LMFDB - Embedded newform 539.2.r.b.23.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [539,2,Mod(23,539)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(539, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([38, 0]))

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

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

chi := DirichletCharacter("539.23");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 539 = 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	539.r (of order $21$, degree $12$, 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:	$4.30393666895$
Analytic rank:	$0$
Dimension:	$276$
Relative dimension:	$23$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			23.19
Character	$\chi$	$=$	539.23
Dual form			539.2.r.b.375.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.130700 - 1.74407i) q^{2} +(-1.64058 + 0.506053i) q^{3} +(-1.04703 - 0.157814i) q^{4} +(2.53334 + 2.35060i) q^{5} +(0.668166 + 2.92743i) q^{6} +(-2.49524 + 0.879644i) q^{7} +(0.366275 - 1.60475i) q^{8} +(-0.0432948 + 0.0295179i) q^{9} +O(q^{10})$	\(q+(0.130700 - 1.74407i) q^{2} +(-1.64058 + 0.506053i) q^{3} +(-1.04703 - 0.157814i) q^{4} +(2.53334 + 2.35060i) q^{5} +(0.668166 + 2.92743i) q^{6} +(-2.49524 + 0.879644i) q^{7} +(0.366275 - 1.60475i) q^{8} +(-0.0432948 + 0.0295179i) q^{9} +(4.43070 - 4.11109i) q^{10} +(0.826239 + 0.563320i) q^{11} +(1.79760 - 0.270944i) q^{12} +(-4.63023 + 2.22980i) q^{13} +(1.20803 + 4.46684i) q^{14} +(-5.34568 - 2.57434i) q^{15} +(-4.77455 - 1.47275i) q^{16} +(-1.07835 + 2.74759i) q^{17} +(0.0458226 + 0.0793671i) q^{18} +(-3.68067 + 6.37510i) q^{19} +(-2.28152 - 2.86094i) q^{20} +(3.64850 - 2.70585i) q^{21} +(1.09046 - 1.36739i) q^{22} +(-2.14040 - 5.45366i) q^{23} +(0.211186 + 2.81809i) q^{24} +(0.518859 + 6.92369i) q^{25} +(3.28375 + 8.36687i) q^{26} +(3.26742 - 4.09722i) q^{27} +(2.75141 - 0.527228i) q^{28} +(5.06532 + 6.35171i) q^{29} +(-5.18851 + 8.98676i) q^{30} +(1.83975 + 3.18654i) q^{31} +(-1.98990 + 5.07018i) q^{32} +(-1.64058 - 0.506053i) q^{33} +(4.65105 + 2.23983i) q^{34} +(-8.38898 - 3.63687i) q^{35} +(0.0499893 - 0.0240736i) q^{36} +(-3.85503 + 0.581052i) q^{37} +(10.6376 + 7.25256i) q^{38} +(6.46788 - 6.00131i) q^{39} +(4.70003 - 3.20442i) q^{40} +(-1.00905 + 4.42094i) q^{41} +(-4.24233 - 6.71689i) q^{42} +(-1.14356 - 5.01025i) q^{43} +(-0.776196 - 0.720204i) q^{44} +(-0.179065 - 0.0269897i) q^{45} +(-9.79131 + 3.02022i) q^{46} +(0.368320 - 4.91489i) q^{47} +8.57834 q^{48} +(5.45245 - 4.38985i) q^{49} +12.1432 q^{50} +(0.378697 - 5.05335i) q^{51} +(5.19988 - 1.60395i) q^{52} +(8.31669 + 1.25354i) q^{53} +(-6.71877 - 6.23411i) q^{54} +(0.769006 + 3.36923i) q^{55} +(0.497668 + 4.32644i) q^{56} +(2.81230 - 12.3215i) q^{57} +(11.7398 - 8.00409i) q^{58} +(7.71352 - 7.15710i) q^{59} +(5.19081 + 3.53903i) q^{60} +(-7.84672 + 1.18270i) q^{61} +(5.79800 - 2.79217i) q^{62} +(0.0820658 - 0.111738i) q^{63} +(-0.420793 - 0.202643i) q^{64} +(-16.9713 - 5.23495i) q^{65} +(-1.09701 + 2.79515i) q^{66} +(6.20901 + 10.7543i) q^{67} +(1.56267 - 2.70663i) q^{68} +(6.27135 + 7.86402i) q^{69} +(-7.43938 + 14.1556i) q^{70} +(-9.21422 + 11.5543i) q^{71} +(0.0315112 + 0.0802892i) q^{72} +(0.763379 + 10.1866i) q^{73} +(0.509543 + 6.79937i) q^{74} +(-4.35498 - 11.0963i) q^{75} +(4.85985 - 6.09405i) q^{76} +(-2.55719 - 0.678824i) q^{77} +(-9.62135 - 12.0648i) q^{78} +(7.15810 - 12.3982i) q^{79} +(-8.63371 - 14.9540i) q^{80} +(-3.22963 + 8.22897i) q^{81} +(7.57853 + 2.33767i) q^{82} +(10.0539 + 4.84172i) q^{83} +(-4.24711 + 2.25732i) q^{84} +(-9.19031 + 4.42582i) q^{85} +(-8.88768 + 1.33960i) q^{86} +(-11.5244 - 7.85718i) q^{87} +(1.20662 - 1.11958i) q^{88} +(4.79915 - 3.27201i) q^{89} +(-0.0704757 + 0.308774i) q^{90} +(9.59211 - 9.63684i) q^{91} +(1.38040 + 6.04793i) q^{92} +(-4.63082 - 4.29678i) q^{93} +(-8.52377 - 1.28475i) q^{94} +(-24.3097 + 7.49854i) q^{95} +(0.698815 - 9.32504i) q^{96} +1.29074 q^{97} +(-6.94355 - 10.0832i) q^{98} -0.0523999 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 276 q + 3 q^{3} + 20 q^{4} + 6 q^{5} - 8 q^{6} + 6 q^{8} + 6 q^{9}+O(q^{10}) $ 276 * q + 3 * q^3 + 20 * q^4 + 6 * q^5 - 8 * q^6 + 6 * q^8 + 6 * q^9	\( 276 q + 3 q^{3} + 20 q^{4} + 6 q^{5} - 8 q^{6} + 6 q^{8} + 6 q^{9} + 3 q^{10} + 23 q^{11} - 32 q^{12} - 27 q^{13} - 23 q^{14} + 6 q^{15} + 70 q^{16} - 3 q^{17} - 20 q^{18} - 61 q^{19} - 12 q^{20} - 23 q^{21} - 6 q^{23} + 6 q^{24} - 11 q^{25} + 9 q^{26} - 12 q^{27} - 3 q^{28} - 24 q^{29} - 26 q^{30} - 75 q^{31} + 137 q^{32} + 3 q^{33} - 58 q^{34} + 15 q^{35} - 36 q^{36} - 29 q^{37} - 6 q^{39} - 53 q^{40} - 25 q^{41} + 4 q^{42} + 20 q^{43} + 6 q^{44} + 3 q^{45} + 52 q^{46} + 25 q^{47} + 288 q^{48} + 84 q^{49} - 218 q^{50} - 160 q^{51} + 65 q^{52} + 5 q^{53} + 66 q^{54} - 12 q^{55} - 178 q^{56} + 23 q^{57} + 5 q^{58} + 28 q^{59} - 54 q^{60} - 65 q^{61} - 92 q^{62} + 85 q^{63} - 50 q^{64} + 201 q^{65} - 38 q^{66} - 16 q^{67} - 91 q^{68} - 42 q^{69} - 255 q^{70} - 63 q^{71} - 165 q^{72} + 6 q^{73} - 166 q^{74} - 117 q^{75} - 87 q^{76} + 33 q^{78} + 2 q^{79} - 48 q^{80} + 5 q^{81} + 53 q^{82} + 37 q^{83} - 84 q^{84} + 26 q^{85} + 67 q^{86} - 59 q^{87} - 3 q^{88} - 155 q^{89} + 9 q^{90} + 47 q^{91} - 19 q^{92} + 81 q^{93} + 126 q^{94} - 37 q^{95} + 395 q^{96} + 302 q^{97} + 90 q^{98} + 268 q^{99}+O(q^{100}) \) 276 * q + 3 * q^3 + 20 * q^4 + 6 * q^5 - 8 * q^6 + 6 * q^8 + 6 * q^9 + 3 * q^10 + 23 * q^11 - 32 * q^12 - 27 * q^13 - 23 * q^14 + 6 * q^15 + 70 * q^16 - 3 * q^17 - 20 * q^18 - 61 * q^19 - 12 * q^20 - 23 * q^21 - 6 * q^23 + 6 * q^24 - 11 * q^25 + 9 * q^26 - 12 * q^27 - 3 * q^28 - 24 * q^29 - 26 * q^30 - 75 * q^31 + 137 * q^32 + 3 * q^33 - 58 * q^34 + 15 * q^35 - 36 * q^36 - 29 * q^37 - 6 * q^39 - 53 * q^40 - 25 * q^41 + 4 * q^42 + 20 * q^43 + 6 * q^44 + 3 * q^45 + 52 * q^46 + 25 * q^47 + 288 * q^48 + 84 * q^49 - 218 * q^50 - 160 * q^51 + 65 * q^52 + 5 * q^53 + 66 * q^54 - 12 * q^55 - 178 * q^56 + 23 * q^57 + 5 * q^58 + 28 * q^59 - 54 * q^60 - 65 * q^61 - 92 * q^62 + 85 * q^63 - 50 * q^64 + 201 * q^65 - 38 * q^66 - 16 * q^67 - 91 * q^68 - 42 * q^69 - 255 * q^70 - 63 * q^71 - 165 * q^72 + 6 * q^73 - 166 * q^74 - 117 * q^75 - 87 * q^76 + 33 * q^78 + 2 * q^79 - 48 * q^80 + 5 * q^81 + 53 * q^82 + 37 * q^83 - 84 * q^84 + 26 * q^85 + 67 * q^86 - 59 * q^87 - 3 * q^88 - 155 * q^89 + 9 * q^90 + 47 * q^91 - 19 * q^92 + 81 * q^93 + 126 * q^94 - 37 * q^95 + 395 * q^96 + 302 * q^97 + 90 * q^98 + 268 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/539\mathbb{Z}\right)^\times$.

$n$	$199$	$442$
$\chi(n)$	$e\left(\frac{19}{21}\right)$	$1$

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 $

$2$	0.130700	−	1.74407i	0.0924187	−	1.23324i	−0.737496	−	0.675352i	$-0.763992\pi$
$2$	0.130700	−	1.74407i	0.0924187	−	1.23324i	0.829915	−	0.557891i	$-0.188389\pi$
$3$	−1.64058	+	0.506053i	−0.947191	+	0.292170i	−0.729603	−	0.683871i	$-0.760295\pi$
$3$	−1.64058	+	0.506053i	−0.947191	+	0.292170i	−0.217588	+	0.976041i	$0.569819\pi$
$4$	−1.04703	−	0.157814i	−0.523514	−	0.0789071i
$5$	2.53334	+	2.35060i	1.13294	+	1.05122i	0.998178	+	0.0603407i	$0.0192187\pi$
$5$	2.53334	+	2.35060i	1.13294	+	1.05122i	0.134766	+	0.990877i	$0.456972\pi$
$6$	0.668166	+	2.92743i	0.272778	+	1.19512i
$7$	−2.49524	+	0.879644i	−0.943112	+	0.332474i
$7$	−2.49524	+	0.879644i	−0.943112	+	0.332474i
$8$	0.366275	−	1.60475i	0.129498	−	0.567366i
$9$	−0.0432948	+	0.0295179i	−0.0144316	+	0.00983931i
$10$	4.43070	−	4.11109i	1.40111	−	1.30004i
$11$	0.826239	+	0.563320i	0.249120	+	0.169847i
$11$	0.826239	+	0.563320i	0.249120	+	0.169847i
$12$	1.79760	−	0.270944i	0.518922	−	0.0782149i
$13$	−4.63023	+	2.22980i	−1.28419	+	0.618436i	−0.946465	−	0.322808i	$-0.895373\pi$
$13$	−4.63023	+	2.22980i	−1.28419	+	0.618436i	−0.337730	+	0.941243i	$0.609659\pi$
$14$	1.20803	+	4.46684i	0.322860	+	1.19381i
$15$	−5.34568	−	2.57434i	−1.38025	−	0.664692i
$16$	−4.77455	−	1.47275i	−1.19364	−	0.368189i
$17$	−1.07835	+	2.74759i	−0.261538	+	0.666389i	−0.999968	−	0.00794104i	$-0.997472\pi$
$17$	−1.07835	+	2.74759i	−0.261538	+	0.666389i	0.738430	+	0.674330i	$0.235568\pi$
$18$	0.0458226	+	0.0793671i	0.0108005	+	0.0187070i
$19$	−3.68067	+	6.37510i	−0.844403	+	1.46255i	0.0417355	+	0.999129i	$0.486711\pi$
$19$	−3.68067	+	6.37510i	−0.844403	+	1.46255i	−0.886139	+	0.463420i	$0.846622\pi$
$20$	−2.28152	−	2.86094i	−0.510164	−	0.639725i
$21$	3.64850	−	2.70585i	0.796169	−	0.590465i
$22$	1.09046	−	1.36739i	0.232486	−	0.291529i
$23$	−2.14040	−	5.45366i	−0.446305	−	1.13717i	−0.960200	−	0.279314i	$-0.909893\pi$
$23$	−2.14040	−	5.45366i	−0.446305	−	1.13717i	0.513895	−	0.857853i	$-0.328202\pi$
$24$	0.211186	+	2.81809i	0.0431082	+	0.575239i
$25$	0.518859	+	6.92369i	0.103772	+	1.38474i
$26$	3.28375	+	8.36687i	0.643997	+	1.64088i
$27$	3.26742	−	4.09722i	0.628815	−	0.788510i
$28$	2.75141	−	0.527228i	0.519967	−	0.0996366i
$29$	5.06532	+	6.35171i	0.940606	+	1.17948i	0.983592	+	0.180406i	$0.0577413\pi$
$29$	5.06532	+	6.35171i	0.940606	+	1.17948i	−0.0429865	+	0.999076i	$0.513687\pi$
$30$	−5.18851	+	8.98676i	−0.947287	+	1.64075i
$31$	1.83975	+	3.18654i	0.330429	+	0.572320i	0.982596	−	0.185755i	$-0.0594732\pi$
$31$	1.83975	+	3.18654i	0.330429	+	0.572320i	−0.652167	+	0.758075i	$0.726140\pi$
$32$	−1.98990	+	5.07018i	−0.351768	+	0.896289i
$33$	−1.64058	−	0.506053i	−0.285589	−	0.0880925i
$34$	4.65105	+	2.23983i	0.797648	+	0.384127i
$35$	−8.38898	−	3.63687i	−1.41800	−	0.614743i
$36$	0.0499893	−	0.0240736i	0.00833155	−	0.00401226i
$37$	−3.85503	+	0.581052i	−0.633763	+	0.0955244i	−0.458063	−	0.888920i	$-0.651457\pi$
$37$	−3.85503	+	0.581052i	−0.633763	+	0.0955244i	−0.175699	+	0.984444i	$0.556219\pi$
$38$	10.6376	+	7.25256i	1.72564	+	1.17652i
$39$	6.46788	−	6.00131i	1.03569	−	0.960979i
$40$	4.70003	−	3.20442i	0.743139	−	0.506664i
$41$	−1.00905	+	4.42094i	−0.157587	+	0.690435i	0.832968	+	0.553321i	$0.186640\pi$
$41$	−1.00905	+	4.42094i	−0.157587	+	0.690435i	−0.990555	+	0.137114i	$0.956217\pi$
$42$	−4.24233	−	6.71689i	−0.654606	−	1.03644i
$43$	−1.14356	−	5.01025i	−0.174391	−	0.764056i	−0.984156	−	0.177303i	$-0.943263\pi$
$43$	−1.14356	−	5.01025i	−0.174391	−	0.764056i	0.809766	−	0.586754i	$-0.199594\pi$
$44$	−0.776196	−	0.720204i	−0.117016	−	0.108575i
$45$	−0.179065	−	0.0269897i	−0.0266935	−	0.00402339i
$46$	−9.79131	+	3.02022i	−1.44365	+	0.445307i
$47$	0.368320	−	4.91489i	0.0537250	−	0.716911i	−0.903688	−	0.428191i	$-0.859151\pi$
$47$	0.368320	−	4.91489i	0.0537250	−	0.716911i	0.957413	−	0.288720i	$-0.0932298\pi$
$48$	8.57834			1.23818
$49$	5.45245	−	4.38985i	0.778922	−	0.627121i
$50$	12.1432			1.71731
$51$	0.378697	−	5.05335i	0.0530281	−	0.707611i
$52$	5.19988	−	1.60395i	0.721093	−	0.222428i
$53$	8.31669	+	1.25354i	1.14238	+	0.172187i	0.692854	−	0.721078i	$-0.256353\pi$
$53$	8.31669	+	1.25354i	1.14238	+	0.172187i	0.449531	+	0.893265i	$0.351591\pi$
$54$	−6.71877	−	6.23411i	−0.914309	−	0.848355i
$55$	0.769006	+	3.36923i	0.103693	+	0.454307i
$56$	0.497668	+	4.32644i	0.0665037	+	0.578145i
$57$	2.81230	−	12.3215i	0.372498	−	1.63202i
$58$	11.7398	−	8.00409i	1.54152	−	1.05099i
$59$	7.71352	−	7.15710i	1.00422	−	0.931776i	0.00654385	−	0.999979i	$-0.497917\pi$
$59$	7.71352	−	7.15710i	1.00422	−	0.931776i	0.997671	+	0.0682029i	$0.0217265\pi$
$60$	5.19081	+	3.53903i	0.670130	+	0.456887i
$61$	−7.84672	+	1.18270i	−1.00467	+	0.151430i	−0.630713	−	0.776016i	$-0.717237\pi$
$61$	−7.84672	+	1.18270i	−1.00467	+	0.151430i	−0.373957	+	0.927446i	$0.621999\pi$
$62$	5.79800	−	2.79217i	0.736347	−	0.354606i
$63$	0.0820658	−	0.111738i	0.0103393	−	0.0140777i
$64$	−0.420793	−	0.202643i	−0.0525991	−	0.0253304i
$65$	−16.9713	−	5.23495i	−2.10503	−	0.649316i
$66$	−1.09701	+	2.79515i	−0.135033	+	0.344059i
$67$	6.20901	+	10.7543i	0.758552	+	1.31385i	0.943589	+	0.331118i	$0.107426\pi$
$67$	6.20901	+	10.7543i	0.758552	+	1.31385i	−0.185038	+	0.982731i	$0.559241\pi$
$68$	1.56267	−	2.70663i	0.189502	−	0.328227i
$69$	6.27135	+	7.86402i	0.754982	+	0.946717i
$70$	−7.43938	+	14.1556i	−0.889176	+	1.69192i
$71$	−9.21422	+	11.5543i	−1.09353	+	1.37124i	−0.171017	+	0.985268i	$0.554705\pi$
$71$	−9.21422	+	11.5543i	−1.09353	+	1.37124i	−0.922511	+	0.385972i	$0.873866\pi$
$72$	0.0315112	+	0.0802892i	0.00371363	+	0.00946218i
$73$	0.763379	+	10.1866i	0.0893468	+	1.19225i	0.844080	+	0.536218i	$0.180147\pi$
$73$	0.763379	+	10.1866i	0.0893468	+	1.19225i	−0.754733	+	0.656032i	$0.772234\pi$
$74$	0.509543	+	6.79937i	0.0592331	+	0.790411i
$75$	−4.35498	−	11.0963i	−0.502870	−	1.28129i
$76$	4.85985	−	6.09405i	0.557463	−	0.699036i
$77$	−2.55719	−	0.678824i	−0.291418	−	0.0773591i
$78$	−9.62135	−	12.0648i	−1.08940	−	1.36607i
$79$	7.15810	−	12.3982i	0.805349	−	1.39491i	−0.110706	−	0.993853i	$-0.535311\pi$
$79$	7.15810	−	12.3982i	0.805349	−	1.39491i	0.916055	−	0.401052i	$-0.131355\pi$
$80$	−8.63371	−	14.9540i	−0.965279	−	1.67191i
$81$	−3.22963	+	8.22897i	−0.358848	+	0.914331i
$82$	7.57853	+	2.33767i	0.836909	+	0.258152i
$83$	10.0539	+	4.84172i	1.10356	+	0.531448i	0.894777	−	0.446514i	$-0.147335\pi$
$83$	10.0539	+	4.84172i	1.10356	+	0.531448i	0.208785	+	0.977961i	$0.433049\pi$
$84$	−4.24711	+	2.25732i	−0.463397	+	0.246294i
$85$	−9.19031	+	4.42582i	−0.996829	+	0.480047i
$86$	−8.88768	+	1.33960i	−0.958383	+	0.144453i
$87$	−11.5244	−	7.85718i	−1.23554	−	0.842378i
$88$	1.20662	−	1.11958i	0.128626	−	0.119348i
$89$	4.79915	−	3.27201i	0.508709	−	0.346832i	−0.281608	−	0.959529i	$-0.590868\pi$
$89$	4.79915	−	3.27201i	0.508709	−	0.346832i	0.790318	+	0.612697i	$0.209916\pi$
$90$	−0.0704757	+	0.308774i	−0.00742879	+	0.0325477i
$91$	9.59211	−	9.63684i	1.00553	−	1.01022i
$92$	1.38040	+	6.04793i	0.143917	+	0.630540i
$93$	−4.63082	−	4.29678i	−0.480194	−	0.445555i
$94$	−8.52377	−	1.28475i	−0.879160	−	0.132512i
$95$	−24.3097	+	7.49854i	−2.49412	+	0.769334i
$96$	0.698815	−	9.32504i	0.0713225	−	0.951733i
$97$	1.29074			0.131054			0.0655272	−	0.997851i	$-0.479127\pi$
$97$	1.29074			0.131054			0.0655272	+	0.997851i	$0.479127\pi$
$98$	−6.94355	−	10.0832i	−0.701405	−	1.01856i
$99$	−0.0523999			−0.00526639
$100$	0.549396	−	7.33118i	0.0549396	−	0.733118i
$101$	1.55220	−	0.478791i	0.154450	−	0.0476415i	−0.216566	−	0.976268i	$-0.569486\pi$
$101$	1.55220	−	0.478791i	0.154450	−	0.0476415i	0.371016	+	0.928626i	$0.379010\pi$
$102$	−8.76390	−	1.32094i	−0.867755	−	0.130793i
$103$	−4.64813	−	4.31284i	−0.457994	−	0.424956i	0.417136	−	0.908844i	$-0.363034\pi$
$103$	−4.64813	−	4.31284i	−0.457994	−	0.424956i	−0.875130	+	0.483888i	$0.839224\pi$
$104$	1.88235	+	8.24710i	0.184579	+	0.808695i
$105$	15.6033	+	1.72131i	1.52272	+	0.167983i
$106$	3.27325	−	14.3410i	0.317926	−	1.39292i
$107$	−12.7827	+	8.71510i	−1.23575	+	0.842520i	−0.991866	−	0.127284i	$-0.959374\pi$
$107$	−12.7827	+	8.71510i	−1.23575	+	0.842520i	−0.243884	+	0.969804i	$0.578422\pi$
$108$	−4.06768	+	3.77426i	−0.391413	+	0.363178i
$109$	4.60539	+	3.13991i	0.441117	+	0.300748i	0.763437	−	0.645882i	$-0.223510\pi$
$109$	4.60539	+	3.13991i	0.441117	+	0.300748i	−0.322320	+	0.946631i	$0.604463\pi$
$110$	5.97668	−	0.900840i	0.569854	−	0.0858917i
$111$	6.03045	−	2.90411i	0.572385	−	0.275646i
$112$	13.2092	−	0.525027i	1.24815	−	0.0496104i
$113$	−12.8590	−	6.19256i	−1.20967	−	0.582547i	−0.283254	−	0.959045i	$-0.591414\pi$
$113$	−12.8590	−	6.19256i	−1.20967	−	0.582547i	−0.926417	+	0.376498i	$0.877128\pi$
$114$	−21.1220	−	6.51526i	−1.97825	−	0.610210i
$115$	7.39698	−	18.8472i	0.689772	−	1.75751i
$116$	−4.30114	−	7.44980i	−0.399351	−	0.691696i
$117$	0.134646	−	0.233214i	0.0124480	−	0.0215606i
$118$	−11.4743	−	14.3883i	−1.05630	−	1.32455i
$119$	0.273843	−	7.80447i	0.0251031	−	0.715435i
$120$	−6.08917	+	7.63558i	−0.555863	+	0.697030i
$121$	0.365341	+	0.930874i	0.0332128	+	0.0846249i
$122$	1.03715	+	13.8398i	0.0938991	+	1.25300i
$123$	−0.581797	−	7.76355i	−0.0524589	−	0.700015i
$124$	−1.42339	−	3.62674i	−0.127824	−	0.325691i
$125$	−4.18682	+	5.25011i	−0.374481	+	0.469584i
$126$	−0.184153	−	0.157732i	−0.0164057	−	0.0140519i
$127$	−4.43620	−	5.56282i	−0.393649	−	0.493620i	0.545028	−	0.838418i	$-0.316519\pi$
$127$	−4.43620	−	5.56282i	−0.393649	−	0.493620i	−0.938677	+	0.344798i	$0.887948\pi$
$128$	−5.85511	+	10.1413i	−0.517523	+	0.896377i
$129$	4.41155	+	7.64103i	0.388415	+	0.672755i
$130$	−11.3483	+	28.9149i	−0.995308	+	2.53600i
$131$	−16.2656	−	5.01728i	−1.42114	−	0.438362i	−0.513488	−	0.858097i	$-0.671647\pi$
$131$	−16.2656	−	5.01728i	−1.42114	−	0.438362i	−0.907647	+	0.419735i	$0.862123\pi$
$132$	1.63787	+	0.788759i	0.142559	+	0.0686526i
$133$	3.57633	−	19.1451i	0.310107	−	1.66009i
$134$	19.5678	−	9.42335i	1.69040	−	0.814054i
$135$	17.9084	−	2.69925i	1.54131	−	0.232315i
$136$	4.01424	+	2.73686i	0.344218	+	0.234684i
$137$	7.72091	−	7.16396i	0.659642	−	0.612058i	−0.277617	−	0.960692i	$-0.589545\pi$
$137$	7.72091	−	7.16396i	0.659642	−	0.612058i	0.937259	+	0.348634i	$0.113354\pi$
$138$	14.5351	−	9.90983i	1.23731	−	0.843581i
$139$	1.41473	−	6.19834i	0.119996	−	0.525737i	−0.878823	−	0.477148i	$-0.841671\pi$
$139$	1.41473	−	6.19834i	0.119996	−	0.525737i	0.998819	−	0.0485885i	$-0.0154723\pi$
$140$	8.20955	+	5.13180i	0.693834	+	0.433716i
$141$	1.88293	+	8.24968i	0.158572	+	0.694748i
$142$	18.9471	+	17.5804i	1.59001	+	1.47531i
$143$	−5.08177	−	0.765953i	−0.424959	−	0.0640522i
$144$	0.250186	−	0.0771722i	0.0208488	−	0.00643102i
$145$	−2.09813	+	27.9975i	−0.174240	+	2.32507i
$146$	17.8659			1.47859
$147$	−6.72371	+	9.96113i	−0.554562	+	0.821580i
$148$	4.12802			0.339321
$149$	−0.286960	+	3.82922i	−0.0235087	+	0.313702i	0.973037	+	0.230651i	$0.0740855\pi$
$149$	−0.286960	+	3.82922i	−0.0235087	+	0.313702i	−0.996545	+	0.0830510i	$0.973534\pi$
$150$	−19.9219	+	6.14510i	−1.62662	+	0.501745i
$151$	−5.54983	−	0.836503i	−0.451639	−	0.0680736i	−0.0807158	−	0.996737i	$-0.525721\pi$
$151$	−5.54983	−	0.836503i	−0.451639	−	0.0680736i	−0.370923	+	0.928664i	$0.620959\pi$
$152$	8.88234	+	8.24161i	0.720453	+	0.668482i
$153$	−0.0344162	−	0.150787i	−0.00278238	−	0.0121904i
$154$	−1.51814	+	4.37118i	−0.122335	+	0.352240i
$155$	−2.82956	+	12.3971i	−0.227276	+	0.995760i
$156$	−7.71914	+	5.26282i	−0.618026	+	0.421363i
$157$	4.79707	−	4.45103i	0.382847	−	0.355231i	−0.465149	−	0.885232i	$-0.653999\pi$
$157$	4.79707	−	4.45103i	0.382847	−	0.355231i	0.847996	+	0.530002i	$0.177809\pi$
$158$	−20.6877	−	14.1046i	−1.64583	−	1.12211i
$159$	−14.2786	+	2.15215i	−1.13236	+	0.170676i
$160$	−16.9590	+	8.16703i	−1.34073	+	0.645661i
$161$	10.1381	+	11.7254i	0.798994	+	0.924091i
$162$	13.9298	+	6.70823i	1.09443	+	0.527048i
$163$	15.8876	+	4.90066i	1.24441	+	0.383849i	0.845913	−	0.533321i	$-0.179056\pi$
$163$	15.8876	+	4.90066i	1.24441	+	0.383849i	0.398496	+	0.917170i	$0.369532\pi$
$164$	1.75419	−	4.46961i	0.136979	−	0.349018i
$165$	−2.96663	−	5.13835i	−0.230952	−	0.400020i
$166$	9.75833	−	16.9019i	0.757393	−	1.31184i
$167$	−6.03909	−	7.57279i	−0.467319	−	0.586000i	0.491193	−	0.871051i	$-0.336561\pi$
$167$	−6.03909	−	7.57279i	−0.467319	−	0.586000i	−0.958512	+	0.285051i	$0.907989\pi$
$168$	−3.00587	−	6.84603i	−0.231908	−	0.528183i
$169$	8.36164	−	10.4852i	0.643203	−	0.806552i
$170$	6.51776	+	16.6070i	0.499889	+	1.27370i
$171$	−0.0288259	−	0.384655i	−0.00220437	−	0.0294153i
$172$	0.406648	+	5.42634i	0.0310066	+	0.413755i
$173$	2.30681	+	5.87765i	0.175383	+	0.446870i	0.991353	−	0.131226i	$-0.0418913\pi$
$173$	2.30681	+	5.87765i	0.175383	+	0.446870i	−0.815969	+	0.578096i	$0.803796\pi$
$174$	−15.2097	+	19.0723i	−1.15304	+	1.44587i
$175$	−7.38506	−	16.8199i	−0.558258	−	1.27146i
$176$	−3.11529	−	3.90645i	−0.234824	−	0.294460i
$177$	−9.03280	+	15.6453i	−0.678947	+	1.17597i
$178$	−5.07935	−	8.79770i	−0.380714	−	0.659415i
$179$	−2.67953	+	6.82734i	−0.200278	+	0.510299i	−0.995362	−	0.0961995i	$-0.969331\pi$
$179$	−2.67953	+	6.82734i	−0.200278	+	0.510299i	0.795084	+	0.606499i	$0.207427\pi$
$180$	0.183227	+	0.0565180i	0.0136569	+	0.00421261i
$181$	−2.68885	−	1.29488i	−0.199861	−	0.0962478i	0.331276	−	0.943534i	$-0.392521\pi$
$181$	−2.68885	−	1.29488i	−0.199861	−	0.0962478i	−0.531137	+	0.847286i	$0.678235\pi$
$182$	−15.5536	−	17.9888i	−1.15291	−	1.33342i
$183$	12.2747	−	5.91118i	0.907371	−	0.436967i
$184$	−9.53576	+	1.43728i	−0.702986	+	0.105958i
$185$	−11.1319	−	7.58961i	−0.818434	−	0.557999i
$186$	−8.09912	+	7.51488i	−0.593856	+	0.551018i
$187$	−2.43875	+	1.66271i	−0.178339	+	0.121589i
$188$	−1.16128	+	5.08791i	−0.0846952	+	0.371074i
$189$	−4.54891	+	13.0977i	−0.330885	+	0.952718i
$190$	9.90069	+	43.3778i	0.718272	+	3.14695i
$191$	−5.56484	−	5.16342i	−0.402658	−	0.373612i	0.452688	−	0.891669i	$-0.350465\pi$
$191$	−5.56484	−	5.16342i	−0.402658	−	0.373612i	−0.855346	+	0.518057i	$0.826656\pi$
$192$	0.792893	+	0.119509i	0.0572222	+	0.00862485i
$193$	16.9217	−	5.21964i	1.21805	−	0.375718i	0.381890	−	0.924208i	$-0.375273\pi$
$193$	16.9217	−	5.21964i	1.21805	−	0.375718i	0.836157	+	0.548490i	$0.184797\pi$
$194$	0.168699	−	2.25113i	0.0121119	−	0.161622i
$195$	30.4920			2.18358
$196$	−6.40165	+	3.73582i	−0.457261	+	0.266844i
$197$	15.5054			1.10472			0.552358	−	0.833607i	$-0.313728\pi$
$197$	15.5054			1.10472			0.552358	+	0.833607i	$0.313728\pi$
$198$	−0.00684866	+	0.0913890i	−0.000486713	+	0.00649473i
$199$	6.39444	−	1.97242i	0.453290	−	0.139821i	−0.0596995	−	0.998216i	$-0.519014\pi$
$199$	6.39444	−	1.97242i	0.453290	−	0.139821i	0.512989	+	0.858395i	$0.328538\pi$
$200$	11.3009	+	1.70333i	0.799092	+	0.120444i
$201$	−15.6287	−	14.5013i	−1.10236	−	1.02284i
$202$	−0.632171	−	2.76972i	−0.0444794	−	0.194877i
$203$	−18.2264	−	11.3934i	−1.27924	−	0.799657i
$204$	−1.19400	+	5.23124i	−0.0835965	+	0.366260i
$205$	−12.9481	+	8.82787i	−0.904335	+	0.616565i
$206$	−8.12939	+	7.54297i	−0.566401	+	0.525544i
$207$	0.253649	+	0.172935i	0.0176298	+	0.0120198i
$208$	25.3912	−	3.82711i	1.76057	−	0.265362i
$209$	−6.63233	+	3.19396i	−0.458768	+	0.220931i
$210$	5.04143	−	26.9882i	0.347892	−	1.86236i
$211$	7.68337	+	3.70012i	0.528945	+	0.254727i	0.679242	−	0.733914i	$-0.262309\pi$
$211$	7.68337	+	3.70012i	0.528945	+	0.254727i	−0.150297	+	0.988641i	$0.548023\pi$
$212$	−8.50998	−	2.62498i	−0.584468	−	0.180284i
$213$	9.26962	−	23.6186i	0.635144	−	1.61832i
$214$	13.5290	+	23.4330i	0.924825	+	1.60184i
$215$	8.88005	−	15.3807i	0.605615	−	1.04896i
$216$	−5.37825	−	6.74411i	−0.365944	−	0.458879i
$217$	−7.39365	−	6.33287i	−0.501913	−	0.429903i
$218$	6.07813	−	7.62174i	0.411663	−	0.516209i
$219$	−6.40734	−	16.3256i	−0.432968	−	1.10318i
$220$	−0.273458	−	3.64904i	−0.0184365	−	0.246018i
$221$	−1.13357	−	15.1265i	−0.0762524	−	1.01752i
$222$	−4.27679	−	10.8971i	−0.287039	−	0.731364i
$223$	4.30485	−	5.39811i	0.288274	−	0.361484i	−0.616516	−	0.787342i	$-0.711456\pi$
$223$	4.30485	−	5.39811i	0.288274	−	0.361484i	0.904790	+	0.425858i	$0.140028\pi$
$224$	0.505326	−	14.4017i	0.0337635	−	0.962255i
$225$	−0.226837	−	0.284444i	−0.0151225	−	0.0189630i
$226$	−12.4809	+	21.6176i	−0.830218	+	1.43798i
$227$	0.795844	+	1.37844i	0.0528220	+	0.0914904i	0.891227	−	0.453557i	$-0.149845\pi$
$227$	0.795844	+	1.37844i	0.0528220	+	0.0914904i	−0.838405	+	0.545047i	$0.816512\pi$
$228$	−4.88907	+	12.4571i	−0.323786	+	0.824994i
$229$	19.4220	+	5.99088i	1.28344	+	0.395889i	0.860120	−	0.510092i	$-0.170389\pi$
$229$	19.4220	+	5.99088i	1.28344	+	0.395889i	0.423320	+	0.905980i	$0.360865\pi$
$230$	−31.9040	−	15.3642i	−2.10369	−	1.01308i
$231$	4.53879	−	0.180404i	0.298631	−	0.0118697i
$232$	12.0482	−	5.80212i	0.791005	−	0.380928i
$233$	6.22412	−	0.938134i	0.407755	−	0.0614592i	0.0580377	−	0.998314i	$-0.481516\pi$
$233$	6.22412	−	0.938134i	0.407755	−	0.0614592i	0.349718	+	0.936855i	$0.386278\pi$
$234$	−0.389142	−	0.265313i	−0.0254390	−	0.0173440i
$235$	12.4860	−	11.5853i	0.814497	−	0.755743i
$236$	−9.20577	+	6.27639i	−0.599245	+	0.408558i
$237$	−5.46931	+	23.9626i	−0.355270	+	1.55654i
$238$	−13.5757	−	1.49764i	−0.879984	−	0.0970778i
$239$	2.73945	+	12.0023i	0.177200	+	0.776364i	0.982915	+	0.184060i	$0.0589242\pi$
$239$	2.73945	+	12.0023i	0.177200	+	0.776364i	−0.805715	+	0.592303i	$0.798219\pi$
$240$	21.7318	+	20.1642i	1.40278	+	1.30159i
$241$	−3.99659	−	0.602390i	−0.257443	−	0.0388033i	0.0190524	−	0.999818i	$-0.493935\pi$
$241$	−3.99659	−	0.602390i	−0.257443	−	0.0388033i	−0.276496	+	0.961015i	$0.589173\pi$
$242$	1.67126	−	0.515514i	0.107432	−	0.0331385i
$243$	−0.0406900	+	0.542971i	−0.00261027	+	0.0348316i
$244$	8.40239			0.537908
$245$	24.1317	+	1.69555i	1.54172	+	0.108325i
$246$	−13.6162			−0.868137
$247$	2.82712	−	37.7253i	0.179886	−	2.40041i
$248$	5.78747	−	1.78520i	0.367505	−	0.113360i
$249$	−18.9445	−	2.85542i	−1.20056	−	0.180955i
$250$	8.60932	+	7.98829i	0.544501	+	0.505224i
$251$	4.87416	+	21.3551i	0.307654	+	1.34792i	0.858286	+	0.513172i	$0.171530\pi$
$251$	4.87416	+	21.3551i	0.307654	+	1.34792i	−0.550632	+	0.834748i	$0.685613\pi$
$252$	−0.103559	+	0.104042i	−0.00652361	+	0.00655404i
$253$	1.30367	−	5.71176i	0.0819611	−	0.359095i
$254$	−10.2817	+	7.00997i	−0.645134	+	0.439845i
$255$	12.8378	−	11.9117i	0.803932	−	0.745939i
$256$	16.1501	+	11.0110i	1.00938	+	0.688187i
$257$	−16.9706	+	2.55791i	−1.05860	+	0.159558i	−0.655192	−	0.755462i	$-0.727412\pi$
$257$	−16.9706	+	2.55791i	−1.05860	+	0.159558i	−0.403407	+	0.915021i	$0.632174\pi$
$258$	13.9031	−	6.69536i	0.865567	−	0.416835i
$259$	9.10811	−	4.84092i	0.565950	−	0.300800i
$260$	16.9433	+	8.15946i	1.05078	+	0.506028i
$261$	−0.406791	−	0.125478i	−0.0251797	−	0.00776692i
$262$	−10.8764	+	27.7126i	−0.671946	+	1.71209i
$263$	−3.64947	−	6.32107i	−0.225036	−	0.389774i	0.731294	−	0.682062i	$-0.238917\pi$
$263$	−3.64947	−	6.32107i	−0.225036	−	0.389774i	−0.956330	+	0.292288i	$0.905583\pi$
$264$	−1.41299	+	2.44738i	−0.0869638	+	0.150626i
$265$	18.1224	+	22.7248i	1.11325	+	1.39597i
$266$	−32.9229	−	8.73963i	−2.01863	−	0.535861i
$267$	−6.21760	+	7.79662i	−0.380511	+	0.477146i
$268$	−4.80383	−	12.2400i	−0.293441	−	0.747674i
$269$	0.874349	+	11.6674i	0.0533100	+	0.711373i	0.958268	+	0.285872i	$0.0922831\pi$
$269$	0.874349	+	11.6674i	0.0533100	+	0.711373i	−0.904958	+	0.425501i	$0.860098\pi$
$270$	−2.36706	−	31.5862i	−0.144055	−	1.92228i
$271$	5.24558	+	13.3655i	0.318646	+	0.811898i	0.997017	+	0.0771782i	$0.0245910\pi$
$271$	5.24558	+	13.3655i	0.318646	+	0.811898i	−0.678371	+	0.734720i	$0.737314\pi$
$272$	9.19517	−	11.5304i	0.557539	−	0.699132i
$273$	−10.8599	+	20.6641i	−0.657271	+	1.25065i
$274$	−11.4853	−	14.4021i	−0.693853	−	0.870064i
$275$	−3.47155	+	6.01291i	−0.209342	+	0.362592i
$276$	−5.32523	−	9.22357i	−0.320541	−	0.555193i
$277$	−6.02116	+	15.3417i	−0.361776	+	0.921791i	0.627877	+	0.778312i	$0.283924\pi$
$277$	−6.02116	+	15.3417i	−0.361776	+	0.921791i	−0.989653	+	0.143478i	$0.954171\pi$
$278$	−10.6254	−	3.27751i	−0.637271	−	0.196572i
$279$	−0.173712	−	0.0836552i	−0.0103999	−	0.00500831i
$280$	−8.90895	+	12.1302i	−0.532411	+	0.724915i
$281$	2.68662	−	1.29381i	0.160270	−	0.0771822i	−0.352029	−	0.935989i	$-0.614508\pi$
$281$	2.68662	−	1.29381i	0.160270	−	0.0771822i	0.512299	+	0.858807i	$0.328794\pi$
$282$	14.6341	−	2.20574i	0.871448	−	0.131350i
$283$	−9.35877	−	6.38070i	−0.556321	−	0.379293i	0.252277	−	0.967655i	$-0.418821\pi$
$283$	−9.35877	−	6.38070i	−0.556321	−	0.379293i	−0.808598	+	0.588362i	$0.799773\pi$
$284$	11.4710	−	10.6435i	0.680678	−	0.631576i
$285$	36.0874	−	24.6039i	2.13763	−	1.45741i
$286$	−2.00006	+	8.76284i	−0.118266	+	0.518157i
$287$	−1.37103	−	11.9189i	−0.0809291	−	0.703551i
$288$	−0.0635088	−	0.278250i	−0.00374229	−	0.0163960i
$289$	6.07546	+	5.63720i	0.357380	+	0.331600i
$290$	48.5554	+	7.31854i	2.85127	+	0.429760i
$291$	−2.11756	+	0.653180i	−0.124133	+	0.0382901i
$292$	0.808308	−	10.7861i	0.0473026	−	0.631210i
$293$	1.13272			0.0661742			0.0330871	−	0.999452i	$-0.489466\pi$
$293$	1.13272			0.0661742			0.0330871	+	0.999452i	$0.489466\pi$
$294$	16.4941	+	13.0285i	0.961956	+	0.759839i
$295$	36.3644			2.11722
$296$	−0.479553	+	6.39920i	−0.0278735	+	0.371946i
$297$	5.00771	−	1.54468i	0.290577	−	0.0896311i
$298$	6.64091	+	1.00096i	0.384698	+	0.0579838i
$299$	22.0711	+	20.4790i	1.27641	+	1.18433i
$300$	2.80864	+	12.3054i	0.162157	+	0.710455i
$301$	7.26068	+	11.4959i	0.418499	+	0.662610i
$302$	−2.18428	+	9.56996i	−0.125691	+	0.550689i
$303$	−2.30422	+	1.57099i	−0.132374	+	0.0902511i
$304$	26.9625	−	25.0176i	1.54641	−	1.43486i
$305$	−22.6585	−	15.4483i	−1.29742	−	0.884566i
$306$	−0.267481	+	0.0403163i	−0.0152909	+	0.00230473i
$307$	−9.78486	+	4.71214i	−0.558451	+	0.268936i	−0.691747	−	0.722140i	$-0.743158\pi$
$307$	−9.78486	+	4.71214i	−0.558451	+	0.268936i	0.133295	+	0.991076i	$0.457444\pi$
$308$	2.57032	+	1.11431i	0.146457	+	0.0634936i
$309$	9.80817	+	4.72336i	0.557967	+	0.268703i
$310$	21.2516	+	6.55524i	1.20701	+	0.372313i
$311$	−10.2449	+	26.1037i	−0.580937	+	1.48020i	0.274134	+	0.961692i	$0.411609\pi$
$311$	−10.2449	+	26.1037i	−0.580937	+	1.48020i	−0.855071	+	0.518511i	$0.826486\pi$
$312$	−7.26161	−	12.5775i	−0.411108	−	0.712060i
$313$	−5.12020	+	8.86844i	−0.289411	+	0.501274i	−0.973669	−	0.227966i	$-0.926793\pi$
$313$	−5.12020	+	8.86844i	−0.289411	+	0.501274i	0.684259	+	0.729239i	$0.260126\pi$
$314$	−7.13592	−	8.94815i	−0.402703	−	0.504974i
$315$	0.470552	−	0.0901676i	0.0265126	−	0.00508037i
$316$	−9.45134	+	11.8516i	−0.531680	+	0.666705i
$317$	−0.597808	−	1.52319i	−0.0335763	−	0.0855509i	0.913102	−	0.407731i	$-0.133680\pi$
$317$	−0.597808	−	1.52319i	−0.0335763	−	0.0855509i	−0.946679	+	0.322180i	$0.895584\pi$
$318$	1.88729	+	25.1841i	0.105834	+	1.41225i
$319$	0.607117	+	8.10142i	0.0339921	+	0.453592i
$320$	−0.589679	−	1.50248i	−0.0329641	−	0.0839910i
$321$	16.5608	−	20.7666i	0.924332	−	1.15908i
$322$	21.7750	−	16.1490i	1.21347	−	0.899950i
$323$	−13.5471	−	16.9876i	−0.753783	−	0.945214i
$324$	4.68017	−	8.10629i	0.260009	−	0.450349i
$325$	−17.8409	−	30.9013i	−0.989634	−	1.71410i
$326$	10.6236	−	27.0685i	0.588386	−	1.49918i
$327$	−9.14449	−	2.82070i	−0.505691	−	0.155985i
$328$	6.72493	+	3.23856i	0.371322	+	0.178819i
$329$	3.40431	+	12.5878i	0.187685	+	0.693990i
$330$	−9.34937	+	4.50242i	−0.514666	+	0.247850i
$331$	−3.56259	+	0.536973i	−0.195817	+	0.0295147i	−0.246219	−	0.969214i	$-0.579188\pi$
$331$	−3.56259	+	0.536973i	−0.195817	+	0.0295147i	0.0504012	+	0.998729i	$0.483950\pi$
$332$	−9.76266	−	6.65607i	−0.535796	−	0.365299i
$333$	0.149751	−	0.138949i	0.00820632	−	0.00761436i
$334$	−13.9968	+	9.54283i	−0.765869	+	0.522160i
$335$	−9.54953	+	41.8392i	−0.521747	+	2.28592i
$336$	−21.4050	+	7.54588i	−1.16774	+	0.411662i
$337$	−1.35099	−	5.91907i	−0.0735931	−	0.322432i	0.924709	−	0.380674i	$-0.124308\pi$
$337$	−1.35099	−	5.91907i	−0.0735931	−	0.322432i	−0.998303	+	0.0582412i	$0.981451\pi$
$338$	−17.1940	−	15.9537i	−0.935229	−	0.867766i
$339$	24.2300	+	3.65208i	1.31599	+	0.198354i
$340$	10.3210	−	3.18360i	0.559733	−	0.172655i
$341$	−0.274970	+	3.66921i	−0.0148904	+	0.198699i
$342$	−0.674631			−0.0364799
$343$	−9.74369	+	15.7499i	−0.526110	+	0.850417i
$344$	−8.45908			−0.456083
$345$	−2.59768	+	34.6636i	−0.139854	+	1.86623i
$346$	10.5525	−	3.25502i	0.567307	−	0.174991i
$347$	−12.8792	−	1.94122i	−0.691390	−	0.104210i	−0.206057	−	0.978540i	$-0.566063\pi$
$347$	−12.8792	−	1.94122i	−0.691390	−	0.104210i	−0.485333	+	0.874330i	$0.661301\pi$
$348$	10.8264	+	10.0454i	0.580354	+	0.538490i
$349$	−2.71449	−	11.8929i	−0.145303	−	0.636615i	−0.994153	−	0.107981i	$-0.965562\pi$
$349$	−2.71449	−	11.8929i	−0.145303	−	0.636615i	0.848850	−	0.528634i	$-0.177296\pi$
$350$	−30.3002	+	10.6817i	−1.61961	+	0.570960i
$351$	−5.99293	+	26.2567i	−0.319879	+	1.40148i
$352$	−4.50026	+	3.06823i	−0.239865	+	0.163537i
$353$	1.61995	−	1.50309i	0.0862212	−	0.0800016i	−0.635885	−	0.771784i	$-0.719365\pi$
$353$	1.61995	−	1.50309i	0.0862212	−	0.0800016i	0.722106	+	0.691782i	$0.243174\pi$
$354$	26.1058	+	17.7987i	1.38751	+	0.945988i
$355$	−50.5022	+	7.61198i	−2.68038	+	0.404002i
$356$	−5.54122	+	2.66851i	−0.293684	+	0.141431i
$357$	3.50021	+	12.9425i	0.185251	+	0.684987i
$358$	11.5571	+	5.56562i	0.610813	+	0.294152i
$359$	5.57246	+	1.71888i	0.294103	+	0.0907188i	0.438296	−	0.898831i	$-0.355582\pi$
$359$	5.57246	+	1.71888i	0.294103	+	0.0907188i	−0.144193	+	0.989550i	$0.546058\pi$
$360$	−0.108899	+	0.277470i	−0.00573948	+	0.0146239i
$361$	−17.5946	−	30.4748i	−0.926033	−	1.60394i
$362$	−2.60979	+	4.52029i	−0.137168	+	0.237581i
$363$	−1.07044	−	1.34229i	−0.0561837	−	0.0704521i
$364$	−11.5640	+	8.57628i	−0.606120	+	0.449519i
$365$	−22.0106	+	27.6005i	−1.15209	+	1.44467i
$366$	−8.70520	−	22.1805i	−0.455028	−	1.15939i
$367$	1.55033	+	20.6877i	0.0809267	+	1.07989i	0.878839	+	0.477118i	$0.158319\pi$
$367$	1.55033	+	20.6877i	0.0809267	+	1.07989i	−0.797912	+	0.602773i	$0.794062\pi$
$368$	2.18757	+	29.1911i	0.114035	+	1.52169i
$369$	−0.0868102	−	0.221189i	−0.00451916	−	0.0115146i
$370$	−14.6917	+	18.4228i	−0.763787	+	0.957758i
$371$	−21.8548	+	4.18784i	−1.13464	+	0.217422i
$372$	4.17051	+	5.22966i	0.216231	+	0.271145i
$373$	11.2730	−	19.5253i	0.583691	−	1.01098i	−0.411346	−	0.911479i	$-0.634941\pi$
$373$	11.2730	−	19.5253i	0.583691	−	1.01098i	0.995037	−	0.0995036i	$-0.0317255\pi$
$374$	2.58114	+	4.47066i	0.133467	+	0.231172i
$375$	4.21199	−	10.7320i	0.217506	−	0.554197i
$376$	−7.75229	−	2.39126i	−0.399794	−	0.123320i
$377$	−37.6166	−	18.1152i	−1.93735	−	0.932981i
$378$	22.2487	+	9.64548i	1.14435	+	0.496110i
$379$	7.21123	−	3.47275i	0.370416	−	0.178383i	−0.239409	−	0.970919i	$-0.576954\pi$
$379$	7.21123	−	3.47275i	0.370416	−	0.178383i	0.609826	+	0.792536i	$0.291240\pi$
$380$	26.6363	−	4.01477i	1.36641	−	0.205954i
$381$	10.0930	+	6.88131i	0.517082	+	0.352540i
$382$	−9.73268	+	9.03060i	−0.497967	+	0.462046i
$383$	7.63602	−	5.20615i	0.390183	−	0.266022i	−0.352300	−	0.935887i	$-0.614600\pi$
$383$	7.63602	−	5.20615i	0.390183	−	0.266022i	0.742483	+	0.669865i	$0.233648\pi$
$384$	4.47373	−	19.6007i	0.228299	−	1.00024i
$385$	−4.88258	−	7.73060i	−0.248839	−	0.393988i
$386$	−6.89175	−	30.1947i	−0.350781	−	1.53687i
$387$	0.197402	+	0.183163i	0.0100345	+	0.00931068i
$388$	−1.35144	−	0.203696i	−0.0686088	−	0.0103411i
$389$	13.1678	−	4.06173i	0.667635	−	0.205938i	0.0576325	−	0.998338i	$-0.481645\pi$
$389$	13.1678	−	4.06173i	0.667635	−	0.205938i	0.610002	+	0.792400i	$0.291169\pi$
$390$	3.98530	−	53.1801i	0.201803	−	2.69288i
$391$	17.2925			0.874522
$392$	−5.04753	−	10.3577i	−0.254939	−	0.523145i
$393$	29.2241			1.47416
$394$	2.02656	−	27.0425i	0.102096	−	1.36238i
$395$	47.2770	−	14.5830i	2.37876	−	0.733752i
$396$	0.0548642	+	0.00826945i	0.00275703	+	0.000415555i
$397$	−20.6847	−	19.1926i	−1.03814	−	0.963251i	−0.0387854	−	0.999248i	$-0.512349\pi$
$397$	−20.6847	−	19.1926i	−1.03814	−	0.963251i	−0.999352	+	0.0359970i	$0.988539\pi$
$398$	−2.60429	−	11.4101i	−0.130541	−	0.571938i
$399$	3.82116	+	33.2189i	0.191297	+	1.66303i
$400$	7.71958	−	33.8217i	0.385979	−	1.69108i
$401$	−12.0519	+	8.21687i	−0.601845	+	0.410331i	−0.825552	−	0.564325i	$-0.809136\pi$
$401$	−12.0519	+	8.21687i	−0.601845	+	0.410331i	0.223707	+	0.974656i	$0.428184\pi$
$402$	−27.3339	+	25.3621i	−1.36329	+	1.26495i
$403$	−15.6238	−	10.6521i	−0.778278	−	0.530621i
$404$	−1.70076	+	0.256348i	−0.0846159	+	0.0127538i
$405$	−27.5247	+	13.2552i	−1.36772	+	0.658657i
$406$	−22.2530	+	30.2990i	−1.10440	+	1.50371i
$407$	−3.51249	−	1.69153i	−0.174108	−	0.0838459i
$408$	−7.97068	−	2.45863i	−0.394608	−	0.121720i
$409$	−3.95849	+	10.0861i	−0.195735	+	0.498724i	−0.994720	−	0.102627i	$-0.967275\pi$
$409$	−3.95849	+	10.0861i	−0.195735	+	0.498724i	0.798985	+	0.601351i	$0.205370\pi$
$410$	13.7041	+	23.7362i	0.676796	+	1.17225i
$411$	−9.04145	+	15.6602i	−0.445982	+	0.772463i
$412$	4.18610	+	5.24920i	0.206234	+	0.258610i
$413$	−12.9514	+	24.6439i	−0.637297	+	1.21264i
$414$	0.334762	−	0.419779i	0.0164527	−	0.0206310i
$415$	14.0891	+	35.8984i	0.691606	+	1.76218i
$416$	−2.09180	−	27.9132i	−0.102559	−	1.36856i
$417$	0.815704	+	10.8848i	0.0399452	+	0.533032i
$418$	4.70364	+	11.9847i	0.230063	+	0.586190i
$419$	2.43800	−	3.05715i	0.119104	−	0.149352i	−0.718705	−	0.695315i	$-0.755265\pi$
$419$	2.43800	−	3.05715i	0.119104	−	0.149352i	0.837809	+	0.545963i	$0.183836\pi$
$420$	−16.0654	−	4.26468i	−0.783911	−	0.208095i
$421$	−3.70249	−	4.64277i	−0.180448	−	0.226275i	0.683378	−	0.730065i	$-0.260510\pi$
$421$	−3.70249	−	4.64277i	−0.180448	−	0.226275i	−0.863826	+	0.503790i	$0.831939\pi$
$422$	7.45747	−	12.9167i	0.363024	−	0.628776i
$423$	0.129131	+	0.223662i	0.00627857	+	0.0108748i
$424$	5.05781	−	12.8871i	0.245629	−	0.625853i
$425$	−19.5830	−	6.04055i	−0.949915	−	0.293010i
$426$	−39.9809	−	19.2538i	−1.93708	−	0.932850i
$427$	18.5391	−	9.85345i	0.897170	−	0.476842i
$428$	14.7592	−	7.10766i	0.713414	−	0.343562i
$429$	8.72467	−	1.31503i	0.421231	−	0.0634904i
$430$	−25.6644	−	17.4977i	−1.23765	−	0.843813i
$431$	16.3426	−	15.1637i	0.787195	−	0.730410i	−0.180215	−	0.983627i	$-0.557679\pi$
$431$	16.3426	−	15.1637i	0.787195	−	0.730410i	0.967409	+	0.253217i	$0.0814888\pi$
$432$	−21.6347	+	14.7503i	−1.04090	+	0.709673i
$433$	−6.12639	+	26.8415i	−0.294416	+	1.28992i	0.583895	+	0.811829i	$0.301528\pi$
$433$	−6.12639	+	26.8415i	−0.294416	+	1.28992i	−0.878311	+	0.478090i	$0.841329\pi$
$434$	−12.0113	+	12.0673i	−0.576561	+	0.579250i
$435$	−10.7261	−	46.9940i	−0.514276	−	2.25319i
$436$	−4.32646	−	4.01437i	−0.207200	−	0.192253i
$437$	42.6458	+	6.42782i	2.04002	+	0.307484i
$438$	−29.3104	+	9.04107i	−1.40051	+	0.431999i
$439$	−2.96382	+	39.5495i	−0.141456	+	1.88759i	0.251239	+	0.967925i	$0.419162\pi$
$439$	−2.96382	+	39.5495i	−0.141456	+	1.88759i	−0.392694	+	0.919669i	$0.628457\pi$
$440$	5.68846			0.271187
$441$	−0.106484	+	0.351003i	−0.00507067	+	0.0167144i
$442$	−26.5298			−1.26189
$443$	0.930101	−	12.4113i	0.0441904	−	0.589680i	−0.930525	−	0.366229i	$-0.880649\pi$
$443$	0.930101	−	12.4113i	0.0441904	−	0.589680i	0.974715	−	0.223451i	$-0.0717323\pi$
$444$	−6.77236	+	2.08900i	−0.321402	+	0.0991394i
$445$	19.8490	+	2.99176i	0.940935	+	0.141823i
$446$	−8.85202	−	8.21348i	−0.419155	−	0.388919i
$447$	−1.46700	−	6.42736i	−0.0693869	−	0.304004i
$448$	1.22823	+	0.135496i	0.0580286	+	0.00640157i
$449$	−6.39116	+	28.0015i	−0.301617	+	1.32147i	0.566068	+	0.824358i	$0.308464\pi$
$449$	−6.39116	+	28.0015i	−0.301617	+	1.32147i	−0.867686	+	0.497113i	$0.834393\pi$
$450$	−0.525738	+	0.358442i	−0.0247835	+	0.0168971i
$451$	−3.32412	+	3.08433i	−0.156527	+	0.145236i
$452$	12.4864	+	8.51312i	0.587313	+	0.400423i
$453$	9.52828	−	1.43616i	0.447677	−	0.0674765i
$454$	2.50811	−	1.20784i	0.117712	−	0.0566869i
$455$	46.9524	−	1.86623i	2.20116	−	0.0874900i
$456$	−18.7429	−	9.02610i	−0.877716	−	0.422686i
$457$	22.7887	+	7.02938i	1.06601	+	0.328821i	0.777648	−	0.628700i	$-0.216413\pi$
$457$	22.7887	+	7.02938i	1.06601	+	0.328821i	0.288363	+	0.957521i	$0.406889\pi$
$458$	12.9870	−	33.0902i	0.606840	−	1.54620i
$459$	7.73406	+	13.3958i	0.360995	+	0.625261i
$460$	−10.7192	+	18.5662i	−0.499785	+	0.865654i
$461$	7.62700	+	9.56395i	0.355225	+	0.445438i	0.927050	−	0.374938i	$-0.122336\pi$
$461$	7.62700	+	9.56395i	0.355225	+	0.445438i	−0.571825	+	0.820375i	$0.693764\pi$
$462$	0.278582	−	7.93954i	0.0129608	−	0.369381i
$463$	−20.2229	+	25.3587i	−0.939836	+	1.17852i	0.0439251	+	0.999035i	$0.486014\pi$
$463$	−20.2229	+	25.3587i	−0.939836	+	1.17852i	−0.983761	+	0.179482i	$0.942558\pi$
$464$	−14.8301	−	37.7865i	−0.688471	−	1.75420i
$465$	−1.63146	−	21.7704i	−0.0756574	−	1.00958i
$466$	−0.822679	−	10.9779i	−0.0381099	−	0.508541i
$467$	8.22208	+	20.9495i	0.380473	+	0.969428i	0.984955	+	0.172810i	$0.0552846\pi$
$467$	8.22208	+	20.9495i	0.380473	+	0.969428i	−0.604483	+	0.796618i	$0.706620\pi$
$468$	−0.177783	+	0.222932i	−0.00821800	+	0.0103050i
$469$	−24.9530	−	21.3729i	−1.15222	−	0.986909i
$470$	−18.5737	−	23.2906i	−0.856739	−	1.07432i
$471$	−5.61753	+	9.72984i	−0.258842	+	0.448327i
$472$	−8.66012	−	14.9998i	−0.398615	−	0.690421i
$473$	1.87752	−	4.78385i	0.0863286	−	0.219962i
$474$	41.0776	+	12.6708i	1.88676	+	0.581987i
$475$	−46.0490	−	22.1760i	−2.11287	−	1.01751i
$476$	−1.51838	+	8.12829i	−0.0695947	+	0.372559i
$477$	−0.397071	+	0.191220i	−0.0181807	+	0.00875534i
$478$	21.2909	−	3.20908i	0.973821	−	0.146780i
$479$	32.8865	+	22.4217i	1.50262	+	1.02447i	0.985713	+	0.168433i	$0.0538708\pi$
$479$	32.8865	+	22.4217i	1.50262	+	1.02447i	0.516912	+	0.856039i	$0.327082\pi$
$480$	23.6897	−	21.9809i	1.08128	−	1.00328i
$481$	16.5540	−	11.2863i	0.754799	−	0.514613i
$482$	−1.57296	+	6.89160i	−0.0716465	+	0.313904i
$483$	−22.5661	−	14.1061i	−1.02679	−	0.641849i
$484$	−0.235617	−	1.03231i	−0.0107099	−	0.0469231i
$485$	3.26987	+	3.03400i	0.148477	+	0.137767i
$486$	0.941659	+	0.141932i	0.0427145	+	0.00643818i
$487$	4.15061	−	1.28029i	0.188082	−	0.0580157i	−0.199283	−	0.979942i	$-0.563861\pi$
$487$	4.15061	−	1.28029i	0.188082	−	0.0580157i	0.387365	+	0.921926i	$0.373385\pi$
$488$	−0.976108	+	13.0253i	−0.0441863	+	0.589626i
$489$	−28.5448			−1.29084
$490$	6.11115	−	41.8657i	0.276074	−	1.89130i
$491$	37.0186			1.67063			0.835313	−	0.549775i	$-0.185287\pi$
$491$	37.0186			1.67063			0.835313	+	0.549775i	$0.185287\pi$
$492$	−0.616039	+	8.22047i	−0.0277732	+	0.370607i
$493$	−22.9141	+	7.06806i	−1.03200	+	0.318329i
$494$	−65.4261	−	9.86139i	−2.94366	−	0.443685i
$495$	−0.132747	−	0.123171i	−0.00596652	−	0.00553612i
$496$	−4.09100	−	17.9238i	−0.183691	−	0.804804i
$497$	12.8281	−	36.9359i	0.575418	−	1.65680i
$498$	−7.45608	+	32.6672i	−0.334115	+	1.46385i
$499$	−11.9127	+	8.12194i	−0.533286	+	0.363588i	−0.799822	−	0.600237i	$-0.795073\pi$
$499$	−11.9127	+	8.12194i	−0.533286	+	0.363588i	0.266537	+	0.963825i	$0.414121\pi$
$500$	5.21226	−	4.83627i	0.233099	−	0.216285i
$501$	13.7399	+	9.36768i	0.613852	+	0.418517i
$502$	37.8818	−	5.70976i	1.69075	−	0.254839i
$503$	30.7477	−	14.8073i	1.37097	−	0.660225i	0.403917	−	0.914796i	$-0.367648\pi$
$503$	30.7477	−	14.8073i	1.37097	−	0.660225i	0.967054	+	0.254571i	$0.0819341\pi$
$504$	−0.149254	−	0.172622i	−0.00664830	−	0.00768921i
$505$	5.05770	+	2.43566i	0.225064	+	0.108385i
$506$	−9.79131	−	3.02022i	−0.435277	−	0.134265i
$507$	−8.41192	+	21.4332i	−0.373586	+	0.951883i
$508$	3.76694	+	6.52452i	0.167131	+	0.289479i
$509$	18.9040	−	32.7426i	0.837903	−	1.45129i	−0.0537417	−	0.998555i	$-0.517115\pi$
$509$	18.9040	−	32.7426i	0.837903	−	1.45129i	0.891645	−	0.452736i	$-0.149552\pi$
$510$	−19.0969	−	23.9468i	−0.845626	−	1.06038i
$511$	−10.8654	−	24.7465i	−0.480656	−	1.09472i
$512$	6.71233	−	8.41699i	0.296646	−	0.371982i
$513$	14.0939	+	35.9106i	0.622260	+	1.58549i
$514$	2.24311	+	29.9323i	0.0989395	+	1.32026i
$515$	−1.63756	−	21.8518i	−0.0721596	−	0.962903i
$516$	−3.41316	−	8.69658i	−0.150256	−	0.382846i
$517$	3.07298	−	3.85339i	0.135149	−	0.169472i
$518$	−7.25246	−	16.5179i	−0.318655	−	0.725753i
$519$	−6.75891	−	8.47541i	−0.296683	−	0.372029i
$520$	−14.6170	+	25.3173i	−0.640997	+	1.11024i
$521$	−3.03122	−	5.25023i	−0.132800	−	0.230017i	0.791955	−	0.610580i	$-0.209064\pi$
$521$	−3.03122	−	5.25023i	−0.132800	−	0.230017i	−0.924755	+	0.380563i	$0.875730\pi$
$522$	−0.272010	+	0.693071i	−0.0119056	+	0.0303349i
$523$	−26.7454	−	8.24988i	−1.16950	−	0.360742i	−0.351624	−	0.936141i	$-0.614370\pi$
$523$	−26.7454	−	8.24988i	−1.16950	−	0.360742i	−0.817873	+	0.575399i	$0.804847\pi$
$524$	16.2388	+	7.82019i	0.709395	+	0.341626i
$525$	20.6275	+	23.8571i	0.900259	+	1.04121i
$526$	−11.5014	+	5.53876i	−0.501483	+	0.241502i
$527$	−10.7392	+	1.61868i	−0.467808	+	0.0705107i
$528$	7.08776	+	4.83235i	0.308455	+	0.210301i
$529$	−8.30090	+	7.70211i	−0.360909	+	0.334874i
$530$	42.0022	−	28.6366i	1.82446	−	1.24389i
$531$	−0.122693	+	0.537553i	−0.00532442	+	0.0233278i
$532$	−6.76589	+	19.4811i	−0.293339	+	0.844611i
$533$	−5.18568	−	22.7199i	−0.224617	−	0.984110i
$534$	12.7852	+	11.8629i	0.553270	+	0.513359i
$535$	−52.8686	−	7.96865i	−2.28571	−	0.344515i
$536$	19.5323	−	6.02490i	0.843665	−	0.260236i
$537$	0.941002	−	12.5568i	0.0406072	−	0.541866i
$538$	20.4630			0.882222
$539$	6.97792	−	0.555583i	0.300560	−	0.0239307i
$540$	−19.1766			−0.825228
$541$	−0.0353830	+	0.472154i	−0.00152124	+	0.0202995i	−0.997913	−	0.0645765i	$-0.979430\pi$
$541$	−0.0353830	+	0.472154i	−0.00152124	+	0.0202995i	0.996392	+	0.0848760i	$0.0270494\pi$
$542$	23.9960	−	7.40178i	1.03072	−	0.317934i
$543$	5.06656	+	0.763661i	0.217427	+	0.0327718i
$544$	−11.7850	−	10.9349i	−0.505277	−	0.468828i
$545$	4.28638	+	18.7799i	0.183608	+	0.804441i
$546$	34.6203	+	21.6412i	1.48161	+	0.926158i
$547$	1.67299	−	7.32986i	0.0715320	−	0.313402i	−0.926486	−	0.376329i	$-0.877186\pi$
$547$	1.67299	−	7.32986i	0.0715320	−	0.313402i	0.998018	+	0.0629267i	$0.0200434\pi$
$548$	−9.21459	+	6.28240i	−0.393628	+	0.268371i
$549$	0.304812	−	0.282824i	0.0130090	−	0.0120706i
$550$	10.0332	+	6.84051i	0.427816	+	0.291680i
$551$	−59.1365	+	8.91340i	−2.51930	+	0.379724i
$552$	14.9169	−	7.18358i	0.634904	−	0.305754i
$553$	−6.95519	+	37.2330i	−0.295765	+	1.58331i
$554$	25.9699	+	12.5065i	1.10336	+	0.531348i
$555$	22.1036	+	6.81805i	0.938244	+	0.289410i
$556$	−2.45945	+	6.26658i	−0.104304	+	0.265762i
$557$	15.9523	+	27.6302i	0.675921	+	1.17073i	0.976199	+	0.216878i	$0.0695874\pi$
$557$	15.9523	+	27.6302i	0.675921	+	1.17073i	−0.300278	+	0.953852i	$0.597079\pi$
$558$	−0.168605	+	0.292032i	−0.00713760	+	0.0123627i
$559$	16.4668	+	20.6487i	0.696471	+	0.873347i
$560$	34.6974	+	29.7193i	1.46623	+	1.25587i
$561$	3.15955	−	3.96195i	0.133396	−	0.167274i
$562$	−1.90535	−	4.85475i	−0.0803723	−	0.204785i
$563$	−0.347148	−	4.63237i	−0.0146305	−	0.195231i	−0.999730	−	0.0232443i	$-0.992600\pi$
$563$	−0.347148	−	4.63237i	−0.0146305	−	0.195231i	0.985099	−	0.171987i	$-0.0550186\pi$
$564$	−0.669571	−	8.93480i	−0.0281940	−	0.376223i
$565$	−18.0200	−	45.9141i	−0.758106	−	1.93162i
$566$	−12.3516	+	15.4884i	−0.519175	+	0.651025i
$567$	0.820152	−	23.3742i	0.0344431	−	0.981624i
$568$	15.1668	+	19.0186i	0.636386	+	0.798003i
$569$	13.3587	−	23.1380i	0.560027	−	0.969996i	−0.437466	−	0.899235i	$-0.644124\pi$
$569$	13.3587	−	23.1380i	0.560027	−	0.969996i	0.997493	−	0.0707609i	$-0.0225427\pi$
$570$	−38.1943	−	66.1545i	−1.59978	−	2.77091i
$571$	13.9515	−	35.5478i	0.583851	−	1.48763i	−0.267777	−	0.963481i	$-0.586289\pi$
$571$	13.9515	−	35.5478i	0.583851	−	1.48763i	0.851628	−	0.524147i	$-0.175616\pi$
$572$	5.19988	+	1.60395i	0.217418	+	0.0670645i
$573$	11.7425	+	5.65491i	0.490552	+	0.236237i
$574$	−20.9666	+	0.833363i	−0.875128	+	0.0347839i
$575$	36.6489	−	17.6492i	1.52836	−	0.736022i
$576$	0.0241998	−	0.00364753i	0.00100832	−	0.000151980i
$577$	−7.27755	−	4.96175i	−0.302968	−	0.206560i	0.402287	−	0.915514i	$-0.368215\pi$
$577$	−7.27755	−	4.96175i	−0.302968	−	0.206560i	−0.705256	+	0.708953i	$0.749168\pi$
$578$	10.6257	−	9.85923i	0.441972	−	0.410090i
$579$	−25.1200	+	17.1265i	−1.04395	+	0.711753i
$580$	6.61520	−	28.9831i	0.274681	−	1.20346i
$581$	−29.3460	−	3.23738i	−1.21748	−	0.134309i
$582$	0.862426	+	3.77853i	0.0357487	+	0.156625i
$583$	6.16542	+	5.72068i	0.255346	+	0.236926i
$584$	16.6266	+	2.50605i	0.688012	+	0.103701i
$585$	0.889295	−	0.274311i	0.0367678	−	0.0113414i
$586$	0.148046	−	1.97554i	0.00611574	−	0.0816089i
$587$	−38.7994			−1.60142			−0.800712	−	0.599049i	$-0.795545\pi$
$587$	−38.7994			−1.60142			−0.800712	+	0.599049i	$0.795545\pi$
$588$	8.61192	−	9.36849i	0.355150	−	0.386350i
$589$	−27.0861			−1.11606
$590$	4.75282	−	63.4220i	0.195671	−	2.61104i
$591$	−25.4379	+	7.84656i	−1.04638	+	0.322764i
$592$	19.2618	+	2.90325i	0.791655	+	0.119323i
$593$	−9.38652	−	8.70942i	−0.385458	−	0.357653i	0.463515	−	0.886089i	$-0.346588\pi$
$593$	−9.38652	−	8.70942i	−0.385458	−	0.357653i	−0.848973	+	0.528436i	$0.822779\pi$
$594$	−2.03951	−	8.93568i	−0.0836821	−	0.366635i
$595$	19.0389	−	19.1277i	0.780518	−	0.784158i
$596$	0.904760	−	3.96401i	0.0370604	−	0.162372i
$597$	−9.49246	+	6.47185i	−0.388500	+	0.264875i
$598$	38.6015	−	35.8170i	1.57853	−	1.46466i
$599$	−12.5408	−	8.55018i	−0.512404	−	0.349351i	0.279352	−	0.960189i	$-0.409880\pi$
$599$	−12.5408	−	8.55018i	−0.512404	−	0.349351i	−0.791756	+	0.610838i	$0.790833\pi$
$600$	−19.4020	+	2.92438i	−0.792082	+	0.119387i
$601$	−26.0443	+	12.5423i	−1.06237	+	0.511609i	−0.881639	−	0.471924i	$-0.843560\pi$
$601$	−26.0443	+	12.5423i	−1.06237	+	0.511609i	−0.180728	+	0.983533i	$0.557845\pi$
$602$	20.9985	−	11.1606i	0.855836	−	0.454873i
$603$	−0.586263	−	0.282330i	−0.0238745	−	0.0114974i
$604$	5.67882	+	1.75168i	0.231068	+	0.0712750i
$605$	−1.26257	+	3.21699i	−0.0513310	+	0.130789i
$606$	2.43875	+	4.22405i	0.0990676	+	0.171590i
$607$	14.1538	−	24.5151i	0.574486	−	0.995039i	−0.421611	−	0.906777i	$-0.638535\pi$
$607$	14.1538	−	24.5151i	0.574486	−	0.995039i	0.996097	−	0.0882625i	$-0.0281314\pi$
$608$	−24.9988	−	31.3474i	−1.01383	−	1.27131i
$609$	35.6676	+	9.46822i	1.44532	+	0.383672i
$610$	−29.9043	+	37.4988i	−1.21079	+	1.51828i
$611$	9.25383	+	23.5784i	0.374370	+	0.953879i
$612$	0.0122384	+	0.163310i	0.000494707	+	0.00660141i
$613$	0.152813	+	2.03915i	0.00617207	+	0.0823606i	0.999439	−	0.0334861i	$-0.0106609\pi$
$613$	0.152813	+	2.03915i	0.00617207	+	0.0823606i	−0.993267	+	0.115847i	$0.963042\pi$
$614$	6.93941	+	17.6813i	0.280052	+	0.713561i
$615$	16.7751	−	21.0353i	0.676436	−	0.848224i
$616$	−2.02598	+	3.85502i	−0.0816290	+	0.155323i
$617$	13.3612	+	16.7544i	0.537902	+	0.674508i	0.974302	−	0.225245i	$-0.0723181\pi$
$617$	13.3612	+	16.7544i	0.537902	+	0.674508i	−0.436400	+	0.899753i	$0.643747\pi$
$618$	9.51979	−	16.4888i	0.382942	−	0.663275i
$619$	−5.68725	−	9.85060i	−0.228590	−	0.395929i	0.728801	−	0.684726i	$-0.240078\pi$
$619$	−5.68725	−	9.85060i	−0.228590	−	0.395929i	−0.957390	+	0.288797i	$0.906745\pi$
$620$	4.91907	−	12.5336i	0.197555	−	0.503361i
$621$	−29.3384	−	9.04971i	−1.17731	−	0.363152i
$622$	44.1875	+	21.2796i	1.77176	+	0.853234i
$623$	−9.09684	+	12.3860i	−0.364457	+	0.496234i
$624$	−39.7197	+	19.1280i	−1.59006	+	0.765733i
$625$	11.3803	−	1.71530i	0.455211	−	0.0686120i
$626$	14.7980	+	10.0891i	0.591445	+	0.403240i
$627$	9.26458	−	8.59627i	0.369992	−	0.343302i
$628$	−5.72510	+	3.90331i	−0.228456	+	0.155759i
$629$	2.56058	−	11.2186i	0.102097	−	0.447316i
$630$	−0.0957574	−	0.832460i	−0.00381507	−	0.0331660i
$631$	4.16432	+	18.2451i	0.165779	+	0.726325i	0.987653	+	0.156656i	$0.0500714\pi$
$631$	4.16432	+	18.2451i	0.165779	+	0.726325i	−0.821874	+	0.569669i	$0.807071\pi$
$632$	−17.2742	−	16.0281i	−0.687131	−	0.637565i
$633$	−14.4777	−	2.18216i	−0.575436	−	0.0867329i
$634$	−2.73468	+	0.843538i	−0.108608	+	0.0335012i
$635$	1.83754	−	24.5202i	0.0729204	−	0.973055i
$636$	15.2897			0.606276
$637$	−15.4576	+	32.4839i	−0.612454	+	1.28706i
$638$	14.2088			0.562531
$639$	0.0578703	−	0.772225i	0.00228931	−	0.0305487i
$640$	−38.6712	+	11.9285i	−1.52861	+	0.471514i
$641$	7.81515	+	1.17794i	0.308680	+	0.0465260i	0.301555	−	0.953449i	$-0.402494\pi$
$641$	7.81515	+	1.17794i	0.308680	+	0.0465260i	0.00712427	+	0.999975i	$0.497732\pi$
$642$	−34.0538	−	31.5973i	−1.34400	−	1.24705i
$643$	7.00472	+	30.6897i	0.276239	+	1.21028i	0.902507	+	0.430675i	$0.141725\pi$
$643$	7.00472	+	30.6897i	0.276239	+	1.21028i	−0.626268	+	0.779608i	$0.715418\pi$
$644$	−8.76445	−	13.8768i	−0.345368	−	0.546821i
$645$	−6.78501	+	29.7271i	−0.267160	+	1.17050i
$646$	−31.3981	+	21.4069i	−1.23534	+	0.842241i
$647$	−13.7183	+	12.7287i	−0.539322	+	0.500417i	−0.902141	−	0.431442i	$-0.858005\pi$
$647$	−13.7183	+	12.7287i	−0.539322	+	0.500417i	0.362819	+	0.931860i	$0.381814\pi$
$648$	12.0225	+	8.19683i	0.472290	+	0.322002i
$649$	10.4050	−	1.56829i	0.408430	−	0.0615609i
$650$	−56.2258	+	27.0769i	−2.20536	+	1.06204i
$651$	15.3347	+	6.64802i	0.601012	+	0.260556i
$652$	−15.8613	−	7.63841i	−0.621177	−	0.299143i
$653$	2.16007	+	0.666294i	0.0845302	+	0.0260741i	0.336732	−	0.941601i	$-0.390678\pi$
$653$	2.16007	+	0.666294i	0.0845302	+	0.0260741i	−0.252202	+	0.967675i	$0.581155\pi$
$654$	−6.11468	+	15.5799i	−0.239103	+	0.609224i
$655$	−29.4128	−	50.9444i	−1.14925	−	1.99056i
$656$	11.3287	−	19.6219i	0.442312	−	0.766107i
$657$	−0.333737	−	0.418493i	−0.0130203	−	0.0163270i
$658$	22.3990	−	4.29211i	0.873203	−	0.167324i
$659$	29.4300	−	36.9041i	1.14643	−	1.43758i	0.265641	−	0.964072i	$-0.414416\pi$
$659$	29.4300	−	36.9041i	1.14643	−	1.43758i	0.880790	−	0.473507i	$-0.157012\pi$
$660$	2.29524	+	5.84817i	0.0893420	+	0.227640i
$661$	−0.296262	−	3.95334i	−0.0115233	−	0.153767i	−0.999997	−	0.00237599i	$-0.999244\pi$
$661$	−0.296262	−	3.95334i	−0.0115233	−	0.153767i	0.988474	−	0.151391i	$-0.0483754\pi$
$662$	0.470889	+	6.28357i	0.0183016	+	0.244218i
$663$	9.51452	+	24.2426i	0.369513	+	0.941505i
$664$	11.4523	−	14.3607i	0.444434	−	0.557303i
$665$	54.0624	−	40.0945i	2.09645	−	1.55480i
$666$	−0.222764	−	0.279337i	−0.00863193	−	0.0108241i
$667$	23.7982	−	41.2197i	0.921471	−	1.59603i
$668$	5.12801	+	8.88198i	0.198409	+	0.343654i
$669$	−4.33073	+	11.0345i	−0.167436	+	0.426619i
$670$	71.7223	+	22.1234i	2.77088	+	0.854702i
$671$	−7.14951	−	3.44302i	−0.276004	−	0.132916i
$672$	6.45900	+	23.8829i	0.249161	+	0.921304i
$673$	−21.5298	+	10.3682i	−0.829914	+	0.399665i	−0.800083	−	0.599890i	$-0.795211\pi$
$673$	−21.5298	+	10.3682i	−0.829914	+	0.399665i	−0.0298310	+	0.999555i	$0.509497\pi$
$674$	−10.4998	+	1.58260i	−0.404439	+	0.0609593i
$675$	30.0632	+	20.4967i	1.15713	+	0.788920i
$676$	−10.4096	+	9.65869i	−0.400369	+	0.371488i
$677$	−17.6997	+	12.0674i	−0.680254	+	0.463789i	−0.853502	−	0.521089i	$-0.825526\pi$
$677$	−17.6997	+	12.0674i	−0.680254	+	0.463789i	0.173249	+	0.984878i	$0.444574\pi$
$678$	9.53633	−	41.7814i	0.366241	−	1.60461i
$679$	−3.22070	+	1.13539i	−0.123599	+	0.0435722i
$680$	3.73617	+	16.3692i	0.143276	+	0.627732i
$681$	−2.00321	−	1.85871i	−0.0767632	−	0.0712259i
$682$	6.36342	+	0.959131i	0.243668	+	0.0367270i
$683$	−25.3312	+	7.81364i	−0.969271	+	0.298981i	−0.738670	−	0.674068i	$-0.764546\pi$
$683$	−25.3312	+	7.81364i	−0.969271	+	0.298981i	−0.230602	+	0.973048i	$0.574069\pi$
$684$	−0.0305224	+	0.407294i	−0.00116705	+	0.0155733i
$685$	36.3992			1.39074
$686$	26.1955	+	19.0522i	1.00015	+	0.727415i
$687$	−34.8950			−1.33133
$688$	−1.91890	+	25.6059i	−0.0731572	+	0.976215i
$689$	−41.3033	+	12.7404i	−1.57353	+	0.485370i
$690$	60.1162	+	9.06106i	2.28859	+	0.344949i
$691$	18.6669	+	17.3203i	0.710121	+	0.658896i	0.950123	−	0.311877i	$-0.100958\pi$
$691$	18.6669	+	17.3203i	0.710121	+	0.658896i	−0.240002	+	0.970772i	$0.577148\pi$
$692$	−1.48772	−	6.51812i	−0.0565546	−	0.247782i
$693$	0.130750	−	0.0460932i	0.00496680	−	0.00175094i
$694$	−5.06893	+	22.2084i	−0.192414	+	0.843020i
$695$	18.1538	−	12.3770i	0.688612	−	0.469488i
$696$	−16.8299	+	15.6159i	−0.637937	+	0.591919i
$697$	−11.0588	−	7.53978i	−0.418883	−	0.285590i
$698$	−21.0969	+	3.17984i	−0.798529	+	0.120359i
$699$	−9.73643	+	4.68882i	−0.368266	+	0.177347i
$700$	5.07795	+	18.7763i	0.191929	+	0.709679i
$701$	−39.7077	−	19.1222i	−1.49974	−	0.722236i	−0.509351	−	0.860559i	$-0.670115\pi$
$701$	−39.7077	−	19.1222i	−1.49974	−	0.722236i	−0.990387	+	0.138323i	$0.955829\pi$
$702$	45.0103	+	13.8838i	1.69880	+	0.524011i
$703$	10.4848	−	26.7149i	0.395442	−	1.00757i
$704$	−0.233522	−	0.404473i	−0.00880121	−	0.0152441i
$705$	−14.6215	+	25.3252i	−0.550679	+	0.953804i
$706$	−2.40977	−	3.02176i	−0.0906929	−	0.113725i
$707$	−3.45195	+	2.56008i	−0.129824	+	0.0962818i
$708$	11.9266	−	14.9555i	0.448231	−	0.562064i
$709$	−3.48902	−	8.88989i	−0.131033	−	0.333867i	0.850267	−	0.526352i	$-0.176441\pi$
$709$	−3.48902	−	8.88989i	−0.131033	−	0.333867i	−0.981300	+	0.192485i	$0.938345\pi$
$710$	6.67518	+	89.0741i	0.250515	+	3.34289i
$711$	0.0560601	+	0.748070i	0.00210242	+	0.0280548i
$712$	−3.49296	−	8.89991i	−0.130904	−	0.333538i
$713$	13.4405	−	16.8539i	0.503351	−	0.631183i
$714$	23.0300	−	4.41303i	0.861876	−	0.165153i
$715$	−11.0734	−	13.8856i	−0.414121	−	0.519292i
$716$	3.88300	−	6.72555i	0.145115	−	0.251346i
$717$	−10.5681	−	18.3045i	−0.394672	−	0.683592i
$718$	3.72616	−	9.49409i	0.139059	−	0.354316i
$719$	20.6540	+	6.37092i	0.770265	+	0.237595i	0.654887	−	0.755726i	$-0.272716\pi$
$719$	20.6540	+	6.37092i	0.770265	+	0.237595i	0.115377	+	0.993322i	$0.463192\pi$
$720$	0.815207	+	0.392583i	0.0303810	+	0.0146307i
$721$	15.3920	+	6.67287i	0.573227	+	0.248511i
$722$	−55.4497	+	26.7032i	−2.06362	+	0.993789i
$723$	6.86158	−	1.03422i	0.255185	−	0.0384630i
$724$	2.61095	+	1.78012i	0.0970352	+	0.0661575i
$725$	−41.3491	+	38.3663i	−1.53567	+	1.42489i
$726$	−2.48096	+	1.69149i	−0.0920770	+	0.0627770i
$727$	4.94768	−	21.6772i	0.183499	−	0.803962i	−0.796448	−	0.604707i	$-0.793290\pi$
$727$	4.94768	−	21.6772i	0.183499	−	0.803962i	0.979948	−	0.199256i	$-0.0638525\pi$
$728$	−11.9514	−	18.9227i	−0.442949	−	0.701322i
$729$	−6.10931	−	26.7666i	−0.226271	−	0.991357i
$730$	45.2603	+	41.9954i	1.67516	+	1.55432i
$731$	14.9993	+	2.26078i	0.554768	+	0.0836179i
$732$	−13.7848	+	4.25205i	−0.509501	+	0.157160i
$733$	0.871590	−	11.6306i	0.0321929	−	0.429585i	−0.957700	−	0.287768i	$-0.907087\pi$
$733$	0.871590	−	11.6306i	0.0321929	−	0.429585i	0.989893	−	0.141816i	$-0.0452943\pi$
$734$	36.2835			1.33925
$735$	−40.4480	+	9.43021i	−1.49195	+	0.347839i
$736$	31.9102			1.17623
$737$	−0.928000	+	12.3833i	−0.0341833	+	0.456145i
$738$	−0.397114	+	0.122494i	−0.0146180	+	0.00450905i
$739$	−17.9370	−	2.70357i	−0.659823	−	0.0994524i	−0.189409	−	0.981898i	$-0.560657\pi$
$739$	−17.9370	−	2.70357i	−0.659823	−	0.0994524i	−0.470414	+	0.882446i	$0.655895\pi$
$740$	10.4577	+	9.70331i	0.384432	+	0.356701i
$741$	14.4529	+	63.3222i	0.530940	+	2.32620i
$742$	4.44745	+	38.6636i	0.163271	+	1.41939i
$743$	−8.83567	+	38.7116i	−0.324149	+	1.42019i	0.505945	+	0.862566i	$0.331144\pi$
$743$	−8.83567	+	38.7116i	−0.324149	+	1.42019i	−0.830094	+	0.557624i	$0.811713\pi$
$744$	−8.59142	+	5.85753i	−0.314977	+	0.214748i
$745$	−9.72791	+	9.02618i	−0.356403	+	0.330694i
$746$	−32.5801	−	22.2127i	−1.19284	−	0.813266i
$747$	−0.578201	+	0.0871497i	−0.0211553	+	0.00318864i
$748$	2.81584	−	1.35604i	0.102957	−	0.0495816i
$749$	24.2297	−	32.9905i	0.885335	−	1.20545i
$750$	−18.1668	−	8.74867i	−0.663358	−	0.319456i
$751$	16.7410	+	5.16392i	0.610888	+	0.188434i	0.584735	−	0.811224i	$-0.301198\pi$
$751$	16.7410	+	5.16392i	0.610888	+	0.188434i	0.0261524	+	0.999658i	$0.491674\pi$
$752$	−8.99700	+	22.9240i	−0.328087	+	0.835951i
$753$	−18.8033	−	32.5682i	−0.685229	−	1.18685i
$754$	−36.5106	+	63.2383i	−1.32964	+	2.30300i
$755$	−12.0933	−	15.1646i	−0.440121	−	0.551895i
$756$	6.82984	−	12.9958i	0.248399	−	0.472652i
$757$	12.8960	−	16.1710i	0.468712	−	0.587746i	−0.490143	−	0.871642i	$-0.663055\pi$
$757$	12.8960	−	16.1710i	0.468712	−	0.587746i	0.958855	+	0.283896i	$0.0916269\pi$
$758$	−5.11420	−	13.0308i	−0.185756	−	0.473299i
$759$	0.751670	+	10.0303i	0.0272839	+	0.364078i
$760$	3.12930	+	41.7576i	0.113512	+	1.51471i
$761$	17.5046	+	44.6011i	0.634543	+	1.61679i	0.778817	+	0.627251i	$0.215820\pi$
$761$	17.5046	+	44.6011i	0.634543	+	1.61679i	−0.144274	+	0.989538i	$0.546085\pi$
$762$	13.3206	−	16.7035i	0.482555	−	0.605105i
$763$	−14.2536	−	3.78371i	−0.516014	−	0.136980i
$764$	5.01169	+	6.28446i	0.181316	+	0.227364i
$765$	0.267252	−	0.462894i	0.00966251	−	0.0167360i
$766$	−8.08186	−	13.9982i	−0.292009	−	0.505775i
$767$	−19.7565	+	50.3387i	−0.713365	+	1.81762i
$768$	−32.0678	−	9.89160i	−1.15715	−	0.356932i
$769$	−4.83892	−	2.33030i	−0.174496	−	0.0840329i	0.344597	−	0.938751i	$-0.388016\pi$
$769$	−4.83892	−	2.33030i	−0.174496	−	0.0840329i	−0.519093	+	0.854718i	$0.673730\pi$
$770$	−14.1208	+	7.50516i	−0.508880	+	0.270467i
$771$	26.5473	−	12.7845i	0.956077	−	0.460423i
$772$	−18.5412	+	2.79463i	−0.667312	+	0.100581i
$773$	−6.13076	−	4.17988i	−0.220508	−	0.150340i	0.448028	−	0.894020i	$-0.352126\pi$
$773$	−6.13076	−	4.17988i	−0.220508	−	0.150340i	−0.668536	+	0.743680i	$0.733079\pi$
$774$	0.345248	−	0.320344i	0.0124097	−	0.0115145i
$775$	−21.1081	+	14.3912i	−0.758224	+	0.516949i
$776$	0.472764	−	2.07131i	0.0169712	−	0.0743558i
$777$	−12.4928	+	12.5511i	−0.448178	+	0.450268i
$778$	−5.36291	−	23.4964i	−0.192269	−	0.842388i
$779$	−24.4700	−	22.7048i	−0.876727	−	0.813484i
$780$	−31.9260	−	4.81207i	−1.14313	−	0.172300i
$781$	−14.1219	+	4.35603i	−0.505321	+	0.155871i
$782$	2.26013	−	30.1594i	0.0808222	−	1.07850i
$783$	42.5748			1.52150
$784$	−32.4982	+	12.9294i	−1.16065	+	0.461765i
$785$	22.6152			0.807169
$786$	3.81959	−	50.9689i	0.136240	−	1.81800i
$787$	−17.7497	+	5.47506i	−0.632708	+	0.195165i	−0.594488	−	0.804105i	$-0.702645\pi$
$787$	−17.7497	+	5.47506i	−0.632708	+	0.195165i	−0.0382206	+	0.999269i	$0.512169\pi$
$788$	−16.2346	−	2.44697i	−0.578334	−	0.0871699i
$789$	9.18606	+	8.52341i	0.327032	+	0.303442i
$790$	−19.2547	−	84.3603i	−0.685051	−	3.00141i
$791$	37.5335	+	4.14061i	1.33454	+	0.147223i
$792$	−0.0191928	+	0.0840890i	−0.000681985	+	0.00298797i
$793$	33.6949	−	22.9728i	1.19654	−	0.815789i
$794$	−36.1767	+	33.5671i	−1.28386	+	1.19125i
$795$	−41.2313	−	28.1110i	−1.46232	−	0.996995i
$796$	−7.00644	+	1.05605i	−0.248337	+	0.0374307i
$797$	−3.80791	+	1.83379i	−0.134883	+	0.0649563i	−0.500108	−	0.865963i	$-0.666706\pi$
$797$	−3.80791	+	1.83379i	−0.134883	+	0.0649563i	0.365225	+	0.930919i	$0.380992\pi$
$798$	58.4355	−	2.32265i	2.06859	−	0.0822208i
$799$	13.1069	+	6.31197i	0.463690	+	0.223302i
$800$	−36.1368	−	11.1467i	−1.27763	−	0.394096i
$801$	−0.111196	+	0.283322i	−0.00392891	+	0.0100107i
$802$	12.7556	+	22.0933i	0.450416	+	0.780143i
$803$	−5.10757	+	8.84658i	−0.180242	+	0.312189i
$804$	14.0751	+	17.6497i	0.496392	+	0.622456i
$805$	−1.87843	+	53.5350i	−0.0662060	+	1.88686i
$806$	−20.6201	+	25.8568i	−0.726312	+	0.910766i
$807$	−7.33875	−	18.6988i	−0.258336	−	0.658230i
$808$	−0.199809	−	2.66627i	−0.00702927	−	0.0937991i
$809$	−0.641176	−	8.55590i	−0.0225426	−	0.300809i	−0.997067	−	0.0765295i	$-0.975616\pi$
$809$	−0.641176	−	8.55590i	−0.0225426	−	0.300809i	0.974525	−	0.224280i	$-0.0720030\pi$
$810$	19.5205	+	49.7375i	0.685881	+	1.74760i
$811$	−3.99581	+	5.01059i	−0.140312	+	0.175946i	−0.847022	−	0.531557i	$-0.821607\pi$
$811$	−3.99581	+	5.01059i	−0.140312	+	0.175946i	0.706710	+	0.707503i	$0.250178\pi$
$812$	17.2855	+	14.8056i	0.606604	+	0.519573i
$813$	−15.3695	−	19.2727i	−0.539031	−	0.675923i
$814$	−3.40922	+	5.90494i	−0.119493	+	0.206968i
$815$	28.7291	+	49.7602i	1.00634	+	1.74303i
$816$	−9.25046	+	23.5698i	−0.323831	+	0.825108i
$817$	36.1499	+	11.1508i	1.26473	+	0.390116i
$818$	17.0734	+	8.22212i	0.596958	+	0.287480i
$819$	−0.130829	+	0.700365i	−0.00457154	+	0.0244727i
$820$	14.9502	−	7.19963i	0.522083	−	0.251422i
$821$	−1.38082	+	0.208125i	−0.0481910	+	0.00726362i	−0.173093	−	0.984905i	$-0.555376\pi$
$821$	−1.38082	+	0.208125i	−0.0481910	+	0.00726362i	0.124903	+	0.992169i	$0.460138\pi$
$822$	26.1308	+	17.8157i	0.911417	+	0.621394i
$823$	−8.29122	+	7.69312i	−0.289014	+	0.268165i	−0.811333	−	0.584585i	$-0.801257\pi$
$823$	−8.29122	+	7.69312i	−0.289014	+	0.268165i	0.522319	+	0.852750i	$0.325067\pi$
$824$	−8.62354	+	5.87943i	−0.300415	+	0.204820i
$825$	2.65252	−	11.6215i	0.0923489	−	0.404607i
$826$	41.2878	+	25.8091i	1.43659	+	0.898012i
$827$	1.38956	+	6.08804i	0.0483196	+	0.211702i	0.993324	−	0.115354i	$-0.0368004\pi$
$827$	1.38956	+	6.08804i	0.0483196	+	0.211702i	−0.945005	+	0.327057i	$0.893943\pi$
$828$	−0.238286	−	0.221097i	−0.00828102	−	0.00768367i
$829$	33.4402	+	5.04030i	1.16143	+	0.175057i	0.701346	−	0.712821i	$-0.252583\pi$
$829$	33.4402	+	5.04030i	1.16143	+	0.175057i	0.460080	+	0.887878i	$0.347821\pi$
$830$	64.4507	−	19.8804i	2.23712	−	0.690059i
$831$	2.11452	−	28.2163i	0.0733518	−	0.978812i
$832$	2.40022			0.0832127
$833$	6.18185	+	19.7149i	0.214188	+	0.683081i
$834$	19.0905			0.661049
$835$	2.50148	−	33.3799i	0.0865672	−	1.15516i
$836$	7.44830	−	2.29749i	0.257605	−	0.0794605i
$837$	19.0672	+	2.87392i	0.659059	+	0.0993371i
$838$	−5.01324	−	4.65161i	−0.173179	−	0.160687i
$839$	−7.09535	−	31.0868i	−0.244959	−	1.07323i	−0.936437	−	0.350837i	$-0.885897\pi$
$839$	−7.09535	−	31.0868i	−0.244959	−	1.07323i	0.691478	−	0.722398i	$-0.256960\pi$
$840$	8.47736	−	24.4089i	0.292497	−	0.842187i
$841$	−8.23363	+	36.0739i	−0.283918	+	1.24393i
$842$	−8.58122	+	5.85058i	−0.295728	+	0.201624i
$843$	−3.75289	+	3.48217i	−0.129256	+	0.119932i
$844$	−7.46078	−	5.08667i	−0.256811	−	0.175091i
$845$	45.8293	−	6.90765i	1.57657	−	0.237630i
$846$	0.406958	−	0.195981i	0.0139915	−	0.00673796i
$847$	−1.73045	−	2.00138i	−0.0594590	−	0.0687684i
$848$	−37.8623	−	18.2335i	−1.30020	−	0.626142i
$849$	18.5828	+	5.73204i	0.637760	+	0.196723i
$850$	−13.0946	+	33.3646i	−0.449142	+	1.14440i
$851$	11.4202	+	19.7803i	0.391479	+	0.678061i
$852$	−13.4329	+	23.2665i	−0.460204	+	0.797097i
$853$	2.60566	+	3.26739i	0.0892161	+	0.111873i	0.824436	−	0.565955i	$-0.191493\pi$
$853$	2.60566	+	3.26739i	0.0892161	+	0.111873i	−0.735220	+	0.677829i	$0.762921\pi$
$854$	−14.7620	−	33.6213i	−0.505146	−	1.15050i
$855$	0.831142	−	1.04222i	0.0284244	−	0.0356431i
$856$	9.30361	+	23.7052i	0.317991	+	0.810227i
$857$	−0.950337	−	12.6814i	−0.0324629	−	0.433187i	−0.989629	−	0.143648i	$-0.954117\pi$
$857$	−0.950337	−	12.6814i	−0.0324629	−	0.433187i	0.957166	−	0.289540i	$-0.0935022\pi$
$858$	−1.15319	−	15.3883i	−0.0393694	−	0.525348i
$859$	−3.89886	−	9.93413i	−0.133027	−	0.338948i	0.848803	−	0.528709i	$-0.177324\pi$
$859$	−3.89886	−	9.93413i	−0.133027	−	0.338948i	−0.981830	+	0.189761i	$0.939229\pi$
$860$	−11.7250	+	14.7026i	−0.399818	+	0.501356i
$861$	8.28088	+	18.8601i	0.282212	+	0.642752i
$862$	−24.3106	−	30.4845i	−0.828021	−	1.03831i
$863$	−3.59350	+	6.22413i	−0.122324	+	0.211872i	−0.920684	−	0.390309i	$-0.872368\pi$
$863$	−3.59350	+	6.22413i	−0.122324	+	0.211872i	0.798360	+	0.602181i	$0.205701\pi$
$864$	14.2718	+	24.7194i	0.485536	+	0.840973i
$865$	−7.97206	+	20.3125i	−0.271058	+	0.690645i
$866$	46.0127	+	14.1930i	1.56357	+	0.482299i
$867$	−12.8200	−	6.17379i	−0.435390	−	0.209673i
$868$	6.74194	+	7.79752i	0.228836	+	0.264665i
$869$	12.8984	−	6.21156i	0.437550	−	0.210713i
$870$	−83.3627	+	12.5649i	−2.82626	+	0.425990i
$871$	−52.7292	−	35.9501i	−1.78666	−	1.21812i
$872$	6.72561	−	6.24046i	0.227758	−	0.211329i
$873$	−0.0558822	+	0.0380998i	−0.00189133	+	0.00128948i
$874$	16.7843	−	73.5370i	0.567739	−	2.48743i
$875$	5.82890	−	16.7832i	0.197053	−	0.567375i
$876$	4.13225	+	18.1046i	0.139616	+	0.611696i
$877$	−4.14879	−	3.84952i	−0.140095	−	0.129989i	0.607013	−	0.794692i	$-0.292368\pi$
$877$	−4.14879	−	3.84952i	−0.140095	−	0.129989i	−0.747108	+	0.664703i	$0.768558\pi$
$878$	68.5896	+	10.3382i	2.31479	+	0.348898i
$879$	−1.85832	+	0.573216i	−0.0626796	+	0.0193341i
$880$	1.29040	−	17.2191i	0.0434993	−	0.580457i
$881$	16.2492			0.547448			0.273724	−	0.961808i	$-0.411744\pi$
$881$	16.2492			0.547448			0.273724	+	0.961808i	$0.411744\pi$
$882$	0.598255	+	0.231591i	0.0201443	+	0.00779809i
$883$	10.6022			0.356791			0.178396	−	0.983959i	$-0.442909\pi$
$883$	10.6022			0.356791			0.178396	+	0.983959i	$0.442909\pi$
$884$	−1.20029	+	16.0168i	−0.0403701	+	0.538702i
$885$	−59.6588	+	18.4023i	−2.00541	+	0.618587i
$886$	−21.5246	−	3.24432i	−0.723135	−	0.108995i
$887$	−37.7798	−	35.0545i	−1.26852	−	1.17702i	−0.975279	−	0.220977i	$-0.929075\pi$
$887$	−37.7798	−	35.0545i	−1.26852	−	1.17702i	−0.293242	−	0.956038i	$-0.594734\pi$
$888$	−2.45158	−	10.7411i	−0.0822698	−	0.360447i
$889$	15.9627	+	9.97830i	0.535371	+	0.334661i
$890$	7.81210	−	34.2271i	0.261862	−	1.14729i
$891$	−7.30400	+	4.97978i	−0.244693	+	0.166829i
$892$	−5.35920	+	4.97261i	−0.179439	+	0.166495i
$893$	29.9773	+	20.4382i	1.00315	+	0.683937i
$894$	−11.4015	+	1.71850i	−0.381323	+	0.0574752i
$895$	−22.8365	+	10.9975i	−0.763340	+	0.367605i
$896$	5.68914	−	30.4555i	0.190061	−	1.01745i
$897$	−46.5730	−	22.4284i	−1.55503	−	0.748862i
$898$	48.0012	+	14.8064i	1.60182	+	0.494096i
$899$	−10.9211	+	27.8264i	−0.364238	+	0.928063i
$900$	0.192615	+	0.333619i	0.00642051	+	0.0111206i
$901$	−12.4125	+	21.4991i	−0.413521	+	0.716239i
$902$	4.94482	+	6.20061i	0.164645	+	0.206458i
$903$	−17.7293	−	15.1856i	−0.589993	−	0.505346i
$904$	−14.6475	+	18.3673i	−0.487167	+	0.610888i
$905$	−3.76802	−	9.60077i	−0.125253	−	0.319140i
$906$	−1.25941	−	16.8057i	−0.0418411	−	0.558331i
$907$	2.54158	+	33.9150i	0.0843918	+	1.12613i	0.865223	+	0.501388i	$0.167177\pi$
$907$	2.54158	+	33.9150i	0.0843918	+	1.12613i	−0.780831	+	0.624742i	$0.785204\pi$
$908$	−0.615733	−	1.56886i	−0.0204338	−	0.0520645i
$909$	−0.0530694	+	0.0665469i	−0.00176020	+	0.00220722i
$910$	2.88184	−	82.1320i	0.0955321	−	2.72265i
$911$	6.41486	+	8.04398i	0.212534	+	0.266509i	0.876659	−	0.481113i	$-0.159767\pi$
$911$	6.41486	+	8.04398i	0.212534	+	0.266509i	−0.664125	+	0.747622i	$0.731196\pi$
$912$	−31.5740	+	54.6878i	−1.04552	+	1.81089i
$913$	5.57951	+	9.66399i	0.184655	+	0.319832i
$914$	15.2382	−	38.8263i	0.504035	−	1.28426i
$915$	44.9907	+	13.8778i	1.48735	+	0.458786i
$916$	−19.3899	−	9.33769i	−0.640660	−	0.308526i
$917$	45.0001	−	1.78863i	1.48603	−	0.0590657i
$918$	24.3740	−	11.7379i	0.804461	−	0.387408i
$919$	−48.0716	+	7.24562i	−1.58573	+	0.239011i	−0.881929	−	0.471382i	$-0.843755\pi$
$919$	−48.0716	+	7.24562i	−1.58573	+	0.239011i	−0.703805	+	0.710393i	$0.748517\pi$
$920$	−27.5358	−	18.7736i	−0.907828	−	0.618947i
$921$	13.6683	−	12.6823i	0.450385	−	0.417896i
$922$	17.6770	−	12.0520i	0.582162	−	0.396911i
$923$	16.9002	−	74.0448i	0.556278	−	2.43721i
$924$	−4.78072	−	0.527397i	−0.157274	−	0.0173501i
$925$	−6.02324	−	26.3895i	−0.198043	−	0.867683i
$926$	41.5841	+	38.5844i	1.36654	+	1.26796i
$927$	0.328546	+	0.0495204i	0.0107909	+	0.00162646i
$928$	−42.2837	+	13.0428i	−1.38803	+	0.428151i
$929$	0.807542	−	10.7759i	0.0264946	−	0.353546i	−0.968163	−	0.250319i	$-0.919464\pi$
$929$	0.807542	−	10.7759i	0.0264946	−	0.353546i	0.994658	−	0.103226i	$-0.0329166\pi$
$930$	−38.1823			−1.25205
$931$	7.91704	+	50.9175i	0.259471	+	1.66875i
$932$	−6.66488			−0.218315
$933$	3.59783	−	48.0097i	0.117788	−	1.57177i
$934$	37.6120	−	11.6018i	1.23070	−	0.379621i
$935$	−10.0865	−	1.52030i	−0.329865	−	0.0497192i
$936$	−0.324933	−	0.301494i	−0.0106208	−	0.00985463i
$937$	4.46056	+	19.5430i	0.145720	+	0.638442i	0.994045	+	0.108967i	$0.0347542\pi$
$937$	4.46056	+	19.5430i	0.145720	+	0.638442i	−0.848325	+	0.529476i	$0.822389\pi$
$938$	−40.5372	+	40.7262i	−1.32359	+	1.32976i
$939$	3.91221	−	17.1405i	0.127670	−	0.559359i
$940$	−14.9015	+	10.1597i	−0.486034	+	0.331373i
$941$	32.9037	−	30.5302i	1.07263	−	0.995256i	0.0726334	−	0.997359i	$-0.476860\pi$
$941$	32.9037	−	30.5302i	1.07263	−	0.995256i	0.999998	+	0.00210238i	$0.000669208\pi$
$942$	16.2353	+	11.0690i	0.528975	+	0.360649i
$943$	26.2701	−	3.95958i	0.855471	−	0.128942i
$944$	−47.3693	+	22.8119i	−1.54174	+	0.742463i
$945$	−42.3113	+	22.4883i	−1.37639	+	0.731544i
$946$	−8.09797	−	3.89978i	−0.263288	−	0.126793i
$947$	8.89217	+	2.74287i	0.288957	+	0.0891314i	0.435845	−	0.900022i	$-0.356450\pi$
$947$	8.89217	+	2.74287i	0.288957	+	0.0891314i	−0.146888	+	0.989153i	$0.546926\pi$
$948$	9.50817	−	24.2264i	0.308811	−	0.786837i
$949$	−26.2487	−	45.4640i	−0.852068	−	1.47583i
$950$	−44.6951	+	77.4142i	−1.45010	+	2.51165i
$951$	1.75157	+	2.19640i	0.0567985	+	0.0712231i
$952$	−12.4240	−	3.29803i	−0.402663	−	0.106890i
$953$	8.94131	−	11.2120i	0.289637	−	0.363194i	−0.615630	−	0.788035i	$-0.711099\pi$
$953$	8.94131	−	11.2120i	0.289637	−	0.363194i	0.905268	+	0.424841i	$0.139670\pi$
$954$	0.281603	+	0.717512i	0.00911722	+	0.0232303i
$955$	−1.96052	−	26.1614i	−0.0634411	−	0.846562i
$956$	−0.974145	−	12.9991i	−0.0315061	−	0.420420i
$957$	−5.09577	−	12.9838i	−0.164723	−	0.419707i
$958$	43.4032	−	54.4259i	1.40229	−	1.75842i
$959$	−12.9638	+	24.6674i	−0.418623	+	0.796553i
$960$	1.72775	+	2.16653i	0.0557629	+	0.0699244i
$961$	8.73063	−	15.1219i	0.281633	−	0.487803i
$962$	−17.5205	−	30.3465i	−0.564885	−	0.978410i
$963$	0.296173	−	0.754637i	0.00954405	−	0.0243178i
$964$	4.08948	+	1.26144i	0.131713	+	0.0406282i
$965$	55.1375	+	26.5528i	1.77494	+	0.854766i
$966$	−27.5513	+	37.5131i	−0.886450	+	1.20696i
$967$	−0.882716	+	0.425094i	−0.0283862	+	0.0136701i	−0.448023	−	0.894022i	$-0.647872\pi$
$967$	−0.882716	+	0.425094i	−0.0283862	+	0.0136701i	0.419637	+	0.907692i	$0.362157\pi$
$968$	1.62764	−	0.245327i	0.0523143	−	0.00788511i
$969$	30.8218	+	21.0139i	0.990139	+	0.675065i
$970$	5.71887	−	5.30633i	0.183622	−	0.170376i
$971$	12.8527	−	8.76282i	0.412463	−	0.281212i	−0.339259	−	0.940693i	$-0.610176\pi$
$971$	12.8527	−	8.76282i	0.412463	−	0.281212i	0.751721	+	0.659481i	$0.229224\pi$
$972$	0.128292	−	0.562084i	0.00411497	−	0.0180289i
$973$	1.92224	+	16.7108i	0.0616241	+	0.535724i
$974$	−1.69044	−	7.40628i	−0.0541651	−	0.237313i
$975$	44.9071	+	41.6677i	1.43818	+	1.33444i
$976$	39.2064	+	5.90942i	1.25497	+	0.189156i
$977$	−7.85746	+	2.42371i	−0.251383	+	0.0775413i	−0.417885	−	0.908500i	$-0.637229\pi$
$977$	−7.85746	+	2.42371i	−0.251383	+	0.0775413i	0.166503	+	0.986041i	$0.446752\pi$
$978$	−3.73080	+	49.7841i	−0.119298	+	1.59192i
$979$	5.80843			0.185638
$980$	−24.9990	−	5.58360i	−0.798562	−	0.178362i
$981$	−0.292073			−0.00932518
$982$	4.83832	−	64.5629i	0.154397	−	2.06029i
$983$	−22.7724	+	7.02434i	−0.726326	+	0.224042i	−0.635802	−	0.771853i	$-0.719330\pi$
$983$	−22.7724	+	7.02434i	−0.726326	+	0.224042i	−0.0905239	+	0.995894i	$0.528854\pi$
$984$	−12.6717	−	1.90995i	−0.403958	−	0.0608869i
$985$	39.2805	+	36.4470i	1.25158	+	1.16130i
$986$	9.33231	+	40.8875i	0.297201	+	1.30212i
$987$	−11.9552	−	18.9286i	−0.380537	−	0.602505i
$988$	−8.91367	+	39.0534i	−0.283582	+	1.24245i
$989$	−24.8765	+	16.9605i	−0.791028	+	0.539314i
$990$	−0.232169	+	0.215421i	−0.00737880	+	0.00684653i
$991$	−13.6543	−	9.30935i	−0.433744	−	0.295721i	0.326697	−	0.945129i	$-0.394064\pi$
$991$	−13.6543	−	9.30935i	−0.433744	−	0.295721i	−0.760440	+	0.649408i	$0.775017\pi$
$992$	−19.8173	+	2.98697i	−0.629199	+	0.0948364i
$993$	5.57298	−	2.68380i	0.176853	−	0.0851680i
$994$	−62.7421	−	27.2005i	−1.99006	−	0.862749i
$995$	20.8357	+	10.0339i	0.660535	+	0.318097i
$996$	19.3848	+	5.97941i	0.614230	+	0.189465i
$997$	18.5043	−	47.1483i	0.586038	−	1.49320i	−0.262961	−	0.964807i	$-0.584699\pi$
$997$	18.5043	−	47.1483i	0.586038	−	1.49320i	0.848999	−	0.528395i	$-0.177206\pi$
$998$	12.6082	+	21.8381i	0.399106	+	0.691273i
$999$	−10.2153	+	17.6934i	−0.323198	+	0.559795i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	539.2.r.b.23.19	✓	276
49.32	even	21	inner	539.2.r.b.375.19	yes	276

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
539.2.r.b.23.19	✓	276	1.1	even	1	trivial
539.2.r.b.375.19	yes	276	49.32	even	21	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:	\( N \)	\(=\)	\( 539 = 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	539.r (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.130700 - 1.74407i) q^{2} +(-1.64058 + 0.506053i) q^{3} +(-1.04703 - 0.157814i) q^{4} +(2.53334 + 2.35060i) q^{5} +(0.668166 + 2.92743i) q^{6} +(-2.49524 + 0.879644i) q^{7} +(0.366275 - 1.60475i) q^{8} +(-0.0432948 + 0.0295179i) q^{9} +O(q^{10})\)	\(q+(0.130700 - 1.74407i) q^{2} +(-1.64058 + 0.506053i) q^{3} +(-1.04703 - 0.157814i) q^{4} +(2.53334 + 2.35060i) q^{5} +(0.668166 + 2.92743i) q^{6} +(-2.49524 + 0.879644i) q^{7} +(0.366275 - 1.60475i) q^{8} +(-0.0432948 + 0.0295179i) q^{9} +(4.43070 - 4.11109i) q^{10} +(0.826239 + 0.563320i) q^{11} +(1.79760 - 0.270944i) q^{12} +(-4.63023 + 2.22980i) q^{13} +(1.20803 + 4.46684i) q^{14} +(-5.34568 - 2.57434i) q^{15} +(-4.77455 - 1.47275i) q^{16} +(-1.07835 + 2.74759i) q^{17} +(0.0458226 + 0.0793671i) q^{18} +(-3.68067 + 6.37510i) q^{19} +(-2.28152 - 2.86094i) q^{20} +(3.64850 - 2.70585i) q^{21} +(1.09046 - 1.36739i) q^{22} +(-2.14040 - 5.45366i) q^{23} +(0.211186 + 2.81809i) q^{24} +(0.518859 + 6.92369i) q^{25} +(3.28375 + 8.36687i) q^{26} +(3.26742 - 4.09722i) q^{27} +(2.75141 - 0.527228i) q^{28} +(5.06532 + 6.35171i) q^{29} +(-5.18851 + 8.98676i) q^{30} +(1.83975 + 3.18654i) q^{31} +(-1.98990 + 5.07018i) q^{32} +(-1.64058 - 0.506053i) q^{33} +(4.65105 + 2.23983i) q^{34} +(-8.38898 - 3.63687i) q^{35} +(0.0499893 - 0.0240736i) q^{36} +(-3.85503 + 0.581052i) q^{37} +(10.6376 + 7.25256i) q^{38} +(6.46788 - 6.00131i) q^{39} +(4.70003 - 3.20442i) q^{40} +(-1.00905 + 4.42094i) q^{41} +(-4.24233 - 6.71689i) q^{42} +(-1.14356 - 5.01025i) q^{43} +(-0.776196 - 0.720204i) q^{44} +(-0.179065 - 0.0269897i) q^{45} +(-9.79131 + 3.02022i) q^{46} +(0.368320 - 4.91489i) q^{47} +8.57834 q^{48} +(5.45245 - 4.38985i) q^{49} +12.1432 q^{50} +(0.378697 - 5.05335i) q^{51} +(5.19988 - 1.60395i) q^{52} +(8.31669 + 1.25354i) q^{53} +(-6.71877 - 6.23411i) q^{54} +(0.769006 + 3.36923i) q^{55} +(0.497668 + 4.32644i) q^{56} +(2.81230 - 12.3215i) q^{57} +(11.7398 - 8.00409i) q^{58} +(7.71352 - 7.15710i) q^{59} +(5.19081 + 3.53903i) q^{60} +(-7.84672 + 1.18270i) q^{61} +(5.79800 - 2.79217i) q^{62} +(0.0820658 - 0.111738i) q^{63} +(-0.420793 - 0.202643i) q^{64} +(-16.9713 - 5.23495i) q^{65} +(-1.09701 + 2.79515i) q^{66} +(6.20901 + 10.7543i) q^{67} +(1.56267 - 2.70663i) q^{68} +(6.27135 + 7.86402i) q^{69} +(-7.43938 + 14.1556i) q^{70} +(-9.21422 + 11.5543i) q^{71} +(0.0315112 + 0.0802892i) q^{72} +(0.763379 + 10.1866i) q^{73} +(0.509543 + 6.79937i) q^{74} +(-4.35498 - 11.0963i) q^{75} +(4.85985 - 6.09405i) q^{76} +(-2.55719 - 0.678824i) q^{77} +(-9.62135 - 12.0648i) q^{78} +(7.15810 - 12.3982i) q^{79} +(-8.63371 - 14.9540i) q^{80} +(-3.22963 + 8.22897i) q^{81} +(7.57853 + 2.33767i) q^{82} +(10.0539 + 4.84172i) q^{83} +(-4.24711 + 2.25732i) q^{84} +(-9.19031 + 4.42582i) q^{85} +(-8.88768 + 1.33960i) q^{86} +(-11.5244 - 7.85718i) q^{87} +(1.20662 - 1.11958i) q^{88} +(4.79915 - 3.27201i) q^{89} +(-0.0704757 + 0.308774i) q^{90} +(9.59211 - 9.63684i) q^{91} +(1.38040 + 6.04793i) q^{92} +(-4.63082 - 4.29678i) q^{93} +(-8.52377 - 1.28475i) q^{94} +(-24.3097 + 7.49854i) q^{95} +(0.698815 - 9.32504i) q^{96} +1.29074 q^{97} +(-6.94355 - 10.0832i) q^{98} -0.0523999 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 276 q + 3 q^{3} + 20 q^{4} + 6 q^{5} - 8 q^{6} + 6 q^{8} + 6 q^{9}+O(q^{10}) \) 276 * q + 3 * q^3 + 20 * q^4 + 6 * q^5 - 8 * q^6 + 6 * q^8 + 6 * q^9	\( 276 q + 3 q^{3} + 20 q^{4} + 6 q^{5} - 8 q^{6} + 6 q^{8} + 6 q^{9} + 3 q^{10} + 23 q^{11} - 32 q^{12} - 27 q^{13} - 23 q^{14} + 6 q^{15} + 70 q^{16} - 3 q^{17} - 20 q^{18} - 61 q^{19} - 12 q^{20} - 23 q^{21} - 6 q^{23} + 6 q^{24} - 11 q^{25} + 9 q^{26} - 12 q^{27} - 3 q^{28} - 24 q^{29} - 26 q^{30} - 75 q^{31} + 137 q^{32} + 3 q^{33} - 58 q^{34} + 15 q^{35} - 36 q^{36} - 29 q^{37} - 6 q^{39} - 53 q^{40} - 25 q^{41} + 4 q^{42} + 20 q^{43} + 6 q^{44} + 3 q^{45} + 52 q^{46} + 25 q^{47} + 288 q^{48} + 84 q^{49} - 218 q^{50} - 160 q^{51} + 65 q^{52} + 5 q^{53} + 66 q^{54} - 12 q^{55} - 178 q^{56} + 23 q^{57} + 5 q^{58} + 28 q^{59} - 54 q^{60} - 65 q^{61} - 92 q^{62} + 85 q^{63} - 50 q^{64} + 201 q^{65} - 38 q^{66} - 16 q^{67} - 91 q^{68} - 42 q^{69} - 255 q^{70} - 63 q^{71} - 165 q^{72} + 6 q^{73} - 166 q^{74} - 117 q^{75} - 87 q^{76} + 33 q^{78} + 2 q^{79} - 48 q^{80} + 5 q^{81} + 53 q^{82} + 37 q^{83} - 84 q^{84} + 26 q^{85} + 67 q^{86} - 59 q^{87} - 3 q^{88} - 155 q^{89} + 9 q^{90} + 47 q^{91} - 19 q^{92} + 81 q^{93} + 126 q^{94} - 37 q^{95} + 395 q^{96} + 302 q^{97} + 90 q^{98} + 268 q^{99}+O(q^{100}) \) 276 * q + 3 * q^3 + 20 * q^4 + 6 * q^5 - 8 * q^6 + 6 * q^8 + 6 * q^9 + 3 * q^10 + 23 * q^11 - 32 * q^12 - 27 * q^13 - 23 * q^14 + 6 * q^15 + 70 * q^16 - 3 * q^17 - 20 * q^18 - 61 * q^19 - 12 * q^20 - 23 * q^21 - 6 * q^23 + 6 * q^24 - 11 * q^25 + 9 * q^26 - 12 * q^27 - 3 * q^28 - 24 * q^29 - 26 * q^30 - 75 * q^31 + 137 * q^32 + 3 * q^33 - 58 * q^34 + 15 * q^35 - 36 * q^36 - 29 * q^37 - 6 * q^39 - 53 * q^40 - 25 * q^41 + 4 * q^42 + 20 * q^43 + 6 * q^44 + 3 * q^45 + 52 * q^46 + 25 * q^47 + 288 * q^48 + 84 * q^49 - 218 * q^50 - 160 * q^51 + 65 * q^52 + 5 * q^53 + 66 * q^54 - 12 * q^55 - 178 * q^56 + 23 * q^57 + 5 * q^58 + 28 * q^59 - 54 * q^60 - 65 * q^61 - 92 * q^62 + 85 * q^63 - 50 * q^64 + 201 * q^65 - 38 * q^66 - 16 * q^67 - 91 * q^68 - 42 * q^69 - 255 * q^70 - 63 * q^71 - 165 * q^72 + 6 * q^73 - 166 * q^74 - 117 * q^75 - 87 * q^76 + 33 * q^78 + 2 * q^79 - 48 * q^80 + 5 * q^81 + 53 * q^82 + 37 * q^83 - 84 * q^84 + 26 * q^85 + 67 * q^86 - 59 * q^87 - 3 * q^88 - 155 * q^89 + 9 * q^90 + 47 * q^91 - 19 * q^92 + 81 * q^93 + 126 * q^94 - 37 * q^95 + 395 * q^96 + 302 * q^97 + 90 * q^98 + 268 * q^99

Introduction

L-functions

Modular forms

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Database

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