LMFDB - Embedded newform 966.2.y.a.121.2

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			121.2
Character	$\chi$	$=$	966.121
Dual form			966.2.y.a.487.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.580057 - 0.814576i) q^{2} +(-0.235759 - 0.971812i) q^{3} +(-0.327068 + 0.945001i) q^{4} +(-0.128045 - 2.68799i) q^{5} +(-0.654861 + 0.755750i) q^{6} +(0.622376 + 2.57151i) q^{7} +(0.959493 - 0.281733i) q^{8} +(-0.888835 + 0.458227i) q^{9} +O(q^{10})$	\(q+(-0.580057 - 0.814576i) q^{2} +(-0.235759 - 0.971812i) q^{3} +(-0.327068 + 0.945001i) q^{4} +(-0.128045 - 2.68799i) q^{5} +(-0.654861 + 0.755750i) q^{6} +(0.622376 + 2.57151i) q^{7} +(0.959493 - 0.281733i) q^{8} +(-0.888835 + 0.458227i) q^{9} +(-2.11530 + 1.66349i) q^{10} +(-0.846403 + 1.18861i) q^{11} +(0.995472 + 0.0950560i) q^{12} +(0.759252 + 5.28072i) q^{13} +(1.73367 - 1.99859i) q^{14} +(-2.58203 + 0.758153i) q^{15} +(-0.786053 - 0.618159i) q^{16} +(8.02100 + 1.54592i) q^{17} +(0.888835 + 0.458227i) q^{18} +(4.17785 - 0.805214i) q^{19} +(2.58203 + 0.758153i) q^{20} +(2.35229 - 1.21109i) q^{21} +1.45917 q^{22} +(2.75650 - 3.92450i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(-2.23153 + 0.213086i) q^{25} +(3.86113 - 3.68158i) q^{26} +(0.654861 + 0.755750i) q^{27} +(-2.63364 - 0.252912i) q^{28} +(-0.144798 + 0.167106i) q^{29} +(2.11530 + 1.66349i) q^{30} +(-1.37512 - 1.31118i) q^{31} +(-0.0475819 + 0.998867i) q^{32} +(1.35465 + 0.542319i) q^{33} +(-3.39336 - 7.43043i) q^{34} +(6.83249 - 2.00221i) q^{35} +(-0.142315 - 0.989821i) q^{36} +(-6.96894 + 3.59274i) q^{37} +(-3.07930 - 2.93610i) q^{38} +(4.95286 - 1.98283i) q^{39} +(-0.880152 - 2.54303i) q^{40} +(-5.88881 + 3.78451i) q^{41} +(-2.35098 - 1.21362i) q^{42} +(8.25722 + 2.42454i) q^{43} +(-0.846403 - 1.18861i) q^{44} +(1.34552 + 2.33051i) q^{45} +(-4.79573 + 0.0310583i) q^{46} +(1.33862 - 2.31857i) q^{47} +(-0.415415 + 0.909632i) q^{48} +(-6.22530 + 3.20089i) q^{49} +(1.46799 + 1.69415i) q^{50} +(-0.388678 - 8.15936i) q^{51} +(-5.23861 - 1.00966i) q^{52} +(-0.339337 + 0.135850i) q^{53} +(0.235759 - 0.971812i) q^{54} +(3.30334 + 2.12293i) q^{55} +(1.32164 + 2.29200i) q^{56} +(-1.76748 - 3.87025i) q^{57} +(0.220112 + 0.0210181i) q^{58} +(-4.96780 + 3.90672i) q^{59} +(0.128045 - 2.68799i) q^{60} +(2.26690 - 9.34427i) q^{61} +(-0.270404 + 1.88070i) q^{62} +(-1.73152 - 2.00046i) q^{63} +(0.841254 - 0.540641i) q^{64} +(14.0973 - 2.71703i) q^{65} +(-0.344013 - 1.41804i) q^{66} +(4.22176 - 0.403129i) q^{67} +(-4.08431 + 7.07423i) q^{68} +(-4.46375 - 1.75356i) q^{69} +(-5.59418 - 4.40419i) q^{70} +(6.60129 - 14.4548i) q^{71} +(-0.723734 + 0.690079i) q^{72} +(2.47099 - 7.13946i) q^{73} +(6.96894 + 3.59274i) q^{74} +(0.733183 + 2.11839i) q^{75} +(-0.605512 + 4.21143i) q^{76} +(-3.58329 - 1.43677i) q^{77} +(-4.48810 - 2.88433i) q^{78} +(6.91264 + 2.76740i) q^{79} +(-1.56096 + 2.19205i) q^{80} +(0.580057 - 0.814576i) q^{81} +(6.49861 + 2.60165i) q^{82} +(7.57158 + 4.86596i) q^{83} +(0.375121 + 2.61902i) q^{84} +(3.12837 - 21.7583i) q^{85} +(-2.81469 - 8.13250i) q^{86} +(0.196533 + 0.101320i) q^{87} +(-0.477248 + 1.37892i) q^{88} +(-0.0608891 + 0.0580576i) q^{89} +(1.11790 - 2.44785i) q^{90} +(-13.1069 + 5.23901i) q^{91} +(2.80710 + 3.88847i) q^{92} +(-0.950021 + 1.64548i) q^{93} +(-2.66513 + 0.254489i) q^{94} +(-2.69936 - 11.1269i) q^{95} +(0.981929 - 0.189251i) q^{96} +(-0.533984 + 0.343170i) q^{97} +(6.21839 + 3.21428i) q^{98} +(0.207662 - 1.44432i) 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
$5$	−0.128045	−	2.68799i	−0.0572633	−	1.20211i	−0.826423	−	0.563049i	$-0.809628\pi$
$5$	−0.128045	−	2.68799i	−0.0572633	−	1.20211i	0.769160	−	0.639056i	$-0.220675\pi$
$6$	−0.654861	+	0.755750i	−0.267346	+	0.308533i
$7$	0.622376	+	2.57151i	0.235236	+	0.971938i
$7$	0.622376	+	2.57151i	0.235236	+	0.971938i
$8$	0.959493	−	0.281733i	0.339232	−	0.0996075i
$9$	−0.888835	+	0.458227i	−0.296278	+	0.152742i
$10$	−2.11530	+	1.66349i	−0.668916	+	0.526041i
$11$	−0.846403	+	1.18861i	−0.255200	+	0.358378i	−0.922223	−	0.386659i	$-0.873629\pi$
$11$	−0.846403	+	1.18861i	−0.255200	+	0.358378i	0.667023	+	0.745037i	$0.267568\pi$
$12$	0.995472	+	0.0950560i	0.287368	+	0.0274403i
$13$	0.759252	+	5.28072i	0.210579	+	1.46461i	0.771231	+	0.636556i	$0.219641\pi$
$13$	0.759252	+	5.28072i	0.210579	+	1.46461i	−0.560652	+	0.828051i	$0.689449\pi$
$14$	1.73367	−	1.99859i	0.463344	−	0.534146i
$15$	−2.58203	+	0.758153i	−0.666678	+	0.195754i
$16$	−0.786053	−	0.618159i	−0.196513	−	0.154540i
$17$	8.02100	+	1.54592i	1.94538	+	0.374941i	0.998590	+	0.0530801i	$0.0169039\pi$
$17$	8.02100	+	1.54592i	1.94538	+	0.374941i	0.946787	+	0.321861i	$0.104308\pi$
$18$	0.888835	+	0.458227i	0.209501	+	0.108005i
$19$	4.17785	−	0.805214i	0.958464	−	0.184729i	0.314051	−	0.949406i	$-0.398314\pi$
$19$	4.17785	−	0.805214i	0.958464	−	0.184729i	0.644413	+	0.764677i	$0.277102\pi$
$20$	2.58203	+	0.758153i	0.577360	+	0.169528i
$21$	2.35229	−	1.21109i	0.513312	−	0.264281i
$22$	1.45917			0.311096
$23$	2.75650	−	3.92450i	0.574769	−	0.818315i
$23$	2.75650	−	3.92450i	0.574769	−	0.818315i
$24$	−0.500000	−	0.866025i	−0.102062	−	0.176777i
$25$	−2.23153	+	0.213086i	−0.446307	+	0.0426171i
$26$	3.86113	−	3.68158i	0.757231	−	0.722018i
$27$	0.654861	+	0.755750i	0.126028	+	0.145444i
$28$	−2.63364	−	0.252912i	−0.497710	−	0.0477958i
$29$	−0.144798	+	0.167106i	−0.0268883	+	0.0310308i	−0.769034	−	0.639207i	$-0.779263\pi$
$29$	−0.144798	+	0.167106i	−0.0268883	+	0.0310308i	0.742146	+	0.670238i	$0.233808\pi$
$30$	2.11530	+	1.66349i	0.386199	+	0.303710i
$31$	−1.37512	−	1.31118i	−0.246980	−	0.235495i	0.556469	−	0.830868i	$-0.312156\pi$
$31$	−1.37512	−	1.31118i	−0.246980	−	0.235495i	−0.803449	+	0.595373i	$0.797004\pi$
$32$	−0.0475819	+	0.998867i	−0.00841137	+	0.176576i
$33$	1.35465	+	0.542319i	0.235814	+	0.0944057i
$34$	−3.39336	−	7.43043i	−0.581957	−	1.27431i
$35$	6.83249	−	2.00221i	1.15490	−	0.338435i
$36$	−0.142315	−	0.989821i	−0.0237191	−	0.164970i
$37$	−6.96894	+	3.59274i	−1.14569	+	0.590643i	−0.923210	−	0.384295i	$-0.874445\pi$
$37$	−6.96894	+	3.59274i	−1.14569	+	0.590643i	−0.222477	+	0.974938i	$0.571414\pi$
$38$	−3.07930	−	2.93610i	−0.499528	−	0.476299i
$39$	4.95286	−	1.98283i	0.793092	−	0.317506i
$40$	−0.880152	−	2.54303i	−0.139164	−	0.402089i
$41$	−5.88881	+	3.78451i	−0.919678	+	0.591041i	−0.912564	−	0.408934i	$-0.865901\pi$
$41$	−5.88881	+	3.78451i	−0.919678	+	0.591041i	−0.00711355	+	0.999975i	$0.502264\pi$
$42$	−2.35098	−	1.21362i	−0.362765	−	0.187265i
$43$	8.25722	+	2.42454i	1.25921	+	0.369739i	0.842202	−	0.539162i	$-0.181259\pi$
$43$	8.25722	+	2.42454i	1.25921	+	0.369739i	0.417012	+	0.908901i	$0.363077\pi$
$44$	−0.846403	−	1.18861i	−0.127600	−	0.179189i
$45$	1.34552	+	2.33051i	0.200578	+	0.347411i
$46$	−4.79573	+	0.0310583i	−0.707092	+	0.00457929i
$47$	1.33862	−	2.31857i	0.195258	−	0.338198i	−0.751727	−	0.659475i	$-0.770779\pi$
$47$	1.33862	−	2.31857i	0.195258	−	0.338198i	0.946985	+	0.321277i	$0.104112\pi$
$48$	−0.415415	+	0.909632i	−0.0599600	+	0.131294i
$49$	−6.22530	+	3.20089i	−0.889328	+	0.457270i
$50$	1.46799	+	1.69415i	0.207605	+	0.239589i
$51$	−0.388678	−	8.15936i	−0.0544258	−	1.14254i
$52$	−5.23861	−	1.00966i	−0.726464	−	0.140015i
$53$	−0.339337	+	0.135850i	−0.0466115	+	0.0186604i	−0.394851	−	0.918745i	$-0.629204\pi$
$53$	−0.339337	+	0.135850i	−0.0466115	+	0.0186604i	0.348240	+	0.937406i	$0.386780\pi$
$54$	0.235759	−	0.971812i	0.0320827	−	0.132247i
$55$	3.30334	+	2.12293i	0.445422	+	0.286255i
$56$	1.32164	+	2.29200i	0.176612	+	0.306281i
$57$	−1.76748	−	3.87025i	−0.234109	−	0.512626i
$58$	0.220112	+	0.0210181i	0.0289021	+	0.00275981i
$59$	−4.96780	+	3.90672i	−0.646753	+	0.508612i	−0.886803	−	0.462149i	$-0.847079\pi$
$59$	−4.96780	+	3.90672i	−0.646753	+	0.508612i	0.240050	+	0.970761i	$0.422836\pi$
$60$	0.128045	−	2.68799i	0.0165305	−	0.347018i
$61$	2.26690	−	9.34427i	0.290246	−	1.19641i	−0.620754	−	0.784005i	$-0.713173\pi$
$61$	2.26690	−	9.34427i	0.290246	−	1.19641i	0.911000	−	0.412406i	$-0.135311\pi$
$62$	−0.270404	+	1.88070i	−0.0343413	+	0.238849i
$63$	−1.73152	−	2.00046i	−0.218151	−	0.252034i
$64$	0.841254	−	0.540641i	0.105157	−	0.0675801i
$65$	14.0973	−	2.71703i	1.74855	−	0.337006i
$66$	−0.344013	−	1.41804i	−0.0423450	−	0.174549i
$67$	4.22176	−	0.403129i	0.515770	−	0.0492500i	0.166074	−	0.986113i	$-0.446891\pi$
$67$	4.22176	−	0.403129i	0.515770	−	0.0492500i	0.349696	+	0.936863i	$0.386285\pi$
$68$	−4.08431	+	7.07423i	−0.495295	+	0.857876i
$69$	−4.46375	−	1.75356i	−0.537372	−	0.211104i
$70$	−5.59418	−	4.40419i	−0.668633	−	0.526401i
$71$	6.60129	−	14.4548i	0.783429	−	1.71547i	0.0888595	−	0.996044i	$-0.471678\pi$
$71$	6.60129	−	14.4548i	0.783429	−	1.71547i	0.694569	−	0.719426i	$-0.255595\pi$
$72$	−0.723734	+	0.690079i	−0.0852929	+	0.0813266i
$73$	2.47099	−	7.13946i	0.289208	−	0.835610i	−0.703020	−	0.711171i	$-0.748165\pi$
$73$	2.47099	−	7.13946i	0.289208	−	0.835610i	0.992227	−	0.124440i	$-0.0397134\pi$
$74$	6.96894	+	3.59274i	0.810123	+	0.417648i
$75$	0.733183	+	2.11839i	0.0846607	+	0.244611i
$76$	−0.605512	+	4.21143i	−0.0694570	+	0.483084i
$77$	−3.58329	−	1.43677i	−0.408354	−	0.163735i
$78$	−4.48810	−	2.88433i	−0.508178	−	0.326586i
$79$	6.91264	+	2.76740i	0.777733	+	0.311357i	0.726353	−	0.687322i	$-0.241214\pi$
$79$	6.91264	+	2.76740i	0.777733	+	0.311357i	0.0513801	+	0.998679i	$0.483638\pi$
$80$	−1.56096	+	2.19205i	−0.174520	+	0.245079i
$81$	0.580057	−	0.814576i	0.0644508	−	0.0905084i
$82$	6.49861	+	2.60165i	0.717652	+	0.287304i
$83$	7.57158	+	4.86596i	0.831089	+	0.534108i	0.885624	−	0.464403i	$-0.153731\pi$
$83$	7.57158	+	4.86596i	0.831089	+	0.534108i	−0.0545348	+	0.998512i	$0.517368\pi$
$84$	0.375121	+	2.61902i	0.0409290	+	0.285759i
$85$	3.12837	−	21.7583i	0.339320	−	2.36002i
$86$	−2.81469	−	8.13250i	−0.303515	−	0.876950i
$87$	0.196533	+	0.101320i	0.0210706	+	0.0108626i
$88$	−0.477248	+	1.37892i	−0.0508748	+	0.146993i
$89$	−0.0608891	+	0.0580576i	−0.00645423	+	0.00615409i	−0.693299	−	0.720650i	$-0.743844\pi$
$89$	−0.0608891	+	0.0580576i	−0.00645423	+	0.00615409i	0.686845	+	0.726804i	$0.258995\pi$
$90$	1.11790	−	2.44785i	0.117837	−	0.258026i
$91$	−13.1069	+	5.23901i	−1.37397	+	0.549198i
$92$	2.80710	+	3.88847i	0.292660	+	0.405401i
$93$	−0.950021	+	1.64548i	−0.0985125	+	0.170629i
$94$	−2.66513	+	0.254489i	−0.274887	+	0.0262485i
$95$	−2.69936	−	11.1269i	−0.276948	−	1.14160i
$96$	0.981929	−	0.189251i	0.100218	−	0.0193154i
$97$	−0.533984	+	0.343170i	−0.0542178	+	0.0348437i	−0.567469	−	0.823395i	$-0.692077\pi$
$97$	−0.533984	+	0.343170i	−0.0542178	+	0.0348437i	0.513251	+	0.858238i	$0.328441\pi$
$98$	6.21839	+	3.21428i	0.628153	+	0.324691i
$99$	0.207662	−	1.44432i	0.0208708	−	0.145160i
$100$	0.528497	−	2.17849i	0.0528497	−	0.217849i
$101$	−0.767668	+	16.1153i	−0.0763859	+	1.60354i	0.557545	+	0.830147i	$0.311743\pi$
$101$	−0.767668	+	16.1153i	−0.0763859	+	1.60354i	−0.633931	+	0.773390i	$0.718560\pi$
$102$	−6.42096	+	5.04950i	−0.635770	+	0.499975i
$103$	−11.4889	−	1.09705i	−1.13203	−	0.108096i	−0.487821	−	0.872944i	$-0.662208\pi$
$103$	−11.4889	−	1.09705i	−1.13203	−	0.108096i	−0.644211	+	0.764848i	$0.722814\pi$
$104$	2.21625	+	4.85290i	0.217321	+	0.475866i
$105$	−3.55659	−	6.16786i	−0.347088	−	0.601921i
$106$	0.307495	+	0.197615i	0.0298666	+	0.0191941i
$107$	1.28557	−	5.29919i	0.124281	−	0.512292i	−0.875307	−	0.483568i	$-0.839341\pi$
$107$	1.28557	−	5.29919i	0.124281	−	0.512292i	0.999587	−	0.0287238i	$-0.00914433\pi$
$108$	−0.928368	+	0.371662i	−0.0893322	+	0.0357632i
$109$	6.03152	+	1.16248i	0.577715	+	0.111345i	0.469735	−	0.882808i	$-0.344350\pi$
$109$	6.03152	+	1.16248i	0.577715	+	0.111345i	0.107980	+	0.994153i	$0.465562\pi$
$110$	−0.186839	−	3.92224i	−0.0178144	−	0.373971i
$111$	5.13446	+	5.92548i	0.487341	+	0.562422i
$112$	1.10038	−	2.40607i	0.103976	−	0.227352i
$113$	1.71910	−	3.76431i	0.161720	−	0.354117i	−0.811374	−	0.584528i	$-0.801280\pi$
$113$	1.71910	−	3.76431i	0.161720	−	0.354117i	0.973093	+	0.230411i	$0.0740070\pi$
$114$	−2.12737	+	3.68471i	−0.199246	+	0.345105i
$115$	−10.9020	−	6.90693i	−1.01661	−	0.644074i
$116$	−0.110556	−	0.191489i	−0.0102649	−	0.0177793i
$117$	−3.09461	−	4.34578i	−0.286097	−	0.401767i
$118$	6.06393	+	1.78053i	0.558230	+	0.163911i
$119$	1.01673	+	21.5882i	0.0932036	+	1.97899i
$120$	−2.26384	+	1.45488i	−0.206660	+	0.132812i
$121$	2.90136	+	8.38293i	0.263760	+	0.762085i
$122$	−8.92655	+	3.57365i	−0.808172	+	0.323543i
$123$	5.06617	+	4.83058i	0.456801	+	0.435559i
$124$	1.68882	−	0.870649i	0.151661	−	0.0781866i
$125$	−1.05636	−	7.34718i	−0.0944842	−	0.657152i
$126$	−0.625143	+	2.57084i	−0.0556921	+	0.229028i
$127$	−0.222703	−	0.487651i	−0.0197617	−	0.0432720i	0.899494	−	0.436934i	$-0.143935\pi$
$127$	−0.222703	−	0.487651i	−0.0197617	−	0.0432720i	−0.919255	+	0.393661i	$0.871208\pi$
$128$	−0.928368	−	0.371662i	−0.0820569	−	0.0328506i
$129$	0.409481	−	8.59607i	0.0360528	−	0.756842i
$130$	−10.3905	−	9.90728i	−0.911304	−	0.868926i
$131$	7.49123	+	5.89117i	0.654512	+	0.514714i	0.889295	−	0.457334i	$-0.151196\pi$
$131$	7.49123	+	5.89117i	0.654512	+	0.514714i	−0.234783	+	0.972048i	$0.575438\pi$
$132$	−0.955554	+	1.10277i	−0.0831703	+	0.0959837i
$133$	4.67081	+	10.2422i	0.405010	+	0.888113i
$134$	−2.77724	−	3.20510i	−0.239917	−	0.276879i
$135$	1.94760	−	1.85703i	0.167622	−	0.159828i
$136$	8.13163	−	0.776476i	0.697281	−	0.0665823i
$137$	3.98437	+	6.90114i	0.340408	+	0.589604i	0.984508	−	0.175337i	$-0.0561015\pi$
$137$	3.98437	+	6.90114i	0.340408	+	0.589604i	−0.644100	+	0.764941i	$0.722768\pi$
$138$	1.16082	+	4.65322i	0.0988155	+	0.396109i
$139$	−3.10616			−0.263461			−0.131730	−	0.991286i	$-0.542053\pi$
$139$	−3.10616			−0.263461			−0.131730	+	0.991286i	$0.542053\pi$
$140$	−0.342601	+	7.11157i	−0.0289551	+	0.601037i
$141$	−2.56880	−	0.754268i	−0.216332	−	0.0635209i
$142$	−15.6037	+	3.00736i	−1.30943	+	0.252372i
$143$	−6.91932	−	3.56716i	−0.578623	−	0.298301i
$144$	0.981929	+	0.189251i	0.0818274	+	0.0157709i
$145$	0.467720	+	0.367819i	0.0388420	+	0.0305457i
$146$	−7.24895	+	2.12848i	−0.599927	+	0.176154i
$147$	4.57833	+	5.29518i	0.377614	+	0.436739i
$148$	−1.11582	−	7.76073i	−0.0917202	−	0.637928i
$149$	2.74208	+	0.261837i	0.224640	+	0.0214505i	0.206769	−	0.978390i	$-0.433705\pi$
$149$	2.74208	+	0.261837i	0.224640	+	0.0214505i	0.0178708	+	0.999840i	$0.494311\pi$
$150$	1.30030	−	1.82602i	0.106169	−	0.149094i
$151$	16.5604	−	13.0232i	1.34766	−	1.05982i	0.355527	−	0.934666i	$-0.384301\pi$
$151$	16.5604	−	13.0232i	1.34766	−	1.05982i	0.992138	−	0.125149i	$-0.0399410\pi$
$152$	3.78176	−	1.94963i	0.306741	−	0.158136i
$153$	−7.83773	+	2.30136i	−0.633643	+	0.186054i
$154$	0.908153	+	3.75227i	0.0731811	+	0.302367i
$155$	−3.34836	+	3.86421i	−0.268947	+	0.310381i
$156$	0.253850	+	5.32898i	0.0203243	+	0.426660i
$157$	−4.47138	+	12.9192i	−0.356855	+	1.03107i	0.613565	+	0.789644i	$0.289735\pi$
$157$	−4.47138	+	12.9192i	−0.356855	+	1.03107i	−0.970420	+	0.241421i	$0.922386\pi$
$158$	−1.75547	−	7.23613i	−0.139657	−	0.575675i
$159$	0.212022	+	0.297744i	0.0168145	+	0.0236126i
$160$	2.69104			0.212745
$161$	11.8075	+	4.64584i	0.930559	+	0.366143i
$162$	−1.00000			−0.0785674
$163$	−2.64532	−	3.71483i	−0.207197	−	0.290968i	0.697880	−	0.716214i	$-0.254127\pi$
$163$	−2.64532	−	3.71483i	−0.207197	−	0.290968i	−0.905077	+	0.425247i	$0.860187\pi$
$164$	−1.65032	−	6.80272i	−0.128869	−	0.531203i
$165$	1.28429	−	3.71072i	0.0999821	−	0.288879i
$166$	−0.428254	−	8.99016i	−0.0332390	−	0.697772i
$167$	13.2608	−	15.3038i	1.02615	−	1.18424i	0.0434483	−	0.999056i	$-0.486166\pi$
$167$	13.2608	−	15.3038i	1.02615	−	1.18424i	0.982703	−	0.185186i	$-0.0592889\pi$
$168$	1.91580	−	1.82475i	0.147807	−	0.140782i
$169$	−14.8361	+	4.35627i	−1.14124	+	0.335098i
$170$	−19.5384	+	10.0728i	−1.49853	+	0.772545i
$171$	−3.34445	+	2.63010i	−0.255756	+	0.201129i
$172$	−4.99186	+	7.01009i	−0.380626	+	0.534514i
$173$	−14.5445	−	1.38883i	−1.10580	−	0.105591i	−0.473853	−	0.880604i	$-0.657137\pi$
$173$	−14.5445	−	1.38883i	−1.10580	−	0.105591i	−0.631945	+	0.775013i	$0.717743\pi$
$174$	−0.0314677	−	0.218862i	−0.00238556	−	0.0165919i
$175$	−1.93680	−	5.60578i	−0.146409	−	0.423757i
$176$	1.40007	−	0.411096i	0.105534	−	0.0309875i
$177$	4.96780	+	3.90672i	0.373403	+	0.293647i
$178$	0.0826114	+	0.0159220i	0.00619199	+	0.00119341i
$179$	5.72952	+	2.95377i	0.428244	+	0.220775i	0.658854	−	0.752271i	$-0.271042\pi$
$179$	5.72952	+	2.95377i	0.428244	+	0.220775i	−0.230609	+	0.973046i	$0.574072\pi$
$180$	−2.64241	+	0.509282i	−0.196953	+	0.0379597i
$181$	−8.95460	−	2.62931i	−0.665590	−	0.195435i	−0.0685518	−	0.997648i	$-0.521838\pi$
$181$	−8.95460	−	2.62931i	−0.665590	−	0.195435i	−0.597038	+	0.802213i	$0.703656\pi$
$182$	11.8703	+	7.63760i	0.879885	+	0.566137i
$183$	−9.61531			−0.710784
$184$	1.53918	−	4.54213i	0.113470	−	0.334850i
$185$	10.5496	+	18.2724i	0.775621	+	1.34341i
$186$	1.89144	−	0.180610i	0.138687	−	0.0132430i
$187$	−8.62648	+	8.22533i	−0.630831	+	0.601496i
$188$	1.75323	+	2.02333i	0.127867	+	0.147567i
$189$	−1.53585	+	2.15434i	−0.111716	+	0.156705i
$190$	−7.49793	+	8.65307i	−0.543957	+	0.627760i
$191$	6.18269	+	4.86212i	0.447364	+	0.351811i	0.816284	−	0.577650i	$-0.196030\pi$
$191$	6.18269	+	4.86212i	0.447364	+	0.351811i	−0.368921	+	0.929461i	$0.620273\pi$
$192$	−0.723734	−	0.690079i	−0.0522310	−	0.0498022i
$193$	−1.19731	+	25.1346i	−0.0861840	+	1.80923i	0.380478	+	0.924790i	$0.375759\pi$
$193$	−1.19731	+	25.1346i	−0.0861840	+	1.80923i	−0.466662	+	0.884436i	$0.654544\pi$
$194$	0.589279	+	0.235912i	0.0423078	+	0.0169375i
$195$	−5.96400	−	13.0593i	−0.427091	−	0.935199i
$196$	−0.988747	−	6.92982i	−0.0706248	−	0.494987i
$197$	−0.866144	−	6.02417i	−0.0617102	−	0.429204i	−0.997133	−	0.0756723i	$-0.975890\pi$
$197$	−0.866144	−	6.02417i	−0.0617102	−	0.429204i	0.935423	−	0.353532i	$-0.115019\pi$
$198$	−1.29696	+	0.668631i	−0.0921712	+	0.0475175i
$199$	9.15891	+	8.73300i	0.649258	+	0.619066i	0.941393	−	0.337311i	$-0.109517\pi$
$199$	9.15891	+	8.73300i	0.649258	+	0.619066i	−0.292136	+	0.956377i	$0.594366\pi$
$200$	−2.08111	+	0.833150i	−0.147157	+	0.0589126i
$201$	−1.38708	−	4.00771i	−0.0978372	−	0.282682i
$202$	13.5725	−	8.72249i	0.954955	−	0.613712i
$203$	−0.519833	−	0.268347i	−0.0364851	−	0.0188343i
$204$	7.83773	+	2.30136i	0.548751	+	0.161128i
$205$	10.9268	+	15.3445i	0.763157	+	1.07170i
$206$	5.77057	+	9.99492i	0.402054	+	0.696379i
$207$	−0.651762	+	4.75134i	−0.0453006	+	0.330241i
$208$	2.66751	−	4.62026i	0.184958	−	0.320358i
$209$	−2.57906	+	5.64735i	−0.178397	+	0.390636i
$210$	−2.96116	+	6.47482i	−0.204340	+	0.446805i
$211$	−11.1810	−	12.9035i	−0.769730	−	0.888315i	0.226594	−	0.973989i	$-0.427241\pi$
$211$	−11.1810	−	12.9035i	−0.769730	−	0.888315i	−0.996323	+	0.0856740i	$0.972696\pi$
$212$	−0.0173921	−	0.365106i	−0.00119450	−	0.0250756i
$213$	−15.6037	−	3.00736i	−1.06915	−	0.206061i
$214$	−5.06230	+	2.02664i	−0.346051	+	0.138538i
$215$	5.45984	−	22.5058i	0.372358	−	1.53488i
$216$	0.841254	+	0.540641i	0.0572401	+	0.0367859i
$217$	2.51586	−	4.35219i	0.170788	−	0.295446i
$218$	−2.55170	−	5.58744i	−0.172823	−	0.378429i
$219$	−7.52077	−	0.718146i	−0.508206	−	0.0485278i
$220$	−3.08658	+	2.42732i	−0.208097	+	0.163650i
$221$	−2.07361	+	43.5303i	−0.139486	+	2.92817i
$222$	1.84848	−	7.61952i	0.124062	−	0.511389i
$223$	1.35205	−	9.40374i	0.0905402	−	0.629721i	−0.893138	−	0.449783i	$-0.851501\pi$
$223$	1.35205	−	9.40374i	0.0905402	−	0.629721i	0.983678	−	0.179938i	$-0.0575897\pi$
$224$	−2.59821	+	0.499314i	−0.173600	+	0.0333618i
$225$	1.88582	−	1.21195i	0.125722	−	0.0807964i
$226$	−4.06350	+	0.783175i	−0.270300	+	0.0520960i
$227$	−5.28603	−	21.7893i	−0.350846	−	1.44621i	−0.824683	−	0.565595i	$-0.808646\pi$
$227$	−5.28603	−	21.7893i	−0.350846	−	1.44621i	0.473836	−	0.880613i	$-0.342869\pi$
$228$	4.23547	−	0.404438i	0.280501	−	0.0267846i
$229$	−1.74881	+	3.02903i	−0.115565	+	0.200164i	−0.918005	−	0.396568i	$-0.870201\pi$
$229$	−1.74881	+	3.02903i	−0.115565	+	0.200164i	0.802441	+	0.596732i	$0.203534\pi$
$230$	0.697552	+	12.8869i	0.0459952	+	0.849737i
$231$	−0.551477	+	3.82101i	−0.0362845	+	0.251404i
$232$	−0.0918536	+	0.201131i	−0.00603049	+	0.0132049i
$233$	−9.14078	+	8.71571i	−0.598832	+	0.570985i	−0.927670	−	0.373401i	$-0.878192\pi$
$233$	−9.14078	+	8.71571i	−0.598832	+	0.570985i	0.328838	+	0.944386i	$0.393343\pi$
$234$	−1.74491	+	5.04160i	−0.114069	+	0.329580i
$235$	−6.40369	−	3.30133i	−0.417730	−	0.215355i
$236$	−2.06705	−	5.97234i	−0.134553	−	0.388766i
$237$	1.05968	−	7.37023i	0.0688335	−	0.478748i
$238$	16.9955	−	13.3506i	1.10165	−	0.865390i
$239$	−9.92175	−	6.37632i	−0.641784	−	0.412450i	0.178872	−	0.983872i	$-0.442755\pi$
$239$	−9.92175	−	6.37632i	−0.641784	−	0.412450i	−0.820656	+	0.571423i	$0.806392\pi$
$240$	2.49827	+	1.00016i	0.161263	+	0.0645599i
$241$	0.371028	−	0.521036i	0.0239000	−	0.0335629i	−0.802453	−	0.596715i	$-0.796472\pi$
$241$	0.371028	−	0.521036i	0.0239000	−	0.0335629i	0.826353	+	0.563152i	$0.190412\pi$
$242$	5.14558	−	7.22595i	0.330770	−	0.464502i
$243$	−0.928368	−	0.371662i	−0.0595548	−	0.0238422i
$244$	8.08892	+	5.19843i	0.517840	+	0.332795i
$245$	9.40107	+	16.3237i	0.600612	+	1.04288i
$246$	0.996210	−	6.92879i	0.0635160	−	0.441764i
$247$	7.42415	+	21.4507i	0.472387	+	1.36487i
$248$	−1.68882	−	0.870649i	−0.107240	−	0.0552863i
$249$	2.94373	−	8.50534i	0.186551	−	0.539004i
$250$	−5.37208	+	5.12227i	−0.339760	+	0.323961i
$251$	−7.26370	+	15.9053i	−0.458481	+	1.00393i	0.529351	+	0.848403i	$0.322436\pi$
$251$	−7.26370	+	15.9053i	−0.458481	+	1.00393i	−0.987831	+	0.155529i	$0.950292\pi$
$252$	2.45676	−	0.982005i	0.154761	−	0.0618605i
$253$	2.33158	+	6.59810i	0.146585	+	0.414819i
$254$	−0.268049	+	0.464274i	−0.0168189	+	0.0291311i
$255$	−21.8825	+	2.08953i	−1.37034	+	0.130851i
$256$	0.235759	+	0.971812i	0.0147349	+	0.0607382i
$257$	18.2550	−	3.51836i	1.13871	−	0.219469i	0.415168	−	0.909745i	$-0.363723\pi$
$257$	18.2550	−	3.51836i	1.13871	−	0.219469i	0.723547	+	0.690275i	$0.242511\pi$
$258$	−7.23967	+	4.65266i	−0.450722	+	0.289662i
$259$	−13.5761	−	15.6847i	−0.843575	−	0.974597i
$260$	−2.04318	+	14.2106i	−0.126712	+	0.881304i
$261$	0.0521294	−	0.214880i	0.00322673	−	0.0133007i
$262$	0.453465	−	9.51939i	0.0280151	−	0.588110i
$263$	−6.42549	+	5.05306i	−0.396213	+	0.311585i	−0.796311	−	0.604887i	$-0.793218\pi$
$263$	−6.42549	+	5.05306i	−0.396213	+	0.311585i	0.400099	+	0.916472i	$0.368976\pi$
$264$	1.45256	+	0.138703i	0.0893992	+	0.00853659i
$265$	0.408614	+	0.894740i	0.0251010	+	0.0549634i
$266$	5.63373	−	9.74580i	0.345426	−	0.597553i
$267$	0.0707762	+	0.0454851i	0.00433143	+	0.00278364i
$268$	−0.999844	+	4.12141i	−0.0610752	+	0.251755i
$269$	−9.14455	+	3.66093i	−0.557553	+	0.223211i	−0.633287	−	0.773917i	$-0.718295\pi$
$269$	−9.14455	+	3.66093i	−0.557553	+	0.223211i	0.0757332	+	0.997128i	$0.475870\pi$
$270$	−2.64241	−	0.509282i	−0.160812	−	0.0309939i
$271$	0.987026	+	20.7202i	0.0599576	+	1.25866i	0.805657	+	0.592382i	$0.201812\pi$
$271$	0.987026	+	20.7202i	0.0599576	+	1.25866i	−0.745700	+	0.666282i	$0.767885\pi$
$272$	−5.34930	−	6.17343i	−0.324349	−	0.374319i
$273$	8.18139	+	11.5023i	0.495160	+	0.696148i
$274$	3.31034	−	7.24863i	0.199985	−	0.437906i
$275$	1.63550	−	2.83277i	0.0986244	−	0.170822i
$276$	3.11706	−	3.64471i	0.187625	−	0.219386i
$277$	0.613312	+	1.06229i	0.0368503	+	0.0638267i	0.883862	−	0.467747i	$-0.154934\pi$
$277$	0.613312	+	1.06229i	0.0368503	+	0.0638267i	−0.847012	+	0.531574i	$0.821601\pi$
$278$	1.80175	+	2.53020i	0.108062	+	0.151751i
$279$	1.82308	+	0.535303i	0.109145	+	0.0320478i
$280$	5.99164	−	3.84604i	0.358069	−	0.229845i
$281$	8.87747	−	5.70520i	0.529586	−	0.340344i	−0.248368	−	0.968666i	$-0.579894\pi$
$281$	8.87747	−	5.70520i	0.529586	−	0.340344i	0.777954	+	0.628322i	$0.216258\pi$
$282$	0.875642	+	2.53000i	0.0521438	+	0.150659i
$283$	−22.3466	+	8.94625i	−1.32837	+	0.531799i	−0.923859	−	0.382734i	$-0.874983\pi$
$283$	−22.3466	+	8.94625i	−1.32837	+	0.531799i	−0.404512	+	0.914533i	$0.632558\pi$
$284$	11.5007	+	10.9659i	0.682443	+	0.650708i
$285$	−10.1769	+	5.24654i	−0.602825	+	0.310778i
$286$	1.10788	+	7.70547i	0.0655103	+	0.455634i
$287$	−13.3969	−	12.7877i	−0.790797	−	0.754836i
$288$	−0.415415	−	0.909632i	−0.0244786	−	0.0536006i
$289$	46.1643	+	18.4814i	2.71554	+	1.08714i
$290$	0.0283123	−	0.594349i	0.00166256	−	0.0349014i
$291$	0.459388	+	0.438026i	0.0269298	+	0.0256775i
$292$	5.93861	+	4.67018i	0.347531	+	0.273301i
$293$	−16.7532	+	19.3342i	−0.978733	+	1.12952i	0.0128332	+	0.999918i	$0.495915\pi$
$293$	−16.7532	+	19.3342i	−0.978733	+	1.12952i	−0.991566	+	0.129601i	$0.958630\pi$
$294$	1.65763	−	6.80090i	0.0966751	−	0.396637i
$295$	11.1373	+	12.8532i	0.648441	+	0.748340i
$296$	−5.67446	+	5.41059i	−0.329821	+	0.314484i
$297$	−1.45256	+	0.138703i	−0.0842863	+	0.00804837i
$298$	−1.37727	−	2.38551i	−0.0797834	−	0.138189i
$299$	22.8171	+	11.5766i	1.31954	+	0.669492i
$300$	−2.24168			−0.129424
$301$	−1.09562	+	22.7425i	−0.0631506	+	1.31085i
$302$	−20.2144	−	5.93548i	−1.16321	−	0.341548i
$303$	15.8421	−	3.05331i	0.910103	−	0.175408i
$304$	−3.78176	−	1.94963i	−0.216899	−	0.111819i
$305$	−25.4076	−	4.89691i	−1.45483	−	0.280396i
$306$	6.42096	+	5.04950i	0.367062	+	0.288661i
$307$	4.39340	−	1.29002i	0.250745	−	0.0736253i	−0.153945	−	0.988079i	$-0.549198\pi$
$307$	4.39340	−	1.29002i	0.250745	−	0.0736253i	0.404689	+	0.914454i	$0.367380\pi$
$308$	2.52973	−	2.91629i	0.144145	−	0.166171i
$309$	1.64247	+	11.4237i	0.0934371	+	0.649869i
$310$	5.08993	+	0.486029i	0.289089	+	0.0276046i
$311$	6.75998	−	9.49307i	0.383324	−	0.538303i	−0.577163	−	0.816629i	$-0.695840\pi$
$311$	6.75998	−	9.49307i	0.383324	−	0.538303i	0.960487	+	0.278326i	$0.0897797\pi$
$312$	4.19361	−	3.29789i	0.237416	−	0.186706i
$313$	−24.2499	+	12.5017i	−1.37069	+	0.706637i	−0.977126	−	0.212662i	$-0.931787\pi$
$313$	−24.2499	+	12.5017i	−1.37069	+	0.706637i	−0.393560	+	0.919299i	$0.628756\pi$
$314$	13.1173	−	3.85160i	0.740254	−	0.217358i
$315$	−5.15550	+	4.91046i	−0.290479	+	0.276673i
$316$	−4.87610	+	5.62732i	−0.274302	+	0.316562i
$317$	−1.53100	−	32.1396i	−0.0859894	−	1.80514i	−0.470901	−	0.882186i	$-0.656071\pi$
$317$	−1.53100	−	32.1396i	−0.0859894	−	1.80514i	0.384911	−	0.922954i	$-0.374232\pi$
$318$	0.119550	−	0.345417i	0.00670403	−	0.0193700i
$319$	−0.0760657	−	0.313547i	−0.00425886	−	0.0175553i
$320$	−1.56096	−	2.19205i	−0.0872600	−	0.122540i
$321$	−5.45290			−0.304351
$322$	−3.06461	−	12.3129i	−0.170784	−	0.686173i
$323$	34.7553			1.93384
$324$	0.580057	+	0.814576i	0.0322254	+	0.0452542i
$325$	−2.81954	−	11.6223i	−0.156400	−	0.644690i
$326$	−1.49157	+	4.30962i	−0.0826106	+	0.238688i
$327$	−0.292273	−	6.13557i	−0.0161627	−	0.339298i
$328$	−4.58405	+	5.29028i	−0.253112	+	0.292107i
$329$	6.79534	+	1.99926i	0.374639	+	0.110223i
$330$	−3.76763	+	1.10628i	−0.207401	+	0.0608985i
$331$	−19.5788	+	10.0936i	−1.07615	+	0.554794i	−0.902798	−	0.430065i	$-0.858490\pi$
$331$	−19.5788	+	10.0936i	−1.07615	+	0.554794i	−0.173353	+	0.984860i	$0.555460\pi$
$332$	−7.07476	+	5.56365i	−0.388278	+	0.305345i
$333$	4.54796	−	6.38671i	0.249226	−	0.349990i
$334$	−20.1581	−	1.92487i	−1.10300	−	0.105324i
$335$	−1.62418	−	11.2964i	−0.0887384	−	0.617189i
$336$	−2.59767	−	0.502109i	−0.141714	−	0.0273923i
$337$	25.3392	−	7.44026i	1.38031	−	0.405297i	0.494436	−	0.869214i	$-0.335375\pi$
$337$	25.3392	−	7.44026i	1.38031	−	0.405297i	0.885878	+	0.463917i	$0.153557\pi$
$338$	12.1543	+	9.55824i	0.661106	+	0.519900i
$339$	−4.06350	−	0.783175i	−0.220699	−	0.0425362i
$340$	19.5384	+	10.0728i	1.05962	+	0.546272i
$341$	2.72238	−	0.524696i	0.147425	−	0.0284139i
$342$	4.08239	+	1.19870i	0.220750	+	0.0648182i
$343$	−12.1056	−	14.0162i	−0.653640	−	0.756806i
$344$	8.60582			0.463994
$345$	−4.14199	+	12.2230i	−0.222997	+	0.658066i
$346$	7.30533	+	12.6532i	0.392737	+	0.680240i
$347$	−23.8748	+	2.27977i	−1.28167	+	0.122384i	−0.713573	−	0.700580i	$-0.752925\pi$
$347$	−23.8748	+	2.27977i	−1.28167	+	0.122384i	−0.568093	+	0.822965i	$0.692318\pi$
$348$	−0.160027	+	0.152585i	−0.00857835	+	0.00817944i
$349$	14.0055	+	16.1632i	0.749695	+	0.865195i	0.994539	−	0.104368i	$-0.0332820\pi$
$349$	14.0055	+	16.1632i	0.749695	+	0.865195i	−0.244843	+	0.969563i	$0.578737\pi$
$350$	−3.44288	+	4.82935i	−0.184030	+	0.258140i
$351$	−3.49369	+	4.03194i	−0.186480	+	0.215209i
$352$	−1.14699	−	0.902000i	−0.0611346	−	0.0480768i
$353$	−19.9079	−	18.9821i	−1.05959	−	1.01032i	−0.999927	−	0.0120978i	$-0.996149\pi$
$353$	−19.9079	−	18.9821i	−1.05959	−	1.01032i	−0.0596625	−	0.998219i	$-0.519002\pi$
$354$	0.300714	−	6.31277i	0.0159828	−	0.335520i
$355$	−39.6996	−	15.8933i	−2.10704	−	0.843531i
$356$	−0.0349496	−	0.0765290i	−0.00185233	−	0.00405603i
$357$	20.7400	−	6.07768i	1.09767	−	0.321665i
$358$	−0.917375	−	6.38048i	−0.0484848	−	0.337219i
$359$	17.2304	−	8.88287i	0.909384	−	0.468820i	0.0609616	−	0.998140i	$-0.480583\pi$
$359$	17.2304	−	8.88287i	0.909384	−	0.468820i	0.848422	+	0.529320i	$0.177553\pi$
$360$	1.94760	+	1.85703i	0.102647	+	0.0978740i
$361$	−0.832943	+	0.333460i	−0.0438391	+	0.0175505i
$362$	3.05241	+	8.81935i	0.160431	+	0.463535i
$363$	7.46261	−	4.79593i	0.391685	−	0.251721i
$364$	−0.664039	−	14.0995i	−0.0348051	−	0.739015i
$365$	−19.5072	−	5.72783i	−1.02105	−	0.299808i
$366$	5.57743	+	7.83240i	0.291537	+	0.409406i
$367$	−14.7172	−	25.4909i	−0.768229	−	1.33061i	−0.938522	−	0.345218i	$-0.887805\pi$
$367$	−14.7172	−	25.4909i	−0.768229	−	1.33061i	0.170293	−	0.985393i	$-0.445528\pi$
$368$	−4.59272	+	1.38091i	−0.239412	+	0.0719851i
$369$	3.50002	−	6.06221i	0.182204	−	0.315586i
$370$	8.76491	−	19.1925i	0.455666	−	0.997770i
$371$	−0.560535	−	0.788058i	−0.0291015	−	0.0409139i
$372$	−1.24426	−	1.43596i	−0.0645120	−	0.0744508i
$373$	0.0128691	+	0.270157i	0.000666339	+	0.0139882i	0.999176	−	0.0405867i	$-0.0129227\pi$
$373$	0.0128691	+	0.270157i	0.000666339	+	0.0139882i	−0.998510	+	0.0545748i	$0.982620\pi$
$374$	11.7040	+	2.25576i	0.605200	+	0.116643i
$375$	−6.89103	+	2.75875i	−0.355851	+	0.142461i
$376$	0.631185	−	2.60178i	0.0325509	−	0.134177i
$377$	−0.992378	−	0.637762i	−0.0511101	−	0.0328464i
$378$	2.64575	+	0.00142353i	0.136083	+	7.32183e-5i
$379$	−2.44744	−	5.35915i	−0.125717	−	0.275281i	0.836300	−	0.548272i	$-0.184714\pi$
$379$	−2.44744	−	5.35915i	−0.125717	−	0.275281i	−0.962017	+	0.272991i	$0.911987\pi$
$380$	11.3978	+	1.08836i	0.584695	+	0.0558316i
$381$	−0.421401	+	0.331393i	−0.0215890	+	0.0169778i
$382$	0.374255	−	7.85657i	0.0191485	−	0.401977i
$383$	7.67375	−	31.6316i	0.392110	−	1.61630i	−0.343677	−	0.939088i	$-0.611672\pi$
$383$	7.67375	−	31.6316i	0.392110	−	1.61630i	0.735787	−	0.677213i	$-0.236812\pi$
$384$	−0.142315	+	0.989821i	−0.00726247	+	0.0505116i
$385$	−3.40320	+	9.81582i	−0.173443	+	0.500260i
$386$	21.1685	−	13.6042i	1.07745	−	0.692434i
$387$	−8.45030	+	1.62866i	−0.429553	+	0.0827895i
$388$	−0.149647	−	0.616855i	−0.00759720	−	0.0313161i
$389$	2.82791	−	0.270033i	0.143381	−	0.0136912i	−0.0231188	−	0.999733i	$-0.507360\pi$
$389$	2.82791	−	0.270033i	0.143381	−	0.0136912i	0.166500	+	0.986042i	$0.446754\pi$
$390$	−7.17837	+	12.4333i	−0.363491	+	0.629585i
$391$	28.1768	−	27.2171i	1.42496	−	1.37643i
$392$	−5.07133	+	4.82510i	−0.256141	+	0.243704i
$393$	3.95898	−	8.66896i	0.199704	−	0.437291i
$394$	−4.40473	+	4.19990i	−0.221907	+	0.211588i
$395$	6.55363	−	18.9355i	0.329749	−	0.952747i
$396$	1.29696	+	0.668631i	0.0651749	+	0.0336000i
$397$	3.27451	+	9.46109i	0.164343	+	0.474838i	0.996862	−	0.0791582i	$-0.0252232\pi$
$397$	3.27451	+	9.46109i	0.164343	+	0.474838i	−0.832519	+	0.553997i	$0.813102\pi$
$398$	1.80100	−	12.5263i	0.0902762	−	0.627885i
$399$	8.85232	−	6.95384i	0.443170	−	0.348127i
$400$	1.88582	+	1.21195i	0.0942912	+	0.0605973i
$401$	−28.4210	−	11.3780i	−1.41928	−	0.568192i	−0.470008	−	0.882662i	$-0.655749\pi$
$401$	−28.4210	−	11.3780i	−1.41928	−	0.568192i	−0.949267	+	0.314470i	$0.898173\pi$
$402$	−2.46000	+	3.45458i	−0.122694	+	0.172299i
$403$	5.87989	−	8.25716i	0.292898	−	0.411318i
$404$	−14.9779	−	5.99626i	−0.745180	−	0.298325i
$405$	−2.26384	−	1.45488i	−0.112491	−	0.0722938i
$406$	0.0829440	+	0.579100i	0.00411644	+	0.0287403i
$407$	1.62818	−	11.3242i	0.0807058	−	0.561322i
$408$	−2.67169	−	7.71935i	−0.132268	−	0.382165i
$409$	−10.7974	−	5.56646i	−0.533898	−	0.275244i	0.170123	−	0.985423i	$-0.445584\pi$
$409$	−10.7974	−	5.56646i	−0.533898	−	0.275244i	−0.704021	+	0.710179i	$0.748614\pi$
$410$	6.16110	−	17.8013i	0.304275	−	0.879145i
$411$	5.76725	−	5.49907i	0.284478	−	0.271249i
$412$	4.79436	−	10.4982i	0.236201	−	0.517208i
$413$	−13.1380	−	10.3433i	−0.646479	−	0.508960i
$414$	4.24838	−	2.22514i	0.208797	−	0.109360i
$415$	12.1101	−	20.9754i	0.594464	−	1.02964i
$416$	−5.31086	+	0.507126i	−0.260386	+	0.0248639i
$417$	0.732305	+	3.01860i	0.0358611	+	0.147822i
$418$	6.09620	−	1.17495i	0.298175	−	0.0574685i
$419$	−27.1193	+	17.4285i	−1.32487	+	0.851439i	−0.995682	−	0.0928266i	$-0.970410\pi$
$419$	−27.1193	+	17.4285i	−1.32487	+	0.851439i	−0.329183	+	0.944266i	$0.606773\pi$
$420$	6.99188	−	1.34367i	0.341169	−	0.0655645i
$421$	0.397355	−	2.76366i	0.0193659	−	0.134693i	−0.977845	−	0.209331i	$-0.932871\pi$
$421$	0.397355	−	2.76366i	0.0193659	−	0.134693i	0.997211	+	0.0746387i	$0.0237804\pi$
$422$	−4.02530	+	16.5925i	−0.195949	+	0.807712i
$423$	−0.127389	+	2.67422i	−0.00619385	+	0.130025i
$424$	−0.287318	+	0.225950i	−0.0139534	+	0.0109731i
$425$	−18.2285	−	1.74061i	−0.884214	−	0.0844322i
$426$	6.60129	+	14.4548i	0.319833	+	0.700338i
$427$	25.4397	+	0.0136877i	1.23111	+	0.000662392i
$428$	4.58727	+	2.94806i	0.221734	+	0.142500i
$429$	−1.83531	+	7.56527i	−0.0886098	+	0.365255i
$430$	−21.4997	+	8.60717i	−1.03681	+	0.415075i
$431$	−29.2726	−	5.64184i	−1.41001	−	0.271758i	−0.573276	−	0.819362i	$-0.694328\pi$
$431$	−29.2726	−	5.64184i	−1.41001	−	0.271758i	−0.836737	+	0.547604i	$0.815540\pi$
$432$	−0.0475819	−	0.998867i	−0.00228929	−	0.0480580i
$433$	−9.57427	−	11.0493i	−0.460110	−	0.530995i	0.477524	−	0.878619i	$-0.341534\pi$
$433$	−9.57427	−	11.0493i	−0.460110	−	0.530995i	−0.937634	+	0.347623i	$0.886989\pi$
$434$	−5.00453	+	0.475158i	−0.240225	+	0.0228083i
$435$	0.247182	−	0.541252i	0.0118515	−	0.0259511i
$436$	−3.07126	+	5.31958i	−0.147087	+	0.254762i
$437$	8.35616	−	18.6155i	0.399730	−	0.890502i
$438$	3.77749	+	6.54280i	0.180495	+	0.312627i
$439$	19.1190	+	26.8489i	0.912502	+	1.28143i	0.959260	+	0.282524i	$0.0911717\pi$
$439$	19.1190	+	26.8489i	0.912502	+	1.28143i	−0.0467579	+	0.998906i	$0.514889\pi$
$440$	3.76763	+	1.10628i	0.179615	+	0.0527396i
$441$	4.06653	−	5.69766i	0.193644	−	0.271317i
$442$	36.6616	−	23.5610i	1.74381	−	1.12068i
$443$	7.31685	+	21.1407i	0.347634	+	1.00442i	0.974323	+	0.225154i	$0.0722884\pi$
$443$	7.31685	+	21.1407i	0.347634	+	1.00442i	−0.626689	+	0.779269i	$0.715590\pi$
$444$	−7.27890	+	2.91403i	−0.345441	+	0.138294i
$445$	0.163855	+	0.156235i	0.00776746	+	0.00740626i
$446$	−8.44433	+	4.35335i	−0.399851	+	0.206137i
$447$	−0.392013	−	2.72651i	−0.0185416	−	0.128960i
$448$	1.91384	+	1.82681i	0.0904203	+	0.0863085i
$449$	−5.06551	−	11.0919i	−0.239056	−	0.523461i	0.751636	−	0.659578i	$-0.229265\pi$
$449$	−5.06551	−	11.0919i	−0.239056	−	0.523461i	−0.990693	+	0.136117i	$0.956538\pi$
$450$	−2.08111	−	0.833150i	−0.0981043	−	0.0392751i
$451$	0.486014	−	10.2027i	0.0228855	−	0.480426i
$452$	2.99502	+	2.85574i	0.140874	+	0.134323i
$453$	−16.5604	−	13.0232i	−0.778075	−	0.611885i
$454$	−14.6829	+	16.9449i	−0.689101	+	0.795265i
$455$	15.7607	+	34.5603i	0.738872	+	1.62021i
$456$	−2.78626	−	3.21552i	−0.130479	−	0.150580i
$457$	26.1859	−	24.9682i	1.22492	−	1.16796i	0.244799	−	0.969574i	$-0.421278\pi$
$457$	26.1859	−	24.9682i	1.22492	−	1.16796i	0.980124	−	0.198388i	$-0.0635705\pi$
$458$	3.48178	−	0.332470i	0.162693	−	0.0155353i
$459$	4.08431	+	7.07423i	0.190639	+	0.330197i
$460$	10.0927	−	8.04334i	0.470576	−	0.375023i
$461$	−25.8972			−1.20615			−0.603076	−	0.797684i	$-0.706058\pi$
$461$	−25.8972			−1.20615			−0.603076	+	0.797684i	$0.706058\pi$
$462$	3.43239	−	1.76719i	0.159689	−	0.0822169i
$463$	−28.6665	−	8.41725i	−1.33225	−	0.391183i	−0.463349	−	0.886176i	$-0.653353\pi$
$463$	−28.6665	−	8.41725i	−1.33225	−	0.391183i	−0.868897	+	0.494993i	$0.835171\pi$
$464$	0.217117	−	0.0418459i	0.0100794	−	0.00194265i
$465$	4.54469	+	2.34295i	0.210755	+	0.108652i
$466$	12.4018	+	2.39025i	0.574501	+	0.110726i
$467$	−18.3273	−	14.4128i	−0.848087	−	0.666943i	0.0964536	−	0.995337i	$-0.469250\pi$
$467$	−18.3273	−	14.4128i	−0.848087	−	0.666943i	−0.944541	+	0.328394i	$0.893492\pi$
$468$	5.11891	−	1.50305i	0.236622	−	0.0694784i
$469$	3.66417	+	10.6054i	0.169196	+	0.489711i
$470$	1.02532	+	7.13125i	0.0472944	+	0.328940i
$471$	13.6092	+	1.29952i	0.627079	+	0.0598788i
$472$	−3.66592	+	5.14807i	−0.168738	+	0.236959i
$473$	−9.87075	+	7.76245i	−0.453858	+	0.356918i
$474$	−6.61828	+	3.41196i	−0.303988	+	0.156717i
$475$	−9.15143	+	2.68710i	−0.419896	+	0.123293i
$476$	−20.7334	−	6.09999i	−0.950314	−	0.279593i
$477$	0.239365	−	0.276242i	0.0109598	−	0.0126482i
$478$	0.561181	+	11.7806i	0.0256678	+	0.538834i
$479$	−7.71030	+	22.2775i	−0.352293	+	1.01788i	0.620098	+	0.784524i	$0.287093\pi$
$479$	−7.71030	+	22.2775i	−0.352293	+	1.01788i	−0.972391	+	0.233359i	$0.925028\pi$
$480$	−0.634436	−	2.61518i	−0.0289579	−	0.119366i
$481$	−24.2634	−	34.0732i	−1.10632	−	1.55361i
$482$	−0.639640			−0.0291348
$483$	1.73116	−	12.5699i	0.0787706	−	0.571952i
$484$	−8.87082			−0.403219
$485$	0.990812	+	1.39140i	0.0449905	+	0.0631803i
$486$	0.235759	+	0.971812i	0.0106942	+	0.0440823i
$487$	4.27886	−	12.3630i	0.193894	−	0.560219i	−0.805586	−	0.592479i	$-0.798149\pi$
$487$	4.27886	−	12.3630i	0.193894	−	0.560219i	0.999480	+	0.0322600i	$0.0102705\pi$
$488$	−0.457515	−	9.60442i	−0.0207107	−	0.434772i
$489$	−2.98645	+	3.44655i	−0.135052	+	0.155858i
$490$	7.84372	−	17.1265i	0.354343	−	0.773699i
$491$	2.04449	−	0.600317i	0.0922666	−	0.0270919i	−0.235273	−	0.971929i	$-0.575599\pi$
$491$	2.04449	−	0.600317i	0.0922666	−	0.0270919i	0.327540	+	0.944837i	$0.393780\pi$
$492$	−6.22189	+	3.20760i	−0.280504	+	0.144610i
$493$	−1.41976	+	1.11651i	−0.0639427	+	0.0502851i
$494$	13.1668	−	18.4901i	0.592401	−	0.831911i
$495$	−3.90891	−	0.373255i	−0.175692	−	0.0167766i
$496$	0.270404	+	1.88070i	0.0121415	+	0.0844460i
$497$	41.2791	+	7.97894i	1.85162	+	0.357904i
$498$	−8.63578	+	2.53569i	−0.386978	+	0.113627i
$499$	25.2901	+	19.8884i	1.13214	+	0.890326i	0.994965	−	0.100220i	$-0.0319548\pi$
$499$	25.2901	+	19.8884i	1.13214	+	0.890326i	0.137177	+	0.990547i	$0.456197\pi$
$500$	7.28859	+	1.40476i	0.325956	+	0.0628228i
$501$	−17.9987	−	9.27900i	−0.804125	−	0.414555i
$502$	17.1694	−	3.30913i	0.766309	−	0.147694i
$503$	12.6235	+	3.70659i	0.562853	+	0.165269i	0.550768	−	0.834658i	$-0.314335\pi$
$503$	12.6235	+	3.70659i	0.562853	+	0.165269i	0.0120850	+	0.999927i	$0.496153\pi$
$504$	−2.22498	−	1.43160i	−0.0991084	−	0.0637685i
$505$	43.4162			1.93199
$506$	4.02220	−	5.72652i	0.178809	−	0.254575i
$507$	7.73121	+	13.3909i	0.343355	+	0.594709i
$508$	0.533670	−	0.0509593i	0.0236778	−	0.00226095i
$509$	−0.234028	+	0.223145i	−0.0103731	+	0.00989074i	−0.695248	−	0.718770i	$-0.744705\pi$
$509$	−0.234028	+	0.223145i	−0.0103731	+	0.00989074i	0.684875	+	0.728661i	$0.259857\pi$
$510$	14.3952	+	16.6129i	0.637429	+	0.735633i
$511$	19.8971	+	1.91074i	0.880194	+	0.0845262i
$512$	0.654861	−	0.755750i	0.0289410	−	0.0333997i
$513$	3.34445	+	2.63010i	0.147661	+	0.116122i
$514$	−13.4549	−	12.8292i	−0.593470	−	0.565873i
$515$	−1.47778	+	31.0225i	−0.0651188	+	1.36701i
$516$	7.98936	+	3.19846i	0.351712	+	0.140804i
$517$	1.62285	+	3.55354i	0.0713727	+	0.156284i
$518$	−4.90145	+	20.1567i	−0.215357	+	0.885636i
$519$	2.07931	+	14.4619i	0.0912717	+	0.634809i
$520$	12.7608	−	6.57864i	0.559597	−	0.288492i
$521$	31.1437	+	29.6954i	1.36443	+	1.30098i	0.912587	+	0.408882i	$0.134081\pi$
$521$	31.1437	+	29.6954i	1.36443	+	1.30098i	0.451842	+	0.892098i	$0.350767\pi$
$522$	−0.205274	+	0.0821794i	−0.00898461	+	0.00359689i
$523$	−1.74872	−	5.05260i	−0.0764663	−	0.220935i	0.900289	−	0.435293i	$-0.143355\pi$
$523$	−1.74872	−	5.05260i	−0.0764663	−	0.220935i	−0.976755	+	0.214358i	$0.931234\pi$
$524$	−8.01730	+	5.15241i	−0.350237	+	0.225084i
$525$	−4.99115	+	3.20382i	−0.217832	+	0.139826i
$526$	7.84326	+	2.30299i	0.341982	+	0.100415i
$527$	−9.00289	−	12.6428i	−0.392172	−	0.550729i
$528$	−0.729586	−	1.26368i	−0.0317511	−	0.0549946i
$529$	−7.80344	−	21.6358i	−0.339280	−	0.940685i
$530$	0.491814	−	0.851847i	0.0213630	−	0.0370019i
$531$	2.62539	−	5.74881i	0.113932	−	0.249477i
$532$	−11.2066	+	1.06401i	−0.485867	+	0.0461309i
$533$	−24.4560	−	28.2237i	−1.05931	−	1.22251i
$534$	−0.00400315	−	0.0840365i	−0.000173233	−	0.00363662i
$535$	−14.4088	−	2.77706i	−0.622946	−	0.120063i
$536$	3.93717	−	1.57621i	0.170060	−	0.0680817i
$537$	1.51972	−	6.26439i	0.0655810	−	0.270328i
$538$	8.28647	+	5.32539i	0.357255	+	0.229594i
$539$	1.46451	−	10.1087i	0.0630810	−	0.435411i
$540$	1.11790	+	2.44785i	0.0481066	+	0.105339i
$541$	31.3800	+	2.99642i	1.34913	+	0.128826i	0.744469	−	0.667657i	$-0.232703\pi$
$541$	31.3800	+	2.99642i	1.34913	+	0.128826i	0.604661	+	0.796483i	$0.293309\pi$
$542$	16.3057	−	12.8229i	0.700388	−	0.550792i
$543$	−0.444065	+	9.32207i	−0.0190566	+	0.400048i
$544$	−1.92582	+	7.93835i	−0.0825690	+	0.340354i
$545$	2.35243	−	16.3615i	0.100767	−	0.700850i
$546$	4.62378	−	13.3363i	0.197880	−	0.570742i
$547$	6.11268	−	3.92838i	0.261359	−	0.167965i	−0.403398	−	0.915024i	$-0.632171\pi$
$547$	6.11268	−	3.92838i	0.261359	−	0.167965i	0.664758	+	0.747059i	$0.268535\pi$
$548$	−7.82474	+	1.50810i	−0.334256	+	0.0644226i
$549$	2.26690	+	9.34427i	0.0967487	+	0.398804i
$550$	−3.25619	+	0.310928i	−0.138844	+	0.0132580i
$551$	−0.470389	+	0.814737i	−0.0200392	+	0.0347090i
$552$	−4.77697	−	0.424946i	−0.203321	−	0.0180869i
$553$	−2.81414	+	19.4983i	−0.119669	+	0.829151i
$554$	0.509558	−	1.11578i	0.0216490	−	0.0474048i
$555$	15.2702	−	14.5601i	0.648183	−	0.618042i
$556$	1.01592	−	2.93532i	0.0430848	−	0.124485i
$557$	−19.0180	−	9.80448i	−0.805820	−	0.415429i	0.00553363	−	0.999985i	$-0.498239\pi$
$557$	−19.0180	−	9.80448i	−0.805820	−	0.415429i	−0.811354	+	0.584556i	$0.801269\pi$
$558$	−0.621443	−	1.79554i	−0.0263078	−	0.0760113i
$559$	−6.53399	+	45.4449i	−0.276358	+	1.92211i
$560$	−6.60838	−	2.64972i	−0.279255	−	0.111971i
$561$	10.0272	+	6.44412i	0.423351	+	0.272071i
$562$	−9.79676	−	3.92203i	−0.413251	−	0.165441i
$563$	10.3228	−	14.4964i	0.435056	−	0.610951i	−0.537600	−	0.843200i	$-0.680669\pi$
$563$	10.3228	−	14.4964i	0.435056	−	0.610951i	0.972656	+	0.232249i	$0.0746085\pi$
$564$	1.55296	−	2.18082i	0.0653913	−	0.0918292i
$565$	−10.3386	−	4.13893i	−0.434946	−	0.174126i
$566$	20.2497	+	13.0137i	0.851159	+	0.547007i
$567$	2.45570	+	0.984648i	0.103130	+	0.0413513i
$568$	2.26150	−	15.7291i	0.0948905	−	0.659978i
$569$	−9.75454	−	28.1839i	−0.408932	−	1.18153i	−0.942045	−	0.335486i	$-0.891099\pi$
$569$	−9.75454	−	28.1839i	−0.408932	−	1.18153i	0.533113	−	0.846044i	$-0.321022\pi$
$570$	10.1769	+	5.24654i	0.426262	+	0.219753i
$571$	−6.07618	+	17.5560i	−0.254280	+	0.734695i	0.743539	+	0.668693i	$0.233146\pi$
$571$	−6.07618	+	17.5560i	−0.254280	+	0.734695i	−0.997819	+	0.0660025i	$0.978975\pi$
$572$	5.63406	−	5.37206i	0.235572	−	0.224617i
$573$	3.26744	−	7.15470i	0.136499	−	0.298892i
$574$	−2.64559	+	18.3304i	−0.110425	+	0.765098i
$575$	−5.31496	+	9.34503i	−0.221649	+	0.389715i
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	28.6672	−	2.73739i	1.19343	−	0.113959i	0.520630	−	0.853782i	$-0.325697\pi$
$577$	28.6672	−	2.73739i	1.19343	−	0.113959i	0.672801	+	0.739823i	$0.265091\pi$
$578$	−11.7234	−	48.3245i	−0.487629	−	2.01004i
$579$	24.7083	−	4.76214i	1.02684	−	0.197908i
$580$	−0.500565	+	0.321694i	−0.0207848	+	0.0133576i
$581$	−7.80048	+	22.4988i	−0.323618	+	0.933409i
$582$	0.0903340	−	0.628287i	0.00374446	−	0.0260433i
$583$	0.125744	−	0.518322i	0.00520777	−	0.0214667i
$584$	0.359480	−	7.54642i	0.0148754	−	0.312273i
$585$	−11.2852	+	8.87475i	−0.466584	+	0.366926i
$586$	25.4670	+	2.43181i	1.05203	+	0.100457i
$587$	−15.1330	−	33.1367i	−0.624608	−	1.36770i	−0.912120	−	0.409923i	$-0.865556\pi$
$587$	−15.1330	−	33.1367i	−0.624608	−	1.36770i	0.287512	−	0.957777i	$-0.407172\pi$
$588$	−6.50137	+	2.59464i	−0.268112	+	0.107001i
$589$	−6.80084	−	4.37064i	−0.280224	−	0.180089i
$590$	4.00959	−	16.5278i	0.165072	−	0.680438i
$591$	−5.65015	+	2.26198i	−0.232416	+	0.0930454i
$592$	7.69885	+	1.48383i	0.316421	+	0.0609851i
$593$	1.57940	+	33.1556i	0.0648580	+	1.36154i	0.763381	+	0.645949i	$0.223538\pi$
$593$	1.57940	+	33.1556i	0.0648580	+	1.36154i	−0.698523	+	0.715588i	$0.746159\pi$
$594$	0.955554	+	1.10277i	0.0392069	+	0.0452471i
$595$	57.8986	−	5.49722i	2.37361	−	0.225364i
$596$	−1.14428	+	2.50563i	−0.0468716	+	0.102634i
$597$	6.32754	−	10.9596i	0.258969	−	0.448547i
$598$	−3.80518	−	25.3013i	−0.155605	−	1.03465i
$599$	−15.4365	−	26.7369i	−0.630720	−	1.09244i	−0.987405	−	0.158214i	$-0.949426\pi$
$599$	−15.4365	−	26.7369i	−0.630720	−	1.09244i	0.356685	−	0.934225i	$-0.383907\pi$
$600$	1.30030	+	1.82602i	0.0530847	+	0.0745470i
$601$	27.6845	+	8.12890i	1.12927	+	0.331585i	0.792422	−	0.609973i	$-0.208820\pi$
$601$	27.6845	+	8.12890i	1.12927	+	0.331585i	0.336852	+	0.941558i	$0.390638\pi$
$602$	19.1610	−	12.2995i	0.780944	−	0.501289i
$603$	−3.56772	+	2.29284i	−0.145289	+	0.0933715i
$604$	6.89059	+	19.9091i	0.280374	+	0.810088i
$605$	22.1617	−	8.87222i	0.901002	−	0.360707i
$606$	−11.6764	−	11.1335i	−0.474323	−	0.452266i
$607$	10.7480	−	5.54097i	0.436247	−	0.224901i	−0.226091	−	0.974106i	$-0.572595\pi$
$607$	10.7480	−	5.54097i	0.436247	−	0.224901i	0.662338	+	0.749205i	$0.269564\pi$
$608$	0.605512	+	4.21143i	0.0245568	+	0.170796i
$609$	−0.138227	+	0.568445i	−0.00560125	+	0.0230346i
$610$	10.7489	+	23.5369i	0.435212	+	0.952980i
$611$	13.2600	+	5.30852i	0.536444	+	0.214760i
$612$	0.388678	−	8.15936i	0.0157114	−	0.329823i
$613$	23.0583	+	21.9860i	0.931314	+	0.888006i	0.993928	−	0.110032i	$-0.0350952\pi$
$613$	23.0583	+	21.9860i	0.931314	+	0.888006i	−0.0626140	+	0.998038i	$0.519944\pi$
$614$	−3.59924	−	2.83047i	−0.145254	−	0.114229i
$615$	12.3359	−	14.2363i	0.497430	−	0.574065i
$616$	−3.84293	−	0.369042i	−0.154836	−	0.0148691i
$617$	7.88948	+	9.10495i	0.317619	+	0.366551i	0.891999	−	0.452037i	$-0.149302\pi$
$617$	7.88948	+	9.10495i	0.317619	+	0.366551i	−0.574381	+	0.818588i	$0.694757\pi$
$618$	8.35271	−	7.96430i	0.335995	−	0.320371i
$619$	10.7241	−	1.02403i	0.431037	−	0.0411590i	0.122717	−	0.992442i	$-0.460839\pi$
$619$	10.7241	−	1.02403i	0.431037	−	0.0411590i	0.308320	+	0.951283i	$0.400233\pi$
$620$	−2.55654	−	4.42806i	−0.102673	−	0.177835i
$621$	4.77106	−	0.486781i	0.191456	−	0.0195338i
$622$	−11.6540			−0.467283
$623$	−0.187191	−	0.120443i	−0.00749966	−	0.00482545i
$624$	−5.11891	−	1.50305i	−0.204921	−	0.0601701i
$625$	−30.6198	+	5.90147i	−1.22479	+	0.236059i
$626$	24.2499	+	12.5017i	0.969221	+	0.499668i
$627$	6.09620	+	1.17495i	0.243459	+	0.0469228i
$628$	−10.7462	−	8.45092i	−0.428821	−	0.337228i
$629$	−61.4520	+	18.0439i	−2.45025	+	0.719458i
$630$	6.99043	+	1.35120i	0.278505	+	0.0538329i
$631$	6.15907	+	42.8373i	0.245189	+	1.70532i	0.625301	+	0.780384i	$0.284976\pi$
$631$	6.15907	+	42.8373i	0.245189	+	1.70532i	−0.380112	+	0.924940i	$0.624115\pi$
$632$	7.41230	+	0.707789i	0.294845	+	0.0281543i
$633$	−9.90378	+	13.9079i	−0.393640	+	0.552790i
$634$	−25.2921	+	19.8899i	−1.00448	+	0.789929i
$635$	−1.28229	+	0.661064i	−0.0508859	+	0.0262335i
$636$	−0.350714	+	0.102979i	−0.0139067	+	0.00408338i
$637$	−21.6296	−	30.4437i	−0.856994	−	1.20622i
$638$	−0.211285	+	0.243836i	−0.00836487	+	0.00965357i
$639$	0.756116	+	15.8728i	0.0299115	+	0.627919i
$640$	−0.880152	+	2.54303i	−0.0347911	+	0.100522i
$641$	−3.14559	−	12.9663i	−0.124243	−	0.512138i	−0.999590	−	0.0286419i	$-0.990882\pi$
$641$	−3.14559	−	12.9663i	−0.124243	−	0.512138i	0.875346	−	0.483496i	$-0.160633\pi$
$642$	3.16299	+	4.44180i	0.124833	+	0.175304i
$643$	−38.9332			−1.53538			−0.767688	−	0.640824i	$-0.778593\pi$
$643$	−38.9332			−1.53538			−0.767688	+	0.640824i	$0.778593\pi$
$644$	−8.25216	+	9.63856i	−0.325181	+	0.379812i
$645$	−23.1586			−0.911868
$646$	−20.1601	−	28.3108i	−0.793187	−	1.11387i
$647$	6.20144	+	25.5627i	0.243804	+	1.00497i	0.953722	+	0.300689i	$0.0972166\pi$
$647$	6.20144	+	25.5627i	0.243804	+	1.00497i	−0.709918	+	0.704284i	$0.751268\pi$
$648$	0.327068	−	0.945001i	0.0128484	−	0.0371231i
$649$	−0.438794	−	9.21142i	−0.0172242	−	0.361580i
$650$	−7.83176	+	9.03833i	−0.307187	+	0.354513i
$651$	−4.82264	−	1.41887i	−0.189014	−	0.0556101i
$652$	4.37571	−	1.28482i	0.171366	−	0.0503176i
$653$	3.39761	−	1.75159i	0.132959	−	0.0685449i	−0.390464	−	0.920618i	$-0.627685\pi$
$653$	3.39761	−	1.75159i	0.132959	−	0.0685449i	0.523422	+	0.852073i	$0.324655\pi$
$654$	−4.82835	+	3.79706i	−0.188803	+	0.148477i
$655$	14.8762	−	20.8907i	0.581261	−	0.816267i
$656$	6.96835	+	0.665396i	0.272068	+	0.0259794i
$657$	1.07519	+	7.47808i	0.0419470	+	0.291748i
$658$	−2.31313	−	6.69500i	−0.0901752	−	0.260998i
$659$	7.78103	−	2.28472i	0.303106	−	0.0890000i	−0.126643	−	0.991948i	$-0.540420\pi$
$659$	7.78103	−	2.28472i	0.303106	−	0.0890000i	0.429749	+	0.902948i	$0.358602\pi$
$660$	3.08658	+	2.42732i	0.120145	+	0.0944832i
$661$	−31.1674	−	6.00702i	−1.21227	−	0.233646i	−0.457245	−	0.889341i	$-0.651164\pi$
$661$	−31.1674	−	6.00702i	−1.21227	−	0.233646i	−0.755026	+	0.655695i	$0.772376\pi$
$662$	19.5788	+	10.0936i	0.760953	+	0.392299i
$663$	42.7922	−	8.24751i	1.66191	−	0.320307i
$664$	8.63578	+	2.53569i	0.335133	+	0.0984040i
$665$	26.9329	−	13.8665i	1.04441	−	0.537721i
$666$	−7.84053			−0.303815
$667$	0.256672	+	1.02889i	0.00993839	+	0.0398387i
$668$	10.1249	+	17.5368i	0.391744	+	0.678521i
$669$	−9.45742	+	0.903074i	−0.365645	+	0.0349149i
$670$	−8.25967	+	7.87558i	−0.319099	+	0.304260i
$671$	9.18795	+	10.6035i	0.354697	+	0.409342i
$672$	1.09779	+	2.40725i	0.0423482	+	0.0928617i
$673$	−17.2276	+	19.8817i	−0.664073	+	0.766382i	−0.983437	−	0.181251i	$-0.941985\pi$
$673$	−17.2276	+	19.8817i	−0.664073	+	0.766382i	0.319363	+	0.947632i	$0.396531\pi$
$674$	−20.7588	−	16.3249i	−0.799600	−	0.628813i
$675$	−1.62238	−	1.54694i	−0.0624455	−	0.0595417i
$676$	0.735732	−	15.4449i	0.0282974	−	0.594035i
$677$	−20.8812	−	8.35958i	−0.802531	−	0.321285i	−0.0661131	−	0.997812i	$-0.521060\pi$
$677$	−20.8812	−	8.35958i	−0.802531	−	0.321285i	−0.736418	+	0.676527i	$0.763484\pi$
$678$	1.71910	+	3.76431i	0.0660218	+	0.144568i
$679$	−1.21480	−	1.15956i	−0.0466199	−	0.0444999i
$680$	−3.12837	−	21.7583i	−0.119968	−	0.834393i
$681$	−19.9289	+	10.2741i	−0.763677	+	0.393703i
$682$	−2.00654	−	1.91323i	−0.0768345	−	0.0732615i
$683$	20.4277	−	8.17802i	0.781644	−	0.312923i	0.0536979	−	0.998557i	$-0.482899\pi$
$683$	20.4277	−	8.17802i	0.781644	−	0.312923i	0.727946	+	0.685634i	$0.240475\pi$
$684$	−1.39159	−	4.02073i	−0.0532087	−	0.153736i
$685$	18.0400	−	11.5936i	0.689273	−	0.442969i
$686$	−4.39536	+	17.9911i	−0.167816	+	0.686905i
$687$	3.35594	+	0.985394i	0.128037	+	0.0375951i
$688$	−4.99186	−	7.01009i	−0.190313	−	0.267257i
$689$	−0.975028	−	1.68880i	−0.0371456	−	0.0643381i
$690$	12.3592	−	3.71609i	0.470506	−	0.141469i
$691$	10.9420	−	18.9520i	0.416252	−	0.720969i	−0.579307	−	0.815109i	$-0.696677\pi$
$691$	10.9420	−	18.9520i	0.416252	−	0.720969i	0.995559	+	0.0941399i	$0.0300101\pi$
$692$	6.06949	−	13.2903i	0.230727	−	0.505222i
$693$	3.84332	−	0.364906i	0.145996	−	0.0138616i
$694$	15.7058	+	18.1254i	0.596183	+	0.688032i
$695$	0.397727	+	8.34932i	0.0150867	+	0.316708i
$696$	0.217117	+	0.0418459i	0.00822980	+	0.00158616i
$697$	−53.0847	+	21.2519i	−2.01073	+	0.804973i
$698$	5.04216	−	20.7841i	0.190849	−	0.786689i
$699$	10.6251	+	6.82831i	0.401876	+	0.258270i
$700$	5.93094	+	0.00319110i	0.224168	+	0.000120612i
$701$	−11.1660	−	24.4501i	−0.421734	−	0.923469i	−0.994596	−	0.103817i	$-0.966894\pi$
$701$	−11.1660	−	24.4501i	−0.421734	−	0.923469i	0.572862	−	0.819652i	$-0.305833\pi$
$702$	5.31086	+	0.507126i	0.200446	+	0.0191402i
$703$	−26.2223	+	20.6214i	−0.988992	+	0.777752i
$704$	−0.0694302	+	1.45752i	−0.00261675	+	0.0549323i
$705$	−1.69854	+	7.00149i	−0.0639709	+	0.263691i
$706$	−3.91468	+	27.2272i	−0.147331	+	1.02471i
$707$	−41.9185	+	8.05574i	−1.57651	+	0.302967i
$708$	−5.31667	+	3.41681i	−0.199813	+	0.128412i
$709$	−36.0146	+	6.94125i	−1.35256	+	0.260684i	−0.813490	−	0.581578i	$-0.802435\pi$
$709$	−36.0146	+	6.94125i	−1.35256	+	0.260684i	−0.539068	+	0.842263i	$0.681223\pi$
$710$	10.0817	+	41.5574i	0.378360	+	1.55962i
$711$	−7.41230	+	0.707789i	−0.277983	+	0.0265442i
$712$	−0.0420659	+	0.0728603i	−0.00157649	+	0.00273055i
$713$	−8.93625	+	1.78242i	−0.334665	+	0.0667521i
$714$	−16.9811	−	13.3689i	−0.635501	−	0.500317i
$715$	−8.70251	+	19.0558i	−0.325455	+	0.712648i
$716$	−4.66526	+	4.44831i	−0.174349	+	0.166241i
$717$	−3.85744	+	11.1453i	−0.144059	+	0.416230i
$718$	−17.2304	−	8.88287i	−0.643031	−	0.331506i
$719$	−7.85164	−	22.6858i	−0.292817	−	0.846038i	−0.991442	−	0.130550i	$-0.958326\pi$
$719$	−7.85164	−	22.6858i	−0.292817	−	0.846038i	0.698625	−	0.715488i	$-0.253796\pi$
$720$	0.382975	−	2.66365i	0.0142726	−	0.0992683i
$721$	−4.32932	−	30.2265i	−0.161232	−	1.12569i
$722$	0.754783	+	0.485070i	0.0280901	+	0.0180524i
$723$	−0.593822	−	0.237730i	−0.0220845	−	0.00884128i
$724$	5.41346	−	7.60214i	0.201190	−	0.282531i
$725$	0.287514	−	0.403757i	0.0106780	−	0.0149952i
$726$	−8.23538	−	3.29695i	−0.305644	−	0.122361i
$727$	−37.2443	−	23.9355i	−1.38132	−	0.887717i	−0.381980	−	0.924171i	$-0.624758\pi$
$727$	−37.2443	−	23.9355i	−1.38132	−	0.887717i	−0.999335	+	0.0364534i	$0.988394\pi$
$728$	−11.0999	+	8.71943i	−0.411391	+	0.323163i
$729$	−0.142315	+	0.989821i	−0.00527092	+	0.0366601i
$730$	6.64953	+	19.2126i	0.246110	+	0.711088i
$731$	62.4830	+	32.2122i	2.31102	+	1.19141i
$732$	3.14486	−	9.08648i	0.116237	−	0.335846i
$733$	−35.7088	+	34.0483i	−1.31894	+	1.25760i	−0.375183	+	0.926951i	$0.622420\pi$
$733$	−35.7088	+	34.0483i	−1.31894	+	1.25760i	−0.943753	+	0.330652i	$0.892731\pi$
$734$	−12.2275	+	26.7744i	−0.451323	+	0.988261i
$735$	13.6471	−	12.9845i	0.503383	−	0.478941i
$736$	3.78890	+	2.94011i	0.139661	+	0.108374i
$737$	−3.09414	+	5.35922i	−0.113974	+	0.197409i
$738$	−6.96835	+	0.665396i	−0.256508	+	0.0244936i
$739$	−5.69054	−	23.4567i	−0.209330	−	0.862870i	−0.975459	−	0.220183i	$-0.929335\pi$
$739$	−5.69054	−	23.4567i	−0.209330	−	0.862870i	0.766129	−	0.642687i	$-0.222181\pi$
$740$	−20.7179	+	3.99304i	−0.761604	+	0.146787i
$741$	19.0957	−	12.2721i	0.701498	−	0.450825i
$742$	−0.316791	+	0.913717i	−0.0116298	+	0.0335436i
$743$	0.493676	−	3.43359i	0.0181112	−	0.125966i	−0.978760	−	0.205010i	$-0.934277\pi$
$743$	0.493676	−	3.43359i	0.0181112	−	0.125966i	0.996871	+	0.0790433i	$0.0251865\pi$
$744$	−0.447952	+	1.84648i	−0.0164227	+	0.0676953i
$745$	0.352706	−	7.40420i	0.0129221	−	0.271269i
$746$	0.212598	−	0.167189i	0.00778378	−	0.00612123i
$747$	−8.95960	−	0.855538i	−0.327815	−	0.0313025i
$748$	−4.95150	−	10.8423i	−0.181045	−	0.396433i
$749$	14.4270	+	0.00776235i	0.527152	+	0.000283630i
$750$	6.24440	+	4.01303i	0.228013	+	0.146535i
$751$	12.0124	−	49.5158i	0.438339	−	1.80686i	−0.138930	−	0.990302i	$-0.544366\pi$
$751$	12.0124	−	49.5158i	0.438339	−	1.80686i	0.577269	−	0.816554i	$-0.304118\pi$
$752$	−2.48547	+	0.995033i	−0.0906359	+	0.0362851i
$753$	17.1694	+	3.30913i	0.625688	+	0.120592i
$754$	0.0561296	+	1.17831i	0.00204412	+	0.0429114i
$755$	−37.1268	−	42.8466i	−1.35118	−	1.55935i
$756$	−1.53353	−	2.15599i	−0.0557738	−	0.0784126i
$757$	10.4398	−	22.8599i	0.379440	−	0.830857i	−0.619508	−	0.784990i	$-0.712668\pi$
$757$	10.4398	−	22.8599i	0.379440	−	0.830857i	0.998948	−	0.0458664i	$-0.0146048\pi$
$758$	−2.94578	+	5.10224i	−0.106996	+	0.185322i
$759$	5.86242	−	3.82142i	0.212792	−	0.138709i
$760$	−5.72483	−	9.91569i	−0.207661	−	0.359680i
$761$	15.3364	+	21.5370i	0.555944	+	0.780714i	0.992923	−	0.118757i	$-0.0378910\pi$
$761$	15.3364	+	21.5370i	0.555944	+	0.780714i	−0.436979	+	0.899472i	$0.643952\pi$
$762$	0.514381	+	0.151036i	0.0186341	+	0.00547146i
$763$	0.764548	+	16.2336i	0.0276785	+	0.587696i
$764$	−6.61687	+	4.25240i	−0.239390	+	0.153846i
$765$	7.18962	+	20.7731i	0.259941	+	0.751051i
$766$	−30.2176	+	12.0973i	−1.09181	+	0.437093i
$767$	−24.4021	−	23.2674i	−0.881109	−	0.840136i
$768$	0.888835	−	0.458227i	0.0320731	−	0.0165348i
$769$	0.0719920	+	0.500715i	0.00259610	+	0.0180563i	0.991078	−	0.133281i	$-0.0425512\pi$
$769$	0.0719920	+	0.500715i	0.00259610	+	0.0180563i	−0.988482	+	0.151337i	$0.951642\pi$
$770$	9.96978	−	2.92157i	0.359286	−	0.105286i
$771$	−7.72296	−	16.9109i	−0.278136	−	0.609032i
$772$	−23.3606	−	9.35217i	−0.840766	−	0.336592i
$773$	1.82513	−	38.3142i	0.0656455	−	1.37807i	−0.690343	−	0.723482i	$-0.742540\pi$
$773$	1.82513	−	38.3142i	0.0656455	−	1.37807i	0.755988	−	0.654585i	$-0.227157\pi$
$774$	6.22832	+	5.93869i	0.223872	+	0.213462i
$775$	3.34803	+	2.63292i	0.120265	+	0.0945773i
$776$	−0.415671	+	0.479710i	−0.0149217	+	0.0172206i
$777$	−12.0418	+	16.8912i	−0.431999	+	0.605967i
$778$	−1.86031	−	2.14692i	−0.0666955	−	0.0769707i
$779$	−21.5552	+	20.5529i	−0.772296	+	0.736383i
$780$	14.2917	−	1.36469i	0.511726	−	0.0488639i
$781$	11.5937	+	20.0809i	0.414856	+	0.718552i
$782$	−38.5146	−	7.16470i	−1.37728	−	0.256209i
$783$	−0.221113			−0.00790193
$784$	6.87207	+	1.33215i	0.245431	+	0.0475769i
$785$	35.2992	+	10.3648i	1.25988	+	0.369935i
$786$	−9.35796	+	1.80360i	−0.333787	+	0.0643323i
$787$	16.6643	+	8.59107i	0.594020	+	0.306238i	0.728896	−	0.684624i	$-0.240034\pi$
$787$	16.6643	+	8.59107i	0.594020	+	0.306238i	−0.134877	+	0.990862i	$0.543064\pi$
$788$	5.97613	+	1.15180i	0.212891	+	0.0410313i
$789$	6.42549	+	5.05306i	0.228754	+	0.179894i
$790$	−19.2259	+	5.64522i	−0.684025	+	0.200848i
$791$	10.7499	+	2.07787i	0.382222	+	0.0738806i
$792$	−0.207662	−	1.44432i	−0.00737894	−	0.0513217i
$793$	51.0656	+	4.87617i	1.81339	+	0.173158i
$794$	5.80737	−	8.15531i	0.206096	−	0.289421i
$795$	0.773184	−	0.608039i	0.0274220	−	0.0215649i
$796$	−11.2483	+	5.79889i	−0.398685	+	0.205536i
$797$	−45.5922	+	13.3871i	−1.61496	+	0.474194i	−0.959657	−	0.281174i	$-0.909276\pi$
$797$	−45.5922	+	13.3871i	−1.61496	+	0.474194i	−0.655301	+	0.755368i	$0.727458\pi$
$798$	−10.7993	−	3.17727i	−0.382290	−	0.112474i
$799$	14.3214	−	16.5278i	0.506655	−	0.584712i
$800$	−0.106664	−	2.23914i	−0.00377113	−	0.0791657i
$801$	0.0275168	−	0.0795046i	0.000972259	−	0.00280916i
$802$	7.21750	+	29.7509i	0.254859	+	1.05054i
$803$	6.39455	+	8.97989i	0.225659	+	0.316893i
$804$	4.24096			0.149567
$805$	10.9761	−	32.3332i	0.386856	−	1.13960i
$806$	−10.1368			−0.357052
$807$	5.71364	+	8.02369i	0.201130	+	0.282447i
$808$	3.80364	+	15.6788i	0.133812	+	0.551579i
$809$	14.1604	−	40.9137i	0.497852	−	1.43845i	−0.364053	−	0.931378i	$-0.618607\pi$
$809$	14.1604	−	40.9137i	0.497852	−	1.43845i	0.861905	−	0.507070i	$-0.169272\pi$
$810$	0.128045	+	2.68799i	0.00449903	+	0.0944463i
$811$	−9.80867	+	11.3198i	−0.344429	+	0.397492i	−0.901363	−	0.433065i	$-0.857432\pi$
$811$	−9.80867	+	11.3198i	−0.344429	+	0.397492i	0.556934	+	0.830557i	$0.311978\pi$
$812$	0.423609	−	0.403475i	0.0148658	−	0.0141592i
$813$	19.9035	−	5.84418i	0.698045	−	0.204964i
$814$	−10.1689	+	5.24243i	−0.356419	+	0.183747i
$815$	−9.64669	+	7.58624i	−0.337909	+	0.265735i
$816$	−4.73826	+	6.65396i	−0.165872	+	0.232935i
$817$	36.4497	+	3.48052i	1.27521	+	0.121768i
$818$	1.72882	+	12.0242i	0.0604466	+	0.420416i
$819$	9.24918	−	10.6625i	0.323193	−	0.372579i
$820$	−18.0743	+	5.30710i	−0.631183	+	0.185332i
$821$	−26.6823	−	20.9832i	−0.931220	−	0.732319i	0.0324340	−	0.999474i	$-0.489674\pi$
$821$	−26.6823	−	20.9832i	−0.931220	−	0.732319i	−0.963654	+	0.267155i	$0.913917\pi$
$822$	−7.82474	−	1.50810i	−0.272919	−	0.0526009i
$823$	31.2940	+	16.1332i	1.09084	+	0.562367i	0.907231	−	0.420632i	$-0.138192\pi$
$823$	31.2940	+	16.1332i	1.09084	+	0.562367i	0.183609	+	0.982999i	$0.441222\pi$
$824$	−11.3326	+	2.18417i	−0.394789	+	0.0760893i
$825$	−3.13850	−	0.921548i	−0.109269	−	0.0320842i
$826$	−0.804602	+	16.7016i	−0.0279957	+	0.581123i
$827$	10.7729			0.374611			0.187305	−	0.982302i	$-0.440025\pi$
$827$	10.7729			0.374611			0.187305	+	0.982302i	$0.440025\pi$
$828$	−4.27685	−	2.16993i	−0.148631	−	0.0754101i
$829$	−1.88052	−	3.25716i	−0.0653132	−	0.113126i	0.831520	−	0.555495i	$-0.187471\pi$
$829$	−1.88052	−	3.25716i	−0.0653132	−	0.113126i	−0.896833	+	0.442369i	$0.854138\pi$
$830$	−24.1106	+	2.30229i	−0.836892	+	0.0799135i
$831$	0.887749	−	0.846467i	0.0307957	−	0.0293636i
$832$	3.49369	+	4.03194i	0.121122	+	0.139782i
$833$	−54.8814	+	16.0505i	−1.90153	+	0.556117i
$834$	2.03410	−	2.34748i	0.0704352	−	0.0812865i
$835$	−42.8344	−	33.6853i	−1.48234	−	1.16573i
$836$	−4.49322	−	4.28428i	−0.155401	−	0.148175i
$837$	0.0904076	−	1.89789i	0.00312494	−	0.0656006i
$838$	29.9276	+	11.9812i	1.03383	+	0.413884i
$839$	−6.58309	−	14.4150i	−0.227274	−	0.497660i	0.761300	−	0.648400i	$-0.224562\pi$
$839$	−6.58309	−	14.4150i	−0.227274	−	0.497660i	−0.988573	+	0.150740i	$0.951834\pi$
$840$	−5.15021	−	4.91601i	−0.177699	−	0.169618i
$841$	4.12017	+	28.6564i	0.142075	+	0.988153i
$842$	−2.48170	+	1.27941i	−0.0855251	+	0.0440912i
$843$	−7.63733	−	7.28218i	−0.263043	−	0.250811i
$844$	15.8508	−	6.34570i	0.545606	−	0.218428i
$845$	13.6093	+	39.3215i	0.468174	+	1.35270i
$846$	2.25225	−	1.44743i	0.0774338	−	0.0497637i
$847$	−19.7510	+	12.6782i	−0.678653	+	0.435628i
$848$	0.350714	+	0.102979i	0.0120436	+	0.00353631i
$849$	13.9625	+	19.6076i	0.479191	+	0.672930i
$850$	9.15572	+	15.8582i	0.314039	+	0.543931i
$851$	−5.11016	+	37.2530i	−0.175174	+	1.27702i
$852$	7.94541	−	13.7619i	0.272205	−	0.471474i
$853$	−4.28807	+	9.38957i	−0.146821	+	0.321493i	−0.968727	−	0.248131i	$-0.920184\pi$
$853$	−4.28807	+	9.38957i	−0.146821	+	0.321493i	0.821906	+	0.569623i	$0.192911\pi$
$854$	−14.7453	−	20.7305i	−0.504575	−	0.709384i
$855$	7.49793	+	8.65307i	0.256424	+	0.295929i
$856$	−0.259459	−	5.44672i	−0.00886814	−	0.186165i
$857$	28.1221	+	5.42008i	0.960631	+	0.185146i	0.645380	−	0.763862i	$-0.276699\pi$
$857$	28.1221	+	5.42008i	0.960631	+	0.185146i	0.315251	+	0.949008i	$0.397911\pi$
$858$	7.22707	−	2.89328i	0.246728	−	0.0987751i
$859$	−11.0014	+	45.3484i	−0.375363	+	1.54727i	0.400459	+	0.916315i	$0.368851\pi$
$859$	−11.0014	+	45.3484i	−0.375363	+	1.54727i	−0.775822	+	0.630952i	$0.782665\pi$
$860$	19.4822	+	12.5205i	0.664339	+	0.426944i
$861$	−9.26881	+	16.0341i	−0.315880	+	0.546442i
$862$	12.3841	+	27.1174i	0.421804	+	0.923622i
$863$	−11.0234	−	1.05261i	−0.375241	−	0.0358312i	−0.0942680	−	0.995547i	$-0.530051\pi$
$863$	−11.0234	−	1.05261i	−0.375241	−	0.0358312i	−0.280973	+	0.959716i	$0.590657\pi$
$864$	−0.786053	+	0.618159i	−0.0267421	+	0.0210302i
$865$	−1.87082	+	39.2733i	−0.0636097	+	1.33533i
$866$	−3.44687	+	14.2082i	−0.117129	+	0.482814i
$867$	7.07678	−	49.2201i	0.240340	−	1.67160i
$868$	3.28996	+	3.80095i	0.111669	+	0.129013i
$869$	−9.14023	+	5.87407i	−0.310061	+	0.199264i
$870$	−0.584270	+	0.112609i	−0.0198086	+	0.00381780i
$871$	5.33419	+	21.9878i	0.180742	+	0.745029i
$872$	6.11471	−	0.583884i	0.207070	−	0.0197728i
$873$	0.317374	−	0.549708i	0.0107415	−	0.0186048i
$874$	−20.0108	+	3.99135i	−0.676876	+	0.135009i
$875$	18.2359	−	7.28916i	0.616485	−	0.246419i
$876$	3.13845	−	6.87225i	0.106038	−	0.232192i
$877$	4.76885	−	4.54709i	0.161033	−	0.153544i	−0.605279	−	0.796014i	$-0.706938\pi$
$877$	4.76885	−	4.54709i	0.161033	−	0.153544i	0.766312	+	0.642469i	$0.222090\pi$
$878$	10.7804	−	31.1478i	0.363820	−	1.05119i
$879$	22.7390	+	11.7227i	0.766966	+	0.395398i
$880$	−1.28429	−	3.71072i	−0.0432935	−	0.125088i
$881$	−4.33978	+	30.1838i	−0.146211	+	1.01692i	0.776138	+	0.630563i	$0.217176\pi$
$881$	−4.33978	+	30.1838i	−0.146211	+	1.01692i	−0.922349	+	0.386357i	$0.873733\pi$
$882$	−7.00000	−	0.00753260i	−0.235702	−	0.000253636i
$883$	27.9809	+	17.9822i	0.941632	+	0.605150i	0.918857	−	0.394590i	$-0.129113\pi$
$883$	27.9809	+	17.9822i	0.941632	+	0.605150i	0.0227752	+	0.999741i	$0.492750\pi$
$884$	−40.4580	−	16.1969i	−1.36075	−	0.544762i
$885$	9.86513	−	13.8536i	0.331613	−	0.465685i
$886$	12.9765	−	18.2229i	0.435954	−	0.612211i
$887$	−3.33946	−	1.33692i	−0.112128	−	0.0448894i	0.314920	−	0.949118i	$-0.398022\pi$
$887$	−3.33946	−	1.33692i	−0.112128	−	0.0448894i	−0.427048	+	0.904229i	$0.640447\pi$
$888$	6.59588	+	4.23891i	0.221343	+	0.142249i
$889$	1.11539	−	0.876184i	0.0374091	−	0.0293863i
$890$	0.0322203	−	0.224097i	0.00108003	−	0.00751176i
$891$	0.477248	+	1.37892i	0.0159884	+	0.0461955i
$892$	8.44433	+	4.35335i	0.282737	+	0.145761i
$893$	3.72563	−	10.7645i	0.124673	−	0.360220i
$894$	−1.99356	+	1.90086i	−0.0666747	+	0.0635742i
$895$	7.20607	−	15.7791i	0.240872	−	0.527437i
$896$	0.377939	−	2.61862i	0.0126260	−	0.0874819i
$897$	5.87094	−	24.9032i	0.196025	−	0.831493i
$898$	−6.09693	+	10.5602i	−0.203457	+	0.352398i
$899$	0.418221	−	0.0399353i	0.0139485	−	0.00133192i
$900$	0.528497	+	2.17849i	0.0176166	+	0.0726165i
$901$	−2.93184	+	0.565065i	−0.0976736	+	0.0188250i
$902$	−8.59279	+	5.52225i	−0.286108	+	0.183871i
$903$	22.3597	−	4.29700i	0.744084	−	0.142995i
$904$	0.588939	−	4.09616i	0.0195878	−	0.136236i
$905$	−5.92096	+	24.4065i	−0.196819	+	0.811301i
$906$	−1.00244	+	21.0439i	−0.0333040	+	0.699137i
$907$	−40.9459	+	32.2002i	−1.35958	+	1.06919i	−0.369423	+	0.929261i	$0.620445\pi$
$907$	−40.9459	+	32.2002i	−1.35958	+	1.06919i	−0.990162	+	0.139928i	$0.955313\pi$
$908$	22.3198	+	2.13128i	0.740709	+	0.0707292i
$909$	−6.70215	−	14.6757i	−0.222296	−	0.486761i
$910$	19.0099	−	32.8852i	0.630171	−	1.09013i
$911$	−0.616325	−	0.396088i	−0.0204198	−	0.0131230i	0.530391	−	0.847753i	$-0.322045\pi$
$911$	−0.616325	−	0.396088i	−0.0204198	−	0.0131230i	−0.550811	+	0.834630i	$0.685681\pi$
$912$	−1.00309	+	4.13480i	−0.0332157	+	0.136917i
$913$	−12.1923	+	4.88107i	−0.403507	+	0.161540i
$914$	−35.5278	−	6.84741i	−1.17515	−	0.226492i
$915$	1.23119	+	25.8459i	0.0407019	+	0.854438i
$916$	−2.29046	−	2.64333i	−0.0756788	−	0.0873380i
$917$	−10.4868	+	22.9303i	−0.346305	+	0.757225i
$918$	3.39336	−	7.43043i	0.111998	−	0.245241i
$919$	1.81361	−	3.14126i	0.0598255	−	0.103621i	−0.834561	−	0.550915i	$-0.814279\pi$
$919$	1.81361	−	3.14126i	0.0598255	−	0.103621i	0.894387	+	0.447294i	$0.147612\pi$
$920$	−12.4063	−	3.55570i	−0.409023	−	0.117228i
$921$	−2.28944	−	3.96542i	−0.0754396	−	0.130665i
$922$	15.0218	+	21.0952i	0.494718	+	0.694734i
$923$	81.3438	+	23.8847i	2.67746	+	0.786174i
$924$	−3.43049	−	1.77088i	−0.112855	−	0.0582576i
$925$	14.7859	−	9.50230i	0.486156	−	0.312434i
$926$	9.77173	+	28.2335i	0.321119	+	0.927812i
$927$	10.7144	−	4.28941i	0.351908	−	0.140883i
$928$	−0.160027	−	0.152585i	−0.00525314	−	0.00500886i
$929$	−52.2651	+	26.9445i	−1.71476	+	0.884022i	−0.736559	+	0.676373i	$0.763551\pi$
$929$	−52.2651	+	26.9445i	−1.71476	+	0.884022i	−0.978203	+	0.207649i	$0.933419\pi$
$930$	−0.727668	−	5.06104i	−0.0238612	−	0.165958i
$931$	−23.4309	+	18.3855i	−0.767918	+	0.602561i
$932$	−5.24670	−	11.4887i	−0.171861	−	0.376324i
$933$	−10.8192	−	4.33135i	−0.354205	−	0.141802i
$934$	−1.10940	+	23.2892i	−0.0363007	+	0.762046i
$935$	23.2142	+	22.1347i	0.759185	+	0.723882i
$936$	−4.19361	−	3.29789i	−0.137072	−	0.107795i
$937$	16.5614	−	19.1128i	0.541036	−	0.624389i	−0.417735	−	0.908569i	$-0.637176\pi$
$937$	16.5614	−	19.1128i	0.541036	−	0.624389i	0.958771	+	0.284180i	$0.0917213\pi$
$938$	6.51346	−	9.13647i	0.212672	−	0.298316i
$939$	17.8664	+	20.6189i	0.583049	+	0.672874i
$940$	5.21420	−	4.97173i	0.170068	−	0.162160i
$941$	−1.62810	+	0.155465i	−0.0530746	+	0.00506801i	−0.121560	−	0.992584i	$-0.538790\pi$
$941$	−1.62810	+	0.155465i	−0.0530746	+	0.00506801i	0.0684849	+	0.997652i	$0.478183\pi$
$942$	−6.83556	−	11.8395i	−0.222714	−	0.385753i
$943$	−1.38018	+	33.5426i	−0.0449448	+	1.09230i
$944$	6.31993			0.205696
$945$	5.98750	+	3.85249i	0.194773	+	0.125321i
$946$	12.0487	+	3.53782i	0.391737	+	0.115024i
$947$	20.4041	−	3.93257i	0.663045	−	0.127791i	0.153384	−	0.988167i	$-0.450983\pi$
$947$	20.4041	−	3.93257i	0.663045	−	0.127791i	0.509661	+	0.860375i	$0.329771\pi$
$948$	6.61828	+	3.41196i	0.214952	+	0.110815i
$949$	39.5776	+	7.62795i	1.28474	+	0.247614i
$950$	7.49720	+	5.89586i	0.243241	+	0.191287i
$951$	−30.8727	+	9.06504i	−1.00112	+	0.293954i
$952$	7.05764	+	20.4273i	0.228740	+	0.662052i
$953$	4.28157	+	29.7790i	0.138694	+	0.964636i	0.933705	+	0.358042i	$0.116556\pi$
$953$	4.28157	+	29.7790i	0.138694	+	0.964636i	−0.795012	+	0.606594i	$0.792535\pi$
$954$	−0.363865	−	0.0347449i	−0.0117806	−	0.00112491i
$955$	12.2777	−	17.2416i	0.397296	−	0.557924i
$956$	9.27071	−	7.29057i	0.299836	−	0.235794i
$957$	−0.286775	+	0.147843i	−0.00927013	+	0.00477909i
$958$	22.6191	−	6.64157i	0.730790	−	0.214579i
$959$	−15.2665	+	14.5409i	−0.492982	+	0.469552i
$960$	−1.76225	+	2.03375i	−0.0568765	+	0.0656390i
$961$	−1.30326	−	27.3588i	−0.0420407	−	0.882543i
$962$	−13.6811	+	39.5288i	−0.441095	+	1.27446i
$963$	1.28557	+	5.29919i	0.0414269	+	0.170764i
$964$	0.371028	+	0.521036i	0.0119500	+	0.0167814i
$965$	67.7147			2.17981
$966$	−11.2433	+	5.88111i	−0.361748	+	0.189222i
$967$	−44.3610			−1.42655			−0.713276	−	0.700883i	$-0.752790\pi$
$967$	−44.3610			−1.42655			−0.713276	+	0.700883i	$0.752790\pi$
$968$	5.14558	+	7.22595i	0.165385	+	0.232251i
$969$	−8.19387	−	33.7756i	−0.263225	−	1.08503i
$970$	0.558675	−	1.61418i	0.0179380	−	0.0518283i
$971$	0.00349475	+	0.0733637i	0.000112152	+	0.00235435i	0.998923	−	0.0464047i	$-0.0147764\pi$
$971$	0.00349475	+	0.0733637i	0.000112152	+	0.00235435i	−0.998811	+	0.0487591i	$0.984473\pi$
$972$	0.654861	−	0.755750i	0.0210047	−	0.0242407i
$973$	−1.93320	−	7.98751i	−0.0619755	−	0.256068i
$974$	−12.5526	+	3.68576i	−0.402210	+	0.118099i
$975$	−10.6300	+	5.48013i	−0.340431	+	0.175504i
$976$	−7.55815	+	5.94379i	−0.241930	+	0.190256i
$977$	18.2463	−	25.6233i	0.583751	−	0.819763i	−0.412064	−	0.911155i	$-0.635192\pi$
$977$	18.2463	−	25.6233i	0.583751	−	0.819763i	0.995815	+	0.0913914i	$0.0291315\pi$
$978$	4.53979	+	0.433497i	0.145166	+	0.0138617i
$979$	−0.0174710	−	0.121513i	−0.000558374	−	0.00388358i
$980$	−18.5007	+	3.54507i	−0.590982	+	0.113243i
$981$	−5.89371	+	1.73055i	−0.188172	+	0.0552522i
$982$	−1.67492	−	1.31718i	−0.0534490	−	0.0420327i
$983$	−8.19068	−	1.57862i	−0.261242	−	0.0503503i	0.0569482	−	0.998377i	$-0.481863\pi$
$983$	−8.19068	−	1.57862i	−0.261242	−	0.0503503i	−0.318190	+	0.948027i	$0.603075\pi$
$984$	6.22189	+	3.20760i	0.198346	+	0.102255i
$985$	−16.0820	+	3.09955i	−0.512415	+	0.0987599i
$986$	1.73302	+	0.508861i	0.0551907	+	0.0162054i
$987$	0.340845	−	7.07513i	0.0108492	−	0.225204i
$988$	−22.6991			−0.722155
$989$	32.2761	−	25.7222i	1.02632	−	0.817920i
$990$	1.96334	+	3.40061i	0.0623991	+	0.108078i
$991$	23.6864	−	2.26178i	0.752423	−	0.0718477i	0.288205	−	0.957569i	$-0.406942\pi$
$991$	23.6864	−	2.26178i	0.752423	−	0.0718477i	0.464218	+	0.885721i	$0.346336\pi$
$992$	1.37512	−	1.31118i	0.0436602	−	0.0416300i
$993$	14.4250	+	16.6473i	0.457762	+	0.528286i
$994$	−17.4448	−	38.2532i	−0.553315	−	1.21332i
$995$	22.3015	−	25.7373i	0.707004	−	0.815926i
$996$	7.07476	+	5.56365i	0.224172	+	0.176291i
$997$	−18.2010	−	17.3546i	−0.576432	−	0.549626i	0.344782	−	0.938683i	$-0.387953\pi$
$997$	−18.2010	−	17.3546i	−0.576432	−	0.549626i	−0.921214	+	0.389056i	$0.872801\pi$
$998$	1.53088	−	32.1371i	0.0484592	−	1.01728i
$999$	−7.27890	−	2.91403i	−0.230294	−	0.0921959i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.y.a.121.2	✓	160
7.4	even	3	inner	966.2.y.a.949.7	yes	160
23.4	even	11	inner	966.2.y.a.625.7	yes	160
161.4	even	33	inner	966.2.y.a.487.2	yes	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.y.a.121.2	✓	160	1.1	even	1	trivial
966.2.y.a.487.2	yes	160	161.4	even	33	inner
966.2.y.a.625.7	yes	160	23.4	even	11	inner
966.2.y.a.949.7	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)

\(f(q)\)	\(=\)	\(q+(-0.580057 - 0.814576i) q^{2} +(-0.235759 - 0.971812i) q^{3} +(-0.327068 + 0.945001i) q^{4} +(-0.128045 - 2.68799i) q^{5} +(-0.654861 + 0.755750i) q^{6} +(0.622376 + 2.57151i) q^{7} +(0.959493 - 0.281733i) q^{8} +(-0.888835 + 0.458227i) q^{9} +O(q^{10})\)	\(q+(-0.580057 - 0.814576i) q^{2} +(-0.235759 - 0.971812i) q^{3} +(-0.327068 + 0.945001i) q^{4} +(-0.128045 - 2.68799i) q^{5} +(-0.654861 + 0.755750i) q^{6} +(0.622376 + 2.57151i) q^{7} +(0.959493 - 0.281733i) q^{8} +(-0.888835 + 0.458227i) q^{9} +(-2.11530 + 1.66349i) q^{10} +(-0.846403 + 1.18861i) q^{11} +(0.995472 + 0.0950560i) q^{12} +(0.759252 + 5.28072i) q^{13} +(1.73367 - 1.99859i) q^{14} +(-2.58203 + 0.758153i) q^{15} +(-0.786053 - 0.618159i) q^{16} +(8.02100 + 1.54592i) q^{17} +(0.888835 + 0.458227i) q^{18} +(4.17785 - 0.805214i) q^{19} +(2.58203 + 0.758153i) q^{20} +(2.35229 - 1.21109i) q^{21} +1.45917 q^{22} +(2.75650 - 3.92450i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(-2.23153 + 0.213086i) q^{25} +(3.86113 - 3.68158i) q^{26} +(0.654861 + 0.755750i) q^{27} +(-2.63364 - 0.252912i) q^{28} +(-0.144798 + 0.167106i) q^{29} +(2.11530 + 1.66349i) q^{30} +(-1.37512 - 1.31118i) q^{31} +(-0.0475819 + 0.998867i) q^{32} +(1.35465 + 0.542319i) q^{33} +(-3.39336 - 7.43043i) q^{34} +(6.83249 - 2.00221i) q^{35} +(-0.142315 - 0.989821i) q^{36} +(-6.96894 + 3.59274i) q^{37} +(-3.07930 - 2.93610i) q^{38} +(4.95286 - 1.98283i) q^{39} +(-0.880152 - 2.54303i) q^{40} +(-5.88881 + 3.78451i) q^{41} +(-2.35098 - 1.21362i) q^{42} +(8.25722 + 2.42454i) q^{43} +(-0.846403 - 1.18861i) q^{44} +(1.34552 + 2.33051i) q^{45} +(-4.79573 + 0.0310583i) q^{46} +(1.33862 - 2.31857i) q^{47} +(-0.415415 + 0.909632i) q^{48} +(-6.22530 + 3.20089i) q^{49} +(1.46799 + 1.69415i) q^{50} +(-0.388678 - 8.15936i) q^{51} +(-5.23861 - 1.00966i) q^{52} +(-0.339337 + 0.135850i) q^{53} +(0.235759 - 0.971812i) q^{54} +(3.30334 + 2.12293i) q^{55} +(1.32164 + 2.29200i) q^{56} +(-1.76748 - 3.87025i) q^{57} +(0.220112 + 0.0210181i) q^{58} +(-4.96780 + 3.90672i) q^{59} +(0.128045 - 2.68799i) q^{60} +(2.26690 - 9.34427i) q^{61} +(-0.270404 + 1.88070i) q^{62} +(-1.73152 - 2.00046i) q^{63} +(0.841254 - 0.540641i) q^{64} +(14.0973 - 2.71703i) q^{65} +(-0.344013 - 1.41804i) q^{66} +(4.22176 - 0.403129i) q^{67} +(-4.08431 + 7.07423i) q^{68} +(-4.46375 - 1.75356i) q^{69} +(-5.59418 - 4.40419i) q^{70} +(6.60129 - 14.4548i) q^{71} +(-0.723734 + 0.690079i) q^{72} +(2.47099 - 7.13946i) q^{73} +(6.96894 + 3.59274i) q^{74} +(0.733183 + 2.11839i) q^{75} +(-0.605512 + 4.21143i) q^{76} +(-3.58329 - 1.43677i) q^{77} +(-4.48810 - 2.88433i) q^{78} +(6.91264 + 2.76740i) q^{79} +(-1.56096 + 2.19205i) q^{80} +(0.580057 - 0.814576i) q^{81} +(6.49861 + 2.60165i) q^{82} +(7.57158 + 4.86596i) q^{83} +(0.375121 + 2.61902i) q^{84} +(3.12837 - 21.7583i) q^{85} +(-2.81469 - 8.13250i) q^{86} +(0.196533 + 0.101320i) q^{87} +(-0.477248 + 1.37892i) q^{88} +(-0.0608891 + 0.0580576i) q^{89} +(1.11790 - 2.44785i) q^{90} +(-13.1069 + 5.23901i) q^{91} +(2.80710 + 3.88847i) q^{92} +(-0.950021 + 1.64548i) q^{93} +(-2.66513 + 0.254489i) q^{94} +(-2.69936 - 11.1269i) q^{95} +(0.981929 - 0.189251i) q^{96} +(-0.533984 + 0.343170i) q^{97} +(6.21839 + 3.21428i) q^{98} +(0.207662 - 1.44432i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q - 8 q^{2} - 8 q^{3} + 8 q^{4} + 2 q^{5} - 16 q^{6} - 2 q^{7} + 16 q^{8} + 8 q^{9}+O(q^{10}) \) 160 * q - 8 * q^2 - 8 * q^3 + 8 * q^4 + 2 * q^5 - 16 * q^6 - 2 * q^7 + 16 * q^8 + 8 * q^9	\( 160 q - 8 q^{2} - 8 q^{3} + 8 q^{4} + 2 q^{5} - 16 q^{6} - 2 q^{7} + 16 q^{8} + 8 q^{9} - 2 q^{10} + 4 q^{11} - 8 q^{12} + 4 q^{13} - 9 q^{14} - 18 q^{15} + 8 q^{16} + 9 q^{17} - 8 q^{18} + 18 q^{20} + 7 q^{21} + 52 q^{22} + 22 q^{23} - 80 q^{24} + 42 q^{25} + 2 q^{26} + 16 q^{27} - 18 q^{28} - 54 q^{29} + 2 q^{30} - 15 q^{31} - 8 q^{32} + 18 q^{33} + 84 q^{34} + 82 q^{35} - 16 q^{36} + 3 q^{37} + 11 q^{38} + 2 q^{39} - 13 q^{40} + 22 q^{41} - 2 q^{42} - 96 q^{43} + 4 q^{44} - 20 q^{45} - 26 q^{47} + 16 q^{48} - 2 q^{49} - 4 q^{50} + 13 q^{51} - 2 q^{52} + 16 q^{53} + 8 q^{54} - 34 q^{55} + 2 q^{56} - 22 q^{57} - 5 q^{58} - 6 q^{59} - 2 q^{60} + 40 q^{61} - 8 q^{62} - 2 q^{63} - 16 q^{64} - 82 q^{65} + 4 q^{66} + 10 q^{67} - 46 q^{68} - 22 q^{69} + 100 q^{70} + 92 q^{71} - 8 q^{72} + 68 q^{73} - 3 q^{74} + 2 q^{75} - 7 q^{77} - 18 q^{78} - 78 q^{79} + 2 q^{80} + 8 q^{81} + 55 q^{82} - 42 q^{83} - 9 q^{84} + 50 q^{85} + 40 q^{86} + 6 q^{87} + 7 q^{88} - 80 q^{89} + 4 q^{90} - 62 q^{91} + 66 q^{92} + 26 q^{93} + 4 q^{94} - 17 q^{95} + 8 q^{96} - 8 q^{97} - 3 q^{98} + 36 q^{99}+O(q^{100}) \) 160 * q - 8 * q^2 - 8 * q^3 + 8 * q^4 + 2 * q^5 - 16 * q^6 - 2 * q^7 + 16 * q^8 + 8 * q^9 - 2 * q^10 + 4 * q^11 - 8 * q^12 + 4 * q^13 - 9 * q^14 - 18 * q^15 + 8 * q^16 + 9 * q^17 - 8 * q^18 + 18 * q^20 + 7 * q^21 + 52 * q^22 + 22 * q^23 - 80 * q^24 + 42 * q^25 + 2 * q^26 + 16 * q^27 - 18 * q^28 - 54 * q^29 + 2 * q^30 - 15 * q^31 - 8 * q^32 + 18 * q^33 + 84 * q^34 + 82 * q^35 - 16 * q^36 + 3 * q^37 + 11 * q^38 + 2 * q^39 - 13 * q^40 + 22 * q^41 - 2 * q^42 - 96 * q^43 + 4 * q^44 - 20 * q^45 - 26 * q^47 + 16 * q^48 - 2 * q^49 - 4 * q^50 + 13 * q^51 - 2 * q^52 + 16 * q^53 + 8 * q^54 - 34 * q^55 + 2 * q^56 - 22 * q^57 - 5 * q^58 - 6 * q^59 - 2 * q^60 + 40 * q^61 - 8 * q^62 - 2 * q^63 - 16 * q^64 - 82 * q^65 + 4 * q^66 + 10 * q^67 - 46 * q^68 - 22 * q^69 + 100 * q^70 + 92 * q^71 - 8 * q^72 + 68 * q^73 - 3 * q^74 + 2 * q^75 - 7 * q^77 - 18 * q^78 - 78 * q^79 + 2 * q^80 + 8 * q^81 + 55 * q^82 - 42 * q^83 - 9 * q^84 + 50 * q^85 + 40 * q^86 + 6 * q^87 + 7 * q^88 - 80 * q^89 + 4 * q^90 - 62 * q^91 + 66 * q^92 + 26 * q^93 + 4 * q^94 - 17 * q^95 + 8 * q^96 - 8 * q^97 - 3 * q^98 + 36 * q^99

Introduction

L-functions

Modular forms

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Database

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