LMFDB - Embedded newform 966.2.y.b.151.4

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			151.4
Character	$\chi$	$=$	966.151
Dual form			966.2.y.b.499.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.327068 - 0.945001i) q^{2} +(-0.888835 + 0.458227i) q^{3} +(-0.786053 - 0.618159i) q^{4} +(-1.13751 + 0.108619i) q^{5} +(0.142315 + 0.989821i) q^{6} +(1.15912 + 2.37833i) q^{7} +(-0.841254 + 0.540641i) q^{8} +(0.580057 - 0.814576i) q^{9} +O(q^{10})$	\(q+(0.327068 - 0.945001i) q^{2} +(-0.888835 + 0.458227i) q^{3} +(-0.786053 - 0.618159i) q^{4} +(-1.13751 + 0.108619i) q^{5} +(0.142315 + 0.989821i) q^{6} +(1.15912 + 2.37833i) q^{7} +(-0.841254 + 0.540641i) q^{8} +(0.580057 - 0.814576i) q^{9} +(-0.269397 + 1.11047i) q^{10} +(-1.64728 - 4.75950i) q^{11} +(0.981929 + 0.189251i) q^{12} +(-0.469068 + 0.137731i) q^{13} +(2.62663 - 0.317494i) q^{14} +(0.961283 - 0.617779i) q^{15} +(0.235759 + 0.971812i) q^{16} +(5.14832 + 2.06108i) q^{17} +(-0.580057 - 0.814576i) q^{18} +(-7.16435 + 2.86817i) q^{19} +(0.961283 + 0.617779i) q^{20} +(-2.12008 - 1.58280i) q^{21} -5.03651 q^{22} +(3.81707 + 2.90344i) q^{23} +(0.500000 - 0.866025i) q^{24} +(-3.62752 + 0.699148i) q^{25} +(-0.0232614 + 0.488317i) q^{26} +(-0.142315 + 0.989821i) q^{27} +(0.559055 - 2.58601i) q^{28} +(0.928999 + 6.46133i) q^{29} +(-0.269397 - 1.11047i) q^{30} +(0.177405 + 3.72420i) q^{31} +(0.995472 + 0.0950560i) q^{32} +(3.64509 + 3.47559i) q^{33} +(3.63157 - 4.19105i) q^{34} +(-1.57684 - 2.57946i) q^{35} +(-0.959493 + 0.281733i) q^{36} +(-1.42670 + 2.00351i) q^{37} +(0.367197 + 7.70840i) q^{38} +(0.353812 - 0.337360i) q^{39} +(0.898207 - 0.706358i) q^{40} +(-4.97936 + 10.9033i) q^{41} +(-2.18916 + 1.48579i) q^{42} +(-2.95462 - 1.89882i) q^{43} +(-1.64728 + 4.75950i) q^{44} +(-0.571340 + 0.989590i) q^{45} +(3.99219 - 2.65752i) q^{46} +(4.74515 + 8.21885i) q^{47} +(-0.654861 - 0.755750i) q^{48} +(-4.31288 + 5.51353i) q^{49} +(-0.525751 + 3.65668i) q^{50} +(-5.52045 + 0.527139i) q^{51} +(0.453852 + 0.181695i) q^{52} +(1.54666 - 1.47474i) q^{53} +(0.888835 + 0.458227i) q^{54} +(2.39076 + 5.23504i) q^{55} +(-2.26093 - 1.37411i) q^{56} +(5.05366 - 5.83223i) q^{57} +(6.40981 + 1.23539i) q^{58} +(2.98403 - 12.3004i) q^{59} +(-1.13751 - 0.108619i) q^{60} +(4.84812 + 2.49938i) q^{61} +(3.57739 + 1.05042i) q^{62} +(2.60968 + 0.435374i) q^{63} +(0.415415 - 0.909632i) q^{64} +(0.518608 - 0.207619i) q^{65} +(4.47663 - 2.30786i) q^{66} +(-3.52686 + 0.679746i) q^{67} +(-2.77278 - 4.80260i) q^{68} +(-4.72318 - 0.831595i) q^{69} +(-2.95332 + 0.646453i) q^{70} +(-5.88381 - 6.79028i) q^{71} +(-0.0475819 + 0.998867i) q^{72} +(1.34646 + 1.05886i) q^{73} +(1.42670 + 2.00351i) q^{74} +(2.90390 - 2.28365i) q^{75} +(7.40455 + 2.17417i) q^{76} +(9.41026 - 9.43461i) q^{77} +(-0.203084 - 0.444693i) q^{78} +(7.43230 + 7.08668i) q^{79} +(-0.373734 - 1.07983i) q^{80} +(-0.327068 - 0.945001i) q^{81} +(8.67501 + 8.27161i) q^{82} +(3.78661 + 8.29152i) q^{83} +(0.688072 + 2.55471i) q^{84} +(-6.08011 - 1.78528i) q^{85} +(-2.76074 + 2.17107i) q^{86} +(-3.78648 - 5.31737i) q^{87} +(3.95896 + 3.11336i) q^{88} +(-0.867409 + 18.2091i) q^{89} +(0.748296 + 0.863580i) q^{90} +(-0.871275 - 0.955951i) q^{91} +(-1.20564 - 4.64181i) q^{92} +(-1.86421 - 3.22891i) q^{93} +(9.31881 - 1.79605i) q^{94} +(7.83795 - 4.04075i) q^{95} +(-0.928368 + 0.371662i) q^{96} +(5.86226 - 12.8366i) q^{97} +(3.79969 + 5.87898i) q^{98} +(-4.83249 - 1.41895i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q - 8 q^{2} + 8 q^{3} + 8 q^{4} + 6 q^{5} + 16 q^{6} - 10 q^{7} + 16 q^{8} + 8 q^{9}+O(q^{10}) $ 160 * q - 8 * q^2 + 8 * q^3 + 8 * q^4 + 6 * q^5 + 16 * q^6 - 10 * q^7 + 16 * q^8 + 8 * q^9	\( 160 q - 8 q^{2} + 8 q^{3} + 8 q^{4} + 6 q^{5} + 16 q^{6} - 10 q^{7} + 16 q^{8} + 8 q^{9} - 6 q^{10} + 8 q^{11} + 8 q^{12} + 4 q^{13} - 13 q^{14} + 10 q^{15} + 8 q^{16} + 9 q^{17} - 8 q^{18} - 8 q^{19} + 10 q^{20} - 3 q^{21} - 28 q^{22} + 22 q^{23} + 80 q^{24} + 46 q^{25} + 2 q^{26} - 16 q^{27} - 14 q^{28} + 62 q^{29} - 6 q^{30} + 7 q^{31} - 8 q^{32} - 14 q^{33} - 4 q^{34} + 24 q^{35} - 16 q^{36} + 15 q^{37} + 19 q^{38} - 2 q^{39} + 5 q^{40} - 14 q^{41} + 10 q^{42} - 56 q^{43} + 8 q^{44} - 16 q^{45} + 66 q^{47} - 16 q^{48} + 42 q^{49} + 4 q^{50} + 9 q^{51} - 2 q^{52} + 12 q^{53} - 8 q^{54} - 14 q^{55} + 10 q^{56} - 6 q^{57} - 13 q^{58} + 62 q^{59} + 6 q^{60} + 16 q^{61} - 8 q^{62} + 2 q^{63} - 16 q^{64} + 70 q^{65} - 8 q^{66} - 14 q^{67} - 46 q^{68} + 22 q^{69} + 24 q^{70} - 108 q^{71} - 8 q^{72} + 40 q^{73} - 15 q^{74} + 2 q^{75} + 16 q^{76} + 29 q^{77} + 18 q^{78} + 22 q^{79} + 6 q^{80} + 8 q^{81} - 7 q^{82} - 18 q^{83} - 9 q^{84} + 26 q^{85} - 6 q^{86} + 2 q^{87} + 3 q^{88} + 112 q^{89} + 12 q^{90} + 18 q^{91} - 66 q^{92} - 26 q^{93} + 23 q^{95} - 8 q^{96} + 8 q^{97} + 9 q^{98} + 28 q^{99}+O(q^{100}) \) 160 * q - 8 * q^2 + 8 * q^3 + 8 * q^4 + 6 * q^5 + 16 * q^6 - 10 * q^7 + 16 * q^8 + 8 * q^9 - 6 * q^10 + 8 * q^11 + 8 * q^12 + 4 * q^13 - 13 * q^14 + 10 * q^15 + 8 * q^16 + 9 * q^17 - 8 * q^18 - 8 * q^19 + 10 * q^20 - 3 * q^21 - 28 * q^22 + 22 * q^23 + 80 * q^24 + 46 * q^25 + 2 * q^26 - 16 * q^27 - 14 * q^28 + 62 * q^29 - 6 * q^30 + 7 * q^31 - 8 * q^32 - 14 * q^33 - 4 * q^34 + 24 * q^35 - 16 * q^36 + 15 * q^37 + 19 * q^38 - 2 * q^39 + 5 * q^40 - 14 * q^41 + 10 * q^42 - 56 * q^43 + 8 * q^44 - 16 * q^45 + 66 * q^47 - 16 * q^48 + 42 * q^49 + 4 * q^50 + 9 * q^51 - 2 * q^52 + 12 * q^53 - 8 * q^54 - 14 * q^55 + 10 * q^56 - 6 * q^57 - 13 * q^58 + 62 * q^59 + 6 * q^60 + 16 * q^61 - 8 * q^62 + 2 * q^63 - 16 * q^64 + 70 * q^65 - 8 * q^66 - 14 * q^67 - 46 * q^68 + 22 * q^69 + 24 * q^70 - 108 * q^71 - 8 * q^72 + 40 * q^73 - 15 * q^74 + 2 * q^75 + 16 * q^76 + 29 * q^77 + 18 * q^78 + 22 * q^79 + 6 * q^80 + 8 * q^81 - 7 * q^82 - 18 * q^83 - 9 * q^84 + 26 * q^85 - 6 * q^86 + 2 * q^87 + 3 * q^88 + 112 * q^89 + 12 * q^90 + 18 * q^91 - 66 * q^92 - 26 * q^93 + 23 * q^95 - 8 * q^96 + 8 * q^97 + 9 * q^98 + 28 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$323$	$829$	$925$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{11}\right)$

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 $

$2$	0.327068	−	0.945001i	0.231272	−	0.668216i
$2$	0.327068	−	0.945001i	0.231272	−	0.668216i
$3$	−0.888835	+	0.458227i	−0.513169	+	0.264557i
$3$	−0.888835	+	0.458227i	−0.513169	+	0.264557i
$4$	−0.786053	−	0.618159i	−0.393027	−	0.309079i
$5$	−1.13751	+	0.108619i	−0.508708	+	0.0485757i	−0.346255	−	0.938141i	$-0.612547\pi$
$5$	−1.13751	+	0.108619i	−0.508708	+	0.0485757i	−0.162453	+	0.986716i	$0.551941\pi$
$6$	0.142315	+	0.989821i	0.0580998	+	0.404093i
$7$	1.15912	+	2.37833i	0.438106	+	0.898923i
$7$	1.15912	+	2.37833i	0.438106	+	0.898923i
$8$	−0.841254	+	0.540641i	−0.297428	+	0.191145i
$9$	0.580057	−	0.814576i	0.193352	−	0.271525i
$10$	−0.269397	+	1.11047i	−0.0851908	+	0.351161i
$11$	−1.64728	−	4.75950i	−0.496674	−	1.43504i	−0.863307	−	0.504679i	$-0.831611\pi$
$11$	−1.64728	−	4.75950i	−0.496674	−	1.43504i	0.366634	−	0.930365i	$-0.380510\pi$
$12$	0.981929	+	0.189251i	0.283458	+	0.0546321i
$13$	−0.469068	+	0.137731i	−0.130096	+	0.0381997i	−0.346132	−	0.938186i	$-0.612505\pi$
$13$	−0.469068	+	0.137731i	−0.130096	+	0.0381997i	0.216036	+	0.976385i	$0.430687\pi$
$14$	2.62663	−	0.317494i	0.701997	−	0.0848540i
$15$	0.961283	−	0.617779i	0.248202	−	0.159510i
$16$	0.235759	+	0.971812i	0.0589397	+	0.242953i
$17$	5.14832	+	2.06108i	1.24865	+	0.499884i	0.899392	−	0.437142i	$-0.144009\pi$
$17$	5.14832	+	2.06108i	1.24865	+	0.499884i	0.349258	+	0.937026i	$0.386434\pi$
$18$	−0.580057	−	0.814576i	−0.136721	−	0.191997i
$19$	−7.16435	+	2.86817i	−1.64361	+	0.658004i	−0.994696	−	0.102854i	$-0.967203\pi$
$19$	−7.16435	+	2.86817i	−1.64361	+	0.658004i	−0.648918	+	0.760858i	$0.724778\pi$
$20$	0.961283	+	0.617779i	0.214950	+	0.138140i
$21$	−2.12008	−	1.58280i	−0.462639	−	0.345396i
$22$	−5.03651			−1.07379
$23$	3.81707	+	2.90344i	0.795915	+	0.605409i
$23$	3.81707	+	2.90344i	0.795915	+	0.605409i
$24$	0.500000	−	0.866025i	0.102062	−	0.176777i
$25$	−3.62752	+	0.699148i	−0.725504	+	0.139830i
$26$	−0.0232614	+	0.488317i	−0.00456194	+	0.0957669i
$27$	−0.142315	+	0.989821i	−0.0273885	+	0.190491i
$28$	0.559055	−	2.58601i	0.105651	−	0.488710i
$29$	0.928999	+	6.46133i	0.172511	+	1.19984i	0.873557	+	0.486722i	$0.161808\pi$
$29$	0.928999	+	6.46133i	0.172511	+	1.19984i	−0.701046	+	0.713116i	$0.747283\pi$
$30$	−0.269397	−	1.11047i	−0.0491849	−	0.202743i
$31$	0.177405	+	3.72420i	0.0318629	+	0.668885i	0.957146	+	0.289607i	$0.0935247\pi$
$31$	0.177405	+	3.72420i	0.0318629	+	0.668885i	−0.925283	+	0.379278i	$0.876172\pi$
$32$	0.995472	+	0.0950560i	0.175976	+	0.0168037i
$33$	3.64509	+	3.47559i	0.634529	+	0.605022i
$34$	3.63157	−	4.19105i	0.622809	−	0.718760i
$35$	−1.57684	−	2.57946i	−0.266534	−	0.436008i
$36$	−0.959493	+	0.281733i	−0.159915	+	0.0469554i
$37$	−1.42670	+	2.00351i	−0.234547	+	0.329376i	−0.915028	−	0.403390i	$-0.867832\pi$
$37$	−1.42670	+	2.00351i	−0.234547	+	0.329376i	0.680481	+	0.732766i	$0.261771\pi$
$38$	0.367197	+	7.70840i	0.0595671	+	1.25047i
$39$	0.353812	−	0.337360i	0.0566553	−	0.0540208i
$40$	0.898207	−	0.706358i	0.142019	−	0.111685i
$41$	−4.97936	+	10.9033i	−0.777645	+	1.70281i	−0.0685979	+	0.997644i	$0.521853\pi$
$41$	−4.97936	+	10.9033i	−0.777645	+	1.70281i	−0.709047	+	0.705161i	$0.750875\pi$
$42$	−2.18916	+	1.48579i	−0.337795	+	0.229263i
$43$	−2.95462	−	1.89882i	−0.450575	−	0.289567i	0.295606	−	0.955310i	$-0.404478\pi$
$43$	−2.95462	−	1.89882i	−0.450575	−	0.289567i	−0.746181	+	0.665743i	$0.768115\pi$
$44$	−1.64728	+	4.75950i	−0.248337	+	0.717522i
$45$	−0.571340	+	0.989590i	−0.0851703	+	0.147519i
$46$	3.99219	−	2.65752i	0.588617	−	0.391829i
$47$	4.74515	+	8.21885i	0.692152	+	1.19884i	0.971131	+	0.238545i	$0.0766705\pi$
$47$	4.74515	+	8.21885i	0.692152	+	1.19884i	−0.278980	+	0.960297i	$0.589996\pi$
$48$	−0.654861	−	0.755750i	−0.0945210	−	0.109083i
$49$	−4.31288	+	5.51353i	−0.616126	+	0.787648i
$50$	−0.525751	+	3.65668i	−0.0743525	+	0.517133i
$51$	−5.52045	+	0.527139i	−0.773017	+	0.0738142i
$52$	0.453852	+	0.181695i	0.0629379	+	0.0251966i
$53$	1.54666	−	1.47474i	0.212450	−	0.202571i	−0.576381	−	0.817181i	$-0.695535\pi$
$53$	1.54666	−	1.47474i	0.212450	−	0.202571i	0.788831	+	0.614611i	$0.210687\pi$
$54$	0.888835	+	0.458227i	0.120955	+	0.0623567i
$55$	2.39076	+	5.23504i	0.322370	+	0.705892i
$56$	−2.26093	−	1.37411i	−0.302130	−	0.183623i
$57$	5.05366	−	5.83223i	0.669373	−	0.772498i
$58$	6.40981	+	1.23539i	0.841649	+	0.162214i
$59$	2.98403	−	12.3004i	0.388488	−	1.60137i	−0.356502	−	0.934295i	$-0.616031\pi$
$59$	2.98403	−	12.3004i	0.388488	−	1.60137i	0.744990	−	0.667075i	$-0.232454\pi$
$60$	−1.13751	−	0.108619i	−0.146851	−	0.0140226i
$61$	4.84812	+	2.49938i	0.620738	+	0.320013i	0.739752	−	0.672880i	$-0.234943\pi$
$61$	4.84812	+	2.49938i	0.620738	+	0.320013i	−0.119014	+	0.992893i	$0.537973\pi$
$62$	3.57739	+	1.05042i	0.454329	+	0.133403i
$63$	2.60968	+	0.435374i	0.328789	+	0.0548520i
$64$	0.415415	−	0.909632i	0.0519269	−	0.113704i
$65$	0.518608	−	0.207619i	0.0643253	−	0.0257520i
$66$	4.47663	−	2.30786i	0.551035	−	0.284078i
$67$	−3.52686	+	0.679746i	−0.430874	+	0.0830442i	−0.400077	−	0.916481i	$-0.631017\pi$
$67$	−3.52686	+	0.679746i	−0.430874	+	0.0830442i	−0.0307971	+	0.999526i	$0.509805\pi$
$68$	−2.77278	−	4.80260i	−0.336249	−	0.582400i
$69$	−4.72318	−	0.831595i	−0.568604	−	0.100112i
$70$	−2.95332	+	0.646453i	−0.352990	+	0.0772659i
$71$	−5.88381	−	6.79028i	−0.698280	−	0.805858i	0.290239	−	0.956954i	$-0.406265\pi$
$71$	−5.88381	−	6.79028i	−0.698280	−	0.805858i	−0.988519	+	0.151096i	$0.951720\pi$
$72$	−0.0475819	+	0.998867i	−0.00560758	+	0.117718i
$73$	1.34646	+	1.05886i	0.157591	+	0.123931i	0.693841	−	0.720128i	$-0.255917\pi$
$73$	1.34646	+	1.05886i	0.157591	+	0.123931i	−0.536250	+	0.844059i	$0.680160\pi$
$74$	1.42670	+	2.00351i	0.165850	+	0.232904i
$75$	2.90390	−	2.28365i	0.335314	−	0.263694i
$76$	7.40455	+	2.17417i	0.849360	+	0.249395i
$77$	9.41026	−	9.43461i	1.07240	−	1.07517i
$78$	−0.203084	−	0.444693i	−0.0229948	−	0.0503515i
$79$	7.43230	+	7.08668i	0.836199	+	0.797314i	0.981377	−	0.192092i	$-0.0615271\pi$
$79$	7.43230	+	7.08668i	0.836199	+	0.797314i	−0.145178	+	0.989406i	$0.546376\pi$
$80$	−0.373734	−	1.07983i	−0.0417847	−	0.120729i
$81$	−0.327068	−	0.945001i	−0.0363409	−	0.105000i
$82$	8.67501	+	8.27161i	0.957995	+	0.913446i
$83$	3.78661	+	8.29152i	0.415634	+	0.910112i	0.995443	+	0.0953596i	$0.0304001\pi$
$83$	3.78661	+	8.29152i	0.415634	+	0.910112i	−0.579809	+	0.814753i	$0.696873\pi$
$84$	0.688072	+	2.55471i	0.0750748	+	0.278742i
$85$	−6.08011	−	1.78528i	−0.659481	−	0.193641i
$86$	−2.76074	+	2.17107i	−0.297699	+	0.234113i
$87$	−3.78648	−	5.31737i	−0.405953	−	0.570081i
$88$	3.95896	+	3.11336i	0.422027	+	0.331886i
$89$	−0.867409	+	18.2091i	−0.0919451	+	1.93017i	0.211614	+	0.977353i	$0.432128\pi$
$89$	−0.867409	+	18.2091i	−0.0919451	+	1.93017i	−0.303559	+	0.952813i	$0.598175\pi$
$90$	0.748296	+	0.863580i	0.0788773	+	0.0910293i
$91$	−0.871275	−	0.955951i	−0.0913345	−	0.100211i
$92$	−1.20564	−	4.64181i	−0.125696	−	0.483943i
$93$	−1.86421	−	3.22891i	−0.193310	−	0.334822i
$94$	9.31881	−	1.79605i	0.961161	−	0.185249i
$95$	7.83795	−	4.04075i	0.804157	−	0.414572i
$96$	−0.928368	+	0.371662i	−0.0947512	+	0.0379326i
$97$	5.86226	−	12.8366i	0.595223	−	1.30336i	−0.337012	−	0.941500i	$-0.609416\pi$
$97$	5.86226	−	12.8366i	0.595223	−	1.30336i	0.932234	−	0.361855i	$-0.117857\pi$
$98$	3.79969	+	5.87898i	0.383826	+	0.593866i
$99$	−4.83249	−	1.41895i	−0.485684	−	0.142610i
$100$	3.28361	+	1.69282i	0.328361	+	0.169282i
$101$	−5.50280	−	0.525454i	−0.547549	−	0.0522846i	−0.182384	−	0.983227i	$-0.558381\pi$
$101$	−5.50280	−	0.525454i	−0.547549	−	0.0522846i	−0.365165	+	0.930943i	$0.618987\pi$
$102$	−1.30742	+	5.38924i	−0.129453	+	0.533614i
$103$	−8.27880	−	1.59561i	−0.815735	−	0.157220i	−0.235715	−	0.971822i	$-0.575743\pi$
$103$	−8.27880	−	1.59561i	−0.815735	−	0.157220i	−0.580020	+	0.814602i	$0.696955\pi$
$104$	0.320142	−	0.369464i	0.0313925	−	0.0362289i
$105$	2.58352	+	1.57017i	0.252126	+	0.153233i
$106$	−0.887764	−	1.94393i	−0.0862273	−	0.188811i
$107$	−1.75002	−	0.902198i	−0.169181	−	0.0872188i	0.371556	−	0.928410i	$-0.378824\pi$
$107$	−1.75002	−	0.902198i	−0.169181	−	0.0872188i	−0.540737	+	0.841192i	$0.681855\pi$
$108$	0.723734	−	0.690079i	0.0696413	−	0.0664029i
$109$	−3.52410	−	1.41084i	−0.337547	−	0.135134i	0.196695	−	0.980465i	$-0.436979\pi$
$109$	−3.52410	−	1.41084i	−0.337547	−	0.135134i	−0.534243	+	0.845331i	$0.679403\pi$
$110$	5.72906	−	0.547058i	0.546244	−	0.0521600i
$111$	0.350035	−	2.43454i	0.0332238	−	0.231077i
$112$	−2.03801	+	1.68716i	−0.192574	+	0.159421i
$113$	−4.82121	−	5.56397i	−0.453541	−	0.523414i	0.482220	−	0.876050i	$-0.339831\pi$
$113$	−4.82121	−	5.56397i	−0.453541	−	0.523414i	−0.935760	+	0.352636i	$0.885285\pi$
$114$	−3.85857	−	6.68324i	−0.361388	−	0.625943i
$115$	−4.65731	−	2.88807i	−0.434296	−	0.269314i
$116$	3.26389	−	5.65322i	0.303044	−	0.524888i
$117$	−0.159894	+	0.461983i	−0.0147822	+	0.0427104i
$118$	−10.6479	−	6.84297i	−0.980215	−	0.629946i
$119$	1.06560	+	14.6334i	0.0976838	+	1.34144i
$120$	−0.474686	+	1.03942i	−0.0433327	+	0.0948855i
$121$	−11.2928	+	8.88072i	−1.02661	+	0.807338i
$122$	3.94758	−	3.76401i	0.357397	−	0.340777i
$123$	−0.570339	−	11.9729i	−0.0514257	−	1.07956i
$124$	2.16270	−	3.03708i	0.194216	−	0.272738i
$125$	9.53235	−	2.79895i	0.852600	−	0.250346i
$126$	1.26497	−	2.32376i	0.112693	−	0.207017i
$127$	−7.21179	+	8.32285i	−0.639943	+	0.738534i	−0.979365	−	0.202101i	$-0.935223\pi$
$127$	−7.21179	+	8.32285i	−0.639943	+	0.738534i	0.339422	+	0.940634i	$0.389769\pi$
$128$	−0.723734	−	0.690079i	−0.0639697	−	0.0609949i
$129$	3.49626	+	0.333852i	0.307828	+	0.0293940i
$130$	−0.0265803	−	0.557990i	−0.00233125	−	0.0489390i
$131$	−3.77369	−	15.5553i	−0.329709	−	1.35908i	−0.859581	−	0.511000i	$-0.829275\pi$
$131$	−3.77369	−	15.5553i	−0.329709	−	1.35908i	0.529872	−	0.848077i	$-0.322240\pi$
$132$	−0.716770	−	4.98524i	−0.0623868	−	0.433910i
$133$	−15.1258	−	13.7146i	−1.31157	−	1.18921i
$134$	−0.511162	+	3.55521i	−0.0441576	+	0.307123i
$135$	0.0543709	−	1.14139i	0.00467950	−	0.0982348i
$136$	−5.44534	+	1.04950i	−0.466934	+	0.0899942i
$137$	−4.18649	+	7.25121i	−0.357676	+	0.619513i	−0.987572	−	0.157166i	$-0.949764\pi$
$137$	−4.18649	+	7.25121i	−0.357676	+	0.619513i	0.629896	+	0.776679i	$0.283097\pi$
$138$	−2.33066	+	4.19142i	−0.198399	+	0.356798i
$139$	−13.2867			−1.12696			−0.563482	−	0.826128i	$-0.690539\pi$
$139$	−13.2867			−1.12696			−0.563482	+	0.826128i	$0.690539\pi$
$140$	−0.355039	+	3.00233i	−0.0300063	+	0.253743i
$141$	−7.98376	−	5.13085i	−0.672353	−	0.432095i
$142$	−8.34122	+	3.33932i	−0.699980	+	0.280230i
$143$	1.42822	+	2.00565i	0.119434	+	0.167721i
$144$	0.928368	+	0.371662i	0.0773640	+	0.0309719i
$145$	−1.75856	−	7.24889i	−0.146041	−	0.601988i
$146$	1.44101	−	0.926081i	0.119259	−	0.0766430i
$147$	1.30700	−	6.87690i	0.107799	−	0.567197i
$148$	2.35995	−	0.692943i	0.193987	−	0.0569596i
$149$	7.51579	+	1.44855i	0.615718	+	0.118670i	0.487568	−	0.873085i	$-0.337884\pi$
$149$	7.51579	+	1.44855i	0.615718	+	0.118670i	0.128150	+	0.991755i	$0.459096\pi$
$150$	−1.20828	−	3.49110i	−0.0986558	−	0.285047i
$151$	5.05207	−	20.8249i	0.411132	−	1.69471i	−0.270258	−	0.962788i	$-0.587109\pi$
$151$	5.05207	−	20.8249i	0.411132	−	1.69471i	0.681390	−	0.731921i	$-0.261376\pi$
$152$	4.47638	−	6.28620i	0.363083	−	0.509878i
$153$	4.66522	−	2.99816i	0.377161	−	0.242387i
$154$	−5.83791	−	11.9785i	−0.470433	−	0.965252i
$155$	−0.606317	−	4.21702i	−0.0487005	−	0.338720i
$156$	−0.486657	+	0.0464701i	−0.0389638	+	0.00372059i
$157$	6.51685	+	5.12491i	0.520101	+	0.409012i	0.843401	−	0.537285i	$-0.180550\pi$
$157$	6.51685	+	5.12491i	0.520101	+	0.409012i	−0.323300	+	0.946297i	$0.604792\pi$
$158$	9.12779	−	4.70570i	0.726168	−	0.374365i
$159$	−0.698962	+	2.01952i	−0.0554313	+	0.160158i
$160$	−1.14268			−0.0903368
$161$	−2.48088	+	12.4437i	−0.195521	+	0.980700i
$162$	−1.00000			−0.0785674
$163$	−2.98224	+	8.61661i	−0.233587	+	0.674905i	0.765903	+	0.642957i	$0.222292\pi$
$163$	−2.98224	+	8.61661i	−0.233587	+	0.674905i	−0.999490	+	0.0319484i	$0.989829\pi$
$164$	10.6540	−	5.49252i	0.831937	−	0.428894i
$165$	−4.52383	−	3.55758i	−0.352179	−	0.276957i
$166$	9.07397	−	0.866459i	0.704277	−	0.0672503i
$167$	−1.24922	−	8.68851i	−0.0966675	−	0.672337i	−0.979321	−	0.202313i	$-0.935154\pi$
$167$	−1.24922	−	8.68851i	−0.0966675	−	0.672337i	0.882654	−	0.470024i	$-0.155755\pi$
$168$	2.63925	+	0.185337i	0.203623	+	0.0142990i
$169$	−10.7352	+	6.89912i	−0.825788	+	0.530702i
$170$	−3.67570	+	5.16180i	−0.281914	+	0.395892i
$171$	−1.81939	+	7.49961i	−0.139132	+	0.573510i
$172$	1.14872	+	3.31899i	0.0875887	+	0.253071i
$173$	6.05939	+	1.16785i	0.460687	+	0.0887901i	0.414314	−	0.910134i	$-0.364022\pi$
$173$	6.05939	+	1.16785i	0.460687	+	0.0887901i	0.0463729	+	0.998924i	$0.485234\pi$
$174$	−6.26335	+	1.83909i	−0.474823	+	0.139421i
$175$	−5.86753	−	7.81704i	−0.443544	−	0.590913i
$176$	4.23698	−	2.72294i	0.319374	−	0.205249i
$177$	2.98403	+	12.3004i	0.224294	+	0.924551i
$178$	16.9240	+	6.77533i	1.26850	+	0.507833i
$179$	13.0511	+	18.3278i	0.975488	+	1.36988i	0.928641	+	0.370979i	$0.120978\pi$
$179$	13.0511	+	18.3278i	0.975488	+	1.36988i	0.0468467	+	0.998902i	$0.485083\pi$
$180$	1.06083	−	0.424691i	0.0790694	−	0.0316546i
$181$	5.98993	+	3.84950i	0.445228	+	0.286131i	0.743982	−	0.668199i	$-0.232935\pi$
$181$	5.98993	+	3.84950i	0.445228	+	0.286131i	−0.298754	+	0.954330i	$0.596571\pi$
$182$	−1.18834	+	0.510695i	−0.0880857	+	0.0378552i
$183$	−5.45446			−0.403205
$184$	−4.78084	−	0.378863i	−0.352448	−	0.0279301i
$185$	1.40526	−	2.43397i	0.103316	−	0.178949i
$186$	−3.66104	+	0.705608i	−0.268441	+	0.0517377i
$187$	1.32897	−	27.8986i	0.0971843	−	2.04015i
$188$	1.35061	−	9.39371i	0.0985035	−	0.685107i
$189$	−2.51908	+	0.808850i	−0.183236	+	0.0588352i
$190$	−1.25496	−	8.72847i	−0.0910447	−	0.633230i
$191$	−5.56520	−	22.9401i	−0.402684	−	1.65989i	−0.706923	−	0.707291i	$-0.749917\pi$
$191$	−5.56520	−	22.9401i	−0.402684	−	1.65989i	0.304239	−	0.952596i	$-0.401598\pi$
$192$	0.0475819	+	0.998867i	0.00343393	+	0.0720870i
$193$	9.72282	+	0.928416i	0.699864	+	0.0668289i	0.438921	−	0.898526i	$-0.355361\pi$
$193$	9.72282	+	0.928416i	0.699864	+	0.0668289i	0.260942	+	0.965354i	$0.415967\pi$
$194$	−10.2132	−	9.73827i	−0.733265	−	0.699167i
$195$	−0.365820	+	0.422179i	−0.0261969	+	0.0302329i
$196$	6.79839	−	1.66788i	0.485600	−	0.119134i
$197$	−5.93615	+	1.74301i	−0.422933	+	0.124184i	−0.486272	−	0.873808i	$-0.661643\pi$
$197$	−5.93615	+	1.74301i	−0.422933	+	0.124184i	0.0633383	+	0.997992i	$0.479825\pi$
$198$	−2.92146	+	4.10262i	−0.207619	+	0.291560i
$199$	0.712411	+	14.9554i	0.0505015	+	1.06016i	0.871863	+	0.489749i	$0.162912\pi$
$199$	0.712411	+	14.9554i	0.0505015	+	1.06016i	−0.821362	+	0.570407i	$0.806785\pi$
$200$	2.67368	−	2.54935i	0.189058	−	0.180266i
$201$	2.82332	−	2.22028i	0.199142	−	0.156607i
$202$	−2.29634	+	5.02829i	−0.161570	+	0.353789i
$203$	−14.2903	+	9.69892i	−1.00298	+	0.680730i
$204$	4.66522	+	2.99816i	0.326631	+	0.209913i
$205$	4.47975	−	12.9434i	0.312879	−	0.904005i
$206$	−4.21558	+	7.30160i	−0.293714	+	0.508727i
$207$	4.57919	−	1.42514i	0.318276	−	0.0990538i
$208$	−0.244435	−	0.423375i	−0.0169485	−	0.0293557i
$209$	25.4528	+	29.3741i	1.76060	+	2.03185i
$210$	2.32880	−	1.92788i	0.160702	−	0.133036i
$211$	2.09824	−	14.5936i	0.144449	−	1.00466i	−0.780659	−	0.624958i	$-0.785116\pi$
$211$	2.09824	−	14.5936i	0.144449	−	1.00466i	0.925107	−	0.379706i	$-0.123975\pi$
$212$	−2.12738	+	0.203140i	−0.146109	+	0.0139517i
$213$	8.34122	+	3.33932i	0.571531	+	0.228807i
$214$	−1.42495	+	1.35869i	−0.0974078	+	0.0928782i
$215$	3.56714	+	1.83899i	0.243277	+	0.125418i
$216$	−0.415415	−	0.909632i	−0.0282654	−	0.0618926i
$217$	−8.65172	+	4.73872i	−0.587317	+	0.321685i
$218$	−2.48586	+	2.86884i	−0.168364	+	0.194302i
$219$	−1.68198	−	0.324175i	−0.113658	−	0.0219057i
$220$	1.35682	−	5.59289i	0.0914768	−	0.377072i
$221$	−2.69879	−	0.257703i	−0.181540	−	0.0173350i
$222$	−2.18616	−	1.12704i	−0.146726	−	0.0756423i
$223$	−0.343947	−	0.100992i	−0.0230324	−	0.00676292i	0.270196	−	0.962805i	$-0.412911\pi$
$223$	−0.343947	−	0.100992i	−0.0230324	−	0.00676292i	−0.293228	+	0.956042i	$0.594730\pi$
$224$	0.927797	+	2.47774i	0.0619910	+	0.165551i
$225$	−1.53466	+	3.36044i	−0.102311	+	0.224029i
$226$	−6.83482	+	2.73625i	−0.454645	+	0.182013i
$227$	2.72711	−	1.40592i	0.181005	−	0.0933145i	−0.365343	−	0.930873i	$-0.619048\pi$
$227$	2.72711	−	1.40592i	0.181005	−	0.0933145i	0.546347	+	0.837559i	$0.316018\pi$
$228$	−7.57769	+	1.46048i	−0.501845	+	0.0967226i
$229$	5.77945	+	10.0103i	0.381917	+	0.661500i	0.991336	−	0.131348i	$-0.0419307\pi$
$229$	5.77945	+	10.0103i	0.381917	+	0.661500i	−0.609419	+	0.792848i	$0.708597\pi$
$230$	−4.25249	+	3.45657i	−0.280401	+	0.227919i
$231$	−4.04099	+	12.6978i	−0.265877	+	0.835457i
$232$	−4.27478	−	4.93336i	−0.280653	−	0.323891i
$233$	1.14189	−	23.9711i	0.0748074	−	1.57040i	−0.580007	−	0.814611i	$-0.696950\pi$
$233$	1.14189	−	23.9711i	0.0748074	−	1.57040i	0.654815	−	0.755790i	$-0.272747\pi$
$234$	0.384278	+	0.302200i	0.0251211	+	0.0197554i
$235$	−6.29036	−	8.83357i	−0.410338	−	0.576239i
$236$	−9.94918	+	7.82413i	−0.647637	+	0.509307i
$237$	−9.85339	−	2.89322i	−0.640047	−	0.187935i
$238$	14.1771	+	3.77913i	0.918966	+	0.244964i
$239$	−12.0826	−	26.4573i	−0.781562	−	1.71138i	−0.699364	−	0.714765i	$-0.746534\pi$
$239$	−12.0826	−	26.4573i	−0.781562	−	1.71138i	−0.0821972	−	0.996616i	$-0.526194\pi$
$240$	0.826996	+	0.788539i	0.0533824	+	0.0509000i
$241$	0.305229	+	0.881903i	0.0196616	+	0.0568083i	0.954405	−	0.298516i	$-0.0964916\pi$
$241$	0.305229	+	0.881903i	0.0196616	+	0.0568083i	−0.934743	+	0.355324i	$0.884370\pi$
$242$	4.69879	+	13.5763i	0.302050	+	0.872715i
$243$	0.723734	+	0.690079i	0.0464276	+	0.0442686i
$244$	−2.26586	−	4.96155i	−0.145057	−	0.317631i
$245$	4.30706	−	6.74013i	0.275168	−	0.430611i
$246$	−11.5009	−	3.37698i	−0.733273	−	0.215308i
$247$	2.96553	−	2.33212i	0.188692	−	0.148389i
$248$	−2.16270	−	3.03708i	−0.137331	−	0.192855i
$249$	−7.16507	−	5.63467i	−0.454068	−	0.357083i
$250$	0.472716	−	9.92353i	0.0298972	−	0.627619i
$251$	−4.08816	−	4.71799i	−0.258042	−	0.297797i	0.611915	−	0.790923i	$-0.290399\pi$
$251$	−4.08816	−	4.71799i	−0.258042	−	0.297797i	−0.869958	+	0.493127i	$0.835854\pi$
$252$	−1.78222	−	1.95543i	−0.112269	−	0.123180i
$253$	7.53114	−	22.9501i	0.473479	−	1.44286i
$254$	5.50636	+	9.53729i	0.345499	+	0.598423i
$255$	6.22228	−	1.19925i	0.389655	−	0.0750998i
$256$	−0.888835	+	0.458227i	−0.0555522	+	0.0286392i
$257$	19.8098	−	7.93064i	1.23570	−	0.494700i	0.340450	−	0.940263i	$-0.389421\pi$
$257$	19.8098	−	7.93064i	1.23570	−	0.494700i	0.895251	+	0.445563i	$0.146996\pi$
$258$	1.45900	−	3.19477i	0.0908336	−	0.198898i
$259$	−6.41872	−	1.07084i	−0.398840	−	0.0665386i
$260$	−0.535995	−	0.157382i	−0.0332410	−	0.00976043i
$261$	5.80211	+	2.99120i	0.359142	+	0.185150i
$262$	−15.9341	−	1.52152i	−0.984410	−	0.0939998i
$263$	1.74478	−	7.19207i	0.107588	−	0.443482i	−0.892382	−	0.451281i	$-0.850967\pi$
$263$	1.74478	−	7.19207i	0.107588	−	0.443482i	0.999970	+	0.00779873i	$0.00248244\pi$
$264$	−4.94549	−	0.953165i	−0.304374	−	0.0586633i
$265$	−1.59915	+	1.84552i	−0.0982350	+	0.113369i
$266$	−17.9075	+	9.80828i	−1.09798	+	0.601384i
$267$	−7.57293	−	16.5824i	−0.463456	−	1.01483i
$268$	3.19249	+	1.64584i	0.195012	+	0.100536i
$269$	17.1131	−	16.3173i	1.04341	−	0.994886i	0.0434153	−	0.999057i	$-0.486176\pi$
$269$	17.1131	−	16.3173i	1.04341	−	0.994886i	0.999991	+	0.00417097i	$0.00132767\pi$
$270$	−1.06083	−	0.424691i	−0.0645599	−	0.0258459i
$271$	−19.0838	+	1.82228i	−1.15926	+	0.110696i	−0.656910	−	0.753969i	$-0.728137\pi$
$271$	−19.0838	+	1.82228i	−1.15926	+	0.110696i	−0.502349	+	0.864665i	$0.667531\pi$
$272$	−0.789215	+	5.48911i	−0.0478532	+	0.332826i
$273$	1.21246	+	0.450442i	0.0733816	+	0.0272620i
$274$	5.48313	+	6.32787i	0.331248	+	0.382281i
$275$	9.30314	+	16.1135i	0.561001	+	0.971681i
$276$	3.19861	+	3.57336i	0.192534	+	0.215091i
$277$	−11.5490	+	20.0034i	−0.693912	+	1.20189i	0.276634	+	0.960975i	$0.410781\pi$
$277$	−11.5490	+	20.0034i	−0.693912	+	1.20189i	−0.970546	+	0.240915i	$0.922552\pi$
$278$	−4.34566	+	12.5560i	−0.260635	+	0.753056i
$279$	3.13655	+	2.01574i	0.187780	+	0.120679i
$280$	2.72108	+	1.31748i	0.162616	+	0.0787343i
$281$	−0.170398	+	0.373120i	−0.0101651	+	0.0222585i	−0.914646	−	0.404255i	$-0.867531\pi$
$281$	−0.170398	+	0.373120i	−0.0101651	+	0.0222585i	0.904481	+	0.426513i	$0.140258\pi$
$282$	−7.45989	+	5.86652i	−0.444230	+	0.349346i
$283$	3.44508	−	3.28488i	0.204789	−	0.195266i	−0.580743	−	0.814087i	$-0.697238\pi$
$283$	3.44508	−	3.28488i	0.204789	−	0.195266i	0.785532	+	0.618821i	$0.212389\pi$
$284$	0.427515	+	8.97465i	0.0253684	+	0.532547i
$285$	−5.11507	+	7.18311i	−0.302991	+	0.425491i
$286$	2.36246	−	0.693682i	0.139695	−	0.0410183i
$287$	−31.7032	+	0.795656i	−1.87138	+	0.0469661i
$288$	0.654861	−	0.755750i	0.0385880	−	0.0445330i
$289$	9.95368	+	9.49081i	0.585511	+	0.558283i
$290$	−7.42538	−	0.709037i	−0.436033	−	0.0416361i
$291$	0.671467	+	14.0958i	0.0393621	+	0.826313i
$292$	−0.403839	−	1.66465i	−0.0236329	−	0.0974162i
$293$	3.29535	+	22.9197i	0.192517	+	1.33898i	0.825318	+	0.564668i	$0.190996\pi$
$293$	3.29535	+	22.9197i	0.192517	+	1.33898i	−0.632802	+	0.774314i	$0.718095\pi$
$294$	−6.07120	−	3.48433i	−0.354080	−	0.203210i
$295$	−2.05831	+	14.3158i	−0.119839	+	0.833501i
$296$	0.117031	−	2.45679i	0.00680232	−	0.142798i
$297$	4.94549	−	0.953165i	0.286966	−	0.0553083i
$298$	3.82706	−	6.62866i	0.221695	−	0.383988i
$299$	−2.19036	−	0.836182i	−0.126672	−	0.0483576i
$300$	−3.69428			−0.213290
$301$	1.09125	−	9.22801i	0.0628988	−	0.531893i
$302$	−18.0272	−	11.5854i	−1.03735	−	0.666664i
$303$	5.13186	−	2.05449i	0.294818	−	0.118027i
$304$	−4.47638	−	6.28620i	−0.256738	−	0.360538i
$305$	−5.78624	−	2.31646i	−0.331319	−	0.132640i
$306$	−1.30742	−	5.38924i	−0.0747399	−	0.308082i
$307$	−16.2115	+	10.4185i	−0.925238	+	0.594614i	−0.914173	−	0.405325i	$-0.867158\pi$
$307$	−16.2115	+	10.4185i	−0.925238	+	0.594614i	−0.0110648	+	0.999939i	$0.503522\pi$
$308$	−13.2291	+	1.59906i	−0.753795	+	0.0911151i
$309$	8.08964	−	2.37533i	0.460204	−	0.135128i
$310$	−4.18340	−	0.806284i	−0.237601	−	0.0457939i
$311$	6.12534	+	17.6980i	0.347336	+	1.00356i	0.974444	+	0.224629i	$0.0721171\pi$
$311$	6.12534	+	17.6980i	0.347336	+	1.00356i	−0.627108	+	0.778932i	$0.715762\pi$
$312$	−0.115256	+	0.475090i	−0.00652507	+	0.0268967i
$313$	11.8896	−	16.6966i	0.672041	−	0.943750i	−0.327958	−	0.944692i	$-0.606360\pi$
$313$	11.8896	−	16.6966i	0.672041	−	0.943750i	1.00000		0.000942088i	$0.000299876\pi$
$314$	6.97449	−	4.48223i	0.393593	−	0.252947i
$315$	−3.01582	−	0.211780i	−0.169922	−	0.0119325i
$316$	−1.46148	−	10.1648i	−0.0822149	−	0.571817i
$317$	25.6817	−	2.45231i	1.44243	−	0.137735i	0.655695	−	0.755026i	$-0.272376\pi$
$317$	25.6817	−	2.45231i	1.44243	−	0.137735i	0.786735	+	0.617290i	$0.211770\pi$
$318$	1.67984	+	1.32104i	0.0942007	+	0.0740802i
$319$	29.2224	−	15.0652i	1.63614	−	0.843489i
$320$	−0.373734	+	1.07983i	−0.0208924	+	0.0603645i
$321$	1.96889			0.109893
$322$	10.9479	+	6.41437i	0.610101	+	0.357459i
$323$	−42.7959			−2.38123
$324$	−0.327068	+	0.945001i	−0.0181704	+	0.0525000i
$325$	1.60526	−	0.827570i	0.0890439	−	0.0459053i
$326$	7.16731	+	5.63643i	0.396961	+	0.312173i
$327$	3.77883	−	0.360834i	0.208970	−	0.0199542i
$328$	−1.70585	−	11.8645i	−0.0941899	−	0.655105i
$329$	−14.0469	+	20.8122i	−0.774431	+	1.14741i
$330$	−4.84151	+	3.11145i	−0.266516	+	0.171280i
$331$	−1.81540	+	2.54938i	−0.0997835	+	0.140126i	−0.861449	−	0.507844i	$-0.830443\pi$
$331$	−1.81540	+	2.54938i	−0.0997835	+	0.140126i	0.761665	+	0.647970i	$0.224382\pi$
$332$	2.14900	−	8.85830i	0.117942	−	0.486162i
$333$	0.804449	+	2.32430i	0.0440836	+	0.127371i
$334$	−8.61923	−	1.66122i	−0.471623	−	0.0908979i
$335$	3.93799	−	1.15630i	0.215155	−	0.0631753i
$336$	1.03836	−	2.43348i	0.0566471	−	0.132757i
$337$	−6.29541	+	4.04582i	−0.342933	+	0.220390i	−0.700758	−	0.713399i	$-0.747155\pi$
$337$	−6.29541	+	4.04582i	−0.342933	+	0.220390i	0.357825	+	0.933789i	$0.383518\pi$
$338$	3.00852	+	12.4013i	0.163642	+	0.674541i
$339$	6.83482	+	2.73625i	0.371216	+	0.148613i
$340$	3.67570	+	5.16180i	0.199343	+	0.279938i
$341$	17.4331	−	6.97916i	0.944055	−	0.377942i
$342$	6.49208	+	4.17220i	0.351051	+	0.225607i
$343$	−18.1121	−	3.86660i	−0.977963	−	0.208777i
$344$	3.51216			0.189363
$345$	5.46297	+	0.432919i	0.294117	+	0.0233076i
$346$	3.08545	−	5.34416i	0.165875	−	0.287304i
$347$	−25.1023	+	4.83807i	−1.34756	+	0.259721i	−0.811448	−	0.584425i	$-0.801320\pi$
$347$	−25.1023	+	4.83807i	−1.34756	+	0.259721i	−0.536113	+	0.844146i	$0.680108\pi$
$348$	−0.310604	+	6.52038i	−0.0166501	+	0.349529i
$349$	−3.09510	+	21.5269i	−0.165677	+	1.15231i	0.722018	+	0.691874i	$0.243215\pi$
$349$	−3.09510	+	21.5269i	−0.165677	+	1.15231i	−0.887695	+	0.460433i	$0.847694\pi$
$350$	−9.30619	+	2.98812i	−0.497437	+	0.159722i
$351$	−0.0695736	−	0.483895i	−0.00371356	−	0.0258284i
$352$	−1.18740	−	4.89454i	−0.0632887	−	0.260880i
$353$	−0.336859	−	7.07154i	−0.0179292	−	0.376380i	−0.989944	−	0.141460i	$-0.954820\pi$
$353$	−0.336859	−	7.07154i	−0.0179292	−	0.376380i	0.972015	−	0.234920i	$-0.0754827\pi$
$354$	12.5998	+	1.20314i	0.669673	+	0.0639461i
$355$	7.43042	+	7.08489i	0.394366	+	0.376027i
$356$	11.9380	−	13.7772i	0.632712	−	0.730188i
$357$	−7.65257	−	12.5184i	−0.405017	−	0.662545i
$358$	21.5884	−	6.33891i	1.14098	−	0.335022i
$359$	−3.78325	+	5.31283i	−0.199672	+	0.280401i	−0.902256	−	0.431200i	$-0.858090\pi$
$359$	−3.78325	+	5.31283i	−0.199672	+	0.280401i	0.702584	+	0.711601i	$0.252030\pi$
$360$	−0.0543709	−	1.14139i	−0.00286560	−	0.0601563i
$361$	29.3506	−	27.9857i	1.54477	−	1.47293i
$362$	5.59689	−	4.40145i	0.294166	−	0.231335i
$363$	5.96802	−	13.0681i	0.313240	−	0.685899i
$364$	0.0939388	+	1.29001i	0.00492373	+	0.0676152i
$365$	−1.64661	−	1.05821i	−0.0861877	−	0.0553895i
$366$	−1.78398	+	5.15447i	−0.0932501	+	0.269428i
$367$	8.17522	−	14.1599i	0.426743	−	0.739140i	−0.569839	−	0.821757i	$-0.692994\pi$
$367$	8.17522	−	14.1599i	0.426743	−	0.739140i	0.996581	+	0.0826164i	$0.0263276\pi$
$368$	−1.92169	+	4.39399i	−0.100175	+	0.229052i
$369$	5.99323	+	10.3806i	0.311995	+	0.540392i
$370$	−1.84049	−	2.12404i	−0.0956827	−	0.110424i
$371$	5.30017	+	1.96907i	0.275171	+	0.102229i
$372$	−0.530609	+	3.69047i	−0.0275108	+	0.191342i
$373$	−3.14187	+	0.300012i	−0.162680	+	0.0155340i	−0.176078	−	0.984376i	$-0.556341\pi$
$373$	−3.14187	+	0.300012i	−0.162680	+	0.0155340i	0.0133982	+	0.999910i	$0.495735\pi$
$374$	−25.9295	−	10.3806i	−1.34078	−	0.536769i
$375$	−7.19014	+	6.85578i	−0.371297	+	0.354031i
$376$	−8.43532	−	4.34871i	−0.435019	−	0.224268i
$377$	−1.32569	−	2.90285i	−0.0682764	−	0.149504i
$378$	−0.0595460	+	2.64508i	−0.00306271	+	0.136048i
$379$	−18.0544	+	20.8359i	−0.927393	+	1.07027i	0.0699597	+	0.997550i	$0.477713\pi$
$379$	−18.0544	+	20.8359i	−0.927393	+	1.07027i	−0.997353	+	0.0727185i	$0.976833\pi$
$380$	−8.65887	−	1.66886i	−0.444191	−	0.0856107i
$381$	2.59635	−	10.7023i	0.133015	−	0.548294i
$382$	−23.4986	−	2.24384i	−1.20229	−	0.114805i
$383$	−2.18921	−	1.12862i	−0.111863	−	0.0576696i	0.401387	−	0.915909i	$-0.368528\pi$
$383$	−2.18921	−	1.12862i	−0.111863	−	0.0576696i	−0.513250	+	0.858239i	$0.671559\pi$
$384$	0.959493	+	0.281733i	0.0489639	+	0.0143771i
$385$	−9.67945	+	11.7540i	−0.493311	+	0.599042i
$386$	4.05738	−	8.88441i	0.206515	−	0.452205i
$387$	−3.26058	+	1.30534i	−0.165744	+	0.0663541i
$388$	−12.5431	+	6.46641i	−0.636779	+	0.328282i
$389$	9.30002	−	1.79243i	0.471530	−	0.0908799i	0.0520498	−	0.998644i	$-0.483425\pi$
$389$	9.30002	−	1.79243i	0.471530	−	0.0908799i	0.419480	+	0.907765i	$0.362212\pi$
$390$	0.279311	+	0.483782i	0.0141435	+	0.0244972i
$391$	13.6673	+	22.8151i	0.691185	+	1.15381i
$392$	0.647387	−	6.97000i	0.0326980	−	0.352038i
$393$	10.4821	+	12.0969i	0.528750	+	0.610210i
$394$	−0.294378	+	6.17975i	−0.0148305	+	0.311331i
$395$	−9.22403	−	7.25385i	−0.464111	−	0.364981i
$396$	2.92146	+	4.10262i	0.146809	+	0.206164i
$397$	−21.2448	+	16.7071i	−1.06624	+	0.838504i	−0.987378	−	0.158381i	$-0.949373\pi$
$397$	−21.2448	+	16.7071i	−1.06624	+	0.838504i	−0.0788668	+	0.996885i	$0.525130\pi$
$398$	14.3658	+	4.21819i	0.720094	+	0.211439i
$399$	19.7287	+	5.25900i	0.987673	+	0.263279i
$400$	−1.53466	−	3.36044i	−0.0767330	−	0.168022i
$401$	18.6607	+	17.7929i	0.931869	+	0.888535i	0.993983	−	0.109534i	$-0.0349359\pi$
$401$	18.6607	+	17.7929i	0.931869	+	0.888535i	−0.0621145	+	0.998069i	$0.519784\pi$
$402$	−1.17475	−	3.39422i	−0.0585913	−	0.169288i
$403$	−0.596152	−	1.72247i	−0.0296964	−	0.0858022i
$404$	4.00068	+	3.81464i	0.199041	+	0.189785i
$405$	0.474686	+	1.03942i	0.0235874	+	0.0516491i
$406$	4.49157	+	16.6766i	0.222913	+	0.827645i
$407$	11.8859	+	3.49001i	0.589162	+	0.172994i
$408$	4.35910	−	3.42804i	0.215808	−	0.169713i
$409$	−6.17990	−	8.67846i	−0.305577	−	0.429122i	0.633022	−	0.774134i	$-0.281814\pi$
$409$	−6.17990	−	8.67846i	−0.305577	−	0.429122i	−0.938598	+	0.345012i	$0.887875\pi$
$410$	−10.7663	−	8.46673i	−0.531711	−	0.418142i
$411$	0.398402	−	8.36349i	0.0196517	−	0.412541i
$412$	5.52124	+	6.37185i	0.272012	+	0.313919i
$413$	32.7131	−	7.16058i	1.60971	−	0.352349i
$414$	0.150952	−	4.79346i	0.00741888	−	0.235585i
$415$	−5.20790	−	9.02035i	−0.255646	−	0.442792i
$416$	−0.480036	+	0.0925194i	−0.0235357	+	0.00453614i
$417$	11.8097	−	6.08832i	0.578323	−	0.298146i
$418$	36.0833	−	14.4456i	1.76489	−	0.706556i
$419$	3.44874	−	7.55169i	0.168482	−	0.368924i	−0.806491	−	0.591246i	$-0.798636\pi$
$419$	3.44874	−	7.55169i	0.168482	−	0.368924i	0.974973	+	0.222322i	$0.0713635\pi$
$420$	−1.06017	−	2.83126i	−0.0517312	−	0.138151i
$421$	25.3884	+	7.45471i	1.23735	+	0.363320i	0.834021	−	0.551733i	$-0.186033\pi$
$421$	25.3884	+	7.45471i	1.23735	+	0.363320i	0.403334	+	0.915053i	$0.367851\pi$
$422$	−13.1047	−	6.75593i	−0.637926	−	0.328873i
$423$	9.44734	+	0.902111i	0.459345	+	0.0438621i
$424$	−0.503830	+	2.07681i	−0.0244681	+	0.100859i
$425$	−20.1166	−	3.87716i	−0.975800	−	0.188070i
$426$	5.88381	−	6.79028i	0.285072	−	0.328990i
$427$	−0.324791	+	14.4275i	−0.0157177	+	0.698195i
$428$	0.817907	+	1.79097i	0.0395350	+	0.0865696i
$429$	−2.18849	−	1.12825i	−0.105661	−	0.0544722i
$430$	2.90454	−	2.76948i	0.140070	−	0.133556i
$431$	5.16401	+	2.06736i	0.248742	+	0.0995812i	0.492683	−	0.870209i	$-0.336016\pi$
$431$	5.16401	+	2.06736i	0.248742	+	0.0995812i	−0.243941	+	0.969790i	$0.578440\pi$
$432$	−0.995472	+	0.0950560i	−0.0478947	+	0.00457339i
$433$	−5.16297	+	35.9093i	−0.248117	+	1.72569i	0.360964	+	0.932580i	$0.382448\pi$
$433$	−5.16297	+	35.9093i	−0.248117	+	1.72569i	−0.609080	+	0.793109i	$0.708461\pi$
$434$	1.64839	+	9.72577i	0.0791253	+	0.466852i
$435$	4.88471	+	5.63725i	0.234204	+	0.270285i
$436$	1.89801	+	3.28744i	0.0908981	+	0.157440i
$437$	−35.6744	−	9.85322i	−1.70654	−	0.471344i
$438$	−0.856466	+	1.48344i	−0.0409235	+	0.0708817i
$439$	5.06819	−	14.6436i	0.241891	−	0.698899i	−0.757070	−	0.653334i	$-0.773370\pi$
$439$	5.06819	−	14.6436i	0.241891	−	0.698899i	0.998961	−	0.0455655i	$-0.0145090\pi$
$440$	−4.84151	−	3.11145i	−0.230810	−	0.148333i
$441$	1.98947	+	6.71133i	0.0947368	+	0.319587i
$442$	−1.12622	+	2.46607i	−0.0535686	+	0.117299i
$443$	2.37379	−	1.86677i	0.112782	−	0.0886927i	−0.560175	−	0.828374i	$-0.689266\pi$
$443$	2.37379	−	1.86677i	0.112782	−	0.0886927i	0.672957	+	0.739681i	$0.265024\pi$
$444$	−1.78008	+	1.69730i	−0.0844789	+	0.0805505i
$445$	−0.991170	−	20.8072i	−0.0469860	−	0.986357i
$446$	−0.207932	+	0.291999i	−0.00984585	+	0.0138266i
$447$	−7.34407	+	2.15641i	−0.347363	+	0.101995i
$448$	2.64492	−	0.0663795i	0.124961	−	0.00313614i
$449$	7.28871	−	8.41162i	0.343975	−	0.396969i	−0.557232	−	0.830357i	$-0.688137\pi$
$449$	7.28871	−	8.41162i	0.343975	−	0.396969i	0.901207	+	0.433388i	$0.142682\pi$
$450$	2.67368	+	2.54935i	0.126038	+	0.120177i
$451$	60.0966	+	5.73853i	2.82984	+	0.270217i
$452$	0.350307	+	7.35385i	0.0164771	+	0.345896i
$453$	5.05207	+	20.8249i	0.237367	+	0.978441i
$454$	−0.436648	−	3.03696i	−0.0204929	−	0.142531i
$455$	1.09491	+	0.992763i	0.0513304	+	0.0465414i
$456$	−1.09826	+	7.63860i	−0.0514309	+	0.357710i
$457$	0.0980539	−	2.05840i	0.00458677	−	0.0962881i	−0.995413	−	0.0956707i	$-0.969500\pi$
$457$	0.0980539	−	2.05840i	0.00458677	−	0.0962881i	1.00000		0.000617425i	$-0.000196533\pi$
$458$	11.3500	−	2.18754i	0.530352	−	0.102217i
$459$	−2.77278	+	4.80260i	−0.129422	+	0.224166i
$460$	1.87560	+	5.14914i	0.0874505	+	0.240080i
$461$	−12.7367			−0.593206			−0.296603	−	0.955001i	$-0.595854\pi$
$461$	−12.7367			−0.593206			−0.296603	+	0.955001i	$0.595854\pi$
$462$	10.6778	+	7.97179i	0.496776	+	0.370881i
$463$	28.6882	+	18.4368i	1.33325	+	0.856829i	0.996404	−	0.0847296i	$-0.0270027\pi$
$463$	28.6882	+	18.4368i	1.33325	+	0.856829i	0.336848	+	0.941559i	$0.390639\pi$
$464$	−6.06017	+	2.42613i	−0.281336	+	0.112630i
$465$	2.47127	+	3.47041i	0.114602	+	0.160936i
$466$	−22.2793	−	8.91927i	−1.03207	−	0.413177i
$467$	2.38606	+	9.83548i	0.110414	+	0.455132i	0.999999	−	0.00163805i	$-0.000521406\pi$
$467$	2.38606	+	9.83548i	0.110414	+	0.455132i	−0.889585	+	0.456770i	$0.849006\pi$
$468$	0.411264	−	0.264304i	0.0190107	−	0.0122174i
$469$	−5.70471	−	7.60012i	−0.263419	−	0.350941i
$470$	−10.4051	+	3.05522i	−0.479952	+	0.140927i
$471$	−8.14077	−	1.56901i	−0.375107	−	0.0722960i
$472$	4.13975	+	11.9610i	0.190547	+	0.550550i
$473$	−4.17035	+	17.1904i	−0.191753	+	0.790415i
$474$	−5.95682	+	8.36519i	−0.273606	+	0.384226i
$475$	23.9836	−	15.4133i	1.10044	−	0.707211i
$476$	8.20816	−	12.1614i	0.376220	−	0.557415i
$477$	−0.304135	−	2.11530i	−0.0139254	−	0.0968530i
$478$	−28.9540	+	2.76477i	−1.32433	+	0.126458i
$479$	3.30260	+	2.59719i	0.150900	+	0.118669i	0.690755	−	0.723089i	$-0.257279\pi$
$479$	3.30260	+	2.59719i	0.150900	+	0.118669i	−0.539855	+	0.841758i	$0.681521\pi$
$480$	1.01565	−	0.523606i	0.0463581	−	0.0238992i
$481$	0.393272	−	1.13628i	0.0179317	−	0.0518101i
$482$	0.933230			0.0425074
$483$	−3.49693	−	12.1972i	−0.159116	−	0.554991i
$484$	14.3664			0.653018
$485$	−5.27407	+	15.2384i	−0.239483	+	0.691941i
$486$	0.888835	−	0.458227i	0.0403184	−	0.0207856i
$487$	−26.9434	−	21.1886i	−1.22092	−	0.960145i	−0.221038	−	0.975265i	$-0.570944\pi$
$487$	−26.9434	−	21.1886i	−1.22092	−	0.960145i	−0.999886	+	0.0151202i	$0.995187\pi$
$488$	−5.42976	+	0.518479i	−0.245794	+	0.0234705i
$489$	−1.29764	−	9.02529i	−0.0586813	−	0.408138i
$490$	−4.96073	−	6.27465i	−0.224103	−	0.283460i
$491$	34.8410	−	22.3910i	1.57235	−	1.01049i	0.593771	−	0.804634i	$-0.297638\pi$
$491$	34.8410	−	22.3910i	1.57235	−	1.01049i	0.978582	−	0.205856i	$-0.0659979\pi$
$492$	−6.95283	+	9.76389i	−0.313458	+	0.440190i
$493$	−8.53451	+	35.1797i	−0.384375	+	1.58441i
$494$	−1.23393	−	3.56519i	−0.0555169	−	0.160406i
$495$	5.65111	+	1.08916i	0.253999	+	0.0489542i
$496$	−3.57739	+	1.05042i	−0.160630	+	0.0471651i
$497$	9.32947	−	21.8644i	0.418484	−	0.980751i
$498$	−7.66823	+	4.92807i	−0.343622	+	0.220832i
$499$	9.81499	+	40.4580i	0.439379	+	1.81115i	0.572329	+	0.820024i	$0.306040\pi$
$499$	9.81499	+	40.4580i	0.439379	+	1.81115i	−0.132950	+	0.991123i	$0.542445\pi$
$500$	−9.22313	−	3.69239i	−0.412471	−	0.165128i
$501$	5.09165	+	7.15023i	0.227478	+	0.319449i
$502$	−5.79561	+	2.32021i	−0.258671	+	0.103556i
$503$	−6.90214	−	4.43574i	−0.307751	−	0.197780i	0.377644	−	0.925951i	$-0.376734\pi$
$503$	−6.90214	−	4.43574i	−0.307751	−	0.197780i	−0.685395	+	0.728171i	$0.740371\pi$
$504$	−2.43079	+	1.04464i	−0.108276	+	0.0465320i
$505$	6.31654			0.281082
$506$	−19.2247	−	14.6232i	−0.854643	−	0.650080i
$507$	6.38050	−	11.0514i	0.283368	−	0.490808i
$508$	10.8137	−	2.08417i	0.479780	−	0.0924701i
$509$	0.674887	−	14.1676i	0.0299139	−	0.627969i	−0.933278	−	0.359155i	$-0.883065\pi$
$509$	0.674887	−	14.1676i	0.0299139	−	0.627969i	0.963192	−	0.268815i	$-0.0866319\pi$
$510$	0.901820	−	6.27230i	0.0399333	−	0.277742i
$511$	−0.957623	+	4.42966i	−0.0423628	+	0.195957i
$512$	0.142315	+	0.989821i	0.00628949	+	0.0437443i
$513$	−1.81939	−	7.49961i	−0.0803279	−	0.331116i
$514$	−1.01532	−	21.3141i	−0.0447837	−	0.940126i
$515$	9.59050	+	0.915782i	0.422608	+	0.0403542i
$516$	−2.54187	−	2.42367i	−0.111900	−	0.106696i
$517$	31.3010	−	36.1233i	1.37662	−	1.58870i
$518$	−3.11130	+	5.71546i	−0.136703	+	0.251123i
$519$	−5.92094	+	1.73854i	−0.259900	+	0.0763136i
$520$	−0.324033	+	0.455041i	−0.0142098	+	0.0199549i
$521$	1.29200	+	27.1224i	0.0566035	+	1.18825i	0.831265	+	0.555877i	$0.187617\pi$
$521$	1.29200	+	27.1224i	0.0566035	+	1.18825i	−0.774661	+	0.632377i	$0.782079\pi$
$522$	4.72437	−	4.50468i	0.206780	−	0.197164i
$523$	20.7221	−	16.2960i	0.906114	−	0.712576i	−0.0520959	−	0.998642i	$-0.516590\pi$
$523$	20.7221	−	16.2960i	0.906114	−	0.712576i	0.958210	+	0.286066i	$0.0923477\pi$
$524$	−6.64936	+	14.5601i	−0.290479	+	0.636060i
$525$	8.79725	+	4.25940i	0.383943	+	0.185896i
$526$	−6.22585	−	4.00111i	−0.271460	−	0.174457i
$527$	−6.76251	+	19.5390i	−0.294580	+	0.851132i
$528$	−2.51825	+	4.36174i	−0.109593	+	0.189821i
$529$	6.14009	+	22.1653i	0.266960	+	0.963708i
$530$	1.22098	+	2.11481i	0.0530362	+	0.0918614i
$531$	−8.28866	−	9.56563i	−0.359697	−	0.415113i
$532$	3.41187	+	20.1306i	0.147923	+	0.872771i
$533$	0.833941	−	5.80019i	0.0361220	−	0.251234i
$534$	−18.1473	+	1.73285i	−0.785308	+	0.0749879i
$535$	2.08865	+	0.836171i	0.0903004	+	0.0361508i
$536$	2.59948	−	2.47860i	0.112281	−	0.107059i
$537$	−19.9986	−	10.3100i	−0.863002	−	0.444909i
$538$	−9.82275	−	21.5088i	−0.423489	−	0.927311i
$539$	33.3462	+	11.4448i	1.43632	+	0.492964i
$540$	−0.748296	+	0.863580i	−0.0322015	+	0.0371626i
$541$	−14.2934	−	2.75482i	−0.614521	−	0.118439i	−0.127513	−	0.991837i	$-0.540699\pi$
$541$	−14.2934	−	2.75482i	−0.614521	−	0.118439i	−0.487008	+	0.873398i	$0.661912\pi$
$542$	−4.51965	+	18.6302i	−0.194135	+	0.800237i
$543$	−7.08801	−	0.676823i	−0.304176	−	0.0290452i
$544$	4.92909	+	2.54112i	0.211333	+	0.108950i
$545$	4.16192	+	1.22205i	0.178277	+	0.0523469i
$546$	0.822225	−	0.998453i	0.0351880	−	0.0427298i
$547$	10.6862	−	23.3994i	0.456907	−	1.00049i	−0.531274	−	0.847200i	$-0.678287\pi$
$547$	10.6862	−	23.3994i	0.456907	−	1.00049i	0.988182	−	0.153288i	$-0.0489861\pi$
$548$	7.77320	−	3.11192i	0.332055	−	0.132935i
$549$	4.84812	−	2.49938i	0.206913	−	0.106671i
$550$	18.2700	−	3.52126i	0.779037	−	0.150147i
$551$	−25.1879	−	43.6267i	−1.07304	−	1.85856i
$552$	4.42299	−	1.85396i	0.188255	−	0.0789099i
$553$	−8.23953	+	25.8907i	−0.350380	+	1.10099i
$554$	15.1260	+	17.4563i	0.642641	+	0.741647i
$555$	−0.133730	+	2.80733i	−0.00567650	+	0.119164i
$556$	10.4441	+	8.21330i	0.442927	+	0.348321i
$557$	−16.3772	−	22.9986i	−0.693926	−	0.974483i	−0.999749	−	0.0223947i	$-0.992871\pi$
$557$	−16.3772	−	22.9986i	−0.693926	−	0.974483i	0.305823	−	0.952088i	$-0.401068\pi$
$558$	2.93074	−	2.30476i	0.124068	−	0.0975681i
$559$	1.64744	+	0.483733i	0.0696794	+	0.0204597i
$560$	2.13499	−	2.14052i	0.0902200	−	0.0904534i
$561$	11.6026	+	25.4062i	0.489864	+	1.07265i
$562$	0.296867	+	0.283062i	0.0125226	+	0.0119402i
$563$	3.53255	+	10.2066i	0.148879	+	0.430158i	0.994639	−	0.103405i	$-0.0329738\pi$
$563$	3.53255	+	10.2066i	0.148879	+	0.430158i	−0.845760	+	0.533563i	$0.820853\pi$
$564$	3.10398	+	8.96835i	0.130701	+	0.377636i
$565$	6.08850	+	5.80537i	0.256145	+	0.244234i
$566$	−1.97744	−	4.32999i	−0.0831179	−	0.182003i
$567$	1.86841	−	1.87324i	0.0784659	−	0.0786688i
$568$	8.62088	+	2.53132i	0.361724	+	0.106212i
$569$	28.9391	−	22.7580i	1.21319	−	0.954063i	0.213452	−	0.976953i	$-0.431529\pi$
$569$	28.9391	−	22.7580i	1.21319	−	0.954063i	0.999738	+	0.0228900i	$0.00728675\pi$
$570$	5.11507	+	7.18311i	0.214247	+	0.300868i
$571$	25.4895	+	20.0451i	1.06670	+	0.838863i	0.987441	−	0.157991i	$-0.0505017\pi$
$571$	25.4895	+	20.0451i	1.06670	+	0.838863i	0.0792604	+	0.996854i	$0.474744\pi$
$572$	0.117156	−	2.45941i	0.00489855	−	0.102833i
$573$	15.4583	+	17.8398i	0.645780	+	0.745270i
$574$	−9.61721	+	30.2198i	−0.401415	+	1.26135i
$575$	−15.8764	−	7.86359i	−0.662094	−	0.327934i
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	−25.0732	+	4.83247i	−1.04381	+	0.201178i	−0.682212	−	0.731155i	$-0.738982\pi$
$577$	−25.0732	+	4.83247i	−1.04381	+	0.201178i	−0.361601	+	0.932333i	$0.617770\pi$
$578$	12.2244	−	6.30209i	0.508466	−	0.262133i
$579$	−9.06741	+	3.63004i	−0.376829	+	0.150859i
$580$	−3.09864	+	6.78508i	−0.128664	+	0.281735i
$581$	−15.3308	+	18.6167i	−0.636029	+	0.772349i
$582$	13.5402	+	3.97576i	0.561259	+	0.164801i
$583$	−9.56679	−	4.93202i	−0.396216	−	0.204264i
$584$	−1.70518	−	0.162825i	−0.0705607	−	0.00673773i
$585$	0.131700	−	0.542876i	0.00544514	−	0.0224452i
$586$	22.7369	+	4.38218i	0.939254	+	0.181026i
$587$	−3.93125	+	4.53690i	−0.162260	+	0.187258i	−0.831057	−	0.556187i	$-0.812264\pi$
$587$	−3.93125	+	4.53690i	−0.162260	+	0.187258i	0.668797	+	0.743445i	$0.266809\pi$
$588$	−5.27839	+	4.59768i	−0.217677	+	0.189605i
$589$	−11.9526	−	26.1726i	−0.492500	−	1.07842i
$590$	12.8553	+	6.62736i	0.529243	+	0.272844i
$591$	4.47757	−	4.26935i	0.184183	−	0.175618i
$592$	−2.28339	−	0.914133i	−0.0938469	−	0.0375706i
$593$	−10.5139	+	1.00395i	−0.431754	+	0.0412275i	−0.308671	−	0.951169i	$-0.599884\pi$
$593$	−10.5139	+	1.00395i	−0.431754	+	0.0412275i	−0.123083	+	0.992396i	$0.539278\pi$
$594$	0.716770	−	4.98524i	0.0294094	−	0.204547i
$595$	−2.80159	−	16.5299i	−0.114854	−	0.677658i
$596$	−5.01238	−	5.78459i	−0.205315	−	0.236946i
$597$	−7.48615	−	12.9664i	−0.306388	−	0.530679i
$598$	−1.50659	+	1.79640i	−0.0616090	+	0.0734604i
$599$	−11.2238	+	19.4402i	−0.458591	+	0.794304i	−0.998887	−	0.0471717i	$-0.984979\pi$
$599$	−11.2238	+	19.4402i	−0.458591	+	0.794304i	0.540295	+	0.841475i	$0.318313\pi$
$600$	−1.20828	+	3.49110i	−0.0493279	+	0.142524i
$601$	−3.06693	−	1.97099i	−0.125103	−	0.0803985i	0.476593	−	0.879124i	$-0.341872\pi$
$601$	−3.06693	−	1.97099i	−0.125103	−	0.0803985i	−0.601696	+	0.798726i	$0.705508\pi$
$602$	−8.36356	−	4.04942i	−0.340873	−	0.165042i
$603$	−1.49207	+	3.26718i	−0.0607619	+	0.133050i
$604$	−16.8443	+	13.2465i	−0.685386	+	0.538993i
$605$	11.8810	−	11.3285i	0.483030	−	0.460568i
$606$	−0.263025	−	5.52157i	−0.0106846	−	0.224298i
$607$	−0.772717	+	1.08513i	−0.0313636	+	0.0440441i	−0.829960	−	0.557823i	$-0.811637\pi$
$607$	−0.772717	+	1.08513i	−0.0313636	+	0.0440441i	0.798596	+	0.601867i	$0.205576\pi$
$608$	−7.40455	+	2.17417i	−0.300294	+	0.0881743i
$609$	8.25745	−	15.1689i	0.334609	−	0.614677i
$610$	−4.08155	+	4.71036i	−0.165257	+	0.190717i
$611$	−3.35779	−	3.20165i	−0.135842	−	0.129525i
$612$	−5.52045	−	0.527139i	−0.223151	−	0.0213083i
$613$	2.06766	+	43.4055i	0.0835120	+	1.75313i	0.520679	+	0.853753i	$0.325679\pi$
$613$	2.06766	+	43.4055i	0.0835120	+	1.75313i	−0.437167	+	0.899380i	$0.644018\pi$
$614$	4.54322	+	18.7274i	0.183349	+	0.755777i
$615$	1.94924	+	13.5573i	0.0786011	+	0.546682i
$616$	−2.81568	+	13.0245i	−0.113447	+	0.524771i
$617$	1.46001	−	10.1546i	0.0587777	−	0.408808i	−0.939097	−	0.343651i	$-0.888336\pi$
$617$	1.46001	−	10.1546i	0.0587777	−	0.408808i	0.997875	−	0.0651565i	$-0.0207547\pi$
$618$	0.401171	−	8.42162i	0.0161375	−	0.338767i
$619$	27.3823	−	5.27751i	1.10059	−	0.212121i	0.393555	−	0.919301i	$-0.371245\pi$
$619$	27.3823	−	5.27751i	1.10059	−	0.212121i	0.707034	+	0.707180i	$0.250033\pi$
$620$	−2.13019	+	3.68961i	−0.0855507	+	0.148178i
$621$	−3.41711	+	3.36502i	−0.137124	+	0.135034i
$622$	18.7280			0.750925
$623$	−44.3127	+	19.0436i	−1.77535	+	0.762966i
$624$	0.411264	+	0.264304i	0.0164637	+	0.0105806i
$625$	6.60918	−	2.64592i	0.264367	−	0.105837i
$626$	−11.8896	−	16.6966i	−0.475205	−	0.667332i
$627$	−36.0833	−	14.4456i	−1.44103	−	0.576901i
$628$	−1.95458	−	8.05690i	−0.0779963	−	0.321505i
$629$	−11.4745	+	7.37420i	−0.457517	+	0.294029i
$630$	−1.18651	+	2.78069i	−0.0472717	+	0.110785i
$631$	−19.8268	+	5.82167i	−0.789293	+	0.231757i	−0.651445	−	0.758696i	$-0.725837\pi$
$631$	−19.8268	+	5.82167i	−0.789293	+	0.231757i	−0.137848	+	0.990453i	$0.544019\pi$
$632$	−10.0838	−	1.94349i	−0.401112	−	0.0773080i
$633$	4.82217	+	13.9328i	0.191664	+	0.553777i
$634$	6.08224	−	25.0713i	0.241557	−	0.995710i
$635$	7.29944	−	10.2506i	0.289669	−	0.406784i
$636$	1.79780	−	1.15538i	0.0712876	−	0.0458138i
$637$	1.26365	−	3.18024i	0.0500677	−	0.126006i
$638$	−4.67891	−	32.5425i	−0.185240	−	1.28837i
$639$	−8.94414	+	0.854062i	−0.353825	+	0.0337862i
$640$	0.898207	+	0.706358i	0.0355047	+	0.0279212i
$641$	34.6534	−	17.8651i	1.36873	−	0.705628i	0.391970	−	0.919978i	$-0.371794\pi$
$641$	34.6534	−	17.8651i	1.36873	−	0.705628i	0.976757	+	0.214350i	$0.0687634\pi$
$642$	0.643961	−	1.86060i	0.0254151	−	0.0734322i
$643$	−6.42506			−0.253380			−0.126690	−	0.991942i	$-0.540435\pi$
$643$	−6.42506			−0.253380			−0.126690	+	0.991942i	$0.540435\pi$
$644$	9.64228	−	8.24781i	0.379959	−	0.325009i
$645$	−4.01328			−0.158023
$646$	−13.9972	+	40.4421i	−0.550711	+	1.59118i
$647$	−10.2241	+	5.27089i	−0.401951	+	0.207220i	−0.647335	−	0.762206i	$-0.724116\pi$
$647$	−10.2241	+	5.27089i	−0.401951	+	0.207220i	0.245384	+	0.969426i	$0.421086\pi$
$648$	0.786053	+	0.618159i	0.0308791	+	0.0242836i
$649$	−63.4591	+	6.05961i	−2.49099	+	0.237861i
$650$	−0.257024	−	1.78764i	−0.0100813	−	0.0701172i
$651$	5.51855	−	8.17639i	0.216289	−	0.320458i
$652$	7.67063	−	4.92962i	0.300405	−	0.193059i
$653$	−3.25371	+	4.56919i	−0.127327	+	0.178806i	−0.873319	−	0.487149i	$-0.838037\pi$
$653$	−3.25371	+	4.56919i	−0.127327	+	0.178806i	0.745991	+	0.665956i	$0.231976\pi$
$654$	0.894944	−	3.68901i	0.0349951	−	0.144252i
$655$	5.98219	+	17.2844i	0.233744	+	0.675358i
$656$	−11.7699	−	2.26845i	−0.459536	−	0.0885682i
$657$	1.64355	−	0.482589i	0.0641209	−	0.0188276i
$658$	15.0732	+	20.0813i	0.587615	+	0.782852i
$659$	0.703247	−	0.451950i	0.0273946	−	0.0176055i	−0.526872	−	0.849945i	$-0.676635\pi$
$659$	0.703247	−	0.451950i	0.0273946	−	0.0176055i	0.554266	+	0.832339i	$0.312999\pi$
$660$	1.35682	+	5.59289i	0.0528141	+	0.217703i
$661$	−23.8393	−	9.54384i	−0.927243	−	0.371212i	−0.141623	−	0.989921i	$-0.545232\pi$
$661$	−23.8393	−	9.54384i	−0.927243	−	0.371212i	−0.785621	+	0.618709i	$0.787656\pi$
$662$	1.81540	+	2.54938i	0.0705576	+	0.0990843i
$663$	2.51686	−	1.00760i	0.0977469	−	0.0391319i
$664$	−7.66823	−	4.92807i	−0.297585	−	0.191246i
$665$	18.6953	+	13.9575i	0.724974	+	0.541249i
$666$	2.45958			0.0953067
$667$	−15.2140	+	27.3606i	−0.589089	+	1.05941i
$668$	−4.38893	+	7.60184i	−0.169813	+	0.294124i
$669$	0.351990	−	0.0678404i	0.0136087	−	0.00262286i
$670$	0.195287	−	4.09959i	0.00754461	−	0.158381i
$671$	3.90959	−	27.1918i	0.150928	−	1.04973i
$672$	−1.96002	−	1.77716i	−0.0756096	−	0.0685555i
$673$	6.23365	+	43.3560i	0.240290	+	1.67125i	0.650688	+	0.759345i	$0.274480\pi$
$673$	6.23365	+	43.3560i	0.240290	+	1.67125i	−0.410399	+	0.911906i	$0.634610\pi$
$674$	1.76427	+	7.27243i	0.0679572	+	0.280123i
$675$	−0.175781	−	3.69010i	−0.00676582	−	0.142032i
$676$	12.7032	+	1.21301i	0.488585	+	0.0466543i
$677$	11.8579	+	11.3064i	0.455735	+	0.434542i	0.882850	−	0.469655i	$-0.155622\pi$
$677$	11.8579	+	11.3064i	0.455735	+	0.434542i	−0.427115	+	0.904197i	$0.640470\pi$
$678$	4.82121	−	5.56397i	0.185157	−	0.213683i
$679$	37.3246	−	0.936736i	1.43239	−	0.0359486i
$680$	6.08011	−	1.78528i	0.233162	−	0.0684625i
$681$	−1.77972	+	2.49927i	−0.0681991	+	0.0957723i
$682$	−0.893503	−	18.7569i	−0.0342140	−	0.718240i
$683$	−10.3097	+	9.83024i	−0.394488	+	0.376144i	−0.861200	−	0.508266i	$-0.830287\pi$
$683$	−10.3097	+	9.83024i	−0.394488	+	0.376144i	0.466712	+	0.884409i	$0.345438\pi$
$684$	6.06609	−	4.77042i	0.231943	−	0.182402i
$685$	3.97454	−	8.70303i	0.151859	−	0.332526i
$686$	−9.57784	+	15.8513i	−0.365684	+	0.605207i
$687$	−9.72397	−	6.24922i	−0.370993	−	0.238423i
$688$	1.14872	−	3.31899i	0.0437944	−	0.126535i
$689$	−0.522372	+	0.904774i	−0.0199008	+	0.0344692i
$690$	2.19587	−	5.02092i	0.0835954	−	0.191143i
$691$	−23.4519	−	40.6199i	−0.892153	−	1.54525i	−0.837289	−	0.546761i	$-0.815861\pi$
$691$	−23.4519	−	40.6199i	−0.892153	−	1.54525i	−0.0548646	−	0.998494i	$-0.517473\pi$
$692$	−4.04108	−	4.66366i	−0.153619	−	0.177286i
$693$	−2.22672	−	13.1380i	−0.0845859	−	0.499071i
$694$	−3.63817	+	25.3041i	−0.138103	+	0.960529i
$695$	15.1137	−	1.44318i	0.573296	−	0.0547431i
$696$	6.06017	+	2.42613i	0.229710	+	0.0919621i
$697$	−48.1078	+	45.8707i	−1.82221	+	1.73748i
$698$	19.3306	+	9.96562i	0.731674	+	0.377204i
$699$	9.96926	+	21.8296i	0.377072	+	0.825673i
$700$	−0.219980	+	9.77168i	−0.00831445	+	0.369335i
$701$	12.9514	−	14.9467i	0.489166	−	0.564527i	−0.456477	−	0.889735i	$-0.650889\pi$
$701$	12.9514	−	14.9467i	0.489166	−	0.564527i	0.945643	+	0.325208i	$0.105434\pi$
$702$	−0.480036	−	0.0925194i	−0.0181178	−	0.00349192i
$703$	4.47492	−	18.4459i	0.168775	−	0.695700i
$704$	−5.01370	−	0.478750i	−0.188961	−	0.0180436i
$705$	9.63887	+	4.96918i	0.363021	+	0.187150i
$706$	−6.79278	−	1.99454i	−0.255650	−	0.0750655i
$707$	−5.12870	−	13.6965i	−0.192885	−	0.515111i
$708$	5.25797	−	11.5133i	0.197606	−	0.432698i
$709$	20.3601	−	8.15095i	0.764639	−	0.306115i	0.0436365	−	0.999047i	$-0.486106\pi$
$709$	20.3601	−	8.15095i	0.764639	−	0.306115i	0.721003	+	0.692932i	$0.243681\pi$
$710$	9.12548	−	4.70451i	0.342473	−	0.176557i
$711$	10.0838	−	1.94349i	0.378172	−	0.0728867i
$712$	−9.11490	−	15.7875i	−0.341595	−	0.591660i
$713$	−10.1358	+	14.7306i	−0.379589	+	0.551666i
$714$	−14.3328	+	3.13731i	−0.536392	+	0.117411i
$715$	−1.84246	−	2.12631i	−0.0689039	−	0.0795194i
$716$	1.07058	−	22.4743i	0.0400095	−	0.839903i
$717$	22.8629	+	17.9796i	0.853832	+	0.671461i
$718$	3.78325	+	5.31283i	0.141190	+	0.198273i
$719$	−20.3875	+	16.0329i	−0.760325	+	0.597927i	−0.921219	−	0.389045i	$-0.872805\pi$
$719$	−20.3875	+	16.0329i	−0.760325	+	0.597927i	0.160893	+	0.986972i	$0.448563\pi$
$720$	−1.09639	−	0.321930i	−0.0408602	−	0.0119976i
$721$	−5.80125	−	21.5392i	−0.216050	−	0.802162i
$722$	−16.8469	−	36.8895i	−0.626976	−	1.37289i
$723$	−0.675410	−	0.644002i	−0.0251188	−	0.0239507i
$724$	−2.32881	−	6.72864i	−0.0865494	−	0.250068i
$725$	−7.88739	−	22.7891i	−0.292930	−	0.846366i
$726$	−10.3975	−	9.91395i	−0.385886	−	0.367941i
$727$	0.992409	+	2.17307i	0.0368064	+	0.0805948i	0.927142	−	0.374710i	$-0.122258\pi$
$727$	0.992409	+	2.17307i	0.0368064	+	0.0805948i	−0.890336	+	0.455305i	$0.849530\pi$
$728$	1.24979	+	0.333150i	0.0463203	+	0.0123474i
$729$	−0.959493	−	0.281733i	−0.0355368	−	0.0104345i
$730$	−1.53857	+	1.20994i	−0.0569450	+	0.0447820i
$731$	−11.2977	−	15.8654i	−0.417861	−	0.586803i
$732$	4.28749	+	3.37172i	0.158470	+	0.124622i
$733$	−0.375956	+	7.89230i	−0.0138863	+	0.291509i	0.981233	+	0.192827i	$0.0617656\pi$
$733$	−0.375956	+	7.89230i	−0.0138863	+	0.291509i	−0.995119	+	0.0986817i	$0.968537\pi$
$734$	−10.7073	−	12.3568i	−0.395212	−	0.456099i
$735$	−0.739756	+	7.96448i	−0.0272863	+	0.293774i
$736$	3.52380	+	3.25313i	0.129889	+	0.119912i
$737$	9.04498	+	15.6664i	0.333176	+	0.577078i
$738$	11.7699	−	2.26845i	0.433254	−	0.0835029i
$739$	−7.99343	+	4.12090i	−0.294043	+	0.151590i	−0.598936	−	0.800797i	$-0.704410\pi$
$739$	−7.99343	+	4.12090i	−0.294043	+	0.151590i	0.304893	+	0.952387i	$0.401379\pi$
$740$	−2.60919	+	1.04456i	−0.0959157	+	0.0383988i
$741$	−1.56723	+	3.43176i	−0.0575737	+	0.126069i
$742$	3.59428	−	4.36465i	0.131950	−	0.160231i
$743$	14.8881	+	4.37153i	0.546190	+	0.160376i	0.543175	−	0.839620i	$-0.317222\pi$
$743$	14.8881	+	4.37153i	0.546190	+	0.160376i	0.00301515	+	0.999995i	$0.499040\pi$
$744$	3.31395	+	1.70846i	0.121495	+	0.0626352i
$745$	−8.70660	−	0.831379i	−0.318985	−	0.0304594i
$746$	−0.744093	+	3.06719i	−0.0272432	+	0.112298i
$747$	8.95052	+	1.72507i	0.327482	+	0.0631171i
$748$	−18.2904	+	21.1083i	−0.668764	+	0.771795i
$749$	0.117240	−	5.20788i	0.00428384	−	0.190292i
$750$	4.12706	+	9.03700i	0.150699	+	0.329984i
$751$	16.5708	+	8.54285i	0.604678	+	0.311733i	0.733242	−	0.679968i	$-0.238006\pi$
$751$	16.5708	+	8.54285i	0.604678	+	0.311733i	−0.128564	+	0.991701i	$0.541037\pi$
$752$	−6.86846	+	6.54906i	−0.250467	+	0.238820i
$753$	5.79561	+	2.32021i	0.211204	+	0.0845532i
$754$	−3.17679	+	0.303346i	−0.115692	+	0.0110472i
$755$	−3.48479	+	24.2372i	−0.126824	+	0.882083i
$756$	2.48013	+	0.921392i	0.0902014	+	0.0335107i
$757$	−10.7204	−	12.3720i	−0.389641	−	0.449669i	0.526711	−	0.850045i	$-0.323425\pi$
$757$	−10.7204	−	12.3720i	−0.389641	−	0.449669i	−0.916351	+	0.400375i	$0.868880\pi$
$758$	13.7849	+	23.8762i	0.500691	+	0.867222i
$759$	3.82242	+	23.8499i	0.138745	+	0.865695i
$760$	−4.40911	+	7.63681i	−0.159935	+	0.277016i
$761$	10.4767	−	30.2706i	0.379782	−	1.09731i	−0.579528	−	0.814952i	$-0.696763\pi$
$761$	10.4767	−	30.2706i	0.379782	−	1.09731i	0.959310	−	0.282355i	$-0.0911156\pi$
$762$	−9.26448	−	5.95392i	−0.335617	−	0.215688i
$763$	−0.729422	−	10.0168i	−0.0264068	−	0.362632i
$764$	−9.80607	+	21.4723i	−0.354771	+	0.776841i
$765$	−4.98106	+	3.91715i	−0.180091	+	0.141625i
$766$	−1.78257	+	1.69967i	−0.0644067	+	0.0614117i
$767$	0.294423	+	6.18070i	0.0106310	+	0.223172i
$768$	0.580057	−	0.814576i	0.0209310	−	0.0293935i
$769$	17.6676	−	5.18767i	0.637110	−	0.187072i	0.0528026	−	0.998605i	$-0.483185\pi$
$769$	17.6676	−	5.18767i	0.637110	−	0.187072i	0.584307	+	0.811533i	$0.301366\pi$
$770$	7.94175	+	12.9915i	0.286201	+	0.468180i
$771$	−13.9736	+	16.1264i	−0.503247	+	0.580778i
$772$	−7.06874	−	6.74003i	−0.254410	−	0.242579i
$773$	−34.0132	−	3.24787i	−1.22337	−	0.116818i	−0.536691	−	0.843779i	$-0.680326\pi$
$773$	−34.0132	−	3.24787i	−1.22337	−	0.116818i	−0.686679	+	0.726961i	$0.740932\pi$
$774$	0.167115	+	3.50818i	0.00600684	+	0.126099i
$775$	−3.24730	−	13.3856i	−0.116647	−	0.480824i
$776$	2.00832	+	13.9682i	0.0720945	+	0.501429i
$777$	6.19587	−	1.98943i	0.222276	−	0.0713704i
$778$	1.34789	−	9.37478i	0.0483242	−	0.336102i
$779$	4.40139	−	92.3965i	0.157696	−	3.31045i
$780$	0.548528	−	0.105720i	0.0196404	−	0.00378539i
$781$	−22.6261	+	39.1895i	−0.809624	+	1.40231i
$782$	26.0304	−	5.45352i	0.930846	−	0.195018i
$783$	−6.52777			−0.233284
$784$	−6.37492	−	2.89144i	−0.227676	−	0.103266i
$785$	−7.96961	−	5.12176i	−0.284448	−	0.182803i
$786$	14.8600	−	5.94903i	0.530037	−	0.212195i
$787$	15.9384	+	22.3823i	0.568143	+	0.797845i	0.994279	−	0.106814i	$-0.0340650\pi$
$787$	15.9384	+	22.3823i	0.568143	+	0.797845i	−0.426136	+	0.904659i	$0.640126\pi$
$788$	5.74359	+	2.29939i	0.204607	+	0.0819123i
$789$	1.74478	+	7.19207i	0.0621157	+	0.256044i
$790$	−9.87178	+	6.34421i	−0.351222	+	0.225717i
$791$	7.64458	−	17.9157i	0.271810	−	0.637009i
$792$	4.83249	−	1.41895i	0.171715	−	0.0504201i
$793$	−2.61834	−	0.504643i	−0.0929799	−	0.0179204i
$794$	8.83972	+	25.5407i	0.313710	+	0.906405i
$795$	0.575716	−	2.37313i	0.0204185	−	0.0841664i
$796$	8.68479	−	12.1961i	0.307824	−	0.432279i
$797$	−33.3381	+	21.4251i	−1.18089	+	0.758915i	−0.975551	−	0.219775i	$-0.929468\pi$
$797$	−33.3381	+	21.4251i	−1.18089	+	0.758915i	−0.205344	+	0.978690i	$0.565831\pi$
$798$	11.4224	−	16.9236i	0.404348	−	0.599090i
$799$	7.48990	+	52.0934i	0.264974	+	1.84293i
$800$	−3.67755	+	0.351164i	−0.130021	+	0.0124155i
$801$	14.3296	+	11.2689i	0.506311	+	0.398167i
$802$	22.9176	−	11.8148i	0.809249	−	0.417197i
$803$	2.82168	−	8.15271i	0.0995749	−	0.287703i
$804$	−3.59177			−0.126672
$805$	1.47040	−	14.4242i	0.0518249	−	0.508387i
$806$	−1.82272			−0.0642024
$807$	−7.73372	+	22.3451i	−0.272240	+	0.786586i
$808$	4.91333	−	2.53300i	0.172850	−	0.0891106i
$809$	5.34972	+	4.20707i	0.188086	+	0.147913i	0.707762	−	0.706451i	$-0.249705\pi$
$809$	5.34972	+	4.20707i	0.188086	+	0.147913i	−0.519676	+	0.854363i	$0.673947\pi$
$810$	1.13751	−	0.108619i	0.0399679	−	0.00381647i
$811$	7.36120	+	51.1983i	0.258487	+	1.79781i	0.543626	+	0.839328i	$0.317051\pi$
$811$	7.36120	+	51.1983i	0.258487	+	1.79781i	−0.285139	+	0.958486i	$0.592040\pi$
$812$	17.2284	+	1.20983i	0.604599	+	0.0424569i
$813$	16.1274	−	10.3644i	0.565611	−	0.363496i
$814$	7.18556	−	10.0907i	0.251854	−	0.353679i
$815$	2.45639	−	10.1254i	0.0860435	−	0.354676i
$816$	−1.81377	−	5.24056i	−0.0634948	−	0.183456i
$817$	26.6141	+	5.12944i	0.931108	+	0.179456i
$818$	−10.2224	+	3.00157i	−0.357418	+	0.104947i
$819$	−1.28408	+	0.155214i	−0.0448695	+	0.00542361i
$820$	−11.5224	+	7.40499i	−0.402379	+	0.258594i
$821$	−4.08540	−	16.8403i	−0.142582	−	0.587729i	−0.997607	−	0.0691428i	$-0.977974\pi$
$821$	−4.08540	−	16.8403i	−0.142582	−	0.587729i	0.855025	−	0.518586i	$-0.173542\pi$
$822$	−7.77320	−	3.11192i	−0.271122	−	0.108541i
$823$	−14.7562	−	20.7223i	−0.514371	−	0.722332i	0.472947	−	0.881091i	$-0.343190\pi$
$823$	−14.7562	−	20.7223i	−0.514371	−	0.722332i	−0.987317	+	0.158759i	$0.949251\pi$
$824$	7.82722	−	3.13355i	0.272674	−	0.109162i
$825$	−15.6526	−	10.0593i	−0.544954	−	0.350220i
$826$	3.93267	−	33.2559i	0.136835	−	1.15712i
$827$	−8.88572			−0.308987			−0.154493	−	0.987994i	$-0.549375\pi$
$827$	−8.88572			−0.308987			−0.154493	+	0.987994i	$0.549375\pi$
$828$	−4.48045	−	1.71044i	−0.155706	−	0.0594417i
$829$	4.63028	−	8.01989i	0.160816	−	0.278542i	−0.774345	−	0.632763i	$-0.781921\pi$
$829$	4.63028	−	8.01989i	0.160816	−	0.278542i	0.935162	+	0.354221i	$0.115254\pi$
$830$	−10.2276	+	1.97120i	−0.355004	+	0.0684215i
$831$	1.09905	−	23.0718i	0.0381255	−	0.800353i
$832$	−0.0695736	+	0.483895i	−0.00241203	+	0.0167760i
$833$	−33.5679	+	19.4962i	−1.16306	+	0.675505i
$834$	−1.89090	−	13.1515i	−0.0654764	−	0.455398i
$835$	2.36473	+	9.74754i	0.0818348	+	0.337327i
$836$	−1.84939	−	38.8234i	−0.0639624	−	1.34274i
$837$	−3.71154	−	0.354409i	−0.128289	−	0.0122502i
$838$	−6.00838	−	5.72898i	−0.207556	−	0.197904i
$839$	−30.5450	+	35.2508i	−1.05453	+	1.21699i	−0.0790599	+	0.996870i	$0.525192\pi$
$839$	−30.5450	+	35.2508i	−1.05453	+	1.21699i	−0.975472	+	0.220125i	$0.929354\pi$
$840$	−3.02229	+	0.0758505i	−0.104279	+	0.00261709i
$841$	−13.0604	+	3.83489i	−0.450359	+	0.132237i
$842$	15.3484	−	21.5539i	0.528942	−	0.742795i
$843$	−0.0195175	−	0.409723i	−0.000672219	−	0.0141116i
$844$	−10.6705	+	10.1743i	−0.367293	+	0.350213i
$845$	11.4620	−	9.01384i	0.394306	−	0.310085i
$846$	3.94242	−	8.63269i	0.135543	−	0.296798i
$847$	−34.2109	−	16.5641i	−1.17550	−	0.569148i
$848$	1.79780	+	1.15538i	0.0617369	+	0.0396759i
$849$	−1.55689	+	4.49835i	−0.0534324	+	0.154383i
$850$	−10.2434	+	17.7421i	−0.351347	+	0.608551i
$851$	−11.2629	+	3.50523i	−0.386087	+	0.120158i
$852$	−4.49241	−	7.78109i	−0.153908	−	0.266576i
$853$	−33.4391	−	38.5907i	−1.14493	−	1.32132i	−0.939460	−	0.342659i	$-0.888672\pi$
$853$	−33.4391	−	38.5907i	−1.14493	−	1.32132i	−0.205472	−	0.978663i	$-0.565873\pi$
$854$	13.5278	+	5.02570i	0.462910	+	0.171976i
$855$	1.25496	−	8.72847i	0.0429189	−	0.298507i
$856$	1.95998	−	0.187155i	0.0669906	−	0.00639683i
$857$	−17.8421	−	7.14289i	−0.609474	−	0.243997i	0.0463319	−	0.998926i	$-0.485247\pi$
$857$	−17.8421	−	7.14289i	−0.609474	−	0.243997i	−0.655806	+	0.754930i	$0.727671\pi$
$858$	−1.78198	+	1.69911i	−0.0608358	+	0.0580068i
$859$	−3.67948	−	1.89690i	−0.125542	−	0.0647215i	0.394311	−	0.918977i	$-0.370983\pi$
$859$	−3.67948	−	1.89690i	−0.125542	−	0.0647215i	−0.519853	+	0.854255i	$0.674013\pi$
$860$	−1.66717	−	3.65060i	−0.0568502	−	0.124485i
$861$	27.8144	−	15.2345i	0.947911	−	0.519189i
$862$	3.64264	−	4.20383i	0.124069	−	0.143183i
$863$	−4.73382	−	0.912369i	−0.161141	−	0.0310574i	0.108042	−	0.994146i	$-0.465542\pi$
$863$	−4.73382	−	0.912369i	−0.161141	−	0.0310574i	−0.269184	+	0.963089i	$0.586754\pi$
$864$	−0.235759	+	0.971812i	−0.00802068	+	0.0330617i
$865$	−7.01944	−	0.670275i	−0.238668	−	0.0227900i
$866$	32.2456	+	16.6238i	1.09575	+	0.564899i
$867$	−13.1961	−	3.87473i	−0.448164	−	0.131593i
$868$	9.73000	+	1.62326i	0.330258	+	0.0550969i
$869$	21.4860	−	47.0478i	0.728863	−	1.59599i
$870$	6.92484	−	2.77229i	0.234774	−	0.0939893i
$871$	1.56071	−	0.804604i	0.0528828	−	0.0272630i
$872$	3.72742	−	0.718400i	0.126226	−	0.0243281i
$873$	−7.05591	−	12.2212i	−0.238806	−	0.413625i
$874$	−20.9793	+	30.4897i	−0.709634	+	1.03133i
$875$	17.7060	+	19.4267i	0.598571	+	0.656744i
$876$	1.12173	+	1.29455i	0.0378998	+	0.0437387i
$877$	1.48679	−	31.2116i	0.0502054	−	1.05394i	−0.823448	−	0.567392i	$-0.807952\pi$
$877$	1.48679	−	31.2116i	0.0502054	−	1.05394i	0.873653	−	0.486549i	$-0.161744\pi$
$878$	−12.1805	−	9.57888i	−0.411073	−	0.323272i
$879$	−13.4314	−	18.8618i	−0.453031	−	0.636193i
$880$	−4.52383	+	3.55758i	−0.152498	+	0.119926i
$881$	−26.2712	−	7.71391i	−0.885099	−	0.259888i	−0.192574	−	0.981282i	$-0.561683\pi$
$881$	−26.2712	−	7.71391i	−0.885099	−	0.259888i	−0.692525	+	0.721394i	$0.743502\pi$
$882$	6.99291	+	0.315008i	0.235463	+	0.0106069i
$883$	9.33953	+	20.4507i	0.314300	+	0.688222i	0.999182	−	0.0404324i	$-0.0128735\pi$
$883$	9.33953	+	20.4507i	0.314300	+	0.688222i	−0.684882	+	0.728654i	$0.740146\pi$
$884$	1.96209	+	1.87085i	0.0659922	+	0.0629234i
$885$	−4.73040	−	13.6676i	−0.159011	−	0.459431i
$886$	−0.987706	−	2.85379i	−0.0331826	−	0.0958749i
$887$	13.2039	+	12.5899i	0.443345	+	0.422729i	0.878585	−	0.477586i	$-0.158488\pi$
$887$	13.2039	+	12.5899i	0.443345	+	0.422729i	−0.435240	+	0.900314i	$0.643336\pi$
$888$	1.02175	+	2.23731i	0.0342876	+	0.0750793i
$889$	−28.1538	−	7.50482i	−0.944248	−	0.251704i
$890$	−19.9870	−	5.86872i	−0.669967	−	0.196720i
$891$	−3.95896	+	3.11336i	−0.132630	+	0.104302i
$892$	0.207932	+	0.291999i	0.00696206	+	0.00977685i
$893$	−57.5690	−	45.2728i	−1.92647	−	1.51500i
$894$	−0.364197	+	7.64544i	−0.0121806	+	0.255702i
$895$	−16.8365	−	19.4303i	−0.562781	−	0.649484i
$896$	0.802339	−	2.52116i	0.0268043	−	0.0842261i
$897$	2.33003	−	0.260453i	0.0777975	−	0.00869627i
$898$	−5.56508	−	9.63901i	−0.185709	−	0.321658i
$899$	−23.8984	+	4.60605i	−0.797058	+	0.153620i
$900$	3.28361	−	1.69282i	0.109454	−	0.0564273i
$901$	11.0022	−	4.40463i	0.366538	−	0.146740i
$902$	25.0786	−	54.9144i	0.835025	−	1.82845i
$903$	3.25857	+	8.70222i	0.108438	+	0.289592i
$904$	7.06397	+	2.07417i	0.234944	+	0.0689858i
$905$	−7.23171	−	3.72821i	−0.240390	−	0.123930i
$906$	21.3319	+	2.03695i	0.708707	+	0.0676733i
$907$	5.30524	−	21.8685i	0.176157	−	0.726131i	−0.813365	−	0.581753i	$-0.802367\pi$
$907$	5.30524	−	21.8685i	0.176157	−	0.726131i	0.989523	−	0.144378i	$-0.0461180\pi$
$908$	−3.01274	−	0.580658i	−0.0999813	−	0.0192698i
$909$	−3.61996	+	4.17765i	−0.120066	+	0.138564i
$910$	1.29627	−	0.709994i	0.0429710	−	0.0235361i
$911$	7.70822	+	16.8786i	0.255385	+	0.559214i	0.993285	−	0.115696i	$-0.0369097\pi$
$911$	7.70822	+	16.8786i	0.255385	+	0.559214i	−0.737900	+	0.674910i	$0.764182\pi$
$912$	6.85927	+	3.53620i	0.227133	+	0.117095i
$913$	33.2259	−	31.6808i	1.09962	−	1.04848i
$914$	−1.91312	−	0.765899i	−0.0632805	−	0.0253337i
$915$	6.20448	−	0.592456i	0.205114	−	0.0195860i
$916$	1.64500	−	11.4413i	0.0543525	−	0.378030i
$917$	32.6216	−	27.0056i	1.07726	−	0.891803i
$918$	3.63157	+	4.19105i	0.119860	+	0.138325i
$919$	8.34066	+	14.4464i	0.275133	+	0.476544i	0.970169	−	0.242431i	$-0.0779448\pi$
$919$	8.34066	+	14.4464i	0.275133	+	0.476544i	−0.695036	+	0.718975i	$0.744611\pi$
$920$	5.47939	−	0.0883303i	0.180650	−	0.00291216i
$921$	9.63531	−	16.6888i	0.317494	−	0.549916i
$922$	−4.16576	+	12.0362i	−0.137192	+	0.396390i
$923$	3.69514	+	2.37472i	0.121627	+	0.0781649i
$924$	11.0257	−	7.48321i	0.362719	−	0.246179i
$925$	3.77462	−	8.26526i	0.124109	−	0.271760i
$926$	26.8057	−	21.0803i	0.880891	−	0.692741i
$927$	−6.10192	+	5.81817i	−0.200413	+	0.191094i
$928$	0.310604	+	6.52038i	0.0101961	+	0.214042i
$929$	−21.7534	+	30.5484i	−0.713706	+	1.00226i	0.285333	+	0.958428i	$0.407896\pi$
$929$	−21.7534	+	30.5484i	−0.713706	+	1.00226i	−0.999039	+	0.0438315i	$0.986044\pi$
$930$	4.08781	−	1.20029i	0.134045	−	0.0393591i
$931$	15.0852	−	51.8710i	0.494399	−	1.70000i
$932$	−15.7156	+	18.1367i	−0.514780	+	0.594088i
$933$	−13.5541	−	12.9238i	−0.443741	−	0.423107i
$934$	10.0749	+	0.962041i	0.329662	+	0.0314789i
$935$	1.51859	+	31.8792i	0.0496633	+	1.04256i
$936$	−0.115256	−	0.475090i	−0.00376725	−	0.0155288i
$937$	−7.44819	−	51.8033i	−0.243322	−	1.69234i	−0.635220	−	0.772331i	$-0.719091\pi$
$937$	−7.44819	−	51.8033i	−0.243322	−	1.69234i	0.391898	−	0.920009i	$-0.371819\pi$
$938$	−9.04794	+	2.90520i	−0.295426	+	0.0948582i
$939$	−2.91708	+	20.2887i	−0.0951952	+	0.662097i
$940$	−0.515997	+	10.8321i	−0.0168300	+	0.353304i
$941$	−29.5238	+	5.69025i	−0.962448	+	0.185497i	−0.646190	−	0.763176i	$-0.723639\pi$
$941$	−29.5238	+	5.69025i	−0.962448	+	0.185497i	−0.316258	+	0.948673i	$0.602427\pi$
$942$	−4.14530	+	7.17987i	−0.135061	+	0.233933i
$943$	−50.6636	+	27.1613i	−1.64983	+	0.884495i
$944$	12.6571			0.411955
$945$	2.77761	−	1.19369i	0.0903557	−	0.0388308i
$946$	14.8810	+	9.56341i	0.483822	+	0.310933i
$947$	32.1617	−	12.8756i	1.04511	−	0.418401i	0.215363	−	0.976534i	$-0.430906\pi$
$947$	32.1617	−	12.8756i	1.04511	−	0.418401i	0.829751	+	0.558133i	$0.188482\pi$
$948$	5.95682	+	8.36519i	0.193469	+	0.271689i
$949$	−0.777418	−	0.311231i	−0.0252361	−	0.0101030i
$950$	−6.72133	−	27.7057i	−0.218069	−	0.898891i
$951$	−21.7031	+	13.9478i	−0.703772	+	0.452287i
$952$	−8.80787	−	11.7343i	−0.285465	−	0.380311i
$953$	−2.21115	+	0.649253i	−0.0716262	+	0.0210314i	−0.317349	−	0.948309i	$-0.602793\pi$
$953$	−2.21115	+	0.649253i	−0.0716262	+	0.0210314i	0.245723	+	0.969340i	$0.420975\pi$
$954$	−2.09844	−	0.404440i	−0.0679393	−	0.0130942i
$955$	8.82217	+	25.4900i	0.285479	+	0.824837i
$956$	−6.85722	+	28.2659i	−0.221778	+	0.914183i
$957$	−19.0706	+	26.7809i	−0.616466	+	0.865705i
$958$	3.53452	−	2.27150i	0.114195	−	0.0733888i
$959$	−22.0984	−	1.55182i	−0.713595	−	0.0501108i
$960$	−0.162620	−	1.13105i	−0.00524855	−	0.0365044i
$961$	17.0215	−	1.62535i	0.549080	−	0.0524307i
$962$	−0.945163	−	0.743285i	−0.0304733	−	0.0239645i
$963$	−1.75002	+	0.902198i	−0.0563936	+	0.0290729i
$964$	0.305229	−	0.881903i	0.00983078	−	0.0284042i
$965$	−11.1606			−0.359272
$966$	−12.6701	−	0.684711i	−0.407653	−	0.0220302i
$967$	22.8729			0.735543			0.367771	−	0.929916i	$-0.380121\pi$
$967$	22.8729			0.735543			0.367771	+	0.929916i	$0.380121\pi$
$968$	4.69879	−	13.5763i	0.151025	−	0.436358i
$969$	38.0385	−	19.6102i	1.22197	−	0.629971i
$970$	12.6753	+	9.96799i	0.406981	+	0.320053i
$971$	−31.5087	+	3.00871i	−1.01116	+	0.0965541i	−0.587464	−	0.809250i	$-0.699874\pi$
$971$	−31.5087	+	3.00871i	−1.01116	+	0.0965541i	−0.423696	+	0.905804i	$0.639268\pi$
$972$	−0.142315	−	0.989821i	−0.00456475	−	0.0317485i
$973$	−15.4009	−	31.6001i	−0.493730	−	1.01305i
$974$	−28.8355	+	18.5315i	−0.923950	+	0.593787i
$975$	−1.04760	+	1.47115i	−0.0335500	+	0.0471144i
$976$	−1.28594	+	5.30071i	−0.0411619	+	0.169671i
$977$	−1.54803	−	4.47273i	−0.0495258	−	0.143095i	0.917526	−	0.397677i	$-0.130184\pi$
$977$	−1.54803	−	4.47273i	−0.0495258	−	0.143095i	−0.967051	+	0.254581i	$0.918062\pi$
$978$	−8.95332	−	1.72561i	−0.286296	−	0.0551790i
$979$	88.0954	−	25.8671i	2.81554	−	0.826717i
$980$	−7.55205	+	2.63566i	−0.241241	+	0.0841930i
$981$	−3.19341	+	2.05228i	−0.101958	+	0.0655243i
$982$	−9.76410	−	40.2482i	−0.311585	−	1.28437i
$983$	14.6854	+	5.87913i	0.468390	+	0.187515i	0.593837	−	0.804585i	$-0.297612\pi$
$983$	14.6854	+	5.87913i	0.468390	+	0.187515i	−0.125447	+	0.992100i	$0.540037\pi$
$984$	6.95283	+	9.76389i	0.221648	+	0.311261i
$985$	6.56309	−	2.62746i	0.209117	−	0.0837179i
$986$	30.4535	+	19.5713i	0.969837	+	0.623276i
$987$	2.94871	−	24.9353i	0.0938584	−	0.793698i
$988$	−3.77269			−0.120025
$989$	−5.76489	−	15.8265i	−0.183313	−	0.503253i
$990$	2.87756	−	4.98408i	0.0914548	−	0.158404i
$991$	−16.6638	+	3.21169i	−0.529344	+	0.102023i	−0.446919	−	0.894575i	$-0.647479\pi$
$991$	−16.6638	+	3.21169i	−0.529344	+	0.102023i	−0.0824253	+	0.996597i	$0.526267\pi$
$992$	−0.177405	+	3.72420i	−0.00563262	+	0.118243i
$993$	0.445402	−	3.09784i	0.0141344	−	0.0983070i
$994$	−17.6105	−	15.9675i	−0.558571	−	0.506458i
$995$	−2.43480	−	16.9344i	−0.0771884	−	0.536857i
$996$	2.14900	+	8.85830i	0.0680937	+	0.280686i
$997$	2.28618	+	47.9929i	0.0724041	+	1.51995i	0.684411	+	0.729097i	$0.260060\pi$
$997$	2.28618	+	47.9929i	0.0724041	+	1.51995i	−0.612006	+	0.790853i	$0.709637\pi$
$998$	41.4430	+	3.95732i	1.31185	+	0.125267i
$999$	−1.78008	−	1.69730i	−0.0563193	−	0.0537003i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.y.b.151.4	✓	160
7.2	even	3	inner	966.2.y.b.289.5	yes	160
23.16	even	11	inner	966.2.y.b.361.5	yes	160
161.16	even	33	inner	966.2.y.b.499.4	yes	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.y.b.151.4	✓	160	1.1	even	1	trivial
966.2.y.b.289.5	yes	160	7.2	even	3	inner
966.2.y.b.361.5	yes	160	23.16	even	11	inner
966.2.y.b.499.4	yes	160	161.16	even	33	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.y (of order \(33\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.327068 - 0.945001i) q^{2} +(-0.888835 + 0.458227i) q^{3} +(-0.786053 - 0.618159i) q^{4} +(-1.13751 + 0.108619i) q^{5} +(0.142315 + 0.989821i) q^{6} +(1.15912 + 2.37833i) q^{7} +(-0.841254 + 0.540641i) q^{8} +(0.580057 - 0.814576i) q^{9} +O(q^{10})\)	\(q+(0.327068 - 0.945001i) q^{2} +(-0.888835 + 0.458227i) q^{3} +(-0.786053 - 0.618159i) q^{4} +(-1.13751 + 0.108619i) q^{5} +(0.142315 + 0.989821i) q^{6} +(1.15912 + 2.37833i) q^{7} +(-0.841254 + 0.540641i) q^{8} +(0.580057 - 0.814576i) q^{9} +(-0.269397 + 1.11047i) q^{10} +(-1.64728 - 4.75950i) q^{11} +(0.981929 + 0.189251i) q^{12} +(-0.469068 + 0.137731i) q^{13} +(2.62663 - 0.317494i) q^{14} +(0.961283 - 0.617779i) q^{15} +(0.235759 + 0.971812i) q^{16} +(5.14832 + 2.06108i) q^{17} +(-0.580057 - 0.814576i) q^{18} +(-7.16435 + 2.86817i) q^{19} +(0.961283 + 0.617779i) q^{20} +(-2.12008 - 1.58280i) q^{21} -5.03651 q^{22} +(3.81707 + 2.90344i) q^{23} +(0.500000 - 0.866025i) q^{24} +(-3.62752 + 0.699148i) q^{25} +(-0.0232614 + 0.488317i) q^{26} +(-0.142315 + 0.989821i) q^{27} +(0.559055 - 2.58601i) q^{28} +(0.928999 + 6.46133i) q^{29} +(-0.269397 - 1.11047i) q^{30} +(0.177405 + 3.72420i) q^{31} +(0.995472 + 0.0950560i) q^{32} +(3.64509 + 3.47559i) q^{33} +(3.63157 - 4.19105i) q^{34} +(-1.57684 - 2.57946i) q^{35} +(-0.959493 + 0.281733i) q^{36} +(-1.42670 + 2.00351i) q^{37} +(0.367197 + 7.70840i) q^{38} +(0.353812 - 0.337360i) q^{39} +(0.898207 - 0.706358i) q^{40} +(-4.97936 + 10.9033i) q^{41} +(-2.18916 + 1.48579i) q^{42} +(-2.95462 - 1.89882i) q^{43} +(-1.64728 + 4.75950i) q^{44} +(-0.571340 + 0.989590i) q^{45} +(3.99219 - 2.65752i) q^{46} +(4.74515 + 8.21885i) q^{47} +(-0.654861 - 0.755750i) q^{48} +(-4.31288 + 5.51353i) q^{49} +(-0.525751 + 3.65668i) q^{50} +(-5.52045 + 0.527139i) q^{51} +(0.453852 + 0.181695i) q^{52} +(1.54666 - 1.47474i) q^{53} +(0.888835 + 0.458227i) q^{54} +(2.39076 + 5.23504i) q^{55} +(-2.26093 - 1.37411i) q^{56} +(5.05366 - 5.83223i) q^{57} +(6.40981 + 1.23539i) q^{58} +(2.98403 - 12.3004i) q^{59} +(-1.13751 - 0.108619i) q^{60} +(4.84812 + 2.49938i) q^{61} +(3.57739 + 1.05042i) q^{62} +(2.60968 + 0.435374i) q^{63} +(0.415415 - 0.909632i) q^{64} +(0.518608 - 0.207619i) q^{65} +(4.47663 - 2.30786i) q^{66} +(-3.52686 + 0.679746i) q^{67} +(-2.77278 - 4.80260i) q^{68} +(-4.72318 - 0.831595i) q^{69} +(-2.95332 + 0.646453i) q^{70} +(-5.88381 - 6.79028i) q^{71} +(-0.0475819 + 0.998867i) q^{72} +(1.34646 + 1.05886i) q^{73} +(1.42670 + 2.00351i) q^{74} +(2.90390 - 2.28365i) q^{75} +(7.40455 + 2.17417i) q^{76} +(9.41026 - 9.43461i) q^{77} +(-0.203084 - 0.444693i) q^{78} +(7.43230 + 7.08668i) q^{79} +(-0.373734 - 1.07983i) q^{80} +(-0.327068 - 0.945001i) q^{81} +(8.67501 + 8.27161i) q^{82} +(3.78661 + 8.29152i) q^{83} +(0.688072 + 2.55471i) q^{84} +(-6.08011 - 1.78528i) q^{85} +(-2.76074 + 2.17107i) q^{86} +(-3.78648 - 5.31737i) q^{87} +(3.95896 + 3.11336i) q^{88} +(-0.867409 + 18.2091i) q^{89} +(0.748296 + 0.863580i) q^{90} +(-0.871275 - 0.955951i) q^{91} +(-1.20564 - 4.64181i) q^{92} +(-1.86421 - 3.22891i) q^{93} +(9.31881 - 1.79605i) q^{94} +(7.83795 - 4.04075i) q^{95} +(-0.928368 + 0.371662i) q^{96} +(5.86226 - 12.8366i) q^{97} +(3.79969 + 5.87898i) q^{98} +(-4.83249 - 1.41895i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q - 8 q^{2} + 8 q^{3} + 8 q^{4} + 6 q^{5} + 16 q^{6} - 10 q^{7} + 16 q^{8} + 8 q^{9}+O(q^{10}) \) 160 * q - 8 * q^2 + 8 * q^3 + 8 * q^4 + 6 * q^5 + 16 * q^6 - 10 * q^7 + 16 * q^8 + 8 * q^9	\( 160 q - 8 q^{2} + 8 q^{3} + 8 q^{4} + 6 q^{5} + 16 q^{6} - 10 q^{7} + 16 q^{8} + 8 q^{9} - 6 q^{10} + 8 q^{11} + 8 q^{12} + 4 q^{13} - 13 q^{14} + 10 q^{15} + 8 q^{16} + 9 q^{17} - 8 q^{18} - 8 q^{19} + 10 q^{20} - 3 q^{21} - 28 q^{22} + 22 q^{23} + 80 q^{24} + 46 q^{25} + 2 q^{26} - 16 q^{27} - 14 q^{28} + 62 q^{29} - 6 q^{30} + 7 q^{31} - 8 q^{32} - 14 q^{33} - 4 q^{34} + 24 q^{35} - 16 q^{36} + 15 q^{37} + 19 q^{38} - 2 q^{39} + 5 q^{40} - 14 q^{41} + 10 q^{42} - 56 q^{43} + 8 q^{44} - 16 q^{45} + 66 q^{47} - 16 q^{48} + 42 q^{49} + 4 q^{50} + 9 q^{51} - 2 q^{52} + 12 q^{53} - 8 q^{54} - 14 q^{55} + 10 q^{56} - 6 q^{57} - 13 q^{58} + 62 q^{59} + 6 q^{60} + 16 q^{61} - 8 q^{62} + 2 q^{63} - 16 q^{64} + 70 q^{65} - 8 q^{66} - 14 q^{67} - 46 q^{68} + 22 q^{69} + 24 q^{70} - 108 q^{71} - 8 q^{72} + 40 q^{73} - 15 q^{74} + 2 q^{75} + 16 q^{76} + 29 q^{77} + 18 q^{78} + 22 q^{79} + 6 q^{80} + 8 q^{81} - 7 q^{82} - 18 q^{83} - 9 q^{84} + 26 q^{85} - 6 q^{86} + 2 q^{87} + 3 q^{88} + 112 q^{89} + 12 q^{90} + 18 q^{91} - 66 q^{92} - 26 q^{93} + 23 q^{95} - 8 q^{96} + 8 q^{97} + 9 q^{98} + 28 q^{99}+O(q^{100}) \) 160 * q - 8 * q^2 + 8 * q^3 + 8 * q^4 + 6 * q^5 + 16 * q^6 - 10 * q^7 + 16 * q^8 + 8 * q^9 - 6 * q^10 + 8 * q^11 + 8 * q^12 + 4 * q^13 - 13 * q^14 + 10 * q^15 + 8 * q^16 + 9 * q^17 - 8 * q^18 - 8 * q^19 + 10 * q^20 - 3 * q^21 - 28 * q^22 + 22 * q^23 + 80 * q^24 + 46 * q^25 + 2 * q^26 - 16 * q^27 - 14 * q^28 + 62 * q^29 - 6 * q^30 + 7 * q^31 - 8 * q^32 - 14 * q^33 - 4 * q^34 + 24 * q^35 - 16 * q^36 + 15 * q^37 + 19 * q^38 - 2 * q^39 + 5 * q^40 - 14 * q^41 + 10 * q^42 - 56 * q^43 + 8 * q^44 - 16 * q^45 + 66 * q^47 - 16 * q^48 + 42 * q^49 + 4 * q^50 + 9 * q^51 - 2 * q^52 + 12 * q^53 - 8 * q^54 - 14 * q^55 + 10 * q^56 - 6 * q^57 - 13 * q^58 + 62 * q^59 + 6 * q^60 + 16 * q^61 - 8 * q^62 + 2 * q^63 - 16 * q^64 + 70 * q^65 - 8 * q^66 - 14 * q^67 - 46 * q^68 + 22 * q^69 + 24 * q^70 - 108 * q^71 - 8 * q^72 + 40 * q^73 - 15 * q^74 + 2 * q^75 + 16 * q^76 + 29 * q^77 + 18 * q^78 + 22 * q^79 + 6 * q^80 + 8 * q^81 - 7 * q^82 - 18 * q^83 - 9 * q^84 + 26 * q^85 - 6 * q^86 + 2 * q^87 + 3 * q^88 + 112 * q^89 + 12 * q^90 + 18 * q^91 - 66 * q^92 - 26 * q^93 + 23 * q^95 - 8 * q^96 + 8 * q^97 + 9 * q^98 + 28 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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