LMFDB - Embedded newform 729.2.k.a.4.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [729,2,Mod(4,729)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(729, base_ring=CyclotomicField(486))

chi = DirichletCharacter(H, H._module([2]))

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

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

chi := DirichletCharacter("729.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 729 = 3^{6} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	729.k (of order $243$, degree $162$, 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:	$5.82109430735$
Analytic rank:	$0$
Dimension:	$12960$
Relative dimension:	$80$ over $\Q(\zeta_{243})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{243}]$

Embedding invariants

Embedding label			4.1
Character	$\chi$	$=$	729.4
Dual form			729.2.k.a.547.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.72490 - 0.0352304i) q^{2} +(-1.51002 - 0.848437i) q^{3} +(5.42450 + 0.140291i) q^{4} +(0.633611 + 0.194162i) q^{5} +(4.08476 + 2.36510i) q^{6} +(1.09035 - 2.71893i) q^{7} +(-9.33012 - 0.362051i) q^{8} +(1.56031 + 2.56231i) q^{9} +O(q^{10})$	\(q+(-2.72490 - 0.0352304i) q^{2} +(-1.51002 - 0.848437i) q^{3} +(5.42450 + 0.140291i) q^{4} +(0.633611 + 0.194162i) q^{5} +(4.08476 + 2.36510i) q^{6} +(1.09035 - 2.71893i) q^{7} +(-9.33012 - 0.362051i) q^{8} +(1.56031 + 2.56231i) q^{9} +(-1.71968 - 0.551395i) q^{10} +(1.46606 + 0.833840i) q^{11} +(-8.07206 - 4.81419i) q^{12} +(2.23325 + 4.99855i) q^{13} +(-3.06688 + 7.37039i) q^{14} +(-0.792029 - 0.830767i) q^{15} +(14.5728 + 0.754280i) q^{16} +(1.23299 + 0.560463i) q^{17} +(-4.16141 - 7.03701i) q^{18} +(1.81231 + 2.64242i) q^{19} +(3.40978 + 1.14212i) q^{20} +(-3.95329 + 3.18054i) q^{21} +(-3.96548 - 2.32378i) q^{22} +(-0.783008 + 2.38882i) q^{23} +(13.7815 + 8.46272i) q^{24} +(-3.77781 - 2.55527i) q^{25} +(-5.90927 - 13.6992i) q^{26} +(-0.182133 - 5.19296i) q^{27} +(6.29604 - 14.5959i) q^{28} +(-6.01114 + 3.84319i) q^{29} +(2.12893 + 2.29166i) q^{30} +(1.42648 + 5.25570i) q^{31} +(-21.0474 - 1.36244i) q^{32} +(-1.50631 - 2.50297i) q^{33} +(-3.34003 - 1.57064i) q^{34} +(1.21877 - 1.51104i) q^{35} +(8.10442 + 14.1182i) q^{36} +(-9.92713 - 1.94962i) q^{37} +(-4.84528 - 7.26417i) q^{38} +(0.868716 - 9.44268i) q^{39} +(-5.84136 - 2.04095i) q^{40} +(-4.95892 + 1.87785i) q^{41} +(10.8844 - 8.52737i) q^{42} +(5.12901 - 2.25187i) q^{43} +(7.83565 + 4.72884i) q^{44} +(0.491124 + 1.92646i) q^{45} +(2.21778 - 6.48170i) q^{46} +(-2.78011 + 10.2430i) q^{47} +(-21.3652 - 13.5030i) q^{48} +(-1.14325 - 1.09266i) q^{49} +(10.2041 + 7.09596i) q^{50} +(-1.38632 - 1.89243i) q^{51} +(11.4130 + 27.4280i) q^{52} +(2.74430 - 2.90879i) q^{53} +(0.313345 + 14.1567i) q^{54} +(0.767010 + 0.812983i) q^{55} +(-11.1575 + 24.9732i) q^{56} +(-0.494700 - 5.52773i) q^{57} +(16.5152 - 10.2605i) q^{58} +(14.3490 - 2.43458i) q^{59} +(-4.17981 - 4.61761i) q^{60} +(-1.85519 + 3.41421i) q^{61} +(-3.70186 - 14.3715i) q^{62} +(8.66802 - 1.44855i) q^{63} +(28.2073 + 2.19245i) q^{64} +(0.444479 + 3.60075i) q^{65} +(4.01637 + 6.87341i) q^{66} +(-7.07605 + 3.66904i) q^{67} +(6.60974 + 3.21321i) q^{68} +(3.20912 - 2.94282i) q^{69} +(-3.37426 + 4.07449i) q^{70} +(6.79467 + 5.26626i) q^{71} +(-13.6302 - 24.4716i) q^{72} +(2.20463 - 0.706886i) q^{73} +(26.9817 + 5.66227i) q^{74} +(3.53656 + 7.06374i) q^{75} +(9.46019 + 14.5881i) q^{76} +(3.86567 - 3.07693i) q^{77} +(-2.69983 + 25.6997i) q^{78} +(-2.76639 + 14.5839i) q^{79} +(9.08700 + 3.30740i) q^{80} +(-4.13088 + 7.99599i) q^{81} +(13.5787 - 4.94225i) q^{82} +(-0.646758 - 3.96720i) q^{83} +(-21.8908 + 16.6982i) q^{84} +(0.672416 + 0.594516i) q^{85} +(-14.0554 + 5.95543i) q^{86} +(12.3376 - 0.703210i) q^{87} +(-13.3766 - 8.31061i) q^{88} +(2.95081 + 1.20554i) q^{89} +(-1.27039 - 5.26671i) q^{90} +(16.0257 - 0.621871i) q^{91} +(-4.58256 + 12.8483i) q^{92} +(2.30512 - 9.14649i) q^{93} +(7.93639 - 27.8132i) q^{94} +(0.635244 + 2.02615i) q^{95} +(30.6260 + 19.9147i) q^{96} +(-0.516441 + 2.24357i) q^{97} +(3.07675 + 3.01766i) q^{98} +(0.150945 + 5.05754i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12960 q - 162 q^{2} - 162 q^{3} - 162 q^{4} - 162 q^{5} - 162 q^{6} - 162 q^{7} - 162 q^{8} - 162 q^{9}+O(q^{10}) $ 12960 * q - 162 * q^2 - 162 * q^3 - 162 * q^4 - 162 * q^5 - 162 * q^6 - 162 * q^7 - 162 * q^8 - 162 * q^9	\( 12960 q - 162 q^{2} - 162 q^{3} - 162 q^{4} - 162 q^{5} - 162 q^{6} - 162 q^{7} - 162 q^{8} - 162 q^{9} - 162 q^{10} - 162 q^{11} - 162 q^{12} - 162 q^{13} - 162 q^{14} - 162 q^{15} - 162 q^{16} - 162 q^{17} - 162 q^{18} - 162 q^{19} - 162 q^{20} - 162 q^{21} - 162 q^{22} - 162 q^{23} - 162 q^{24} - 162 q^{25} - 162 q^{26} - 162 q^{27} - 162 q^{28} - 162 q^{29} - 162 q^{30} - 162 q^{31} - 162 q^{32} - 162 q^{33} - 162 q^{34} - 162 q^{35} - 162 q^{36} - 162 q^{37} - 162 q^{38} - 162 q^{39} - 162 q^{40} - 162 q^{41} - 162 q^{42} - 162 q^{43} - 162 q^{44} - 162 q^{45} - 162 q^{46} - 162 q^{47} - 162 q^{48} - 162 q^{49} - 162 q^{50} - 162 q^{51} - 162 q^{52} - 162 q^{53} - 162 q^{54} - 162 q^{55} - 162 q^{56} - 162 q^{57} - 162 q^{58} - 162 q^{59} - 162 q^{60} - 162 q^{61} - 162 q^{62} - 162 q^{63} - 162 q^{64} - 162 q^{65} - 162 q^{66} - 162 q^{67} - 162 q^{68} - 162 q^{69} - 162 q^{70} - 162 q^{71} - 162 q^{72} - 162 q^{73} - 162 q^{74} - 162 q^{75} - 162 q^{76} - 162 q^{77} - 162 q^{78} - 162 q^{79} - 162 q^{80} - 162 q^{81} - 162 q^{82} - 162 q^{83} - 162 q^{84} - 162 q^{85} - 162 q^{86} - 162 q^{87} - 162 q^{88} - 162 q^{89} - 162 q^{90} - 162 q^{91} - 162 q^{92} - 162 q^{93} - 162 q^{94} - 162 q^{95} - 162 q^{96} - 162 q^{97} - 162 q^{98} - 162 q^{99}+O(q^{100}) \) 12960 * q - 162 * q^2 - 162 * q^3 - 162 * q^4 - 162 * q^5 - 162 * q^6 - 162 * q^7 - 162 * q^8 - 162 * q^9 - 162 * q^10 - 162 * q^11 - 162 * q^12 - 162 * q^13 - 162 * q^14 - 162 * q^15 - 162 * q^16 - 162 * q^17 - 162 * q^18 - 162 * q^19 - 162 * q^20 - 162 * q^21 - 162 * q^22 - 162 * q^23 - 162 * q^24 - 162 * q^25 - 162 * q^26 - 162 * q^27 - 162 * q^28 - 162 * q^29 - 162 * q^30 - 162 * q^31 - 162 * q^32 - 162 * q^33 - 162 * q^34 - 162 * q^35 - 162 * q^36 - 162 * q^37 - 162 * q^38 - 162 * q^39 - 162 * q^40 - 162 * q^41 - 162 * q^42 - 162 * q^43 - 162 * q^44 - 162 * q^45 - 162 * q^46 - 162 * q^47 - 162 * q^48 - 162 * q^49 - 162 * q^50 - 162 * q^51 - 162 * q^52 - 162 * q^53 - 162 * q^54 - 162 * q^55 - 162 * q^56 - 162 * q^57 - 162 * q^58 - 162 * q^59 - 162 * q^60 - 162 * q^61 - 162 * q^62 - 162 * q^63 - 162 * q^64 - 162 * q^65 - 162 * q^66 - 162 * q^67 - 162 * q^68 - 162 * q^69 - 162 * q^70 - 162 * q^71 - 162 * q^72 - 162 * q^73 - 162 * q^74 - 162 * q^75 - 162 * q^76 - 162 * q^77 - 162 * q^78 - 162 * q^79 - 162 * q^80 - 162 * q^81 - 162 * q^82 - 162 * q^83 - 162 * q^84 - 162 * q^85 - 162 * q^86 - 162 * q^87 - 162 * q^88 - 162 * q^89 - 162 * q^90 - 162 * q^91 - 162 * q^92 - 162 * q^93 - 162 * q^94 - 162 * q^95 - 162 * q^96 - 162 * q^97 - 162 * q^98 - 162 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/729\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{243}\right)$

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 $

$2$	−2.72490	−	0.0352304i	−1.92679	−	0.0249117i	−0.959935	−	0.280222i	$-0.909592\pi$
$2$	−2.72490	−	0.0352304i	−1.92679	−	0.0249117i	−0.966859	+	0.255310i	$0.917822\pi$
$3$	−1.51002	−	0.848437i	−0.871809	−	0.489845i
$3$	−1.51002	−	0.848437i	−0.871809	−	0.489845i
$4$	5.42450	+	0.140291i	2.71225	+	0.0701456i
$5$	0.633611	+	0.194162i	0.283359	+	0.0868319i	0.431435	−	0.902144i	$-0.358007\pi$
$5$	0.633611	+	0.194162i	0.283359	+	0.0868319i	−0.148076	+	0.988976i	$0.547308\pi$
$6$	4.08476	+	2.36510i	1.66759	+	0.965550i
$7$	1.09035	−	2.71893i	0.412113	−	1.02766i	−0.566886	−	0.823796i	$-0.691852\pi$
$7$	1.09035	−	2.71893i	0.412113	−	1.02766i	0.979000	−	0.203862i	$-0.0653495\pi$
$8$	−9.33012	−	0.362051i	−3.29869	−	0.128004i
$9$	1.56031	+	2.56231i	0.520103	+	0.854104i
$10$	−1.71968	−	0.551395i	−0.543812	−	0.174366i
$11$	1.46606	+	0.833840i	0.442033	+	0.251412i	0.699160	−	0.714966i	$-0.253558\pi$
$11$	1.46606	+	0.833840i	0.442033	+	0.251412i	−0.257127	+	0.966378i	$0.582776\pi$
$12$	−8.07206	−	4.81419i	−2.33020	−	1.38974i
$13$	2.23325	+	4.99855i	0.619391	+	1.38635i	0.903928	+	0.427684i	$0.140670\pi$
$13$	2.23325	+	4.99855i	0.619391	+	1.38635i	−0.284537	+	0.958665i	$0.591840\pi$
$14$	−3.06688	+	7.37039i	−0.819658	+	1.96982i
$15$	−0.792029	−	0.830767i	−0.204501	−	0.214503i
$16$	14.5728	+	0.754280i	3.64319	+	0.188570i
$17$	1.23299	+	0.560463i	0.299044	+	0.135932i	0.557713	−	0.830034i	$-0.311679\pi$
$17$	1.23299	+	0.560463i	0.299044	+	0.135932i	−0.258669	+	0.965966i	$0.583284\pi$
$18$	−4.16141	−	7.03701i	−0.980854	−	1.65864i
$19$	1.81231	+	2.64242i	0.415773	+	0.606212i	0.974839	−	0.222911i	$-0.0715560\pi$
$19$	1.81231	+	2.64242i	0.415773	+	0.606212i	−0.559065	+	0.829124i	$0.688840\pi$
$20$	3.40978	+	1.14212i	0.762450	+	0.255386i
$21$	−3.95329	+	3.18054i	−0.862678	+	0.694050i
$22$	−3.96548	−	2.32378i	−0.845444	−	0.495431i
$23$	−0.783008	+	2.38882i	−0.163268	+	0.498103i	−0.998671	−	0.0515358i	$-0.983588\pi$
$23$	−0.783008	+	2.38882i	−0.163268	+	0.498103i	0.835403	+	0.549638i	$0.185234\pi$
$24$	13.7815	+	8.46272i	2.81313	+	1.72745i
$25$	−3.77781	−	2.55527i	−0.755561	−	0.511055i
$26$	−5.90927	−	13.6992i	−1.15890	−	2.68664i
$27$	−0.182133	−	5.19296i	−0.0350516	−	0.999386i
$28$	6.29604	−	14.5959i	1.18984	−	2.75836i
$29$	−6.01114	+	3.84319i	−1.11624	+	0.713663i	−0.961640	−	0.274314i	$-0.911549\pi$
$29$	−6.01114	+	3.84319i	−1.11624	+	0.713663i	−0.154601	+	0.987977i	$0.549409\pi$
$30$	2.12893	+	2.29166i	0.388688	+	0.418398i
$31$	1.42648	+	5.25570i	0.256204	+	0.943952i	0.969901	+	0.243498i	$0.0782949\pi$
$31$	1.42648	+	5.25570i	0.256204	+	0.943952i	−0.713697	+	0.700454i	$0.752981\pi$
$32$	−21.0474	−	1.36244i	−3.72069	−	0.240848i
$33$	−1.50631	−	2.50297i	−0.262215	−	0.435711i
$34$	−3.34003	−	1.57064i	−0.572811	−	0.269363i
$35$	1.21877	−	1.51104i	0.206010	−	0.255412i
$36$	8.10442	+	14.1182i	1.35074	+	2.35303i
$37$	−9.92713	−	1.94962i	−1.63201	−	0.320516i	−0.708975	−	0.705234i	$-0.750842\pi$
$37$	−9.92713	−	1.94962i	−1.63201	−	0.320516i	−0.923034	+	0.384717i	$0.874299\pi$
$38$	−4.84528	−	7.26417i	−0.786008	−	1.17840i
$39$	0.868716	−	9.44268i	0.139106	−	1.51204i
$40$	−5.84136	−	2.04095i	−0.923601	−	0.322703i
$41$	−4.95892	+	1.87785i	−0.774454	+	0.293271i	−0.709582	−	0.704622i	$-0.751116\pi$
$41$	−4.95892	+	1.87785i	−0.774454	+	0.293271i	−0.0648713	+	0.997894i	$0.520664\pi$
$42$	10.8844	−	8.52737i	1.67949	−	1.31580i
$43$	5.12901	−	2.25187i	0.782166	−	0.343407i	0.0275897	−	0.999619i	$-0.491217\pi$
$43$	5.12901	−	2.25187i	0.782166	−	0.343407i	0.754577	+	0.656212i	$0.227842\pi$
$44$	7.83565	+	4.72884i	1.18127	+	0.712900i
$45$	0.491124	+	1.92646i	0.0732124	+	0.287180i
$46$	2.21778	−	6.48170i	0.326993	−	0.955674i
$47$	−2.78011	+	10.2430i	−0.405521	+	1.49409i	0.408230	+	0.912879i	$0.366146\pi$
$47$	−2.78011	+	10.2430i	−0.405521	+	1.49409i	−0.813751	+	0.581214i	$0.802578\pi$
$48$	−21.3652	−	13.5030i	−3.08379	−	1.94900i
$49$	−1.14325	−	1.09266i	−0.163322	−	0.156094i
$50$	10.2041	+	7.09596i	1.44308	+	1.00352i
$51$	−1.38632	−	1.89243i	−0.194124	−	0.264993i
$52$	11.4130	+	27.4280i	1.58270	+	3.80357i
$53$	2.74430	−	2.90879i	0.376959	−	0.399553i	−0.510922	−	0.859627i	$-0.670696\pi$
$53$	2.74430	−	2.90879i	0.376959	−	0.399553i	0.887880	+	0.460074i	$0.152177\pi$
$54$	0.313345	+	14.1567i	0.0426408	+	1.92648i
$55$	0.767010	+	0.812983i	0.103424	+	0.109623i
$56$	−11.1575	+	24.9732i	−1.49098	+	3.33718i
$57$	−0.494700	−	5.52773i	−0.0655247	−	0.732166i
$58$	16.5152	−	10.2605i	2.16855	−	1.34727i
$59$	14.3490	−	2.43458i	1.86808	−	0.316955i	0.880494	−	0.474056i	$-0.157211\pi$
$59$	14.3490	−	2.43458i	1.86808	−	0.316955i	0.987583	+	0.157101i	$0.0502148\pi$
$60$	−4.17981	−	4.61761i	−0.539611	−	0.596131i
$61$	−1.85519	+	3.41421i	−0.237533	+	0.437145i	−0.969810	−	0.243863i	$-0.921585\pi$
$61$	−1.85519	+	3.41421i	−0.237533	+	0.437145i	0.732277	+	0.681007i	$0.238458\pi$
$62$	−3.70186	−	14.3715i	−0.470137	−	1.82518i
$63$	8.66802	−	1.44855i	1.09207	−	0.182501i
$64$	28.2073	+	2.19245i	3.52592	+	0.274056i
$65$	0.444479	+	3.60075i	0.0551309	+	0.446618i
$66$	4.01637	+	6.87341i	0.494381	+	0.846059i
$67$	−7.07605	+	3.66904i	−0.864477	+	0.448244i	−0.834307	−	0.551301i	$-0.814132\pi$
$67$	−7.07605	+	3.66904i	−0.864477	+	0.448244i	−0.0301705	+	0.999545i	$0.509605\pi$
$68$	6.60974	+	3.21321i	0.801548	+	0.389659i
$69$	3.20912	−	2.94282i	0.386332	−	0.354274i
$70$	−3.37426	+	4.07449i	−0.403301	+	0.486994i
$71$	6.79467	+	5.26626i	0.806378	+	0.624990i	0.930092	−	0.367328i	$-0.119727\pi$
$71$	6.79467	+	5.26626i	0.806378	+	0.624990i	−0.123713	+	0.992318i	$0.539480\pi$
$72$	−13.6302	−	24.4716i	−1.60633	−	2.88400i
$73$	2.20463	−	0.706886i	0.258032	−	0.0827348i	−0.173494	−	0.984835i	$-0.555506\pi$
$73$	2.20463	−	0.706886i	0.258032	−	0.0827348i	0.431527	+	0.902100i	$0.357975\pi$
$74$	26.9817	+	5.66227i	3.13656	+	0.658225i
$75$	3.53656	+	7.06374i	0.408367	+	0.815651i
$76$	9.46019	+	14.5881i	1.08516	+	1.67336i
$77$	3.86567	−	3.07693i	0.440534	−	0.350649i
$78$	−2.69983	+	25.6997i	−0.305696	+	2.90992i
$79$	−2.76639	+	14.5839i	−0.311244	+	1.64081i	0.384933	+	0.922944i	$0.374225\pi$
$79$	−2.76639	+	14.5839i	−0.311244	+	1.64081i	−0.696177	+	0.717870i	$0.745117\pi$
$80$	9.08700	+	3.30740i	1.01596	+	0.369778i
$81$	−4.13088	+	7.99599i	−0.458986	+	0.888443i
$82$	13.5787	−	4.94225i	1.49952	−	0.545780i
$83$	−0.646758	−	3.96720i	−0.0709909	−	0.435457i	−0.998151	−	0.0607904i	$-0.980638\pi$
$83$	−0.646758	−	3.96720i	−0.0709909	−	0.435457i	0.927160	−	0.374666i	$-0.122243\pi$
$84$	−21.8908	+	16.6982i	−2.38848	+	1.82192i
$85$	0.672416	+	0.594516i	0.0729337	+	0.0644843i
$86$	−14.0554	+	5.95543i	−1.51563	+	0.642190i
$87$	12.3376	−	0.703210i	1.32273	−	0.0753921i
$88$	−13.3766	−	8.31061i	−1.42595	−	0.885914i
$89$	2.95081	+	1.20554i	0.312785	+	0.127787i	0.529156	−	0.848524i	$-0.322509\pi$
$89$	2.95081	+	1.20554i	0.312785	+	0.127787i	−0.216371	+	0.976311i	$0.569422\pi$
$90$	−1.27039	−	5.26671i	−0.133911	−	0.555160i
$91$	16.0257	−	0.621871i	1.67995	−	0.0651898i
$92$	−4.58256	+	12.8483i	−0.477764	+	1.33953i
$93$	2.30512	−	9.14649i	0.239030	−	0.948447i
$94$	7.93639	−	27.8132i	0.818576	−	2.86871i
$95$	0.635244	+	2.02615i	0.0651746	+	0.207878i
$96$	30.6260	+	19.9147i	3.12576	+	2.03254i
$97$	−0.516441	+	2.24357i	−0.0524366	+	0.227800i	−0.994054	−	0.108884i	$-0.965272\pi$
$97$	−0.516441	+	2.24357i	−0.0524366	+	0.227800i	0.941618	+	0.336684i	$0.109305\pi$
$98$	3.07675	+	3.01766i	0.310799	+	0.304829i
$99$	0.150945	+	5.05754i	0.0151706	+	0.508302i
$100$	−20.1342	−	14.3911i	−2.01342	−	1.43911i
$101$	−0.471912	+	3.15067i	−0.0469570	+	0.313503i	0.952988	+	0.303008i	$0.0979909\pi$
$101$	−0.471912	+	3.15067i	−0.0469570	+	0.313503i	−0.999945	+	0.0104950i	$0.996659\pi$
$102$	3.71091	+	5.20551i	0.367435	+	0.515422i
$103$	1.42865	+	4.00557i	0.140770	+	0.394681i	0.991364	−	0.131142i	$-0.0418644\pi$
$103$	1.42865	+	4.00557i	0.140770	+	0.394681i	−0.850594	+	0.525823i	$0.823757\pi$
$104$	−19.0267	−	47.4456i	−1.86572	−	4.65243i
$105$	−3.12238	+	1.24764i	−0.304713	+	0.121758i
$106$	−7.58042	+	7.82948i	−0.736276	+	0.760466i
$107$	−0.593389	−	10.1881i	−0.0573651	−	0.984921i	−0.897073	−	0.441882i	$-0.854311\pi$
$107$	−0.593389	−	10.1881i	−0.0573651	−	0.984921i	0.839708	−	0.543038i	$-0.182726\pi$
$108$	−0.259456	−	28.1948i	−0.0249662	−	2.71304i
$109$	−0.245628	+	4.21728i	−0.0235269	+	0.403942i	0.965901	+	0.258913i	$0.0833644\pi$
$109$	−0.245628	+	4.21728i	−0.0235269	+	0.403942i	−0.989427	+	0.145028i	$0.953673\pi$
$110$	−2.06138	−	2.24232i	−0.196545	−	0.213797i
$111$	13.3360	+	11.3665i	1.26580	+	1.07886i
$112$	17.9402	−	38.7998i	1.69519	−	3.66624i
$113$	−2.40371	+	1.76546i	−0.226122	+	0.166081i	−0.699169	−	0.714957i	$-0.746446\pi$
$113$	−2.40371	+	1.76546i	−0.226122	+	0.166081i	0.473047	+	0.881037i	$0.343154\pi$
$114$	1.15326	+	15.0799i	0.108013	+	1.41237i
$115$	−0.959940	+	1.36155i	−0.0895148	+	0.126965i
$116$	−33.1466	+	20.0041i	−3.07759	+	1.85733i
$117$	−9.32330	+	13.5216i	−0.861939	+	1.25007i
$118$	−39.1853	+	6.12846i	−3.60730	+	0.564171i
$119$	2.86825	−	2.74131i	0.262932	−	0.251296i
$120$	7.08894	+	8.03791i	0.647129	+	0.733757i
$121$	−4.16866	−	7.00946i	−0.378969	−	0.637224i
$122$	5.17550	−	9.23802i	0.468568	−	0.836371i
$123$	9.08130	+	1.37175i	0.818833	+	0.123686i
$124$	7.00063	+	28.7097i	0.628675	+	2.57821i
$125$	−3.97775	−	4.93164i	−0.355781	−	0.441099i
$126$	−23.6705	+	3.64178i	−2.10874	+	0.324436i
$127$	0.409141	+	21.0952i	0.0363054	+	1.87190i	0.369757	+	0.929129i	$0.379441\pi$
$127$	0.409141	+	21.0952i	0.0363054	+	1.87190i	−0.333451	+	0.942767i	$0.608213\pi$
$128$	−34.7745	−	3.15567i	−3.07366	−	0.278924i
$129$	−9.65546	−	0.951273i	−0.850116	−	0.0837550i
$130$	−1.08430	−	9.82733i	−0.0950998	−	0.861914i
$131$	0.476593	−	0.0432491i	0.0416401	−	0.00377869i	−0.0695353	−	0.997579i	$-0.522152\pi$
$131$	0.476593	−	0.0432491i	0.0416401	−	0.00377869i	0.111175	+	0.993801i	$0.464538\pi$
$132$	−7.81985	−	13.7887i	−0.680631	−	1.20015i
$133$	9.16060	−	2.04639i	0.794325	−	0.177445i
$134$	19.4108	−	9.74846i	1.67684	−	0.842139i
$135$	0.892874	−	3.32568i	0.0768464	−	0.286229i
$136$	−11.3010	−	5.67560i	−0.969056	−	0.486678i
$137$	19.1363	+	4.79750i	1.63492	+	0.409878i	0.948361	−	0.317194i	$-0.102741\pi$
$137$	19.1363	+	4.79750i	1.63492	+	0.409878i	0.686562	+	0.727072i	$0.259119\pi$
$138$	−8.84819	+	7.90583i	−0.753208	+	0.672989i
$139$	7.68551	+	1.10040i	0.651876	+	0.0933347i	0.459768	−	0.888039i	$-0.347933\pi$
$139$	7.68551	+	1.10040i	0.651876	+	0.0933347i	0.192108	+	0.981374i	$0.438468\pi$
$140$	6.82320	−	8.02564i	0.576666	−	0.678290i
$141$	12.8886	−	13.1083i	1.08541	−	1.10392i
$142$	−18.3292	−	14.5894i	−1.53816	−	1.22432i
$143$	−0.893924	+	9.19034i	−0.0747537	+	0.768535i
$144$	20.8053	+	38.5168i	1.73377	+	3.20974i
$145$	−4.55493	+	1.26795i	−0.378266	+	0.105298i
$146$	−6.03230	+	1.84852i	−0.499237	+	0.152985i
$147$	0.799280	+	2.61991i	0.0659235	+	0.216086i
$148$	−53.5762	−	11.9684i	−4.40394	−	0.983798i
$149$	15.2118	−	3.81363i	1.24620	−	0.312425i	0.436734	−	0.899590i	$-0.356135\pi$
$149$	15.2118	−	3.81363i	1.24620	−	0.312425i	0.809467	+	0.587166i	$0.199756\pi$
$150$	−9.38792	−	19.3726i	−0.766521	−	1.58176i
$151$	−13.3370	−	15.6873i	−1.08535	−	1.27661i	−0.958624	−	0.284677i	$-0.908114\pi$
$151$	−13.3370	−	15.6873i	−1.08535	−	1.27661i	−0.126723	−	0.991938i	$-0.540446\pi$
$152$	−15.9524	−	25.3102i	−1.29391	−	2.05293i
$153$	0.487765	+	4.03380i	0.0394335	+	0.326114i
$154$	−10.6419	+	8.24813i	−0.857553	+	0.664654i
$155$	−0.116623	+	3.60704i	−0.00936741	+	0.289724i
$156$	6.03707	−	51.0999i	0.483353	−	4.09127i
$157$	−0.945745	+	7.66153i	−0.0754787	+	0.611457i	0.906465	+	0.422282i	$0.138771\pi$
$157$	−0.945745	+	7.66153i	−0.0754787	+	0.611457i	−0.981943	+	0.189175i	$0.939419\pi$
$158$	8.05194	−	39.6421i	0.640578	−	3.15376i
$159$	−6.61187	+	2.06396i	−0.524356	+	0.163682i
$160$	−13.0713	−	4.94987i	−1.03338	−	0.391321i
$161$	5.64127	+	4.73358i	0.444594	+	0.373059i
$162$	11.5379	−	21.6427i	0.906505	−	1.70041i
$163$	11.1180	−	9.32912i	0.870830	−	0.730713i	−0.0934426	−	0.995625i	$-0.529787\pi$
$163$	11.1180	−	9.32912i	0.870830	−	0.730713i	0.964273	+	0.264911i	$0.0853427\pi$
$164$	−27.1631	+	9.49071i	−2.12108	+	0.741100i
$165$	−0.468433	−	1.87838i	−0.0364675	−	0.146232i
$166$	1.62258	+	10.8330i	0.125937	+	0.840804i
$167$	4.97299	−	9.74447i	0.384822	−	0.754050i	−0.614572	−	0.788861i	$-0.710671\pi$
$167$	4.97299	−	9.74447i	0.384822	−	0.754050i	0.999394	+	0.0348109i	$0.0110829\pi$
$168$	38.0361	−	28.2435i	2.93455	−	2.17903i
$169$	−11.3245	+	12.6427i	−0.871112	+	0.972513i
$170$	−1.81132	−	1.64368i	−0.138922	−	0.126065i
$171$	−3.94293	+	8.76670i	−0.301523	+	0.670406i
$172$	28.1382	−	11.4957i	2.14552	−	0.876541i
$173$	0.882334	+	0.149705i	0.0670826	+	0.0113819i	0.200723	−	0.979648i	$-0.435671\pi$
$173$	0.882334	+	0.149705i	0.0670826	+	0.0113819i	−0.133640	+	0.991030i	$0.542667\pi$
$174$	−33.6436	+	1.48152i	−2.55052	+	0.112313i
$175$	−11.0667	+	7.48544i	−0.836567	+	0.565846i
$176$	20.7355	+	13.2572i	1.56300	+	0.999296i
$177$	−23.7328	−	8.49794i	−1.78387	−	0.638745i
$178$	−7.99818	−	3.38892i	−0.599489	−	0.254011i
$179$	−10.2758	−	21.4901i	−0.768052	−	1.60625i	−0.795001	−	0.606608i	$-0.792530\pi$
$179$	−10.2758	−	21.4901i	−0.768052	−	1.60625i	0.0269487	−	0.999637i	$-0.491421\pi$
$180$	2.39384	+	10.5190i	0.178426	+	0.784039i
$181$	18.1807	+	5.06095i	1.35136	+	0.376178i	0.866834	−	0.498597i	$-0.166151\pi$
$181$	18.1807	+	5.06095i	1.35136	+	0.376178i	0.484530	+	0.874775i	$0.338991\pi$
$182$	−43.6904	+	1.12994i	−3.23855	+	0.0837569i
$183$	5.69812	−	3.58150i	0.421217	−	0.264752i
$184$	8.17043	−	22.0044i	0.602332	−	1.62219i
$185$	−5.91139	−	3.16277i	−0.434614	−	0.232532i
$186$	−6.60345	+	24.8420i	−0.484188	+	1.82151i
$187$	1.34030	+	1.84979i	0.0980125	+	0.135270i
$188$	−16.5177	+	55.1731i	−1.20468	+	4.02391i
$189$	−14.3179	−	5.16693i	−1.04147	−	0.375839i
$190$	−1.65959	−	5.54343i	−0.120400	−	0.402162i
$191$	10.5756	−	13.8287i	0.765226	−	1.00061i	−0.234369	−	0.972148i	$-0.575302\pi$
$191$	10.5756	−	13.8287i	0.765226	−	1.00061i	0.999595	−	0.0284584i	$-0.00905982\pi$
$192$	−40.7334	−	27.2428i	−2.93968	−	1.96608i
$193$	11.9317	−	5.61084i	0.858859	−	0.403877i	0.0548503	−	0.998495i	$-0.482532\pi$
$193$	11.9317	−	5.61084i	0.858859	−	0.403877i	0.804009	+	0.594617i	$0.202696\pi$
$194$	1.48629	−	6.09530i	0.106709	−	0.437617i
$195$	2.38384	−	5.81431i	0.170710	−	0.416371i
$196$	−6.04828	−	6.08751i	−0.432020	−	0.434822i
$197$	−13.0345	+	2.55989i	−0.928670	+	0.182385i	−0.634105	−	0.773247i	$-0.718631\pi$
$197$	−13.0345	+	2.55989i	−0.928670	+	0.182385i	−0.294565	+	0.955632i	$0.595175\pi$
$198$	−0.233131	−	13.7866i	−0.0165679	−	0.979772i
$199$	8.56591	−	4.72647i	0.607221	−	0.335050i	−0.149526	−	0.988758i	$-0.547775\pi$
$199$	8.56591	−	4.72647i	0.607221	−	0.335050i	0.756747	+	0.653707i	$0.226787\pi$
$200$	34.3222	+	25.2088i	2.42695	+	1.78253i
$201$	13.7979	+	0.463274i	0.973230	+	0.0326768i
$202$	1.39691	−	8.56862i	0.0982863	−	0.602886i
$203$	3.89512	+	20.5343i	0.273384	+	1.44122i
$204$	−7.25461	−	10.4600i	−0.507924	−	0.732343i
$205$	−3.50663	+	0.226991i	−0.244914	+	0.0158538i
$206$	−3.75182	−	10.9651i	−0.261402	−	0.763975i
$207$	−7.34262	+	1.72098i	−0.510348	+	0.119616i
$208$	28.7742	+	74.5272i	1.99514	+	5.16753i
$209$	0.453603	+	5.38512i	0.0313764	+	0.372497i
$210$	8.55214	−	3.28970i	0.590153	−	0.227011i
$211$	−10.8114	+	16.2088i	−0.744291	+	1.11586i	0.244946	+	0.969537i	$0.421230\pi$
$211$	−10.8114	+	16.2088i	−0.744291	+	1.11586i	−0.989237	+	0.146324i	$0.953256\pi$
$212$	15.2945	−	15.3937i	1.05043	−	1.05725i
$213$	−5.79197	−	13.7170i	−0.396859	−	0.939873i
$214$	1.25799	+	27.7824i	0.0859947	+	1.89917i
$215$	3.68702	−	0.430951i	0.251453	−	0.0293906i
$216$	−0.180791	+	48.5169i	−0.0123013	+	3.30115i
$217$	15.8452	+	1.85204i	1.07565	+	0.125725i
$218$	0.817889	−	11.4830i	0.0553944	−	0.777727i
$219$	−3.92878	−	0.803080i	−0.265482	−	0.0542671i
$220$	4.04659	+	4.51763i	0.272821	+	0.304579i
$221$	−0.0479315	+	7.41483i	−0.00322422	+	0.498775i
$222$	−35.9388	−	31.4424i	−2.41206	−	2.11028i
$223$	4.57967	−	4.04911i	0.306677	−	0.271148i	−0.495016	−	0.868884i	$-0.664838\pi$
$223$	4.57967	−	4.04911i	0.306677	−	0.271148i	0.801694	+	0.597735i	$0.203933\pi$
$224$	−26.6534	+	55.7409i	−1.78086	+	3.72434i
$225$	0.652866	−	13.6669i	0.0435244	−	0.911129i
$226$	6.61207	−	4.72602i	0.439828	−	0.314370i
$227$	6.15563	+	12.0618i	0.408564	+	0.800571i	0.999983	−	0.00579262i	$-0.00184386\pi$
$227$	6.15563	+	12.0618i	0.408564	+	0.800571i	−0.591420	+	0.806364i	$0.701432\pi$
$228$	−1.90801	−	30.0546i	−0.126361	−	1.99041i
$229$	−14.7968	−	19.3482i	−0.977797	−	1.27856i	−0.960374	−	0.278714i	$-0.910092\pi$
$229$	−14.7968	−	19.3482i	−0.977797	−	1.27856i	−0.0174229	−	0.999848i	$-0.505546\pi$
$230$	2.66371	−	3.67626i	0.175640	−	0.242406i
$231$	−8.44781	+	1.36644i	−0.555825	+	0.0899054i
$232$	57.4761	−	33.6811i	3.77349	−	2.21127i
$233$	1.76446	+	8.14564i	0.115593	+	0.533639i	0.998004	+	0.0631578i	$0.0201171\pi$
$233$	1.76446	+	8.14564i	0.115593	+	0.533639i	−0.882410	+	0.470481i	$0.844080\pi$
$234$	25.8814	−	36.5164i	1.69192	−	2.38715i
$235$	−3.75031	+	5.95027i	−0.244643	+	0.388153i
$236$	78.1776	−	11.1933i	5.08893	−	0.728625i
$237$	16.5508	−	19.6748i	1.07509	−	1.27802i
$238$	−7.91227	+	7.36876i	−0.512876	+	0.477645i
$239$	9.39796	+	17.2956i	0.607903	+	1.11876i	0.981554	+	0.191187i	$0.0612335\pi$
$239$	9.39796	+	17.2956i	0.607903	+	1.11876i	−0.373650	+	0.927570i	$0.621894\pi$
$240$	−10.9154	−	12.7040i	−0.704587	−	0.820038i
$241$	1.39343	−	2.34300i	0.0897584	−	0.150926i	−0.811291	−	0.584643i	$-0.801235\pi$
$241$	1.39343	−	2.34300i	0.0897584	−	0.150926i	0.901049	+	0.433717i	$0.142798\pi$
$242$	11.1122	+	19.2469i	0.714321	+	1.23724i
$243$	13.0218	−	8.56930i	0.835348	−	0.549721i
$244$	−10.5425	+	18.2601i	−0.674913	+	1.16898i
$245$	−0.512224	−	0.914295i	−0.0327248	−	0.0584122i
$246$	−24.6973	−	4.05781i	−1.57464	−	0.258716i
$247$	−9.16093	+	14.9601i	−0.582896	+	0.951890i
$248$	−11.4064	−	49.5528i	−0.724309	−	3.14660i
$249$	−2.38931	+	6.53928i	−0.151416	+	0.414410i
$250$	10.6652	+	13.5784i	0.674528	+	0.858770i
$251$	−11.8592	−	22.5142i	−0.748549	−	1.42108i	−0.901468	−	0.432846i	$-0.857509\pi$
$251$	−11.8592	−	22.5142i	−0.748549	−	1.42108i	0.152919	−	0.988239i	$-0.451133\pi$
$252$	47.2229	−	6.64163i	2.97476	−	0.418383i
$253$	−3.13983	+	2.84924i	−0.197399	+	0.179130i
$254$	−0.371674	−	57.4967i	−0.0233209	−	3.60766i
$255$	−0.510950	−	1.46823i	−0.0319970	−	0.0919443i
$256$	38.3635	+	3.98203i	2.39772	+	0.248877i
$257$	−0.775567	+	0.100831i	−0.0483785	+	0.00628963i	−0.153075	−	0.988215i	$-0.548918\pi$
$257$	−0.775567	+	0.100831i	−0.0483785	+	0.00628963i	0.104696	+	0.994504i	$0.466613\pi$
$258$	26.2766	+	2.93229i	1.63591	+	0.182556i
$259$	−16.1249	+	24.8654i	−1.00195	+	1.54506i
$260$	1.90592	+	19.5946i	0.118200	+	1.21521i
$261$	−19.2267	−	9.40586i	−1.19010	−	0.582208i
$262$	−1.30019	+	0.101059i	−0.0803260	+	0.00624343i
$263$	4.31224	+	21.2304i	0.265904	+	1.30913i	0.862285	+	0.506424i	$0.169033\pi$
$263$	4.31224	+	21.2304i	0.265904	+	1.30913i	−0.596381	+	0.802702i	$0.703395\pi$
$264$	13.1479	+	23.8984i	0.809196	+	1.47084i
$265$	2.30360	−	1.31020i	0.141509	−	0.0804850i
$266$	−25.0338	+	5.25348i	−1.53492	+	0.322112i
$267$	−3.43295	−	4.32396i	−0.210093	−	0.264622i
$268$	−38.8988	+	18.9100i	−2.37612	+	1.15511i
$269$	−5.53590	+	7.43601i	−0.337530	+	0.453381i	−0.938189	−	0.346124i	$-0.887498\pi$
$269$	−5.53590	+	7.43601i	−0.337530	+	0.453381i	0.600659	+	0.799505i	$0.294905\pi$
$270$	−2.55016	+	9.03068i	−0.155198	+	0.549590i
$271$	−15.1913	−	20.4055i	−0.922808	−	1.23955i	−0.970602	−	0.240688i	$-0.922627\pi$
$271$	−15.1913	−	20.4055i	−0.922808	−	1.23955i	0.0477949	−	0.998857i	$-0.484781\pi$
$272$	17.5453	+	9.09751i	1.06384	+	0.551618i
$273$	−24.7268	−	12.6578i	−1.49653	−	0.766084i
$274$	−51.9754	−	13.7469i	−3.13995	−	0.830479i
$275$	−3.40779	−	6.89627i	−0.205498	−	0.415861i
$276$	17.8207	−	15.5131i	1.07268	−	0.933780i
$277$	4.87517	−	3.39020i	0.292920	−	0.203697i	−0.415308	−	0.909681i	$-0.636326\pi$
$277$	4.87517	−	3.39020i	0.292920	−	0.203697i	0.708228	+	0.705984i	$0.249495\pi$
$278$	−20.9035	−	3.26924i	−1.25371	−	0.196076i
$279$	−11.2410	+	11.8556i	−0.672981	+	0.709777i
$280$	−11.9183	+	13.6569i	−0.712257	+	0.816156i
$281$	−1.83581	+	3.71509i	−0.109515	+	0.221624i	−0.944398	−	0.328804i	$-0.893354\pi$
$281$	−1.83581	+	3.71509i	−0.109515	+	0.221624i	0.834883	+	0.550428i	$0.185535\pi$
$282$	−35.5818	+	35.2648i	−2.11887	+	2.09999i
$283$	−18.4876	+	15.9248i	−1.09898	+	0.946628i	−0.998831	−	0.0483446i	$-0.984605\pi$
$283$	−18.4876	+	15.9248i	−1.09898	+	0.946628i	−0.100145	+	0.994973i	$0.531931\pi$
$284$	36.1189	+	29.5201i	2.14326	+	1.75169i
$285$	0.759829	−	3.59848i	0.0450084	−	0.213156i
$286$	2.75963	−	25.0113i	0.163180	−	1.47895i
$287$	−0.301213	+	15.5305i	−0.0177800	+	0.916735i
$288$	−29.3495	−	56.0559i	−1.72943	−	3.30312i
$289$	−9.97171	−	11.4263i	−0.586571	−	0.672136i
$290$	12.4564	−	3.29456i	0.731464	−	0.193464i
$291$	2.68336	−	2.94966i	0.157301	−	0.172912i
$292$	12.0582	−	3.52522i	0.705652	−	0.206298i
$293$	−1.25567	+	14.9072i	−0.0733572	+	0.870887i	0.859616	+	0.510941i	$0.170703\pi$
$293$	−1.25567	+	14.9072i	−0.0733572	+	0.870887i	−0.932973	+	0.359946i	$0.882795\pi$
$294$	−2.08566	−	7.16715i	−0.121638	−	0.417996i
$295$	9.56436	+	1.24345i	0.556859	+	0.0723965i
$296$	91.9154	+	21.7843i	5.34247	+	1.26619i
$297$	4.06308	−	7.76505i	0.235764	−	0.450574i
$298$	−41.5850	+	9.85583i	−2.40896	+	0.570933i
$299$	−13.6893	+	1.42091i	−0.791671	+	0.0821733i
$300$	18.1931	+	38.8134i	1.05038	+	2.24089i
$301$	−0.530271	−	16.4007i	−0.0305643	−	0.945322i
$302$	35.7892	+	43.2162i	2.05944	+	2.48681i
$303$	3.38574	−	4.35718i	0.194506	−	0.250313i
$304$	24.4173	+	39.8743i	1.40043	+	2.28695i
$305$	−1.83838	+	1.80307i	−0.105265	+	0.103244i
$306$	−1.18700	−	11.0089i	−0.0678562	−	0.629336i
$307$	5.53320	−	8.06760i	0.315796	−	0.460442i	−0.633990	−	0.773341i	$-0.718584\pi$
$307$	5.53320	−	8.06760i	0.315796	−	0.460442i	0.949786	+	0.312899i	$0.101300\pi$
$308$	21.4010	−	16.1485i	1.21943	−	0.920146i
$309$	1.24118	−	7.26061i	0.0706084	−	0.413042i
$310$	0.444864	−	9.82470i	0.0252666	−	0.558006i
$311$	−2.19652	−	30.8387i	−0.124553	−	1.74870i	−0.542343	−	0.840157i	$-0.682463\pi$
$311$	−2.19652	−	30.8387i	−0.124553	−	1.74870i	0.417790	−	0.908544i	$-0.362805\pi$
$312$	−11.5240	+	87.7868i	−0.652415	+	4.96995i
$313$	−3.57430	−	9.62624i	−0.202031	−	0.544107i	0.796103	−	0.605161i	$-0.206891\pi$
$313$	−3.57430	−	9.62624i	−0.202031	−	0.544107i	−0.998134	+	0.0610539i	$0.980554\pi$
$314$	2.84698	−	20.8436i	0.160664	−	1.17627i
$315$	5.77340	+	0.765183i	0.325294	+	0.0431132i
$316$	−17.0523	+	78.7222i	−0.959267	+	4.42847i
$317$	−2.33888	−	7.13549i	−0.131364	−	0.400769i	0.863204	−	0.504855i	$-0.168454\pi$
$317$	−2.33888	−	7.13549i	−0.131364	−	0.400769i	−0.994568	+	0.104086i	$0.966808\pi$
$318$	18.0894	−	5.39114i	1.01440	−	0.302320i
$319$	−12.0173	+	0.622010i	−0.672839	+	0.0348259i
$320$	17.4468	+	6.86595i	0.975304	+	0.383818i
$321$	−7.74793	+	15.8877i	−0.432447	+	0.886763i
$322$	−15.2051	−	13.0973i	−0.847348	−	0.729883i
$323$	0.753589	+	4.27382i	0.0419308	+	0.237801i
$324$	−23.5297	+	42.7947i	−1.30721	+	2.37748i
$325$	4.33590	−	24.5901i	0.240513	−	1.36401i
$326$	−30.6241	+	25.0292i	−1.69611	+	1.38624i
$327$	3.94900	−	6.15976i	0.218380	−	0.340636i
$328$	46.9472	−	15.7252i	2.59223	−	0.868279i
$329$	24.8186	+	18.7274i	1.36830	+	1.03247i
$330$	1.21026	+	5.13489i	0.0666225	+	0.282667i
$331$	10.0823	−	5.39436i	0.554175	−	0.296501i	−0.170766	−	0.985312i	$-0.554624\pi$
$331$	10.0823	−	5.39436i	0.554175	−	0.296501i	0.724941	+	0.688811i	$0.241867\pi$
$332$	−2.95178	−	21.6108i	−0.162000	−	1.18605i
$333$	−10.4938	−	28.4784i	−0.575059	−	1.56061i
$334$	−13.8942	+	26.3775i	−0.760257	+	1.44331i
$335$	−5.19585	+	0.950839i	−0.283880	+	0.0519499i
$336$	−60.0093	+	43.3673i	−3.27377	+	2.36588i
$337$	14.4936	+	14.9698i	0.789517	+	0.815456i	0.986295	−	0.164992i	$-0.0527597\pi$
$337$	14.4936	+	14.9698i	0.789517	+	0.815456i	−0.196778	+	0.980448i	$0.563048\pi$
$338$	31.3034	−	34.0510i	1.70268	−	1.85213i
$339$	5.12753	−	0.626481i	0.278489	−	0.0340258i
$340$	3.56411	+	3.31929i	0.193291	+	0.180014i
$341$	−2.29111	+	8.89462i	−0.124070	+	0.481671i
$342$	11.0529	−	23.7495i	0.597675	−	1.28422i
$343$	14.4504	−	6.56850i	0.780247	−	0.354666i
$344$	−48.6695	+	19.1533i	−2.62409	+	1.03268i
$345$	2.60471	−	1.24151i	0.140233	−	0.0668409i
$346$	−2.39900	−	0.439016i	−0.128971	−	0.0236017i
$347$	−13.0772	+	16.6491i	−0.702021	+	0.893773i	−0.998114	−	0.0613860i	$-0.980448\pi$
$347$	−13.0772	+	16.6491i	−0.702021	+	0.893773i	0.296093	+	0.955159i	$0.404316\pi$
$348$	67.0242	−	2.08370i	3.59287	−	0.111698i
$349$	6.28726	+	22.0338i	0.336549	+	1.17944i	0.927839	+	0.372981i	$0.121664\pi$
$349$	6.28726	+	22.0338i	0.336549	+	1.17944i	−0.591290	+	0.806459i	$0.701381\pi$
$350$	30.4195	−	20.0072i	1.62599	−	1.06943i
$351$	25.5505	−	12.5076i	1.36379	−	0.667604i
$352$	−29.7207	−	19.5476i	−1.58412	−	1.04189i
$353$	−7.02250	+	22.3987i	−0.373770	+	1.19216i	0.558224	+	0.829690i	$0.311483\pi$
$353$	−7.02250	+	22.3987i	−0.373770	+	1.19216i	−0.931995	+	0.362472i	$0.881933\pi$
$354$	64.3701	+	23.9922i	3.42123	+	1.27517i
$355$	3.28266	+	4.65603i	0.174226	+	0.247116i
$356$	15.8375	+	6.95341i	0.839387	+	0.368530i
$357$	−6.65694	+	1.70590i	−0.352323	+	0.0902860i
$358$	27.2435	+	58.9204i	1.43986	+	3.11404i
$359$	19.9361	+	11.0003i	1.05219	+	0.580572i	0.912269	−	0.409591i	$-0.134329\pi$
$359$	19.9361	+	11.0003i	1.05219	+	0.580572i	0.139917	+	0.990163i	$0.455316\pi$
$360$	−3.88477	−	18.1519i	−0.204745	−	0.956690i
$361$	3.14548	−	8.14700i	0.165552	−	0.428790i
$362$	−49.3624	−	14.4311i	−2.59443	−	0.758482i
$363$	0.347660	+	14.1213i	0.0182474	+	0.741174i
$364$	87.0188	−	1.12507i	4.56102	−	0.0589699i
$365$	1.53413	−	0.0198349i	0.0802999	−	0.00103820i
$366$	−15.6530	+	9.55849i	−0.818194	+	0.499630i
$367$	13.3386	+	3.89955i	0.696271	+	0.203555i	0.609632	−	0.792685i	$-0.291317\pi$
$367$	13.3386	+	3.89955i	0.696271	+	0.203555i	0.0866391	+	0.996240i	$0.472387\pi$
$368$	−13.2124	+	34.2210i	−0.688745	+	1.78389i
$369$	−12.5491	−	9.77628i	−0.653280	−	0.508933i
$370$	15.9965	+	8.82650i	0.831619	+	0.458868i
$371$	−4.91654	−	10.6332i	−0.255254	−	0.552046i
$372$	13.7873	−	49.2917i	0.714837	−	2.55566i
$373$	−32.6479	−	14.3340i	−1.69045	−	0.742184i	−0.999820	−	0.0189710i	$-0.993961\pi$
$373$	−32.6479	−	14.3340i	−1.69045	−	0.742184i	−0.690625	−	0.723213i	$-0.742665\pi$
$374$	−3.58701	−	5.08771i	−0.185480	−	0.263079i
$375$	1.82229	+	10.8217i	0.0941027	+	0.558832i
$376$	29.6473	−	94.5617i	1.52894	−	4.87665i
$377$	−32.6348	−	21.4642i	−1.68078	−	1.10546i
$378$	38.8327	+	14.5838i	1.99734	+	0.750109i
$379$	13.7436	−	9.03931i	0.705961	−	0.464318i	−0.145078	−	0.989420i	$-0.546343\pi$
$379$	13.7436	−	9.03931i	0.705961	−	0.464318i	0.851039	+	0.525102i	$0.175973\pi$
$380$	3.16163	+	11.0800i	0.162188	+	0.568390i
$381$	17.2801	−	32.2013i	0.885288	−	1.64972i
$382$	−29.3047	+	37.3091i	−1.49936	+	1.90890i
$383$	−1.61065	−	0.294748i	−0.0823003	−	0.0150609i	0.138703	−	0.990334i	$-0.455707\pi$
$383$	−1.61065	−	0.294748i	−0.0823003	−	0.0150609i	−0.221003	+	0.975273i	$0.570933\pi$
$384$	49.8328	+	34.2691i	2.54302	+	1.74879i
$385$	3.04675	−	1.19901i	0.155277	−	0.0611072i
$386$	−32.7102	+	14.8686i	−1.66491	+	0.756793i
$387$	13.7728	+	9.62850i	0.700112	+	0.489444i
$388$	−3.11619	+	12.0978i	−0.158200	+	0.614171i
$389$	−7.29745	−	6.79617i	−0.369995	−	0.344579i	0.474391	−	0.880314i	$-0.342668\pi$
$389$	−7.29745	−	6.79617i	−0.369995	−	0.344579i	−0.844386	+	0.535735i	$0.820035\pi$
$390$	−6.70056	+	15.7594i	−0.339296	+	0.798009i
$391$	−2.30429	+	2.50654i	−0.116533	+	0.126761i
$392$	10.2711	+	10.6085i	0.518768	+	0.535812i
$393$	−0.756358	−	0.339052i	−0.0381532	−	0.0171029i
$394$	35.6079	−	6.51624i	1.79390	−	0.328283i
$395$	−4.58445	+	8.70337i	−0.230669	+	0.437914i
$396$	0.109274	+	27.4558i	0.00549121	+	1.37971i
$397$	−1.80475	−	13.2131i	−0.0905777	−	0.663146i	−0.978962	−	0.204045i	$-0.934591\pi$
$397$	−1.80475	−	13.2131i	−0.0905777	−	0.663146i	0.888384	−	0.459101i	$-0.151829\pi$
$398$	−23.5077	+	12.5774i	−1.17834	+	0.630446i
$399$	−15.5689	−	4.68211i	−0.779420	−	0.234398i
$400$	−53.1256	−	40.0869i	−2.65628	−	2.00435i
$401$	−3.58440	+	1.20061i	−0.178997	+	0.0599557i	−0.405692	−	0.914010i	$-0.632969\pi$
$401$	−3.58440	+	1.20061i	−0.178997	+	0.0599557i	0.226695	+	0.973966i	$0.427208\pi$
$402$	−37.5816	−	1.74848i	−1.87440	−	0.0872063i
$403$	−23.0852	+	18.8676i	−1.14996	+	0.939864i
$404$	−3.00189	+	17.0246i	−0.149350	+	0.847005i
$405$	−4.16988	+	4.26428i	−0.207203	+	0.211894i
$406$	−9.89037	−	56.0911i	−0.490851	−	2.78375i
$407$	−12.9281	−	11.1359i	−0.640821	−	0.551986i
$408$	12.2494	+	18.1585i	0.606435	+	0.898978i
$409$	−3.73574	−	1.47015i	−0.184720	−	0.0726943i	0.272032	−	0.962288i	$-0.412304\pi$
$409$	−3.73574	−	1.47015i	−0.184720	−	0.0726943i	−0.456752	+	0.889594i	$0.650987\pi$
$410$	9.56322	−	0.494988i	0.472294	−	0.0244457i
$411$	−24.8257	−	23.4802i	−1.22456	−	1.15819i
$412$	7.18779	+	21.9287i	0.354117	+	1.08035i
$413$	9.02594	−	41.6684i	0.444137	−	2.05037i
$414$	20.0685	−	4.43081i	0.986315	−	0.217762i
$415$	0.360488	−	2.63924i	0.0176956	−	0.129555i
$416$	−40.1939	−	108.249i	−1.97067	−	5.30736i
$417$	−10.6716	−	8.18229i	−0.522592	−	0.400689i
$418$	−1.04630	−	14.6899i	−0.0511764	−	0.718506i
$419$	−1.08223	+	23.9007i	−0.0528704	+	1.16763i	0.784191	+	0.620519i	$0.213078\pi$
$419$	−1.08223	+	23.9007i	−0.0528704	+	1.16763i	−0.837062	+	0.547109i	$0.815728\pi$
$420$	−17.1124	+	6.32980i	−0.835000	+	0.308863i
$421$	3.99670	−	3.01578i	0.194787	−	0.146980i	−0.500437	−	0.865773i	$-0.666827\pi$
$421$	3.99670	−	3.01578i	0.194787	−	0.146980i	0.695225	+	0.718792i	$0.255305\pi$
$422$	30.0311	−	43.7865i	1.46189	−	2.13149i
$423$	−30.5835	+	8.85870i	−1.48702	+	0.430725i
$424$	−26.6578	+	26.1458i	−1.29462	+	1.26975i
$425$	−3.22587	−	5.26795i	−0.156477	−	0.255533i
$426$	15.2993	+	37.5815i	0.741253	+	1.82083i
$427$	7.26018	+	8.76682i	0.351345	+	0.424256i
$428$	−1.78954	−	55.3486i	−0.0865007	−	2.67537i
$429$	9.14727	−	13.1191i	0.441634	−	0.633398i
$430$	−10.0619	+	1.04440i	−0.485230	+	0.0503656i
$431$	34.8272	−	8.25421i	1.67757	−	0.397591i	0.721891	−	0.692007i	$-0.243273\pi$
$431$	34.8272	−	8.25421i	1.67757	−	0.397591i	0.955678	+	0.294415i	$0.0951249\pi$
$432$	1.26276	−	75.8131i	0.0607546	−	3.64756i
$433$	−3.40702	−	0.807479i	−0.163731	−	0.0388049i	0.147933	−	0.988997i	$-0.452738\pi$
$433$	−3.40702	−	0.807479i	−0.163731	−	0.0388049i	−0.311664	+	0.950192i	$0.600886\pi$
$434$	−43.1114	−	5.60487i	−2.06942	−	0.269042i
$435$	7.95380	+	1.94994i	0.381355	+	0.0934926i
$436$	−1.92406	+	22.8422i	−0.0921456	+	1.09394i
$437$	−7.73131	+	2.26025i	−0.369839	+	0.108122i
$438$	10.6772	+	2.32672i	0.510178	+	0.111175i
$439$	37.5599	−	9.93414i	1.79264	−	0.474131i	0.800504	−	0.599327i	$-0.204565\pi$
$439$	37.5599	−	9.93414i	1.79264	−	0.474131i	0.992132	+	0.125196i	$0.0399560\pi$
$440$	−6.86195	−	7.86292i	−0.327131	−	0.374850i
$441$	1.01590	−	4.63425i	0.0483762	−	0.220679i
$442$	0.391836	−	20.2030i	0.0186377	−	0.960957i
$443$	0.190242	−	1.72421i	0.00903867	−	0.0819198i	−0.988604	−	0.150537i	$-0.951900\pi$
$443$	0.190242	−	1.72421i	0.00903867	−	0.0819198i	0.997643	+	0.0686170i	$0.0218587\pi$
$444$	70.7465	+	63.5286i	3.35748	+	3.01493i
$445$	1.63559	+	1.33678i	0.0775345	+	0.0633692i
$446$	−12.6218	+	10.8721i	−0.597659	+	0.514807i
$447$	−26.2058	−	7.14763i	−1.23949	−	0.338071i
$448$	36.7169	−	74.3032i	1.73471	−	3.51049i
$449$	−12.4655	+	14.2838i	−0.588282	+	0.674096i	−0.967984	−	0.251013i	$-0.919236\pi$
$449$	−12.4655	+	14.2838i	−0.588282	+	0.674096i	0.379702	+	0.925109i	$0.376026\pi$
$450$	−2.26049	+	37.2180i	−0.106560	+	1.75447i
$451$	−8.83590	−	1.38191i	−0.416066	−	0.0650716i
$452$	−13.2866	+	9.23953i	−0.624949	+	0.434591i
$453$	6.82936	+	35.0037i	0.320871	+	1.64462i
$454$	−16.3485	−	33.0841i	−0.767274	−	1.55271i
$455$	10.2748	+	2.71757i	0.481691	+	0.127401i
$456$	2.61429	+	51.7535i	0.122425	+	2.42358i
$457$	23.4798	+	12.1746i	1.09834	+	0.569505i	0.910840	−	0.412759i	$-0.135435\pi$
$457$	23.4798	+	12.1746i	1.09834	+	0.569505i	0.187500	+	0.982265i	$0.439962\pi$
$458$	39.6380	+	53.2431i	1.85216	+	2.48789i
$459$	2.68589	−	6.50495i	0.125367	−	0.303625i
$460$	−5.39821	+	7.25105i	−0.251693	+	0.338082i
$461$	3.74194	−	1.81908i	0.174280	−	0.0847231i	−0.348012	−	0.937490i	$-0.613143\pi$
$461$	3.74194	−	1.81908i	0.174280	−	0.0847231i	0.522292	+	0.852767i	$0.325077\pi$
$462$	23.0676	−	3.42580i	1.07320	−	0.159383i
$463$	6.91279	−	1.45069i	0.321265	−	0.0674192i	−0.0419641	−	0.999119i	$-0.513362\pi$
$463$	6.91279	−	1.45069i	0.321265	−	0.0674192i	0.363229	+	0.931700i	$0.381674\pi$
$464$	−90.4978	+	51.4718i	−4.20125	+	2.38952i
$465$	3.23645	−	5.34774i	0.150087	−	0.247996i
$466$	−4.52099	−	22.2582i	−0.209431	−	1.03109i
$467$	18.2859	−	1.42129i	0.846169	−	0.0657694i	0.352916	−	0.935655i	$-0.385190\pi$
$467$	18.2859	−	1.42129i	0.846169	−	0.0657694i	0.493253	+	0.869886i	$0.335808\pi$
$468$	−52.4712	+	72.0397i	−2.42548	+	3.33004i
$469$	2.26048	+	23.2398i	0.104379	+	1.07311i
$470$	10.4288	−	16.0818i	0.481047	−	0.741796i
$471$	7.92842	−	10.7666i	0.365322	−	0.496101i
$472$	−134.759	+	17.5199i	−6.20279	+	0.806417i
$473$	9.39712	+	0.975396i	0.432080	+	0.0448488i
$474$	−45.7924	+	53.0288i	−2.10332	+	2.43569i
$475$	−0.0944657	−	14.6135i	−0.00433438	−	0.670514i
$476$	15.9434	−	14.4679i	0.730765	−	0.663134i
$477$	11.7352	+	2.49315i	0.537317	+	0.114153i
$478$	−24.9992	−	47.4597i	−1.14343	−	2.17076i
$479$	−10.4808	−	13.3436i	−0.478882	−	0.609685i	0.485488	−	0.874243i	$-0.338642\pi$
$479$	−10.4808	−	13.3436i	−0.478882	−	0.609685i	−0.964370	+	0.264559i	$0.914774\pi$
$480$	15.5383	+	18.5646i	0.709223	+	0.847354i
$481$	−12.4244	−	53.9753i	−0.566505	−	2.46106i
$482$	−3.87949	+	6.33535i	−0.176706	+	0.288567i
$483$	−4.50226	−	11.9341i	−0.204860	−	0.543018i
$484$	−21.6295	−	38.6077i	−0.983160	−	1.75489i
$485$	−0.762838	+	1.32127i	−0.0346387	+	0.0599960i
$486$	−35.7850	+	22.8917i	−1.62324	+	1.03839i
$487$	−0.771325	−	1.33597i	−0.0349521	−	0.0605387i	0.848020	−	0.529964i	$-0.177795\pi$
$487$	−0.771325	−	1.33597i	−0.0349521	−	0.0605387i	−0.882972	+	0.469425i	$0.844461\pi$
$488$	18.5453	−	31.1833i	0.839506	−	1.41160i
$489$	−24.7036	+	4.65420i	−1.11713	+	0.210470i
$490$	1.36355	+	2.50941i	0.0615988	+	0.113363i
$491$	−1.18496	+	1.10356i	−0.0534766	+	0.0498031i	−0.707809	−	0.706404i	$-0.750316\pi$
$491$	−1.18496	+	1.10356i	−0.0534766	+	0.0498031i	0.654332	+	0.756207i	$0.272950\pi$
$492$	49.0691	+	8.71506i	2.21221	+	0.392905i
$493$	−9.56566	+	1.36960i	−0.430816	+	0.0616836i
$494$	25.4896	−	40.4421i	1.14683	−	1.81958i
$495$	−0.886343	+	3.23382i	−0.0398382	+	0.145349i
$496$	16.8235	+	77.6660i	0.755398	+	3.48731i
$497$	21.7271	−	12.7321i	0.974596	−	0.571115i
$498$	6.74100	−	17.7347i	0.302071	−	0.794711i
$499$	14.7988	−	20.4243i	0.662485	−	0.914316i	−0.337146	−	0.941452i	$-0.609462\pi$
$499$	14.7988	−	20.4243i	0.662485	−	0.914316i	0.999632	+	0.0271358i	$0.00863866\pi$
$500$	−20.8855	−	27.3097i	−0.934026	−	1.22133i
$501$	−15.7769	+	10.4951i	−0.704859	+	0.468884i
$502$	31.5220	+	61.7668i	1.40690	+	2.75679i
$503$	−21.8407	+	15.6108i	−0.973828	+	0.696050i	−0.952759	−	0.303728i	$-0.901769\pi$
$503$	−21.8407	+	15.6108i	−0.973828	+	0.696050i	−0.0210692	+	0.999778i	$0.506707\pi$
$504$	−81.3981	+	10.3769i	−3.62576	+	0.462224i
$505$	−0.910748	+	1.90467i	−0.0405278	+	0.0847566i
$506$	8.65609	−	7.65327i	0.384810	−	0.340229i
$507$	27.8266	−	9.48257i	1.23582	−	0.421136i
$508$	−0.740083	+	114.488i	−0.0328359	+	5.07960i
$509$	−12.6556	−	14.1288i	−0.560951	−	0.626248i	0.395386	−	0.918515i	$-0.370611\pi$
$509$	−12.6556	−	14.1288i	−0.560951	−	0.626248i	−0.956337	+	0.292267i	$0.905590\pi$
$510$	1.34056	+	4.01878i	0.0593611	+	0.177955i
$511$	0.481843	−	6.76498i	0.0213155	−	0.299265i
$512$	−35.0337	−	4.09486i	−1.54829	−	0.180969i
$513$	13.3919	−	9.89255i	0.591266	−	0.436767i
$514$	2.11689	−	0.247429i	0.0933722	−	0.0109136i
$515$	0.127480	+	2.81536i	0.00561745	+	0.124060i
$516$	−52.2426	−	6.51476i	−2.29985	−	0.286796i
$517$	−12.6168	+	12.6986i	−0.554887	+	0.558486i
$518$	44.8148	−	67.1875i	1.96905	−	2.95205i
$519$	−1.20533	−	0.974663i	−0.0529079	−	0.0427829i
$520$	−2.84339	−	33.7563i	−0.124691	−	1.48031i
$521$	−8.91924	−	23.1014i	−0.390759	−	1.01209i	−0.979082	−	0.203465i	$-0.934780\pi$
$521$	−8.91924	−	23.1014i	−0.390759	−	1.01209i	0.588323	−	0.808626i	$-0.299788\pi$
$522$	52.0594	+	26.3074i	2.27858	+	1.15144i
$523$	−1.84732	−	5.39900i	−0.0807777	−	0.236082i	0.898367	−	0.439246i	$-0.144754\pi$
$523$	−1.84732	−	5.39900i	−0.0807777	−	0.236082i	−0.979145	+	0.203164i	$0.934878\pi$
$524$	2.59134	−	0.167743i	0.113203	−	0.00732788i
$525$	23.0619	−	1.91372i	1.00650	−	0.0835216i
$526$	−11.0025	−	58.0027i	−0.479730	−	2.52904i
$527$	−1.18679	+	7.27973i	−0.0516972	+	0.317110i
$528$	−20.0632	−	37.6114i	−0.873138	−	1.63682i
$529$	13.4439	+	9.87418i	0.584517	+	0.429312i
$530$	−6.32322	+	3.48901i	−0.274663	+	0.151553i
$531$	28.6270	+	32.9678i	1.24230	+	1.43068i
$532$	49.9788	−	9.81551i	2.16685	−	0.425556i
$533$	−20.4610	−	20.5937i	−0.886266	−	0.892014i
$534$	9.20210	+	11.9033i	0.398214	+	0.515106i
$535$	1.60217	−	6.57050i	0.0692676	−	0.284067i
$536$	67.3488	−	31.6707i	2.90902	−	1.36796i
$537$	−2.71630	+	41.1688i	−0.117217	+	1.77657i
$538$	15.3467	−	20.0673i	0.661645	−	0.865164i
$539$	−0.764973	−	2.55519i	−0.0329497	−	0.110060i
$540$	5.30996	−	17.9149i	0.228504	−	0.770933i
$541$	−5.88032	+	19.6417i	−0.252815	+	0.844461i	0.733514	+	0.679674i	$0.237879\pi$
$541$	−5.88032	+	19.6417i	−0.252815	+	0.844461i	−0.986329	+	0.164787i	$0.947306\pi$
$542$	40.6759	+	56.1381i	1.74718	+	2.41134i
$543$	−23.1593	−	23.0673i	−0.993862	−	0.989915i
$544$	−25.1877	−	13.4762i	−1.07991	−	0.577787i
$545$	−0.974468	+	2.62442i	−0.0417416	+	0.112418i
$546$	66.9320	+	35.3623i	2.86442	+	1.51337i
$547$	−33.1434	+	0.857171i	−1.41711	+	0.0366500i	−0.726793	−	0.686857i	$-0.758990\pi$
$547$	−33.1434	+	0.857171i	−1.41711	+	0.0366500i	−0.690317	+	0.723507i	$0.742529\pi$
$548$	103.132	+	28.7087i	4.40557	+	1.22637i
$549$	−11.6429	+	0.573637i	−0.496909	+	0.0244822i
$550$	9.04293	+	18.9117i	0.385592	+	0.806397i
$551$	−21.0494	−	8.91889i	−0.896735	−	0.379957i
$552$	−31.0069	+	26.2950i	−1.31974	+	1.11919i
$553$	36.6362	+	23.4231i	1.55793	+	0.996054i
$554$	−13.4038	+	9.06619i	−0.569472	+	0.385186i
$555$	6.24289	+	9.79129i	0.264996	+	0.415617i
$556$	41.5357	+	7.04733i	1.76150	+	0.298873i
$557$	3.07611	−	1.25673i	0.130339	−	0.0532494i	−0.312092	−	0.950052i	$-0.601030\pi$
$557$	3.07611	−	1.25673i	0.130339	−	0.0532494i	0.442431	+	0.896803i	$0.354116\pi$
$558$	31.0482	−	31.9093i	1.31438	−	1.35083i
$559$	22.7104	+	20.6086i	0.960549	+	0.871652i
$560$	18.9006	−	21.1007i	0.798695	−	0.891666i
$561$	−0.454447	−	3.93038i	−0.0191868	−	0.165941i
$562$	5.13329	−	10.0586i	0.216535	−	0.424295i
$563$	−1.45594	−	9.72041i	−0.0613604	−	0.409666i	−0.998203	−	0.0599162i	$-0.980917\pi$
$563$	−1.45594	−	9.72041i	−0.0613604	−	0.409666i	0.936843	−	0.349750i	$-0.113734\pi$
$564$	71.7529	−	69.2980i	3.02134	−	2.91797i
$565$	−1.86580	+	0.651906i	−0.0784949	+	0.0274259i
$566$	50.9379	−	42.7420i	2.14108	−	1.79658i
$567$	17.2364	+	19.9500i	0.723862	+	0.837820i
$568$	−61.4884	−	51.5949i	−2.57999	−	2.16487i
$569$	−18.0601	−	6.83902i	−0.757118	−	0.286707i	−0.0547305	−	0.998501i	$-0.517430\pi$
$569$	−18.0601	−	6.83902i	−0.757118	−	0.286707i	−0.702388	+	0.711795i	$0.747883\pi$
$570$	−2.19723	+	9.77873i	−0.0920320	+	0.409586i
$571$	−3.61313	+	17.7885i	−0.151205	+	0.744426i	0.830949	+	0.556348i	$0.187798\pi$
$571$	−3.61313	+	17.7885i	−0.151205	+	0.744426i	−0.982154	+	0.188078i	$0.939774\pi$
$572$	−6.13841	+	49.7276i	−0.256660	+	2.07922i
$573$	−27.7021	+	11.9087i	−1.15727	+	0.497495i
$574$	1.36792	−	42.3083i	0.0570959	−	1.76592i
$575$	9.06213	−	7.02368i	0.377917	−	0.292908i
$576$	38.3944	+	75.6968i	1.59977	+	3.15403i
$577$	17.6481	+	28.0007i	0.734702	+	1.16568i	0.980530	+	0.196370i	$0.0629154\pi$
$577$	17.6481	+	28.0007i	0.734702	+	1.16568i	−0.245828	+	0.969313i	$0.579060\pi$
$578$	26.7694	+	31.4869i	1.11346	+	1.30968i
$579$	−22.7775	−	1.65079i	−0.946599	−	0.0686044i
$580$	−24.8861	+	6.23898i	−1.03334	+	0.259060i
$581$	−11.4917	−	2.56715i	−0.476757	−	0.106503i
$582$	−7.41580	+	7.94298i	−0.307395	+	0.329247i
$583$	6.44877	−	1.97615i	0.267081	−	0.0818436i
$584$	−20.8254	+	5.79714i	−0.861761	+	0.239888i
$585$	−8.53271	+	6.75717i	−0.352784	+	0.279375i
$586$	3.94677	−	40.5763i	0.163039	−	1.67619i
$587$	1.14141	+	0.908524i	0.0471112	+	0.0374988i	0.646041	−	0.763303i	$-0.276424\pi$
$587$	1.14141	+	0.908524i	0.0471112	+	0.0374988i	−0.598930	+	0.800802i	$0.704407\pi$
$588$	3.96815	+	14.3238i	0.163644	+	0.590705i
$589$	−11.3025	+	13.2944i	−0.465713	+	0.547784i
$590$	−26.0181	−	3.72524i	−1.07115	−	0.153366i
$591$	21.8542	+	7.19347i	0.898963	+	0.295900i
$592$	−143.195	−	35.8992i	−5.88528	−	1.47545i
$593$	−10.5508	−	5.29880i	−0.433268	−	0.217596i	0.218778	−	0.975775i	$-0.429793\pi$
$593$	−10.5508	−	5.29880i	−0.433268	−	0.217596i	−0.652046	+	0.758179i	$0.726089\pi$
$594$	−11.3450	+	21.0158i	−0.465493	+	0.862290i
$595$	2.34961	−	1.18002i	0.0963248	−	0.0483761i
$596$	83.0516	−	18.5530i	3.40192	−	0.759958i
$597$	−16.9448	−	0.130584i	−0.693504	−	0.00534445i
$598$	37.3519	−	3.38956i	1.52743	−	0.138609i
$599$	4.49819	+	40.7683i	0.183791	+	1.66575i	0.634385	+	0.773017i	$0.281253\pi$
$599$	4.49819	+	40.7683i	0.183791	+	1.66575i	−0.450594	+	0.892729i	$0.648788\pi$
$600$	−30.4391	−	67.1860i	−1.24267	−	2.74286i
$601$	−31.5993	−	2.86753i	−1.28896	−	0.116969i	−0.575582	−	0.817744i	$-0.695224\pi$
$601$	−31.5993	−	2.86753i	−1.28896	−	0.116969i	−0.713382	+	0.700775i	$0.752838\pi$
$602$	0.867130	+	44.7090i	0.0353416	+	1.82220i
$603$	−20.4420	−	12.4062i	−0.832464	−	0.505220i
$604$	−70.1456	−	86.9669i	−2.85418	−	3.53863i
$605$	−1.28033	−	5.25067i	−0.0520530	−	0.213470i
$606$	−9.37930	+	11.7536i	−0.381008	+	0.477457i
$607$	−4.49394	+	8.02147i	−0.182403	+	0.325581i	−0.948296	−	0.317387i	$-0.897195\pi$
$607$	−4.49394	+	8.02147i	−0.182403	+	0.325581i	0.765893	+	0.642969i	$0.222297\pi$
$608$	−34.5444	−	58.0853i	−1.40096	−	2.35567i
$609$	11.5404	−	34.3119i	0.467639	−	1.39039i
$610$	5.07293	−	4.84842i	0.205397	−	0.196307i
$611$	−57.4088	+	8.97857i	−2.32251	+	0.363234i
$612$	2.07998	+	21.9498i	0.0840781	+	0.887268i
$613$	4.53773	−	2.73853i	0.183277	−	0.110608i	−0.422093	−	0.906553i	$-0.638704\pi$
$613$	4.53773	−	2.73853i	0.183277	−	0.110608i	0.605370	+	0.795944i	$0.293025\pi$
$614$	−15.3616	+	21.7885i	−0.619945	+	0.879310i
$615$	5.48767	+	2.63240i	0.221284	+	0.106149i
$616$	−37.1811	+	27.3086i	−1.49807	+	1.10029i
$617$	−15.8646	+	34.3109i	−0.638687	+	1.38131i	0.269606	+	0.962971i	$0.413107\pi$
$617$	−15.8646	+	34.3109i	−0.638687	+	1.38131i	−0.908293	+	0.418336i	$0.862614\pi$
$618$	−3.63789	+	19.7407i	−0.146337	+	0.794087i
$619$	−8.29809	−	9.02645i	−0.333528	−	0.362804i	0.546721	−	0.837315i	$-0.315876\pi$
$619$	−8.29809	−	9.02645i	−0.333528	−	0.362804i	−0.880249	+	0.474511i	$0.842625\pi$
$620$	−1.13866	+	19.5500i	−0.0457296	+	0.785148i
$621$	12.5476	+	3.63104i	0.503519	+	0.145709i
$622$	4.89883	+	84.1096i	0.196425	+	3.37249i
$623$	6.49518	−	6.70857i	0.260224	−	0.268773i
$624$	19.7820	−	136.951i	0.791914	−	5.48241i
$625$	6.92509	+	17.2686i	0.277004	+	0.690745i
$626$	9.40047	+	26.3564i	0.375718	+	1.05342i
$627$	3.88399	−	8.51648i	0.155112	−	0.340115i
$628$	−6.20504	+	41.4273i	−0.247608	+	1.65313i
$629$	−11.1474	−	7.96766i	−0.444475	−	0.317691i
$630$	−15.7050	−	2.28845i	−0.625701	−	0.0911738i
$631$	12.0750	+	11.8431i	0.480698	+	0.471465i	0.899693	−	0.436523i	$-0.143790\pi$
$631$	12.0750	+	11.8431i	0.480698	+	0.471465i	−0.418995	+	0.907989i	$0.637617\pi$
$632$	31.0909	−	135.068i	1.23673	−	5.37271i
$633$	30.0776	−	15.3028i	1.19548	−	0.608230i
$634$	6.12181	+	19.5259i	0.243128	+	0.775472i
$635$	−3.83665	+	13.4456i	−0.152253	+	0.533571i
$636$	−36.1557	+	10.2683i	−1.43366	+	0.407167i
$637$	2.90854	−	8.15478i	0.115241	−	0.323104i
$638$	32.7678	−	1.27154i	1.29729	−	0.0503408i
$639$	−2.89203	+	25.6270i	−0.114407	+	1.01379i
$640$	−21.4208	−	8.75136i	−0.846732	−	0.345928i
$641$	−11.4448	−	7.11045i	−0.452044	−	0.280846i	0.282677	−	0.959215i	$-0.408777\pi$
$641$	−11.4448	−	7.11045i	−0.452044	−	0.280846i	−0.734721	+	0.678369i	$0.762687\pi$
$642$	21.6721	−	43.0193i	0.855328	−	1.69784i
$643$	16.0008	−	6.77974i	0.631011	−	0.267367i	−0.0510118	−	0.998698i	$-0.516245\pi$
$643$	16.0008	−	6.77974i	0.631011	−	0.267367i	0.682023	+	0.731331i	$0.261101\pi$
$644$	29.9370	+	26.4688i	1.17968	+	1.04301i
$645$	−5.93310	−	2.47746i	−0.233616	−	0.0975500i
$646$	−1.90289	−	11.6723i	−0.0748680	−	0.459239i
$647$	10.4424	−	3.80074i	0.410535	−	0.149422i	−0.128493	−	0.991710i	$-0.541014\pi$
$647$	10.4424	−	3.80074i	0.410535	−	0.149422i	0.539028	+	0.842288i	$0.318792\pi$
$648$	41.4365	−	73.1079i	1.62778	−	2.87195i
$649$	23.0665	+	8.39551i	0.905438	+	0.329553i
$650$	−12.6812	+	66.8529i	−0.497398	+	2.62218i
$651$	−22.3553	−	16.2403i	−0.876172	−	0.636508i
$652$	61.6185	−	49.0461i	2.41317	−	1.92079i
$653$	−7.70605	−	11.8831i	−0.301561	−	0.465021i	0.655382	−	0.755298i	$-0.272508\pi$
$653$	−7.70605	−	11.8831i	−0.301561	−	0.465021i	−0.956943	+	0.290277i	$0.906253\pi$
$654$	−10.9776	+	16.6456i	−0.429259	+	0.650895i
$655$	0.310371	+	0.0651332i	0.0121272	+	0.00254496i
$656$	−73.6816	+	23.6250i	−2.87678	+	0.922403i
$657$	5.25117	+	4.54599i	0.204867	+	0.177356i
$658$	−66.9685	−	51.9045i	−2.61071	−	2.02345i
$659$	6.49698	−	7.84523i	0.253086	−	0.305607i	−0.628330	−	0.777947i	$-0.716261\pi$
$659$	6.49698	−	7.84523i	0.253086	−	0.305607i	0.881416	+	0.472340i	$0.156591\pi$
$660$	−2.27750	−	10.2550i	−0.0886515	−	0.399175i
$661$	−3.80333	−	1.84893i	−0.147933	−	0.0719149i	0.361761	−	0.932271i	$-0.382176\pi$
$661$	−3.80333	−	1.84893i	−0.147933	−	0.0719149i	−0.509694	+	0.860356i	$0.670241\pi$
$662$	−27.6634	+	14.3439i	−1.07517	+	0.557491i
$663$	6.36339	−	11.1559i	0.247134	−	0.433258i
$664$	4.59800	+	37.2486i	0.178437	+	1.44553i
$665$	6.20159	+	0.482025i	0.240487	+	0.0186921i
$666$	27.5913	+	77.9705i	1.06914	+	3.02129i
$667$	−4.47391	−	17.3688i	−0.173230	−	0.672521i
$668$	28.3431	−	52.1612i	1.09663	−	2.01818i
$669$	−10.3508	+	2.22867i	−0.400185	+	0.0861652i
$670$	14.1917	−	2.40789i	0.548272	−	0.0930249i
$671$	−5.56673	+	3.45850i	−0.214901	+	0.133514i
$672$	87.5398	−	61.5560i	3.37692	−	2.37457i
$673$	6.12658	−	13.7128i	0.236162	−	0.528589i	−0.755848	−	0.654747i	$-0.772775\pi$
$673$	6.12658	−	13.7128i	0.236162	−	0.528589i	0.992010	+	0.126158i	$0.0402648\pi$
$674$	−38.9662	−	41.3018i	−1.50092	−	1.59089i
$675$	−12.5814	+	20.0834i	−0.484257	+	0.773010i
$676$	−63.2032	+	66.9915i	−2.43089	+	2.57659i
$677$	−4.24359	−	10.1983i	−0.163094	−	0.391952i	0.820673	−	0.571397i	$-0.193598\pi$
$677$	−4.24359	−	10.1983i	−0.163094	−	0.391952i	−0.983768	+	0.179445i	$0.942570\pi$
$678$	−13.9941	+	1.52645i	−0.537439	+	0.0586231i
$679$	5.53700	+	3.85044i	0.212490	+	0.147766i
$680$	−6.05847	−	5.79035i	−0.232332	−	0.222050i
$681$	0.938588	−	23.4362i	0.0359668	−	0.898078i
$682$	6.55640	−	24.1562i	0.251057	−	0.924990i
$683$	7.92939	−	23.1745i	0.303410	−	0.886748i	−0.684128	−	0.729362i	$-0.739817\pi$
$683$	7.92939	−	23.1745i	0.303410	−	0.886748i	0.987537	−	0.157386i	$-0.0503066\pi$
$684$	−22.6183	+	47.0018i	−0.864833	+	1.79716i
$685$	11.1935	+	6.75528i	0.427680	+	0.258106i
$686$	−39.6072	+	17.3894i	−1.51221	+	0.663931i
$687$	5.92766	+	41.7702i	0.226154	+	1.59363i
$688$	76.4423	−	28.9473i	2.91433	−	1.10360i
$689$	20.6684	+	7.22149i	0.787405	+	0.275117i
$690$	−7.14132	+	3.29123i	−0.271865	+	0.125295i
$691$	−10.4774	−	15.7080i	−0.398579	−	0.597561i	0.577124	−	0.816656i	$-0.304175\pi$
$691$	−10.4774	−	15.7080i	−0.398579	−	0.597561i	−0.975703	+	0.219096i	$0.929689\pi$
$692$	4.76522	+	0.935859i	0.181146	+	0.0355760i
$693$	13.9157	+	5.10408i	0.528613	+	0.193888i
$694$	36.2206	−	44.9065i	1.37492	−	1.70463i
$695$	4.65596	+	2.18946i	0.176611	+	0.0830509i
$696$	−115.366	+	2.09418i	−4.37295	+	0.0793796i
$697$	−7.16678	−	0.463920i	−0.271461	−	0.0175722i
$698$	−16.3559	−	60.2612i	−0.619079	−	2.28092i
$699$	4.24671	−	13.7971i	0.160625	−	0.521854i
$700$	−61.0817	+	39.0522i	−2.30867	+	1.47604i
$701$	−17.2417	+	39.9708i	−0.651211	+	1.50968i	0.197213	+	0.980361i	$0.436811\pi$
$701$	−17.2417	+	39.9708i	−0.651211	+	1.50968i	−0.848424	+	0.529317i	$0.822448\pi$
$702$	−70.0633	+	33.1817i	−2.64437	+	1.25236i
$703$	−12.8393	−	29.7650i	−0.484245	−	1.12261i
$704$	39.5254	+	26.7347i	1.48967	+	1.00760i
$705$	10.7115	−	5.80311i	0.403417	−	0.218558i
$706$	19.9247	−	60.7868i	0.749877	−	2.28774i
$707$	8.05189	+	4.71842i	0.302823	+	0.177454i
$708$	−127.546	−	49.4266i	−4.79349	−	1.85757i
$709$	22.3976	+	7.50217i	0.841158	+	0.281750i	0.705239	−	0.708970i	$-0.250840\pi$
$709$	22.3976	+	7.50217i	0.841158	+	0.281750i	0.135919	+	0.990720i	$0.456601\pi$
$710$	−8.78089	−	12.8029i	−0.329541	−	0.480482i
$711$	−41.6849	+	15.6670i	−1.56330	+	0.587558i
$712$	−27.0949	−	12.3161i	−1.01542	−	0.461567i
$713$	−13.6719	−	0.707650i	−0.512015	−	0.0265017i
$714$	18.1996	−	4.41389i	0.681103	−	0.165186i
$715$	−2.35082	+	5.64953i	−0.0879155	+	0.211280i
$716$	−52.7264	−	118.015i	−1.97048	−	4.41041i
$717$	0.483106	−	34.0902i	0.0180419	−	1.27312i
$718$	−53.9363	−	30.6770i	−2.01288	−	1.14485i
$719$	−33.1478	−	10.6284i	−1.23620	−	0.396373i	−0.385839	−	0.922566i	$-0.626088\pi$
$719$	−33.1478	−	10.6284i	−1.23620	−	0.396373i	−0.850365	+	0.526194i	$0.823619\pi$
$720$	5.70394	+	28.4443i	0.212573	+	1.06006i
$721$	12.4486	+	0.483062i	0.463610	+	0.0179902i
$722$	−8.85814	+	22.0889i	−0.329666	+	0.822065i
$723$	−4.09199	+	2.35574i	−0.152183	+	0.0876108i
$724$	97.9114	+	30.0037i	3.63885	+	1.11508i
$725$	32.5294	+	0.841290i	1.20811	+	0.0312447i
$726$	−0.449839	−	38.4913i	−0.0166951	−	1.42854i
$727$	28.5516	+	0.369147i	1.05892	+	0.0136909i	0.540428	−	0.841390i	$-0.318262\pi$
$727$	28.5516	+	0.369147i	1.05892	+	0.0136909i	0.518494	+	0.855081i	$0.326493\pi$
$728$	−149.747			−5.55000
$729$	−26.9337	+	1.89162i	−0.997543	+	0.0700601i
$730$	−4.18104			−0.154747
$731$	7.58611	+	0.0980815i	0.280583	+	0.00362768i
$732$	31.4119	−	18.6285i	1.16102	−	0.688528i
$733$	−48.9054	−	1.26482i	−1.80636	−	0.0467170i	−0.892100	−	0.451839i	$-0.850768\pi$
$733$	−48.9054	−	1.26482i	−1.80636	−	0.0467170i	−0.914263	+	0.405122i	$0.867229\pi$
$734$	−36.2090	−	11.0958i	−1.33650	−	0.409554i
$735$	−0.00225467	+	1.81519i	−8.31648e−5	+	0.0669544i
$736$	19.7349	−	49.2116i	0.727439	−	1.81396i
$737$	−13.4333	−	0.521273i	−0.494822	−	0.0192013i
$738$	33.8506	+	27.0815i	1.24606	+	0.996883i
$739$	−7.46137	−	2.39239i	−0.274471	−	0.0880056i	0.164903	−	0.986310i	$-0.447269\pi$
$739$	−7.46137	−	2.39239i	−0.274471	−	0.0880056i	−0.439374	+	0.898304i	$0.644800\pi$
$740$	−31.6226	−	17.9858i	−1.16247	−	0.661171i
$741$	26.5259	−	14.8176i	0.974453	−	0.544338i
$742$	13.0225	+	29.1475i	0.478070	+	1.07004i
$743$	4.51540	−	10.8515i	0.165654	−	0.398104i	−0.818720	−	0.574193i	$-0.805316\pi$
$743$	4.51540	−	10.8515i	0.165654	−	0.398104i	0.984374	+	0.176089i	$0.0563448\pi$
$744$	−24.8185	+	84.5032i	−0.909891	+	3.09804i
$745$	10.3788	+	0.537204i	0.380251	+	0.0196816i
$746$	88.4573	+	40.2088i	3.23865	+	1.47215i
$747$	9.15606	−	7.84725i	0.335003	−	0.287116i
$748$	7.01095	+	10.2222i	0.256346	+	0.373761i
$749$	−28.3477	−	9.49520i	−1.03580	−	0.346947i
$750$	−4.58430	−	29.5523i	−0.167395	−	1.07910i
$751$	−19.3707	−	11.3513i	−0.706847	−	0.414213i	0.107798	−	0.994173i	$-0.465620\pi$
$751$	−19.3707	−	11.3513i	−0.706847	−	0.414213i	−0.814645	+	0.579959i	$0.803068\pi$
$752$	−48.2400	+	147.171i	−1.75913	+	5.36679i
$753$	−1.19423	+	44.0587i	−0.0435202	+	1.60559i
$754$	88.1703	+	59.6376i	3.21097	+	2.17187i
$755$	−5.40456	−	12.5292i	−0.196692	−	0.455983i
$756$	−76.9424	−	30.0367i	−2.79837	−	1.09242i
$757$	−0.544585	+	1.26249i	−0.0197933	+	0.0458860i	−0.927826	−	0.373013i	$-0.878325\pi$
$757$	−0.544585	+	1.26249i	−0.0197933	+	0.0458860i	0.908033	+	0.418899i	$0.137584\pi$
$758$	−37.7684	+	24.1470i	−1.37181	+	0.877059i
$759$	7.15859	−	1.63846i	0.259840	−	0.0594723i
$760$	−5.19333	−	19.1342i	−0.188382	−	0.694070i
$761$	21.7948	+	1.41082i	0.790061	+	0.0511422i	0.454350	−	0.890823i	$-0.349871\pi$
$761$	21.7948	+	1.41082i	0.790061	+	0.0511422i	0.335710	+	0.941965i	$0.391024\pi$
$762$	−48.2211	+	87.1364i	−1.74687	+	3.15662i
$763$	11.1986	+	5.26615i	0.405418	+	0.190647i
$764$	59.3076	−	73.5299i	2.14567	−	2.66022i
$765$	−0.474159	+	2.65057i	−0.0171432	+	0.0958314i
$766$	4.37847	+	0.859904i	0.158201	+	0.0310696i
$767$	44.2142	+	66.2871i	1.59648	+	2.39349i
$768$	−54.5511	−	38.5620i	−1.96844	−	1.39149i
$769$	16.9568	+	5.92464i	0.611476	+	0.213648i	0.617804	−	0.786332i	$-0.288022\pi$
$769$	16.9568	+	5.92464i	0.611476	+	0.213648i	−0.00632774	+	0.999980i	$0.502014\pi$
$770$	−8.34433	+	3.15984i	−0.300709	+	0.113873i
$771$	1.25667	+	0.505764i	0.0452578	+	0.0182146i
$772$	65.5104	−	28.7621i	2.35777	−	1.03517i
$773$	−24.7631	−	14.9446i	−0.890667	−	0.537520i	−0.00403274	−	0.999992i	$-0.501284\pi$
$773$	−24.7631	−	14.9446i	−0.890667	−	0.537520i	−0.886634	+	0.462472i	$0.846963\pi$
$774$	−37.1903	−	26.7219i	−1.33678	−	0.960499i
$775$	8.04079	−	23.5001i	0.288834	−	0.844148i
$776$	5.63074	−	20.7458i	0.202132	−	0.744729i
$777$	45.4456	−	23.8662i	1.63035	−	0.856194i
$778$	19.6454	+	18.7760i	0.704321	+	0.673151i
$779$	−13.9492	−	9.70030i	−0.499782	−	0.347549i
$780$	13.7468	−	31.2053i	0.492215	−	1.11733i
$781$	5.57015	+	13.3863i	0.199316	+	0.479000i
$782$	6.36725	−	6.74889i	0.227692	−	0.241340i
$783$	21.0524	+	30.5157i	0.752350	+	1.09054i
$784$	−15.8362	−	16.7853i	−0.565577	−	0.599477i
$785$	−2.08681	+	4.67080i	−0.0744816	+	0.166708i
$786$	2.04905	+	0.950529i	0.0730873	+	0.0339043i
$787$	−34.8109	+	21.6273i	−1.24087	+	0.770930i	−0.980867	−	0.194677i	$-0.937634\pi$
$787$	−34.8109	+	21.6273i	−1.24087	+	0.770930i	−0.260006	+	0.965607i	$0.583725\pi$
$788$	−71.0648	+	12.0575i	−2.53158	+	0.429531i
$789$	11.5011	−	35.7170i	0.409452	−	1.27156i
$790$	12.7988	−	23.5543i	0.455361	−	0.838024i
$791$	2.17928	+	8.46049i	0.0774863	+	0.300820i
$792$	0.422753	−	47.2421i	0.0150219	−	1.67868i
$793$	−21.2092	−	1.64851i	−0.753162	−	0.0585404i
$794$	4.45225	+	36.0679i	0.158004	+	1.28000i
$795$	−4.59009	+	0.0239700i	−0.162794	+	0.000850129i
$796$	47.1288	−	24.4370i	1.67044	−	0.866147i
$797$	−31.8267	−	15.4720i	−1.12736	−	0.548047i	−0.223000	−	0.974818i	$-0.571585\pi$
$797$	−31.8267	−	15.4720i	−1.12736	−	0.548047i	−0.904359	+	0.426772i	$0.859651\pi$
$798$	42.2587	+	13.3068i	1.49594	+	0.471054i
$799$	−9.16868	+	11.0714i	−0.324364	+	0.391677i
$800$	76.0317	+	58.9290i	2.68812	+	2.08345i
$801$	1.51521	+	9.44189i	0.0535372	+	0.333613i
$802$	9.80943	−	3.14527i	0.346383	−	0.111063i
$803$	3.82155	+	0.801973i	0.134859	+	0.0283010i
$804$	74.7818	+	4.44875i	2.63735	+	0.156895i
$805$	2.65528	+	4.09457i	0.0935864	+	0.144315i
$806$	63.5696	−	50.5991i	2.23914	−	1.78228i
$807$	14.6683	−	6.53164i	0.516349	−	0.229925i
$808$	5.54369	−	29.2252i	0.195026	−	1.02814i
$809$	−2.84870	−	1.03684i	−0.100155	−	0.0364535i	0.291457	−	0.956584i	$-0.405860\pi$
$809$	−2.84870	−	1.03684i	−0.100155	−	0.0364535i	−0.391612	+	0.920131i	$0.628082\pi$
$810$	11.5127	−	11.4728i	0.404517	−	0.403114i
$811$	51.9483	−	18.9076i	1.82415	−	0.663937i	0.829769	−	0.558107i	$-0.188472\pi$
$811$	51.9483	−	18.9076i	1.82415	−	0.663937i	0.994384	−	0.105830i	$-0.0337499\pi$
$812$	18.2483	+	111.935i	0.640390	+	3.92814i
$813$	5.62640	+	43.7016i	0.197326	+	1.53268i
$814$	34.8354	+	30.7997i	1.22098	+	1.07953i
$815$	8.85585	−	3.75233i	0.310207	−	0.131438i
$816$	−18.7751	−	28.6235i	−0.657260	−	1.00202i
$817$	15.2458	+	9.47188i	0.533382	+	0.331379i
$818$	10.1277	+	4.13763i	0.354107	+	0.144669i
$819$	26.5985	+	40.0926i	0.929427	+	1.40095i
$820$	−19.0536	+	0.739366i	−0.665380	+	0.0258198i
$821$	−14.5114	+	40.6862i	−0.506452	+	1.41996i	0.365704	+	0.930731i	$0.380828\pi$
$821$	−14.5114	+	40.6862i	−0.506452	+	1.41996i	−0.872156	+	0.489227i	$0.837279\pi$
$822$	66.8204	+	64.8559i	2.33063	+	2.26211i
$823$	12.9430	−	45.3587i	0.451163	−	1.58111i	−0.321898	−	0.946774i	$-0.604321\pi$
$823$	12.9430	−	45.3587i	0.451163	−	1.58111i	0.773061	−	0.634331i	$-0.218724\pi$
$824$	−11.8793	−	37.8897i	−0.413835	−	1.31995i
$825$	−0.705222	+	13.3048i	−0.0245527	+	0.463213i
$826$	−26.0628	+	113.224i	−0.906839	+	3.93957i
$827$	22.7618	+	22.3246i	0.791506	+	0.776303i	0.978542	−	0.206050i	$-0.0660608\pi$
$827$	22.7618	+	22.3246i	0.791506	+	0.776303i	−0.187036	+	0.982353i	$0.559888\pi$
$828$	−40.0715	+	8.30535i	−1.39258	+	0.288631i
$829$	9.53825	+	6.81753i	0.331277	+	0.236783i	0.734951	−	0.678120i	$-0.237205\pi$
$829$	9.53825	+	6.81753i	0.331277	+	0.236783i	−0.403674	+	0.914903i	$0.632267\pi$
$830$	−1.07527	+	7.17895i	−0.0373233	+	0.249185i
$831$	−10.2380	+	0.982988i	−0.355151	+	0.0340995i
$832$	52.0349	+	145.892i	1.80398	+	5.05790i
$833$	−0.797226	−	1.98799i	−0.0276222	−	0.0688797i
$834$	28.7909	+	22.6719i	0.996946	+	0.785063i
$835$	5.04295	−	5.20863i	0.174518	−	0.180252i
$836$	1.70509	+	29.2752i	0.0589717	+	1.01250i
$837$	27.0328	−	8.36491i	0.934392	−	0.289134i
$838$	3.79100	−	65.0890i	0.130958	−	2.24846i
$839$	−1.05829	−	1.15118i	−0.0365361	−	0.0397431i	0.717648	−	0.696406i	$-0.245219\pi$
$839$	−1.05829	−	1.15118i	−0.0365361	−	0.0397431i	−0.754184	+	0.656663i	$0.771968\pi$
$840$	29.5839	−	10.5102i	1.02074	−	0.362636i
$841$	9.19282	−	19.8816i	0.316994	−	0.685572i
$842$	−10.9969	+	8.07690i	−0.378977	+	0.278348i
$843$	5.92413	−	4.05228i	0.204038	−	0.139568i
$844$	−60.9207	+	86.4080i	−2.09698	+	2.97428i
$845$	−9.63002	+	5.81175i	−0.331283	+	0.199930i
$846$	83.6492	−	23.0616i	2.87592	−	0.792874i
$847$	−23.6035	+	3.69152i	−0.811027	+	0.126842i
$848$	42.1861	−	40.3191i	1.44868	−	1.38456i
$849$	41.4278	−	8.36107i	1.42180	−	0.286951i
$850$	8.60456	+	14.4683i	0.295134	+	0.496258i
$851$	12.4303	−	22.1875i	0.426106	−	0.760578i
$852$	−29.4942	−	75.2204i	−1.01045	−	2.57701i
$853$	−5.98696	−	24.5526i	−0.204989	−	0.840665i	−0.978394	−	0.206751i	$-0.933711\pi$
$853$	−5.98696	−	24.5526i	−0.204989	−	0.840665i	0.773404	−	0.633913i	$-0.218552\pi$
$854$	−19.4744	−	24.1445i	−0.666401	−	0.826207i
$855$	−4.20044	+	4.78911i	−0.143652	+	0.163784i
$856$	1.84778	+	95.2710i	0.0631558	+	3.25630i
$857$	19.8679	+	1.80294i	0.678673	+	0.0615872i	0.424304	−	0.905520i	$-0.360519\pi$
$857$	19.8679	+	1.80294i	0.678673	+	0.0615872i	0.254369	+	0.967107i	$0.418132\pi$
$858$	−25.3876	+	35.4261i	−0.866718	+	1.20943i
$859$	0.186856	+	1.69352i	0.00637543	+	0.0577822i	0.996736	−	0.0807326i	$-0.0257260\pi$
$859$	0.186856	+	1.69352i	0.00637543	+	0.0577822i	−0.990360	+	0.138515i	$0.955767\pi$
$860$	20.0607	−	1.82044i	0.684064	−	0.0620764i
$861$	13.6315	−	23.1957i	0.464559	−	0.790508i
$862$	−95.1915	+	21.2649i	−3.24223	+	0.724285i
$863$	51.3274	−	25.7776i	1.74721	−	0.877480i	0.779115	−	0.626881i	$-0.215669\pi$
$863$	51.3274	−	25.7776i	1.74721	−	0.877480i	0.968091	−	0.250599i	$-0.0806274\pi$
$864$	−3.24167	+	109.547i	−0.110284	+	3.72685i
$865$	0.529989	+	0.266171i	0.0180202	+	0.00905007i
$866$	9.25534	+	2.32033i	0.314509	+	0.0788480i
$867$	5.36295	+	25.7143i	0.182135	+	0.873304i
$868$	85.6927	+	12.2694i	2.90860	+	0.416449i
$869$	−16.2163	+	19.0741i	−0.550101	+	0.647044i
$870$	−21.6046	−	5.59361i	−0.732464	−	0.189641i
$871$	−34.1424	−	27.1762i	−1.15687	−	0.920829i
$872$	3.81861	−	39.2587i	0.129314	−	1.32947i
$873$	−6.55452	+	2.17737i	−0.221837	+	0.0736929i
$874$	21.1467	−	5.88658i	0.715296	−	0.199116i
$875$	−17.7459	+	5.43801i	−0.599921	+	0.183838i
$876$	−21.1990	−	4.90748i	−0.716248	−	0.165808i
$877$	41.3089	+	9.22802i	1.39490	+	0.311608i	0.849952	−	0.526860i	$-0.176631\pi$
$877$	41.3089	+	9.22802i	1.39490	+	0.311608i	0.544950	+	0.838468i	$0.316549\pi$
$878$	−102.697	+	25.7463i	−3.46585	+	0.868895i
$879$	14.5439	−	21.4447i	0.490553	−	0.723313i
$880$	10.5642	+	12.4259i	0.356120	+	0.418878i
$881$	−10.5112	−	16.6771i	−0.354131	−	0.561867i	0.620913	−	0.783879i	$-0.286762\pi$
$881$	−10.5112	−	16.6771i	−0.354131	−	0.561867i	−0.975044	+	0.222013i	$0.928737\pi$
$882$	−2.93149	+	12.5921i	−0.0987085	+	0.423997i
$883$	5.72826	−	4.43973i	0.192771	−	0.149409i	−0.511643	−	0.859198i	$-0.670963\pi$
$883$	5.72826	−	4.43973i	0.192771	−	0.149409i	0.704414	+	0.709789i	$0.251210\pi$
$884$	−1.30024	+	40.2150i	−0.0437318	+	1.35258i
$885$	−13.3874	−	9.99240i	−0.450011	−	0.335891i
$886$	−0.579135	+	4.69160i	−0.0194564	+	0.157617i
$887$	−2.62093	+	12.9036i	−0.0880023	+	0.433262i	0.911744	+	0.410758i	$0.134736\pi$
$887$	−2.62093	+	12.9036i	−0.0880023	+	0.433262i	−0.999747	+	0.0225039i	$0.992836\pi$
$888$	−120.311	−	110.879i	−4.03738	−	3.72086i
$889$	57.8024	+	21.8887i	1.93863	+	0.734123i
$890$	−4.40973	−	3.70020i	−0.147814	−	0.124031i
$891$	−12.7235	+	8.27810i	−0.426253	+	0.277327i
$892$	25.4105	−	21.3219i	0.850805	−	0.713910i
$893$	−32.1047	+	11.2173i	−1.07434	+	0.375372i
$894$	71.1562	+	20.3998i	2.37982	+	0.682272i
$895$	−2.33832	−	15.6115i	−0.0781613	−	0.521836i
$896$	−46.4964	+	91.1087i	−1.55334	+	3.04373i
$897$	21.8766	+	9.46889i	0.730439	+	0.316157i
$898$	34.4703	−	38.4828i	1.15029	−	1.28419i
$899$	−28.7735	−	26.1105i	−0.959649	−	0.870835i
$900$	5.45882	−	74.0447i	0.181961	−	2.46816i
$901$	5.01397	−	2.04843i	0.167040	−	0.0682432i
$902$	24.0282	+	4.07686i	0.800053	+	0.135744i
$903$	−13.1143	+	25.2153i	−0.436416	+	0.839112i
$904$	23.0661	−	15.6017i	0.767167	−	0.518905i
$905$	10.5369	+	6.73668i	0.350257	+	0.223935i
$906$	−17.3761	−	95.6221i	−0.577283	−	3.17683i
$907$	−25.5326	−	10.8185i	−0.847795	−	0.359221i	−0.0775648	−	0.996987i	$-0.524714\pi$
$907$	−25.5326	−	10.8185i	−0.847795	−	0.359221i	−0.770230	+	0.637766i	$0.779858\pi$
$908$	31.6991	+	66.2929i	1.05197	+	2.20001i
$909$	−8.80932	+	3.70683i	−0.292187	+	0.122948i
$910$	−27.9021	−	7.76708i	−0.924945	−	0.257476i
$911$	9.93638	−	0.256980i	0.329207	−	0.00851412i	0.139103	−	0.990278i	$-0.455578\pi$
$911$	9.93638	−	0.256980i	0.329207	−	0.00851412i	0.190105	+	0.981764i	$0.439117\pi$
$912$	−3.03969	−	80.9274i	−0.100654	−	2.67978i
$913$	2.35983	−	6.35544i	0.0780989	−	0.210334i
$914$	−63.5512	−	34.0019i	−2.10209	−	1.12468i
$915$	4.30578	−	1.16292i	0.142345	−	0.0384449i
$916$	−77.5506	−	107.030i	−2.56234	−	3.53637i
$917$	0.402061	−	1.34298i	0.0132772	−	0.0443490i
$918$	−7.54796	+	17.6307i	−0.249120	+	0.581900i
$919$	5.91708	+	19.7644i	0.195187	+	0.651969i	0.998414	+	0.0562963i	$0.0179291\pi$
$919$	5.91708	+	19.7644i	0.195187	+	0.651969i	−0.803228	+	0.595672i	$0.796886\pi$
$920$	9.44930	−	12.3559i	0.311534	−	0.407361i
$921$	−15.2001	+	7.48765i	−0.500860	+	0.246726i
$922$	−10.2605	+	4.82498i	−0.337912	+	0.158902i
$923$	−11.1495	+	45.7244i	−0.366991	+	1.50504i
$924$	−46.0168	+	6.22713i	−1.51384	+	0.204857i
$925$	32.5209	+	32.7318i	1.06928	+	1.07622i
$926$	−18.8878	+	3.70944i	−0.620691	+	0.121900i
$927$	−8.03438	+	9.91058i	−0.263884	+	0.325506i
$928$	131.755	−	72.6994i	4.32508	−	2.38648i
$929$	2.72869	+	2.00415i	0.0895256	+	0.0657542i	0.635810	−	0.771845i	$-0.280666\pi$
$929$	2.72869	+	2.00415i	0.0895256	+	0.0657542i	−0.546285	+	0.837600i	$0.683958\pi$
$930$	−9.00740	+	14.4580i	−0.295364	+	0.474098i
$931$	0.815325	−	5.00119i	0.0267212	−	0.163907i
$932$	8.42854	+	44.4336i	0.276086	+	1.45547i
$933$	−22.8479	+	48.4306i	−0.748007	+	1.58555i
$934$	−49.8772	+	3.22865i	−1.63203	+	0.105645i
$935$	0.490069	+	1.43228i	0.0160270	+	0.0468406i
$936$	91.8829	−	122.782i	3.00329	−	4.01326i
$937$	−19.6397	−	50.8680i	−0.641600	−	1.66179i	−0.744933	−	0.667140i	$-0.767518\pi$
$937$	−19.6397	−	50.8680i	−0.641600	−	1.66179i	0.103332	−	0.994647i	$-0.467050\pi$
$938$	−5.34084	−	63.4057i	−0.174385	−	2.07027i
$939$	−2.77000	+	17.5684i	−0.0903956	+	0.573322i
$940$	−21.1783	+	31.7511i	−0.690761	+	1.03561i
$941$	4.58404	−	4.61377i	0.149435	−	0.150405i	−0.630673	−	0.776048i	$-0.717221\pi$
$941$	4.58404	−	4.61377i	0.149435	−	0.150405i	0.780109	+	0.625644i	$0.215164\pi$
$942$	−21.9835	+	29.0587i	−0.716260	+	0.946783i
$943$	−0.602966	−	13.3163i	−0.0196353	−	0.433639i
$944$	210.940	−	24.6554i	6.86552	−	0.802465i
$945$	−8.06873	−	6.05381i	−0.262476	−	0.196930i
$946$	−25.5718	−	2.98892i	−0.831412	−	0.0971782i
$947$	1.22587	−	17.2110i	0.0398355	−	0.559282i	−0.937555	−	0.347838i	$-0.886916\pi$
$947$	1.22587	−	17.2110i	0.0398355	−	0.559282i	0.977390	−	0.211444i	$-0.0678166\pi$
$948$	92.5401	−	104.404i	3.00556	−	3.39089i
$949$	8.45689	+	9.44131i	0.274522	+	0.306478i
$950$	−0.257431	+	39.8237i	−0.00835216	+	1.29205i
$951$	−2.52227	+	12.7591i	−0.0817902	+	0.413742i
$952$	−27.7536	+	24.5383i	−0.899500	+	0.795292i
$953$	−16.7441	+	35.0174i	−0.542395	+	1.13432i	0.430396	+	0.902640i	$0.358374\pi$
$953$	−16.7441	+	35.0174i	−0.542395	+	1.13432i	−0.972791	+	0.231683i	$0.925577\pi$
$954$	−31.8893	−	7.20701i	−1.03246	−	0.233335i
$955$	9.38584	−	6.70859i	0.303718	−	0.217085i
$956$	48.5528	+	95.1382i	1.57031	+	3.07699i
$957$	18.6741	+	9.25667i	0.603647	+	0.299226i
$958$	28.0891	+	36.7292i	0.907518	+	1.18667i
$959$	33.9093	−	46.7992i	1.09499	−	1.51123i
$960$	−20.5196	−	25.1702i	−0.662267	−	0.812365i
$961$	1.15848	−	0.678869i	0.0373702	−	0.0218990i
$962$	31.9537	+	147.515i	1.03023	+	4.75607i
$963$	25.1792	−	17.4170i	0.811389	−	0.561256i
$964$	7.88734	−	12.5141i	0.254034	−	0.403053i
$965$	8.64943	−	1.23841i	0.278435	−	0.0398659i
$966$	11.8478	+	32.6777i	0.381196	+	1.05139i
$967$	16.4589	−	15.3283i	0.529282	−	0.492924i	−0.370759	−	0.928729i	$-0.620903\pi$
$967$	16.4589	−	15.3283i	0.529282	−	0.492924i	0.900041	+	0.435805i	$0.143536\pi$
$968$	36.3563	+	66.9084i	1.16854	+	2.15052i
$969$	2.48813	−	7.09291i	0.0799303	−	0.227857i
$970$	2.12521	−	3.57346i	0.0682362	−	0.114737i
$971$	−20.2183	−	35.0191i	−0.648836	−	1.12382i	−0.983401	−	0.181444i	$-0.941923\pi$
$971$	−20.2183	−	35.0191i	−0.648836	−	1.12382i	0.334565	−	0.942373i	$-0.391410\pi$
$972$	71.8389	−	44.6573i	2.30423	−	1.43238i
$973$	11.3718	−	19.6965i	0.364563	−	0.631441i
$974$	2.05471	+	3.66757i	0.0658373	+	0.117516i
$975$	−27.4105	+	33.4528i	−0.877838	+	1.07135i
$976$	−29.6106	+	48.3551i	−0.947811	+	1.54781i
$977$	−5.06367	−	21.9980i	−0.162001	−	0.703779i	−0.989765	−	0.142703i	$-0.954420\pi$
$977$	−5.06367	−	21.9980i	−0.162001	−	0.703779i	0.827764	−	0.561076i	$-0.189612\pi$
$978$	67.4787	−	11.8119i	2.15773	−	0.377703i
$979$	3.32083	+	4.22789i	0.106134	+	0.135124i
$980$	−2.65029	−	5.03146i	−0.0846605	−	0.160724i
$981$	−11.1892	+	5.95087i	−0.357245	+	0.189997i
$982$	3.26778	−	2.96535i	0.104279	−	0.0946282i
$983$	0.131948	+	20.4119i	0.00420850	+	0.651039i	0.947617	+	0.319408i	$0.103484\pi$
$983$	0.131948	+	20.4119i	0.00420850	+	0.651039i	−0.943409	+	0.331632i	$0.892401\pi$
$984$	−84.2330	−	16.0864i	−2.68525	−	0.512817i
$985$	−8.75583	−	0.908832i	−0.278984	−	0.0289578i
$986$	26.1137	−	3.39501i	0.831630	−	0.108119i
$987$	−21.5876	−	49.3357i	−0.687141	−	1.57037i
$988$	−51.7922	+	79.8660i	−1.64773	+	2.54088i
$989$	1.36325	+	14.0155i	0.0433490	+	0.445667i
$990$	2.52912	−	8.78061i	0.0803808	−	0.279066i
$991$	9.44202	−	0.733892i	0.299936	−	0.0233129i	0.0733572	−	0.997306i	$-0.476629\pi$
$991$	9.44202	−	0.733892i	0.299936	−	0.0233129i	0.226579	+	0.973993i	$0.427246\pi$
$992$	−22.8632	−	112.562i	−0.725908	−	3.57386i
$993$	−19.8013	−	0.408651i	−0.628375	−	0.0129681i
$994$	−59.6528	+	33.9283i	−1.89207	+	1.07614i
$995$	6.34515	−	1.33156i	0.201155	−	0.0422134i
$996$	−13.8782	+	35.1371i	−0.439747	+	1.11336i
$997$	−6.24046	+	3.03369i	−0.197637	+	0.0960780i	−0.533380	−	0.845876i	$-0.679078\pi$
$997$	−6.24046	+	3.03369i	−0.197637	+	0.0960780i	0.335743	+	0.941954i	$0.391013\pi$
$998$	−41.0448	+	55.1327i	−1.29925	+	1.74520i
$999$	−8.31626	+	51.9063i	−0.263115	+	1.64224i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	729.2.k.a.4.1	✓	12960
729.547	even	243	inner	729.2.k.a.547.1	yes	12960

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
729.2.k.a.4.1	✓	12960	1.1	even	1	trivial
729.2.k.a.547.1	yes	12960	729.547	even	243	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:	\( N \)	\(=\)	\( 729 = 3^{6} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	729.k (of order \(243\), degree \(162\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.72490 - 0.0352304i) q^{2} +(-1.51002 - 0.848437i) q^{3} +(5.42450 + 0.140291i) q^{4} +(0.633611 + 0.194162i) q^{5} +(4.08476 + 2.36510i) q^{6} +(1.09035 - 2.71893i) q^{7} +(-9.33012 - 0.362051i) q^{8} +(1.56031 + 2.56231i) q^{9} +O(q^{10})\)	\(q+(-2.72490 - 0.0352304i) q^{2} +(-1.51002 - 0.848437i) q^{3} +(5.42450 + 0.140291i) q^{4} +(0.633611 + 0.194162i) q^{5} +(4.08476 + 2.36510i) q^{6} +(1.09035 - 2.71893i) q^{7} +(-9.33012 - 0.362051i) q^{8} +(1.56031 + 2.56231i) q^{9} +(-1.71968 - 0.551395i) q^{10} +(1.46606 + 0.833840i) q^{11} +(-8.07206 - 4.81419i) q^{12} +(2.23325 + 4.99855i) q^{13} +(-3.06688 + 7.37039i) q^{14} +(-0.792029 - 0.830767i) q^{15} +(14.5728 + 0.754280i) q^{16} +(1.23299 + 0.560463i) q^{17} +(-4.16141 - 7.03701i) q^{18} +(1.81231 + 2.64242i) q^{19} +(3.40978 + 1.14212i) q^{20} +(-3.95329 + 3.18054i) q^{21} +(-3.96548 - 2.32378i) q^{22} +(-0.783008 + 2.38882i) q^{23} +(13.7815 + 8.46272i) q^{24} +(-3.77781 - 2.55527i) q^{25} +(-5.90927 - 13.6992i) q^{26} +(-0.182133 - 5.19296i) q^{27} +(6.29604 - 14.5959i) q^{28} +(-6.01114 + 3.84319i) q^{29} +(2.12893 + 2.29166i) q^{30} +(1.42648 + 5.25570i) q^{31} +(-21.0474 - 1.36244i) q^{32} +(-1.50631 - 2.50297i) q^{33} +(-3.34003 - 1.57064i) q^{34} +(1.21877 - 1.51104i) q^{35} +(8.10442 + 14.1182i) q^{36} +(-9.92713 - 1.94962i) q^{37} +(-4.84528 - 7.26417i) q^{38} +(0.868716 - 9.44268i) q^{39} +(-5.84136 - 2.04095i) q^{40} +(-4.95892 + 1.87785i) q^{41} +(10.8844 - 8.52737i) q^{42} +(5.12901 - 2.25187i) q^{43} +(7.83565 + 4.72884i) q^{44} +(0.491124 + 1.92646i) q^{45} +(2.21778 - 6.48170i) q^{46} +(-2.78011 + 10.2430i) q^{47} +(-21.3652 - 13.5030i) q^{48} +(-1.14325 - 1.09266i) q^{49} +(10.2041 + 7.09596i) q^{50} +(-1.38632 - 1.89243i) q^{51} +(11.4130 + 27.4280i) q^{52} +(2.74430 - 2.90879i) q^{53} +(0.313345 + 14.1567i) q^{54} +(0.767010 + 0.812983i) q^{55} +(-11.1575 + 24.9732i) q^{56} +(-0.494700 - 5.52773i) q^{57} +(16.5152 - 10.2605i) q^{58} +(14.3490 - 2.43458i) q^{59} +(-4.17981 - 4.61761i) q^{60} +(-1.85519 + 3.41421i) q^{61} +(-3.70186 - 14.3715i) q^{62} +(8.66802 - 1.44855i) q^{63} +(28.2073 + 2.19245i) q^{64} +(0.444479 + 3.60075i) q^{65} +(4.01637 + 6.87341i) q^{66} +(-7.07605 + 3.66904i) q^{67} +(6.60974 + 3.21321i) q^{68} +(3.20912 - 2.94282i) q^{69} +(-3.37426 + 4.07449i) q^{70} +(6.79467 + 5.26626i) q^{71} +(-13.6302 - 24.4716i) q^{72} +(2.20463 - 0.706886i) q^{73} +(26.9817 + 5.66227i) q^{74} +(3.53656 + 7.06374i) q^{75} +(9.46019 + 14.5881i) q^{76} +(3.86567 - 3.07693i) q^{77} +(-2.69983 + 25.6997i) q^{78} +(-2.76639 + 14.5839i) q^{79} +(9.08700 + 3.30740i) q^{80} +(-4.13088 + 7.99599i) q^{81} +(13.5787 - 4.94225i) q^{82} +(-0.646758 - 3.96720i) q^{83} +(-21.8908 + 16.6982i) q^{84} +(0.672416 + 0.594516i) q^{85} +(-14.0554 + 5.95543i) q^{86} +(12.3376 - 0.703210i) q^{87} +(-13.3766 - 8.31061i) q^{88} +(2.95081 + 1.20554i) q^{89} +(-1.27039 - 5.26671i) q^{90} +(16.0257 - 0.621871i) q^{91} +(-4.58256 + 12.8483i) q^{92} +(2.30512 - 9.14649i) q^{93} +(7.93639 - 27.8132i) q^{94} +(0.635244 + 2.02615i) q^{95} +(30.6260 + 19.9147i) q^{96} +(-0.516441 + 2.24357i) q^{97} +(3.07675 + 3.01766i) q^{98} +(0.150945 + 5.05754i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12960 q - 162 q^{2} - 162 q^{3} - 162 q^{4} - 162 q^{5} - 162 q^{6} - 162 q^{7} - 162 q^{8} - 162 q^{9}+O(q^{10}) \) 12960 * q - 162 * q^2 - 162 * q^3 - 162 * q^4 - 162 * q^5 - 162 * q^6 - 162 * q^7 - 162 * q^8 - 162 * q^9	\( 12960 q - 162 q^{2} - 162 q^{3} - 162 q^{4} - 162 q^{5} - 162 q^{6} - 162 q^{7} - 162 q^{8} - 162 q^{9} - 162 q^{10} - 162 q^{11} - 162 q^{12} - 162 q^{13} - 162 q^{14} - 162 q^{15} - 162 q^{16} - 162 q^{17} - 162 q^{18} - 162 q^{19} - 162 q^{20} - 162 q^{21} - 162 q^{22} - 162 q^{23} - 162 q^{24} - 162 q^{25} - 162 q^{26} - 162 q^{27} - 162 q^{28} - 162 q^{29} - 162 q^{30} - 162 q^{31} - 162 q^{32} - 162 q^{33} - 162 q^{34} - 162 q^{35} - 162 q^{36} - 162 q^{37} - 162 q^{38} - 162 q^{39} - 162 q^{40} - 162 q^{41} - 162 q^{42} - 162 q^{43} - 162 q^{44} - 162 q^{45} - 162 q^{46} - 162 q^{47} - 162 q^{48} - 162 q^{49} - 162 q^{50} - 162 q^{51} - 162 q^{52} - 162 q^{53} - 162 q^{54} - 162 q^{55} - 162 q^{56} - 162 q^{57} - 162 q^{58} - 162 q^{59} - 162 q^{60} - 162 q^{61} - 162 q^{62} - 162 q^{63} - 162 q^{64} - 162 q^{65} - 162 q^{66} - 162 q^{67} - 162 q^{68} - 162 q^{69} - 162 q^{70} - 162 q^{71} - 162 q^{72} - 162 q^{73} - 162 q^{74} - 162 q^{75} - 162 q^{76} - 162 q^{77} - 162 q^{78} - 162 q^{79} - 162 q^{80} - 162 q^{81} - 162 q^{82} - 162 q^{83} - 162 q^{84} - 162 q^{85} - 162 q^{86} - 162 q^{87} - 162 q^{88} - 162 q^{89} - 162 q^{90} - 162 q^{91} - 162 q^{92} - 162 q^{93} - 162 q^{94} - 162 q^{95} - 162 q^{96} - 162 q^{97} - 162 q^{98} - 162 q^{99}+O(q^{100}) \) 12960 * q - 162 * q^2 - 162 * q^3 - 162 * q^4 - 162 * q^5 - 162 * q^6 - 162 * q^7 - 162 * q^8 - 162 * q^9 - 162 * q^10 - 162 * q^11 - 162 * q^12 - 162 * q^13 - 162 * q^14 - 162 * q^15 - 162 * q^16 - 162 * q^17 - 162 * q^18 - 162 * q^19 - 162 * q^20 - 162 * q^21 - 162 * q^22 - 162 * q^23 - 162 * q^24 - 162 * q^25 - 162 * q^26 - 162 * q^27 - 162 * q^28 - 162 * q^29 - 162 * q^30 - 162 * q^31 - 162 * q^32 - 162 * q^33 - 162 * q^34 - 162 * q^35 - 162 * q^36 - 162 * q^37 - 162 * q^38 - 162 * q^39 - 162 * q^40 - 162 * q^41 - 162 * q^42 - 162 * q^43 - 162 * q^44 - 162 * q^45 - 162 * q^46 - 162 * q^47 - 162 * q^48 - 162 * q^49 - 162 * q^50 - 162 * q^51 - 162 * q^52 - 162 * q^53 - 162 * q^54 - 162 * q^55 - 162 * q^56 - 162 * q^57 - 162 * q^58 - 162 * q^59 - 162 * q^60 - 162 * q^61 - 162 * q^62 - 162 * q^63 - 162 * q^64 - 162 * q^65 - 162 * q^66 - 162 * q^67 - 162 * q^68 - 162 * q^69 - 162 * q^70 - 162 * q^71 - 162 * q^72 - 162 * q^73 - 162 * q^74 - 162 * q^75 - 162 * q^76 - 162 * q^77 - 162 * q^78 - 162 * q^79 - 162 * q^80 - 162 * q^81 - 162 * q^82 - 162 * q^83 - 162 * q^84 - 162 * q^85 - 162 * q^86 - 162 * q^87 - 162 * q^88 - 162 * q^89 - 162 * q^90 - 162 * q^91 - 162 * q^92 - 162 * q^93 - 162 * q^94 - 162 * q^95 - 162 * q^96 - 162 * q^97 - 162 * q^98 - 162 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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