LMFDB - Embedded newform 1110.2.bb.d.1009.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1110,2,Mod(1009,1110)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1110, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 4]))

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

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

chi := DirichletCharacter("1110.1009");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1110 = 2 \cdot 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1110.bb (of order $6$, degree $2$, 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:	$8.86339462436$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1009.1
Character	$\chi$	$=$	1110.1009
Dual form			1110.2.bb.d.1099.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.00835632 + 2.23605i) q^{5} +1.00000 q^{6} +(3.70065 - 2.13657i) q^{7} -1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.00835632 + 2.23605i) q^{5} +1.00000 q^{6} +(3.70065 - 2.13657i) q^{7} -1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +(1.12526 - 1.93230i) q^{10} -5.93869 q^{11} +(-0.866025 - 0.500000i) q^{12} +(-1.08299 + 0.625263i) q^{13} -4.27314 q^{14} +(-1.11079 - 1.94066i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-6.29873 - 3.63657i) q^{17} +(-0.866025 + 0.500000i) q^{18} +(2.05756 + 3.56380i) q^{19} +(-1.94066 + 1.11079i) q^{20} +(-2.13657 + 3.70065i) q^{21} +(5.14305 + 2.96934i) q^{22} -6.89816i q^{23} +(0.500000 + 0.866025i) q^{24} +(-4.99986 - 0.0373703i) q^{25} +1.25053 q^{26} +1.00000i q^{27} +(3.70065 + 2.13657i) q^{28} +3.27314 q^{29} +(-0.00835632 + 2.23605i) q^{30} -2.68816 q^{31} +(0.866025 - 0.500000i) q^{32} +(5.14305 - 2.96934i) q^{33} +(3.63657 + 6.29873i) q^{34} +(4.74656 + 8.29270i) q^{35} +1.00000 q^{36} +(-3.08237 - 5.24395i) q^{37} -4.11513i q^{38} +(0.625263 - 1.08299i) q^{39} +(2.23605 + 0.00835632i) q^{40} +(-1.33327 - 2.30929i) q^{41} +(3.70065 - 2.13657i) q^{42} +9.04279i q^{43} +(-2.96934 - 5.14305i) q^{44} +(1.93230 + 1.12526i) q^{45} +(-3.44908 + 5.97399i) q^{46} +4.62329i q^{47} -1.00000i q^{48} +(5.62987 - 9.75123i) q^{49} +(4.31132 + 2.53229i) q^{50} +7.27314 q^{51} +(-1.08299 - 0.625263i) q^{52} +(-1.31601 - 0.759799i) q^{53} +(0.500000 - 0.866025i) q^{54} +(0.0496256 - 13.2792i) q^{55} +(-2.13657 - 3.70065i) q^{56} +(-3.56380 - 2.05756i) q^{57} +(-2.83462 - 1.63657i) q^{58} +(-0.0555279 + 0.0961772i) q^{59} +(1.12526 - 1.93230i) q^{60} +(-6.14118 - 10.6368i) q^{61} +(2.32802 + 1.34408i) q^{62} -4.27314i q^{63} -1.00000 q^{64} +(-1.38907 - 2.42684i) q^{65} -5.93869 q^{66} +(-4.44547 + 2.56660i) q^{67} -7.27314i q^{68} +(3.44908 + 5.97399i) q^{69} +(0.0357078 - 9.55497i) q^{70} +(-3.59953 - 6.23456i) q^{71} +(-0.866025 - 0.500000i) q^{72} -3.36158i q^{73} +(0.0474386 + 6.08258i) q^{74} +(4.34869 - 2.46757i) q^{75} +(-2.05756 + 3.56380i) q^{76} +(-21.9770 + 12.6884i) q^{77} +(-1.08299 + 0.625263i) q^{78} +(-3.41867 - 5.92130i) q^{79} +(-1.93230 - 1.12526i) q^{80} +(-0.500000 - 0.866025i) q^{81} +2.66654i q^{82} +(-6.46021 - 3.72981i) q^{83} -4.27314 q^{84} +(8.18420 - 14.0539i) q^{85} +(4.52139 - 7.83128i) q^{86} +(-2.83462 + 1.63657i) q^{87} +5.93869i q^{88} +(4.39703 - 7.61589i) q^{89} +(-1.11079 - 1.94066i) q^{90} +(-2.67184 + 4.62776i) q^{91} +(5.97399 - 3.44908i) q^{92} +(2.32802 - 1.34408i) q^{93} +(2.31165 - 4.00389i) q^{94} +(-7.98605 + 4.57104i) q^{95} +(-0.500000 + 0.866025i) q^{96} -12.1077i q^{97} +(-9.75123 + 5.62987i) q^{98} +(-2.96934 + 5.14305i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 14 q^{4} + 2 q^{5} + 28 q^{6} + 14 q^{9}+O(q^{10}) $ 28 * q + 14 * q^4 + 2 * q^5 + 28 * q^6 + 14 * q^9	$ 28 q + 14 q^{4} + 2 q^{5} + 28 q^{6} + 14 q^{9} + 4 q^{10} - 12 q^{11} + 8 q^{14} + 2 q^{15} - 14 q^{16} - 20 q^{19} - 2 q^{20} + 4 q^{21} + 14 q^{24} - 8 q^{25} - 20 q^{26} - 36 q^{29} + 2 q^{30} + 24 q^{31} + 38 q^{34} - 2 q^{35} + 28 q^{36} - 10 q^{39} + 2 q^{40} - 6 q^{44} + 4 q^{45} + 8 q^{46} + 50 q^{49} - 4 q^{50} + 76 q^{51} + 14 q^{54} - 28 q^{55} + 4 q^{56} - 26 q^{59} + 4 q^{60} - 28 q^{61} - 28 q^{64} + 60 q^{65} - 12 q^{66} - 8 q^{69} - 10 q^{70} - 64 q^{71} + 24 q^{74} - 8 q^{75} + 20 q^{76} + 32 q^{79} - 4 q^{80} - 14 q^{81} + 8 q^{84} + 16 q^{85} - 8 q^{86} + 76 q^{89} + 2 q^{90} - 8 q^{91} - 38 q^{94} - 70 q^{95} - 14 q^{96} - 6 q^{99}+O(q^{100}) $ 28 * q + 14 * q^4 + 2 * q^5 + 28 * q^6 + 14 * q^9 + 4 * q^10 - 12 * q^11 + 8 * q^14 + 2 * q^15 - 14 * q^16 - 20 * q^19 - 2 * q^20 + 4 * q^21 + 14 * q^24 - 8 * q^25 - 20 * q^26 - 36 * q^29 + 2 * q^30 + 24 * q^31 + 38 * q^34 - 2 * q^35 + 28 * q^36 - 10 * q^39 + 2 * q^40 - 6 * q^44 + 4 * q^45 + 8 * q^46 + 50 * q^49 - 4 * q^50 + 76 * q^51 + 14 * q^54 - 28 * q^55 + 4 * q^56 - 26 * q^59 + 4 * q^60 - 28 * q^61 - 28 * q^64 + 60 * q^65 - 12 * q^66 - 8 * q^69 - 10 * q^70 - 64 * q^71 + 24 * q^74 - 8 * q^75 + 20 * q^76 + 32 * q^79 - 4 * q^80 - 14 * q^81 + 8 * q^84 + 16 * q^85 - 8 * q^86 + 76 * q^89 + 2 * q^90 - 8 * q^91 - 38 * q^94 - 70 * q^95 - 14 * q^96 - 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times$.

$n$	$371$	$631$	$667$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$-1$

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 $

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	−0.00835632	+	2.23605i	−0.00373706	+	0.999993i
$5$	−0.00835632	+	2.23605i	−0.00373706	+	0.999993i
$6$	1.00000			0.408248
$7$	3.70065	−	2.13657i	1.39871	−	0.807548i	0.404456	−	0.914557i	$-0.367461\pi$
$7$	3.70065	−	2.13657i	1.39871	−	0.807548i	0.994258	+	0.107009i	$0.0341275\pi$
$8$		−	1.00000i		−	0.353553i
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$	1.12526	−	1.93230i	0.355839	−	0.611047i
$11$	−5.93869			−1.79058			−0.895291	−	0.445482i	$-0.853032\pi$
$11$	−5.93869			−1.79058			−0.895291	+	0.445482i	$0.853032\pi$
$12$	−0.866025	−	0.500000i	−0.250000	−	0.144338i
$13$	−1.08299	+	0.625263i	−0.300367	+	0.173417i	−0.642608	−	0.766195i	$-0.722147\pi$
$13$	−1.08299	+	0.625263i	−0.300367	+	0.173417i	0.342241	+	0.939612i	$0.388814\pi$
$14$	−4.27314			−1.14205
$15$	−1.11079	−	1.94066i	−0.286805	−	0.501075i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−6.29873	−	3.63657i	−1.52767	−	0.881998i	−0.999459	−	0.0328820i	$-0.989531\pi$
$17$	−6.29873	−	3.63657i	−1.52767	−	0.881998i	−0.528206	−	0.849116i	$-0.677135\pi$
$18$	−0.866025	+	0.500000i	−0.204124	+	0.117851i
$19$	2.05756	+	3.56380i	0.472037	+	0.817593i	0.999488	−	0.0319930i	$-0.0101854\pi$
$19$	2.05756	+	3.56380i	0.472037	+	0.817593i	−0.527451	+	0.849586i	$0.676852\pi$
$20$	−1.94066	+	1.11079i	−0.433944	+	0.248380i
$21$	−2.13657	+	3.70065i	−0.466238	+	0.807548i
$22$	5.14305	+	2.96934i	1.09650	+	0.633066i
$23$		−	6.89816i		−	1.43837i	−0.694820	−	0.719183i	$-0.744516\pi$
$23$		−	6.89816i		−	1.43837i	0.694820	−	0.719183i	$-0.255484\pi$
$24$	0.500000	+	0.866025i	0.102062	+	0.176777i
$25$	−4.99986	−	0.0373703i	−0.999972	−	0.00747407i
$26$	1.25053			0.245248
$27$			1.00000i			0.192450i
$28$	3.70065	+	2.13657i	0.699357	+	0.403774i
$29$	3.27314			0.607807			0.303904	−	0.952703i	$-0.401710\pi$
$29$	3.27314			0.607807			0.303904	+	0.952703i	$0.401710\pi$
$30$	−0.00835632	+	2.23605i	−0.00152565	+	0.408245i
$31$	−2.68816			−0.482808			−0.241404	−	0.970425i	$-0.577608\pi$
$31$	−2.68816			−0.482808			−0.241404	+	0.970425i	$0.577608\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$	5.14305	−	2.96934i	0.895291	−	0.516896i
$34$	3.63657	+	6.29873i	0.623667	+	1.08022i
$35$	4.74656	+	8.29270i	0.802315	+	1.40172i
$36$	1.00000			0.166667
$37$	−3.08237	−	5.24395i	−0.506739	−	0.862100i
$37$	−3.08237	−	5.24395i	−0.506739	−	0.862100i
$38$		−	4.11513i		−	0.667562i
$39$	0.625263	−	1.08299i	0.100122	−	0.173417i
$40$	2.23605	+	0.00835632i	0.353551	+	0.00132125i
$41$	−1.33327	−	2.30929i	−0.208222	−	0.360651i	0.742933	−	0.669366i	$-0.233434\pi$
$41$	−1.33327	−	2.30929i	−0.208222	−	0.360651i	−0.951154	+	0.308715i	$0.900101\pi$
$42$	3.70065	−	2.13657i	0.571023	−	0.329680i
$43$			9.04279i			1.37901i	0.724280	+	0.689506i	$0.242172\pi$
$43$			9.04279i			1.37901i	−0.724280	+	0.689506i	$0.757828\pi$
$44$	−2.96934	−	5.14305i	−0.447645	−	0.775345i
$45$	1.93230	+	1.12526i	0.288050	+	0.167744i
$46$	−3.44908	+	5.97399i	−0.508539	+	0.880816i
$47$			4.62329i			0.674377i	0.941437	+	0.337188i	$0.109476\pi$
$47$			4.62329i			0.674377i	−0.941437	+	0.337188i	$0.890524\pi$
$48$		−	1.00000i		−	0.144338i
$49$	5.62987	−	9.75123i	0.804268	−	1.39303i
$50$	4.31132	+	2.53229i	0.609713	+	0.358120i
$51$	7.27314			1.01844
$52$	−1.08299	−	0.625263i	−0.150183	−	0.0867084i
$53$	−1.31601	−	0.759799i	−0.180768	−	0.104366i	0.406885	−	0.913479i	$-0.366615\pi$
$53$	−1.31601	−	0.759799i	−0.180768	−	0.104366i	−0.587653	+	0.809113i	$0.699948\pi$
$54$	0.500000	−	0.866025i	0.0680414	−	0.117851i
$55$	0.0496256	−	13.2792i	0.00669151	−	1.79057i
$56$	−2.13657	−	3.70065i	−0.285511	−	0.494520i
$57$	−3.56380	−	2.05756i	−0.472037	−	0.272531i
$58$	−2.83462	−	1.63657i	−0.372204	−	0.214892i
$59$	−0.0555279	+	0.0961772i	−0.00722912	+	0.0125212i	−0.869617	−	0.493726i	$-0.835634\pi$
$59$	−0.0555279	+	0.0961772i	−0.00722912	+	0.0125212i	0.862388	+	0.506248i	$0.168968\pi$
$60$	1.12526	−	1.93230i	0.145271	−	0.249459i
$61$	−6.14118	−	10.6368i	−0.786298	−	1.36191i	−0.928221	−	0.372030i	$-0.878662\pi$
$61$	−6.14118	−	10.6368i	−0.786298	−	1.36191i	0.141923	−	0.989878i	$-0.454671\pi$
$62$	2.32802	+	1.34408i	0.295658	+	0.170698i
$63$		−	4.27314i		−	0.538365i
$64$	−1.00000			−0.125000
$65$	−1.38907	−	2.42684i	−0.172293	−	0.301013i
$66$	−5.93869			−0.731002
$67$	−4.44547	+	2.56660i	−0.543101	+	0.313560i	−0.746335	−	0.665571i	$-0.768188\pi$
$67$	−4.44547	+	2.56660i	−0.543101	+	0.313560i	0.203234	+	0.979130i	$0.434855\pi$
$68$		−	7.27314i		−	0.881998i
$69$	3.44908	+	5.97399i	0.415221	+	0.719183i
$70$	0.0357078	−	9.55497i	0.00426789	−	1.14204i
$71$	−3.59953	−	6.23456i	−0.427185	−	0.739907i	0.569436	−	0.822035i	$-0.307161\pi$
$71$	−3.59953	−	6.23456i	−0.427185	−	0.739907i	−0.996622	+	0.0821287i	$0.973828\pi$
$72$	−0.866025	−	0.500000i	−0.102062	−	0.0589256i
$73$		−	3.36158i		−	0.393443i	−0.980459	−	0.196722i	$-0.936970\pi$
$73$		−	3.36158i		−	0.393443i	0.980459	−	0.196722i	$-0.0630295\pi$
$74$	0.0474386	+	6.08258i	0.00551462	+	0.707085i
$75$	4.34869	−	2.46757i	0.502144	−	0.284930i
$76$	−2.05756	+	3.56380i	−0.236019	+	0.408796i
$77$	−21.9770	+	12.6884i	−2.50451	+	1.44598i
$78$	−1.08299	+	0.625263i	−0.122624	+	0.0707971i
$79$	−3.41867	−	5.92130i	−0.384630	−	0.666199i	0.607088	−	0.794635i	$-0.292338\pi$
$79$	−3.41867	−	5.92130i	−0.384630	−	0.666199i	−0.991718	+	0.128436i	$0.959004\pi$
$80$	−1.93230	−	1.12526i	−0.216038	−	0.125808i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$			2.66654i			0.294470i
$83$	−6.46021	−	3.72981i	−0.709101	−	0.409399i	0.101627	−	0.994823i	$-0.467595\pi$
$83$	−6.46021	−	3.72981i	−0.709101	−	0.409399i	−0.810728	+	0.585423i	$0.800928\pi$
$84$	−4.27314			−0.466238
$85$	8.18420	−	14.0539i	0.887701	−	1.52436i
$86$	4.52139	−	7.83128i	0.487554	−	0.844469i
$87$	−2.83462	+	1.63657i	−0.303904	+	0.175459i
$88$			5.93869i			0.633066i
$89$	4.39703	−	7.61589i	0.466085	−	0.807282i	−0.533165	−	0.846011i	$-0.678998\pi$
$89$	4.39703	−	7.61589i	0.466085	−	0.807282i	0.999250	+	0.0387290i	$0.0123309\pi$
$90$	−1.11079	−	1.94066i	−0.117087	−	0.204563i
$91$	−2.67184	+	4.62776i	−0.280085	+	0.485121i
$92$	5.97399	−	3.44908i	0.622831	−	0.359592i
$93$	2.32802	−	1.34408i	0.241404	−	0.139375i
$94$	2.31165	−	4.00389i	0.238428	−	0.412970i
$95$	−7.98605	+	4.57104i	−0.819351	+	0.468979i
$96$	−0.500000	+	0.866025i	−0.0510310	+	0.0883883i
$97$		−	12.1077i		−	1.22935i	−0.788782	−	0.614673i	$-0.789288\pi$
$97$		−	12.1077i		−	1.22935i	0.788782	−	0.614673i	$-0.210712\pi$
$98$	−9.75123	+	5.62987i	−0.985023	+	0.568703i
$99$	−2.96934	+	5.14305i	−0.298430	+	0.516896i
$100$	−2.46757	−	4.34869i	−0.246757	−	0.434869i
$101$	−7.20776			−0.717199			−0.358599	−	0.933492i	$-0.616746\pi$
$101$	−7.20776			−0.717199			−0.358599	+	0.933492i	$0.616746\pi$
$102$	−6.29873	−	3.63657i	−0.623667	−	0.360074i
$103$			3.19806i			0.315114i	0.987510	+	0.157557i	$0.0503618\pi$
$103$			3.19806i			0.315114i	−0.987510	+	0.157557i	$0.949638\pi$
$104$	0.625263	+	1.08299i	0.0613121	+	0.106196i
$105$	−8.25699	−	4.80841i	−0.805800	−	0.469253i
$106$	0.759799	+	1.31601i	0.0737982	+	0.127822i
$107$	−6.68208	+	3.85790i	−0.645981	+	0.372957i	−0.786915	−	0.617062i	$-0.788323\pi$
$107$	−6.68208	+	3.85790i	−0.645981	+	0.372957i	0.140934	+	0.990019i	$0.454990\pi$
$108$	−0.866025	+	0.500000i	−0.0833333	+	0.0481125i
$109$	−3.85417	+	6.67561i	−0.369162	+	0.639408i	−0.989435	−	0.144979i	$-0.953689\pi$
$109$	−3.85417	+	6.67561i	−0.369162	+	0.639408i	0.620273	+	0.784386i	$0.287022\pi$
$110$	−6.68259	+	11.4753i	−0.637160	+	1.09413i
$111$	5.29139	+	3.00021i	0.502236	+	0.284767i
$112$			4.27314i			0.403774i
$113$	13.4168	+	7.74618i	1.26214	+	0.728700i	0.973489	−	0.228733i	$-0.0734584\pi$
$113$	13.4168	+	7.74618i	1.26214	+	0.728700i	0.288656	+	0.957433i	$0.406792\pi$
$114$	2.05756	+	3.56380i	0.192708	+	0.333781i
$115$	15.4247	+	0.0576433i	1.43836	+	0.00537526i
$116$	1.63657	+	2.83462i	0.151952	+	0.263188i
$117$			1.25053i			0.115611i
$118$	0.0961772	−	0.0555279i	0.00885383	−	0.00511176i
$119$	−31.0792			−2.84902
$120$	−1.94066	+	1.11079i	−0.177157	+	0.101401i
$121$	24.2680			2.20618
$122$			12.2824i			1.11199i
$123$	2.30929	+	1.33327i	0.208222	+	0.120217i
$124$	−1.34408	−	2.32802i	−0.120702	−	0.209062i
$125$	0.125342	−	11.1796i	0.0112110	−	0.999937i
$126$	−2.13657	+	3.70065i	−0.190341	+	0.329680i
$127$	−13.1682	−	7.60268i	−1.16849	−	0.674628i	−0.215167	−	0.976577i	$-0.569029\pi$
$127$	−13.1682	−	7.60268i	−1.16849	−	0.674628i	−0.953324	+	0.301949i	$0.902363\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	−4.52139	−	7.83128i	−0.398086	−	0.689506i
$130$	−0.0104498	+	2.79624i	−0.000916508	+	0.245247i
$131$	8.24808	−	14.2861i	0.720638	−	1.24818i	−0.240106	−	0.970747i	$-0.577182\pi$
$131$	8.24808	−	14.2861i	0.720638	−	1.24818i	0.960744	−	0.277435i	$-0.0894844\pi$
$132$	5.14305	+	2.96934i	0.447645	+	0.258448i
$133$	15.2286	+	8.79226i	1.32049	+	0.762386i
$134$	5.13319			0.443440
$135$	−2.23605	−	0.00835632i	−0.192449	−	0.000719198i
$136$	−3.63657	+	6.29873i	−0.311833	+	0.540111i
$137$			23.0633i			1.97043i	0.171327	+	0.985214i	$0.445194\pi$
$137$			23.0633i			1.97043i	−0.171327	+	0.985214i	$0.554806\pi$
$138$		−	6.89816i		−	0.587211i
$139$	−4.48645	+	7.77075i	−0.380535	+	0.659107i	−0.991139	−	0.132830i	$-0.957594\pi$
$139$	−4.48645	+	7.77075i	−0.380535	+	0.659107i	0.610603	+	0.791937i	$0.290927\pi$
$140$	−4.80841	+	8.25699i	−0.406385	+	0.697843i
$141$	−2.31165	−	4.00389i	−0.194676	−	0.337188i
$142$			7.19905i			0.604131i
$143$	6.43152	−	3.71324i	0.537831	−	0.310517i
$144$	0.500000	+	0.866025i	0.0416667	+	0.0721688i
$145$	−0.0273514	+	7.31892i	−0.00227141	+	0.607803i
$146$	−1.68079	+	2.91122i	−0.139103	+	0.240934i
$147$			11.2597i			0.928688i
$148$	3.00021	−	5.29139i	0.246615	−	0.434949i
$149$	12.1069			0.991838			0.495919	−	0.868369i	$-0.334831\pi$
$149$	12.1069			0.991838			0.495919	+	0.868369i	$0.334831\pi$
$150$	−4.99986	−	0.0373703i	−0.408237	−	0.00305128i
$151$	4.81068	+	8.33235i	0.391488	+	0.678077i	0.992646	−	0.121053i	$-0.0386271\pi$
$151$	4.81068	+	8.33235i	0.391488	+	0.678077i	−0.601158	+	0.799130i	$0.705294\pi$
$152$	3.56380	−	2.05756i	0.289063	−	0.166890i
$153$	−6.29873	+	3.63657i	−0.509222	+	0.293999i
$154$	25.3769			2.04493
$155$	0.0224631	−	6.01087i	0.00180428	−	0.482805i
$156$	1.25053			0.100122
$157$	−7.43290	−	4.29139i	−0.593210	−	0.342490i	0.173156	−	0.984894i	$-0.444604\pi$
$157$	−7.43290	−	4.29139i	−0.593210	−	0.342490i	−0.766366	+	0.642405i	$0.777937\pi$
$158$			6.83733i			0.543949i
$159$	1.51960			0.120512
$160$	1.11079	+	1.94066i	0.0878156	+	0.153422i
$161$	−14.7384	−	25.5277i	−1.16155	−	2.01186i
$162$			1.00000i			0.0785674i
$163$	−19.6684	−	11.3555i	−1.54055	−	0.889434i	−0.998804	−	0.0488890i	$-0.984432\pi$
$163$	−19.6684	−	11.3555i	−1.54055	−	0.889434i	−0.541741	−	0.840545i	$-0.682235\pi$
$164$	1.33327	−	2.30929i	0.104111	−	0.180325i
$165$	6.59663	+	11.5250i	0.513547	+	0.897216i
$166$	3.72981	+	6.46021i	0.289489	+	0.501410i
$167$	−3.96167	+	2.28727i	−0.306564	+	0.176995i	−0.645388	−	0.763855i	$-0.723304\pi$
$167$	−3.96167	+	2.28727i	−0.306564	+	0.176995i	0.338824	+	0.940850i	$0.389971\pi$
$168$	3.70065	+	2.13657i	0.285511	+	0.164840i
$169$	−5.71809	+	9.90403i	−0.439853	+	0.761848i
$170$	−14.1147	+	8.07893i	−1.08255	+	0.619626i
$171$	4.11513			0.314692
$172$	−7.83128	+	4.52139i	−0.597130	+	0.344753i
$173$	1.24331	+	0.717825i	0.0945270	+	0.0545752i	0.546518	−	0.837447i	$-0.315953\pi$
$173$	1.24331	+	0.717825i	0.0945270	+	0.0545752i	−0.451991	+	0.892022i	$0.649286\pi$
$174$	3.27314			0.248136
$175$	−18.5826	+	10.5443i	−1.40471	+	0.797071i
$176$	2.96934	−	5.14305i	0.223823	−	0.387672i
$177$		−	0.111056i		−	0.00834747i
$178$	−7.61589	+	4.39703i	−0.570835	+	0.329572i
$179$	11.3781			0.850437			0.425218	−	0.905091i	$-0.360197\pi$
$179$	11.3781			0.850437			0.425218	+	0.905091i	$0.360197\pi$
$180$	−0.00835632	+	2.23605i	−0.000622843	+	0.166666i
$181$	−9.91980	−	17.1816i	−0.737333	−	1.27710i	−0.953692	−	0.300784i	$-0.902752\pi$
$181$	−9.91980	−	17.1816i	−0.737333	−	1.27710i	0.216359	−	0.976314i	$-0.430582\pi$
$182$	4.62776	−	2.67184i	0.343032	−	0.198050i
$183$	10.6368	+	6.14118i	0.786298	+	0.453969i
$184$	−6.89816			−0.508539
$185$	11.7515	−	6.84852i	0.863987	−	0.503514i
$186$	−2.68816			−0.197106
$187$	37.4062	+	21.5965i	2.73541	+	1.57929i
$188$	−4.00389	+	2.31165i	−0.292014	+	0.168594i
$189$	2.13657	+	3.70065i	0.155413	+	0.269183i
$190$	9.20164	+	0.0343873i	0.667557	+	0.00249472i
$191$	11.1024			0.803339			0.401670	−	0.915785i	$-0.368430\pi$
$191$	11.1024			0.803339			0.401670	+	0.915785i	$0.368430\pi$
$192$	0.866025	−	0.500000i	0.0625000	−	0.0360844i
$193$		−	25.1326i		−	1.80909i	−0.426382	−	0.904543i	$-0.640212\pi$
$193$		−	25.1326i		−	1.80909i	0.426382	−	0.904543i	$-0.359788\pi$
$194$	−6.05383	+	10.4855i	−0.434639	+	0.752818i
$195$	2.41639	+	1.40717i	0.173041	+	0.100770i
$196$	11.2597			0.804268
$197$	−0.993932	−	0.573847i	−0.0708148	−	0.0408849i	0.464175	−	0.885744i	$-0.346351\pi$
$197$	−0.993932	−	0.573847i	−0.0708148	−	0.0408849i	−0.534989	+	0.844859i	$0.679684\pi$
$198$	5.14305	−	2.96934i	0.365501	−	0.211022i
$199$	6.59776			0.467703			0.233851	−	0.972272i	$-0.424867\pi$
$199$	6.59776			0.467703			0.233851	+	0.972272i	$0.424867\pi$
$200$	−0.0373703	+	4.99986i	−0.00264248	+	0.353544i
$201$	2.56660	−	4.44547i	0.181034	−	0.313560i
$202$	6.24210	+	3.60388i	0.439193	+	0.253568i
$203$	12.1128	−	6.99330i	0.850149	−	0.490834i
$204$	3.63657	+	6.29873i	0.254611	+	0.440999i
$205$	5.17484	−	2.96197i	0.361427	−	0.206873i
$206$	1.59903	−	2.76960i	0.111410	−	0.192967i
$207$	−5.97399	−	3.44908i	−0.415221	−	0.239728i
$208$		−	1.25053i		−	0.0867084i
$209$	−12.2192	−	21.1643i	−0.845221	−	1.46397i
$210$	4.74656	+	8.29270i	0.327544	+	0.572251i
$211$	18.6041			1.28076			0.640380	−	0.768058i	$-0.278777\pi$
$211$	18.6041			1.28076			0.640380	+	0.768058i	$0.278777\pi$
$212$		−	1.51960i		−	0.104366i
$213$	6.23456	+	3.59953i	0.427185	+	0.246636i
$214$	7.71580			0.527442
$215$	−20.2201	−	0.0755644i	−1.37900	−	0.00515345i
$216$	1.00000			0.0680414
$217$	−9.94795	+	5.74345i	−0.675311	+	0.389891i
$218$	6.67561	−	3.85417i	0.452129	−	0.261037i
$219$	1.68079	+	2.91122i	0.113577	+	0.196722i
$220$	11.5250	−	6.59663i	0.777012	−	0.444745i
$221$	9.09525			0.611813
$222$	−3.08237	−	5.24395i	−0.206875	−	0.351951i
$223$		−	19.3854i		−	1.29814i	−0.760727	−	0.649072i	$-0.775157\pi$
$223$		−	19.3854i		−	1.29814i	0.760727	−	0.649072i	$-0.224843\pi$
$224$	2.13657	−	3.70065i	0.142756	−	0.247260i
$225$	−2.53229	+	4.31132i	−0.168820	+	0.287421i
$226$	−7.74618	−	13.4168i	−0.515268	−	0.892471i
$227$	−5.15116	+	2.97402i	−0.341895	+	0.197393i	−0.661109	−	0.750289i	$-0.729914\pi$
$227$	−5.15116	+	2.97402i	−0.341895	+	0.197393i	0.319215	+	0.947682i	$0.396581\pi$
$228$		−	4.11513i		−	0.272531i
$229$	4.45902	+	7.72325i	0.294660	+	0.510367i	0.974906	−	0.222618i	$-0.0714602\pi$
$229$	4.45902	+	7.72325i	0.294660	+	0.510367i	−0.680246	+	0.732984i	$0.738127\pi$
$230$	−13.3293	−	7.76225i	−0.878910	−	0.511828i
$231$	12.6884	−	21.9770i	0.834837	−	1.44598i
$232$		−	3.27314i		−	0.214892i
$233$			1.91329i			0.125344i	0.998034	+	0.0626718i	$0.0199621\pi$
$233$			1.91329i			0.125344i	−0.998034	+	0.0626718i	$0.980038\pi$
$234$	0.625263	−	1.08299i	0.0408747	−	0.0707971i
$235$	−10.3379	−	0.0386337i	−0.674372	−	0.00252019i
$236$	−0.111056			−0.00722912
$237$	5.92130	+	3.41867i	0.384630	+	0.222066i
$238$	26.9154	+	15.5396i	1.74466	+	1.00728i
$239$	−7.76415	+	13.4479i	−0.502221	+	0.869872i	0.497776	+	0.867306i	$0.334150\pi$
$239$	−7.76415	+	13.4479i	−0.502221	+	0.869872i	−0.999997	+	0.00256635i	$0.999183\pi$
$240$	2.23605	+	0.00835632i	0.144337	+	0.000539398i
$241$	−5.55610	−	9.62345i	−0.357900	−	0.619901i	0.629710	−	0.776830i	$-0.283174\pi$
$241$	−5.55610	−	9.62345i	−0.357900	−	0.619901i	−0.987610	+	0.156929i	$0.949840\pi$
$242$	−21.0167	−	12.1340i	−1.35101	−	0.780003i
$243$	0.866025	+	0.500000i	0.0555556	+	0.0320750i
$244$	6.14118	−	10.6368i	0.393149	−	0.680954i
$245$	21.7572	+	12.6702i	1.39002	+	0.809468i
$246$	−1.33327	−	2.30929i	−0.0850062	−	0.147235i
$247$	−4.45663	−	2.57304i	−0.283569	−	0.163718i
$248$			2.68816i			0.170698i
$249$	7.45961			0.472734
$250$	−5.69837	+	9.61918i	−0.360396	+	0.608370i
$251$	13.3364			0.841789			0.420894	−	0.907110i	$-0.361716\pi$
$251$	13.3364			0.841789			0.420894	+	0.907110i	$0.361716\pi$
$252$	3.70065	−	2.13657i	0.233119	−	0.134591i
$253$			40.9660i			2.57551i
$254$	7.60268	+	13.1682i	0.477034	+	0.826248i
$255$	−0.0607767	+	16.2631i	−0.00380599	+	1.01844i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	21.3805	+	12.3440i	1.33368	+	0.769999i	0.985861	−	0.167563i	$-0.0535898\pi$
$257$	21.3805	+	12.3440i	1.33368	+	0.769999i	0.347817	+	0.937563i	$0.386923\pi$
$258$			9.04279i			0.562979i
$259$	−22.6108	−	12.8203i	−1.40497	−	0.796615i
$260$	1.40717	−	2.41639i	0.0872690	−	0.149858i
$261$	1.63657	−	2.83462i	0.101301	−	0.175459i
$262$	−14.2861	+	8.24808i	−0.882598	+	0.509568i
$263$	−21.8902	+	12.6383i	−1.34981	+	0.779311i	−0.988222	−	0.153029i	$-0.951097\pi$
$263$	−21.8902	+	12.6383i	−1.34981	+	0.779311i	−0.361584	+	0.932340i	$0.617764\pi$
$264$	−2.96934	−	5.14305i	−0.182750	−	0.316533i
$265$	1.70995	−	2.93632i	0.105041	−	0.180377i
$266$	−8.79226	−	15.2286i	−0.539088	−	0.933728i
$267$			8.79407i			0.538188i
$268$	−4.44547	−	2.56660i	−0.271551	−	0.156780i
$269$	−25.0272			−1.52594			−0.762968	−	0.646436i	$-0.776259\pi$
$269$	−25.0272			−1.52594			−0.762968	+	0.646436i	$0.776259\pi$
$270$	1.93230	+	1.12526i	0.117596	+	0.0684813i
$271$	−6.67337	+	11.5586i	−0.405379	+	0.702136i	−0.994365	−	0.106006i	$-0.966194\pi$
$271$	−6.67337	+	11.5586i	−0.405379	+	0.702136i	0.588987	+	0.808143i	$0.299527\pi$
$272$	6.29873	−	3.63657i	0.381916	−	0.220500i
$273$		−	5.34368i		−	0.323414i
$274$	11.5316	−	19.9734i	0.696652	−	1.20664i
$275$	29.6926	+	0.221931i	1.79053	+	0.0133829i
$276$	−3.44908	+	5.97399i	−0.207610	+	0.359592i
$277$	16.1983	−	9.35210i	0.973262	−	0.561913i	0.0730329	−	0.997330i	$-0.476732\pi$
$277$	16.1983	−	9.35210i	0.973262	−	0.561913i	0.900229	+	0.435416i	$0.143399\pi$
$278$	7.77075	−	4.48645i	0.466059	−	0.269079i
$279$	−1.34408	+	2.32802i	−0.0804680	+	0.139375i
$280$	8.29270	−	4.74656i	0.495584	−	0.283661i
$281$	−5.15883	+	8.93535i	−0.307750	+	0.533038i	−0.977870	−	0.209214i	$-0.932909\pi$
$281$	−5.15883	+	8.93535i	−0.307750	+	0.533038i	0.670120	+	0.742253i	$0.266243\pi$
$282$			4.62329i			0.275313i
$283$	−5.24310	+	3.02711i	−0.311670	+	0.179943i	−0.647674	−	0.761918i	$-0.724258\pi$
$283$	−5.24310	+	3.02711i	−0.311670	+	0.179943i	0.336003	+	0.941861i	$0.390925\pi$
$284$	3.59953	−	6.23456i	0.213593	−	0.369953i
$285$	4.63060	−	7.95166i	0.274293	−	0.471016i
$286$	−7.42648			−0.439137
$287$	−9.86794	−	5.69726i	−0.582486	−	0.336298i
$288$		−	1.00000i		−	0.0589256i
$289$	17.9493	+	31.0891i	1.05584	+	1.82877i
$290$	3.68315	−	6.32469i	0.216282	−	0.371399i
$291$	6.05383	+	10.4855i	0.354882	+	0.614673i
$292$	2.91122	−	1.68079i	0.170366	−	0.0983608i
$293$	4.60340	−	2.65778i	0.268934	−	0.155269i	−0.359469	−	0.933157i	$-0.617042\pi$
$293$	4.60340	−	2.65778i	0.268934	−	0.155269i	0.628403	+	0.777888i	$0.283709\pi$
$294$	5.62987	−	9.75123i	0.328341	−	0.568703i
$295$	−0.214593	−	0.124967i	−0.0124941	−	0.00727586i
$296$	−5.24395	+	3.08237i	−0.304798	+	0.179159i
$297$		−	5.93869i		−	0.344598i
$298$	−10.4849	−	6.05346i	−0.607374	−	0.350668i
$299$	4.31317	+	7.47062i	0.249437	+	0.432037i
$300$	4.31132	+	2.53229i	0.248914	+	0.146202i
$301$	19.3206	+	33.4642i	1.11362	+	1.92884i
$302$		−	9.62137i		−	0.553648i
$303$	6.24210	−	3.60388i	0.358599	−	0.207037i
$304$	−4.11513			−0.236019
$305$	23.8358	−	13.6431i	1.36484	−	0.781203i
$306$	7.27314			0.415778
$307$			18.2790i			1.04324i	0.853178	+	0.521620i	$0.174672\pi$
$307$			18.2790i			1.04324i	−0.853178	+	0.521620i	$0.825328\pi$
$308$	−21.9770	−	12.6884i	−1.25226	−	0.722990i
$309$	−1.59903	−	2.76960i	−0.0909656	−	0.157557i
$310$	−3.02489	+	5.19433i	−0.171802	+	0.295018i
$311$	−16.0222	+	27.7513i	−0.908537	+	1.57363i	−0.0924383	+	0.995718i	$0.529466\pi$
$311$	−16.0222	+	27.7513i	−0.908537	+	1.57363i	−0.816098	+	0.577913i	$0.803867\pi$
$312$	−1.08299	−	0.625263i	−0.0613121	−	0.0353985i
$313$	7.68688	+	4.43802i	0.434488	+	0.250852i	0.701257	−	0.712909i	$-0.252623\pi$
$313$	7.68688	+	4.43802i	0.434488	+	0.250852i	−0.266769	+	0.963761i	$0.585956\pi$
$314$	4.29139	+	7.43290i	0.242177	+	0.419463i
$315$	9.55497	+	0.0357078i	0.538362	+	0.00201190i
$316$	3.41867	−	5.92130i	0.192315	−	0.333099i
$317$	3.82489	+	2.20830i	0.214827	+	0.124031i	0.603553	−	0.797323i	$-0.293751\pi$
$317$	3.82489	+	2.20830i	0.214827	+	0.124031i	−0.388725	+	0.921354i	$0.627085\pi$
$318$	−1.31601	−	0.759799i	−0.0737982	−	0.0426074i
$319$	−19.4382			−1.08833
$320$	0.00835632	−	2.23605i	0.000467133	−	0.124999i
$321$	3.85790	−	6.68208i	0.215327	−	0.372957i
$322$			29.4768i			1.64268i
$323$		−	29.9299i		−	1.66534i
$324$	0.500000	−	0.866025i	0.0277778	−	0.0481125i
$325$	5.43815	−	3.08576i	0.301654	−	0.171167i
$326$	11.3555	+	19.6684i	0.628925	+	1.08933i
$327$		−	7.70833i		−	0.426272i
$328$	−2.30929	+	1.33327i	−0.127509	+	0.0736176i
$329$	9.87800	+	17.1092i	0.544592	+	0.943260i
$330$	0.0496256	−	13.2792i	0.00273180	−	0.730997i
$331$	−15.1841	+	26.2996i	−0.834592	+	1.44556i	0.0597696	+	0.998212i	$0.480963\pi$
$331$	−15.1841	+	26.2996i	−0.834592	+	1.44556i	−0.894362	+	0.447344i	$0.852370\pi$
$332$		−	7.45961i		−	0.409399i
$333$	−6.08258	+	0.0474386i	−0.333323	+	0.00259962i
$334$	4.57455			0.250308
$335$	−5.70189	−	9.96176i	−0.311528	−	0.544269i
$336$	−2.13657	−	3.70065i	−0.116560	−	0.201887i
$337$	−20.8921	+	12.0621i	−1.13807	+	0.657063i	−0.945951	−	0.324310i	$-0.894868\pi$
$337$	−20.8921	+	12.0621i	−1.13807	+	0.657063i	−0.192115	+	0.981372i	$0.561535\pi$
$338$	9.90403	−	5.71809i	0.538708	−	0.311023i
$339$	−15.4924			−0.841430
$340$	16.2631	+	0.0607767i	0.881992	+	0.00329608i
$341$	15.9642			0.864507
$342$	−3.56380	−	2.05756i	−0.192708	−	0.111260i
$343$		−	18.2025i		−	0.982843i
$344$	9.04279			0.487554
$345$	−13.3870	+	7.66241i	−0.720730	+	0.412530i
$346$	−0.717825	−	1.24331i	−0.0385905	−	0.0668407i
$347$			28.8375i			1.54808i	0.633139	+	0.774038i	$0.281766\pi$
$347$			28.8375i			1.54808i	−0.633139	+	0.774038i	$0.718234\pi$
$348$	−2.83462	−	1.63657i	−0.151952	−	0.0877294i
$349$	11.6328	−	20.1486i	0.622689	−	1.07853i	−0.366294	−	0.930499i	$-0.619374\pi$
$349$	11.6328	−	20.1486i	0.622689	−	1.07853i	0.988983	−	0.148029i	$-0.0472930\pi$
$350$	21.3651	+	0.159689i	1.14201	+	0.00853573i
$351$	−0.625263	−	1.08299i	−0.0333741	−	0.0578056i
$352$	−5.14305	+	2.96934i	−0.274126	+	0.158267i
$353$	−0.169377	−	0.0977899i	−0.00901503	−	0.00520483i	0.495486	−	0.868616i	$-0.334990\pi$
$353$	−0.169377	−	0.0977899i	−0.00901503	−	0.00520483i	−0.504501	+	0.863411i	$0.668323\pi$
$354$	−0.0555279	+	0.0961772i	−0.00295128	+	0.00511176i
$355$	13.9709	−	7.99663i	0.741498	−	0.424417i
$356$	8.79407			0.466085
$357$	26.9154	−	15.5396i	1.42451	−	0.822442i
$358$	−9.85370	−	5.68904i	−0.520784	−	0.300675i
$359$	3.52995			0.186303			0.0931517	−	0.995652i	$-0.470306\pi$
$359$	3.52995			0.186303			0.0931517	+	0.995652i	$0.470306\pi$
$360$	1.12526	−	1.93230i	0.0593066	−	0.101841i
$361$	1.03287	−	1.78898i	0.0543615	−	0.0941570i
$362$			19.8396i			1.04275i
$363$	−21.0167	+	12.1340i	−1.10309	+	0.636870i
$364$	−5.34368			−0.280085
$365$	7.51667	+	0.0280905i	0.393441	+	0.00147032i
$366$	−6.14118	−	10.6368i	−0.321005	−	0.555996i
$367$	1.73122	−	0.999522i	0.0903691	−	0.0521746i	−0.454134	−	0.890933i	$-0.650051\pi$
$367$	1.73122	−	0.999522i	0.0903691	−	0.0521746i	0.544504	+	0.838759i	$0.316718\pi$
$368$	5.97399	+	3.44908i	0.311416	+	0.179796i
$369$	−2.66654			−0.138815
$370$	−13.6014	+	0.0552472i	−0.707101	+	0.00287217i
$371$	−6.49346			−0.337124
$372$	2.32802	+	1.34408i	0.120702	+	0.0696873i
$373$	11.9568	−	6.90326i	0.619099	−	0.357437i	−0.157419	−	0.987532i	$-0.550317\pi$
$373$	11.9568	−	6.90326i	0.619099	−	0.357437i	0.776518	+	0.630095i	$0.216984\pi$
$374$	−21.5965	−	37.4062i	−1.11673	−	1.93423i
$375$	5.48127	+	9.74452i	0.283052	+	0.503205i
$376$	4.62329			0.238428
$377$	−3.54477	+	2.04657i	−0.182565	+	0.105404i
$378$		−	4.27314i		−	0.219787i
$379$	−3.38018	+	5.85465i	−0.173628	+	0.300733i	−0.939686	−	0.342039i	$-0.888882\pi$
$379$	−3.38018	+	5.85465i	−0.173628	+	0.300733i	0.766057	+	0.642772i	$0.222216\pi$
$380$	−7.95166	−	4.63060i	−0.407911	−	0.237545i
$381$	15.2054			0.778994
$382$	−9.61493	−	5.55119i	−0.491943	−	0.284023i
$383$	−12.2108	+	7.04991i	−0.623943	+	0.360233i	−0.778402	−	0.627766i	$-0.783970\pi$
$383$	−12.2108	+	7.04991i	−0.623943	+	0.360233i	0.154460	+	0.987999i	$0.450636\pi$
$384$	−1.00000			−0.0510310
$385$	−28.1883	−	49.2478i	−1.43661	−	2.50990i
$386$	−12.5663	+	21.7655i	−0.639609	+	1.10783i
$387$	7.83128	+	4.52139i	0.398086	+	0.229835i
$388$	10.4855	−	6.05383i	0.532322	−	0.307336i
$389$	2.87886	+	4.98634i	0.145964	+	0.252817i	0.929732	−	0.368236i	$-0.120038\pi$
$389$	2.87886	+	4.98634i	0.145964	+	0.252817i	−0.783768	+	0.621054i	$0.786705\pi$
$390$	−1.38907	−	2.42684i	−0.0703383	−	0.122888i
$391$	−25.0857	+	43.4497i	−1.26864	+	2.19734i
$392$	−9.75123	−	5.62987i	−0.492511	−	0.284352i
$393$			16.4962i			0.832121i
$394$	0.573847	+	0.993932i	0.0289100	+	0.0500736i
$395$	13.2689	−	7.59484i	0.667632	−	0.382138i
$396$	−5.93869			−0.298430
$397$		−	11.8180i		−	0.593130i	−0.955013	−	0.296565i	$-0.904159\pi$
$397$		−	11.8180i		−	0.593130i	0.955013	−	0.296565i	$-0.0958411\pi$
$398$	−5.71382	−	3.29888i	−0.286408	−	0.165358i
$399$	−17.5845			−0.880327
$400$	2.53229	−	4.31132i	0.126615	−	0.215566i
$401$	5.04044			0.251708			0.125854	−	0.992049i	$-0.459833\pi$
$401$	5.04044			0.251708			0.125854	+	0.992049i	$0.459833\pi$
$402$	−4.44547	+	2.56660i	−0.221720	+	0.128010i
$403$	2.91124	−	1.68081i	0.145019	−	0.0837270i
$404$	−3.60388	−	6.24210i	−0.179300	−	0.310556i
$405$	1.94066	−	1.11079i	0.0964320	−	0.0551956i
$406$	−13.9866			−0.694144
$407$	18.3052	+	31.1422i	0.907357	+	1.54366i
$408$		−	7.27314i		−	0.360074i
$409$	1.41880	−	2.45743i	0.0701549	−	0.121512i	−0.828814	−	0.559524i	$-0.810984\pi$
$409$	1.41880	−	2.45743i	0.0701549	−	0.121512i	0.898969	+	0.438012i	$0.144317\pi$
$410$	−5.96253	−	0.0222825i	−0.294468	−	0.00110045i
$411$	−11.5316	−	19.9734i	−0.568814	−	0.985214i
$412$	−2.76960	+	1.59903i	−0.136448	+	0.0787785i
$413$			0.474557i			0.0233514i
$414$	3.44908	+	5.97399i	0.169513	+	0.293605i
$415$	8.39403	−	14.4142i	0.412046	−	0.707566i
$416$	−0.625263	+	1.08299i	−0.0306560	+	0.0530978i
$417$		−	8.97289i		−	0.439404i
$418$			24.4384i			1.19532i
$419$	2.45402	−	4.25048i	0.119887	−	0.207650i	−0.799836	−	0.600219i	$-0.795080\pi$
$419$	2.45402	−	4.25048i	0.119887	−	0.207650i	0.919723	+	0.392569i	$0.128414\pi$
$420$	0.0357078	−	9.55497i	0.00174236	−	0.466235i
$421$	−25.3784			−1.23687			−0.618433	−	0.785837i	$-0.712232\pi$
$421$	−25.3784			−1.23687			−0.618433	+	0.785837i	$0.712232\pi$
$422$	−16.1116	−	9.30206i	−0.784303	−	0.452817i
$423$	4.00389	+	2.31165i	0.194676	+	0.112396i
$424$	−0.759799	+	1.31601i	−0.0368991	+	0.0639111i
$425$	31.3569	+	18.4177i	1.52103	+	0.893391i
$426$	−3.59953	−	6.23456i	−0.174398	−	0.302066i
$427$	−45.4527	−	26.2421i	−2.19961	−	1.26995i
$428$	−6.68208	−	3.85790i	−0.322991	−	0.186479i
$429$	−3.71324	+	6.43152i	−0.179277	+	0.310517i
$430$	17.4734	+	10.1755i	0.842641	+	0.490707i
$431$	−6.96555	−	12.0647i	−0.335519	−	0.581136i	0.648065	−	0.761585i	$-0.275578\pi$
$431$	−6.96555	−	12.0647i	−0.335519	−	0.581136i	−0.983584	+	0.180449i	$0.942245\pi$
$432$	−0.866025	−	0.500000i	−0.0416667	−	0.0240563i
$433$			22.8789i			1.09949i	0.835332	+	0.549746i	$0.185275\pi$
$433$			22.8789i			1.09949i	−0.835332	+	0.549746i	$0.814725\pi$
$434$	11.4869			0.551389
$435$	−3.63577	−	6.35204i	−0.174322	−	0.304557i
$436$	−7.70833			−0.369162
$437$	24.5837	−	14.1934i	1.17600	−	0.678963i
$438$		−	3.36158i		−	0.160623i
$439$	−5.14932	−	8.91889i	−0.245764	−	0.425675i	0.716582	−	0.697502i	$-0.245705\pi$
$439$	−5.14932	−	8.91889i	−0.245764	−	0.425675i	−0.962346	+	0.271827i	$0.912372\pi$
$440$	−13.2792	−	0.0496256i	−0.633062	−	0.00236581i
$441$	−5.62987	−	9.75123i	−0.268089	−	0.464344i
$442$	−7.87672	−	4.54763i	−0.374657	−	0.216309i
$443$			21.4199i			1.01769i	0.860859	+	0.508844i	$0.169927\pi$
$443$			21.4199i			1.01769i	−0.860859	+	0.508844i	$0.830073\pi$
$444$	0.0474386	+	6.08258i	0.00225134	+	0.288666i
$445$	16.9928	+	9.89564i	0.805535	+	0.469098i
$446$	−9.69271	+	16.7883i	−0.458963	+	0.794947i
$447$	−10.4849	+	6.05346i	−0.495919	+	0.286319i
$448$	−3.70065	+	2.13657i	−0.174839	+	0.100944i
$449$	−16.3407	−	28.3030i	−0.771167	−	1.33570i	−0.936924	−	0.349533i	$-0.886340\pi$
$449$	−16.3407	−	28.3030i	−0.771167	−	1.33570i	0.165757	−	0.986167i	$-0.446993\pi$
$450$	4.34869	−	2.46757i	0.204999	−	0.116322i
$451$	7.91788	+	13.7142i	0.372838	+	0.645775i
$452$			15.4924i			0.728700i
$453$	−8.33235	−	4.81068i	−0.391488	−	0.226026i
$454$	5.94805			0.279156
$455$	−10.3256	−	6.01304i	−0.484071	−	0.281896i
$456$	−2.05756	+	3.56380i	−0.0963542	+	0.166890i
$457$	−9.41322	+	5.43472i	−0.440332	+	0.254226i	−0.703738	−	0.710459i	$-0.748487\pi$
$457$	−9.41322	+	5.43472i	−0.440332	+	0.254226i	0.263407	+	0.964685i	$0.415154\pi$
$458$		−	8.91804i		−	0.416713i
$459$	3.63657	−	6.29873i	0.169741	−	0.293999i
$460$	7.66241	+	13.3870i	0.357262	+	0.624171i
$461$	14.4531	−	25.0336i	0.673150	−	1.16593i	−0.303856	−	0.952718i	$-0.598274\pi$
$461$	14.4531	−	25.0336i	0.673150	−	1.16593i	0.977006	−	0.213212i	$-0.0683925\pi$
$462$	−21.9770	+	12.6884i	−1.02246	+	0.590319i
$463$	32.1719	−	18.5745i	1.49516	−	0.863229i	0.495172	−	0.868795i	$-0.335105\pi$
$463$	32.1719	−	18.5745i	1.49516	−	0.863229i	0.999985	+	0.00556589i	$0.00177169\pi$
$464$	−1.63657	+	2.83462i	−0.0759759	+	0.131594i
$465$	2.98598	+	5.21680i	0.138472	+	0.241923i
$466$	0.956644	−	1.65696i	0.0443157	−	0.0767570i
$467$			22.3568i			1.03455i	0.855819	+	0.517276i	$0.173054\pi$
$467$			22.3568i			1.03455i	−0.855819	+	0.517276i	$0.826946\pi$
$468$	−1.08299	+	0.625263i	−0.0500611	+	0.0289028i
$469$	−10.9674	+	18.9961i	−0.506429	+	0.877160i
$470$	8.93359	+	5.20242i	0.412076	+	0.239970i
$471$	8.58277			0.395473
$472$	0.0961772	+	0.0555279i	0.00442691	+	0.00255588i
$473$		−	53.7023i		−	2.46923i
$474$	−3.41867	−	5.92130i	−0.157025	−	0.271975i
$475$	−10.1543	−	17.8954i	−0.465913	−	0.821098i
$476$	−15.5396	−	26.9154i	−0.712256	−	1.23366i
$477$	−1.31601	+	0.759799i	−0.0602560	+	0.0347888i
$478$	13.4479	−	7.76415i	0.615092	−	0.355124i
$479$	5.34678	−	9.26089i	0.244300	−	0.423141i	−0.717634	−	0.696420i	$-0.754775\pi$
$479$	5.34678	−	9.26089i	0.244300	−	0.423141i	0.961935	+	0.273279i	$0.0881084\pi$
$480$	−1.93230	−	1.12526i	−0.0881970	−	0.0513610i
$481$	6.61702	+	3.75184i	0.301710	+	0.171069i
$482$			11.1122i			0.506147i
$483$	25.5277	+	14.7384i	1.16155	+	0.670621i
$484$	12.1340	+	21.0167i	0.551546	+	0.955305i
$485$	27.0733	+	0.101175i	1.22934	+	0.00459414i
$486$	−0.500000	−	0.866025i	−0.0226805	−	0.0392837i
$487$			12.8937i			0.584270i	0.956377	+	0.292135i	$0.0943656\pi$
$487$			12.8937i			0.584270i	−0.956377	+	0.292135i	$0.905634\pi$
$488$	−10.6368	+	6.14118i	−0.481507	+	0.277998i
$489$	22.7111			1.02703
$490$	−12.5072	−	21.8513i	−0.565018	−	0.987141i
$491$	−38.5951			−1.74177			−0.870885	−	0.491486i	$-0.836454\pi$
$491$	−38.5951			−1.74177			−0.870885	+	0.491486i	$0.836454\pi$
$492$			2.66654i			0.120217i
$493$	−20.6166	−	11.9030i	−0.928526	−	0.536085i
$494$	2.57304	+	4.45663i	0.115766	+	0.200513i
$495$	−11.4753	−	6.68259i	−0.515778	−	0.300360i
$496$	1.34408	−	2.32802i	0.0603510	−	0.104531i
$497$	−26.6412	−	15.3813i	−1.19502	−	0.689945i
$498$	−6.46021	−	3.72981i	−0.289489	−	0.167137i
$499$	−5.68234	−	9.84210i	−0.254376	−	0.440593i	0.710350	−	0.703849i	$-0.248537\pi$
$499$	−5.68234	−	9.84210i	−0.254376	−	0.440593i	−0.964726	+	0.263256i	$0.915204\pi$
$500$	9.74452	−	5.48127i	0.435788	−	0.245130i
$501$	2.28727	−	3.96167i	0.102188	−	0.176995i
$502$	−11.5497	−	6.66822i	−0.515488	−	0.297617i
$503$	5.76066	+	3.32592i	0.256855	+	0.148295i	0.622899	−	0.782302i	$-0.285955\pi$
$503$	5.76066	+	3.32592i	0.256855	+	0.148295i	−0.366044	+	0.930598i	$0.619288\pi$
$504$	−4.27314			−0.190341
$505$	0.0602304	−	16.1169i	0.00268022	−	0.717194i
$506$	20.4830	−	35.4776i	0.910581	−	1.57717i
$507$		−	11.4362i		−	0.507899i
$508$		−	15.2054i		−	0.674628i
$509$	3.93391	−	6.81372i	0.174367	−	0.302013i	−0.765575	−	0.643347i	$-0.777545\pi$
$509$	3.93391	−	6.81372i	0.174367	−	0.302013i	0.939942	+	0.341334i	$0.110879\pi$
$510$	8.18420	−	14.0539i	0.362402	−	0.622317i
$511$	−7.18226	−	12.4400i	−0.317724	−	0.550315i
$512$			1.00000i			0.0441942i
$513$	−3.56380	+	2.05756i	−0.157346	+	0.0908436i
$514$	−12.3440	−	21.3805i	−0.544472	−	0.943053i
$515$	−7.15103	−	0.0267240i	−0.315112	−	0.00117760i
$516$	4.52139	−	7.83128i	0.199043	−	0.344753i
$517$		−	27.4563i		−	1.20753i
$518$	13.1714	+	22.4081i	0.578719	+	0.984557i
$519$	−1.43565			−0.0630180
$520$	−2.42684	+	1.38907i	−0.106424	+	0.0609148i
$521$	16.2960	+	28.2255i	0.713941	+	1.23658i	0.963367	+	0.268188i	$0.0864249\pi$
$521$	16.2960	+	28.2255i	0.713941	+	1.23658i	−0.249425	+	0.968394i	$0.580242\pi$
$522$	−2.83462	+	1.63657i	−0.124068	+	0.0716308i
$523$	10.8426	−	6.26000i	0.474116	−	0.273731i	−0.243845	−	0.969814i	$-0.578409\pi$
$523$	10.8426	−	6.26000i	0.474116	−	0.273731i	0.717961	+	0.696083i	$0.245076\pi$
$524$	16.4962			0.720638
$525$	10.8209	−	18.4229i	0.472261	−	0.804041i
$526$	25.2766			1.10211
$527$	16.9320	+	9.77569i	0.737569	+	0.425836i
$528$			5.93869i			0.258448i
$529$	−24.5847			−1.06890
$530$	−2.94902	+	1.68795i	−0.128097	+	0.0733200i
$531$	0.0555279	+	0.0961772i	0.00240971	+	0.00417373i
$532$			17.5845i			0.762386i
$533$	2.88783	+	1.66729i	0.125086	+	0.0722183i
$534$	4.39703	−	7.61589i	0.190278	−	0.329572i
$535$	−8.57063	−	14.9737i	−0.370541	−	0.647371i
$536$	2.56660	+	4.44547i	0.110860	+	0.192015i
$537$	−9.85370	+	5.68904i	−0.425218	+	0.245500i
$538$	21.6742	+	12.5136i	0.934442	+	0.539500i
$539$	−33.4341	+	57.9095i	−1.44011	+	2.49434i
$540$	−1.11079	−	1.94066i	−0.0478008	−	0.0835126i
$541$	4.12381			0.177297			0.0886483	−	0.996063i	$-0.471745\pi$
$541$	4.12381			0.177297			0.0886483	+	0.996063i	$0.471745\pi$
$542$	11.5586	−	6.67337i	0.496485	−	0.286646i
$543$	17.1816	+	9.91980i	0.737333	+	0.425699i
$544$	−7.27314			−0.311833
$545$	−14.8948	−	8.67390i	−0.638023	−	0.371549i
$546$	−2.67184	+	4.62776i	−0.114344	+	0.198050i
$547$			35.3451i			1.51125i	0.655006	+	0.755624i	$0.272666\pi$
$547$			35.3451i			1.51125i	−0.655006	+	0.755624i	$0.727334\pi$
$548$	−19.9734	+	11.5316i	−0.853221	+	0.492607i
$549$	−12.2824			−0.524198
$550$	−25.6036	−	15.0385i	−1.09174	−	0.641244i
$551$	6.73470	+	11.6648i	0.286908	+	0.496939i
$552$	5.97399	−	3.44908i	0.254270	−	0.146803i
$553$	−25.3026	−	14.6085i	−1.07598	−	0.621215i
$554$	−18.7042			−0.794665
$555$	−6.75283	+	11.8067i	−0.286642	+	0.501168i
$556$	−8.97289			−0.380535
$557$	−5.17687	−	2.98887i	−0.219351	−	0.126642i	0.386299	−	0.922374i	$-0.373753\pi$
$557$	−5.17687	−	2.98887i	−0.219351	−	0.126642i	−0.605650	+	0.795731i	$0.707087\pi$
$558$	2.32802	−	1.34408i	0.0985528	−	0.0568995i
$559$	−5.65412	−	9.79322i	−0.239144	−	0.414209i
$560$	−9.55497	−	0.0357078i	−0.403771	−	0.00150893i
$561$	−43.1929			−1.82361
$562$	8.93535	−	5.15883i	0.376915	−	0.217612i
$563$		−	12.8905i		−	0.543268i	−0.962401	−	0.271634i	$-0.912436\pi$
$563$		−	12.8905i		−	0.543268i	0.962401	−	0.271634i	$-0.0875641\pi$
$564$	2.31165	−	4.00389i	0.0973379	−	0.168594i
$565$	−17.4330	+	29.9359i	−0.733411	+	1.25941i
$566$	6.05422			0.254478
$567$	−3.70065	−	2.13657i	−0.155413	−	0.0897276i
$568$	−6.23456	+	3.59953i	−0.261597	+	0.151033i
$569$	10.8120			0.453261			0.226631	−	0.973981i	$-0.427229\pi$
$569$	10.8120			0.453261			0.226631	+	0.973981i	$0.427229\pi$
$570$	−7.98605	+	4.57104i	−0.334499	+	0.191460i
$571$	12.4430	−	21.5520i	0.520725	−	0.901922i	−0.478985	−	0.877823i	$-0.658995\pi$
$571$	12.4430	−	21.5520i	0.520725	−	0.901922i	0.999710	−	0.0240989i	$-0.00767165\pi$
$572$	6.43152	+	3.71324i	0.268915	+	0.155258i
$573$	−9.61493	+	5.55119i	−0.401670	+	0.231904i
$574$	5.69726	+	9.86794i	0.237799	+	0.411880i
$575$	−0.257787	+	34.4899i	−0.0107505	+	1.43833i
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	−6.17293	−	3.56394i	−0.256982	−	0.148369i	0.365975	−	0.930625i	$-0.380736\pi$
$577$	−6.17293	−	3.56394i	−0.256982	−	0.148369i	−0.622957	+	0.782256i	$0.714069\pi$
$578$		−	35.8986i		−	1.49318i
$579$	12.5663	+	21.7655i	0.522238	+	0.904543i
$580$	−6.35204	+	3.63577i	−0.263754	+	0.150967i
$581$	−31.8760			−1.32244
$582$		−	12.1077i		−	0.501878i
$583$	7.81538	+	4.51221i	0.323680	+	0.186877i
$584$	−3.36158			−0.139103
$585$	−2.79624	−	0.0104498i	−0.115610	−	0.000432046i
$586$	−5.31555			−0.219583
$587$	−8.55022	+	4.93647i	−0.352905	+	0.203750i	−0.665964	−	0.745984i	$-0.731980\pi$
$587$	−8.55022	+	4.93647i	−0.352905	+	0.203750i	0.313059	+	0.949734i	$0.398646\pi$
$588$	−9.75123	+	5.62987i	−0.402134	+	0.232172i
$589$	−5.53106	−	9.58008i	−0.227903	−	0.394740i
$590$	0.123360	+	0.215521i	0.00507864	+	0.00887287i
$591$	1.14769			0.0472098
$592$	6.08258	−	0.0474386i	0.249992	−	0.00194971i
$593$		−	27.6314i		−	1.13469i	−0.823481	−	0.567343i	$-0.807971\pi$
$593$		−	27.6314i		−	1.13469i	0.823481	−	0.567343i	$-0.192029\pi$
$594$	−2.96934	+	5.14305i	−0.121834	+	0.211022i
$595$	0.259708	−	69.4947i	0.0106470	−	2.84900i
$596$	6.05346	+	10.4849i	0.247959	+	0.429478i
$597$	−5.71382	+	3.29888i	−0.233851	+	0.135014i
$598$		−	8.62633i		−	0.352757i
$599$	9.52530	+	16.4983i	0.389193	+	0.674102i	0.992341	−	0.123527i	$-0.0394205\pi$
$599$	9.52530	+	16.4983i	0.389193	+	0.674102i	−0.603148	+	0.797629i	$0.706087\pi$
$600$	−2.46757	−	4.34869i	−0.100738	−	0.177535i
$601$	−17.3651	+	30.0773i	−0.708338	+	1.22688i	0.257135	+	0.966375i	$0.417221\pi$
$601$	−17.3651	+	30.0773i	−0.708338	+	1.22688i	−0.965473	+	0.260502i	$0.916112\pi$
$602$		−	38.6411i		−	1.57489i
$603$			5.13319i			0.209040i
$604$	−4.81068	+	8.33235i	−0.195744	+	0.339039i
$605$	−0.202791	+	54.2645i	−0.00824464	+	2.20617i
$606$	−7.20776			−0.292795
$607$	−3.78634	−	2.18604i	−0.153683	−	0.0887288i	0.421187	−	0.906974i	$-0.361614\pi$
$607$	−3.78634	−	2.18604i	−0.153683	−	0.0887288i	−0.574869	+	0.818245i	$0.694947\pi$
$608$	3.56380	+	2.05756i	0.144531	+	0.0834452i
$609$	−6.99330	+	12.1128i	−0.283383	+	0.490834i
$610$	−27.4640	−	0.102635i	−1.11199	−	0.00415559i
$611$	−2.89078	−	5.00697i	−0.116948	−	0.202560i
$612$	−6.29873	−	3.63657i	−0.254611	−	0.147000i
$613$	0.371275	+	0.214356i	0.0149957	+	0.00865775i	0.507479	−	0.861664i	$-0.330577\pi$
$613$	0.371275	+	0.214356i	0.0149957	+	0.00865775i	−0.492483	+	0.870322i	$0.663911\pi$
$614$	9.13952	−	15.8301i	0.368841	−	0.638851i
$615$	−3.00056	+	5.15256i	−0.120994	+	0.207771i
$616$	12.6884	+	21.9770i	0.511231	+	0.885479i
$617$	−12.3649	−	7.13885i	−0.497790	−	0.287399i	0.230010	−	0.973188i	$-0.426124\pi$
$617$	−12.3649	−	7.13885i	−0.497790	−	0.287399i	−0.727801	+	0.685789i	$0.759457\pi$
$618$			3.19806i			0.128645i
$619$	12.0527			0.484441			0.242220	−	0.970221i	$-0.422124\pi$
$619$	12.0527			0.484441			0.242220	+	0.970221i	$0.422124\pi$
$620$	5.21680	−	2.98598i	0.209512	−	0.119920i
$621$	6.89816			0.276814
$622$	27.7513	−	16.0222i	1.11273	−	0.642432i
$623$		−	37.5783i		−	1.50554i
$624$	0.625263	+	1.08299i	0.0250306	+	0.0433542i
$625$	24.9972	+	0.373693i	0.999888	+	0.0149477i
$626$	−4.43802	−	7.68688i	−0.177379	−	0.307230i
$627$	21.1643	+	12.2192i	0.845221	+	0.487989i
$628$		−	8.58277i		−	0.342490i
$629$	0.345028	+	44.2395i	0.0137572	+	1.76394i
$630$	−8.25699	−	4.80841i	−0.328966	−	0.191572i
$631$	−7.44379	+	12.8930i	−0.296333	+	0.513263i	−0.975294	−	0.220911i	$-0.929097\pi$
$631$	−7.44379	+	12.8930i	−0.296333	+	0.513263i	0.678961	+	0.734174i	$0.262430\pi$
$632$	−5.92130	+	3.41867i	−0.235537	+	0.135987i
$633$	−16.1116	+	9.30206i	−0.640380	+	0.369724i
$634$	−2.20830	−	3.82489i	−0.0877029	−	0.151906i
$635$	17.1100	−	29.3813i	0.678990	−	1.16596i
$636$	0.759799	+	1.31601i	0.0301280	+	0.0521832i
$637$			14.0806i			0.557894i
$638$	16.8339	+	9.71909i	0.666462	+	0.384782i
$639$	−7.19905			−0.284790
$640$	−1.12526	+	1.93230i	−0.0444799	+	0.0763809i
$641$	−15.4399	+	26.7427i	−0.609840	+	1.05627i	0.381426	+	0.924399i	$0.375433\pi$
$641$	−15.4399	+	26.7427i	−0.609840	+	1.05627i	−0.991266	+	0.131875i	$0.957900\pi$
$642$	−6.68208	+	3.85790i	−0.263721	+	0.152259i
$643$		−	6.52207i		−	0.257205i	−0.991696	−	0.128603i	$-0.958951\pi$
$643$		−	6.52207i		−	0.257205i	0.991696	−	0.128603i	$-0.0410492\pi$
$644$	14.7384	−	25.5277i	0.580775	−	1.00593i
$645$	17.5489	−	10.0446i	0.690989	−	0.395507i
$646$	−14.9649	+	25.9201i	−0.588788	+	1.01981i
$647$	19.3536	−	11.1738i	0.760870	−	0.439288i	−0.0687382	−	0.997635i	$-0.521897\pi$
$647$	19.3536	−	11.1738i	0.760870	−	0.439288i	0.829608	+	0.558346i	$0.188564\pi$
$648$	−0.866025	+	0.500000i	−0.0340207	+	0.0196419i
$649$	0.329763	−	0.571166i	0.0129443	−	0.0224202i
$650$	−6.25246	−	0.0467326i	−0.245241	−	0.00183300i
$651$	5.74345	−	9.94795i	0.225104	−	0.389891i
$652$		−	22.7111i		−	0.889434i
$653$	30.6001	−	17.6670i	1.19747	−	0.691362i	0.237483	−	0.971392i	$-0.423678\pi$
$653$	30.6001	−	17.6670i	1.19747	−	0.691362i	0.959991	+	0.280030i	$0.0903443\pi$
$654$	−3.85417	+	6.67561i	−0.150710	+	0.261037i
$655$	31.8755	+	18.5625i	1.24548	+	0.725298i
$656$	2.66654			0.104111
$657$	−2.91122	−	1.68079i	−0.113577	−	0.0655739i
$658$		−	19.7560i		−	0.770169i
$659$	0.235145	+	0.407284i	0.00915996	+	0.0158655i	0.870569	−	0.492046i	$-0.163751\pi$
$659$	0.235145	+	0.407284i	0.00915996	+	0.0158655i	−0.861409	+	0.507912i	$0.830418\pi$
$660$	−6.68259	+	11.4753i	−0.260119	+	0.446676i
$661$	9.15487	+	15.8567i	0.356083	+	0.616754i	0.987303	−	0.158850i	$-0.0507787\pi$
$661$	9.15487	+	15.8567i	0.356083	+	0.616754i	−0.631220	+	0.775604i	$0.717445\pi$
$662$	26.2996	−	15.1841i	1.02216	−	0.590146i
$663$	−7.87672	+	4.54763i	−0.305906	+	0.176615i
$664$	−3.72981	+	6.46021i	−0.144745	+	0.250705i
$665$	−19.7872	+	33.9786i	−0.767315	+	1.31763i
$666$	5.29139	+	3.00021i	0.205037	+	0.116256i
$667$		−	22.5787i		−	0.874250i
$668$	−3.96167	−	2.28727i	−0.153282	−	0.0884973i
$669$	9.69271	+	16.7883i	0.374742	+	0.649072i
$670$	−0.0428946	+	11.4781i	−0.00165716	+	0.443437i
$671$	36.4706	+	63.1689i	1.40793	+	2.43861i
$672$			4.27314i			0.164840i
$673$	2.70882	−	1.56394i	0.104418	−	0.0602855i	−0.446882	−	0.894593i	$-0.647466\pi$
$673$	2.70882	−	1.56394i	0.104418	−	0.0602855i	0.551299	+	0.834308i	$0.314132\pi$
$674$	24.1241			0.929227
$675$	0.0373703	−	4.99986i	0.00143839	−	0.192445i
$676$	−11.4362			−0.439853
$677$		−	26.3204i		−	1.01157i	−0.862658	−	0.505787i	$-0.831202\pi$
$677$		−	26.3204i		−	1.01157i	0.862658	−	0.505787i	$-0.168798\pi$
$678$	13.4168	+	7.74618i	0.515268	+	0.297490i
$679$	−25.8689	−	44.8062i	−0.992756	−	1.71950i
$680$	−14.0539	−	8.18420i	−0.538942	−	0.313850i
$681$	2.97402	−	5.15116i	0.113965	−	0.197393i
$682$	−13.8254	−	7.98208i	−0.529400	−	0.305650i
$683$	−0.297050	−	0.171502i	−0.0113663	−	0.00656234i	0.494306	−	0.869288i	$-0.335422\pi$
$683$	−0.297050	−	0.171502i	−0.0113663	−	0.00656234i	−0.505672	+	0.862726i	$0.668756\pi$
$684$	2.05756	+	3.56380i	0.0786729	+	0.136265i
$685$	−51.5707	−	0.192724i	−1.97041	−	0.00736361i
$686$	−9.10125	+	15.7638i	−0.347487	+	0.601866i
$687$	−7.72325	−	4.45902i	−0.294660	−	0.170122i
$688$	−7.83128	−	4.52139i	−0.298565	−	0.172376i
$689$	1.90030			0.0723956
$690$	15.4247	+	0.0576433i	0.587207	+	0.00219444i
$691$	−11.6638	+	20.2023i	−0.443711	+	0.768531i	−0.997961	−	0.0638196i	$-0.979672\pi$
$691$	−11.6638	+	20.2023i	−0.443711	+	0.768531i	0.554250	+	0.832350i	$0.313005\pi$
$692$			1.43565i			0.0545752i
$693$			25.3769i			0.963987i
$694$	14.4187	−	24.9740i	0.547328	−	0.947999i
$695$	−17.3383	−	10.0969i	−0.657680	−	0.382996i
$696$	1.63657	+	2.83462i	0.0620341	+	0.107446i
$697$			19.3941i			0.734605i
$698$	−20.1486	+	11.6328i	−0.762635	+	0.440307i
$699$	−0.956644	−	1.65696i	−0.0361836	−	0.0626718i
$700$	−18.4229	−	10.8209i	−0.696320	−	0.408990i
$701$	25.0713	−	43.4248i	0.946930	−	1.64013i	0.195091	−	0.980785i	$-0.437500\pi$
$701$	25.0713	−	43.4248i	0.946930	−	1.64013i	0.751839	−	0.659347i	$-0.229167\pi$
$702$			1.25053i			0.0471981i
$703$	12.3462	−	21.7747i	0.465647	−	0.821249i
$704$	5.93869			0.223823
$705$	8.97223	−	5.13551i	0.337914	−	0.193414i
$706$	0.0977899	+	0.169377i	0.00368037	+	0.00637459i
$707$	−26.6734	+	15.3999i	−1.00316	+	0.579173i
$708$	0.0961772	−	0.0555279i	0.00361456	−	0.00208687i
$709$	−39.5030			−1.48357			−0.741784	−	0.670639i	$-0.766020\pi$
$709$	−39.5030			−1.48357			−0.741784	+	0.670639i	$0.766020\pi$
$710$	−16.0975	−	0.0601576i	−0.604127	−	0.00225768i
$711$	−6.83733			−0.256420
$712$	−7.61589	−	4.39703i	−0.285417	−	0.164786i
$713$			18.5434i			0.694455i
$714$	−31.0792			−1.16311
$715$	8.24926	+	14.4123i	0.308505	+	0.538988i
$716$	5.68904	+	9.85370i	0.212609	+	0.368250i
$717$		−	15.5283i		−	0.579915i
$718$	−3.05702	−	1.76497i	−0.114087	−	0.0658682i
$719$	10.0711	−	17.4437i	0.375589	−	0.650540i	−0.614826	−	0.788663i	$-0.710774\pi$
$719$	10.0711	−	17.4437i	0.375589	−	0.650540i	0.990415	+	0.138123i	$0.0441070\pi$
$720$	−1.94066	+	1.11079i	−0.0723240	+	0.0413967i
$721$	6.83288	+	11.8349i	0.254470	+	0.440754i
$722$	−1.78898	+	1.03287i	−0.0665790	+	0.0384394i
$723$	9.62345	+	5.55610i	0.357900	+	0.206634i
$724$	9.91980	−	17.1816i	0.368666	−	0.638549i
$725$	−16.3653	−	0.122318i	−0.607790	−	0.00454279i
$726$	24.2680			0.900670
$727$	30.2818	−	17.4832i	1.12309	−	0.648417i	0.180903	−	0.983501i	$-0.442098\pi$
$727$	30.2818	−	17.4832i	1.12309	−	0.648417i	0.942188	+	0.335084i	$0.108765\pi$
$728$	4.62776	+	2.67184i	0.171516	+	0.0990249i
$729$	−1.00000			−0.0370370
$730$	−6.49558	−	3.78266i	−0.240412	−	0.140003i
$731$	32.8847	−	56.9580i	1.21629	−	2.10667i
$732$			12.2824i			0.453969i
$733$	−4.06319	+	2.34588i	−0.150077	+	0.0866471i	−0.573158	−	0.819445i	$-0.694282\pi$
$733$	−4.06319	+	2.34588i	−0.150077	+	0.0866471i	0.423081	+	0.906092i	$0.360949\pi$
$734$	−1.99904			−0.0737861
$735$	−25.1774	−	0.0940901i	−0.928682	−	0.00347056i
$736$	−3.44908	−	5.97399i	−0.127135	−	0.220204i
$737$	26.4003	−	15.2422i	0.972467	−	0.561454i
$738$	2.30929	+	1.33327i	0.0850062	+	0.0490784i
$739$	19.3032			0.710079			0.355040	−	0.934851i	$-0.384467\pi$
$739$	19.3032			0.710079			0.355040	+	0.934851i	$0.384467\pi$
$740$	11.8067	+	6.75283i	0.434025	+	0.248239i
$741$	5.14607			0.189046
$742$	5.62350	+	3.24673i	0.206445	+	0.119191i
$743$	−34.6971	+	20.0324i	−1.27291	+	0.734917i	−0.975535	−	0.219843i	$-0.929445\pi$
$743$	−34.6971	+	20.0324i	−1.27291	+	0.734917i	−0.297378	+	0.954760i	$0.596112\pi$
$744$	−1.34408	−	2.32802i	−0.0492764	−	0.0853492i
$745$	−0.101169	+	27.0717i	−0.00370656	+	0.991831i
$746$	−13.8065			−0.505492
$747$	−6.46021	+	3.72981i	−0.236367	+	0.136466i
$748$			43.1929i			1.57929i
$749$	−16.4854	+	28.5535i	−0.602362	+	1.04332i
$750$	0.125342	−	11.1796i	0.00457686	−	0.408223i
$751$	−9.68222			−0.353309			−0.176655	−	0.984273i	$-0.556528\pi$
$751$	−9.68222			−0.353309			−0.176655	+	0.984273i	$0.556528\pi$
$752$	−4.00389	−	2.31165i	−0.146007	−	0.0842971i
$753$	−11.5497	+	6.66822i	−0.420894	+	0.243003i
$754$	4.09315			0.149064
$755$	−18.6718	+	10.6873i	−0.679535	+	0.388951i
$756$	−2.13657	+	3.70065i	−0.0777063	+	0.134591i
$757$	−28.5617	−	16.4901i	−1.03809	−	0.599342i	−0.118799	−	0.992918i	$-0.537904\pi$
$757$	−28.5617	−	16.4901i	−1.03809	−	0.599342i	−0.919292	+	0.393576i	$0.871238\pi$
$758$	5.85465	−	3.38018i	0.212650	−	0.122774i
$759$	−20.4830	−	35.4776i	−0.743487	−	1.28776i
$760$	4.57104	+	7.98605i	0.165809	+	0.289684i
$761$	24.2801	−	42.0544i	0.880155	−	1.52447i	0.0289860	−	0.999580i	$-0.490772\pi$
$761$	24.2801	−	42.0544i	0.880155	−	1.52447i	0.851169	−	0.524893i	$-0.175894\pi$
$762$	−13.1682	−	7.60268i	−0.477034	−	0.275416i
$763$			32.9388i			1.19246i
$764$	5.55119	+	9.61493i	0.200835	+	0.347856i
$765$	−8.07893	−	14.1147i	−0.292094	−	0.510317i
$766$	14.0998			0.509447
$767$		−	0.138878i		−	0.00501460i
$768$	0.866025	+	0.500000i	0.0312500	+	0.0180422i
$769$	41.0894			1.48172			0.740861	−	0.671659i	$-0.234418\pi$
$769$	41.0894			1.48172			0.740861	+	0.671659i	$0.234418\pi$
$770$	−0.212057	+	56.7440i	−0.00764201	+	2.04491i
$771$	−24.6881			−0.889119
$772$	21.7655	−	12.5663i	0.783357	−	0.452272i
$773$	−16.2676	+	9.39211i	−0.585105	+	0.337811i	−0.763160	−	0.646210i	$-0.776353\pi$
$773$	−16.2676	+	9.39211i	−0.585105	+	0.337811i	0.178054	+	0.984021i	$0.443020\pi$
$774$	−4.52139	−	7.83128i	−0.162518	−	0.281490i
$775$	13.4404	+	0.100458i	0.482795	+	0.00360854i
$776$	−12.1077			−0.434639
$777$	25.9917	−	0.202712i	0.932448	−	0.00727225i
$778$		−	5.75772i		−	0.206424i
$779$	5.48658	−	9.50303i	0.196577	−	0.340481i
$780$	−0.0104498	+	2.79624i	−0.000374163	+	0.100122i
$781$	21.3765	+	37.0251i	0.764910	+	1.32486i
$782$	43.4497	−	25.0857i	1.55376	−	0.897062i
$783$			3.27314i			0.116973i
$784$	5.62987	+	9.75123i	0.201067	+	0.348258i
$785$	9.65788	−	16.5845i	0.344704	−	0.591926i
$786$	8.24808	−	14.2861i	0.294199	−	0.509568i
$787$			9.59991i			0.342200i	0.985254	+	0.171100i	$0.0547321\pi$
$787$			9.59991i			0.342200i	−0.985254	+	0.171100i	$0.945268\pi$
$788$		−	1.14769i		−	0.0408849i
$789$	12.6383	−	21.8902i	0.449935	−	0.779311i
$790$	−15.2886	−	0.0571350i	−0.543945	−	0.00203277i
$791$	66.2011			2.35384
$792$	5.14305	+	2.96934i	0.182750	+	0.105511i
$793$	13.3016	+	7.67971i	0.472355	+	0.272714i
$794$	−5.90901	+	10.2347i	−0.209703	+	0.363216i
$795$	−0.0126983	+	3.39790i	−0.000450361	+	0.120511i
$796$	3.29888	+	5.71382i	0.116926	+	0.202521i
$797$	−43.8239	−	25.3018i	−1.55232	−	0.896234i	−0.997952	−	0.0639644i	$-0.979626\pi$
$797$	−43.8239	−	25.3018i	−1.55232	−	0.896234i	−0.554371	−	0.832270i	$-0.687041\pi$
$798$	15.2286	+	8.79226i	0.539088	+	0.311243i
$799$	16.8129	−	29.1209i	0.594799	−	1.03022i
$800$	−4.34869	+	2.46757i	−0.153749	+	0.0872417i
$801$	−4.39703	−	7.61589i	−0.155362	−	0.269094i
$802$	−4.36515	−	2.52022i	−0.154139	−	0.0889921i
$803$			19.9634i			0.704493i
$804$	5.13319			0.181034
$805$	57.2044	−	32.7426i	2.01619	−	1.15402i
$806$	−3.36162			−0.118408
$807$	21.6742	−	12.5136i	0.762968	−	0.440500i
$808$			7.20776i			0.253568i
$809$	−16.5378	−	28.6443i	−0.581439	−	1.00708i	−0.995309	−	0.0967455i	$-0.969157\pi$
$809$	−16.5378	−	28.6443i	−0.581439	−	1.00708i	0.413871	−	0.910336i	$-0.364177\pi$
$810$	−2.23605	−	0.00835632i	−0.0785669	−	0.000293611i
$811$	−12.6537	−	21.9168i	−0.444330	−	0.769603i	0.553675	−	0.832733i	$-0.313225\pi$
$811$	−12.6537	−	21.9168i	−0.444330	−	0.769603i	−0.998005	+	0.0631300i	$0.979892\pi$
$812$	12.1128	+	6.99330i	0.425074	+	0.245417i
$813$		−	13.3467i		−	0.468091i
$814$	−0.281723	−	36.1225i	−0.00987439	−	1.26609i
$815$	25.5559	−	43.8846i	0.895185	−	1.53721i
$816$	−3.63657	+	6.29873i	−0.127305	+	0.220500i
$817$	−32.2267	+	18.6061i	−1.12747	+	0.650945i
$818$	−2.45743	+	1.41880i	−0.0859219	+	0.0496070i
$819$	2.67184	+	4.62776i	0.0933616	+	0.161707i
$820$	5.15256	+	3.00056i	0.179935	+	0.104784i
$821$	18.3900	+	31.8525i	0.641816	+	1.11166i	0.985027	+	0.172400i	$0.0551522\pi$
$821$	18.3900	+	31.8525i	0.641816	+	1.11166i	−0.343211	+	0.939258i	$0.611514\pi$
$822$			23.0633i			0.804424i
$823$	−22.9721	−	13.2629i	−0.800757	−	0.462317i	0.0429791	−	0.999076i	$-0.486315\pi$
$823$	−22.9721	−	13.2629i	−0.800757	−	0.462317i	−0.843736	+	0.536759i	$0.819648\pi$
$824$	3.19806			0.111410
$825$	−25.8255	+	14.6541i	−0.899129	+	0.510191i
$826$	0.237279	−	0.410979i	0.00825598	−	0.0142998i
$827$	25.5843	−	14.7711i	0.889653	−	0.513641i	0.0158239	−	0.999875i	$-0.494963\pi$
$827$	25.5843	−	14.7711i	0.889653	−	0.513641i	0.873829	+	0.486234i	$0.161630\pi$
$828$		−	6.89816i		−	0.239728i
$829$	7.11508	−	12.3237i	0.247117	−	0.428019i	−0.715608	−	0.698502i	$-0.753850\pi$
$829$	7.11508	−	12.3237i	0.247117	−	0.428019i	0.962725	+	0.270483i	$0.0871835\pi$
$830$	−14.4765	+	8.28606i	−0.502488	+	0.287613i
$831$	−9.35210	+	16.1983i	−0.324421	+	0.561913i
$832$	1.08299	−	0.625263i	0.0375458	−	0.0216771i
$833$	−70.9221	+	40.9469i	−2.45730	+	1.41872i
$834$	−4.48645	+	7.77075i	−0.155353	+	0.269079i
$835$	−5.08136	−	8.87762i	−0.175848	−	0.307223i
$836$	12.2192	−	21.1643i	0.422611	−	0.731983i
$837$		−	2.68816i		−	0.0929165i
$838$	−4.25048	+	2.45402i	−0.146831	+	0.0847727i
$839$	−1.18772	+	2.05719i	−0.0410045	+	0.0710219i	−0.885799	−	0.464069i	$-0.846389\pi$
$839$	−1.18772	+	2.05719i	−0.0410045	+	0.0710219i	0.844795	+	0.535090i	$0.179722\pi$
$840$	−4.80841	+	8.25699i	−0.165906	+	0.284893i
$841$	−18.2865			−0.630570
$842$	21.9783	+	12.6892i	0.757423	+	0.437299i
$843$		−	10.3177i		−	0.355359i
$844$	9.30206	+	16.1116i	0.320190	+	0.554586i
$845$	−22.0981	−	12.8687i	−0.760199	−	0.442697i
$846$	−2.31165	−	4.00389i	−0.0794761	−	0.137657i
$847$	89.8074	−	51.8503i	3.08582	−	1.78160i
$848$	1.31601	−	0.759799i	0.0451920	−	0.0260916i
$849$	3.02711	−	5.24310i	0.103890	−	0.179943i
$850$	−17.9470	−	31.6287i	−0.615576	−	1.08485i
$851$	−36.1736	+	21.2627i	−1.24002	+	0.728876i
$852$			7.19905i			0.246636i
$853$	−11.4895	−	6.63345i	−0.393392	−	0.227125i	0.290237	−	0.956955i	$-0.406266\pi$
$853$	−11.4895	−	6.63345i	−0.393392	−	0.227125i	−0.683629	+	0.729830i	$0.739599\pi$
$854$	26.2421	+	45.4527i	0.897988	+	1.55536i
$855$	−0.0343873	+	9.20164i	−0.00117602	+	0.314689i
$856$	3.85790	+	6.68208i	0.131860	+	0.228389i
$857$		−	34.3574i		−	1.17363i	−0.809723	−	0.586813i	$-0.800383\pi$
$857$		−	34.3574i		−	1.17363i	0.809723	−	0.586813i	$-0.199617\pi$
$858$	6.43152	−	3.71324i	0.219569	−	0.126768i
$859$	−31.1897			−1.06418			−0.532089	−	0.846689i	$-0.678593\pi$
$859$	−31.1897			−1.06418			−0.532089	+	0.846689i	$0.678593\pi$
$860$	−10.0446	−	17.5489i	−0.342519	−	0.598414i
$861$	11.3945			0.388324
$862$			13.9311i			0.474495i
$863$	39.5069	+	22.8093i	1.34483	+	0.776438i	0.987512	−	0.157544i	$-0.0503576\pi$
$863$	39.5069	+	22.8093i	1.34483	+	0.776438i	0.357319	+	0.933982i	$0.383691\pi$
$864$	0.500000	+	0.866025i	0.0170103	+	0.0294628i
$865$	−1.61548	+	2.77411i	−0.0549281	+	0.0943224i
$866$	11.4395	−	19.8137i	0.388729	−	0.673299i
$867$	−31.0891	−	17.9493i	−1.05584	−	0.609590i
$868$	−9.94795	−	5.74345i	−0.337655	−	0.194945i
$869$	20.3024	+	35.1648i	0.688712	+	1.19288i
$870$	−0.0273514	+	7.31892i	−0.000927300	+	0.248135i
$871$	3.20959	−	5.55918i	0.108753	−	0.188366i
$872$	6.67561	+	3.85417i	0.226065	+	0.130519i
$873$	−10.4855	−	6.05383i	−0.354882	−	0.204891i
$874$	−28.3868			−0.960198
$875$	−23.4222	−	41.6397i	−0.791816	−	1.40768i
$876$	−1.68079	+	2.91122i	−0.0567887	+	0.0983608i
$877$			19.9901i			0.675019i	0.941322	+	0.337510i	$0.109585\pi$
$877$			19.9901i			0.675019i	−0.941322	+	0.337510i	$0.890415\pi$
$878$			10.2986i			0.347562i
$879$	−2.65778	+	4.60340i	−0.0896446	+	0.155269i
$880$	11.4753	+	6.68259i	0.386833	+	0.225270i
$881$	−23.3579	−	40.4571i	−0.786948	−	1.36303i	−0.927829	−	0.373007i	$-0.878327\pi$
$881$	−23.3579	−	40.4571i	−0.786948	−	1.36303i	0.140881	−	0.990027i	$-0.455007\pi$
$882$			11.2597i			0.379135i
$883$	1.18063	−	0.681638i	0.0397314	−	0.0229389i	−0.480003	−	0.877267i	$-0.659364\pi$
$883$	1.18063	−	0.681638i	0.0397314	−	0.0229389i	0.519734	+	0.854328i	$0.326031\pi$
$884$	4.54763	+	7.87672i	0.152953	+	0.264923i
$885$	0.248327		0.000928018i	0.00834741		3.11950e-5i
$886$	10.7099	−	18.5501i	0.359807	−	0.623204i
$887$		−	17.3078i		−	0.581139i	−0.956854	−	0.290569i	$-0.906155\pi$
$887$		−	17.3078i		−	0.581139i	0.956854	−	0.290569i	$-0.0938447\pi$
$888$	3.00021	−	5.29139i	0.100680	−	0.177567i
$889$	−64.9746			−2.17918
$890$	−9.76836	−	17.0663i	−0.327436	−	0.572062i
$891$	2.96934	+	5.14305i	0.0994768	+	0.172299i
$892$	16.7883	−	9.69271i	0.562113	−	0.324536i
$893$	−16.4765	+	9.51272i	−0.551366	+	0.318331i
$894$	12.1069			0.404916
$895$	−0.0950788	+	25.4420i	−0.00317813	+	0.850431i
$896$	4.27314			0.142756
$897$	−7.47062	−	4.31317i	−0.249437	−	0.144012i
$898$			32.6815i			1.09059i
$899$	−8.79874			−0.293454
$900$	−4.99986	−	0.0373703i	−0.166662	−	0.00124568i
$901$	5.52613	+	9.57153i	0.184102	+	0.318874i
$902$		−	15.8358i		−	0.527273i
$903$	−33.4642	−	19.3206i	−1.11362	−	0.642948i
$904$	7.74618	−	13.4168i	0.257634	−	0.446236i
$905$	38.5018	−	22.0376i	1.27984	−	0.732555i
$906$	4.81068	+	8.33235i	0.159824	+	0.276824i
$907$	18.0725	−	10.4341i	0.600087	−	0.346460i	−0.168989	−	0.985618i	$-0.554050\pi$
$907$	18.0725	−	10.4341i	0.600087	−	0.346460i	0.769076	+	0.639158i	$0.220717\pi$
$908$	−5.15116	−	2.97402i	−0.170947	−	0.0986964i
$909$	−3.60388	+	6.24210i	−0.119533	+	0.207037i
$910$	5.93570	+	10.3702i	0.196766	+	0.343770i
$911$	45.8100			1.51775			0.758877	−	0.651234i	$-0.225748\pi$
$911$	45.8100			1.51775			0.758877	+	0.651234i	$0.225748\pi$
$912$	3.56380	−	2.05756i	0.118009	−	0.0681327i
$913$	38.3652	+	22.1502i	1.26970	+	0.733063i
$914$	10.8694			0.359529
$915$	−13.8209	+	23.7332i	−0.456904	+	0.784596i
$916$	−4.45902	+	7.72325i	−0.147330	+	0.255183i
$917$		−	70.4904i		−	2.32780i
$918$	−6.29873	+	3.63657i	−0.207889	+	0.120025i
$919$	48.7717			1.60883			0.804415	−	0.594068i	$-0.202479\pi$
$919$	48.7717			1.60883			0.804415	+	0.594068i	$0.202479\pi$
$920$	0.0576433	−	15.4247i	0.00190044	−	0.508536i
$921$	−9.13952	−	15.8301i	−0.301157	−	0.521620i
$922$	−25.0336	+	14.4531i	−0.824437	+	0.475989i
$923$	7.79648	+	4.50130i	0.256624	+	0.148162i
$924$	25.3769			0.834837
$925$	15.2155	+	26.3342i	0.500281	+	0.865863i
$926$	−37.1489			−1.22079
$927$	2.76960	+	1.59903i	0.0909656	+	0.0525190i
$928$	2.83462	−	1.63657i	0.0930511	−	0.0537231i
$929$	−21.4366	−	37.1293i	−0.703312	−	1.21817i	−0.967297	−	0.253645i	$-0.918370\pi$
$929$	−21.4366	−	37.1293i	−0.703312	−	1.21817i	0.263985	−	0.964527i	$-0.414963\pi$
$930$	0.0224631	−	6.01087i	0.000736596	−	0.197104i
$931$	46.3353			1.51858
$932$	−1.65696	+	0.956644i	−0.0542754	+	0.0313359i
$933$		−	32.0444i		−	1.04909i
$934$	11.1784	−	19.3616i	0.365769	−	0.633531i
$935$	−48.6034	+	83.4617i	−1.58950	+	2.72949i
$936$	1.25053			0.0408747
$937$	47.5708	+	27.4650i	1.55407	+	0.897242i	0.997804	+	0.0662376i	$0.0210995\pi$
$937$	47.5708	+	27.4650i	1.55407	+	0.897242i	0.556265	+	0.831005i	$0.312234\pi$
$938$	18.9961	−	10.9674i	0.620246	−	0.358099i
$939$	−8.87605			−0.289659
$940$	−5.13551	−	8.97223i	−0.167502	−	0.292642i
$941$	11.3474	−	19.6542i	0.369913	−	0.640709i	−0.619638	−	0.784888i	$-0.712721\pi$
$941$	11.3474	−	19.6542i	0.369913	−	0.640709i	0.989552	+	0.144179i	$0.0460540\pi$
$942$	−7.43290	−	4.29139i	−0.242177	−	0.139821i
$943$	−15.9299	+	9.19712i	−0.518748	+	0.299500i
$944$	−0.0555279	−	0.0961772i	−0.00180728	−	0.00313030i
$945$	−8.29270	+	4.74656i	−0.269762	+	0.154406i
$946$	−26.8511	+	46.5075i	−0.873006	+	1.51209i
$947$	−6.95546	−	4.01574i	−0.226022	−	0.130494i	0.382713	−	0.923867i	$-0.374990\pi$
$947$	−6.95546	−	4.01574i	−0.226022	−	0.130494i	−0.608736	+	0.793373i	$0.708323\pi$
$948$			6.83733i			0.222066i
$949$	2.10187	+	3.64055i	0.0682297	+	0.118177i
$950$	−0.153784	+	20.5751i	−0.00498940	+	0.667543i
$951$	−4.41661			−0.143218
$952$			31.0792i			1.00728i
$953$	40.2906	+	23.2618i	1.30514	+	0.753524i	0.981281	−	0.192581i	$-0.0616859\pi$
$953$	40.2906	+	23.2618i	1.30514	+	0.753524i	0.323860	+	0.946105i	$0.395019\pi$
$954$	1.51960			0.0491988
$955$	−0.0927750	+	24.8255i	−0.00300213	+	0.803334i
$956$	−15.5283			−0.502221
$957$	16.8339	−	9.71909i	0.544164	−	0.314173i
$958$	−9.26089	+	5.34678i	−0.299206	+	0.172746i
$959$	49.2763	+	85.3491i	1.59122	+	2.75607i
$960$	1.11079	+	1.94066i	0.0358506	+	0.0626344i
$961$	−23.7738			−0.766896
$962$	−3.85459	−	6.55769i	−0.124277	−	0.211428i
$963$			7.71580i			0.248638i
$964$	5.55610	−	9.62345i	0.178950	−	0.309950i
$965$	56.1979	+	0.210016i	1.80907	+	0.00676067i
$966$	−14.7384	−	25.5277i	−0.474201	−	0.821340i
$967$	32.0985	−	18.5321i	1.03222	−	0.595951i	0.114598	−	0.993412i	$-0.463442\pi$
$967$	32.0985	−	18.5321i	1.03222	−	0.595951i	0.917619	+	0.397461i	$0.130109\pi$
$968$		−	24.2680i		−	0.780003i
$969$	14.9649	+	25.9201i	0.480743	+	0.832672i
$970$	−23.3956	−	13.6243i	−0.751188	−	0.437450i
$971$	2.81026	−	4.86752i	0.0901856	−	0.156206i	−0.817404	−	0.576066i	$-0.804587\pi$
$971$	2.81026	−	4.86752i	0.0901856	−	0.156206i	0.907589	+	0.419859i	$0.137921\pi$
$972$			1.00000i			0.0320750i
$973$			38.3424i			1.22920i
$974$	6.44686	−	11.1663i	0.206571	−	0.357791i
$975$	−3.16670	+	5.39142i	−0.101416	+	0.172664i
$976$	12.2824			0.393149
$977$	36.1619	+	20.8781i	1.15692	+	0.667948i	0.950564	−	0.310528i	$-0.100506\pi$
$977$	36.1619	+	20.8781i	1.15692	+	0.667948i	0.206357	+	0.978477i	$0.433839\pi$
$978$	−19.6684	−	11.3555i	−0.628925	−	0.363110i
$979$	−26.1126	+	45.2284i	−0.834563	+	1.44550i
$980$	−0.0940901	+	25.1774i	−0.00300560	+	0.804262i
$981$	3.85417	+	6.67561i	0.123054	+	0.213136i
$982$	33.4243	+	19.2975i	1.06661	+	0.615809i
$983$	33.0554	+	19.0845i	1.05430	+	0.608702i	0.923851	−	0.382753i	$-0.125024\pi$
$983$	33.0554	+	19.0845i	1.05430	+	0.608702i	0.130452	+	0.991455i	$0.458357\pi$
$984$	1.33327	−	2.30929i	0.0425031	−	0.0736176i
$985$	1.29146	−	2.21769i	0.0411493	−	0.0706615i
$986$	11.9030	+	20.6166i	0.379069	+	0.656567i
$987$	−17.1092	−	9.87800i	−0.544592	−	0.314420i
$988$		−	5.14607i		−	0.163718i
$989$	62.3786			1.98352
$990$	6.59663	+	11.5250i	0.209655	+	0.366287i
$991$	−10.2413			−0.325325			−0.162662	−	0.986682i	$-0.552008\pi$
$991$	−10.2413			−0.325325			−0.162662	+	0.986682i	$0.552008\pi$
$992$	−2.32802	+	1.34408i	−0.0739146	+	0.0426746i
$993$		−	30.3682i		−	0.963704i
$994$	15.3813	+	26.6412i	0.487865	+	0.845007i
$995$	−0.0551330	+	14.7529i	−0.00174783	+	0.467699i
$996$	3.72981	+	6.46021i	0.118183	+	0.204700i
$997$	−42.0769	−	24.2931i	−1.33259	−	0.769371i	−0.346893	−	0.937905i	$-0.612763\pi$
$997$	−42.0769	−	24.2931i	−1.33259	−	0.769371i	−0.985696	+	0.168534i	$0.946097\pi$
$998$			11.3647i			0.359743i
$999$	5.24395	−	3.08237i	0.165911	−	0.0975219i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.bb.d.1009.1	✓	28
5.4	even	2	inner	1110.2.bb.d.1009.14	yes	28
37.26	even	3	inner	1110.2.bb.d.1099.14	yes	28
185.174	even	6	inner	1110.2.bb.d.1099.1	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.bb.d.1009.1	✓	28	1.1	even	1	trivial
1110.2.bb.d.1009.14	yes	28	5.4	even	2	inner
1110.2.bb.d.1099.1	yes	28	185.174	even	6	inner
1110.2.bb.d.1099.14	yes	28	37.26	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1110.bb (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.00835632 + 2.23605i) q^{5} +1.00000 q^{6} +(3.70065 - 2.13657i) q^{7} -1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.00835632 + 2.23605i) q^{5} +1.00000 q^{6} +(3.70065 - 2.13657i) q^{7} -1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +(1.12526 - 1.93230i) q^{10} -5.93869 q^{11} +(-0.866025 - 0.500000i) q^{12} +(-1.08299 + 0.625263i) q^{13} -4.27314 q^{14} +(-1.11079 - 1.94066i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-6.29873 - 3.63657i) q^{17} +(-0.866025 + 0.500000i) q^{18} +(2.05756 + 3.56380i) q^{19} +(-1.94066 + 1.11079i) q^{20} +(-2.13657 + 3.70065i) q^{21} +(5.14305 + 2.96934i) q^{22} -6.89816i q^{23} +(0.500000 + 0.866025i) q^{24} +(-4.99986 - 0.0373703i) q^{25} +1.25053 q^{26} +1.00000i q^{27} +(3.70065 + 2.13657i) q^{28} +3.27314 q^{29} +(-0.00835632 + 2.23605i) q^{30} -2.68816 q^{31} +(0.866025 - 0.500000i) q^{32} +(5.14305 - 2.96934i) q^{33} +(3.63657 + 6.29873i) q^{34} +(4.74656 + 8.29270i) q^{35} +1.00000 q^{36} +(-3.08237 - 5.24395i) q^{37} -4.11513i q^{38} +(0.625263 - 1.08299i) q^{39} +(2.23605 + 0.00835632i) q^{40} +(-1.33327 - 2.30929i) q^{41} +(3.70065 - 2.13657i) q^{42} +9.04279i q^{43} +(-2.96934 - 5.14305i) q^{44} +(1.93230 + 1.12526i) q^{45} +(-3.44908 + 5.97399i) q^{46} +4.62329i q^{47} -1.00000i q^{48} +(5.62987 - 9.75123i) q^{49} +(4.31132 + 2.53229i) q^{50} +7.27314 q^{51} +(-1.08299 - 0.625263i) q^{52} +(-1.31601 - 0.759799i) q^{53} +(0.500000 - 0.866025i) q^{54} +(0.0496256 - 13.2792i) q^{55} +(-2.13657 - 3.70065i) q^{56} +(-3.56380 - 2.05756i) q^{57} +(-2.83462 - 1.63657i) q^{58} +(-0.0555279 + 0.0961772i) q^{59} +(1.12526 - 1.93230i) q^{60} +(-6.14118 - 10.6368i) q^{61} +(2.32802 + 1.34408i) q^{62} -4.27314i q^{63} -1.00000 q^{64} +(-1.38907 - 2.42684i) q^{65} -5.93869 q^{66} +(-4.44547 + 2.56660i) q^{67} -7.27314i q^{68} +(3.44908 + 5.97399i) q^{69} +(0.0357078 - 9.55497i) q^{70} +(-3.59953 - 6.23456i) q^{71} +(-0.866025 - 0.500000i) q^{72} -3.36158i q^{73} +(0.0474386 + 6.08258i) q^{74} +(4.34869 - 2.46757i) q^{75} +(-2.05756 + 3.56380i) q^{76} +(-21.9770 + 12.6884i) q^{77} +(-1.08299 + 0.625263i) q^{78} +(-3.41867 - 5.92130i) q^{79} +(-1.93230 - 1.12526i) q^{80} +(-0.500000 - 0.866025i) q^{81} +2.66654i q^{82} +(-6.46021 - 3.72981i) q^{83} -4.27314 q^{84} +(8.18420 - 14.0539i) q^{85} +(4.52139 - 7.83128i) q^{86} +(-2.83462 + 1.63657i) q^{87} +5.93869i q^{88} +(4.39703 - 7.61589i) q^{89} +(-1.11079 - 1.94066i) q^{90} +(-2.67184 + 4.62776i) q^{91} +(5.97399 - 3.44908i) q^{92} +(2.32802 - 1.34408i) q^{93} +(2.31165 - 4.00389i) q^{94} +(-7.98605 + 4.57104i) q^{95} +(-0.500000 + 0.866025i) q^{96} -12.1077i q^{97} +(-9.75123 + 5.62987i) q^{98} +(-2.96934 + 5.14305i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 14 q^{4} + 2 q^{5} + 28 q^{6} + 14 q^{9}+O(q^{10}) \) 28 * q + 14 * q^4 + 2 * q^5 + 28 * q^6 + 14 * q^9	\( 28 q + 14 q^{4} + 2 q^{5} + 28 q^{6} + 14 q^{9} + 4 q^{10} - 12 q^{11} + 8 q^{14} + 2 q^{15} - 14 q^{16} - 20 q^{19} - 2 q^{20} + 4 q^{21} + 14 q^{24} - 8 q^{25} - 20 q^{26} - 36 q^{29} + 2 q^{30} + 24 q^{31} + 38 q^{34} - 2 q^{35} + 28 q^{36} - 10 q^{39} + 2 q^{40} - 6 q^{44} + 4 q^{45} + 8 q^{46} + 50 q^{49} - 4 q^{50} + 76 q^{51} + 14 q^{54} - 28 q^{55} + 4 q^{56} - 26 q^{59} + 4 q^{60} - 28 q^{61} - 28 q^{64} + 60 q^{65} - 12 q^{66} - 8 q^{69} - 10 q^{70} - 64 q^{71} + 24 q^{74} - 8 q^{75} + 20 q^{76} + 32 q^{79} - 4 q^{80} - 14 q^{81} + 8 q^{84} + 16 q^{85} - 8 q^{86} + 76 q^{89} + 2 q^{90} - 8 q^{91} - 38 q^{94} - 70 q^{95} - 14 q^{96} - 6 q^{99}+O(q^{100}) \) 28 * q + 14 * q^4 + 2 * q^5 + 28 * q^6 + 14 * q^9 + 4 * q^10 - 12 * q^11 + 8 * q^14 + 2 * q^15 - 14 * q^16 - 20 * q^19 - 2 * q^20 + 4 * q^21 + 14 * q^24 - 8 * q^25 - 20 * q^26 - 36 * q^29 + 2 * q^30 + 24 * q^31 + 38 * q^34 - 2 * q^35 + 28 * q^36 - 10 * q^39 + 2 * q^40 - 6 * q^44 + 4 * q^45 + 8 * q^46 + 50 * q^49 - 4 * q^50 + 76 * q^51 + 14 * q^54 - 28 * q^55 + 4 * q^56 - 26 * q^59 + 4 * q^60 - 28 * q^61 - 28 * q^64 + 60 * q^65 - 12 * q^66 - 8 * q^69 - 10 * q^70 - 64 * q^71 + 24 * q^74 - 8 * q^75 + 20 * q^76 + 32 * q^79 - 4 * q^80 - 14 * q^81 + 8 * q^84 + 16 * q^85 - 8 * q^86 + 76 * q^89 + 2 * q^90 - 8 * q^91 - 38 * q^94 - 70 * q^95 - 14 * q^96 - 6 * q^99

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