	23.6316i	0.312959	+	0.904236i	−0.673349	+	0.739325i	$0.735145\pi$
$684$	−1.33097	+	0.127092i	−0.0508908	+	0.00485948i
$685$	14.8525	+	4.36108i	0.567484	+	0.166628i
$686$	−12.8285	−	13.3577i	−0.489796	−	0.510000i
$687$	0.464232	+	3.22880i	0.0177115	+	0.123186i
$688$	−0.437156	+	9.17702i	−0.0166664	+	0.349871i
$689$	9.48628	−	16.4307i	0.361398	−	0.625960i
$690$	−3.00445	+	6.76671i	−0.114378	+	0.257604i
$691$	15.1098	+	26.1709i	0.574803	+	0.995589i	0.996063	+	0.0886486i	$0.0282548\pi$
$691$	15.1098	+	26.1709i	0.574803	+	0.995589i	−0.421260	+	0.906940i	$0.638412\pi$
$692$	−17.7746	−	11.4231i	−0.675691	−	0.434240i
$693$	0.250060	+	0.362292i	0.00949901	+	0.0137623i
$694$	−5.28883	−	11.5809i	−0.200761	−	0.439606i
$695$	−2.75863	−	11.3712i	−0.104641	−	0.431336i
$696$	6.02314	+	8.45832i	0.228307	+	0.320612i
$697$	−11.3951	−	32.9239i	−0.431619	−	1.24708i
$698$	−1.81842	+	0.727986i	−0.0688282	+	0.0275547i
$699$	22.6878	−	6.66175i	0.858132	−	0.251970i
$700$	−0.884656	−	6.86647i	−0.0334369	−	0.259528i
$701$	−14.5413	+	9.34510i	−0.549216	+	0.352960i	−0.785634	−	0.618692i	$-0.787663\pi$
$701$	−14.5413	+	9.34510i	−0.549216	+	0.352960i	0.236418	+	0.971651i	$0.424027\pi$
$702$	−5.58234	−	2.87790i	−0.210692	−	0.108619i
$703$	−8.20000	+	1.58042i	−0.309269	+	0.0596067i
$704$	−0.0392266	+	0.161694i	−0.00147841	+	0.00609408i
$705$	7.71403	−	3.08823i	0.290527	−	0.116309i
$706$	−17.7465	+	20.4806i	−0.667899	+	0.770797i
$707$	21.0279	+	11.2341i	0.790836	+	0.422501i
$708$	9.06880	+	2.66284i	0.340826	+	0.100076i
$709$	16.1336	−	22.6565i	0.605911	−	0.850882i	−0.391691	−	0.920097i	$-0.628110\pi$
$709$	16.1336	−	22.6565i	0.605911	−	0.850882i	0.997602	+	0.0692144i	$0.0220493\pi$
$710$	−20.0308	−	8.01913i	−0.751743	−	0.300953i
$711$	7.20492	−	3.71439i	0.270206	−	0.139301i
$712$	−2.45624	−	4.25433i	−0.0920514	−	0.159438i
$713$	−14.4977	+	11.6506i	−0.542943	+	0.436317i
$714$	1.01334	−	16.2527i	0.0379231	−	0.608241i
$715$	1.35713	+	0.872172i	0.0507536	+	0.0326174i
$716$	−5.94641	+	4.67631i	−0.222228	+	0.174762i
$717$	11.4245	+	1.09091i	0.426657	+	0.0407408i
$718$	3.09868	−	2.95459i	0.115642	−	0.110264i
$719$	−0.621665	+	0.0593618i	−0.0231842	+	0.00221382i	−0.106642	−	0.994298i	$-0.534010\pi$
$719$	−0.621665	+	0.0593618i	−0.0231842	+	0.00221382i	0.0834575	+	0.996511i	$0.473404\pi$
$720$	1.01096	−	1.16671i	0.0376764	−	0.0434809i
$721$	−9.86165	+	11.0492i	−0.367267	+	0.411495i
$722$	16.5152	−	4.84929i	0.614630	−	0.180472i
$723$	3.29650	−	9.52460i	0.122598	−	0.354224i
$724$	0.866274	+	18.1853i	0.0321948	+	0.675852i
$725$	−1.29287	−	27.1406i	−0.0480158	−	1.00798i
$726$	3.58869	−	10.3688i	0.133189	−	0.384824i
$727$	−18.0087	+	5.28783i	−0.667905	+	0.196115i	−0.598070	−	0.801444i	$-0.704066\pi$
$727$	−18.0087	+	5.28783i	−0.667905	+	0.196115i	−0.0698353	+	0.997559i	$0.522247\pi$
$728$	5.20387	+	15.7808i	0.192868	+	0.584875i
$729$	−0.654861	+	0.755750i	−0.0242541	+	0.0279907i
$730$	21.4168	−	2.04505i	0.792671	−	0.0756909i
$731$	40.9252	−	39.0221i	1.51367	−	1.44329i
$732$	−2.93761	−	0.280507i	−0.108577	−	0.0103679i
$733$	23.4800	−	18.4649i	0.867254	−	0.682016i	−0.0819640	−	0.996635i	$-0.526119\pi$
$733$	23.4800	−	18.4649i	0.867254	−	0.682016i	0.949218	+	0.314619i	$0.101877\pi$
$734$	−10.5482	−	6.77893i	−0.389342	−	0.250215i
$735$	−6.52389	+	8.61505i	−0.240637	+	0.317771i
$736$	−4.28563	−	2.15252i	−0.157971	−	0.0793429i
$737$	0.706250	+	1.22326i	0.0260151	+	0.0450594i
$738$	5.03132	−	2.59383i	0.185206	−	0.0954801i
$739$	40.1406	+	16.0699i	1.47659	+	0.591139i	0.963623	−	0.267266i	$-0.0861204\pi$
$739$	40.1406	+	16.0699i	1.47659	+	0.591139i	0.512972	+	0.858406i	$0.328545\pi$
$740$	5.59310	−	7.85441i	0.205607	−	0.288734i
$741$	−8.05703	−	2.36576i	−0.295982	−	0.0869083i
$742$	0.263155	+	7.98812i	0.00966074	+	0.293253i
$743$	12.9106	−	14.8996i	0.473644	−	0.546614i	−0.467778	−	0.883846i	$-0.654945\pi$
$743$	12.9106	−	14.8996i	0.473644	−	0.546614i	0.941422	+	0.337232i	$0.109491\pi$
$744$	3.60034	−	1.44136i	0.131995	−	0.0528428i
$745$	6.86894	−	28.3141i	0.251658	−	1.03735i
$746$	35.1065	−	6.76623i	1.28534	−	0.247729i
$747$	7.36025	+	3.79447i	0.269297	+	0.138832i
$748$	0.861503	−	0.553655i	0.0314997	−	0.0202436i
$749$	−3.49791	−	27.1499i	−0.127811	−	0.992036i
$750$	−11.2823	+	3.31278i	−0.411971	+	0.120965i
$751$	−26.3142	+	10.5346i	−0.960217	+	0.384413i	−0.798212	−	0.602377i	$-0.794220\pi$
$751$	−26.3142	+	10.5346i	−0.960217	+	0.384413i	−0.162006	+	0.986790i	$0.551796\pi$
$752$	1.76041	+	5.08636i	0.0641954	+	0.185480i
$753$	−15.3555	−	21.5638i	−0.559585	−	0.785827i
$754$	15.3750	+	63.3766i	0.559925	+	2.30804i
$755$	9.51021	+	20.8245i	0.346112	+	0.757879i
$756$	2.63718	−	0.212836i	0.0959132	−	0.00774076i
$757$	−25.4795	−	16.3747i	−0.926069	−	0.595149i	−0.0116567	−	0.999932i	$-0.503711\pi$
$757$	−25.4795	−	16.3747i	−0.926069	−	0.595149i	−0.914413	+	0.404783i	$0.867347\pi$
$758$	−7.27566	−	12.6018i	−0.264264	−	0.457718i
$759$	−0.675789	−	0.424304i	−0.0245296	−	0.0154013i
$760$	1.03204	−	1.78754i	0.0374359	−	0.0648408i
$761$	0.773336	−	16.2343i	0.0280334	−	0.588493i	−0.940528	−	0.339717i	$-0.889669\pi$
$761$	0.773336	−	16.2343i	0.0280334	−	0.588493i	0.968561	−	0.248776i	$-0.0800284\pi$
$762$	0.0560255	+	0.389666i	0.00202959	+	0.0141161i
$763$	−2.25262	+	0.863695i	−0.0815502	+	0.0312678i
$764$	4.07363	+	1.19612i	0.147379	+	0.0432743i
$765$	−9.45874	+	0.903200i	−0.341982	+	0.0326553i
$766$	−6.88062	−	19.8803i	−0.248607	−	0.718303i
$767$	46.6611	+	36.6947i	1.68483	+	1.32497i
$768$	0.723734	+	0.690079i	0.0261155	+	0.0249011i
$769$	14.6134	+	16.8648i	0.526974	+	0.608160i	0.955363	−	0.295434i	$-0.0954643\pi$
$769$	14.6134	+	16.8648i	0.526974	+	0.608160i	−0.428389	+	0.903594i	$0.640919\pi$
$770$	−0.679518	−	0.00996817i	−0.0244881	−	0.000359228i
$771$	6.24317	−	4.01224i	0.224842	−	0.144497i
$772$	3.14531	−	9.08779i	0.113202	−	0.327077i
$773$	3.17414	−	13.0840i	0.114166	−	0.470598i	−0.885813	−	0.464043i	$-0.846398\pi$
$773$	3.17414	−	13.0840i	0.114166	−	0.470598i	0.999979	−	0.00655513i	$-0.00208658\pi$
$774$	7.22181	+	5.67929i	0.259583	+	0.204138i
$775$	−9.96466	−	1.92053i	−0.357941	−	0.0689875i
$776$	−1.11391	+	2.43913i	−0.0399872	+	0.0875597i
$777$	16.2706	−	2.88906i	0.583705	−	0.103644i
$778$	11.1687	+	24.4560i	0.400417	+	0.876790i
$779$	5.94910	−	4.67842i	0.213149	−	0.167622i
$780$	8.61792	−	4.44285i	0.308571	−	0.159079i
$781$	1.16272	−	2.01389i	0.0416053	−	0.0720625i
$782$	9.94780	+	27.7909i	0.355733	+	0.993800i
$783$	10.3837			0.371083
$784$	−5.37308	−	4.48665i	−0.191896	−	0.160238i
$785$	2.21260	+	15.3890i	0.0789712	+	0.549257i
$786$	−4.19051	+	5.88475i	−0.149471	+	0.209902i
$787$	−14.8927	+	14.2002i	−0.530868	+	0.506182i	−0.907426	−	0.420211i	$-0.861956\pi$
$787$	−14.8927	+	14.2002i	−0.530868	+	0.506182i	0.376558	+	0.926393i	$0.377108\pi$
$788$	0.800679	+	1.12440i	0.0285230	+	0.0400549i
$789$	16.5318	+	3.18625i	0.588548	+	0.113433i
$790$	−1.78092	+	12.3866i	−0.0633623	+	0.440694i
$791$	−7.59523	+	7.03225i	−0.270055	+	0.250038i
$792$	0.108958	+	0.125745i	0.00387167	+	0.00446815i
$793$	−16.4733	−	8.49258i	−0.584985	−	0.301580i
$794$	0.295450	+	6.20225i	0.0104851	+	0.220110i
$795$	4.57928	−	0.882584i	0.162410	−	0.0313020i
$796$	−14.9821	−	14.2855i	−0.531028	−	0.506334i
$797$	1.11297	−	7.74085i	0.0394233	−	0.274195i	−0.960569	−	0.278041i	$-0.910315\pi$
$797$	1.11297	−	7.74085i	0.0394233	−	0.274195i	0.999993	+	0.00384567i	$0.00122412\pi$
$798$	3.40839	−	0.946716i	0.120656	−	0.0335134i
$799$	13.7618	−	30.1341i	0.486857	−	1.06607i
$800$	−0.616918	−	2.54297i	−0.0218113	−	0.0899076i
$801$	−4.89023	−	0.466960i	−0.172788	−	0.0164992i
$802$	7.51519	+	3.00863i	0.265371	+	0.106238i
$803$	−0.110330	+	2.31611i	−0.00389345	+	0.0817337i
$804$	8.48939			0.299398
$805$	4.69666	−	19.0170i	0.165535	−	0.670262i
$806$	24.3567			0.857928
$807$	0.195065	−	4.09491i	0.00686660	−	0.144148i
$808$	8.36545	+	3.34902i	0.294296	+	0.117818i
$809$	25.8346	+	2.46690i	0.908295	+	0.0867317i	0.538735	−	0.842475i	$-0.318902\pi$
$809$	25.8346	+	2.46690i	0.908295	+	0.0867317i	0.369560	+	0.929207i	$0.379508\pi$
$810$	−0.363961	−	1.50027i	−0.0127883	−	0.0527140i
$811$	13.9438	−	30.5327i	0.489634	−	1.07215i	−0.490066	−	0.871685i	$-0.663028\pi$
$811$	13.9438	−	30.5327i	0.489634	−	1.07215i	0.979701	−	0.200465i	$-0.0642452\pi$
$812$	−19.6027	−	19.2479i	−0.687920	−	0.675470i
$813$	−1.86004	+	12.9368i	−0.0652344	+	0.453715i
$814$	0.752120	+	0.717145i	0.0263618	+	0.0251359i
$815$	−20.6625	+	3.98237i	−0.723775	+	0.139496i
$816$	−0.292860	−	6.14789i	−0.0102521	−	0.215219i
$817$	10.9183	+	5.62876i	0.381982	+	0.196925i
$818$	21.1987	+	24.4647i	0.741197	+	0.855387i
$819$	15.8732	+	4.91481i	0.554654	+	0.171737i
$820$	−1.24365	+	8.64976i	−0.0434301	+	0.302063i
$821$	2.32441	+	0.447993i	0.0811224	+	0.0156351i	0.229651	−	0.973273i	$-0.426242\pi$
$821$	2.32441	+	0.447993i	0.0811224	+	0.0156351i	−0.148529	+	0.988908i	$0.547454\pi$
$822$	5.81623	+	8.16775i	0.202864	+	0.284883i
$823$	−24.8673	+	23.7109i	−0.866819	+	0.826510i	−0.986066	−	0.166354i	$-0.946800\pi$
$823$	−24.8673	+	23.7109i	−0.866819	+	0.826510i	0.119247	+	0.992865i	$0.461952\pi$
$824$	−3.24697	+	4.55973i	−0.113114	+	0.158846i
$825$	−0.0619615	−	0.430951i	−0.00215722	−	0.0150038i
$826$	−24.8560	−	2.74192i	−0.864849	−	0.0954036i
$827$	5.97934			0.207922			0.103961	−	0.994581i	$-0.466848\pi$
$827$	5.97934			0.207922			0.103961	+	0.994581i	$0.466848\pi$
$828$	−4.23930	+	2.24239i	−0.147326	+	0.0779285i
$829$	14.7998	−	25.6340i	0.514018	−	0.890305i	−0.485850	−	0.874042i	$-0.661490\pi$
$829$	14.7998	−	25.6340i	0.514018	−	0.890305i	0.999868	−	0.0162631i	$-0.00517692\pi$
$830$	−11.3626	+	5.85784i	−0.394403	+	0.203329i
$831$	17.7657	−	13.9711i	0.616285	−	0.484652i
$832$	2.60902	+	5.71295i	0.0904514	+	0.198061i
$833$	4.87795	+	42.8070i	0.169011	+	1.48317i
$834$	3.14863	−	6.89454i	0.109028	−	0.238738i
$835$	12.7712	+	2.46145i	0.441966	+	0.0851819i
$836$	0.174865	+	0.137515i	0.00604782	+	0.00475606i
$837$	0.914306	−	3.76882i	0.0316030	−	0.130269i
$838$	1.29758	−	3.74910i	0.0448240	−	0.129511i
$839$	−38.8121	+	24.9430i	−1.33994	+	0.861129i	−0.996937	−	0.0782047i	$-0.975081\pi$
$839$	−38.8121	+	24.9430i	−1.33994	+	0.861129i	−0.343005	+	0.939333i	$0.611445\pi$
$840$	−2.09390	+	3.50692i	−0.0722463	+	0.121000i
$841$	−51.6170	−	59.5692i	−1.77990	−	2.05411i
$842$	2.77761	+	2.64845i	0.0957229	+	0.0912716i
$843$	24.5118	+	19.2763i	0.844230	+	0.663910i
$844$	8.29143	+	23.9565i	0.285403	+	0.824617i
$845$	40.6402	−	3.88067i	1.39806	−	0.133499i
$846$	5.16436	+	1.51639i	0.177554	+	0.0521347i
$847$	−4.55243	+	28.6708i	−0.156423	+	0.985142i
$848$	0.429913	+	2.99011i	0.0147633	+	0.102681i
$849$	−0.577993	+	12.1336i	−0.0198367	+	0.416423i
$850$	−8.05281	+	13.9479i	−0.276209	+	0.478408i
$851$	−25.0271	+	16.4593i	−0.857917	+	0.564217i
$852$	−6.98815	−	12.1038i	−0.239410	−	0.414670i
$853$	−5.75011	−	3.69537i	−0.196880	−	0.126527i	0.438487	−	0.898738i	$-0.355515\pi$
$853$	−5.75011	−	3.69537i	−0.196880	−	0.126527i	−0.635367	+	0.772211i	$0.719151\pi$
$854$	7.78223	−	0.628072i	0.266302	−	0.0214922i
$855$	−0.857446	−	1.87755i	−0.0293240	−	0.0642107i
$856$	−2.43928	−	10.0549i	−0.0833730	−	0.343668i
$857$	−21.1922	−	29.7603i	−0.723913	−	1.01659i	−0.998485	−	0.0550273i	$-0.982475\pi$
$857$	−21.1922	−	29.7603i	−0.723913	−	1.01659i	0.274572	−	0.961567i	$-0.411464\pi$
$858$	0.341779	+	0.987505i	0.0116681	+	0.0337129i
$859$	33.5164	−	13.4179i	1.14356	−	0.457814i	0.278978	−	0.960298i	$-0.410004\pi$
$859$	33.5164	−	13.4179i	1.14356	−	0.457814i	0.864587	+	0.502483i	$0.167580\pi$
$860$	−13.6089	+	3.99593i	−0.464059	+	0.136260i
$861$	−11.9068	+	9.08418i	−0.405784	+	0.309588i
$862$	−26.9018	+	17.2887i	−0.916279	+	0.588857i
$863$	32.8138	+	16.9167i	1.11700	+	0.575851i	0.914967	−	0.403529i	$-0.132216\pi$
$863$	32.8138	+	16.9167i	1.11700	+	0.575851i	0.202028	+	0.979380i	$0.435247\pi$
$864$	0.981929	−	0.189251i	0.0334059	−	0.00643846i
$865$	7.69004	−	31.6988i	0.261469	−	1.07779i
$866$	26.8978	−	10.7683i	0.914024	−	0.365920i
$867$	−13.6750	+	15.7818i	−0.464427	+	0.535977i
$868$	−8.71220	+	5.42009i	−0.295711	+	0.183970i
$869$	−1.29408	−	0.379977i	−0.0438987	−	0.0128898i
$870$	−9.29842	+	13.0578i	−0.315246	+	0.442701i
$871$	49.4985	+	19.8162i	1.67719	+	0.671446i
$872$	−0.810482	+	0.417832i	−0.0274464	+	0.0141496i
$873$	1.34072	+	2.32220i	0.0453766	+	0.0785947i
$874$	−4.99821	+	4.01663i	−0.169067	+	0.135864i
$875$	27.8581	−	13.8484i	0.941774	−	0.468162i
$876$	11.7237	+	7.53438i	0.396108	+	0.254563i
$877$	−31.0280	+	24.4007i	−1.04774	+	0.823952i	−0.984735	−	0.174061i	$-0.944311\pi$
$877$	−31.0280	+	24.4007i	−1.04774	+	0.823952i	−0.0630053	+	0.998013i	$0.520069\pi$
$878$	−30.3731	−	2.90028i	−1.02504	−	0.0978798i
$879$	11.7681	−	11.2209i	0.396928	−	0.378470i
$880$	−0.255698	+	0.0244162i	−0.00861958	+	0.000823070i
$881$	10.9501	−	12.6371i	0.368918	−	0.425754i	−0.540690	−	0.841222i	$-0.681837\pi$
$881$	10.9501	−	12.6371i	0.368918	−	0.425754i	0.909608	+	0.415468i	$0.136382\pi$
$882$	−6.77141	+	1.77427i	−0.228005	+	0.0597427i
$883$	−1.30262	+	0.382484i	−0.0438366	+	0.0128716i	−0.303577	−	0.952807i	$-0.598181\pi$
$883$	−1.30262	+	0.382484i	−0.0438366	+	0.0128716i	0.259741	+	0.965678i	$0.416363\pi$
$884$	12.6430	−	36.5296i	0.425231	−	1.22862i
$885$	0.694283	+	14.5748i	0.0233381	+	0.489926i
$886$	0.163424	+	3.43070i	0.00549035	+	0.115257i
$887$	−2.91741	+	8.42929i	−0.0979569	+	0.283028i	−0.983323	−	0.181866i	$-0.941786\pi$
$887$	−2.91741	+	8.42929i	−0.0979569	+	0.283028i	0.885366	+	0.464894i	$0.153908\pi$
$888$	5.99291	−	1.75968i	0.201109	−	0.0590509i
$889$	−0.326187	−	0.989166i	−0.0109400	−	0.0331756i
$890$	4.96633	−	5.73145i	0.166472	−	0.192119i
$891$	0.165631	−	0.0158158i	0.00554884	−	0.000529850i
$892$	6.60967	−	6.30230i	0.221308	−	0.211017i
$893$	7.16378	+	0.684058i	0.239727	+	0.0228911i
$894$	14.8350	−	11.6664i	0.496156	−	0.390181i
$895$	−9.82462	−	6.31390i	−0.328401	−	0.211050i
$896$	−2.20453	−	1.46289i	−0.0736481	−	0.0488719i
$897$	−29.9520	+	3.17904i	−1.00007	+	0.106145i
$898$	−14.2952	−	24.7599i	−0.477035	−	0.826250i
$899$	−35.7929	+	18.4525i	−1.19376	+	0.615426i
$900$	−2.42929	−	0.972541i	−0.0809764	−	0.0324180i
$901$	10.7850	−	15.1454i	0.359300	−	0.504566i
$902$	−0.903680	−	0.265344i	−0.0300893	−	0.00883501i
$903$	−21.4398	−	11.4541i	−0.713472	−	0.381169i
$904$	−2.56198	+	2.95668i	−0.0852102	+	0.0983378i
$905$	−26.0927	+	10.4460i	−0.867352	+	0.347235i
$906$	−3.49615	+	14.4113i	−0.116152	+	0.478784i
$907$	−50.6325	+	9.75862i	−1.68122	+	0.324030i	−0.938425	−	0.345484i	$-0.887715\pi$
$907$	−50.6325	+	9.75862i	−1.68122	+	0.324030i	−0.742800	+	0.669513i	$0.766503\pi$
$908$	−11.0429	−	5.69299i	−0.366470	−	0.188929i
$909$	7.58047	−	4.87167i	0.251428	−	0.161583i
$910$	−20.3947	+	15.5599i	−0.676077	+	0.515805i
$911$	15.4582	−	4.53895i	0.512154	−	0.150382i	−0.0154364	−	0.999881i	$-0.504914\pi$
$911$	15.4582	−	4.53895i	0.512154	−	0.150382i	0.527590	+	0.849499i	$0.323096\pi$
$912$	1.24125	−	0.496921i	0.0411018	−	0.0164547i
$913$	−0.450631	−	1.30201i	−0.0149137	−	0.0430903i
$914$	22.1092	+	31.0480i	0.731306	+	1.02698i
$915$	−1.07404	−	4.42724i	−0.0355066	−	0.146360i
$916$	−1.35509	−	2.96722i	−0.0447733	−	0.0980398i
$917$	8.19429	−	17.2681i	0.270599	−	0.570243i
$918$	−5.17780	−	3.32757i	−0.170893	−	0.109826i
$919$	0.984772	+	1.70568i	0.0324846	+	0.0562650i	0.881811	−	0.471604i	$-0.156325\pi$
$919$	0.984772	+	1.70568i	0.0324846	+	0.0562650i	−0.849326	+	0.527869i	$0.822991\pi$
$920$	0.976348	−	7.33907i	0.0321892	−	0.241962i
$921$	15.2159	−	26.3547i	0.501381	−	0.868418i
$922$	0.866160	−	18.1829i	0.0285255	−	0.598823i
$923$	−12.4922	−	86.8848i	−0.411184	−	2.85985i
$924$	−0.342001	−	0.277167i	−0.0112510	−	0.00911812i
$925$	−15.6818	−	4.60460i	−0.515616	−	0.151398i
$926$	−9.15212	+	0.873922i	−0.300757	+	0.0287189i
$927$	1.83082	+	5.28981i	0.0601320	+	0.173740i
$928$	−8.16214	−	6.41878i	−0.267935	−	0.210707i
$929$	−12.2635	−	11.6932i	−0.402352	−	0.383641i	0.461707	−	0.887032i	$-0.347237\pi$
$929$	−12.2635	−	11.6932i	−0.402352	−	0.383641i	−0.864059	+	0.503391i	$0.832086\pi$
$930$	3.92065	+	4.52468i	0.128563	+	0.148370i
$931$	−8.44096	+	4.04275i	−0.276641	+	0.132496i
$932$	−19.8920	+	12.7838i	−0.651584	+	0.418747i
$933$	6.91191	−	19.9707i	0.226286	−	0.653810i
$934$	−7.63243	+	31.4613i	−0.249741	+	1.02944i
$935$	1.24271	+	0.977275i	0.0406408	+	0.0319603i
$936$	6.16701	+	1.18859i	0.201575	+	0.0388504i
$937$	−14.9046	+	32.6365i	−0.486912	+	1.06619i	0.493593	+	0.869693i	$0.335683\pi$
$937$	−14.9046	+	32.6365i	−0.486912	+	1.06619i	−0.980505	+	0.196495i	$0.937044\pi$
$938$	−22.1149	+	3.92678i	−0.722077	+	0.128214i
$939$	−0.393875	−	0.862466i	−0.0128536	−	0.0281455i
$940$	−6.53150	+	5.13643i	−0.213034	+	0.167532i
$941$	35.2424	−	18.1687i	1.14887	−	0.592283i	0.224760	−	0.974414i	$-0.427840\pi$
$941$	35.2424	−	18.1687i	1.14887	−	0.592283i	0.924108	+	0.382131i	$0.124810\pi$
$942$	−5.03544	+	8.72163i	−0.164063	+	0.284166i
$943$	13.3250	−	23.6519i	0.433922	−	0.770213i
$944$	−9.45166			−0.307625
$945$	1.64207	+	3.73985i	0.0534165	+	0.121657i
$946$	−0.217549	−	1.51308i	−0.00707312	−	0.0491946i
$947$	6.99067	−	9.81702i	0.227166	−	0.319010i	−0.685224	−	0.728333i	$-0.740296\pi$
$947$	6.99067	−	9.81702i	0.227166	−	0.319010i	0.912390	+	0.409323i	$0.134235\pi$
$948$	−5.86660	+	5.59380i	−0.190538	+	0.181678i
$949$	50.7697	+	71.2960i	1.64805	+	2.31437i
$950$	−3.43540	−	0.662120i	−0.111459	−	0.0214820i
$951$	3.16891	−	22.0402i	0.102759	−	0.714704i
$952$	3.60662	+	15.8798i	0.116891	+	0.514667i
$953$	7.22317	+	8.33599i	0.233982	+	0.270029i	0.860582	−	0.509311i	$-0.170100\pi$
$953$	7.22317	+	8.33599i	0.233982	+	0.270029i	−0.626601	+	0.779340i	$0.715554\pi$
$954$	2.68505	+	1.38424i	0.0869317	+	0.0448164i
$955$	0.311866	+	6.54687i	0.0100917	+	0.211852i
$956$	−11.2691	+	2.17194i	−0.364469	+	0.0702456i
$957$	−1.25038	−	1.19224i	−0.0404192	−	0.0385396i
$958$	0.865378	−	6.01884i	0.0279591	−	0.194460i
$959$	−18.9293	−	18.5867i	−0.611259	−	0.600197i
$960$	−0.641311	+	1.40427i	−0.0206982	+	0.0453228i
$961$	−3.76272	−	15.5102i	−0.121378	−	0.500328i
$962$	39.0499	+	3.72881i	1.25902	+	0.120222i
$963$	−9.60537	−	3.84541i	−0.309529	−	0.123917i
$964$	−0.479575	+	10.0675i	−0.0154461	+	0.324253i
$965$	14.8461			0.477913
$966$	10.0062	−	7.80233i	0.321943	−	0.251036i
$967$	−20.7065			−0.665877			−0.332938	−	0.942949i	$-0.608040\pi$
$967$	−20.7065			−0.665877			−0.332938	+	0.942949i	$0.608040\pi$
$968$	−0.522084	+	10.9599i	−0.0167804	+	0.352264i
$969$	−7.63970	−	3.05848i	−0.245423	−	0.0982524i
$970$	−4.12083	−	0.393492i	−0.132312	−	0.0126343i
$971$	7.65472	+	31.5532i	0.245652	+	1.01259i	0.952334	+	0.305058i	$0.0986759\pi$
$971$	7.65472	+	31.5532i	0.245652	+	1.01259i	−0.706682	+	0.707531i	$0.749809\pi$
$972$	0.415415	−	0.909632i	0.0133244	−	0.0291765i
$973$	−5.01312	+	19.4167i	−0.160713	+	0.622471i
$974$	−2.49521	+	17.3546i	−0.0799516	+	0.556076i
$975$	−11.8941	−	11.3410i	−0.380918	−	0.363204i
$976$	2.89764	−	0.558475i	0.0927512	−	0.0178763i
$977$	0.320947	+	6.73752i	0.0102680	+	0.215552i	0.998170	+	0.0604720i	$0.0192606\pi$
$977$	0.320947	+	6.73752i	0.0102680	+	0.215552i	−0.987902	+	0.155080i	$0.950436\pi$
$978$	−12.1154	−	6.24592i	−0.387408	−	0.199722i
$979$	0.535256	+	0.617718i	0.0171068	+	0.0197423i
$980$	3.83248	−	10.1041i	0.122424	−	0.322763i
$981$	−0.129769	+	0.902565i	−0.00414322	+	0.0288167i
$982$	2.51166	+	0.484084i	0.0801504	+	0.0154477i
$983$	−14.3329	−	20.1277i	−0.457148	−	0.641975i	0.520092	−	0.854110i	$-0.325898\pi$
$983$	−14.3329	−	20.1277i	−0.457148	−	0.641975i	−0.977240	+	0.212135i	$0.931958\pi$
$984$	−4.09675	+	3.90625i	−0.130600	+	0.124527i
$985$	−1.23607	+	1.73582i	−0.0393846	+	0.0553079i
$986$	9.09537	+	63.2597i	0.289656	+	2.01460i
$987$	−14.1546	−	1.56143i	−0.450545	−	0.0497008i
$988$	8.39717			0.267150
$989$	43.9036	+	3.72569i	1.39605	+	0.118470i
$990$	−0.128431	+	0.222448i	−0.00408179	+	0.00706987i
$991$	27.4059	−	14.1287i	0.870577	−	0.448813i	0.0357721	−	0.999360i	$-0.488611\pi$
$991$	27.4059	−	14.1287i	0.870577	−	0.448813i	0.834804	+	0.550547i	$0.185581\pi$
$992$	−3.04842	+	2.39731i	−0.0967875	+	0.0761145i
$993$	6.74983	+	14.7801i	0.214199	+	0.469031i
$994$	23.8028	+	28.2981i	0.754979	+	0.897563i
$995$	13.2759	−	29.0701i	0.420874	−	0.921586i
$996$	−8.13113	−	1.56715i	−0.257645	−	0.0496570i
$997$	34.2970	+	26.9715i	1.08620	+	0.854195i	0.989986	−	0.141166i	$-0.0450851\pi$
$997$	34.2970	+	26.9715i	1.08620	+	0.854195i	0.0962112	+	0.995361i	$0.469328\pi$
$998$	−6.99919	+	28.8510i	−0.221555	+	0.913264i
$999$	2.04284	−	5.90239i	0.0646325	−	0.186743i

Twists

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

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

\(f(q)\)	\(=\)	\(q+(0.0475819 - 0.998867i) q^{2} +(0.928368 + 0.371662i) q^{3} +(-0.995472 - 0.0950560i) q^{4} +(-0.363961 - 1.50027i) q^{5} +(0.415415 - 0.909632i) q^{6} +(-0.661406 + 2.56175i) q^{7} +(-0.142315 + 0.989821i) q^{8} +(0.723734 + 0.690079i) q^{9} +O(q^{10})\)	\(q+(0.0475819 - 0.998867i) q^{2} +(0.928368 + 0.371662i) q^{3} +(-0.995472 - 0.0950560i) q^{4} +(-0.363961 - 1.50027i) q^{5} +(0.415415 - 0.909632i) q^{6} +(-0.661406 + 2.56175i) q^{7} +(-0.142315 + 0.989821i) q^{8} +(0.723734 + 0.690079i) q^{9} +(-1.51589 + 0.292163i) q^{10} +(-0.00791688 - 0.166196i) q^{11} +(-0.888835 - 0.458227i) q^{12} +(-4.11286 - 4.74649i) q^{13} +(2.52737 + 0.782550i) q^{14} +(0.219703 - 1.52807i) q^{15} +(0.981929 + 0.189251i) q^{16} +(-3.57017 - 5.01360i) q^{17} +(0.723734 - 0.690079i) q^{18} +(0.775548 - 1.08911i) q^{19} +(0.219703 + 1.52807i) q^{20} +(-1.56613 + 2.13242i) q^{21} -0.166384 q^{22} +(1.08147 - 4.67230i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(2.32584 - 1.19906i) q^{25} +(-4.93681 + 3.88235i) q^{26} +(0.415415 + 0.909632i) q^{27} +(0.901921 - 2.48728i) q^{28} +(4.31355 - 9.44535i) q^{29} +(-1.51589 - 0.292163i) q^{30} +(-3.04842 - 2.39731i) q^{31} +(0.235759 - 0.971812i) q^{32} +(0.0544189 - 0.157233i) q^{33} +(-5.17780 + 3.32757i) q^{34} +(4.08403 + 0.0599106i) q^{35} +(-0.654861 - 0.755750i) q^{36} +(-4.52038 - 4.31017i) q^{37} +(-1.05097 - 0.826492i) q^{38} +(-2.05415 - 5.93509i) q^{39} +(1.53679 - 0.146746i) q^{40} +(5.43129 + 1.59477i) q^{41} +(2.05549 + 1.66582i) q^{42} +(1.30751 + 9.09392i) q^{43} +(-0.00791688 + 0.166196i) q^{44} +(0.771892 - 1.33696i) q^{45} +(-4.61555 - 1.30256i) q^{46} +(2.69119 + 4.66128i) q^{47} +(0.841254 + 0.540641i) q^{48} +(-6.12508 - 3.38871i) q^{49} +(-1.08703 - 2.38026i) q^{50} +(-1.45106 - 5.98136i) q^{51} +(3.64305 + 5.11595i) q^{52} +(0.988027 + 2.85472i) q^{53} +(0.928368 - 0.371662i) q^{54} +(-0.246456 + 0.0723662i) q^{55} +(-2.44154 - 1.01925i) q^{56} +(1.12477 - 0.722848i) q^{57} +(-9.22940 - 4.75809i) q^{58} +(-9.28085 + 1.78874i) q^{59} +(-0.363961 + 1.50027i) q^{60} +(2.73959 - 1.09676i) q^{61} +(-2.53964 + 2.93090i) q^{62} +(-2.24649 + 1.39760i) q^{63} +(-0.959493 - 0.281733i) q^{64} +(-5.62408 + 7.89792i) q^{65} +(-0.154466 - 0.0618388i) q^{66} +(-7.54567 + 3.89007i) q^{67} +(3.07743 + 5.33026i) q^{68} +(2.74052 - 3.93568i) q^{69} +(0.254169 - 4.07655i) q^{70} +(11.7576 + 7.55616i) q^{71} +(-0.786053 + 0.618159i) q^{72} +(-13.8729 - 1.32470i) q^{73} +(-4.52038 + 4.31017i) q^{74} +(2.60488 - 0.248736i) q^{75} +(-0.875563 + 1.01045i) q^{76} +(0.430988 + 0.0896418i) q^{77} +(-6.02610 + 1.76942i) q^{78} +(2.65122 - 7.66020i) q^{79} +(-0.0734562 - 1.54203i) q^{80} +(0.0475819 + 0.998867i) q^{81} +(1.85139 - 5.34925i) q^{82} +(7.94535 - 2.33296i) q^{83} +(1.76174 - 1.97390i) q^{84} +(-6.22233 + 7.18096i) q^{85} +(9.14583 - 0.873321i) q^{86} +(7.51504 - 7.16558i) q^{87} +(0.165631 + 0.0158158i) q^{88} +(-3.86146 + 3.03669i) q^{89} +(-1.29871 - 0.834632i) q^{90} +(14.8796 - 7.39674i) q^{91} +(-1.52070 + 4.54835i) q^{92} +(-1.93907 - 3.35857i) q^{93} +(4.78405 - 2.46635i) q^{94} +(-1.91622 - 0.767138i) q^{95} +(0.580057 - 0.814576i) q^{96} +(2.57283 + 0.755451i) q^{97} +(-3.67631 + 5.95691i) q^{98} +(0.108958 - 0.125745i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q + 8 q^{2} + 8 q^{3} + 8 q^{4} - 2 q^{5} - 16 q^{6} + 6 q^{7} - 16 q^{8} + 8 q^{9}+O(q^{10}) \) 160 * q + 8 * q^2 + 8 * q^3 + 8 * q^4 - 2 * q^5 - 16 * q^6 + 6 * q^7 - 16 * q^8 + 8 * q^9	\( 160 q + 8 q^{2} + 8 q^{3} + 8 q^{4} - 2 q^{5} - 16 q^{6} + 6 q^{7} - 16 q^{8} + 8 q^{9} - 2 q^{10} - 4 q^{11} + 8 q^{12} - 4 q^{13} + 5 q^{14} + 26 q^{15} + 8 q^{16} - 13 q^{17} + 8 q^{18} + 4 q^{19} + 26 q^{20} + 11 q^{21} - 124 q^{22} + 26 q^{23} - 80 q^{24} + 14 q^{25} + 2 q^{26} - 16 q^{27} - 22 q^{28} + 54 q^{29} - 2 q^{30} + 15 q^{31} + 8 q^{32} - 4 q^{33} + 4 q^{34} - 2 q^{35} - 16 q^{36} + 7 q^{37} - 7 q^{38} + 2 q^{39} + 9 q^{40} - 30 q^{41} + 6 q^{42} + 36 q^{43} - 4 q^{44} + 20 q^{45} + 4 q^{46} - 6 q^{47} - 16 q^{48} + 14 q^{49} - 28 q^{50} + 9 q^{51} + 2 q^{52} - 24 q^{53} + 8 q^{54} - 14 q^{55} + 6 q^{56} - 30 q^{57} - 5 q^{58} + 4 q^{59} - 2 q^{60} + 32 q^{61} - 8 q^{62} - 6 q^{63} - 16 q^{64} + 38 q^{65} - 4 q^{66} + 6 q^{67} + 42 q^{68} - 30 q^{69} - 8 q^{70} - 180 q^{71} + 8 q^{72} - 32 q^{73} + 7 q^{74} + 14 q^{75} - 8 q^{76} + 61 q^{77} + 18 q^{78} - 66 q^{79} - 2 q^{80} + 8 q^{81} - 7 q^{82} + 130 q^{83} + 5 q^{84} - 70 q^{85} - 40 q^{86} + 6 q^{87} - 15 q^{88} - 4 q^{89} + 4 q^{90} - 6 q^{91} + 58 q^{92} - 18 q^{93} + 16 q^{94} + 19 q^{95} + 8 q^{96} + 40 q^{97} + 43 q^{98} + 8 q^{99}+O(q^{100}) \) 160 * q + 8 * q^2 + 8 * q^3 + 8 * q^4 - 2 * q^5 - 16 * q^6 + 6 * q^7 - 16 * q^8 + 8 * q^9 - 2 * q^10 - 4 * q^11 + 8 * q^12 - 4 * q^13 + 5 * q^14 + 26 * q^15 + 8 * q^16 - 13 * q^17 + 8 * q^18 + 4 * q^19 + 26 * q^20 + 11 * q^21 - 124 * q^22 + 26 * q^23 - 80 * q^24 + 14 * q^25 + 2 * q^26 - 16 * q^27 - 22 * q^28 + 54 * q^29 - 2 * q^30 + 15 * q^31 + 8 * q^32 - 4 * q^33 + 4 * q^34 - 2 * q^35 - 16 * q^36 + 7 * q^37 - 7 * q^38 + 2 * q^39 + 9 * q^40 - 30 * q^41 + 6 * q^42 + 36 * q^43 - 4 * q^44 + 20 * q^45 + 4 * q^46 - 6 * q^47 - 16 * q^48 + 14 * q^49 - 28 * q^50 + 9 * q^51 + 2 * q^52 - 24 * q^53 + 8 * q^54 - 14 * q^55 + 6 * q^56 - 30 * q^57 - 5 * q^58 + 4 * q^59 - 2 * q^60 + 32 * q^61 - 8 * q^62 - 6 * q^63 - 16 * q^64 + 38 * q^65 - 4 * q^66 + 6 * q^67 + 42 * q^68 - 30 * q^69 - 8 * q^70 - 180 * q^71 + 8 * q^72 - 32 * q^73 + 7 * q^74 + 14 * q^75 - 8 * q^76 + 61 * q^77 + 18 * q^78 - 66 * q^79 - 2 * q^80 + 8 * q^81 - 7 * q^82 + 130 * q^83 + 5 * q^84 - 70 * q^85 - 40 * q^86 + 6 * q^87 - 15 * q^88 - 4 * q^89 + 4 * q^90 - 6 * q^91 + 58 * q^92 - 18 * q^93 + 16 * q^94 + 19 * q^95 + 8 * q^96 + 40 * q^97 + 43 * q^98 + 8 * q^99

Introduction

L-functions

Modular forms

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