LMFDB - Embedded newform 1110.2.bb.d.1099.14

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			1099.14
Character	$\chi$	$=$	1110.1099
Dual form			1110.2.bb.d.1009.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} +(0.866025 + 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(1.94066 - 1.11079i) q^{5} +1.00000 q^{6} +(-3.70065 - 2.13657i) q^{7} -1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.866025 - 0.500000i) q^{2} +(0.866025 + 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(1.94066 - 1.11079i) 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} +(2.23605 + 0.00835632i) 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} +(0.00835632 - 2.23605i) q^{20} +(-2.13657 - 3.70065i) q^{21} +(-5.14305 + 2.96934i) q^{22} -6.89816i q^{23} +(0.500000 - 0.866025i) q^{24} +(2.53229 - 4.31132i) q^{25} +1.25053 q^{26} +1.00000i q^{27} +(-3.70065 + 2.13657i) q^{28} +3.27314 q^{29} +(1.94066 - 1.11079i) q^{30} -2.68816 q^{31} +(-0.866025 - 0.500000i) q^{32} +(-5.14305 - 2.96934i) q^{33} +(3.63657 - 6.29873i) q^{34} +(-9.55497 - 0.0357078i) q^{35} +1.00000 q^{36} +(3.08237 - 5.24395i) q^{37} -4.11513i q^{38} +(0.625263 + 1.08299i) q^{39} +(-1.11079 - 1.94066i) 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} +(0.0373703 - 4.99986i) q^{50} +7.27314 q^{51} +(1.08299 - 0.625263i) q^{52} +(1.31601 - 0.759799i) q^{53} +(0.500000 + 0.866025i) q^{54} +(-11.5250 + 6.59663i) 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} +(2.79624 + 0.0104498i) q^{65} -5.93869 q^{66} +(4.44547 + 2.56660i) q^{67} -7.27314i q^{68} +(3.44908 - 5.97399i) q^{69} +(-8.29270 + 4.74656i) 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} +(2.23605 + 0.00835632i) 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} +(0.0343873 - 9.20164i) 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 $\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times$.

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

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
$5$	1.94066	−	1.11079i	0.867888	−	0.496760i
$5$	1.94066	−	1.11079i	0.867888	−	0.496760i
$6$	1.00000			0.408248
$7$	−3.70065	−	2.13657i	−1.39871	−	0.807548i	−0.404456	−	0.914557i	$-0.632539\pi$
$7$	−3.70065	−	2.13657i	−1.39871	−	0.807548i	−0.994258	+	0.107009i	$0.965873\pi$
$8$		−	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	$-0.277853\pi$
$13$	1.08299	+	0.625263i	0.300367	+	0.173417i	−0.342241	+	0.939612i	$0.611186\pi$
$14$	−4.27314			−1.14205
$15$	2.23605	+	0.00835632i	0.577346	+	0.00215759i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	6.29873	−	3.63657i	1.52767	−	0.881998i	0.528206	−	0.849116i	$-0.322865\pi$
$17$	6.29873	−	3.63657i	1.52767	−	0.881998i	0.999459	−	0.0328820i	$-0.0104685\pi$
$18$	0.866025	+	0.500000i	0.204124	+	0.117851i
$19$	2.05756	−	3.56380i	0.472037	−	0.817593i	−0.527451	−	0.849586i	$-0.676852\pi$
$19$	2.05756	−	3.56380i	0.472037	−	0.817593i	0.999488	+	0.0319930i	$0.0101854\pi$
$20$	0.00835632	−	2.23605i	0.00186853	−	0.499997i
$21$	−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
$25$	2.53229	−	4.31132i	0.506459	−	0.862264i
$26$	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	$0.401710\pi$
$30$	1.94066	−	1.11079i	0.354314	−	0.202801i
$31$	−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
$35$	−9.55497	−	0.0357078i	−1.61508	−	0.00603571i
$36$	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
$40$	−1.11079	−	1.94066i	−0.175631	−	0.306845i
$41$	−1.33327	+	2.30929i	−0.208222	+	0.360651i	−0.951154	−	0.308715i	$-0.900101\pi$
$41$	−1.33327	+	2.30929i	−0.208222	+	0.360651i	0.742933	+	0.669366i	$0.233434\pi$
$42$	−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
$50$	0.0373703	−	4.99986i	0.00528497	−	0.707087i
$51$	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	$-0.633385\pi$
$53$	1.31601	−	0.759799i	0.180768	−	0.104366i	0.587653	+	0.809113i	$0.300052\pi$
$54$	0.500000	+	0.866025i	0.0680414	+	0.117851i
$55$	−11.5250	+	6.59663i	−1.55402	+	0.889490i
$56$	−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	0.862388	−	0.506248i	$-0.168968\pi$
$59$	−0.0555279	−	0.0961772i	−0.00722912	−	0.0125212i	−0.869617	+	0.493726i	$0.835634\pi$
$60$	1.12526	−	1.93230i	0.145271	−	0.249459i
$61$	−6.14118	+	10.6368i	−0.786298	+	1.36191i	0.141923	+	0.989878i	$0.454671\pi$
$61$	−6.14118	+	10.6368i	−0.786298	+	1.36191i	−0.928221	+	0.372030i	$0.878662\pi$
$62$	−2.32802	+	1.34408i	−0.295658	+	0.170698i
$63$		−	4.27314i		−	0.538365i
$64$	−1.00000			−0.125000
$65$	2.79624	+	0.0104498i	0.346831	+	0.00129614i
$66$	−5.93869			−0.731002
$67$	4.44547	+	2.56660i	0.543101	+	0.313560i	0.746335	−	0.665571i	$-0.231812\pi$
$67$	4.44547	+	2.56660i	0.543101	+	0.313560i	−0.203234	+	0.979130i	$0.565145\pi$
$68$		−	7.27314i		−	0.881998i
$69$	3.44908	−	5.97399i	0.415221	−	0.719183i
$70$	−8.29270	+	4.74656i	−0.991167	+	0.567323i
$71$	−3.59953	+	6.23456i	−0.427185	+	0.739907i	−0.996622	−	0.0821287i	$-0.973828\pi$
$71$	−3.59953	+	6.23456i	−0.427185	+	0.739907i	0.569436	+	0.822035i	$0.307161\pi$
$72$	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	−0.991718	−	0.128436i	$-0.959004\pi$
$79$	−3.41867	+	5.92130i	−0.384630	+	0.666199i	0.607088	+	0.794635i	$0.292338\pi$
$80$	−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	$-0.532405\pi$
$83$	6.46021	−	3.72981i	0.709101	−	0.409399i	0.810728	+	0.585423i	$0.199072\pi$
$84$	−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	0.999250	−	0.0387290i	$-0.0123309\pi$
$89$	4.39703	+	7.61589i	0.466085	+	0.807282i	−0.533165	+	0.846011i	$0.678998\pi$
$90$	2.23605	+	0.00835632i	0.235701	+	0.000880834i
$91$	−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
$95$	0.0343873	−	9.20164i	0.00352806	−	0.944068i
$96$	−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	$-0.211677\pi$
$107$	6.68208	+	3.85790i	0.645981	+	0.372957i	−0.140934	+	0.990019i	$0.545010\pi$
$108$	0.866025	+	0.500000i	0.0833333	+	0.0481125i
$109$	−3.85417	−	6.67561i	−0.369162	−	0.639408i	0.620273	−	0.784386i	$-0.287022\pi$
$109$	−3.85417	−	6.67561i	−0.369162	−	0.639408i	−0.989435	+	0.144979i	$0.953689\pi$
$110$	−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	$-0.926542\pi$
$113$	−13.4168	+	7.74618i	−1.26214	+	0.728700i	−0.288656	+	0.957433i	$0.593208\pi$
$114$	2.05756	−	3.56380i	0.192708	−	0.333781i
$115$	−7.66241	−	13.3870i	−0.714523	−	1.24834i
$116$	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
$120$	0.00835632	−	2.23605i	0.000762824	−	0.204123i
$121$	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	$-0.430971\pi$
$127$	13.1682	−	7.60268i	1.16849	−	0.674628i	0.953324	+	0.301949i	$0.0976372\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$	−4.52139	+	7.83128i	−0.398086	+	0.689506i
$130$	2.42684	−	1.38907i	0.212848	−	0.121830i
$131$	8.24808	+	14.2861i	0.720638	+	1.24818i	0.960744	+	0.277435i	$0.0894844\pi$
$131$	8.24808	+	14.2861i	0.720638	+	1.24818i	−0.240106	+	0.970747i	$0.577182\pi$
$132$	−5.14305	+	2.96934i	−0.447645	+	0.258448i
$133$	−15.2286	+	8.79226i	−1.32049	+	0.762386i
$134$	5.13319			0.443440
$135$	1.11079	+	1.94066i	0.0956015	+	0.167025i
$136$	−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	0.610603	−	0.791937i	$-0.290927\pi$
$139$	−4.48645	−	7.77075i	−0.380535	−	0.659107i	−0.991139	+	0.132830i	$0.957594\pi$
$140$	−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
$145$	6.35204	−	3.63577i	0.527509	−	0.301934i
$146$	−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	$0.334831\pi$
$150$	2.53229	−	4.31132i	0.206761	−	0.352018i
$151$	4.81068	−	8.33235i	0.391488	−	0.678077i	−0.601158	−	0.799130i	$-0.705294\pi$
$151$	4.81068	−	8.33235i	0.391488	−	0.678077i	0.992646	+	0.121053i	$0.0386271\pi$
$152$	−3.56380	−	2.05756i	−0.289063	−	0.166890i
$153$	6.29873	+	3.63657i	0.509222	+	0.293999i
$154$	25.3769			2.04493
$155$	−5.21680	+	2.98598i	−0.419023	+	0.239840i
$156$	1.25053			0.100122
$157$	7.43290	−	4.29139i	0.593210	−	0.342490i	−0.173156	−	0.984894i	$-0.555396\pi$
$157$	7.43290	−	4.29139i	0.593210	−	0.342490i	0.766366	+	0.642405i	$0.222063\pi$
$158$			6.83733i			0.543949i
$159$	1.51960			0.120512
$160$	−2.23605	−	0.00835632i	−0.176775	−	0.000660625i
$161$	−14.7384	+	25.5277i	−1.16155	+	2.01186i
$162$			1.00000i			0.0785674i
$163$	19.6684	−	11.3555i	1.54055	−	0.889434i	0.541741	−	0.840545i	$-0.317765\pi$
$163$	19.6684	−	11.3555i	1.54055	−	0.889434i	0.998804	−	0.0488890i	$-0.0155681\pi$
$164$	1.33327	+	2.30929i	0.104111	+	0.180325i
$165$	−13.2792	−	0.0496256i	−1.03379	−	0.00386335i
$166$	3.72981	−	6.46021i	0.289489	−	0.501410i
$167$	3.96167	+	2.28727i	0.306564	+	0.176995i	0.645388	−	0.763855i	$-0.276696\pi$
$167$	3.96167	+	2.28727i	0.306564	+	0.176995i	−0.338824	+	0.940850i	$0.610029\pi$
$168$	−3.70065	+	2.13657i	−0.285511	+	0.164840i
$169$	−5.71809	−	9.90403i	−0.439853	−	0.761848i
$170$	0.0607767	−	16.2631i	0.00466136	−	1.24732i
$171$	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	$-0.684047\pi$
$173$	−1.24331	+	0.717825i	−0.0945270	+	0.0545752i	0.451991	+	0.892022i	$0.350714\pi$
$174$	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	$0.360197\pi$
$180$	1.94066	−	1.11079i	0.144648	−	0.0827934i
$181$	−9.91980	+	17.1816i	−0.737333	+	1.27710i	0.216359	+	0.976314i	$0.430582\pi$
$181$	−9.91980	+	17.1816i	−0.737333	+	1.27710i	−0.953692	+	0.300784i	$0.902752\pi$
$182$	−4.62776	−	2.67184i	−0.343032	−	0.198050i
$183$	−10.6368	+	6.14118i	−0.786298	+	0.453969i
$184$	−6.89816			−0.508539
$185$	0.156903	−	13.6006i	0.0115357	−	0.999933i
$186$	−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
$190$	−4.57104	−	7.98605i	−0.331618	−	0.579369i
$191$	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	$-0.653649\pi$
$197$	0.993932	−	0.573847i	0.0708148	−	0.0408849i	0.534989	+	0.844859i	$0.320316\pi$
$198$	−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	$0.424867\pi$
$200$	−4.31132	−	2.53229i	−0.304856	−	0.179060i
$201$	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
$205$	−0.0222825	+	5.96253i	−0.00155628	+	0.416441i
$206$	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
$210$	−9.55497	−	0.0357078i	−0.659356	−	0.00246407i
$211$	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
$215$	10.0446	+	17.5489i	0.685038	+	1.19683i
$216$	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
$220$	−0.0496256	+	13.2792i	−0.00334576	+	0.895285i
$221$	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
$225$	4.99986	+	0.0373703i	0.333324	+	0.00249136i
$226$	−7.74618	+	13.4168i	−0.515268	+	0.892471i
$227$	5.15116	+	2.97402i	0.341895	+	0.197393i	0.661109	−	0.750289i	$-0.270086\pi$
$227$	5.15116	+	2.97402i	0.341895	+	0.197393i	−0.319215	+	0.947682i	$0.603419\pi$
$228$		−	4.11513i		−	0.272531i
$229$	4.45902	−	7.72325i	0.294660	−	0.510367i	−0.680246	−	0.732984i	$-0.738127\pi$
$229$	4.45902	−	7.72325i	0.294660	−	0.510367i	0.974906	+	0.222618i	$0.0714602\pi$
$230$	−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
$235$	5.13551	+	8.97223i	0.335004	+	0.585284i
$236$	−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	−0.999997	−	0.00256635i	$-0.999183\pi$
$239$	−7.76415	−	13.4479i	−0.502221	−	0.869872i	0.497776	−	0.867306i	$-0.334150\pi$
$240$	−1.11079	−	1.94066i	−0.0717011	−	0.125269i
$241$	−5.55610	+	9.62345i	−0.357900	+	0.619901i	−0.987610	−	0.156929i	$-0.949840\pi$
$241$	−5.55610	+	9.62345i	−0.357900	+	0.619901i	0.629710	+	0.776830i	$0.283174\pi$
$242$	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
$250$	−5.48127	−	9.74452i	−0.346666	−	0.616298i
$251$	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
$255$	14.1147	−	8.07893i	0.883895	−	0.505922i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−21.3805	+	12.3440i	−1.33368	+	0.769999i	−0.985861	−	0.167563i	$-0.946410\pi$
$257$	−21.3805	+	12.3440i	−1.33368	+	0.769999i	−0.347817	+	0.937563i	$0.613077\pi$
$258$			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	$-0.0489027\pi$
$263$	21.8902	+	12.6383i	1.34981	+	0.779311i	0.361584	+	0.932340i	$0.382236\pi$
$264$	−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	0.588987	−	0.808143i	$-0.299527\pi$
$271$	−6.67337	−	11.5586i	−0.405379	−	0.702136i	−0.994365	+	0.106006i	$0.966194\pi$
$272$	−6.29873	−	3.63657i	−0.381916	−	0.220500i
$273$		−	5.34368i		−	0.323414i
$274$	11.5316	+	19.9734i	0.696652	+	1.20664i
$275$	−15.0385	+	25.6036i	−0.906856	+	1.54395i
$276$	−3.44908	−	5.97399i	−0.207610	−	0.359592i
$277$	−16.1983	−	9.35210i	−0.973262	−	0.561913i	−0.0730329	−	0.997330i	$-0.523268\pi$
$277$	−16.1983	−	9.35210i	−0.973262	−	0.561913i	−0.900229	+	0.435416i	$0.856601\pi$
$278$	−7.77075	−	4.48645i	−0.466059	−	0.269079i
$279$	−1.34408	−	2.32802i	−0.0804680	−	0.139375i
$280$	−0.0357078	+	9.55497i	−0.00213395	+	0.571019i
$281$	−5.15883	−	8.93535i	−0.307750	−	0.533038i	0.670120	−	0.742253i	$-0.266243\pi$
$281$	−5.15883	−	8.93535i	−0.307750	−	0.533038i	−0.977870	+	0.209214i	$0.932909\pi$
$282$			4.62329i			0.275313i
$283$	5.24310	+	3.02711i	0.311670	+	0.179943i	0.647674	−	0.761918i	$-0.275742\pi$
$283$	5.24310	+	3.02711i	0.311670	+	0.179943i	−0.336003	+	0.941861i	$0.609075\pi$
$284$	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	$-0.382958\pi$
$293$	−4.60340	−	2.65778i	−0.268934	−	0.155269i	−0.628403	+	0.777888i	$0.716291\pi$
$294$	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
$300$	0.0373703	−	4.99986i	0.00215758	−	0.288667i
$301$	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
$305$	−0.102635	+	27.4640i	−0.00587688	+	1.57258i
$306$	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	−0.816098	−	0.577913i	$-0.803867\pi$
$311$	−16.0222	−	27.7513i	−0.908537	−	1.57363i	−0.0924383	−	0.995718i	$-0.529466\pi$
$312$	1.08299	−	0.625263i	0.0613121	−	0.0353985i
$313$	−7.68688	+	4.43802i	−0.434488	+	0.250852i	−0.701257	−	0.712909i	$-0.747377\pi$
$313$	−7.68688	+	4.43802i	−0.434488	+	0.250852i	0.266769	+	0.963761i	$0.414044\pi$
$314$	4.29139	−	7.43290i	0.242177	−	0.419463i
$315$	−4.74656	−	8.29270i	−0.267438	−	0.467241i
$316$	3.41867	+	5.92130i	0.192315	+	0.333099i
$317$	−3.82489	+	2.20830i	−0.214827	+	0.124031i	−0.603553	−	0.797323i	$-0.706249\pi$
$317$	−3.82489	+	2.20830i	−0.214827	+	0.124031i	0.388725	+	0.921354i	$0.372915\pi$
$318$	1.31601	−	0.759799i	0.0737982	−	0.0426074i
$319$	−19.4382			−1.08833
$320$	−1.94066	+	1.11079i	−0.108486	+	0.0620950i
$321$	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
$330$	−11.5250	+	6.59663i	−0.634428	+	0.363133i
$331$	−15.1841	−	26.2996i	−0.834592	−	1.44556i	−0.894362	−	0.447344i	$-0.852370\pi$
$331$	−15.1841	−	26.2996i	−0.834592	−	1.44556i	0.0597696	−	0.998212i	$-0.480963\pi$
$332$		−	7.45961i		−	0.409399i
$333$	6.08258	+	0.0474386i	0.333323	+	0.00259962i
$334$	4.57455			0.250308
$335$	11.4781	+	0.0428946i	0.627115	+	0.00234358i
$336$	−2.13657	+	3.70065i	−0.116560	+	0.201887i
$337$	20.8921	+	12.0621i	1.13807	+	0.657063i	0.945951	−	0.324310i	$-0.105132\pi$
$337$	20.8921	+	12.0621i	1.13807	+	0.657063i	0.192115	+	0.981372i	$0.438465\pi$
$338$	−9.90403	−	5.71809i	−0.538708	−	0.311023i
$339$	−15.4924			−0.841430
$340$	−8.07893	−	14.1147i	−0.438141	−	0.765475i
$341$	15.9642			0.864507
$342$	3.56380	−	2.05756i	0.192708	−	0.111260i
$343$		−	18.2025i		−	0.982843i
$344$	9.04279			0.487554
$345$	0.0576433	−	15.4247i	0.00310341	−	0.830436i
$346$	−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	0.988983	+	0.148029i	$0.0472930\pi$
$349$	11.6328	+	20.1486i	0.622689	+	1.07853i	−0.366294	+	0.930499i	$0.619374\pi$
$350$	−10.8209	+	18.4229i	−0.578399	+	0.984745i
$351$	−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	$-0.665010\pi$
$353$	0.169377	−	0.0977899i	0.00901503	−	0.00520483i	0.504501	+	0.863411i	$0.331677\pi$
$354$	−0.0555279	−	0.0961772i	−0.00295128	−	0.00511176i
$355$	−0.0601576	+	16.0975i	−0.00319283	+	0.854365i
$356$	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
$365$	−3.73401	−	6.52367i	−0.195447	−	0.341465i
$366$	−6.14118	+	10.6368i	−0.321005	+	0.555996i
$367$	−1.73122	−	0.999522i	−0.0903691	−	0.0521746i	0.454134	−	0.890933i	$-0.349949\pi$
$367$	−1.73122	−	0.999522i	−0.0903691	−	0.0521746i	−0.544504	+	0.838759i	$0.683282\pi$
$368$	−5.97399	+	3.44908i	−0.311416	+	0.179796i
$369$	−2.66654			−0.138815
$370$	−6.66440	−	11.8569i	−0.346466	−	0.616410i
$371$	−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	$-0.449683\pi$
$373$	−11.9568	−	6.90326i	−0.619099	−	0.357437i	−0.776518	+	0.630095i	$0.783016\pi$
$374$	−21.5965	+	37.4062i	−1.11673	+	1.93423i
$375$	5.69837	−	9.61918i	0.294262	−	0.496732i
$376$	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	0.766057	−	0.642772i	$-0.222216\pi$
$379$	−3.38018	−	5.85465i	−0.173628	−	0.300733i	−0.939686	+	0.342039i	$0.888882\pi$
$380$	−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	$-0.216030\pi$
$383$	12.2108	+	7.04991i	0.623943	+	0.360233i	−0.154460	+	0.987999i	$0.549364\pi$
$384$	−1.00000			−0.0510310
$385$	56.7440	+	0.212057i	2.89194	+	0.0108074i
$386$	−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	−0.783768	−	0.621054i	$-0.786705\pi$
$389$	2.87886	−	4.98634i	0.145964	−	0.252817i	0.929732	+	0.368236i	$0.120038\pi$
$390$	2.79624	+	0.0104498i	0.141593	+	0.000529146i
$391$	−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
$395$	−0.0571350	+	15.2886i	−0.00287477	+	0.769255i
$396$	−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
$400$	−4.99986	−	0.0373703i	−0.249993	−	0.00186852i
$401$	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
$405$	−0.00835632	+	2.23605i	−0.000415229	+	0.111110i
$406$	−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	0.898969	−	0.438012i	$-0.144317\pi$
$409$	1.41880	+	2.45743i	0.0701549	+	0.121512i	−0.828814	+	0.559524i	$0.810984\pi$
$410$	2.96197	+	5.17484i	0.146281	+	0.255567i
$411$	−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	0.919723	−	0.392569i	$-0.128414\pi$
$419$	2.45402	+	4.25048i	0.119887	+	0.207650i	−0.799836	+	0.600219i	$0.795080\pi$
$420$	−8.29270	+	4.74656i	−0.404642	+	0.231608i
$421$	−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
$425$	0.271800	−	36.3647i	0.0131842	−	1.76395i
$426$	−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	−0.983584	−	0.180449i	$-0.942245\pi$
$431$	−6.96555	+	12.0647i	−0.335519	+	0.581136i	0.648065	+	0.761585i	$0.275578\pi$
$432$	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
$435$	7.31892	+	0.0273514i	0.350915	+	0.00131140i
$436$	−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	−0.962346	−	0.271827i	$-0.912372\pi$
$439$	−5.14932	+	8.91889i	−0.245764	+	0.425675i	0.716582	+	0.697502i	$0.245705\pi$
$440$	6.59663	+	11.5250i	0.314482	+	0.549431i
$441$	−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	0.165757	+	0.986167i	$0.446993\pi$
$449$	−16.3407	+	28.3030i	−0.771167	+	1.33570i	−0.936924	+	0.349533i	$0.886340\pi$
$450$	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	$-0.251513\pi$
$457$	9.41322	+	5.43472i	0.440332	+	0.254226i	−0.263407	+	0.964685i	$0.584846\pi$
$458$		−	8.91804i		−	0.416713i
$459$	3.63657	+	6.29873i	0.169741	+	0.293999i
$460$	−15.4247	−	0.0576433i	−0.719178	−	0.00268763i
$461$	14.4531	+	25.0336i	0.673150	+	1.16593i	0.977006	+	0.213212i	$0.0683925\pi$
$461$	14.4531	+	25.0336i	0.673150	+	1.16593i	−0.303856	+	0.952718i	$0.598274\pi$
$462$	21.9770	+	12.6884i	1.02246	+	0.590319i
$463$	−32.1719	−	18.5745i	−1.49516	−	0.863229i	−0.495172	−	0.868795i	$-0.664895\pi$
$463$	−32.1719	−	18.5745i	−1.49516	−	0.863229i	−0.999985	+	0.00556589i	$0.998228\pi$
$464$	−1.63657	−	2.83462i	−0.0759759	−	0.131594i
$465$	−6.01087	−	0.0224631i	−0.278747	−	0.00104170i
$466$	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	0.961935	−	0.273279i	$-0.0881084\pi$
$479$	5.34678	+	9.26089i	0.244300	+	0.423141i	−0.717634	+	0.696420i	$0.754775\pi$
$480$	−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
$485$	−13.4491	−	23.4968i	−0.610690	−	1.06693i
$486$	−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
$490$	25.1774	+	0.0940901i	1.13740	+	0.00425056i
$491$	−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	−0.964726	−	0.263256i	$-0.915204\pi$
$499$	−5.68234	+	9.84210i	−0.254376	+	0.440593i	0.710350	+	0.703849i	$0.248537\pi$
$500$	−9.61918	−	5.69837i	−0.430183	−	0.254839i
$501$	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	$-0.714045\pi$
$503$	−5.76066	+	3.32592i	−0.256855	+	0.148295i	0.366044	+	0.930598i	$0.380712\pi$
$504$	−4.27314			−0.190341
$505$	−13.9878	+	8.00630i	−0.622448	+	0.356276i
$506$	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	0.939942	−	0.341334i	$-0.110879\pi$
$509$	3.93391	+	6.81372i	0.174367	+	0.302013i	−0.765575	+	0.643347i	$0.777545\pi$
$510$	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
$515$	3.55237	+	6.20633i	0.156536	+	0.273484i
$516$	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
$520$	0.0104498	−	2.79624i	0.000458254	−	0.122623i
$521$	16.2960	−	28.2255i	0.713941	−	1.23658i	−0.249425	−	0.968394i	$-0.580242\pi$
$521$	16.2960	−	28.2255i	0.713941	−	1.23658i	0.963367	−	0.268188i	$-0.0864249\pi$
$522$	2.83462	+	1.63657i	0.124068	+	0.0716308i
$523$	−10.8426	−	6.26000i	−0.474116	−	0.273731i	0.243845	−	0.969814i	$-0.421591\pi$
$523$	−10.8426	−	6.26000i	−0.474116	−	0.273731i	−0.717961	+	0.696083i	$0.754924\pi$
$524$	16.4962			0.720638
$525$	−21.3651	−	0.159689i	−0.932450	−	0.00696939i
$526$	25.2766			1.10211
$527$	−16.9320	+	9.77569i	−0.737569	+	0.425836i
$528$			5.93869i			0.258448i
$529$	−24.5847			−1.06890
$530$	0.0126983	−	3.39790i	0.000551577	−	0.147595i
$531$	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
$535$	17.2529	+	0.0644757i	0.745910	+	0.00278753i
$536$	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
$540$	2.23605	+	0.00835632i	0.0962244	+	0.000359599i
$541$	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
$550$	−0.221931	+	29.6926i	−0.00946316	+	1.26610i
$551$	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
$555$	6.93616	−	11.7000i	0.294424	−	0.496637i
$556$	−8.97289			−0.380535
$557$	5.17687	−	2.98887i	0.219351	−	0.126642i	−0.386299	−	0.922374i	$-0.626247\pi$
$557$	5.17687	−	2.98887i	0.219351	−	0.126642i	0.605650	+	0.795731i	$0.292913\pi$
$558$	−2.32802	−	1.34408i	−0.0985528	−	0.0568995i
$559$	−5.65412	+	9.79322i	−0.239144	+	0.414209i
$560$	4.74656	+	8.29270i	0.200579	+	0.350431i
$561$	−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	$0.427229\pi$
$570$	0.0343873	−	9.20164i	0.00144033	−	0.385414i
$571$	12.4430	+	21.5520i	0.520725	+	0.901922i	0.999710	+	0.0240989i	$0.00767165\pi$
$571$	12.4430	+	21.5520i	0.520725	+	0.901922i	−0.478985	+	0.877823i	$0.658995\pi$
$572$	−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
$575$	−29.7402	−	17.4682i	−1.24025	−	0.728473i
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	6.17293	−	3.56394i	0.256982	−	0.148369i	−0.365975	−	0.930625i	$-0.619264\pi$
$577$	6.17293	−	3.56394i	0.256982	−	0.148369i	0.622957	+	0.782256i	$0.285931\pi$
$578$		−	35.8986i		−	1.49318i
$579$	12.5663	−	21.7655i	0.522238	−	0.904543i
$580$	0.0273514	−	7.31892i	0.00113571	−	0.303902i
$581$	−31.8760			−1.32244
$582$		−	12.1077i		−	0.501878i
$583$	−7.81538	+	4.51221i	−0.323680	+	0.186877i
$584$	−3.36158			−0.139103
$585$	1.38907	+	2.42684i	0.0574310	+	0.100338i
$586$	−5.31555			−0.219583
$587$	8.55022	+	4.93647i	0.352905	+	0.203750i	0.665964	−	0.745984i	$-0.268020\pi$
$587$	8.55022	+	4.93647i	0.352905	+	0.203750i	−0.313059	+	0.949734i	$0.601354\pi$
$588$	9.75123	+	5.62987i	0.402134	+	0.232172i
$589$	−5.53106	+	9.58008i	−0.227903	+	0.394740i
$590$	−0.248327		0.000928018i	−0.0102234		3.82059e-5i
$591$	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
$595$	−60.3140	+	34.5224i	−2.47263	+	1.41528i
$596$	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	−0.603148	−	0.797629i	$-0.706087\pi$
$599$	9.52530	−	16.4983i	0.389193	−	0.674102i	0.992341	+	0.123527i	$0.0394205\pi$
$600$	−2.46757	−	4.34869i	−0.100738	−	0.177535i
$601$	−17.3651	−	30.0773i	−0.708338	−	1.22688i	−0.965473	−	0.260502i	$-0.916112\pi$
$601$	−17.3651	−	30.0773i	−0.708338	−	1.22688i	0.257135	−	0.966375i	$-0.417221\pi$
$602$		−	38.6411i		−	1.57489i
$603$			5.13319i			0.209040i
$604$	−4.81068	−	8.33235i	−0.195744	−	0.339039i
$605$	47.0959	−	26.9566i	1.91472	−	1.09594i
$606$	−7.20776			−0.292795
$607$	3.78634	−	2.18604i	0.153683	−	0.0887288i	−0.421187	−	0.906974i	$-0.638386\pi$
$607$	3.78634	−	2.18604i	0.153683	−	0.0887288i	0.574869	+	0.818245i	$0.305053\pi$
$608$	−3.56380	+	2.05756i	−0.144531	+	0.0834452i
$609$	−6.99330	−	12.1128i	−0.283383	−	0.490834i
$610$	13.6431	+	23.8358i	0.552394	+	0.965085i
$611$	−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	$-0.669423\pi$
$613$	−0.371275	+	0.214356i	−0.0149957	+	0.00865775i	0.492483	+	0.870322i	$0.336089\pi$
$614$	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	$-0.573876\pi$
$617$	12.3649	−	7.13885i	0.497790	−	0.287399i	0.727801	+	0.685789i	$0.240543\pi$
$618$			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	$0.422124\pi$
$620$	−0.0224631	+	6.01087i	−0.000902142	+	0.241402i
$621$	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
$625$	−12.1750	−	21.8351i	−0.486999	−	0.873403i
$626$	−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	0.678961	−	0.734174i	$-0.262430\pi$
$631$	−7.44379	−	12.8930i	−0.296333	−	0.513263i	−0.975294	+	0.220911i	$0.929097\pi$
$632$	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	−0.991266	−	0.131875i	$-0.957900\pi$
$641$	−15.4399	−	26.7427i	−0.609840	−	1.05627i	0.381426	−	0.924399i	$-0.375433\pi$
$642$	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
$645$	−0.0755644	+	20.2201i	−0.00297535	+	0.796167i
$646$	−14.9649	−	25.9201i	−0.588788	−	1.01981i
$647$	−19.3536	−	11.1738i	−0.760870	−	0.439288i	0.0687382	−	0.997635i	$-0.478103\pi$
$647$	−19.3536	−	11.1738i	−0.760870	−	0.439288i	−0.829608	+	0.558346i	$0.811436\pi$
$648$	0.866025	+	0.500000i	0.0340207	+	0.0196419i
$649$	0.329763	+	0.571166i	0.0129443	+	0.0224202i
$650$	3.16670	−	5.39142i	0.124208	−	0.211469i
$651$	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	$-0.576322\pi$
$653$	−30.6001	−	17.6670i	−1.19747	−	0.691362i	−0.959991	+	0.280030i	$0.909656\pi$
$654$	−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	−0.861409	−	0.507912i	$-0.830418\pi$
$659$	0.235145	−	0.407284i	0.00915996	−	0.0158655i	0.870569	+	0.492046i	$0.163751\pi$
$660$	−6.68259	+	11.4753i	−0.260119	+	0.446676i
$661$	9.15487	−	15.8567i	0.356083	−	0.616754i	−0.631220	−	0.775604i	$-0.717445\pi$
$661$	9.15487	−	15.8567i	0.356083	−	0.616754i	0.987303	+	0.158850i	$0.0507787\pi$
$662$	−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
$670$	9.96176	−	5.70189i	0.384856	−	0.220283i
$671$	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	$-0.352534\pi$
$673$	−2.70882	−	1.56394i	−0.104418	−	0.0602855i	−0.551299	+	0.834308i	$0.685868\pi$
$674$	24.1241			0.929227
$675$	4.31132	+	2.53229i	0.165943	+	0.0974680i
$676$	−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	$-0.664578\pi$
$683$	0.297050	−	0.171502i	0.0113663	−	0.00656234i	0.505672	+	0.862726i	$0.331244\pi$
$684$	2.05756	−	3.56380i	0.0786729	−	0.136265i
$685$	25.6184	+	44.7579i	0.978830	+	1.71011i
$686$	−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
$690$	−7.66241	−	13.3870i	−0.291703	−	0.509633i
$691$	−11.6638	−	20.2023i	−0.443711	−	0.768531i	0.554250	−	0.832350i	$-0.313005\pi$
$691$	−11.6638	−	20.2023i	−0.443711	−	0.768531i	−0.997961	+	0.0638196i	$0.979672\pi$
$692$			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
$700$	−0.159689	+	21.3651i	−0.00603567	+	0.807525i
$701$	25.0713	+	43.4248i	0.946930	+	1.64013i	0.751839	+	0.659347i	$0.229167\pi$
$701$	25.0713	+	43.4248i	0.946930	+	1.64013i	0.195091	+	0.980785i	$0.437500\pi$
$702$			1.25053i			0.0471981i
$703$	−12.3462	−	21.7747i	−0.465647	−	0.821249i
$704$	5.93869			0.223823
$705$	−0.0386337	+	10.3379i	−0.00145503	+	0.389349i
$706$	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	$0.766020\pi$
$710$	7.99663	+	13.9709i	0.300108	+	0.524318i
$711$	−6.83733			−0.256420
$712$	7.61589	−	4.39703i	0.285417	−	0.164786i
$713$			18.5434i			0.694455i
$714$	−31.0792			−1.16311
$715$	−16.6060	−	0.0620581i	−0.621029	−	0.00232084i
$716$	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	0.990415	−	0.138123i	$-0.0441070\pi$
$719$	10.0711	+	17.4437i	0.375589	+	0.650540i	−0.614826	+	0.788663i	$0.710774\pi$
$720$	0.00835632	−	2.23605i	0.000311422	−	0.0833328i
$721$	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
$725$	8.28856	−	14.1116i	0.307829	−	0.524090i
$726$	24.2680			0.900670
$727$	−30.2818	−	17.4832i	−1.12309	−	0.648417i	−0.180903	−	0.983501i	$-0.557902\pi$
$727$	−30.2818	−	17.4832i	−1.12309	−	0.648417i	−0.942188	+	0.335084i	$0.891235\pi$
$728$	−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	$-0.305718\pi$
$733$	4.06319	+	2.34588i	0.150077	+	0.0866471i	−0.423081	+	0.906092i	$0.639051\pi$
$734$	−1.99904			−0.0737861
$735$	12.5072	+	21.8513i	0.461335	+	0.805997i
$736$	−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	$0.384467\pi$
$740$	−11.7000	−	6.93616i	−0.430100	−	0.254978i
$741$	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	$-0.0705546\pi$
$743$	34.6971	+	20.0324i	1.27291	+	0.734917i	0.297378	+	0.954760i	$0.403888\pi$
$744$	−1.34408	+	2.32802i	−0.0492764	+	0.0853492i
$745$	23.4954	−	13.4482i	0.860804	−	0.492705i
$746$	−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
$755$	0.0803993	−	21.5139i	0.00292603	−	0.782970i
$756$	−2.13657	−	3.70065i	−0.0777063	−	0.134591i
$757$	28.5617	−	16.4901i	1.03809	−	0.599342i	0.118799	−	0.992918i	$-0.462096\pi$
$757$	28.5617	−	16.4901i	1.03809	−	0.599342i	0.919292	+	0.393576i	$0.128762\pi$
$758$	−5.85465	−	3.38018i	−0.212650	−	0.122774i
$759$	−20.4830	+	35.4776i	−0.743487	+	1.28776i
$760$	−9.20164	−	0.0343873i	−0.333778	−	0.00124736i
$761$	24.2801	+	42.0544i	0.880155	+	1.52447i	0.851169	+	0.524893i	$0.175894\pi$
$761$	24.2801	+	42.0544i	0.880155	+	1.52447i	0.0289860	+	0.999580i	$0.490772\pi$
$762$	13.1682	−	7.60268i	0.477034	−	0.275416i
$763$			32.9388i			1.19246i
$764$	5.55119	−	9.61493i	0.200835	−	0.347856i
$765$	16.2631	+	0.0607767i	0.587995	+	0.00219739i
$766$	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	$0.234418\pi$
$770$	49.2478	−	28.1883i	1.77477	−	1.01584i
$771$	−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	$-0.223647\pi$
$773$	16.2676	+	9.39211i	0.585105	+	0.337811i	−0.178054	+	0.984021i	$0.556980\pi$
$774$	−4.52139	+	7.83128i	−0.162518	+	0.281490i
$775$	−6.80722	+	11.5895i	−0.244522	+	0.416308i
$776$	−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
$780$	2.42684	−	1.38907i	0.0868948	−	0.0497367i
$781$	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
$790$	7.59484	+	13.2689i	0.270212	+	0.472087i
$791$	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
$795$	2.94902	−	1.68795i	0.104591	−	0.0598655i
$796$	3.29888	−	5.71382i	0.116926	−	0.202521i
$797$	43.8239	−	25.3018i	1.55232	−	0.896234i	0.554371	−	0.832270i	$-0.312959\pi$
$797$	43.8239	−	25.3018i	1.55232	−	0.896234i	0.997952	−	0.0639644i	$-0.0203744\pi$
$798$	−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
$805$	−0.246318	+	65.9118i	−0.00868157	+	2.32308i
$806$	−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	0.413871	+	0.910336i	$0.364177\pi$
$809$	−16.5378	+	28.6443i	−0.581439	+	1.00708i	−0.995309	+	0.0967455i	$0.969157\pi$
$810$	1.11079	+	1.94066i	0.0390292	+	0.0681877i
$811$	−12.6537	+	21.9168i	−0.444330	+	0.769603i	−0.998005	−	0.0631300i	$-0.979892\pi$
$811$	−12.6537	+	21.9168i	−0.444330	+	0.769603i	0.553675	+	0.832733i	$0.313225\pi$
$812$	−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	−0.343211	−	0.939258i	$-0.611514\pi$
$821$	18.3900	−	31.8525i	0.641816	−	1.11166i	0.985027	−	0.172400i	$-0.0551522\pi$
$822$			23.0633i			0.804424i
$823$	22.9721	−	13.2629i	0.800757	−	0.462317i	−0.0429791	−	0.999076i	$-0.513685\pi$
$823$	22.9721	−	13.2629i	0.800757	−	0.462317i	0.843736	+	0.536759i	$0.180352\pi$
$824$	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	$-0.505037\pi$
$827$	−25.5843	−	14.7711i	−0.889653	−	0.513641i	−0.873829	+	0.486234i	$0.838370\pi$
$828$		−	6.89816i		−	0.239728i
$829$	7.11508	+	12.3237i	0.247117	+	0.428019i	0.962725	−	0.270483i	$-0.0871835\pi$
$829$	7.11508	+	12.3237i	0.247117	+	0.428019i	−0.715608	+	0.698502i	$0.753850\pi$
$830$	0.0623349	−	16.6801i	0.00216368	−	0.578974i
$831$	−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
$835$	10.2289	+	0.0382264i	0.353987	+	0.00132288i
$836$	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	0.844795	−	0.535090i	$-0.179722\pi$
$839$	−1.18772	−	2.05719i	−0.0410045	−	0.0710219i	−0.885799	+	0.464069i	$0.846389\pi$
$840$	−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	$-0.593734\pi$
$853$	11.4895	−	6.63345i	0.393392	−	0.227125i	0.683629	+	0.729830i	$0.260401\pi$
$854$	26.2421	−	45.4527i	0.897988	−	1.55536i
$855$	7.98605	−	4.57104i	0.273117	−	0.156326i
$856$	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	$0.678593\pi$
$860$	20.2201	+	0.0755644i	0.689501	+	0.00257673i
$861$	11.3945			0.388324
$862$			13.9311i			0.474495i
$863$	−39.5069	+	22.8093i	−1.34483	+	0.776438i	−0.987512	−	0.157544i	$-0.949642\pi$
$863$	−39.5069	+	22.8093i	−1.34483	+	0.776438i	−0.357319	+	0.933982i	$0.616309\pi$
$864$	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
$870$	6.35204	−	3.63577i	0.215354	−	0.123264i
$871$	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
$875$	−24.3499	+	41.1041i	−0.823178	+	1.38957i
$876$	−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	0.140881	+	0.990027i	$0.455007\pi$
$881$	−23.3579	+	40.4571i	−0.786948	+	1.36303i	−0.927829	+	0.373007i	$0.878327\pi$
$882$			11.2597i			0.379135i
$883$	−1.18063	−	0.681638i	−0.0397314	−	0.0229389i	0.480003	−	0.877267i	$-0.340636\pi$
$883$	−1.18063	−	0.681638i	−0.0397314	−	0.0229389i	−0.519734	+	0.854328i	$0.673969\pi$
$884$	4.54763	−	7.87672i	0.152953	−	0.264923i
$885$	−0.123360	−	0.215521i	−0.00414669	−	0.00724467i
$886$	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
$890$	19.6640	+	0.0734861i	0.659139	+	0.00246326i
$891$	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
$895$	22.0809	−	12.6386i	0.738084	−	0.422463i
$896$	4.27314			0.142756
$897$	7.47062	−	4.31317i	0.249437	−	0.144012i
$898$			32.6815i			1.09059i
$899$	−8.79874			−0.293454
$900$	2.53229	−	4.31132i	0.0844098	−	0.143711i
$901$	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
$905$	−0.165786	+	44.3624i	−0.00551091	+	1.47466i
$906$	4.81068	−	8.33235i	0.159824	−	0.276824i
$907$	−18.0725	−	10.4341i	−0.600087	−	0.346460i	0.168989	−	0.985618i	$-0.445950\pi$
$907$	−18.0725	−	10.4341i	−0.600087	−	0.346460i	−0.769076	+	0.639158i	$0.779283\pi$
$908$	5.15116	−	2.97402i	0.170947	−	0.0986964i
$909$	−3.60388	−	6.24210i	−0.119533	−	0.207037i
$910$	−11.9487	−	0.0446535i	−0.396097	−	0.00148025i
$911$	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	$0.202479\pi$
$920$	−13.3870	+	7.66241i	−0.441355	+	0.252622i
$921$	−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
$925$	−14.8029	−	26.5683i	−0.486715	−	0.873561i
$926$	−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	0.263985	+	0.964527i	$0.414963\pi$
$929$	−21.4366	+	37.1293i	−0.703312	+	1.21817i	−0.967297	+	0.253645i	$0.918370\pi$
$930$	−5.21680	+	2.98598i	−0.171066	+	0.0979142i
$931$	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	−0.556265	+	0.831005i	$0.687766\pi$
$937$	−47.5708	+	27.4650i	−1.55407	+	0.897242i	−0.997804	+	0.0662376i	$0.978900\pi$
$938$	−18.9961	−	10.9674i	−0.620246	−	0.358099i
$939$	−8.87605			−0.289659
$940$	10.3379	+	0.0386337i	0.337186	+	0.00126009i
$941$	11.3474	+	19.6542i	0.369913	+	0.640709i	0.989552	−	0.144179i	$-0.0460540\pi$
$941$	11.3474	+	19.6542i	0.369913	+	0.640709i	−0.619638	+	0.784888i	$0.712721\pi$
$942$	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
$945$	0.0357078	−	9.55497i	0.00116157	−	0.310823i
$946$	−26.8511	−	46.5075i	−0.873006	−	1.51209i
$947$	6.95546	−	4.01574i	0.226022	−	0.130494i	−0.382713	−	0.923867i	$-0.625010\pi$
$947$	6.95546	−	4.01574i	0.226022	−	0.130494i	0.608736	+	0.793373i	$0.291677\pi$
$948$			6.83733i			0.222066i
$949$	2.10187	−	3.64055i	0.0682297	−	0.118177i
$950$	−17.7416	−	10.4207i	−0.575614	−	0.338092i
$951$	−4.41661			−0.143218
$952$			31.0792i			1.00728i
$953$	−40.2906	+	23.2618i	−1.30514	+	0.753524i	−0.981281	−	0.192581i	$-0.938314\pi$
$953$	−40.2906	+	23.2618i	−1.30514	+	0.753524i	−0.323860	+	0.946105i	$0.604981\pi$
$954$	1.51960			0.0491988
$955$	21.5459	−	12.3324i	0.697208	−	0.399067i
$956$	−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
$960$	−2.23605	−	0.00835632i	−0.0721683	−	0.000269699i
$961$	−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
$965$	−27.9171	−	48.7738i	−0.898682	−	1.57008i
$966$	−14.7384	+	25.5277i	−0.474201	+	0.821340i
$967$	−32.0985	−	18.5321i	−1.03222	−	0.595951i	−0.114598	−	0.993412i	$-0.536558\pi$
$967$	−32.0985	−	18.5321i	−1.03222	−	0.595951i	−0.917619	+	0.397461i	$0.869891\pi$
$968$		−	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	0.907589	−	0.419859i	$-0.137921\pi$
$971$	2.81026	+	4.86752i	0.0901856	+	0.156206i	−0.817404	+	0.576066i	$0.804587\pi$
$972$			1.00000i			0.0320750i
$973$			38.3424i			1.22920i
$974$	6.44686	+	11.1663i	0.206571	+	0.357791i
$975$	6.25246	+	0.0467326i	0.200239	+	0.00149664i
$976$	12.2824			0.393149
$977$	−36.1619	+	20.8781i	−1.15692	+	0.667948i	−0.950564	−	0.310528i	$-0.899494\pi$
$977$	−36.1619	+	20.8781i	−1.15692	+	0.667948i	−0.206357	+	0.978477i	$0.566161\pi$
$978$	19.6684	−	11.3555i	0.628925	−	0.363110i
$979$	−26.1126	−	45.2284i	−0.834563	−	1.44550i
$980$	21.8513	−	12.5072i	0.698014	−	0.399528i
$981$	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	$-0.874976\pi$
$983$	−33.0554	+	19.0845i	−1.05430	+	0.608702i	−0.130452	+	0.991455i	$0.541643\pi$
$984$	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
$990$	−13.2792	−	0.0496256i	−0.422041	−	0.00157720i
$991$	−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
$995$	12.8040	−	7.32872i	0.405913	−	0.232336i
$996$	3.72981	−	6.46021i	0.118183	−	0.204700i
$997$	42.0769	−	24.2931i	1.33259	−	0.769371i	0.346893	−	0.937905i	$-0.387237\pi$
$997$	42.0769	−	24.2931i	1.33259	−	0.769371i	0.985696	+	0.168534i	$0.0539033\pi$
$998$			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.1099.14	yes	28
5.4	even	2	inner	1110.2.bb.d.1099.1	yes	28
37.10	even	3	inner	1110.2.bb.d.1009.1	✓	28
185.84	even	6	inner	1110.2.bb.d.1009.14	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.bb.d.1009.1	✓	28	37.10	even	3	inner
1110.2.bb.d.1009.14	yes	28	185.84	even	6	inner
1110.2.bb.d.1099.1	yes	28	5.4	even	2	inner
1110.2.bb.d.1099.14	yes	28	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(0.866025 + 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(1.94066 - 1.11079i) q^{5} +1.00000 q^{6} +(-3.70065 - 2.13657i) q^{7} -1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.866025 - 0.500000i) q^{2} +(0.866025 + 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(1.94066 - 1.11079i) 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} +(2.23605 + 0.00835632i) 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} +(0.00835632 - 2.23605i) q^{20} +(-2.13657 - 3.70065i) q^{21} +(-5.14305 + 2.96934i) q^{22} -6.89816i q^{23} +(0.500000 - 0.866025i) q^{24} +(2.53229 - 4.31132i) q^{25} +1.25053 q^{26} +1.00000i q^{27} +(-3.70065 + 2.13657i) q^{28} +3.27314 q^{29} +(1.94066 - 1.11079i) q^{30} -2.68816 q^{31} +(-0.866025 - 0.500000i) q^{32} +(-5.14305 - 2.96934i) q^{33} +(3.63657 - 6.29873i) q^{34} +(-9.55497 - 0.0357078i) q^{35} +1.00000 q^{36} +(3.08237 - 5.24395i) q^{37} -4.11513i q^{38} +(0.625263 + 1.08299i) q^{39} +(-1.11079 - 1.94066i) 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} +(0.0373703 - 4.99986i) q^{50} +7.27314 q^{51} +(1.08299 - 0.625263i) q^{52} +(1.31601 - 0.759799i) q^{53} +(0.500000 + 0.866025i) q^{54} +(-11.5250 + 6.59663i) 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} +(2.79624 + 0.0104498i) q^{65} -5.93869 q^{66} +(4.44547 + 2.56660i) q^{67} -7.27314i q^{68} +(3.44908 - 5.97399i) q^{69} +(-8.29270 + 4.74656i) 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} +(2.23605 + 0.00835632i) 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} +(0.0343873 - 9.20164i) 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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