LMFDB - Embedded newform 1110.2.i.l.211.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1110,2,Mod(121,1110)]

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, 0, 4]))

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

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

chi := DirichletCharacter("1110.121");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1110 = 2 \cdot 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1110.i (of order $3$, 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:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-5})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 5x^{2} + 25 $ x^4 - 5*x^2 + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			211.2
Root			$1.93649 - 1.11803i$ of defining polynomial
Character	$\chi$	$=$	1110.211
Dual form			1110.2.i.l.121.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} -1.00000 q^{6} +(1.43649 - 2.48808i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} -1.00000 q^{6} +(1.43649 - 2.48808i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +1.00000 q^{10} -5.00000 q^{11} +(-0.500000 - 0.866025i) q^{12} +(0.500000 - 0.866025i) q^{13} +2.87298 q^{14} +(0.500000 + 0.866025i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-3.93649 - 6.81820i) q^{17} +(0.500000 - 0.866025i) q^{18} +(-3.87298 + 6.70820i) q^{19} +(0.500000 + 0.866025i) q^{20} +(1.43649 + 2.48808i) q^{21} +(-2.50000 - 4.33013i) q^{22} -6.00000 q^{23} +(0.500000 - 0.866025i) q^{24} +(-0.500000 - 0.866025i) q^{25} +1.00000 q^{26} +1.00000 q^{27} +(1.43649 + 2.48808i) q^{28} -3.87298 q^{29} +(-0.500000 + 0.866025i) q^{30} -7.74597 q^{31} +(0.500000 - 0.866025i) q^{32} +(2.50000 - 4.33013i) q^{33} +(3.93649 - 6.81820i) q^{34} +(-1.43649 - 2.48808i) q^{35} +1.00000 q^{36} +(-5.50000 + 2.59808i) q^{37} -7.74597 q^{38} +(0.500000 + 0.866025i) q^{39} +(-0.500000 + 0.866025i) q^{40} +(3.43649 - 5.95218i) q^{41} +(-1.43649 + 2.48808i) q^{42} +5.74597 q^{43} +(2.50000 - 4.33013i) q^{44} -1.00000 q^{45} +(-3.00000 - 5.19615i) q^{46} +4.74597 q^{47} +1.00000 q^{48} +(-0.627017 - 1.08602i) q^{49} +(0.500000 - 0.866025i) q^{50} +7.87298 q^{51} +(0.500000 + 0.866025i) q^{52} +(3.43649 + 5.95218i) q^{53} +(0.500000 + 0.866025i) q^{54} +(-2.50000 + 4.33013i) q^{55} +(-1.43649 + 2.48808i) q^{56} +(-3.87298 - 6.70820i) q^{57} +(-1.93649 - 3.35410i) q^{58} +(-2.50000 - 4.33013i) q^{59} -1.00000 q^{60} +(0.563508 - 0.976025i) q^{61} +(-3.87298 - 6.70820i) q^{62} -2.87298 q^{63} +1.00000 q^{64} +(-0.500000 - 0.866025i) q^{65} +5.00000 q^{66} +(-6.93649 + 12.0144i) q^{67} +7.87298 q^{68} +(3.00000 - 5.19615i) q^{69} +(1.43649 - 2.48808i) q^{70} +(4.30948 - 7.46423i) q^{71} +(0.500000 + 0.866025i) q^{72} +12.0000 q^{73} +(-5.00000 - 3.46410i) q^{74} +1.00000 q^{75} +(-3.87298 - 6.70820i) q^{76} +(-7.18246 + 12.4404i) q^{77} +(-0.500000 + 0.866025i) q^{78} +(7.74597 - 13.4164i) q^{79} -1.00000 q^{80} +(-0.500000 + 0.866025i) q^{81} +6.87298 q^{82} +(2.43649 + 4.22013i) q^{83} -2.87298 q^{84} -7.87298 q^{85} +(2.87298 + 4.97615i) q^{86} +(1.93649 - 3.35410i) q^{87} +5.00000 q^{88} +(1.87298 + 3.24410i) q^{89} +(-0.500000 - 0.866025i) q^{90} +(-1.43649 - 2.48808i) q^{91} +(3.00000 - 5.19615i) q^{92} +(3.87298 - 6.70820i) q^{93} +(2.37298 + 4.11013i) q^{94} +(3.87298 + 6.70820i) q^{95} +(0.500000 + 0.866025i) q^{96} -10.0000 q^{97} +(0.627017 - 1.08602i) q^{98} +(2.50000 + 4.33013i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + 2 q^{5} - 4 q^{6} - 2 q^{7} - 4 q^{8} - 2 q^{9}+O(q^{10}) $ 4 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 + 2 * q^5 - 4 * q^6 - 2 * q^7 - 4 * q^8 - 2 * q^9	$ 4 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + 2 q^{5} - 4 q^{6} - 2 q^{7} - 4 q^{8} - 2 q^{9} + 4 q^{10} - 20 q^{11} - 2 q^{12} + 2 q^{13} - 4 q^{14} + 2 q^{15} - 2 q^{16} - 8 q^{17} + 2 q^{18} + 2 q^{20} - 2 q^{21} - 10 q^{22} - 24 q^{23} + 2 q^{24} - 2 q^{25} + 4 q^{26} + 4 q^{27} - 2 q^{28} - 2 q^{30} + 2 q^{32} + 10 q^{33} + 8 q^{34} + 2 q^{35} + 4 q^{36} - 22 q^{37} + 2 q^{39} - 2 q^{40} + 6 q^{41} + 2 q^{42} - 8 q^{43} + 10 q^{44} - 4 q^{45} - 12 q^{46} - 12 q^{47} + 4 q^{48} - 18 q^{49} + 2 q^{50} + 16 q^{51} + 2 q^{52} + 6 q^{53} + 2 q^{54} - 10 q^{55} + 2 q^{56} - 10 q^{59} - 4 q^{60} + 10 q^{61} + 4 q^{63} + 4 q^{64} - 2 q^{65} + 20 q^{66} - 20 q^{67} + 16 q^{68} + 12 q^{69} - 2 q^{70} - 6 q^{71} + 2 q^{72} + 48 q^{73} - 20 q^{74} + 4 q^{75} + 10 q^{77} - 2 q^{78} - 4 q^{80} - 2 q^{81} + 12 q^{82} + 2 q^{83} + 4 q^{84} - 16 q^{85} - 4 q^{86} + 20 q^{88} - 8 q^{89} - 2 q^{90} + 2 q^{91} + 12 q^{92} - 6 q^{94} + 2 q^{96} - 40 q^{97} + 18 q^{98} + 10 q^{99}+O(q^{100}) $ 4 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 + 2 * q^5 - 4 * q^6 - 2 * q^7 - 4 * q^8 - 2 * q^9 + 4 * q^10 - 20 * q^11 - 2 * q^12 + 2 * q^13 - 4 * q^14 + 2 * q^15 - 2 * q^16 - 8 * q^17 + 2 * q^18 + 2 * q^20 - 2 * q^21 - 10 * q^22 - 24 * q^23 + 2 * q^24 - 2 * q^25 + 4 * q^26 + 4 * q^27 - 2 * q^28 - 2 * q^30 + 2 * q^32 + 10 * q^33 + 8 * q^34 + 2 * q^35 + 4 * q^36 - 22 * q^37 + 2 * q^39 - 2 * q^40 + 6 * q^41 + 2 * q^42 - 8 * q^43 + 10 * q^44 - 4 * q^45 - 12 * q^46 - 12 * q^47 + 4 * q^48 - 18 * q^49 + 2 * q^50 + 16 * q^51 + 2 * q^52 + 6 * q^53 + 2 * q^54 - 10 * q^55 + 2 * q^56 - 10 * q^59 - 4 * q^60 + 10 * q^61 + 4 * q^63 + 4 * q^64 - 2 * q^65 + 20 * q^66 - 20 * q^67 + 16 * q^68 + 12 * q^69 - 2 * q^70 - 6 * q^71 + 2 * q^72 + 48 * q^73 - 20 * q^74 + 4 * q^75 + 10 * q^77 - 2 * q^78 - 4 * q^80 - 2 * q^81 + 12 * q^82 + 2 * q^83 + 4 * q^84 - 16 * q^85 - 4 * q^86 + 20 * q^88 - 8 * q^89 - 2 * q^90 + 2 * q^91 + 12 * q^92 - 6 * q^94 + 2 * q^96 - 40 * q^97 + 18 * q^98 + 10 * 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 $

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$	−1.00000			−0.408248
$7$	1.43649	−	2.48808i	0.542943	−	0.940405i	−0.455790	−	0.890087i	$-0.650643\pi$
$7$	1.43649	−	2.48808i	0.542943	−	0.940405i	0.998733	−	0.0503174i	$-0.0160233\pi$
$8$	−1.00000			−0.353553
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	1.00000			0.316228
$11$	−5.00000			−1.50756			−0.753778	−	0.657129i	$-0.771771\pi$
$11$	−5.00000			−1.50756			−0.753778	+	0.657129i	$0.771771\pi$
$12$	−0.500000	−	0.866025i	−0.144338	−	0.250000i
$13$	0.500000	−	0.866025i	0.138675	−	0.240192i	−0.788320	−	0.615265i	$-0.789049\pi$
$13$	0.500000	−	0.866025i	0.138675	−	0.240192i	0.926995	+	0.375073i	$0.122382\pi$
$14$	2.87298			0.767837
$15$	0.500000	+	0.866025i	0.129099	+	0.223607i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−3.93649	−	6.81820i	−0.954739	−	1.65366i	−0.734963	−	0.678107i	$-0.762801\pi$
$17$	−3.93649	−	6.81820i	−0.954739	−	1.65366i	−0.219776	−	0.975550i	$-0.570533\pi$
$18$	0.500000	−	0.866025i	0.117851	−	0.204124i
$19$	−3.87298	+	6.70820i	−0.888523	+	1.53897i	−0.0469020	+	0.998899i	$0.514935\pi$
$19$	−3.87298	+	6.70820i	−0.888523	+	1.53897i	−0.841621	+	0.540068i	$0.818398\pi$
$20$	0.500000	+	0.866025i	0.111803	+	0.193649i
$21$	1.43649	+	2.48808i	0.313468	+	0.542943i
$22$	−2.50000	−	4.33013i	−0.533002	−	0.923186i
$23$	−6.00000			−1.25109			−0.625543	−	0.780189i	$-0.715123\pi$
$23$	−6.00000			−1.25109			−0.625543	+	0.780189i	$0.715123\pi$
$24$	0.500000	−	0.866025i	0.102062	−	0.176777i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	1.00000			0.196116
$27$	1.00000			0.192450
$28$	1.43649	+	2.48808i	0.271471	+	0.470202i
$29$	−3.87298			−0.719195			−0.359597	−	0.933108i	$-0.617086\pi$
$29$	−3.87298			−0.719195			−0.359597	+	0.933108i	$0.617086\pi$
$30$	−0.500000	+	0.866025i	−0.0912871	+	0.158114i
$31$	−7.74597			−1.39122			−0.695608	−	0.718421i	$-0.744865\pi$
$31$	−7.74597			−1.39122			−0.695608	+	0.718421i	$0.744865\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	2.50000	−	4.33013i	0.435194	−	0.753778i
$34$	3.93649	−	6.81820i	0.675103	−	1.16931i
$35$	−1.43649	−	2.48808i	−0.242811	−	0.420562i
$36$	1.00000			0.166667
$37$	−5.50000	+	2.59808i	−0.904194	+	0.427121i
$37$	−5.50000	+	2.59808i	−0.904194	+	0.427121i
$38$	−7.74597			−1.25656
$39$	0.500000	+	0.866025i	0.0800641	+	0.138675i
$40$	−0.500000	+	0.866025i	−0.0790569	+	0.136931i
$41$	3.43649	−	5.95218i	0.536690	−	0.929574i	−0.462390	−	0.886677i	$-0.653008\pi$
$41$	3.43649	−	5.95218i	0.536690	−	0.929574i	0.999079	−	0.0428972i	$-0.0136588\pi$
$42$	−1.43649	+	2.48808i	−0.221655	+	0.383919i
$43$	5.74597			0.876252			0.438126	−	0.898914i	$-0.355642\pi$
$43$	5.74597			0.876252			0.438126	+	0.898914i	$0.355642\pi$
$44$	2.50000	−	4.33013i	0.376889	−	0.652791i
$45$	−1.00000			−0.149071
$46$	−3.00000	−	5.19615i	−0.442326	−	0.766131i
$47$	4.74597			0.692270			0.346135	−	0.938185i	$-0.387494\pi$
$47$	4.74597			0.692270			0.346135	+	0.938185i	$0.387494\pi$
$48$	1.00000			0.144338
$49$	−0.627017	−	1.08602i	−0.0895738	−	0.155146i
$50$	0.500000	−	0.866025i	0.0707107	−	0.122474i
$51$	7.87298			1.10244
$52$	0.500000	+	0.866025i	0.0693375	+	0.120096i
$53$	3.43649	+	5.95218i	0.472038	+	0.817595i	0.999488	−	0.0319917i	$-0.0101850\pi$
$53$	3.43649	+	5.95218i	0.472038	+	0.817595i	−0.527450	+	0.849586i	$0.676852\pi$
$54$	0.500000	+	0.866025i	0.0680414	+	0.117851i
$55$	−2.50000	+	4.33013i	−0.337100	+	0.583874i
$56$	−1.43649	+	2.48808i	−0.191959	+	0.332483i
$57$	−3.87298	−	6.70820i	−0.512989	−	0.888523i
$58$	−1.93649	−	3.35410i	−0.254274	−	0.440415i
$59$	−2.50000	−	4.33013i	−0.325472	−	0.563735i	0.656136	−	0.754643i	$-0.272190\pi$
$59$	−2.50000	−	4.33013i	−0.325472	−	0.563735i	−0.981608	+	0.190909i	$0.938857\pi$
$60$	−1.00000			−0.129099
$61$	0.563508	−	0.976025i	0.0721498	−	0.124967i	−0.827693	−	0.561181i	$-0.810347\pi$
$61$	0.563508	−	0.976025i	0.0721498	−	0.124967i	0.899843	+	0.436213i	$0.143681\pi$
$62$	−3.87298	−	6.70820i	−0.491869	−	0.851943i
$63$	−2.87298			−0.361962
$64$	1.00000			0.125000
$65$	−0.500000	−	0.866025i	−0.0620174	−	0.107417i
$66$	5.00000			0.615457
$67$	−6.93649	+	12.0144i	−0.847427	+	1.46779i	0.0360691	+	0.999349i	$0.488516\pi$
$67$	−6.93649	+	12.0144i	−0.847427	+	1.46779i	−0.883496	+	0.468438i	$0.844817\pi$
$68$	7.87298			0.954739
$69$	3.00000	−	5.19615i	0.361158	−	0.625543i
$70$	1.43649	−	2.48808i	0.171694	−	0.297382i
$71$	4.30948	−	7.46423i	0.511441	−	0.885841i	−0.488471	−	0.872580i	$-0.662445\pi$
$71$	4.30948	−	7.46423i	0.511441	−	0.885841i	0.999912	−	0.0132612i	$-0.00422130\pi$
$72$	0.500000	+	0.866025i	0.0589256	+	0.102062i
$73$	12.0000			1.40449			0.702247	−	0.711934i	$-0.252180\pi$
$73$	12.0000			1.40449			0.702247	+	0.711934i	$0.252180\pi$
$74$	−5.00000	−	3.46410i	−0.581238	−	0.402694i
$75$	1.00000			0.115470
$76$	−3.87298	−	6.70820i	−0.444262	−	0.769484i
$77$	−7.18246	+	12.4404i	−0.818517	+	1.41771i
$78$	−0.500000	+	0.866025i	−0.0566139	+	0.0980581i
$79$	7.74597	−	13.4164i	0.871489	−	1.50946i	0.0110333	−	0.999939i	$-0.496488\pi$
$79$	7.74597	−	13.4164i	0.871489	−	1.50946i	0.860456	−	0.509525i	$-0.170179\pi$
$80$	−1.00000			−0.111803
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	6.87298			0.758994
$83$	2.43649	+	4.22013i	0.267440	+	0.463219i	0.968200	−	0.250178i	$-0.0804890\pi$
$83$	2.43649	+	4.22013i	0.267440	+	0.463219i	−0.700760	+	0.713397i	$0.747156\pi$
$84$	−2.87298			−0.313468
$85$	−7.87298			−0.853945
$86$	2.87298	+	4.97615i	0.309802	+	0.536592i
$87$	1.93649	−	3.35410i	0.207614	−	0.359597i
$88$	5.00000			0.533002
$89$	1.87298	+	3.24410i	0.198536	+	0.343874i	0.948054	−	0.318110i	$-0.103048\pi$
$89$	1.87298	+	3.24410i	0.198536	+	0.343874i	−0.749518	+	0.661984i	$0.769715\pi$
$90$	−0.500000	−	0.866025i	−0.0527046	−	0.0912871i
$91$	−1.43649	−	2.48808i	−0.150585	−	0.260821i
$92$	3.00000	−	5.19615i	0.312772	−	0.541736i
$93$	3.87298	−	6.70820i	0.401610	−	0.695608i
$94$	2.37298	+	4.11013i	0.244755	+	0.423927i
$95$	3.87298	+	6.70820i	0.397360	+	0.688247i
$96$	0.500000	+	0.866025i	0.0510310	+	0.0883883i
$97$	−10.0000			−1.01535			−0.507673	−	0.861550i	$-0.669494\pi$
$97$	−10.0000			−1.01535			−0.507673	+	0.861550i	$0.669494\pi$
$98$	0.627017	−	1.08602i	0.0633382	−	0.109705i
$99$	2.50000	+	4.33013i	0.251259	+	0.435194i
$100$	1.00000			0.100000
$101$	11.6190			1.15613			0.578064	−	0.815991i	$-0.303808\pi$
$101$	11.6190			1.15613			0.578064	+	0.815991i	$0.303808\pi$
$102$	3.93649	+	6.81820i	0.389771	+	0.675103i
$103$	7.12702			0.702246			0.351123	−	0.936329i	$-0.385800\pi$
$103$	7.12702			0.702246			0.351123	+	0.936329i	$0.385800\pi$
$104$	−0.500000	+	0.866025i	−0.0490290	+	0.0849208i
$105$	2.87298			0.280374
$106$	−3.43649	+	5.95218i	−0.333782	+	0.578127i
$107$	6.43649	−	11.1483i	0.622239	−	1.07775i	−0.366829	−	0.930289i	$-0.619556\pi$
$107$	6.43649	−	11.1483i	0.622239	−	1.07775i	0.989068	−	0.147461i	$-0.0471102\pi$
$108$	−0.500000	+	0.866025i	−0.0481125	+	0.0833333i
$109$	−9.30948	−	16.1245i	−0.891686	−	1.54445i	−0.837853	−	0.545895i	$-0.816190\pi$
$109$	−9.30948	−	16.1245i	−0.891686	−	1.54445i	−0.0538327	−	0.998550i	$-0.517144\pi$
$110$	−5.00000			−0.476731
$111$	0.500000	−	6.06218i	0.0474579	−	0.575396i
$112$	−2.87298			−0.271471
$113$	−3.80948	−	6.59820i	−0.358365	−	0.620707i	0.629323	−	0.777144i	$-0.283332\pi$
$113$	−3.80948	−	6.59820i	−0.358365	−	0.620707i	−0.987688	+	0.156437i	$0.949999\pi$
$114$	3.87298	−	6.70820i	0.362738	−	0.628281i
$115$	−3.00000	+	5.19615i	−0.279751	+	0.484544i
$116$	1.93649	−	3.35410i	0.179799	−	0.311421i
$117$	−1.00000			−0.0924500
$118$	2.50000	−	4.33013i	0.230144	−	0.398621i
$119$	−22.6190			−2.07348
$120$	−0.500000	−	0.866025i	−0.0456435	−	0.0790569i
$121$	14.0000			1.27273
$122$	1.12702			0.102035
$123$	3.43649	+	5.95218i	0.309858	+	0.536690i
$124$	3.87298	−	6.70820i	0.347804	−	0.602414i
$125$	−1.00000			−0.0894427
$126$	−1.43649	−	2.48808i	−0.127973	−	0.221655i
$127$	3.43649	+	5.95218i	0.304939	+	0.528170i	0.977248	−	0.212101i	$-0.0680305\pi$
$127$	3.43649	+	5.95218i	0.304939	+	0.528170i	−0.672308	+	0.740271i	$0.734697\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	−2.87298	+	4.97615i	−0.252952	+	0.438126i
$130$	0.500000	−	0.866025i	0.0438529	−	0.0759555i
$131$	−0.500000	−	0.866025i	−0.0436852	−	0.0756650i	0.843356	−	0.537355i	$-0.180577\pi$
$131$	−0.500000	−	0.866025i	−0.0436852	−	0.0756650i	−0.887041	+	0.461690i	$0.847243\pi$
$132$	2.50000	+	4.33013i	0.217597	+	0.376889i
$133$	11.1270	+	19.2726i	0.964835	+	1.67114i
$134$	−13.8730			−1.19844
$135$	0.500000	−	0.866025i	0.0430331	−	0.0745356i
$136$	3.93649	+	6.81820i	0.337551	+	0.584656i
$137$	−10.1270			−0.865209			−0.432605	−	0.901584i	$-0.642405\pi$
$137$	−10.1270			−0.865209			−0.432605	+	0.901584i	$0.642405\pi$
$138$	6.00000			0.510754
$139$	2.87298	+	4.97615i	0.243683	+	0.422072i	0.961761	−	0.273892i	$-0.0883109\pi$
$139$	2.87298	+	4.97615i	0.243683	+	0.422072i	−0.718077	+	0.695963i	$0.754978\pi$
$140$	2.87298			0.242811
$141$	−2.37298	+	4.11013i	−0.199841	+	0.346135i
$142$	8.61895			0.723286
$143$	−2.50000	+	4.33013i	−0.209061	+	0.362103i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	−1.93649	+	3.35410i	−0.160817	+	0.278543i
$146$	6.00000	+	10.3923i	0.496564	+	0.860073i
$147$	1.25403			0.103431
$148$	0.500000	−	6.06218i	0.0410997	−	0.498308i
$149$	−13.8730			−1.13652			−0.568260	−	0.822849i	$-0.692383\pi$
$149$	−13.8730			−1.13652			−0.568260	+	0.822849i	$0.692383\pi$
$150$	0.500000	+	0.866025i	0.0408248	+	0.0707107i
$151$	−6.00000	+	10.3923i	−0.488273	+	0.845714i	−0.999909	−	0.0134886i	$-0.995706\pi$
$151$	−6.00000	+	10.3923i	−0.488273	+	0.845714i	0.511636	+	0.859202i	$0.329040\pi$
$152$	3.87298	−	6.70820i	0.314140	−	0.544107i
$153$	−3.93649	+	6.81820i	−0.318246	+	0.551219i
$154$	−14.3649			−1.15756
$155$	−3.87298	+	6.70820i	−0.311086	+	0.538816i
$156$	−1.00000			−0.0800641
$157$	−4.37298	−	7.57423i	−0.349002	−	0.604489i	0.637070	−	0.770806i	$-0.280146\pi$
$157$	−4.37298	−	7.57423i	−0.349002	−	0.604489i	−0.986072	+	0.166316i	$0.946813\pi$
$158$	15.4919			1.23247
$159$	−6.87298			−0.545063
$160$	−0.500000	−	0.866025i	−0.0395285	−	0.0684653i
$161$	−8.61895	+	14.9285i	−0.679268	+	1.17653i
$162$	−1.00000			−0.0785674
$163$	8.93649	+	15.4785i	0.699960	+	1.21237i	0.968480	+	0.249092i	$0.0801322\pi$
$163$	8.93649	+	15.4785i	0.699960	+	1.21237i	−0.268520	+	0.963274i	$0.586534\pi$
$164$	3.43649	+	5.95218i	0.268345	+	0.464787i
$165$	−2.50000	−	4.33013i	−0.194625	−	0.337100i
$166$	−2.43649	+	4.22013i	−0.189108	+	0.327545i
$167$	4.37298	−	7.57423i	0.338392	−	0.586111i	−0.645739	−	0.763558i	$-0.723450\pi$
$167$	4.37298	−	7.57423i	0.338392	−	0.586111i	0.984130	+	0.177447i	$0.0567838\pi$
$168$	−1.43649	−	2.48808i	−0.110828	−	0.191959i
$169$	6.00000	+	10.3923i	0.461538	+	0.799408i
$170$	−3.93649	−	6.81820i	−0.301915	−	0.522932i
$171$	7.74597			0.592349
$172$	−2.87298	+	4.97615i	−0.219063	+	0.379428i
$173$	−8.30948	−	14.3924i	−0.631758	−	1.09424i	−0.987192	−	0.159535i	$-0.949000\pi$
$173$	−8.30948	−	14.3924i	−0.631758	−	1.09424i	0.355435	−	0.934701i	$-0.384333\pi$
$174$	3.87298			0.293610
$175$	−2.87298			−0.217177
$176$	2.50000	+	4.33013i	0.188445	+	0.326396i
$177$	5.00000			0.375823
$178$	−1.87298	+	3.24410i	−0.140386	+	0.243156i
$179$	−10.0000			−0.747435			−0.373718	−	0.927543i	$-0.621917\pi$
$179$	−10.0000			−0.747435			−0.373718	+	0.927543i	$0.621917\pi$
$180$	0.500000	−	0.866025i	0.0372678	−	0.0645497i
$181$	−1.00000	+	1.73205i	−0.0743294	+	0.128742i	−0.900794	−	0.434246i	$-0.857015\pi$
$181$	−1.00000	+	1.73205i	−0.0743294	+	0.128742i	0.826465	+	0.562988i	$0.190348\pi$
$182$	1.43649	−	2.48808i	0.106480	−	0.184429i
$183$	0.563508	+	0.976025i	0.0416557	+	0.0721498i
$184$	6.00000			0.442326
$185$	−0.500000	+	6.06218i	−0.0367607	+	0.445700i
$186$	7.74597			0.567962
$187$	19.6825	+	34.0910i	1.43932	+	2.49298i
$188$	−2.37298	+	4.11013i	−0.173068	+	0.299762i
$189$	1.43649	−	2.48808i	0.104489	−	0.180981i
$190$	−3.87298	+	6.70820i	−0.280976	+	0.486664i
$191$	−18.6190			−1.34722			−0.673610	−	0.739087i	$-0.735257\pi$
$191$	−18.6190			−1.34722			−0.673610	+	0.739087i	$0.735257\pi$
$192$	−0.500000	+	0.866025i	−0.0360844	+	0.0625000i
$193$	6.61895			0.476442			0.238221	−	0.971211i	$-0.423436\pi$
$193$	6.61895			0.476442			0.238221	+	0.971211i	$0.423436\pi$
$194$	−5.00000	−	8.66025i	−0.358979	−	0.621770i
$195$	1.00000			0.0716115
$196$	1.25403			0.0895738
$197$	−6.12702	−	10.6123i	−0.436532	−	0.756095i	0.560887	−	0.827892i	$-0.310460\pi$
$197$	−6.12702	−	10.6123i	−0.436532	−	0.756095i	−0.997419	+	0.0717967i	$0.977127\pi$
$198$	−2.50000	+	4.33013i	−0.177667	+	0.307729i
$199$	−14.1270			−1.00144			−0.500719	−	0.865610i	$-0.666931\pi$
$199$	−14.1270			−1.00144			−0.500719	+	0.865610i	$0.666931\pi$
$200$	0.500000	+	0.866025i	0.0353553	+	0.0612372i
$201$	−6.93649	−	12.0144i	−0.489262	−	0.847427i
$202$	5.80948	+	10.0623i	0.408753	+	0.707981i
$203$	−5.56351	+	9.63628i	−0.390482	+	0.676334i
$204$	−3.93649	+	6.81820i	−0.275610	+	0.477370i
$205$	−3.43649	−	5.95218i	−0.240015	−	0.415718i
$206$	3.56351	+	6.17218i	0.248281	+	0.430036i
$207$	3.00000	+	5.19615i	0.208514	+	0.361158i
$208$	−1.00000			−0.0693375
$209$	19.3649	−	33.5410i	1.33950	−	2.32008i
$210$	1.43649	+	2.48808i	0.0991273	+	0.171694i
$211$	17.7460			1.22168			0.610841	−	0.791753i	$-0.290831\pi$
$211$	17.7460			1.22168			0.610841	+	0.791753i	$0.290831\pi$
$212$	−6.87298			−0.472038
$213$	4.30948	+	7.46423i	0.295280	+	0.511441i
$214$	12.8730			0.879979
$215$	2.87298	−	4.97615i	0.195936	−	0.339371i
$216$	−1.00000			−0.0680414
$217$	−11.1270	+	19.2726i	−0.755351	+	1.30831i
$218$	9.30948	−	16.1245i	0.630517	−	1.09209i
$219$	−6.00000	+	10.3923i	−0.405442	+	0.702247i
$220$	−2.50000	−	4.33013i	−0.168550	−	0.291937i
$221$	−7.87298			−0.529594
$222$	5.50000	−	2.59808i	0.369136	−	0.174371i
$223$	−23.4919			−1.57314			−0.786568	−	0.617504i	$-0.788144\pi$
$223$	−23.4919			−1.57314			−0.786568	+	0.617504i	$0.788144\pi$
$224$	−1.43649	−	2.48808i	−0.0959796	−	0.166242i
$225$	−0.500000	+	0.866025i	−0.0333333	+	0.0577350i
$226$	3.80948	−	6.59820i	0.253403	−	0.438906i
$227$	−12.1825	+	21.1006i	−0.808578	+	1.40050i	0.105271	+	0.994444i	$0.466429\pi$
$227$	−12.1825	+	21.1006i	−0.808578	+	1.40050i	−0.913849	+	0.406055i	$0.866904\pi$
$228$	7.74597			0.512989
$229$	10.3095	−	17.8565i	0.681269	−	1.17999i	−0.293324	−	0.956013i	$-0.594762\pi$
$229$	10.3095	−	17.8565i	0.681269	−	1.17999i	0.974594	−	0.223980i	$-0.0719051\pi$
$230$	−6.00000			−0.395628
$231$	−7.18246	−	12.4404i	−0.472571	−	0.818517i
$232$	3.87298			0.254274
$233$	−2.00000			−0.131024			−0.0655122	−	0.997852i	$-0.520868\pi$
$233$	−2.00000			−0.131024			−0.0655122	+	0.997852i	$0.520868\pi$
$234$	−0.500000	−	0.866025i	−0.0326860	−	0.0566139i
$235$	2.37298	−	4.11013i	0.154796	−	0.268115i
$236$	5.00000			0.325472
$237$	7.74597	+	13.4164i	0.503155	+	0.871489i
$238$	−11.3095	−	19.5886i	−0.733084	−	1.26974i
$239$	−0.872983	−	1.51205i	−0.0564686	−	0.0978065i	0.836409	−	0.548105i	$-0.184651\pi$
$239$	−0.872983	−	1.51205i	−0.0564686	−	0.0978065i	−0.892878	+	0.450299i	$0.851317\pi$
$240$	0.500000	−	0.866025i	0.0322749	−	0.0559017i
$241$	10.1190	−	17.5265i	0.651819	−	1.12898i	−0.330862	−	0.943679i	$-0.607340\pi$
$241$	10.1190	−	17.5265i	0.651819	−	1.12898i	0.982681	−	0.185304i	$-0.0593271\pi$
$242$	7.00000	+	12.1244i	0.449977	+	0.779383i
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	0.563508	+	0.976025i	0.0360749	+	0.0624836i
$245$	−1.25403			−0.0801172
$246$	−3.43649	+	5.95218i	−0.219103	+	0.379497i
$247$	3.87298	+	6.70820i	0.246432	+	0.426833i
$248$	7.74597			0.491869
$249$	−4.87298			−0.308813
$250$	−0.500000	−	0.866025i	−0.0316228	−	0.0547723i
$251$	−0.491933			−0.0310506			−0.0155253	−	0.999879i	$-0.504942\pi$
$251$	−0.491933			−0.0310506			−0.0155253	+	0.999879i	$0.504942\pi$
$252$	1.43649	−	2.48808i	0.0904905	−	0.156734i
$253$	30.0000			1.88608
$254$	−3.43649	+	5.95218i	−0.215625	+	0.373473i
$255$	3.93649	−	6.81820i	0.246513	−	0.426972i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	0.190525	+	0.329999i	0.0118846	+	0.0205848i	0.871907	−	0.489672i	$-0.162884\pi$
$257$	0.190525	+	0.329999i	0.0118846	+	0.0205848i	−0.860022	+	0.510257i	$0.829550\pi$
$258$	−5.74597			−0.357728
$259$	−1.43649	+	17.4165i	−0.0892592	+	1.08221i
$260$	1.00000			0.0620174
$261$	1.93649	+	3.35410i	0.119866	+	0.207614i
$262$	0.500000	−	0.866025i	0.0308901	−	0.0535032i
$263$	−3.87298	+	6.70820i	−0.238818	+	0.413646i	−0.960376	−	0.278709i	$-0.910093\pi$
$263$	−3.87298	+	6.70820i	−0.238818	+	0.413646i	0.721557	+	0.692355i	$0.243427\pi$
$264$	−2.50000	+	4.33013i	−0.153864	+	0.266501i
$265$	6.87298			0.422204
$266$	−11.1270	+	19.2726i	−0.682241	+	1.18168i
$267$	−3.74597			−0.229249
$268$	−6.93649	−	12.0144i	−0.423714	−	0.733894i
$269$	7.74597			0.472280			0.236140	−	0.971719i	$-0.424118\pi$
$269$	7.74597			0.472280			0.236140	+	0.971719i	$0.424118\pi$
$270$	1.00000			0.0608581
$271$	−8.93649	−	15.4785i	−0.542853	−	0.940249i	−0.998739	−	0.0502109i	$-0.984011\pi$
$271$	−8.93649	−	15.4785i	−0.542853	−	0.940249i	0.455885	−	0.890038i	$-0.349323\pi$
$272$	−3.93649	+	6.81820i	−0.238685	+	0.413414i
$273$	2.87298			0.173881
$274$	−5.06351	−	8.77025i	−0.305898	−	0.529830i
$275$	2.50000	+	4.33013i	0.150756	+	0.261116i
$276$	3.00000	+	5.19615i	0.180579	+	0.312772i
$277$	8.11895	−	14.0624i	0.487820	−	0.844930i	−0.512081	−	0.858937i	$-0.671125\pi$
$277$	8.11895	−	14.0624i	0.487820	−	0.844930i	0.999902	+	0.0140071i	$0.00445875\pi$
$278$	−2.87298	+	4.97615i	−0.172310	+	0.298450i
$279$	3.87298	+	6.70820i	0.231869	+	0.401610i
$280$	1.43649	+	2.48808i	0.0858468	+	0.148691i
$281$	1.87298	+	3.24410i	0.111733	+	0.193527i	0.916469	−	0.400106i	$-0.131027\pi$
$281$	1.87298	+	3.24410i	0.111733	+	0.193527i	−0.804736	+	0.593633i	$0.797693\pi$
$282$	−4.74597			−0.282618
$283$	−2.93649	+	5.08615i	−0.174556	+	0.302340i	−0.940008	−	0.341153i	$-0.889182\pi$
$283$	−2.93649	+	5.08615i	−0.174556	+	0.302340i	0.765451	+	0.643494i	$0.222516\pi$
$284$	4.30948	+	7.46423i	0.255720	+	0.442921i
$285$	−7.74597			−0.458831
$286$	−5.00000			−0.295656
$287$	−9.87298	−	17.1005i	−0.582784	−	1.00941i
$288$	−1.00000			−0.0589256
$289$	−22.4919	+	38.9572i	−1.32305	+	2.29160i
$290$	−3.87298			−0.227429
$291$	5.00000	−	8.66025i	0.293105	−	0.507673i
$292$	−6.00000	+	10.3923i	−0.351123	+	0.608164i
$293$	−5.87298	+	10.1723i	−0.343103	+	0.594272i	−0.985007	−	0.172513i	$-0.944811\pi$
$293$	−5.87298	+	10.1723i	−0.343103	+	0.594272i	0.641904	+	0.766785i	$0.278145\pi$
$294$	0.627017	+	1.08602i	0.0365684	+	0.0633382i
$295$	−5.00000			−0.291111
$296$	5.50000	−	2.59808i	0.319681	−	0.151010i
$297$	−5.00000			−0.290129
$298$	−6.93649	−	12.0144i	−0.401820	−	0.695973i
$299$	−3.00000	+	5.19615i	−0.173494	+	0.300501i
$300$	−0.500000	+	0.866025i	−0.0288675	+	0.0500000i
$301$	8.25403	−	14.2964i	0.475755	−	0.824031i
$302$	−12.0000			−0.690522
$303$	−5.80948	+	10.0623i	−0.333746	+	0.578064i
$304$	7.74597			0.444262
$305$	−0.563508	−	0.976025i	−0.0322664	−	0.0558870i
$306$	−7.87298			−0.450069
$307$	−7.74597			−0.442086			−0.221043	−	0.975264i	$-0.570946\pi$
$307$	−7.74597			−0.442086			−0.221043	+	0.975264i	$0.570946\pi$
$308$	−7.18246	−	12.4404i	−0.409259	−	0.708857i
$309$	−3.56351	+	6.17218i	−0.202721	+	0.351123i
$310$	−7.74597			−0.439941
$311$	−2.30948	−	4.00013i	−0.130958	−	0.226826i	0.793088	−	0.609107i	$-0.208472\pi$
$311$	−2.30948	−	4.00013i	−0.130958	−	0.226826i	−0.924046	+	0.382281i	$0.875139\pi$
$312$	−0.500000	−	0.866025i	−0.0283069	−	0.0490290i
$313$	9.87298	+	17.1005i	0.558054	+	0.966578i	0.997659	+	0.0683866i	$0.0217851\pi$
$313$	9.87298	+	17.1005i	0.558054	+	0.966578i	−0.439605	+	0.898191i	$0.644882\pi$
$314$	4.37298	−	7.57423i	0.246782	−	0.427438i
$315$	−1.43649	+	2.48808i	−0.0809371	+	0.140187i
$316$	7.74597	+	13.4164i	0.435745	+	0.754732i
$317$	6.30948	+	10.9283i	0.354375	+	0.613796i	0.987011	−	0.160653i	$-0.0513602\pi$
$317$	6.30948	+	10.9283i	0.354375	+	0.613796i	−0.632635	+	0.774450i	$0.718027\pi$
$318$	−3.43649	−	5.95218i	−0.192709	−	0.333782i
$319$	19.3649			1.08423
$320$	0.500000	−	0.866025i	0.0279508	−	0.0484123i
$321$	6.43649	+	11.1483i	0.359250	+	0.622239i
$322$	−17.2379			−0.960631
$323$	60.9839			3.39323
$324$	−0.500000	−	0.866025i	−0.0277778	−	0.0481125i
$325$	−1.00000			−0.0554700
$326$	−8.93649	+	15.4785i	−0.494946	+	0.857272i
$327$	18.6190			1.02963
$328$	−3.43649	+	5.95218i	−0.189749	+	0.328654i
$329$	6.81754	−	11.8083i	0.375863	−	0.651014i
$330$	2.50000	−	4.33013i	0.137620	−	0.238366i
$331$	−1.56351	−	2.70808i	−0.0859382	−	0.148849i	0.819852	−	0.572575i	$-0.194055\pi$
$331$	−1.56351	−	2.70808i	−0.0859382	−	0.148849i	−0.905791	+	0.423726i	$0.860722\pi$
$332$	−4.87298			−0.267440
$333$	5.00000	+	3.46410i	0.273998	+	0.189832i
$334$	8.74597			0.478558
$335$	6.93649	+	12.0144i	0.378981	+	0.656414i
$336$	1.43649	−	2.48808i	0.0783670	−	0.135736i
$337$	13.3095	−	23.0527i	0.725013	−	1.25576i	−0.233955	−	0.972247i	$-0.575167\pi$
$337$	13.3095	−	23.0527i	0.725013	−	1.25576i	0.958969	−	0.283513i	$-0.0914997\pi$
$338$	−6.00000	+	10.3923i	−0.326357	+	0.565267i
$339$	7.61895			0.413805
$340$	3.93649	−	6.81820i	0.213486	−	0.369769i
$341$	38.7298			2.09734
$342$	3.87298	+	6.70820i	0.209427	+	0.362738i
$343$	16.5081			0.891352
$344$	−5.74597			−0.309802
$345$	−3.00000	−	5.19615i	−0.161515	−	0.279751i
$346$	8.30948	−	14.3924i	0.446720	−	0.773742i
$347$	−21.4919			−1.15375			−0.576874	−	0.816833i	$-0.695728\pi$
$347$	−21.4919			−1.15375			−0.576874	+	0.816833i	$0.695728\pi$
$348$	1.93649	+	3.35410i	0.103807	+	0.179799i
$349$	−15.4919	−	26.8328i	−0.829264	−	1.43633i	−0.898616	−	0.438735i	$-0.855427\pi$
$349$	−15.4919	−	26.8328i	−0.829264	−	1.43633i	0.0693521	−	0.997592i	$-0.477907\pi$
$350$	−1.43649	−	2.48808i	−0.0767837	−	0.132993i
$351$	0.500000	−	0.866025i	0.0266880	−	0.0462250i
$352$	−2.50000	+	4.33013i	−0.133250	+	0.230797i
$353$	−5.00000	−	8.66025i	−0.266123	−	0.460939i	0.701734	−	0.712439i	$-0.252409\pi$
$353$	−5.00000	−	8.66025i	−0.266123	−	0.460939i	−0.967857	+	0.251500i	$0.919076\pi$
$354$	2.50000	+	4.33013i	0.132874	+	0.230144i
$355$	−4.30948	−	7.46423i	−0.228723	−	0.396160i
$356$	−3.74597			−0.198536
$357$	11.3095	−	19.5886i	0.598561	−	1.03674i
$358$	−5.00000	−	8.66025i	−0.264258	−	0.457709i
$359$	−19.7460			−1.04215			−0.521076	−	0.853510i	$-0.674469\pi$
$359$	−19.7460			−1.04215			−0.521076	+	0.853510i	$0.674469\pi$
$360$	1.00000			0.0527046
$361$	−20.5000	−	35.5070i	−1.07895	−	1.86879i
$362$	−2.00000			−0.105118
$363$	−7.00000	+	12.1244i	−0.367405	+	0.636364i
$364$	2.87298			0.150585
$365$	6.00000	−	10.3923i	0.314054	−	0.543958i
$366$	−0.563508	+	0.976025i	−0.0294551	+	0.0510176i
$367$	−8.87298	+	15.3685i	−0.463166	+	0.802227i	−0.999117	−	0.0420223i	$-0.986620\pi$
$367$	−8.87298	+	15.3685i	−0.463166	+	0.802227i	0.535951	+	0.844249i	$0.319953\pi$
$368$	3.00000	+	5.19615i	0.156386	+	0.270868i
$369$	−6.87298			−0.357793
$370$	−5.50000	+	2.59808i	−0.285931	+	0.135068i
$371$	19.7460			1.02516
$372$	3.87298	+	6.70820i	0.200805	+	0.347804i
$373$	−4.87298	+	8.44025i	−0.252314	+	0.437020i	−0.964162	−	0.265313i	$-0.914525\pi$
$373$	−4.87298	+	8.44025i	−0.252314	+	0.437020i	0.711849	+	0.702333i	$0.247858\pi$
$374$	−19.6825	+	34.0910i	−1.01776	+	1.76280i
$375$	0.500000	−	0.866025i	0.0258199	−	0.0447214i
$376$	−4.74597			−0.244755
$377$	−1.93649	+	3.35410i	−0.0997344	+	0.172745i
$378$	2.87298			0.147770
$379$	−6.30948	−	10.9283i	−0.324096	−	0.561351i	0.657233	−	0.753687i	$-0.271727\pi$
$379$	−6.30948	−	10.9283i	−0.324096	−	0.561351i	−0.981329	+	0.192337i	$0.938393\pi$
$380$	−7.74597			−0.397360
$381$	−6.87298			−0.352114
$382$	−9.30948	−	16.1245i	−0.476314	−	0.825000i
$383$	5.37298	−	9.30628i	0.274547	−	0.475529i	−0.695474	−	0.718551i	$-0.744806\pi$
$383$	5.37298	−	9.30628i	0.274547	−	0.475529i	0.970021	+	0.243023i	$0.0781389\pi$
$384$	−1.00000			−0.0510310
$385$	7.18246	+	12.4404i	0.366052	+	0.634021i
$386$	3.30948	+	5.73218i	0.168448	+	0.291760i
$387$	−2.87298	−	4.97615i	−0.146042	−	0.252952i
$388$	5.00000	−	8.66025i	0.253837	−	0.439658i
$389$	1.87298	−	3.24410i	0.0949640	−	0.164483i	−0.814630	−	0.579982i	$-0.803060\pi$
$389$	1.87298	−	3.24410i	0.0949640	−	0.164483i	0.909594	+	0.415499i	$0.136393\pi$
$390$	0.500000	+	0.866025i	0.0253185	+	0.0438529i
$391$	23.6190	+	40.9092i	1.19446	+	2.06887i
$392$	0.627017	+	1.08602i	0.0316691	+	0.0548525i
$393$	1.00000			0.0504433
$394$	6.12702	−	10.6123i	0.308675	−	0.534640i
$395$	−7.74597	−	13.4164i	−0.389742	−	0.675053i
$396$	−5.00000			−0.251259
$397$	−20.2379			−1.01571			−0.507856	−	0.861442i	$-0.669562\pi$
$397$	−20.2379			−1.01571			−0.507856	+	0.861442i	$0.669562\pi$
$398$	−7.06351	−	12.2344i	−0.354062	−	0.613253i
$399$	−22.2540			−1.11410
$400$	−0.500000	+	0.866025i	−0.0250000	+	0.0433013i
$401$	−20.6190			−1.02966			−0.514831	−	0.857292i	$-0.672145\pi$
$401$	−20.6190			−1.02966			−0.514831	+	0.857292i	$0.672145\pi$
$402$	6.93649	−	12.0144i	0.345961	−	0.599222i
$403$	−3.87298	+	6.70820i	−0.192927	+	0.334159i
$404$	−5.80948	+	10.0623i	−0.289032	+	0.500618i
$405$	0.500000	+	0.866025i	0.0248452	+	0.0430331i
$406$	−11.1270			−0.552225
$407$	27.5000	−	12.9904i	1.36312	−	0.643909i
$408$	−7.87298			−0.389771
$409$	−16.1190	−	27.9188i	−0.797031	−	1.38050i	−0.921542	−	0.388280i	$-0.873069\pi$
$409$	−16.1190	−	27.9188i	−0.797031	−	1.38050i	0.124511	−	0.992218i	$-0.460264\pi$
$410$	3.43649	−	5.95218i	0.169716	−	0.293957i
$411$	5.06351	−	8.77025i	0.249764	−	0.432605i
$412$	−3.56351	+	6.17218i	−0.175561	+	0.304081i
$413$	−14.3649			−0.706851
$414$	−3.00000	+	5.19615i	−0.147442	+	0.255377i
$415$	4.87298			0.239205
$416$	−0.500000	−	0.866025i	−0.0245145	−	0.0424604i
$417$	−5.74597			−0.281381
$418$	38.7298			1.89434
$419$	−7.00000	−	12.1244i	−0.341972	−	0.592314i	0.642827	−	0.766012i	$-0.277762\pi$
$419$	−7.00000	−	12.1244i	−0.341972	−	0.592314i	−0.984799	+	0.173698i	$0.944428\pi$
$420$	−1.43649	+	2.48808i	−0.0700936	+	0.121406i
$421$	−8.61895			−0.420062			−0.210031	−	0.977695i	$-0.567356\pi$
$421$	−8.61895			−0.420062			−0.210031	+	0.977695i	$0.567356\pi$
$422$	8.87298	+	15.3685i	0.431930	+	0.748125i
$423$	−2.37298	−	4.11013i	−0.115378	−	0.199841i
$424$	−3.43649	−	5.95218i	−0.166891	−	0.289063i
$425$	−3.93649	+	6.81820i	−0.190948	+	0.330731i
$426$	−4.30948	+	7.46423i	−0.208795	+	0.361643i
$427$	−1.61895	−	2.80410i	−0.0783465	−	0.135700i
$428$	6.43649	+	11.1483i	0.311120	+	0.538875i
$429$	−2.50000	−	4.33013i	−0.120701	−	0.209061i
$430$	5.74597			0.277095
$431$	−17.1825	+	29.7609i	−0.827650	+	1.43353i	0.0722272	+	0.997388i	$0.476989\pi$
$431$	−17.1825	+	29.7609i	−0.827650	+	1.43353i	−0.899877	+	0.436143i	$0.856344\pi$
$432$	−0.500000	−	0.866025i	−0.0240563	−	0.0416667i
$433$	27.4919			1.32118			0.660589	−	0.750748i	$-0.270307\pi$
$433$	27.4919			1.32118			0.660589	+	0.750748i	$0.270307\pi$
$434$	−22.2540			−1.06823
$435$	−1.93649	−	3.35410i	−0.0928477	−	0.160817i
$436$	18.6190			0.891686
$437$	23.2379	−	40.2492i	1.11162	−	1.92538i
$438$	−12.0000			−0.573382
$439$	−3.68246	+	6.37820i	−0.175754	+	0.304415i	−0.940422	−	0.340009i	$-0.889570\pi$
$439$	−3.68246	+	6.37820i	−0.175754	+	0.304415i	0.764668	+	0.644425i	$0.222903\pi$
$440$	2.50000	−	4.33013i	0.119183	−	0.206431i
$441$	−0.627017	+	1.08602i	−0.0298579	+	0.0517155i
$442$	−3.93649	−	6.81820i	−0.187240	−	0.324309i
$443$	0.364917			0.0173377			0.00866886	−	0.999962i	$-0.497241\pi$
$443$	0.364917			0.0173377			0.00866886	+	0.999962i	$0.497241\pi$
$444$	5.00000	+	3.46410i	0.237289	+	0.164399i
$445$	3.74597			0.177576
$446$	−11.7460	−	20.3446i	−0.556188	−	0.963345i
$447$	6.93649	−	12.0144i	0.328085	−	0.568260i
$448$	1.43649	−	2.48808i	0.0678679	−	0.117551i
$449$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$449$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$450$	−1.00000			−0.0471405
$451$	−17.1825	+	29.7609i	−0.809090	+	1.40139i
$452$	7.61895			0.358365
$453$	−6.00000	−	10.3923i	−0.281905	−	0.488273i
$454$	−24.3649			−1.14350
$455$	−2.87298			−0.134688
$456$	3.87298	+	6.70820i	0.181369	+	0.314140i
$457$	10.8730	−	18.8326i	0.508617	−	0.880950i	−0.491334	−	0.870972i	$-0.663490\pi$
$457$	10.8730	−	18.8326i	0.508617	−	0.880950i	0.999950	−	0.00997846i	$-0.00317630\pi$
$458$	20.6190			0.963460
$459$	−3.93649	−	6.81820i	−0.183740	−	0.318246i
$460$	−3.00000	−	5.19615i	−0.139876	−	0.242272i
$461$	−0.809475	−	1.40205i	−0.0377010	−	0.0653001i	0.846559	−	0.532295i	$-0.178670\pi$
$461$	−0.809475	−	1.40205i	−0.0377010	−	0.0653001i	−0.884260	+	0.466994i	$0.845337\pi$
$462$	7.18246	−	12.4404i	0.334158	−	0.578779i
$463$	11.0000	−	19.0526i	0.511213	−	0.885448i	−0.488702	−	0.872451i	$-0.662530\pi$
$463$	11.0000	−	19.0526i	0.511213	−	0.885448i	0.999916	−	0.0129968i	$-0.00413714\pi$
$464$	1.93649	+	3.35410i	0.0898994	+	0.155710i
$465$	−3.87298	−	6.70820i	−0.179605	−	0.311086i
$466$	−1.00000	−	1.73205i	−0.0463241	−	0.0802357i
$467$	31.7460			1.46903			0.734514	−	0.678593i	$-0.237410\pi$
$467$	31.7460			1.46903			0.734514	+	0.678593i	$0.237410\pi$
$468$	0.500000	−	0.866025i	0.0231125	−	0.0400320i
$469$	19.9284	+	34.5170i	0.920209	+	1.59385i
$470$	4.74597			0.218915
$471$	8.74597			0.402993
$472$	2.50000	+	4.33013i	0.115072	+	0.199310i
$473$	−28.7298			−1.32100
$474$	−7.74597	+	13.4164i	−0.355784	+	0.616236i
$475$	7.74597			0.355409
$476$	11.3095	−	19.5886i	0.518369	−	0.897841i
$477$	3.43649	−	5.95218i	0.157346	−	0.272532i
$478$	0.872983	−	1.51205i	0.0399293	−	0.0691596i
$479$	18.4919	+	32.0290i	0.844918	+	1.46344i	0.885692	+	0.464273i	$0.153684\pi$
$479$	18.4919	+	32.0290i	0.844918	+	1.46344i	−0.0407744	+	0.999168i	$0.512982\pi$
$480$	1.00000			0.0456435
$481$	−0.500000	+	6.06218i	−0.0227980	+	0.276412i
$482$	20.2379			0.921811
$483$	−8.61895	−	14.9285i	−0.392176	−	0.679268i
$484$	−7.00000	+	12.1244i	−0.318182	+	0.551107i
$485$	−5.00000	+	8.66025i	−0.227038	+	0.393242i
$486$	0.500000	−	0.866025i	0.0226805	−	0.0392837i
$487$	0.254033			0.0115113			0.00575567	−	0.999983i	$-0.498168\pi$
$487$	0.254033			0.0115113			0.00575567	+	0.999983i	$0.498168\pi$
$488$	−0.563508	+	0.976025i	−0.0255088	+	0.0441826i
$489$	−17.8730			−0.808244
$490$	−0.627017	−	1.08602i	−0.0283257	−	0.0490616i
$491$	30.0000			1.35388			0.676941	−	0.736038i	$-0.263305\pi$
$491$	30.0000			1.35388			0.676941	+	0.736038i	$0.263305\pi$
$492$	−6.87298			−0.309858
$493$	15.2460	+	26.4068i	0.686644	+	1.18930i
$494$	−3.87298	+	6.70820i	−0.174254	+	0.301816i
$495$	5.00000			0.224733
$496$	3.87298	+	6.70820i	0.173902	+	0.301207i
$497$	−12.3810	−	21.4446i	−0.555366	−	0.961922i
$498$	−2.43649	−	4.22013i	−0.109182	−	0.189108i
$499$	13.0554	−	22.6127i	0.584442	−	1.01228i	−0.410503	−	0.911859i	$-0.634647\pi$
$499$	13.0554	−	22.6127i	0.584442	−	1.01228i	0.994945	−	0.100424i	$-0.0320198\pi$
$500$	0.500000	−	0.866025i	0.0223607	−	0.0387298i
$501$	4.37298	+	7.57423i	0.195370	+	0.338392i
$502$	−0.245967	−	0.426027i	−0.0109780	−	0.0190145i
$503$	14.1190	+	24.4547i	0.629533	+	1.09038i	0.987646	+	0.156705i	$0.0500870\pi$
$503$	14.1190	+	24.4547i	0.629533	+	1.09038i	−0.358113	+	0.933678i	$0.616580\pi$
$504$	2.87298			0.127973
$505$	5.80948	−	10.0623i	0.258518	−	0.447767i
$506$	15.0000	+	25.9808i	0.666831	+	1.15499i
$507$	−12.0000			−0.532939
$508$	−6.87298			−0.304939
$509$	9.49193	+	16.4405i	0.420723	+	0.728713i	0.996010	−	0.0892383i	$-0.0284433\pi$
$509$	9.49193	+	16.4405i	0.420723	+	0.728713i	−0.575288	+	0.817951i	$0.695110\pi$
$510$	7.87298			0.348622
$511$	17.2379	−	29.8569i	0.762560	−	1.32079i
$512$	−1.00000			−0.0441942
$513$	−3.87298	+	6.70820i	−0.170996	+	0.296174i
$514$	−0.190525	+	0.329999i	−0.00840370	+	0.0145556i
$515$	3.56351	−	6.17218i	0.157027	−	0.271979i
$516$	−2.87298	−	4.97615i	−0.126476	−	0.219063i
$517$	−23.7298			−1.04364
$518$	−15.8014	+	7.46423i	−0.694274	+	0.327959i
$519$	16.6190			0.729491
$520$	0.500000	+	0.866025i	0.0219265	+	0.0379777i
$521$	−18.8730	+	32.6890i	−0.826840	+	1.43213i	0.0736642	+	0.997283i	$0.476531\pi$
$521$	−18.8730	+	32.6890i	−0.826840	+	1.43213i	−0.900505	+	0.434847i	$0.856803\pi$
$522$	−1.93649	+	3.35410i	−0.0847579	+	0.146805i
$523$	2.61895	−	4.53615i	0.114519	−	0.198352i	−0.803069	−	0.595887i	$-0.796801\pi$
$523$	2.61895	−	4.53615i	0.114519	−	0.198352i	0.917587	+	0.397534i	$0.130134\pi$
$524$	1.00000			0.0436852
$525$	1.43649	−	2.48808i	0.0626936	−	0.108589i
$526$	−7.74597			−0.337740
$527$	30.4919	+	52.8136i	1.32825	+	2.30060i
$528$	−5.00000			−0.217597
$529$	13.0000			0.565217
$530$	3.43649	+	5.95218i	0.149272	+	0.258546i
$531$	−2.50000	+	4.33013i	−0.108491	+	0.187912i
$532$	−22.2540			−0.964835
$533$	−3.43649	−	5.95218i	−0.148851	−	0.257817i
$534$	−1.87298	−	3.24410i	−0.0810519	−	0.140386i
$535$	−6.43649	−	11.1483i	−0.278274	−	0.481984i
$536$	6.93649	−	12.0144i	0.299611	−	0.518941i
$537$	5.00000	−	8.66025i	0.215766	−	0.373718i
$538$	3.87298	+	6.70820i	0.166976	+	0.289211i
$539$	3.13508	+	5.43012i	0.135038	+	0.233892i
$540$	0.500000	+	0.866025i	0.0215166	+	0.0372678i
$541$	11.3810			0.489310			0.244655	−	0.969610i	$-0.421325\pi$
$541$	11.3810			0.489310			0.244655	+	0.969610i	$0.421325\pi$
$542$	8.93649	−	15.4785i	0.383855	−	0.664857i
$543$	−1.00000	−	1.73205i	−0.0429141	−	0.0743294i
$544$	−7.87298			−0.337551
$545$	−18.6190			−0.797548
$546$	1.43649	+	2.48808i	0.0614762	+	0.106480i
$547$	−4.00000			−0.171028			−0.0855138	−	0.996337i	$-0.527253\pi$
$547$	−4.00000			−0.171028			−0.0855138	+	0.996337i	$0.527253\pi$
$548$	5.06351	−	8.77025i	0.216302	−	0.374647i
$549$	−1.12702			−0.0480999
$550$	−2.50000	+	4.33013i	−0.106600	+	0.184637i
$551$	15.0000	−	25.9808i	0.639021	−	1.10682i
$552$	−3.00000	+	5.19615i	−0.127688	+	0.221163i
$553$	−22.2540	−	38.5451i	−0.946338	−	1.63911i
$554$	16.2379			0.689882
$555$	−5.00000	−	3.46410i	−0.212238	−	0.147043i
$556$	−5.74597			−0.243683
$557$	−10.7460	−	18.6126i	−0.455321	−	0.788639i	0.543385	−	0.839483i	$-0.317142\pi$
$557$	−10.7460	−	18.6126i	−0.455321	−	0.788639i	−0.998707	+	0.0508439i	$0.983809\pi$
$558$	−3.87298	+	6.70820i	−0.163956	+	0.283981i
$559$	2.87298	−	4.97615i	0.121514	−	0.210469i
$560$	−1.43649	+	2.48808i	−0.0607029	+	0.105140i
$561$	−39.3649			−1.66199
$562$	−1.87298	+	3.24410i	−0.0790070	+	0.136844i
$563$	−25.1270			−1.05898			−0.529489	−	0.848317i	$-0.677616\pi$
$563$	−25.1270			−1.05898			−0.529489	+	0.848317i	$0.677616\pi$
$564$	−2.37298	−	4.11013i	−0.0999206	−	0.173068i
$565$	−7.61895			−0.320532
$566$	−5.87298			−0.246860
$567$	1.43649	+	2.48808i	0.0603270	+	0.104489i
$568$	−4.30948	+	7.46423i	−0.180822	+	0.313192i
$569$	−36.6190			−1.53515			−0.767573	−	0.640961i	$-0.778536\pi$
$569$	−36.6190			−1.53515			−0.767573	+	0.640961i	$0.778536\pi$
$570$	−3.87298	−	6.70820i	−0.162221	−	0.280976i
$571$	−20.7460	−	35.9331i	−0.868192	−	1.50375i	−0.863843	−	0.503762i	$-0.831949\pi$
$571$	−20.7460	−	35.9331i	−0.868192	−	1.50375i	−0.00434894	−	0.999991i	$-0.501384\pi$
$572$	−2.50000	−	4.33013i	−0.104530	−	0.181052i
$573$	9.30948	−	16.1245i	0.388909	−	0.673610i
$574$	9.87298	−	17.1005i	0.412090	−	0.713761i
$575$	3.00000	+	5.19615i	0.125109	+	0.216695i
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	14.9284	+	25.8568i	0.621478	+	1.07643i	0.989211	+	0.146501i	$0.0468010\pi$
$577$	14.9284	+	25.8568i	0.621478	+	1.07643i	−0.367732	+	0.929932i	$0.619866\pi$
$578$	−44.9839			−1.87108
$579$	−3.30948	+	5.73218i	−0.137537	+	0.238221i
$580$	−1.93649	−	3.35410i	−0.0804084	−	0.139272i
$581$	14.0000			0.580818
$582$	10.0000			0.414513
$583$	−17.1825	−	29.7609i	−0.711625	−	1.23257i
$584$	−12.0000			−0.496564
$585$	−0.500000	+	0.866025i	−0.0206725	+	0.0358057i
$586$	−11.7460			−0.485221
$587$	12.4365	−	21.5406i	0.513309	−	0.889077i	−0.486572	−	0.873641i	$-0.661753\pi$
$587$	12.4365	−	21.5406i	0.513309	−	0.889077i	0.999881	−	0.0154366i	$-0.00491383\pi$
$588$	−0.627017	+	1.08602i	−0.0258577	+	0.0447869i
$589$	30.0000	−	51.9615i	1.23613	−	2.14104i
$590$	−2.50000	−	4.33013i	−0.102923	−	0.178269i
$591$	12.2540			0.504064
$592$	5.00000	+	3.46410i	0.205499	+	0.142374i
$593$	−21.1109			−0.866920			−0.433460	−	0.901173i	$-0.642707\pi$
$593$	−21.1109			−0.866920			−0.433460	+	0.901173i	$0.642707\pi$
$594$	−2.50000	−	4.33013i	−0.102576	−	0.177667i
$595$	−11.3095	+	19.5886i	−0.463643	+	0.803054i
$596$	6.93649	−	12.0144i	0.284130	−	0.492127i
$597$	7.06351	−	12.2344i	0.289090	−	0.500719i
$598$	−6.00000			−0.245358
$599$	23.9284	−	41.4452i	0.977689	−	1.69341i	0.306929	−	0.951732i	$-0.400699\pi$
$599$	23.9284	−	41.4452i	0.977689	−	1.69341i	0.670760	−	0.741675i	$-0.265968\pi$
$600$	−1.00000			−0.0408248
$601$	21.9919	+	38.0911i	0.897070	+	1.55377i	0.831222	+	0.555941i	$0.187642\pi$
$601$	21.9919	+	38.0911i	0.897070	+	1.55377i	0.0658476	+	0.997830i	$0.479025\pi$
$602$	16.5081			0.672819
$603$	13.8730			0.564952
$604$	−6.00000	−	10.3923i	−0.244137	−	0.422857i
$605$	7.00000	−	12.1244i	0.284590	−	0.492925i
$606$	−11.6190			−0.471988
$607$	−21.0000	−	36.3731i	−0.852364	−	1.47634i	−0.879069	−	0.476694i	$-0.841835\pi$
$607$	−21.0000	−	36.3731i	−0.852364	−	1.47634i	0.0267056	−	0.999643i	$-0.491498\pi$
$608$	3.87298	+	6.70820i	0.157070	+	0.272054i
$609$	−5.56351	−	9.63628i	−0.225445	−	0.390482i
$610$	0.563508	−	0.976025i	0.0228158	−	0.0395181i
$611$	2.37298	−	4.11013i	0.0960006	−	0.166278i
$612$	−3.93649	−	6.81820i	−0.159123	−	0.275610i
$613$	3.37298	+	5.84218i	0.136234	+	0.235963i	0.926068	−	0.377357i	$-0.123167\pi$
$613$	3.37298	+	5.84218i	0.136234	+	0.235963i	−0.789834	+	0.613320i	$0.789834\pi$
$614$	−3.87298	−	6.70820i	−0.156301	−	0.270721i
$615$	6.87298			0.277145
$616$	7.18246	−	12.4404i	0.289389	−	0.501237i
$617$	−7.68246	−	13.3064i	−0.309284	−	0.535696i	0.668922	−	0.743333i	$-0.266756\pi$
$617$	−7.68246	−	13.3064i	−0.309284	−	0.535696i	−0.978206	+	0.207637i	$0.933423\pi$
$618$	−7.12702			−0.286691
$619$	−14.8730			−0.597796			−0.298898	−	0.954285i	$-0.596619\pi$
$619$	−14.8730			−0.597796			−0.298898	+	0.954285i	$0.596619\pi$
$620$	−3.87298	−	6.70820i	−0.155543	−	0.269408i
$621$	−6.00000			−0.240772
$622$	2.30948	−	4.00013i	0.0926015	−	0.160391i
$623$	10.7621			0.431174
$624$	0.500000	−	0.866025i	0.0200160	−	0.0346688i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−9.87298	+	17.1005i	−0.394604	+	0.683474i
$627$	19.3649	+	33.5410i	0.773360	+	1.33950i
$628$	8.74597			0.349002
$629$	39.3649	+	27.2728i	1.56958	+	1.08744i
$630$	−2.87298			−0.114462
$631$	−0.317542	−	0.549998i	−0.0126411	−	0.0218951i	0.859636	−	0.510908i	$-0.170691\pi$
$631$	−0.317542	−	0.549998i	−0.0126411	−	0.0218951i	−0.872277	+	0.489013i	$0.837357\pi$
$632$	−7.74597	+	13.4164i	−0.308118	+	0.533676i
$633$	−8.87298	+	15.3685i	−0.352669	+	0.610841i
$634$	−6.30948	+	10.9283i	−0.250581	+	0.434019i
$635$	6.87298			0.272746
$636$	3.43649	−	5.95218i	0.136266	−	0.236019i
$637$	−1.25403			−0.0496866
$638$	9.68246	+	16.7705i	0.383332	+	0.663951i
$639$	−8.61895			−0.340960
$640$	1.00000			0.0395285
$641$	−18.4365	−	31.9329i	−0.728198	−	1.26128i	−0.957644	−	0.287954i	$-0.907025\pi$
$641$	−18.4365	−	31.9329i	−0.728198	−	1.26128i	0.229447	−	0.973321i	$-0.426308\pi$
$642$	−6.43649	+	11.1483i	−0.254028	+	0.439990i
$643$	−21.6190			−0.852568			−0.426284	−	0.904589i	$-0.640178\pi$
$643$	−21.6190			−0.852568			−0.426284	+	0.904589i	$0.640178\pi$
$644$	−8.61895	−	14.9285i	−0.339634	−	0.588264i
$645$	2.87298	+	4.97615i	0.113124	+	0.195936i
$646$	30.4919	+	52.8136i	1.19969	+	2.07792i
$647$	−4.11895	+	7.13423i	−0.161933	+	0.280476i	−0.935562	−	0.353163i	$-0.885106\pi$
$647$	−4.11895	+	7.13423i	−0.161933	+	0.280476i	0.773629	+	0.633639i	$0.218439\pi$
$648$	0.500000	−	0.866025i	0.0196419	−	0.0340207i
$649$	12.5000	+	21.6506i	0.490668	+	0.849862i
$650$	−0.500000	−	0.866025i	−0.0196116	−	0.0339683i
$651$	−11.1270	−	19.2726i	−0.436102	−	0.755351i
$652$	−17.8730			−0.699960
$653$	14.6190	−	25.3208i	0.572084	−	0.990878i	−0.424268	−	0.905537i	$-0.639469\pi$
$653$	14.6190	−	25.3208i	0.572084	−	0.990878i	0.996352	−	0.0853414i	$-0.0271981\pi$
$654$	9.30948	+	16.1245i	0.364029	+	0.630517i
$655$	−1.00000			−0.0390732
$656$	−6.87298			−0.268345
$657$	−6.00000	−	10.3923i	−0.234082	−	0.405442i
$658$	13.6351			0.531551
$659$	−17.2460	+	29.8709i	−0.671807	+	1.16360i	0.305584	+	0.952165i	$0.401148\pi$
$659$	−17.2460	+	29.8709i	−0.671807	+	1.16360i	−0.977391	+	0.211439i	$0.932185\pi$
$660$	5.00000			0.194625
$661$	−2.87298	+	4.97615i	−0.111746	+	0.193550i	−0.916474	−	0.400093i	$-0.868978\pi$
$661$	−2.87298	+	4.97615i	−0.111746	+	0.193550i	0.804728	+	0.593643i	$0.202311\pi$
$662$	1.56351	−	2.70808i	0.0607675	−	0.105252i
$663$	3.93649	−	6.81820i	0.152881	−	0.264797i
$664$	−2.43649	−	4.22013i	−0.0945542	−	0.163773i
$665$	22.2540			0.862974
$666$	−0.500000	+	6.06218i	−0.0193746	+	0.234905i
$667$	23.2379			0.899775
$668$	4.37298	+	7.57423i	0.169196	+	0.293056i
$669$	11.7460	−	20.3446i	0.454125	−	0.786568i
$670$	−6.93649	+	12.0144i	−0.267980	+	0.464155i
$671$	−2.81754	+	4.88013i	−0.108770	+	0.188395i
$672$	2.87298			0.110828
$673$	−8.43649	+	14.6124i	−0.325203	+	0.563268i	−0.981553	−	0.191188i	$-0.938766\pi$
$673$	−8.43649	+	14.6124i	−0.325203	+	0.563268i	0.656351	+	0.754456i	$0.272099\pi$
$674$	26.6190			1.02532
$675$	−0.500000	−	0.866025i	−0.0192450	−	0.0333333i
$676$	−12.0000			−0.461538
$677$	−0.872983			−0.0335515			−0.0167757	−	0.999859i	$-0.505340\pi$
$677$	−0.872983			−0.0335515			−0.0167757	+	0.999859i	$0.505340\pi$
$678$	3.80948	+	6.59820i	0.146302	+	0.253403i
$679$	−14.3649	+	24.8808i	−0.551275	+	0.954836i
$680$	7.87298			0.301915
$681$	−12.1825	−	21.1006i	−0.466833	−	0.808578i
$682$	19.3649	+	33.5410i	0.741521	+	1.28435i
$683$	17.6190	+	30.5169i	0.674170	+	1.16770i	0.976711	+	0.214561i	$0.0688320\pi$
$683$	17.6190	+	30.5169i	0.674170	+	1.16770i	−0.302540	+	0.953137i	$0.597835\pi$
$684$	−3.87298	+	6.70820i	−0.148087	+	0.256495i
$685$	−5.06351	+	8.77025i	−0.193467	+	0.335094i
$686$	8.25403	+	14.2964i	0.315140	+	0.545839i
$687$	10.3095	+	17.8565i	0.393331	+	0.681269i
$688$	−2.87298	−	4.97615i	−0.109531	−	0.189714i
$689$	6.87298			0.261840
$690$	3.00000	−	5.19615i	0.114208	−	0.197814i
$691$	−13.8730	−	24.0287i	−0.527753	−	0.914095i	−0.999477	−	0.0323487i	$-0.989701\pi$
$691$	−13.8730	−	24.0287i	−0.527753	−	0.914095i	0.471723	−	0.881747i	$-0.343632\pi$
$692$	16.6190			0.631758
$693$	14.3649			0.545678
$694$	−10.7460	−	18.6126i	−0.407911	−	0.706523i
$695$	5.74597			0.217957
$696$	−1.93649	+	3.35410i	−0.0734025	+	0.127137i
$697$	−54.1109			−2.04960
$698$	15.4919	−	26.8328i	0.586378	−	1.01564i
$699$	1.00000	−	1.73205i	0.0378235	−	0.0655122i
$700$	1.43649	−	2.48808i	0.0542943	−	0.0940405i
$701$	−6.68246	−	11.5744i	−0.252393	−	0.437157i	0.711791	−	0.702391i	$-0.247884\pi$
$701$	−6.68246	−	11.5744i	−0.252393	−	0.437157i	−0.964184	+	0.265234i	$0.914551\pi$
$702$	1.00000			0.0377426
$703$	3.87298	−	46.9574i	0.146072	−	1.77103i
$704$	−5.00000			−0.188445
$705$	2.37298	+	4.11013i	0.0893717	+	0.154796i
$706$	5.00000	−	8.66025i	0.188177	−	0.325933i
$707$	16.6905	−	28.9088i	0.627712	−	1.08723i
$708$	−2.50000	+	4.33013i	−0.0939558	+	0.162736i
$709$	21.1270			0.793442			0.396721	−	0.917939i	$-0.370148\pi$
$709$	21.1270			0.793442			0.396721	+	0.917939i	$0.370148\pi$
$710$	4.30948	−	7.46423i	0.161732	−	0.280128i
$711$	−15.4919			−0.580993
$712$	−1.87298	−	3.24410i	−0.0701930	−	0.121578i
$713$	46.4758			1.74053
$714$	22.6190			0.846493
$715$	2.50000	+	4.33013i	0.0934947	+	0.161938i
$716$	5.00000	−	8.66025i	0.186859	−	0.323649i
$717$	1.74597			0.0652043
$718$	−9.87298	−	17.1005i	−0.368456	−	0.638185i
$719$	−11.9284	−	20.6606i	−0.444855	−	0.770512i	0.553187	−	0.833057i	$-0.313412\pi$
$719$	−11.9284	−	20.6606i	−0.444855	−	0.770512i	−0.998042	+	0.0625454i	$0.980078\pi$
$720$	0.500000	+	0.866025i	0.0186339	+	0.0322749i
$721$	10.2379	−	17.7326i	0.381279	−	0.660395i
$722$	20.5000	−	35.5070i	0.762931	−	1.32144i
$723$	10.1190	+	17.5265i	0.376328	+	0.651819i
$724$	−1.00000	−	1.73205i	−0.0371647	−	0.0643712i
$725$	1.93649	+	3.35410i	0.0719195	+	0.124568i
$726$	−14.0000			−0.519589
$727$	−20.6190	+	35.7131i	−0.764715	+	1.32452i	0.175683	+	0.984447i	$0.443787\pi$
$727$	−20.6190	+	35.7131i	−0.764715	+	1.32452i	−0.940397	+	0.340078i	$0.889547\pi$
$728$	1.43649	+	2.48808i	0.0532399	+	0.0922143i
$729$	1.00000			0.0370370
$730$	12.0000			0.444140
$731$	−22.6190	−	39.1772i	−0.836592	−	1.44902i
$732$	−1.12702			−0.0416557
$733$	−24.5000	+	42.4352i	−0.904928	+	1.56738i	−0.0839145	+	0.996473i	$0.526742\pi$
$733$	−24.5000	+	42.4352i	−0.904928	+	1.56738i	−0.821014	+	0.570909i	$0.806591\pi$
$734$	−17.7460			−0.655016
$735$	0.627017	−	1.08602i	0.0231279	−	0.0400586i
$736$	−3.00000	+	5.19615i	−0.110581	+	0.191533i
$737$	34.6825	−	60.0718i	1.27754	−	2.21277i
$738$	−3.43649	−	5.95218i	−0.126499	−	0.219103i
$739$	−11.7460			−0.432082			−0.216041	−	0.976384i	$-0.569315\pi$
$739$	−11.7460			−0.432082			−0.216041	+	0.976384i	$0.569315\pi$
$740$	−5.00000	−	3.46410i	−0.183804	−	0.127343i
$741$	−7.74597			−0.284555
$742$	9.87298	+	17.1005i	0.362449	+	0.627779i
$743$	26.1190	−	45.2393i	0.958211	−	1.65967i	0.231369	−	0.972866i	$-0.425679\pi$
$743$	26.1190	−	45.2393i	0.958211	−	1.65967i	0.726842	−	0.686805i	$-0.240987\pi$
$744$	−3.87298	+	6.70820i	−0.141990	+	0.245935i
$745$	−6.93649	+	12.0144i	−0.254133	+	0.440172i
$746$	−9.74597			−0.356825
$747$	2.43649	−	4.22013i	0.0891466	−	0.154406i
$748$	−39.3649			−1.43932
$749$	−18.4919	−	32.0290i	−0.675681	−	1.17031i
$750$	1.00000			0.0365148
$751$	33.6190			1.22677			0.613386	−	0.789783i	$-0.289807\pi$
$751$	33.6190			1.22677			0.613386	+	0.789783i	$0.289807\pi$
$752$	−2.37298	−	4.11013i	−0.0865338	−	0.149881i
$753$	0.245967	−	0.426027i	0.00896352	−	0.0155253i
$754$	−3.87298			−0.141046
$755$	6.00000	+	10.3923i	0.218362	+	0.378215i
$756$	1.43649	+	2.48808i	0.0522447	+	0.0904905i
$757$	10.4919	+	18.1726i	0.381336	+	0.660493i	0.991253	−	0.131972i	$-0.0421308\pi$
$757$	10.4919	+	18.1726i	0.381336	+	0.660493i	−0.609918	+	0.792465i	$0.708797\pi$
$758$	6.30948	−	10.9283i	0.229170	−	0.396935i
$759$	−15.0000	+	25.9808i	−0.544466	+	0.943042i
$760$	−3.87298	−	6.70820i	−0.140488	−	0.243332i
$761$	−5.56351	−	9.63628i	−0.201677	−	0.349315i	0.747392	−	0.664383i	$-0.231306\pi$
$761$	−5.56351	−	9.63628i	−0.201677	−	0.349315i	−0.949069	+	0.315069i	$0.897972\pi$
$762$	−3.43649	−	5.95218i	−0.124491	−	0.215625i
$763$	−53.4919			−1.93654
$764$	9.30948	−	16.1245i	0.336805	−	0.583363i
$765$	3.93649	+	6.81820i	0.142324	+	0.246513i
$766$	10.7460			0.388268
$767$	−5.00000			−0.180540
$768$	−0.500000	−	0.866025i	−0.0180422	−	0.0312500i
$769$	12.2379			0.441310			0.220655	−	0.975352i	$-0.429181\pi$
$769$	12.2379			0.441310			0.220655	+	0.975352i	$0.429181\pi$
$770$	−7.18246	+	12.4404i	−0.258838	+	0.448320i
$771$	−0.381050			−0.0137232
$772$	−3.30948	+	5.73218i	−0.119111	+	0.206306i
$773$	−24.0554	+	41.6652i	−0.865214	+	1.49859i	0.00162033	+	0.999999i	$0.499484\pi$
$773$	−24.0554	+	41.6652i	−0.865214	+	1.49859i	−0.866834	+	0.498596i	$0.833849\pi$
$774$	2.87298	−	4.97615i	0.103267	−	0.178864i
$775$	3.87298	+	6.70820i	0.139122	+	0.240966i
$776$	10.0000			0.358979
$777$	−14.3649	−	9.95231i	−0.515339	−	0.357037i
$778$	3.74597			0.134299
$779$	26.6190	+	46.1054i	0.953723	+	1.65190i
$780$	−0.500000	+	0.866025i	−0.0179029	+	0.0310087i
$781$	−21.5474	+	37.3211i	−0.771026	+	1.33546i
$782$	−23.6190	+	40.9092i	−0.844612	+	1.46291i
$783$	−3.87298			−0.138409
$784$	−0.627017	+	1.08602i	−0.0223935	+	0.0387866i
$785$	−8.74597			−0.312157
$786$	0.500000	+	0.866025i	0.0178344	+	0.0308901i
$787$	−20.1270			−0.717451			−0.358725	−	0.933443i	$-0.616789\pi$
$787$	−20.1270			−0.717451			−0.358725	+	0.933443i	$0.616789\pi$
$788$	12.2540			0.436532
$789$	−3.87298	−	6.70820i	−0.137882	−	0.238818i
$790$	7.74597	−	13.4164i	0.275589	−	0.477334i
$791$	−21.8891			−0.778287
$792$	−2.50000	−	4.33013i	−0.0888336	−	0.153864i
$793$	−0.563508	−	0.976025i	−0.0200108	−	0.0346597i
$794$	−10.1190	−	17.5265i	−0.359108	−	0.621993i
$795$	−3.43649	+	5.95218i	−0.121880	+	0.211102i
$796$	7.06351	−	12.2344i	0.250359	−	0.433635i
$797$	5.74597	+	9.95231i	0.203533	+	0.352529i	0.949664	−	0.313270i	$-0.101424\pi$
$797$	5.74597	+	9.95231i	0.203533	+	0.352529i	−0.746132	+	0.665798i	$0.768091\pi$
$798$	−11.1270	−	19.2726i	−0.393892	−	0.682241i
$799$	−18.6825	−	32.3590i	−0.660938	−	1.14478i
$800$	−1.00000			−0.0353553
$801$	1.87298	−	3.24410i	0.0661786	−	0.114625i
$802$	−10.3095	−	17.8565i	−0.364040	−	0.630536i
$803$	−60.0000			−2.11735
$804$	13.8730			0.489262
$805$	8.61895	+	14.9285i	0.303778	+	0.526159i
$806$	−7.74597			−0.272840
$807$	−3.87298	+	6.70820i	−0.136335	+	0.236140i
$808$	−11.6190			−0.408753
$809$	−0.381050	+	0.659998i	−0.0133970	+	0.0232043i	−0.872646	−	0.488353i	$-0.837598\pi$
$809$	−0.381050	+	0.659998i	−0.0133970	+	0.0232043i	0.859249	+	0.511557i	$0.170931\pi$
$810$	−0.500000	+	0.866025i	−0.0175682	+	0.0304290i
$811$	−15.3095	+	26.5168i	−0.537588	+	0.931130i	0.461445	+	0.887169i	$0.347331\pi$
$811$	−15.3095	+	26.5168i	−0.537588	+	0.931130i	−0.999033	+	0.0439615i	$0.986002\pi$
$812$	−5.56351	−	9.63628i	−0.195241	−	0.338167i
$813$	17.8730			0.626833
$814$	25.0000	+	17.3205i	0.876250	+	0.607083i
$815$	17.8730			0.626063
$816$	−3.93649	−	6.81820i	−0.137805	−	0.238685i
$817$	−22.2540	+	38.5451i	−0.778570	+	1.34852i
$818$	16.1190	−	27.9188i	0.563586	−	0.976159i
$819$	−1.43649	+	2.48808i	−0.0501951	+	0.0869404i
$820$	6.87298			0.240015
$821$	−3.19052	+	5.52615i	−0.111350	+	0.192864i	−0.916315	−	0.400459i	$-0.868851\pi$
$821$	−3.19052	+	5.52615i	−0.111350	+	0.192864i	0.804965	+	0.593323i	$0.202184\pi$
$822$	10.1270			0.353220
$823$	−9.69052	−	16.7845i	−0.337790	−	0.585070i	0.646226	−	0.763146i	$-0.276346\pi$
$823$	−9.69052	−	16.7845i	−0.337790	−	0.585070i	−0.984017	+	0.178076i	$0.943013\pi$
$824$	−7.12702			−0.248281
$825$	−5.00000			−0.174078
$826$	−7.18246	−	12.4404i	−0.249910	−	0.432856i
$827$	4.74597	−	8.22026i	0.165033	−	0.285846i	−0.771634	−	0.636067i	$-0.780560\pi$
$827$	4.74597	−	8.22026i	0.165033	−	0.285846i	0.936667	+	0.350221i	$0.113893\pi$
$828$	−6.00000			−0.208514
$829$	−23.0554	−	39.9332i	−0.800749	−	1.38694i	−0.919124	−	0.393968i	$-0.871102\pi$
$829$	−23.0554	−	39.9332i	−0.800749	−	1.38694i	0.118375	−	0.992969i	$-0.462231\pi$
$830$	2.43649	+	4.22013i	0.0845719	+	0.146483i
$831$	8.11895	+	14.0624i	0.281643	+	0.487820i
$832$	0.500000	−	0.866025i	0.0173344	−	0.0300240i
$833$	−4.93649	+	8.55025i	−0.171039	+	0.296249i
$834$	−2.87298	−	4.97615i	−0.0994833	−	0.172310i
$835$	−4.37298	−	7.57423i	−0.151333	−	0.262117i
$836$	19.3649	+	33.5410i	0.669750	+	1.16004i
$837$	−7.74597			−0.267740
$838$	7.00000	−	12.1244i	0.241811	−	0.418829i
$839$	12.0554	+	20.8806i	0.416200	+	0.720880i	0.995554	−	0.0941967i	$-0.0300283\pi$
$839$	12.0554	+	20.8806i	0.416200	+	0.720880i	−0.579354	+	0.815076i	$0.696695\pi$
$840$	−2.87298			−0.0991273
$841$	−14.0000			−0.482759
$842$	−4.30948	−	7.46423i	−0.148514	−	0.257234i
$843$	−3.74597			−0.129018
$844$	−8.87298	+	15.3685i	−0.305421	+	0.529004i
$845$	12.0000			0.412813
$846$	2.37298	−	4.11013i	0.0815848	−	0.141309i
$847$	20.1109	−	34.8331i	0.691018	−	1.19688i
$848$	3.43649	−	5.95218i	0.118010	−	0.204399i
$849$	−2.93649	−	5.08615i	−0.100780	−	0.174556i
$850$	−7.87298			−0.270041
$851$	33.0000	−	15.5885i	1.13123	−	0.534365i
$852$	−8.61895			−0.295280
$853$	14.5000	+	25.1147i	0.496471	+	0.859912i	0.999992	−	0.00407068i	$-0.00129574\pi$
$853$	14.5000	+	25.1147i	0.496471	+	0.859912i	−0.503521	+	0.863983i	$0.667962\pi$
$854$	1.61895	−	2.80410i	0.0553993	−	0.0959545i
$855$	3.87298	−	6.70820i	0.132453	−	0.229416i
$856$	−6.43649	+	11.1483i	−0.219995	+	0.381042i
$857$	39.8730			1.36204			0.681018	−	0.732267i	$-0.261538\pi$
$857$	39.8730			1.36204			0.681018	+	0.732267i	$0.261538\pi$
$858$	2.50000	−	4.33013i	0.0853486	−	0.147828i
$859$	−6.36492			−0.217168			−0.108584	−	0.994087i	$-0.534632\pi$
$859$	−6.36492			−0.217168			−0.108584	+	0.994087i	$0.534632\pi$
$860$	2.87298	+	4.97615i	0.0979679	+	0.169685i
$861$	19.7460			0.672941
$862$	−34.3649			−1.17047
$863$	−2.37298	−	4.11013i	−0.0807773	−	0.139910i	0.822807	−	0.568321i	$-0.192407\pi$
$863$	−2.37298	−	4.11013i	−0.0807773	−	0.139910i	−0.903584	+	0.428411i	$0.859074\pi$
$864$	0.500000	−	0.866025i	0.0170103	−	0.0294628i
$865$	−16.6190			−0.565061
$866$	13.7460	+	23.8087i	0.467107	+	0.809053i
$867$	−22.4919	−	38.9572i	−0.763866	−	1.32305i
$868$	−11.1270	−	19.2726i	−0.377676	−	0.654153i
$869$	−38.7298	+	67.0820i	−1.31382	+	2.27560i
$870$	1.93649	−	3.35410i	0.0656532	−	0.113715i
$871$	6.93649	+	12.0144i	0.235034	+	0.407091i
$872$	9.30948	+	16.1245i	0.315259	+	0.546044i
$873$	5.00000	+	8.66025i	0.169224	+	0.293105i
$874$	46.4758			1.57207
$875$	−1.43649	+	2.48808i	−0.0485623	+	0.0841123i
$876$	−6.00000	−	10.3923i	−0.202721	−	0.351123i
$877$	9.25403			0.312487			0.156243	−	0.987719i	$-0.450062\pi$
$877$	9.25403			0.312487			0.156243	+	0.987719i	$0.450062\pi$
$878$	−7.36492			−0.248554
$879$	−5.87298	−	10.1723i	−0.198091	−	0.343103i
$880$	5.00000			0.168550
$881$	−19.4919	+	33.7610i	−0.656700	+	1.13744i	0.324765	+	0.945795i	$0.394715\pi$
$881$	−19.4919	+	33.7610i	−0.656700	+	1.13744i	−0.981465	+	0.191643i	$0.938618\pi$
$882$	−1.25403			−0.0422255
$883$	−0.190525	+	0.329999i	−0.00641168	+	0.0111053i	−0.869213	−	0.494437i	$-0.835374\pi$
$883$	−0.190525	+	0.329999i	−0.00641168	+	0.0111053i	0.862802	+	0.505542i	$0.168708\pi$
$884$	3.93649	−	6.81820i	0.132399	−	0.229321i
$885$	2.50000	−	4.33013i	0.0840366	−	0.145556i
$886$	0.182458	+	0.316027i	0.00612981	+	0.0106171i
$887$	22.0000			0.738688			0.369344	−	0.929293i	$-0.379582\pi$
$887$	22.0000			0.738688			0.369344	+	0.929293i	$0.379582\pi$
$888$	−0.500000	+	6.06218i	−0.0167789	+	0.203433i
$889$	19.7460			0.662258
$890$	1.87298	+	3.24410i	0.0627825	+	0.108743i
$891$	2.50000	−	4.33013i	0.0837532	−	0.145065i
$892$	11.7460	−	20.3446i	0.393284	−	0.681188i
$893$	−18.3810	+	31.8369i	−0.615098	+	1.06538i
$894$	13.8730			0.463982
$895$	−5.00000	+	8.66025i	−0.167132	+	0.289480i
$896$	2.87298			0.0959796
$897$	−3.00000	−	5.19615i	−0.100167	−	0.173494i
$898$		0			0
$899$	30.0000			1.00056
$900$	−0.500000	−	0.866025i	−0.0166667	−	0.0288675i
$901$	27.0554	−	46.8614i	0.901347	−	1.56118i
$902$	−34.3649			−1.14423
$903$	8.25403	+	14.2964i	0.274677	+	0.475755i
$904$	3.80948	+	6.59820i	0.126701	+	0.219453i
$905$	1.00000	+	1.73205i	0.0332411	+	0.0575753i
$906$	6.00000	−	10.3923i	0.199337	−	0.345261i
$907$	−2.00000	+	3.46410i	−0.0664089	+	0.115024i	−0.897318	−	0.441384i	$-0.854488\pi$
$907$	−2.00000	+	3.46410i	−0.0664089	+	0.115024i	0.830909	+	0.556408i	$0.187821\pi$
$908$	−12.1825	−	21.1006i	−0.404289	−	0.700249i
$909$	−5.80948	−	10.0623i	−0.192688	−	0.333746i
$910$	−1.43649	−	2.48808i	−0.0476192	−	0.0824789i
$911$	−34.7298			−1.15065			−0.575325	−	0.817925i	$-0.695125\pi$
$911$	−34.7298			−1.15065			−0.575325	+	0.817925i	$0.695125\pi$
$912$	−3.87298	+	6.70820i	−0.128247	+	0.222131i
$913$	−12.1825	−	21.1006i	−0.403181	−	0.698329i
$914$	21.7460			0.719293
$915$	1.12702			0.0372580
$916$	10.3095	+	17.8565i	0.340635	+	0.589997i
$917$	−2.87298			−0.0948743
$918$	3.93649	−	6.81820i	0.129924	−	0.225034i
$919$	45.6190			1.50483			0.752415	−	0.658689i	$-0.228889\pi$
$919$	45.6190			1.50483			0.752415	+	0.658689i	$0.228889\pi$
$920$	3.00000	−	5.19615i	0.0989071	−	0.171312i
$921$	3.87298	−	6.70820i	0.127619	−	0.221043i
$922$	0.809475	−	1.40205i	0.0266586	−	0.0461741i
$923$	−4.30948	−	7.46423i	−0.141848	−	0.245688i
$924$	14.3649			0.472571
$925$	5.00000	+	3.46410i	0.164399	+	0.113899i
$926$	22.0000			0.722965
$927$	−3.56351	−	6.17218i	−0.117041	−	0.202721i
$928$	−1.93649	+	3.35410i	−0.0635685	+	0.110104i
$929$	2.87298	−	4.97615i	0.0942595	−	0.163262i	−0.815040	−	0.579405i	$-0.803285\pi$
$929$	2.87298	−	4.97615i	0.0942595	−	0.163262i	0.909299	+	0.416143i	$0.136618\pi$
$930$	3.87298	−	6.70820i	0.127000	−	0.219971i
$931$	9.71370			0.318354
$932$	1.00000	−	1.73205i	0.0327561	−	0.0567352i
$933$	4.61895			0.151218
$934$	15.8730	+	27.4928i	0.519380	+	0.899592i
$935$	39.3649			1.28737
$936$	1.00000			0.0326860
$937$	3.30948	+	5.73218i	0.108116	+	0.187262i	0.915007	−	0.403438i	$-0.132185\pi$
$937$	3.30948	+	5.73218i	0.108116	+	0.187262i	−0.806891	+	0.590700i	$0.798852\pi$
$938$	−19.9284	+	34.5170i	−0.650686	+	1.12702i
$939$	−19.7460			−0.644385
$940$	2.37298	+	4.11013i	0.0773982	+	0.134058i
$941$	−2.25403	−	3.90410i	−0.0734794	−	0.127270i	0.826945	−	0.562283i	$-0.190077\pi$
$941$	−2.25403	−	3.90410i	−0.0734794	−	0.127270i	−0.900424	+	0.435013i	$0.856744\pi$
$942$	4.37298	+	7.57423i	0.142479	+	0.246782i
$943$	−20.6190	+	35.7131i	−0.671445	+	1.16298i
$944$	−2.50000	+	4.33013i	−0.0813681	+	0.140934i
$945$	−1.43649	−	2.48808i	−0.0467291	−	0.0809371i
$946$	−14.3649	−	24.8808i	−0.467044	−	0.808943i
$947$	−26.4919	−	45.8854i	−0.860872	−	1.49107i	−0.871088	−	0.491127i	$-0.836585\pi$
$947$	−26.4919	−	45.8854i	−0.860872	−	1.49107i	0.0102161	−	0.999948i	$-0.496748\pi$
$948$	−15.4919			−0.503155
$949$	6.00000	−	10.3923i	0.194768	−	0.337348i
$950$	3.87298	+	6.70820i	0.125656	+	0.217643i
$951$	−12.6190			−0.409197
$952$	22.6190			0.733084
$953$	13.8095	+	23.9187i	0.447333	+	0.774803i	0.998211	−	0.0597822i	$-0.0190406\pi$
$953$	13.8095	+	23.9187i	0.447333	+	0.774803i	−0.550879	+	0.834585i	$0.685707\pi$
$954$	6.87298			0.222521
$955$	−9.30948	+	16.1245i	−0.301248	+	0.521776i
$956$	1.74597			0.0564686
$957$	−9.68246	+	16.7705i	−0.312989	+	0.542114i
$958$	−18.4919	+	32.0290i	−0.597447	+	1.03481i
$959$	−14.5474	+	25.1968i	−0.469759	+	0.813647i
$960$	0.500000	+	0.866025i	0.0161374	+	0.0279508i
$961$	29.0000			0.935484
$962$	−5.50000	+	2.59808i	−0.177327	+	0.0837653i
$963$	−12.8730			−0.414826
$964$	10.1190	+	17.5265i	0.325909	+	0.564492i
$965$	3.30948	−	5.73218i	0.106536	−	0.184525i
$966$	8.61895	−	14.9285i	0.277310	−	0.480315i
$967$	−2.56351	+	4.44013i	−0.0824369	+	0.142785i	−0.904296	−	0.426906i	$-0.859604\pi$
$967$	−2.56351	+	4.44013i	−0.0824369	+	0.142785i	0.821859	+	0.569691i	$0.192937\pi$
$968$	−14.0000			−0.449977
$969$	−30.4919	+	52.8136i	−0.979542	+	1.69662i
$970$	−10.0000			−0.321081
$971$	25.6190	+	44.3733i	0.822151	+	1.42401i	0.904077	+	0.427369i	$0.140560\pi$
$971$	25.6190	+	44.3733i	0.822151	+	1.42401i	−0.0819259	+	0.996638i	$0.526107\pi$
$972$	1.00000			0.0320750
$973$	16.5081			0.529224
$974$	0.127017	+	0.219999i	0.00406988	+	0.00704923i
$975$	0.500000	−	0.866025i	0.0160128	−	0.0277350i
$976$	−1.12702			−0.0360749
$977$	−3.19052	−	5.52615i	−0.102074	−	0.176797i	0.810465	−	0.585787i	$-0.199214\pi$
$977$	−3.19052	−	5.52615i	−0.102074	−	0.176797i	−0.912539	+	0.408990i	$0.865881\pi$
$978$	−8.93649	−	15.4785i	−0.285757	−	0.494946i
$979$	−9.36492	−	16.2205i	−0.299304	−	0.518410i
$980$	0.627017	−	1.08602i	0.0200293	−	0.0346918i
$981$	−9.30948	+	16.1245i	−0.297229	+	0.514815i
$982$	15.0000	+	25.9808i	0.478669	+	0.829079i
$983$	11.0000	+	19.0526i	0.350846	+	0.607682i	0.986398	−	0.164376i	$-0.0525609\pi$
$983$	11.0000	+	19.0526i	0.350846	+	0.607682i	−0.635552	+	0.772058i	$0.719228\pi$
$984$	−3.43649	−	5.95218i	−0.109551	−	0.189749i
$985$	−12.2540			−0.390446
$986$	−15.2460	+	26.4068i	−0.485530	+	0.840963i
$987$	6.81754	+	11.8083i	0.217005	+	0.375863i
$988$	−7.74597			−0.246432
$989$	−34.4758			−1.09627
$990$	2.50000	+	4.33013i	0.0794552	+	0.137620i
$991$	−33.6190			−1.06794			−0.533971	−	0.845503i	$-0.679301\pi$
$991$	−33.6190			−1.06794			−0.533971	+	0.845503i	$0.679301\pi$
$992$	−3.87298	+	6.70820i	−0.122967	+	0.212986i
$993$	3.12702			0.0992329
$994$	12.3810	−	21.4446i	0.392703	−	0.680182i
$995$	−7.06351	+	12.2344i	−0.223928	+	0.387855i
$996$	2.43649	−	4.22013i	0.0772032	−	0.133720i
$997$	6.24597	+	10.8183i	0.197812	+	0.342620i	0.947819	−	0.318810i	$-0.103283\pi$
$997$	6.24597	+	10.8183i	0.197812	+	0.342620i	−0.750007	+	0.661430i	$0.769950\pi$
$998$	26.1109			0.826526
$999$	−5.50000	+	2.59808i	−0.174012	+	0.0821995i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.i.l.211.2	yes	4
37.10	even	3	inner	1110.2.i.l.121.2	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.i.l.121.2	✓	4	37.10	even	3	inner
1110.2.i.l.211.2	yes	4	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.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} -1.00000 q^{6} +(1.43649 - 2.48808i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} -1.00000 q^{6} +(1.43649 - 2.48808i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +1.00000 q^{10} -5.00000 q^{11} +(-0.500000 - 0.866025i) q^{12} +(0.500000 - 0.866025i) q^{13} +2.87298 q^{14} +(0.500000 + 0.866025i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-3.93649 - 6.81820i) q^{17} +(0.500000 - 0.866025i) q^{18} +(-3.87298 + 6.70820i) q^{19} +(0.500000 + 0.866025i) q^{20} +(1.43649 + 2.48808i) q^{21} +(-2.50000 - 4.33013i) q^{22} -6.00000 q^{23} +(0.500000 - 0.866025i) q^{24} +(-0.500000 - 0.866025i) q^{25} +1.00000 q^{26} +1.00000 q^{27} +(1.43649 + 2.48808i) q^{28} -3.87298 q^{29} +(-0.500000 + 0.866025i) q^{30} -7.74597 q^{31} +(0.500000 - 0.866025i) q^{32} +(2.50000 - 4.33013i) q^{33} +(3.93649 - 6.81820i) q^{34} +(-1.43649 - 2.48808i) q^{35} +1.00000 q^{36} +(-5.50000 + 2.59808i) q^{37} -7.74597 q^{38} +(0.500000 + 0.866025i) q^{39} +(-0.500000 + 0.866025i) q^{40} +(3.43649 - 5.95218i) q^{41} +(-1.43649 + 2.48808i) q^{42} +5.74597 q^{43} +(2.50000 - 4.33013i) q^{44} -1.00000 q^{45} +(-3.00000 - 5.19615i) q^{46} +4.74597 q^{47} +1.00000 q^{48} +(-0.627017 - 1.08602i) q^{49} +(0.500000 - 0.866025i) q^{50} +7.87298 q^{51} +(0.500000 + 0.866025i) q^{52} +(3.43649 + 5.95218i) q^{53} +(0.500000 + 0.866025i) q^{54} +(-2.50000 + 4.33013i) q^{55} +(-1.43649 + 2.48808i) q^{56} +(-3.87298 - 6.70820i) q^{57} +(-1.93649 - 3.35410i) q^{58} +(-2.50000 - 4.33013i) q^{59} -1.00000 q^{60} +(0.563508 - 0.976025i) q^{61} +(-3.87298 - 6.70820i) q^{62} -2.87298 q^{63} +1.00000 q^{64} +(-0.500000 - 0.866025i) q^{65} +5.00000 q^{66} +(-6.93649 + 12.0144i) q^{67} +7.87298 q^{68} +(3.00000 - 5.19615i) q^{69} +(1.43649 - 2.48808i) q^{70} +(4.30948 - 7.46423i) q^{71} +(0.500000 + 0.866025i) q^{72} +12.0000 q^{73} +(-5.00000 - 3.46410i) q^{74} +1.00000 q^{75} +(-3.87298 - 6.70820i) q^{76} +(-7.18246 + 12.4404i) q^{77} +(-0.500000 + 0.866025i) q^{78} +(7.74597 - 13.4164i) q^{79} -1.00000 q^{80} +(-0.500000 + 0.866025i) q^{81} +6.87298 q^{82} +(2.43649 + 4.22013i) q^{83} -2.87298 q^{84} -7.87298 q^{85} +(2.87298 + 4.97615i) q^{86} +(1.93649 - 3.35410i) q^{87} +5.00000 q^{88} +(1.87298 + 3.24410i) q^{89} +(-0.500000 - 0.866025i) q^{90} +(-1.43649 - 2.48808i) q^{91} +(3.00000 - 5.19615i) q^{92} +(3.87298 - 6.70820i) q^{93} +(2.37298 + 4.11013i) q^{94} +(3.87298 + 6.70820i) q^{95} +(0.500000 + 0.866025i) q^{96} -10.0000 q^{97} +(0.627017 - 1.08602i) q^{98} +(2.50000 + 4.33013i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + 2 q^{5} - 4 q^{6} - 2 q^{7} - 4 q^{8} - 2 q^{9}+O(q^{10}) \) 4 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 + 2 * q^5 - 4 * q^6 - 2 * q^7 - 4 * q^8 - 2 * q^9	\( 4 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + 2 q^{5} - 4 q^{6} - 2 q^{7} - 4 q^{8} - 2 q^{9} + 4 q^{10} - 20 q^{11} - 2 q^{12} + 2 q^{13} - 4 q^{14} + 2 q^{15} - 2 q^{16} - 8 q^{17} + 2 q^{18} + 2 q^{20} - 2 q^{21} - 10 q^{22} - 24 q^{23} + 2 q^{24} - 2 q^{25} + 4 q^{26} + 4 q^{27} - 2 q^{28} - 2 q^{30} + 2 q^{32} + 10 q^{33} + 8 q^{34} + 2 q^{35} + 4 q^{36} - 22 q^{37} + 2 q^{39} - 2 q^{40} + 6 q^{41} + 2 q^{42} - 8 q^{43} + 10 q^{44} - 4 q^{45} - 12 q^{46} - 12 q^{47} + 4 q^{48} - 18 q^{49} + 2 q^{50} + 16 q^{51} + 2 q^{52} + 6 q^{53} + 2 q^{54} - 10 q^{55} + 2 q^{56} - 10 q^{59} - 4 q^{60} + 10 q^{61} + 4 q^{63} + 4 q^{64} - 2 q^{65} + 20 q^{66} - 20 q^{67} + 16 q^{68} + 12 q^{69} - 2 q^{70} - 6 q^{71} + 2 q^{72} + 48 q^{73} - 20 q^{74} + 4 q^{75} + 10 q^{77} - 2 q^{78} - 4 q^{80} - 2 q^{81} + 12 q^{82} + 2 q^{83} + 4 q^{84} - 16 q^{85} - 4 q^{86} + 20 q^{88} - 8 q^{89} - 2 q^{90} + 2 q^{91} + 12 q^{92} - 6 q^{94} + 2 q^{96} - 40 q^{97} + 18 q^{98} + 10 q^{99}+O(q^{100}) \) 4 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 + 2 * q^5 - 4 * q^6 - 2 * q^7 - 4 * q^8 - 2 * q^9 + 4 * q^10 - 20 * q^11 - 2 * q^12 + 2 * q^13 - 4 * q^14 + 2 * q^15 - 2 * q^16 - 8 * q^17 + 2 * q^18 + 2 * q^20 - 2 * q^21 - 10 * q^22 - 24 * q^23 + 2 * q^24 - 2 * q^25 + 4 * q^26 + 4 * q^27 - 2 * q^28 - 2 * q^30 + 2 * q^32 + 10 * q^33 + 8 * q^34 + 2 * q^35 + 4 * q^36 - 22 * q^37 + 2 * q^39 - 2 * q^40 + 6 * q^41 + 2 * q^42 - 8 * q^43 + 10 * q^44 - 4 * q^45 - 12 * q^46 - 12 * q^47 + 4 * q^48 - 18 * q^49 + 2 * q^50 + 16 * q^51 + 2 * q^52 + 6 * q^53 + 2 * q^54 - 10 * q^55 + 2 * q^56 - 10 * q^59 - 4 * q^60 + 10 * q^61 + 4 * q^63 + 4 * q^64 - 2 * q^65 + 20 * q^66 - 20 * q^67 + 16 * q^68 + 12 * q^69 - 2 * q^70 - 6 * q^71 + 2 * q^72 + 48 * q^73 - 20 * q^74 + 4 * q^75 + 10 * q^77 - 2 * q^78 - 4 * q^80 - 2 * q^81 + 12 * q^82 + 2 * q^83 + 4 * q^84 - 16 * q^85 - 4 * q^86 + 20 * q^88 - 8 * q^89 - 2 * q^90 + 2 * q^91 + 12 * q^92 - 6 * q^94 + 2 * q^96 - 40 * q^97 + 18 * q^98 + 10 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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