LMFDB - Embedded newform 966.2.be.a.19.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(19,966)]

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, 55, 45]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("966.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.be (of order $66$, 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:	$320$
Relative dimension:	$16$ over $\Q(\zeta_{66})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{66}]$

Embedding invariants

Embedding label			19.13
Character	$\chi$	$=$	966.19
Dual form			966.2.be.a.661.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.995472 + 0.0950560i) q^{2} +(0.690079 - 0.723734i) q^{3} +(0.981929 + 0.189251i) q^{4} +(0.525481 - 0.270904i) q^{5} +(0.755750 - 0.654861i) q^{6} +(-0.753581 - 2.53616i) q^{7} +(0.959493 + 0.281733i) q^{8} +(-0.0475819 - 0.998867i) q^{9} +O(q^{10})$	\(q+(0.995472 + 0.0950560i) q^{2} +(0.690079 - 0.723734i) q^{3} +(0.981929 + 0.189251i) q^{4} +(0.525481 - 0.270904i) q^{5} +(0.755750 - 0.654861i) q^{6} +(-0.753581 - 2.53616i) q^{7} +(0.959493 + 0.281733i) q^{8} +(-0.0475819 - 0.998867i) q^{9} +(0.548853 - 0.219728i) q^{10} +(-0.179928 - 1.88430i) q^{11} +(0.814576 - 0.580057i) q^{12} +(5.40460 + 0.777064i) q^{13} +(-0.509091 - 2.59631i) q^{14} +(0.166561 - 0.567254i) q^{15} +(0.928368 + 0.371662i) q^{16} +(-1.88958 + 5.45960i) q^{17} +(0.0475819 - 0.998867i) q^{18} +(-2.65070 - 7.65869i) q^{19} +(0.567254 - 0.166561i) q^{20} +(-2.35554 - 1.20476i) q^{21} -1.89287i q^{22} +(-1.11599 - 4.66418i) q^{23} +(0.866025 - 0.500000i) q^{24} +(-2.69754 + 3.78817i) q^{25} +(5.30626 + 1.28729i) q^{26} +(-0.755750 - 0.654861i) q^{27} +(-0.259991 - 2.63295i) q^{28} +(3.54180 + 4.08746i) q^{29} +(0.219728 - 0.548853i) q^{30} +(0.563798 - 0.136776i) q^{31} +(0.888835 + 0.458227i) q^{32} +(-1.48789 - 1.17009i) q^{33} +(-2.40000 + 5.25526i) q^{34} +(-1.08305 - 1.12856i) q^{35} +(0.142315 - 0.989821i) q^{36} +(6.11678 - 0.291378i) q^{37} +(-1.91069 - 7.87598i) q^{38} +(4.29199 - 3.37526i) q^{39} +(0.580518 - 0.111886i) q^{40} +(3.16017 - 4.91732i) q^{41} +(-2.23035 - 1.42321i) q^{42} +(-1.25354 - 4.26915i) q^{43} +(0.179928 - 1.88430i) q^{44} +(-0.295601 - 0.511996i) q^{45} +(-0.667578 - 4.74914i) q^{46} +(-1.48945 - 0.859932i) q^{47} +(0.909632 - 0.415415i) q^{48} +(-5.86423 + 3.82241i) q^{49} +(-3.04542 + 3.51460i) q^{50} +(2.64733 + 5.13511i) q^{51} +(5.15987 + 1.78585i) q^{52} +(-1.07438 - 1.36618i) q^{53} +(-0.690079 - 0.723734i) q^{54} +(-0.605013 - 0.941419i) q^{55} +(-0.00853607 - 2.64574i) q^{56} +(-7.37205 - 3.36670i) q^{57} +(3.13723 + 4.40562i) q^{58} +(2.51648 + 6.28587i) q^{59} +(0.270904 - 0.525481i) q^{60} +(1.84485 - 1.75906i) q^{61} +(0.574246 - 0.0825641i) q^{62} +(-2.49743 + 0.873403i) q^{63} +(0.841254 + 0.540641i) q^{64} +(3.05053 - 1.05580i) q^{65} +(-1.36993 - 1.30623i) q^{66} +(11.8733 + 8.45495i) q^{67} +(-2.88867 + 5.00333i) q^{68} +(-4.14575 - 2.41097i) q^{69} +(-0.970870 - 1.22640i) q^{70} +(4.47211 + 9.79255i) q^{71} +(0.235759 - 0.971812i) q^{72} +(-1.39185 + 7.22162i) q^{73} +(6.11678 + 0.291378i) q^{74} +(0.880109 + 4.56644i) q^{75} +(-1.15338 - 8.02194i) q^{76} +(-4.64329 + 1.87630i) q^{77} +(4.59339 - 2.95200i) q^{78} +(-5.84853 + 7.43701i) q^{79} +(0.588525 - 0.0561973i) q^{80} +(-0.995472 + 0.0950560i) q^{81} +(3.61328 - 4.59466i) q^{82} +(-9.75156 + 6.26695i) q^{83} +(-2.08497 - 1.62878i) q^{84} +(0.486087 + 3.38081i) q^{85} +(-0.842051 - 4.36897i) q^{86} +(5.40236 + 0.257346i) q^{87} +(0.358227 - 1.85866i) q^{88} +(-2.13922 + 8.81798i) q^{89} +(-0.245594 - 0.537776i) q^{90} +(-2.10204 - 14.2925i) q^{91} +(-0.213120 - 4.79109i) q^{92} +(0.290076 - 0.502426i) q^{93} +(-1.40096 - 0.997619i) q^{94} +(-3.46767 - 3.30641i) q^{95} +(0.945001 - 0.327068i) q^{96} +(-13.6131 - 8.74859i) q^{97} +(-6.20102 + 3.24767i) q^{98} +(-1.87360 + 0.269383i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 320 q - 16 q^{2} + 16 q^{4} + 32 q^{8} - 16 q^{9}+O(q^{10}) $ 320 * q - 16 * q^2 + 16 * q^4 + 32 * q^8 - 16 * q^9	$ 320 q - 16 q^{2} + 16 q^{4} + 32 q^{8} - 16 q^{9} - 22 q^{14} + 16 q^{16} + 66 q^{17} + 16 q^{18} + 40 q^{23} - 48 q^{25} + 12 q^{26} + 44 q^{28} - 24 q^{29} + 24 q^{31} - 16 q^{32} + 98 q^{35} + 32 q^{36} - 22 q^{37} - 66 q^{38} - 8 q^{39} - 88 q^{43} + 4 q^{46} - 144 q^{47} - 24 q^{49} + 80 q^{50} - 22 q^{51} + 12 q^{52} + 44 q^{53} + 44 q^{57} + 10 q^{58} + 12 q^{59} - 32 q^{64} + 108 q^{70} - 16 q^{71} + 16 q^{72} - 180 q^{73} - 22 q^{74} - 12 q^{75} + 18 q^{77} - 16 q^{78} + 44 q^{79} + 16 q^{81} + 36 q^{82} + 22 q^{84} + 68 q^{85} - 22 q^{86} + 48 q^{87} + 22 q^{88} + 8 q^{92} + 8 q^{93} - 12 q^{94} + 66 q^{95} - 90 q^{98}+O(q^{100}) $ 320 * q - 16 * q^2 + 16 * q^4 + 32 * q^8 - 16 * q^9 - 22 * q^14 + 16 * q^16 + 66 * q^17 + 16 * q^18 + 40 * q^23 - 48 * q^25 + 12 * q^26 + 44 * q^28 - 24 * q^29 + 24 * q^31 - 16 * q^32 + 98 * q^35 + 32 * q^36 - 22 * q^37 - 66 * q^38 - 8 * q^39 - 88 * q^43 + 4 * q^46 - 144 * q^47 - 24 * q^49 + 80 * q^50 - 22 * q^51 + 12 * q^52 + 44 * q^53 + 44 * q^57 + 10 * q^58 + 12 * q^59 - 32 * q^64 + 108 * q^70 - 16 * q^71 + 16 * q^72 - 180 * q^73 - 22 * q^74 - 12 * q^75 + 18 * q^77 - 16 * q^78 + 44 * q^79 + 16 * q^81 + 36 * q^82 + 22 * q^84 + 68 * q^85 - 22 * q^86 + 48 * q^87 + 22 * q^88 + 8 * q^92 + 8 * q^93 - 12 * q^94 + 66 * q^95 - 90 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$323$	$829$	$925$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{15}{22}\right)$

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 $

$2$	0.995472	+	0.0950560i	0.703905	+	0.0672148i
$2$	0.995472	+	0.0950560i	0.703905	+	0.0672148i
$3$	0.690079	−	0.723734i	0.398417	−	0.417848i
$3$	0.690079	−	0.723734i	0.398417	−	0.417848i
$4$	0.981929	+	0.189251i	0.490964	+	0.0946256i
$5$	0.525481	−	0.270904i	0.235002	−	0.121152i	−0.336704	−	0.941611i	$-0.609312\pi$
$5$	0.525481	−	0.270904i	0.235002	−	0.121152i	0.571706	+	0.820458i	$0.306282\pi$
$6$	0.755750	−	0.654861i	0.308533	−	0.267346i
$7$	−0.753581	−	2.53616i	−0.284827	−	0.958579i
$7$	−0.753581	−	2.53616i	−0.284827	−	0.958579i
$8$	0.959493	+	0.281733i	0.339232	+	0.0996075i
$9$	−0.0475819	−	0.998867i	−0.0158606	−	0.332956i
$10$	0.548853	−	0.219728i	0.173563	−	0.0694840i
$11$	−0.179928	−	1.88430i	−0.0542505	−	0.568137i	−0.981206	−	0.192965i	$-0.938190\pi$
$11$	−0.179928	−	1.88430i	−0.0542505	−	0.568137i	0.926955	−	0.375172i	$-0.122416\pi$
$12$	0.814576	−	0.580057i	0.235148	−	0.167448i
$13$	5.40460	+	0.777064i	1.49897	+	0.215519i	0.842443	−	0.538786i	$-0.181117\pi$
$13$	5.40460	+	0.777064i	1.49897	+	0.215519i	0.656524	+	0.754305i	$0.272026\pi$
$14$	−0.509091	−	2.59631i	−0.136060	−	0.693893i
$15$	0.166561	−	0.567254i	0.0430058	−	0.146464i
$16$	0.928368	+	0.371662i	0.232092	+	0.0929156i
$17$	−1.88958	+	5.45960i	−0.458292	+	1.32415i	0.445158	+	0.895452i	$0.353148\pi$
$17$	−1.88958	+	5.45960i	−0.458292	+	1.32415i	−0.903450	+	0.428694i	$0.858974\pi$
$18$	0.0475819	−	0.998867i	0.0112152	−	0.235435i
$19$	−2.65070	−	7.65869i	−0.608112	−	1.75702i	−0.652255	−	0.757999i	$-0.726177\pi$
$19$	−2.65070	−	7.65869i	−0.608112	−	1.75702i	0.0441430	−	0.999025i	$-0.485944\pi$
$20$	0.567254	−	0.166561i	0.126842	−	0.0372441i
$21$	−2.35554	−	1.20476i	−0.514020	−	0.262900i
$22$		−	1.89287i		−	0.403561i
$23$	−1.11599	−	4.66418i	−0.232700	−	0.972549i
$23$	−1.11599	−	4.66418i	−0.232700	−	0.972549i
$24$	0.866025	−	0.500000i	0.176777	−	0.102062i
$25$	−2.69754	+	3.78817i	−0.539509	+	0.757634i
$26$	5.30626	+	1.28729i	1.04064	+	0.252458i
$27$	−0.755750	−	0.654861i	−0.145444	−	0.126028i
$28$	−0.259991	−	2.63295i	−0.0491336	−	0.497580i
$29$	3.54180	+	4.08746i	0.657697	+	0.759022i	0.982399	−	0.186794i	$-0.0598096\pi$
$29$	3.54180	+	4.08746i	0.657697	+	0.759022i	−0.324702	+	0.945816i	$0.605264\pi$
$30$	0.219728	−	0.548853i	0.0401166	−	0.100206i
$31$	0.563798	−	0.136776i	0.101261	−	0.0245657i	−0.184808	−	0.982775i	$-0.559166\pi$
$31$	0.563798	−	0.136776i	0.101261	−	0.0245657i	0.286069	+	0.958209i	$0.407651\pi$
$32$	0.888835	+	0.458227i	0.157125	+	0.0810038i
$33$	−1.48789	−	1.17009i	−0.259009	−	0.203687i
$34$	−2.40000	+	5.25526i	−0.411596	+	0.901269i
$35$	−1.08305	−	1.12856i	−0.183069	−	0.190761i
$36$	0.142315	−	0.989821i	0.0237191	−	0.164970i
$37$	6.11678	−	0.291378i	1.00559	−	0.0479023i	0.461682	−	0.887046i	$-0.347246\pi$
$37$	6.11678	−	0.291378i	1.00559	−	0.0479023i	0.543910	+	0.839143i	$0.316943\pi$
$38$	−1.91069	−	7.87598i	−0.309955	−	1.27765i
$39$	4.29199	−	3.37526i	0.687268	−	0.540474i
$40$	0.580518	−	0.111886i	0.0917880	−	0.0176907i
$41$	3.16017	−	4.91732i	0.493536	−	0.767957i	−0.501743	−	0.865017i	$-0.667308\pi$
$41$	3.16017	−	4.91732i	0.493536	−	0.767957i	0.995279	+	0.0970603i	$0.0309440\pi$
$42$	−2.23035	−	1.42321i	−0.344151	−	0.219606i
$43$	−1.25354	−	4.26915i	−0.191162	−	0.651039i	−0.998168	−	0.0604960i	$-0.980732\pi$
$43$	−1.25354	−	4.26915i	−0.191162	−	0.651039i	0.807006	−	0.590543i	$-0.201086\pi$
$44$	0.179928	−	1.88430i	0.0271252	−	0.284068i
$45$	−0.295601	−	0.511996i	−0.0440656	−	0.0763239i
$46$	−0.667578	−	4.74914i	−0.0984290	−	0.700223i
$47$	−1.48945	−	0.859932i	−0.217258	−	0.125434i	0.387422	−	0.921902i	$-0.373366\pi$
$47$	−1.48945	−	0.859932i	−0.217258	−	0.125434i	−0.604680	+	0.796469i	$0.706699\pi$
$48$	0.909632	−	0.415415i	0.131294	−	0.0599600i
$49$	−5.86423	+	3.82241i	−0.837747	+	0.546058i
$50$	−3.04542	+	3.51460i	−0.430687	+	0.497039i
$51$	2.64733	+	5.13511i	0.370701	+	0.719059i
$52$	5.15987	+	1.78585i	0.715546	+	0.247653i
$53$	−1.07438	−	1.36618i	−0.147577	−	0.187659i	0.706644	−	0.707569i	$-0.250208\pi$
$53$	−1.07438	−	1.36618i	−0.147577	−	0.187659i	−0.854221	+	0.519910i	$0.825966\pi$
$54$	−0.690079	−	0.723734i	−0.0939079	−	0.0984877i
$55$	−0.605013	−	0.941419i	−0.0815800	−	0.126941i
$56$	−0.00853607	−	2.64574i	−0.00114068	−	0.353552i
$57$	−7.37205	−	3.36670i	−0.976452	−	0.445931i
$58$	3.13723	+	4.40562i	0.411938	+	0.578487i
$59$	2.51648	+	6.28587i	0.327618	+	0.818350i	0.997141	+	0.0755590i	$0.0240741\pi$
$59$	2.51648	+	6.28587i	0.327618	+	0.818350i	−0.669523	+	0.742791i	$0.733502\pi$
$60$	0.270904	−	0.525481i	0.0349736	−	0.0678394i
$61$	1.84485	−	1.75906i	0.236209	−	0.225225i	−0.562724	−	0.826645i	$-0.690247\pi$
$61$	1.84485	−	1.75906i	0.236209	−	0.225225i	0.798933	+	0.601420i	$0.205398\pi$
$62$	0.574246	−	0.0825641i	0.0729293	−	0.0104857i
$63$	−2.49743	+	0.873403i	−0.314647	+	0.110038i
$64$	0.841254	+	0.540641i	0.105157	+	0.0675801i
$65$	3.05053	−	1.05580i	0.378371	−	0.130956i
$66$	−1.36993	−	1.30623i	−0.168627	−	0.160786i
$67$	11.8733	+	8.45495i	1.45056	+	1.03294i	0.989336	+	0.145652i	$0.0465278\pi$
$67$	11.8733	+	8.45495i	1.45056	+	1.03294i	0.461221	+	0.887285i	$0.347412\pi$
$68$	−2.88867	+	5.00333i	−0.350303	+	0.606743i
$69$	−4.14575	−	2.41097i	−0.499089	−	0.290247i
$70$	−0.970870	−	1.22640i	−0.116041	−	0.146583i
$71$	4.47211	+	9.79255i	0.530742	+	1.16216i	0.965210	+	0.261475i	$0.0842089\pi$
$71$	4.47211	+	9.79255i	0.530742	+	1.16216i	−0.434469	+	0.900687i	$0.643064\pi$
$72$	0.235759	−	0.971812i	0.0277845	−	0.114529i
$73$	−1.39185	+	7.22162i	−0.162904	+	0.845227i	0.804878	+	0.593440i	$0.202230\pi$
$73$	−1.39185	+	7.22162i	−0.162904	+	0.845227i	−0.967783	+	0.251787i	$0.918982\pi$
$74$	6.11678	+	0.291378i	0.711061	+	0.0338720i
$75$	0.880109	+	4.56644i	0.101626	+	0.527287i
$76$	−1.15338	−	8.02194i	−0.132302	−	0.920179i
$77$	−4.64329	+	1.87630i	−0.529152	+	0.213824i
$78$	4.59339	−	2.95200i	0.520099	−	0.334248i
$79$	−5.84853	+	7.43701i	−0.658011	+	0.836730i	−0.994476	−	0.104967i	$-0.966526\pi$
$79$	−5.84853	+	7.43701i	−0.658011	+	0.836730i	0.336464	+	0.941696i	$0.390769\pi$
$80$	0.588525	−	0.0561973i	0.0657991	−	0.00628305i
$81$	−0.995472	+	0.0950560i	−0.110608	+	0.0105618i
$82$	3.61328	−	4.59466i	0.399020	−	0.507396i
$83$	−9.75156	+	6.26695i	−1.07037	+	0.687887i	−0.952314	−	0.305120i	$-0.901304\pi$
$83$	−9.75156	+	6.26695i	−1.07037	+	0.687887i	−0.118059	+	0.993007i	$0.537667\pi$
$84$	−2.08497	−	1.62878i	−0.227489	−	0.177714i
$85$	0.486087	+	3.38081i	0.0527236	+	0.366701i
$86$	−0.842051	−	4.36897i	−0.0908007	−	0.471119i
$87$	5.40236	+	0.257346i	0.579194	+	0.0275904i
$88$	0.358227	−	1.85866i	0.0381872	−	0.198134i
$89$	−2.13922	+	8.81798i	−0.226757	+	0.934704i	0.738678	+	0.674059i	$0.235450\pi$
$89$	−2.13922	+	8.81798i	−0.226757	+	0.934704i	−0.965435	+	0.260645i	$0.916065\pi$
$90$	−0.245594	−	0.537776i	−0.0258879	−	0.0566866i
$91$	−2.10204	−	14.2925i	−0.220354	−	1.49826i
$92$	−0.213120	−	4.79109i	−0.0222193	−	0.499506i
$93$	0.290076	−	0.502426i	0.0300794	−	0.0520991i
$94$	−1.40096	−	0.997619i	−0.144498	−	0.102897i
$95$	−3.46767	−	3.30641i	−0.355775	−	0.339231i
$96$	0.945001	−	0.327068i	0.0964487	−	0.0333812i
$97$	−13.6131	−	8.74859i	−1.38220	−	0.888285i	−0.382830	−	0.923819i	$-0.625050\pi$
$97$	−13.6131	−	8.74859i	−1.38220	−	0.888285i	−0.999368	+	0.0355340i	$0.988687\pi$
$98$	−6.20102	+	3.24767i	−0.626398	+	0.328064i
$99$	−1.87360	+	0.269383i	−0.188304	+	0.0270740i
$100$	−3.36571	+	3.20920i	−0.336571	+	0.320920i
$101$	−0.0687034	+	0.133266i	−0.00683625	+	0.0132605i	−0.892229	−	0.451584i	$-0.850859\pi$
$101$	−0.0687034	+	0.133266i	−0.00683625	+	0.0132605i	0.885393	+	0.464844i	$0.153890\pi$
$102$	2.14722	+	5.36350i	0.212607	+	0.531066i
$103$	−9.44367	−	13.2618i	−0.930513	−	1.30672i	−0.951727	−	0.306947i	$-0.900692\pi$
$103$	−9.44367	−	13.2618i	−0.930513	−	1.30672i	0.0212139	−	0.999775i	$-0.493247\pi$
$104$	4.96675	+	2.26824i	0.487030	+	0.222419i
$105$	−1.56417	+	0.00504654i	−0.152647	+	0.000492492i
$106$	−0.939647	−	1.46212i	−0.0912666	−	0.142014i
$107$	11.0343	+	11.5725i	1.06673	+	1.11875i	0.992591	+	0.121505i	$0.0387719\pi$
$107$	11.0343	+	11.5725i	1.06673	+	1.11875i	0.0741375	+	0.997248i	$0.476380\pi$
$108$	−0.618159	−	0.786053i	−0.0594824	−	0.0756380i
$109$	9.46916	+	3.27731i	0.906981	+	0.313909i	0.740438	−	0.672125i	$-0.234618\pi$
$109$	9.46916	+	3.27731i	0.906981	+	0.313909i	0.166543	+	0.986034i	$0.446739\pi$
$110$	−0.512786	−	0.994666i	−0.0488922	−	0.0948377i
$111$	4.01018	−	4.62800i	0.380630	−	0.439270i
$112$	0.242996	−	2.63457i	0.0229610	−	0.248943i
$113$	9.85337	−	4.49988i	0.926927	−	0.423313i	0.106013	−	0.994365i	$-0.466192\pi$
$113$	9.85337	−	4.49988i	0.926927	−	0.423313i	0.820914	+	0.571051i	$0.193464\pi$
$114$	−7.01864	−	4.05222i	−0.657356	−	0.379525i
$115$	−1.84998	−	2.14861i	−0.172511	−	0.200359i
$116$	2.70424	+	4.68389i	0.251083	+	0.434888i
$117$	0.519023	−	5.43545i	0.0479837	−	0.502508i
$118$	1.90758	+	6.49661i	0.175607	+	0.598061i
$119$	15.2704	+	0.678046i	1.39983	+	0.0621564i
$120$	0.319628	−	0.497351i	0.0291779	−	0.0454017i
$121$	7.28302	−	1.40369i	0.662093	−	0.127608i
$122$	2.00371	−	1.57573i	0.181407	−	0.142660i
$123$	−1.37807	−	5.68046i	−0.124256	−	0.512190i
$124$	0.579494	−	0.0276047i	0.0520401	−	0.00247898i
$125$	−0.811961	+	5.64731i	−0.0726240	+	0.505111i
$126$	−2.56915	+	0.632052i	−0.228878	+	0.0563076i
$127$	−1.46543	+	3.20885i	−0.130036	+	0.284739i	−0.963440	−	0.267926i	$-0.913662\pi$
$127$	−1.46543	+	3.20885i	−0.130036	+	0.284739i	0.833404	+	0.552665i	$0.186389\pi$
$128$	0.786053	+	0.618159i	0.0694779	+	0.0546381i
$129$	−3.95477	−	2.03882i	−0.348198	−	0.179508i
$130$	3.13707	−	0.761046i	0.275140	−	0.0667482i
$131$	−4.48646	+	11.2066i	−0.391984	+	0.979129i	0.592800	+	0.805349i	$0.298022\pi$
$131$	−4.48646	+	11.2066i	−0.391984	+	0.979129i	−0.984785	+	0.173780i	$0.944402\pi$
$132$	−1.23956	−	1.43053i	−0.107890	−	0.124512i
$133$	−17.4262	+	12.4940i	−1.51104	+	1.08337i
$134$	11.0159	+	9.54530i	0.951626	+	0.824588i
$135$	−0.574537	−	0.139381i	−0.0494483	−	0.0119960i
$136$	−3.35119	+	4.70609i	−0.287362	+	0.403544i
$137$	−10.4788	+	6.04992i	−0.895262	+	0.516880i	−0.875660	−	0.482928i	$-0.839573\pi$
$137$	−10.4788	+	6.04992i	−0.895262	+	0.516880i	−0.0196018	+	0.999808i	$0.506240\pi$
$138$	−3.89780	−	2.79413i	−0.331802	−	0.237852i
$139$		−	14.6047i		−	1.23875i	−0.785095	−	0.619376i	$-0.787386\pi$
$139$		−	14.6047i		−	1.23875i	0.785095	−	0.619376i	$-0.212614\pi$
$140$	−0.849897	−	1.31313i	−0.0718294	−	0.110980i
$141$	−1.65020	+	0.484542i	−0.138972	+	0.0408058i
$142$	3.52102	+	10.1733i	0.295477	+	0.853725i
$143$	0.491778	−	10.3237i	0.0411245	−	0.863310i
$144$	0.327068	−	0.945001i	0.0272557	−	0.0787501i
$145$	2.96846	+	1.18839i	0.246517	+	0.0986907i
$146$	−2.07201	+	7.05662i	−0.171481	+	0.584010i
$147$	−1.28038	+	6.88191i	−0.105604	+	0.567610i
$148$	6.06138	+	0.871496i	0.498243	+	0.0716365i
$149$	5.06133	−	3.60416i	0.414640	−	0.295264i	−0.353635	−	0.935383i	$-0.615055\pi$
$149$	5.06133	−	3.60416i	0.414640	−	0.295264i	0.768275	+	0.640119i	$0.221115\pi$
$150$	0.442056	+	4.62942i	0.0360937	+	0.377991i
$151$	−6.92286	+	2.77149i	−0.563374	+	0.225541i	−0.635828	−	0.771831i	$-0.719341\pi$
$151$	−6.92286	+	2.77149i	−0.563374	+	0.225541i	0.0724537	+	0.997372i	$0.476917\pi$
$152$	−0.385624	−	8.09525i	−0.0312783	−	0.656612i
$153$	5.54332	+	1.62767i	0.448151	+	0.131589i
$154$	−4.80062	+	1.42643i	−0.386845	+	0.114945i
$155$	0.259212	−	0.224609i	0.0208204	−	0.0180410i
$156$	4.85320	−	2.50200i	0.388567	−	0.200320i
$157$	−6.95080	−	1.33966i	−0.554734	−	0.106916i	−0.0958228	−	0.995398i	$-0.530548\pi$
$157$	−6.95080	−	1.33966i	−0.554734	−	0.106916i	−0.458911	+	0.888482i	$0.651760\pi$
$158$	−6.52898	+	6.84740i	−0.519418	+	0.544750i
$159$	−1.73016	−	0.165210i	−0.137210	−	0.0131020i
$160$	0.591202			0.0467386
$161$	−10.9881	+	6.34517i	−0.865986	+	0.500069i
$162$	−1.00000			−0.0785674
$163$	−5.63148	−	0.537741i	−0.441091	−	0.0421191i	−0.127852	−	0.991793i	$-0.540808\pi$
$163$	−5.63148	−	0.537741i	−0.441091	−	0.0421191i	−0.313239	+	0.949674i	$0.601414\pi$
$164$	4.03367	−	4.23039i	0.314977	−	0.330338i
$165$	−1.09884	−	0.211785i	−0.0855449	−	0.0164874i
$166$	−10.3031	+	5.31163i	−0.799677	+	0.412262i
$167$	−15.4815	+	13.4148i	−1.19799	+	1.03807i	−0.199689	+	0.979859i	$0.563993\pi$
$167$	−15.4815	+	13.4148i	−1.19799	+	1.03807i	−0.998304	+	0.0582081i	$0.981461\pi$
$168$	−1.92070	−	1.81959i	−0.148185	−	0.140384i
$169$	16.1325	+	4.73692i	1.24096	+	0.364379i
$170$	0.162520	+	3.41171i	0.0124647	+	0.261666i
$171$	−7.52389	+	3.01211i	−0.575366	+	0.230342i
$172$	−0.422940	−	4.42923i	−0.0322489	−	0.337726i
$173$	7.97147	−	5.67646i	0.606060	−	0.431573i	−0.235396	−	0.971900i	$-0.575639\pi$
$173$	7.97147	−	5.67646i	0.606060	−	0.431573i	0.841456	+	0.540326i	$0.181699\pi$
$174$	5.35343	+	0.769708i	0.405843	+	0.0583514i
$175$	11.6402	+	3.98671i	0.879918	+	0.301367i
$176$	0.533282	−	1.81619i	0.0401977	−	0.136901i
$177$	6.28587	+	2.51648i	0.472475	+	0.189150i
$178$	−2.96773	+	8.57471i	−0.222441	+	0.642701i
$179$	0.186027	−	3.90519i	0.0139043	−	0.291888i	−0.981196	−	0.193015i	$-0.938173\pi$
$179$	0.186027	−	3.90519i	0.0139043	−	0.291888i	0.995100	−	0.0988727i	$-0.0315237\pi$
$180$	−0.193363	−	0.558686i	−0.0144124	−	0.0416420i
$181$	4.44711	−	1.30579i	0.330551	−	0.0970585i	−0.112246	−	0.993680i	$-0.535804\pi$
$181$	4.44711	−	1.30579i	0.330551	−	0.0970585i	0.442797	+	0.896622i	$0.353986\pi$
$182$	−0.733933	−	14.4276i	−0.0544028	−	1.06945i
$183$		−	2.54907i		−	0.188433i
$184$	0.243267	−	4.78966i	0.0179339	−	0.353098i
$185$	3.13532	−	1.81018i	0.230513	−	0.133087i
$186$	0.336521	−	0.472577i	0.0246749	−	0.0346511i
$187$	10.6275	+	2.57820i	0.777159	+	0.188537i
$188$	−1.29979	−	1.12627i	−0.0947967	−	0.0821418i
$189$	−1.09131	+	2.41019i	−0.0793814	+	0.175316i
$190$	−3.13767	−	3.62107i	−0.227631	−	0.262700i
$191$	−6.57619	+	16.4265i	−0.475837	+	1.18858i	0.475303	+	0.879822i	$0.342338\pi$
$191$	−6.57619	+	16.4265i	−0.475837	+	1.18858i	−0.951140	+	0.308760i	$0.900086\pi$
$192$	0.971812	−	0.235759i	0.0701345	−	0.0170144i
$193$	−15.1024	−	7.78583i	−1.08709	−	0.560436i	−0.180988	−	0.983485i	$-0.557929\pi$
$193$	−15.1024	−	7.78583i	−1.08709	−	0.560436i	−0.906107	+	0.423049i	$0.860960\pi$
$194$	−12.7198	−	10.0030i	−0.913230	−	0.718172i
$195$	1.34099	−	2.93635i	0.0960302	−	0.210277i
$196$	−6.48165	+	2.64352i	−0.462975	+	0.188823i
$197$	−1.27349	+	8.85735i	−0.0907328	+	0.631060i	0.892817	+	0.450420i	$0.148726\pi$
$197$	−1.27349	+	8.85735i	−0.0907328	+	0.631060i	−0.983549	+	0.180640i	$0.942183\pi$
$198$	−1.89072	+	0.0900663i	−0.134368	+	0.00640073i
$199$	3.34479	+	13.7874i	0.237106	+	0.977364i	0.958558	+	0.284899i	$0.0919601\pi$
$199$	3.34479	+	13.7874i	0.237106	+	0.977364i	−0.721452	+	0.692465i	$0.756525\pi$
$200$	−3.65552	+	2.87474i	−0.258485	+	0.203275i
$201$	14.3127	−	2.75854i	1.00954	−	0.194572i
$202$	−0.0810601	+	0.126132i	−0.00570337	+	0.00887461i
$203$	7.69743	−	12.0628i	0.540253	−	0.846644i
$204$	1.62767	+	5.54332i	0.113959	+	0.388110i
$205$	0.328486	−	3.44007i	0.0229425	−	0.240265i
$206$	−8.14030	−	14.0994i	−0.567161	−	0.982352i
$207$	−4.60580	+	1.33666i	−0.320125	+	0.0929040i
$208$	4.72865	+	2.73009i	0.327873	+	0.189298i
$209$	−13.9543	+	6.37272i	−0.965240	+	0.440810i
$210$	−1.55756	−	0.143660i	−0.107482	−	0.00991346i
$211$	4.28185	−	4.94152i	0.294775	−	0.340188i	−0.588972	−	0.808153i	$-0.700467\pi$
$211$	4.28185	−	4.94152i	0.294775	−	0.340188i	0.883747	+	0.467965i	$0.155013\pi$
$212$	−0.796409	−	1.54482i	−0.0546976	−	0.106099i
$213$	10.1733	+	3.52102i	0.697064	+	0.241256i
$214$	9.88433	+	12.5689i	0.675679	+	0.859195i
$215$	−1.81524	−	1.90377i	−0.123798	−	0.129836i
$216$	−0.540641	−	0.841254i	−0.0367859	−	0.0572401i
$217$	−0.771753	−	1.32681i	−0.0523900	−	0.0900698i
$218$	9.11475	+	4.16257i	0.617329	+	0.281925i
$219$	4.26605	+	5.99082i	0.288273	+	0.404822i
$220$	−0.415915	−	1.03891i	−0.0280410	−	0.0700430i
$221$	−14.4549	+	28.0386i	−0.972342	+	1.88608i
$222$	4.43194	−	4.22585i	0.297452	−	0.283620i
$223$	−12.8895	+	1.85323i	−0.863146	+	0.124102i	−0.559648	−	0.828730i	$-0.689064\pi$
$223$	−12.8895	+	1.85323i	−0.863146	+	0.124102i	−0.303498	+	0.952832i	$0.598155\pi$
$224$	0.492327	−	2.59954i	0.0328950	−	0.173689i
$225$	3.91223	+	2.51424i	0.260816	+	0.167616i
$226$	10.2365	−	3.54289i	0.680922	−	0.235669i
$227$	15.1834	+	14.4773i	1.00776	+	0.960895i	0.999237	−	0.0390683i	$-0.0124390\pi$
$227$	15.1834	+	14.4773i	1.00776	+	0.960895i	0.00852157	+	0.999964i	$0.497287\pi$
$228$	−6.60167	−	4.70103i	−0.437207	−	0.311333i
$229$	1.01137	−	1.75174i	0.0668332	−	0.115758i	−0.830673	−	0.556761i	$-0.812044\pi$
$229$	1.01137	−	1.75174i	0.0668332	−	0.115758i	0.897506	+	0.441003i	$0.145377\pi$
$230$	−1.63736	−	2.31474i	−0.107965	−	0.152629i
$231$	−1.84630	+	4.65530i	−0.121477	+	0.306296i
$232$	2.24677	+	4.91973i	0.147507	+	0.322996i
$233$	−3.12767	+	12.8924i	−0.204901	+	0.844612i	0.772807	+	0.634641i	$0.218852\pi$
$233$	−3.12767	+	12.8924i	−0.204901	+	0.844612i	−0.977708	+	0.209971i	$0.932663\pi$
$234$	1.03335	−	5.36151i	0.0675519	−	0.350493i
$235$	−1.01564	−	0.0483807i	−0.0662528	−	0.00315601i
$236$	1.28140	+	6.64852i	0.0834118	+	0.432782i
$237$	1.34647	+	9.36491i	0.0874627	+	0.608316i
$238$	15.1368	+	2.12652i	0.981171	+	0.137842i
$239$	6.23571	−	4.00745i	0.403354	−	0.259220i	−0.323198	−	0.946331i	$-0.604758\pi$
$239$	6.23571	−	4.00745i	0.403354	−	0.259220i	0.726552	+	0.687111i	$0.241122\pi$
$240$	0.365457	−	0.464716i	0.0235901	−	0.0299973i
$241$	17.0611	−	1.62913i	1.09900	−	0.104942i	0.470238	−	0.882540i	$-0.344168\pi$
$241$	17.0611	−	1.62913i	1.09900	−	0.104942i	0.628762	+	0.777598i	$0.283562\pi$
$242$	7.38347	−	0.705036i	0.474627	−	0.0453214i
$243$	−0.618159	+	0.786053i	−0.0396549	+	0.0504253i
$244$	2.14442	−	1.37813i	0.137282	−	0.0882259i
$245$	−2.04604	+	3.59725i	−0.130717	+	0.229820i
$246$	−0.831863	−	5.78574i	−0.0530377	−	0.368885i
$247$	−8.37468	−	43.4519i	−0.532868	−	2.76478i
$248$	0.579494	+	0.0276047i	0.0367979	+	0.00175290i
$249$	−2.19374	+	11.3822i	−0.139023	+	0.721319i
$250$	−1.34510	+	5.54456i	−0.0850713	+	0.350669i
$251$	−9.01545	−	19.7411i	−0.569050	−	1.24605i	−0.947302	−	0.320343i	$-0.896202\pi$
$251$	−9.01545	−	19.7411i	−0.569050	−	1.24605i	0.378252	−	0.925703i	$-0.376525\pi$
$252$	−2.61759	+	0.384977i	−0.164893	+	0.0242513i
$253$	−8.58790	+	2.94207i	−0.539916	+	0.184967i
$254$	−1.76382	+	3.05502i	−0.110672	+	0.191689i
$255$	2.78225	+	1.98123i	0.174231	+	0.124069i
$256$	0.723734	+	0.690079i	0.0452334	+	0.0431299i
$257$	8.35874	−	2.89299i	0.521404	−	0.180460i	−0.0536736	−	0.998559i	$-0.517093\pi$
$257$	8.35874	−	2.89299i	0.521404	−	0.180460i	0.575078	+	0.818099i	$0.304972\pi$
$258$	−3.74306	−	2.40552i	−0.233033	−	0.149761i
$259$	−5.34847	−	15.2936i	−0.332338	−	0.950296i
$260$	3.19521	−	0.459402i	0.198159	−	0.0284909i
$261$	3.91431	−	3.73228i	0.242289	−	0.231022i
$262$	−5.53141	+	10.7294i	−0.341732	+	0.662867i
$263$	9.64909	+	24.1023i	0.594988	+	1.48621i	0.853968	+	0.520326i	$0.174189\pi$
$263$	9.64909	+	24.1023i	0.594988	+	1.48621i	−0.258980	+	0.965883i	$0.583386\pi$
$264$	−1.09797	−	1.54188i	−0.0675754	−	0.0948964i
$265$	−0.934669	−	0.426849i	−0.0574163	−	0.0262211i
$266$	−18.5349	+	10.7810i	−1.13645	+	0.661026i
$267$	4.90564	+	7.63333i	0.300220	+	0.467152i
$268$	10.0586	+	10.5492i	0.614429	+	0.644395i
$269$	−13.6255	−	17.3262i	−0.830759	−	1.05640i	−0.997519	−	0.0703987i	$-0.977573\pi$
$269$	−13.6255	−	17.3262i	−0.830759	−	1.05640i	0.166760	−	0.985998i	$-0.446670\pi$
$270$	−0.558686	−	0.193363i	−0.0340006	−	0.0117677i
$271$	−6.39695	−	12.4084i	−0.388587	−	0.753754i	0.610686	−	0.791873i	$-0.290894\pi$
$271$	−6.39695	−	12.4084i	−0.388587	−	0.753754i	−0.999273	+	0.0381187i	$0.987864\pi$
$272$	−3.78336	+	4.36623i	−0.229400	+	0.264741i
$273$	−11.7946	−	8.34165i	−0.713839	−	0.504860i
$274$	−11.0064	+	5.02646i	−0.664921	+	0.303659i
$275$	7.62340	+	4.40137i	0.459708	+	0.265413i
$276$	−3.61455	−	3.15199i	−0.217570	−	0.189728i
$277$	4.89429	+	8.47715i	0.294069	+	0.509343i	0.974768	−	0.223221i	$-0.0716570\pi$
$277$	4.89429	+	8.47715i	0.294069	+	0.509343i	−0.680699	+	0.732563i	$0.738324\pi$
$278$	1.38826	−	14.5385i	0.0832624	−	0.871963i
$279$	−0.163448	−	0.556651i	−0.00978535	−	0.0333258i
$280$	−0.721228	−	1.38797i	−0.0431016	−	0.0829473i
$281$	−5.69875	+	8.86743i	−0.339959	+	0.528986i	−0.968573	−	0.248731i	$-0.919986\pi$
$281$	−5.69875	+	8.86743i	−0.339959	+	0.528986i	0.628614	+	0.777718i	$0.283623\pi$
$282$	−1.68878	+	0.325486i	−0.100566	+	0.0193824i
$283$	8.23583	−	6.47673i	0.489569	−	0.385002i	−0.342637	−	0.939468i	$-0.611320\pi$
$283$	8.23583	−	6.47673i	0.489569	−	0.385002i	0.832206	+	0.554466i	$0.187078\pi$
$284$	2.53804	+	10.4619i	0.150605	+	0.620802i
$285$	−4.78593	+	0.227982i	−0.283494	+	0.0135045i
$286$	1.47088	−	10.2302i	0.0869749	−	0.604924i
$287$	−14.8526	−	4.30911i	−0.876719	−	0.254358i
$288$	0.415415	−	0.909632i	0.0244786	−	0.0536006i
$289$	−12.8738	−	10.1240i	−0.757280	−	0.595531i
$290$	2.84206	+	1.46518i	0.166891	+	0.0860385i
$291$	−15.7258	+	3.81503i	−0.921860	+	0.223641i
$292$	−2.73340	+	6.82771i	−0.159960	+	0.399562i
$293$	−5.05603	−	5.83497i	−0.295376	−	0.340883i	0.588591	−	0.808431i	$-0.299683\pi$
$293$	−5.05603	−	5.83497i	−0.295376	−	0.340883i	−0.883968	+	0.467548i	$0.845137\pi$
$294$	−1.92875	+	6.72904i	−0.112487	+	0.392445i
$295$	3.02523	+	2.62138i	0.176136	+	0.152623i
$296$	5.95110	+	1.44372i	0.345901	+	0.0839146i
$297$	−1.09797	+	1.54188i	−0.0637107	+	0.0894692i
$298$	5.38101	−	3.10673i	0.311714	−	0.179968i
$299$	−2.40711	−	26.0752i	−0.139207	−	1.50797i
$300$			4.65048i			0.268496i
$301$	−9.88261	+	6.39632i	−0.569624	+	0.368678i
$302$	−7.15496	+	2.10089i	−0.411722	+	0.120892i
$303$	0.0490384	+	0.141687i	0.00281718	+	0.00813971i
$304$	0.385624	−	8.09525i	0.0221171	−	0.464294i
$305$	0.492897	−	1.42413i	0.0282232	−	0.0815456i
$306$	5.36350	+	2.14722i	0.306611	+	0.122749i
$307$	−1.61352	+	5.49516i	−0.0920886	+	0.313625i	−0.992636	−	0.121132i	$-0.961348\pi$
$307$	−1.61352	+	5.49516i	−0.0920886	+	0.313625i	0.900548	+	0.434757i	$0.143166\pi$
$308$	−4.91447	+	0.963642i	−0.280028	+	0.0549086i
$309$	−16.1149	−	2.31697i	−0.916744	−	0.131808i
$310$	0.279389	−	0.198952i	0.0158682	−	0.0112997i
$311$	1.60566	+	16.8152i	0.0910485	+	0.953503i	0.919408	+	0.393306i	$0.128669\pi$
$311$	1.60566	+	16.8152i	0.0910485	+	0.953503i	−0.828359	+	0.560197i	$0.810725\pi$
$312$	5.06905	−	2.02934i	0.286979	−	0.114889i
$313$	−0.694293	−	14.5750i	−0.0392438	−	0.823828i	−0.929601	−	0.368567i	$-0.879849\pi$
$313$	−0.694293	−	14.5750i	−0.0392438	−	0.823828i	0.890358	−	0.455262i	$-0.150454\pi$
$314$	−6.79198	−	1.99431i	−0.383294	−	0.112545i
$315$	−1.07575	+	1.13552i	−0.0606114	+	0.0639794i
$316$	−7.15031	+	6.19578i	−0.402236	+	0.348540i
$317$	−4.95369	+	2.55381i	−0.278227	+	0.143436i	−0.591693	−	0.806163i	$-0.701540\pi$
$317$	−4.95369	+	2.55381i	−0.278227	+	0.143436i	0.313466	+	0.949600i	$0.398510\pi$
$318$	−1.70662	−	0.328923i	−0.0957023	−	0.0184451i
$319$	7.06472	−	7.40926i	0.395548	−	0.414839i
$320$	0.588525	+	0.0561973i	0.0328996	+	0.00314153i
$321$	15.9899			0.892472
$322$	−11.5415	+	5.27195i	−0.643184	+	0.293794i
$323$	46.8221			2.60525
$324$	−0.995472	−	0.0950560i	−0.0553040	−	0.00528089i
$325$	−17.5228	+	18.3774i	−0.971990	+	1.01939i
$326$	−5.55486	−	1.07061i	−0.307655	−	0.0592957i
$327$	8.90637	−	4.59155i	0.492523	−	0.253913i
$328$	4.41753	−	3.82781i	0.243917	−	0.211356i
$329$	−1.05851	+	4.42550i	−0.0583575	+	0.243986i
$330$	−1.07374	−	0.315278i	−0.0591073	−	0.0173555i
$331$	−0.466278	−	9.78838i	−0.0256290	−	0.538018i	−0.974776	−	0.223185i	$-0.928355\pi$
$331$	−0.466278	−	9.78838i	−0.0256290	−	0.538018i	0.949147	−	0.314833i	$-0.101949\pi$
$332$	−10.7614	+	4.30820i	−0.590607	+	0.236443i
$333$	−0.582096	−	6.09599i	−0.0318987	−	0.334058i
$334$	−16.6865	+	11.8824i	−0.913047	+	0.650178i
$335$	8.52969	+	1.22638i	0.466027	+	0.0670046i
$336$	−1.73904	−	1.99393i	−0.0948725	−	0.108778i
$337$	8.11241	−	27.6283i	0.441911	−	1.50501i	−0.374327	−	0.927297i	$-0.622126\pi$
$337$	8.11241	−	27.6283i	0.441911	−	1.50501i	0.816239	−	0.577715i	$-0.196056\pi$
$338$	15.6092	+	6.24896i	0.849026	+	0.339899i
$339$	3.54289	−	10.2365i	0.192423	−	0.555970i
$340$	−0.162520	+	3.41171i	−0.00881387	+	0.185026i
$341$	−0.359170	−	1.03775i	−0.0194501	−	0.0561974i
$342$	−7.77614	+	2.28328i	−0.420486	+	0.123466i
$343$	14.1134	+	11.9922i	0.762052	+	0.647515i
$344$		−	4.44938i		−	0.239894i
$345$	−2.83166	−	0.143820i	−0.152451	−	0.00774301i
$346$	8.47496	−	4.89302i	0.455617	−	0.263050i
$347$	12.0191	−	16.8784i	0.645217	−	0.906081i	−0.354361	−	0.935109i	$-0.615302\pi$
$347$	12.0191	−	16.8784i	0.645217	−	0.906081i	0.999579	+	0.0290275i	$0.00924103\pi$
$348$	5.25603	+	1.27510i	0.281753	+	0.0683525i
$349$	−24.2930	−	21.0500i	−1.30037	−	1.12678i	−0.984005	−	0.178142i	$-0.942991\pi$
$349$	−24.2930	−	21.0500i	−1.30037	−	1.12678i	−0.316367	−	0.948637i	$-0.602463\pi$
$350$	11.2086	+	5.07514i	0.599123	+	0.271277i
$351$	−3.57566	−	4.12653i	−0.190854	−	0.220258i
$352$	0.703508	−	1.75728i	0.0374971	−	0.0936632i
$353$	27.8398	−	6.75387i	1.48176	−	0.359472i	0.588314	−	0.808633i	$-0.299792\pi$
$353$	27.8398	−	6.75387i	1.48176	−	0.359472i	0.893451	+	0.449161i	$0.148277\pi$
$354$	6.01820	+	3.10260i	0.319864	+	0.164901i
$355$	5.00285	+	3.93429i	0.265524	+	0.208810i
$356$	−3.76937	+	8.25378i	−0.199776	+	0.437449i
$357$	11.0285	−	10.5838i	0.583689	−	0.560153i
$358$	0.556397	−	3.86983i	0.0294065	−	0.204527i
$359$	13.9088	−	0.662557i	0.734078	−	0.0349684i	0.322786	−	0.946472i	$-0.395381\pi$
$359$	13.9088	−	0.662557i	0.734078	−	0.0349684i	0.411292	+	0.911504i	$0.365078\pi$
$360$	−0.139381	−	0.574537i	−0.00734603	−	0.0302808i
$361$	−36.6944	+	28.8568i	−1.93128	+	1.51878i
$362$	4.55109	−	0.877152i	0.239200	−	0.0461021i
$363$	4.00996	−	6.23962i	0.210468	−	0.327495i
$364$	0.640822	−	14.4321i	0.0335882	−	0.756445i
$365$	1.22498	+	4.17189i	0.0641182	+	0.218367i
$366$	0.242305	−	2.53753i	0.0126655	−	0.132639i
$367$	5.96846	+	10.3377i	0.311551	+	0.539623i	0.978698	−	0.205303i	$-0.0658181\pi$
$367$	5.96846	+	10.3377i	0.311551	+	0.539623i	−0.667147	+	0.744926i	$0.732485\pi$
$368$	0.697451	−	4.74485i	0.0363572	−	0.247342i
$369$	−5.06212	−	2.92262i	−0.263523	−	0.152145i
$370$	3.29319	−	1.50395i	0.171205	−	0.0781866i
$371$	−2.65522	+	3.75432i	−0.137852	+	0.194914i
$372$	0.379918	−	0.438449i	0.0196978	−	0.0227325i
$373$	−8.06245	−	15.6390i	−0.417458	−	0.809755i	0.582538	−	0.812804i	$-0.302060\pi$
$373$	−8.06245	−	15.6390i	−0.417458	−	0.809755i	−0.999995	+	0.00304870i	$0.999030\pi$
$374$	10.3343	+	3.57673i	0.534373	+	0.184948i
$375$	3.52683	+	4.48473i	0.182125	+	0.231591i
$376$	−1.18684	−	1.24472i	−0.0612067	−	0.0641917i
$377$	15.9658	+	24.8433i	0.822282	+	1.27950i
$378$	−1.31548	+	2.29554i	−0.0676608	+	0.118070i
$379$	−34.1326	−	15.5878i	−1.75328	−	0.800694i	−0.987507	−	0.157578i	$-0.949631\pi$
$379$	−34.1326	−	15.5878i	−1.75328	−	0.800694i	−0.765769	−	0.643116i	$-0.777641\pi$
$380$	−2.77926	−	3.90292i	−0.142573	−	0.200216i
$381$	1.31109	+	3.27494i	0.0671691	+	0.167780i
$382$	−8.10786	+	15.7270i	−0.414834	+	0.804666i
$383$	14.0725	−	13.4181i	0.719070	−	0.685632i	−0.239369	−	0.970929i	$-0.576941\pi$
$383$	14.0725	−	13.4181i	0.719070	−	0.685632i	0.958439	+	0.285296i	$0.0920920\pi$
$384$	0.989821	−	0.142315i	0.0505116	−	0.00726247i
$385$	−1.93166	+	2.24385i	−0.0984468	+	0.114357i
$386$	−14.2939	−	9.18615i	−0.727542	−	0.467563i
$387$	−4.20467	+	1.45525i	−0.213735	+	0.0739745i
$388$	−11.7114	−	11.1668i	−0.594556	−	0.566908i
$389$	−10.4063	−	7.41027i	−0.527619	−	0.375716i	0.284985	−	0.958532i	$-0.408011\pi$
$389$	−10.4063	−	7.41027i	−0.527619	−	0.375716i	−0.812604	+	0.582816i	$0.801951\pi$
$390$	1.61403	−	2.79559i	0.0817298	−	0.141560i
$391$	27.5733	+	2.72051i	1.39444	+	0.137582i
$392$	−6.70359	+	2.01543i	−0.338582	+	0.101794i
$393$	5.01462	+	10.9805i	0.252954	+	0.553892i
$394$	−2.10967	+	8.69619i	−0.106284	+	0.438108i
$395$	−1.05857	+	5.49241i	−0.0532627	+	0.276353i
$396$	−1.89072	−	0.0900663i	−0.0950124	−	0.00452600i
$397$	0.435619	+	2.26021i	0.0218631	+	0.113437i	0.991221	−	0.132217i	$-0.0422096\pi$
$397$	0.435619	+	2.26021i	0.0218631	+	0.113437i	−0.969358	+	0.245654i	$0.920997\pi$
$398$	2.01907	+	14.0429i	0.101207	+	0.703908i
$399$	−2.98307	+	21.2338i	−0.149340	+	1.06302i
$400$	−3.91223	+	2.51424i	−0.195612	+	0.125712i
$401$	10.3303	−	13.1360i	0.515868	−	0.655980i	−0.456420	−	0.889764i	$-0.650869\pi$
$401$	10.3303	−	13.1360i	0.515868	−	0.655980i	0.972288	+	0.233784i	$0.0751110\pi$
$402$	14.5101	−	1.38554i	0.723697	−	0.0691047i
$403$	3.15339	−	0.301112i	0.157081	−	0.0149995i
$404$	−0.0926826	+	0.117856i	−0.00461113	+	0.00586353i
$405$	−0.497351	+	0.319628i	−0.0247136	+	0.0158824i
$406$	8.80921	−	11.2765i	0.437194	−	0.559644i
$407$	−1.64963	−	11.4734i	−0.0817689	−	0.568715i
$408$	1.09337	+	5.67294i	0.0541299	+	0.280852i
$409$	18.7794	+	0.894573i	0.928581	+	0.0442338i	0.506420	−	0.862287i	$-0.330969\pi$
$409$	18.7794	+	0.894573i	0.928581	+	0.0442338i	0.422161	+	0.906521i	$0.361272\pi$
$410$	0.653998	−	3.39326i	0.0322987	−	0.167581i
$411$	−2.85265	+	11.7588i	−0.140711	+	0.580017i
$412$	−6.76320	−	14.8094i	−0.333199	−	0.729604i
$413$	14.0456	−	11.1191i	0.691139	−	0.547136i
$414$	−4.71200	+	0.892795i	−0.231582	+	0.0438785i
$415$	−3.42652	+	5.93491i	−0.168201	+	0.291333i
$416$	4.44773	+	3.16721i	0.218068	+	0.155285i
$417$	−10.5699	−	10.0784i	−0.517610	−	0.493540i
$418$	−14.4969	+	5.01742i	−0.709066	+	0.245410i
$419$	−12.2043	−	7.84322i	−0.596219	−	0.383166i	0.207448	−	0.978246i	$-0.433484\pi$
$419$	−12.2043	−	7.84322i	−0.596219	−	0.383166i	−0.803667	+	0.595080i	$0.797121\pi$
$420$	−1.53685	−	0.291065i	−0.0749908	−	0.0142025i
$421$	22.0413	−	3.16906i	1.07423	−	0.154451i	0.417574	−	0.908643i	$-0.362880\pi$
$421$	22.0413	−	3.16906i	1.07423	−	0.154451i	0.656654	+	0.754192i	$0.271971\pi$
$422$	4.73218	−	4.51213i	0.230359	−	0.219647i
$423$	−0.788087	+	1.52868i	−0.0383181	+	0.0743268i
$424$	−0.645959	−	1.61353i	−0.0313705	−	0.0783598i
$425$	−15.5846	−	21.8856i	−0.755966	−	1.06161i
$426$	9.79255	+	4.47211i	0.474451	+	0.216674i
$427$	−5.85151	−	3.35324i	−0.283174	−	0.162275i
$428$	8.64482	+	13.4516i	0.417863	+	0.650207i
$429$	−7.13224	−	7.48008i	−0.344348	−	0.361141i
$430$	−1.62606	−	2.06770i	−0.0784154	−	0.0997133i
$431$	−16.8936	−	5.84694i	−0.813737	−	0.281637i	−0.111667	−	0.993746i	$-0.535619\pi$
$431$	−16.8936	−	5.84694i	−0.813737	−	0.281637i	−0.702069	+	0.712109i	$0.747740\pi$
$432$	−0.458227	−	0.888835i	−0.0220464	−	0.0427641i
$433$	−4.87438	+	5.62533i	−0.234248	+	0.270336i	−0.860688	−	0.509134i	$-0.829966\pi$
$433$	−4.87438	+	5.62533i	−0.234248	+	0.270336i	0.626440	+	0.779470i	$0.284511\pi$
$434$	−0.642137	−	1.39416i	−0.0308236	−	0.0669219i
$435$	2.90856	−	1.32829i	0.139455	−	0.0636868i
$436$	8.67780	+	5.01013i	0.415591	+	0.239942i
$437$	−32.7634	+	20.9104i	−1.56728	+	1.00028i
$438$	3.67727	+	6.36921i	0.175707	+	0.304333i
$439$	2.98045	−	31.2127i	0.142249	−	1.48970i	−0.589302	−	0.807913i	$-0.700597\pi$
$439$	2.98045	−	31.2127i	0.142249	−	1.48970i	0.731551	−	0.681787i	$-0.238797\pi$
$440$	−0.315278	−	1.07374i	−0.0150303	−	0.0511884i
$441$	4.09711	+	5.67571i	0.195100	+	0.270272i
$442$	−17.0547	+	26.5376i	−0.811209	+	1.26227i
$443$	38.9174	−	7.50072i	1.84902	−	0.356370i	0.860744	−	0.509037i	$-0.169998\pi$
$443$	38.9174	−	7.50072i	1.84902	−	0.356370i	0.988278	+	0.152668i	$0.0487864\pi$
$444$	4.81357	−	3.78543i	0.228442	−	0.179649i
$445$	1.26471	+	5.21321i	0.0599530	+	0.247130i
$446$	−13.0073	+	0.619615i	−0.615914	+	0.0293396i
$447$	0.884267	−	6.15021i	0.0418244	−	0.290895i
$448$	0.737200	−	2.54097i	0.0348294	−	0.120050i
$449$	−9.14679	+	20.0287i	−0.431664	+	0.945212i	0.561390	+	0.827551i	$0.310267\pi$
$449$	−9.14679	+	20.0287i	−0.431664	+	0.945212i	−0.993054	+	0.117661i	$0.962460\pi$
$450$	3.65552	+	2.87474i	0.172323	+	0.135516i
$451$	−9.83430	−	5.06993i	−0.463079	−	0.238734i
$452$	10.5269	−	2.55380i	0.495144	−	0.120121i
$453$	−2.77149	+	6.92286i	−0.130216	+	0.325264i
$454$	13.7385	+	15.8551i	0.644780	+	0.744115i
$455$	−4.97649	−	6.94100i	−0.233302	−	0.325399i
$456$	−6.12492	−	5.30727i	−0.286826	−	0.248536i
$457$	34.4623	+	8.36047i	1.61208	+	0.391086i	0.937741	−	0.347336i	$-0.112914\pi$
$457$	34.4623	+	8.36047i	1.61208	+	0.391086i	0.674339	+	0.738422i	$0.264429\pi$
$458$	1.17330	−	1.64767i	0.0548249	−	0.0769908i
$459$	5.00333	−	2.88867i	0.233535	−	0.134832i
$460$	−1.40992	−	2.45990i	−0.0657378	−	0.114693i
$461$			0.969860i			0.0451709i	0.999745	+	0.0225854i	$0.00718978\pi$
$461$			0.969860i			0.0451709i	−0.999745	+	0.0225854i	$0.992810\pi$
$462$	−2.28045	+	4.45872i	−0.106096	+	0.207438i
$463$	7.64415	−	2.24453i	0.355254	−	0.104312i	−0.0992359	−	0.995064i	$-0.531640\pi$
$463$	7.64415	−	2.24453i	0.355254	−	0.104312i	0.454490	+	0.890752i	$0.349822\pi$
$464$	1.76894	+	5.11102i	0.0821211	+	0.237273i
$465$	0.0163200	−	0.342598i	0.000756820	−	0.0158876i
$466$	−4.33901	+	12.5368i	−0.201001	+	0.580754i
$467$	−9.02327	−	3.61237i	−0.417547	−	0.167161i	0.153369	−	0.988169i	$-0.450988\pi$
$467$	−9.02327	−	3.61237i	−0.417547	−	0.167161i	−0.570916	+	0.821008i	$0.693412\pi$
$468$	1.53831	−	5.23900i	0.0711084	−	0.242173i
$469$	12.4956	−	36.4841i	0.576994	−	1.68468i
$470$	−1.00644	−	0.144704i	−0.0464235	−	0.00667469i
$471$	−5.76615	+	4.10606i	−0.265690	+	0.189197i
$472$	0.643613	+	6.74022i	0.0296247	+	0.310244i
$473$	−7.81879	+	3.13017i	−0.359509	+	0.143926i
$474$	0.450183	+	9.45050i	0.0206776	+	0.434076i
$475$	36.1628	+	10.6184i	1.65926	+	0.487204i
$476$	14.8661	+	3.55573i	0.681386	+	0.162977i
$477$	−1.31351	+	1.13816i	−0.0601416	+	0.0521130i
$478$	6.58840	−	3.39656i	0.301347	−	0.155355i
$479$	−36.6262	−	7.05912i	−1.67349	−	0.322539i	−0.737710	−	0.675117i	$-0.764093\pi$
$479$	−36.6262	−	7.05912i	−1.67349	−	0.322539i	−0.935782	+	0.352578i	$0.885305\pi$
$480$	0.407976	−	0.427873i	0.0186215	−	0.0195296i
$481$	33.2852	+	3.17835i	1.51767	+	0.144920i
$482$	17.1387			0.780645
$483$	−2.99046	+	12.3311i	−0.136071	+	0.561087i
$484$	7.41705			0.337139
$485$	−9.52345	−	0.909379i	−0.432438	−	0.0412928i
$486$	−0.690079	+	0.723734i	−0.0313026	+	0.0328292i
$487$	36.3392	+	7.00381i	1.64669	+	0.317373i	0.926468	−	0.376373i	$-0.122829\pi$
$487$	36.3392	+	7.00381i	1.64669	+	0.317373i	0.720219	+	0.693746i	$0.244041\pi$
$488$	2.26571	−	1.16805i	0.102564	−	0.0528753i
$489$	−4.27534	+	3.70461i	−0.193338	+	0.167528i
$490$	−2.37871	+	3.38647i	−0.107459	+	0.152985i
$491$	−9.20539	−	2.70295i	−0.415434	−	0.121982i	0.0673347	−	0.997730i	$-0.478550\pi$
$491$	−9.20539	−	2.70295i	−0.415434	−	0.121982i	−0.482768	+	0.875748i	$0.660369\pi$
$492$	−0.278127	−	5.83861i	−0.0125389	−	0.263225i
$493$	−29.0084	+	11.6132i	−1.30647	+	0.523033i
$494$	−4.20639	−	44.0513i	−0.189254	−	1.98196i
$495$	−0.911565	+	0.649123i	−0.0409718	+	0.0291759i
$496$	0.574246	+	0.0825641i	0.0257844	+	0.00370724i
$497$	21.4654	−	18.7215i	0.962855	−	0.839772i
$498$	−3.26576	+	11.1222i	−0.146342	+	0.498396i
$499$	28.5076	+	11.4127i	1.27618	+	0.510904i	0.908046	−	0.418870i	$-0.137574\pi$
$499$	28.5076	+	11.4127i	1.27618	+	0.510904i	0.368131	+	0.929774i	$0.379998\pi$
$500$	−1.86605	+	5.39159i	−0.0834522	+	0.241119i
$501$	−0.974713	+	20.4617i	−0.0435470	+	0.914163i
$502$	−7.09811	−	20.5087i	−0.316804	−	0.915346i
$503$	−27.6109	+	8.10729i	−1.23111	+	0.361486i	−0.831668	−	0.555273i	$-0.812614\pi$
$503$	−27.6109	+	8.10729i	−1.23111	+	0.361486i	−0.399440	+	0.916759i	$0.630796\pi$
$504$	−2.64233	+	0.134416i	−0.117699	+	0.00598735i
$505$			0.0886409i			0.00394447i
$506$	−8.82867	+	2.11242i	−0.392482	+	0.0939085i
$507$	14.5610	−	8.40677i	0.646675	−	0.373358i
$508$	−2.04623	+	2.87352i	−0.0907867	+	0.127492i
$509$	−14.0782	−	3.41533i	−0.624005	−	0.151382i	−0.0887242	−	0.996056i	$-0.528279\pi$
$509$	−14.0782	−	3.41533i	−0.624005	−	0.151382i	−0.535281	+	0.844674i	$0.679794\pi$
$510$	2.58132	+	2.23673i	0.114303	+	0.0990440i
$511$	19.3641	−	1.91211i	0.856617	−	0.0845868i
$512$	0.654861	+	0.755750i	0.0289410	+	0.0333997i
$513$	−3.01211	+	7.52389i	−0.132988	+	0.332188i
$514$	8.59589	−	2.08534i	0.379148	−	0.0919804i
$515$	−8.55515	−	4.41049i	−0.376985	−	0.194349i
$516$	−3.49745	−	2.75042i	−0.153967	−	0.121081i
$517$	−1.35237	+	2.96128i	−0.0594773	+	0.130237i
$518$	−3.87050	−	15.7327i	−0.170060	−	0.691256i
$519$	1.39270	−	9.68643i	0.0611327	−	0.425187i
$520$	3.22441	−	0.153598i	0.141400	−	0.00673570i
$521$	−9.14997	−	37.7167i	−0.400867	−	1.65240i	−0.712111	−	0.702067i	$-0.752261\pi$
$521$	−9.14997	−	37.7167i	−0.400867	−	1.65240i	0.311243	−	0.950330i	$-0.399255\pi$
$522$	4.25136	−	3.34330i	0.186077	−	0.146332i
$523$	4.77485	−	0.920277i	0.208790	−	0.0402409i	−0.0837838	−	0.996484i	$-0.526701\pi$
$523$	4.77485	−	0.920277i	0.208790	−	0.0402409i	0.292573	+	0.956243i	$0.405488\pi$
$524$	−6.52626	+	10.1551i	−0.285101	+	0.443626i
$525$	10.9180	−	5.67328i	0.476500	−	0.247602i
$526$	7.31433	+	24.9103i	0.318920	+	1.08614i
$527$	−0.318603	+	3.33656i	−0.0138785	+	0.145343i
$528$	−0.946434	−	1.63927i	−0.0411882	−	0.0713401i
$529$	−20.5091	+	10.4104i	−0.891702	+	0.452624i
$530$	−0.889862	−	0.513762i	−0.0386531	−	0.0223164i
$531$	6.15901	−	2.81272i	0.267278	−	0.122062i
$532$	−19.4758	+	8.97034i	−0.844382	+	0.388913i
$533$	20.9005	−	24.1205i	0.905303	−	1.04478i
$534$	4.15784	+	8.06508i	0.179927	+	0.349010i
$535$	8.93336	+	3.09187i	0.386223	+	0.133673i
$536$	9.01033	+	11.4576i	0.389187	+	0.494892i
$537$	−2.69795	−	2.82953i	−0.116425	−	0.122103i
$538$	−11.9168	−	18.5429i	−0.513770	−	0.799442i
$539$	8.25769	+	10.3622i	0.355684	+	0.446331i
$540$	−0.537776	−	0.245594i	−0.0231422	−	0.0105687i
$541$	6.29983	+	8.84687i	0.270851	+	0.380357i	0.927490	−	0.373848i	$-0.121962\pi$
$541$	6.29983	+	8.84687i	0.270851	+	0.380357i	−0.656639	+	0.754205i	$0.728023\pi$
$542$	−5.18850	−	12.9602i	−0.222865	−	0.556690i
$543$	2.12381	−	4.11962i	0.0911415	−	0.176790i
$544$	−4.18126	+	3.98682i	−0.179270	+	0.170934i
$545$	5.86370	−	0.843073i	0.251173	−	0.0361133i
$546$	−10.9482	−	9.42502i	−0.468541	−	0.403354i
$547$	−30.2047	−	19.4114i	−1.29146	−	0.829971i	−0.299206	−	0.954189i	$-0.596722\pi$
$547$	−30.2047	−	19.4114i	−1.29146	−	0.829971i	−0.992255	+	0.124217i	$0.960358\pi$
$548$	−11.4344	+	3.95747i	−0.488452	+	0.169055i
$549$	−1.84485	−	1.75906i	−0.0787363	−	0.0750749i
$550$	7.17050	+	5.10609i	0.305751	+	0.217724i
$551$	21.9163	−	37.9602i	0.933668	−	1.61716i
$552$	−3.29856	−	3.48130i	−0.140396	−	0.148174i
$553$	23.2688	+	9.22843i	0.989491	+	0.392433i
$554$	4.06632	+	8.90400i	0.172761	+	0.378295i
$555$	0.853531	−	3.51830i	0.0362304	−	0.149344i
$556$	2.76395	−	14.3407i	0.117218	−	0.608183i
$557$	15.8361	+	0.754368i	0.670998	+	0.0319636i	0.380317	−	0.924856i	$-0.375815\pi$
$557$	15.8361	+	0.754368i	0.670998	+	0.0319636i	0.290681	+	0.956820i	$0.406118\pi$
$558$	−0.109794	−	0.569667i	−0.00464797	−	0.0241159i
$559$	−3.45745	−	24.0471i	−0.146235	−	1.01709i
$560$	−0.586027	−	1.45025i	−0.0247641	−	0.0612841i
$561$	9.19974	−	5.91231i	0.388413	−	0.249618i
$562$	−6.51585	+	8.28557i	−0.274854	+	0.349506i
$563$	−24.7657	+	2.36484i	−1.04375	+	0.0996660i	−0.602821	−	0.797876i	$-0.705957\pi$
$563$	−24.7657	+	2.36484i	−1.04375	+	0.0996660i	−0.440928	+	0.897542i	$0.645351\pi$
$564$	−1.71208	+	0.163483i	−0.0720914	+	0.00688390i
$565$	3.95872	−	5.03393i	0.166545	−	0.211779i
$566$	8.81419	−	5.66454i	0.370488	−	0.238098i
$567$	0.991246	+	2.45305i	0.0416284	+	0.103018i
$568$	1.53208	+	10.6558i	0.0642845	+	0.447108i
$569$	−3.13133	−	16.2469i	−0.131272	−	0.681106i	−0.986618	−	0.163048i	$-0.947867\pi$
$569$	−3.13133	−	16.2469i	−0.131272	−	0.681106i	0.855346	−	0.518058i	$-0.173345\pi$
$570$	−4.78593	−	0.227982i	−0.200461	−	0.00954911i
$571$	0.538849	−	2.79581i	0.0225501	−	0.117001i	−0.968909	−	0.247416i	$-0.920419\pi$
$571$	0.538849	−	2.79581i	0.0225501	−	0.117001i	0.991460	+	0.130415i	$0.0416308\pi$
$572$	2.43666	−	10.0441i	0.101882	−	0.419963i
$573$	7.35035	+	16.0950i	0.307065	+	0.672379i
$574$	−14.3757	−	5.70142i	−0.600030	−	0.237973i
$575$	20.6791	+	8.35427i	0.862379	+	0.348397i
$576$	0.500000	−	0.866025i	0.0208333	−	0.0360844i
$577$	27.0412	+	19.2560i	1.12574	+	0.801636i	0.982168	−	0.188004i	$-0.0602018\pi$
$577$	27.0412	+	19.2560i	1.12574	+	0.801636i	0.143572	+	0.989640i	$0.454141\pi$
$578$	−11.8531	−	11.3019i	−0.493024	−	0.470098i
$579$	−16.0567	+	5.55728i	−0.667294	+	0.230953i
$580$	2.68991	+	1.72870i	0.111693	+	0.0717805i
$581$	23.2426	+	20.0089i	0.964265	+	0.830108i
$582$	−16.0172	+	2.30292i	−0.663934	+	0.0954592i
$583$	−2.38098	+	2.27026i	−0.0986100	+	0.0940245i
$584$	−3.37004	+	6.53697i	−0.139453	+	0.270502i
$585$	−1.19975	−	2.99684i	−0.0496036	−	0.123904i
$586$	−4.47849	−	6.28916i	−0.185005	−	0.259803i
$587$	35.4600	+	16.1940i	1.46359	+	0.668399i	0.978534	−	0.206084i	$-0.0660720\pi$
$587$	35.4600	+	16.1940i	1.46359	+	0.668399i	0.485056	+	0.874483i	$0.338799\pi$
$588$	−2.55965	+	6.51523i	−0.105558	+	0.268683i
$589$	−2.54198	−	3.95540i	−0.104741	−	0.162980i
$590$	2.76236	+	2.89708i	0.113724	+	0.119271i
$591$	5.53155	+	7.03394i	0.227538	+	0.289338i
$592$	5.78692	+	2.00287i	0.237841	+	0.0823175i
$593$	−19.8327	−	38.4701i	−0.814431	−	1.57978i	−0.814775	−	0.579777i	$-0.803140\pi$
$593$	−19.8327	−	38.4701i	−0.814431	−	1.57978i	0.000343912	−	1.00000i	$-0.499891\pi$
$594$	−1.23956	+	1.43053i	−0.0508599	+	0.0586955i
$595$	8.20798	−	3.78051i	0.336494	−	0.154986i
$596$	5.65196	−	2.58116i	0.231513	−	0.105729i
$597$	12.2866	+	7.09367i	0.502857	+	0.290324i
$598$	0.0823963	−	26.1860i	0.00336943	−	1.07082i
$599$	−23.4220	−	40.5681i	−0.956996	−	1.65757i	−0.729732	−	0.683733i	$-0.760355\pi$
$599$	−23.4220	−	40.5681i	−0.956996	−	1.65757i	−0.227264	−	0.973833i	$-0.572978\pi$
$600$	−0.442056	+	4.62942i	−0.0180469	+	0.188995i
$601$	−3.31754	−	11.2985i	−0.135325	−	0.460875i	0.863748	−	0.503924i	$-0.168111\pi$
$601$	−3.31754	−	11.2985i	−0.135325	−	0.460875i	−0.999073	+	0.0430493i	$0.986293\pi$
$602$	−10.4459	+	5.42795i	−0.425742	+	0.221227i
$603$	7.88042	−	12.2622i	0.320916	−	0.499354i
$604$	−7.32226	+	1.41125i	−0.297939	+	0.0574230i
$605$	3.44683	−	2.71061i	0.140133	−	0.110202i
$606$	0.0353481	+	0.145707i	0.00143592	+	0.00591894i
$607$	−0.539591	+	0.0257039i	−0.0219013	+	0.00104329i	−0.0585297	−	0.998286i	$-0.518641\pi$
$607$	−0.539591	+	0.0257039i	−0.0219013	+	0.00104329i	0.0366284	+	0.999329i	$0.488338\pi$
$608$	1.15338	−	8.02194i	0.0467758	−	0.325333i
$609$	−3.41844	−	13.8952i	−0.138522	−	0.563061i
$610$	0.626038	−	1.37083i	0.0253475	−	0.0555033i
$611$	−7.38164	−	5.80499i	−0.298629	−	0.234845i
$612$	5.13511	+	2.64733i	0.207574	+	0.107012i
$613$	−30.2053	+	7.32774i	−1.21998	+	0.295965i	−0.793522	−	0.608542i	$-0.791755\pi$
$613$	−30.2053	+	7.32774i	−1.21998	+	0.295965i	−0.426461	+	0.904506i	$0.640240\pi$
$614$	−2.12856	+	5.31690i	−0.0859019	+	0.214573i
$615$	−2.26301	−	2.61165i	−0.0912534	−	0.105312i
$616$	−4.98382	+	0.492128i	−0.200804	+	0.0198284i
$617$	−6.61022	−	5.72778i	−0.266117	−	0.230592i	0.511573	−	0.859240i	$-0.329063\pi$
$617$	−6.61022	−	5.72778i	−0.266117	−	0.230592i	−0.777690	+	0.628648i	$0.783609\pi$
$618$	−15.8217	−	3.83830i	−0.636441	−	0.154399i
$619$	−6.43121	+	9.03137i	−0.258492	+	0.363001i	−0.923344	−	0.383974i	$-0.874555\pi$
$619$	−6.43121	+	9.03137i	−0.258492	+	0.363001i	0.664852	+	0.746975i	$0.268495\pi$
$620$	0.297035	−	0.171493i	0.0119292	−	0.00688734i
$621$	−2.21098	+	4.25577i	−0.0887235	+	0.170778i
$622$			16.8917i			0.677295i
$623$	23.9759	−	1.21965i	0.960574	−	0.0488644i
$624$	5.23900	−	1.53831i	0.209728	−	0.0615817i
$625$	−6.50190	−	18.7860i	−0.260076	−	0.751441i
$626$	0.694293	−	14.5750i	0.0277495	−	0.582535i
$627$	−5.01742	+	14.4969i	−0.200377	+	0.578950i
$628$	−6.57165	−	2.63089i	−0.262238	−	0.104984i
$629$	−9.96736	+	33.9457i	−0.397425	+	1.35350i
$630$	−1.17881	+	1.02812i	−0.0469650	+	0.0409615i
$631$	−44.5072	−	6.39917i	−1.77180	−	0.254747i	−0.822424	−	0.568876i	$-0.807379\pi$
$631$	−44.5072	−	6.39917i	−1.77180	−	0.254747i	−0.949380	+	0.314129i	$0.898288\pi$
$632$	−7.70688	+	5.48804i	−0.306563	+	0.218303i
$633$	−0.621530	−	6.50896i	−0.0247036	−	0.258708i
$634$	−5.17402	+	2.07136i	−0.205487	+	0.0822644i
$635$	0.0992341	+	2.08318i	0.00393799	+	0.0826685i
$636$	−1.66762	−	0.489658i	−0.0661256	−	0.0194162i
$637$	−34.6641	+	16.1017i	−1.37344	+	0.637972i
$638$	7.73702	−	6.70417i	0.306312	−	0.265420i
$639$	9.56867	−	4.93299i	0.378531	−	0.195146i
$640$	0.580518	+	0.111886i	0.0229470	+	0.00442267i
$641$	22.0561	−	23.1317i	0.871162	−	0.913648i	−0.125759	−	0.992061i	$-0.540137\pi$
$641$	22.0561	−	23.1317i	0.871162	−	0.913648i	0.996921	+	0.0784126i	$0.0249852\pi$
$642$	15.9175	+	1.51994i	0.628215	+	0.0599873i
$643$	−10.6368			−0.419473			−0.209736	−	0.977758i	$-0.567261\pi$
$643$	−10.6368			−0.419473			−0.209736	+	0.977758i	$0.567261\pi$
$644$	−11.9904	+	4.15098i	−0.472487	+	0.163572i
$645$	−2.63048			−0.103575
$646$	46.6101	+	4.45072i	1.83385	+	0.175111i
$647$	5.01791	−	5.26263i	0.197274	−	0.206895i	−0.617665	−	0.786441i	$-0.711921\pi$
$647$	5.01791	−	5.26263i	0.197274	−	0.206895i	0.814940	+	0.579545i	$0.196770\pi$
$648$	−0.981929	−	0.189251i	−0.0385738	−	0.00743449i
$649$	11.3916	−	5.87280i	0.447161	−	0.230528i
$650$	−19.1903	+	16.6285i	−0.752707	+	0.652224i
$651$	−1.49283	−	0.357060i	−0.0585086	−	0.0139943i
$652$	−5.42794	−	1.59379i	−0.212575	−	0.0624175i
$653$	0.832041	+	17.4667i	0.0325603	+	0.683524i	0.954861	+	0.297052i	$0.0960035\pi$
$653$	0.832041	+	17.4667i	0.0325603	+	0.683524i	−0.922301	+	0.386472i	$0.873693\pi$
$654$	9.30249	−	3.72416i	0.363756	−	0.145626i
$655$	0.678377	+	7.10429i	0.0265064	+	0.277587i
$656$	4.76138	−	3.39057i	0.185901	−	0.132379i
$657$	7.27967	+	1.04666i	0.284007	+	0.0408340i
$658$	−1.47439	+	4.30485i	−0.0574776	+	0.167820i
$659$	6.95031	−	23.6706i	0.270746	−	0.922075i	−0.706097	−	0.708115i	$-0.749546\pi$
$659$	6.95031	−	23.6706i	0.270746	−	0.922075i	0.976842	−	0.213960i	$-0.0686362\pi$
$660$	−1.03891	−	0.415915i	−0.0404394	−	0.0161895i
$661$	−8.67368	+	25.0610i	−0.337367	+	0.974758i	0.640939	+	0.767592i	$0.278545\pi$
$661$	−8.67368	+	25.0610i	−0.337367	+	0.974758i	−0.978306	+	0.207166i	$0.933576\pi$
$662$	0.466278	−	9.78838i	0.0181224	−	0.380436i
$663$	10.3175	+	29.8104i	0.400697	+	1.15774i
$664$	−11.1222	+	3.26576i	−0.431623	+	0.126736i
$665$	−5.77243	+	11.2862i	−0.223845	+	0.437661i
$666$		−	6.12372i		−	0.237289i
$667$	15.1120	−	21.0812i	0.585140	−	0.816266i
$668$	−17.7405	+	10.2425i	−0.686400	+	0.396293i
$669$	−7.55354	+	10.6075i	−0.292037	+	0.410108i
$670$	8.37449	+	2.03163i	0.323535	+	0.0784887i
$671$	−3.64653	−	3.15974i	−0.140773	−	0.121980i
$672$	−1.54163	−	2.15020i	−0.0594697	−	0.0829459i
$673$	21.9578	+	25.3406i	0.846411	+	0.976810i	0.999936	−	0.0113346i	$-0.00360800\pi$
$673$	21.9578	+	25.3406i	0.846411	+	0.976810i	−0.153525	+	0.988145i	$0.549063\pi$
$674$	10.7019	−	26.7321i	0.412223	−	1.02968i
$675$	4.51939	−	1.09639i	0.173951	−	0.0422002i
$676$	14.9445	+	7.70441i	0.574788	+	0.296324i
$677$	−30.4395	−	23.9379i	−1.16989	−	0.920008i	−0.172006	−	0.985096i	$-0.555025\pi$
$677$	−30.4395	−	23.9379i	−1.16989	−	0.920008i	−0.997880	+	0.0650877i	$0.979267\pi$
$678$	4.49988	−	9.85337i	0.172817	−	0.378416i
$679$	−11.9293	+	41.1177i	−0.457804	+	1.57795i
$680$	−0.486087	+	3.38081i	−0.0186406	+	0.129648i
$681$	20.9555	−	0.998234i	0.803017	−	0.0382524i
$682$	−0.258899	−	1.06719i	−0.00991374	−	0.0408650i
$683$	−10.6112	+	8.34478i	−0.406028	+	0.319304i	−0.800201	−	0.599732i	$-0.795274\pi$
$683$	−10.6112	+	8.34478i	−0.406028	+	0.319304i	0.394172	+	0.919036i	$0.371031\pi$
$684$	−7.95797	+	1.53377i	−0.304281	+	0.0586453i
$685$	−3.86745	+	6.01787i	−0.147768	+	0.229931i
$686$	12.9096	+	13.2794i	0.492890	+	0.507010i
$687$	−0.569871	−	1.94080i	−0.0217419	−	0.0740463i
$688$	0.422940	−	4.42923i	0.0161245	−	0.168863i
$689$	−4.74496	−	8.21852i	−0.180769	−	0.313101i
$690$	−2.80516	−	0.412335i	−0.106791	−	0.0156973i
$691$	33.5638	+	19.3781i	1.27683	+	0.737177i	0.976264	−	0.216584i	$-0.0694916\pi$
$691$	33.5638	+	19.3781i	1.27683	+	0.737177i	0.300564	+	0.953762i	$0.402825\pi$
$692$	8.90170	−	4.06527i	0.338392	−	0.154538i
$693$	2.09511	+	4.54875i	0.0795866	+	0.172793i
$694$	13.5690	−	15.6595i	0.515074	−	0.594427i
$695$	−3.95647	−	7.67448i	−0.150077	−	0.291110i
$696$	5.11102	+	1.76894i	0.193733	+	0.0670516i
$697$	20.8752	+	26.5449i	0.790704	+	1.00546i
$698$	−22.1820	−	23.2638i	−0.839602	−	0.880549i
$699$	7.17236	+	11.1604i	0.271283	+	0.422125i
$700$	10.6754	+	6.11760i	0.403491	+	0.231223i
$701$	8.03271	+	3.66842i	0.303391	+	0.138554i	0.561293	−	0.827617i	$-0.310304\pi$
$701$	8.03271	+	3.66842i	0.303391	+	0.138554i	−0.257902	+	0.966171i	$0.583031\pi$
$702$	−3.16721	−	4.44773i	−0.119539	−	0.167869i
$703$	−18.4453	−	46.0742i	−0.695678	−	1.73772i
$704$	0.867362	−	1.68245i	0.0326899	−	0.0634096i
$705$	−0.735884	+	0.701664i	−0.0277150	+	0.0264262i
$706$	28.3558	−	4.07694i	1.06718	−	0.153438i
$707$	0.389758	+	0.0738163i	0.0146584	+	0.00277615i
$708$	5.69602	+	3.66061i	0.214070	+	0.137574i
$709$	8.51445	−	2.94688i	0.319767	−	0.110672i	−0.162469	−	0.986714i	$-0.551946\pi$
$709$	8.51445	−	2.94688i	0.319767	−	0.110672i	0.482236	+	0.876041i	$0.339825\pi$
$710$	4.60622	+	4.39203i	0.172868	+	0.164830i
$711$	7.70688	+	5.48804i	0.289030	+	0.205818i
$712$	−4.53688	+	7.85810i	−0.170027	+	0.294495i
$713$	−1.26714	−	2.47701i	−0.0474548	−	0.0927649i
$714$	11.9846	−	9.48753i	0.448512	−	0.355062i
$715$	−2.53831	−	5.55813i	−0.0949275	−	0.207862i
$716$	0.921728	−	3.79942i	0.0344466	−	0.141991i
$717$	1.40281	−	7.27845i	0.0523888	−	0.271819i
$718$	13.9088	+	0.662557i	0.519071	+	0.0247264i
$719$	7.09560	+	36.8155i	0.264621	+	1.37299i	0.834387	+	0.551178i	$0.185822\pi$
$719$	7.09560	+	36.8155i	0.264621	+	1.37299i	−0.569766	+	0.821807i	$0.692966\pi$
$720$	−0.0841368	−	0.585184i	−0.00313559	−	0.0218085i
$721$	−26.5175	+	33.9445i	−0.987562	+	1.26416i
$722$	−39.2712	+	25.2381i	−1.46152	+	0.939264i
$723$	10.5944	−	13.4719i	0.394011	−	0.501025i
$724$	4.61387	−	0.440571i	0.171473	−	0.0163737i
$725$	−25.0382	+	2.39085i	−0.929894	+	0.0887941i
$726$	4.58492	−	5.83020i	0.170162	−	0.216379i
$727$	16.0315	−	10.3028i	0.594577	−	0.382111i	−0.208469	−	0.978029i	$-0.566848\pi$
$727$	16.0315	−	10.3028i	0.594577	−	0.382111i	0.803046	+	0.595918i	$0.203212\pi$
$728$	2.00977	−	14.3058i	0.0744872	−	0.530208i
$729$	0.142315	+	0.989821i	0.00527092	+	0.0366601i
$730$	0.822867	+	4.26944i	0.0304557	+	0.158019i
$731$	25.6765	+	1.22312i	0.949679	+	0.0452388i
$732$	0.482415	−	2.50301i	0.0178306	−	0.0925138i
$733$	−11.3425	+	46.7544i	−0.418944	+	1.72691i	0.236467	+	0.971640i	$0.424011\pi$
$733$	−11.3425	+	46.7544i	−0.418944	+	1.72691i	−0.655411	+	0.755272i	$0.727505\pi$
$734$	4.95878	+	10.8582i	0.183032	+	0.400784i
$735$	1.19152	+	3.96317i	0.0439500	+	0.146184i
$736$	1.14532	−	4.65706i	0.0422170	−	0.171662i
$737$	13.7953	−	23.8941i	0.508156	−	0.880152i
$738$	−4.76138	−	3.39057i	−0.175269	−	0.124808i
$739$	−0.293389	−	0.279746i	−0.0107925	−	0.0102906i	0.684664	−	0.728859i	$-0.259949\pi$
$739$	−0.293389	−	0.279746i	−0.0107925	−	0.0102906i	−0.695456	+	0.718569i	$0.744798\pi$
$740$	3.42124	−	1.18410i	0.125767	−	0.0435284i
$741$	−37.2268	−	23.9242i	−1.36756	−	0.878879i
$742$	−3.00007	+	3.48492i	−0.110136	+	0.127936i
$743$	−32.3407	+	4.64989i	−1.18647	+	0.170588i	−0.707156	−	0.707058i	$-0.750022\pi$
$743$	−32.3407	+	4.64989i	−1.18647	+	0.170588i	−0.479310	+	0.877646i	$0.659113\pi$
$744$	0.419875	−	0.400350i	0.0153934	−	0.0146776i
$745$	1.68325	−	3.26506i	0.0616696	−	0.119622i
$746$	−6.53936	−	16.3345i	−0.239423	−	0.598050i
$747$	6.72385	+	9.44232i	0.246013	+	0.345477i
$748$	9.94751	+	4.54287i	0.363717	+	0.166104i
$749$	21.0344	−	36.7056i	0.768580	−	1.34119i
$750$	3.08456	+	4.79967i	0.112632	+	0.175259i
$751$	−19.9090	−	20.8800i	−0.726490	−	0.761921i	0.252109	−	0.967699i	$-0.418876\pi$
$751$	−19.9090	−	20.8800i	−0.726490	−	0.761921i	−0.978599	+	0.205778i	$0.934027\pi$
$752$	−1.06315	−	1.35190i	−0.0387691	−	0.0492989i
$753$	−20.5087	−	7.09811i	−0.747377	−	0.258670i
$754$	13.5320	+	26.2485i	0.492807	+	0.955913i
$755$	−2.88702	+	3.33180i	−0.105070	+	0.121257i
$756$	−1.52773	+	2.16011i	−0.0555628	+	0.0785623i
$757$	−17.3072	+	7.90394i	−0.629041	+	0.287273i	−0.704313	−	0.709890i	$-0.748745\pi$
$757$	−17.3072	+	7.90394i	−0.629041	+	0.287273i	0.0752718	+	0.997163i	$0.476018\pi$
$758$	−32.4964	−	18.7618i	−1.18032	−	0.681458i
$759$	−3.79705	+	8.24562i	−0.137824	+	0.299297i
$760$	−2.39568	−	4.14944i	−0.0869004	−	0.150516i
$761$	1.03119	−	10.7991i	0.0373807	−	0.391468i	−0.957349	−	0.288935i	$-0.906699\pi$
$761$	1.03119	−	10.7991i	0.0373807	−	0.391468i	0.994730	−	0.102534i	$-0.0326950\pi$
$762$	0.993849	+	3.38474i	0.0360033	+	0.122616i
$763$	1.17601	−	26.4850i	0.0425743	−	0.958822i
$764$	−9.56609	+	14.8851i	−0.346089	+	0.538525i
$765$	3.35385	−	0.646402i	0.121259	−	0.0233707i
$766$	15.2842	−	12.0197i	0.552242	−	0.434288i
$767$	8.71605	+	35.9281i	0.314718	+	1.29729i
$768$	0.998867	−	0.0475819i	0.0360435	−	0.00171696i
$769$	1.55893	−	10.8426i	0.0562164	−	0.390994i	−0.942215	−	0.335008i	$-0.891261\pi$
$769$	1.55893	−	10.8426i	0.0562164	−	0.390994i	0.998432	−	0.0559853i	$-0.0178300\pi$
$770$	−2.13621	+	2.05007i	−0.0769836	+	0.0738794i
$771$	3.67444	−	8.04590i	0.132332	−	0.289766i
$772$	−13.3560	−	10.5033i	−0.480693	−	0.378021i
$773$	10.1364	+	5.22566i	0.364580	+	0.187954i	0.630776	−	0.775965i	$-0.282737\pi$
$773$	10.1364	+	5.22566i	0.364580	+	0.187954i	−0.266196	+	0.963919i	$0.585767\pi$
$774$	−4.32396	+	1.04898i	−0.155421	+	0.0377048i
$775$	−1.00274	+	2.50472i	−0.0360194	+	0.0899722i
$776$	−10.5969	−	12.2295i	−0.380406	−	0.439012i
$777$	−14.7593	−	6.68290i	−0.529488	−	0.239748i
$778$	−9.65476	−	8.36590i	−0.346140	−	0.299932i
$779$	−46.0369	−	11.1684i	−1.64944	−	0.400151i
$780$	1.87246	−	2.62951i	0.0670450	−	0.0941515i
$781$	17.6474	−	10.1887i	0.631474	−	0.364582i
$782$	27.1898	+	5.32920i	0.972307	+	0.190572i
$783$		−	5.40849i		−	0.193284i
$784$	−6.86481	+	1.36908i	−0.245172	+	0.0488958i
$785$	−4.01543	+	1.17904i	−0.143317	+	0.0420816i
$786$	3.94815	+	11.4074i	0.140826	+	0.406889i
$787$	−1.80472	+	37.8857i	−0.0643313	+	1.35048i	0.703896	+	0.710303i	$0.251442\pi$
$787$	−1.80472	+	37.8857i	−0.0643313	+	1.35048i	−0.768227	+	0.640177i	$0.778861\pi$
$788$	−2.92675	+	8.45628i	−0.104261	+	0.301242i
$789$	24.1023	+	9.64909i	0.858063	+	0.343517i
$790$	−1.57587	+	5.36691i	−0.0560669	+	0.190946i
$791$	−18.8377	−	21.5987i	−0.669793	−	0.767962i
$792$	−1.87360	−	0.269383i	−0.0665755	−	0.00957211i
$793$	11.3376	−	8.07346i	0.402610	−	0.286697i
$794$	0.218800	+	2.29138i	0.00776494	+	0.0813181i
$795$	−0.953920	+	0.381892i	−0.0338321	+	0.0135443i
$796$	0.675061	+	14.1713i	0.0239269	+	0.502287i
$797$	8.53921	+	2.50734i	0.302474	+	0.0888145i	0.429448	−	0.903092i	$-0.358708\pi$
$797$	8.53921	+	2.50734i	0.302474	+	0.0888145i	−0.126974	+	0.991906i	$0.540526\pi$
$798$	−4.98796	+	20.8541i	−0.176572	+	0.738227i
$799$	7.50932	−	6.50686i	0.265660	−	0.230196i
$800$	−4.13351	+	2.13097i	−0.146142	+	0.0753413i
$801$	8.90978	+	1.71722i	0.314812	+	0.0606750i
$802$	11.5321	−	12.0946i	0.407214	−	0.427074i
$803$	13.8581	+	1.32329i	0.489042	+	0.0466979i
$804$	14.5761			0.514059
$805$	−4.05512	+	6.31100i	−0.142924	+	0.222433i
$806$	3.16773			0.111579
$807$	−21.9422	−	2.09523i	−0.772402	−	0.0737554i
$808$	−0.103466	+	0.108512i	−0.00363992	+	0.00381743i
$809$	−13.8624	−	2.67176i	−0.487376	−	0.0939340i	−0.0603573	−	0.998177i	$-0.519224\pi$
$809$	−13.8624	−	2.67176i	−0.487376	−	0.0939340i	−0.427019	+	0.904243i	$0.640436\pi$
$810$	−0.525481	+	0.270904i	−0.0184635	+	0.00951861i
$811$	−13.9005	+	12.0448i	−0.488111	+	0.422950i	−0.863830	−	0.503783i	$-0.831941\pi$
$811$	−13.9005	+	12.0448i	−0.488111	+	0.422950i	0.375719	+	0.926733i	$0.377396\pi$
$812$	9.84123	−	10.3881i	0.345359	−	0.364550i
$813$	−13.3948	−	3.93306i	−0.469775	−	0.137938i
$814$	−0.551540	−	11.5783i	−0.0193315	−	0.405817i
$815$	−3.10491	+	1.24302i	−0.108760	+	0.0435411i
$816$	0.549172	+	5.75118i	0.0192248	+	0.201332i
$817$	−29.3734	+	20.9167i	−1.02764	+	0.731782i
$818$	18.6093	+	2.67562i	0.650660	+	0.0935508i
$819$	−14.1763	+	2.77973i	−0.495361	+	0.0971315i
$820$	0.973587	−	3.31573i	0.0339991	−	0.115790i
$821$	−1.11792	−	0.447547i	−0.0390156	−	0.0156195i	0.352073	−	0.935973i	$-0.385477\pi$
$821$	−1.11792	−	0.447547i	−0.0390156	−	0.0156195i	−0.391088	+	0.920353i	$0.627901\pi$
$822$	−3.95747	+	11.4344i	−0.138033	+	0.398819i
$823$	1.45947	−	30.6380i	0.0508739	−	1.06798i	−0.818715	−	0.574199i	$-0.805313\pi$
$823$	1.45947	−	30.6380i	0.0508739	−	1.06798i	0.869589	−	0.493776i	$-0.164384\pi$
$824$	−5.32486	−	15.3852i	−0.185500	−	0.535968i
$825$	8.44617	−	2.48002i	0.294058	−	0.0863432i
$826$	15.0389	−	9.73364i	0.523272	−	0.338677i
$827$		−	4.26723i		−	0.148386i	−0.997244	−	0.0741930i	$-0.976362\pi$
$827$		−	4.26723i		−	0.148386i	0.997244	−	0.0741930i	$-0.0236381\pi$
$828$	−4.77553	+	0.440848i	−0.165961	+	0.0153205i
$829$	−22.7701	+	13.1463i	−0.790839	+	0.456591i	−0.840258	−	0.542187i	$-0.817596\pi$
$829$	−22.7701	+	13.1463i	−0.790839	+	0.456591i	0.0494189	+	0.998778i	$0.484263\pi$
$830$	−3.97515	+	5.58232i	−0.137980	+	0.193765i
$831$	9.51265	+	2.30774i	0.329990	+	0.0800548i
$832$	4.12653	+	3.57566i	0.143062	+	0.123964i
$833$	−9.78782	−	39.2391i	−0.339128	−	1.35955i
$834$	−9.56402	−	11.0375i	−0.331175	−	0.382196i
$835$	−4.50111	+	11.2432i	−0.155767	+	0.389088i
$836$	−14.9082	+	3.61669i	−0.515610	+	0.125086i
$837$	−0.515659	−	0.265841i	−0.0178238	−	0.00918880i
$838$	−11.4035	−	8.96780i	−0.393927	−	0.309787i
$839$	12.0163	−	26.3121i	0.414850	−	0.908395i	−0.580696	−	0.814120i	$-0.697220\pi$
$839$	12.0163	−	26.3121i	0.414850	−	0.908395i	0.995546	−	0.0942748i	$-0.0300532\pi$
$840$	−1.50223	−	0.435834i	−0.0518318	−	0.0150377i
$841$	−0.0358229	+	0.249154i	−0.00123527	+	0.00859150i
$842$	22.2427	−	1.05955i	0.766535	−	0.0365146i
$843$	2.48507	+	10.2436i	0.0855904	+	0.352808i
$844$	5.13966	−	4.04187i	0.176914	−	0.139127i
$845$	9.76057	−	1.88120i	0.335774	−	0.0647151i
$846$	−0.929829	+	1.44684i	−0.0319682	+	0.0497434i
$847$	−9.04832	−	17.4131i	−0.310904	−	0.598322i
$848$	−0.489658	−	1.66762i	−0.0168149	−	0.0572664i
$849$	0.995945	−	10.4300i	0.0341807	−	0.357957i
$850$	−13.4337	−	23.2679i	−0.460773	−	0.798082i
$851$	−8.18530	−	28.2046i	−0.280589	−	0.966841i
$852$	9.32311	+	5.38270i	0.319404	+	0.184408i
$853$	−18.2499	+	8.33444i	−0.624864	+	0.285366i	−0.702575	−	0.711610i	$-0.747966\pi$
$853$	−18.2499	+	8.33444i	−0.624864	+	0.285366i	0.0777105	+	0.996976i	$0.475239\pi$
$854$	−5.50627	−	3.89428i	−0.188421	−	0.133260i
$855$	−3.13767	+	3.62107i	−0.107306	+	0.123838i
$856$	7.32702	+	14.2124i	0.250432	+	0.485771i
$857$	−6.64503	−	2.29987i	−0.226990	−	0.0785620i	0.211206	−	0.977442i	$-0.432261\pi$
$857$	−6.64503	−	2.29987i	−0.226990	−	0.0785620i	−0.438196	+	0.898880i	$0.644382\pi$
$858$	−6.38892	−	8.12417i	−0.218114	−	0.277355i
$859$	28.5014	+	29.8914i	0.972456	+	1.01988i	0.999795	+	0.0202559i	$0.00644809\pi$
$859$	28.5014	+	29.8914i	0.972456	+	1.01988i	−0.0273392	+	0.999626i	$0.508703\pi$
$860$	−1.42215	−	2.21290i	−0.0484948	−	0.0754594i
$861$	−13.3681	+	7.77568i	−0.455583	+	0.264995i
$862$	−16.2613	−	7.42630i	−0.553863	−	0.252941i
$863$	−11.3891	−	15.9937i	−0.387688	−	0.544432i	0.573901	−	0.818925i	$-0.305429\pi$
$863$	−11.3891	−	15.9937i	−0.387688	−	0.544432i	−0.961589	+	0.274493i	$0.911490\pi$
$864$	−0.371662	−	0.928368i	−0.0126442	−	0.0315837i
$865$	2.65108	−	5.14238i	0.0901395	−	0.174846i
$866$	−5.38703	+	5.13652i	−0.183059	+	0.174546i
$867$	−16.2110	+	2.33079i	−0.550555	+	0.0791578i
$868$	−0.506706	−	1.44889i	−0.0171987	−	0.0491785i
$869$	15.0659	+	9.68224i	0.511074	+	0.328447i
$870$	3.02165	−	1.04580i	0.102443	−	0.0354560i
$871$	57.6005	+	54.9220i	1.95172	+	1.86096i
$872$	8.16227	+	5.81232i	0.276409	+	0.196830i
$873$	−8.09095	+	14.0139i	−0.273837	+	0.474300i
$874$	−34.6027	+	17.7013i	−1.17045	+	0.598756i
$875$	14.9344	−	2.19644i	0.504874	−	0.0742533i
$876$	3.05518	+	6.68992i	0.103225	+	0.226031i
$877$	−10.3193	+	42.5367i	−0.348458	+	1.43636i	0.480471	+	0.877010i	$0.340466\pi$
$877$	−10.3193	+	42.5367i	−0.348458	+	1.43636i	−0.828929	+	0.559353i	$0.811050\pi$
$878$	5.93391	−	30.7880i	0.200260	−	1.03905i
$879$	−7.71203	−	0.367369i	−0.260120	−	0.0123911i
$880$	−0.211785	−	1.09884i	−0.00713927	−	0.0370420i
$881$	1.88297	+	13.0964i	0.0634390	+	0.441228i	0.996642	+	0.0818788i	$0.0260921\pi$
$881$	1.88297	+	13.0964i	0.0634390	+	0.441228i	−0.933203	+	0.359349i	$0.882999\pi$
$882$	3.53904	+	6.03947i	0.119166	+	0.203359i
$883$	−21.6580	+	13.9188i	−0.728851	+	0.468404i	−0.851706	−	0.524020i	$-0.824432\pi$
$883$	−21.6580	+	13.9188i	−0.728851	+	0.468404i	0.122854	+	0.992425i	$0.460795\pi$
$884$	−19.5000	+	24.7963i	−0.655857	+	0.833990i
$885$	3.98483	−	0.380505i	0.133949	−	0.0127905i
$886$	39.4542	−	3.76742i	1.32549	−	0.126569i
$887$	−27.4158	+	34.8621i	−0.920534	+	1.17055i	0.0644521	+	0.997921i	$0.479470\pi$
$887$	−27.4158	+	34.8621i	−0.920534	+	1.17055i	−0.984986	+	0.172633i	$0.944772\pi$
$888$	5.15160	−	3.31073i	0.172876	−	0.111101i
$889$	9.24247	+	1.29845i	0.309983	+	0.0435485i
$890$	0.763437	+	5.30982i	0.0255905	+	0.177986i
$891$	0.358227	+	1.85866i	0.0120011	+	0.0622675i
$892$	−13.0073	−	0.619615i	−0.435517	−	0.0207462i
$893$	−2.63788	+	13.6866i	−0.0882734	+	0.458006i
$894$	1.46488	−	6.03831i	0.0489928	−	0.201951i
$895$	−0.960181	−	2.10250i	−0.0320953	−	0.0702789i
$896$	0.975397	−	2.45939i	0.0325857	−	0.0821625i
$897$	−20.5326	−	16.2519i	−0.685564	−	0.542634i
$898$	−11.0092	+	19.0685i	−0.367383	+	0.636325i
$899$	2.55593	+	1.82007i	0.0852450	+	0.0607027i
$900$	3.36571	+	3.20920i	0.112190	+	0.106973i
$901$	9.48892	−	3.28415i	0.316122	−	0.109411i
$902$	−9.30784	−	5.98178i	−0.309917	−	0.199172i
$903$	−2.19055	+	11.5663i	−0.0728970	+	0.384904i
$904$	10.7220	−	1.54159i	0.356609	−	0.0512726i
$905$	1.98313	−	1.89091i	0.0659214	−	0.0628559i
$906$	−3.41701	+	6.62807i	−0.113522	+	0.220203i
$907$	−13.5104	−	33.7474i	−0.448607	−	1.12057i	−0.964540	−	0.263937i	$-0.914979\pi$
$907$	−13.5104	−	33.7474i	−0.448607	−	1.12057i	0.515933	−	0.856629i	$-0.327445\pi$
$908$	12.1692	+	17.0892i	0.403848	+	0.567125i
$909$	0.136384	+	0.0622846i	0.00452358	+	0.00206585i
$910$	−4.29417	−	7.38262i	−0.142351	−	0.244731i
$911$	23.5280	+	36.6103i	0.779518	+	1.21295i	0.972763	+	0.231803i	$0.0744624\pi$
$911$	23.5280	+	36.6103i	0.779518	+	1.21295i	−0.193245	+	0.981151i	$0.561901\pi$
$912$	−5.59270	−	5.86545i	−0.185193	−	0.194225i
$913$	13.5634	+	17.2472i	0.448882	+	0.570800i
$914$	33.5116	+	11.5985i	1.10846	+	0.383643i
$915$	−0.690555	−	1.33949i	−0.0228291	−	0.0442822i
$916$	1.32461	−	1.52868i	0.0437664	−	0.0505091i
$917$	31.8028	+	2.93329i	1.05022	+	0.0968657i
$918$	5.25526	−	2.40000i	0.173449	−	0.0792117i
$919$	−31.0900	−	17.9498i	−1.02556	−	0.592110i	−0.109853	−	0.993948i	$-0.535038\pi$
$919$	−31.0900	−	17.9498i	−1.02556	−	0.592110i	−0.915711	+	0.401838i	$0.868371\pi$
$920$	−1.16971	−	2.58278i	−0.0385641	−	0.0851517i
$921$	2.86357	+	4.95985i	0.0943579	+	0.163433i
$922$	−0.0921910	+	0.965468i	−0.00303615	+	0.0317960i
$923$	16.5605	+	56.3999i	0.545096	+	1.85643i
$924$	−2.69395	+	4.22176i	−0.0886245	+	0.138886i
$925$	−15.3965	+	23.9574i	−0.506233	+	0.787714i
$926$	7.82289	−	1.50774i	0.257076	−	0.0495474i
$927$	−12.7974	+	10.0640i	−0.420322	+	0.330545i
$928$	1.27510	+	5.25603i	0.0418572	+	0.172538i
$929$	−50.3316	+	2.39759i	−1.65133	+	0.0786623i	−0.852441	−	0.522823i	$-0.824879\pi$
$929$	−50.3316	+	2.39759i	−1.65133	+	0.0786623i	−0.798884	+	0.601485i	$0.794576\pi$
$930$	0.0488121	−	0.339496i	0.00160061	−	0.0111325i
$931$	44.8189	+	34.7803i	1.46888	+	1.13988i
$932$	−5.51106	+	12.0675i	−0.180521	+	0.395285i
$933$	13.2778	+	10.4418i	0.434695	+	0.341848i
$934$	−8.63903	−	4.45373i	−0.282678	−	0.145730i
$935$	6.28299	−	1.52424i	0.205476	−	0.0498479i
$936$	2.02934	−	5.06905i	0.0663312	−	0.165687i
$937$	16.7135	+	19.2884i	0.546005	+	0.630124i	0.959948	−	0.280179i	$-0.0903939\pi$
$937$	16.7135	+	19.2884i	0.546005	+	0.630124i	−0.413942	+	0.910303i	$0.635848\pi$
$938$	15.9071	−	35.1312i	0.519385	−	1.14707i
$939$	−11.0276	−	9.55543i	−0.359871	−	0.311830i
$940$	−0.988126	−	0.239717i	−0.0322291	−	0.00781870i
$941$	−2.74298	+	3.85198i	−0.0894186	+	0.125571i	−0.856862	−	0.515546i	$-0.827589\pi$
$941$	−2.74298	+	3.85198i	−0.0894186	+	0.125571i	0.767443	+	0.641117i	$0.221529\pi$
$942$	−6.13035	+	3.53936i	−0.199738	+	0.115319i
$943$	−26.4620	−	9.25192i	−0.861721	−	0.301284i
$944$			6.77088i			0.220373i
$945$	0.0794668	+	1.56215i	0.00258506	+	0.0508169i
$946$	−8.08093	+	2.37278i	−0.262734	+	0.0771456i
$947$	1.31328	+	3.79447i	0.0426758	+	0.123304i	0.964326	−	0.264719i	$-0.0852793\pi$
$947$	1.31328	+	3.79447i	0.0426758	+	0.123304i	−0.921650	+	0.388023i	$0.873158\pi$
$948$	−0.450183	+	9.45050i	−0.0146213	+	0.306938i
$949$	−13.1341	+	37.9484i	−0.426350	+	1.23186i
$950$	34.9897	+	14.0078i	1.13522	+	0.454472i
$951$	−1.57016	+	5.34749i	−0.0509160	+	0.173404i
$952$	14.4608	+	4.95274i	0.468677	+	0.160519i
$953$	−8.92011	−	1.28252i	−0.288951	−	0.0415448i	−0.00368459	−	0.999993i	$-0.501173\pi$
$953$	−8.92011	−	1.28252i	−0.288951	−	0.0415448i	−0.285266	+	0.958448i	$0.592082\pi$
$954$	−1.41575	+	1.00815i	−0.0458367	+	0.0326402i
$955$	0.994355	+	10.4134i	0.0321766	+	0.336968i
$956$	6.88143	−	2.75491i	0.222562	−	0.0891002i
$957$	−0.487122	−	10.2259i	−0.0157464	−	0.330558i
$958$	−35.7893	−	10.5087i	−1.15630	−	0.339520i
$959$	23.2402	+	22.0168i	0.750464	+	0.710958i
$960$	0.446801	−	0.387155i	0.0144204	−	0.0124954i
$961$	−27.2547	+	14.0508i	−0.879185	+	0.453251i
$962$	32.8323	+	6.32791i	1.05856	+	0.204020i
$963$	11.0343	−	11.5725i	0.355576	−	0.372918i
$964$	17.0611	+	1.62913i	0.549500	+	0.0524708i
$965$	−10.0452			−0.323368
$966$	−4.14907	+	11.9910i	−0.133494	+	0.385806i
$967$	25.1266			0.808017			0.404008	−	0.914755i	$-0.367617\pi$
$967$	25.1266			0.808017			0.404008	+	0.914755i	$0.367617\pi$
$968$	7.38347	+	0.705036i	0.237314	+	0.0226607i
$969$	32.3109	−	33.8867i	1.03798	−	1.08860i
$970$	−9.39388	−	1.81052i	−0.301619	−	0.0581324i
$971$	−10.0226	+	5.16703i	−0.321642	+	0.165818i	−0.611484	−	0.791256i	$-0.709427\pi$
$971$	−10.0226	+	5.16703i	−0.321642	+	0.165818i	0.289843	+	0.957074i	$0.406397\pi$
$972$	−0.755750	+	0.654861i	−0.0242407	+	0.0210047i
$973$	−37.0398	+	11.0058i	−1.18744	+	0.352829i
$974$	35.5089	+	10.4264i	1.13778	+	0.334082i
$975$	1.20822	+	25.3637i	0.0386941	+	0.812288i
$976$	2.36648	−	0.947395i	0.0757491	−	0.0303254i
$977$	−2.79466	−	29.2670i	−0.0894091	−	0.936335i	−0.923217	−	0.384280i	$-0.874450\pi$
$977$	−2.79466	−	29.2670i	−0.0894091	−	0.936335i	0.833808	−	0.552055i	$-0.186156\pi$
$978$	−4.60813	+	3.28143i	−0.147352	+	0.104929i
$979$	17.0006	+	2.44432i	0.543341	+	0.0781207i
$980$	−2.68985	+	3.14503i	−0.0859240	+	0.100464i
$981$	2.82303	−	9.61437i	0.0901326	−	0.306963i
$982$	−8.90678	−	3.56574i	−0.284227	−	0.113787i
$983$	1.16070	−	3.35363i	0.0370207	−	0.106964i	−0.924976	−	0.380026i	$-0.875915\pi$
$983$	1.16070	−	3.35363i	0.0370207	−	0.106964i	0.961997	+	0.273062i	$0.0880363\pi$
$984$	0.278127	−	5.83861i	0.00886637	−	0.186128i
$985$	1.73030	+	4.99937i	0.0551319	+	0.159293i
$986$	−29.9810	+	8.80321i	−0.954789	+	0.280351i
$987$	2.47243	+	3.82003i	0.0786984	+	0.121593i
$988$		−	44.2516i		−	1.40783i
$989$	−18.5131	+	10.6110i	−0.588684	+	0.337411i
$990$	−0.969140	+	0.559534i	−0.0308013	+	0.0177831i
$991$	17.3093	−	24.3075i	0.549847	−	0.772152i	−0.442348	−	0.896843i	$-0.645855\pi$
$991$	17.3093	−	24.3075i	0.549847	−	0.772152i	0.992196	+	0.124691i	$0.0397939\pi$
$992$	0.563798	+	0.136776i	0.0179006	+	0.00434264i
$993$	−7.40596	−	6.41730i	−0.235021	−	0.203647i
$994$	23.1478	−	16.5963i	0.734203	−	0.526402i
$995$	5.49270	+	6.33891i	0.174130	+	0.200957i
$996$	−4.30820	+	10.7614i	−0.136511	+	0.340987i
$997$	−6.21238	+	1.50711i	−0.196748	+	0.0477306i	−0.332922	−	0.942954i	$-0.608035\pi$
$997$	−6.21238	+	1.50711i	−0.196748	+	0.0477306i	0.136174	+	0.990685i	$0.456519\pi$
$998$	27.2937	+	14.0709i	0.863967	+	0.445406i
$999$	−4.81357	−	3.78543i	−0.152294	−	0.119766i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.be.a.19.13	✓	320
7.3	odd	6	inner	966.2.be.a.157.13	yes	320
23.17	odd	22	inner	966.2.be.a.523.13	yes	320
161.17	even	66	inner	966.2.be.a.661.13	yes	320

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.be.a.19.13	✓	320	1.1	even	1	trivial
966.2.be.a.157.13	yes	320	7.3	odd	6	inner
966.2.be.a.523.13	yes	320	23.17	odd	22	inner
966.2.be.a.661.13	yes	320	161.17	even	66	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.be (of order \(66\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.995472 + 0.0950560i) q^{2} +(0.690079 - 0.723734i) q^{3} +(0.981929 + 0.189251i) q^{4} +(0.525481 - 0.270904i) q^{5} +(0.755750 - 0.654861i) q^{6} +(-0.753581 - 2.53616i) q^{7} +(0.959493 + 0.281733i) q^{8} +(-0.0475819 - 0.998867i) q^{9} +O(q^{10})\)	\(q+(0.995472 + 0.0950560i) q^{2} +(0.690079 - 0.723734i) q^{3} +(0.981929 + 0.189251i) q^{4} +(0.525481 - 0.270904i) q^{5} +(0.755750 - 0.654861i) q^{6} +(-0.753581 - 2.53616i) q^{7} +(0.959493 + 0.281733i) q^{8} +(-0.0475819 - 0.998867i) q^{9} +(0.548853 - 0.219728i) q^{10} +(-0.179928 - 1.88430i) q^{11} +(0.814576 - 0.580057i) q^{12} +(5.40460 + 0.777064i) q^{13} +(-0.509091 - 2.59631i) q^{14} +(0.166561 - 0.567254i) q^{15} +(0.928368 + 0.371662i) q^{16} +(-1.88958 + 5.45960i) q^{17} +(0.0475819 - 0.998867i) q^{18} +(-2.65070 - 7.65869i) q^{19} +(0.567254 - 0.166561i) q^{20} +(-2.35554 - 1.20476i) q^{21} -1.89287i q^{22} +(-1.11599 - 4.66418i) q^{23} +(0.866025 - 0.500000i) q^{24} +(-2.69754 + 3.78817i) q^{25} +(5.30626 + 1.28729i) q^{26} +(-0.755750 - 0.654861i) q^{27} +(-0.259991 - 2.63295i) q^{28} +(3.54180 + 4.08746i) q^{29} +(0.219728 - 0.548853i) q^{30} +(0.563798 - 0.136776i) q^{31} +(0.888835 + 0.458227i) q^{32} +(-1.48789 - 1.17009i) q^{33} +(-2.40000 + 5.25526i) q^{34} +(-1.08305 - 1.12856i) q^{35} +(0.142315 - 0.989821i) q^{36} +(6.11678 - 0.291378i) q^{37} +(-1.91069 - 7.87598i) q^{38} +(4.29199 - 3.37526i) q^{39} +(0.580518 - 0.111886i) q^{40} +(3.16017 - 4.91732i) q^{41} +(-2.23035 - 1.42321i) q^{42} +(-1.25354 - 4.26915i) q^{43} +(0.179928 - 1.88430i) q^{44} +(-0.295601 - 0.511996i) q^{45} +(-0.667578 - 4.74914i) q^{46} +(-1.48945 - 0.859932i) q^{47} +(0.909632 - 0.415415i) q^{48} +(-5.86423 + 3.82241i) q^{49} +(-3.04542 + 3.51460i) q^{50} +(2.64733 + 5.13511i) q^{51} +(5.15987 + 1.78585i) q^{52} +(-1.07438 - 1.36618i) q^{53} +(-0.690079 - 0.723734i) q^{54} +(-0.605013 - 0.941419i) q^{55} +(-0.00853607 - 2.64574i) q^{56} +(-7.37205 - 3.36670i) q^{57} +(3.13723 + 4.40562i) q^{58} +(2.51648 + 6.28587i) q^{59} +(0.270904 - 0.525481i) q^{60} +(1.84485 - 1.75906i) q^{61} +(0.574246 - 0.0825641i) q^{62} +(-2.49743 + 0.873403i) q^{63} +(0.841254 + 0.540641i) q^{64} +(3.05053 - 1.05580i) q^{65} +(-1.36993 - 1.30623i) q^{66} +(11.8733 + 8.45495i) q^{67} +(-2.88867 + 5.00333i) q^{68} +(-4.14575 - 2.41097i) q^{69} +(-0.970870 - 1.22640i) q^{70} +(4.47211 + 9.79255i) q^{71} +(0.235759 - 0.971812i) q^{72} +(-1.39185 + 7.22162i) q^{73} +(6.11678 + 0.291378i) q^{74} +(0.880109 + 4.56644i) q^{75} +(-1.15338 - 8.02194i) q^{76} +(-4.64329 + 1.87630i) q^{77} +(4.59339 - 2.95200i) q^{78} +(-5.84853 + 7.43701i) q^{79} +(0.588525 - 0.0561973i) q^{80} +(-0.995472 + 0.0950560i) q^{81} +(3.61328 - 4.59466i) q^{82} +(-9.75156 + 6.26695i) q^{83} +(-2.08497 - 1.62878i) q^{84} +(0.486087 + 3.38081i) q^{85} +(-0.842051 - 4.36897i) q^{86} +(5.40236 + 0.257346i) q^{87} +(0.358227 - 1.85866i) q^{88} +(-2.13922 + 8.81798i) q^{89} +(-0.245594 - 0.537776i) q^{90} +(-2.10204 - 14.2925i) q^{91} +(-0.213120 - 4.79109i) q^{92} +(0.290076 - 0.502426i) q^{93} +(-1.40096 - 0.997619i) q^{94} +(-3.46767 - 3.30641i) q^{95} +(0.945001 - 0.327068i) q^{96} +(-13.6131 - 8.74859i) q^{97} +(-6.20102 + 3.24767i) q^{98} +(-1.87360 + 0.269383i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 320 q - 16 q^{2} + 16 q^{4} + 32 q^{8} - 16 q^{9}+O(q^{10}) \) 320 * q - 16 * q^2 + 16 * q^4 + 32 * q^8 - 16 * q^9	\( 320 q - 16 q^{2} + 16 q^{4} + 32 q^{8} - 16 q^{9} - 22 q^{14} + 16 q^{16} + 66 q^{17} + 16 q^{18} + 40 q^{23} - 48 q^{25} + 12 q^{26} + 44 q^{28} - 24 q^{29} + 24 q^{31} - 16 q^{32} + 98 q^{35} + 32 q^{36} - 22 q^{37} - 66 q^{38} - 8 q^{39} - 88 q^{43} + 4 q^{46} - 144 q^{47} - 24 q^{49} + 80 q^{50} - 22 q^{51} + 12 q^{52} + 44 q^{53} + 44 q^{57} + 10 q^{58} + 12 q^{59} - 32 q^{64} + 108 q^{70} - 16 q^{71} + 16 q^{72} - 180 q^{73} - 22 q^{74} - 12 q^{75} + 18 q^{77} - 16 q^{78} + 44 q^{79} + 16 q^{81} + 36 q^{82} + 22 q^{84} + 68 q^{85} - 22 q^{86} + 48 q^{87} + 22 q^{88} + 8 q^{92} + 8 q^{93} - 12 q^{94} + 66 q^{95} - 90 q^{98}+O(q^{100}) \) 320 * q - 16 * q^2 + 16 * q^4 + 32 * q^8 - 16 * q^9 - 22 * q^14 + 16 * q^16 + 66 * q^17 + 16 * q^18 + 40 * q^23 - 48 * q^25 + 12 * q^26 + 44 * q^28 - 24 * q^29 + 24 * q^31 - 16 * q^32 + 98 * q^35 + 32 * q^36 - 22 * q^37 - 66 * q^38 - 8 * q^39 - 88 * q^43 + 4 * q^46 - 144 * q^47 - 24 * q^49 + 80 * q^50 - 22 * q^51 + 12 * q^52 + 44 * q^53 + 44 * q^57 + 10 * q^58 + 12 * q^59 - 32 * q^64 + 108 * q^70 - 16 * q^71 + 16 * q^72 - 180 * q^73 - 22 * q^74 - 12 * q^75 + 18 * q^77 - 16 * q^78 + 44 * q^79 + 16 * q^81 + 36 * q^82 + 22 * q^84 + 68 * q^85 - 22 * q^86 + 48 * q^87 + 22 * q^88 + 8 * q^92 + 8 * q^93 - 12 * q^94 + 66 * q^95 - 90 * q^98

Introduction

L-functions

Modular forms

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