LMFDB - Embedded newform 1110.2.i.o.121.3

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:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.45911232.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} + 11x^{4} - 4x^{3} + 121x^{2} - 22x + 4 $ x^6 + 11x^4 - 4x^3 + 121x^2 - 22x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			121.3
Root			$-1.70202 + 2.94799i$ of defining polynomial
Character	$\chi$	$=$	1110.121
Dual form			1110.2.i.o.211.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} -1.00000 q^{6} +(1.74790 + 3.02744i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(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} +(1.74790 + 3.02744i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} -1.00000 q^{10} +3.40405 q^{11} +(0.500000 - 0.866025i) q^{12} +(-0.500000 - 0.866025i) q^{13} -3.49579 q^{14} +(-0.500000 + 0.866025i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-3.24790 + 5.62552i) q^{17} +(-0.500000 - 0.866025i) q^{18} +(-1.20202 - 2.08197i) q^{19} +(0.500000 - 0.866025i) q^{20} +(-1.74790 + 3.02744i) q^{21} +(-1.70202 + 2.94799i) q^{22} -0.183489 q^{23} +(0.500000 + 0.866025i) q^{24} +(-0.500000 + 0.866025i) q^{25} +1.00000 q^{26} -1.00000 q^{27} +(1.74790 - 3.02744i) q^{28} +8.71635 q^{29} +(-0.500000 - 0.866025i) q^{30} +10.8081 q^{31} +(-0.500000 - 0.866025i) q^{32} +(1.70202 + 2.94799i) q^{33} +(-3.24790 - 5.62552i) q^{34} +(-1.74790 + 3.02744i) q^{35} +1.00000 q^{36} +(-5.99579 + 1.02493i) q^{37} +2.40405 q^{38} +(0.500000 - 0.866025i) q^{39} +(0.500000 + 0.866025i) q^{40} +(-2.85817 - 4.95050i) q^{41} +(-1.74790 - 3.02744i) q^{42} -6.99158 q^{43} +(-1.70202 - 2.94799i) q^{44} -1.00000 q^{45} +(0.0917445 - 0.158906i) q^{46} +3.22056 q^{47} -1.00000 q^{48} +(-2.61028 + 4.52114i) q^{49} +(-0.500000 - 0.866025i) q^{50} -6.49579 q^{51} +(-0.500000 + 0.866025i) q^{52} +(-3.94992 + 6.84146i) q^{53} +(0.500000 - 0.866025i) q^{54} +(1.70202 + 2.94799i) q^{55} +(1.74790 + 3.02744i) q^{56} +(1.20202 - 2.08197i) q^{57} +(-4.35817 + 7.54858i) q^{58} +(-6.19781 + 10.7349i) q^{59} +1.00000 q^{60} +(-0.454128 - 0.786572i) q^{61} +(-5.40405 + 9.36008i) q^{62} -3.49579 q^{63} +1.00000 q^{64} +(0.500000 - 0.866025i) q^{65} -3.40405 q^{66} +(-6.65194 - 11.5215i) q^{67} +6.49579 q^{68} +(-0.0917445 - 0.158906i) q^{69} +(-1.74790 - 3.02744i) q^{70} +(2.83964 + 4.91840i) q^{71} +(-0.500000 + 0.866025i) q^{72} +4.80809 q^{73} +(2.11028 - 5.70497i) q^{74} -1.00000 q^{75} +(-1.20202 + 2.08197i) q^{76} +(5.94992 + 10.3056i) q^{77} +(0.500000 + 0.866025i) q^{78} +(-8.58754 - 14.8740i) q^{79} -1.00000 q^{80} +(-0.500000 - 0.866025i) q^{81} +5.71635 q^{82} +(-2.34385 + 4.05967i) q^{83} +3.49579 q^{84} -6.49579 q^{85} +(3.49579 - 6.05489i) q^{86} +(4.35817 + 7.54858i) q^{87} +3.40405 q^{88} +(0.495791 - 0.858736i) q^{89} +(0.500000 - 0.866025i) q^{90} +(1.74790 - 3.02744i) q^{91} +(0.0917445 + 0.158906i) q^{92} +(5.40405 + 9.36008i) q^{93} +(-1.61028 + 2.78909i) q^{94} +(1.20202 - 2.08197i) q^{95} +(0.500000 - 0.866025i) q^{96} +2.00000 q^{97} +(-2.61028 - 4.52114i) q^{98} +(-1.70202 + 2.94799i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{2} + 3 q^{3} - 3 q^{4} + 3 q^{5} - 6 q^{6} - q^{7} + 6 q^{8} - 3 q^{9}+O(q^{10}) $ 6 * q - 3 * q^2 + 3 * q^3 - 3 * q^4 + 3 * q^5 - 6 * q^6 - q^7 + 6 * q^8 - 3 * q^9	$ 6 q - 3 q^{2} + 3 q^{3} - 3 q^{4} + 3 q^{5} - 6 q^{6} - q^{7} + 6 q^{8} - 3 q^{9} - 6 q^{10} + 3 q^{12} - 3 q^{13} + 2 q^{14} - 3 q^{15} - 3 q^{16} - 8 q^{17} - 3 q^{18} + 3 q^{19} + 3 q^{20} + q^{21} + 4 q^{23} + 3 q^{24} - 3 q^{25} + 6 q^{26} - 6 q^{27} - q^{28} + 14 q^{29} - 3 q^{30} + 24 q^{31} - 3 q^{32} - 8 q^{34} + q^{35} + 6 q^{36} - 13 q^{37} - 6 q^{38} + 3 q^{39} + 3 q^{40} + 2 q^{41} + q^{42} + 4 q^{43} - 6 q^{45} - 2 q^{46} + 4 q^{47} - 6 q^{48} - 8 q^{49} - 3 q^{50} - 16 q^{51} - 3 q^{52} - 2 q^{53} + 3 q^{54} - q^{56} - 3 q^{57} - 7 q^{58} - 4 q^{59} + 6 q^{60} - 4 q^{61} - 12 q^{62} + 2 q^{63} + 6 q^{64} + 3 q^{65} - 8 q^{67} + 16 q^{68} + 2 q^{69} + q^{70} + 3 q^{71} - 3 q^{72} - 12 q^{73} + 5 q^{74} - 6 q^{75} + 3 q^{76} + 14 q^{77} + 3 q^{78} - 26 q^{79} - 6 q^{80} - 3 q^{81} - 4 q^{82} - 23 q^{83} - 2 q^{84} - 16 q^{85} - 2 q^{86} + 7 q^{87} - 20 q^{89} + 3 q^{90} - q^{91} - 2 q^{92} + 12 q^{93} - 2 q^{94} - 3 q^{95} + 3 q^{96} + 12 q^{97} - 8 q^{98}+O(q^{100}) $ 6 * q - 3 * q^2 + 3 * q^3 - 3 * q^4 + 3 * q^5 - 6 * q^6 - q^7 + 6 * q^8 - 3 * q^9 - 6 * q^10 + 3 * q^12 - 3 * q^13 + 2 * q^14 - 3 * q^15 - 3 * q^16 - 8 * q^17 - 3 * q^18 + 3 * q^19 + 3 * q^20 + q^21 + 4 * q^23 + 3 * q^24 - 3 * q^25 + 6 * q^26 - 6 * q^27 - q^28 + 14 * q^29 - 3 * q^30 + 24 * q^31 - 3 * q^32 - 8 * q^34 + q^35 + 6 * q^36 - 13 * q^37 - 6 * q^38 + 3 * q^39 + 3 * q^40 + 2 * q^41 + q^42 + 4 * q^43 - 6 * q^45 - 2 * q^46 + 4 * q^47 - 6 * q^48 - 8 * q^49 - 3 * q^50 - 16 * q^51 - 3 * q^52 - 2 * q^53 + 3 * q^54 - q^56 - 3 * q^57 - 7 * q^58 - 4 * q^59 + 6 * q^60 - 4 * q^61 - 12 * q^62 + 2 * q^63 + 6 * q^64 + 3 * q^65 - 8 * q^67 + 16 * q^68 + 2 * q^69 + q^70 + 3 * q^71 - 3 * q^72 - 12 * q^73 + 5 * q^74 - 6 * q^75 + 3 * q^76 + 14 * q^77 + 3 * q^78 - 26 * q^79 - 6 * q^80 - 3 * q^81 - 4 * q^82 - 23 * q^83 - 2 * q^84 - 16 * q^85 - 2 * q^86 + 7 * q^87 - 20 * q^89 + 3 * q^90 - q^91 - 2 * q^92 + 12 * q^93 - 2 * q^94 - 3 * q^95 + 3 * q^96 + 12 * q^97 - 8 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.500000	+	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
$7$	1.74790	+	3.02744i	0.660642	+	1.14427i	0.980447	+	0.196783i	$0.0630494\pi$
$7$	1.74790	+	3.02744i	0.660642	+	1.14427i	−0.319805	+	0.947484i	$0.603617\pi$
$8$	1.00000			0.353553
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−1.00000			−0.316228
$11$	3.40405			1.02636			0.513179	−	0.858281i	$-0.328468\pi$
$11$	3.40405			1.02636			0.513179	+	0.858281i	$0.328468\pi$
$12$	0.500000	−	0.866025i	0.144338	−	0.250000i
$13$	−0.500000	−	0.866025i	−0.138675	−	0.240192i	0.788320	−	0.615265i	$-0.210951\pi$
$13$	−0.500000	−	0.866025i	−0.138675	−	0.240192i	−0.926995	+	0.375073i	$0.877618\pi$
$14$	−3.49579			−0.934290
$15$	−0.500000	+	0.866025i	−0.129099	+	0.223607i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−3.24790	+	5.62552i	−0.787730	+	1.36439i	0.139624	+	0.990205i	$0.455411\pi$
$17$	−3.24790	+	5.62552i	−0.787730	+	1.36439i	−0.927354	+	0.374185i	$0.877923\pi$
$18$	−0.500000	−	0.866025i	−0.117851	−	0.204124i
$19$	−1.20202	−	2.08197i	−0.275763	−	0.477636i	0.694564	−	0.719431i	$-0.255597\pi$
$19$	−1.20202	−	2.08197i	−0.275763	−	0.477636i	−0.970327	+	0.241795i	$0.922264\pi$
$20$	0.500000	−	0.866025i	0.111803	−	0.193649i
$21$	−1.74790	+	3.02744i	−0.381422	+	0.660642i
$22$	−1.70202	+	2.94799i	−0.362873	+	0.628514i
$23$	−0.183489			−0.0382601			−0.0191300	−	0.999817i	$-0.506090\pi$
$23$	−0.183489			−0.0382601			−0.0191300	+	0.999817i	$0.506090\pi$
$24$	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
$28$	1.74790	−	3.02744i	0.330321	−	0.572133i
$29$	8.71635			1.61859			0.809293	−	0.587406i	$-0.199851\pi$
$29$	8.71635			1.61859			0.809293	+	0.587406i	$0.199851\pi$
$30$	−0.500000	−	0.866025i	−0.0912871	−	0.158114i
$31$	10.8081			1.94119			0.970595	−	0.240716i	$-0.0773824\pi$
$31$	10.8081			1.94119			0.970595	+	0.240716i	$0.0773824\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	1.70202	+	2.94799i	0.296284	+	0.513179i
$34$	−3.24790	−	5.62552i	−0.557010	−	0.964769i
$35$	−1.74790	+	3.02744i	−0.295448	+	0.511731i
$36$	1.00000			0.166667
$37$	−5.99579	+	1.02493i	−0.985702	+	0.168498i
$37$	−5.99579	+	1.02493i	−0.985702	+	0.168498i
$38$	2.40405			0.389988
$39$	0.500000	−	0.866025i	0.0800641	−	0.138675i
$40$	0.500000	+	0.866025i	0.0790569	+	0.136931i
$41$	−2.85817	−	4.95050i	−0.446372	−	0.773139i	0.551775	−	0.833993i	$-0.313951\pi$
$41$	−2.85817	−	4.95050i	−0.446372	−	0.773139i	−0.998147	+	0.0608544i	$0.980617\pi$
$42$	−1.74790	−	3.02744i	−0.269706	−	0.467145i
$43$	−6.99158			−1.06621			−0.533103	−	0.846050i	$-0.678974\pi$
$43$	−6.99158			−1.06621			−0.533103	+	0.846050i	$0.678974\pi$
$44$	−1.70202	−	2.94799i	−0.256590	−	0.444426i
$45$	−1.00000			−0.149071
$46$	0.0917445	−	0.158906i	0.0135270	−	0.0234294i
$47$	3.22056			0.469767			0.234883	−	0.972024i	$-0.424529\pi$
$47$	3.22056			0.469767			0.234883	+	0.972024i	$0.424529\pi$
$48$	−1.00000			−0.144338
$49$	−2.61028	+	4.52114i	−0.372897	+	0.645877i
$50$	−0.500000	−	0.866025i	−0.0707107	−	0.122474i
$51$	−6.49579			−0.909593
$52$	−0.500000	+	0.866025i	−0.0693375	+	0.120096i
$53$	−3.94992	+	6.84146i	−0.542563	+	0.939747i	0.456193	+	0.889881i	$0.349213\pi$
$53$	−3.94992	+	6.84146i	−0.542563	+	0.939747i	−0.998756	+	0.0498659i	$0.984121\pi$
$54$	0.500000	−	0.866025i	0.0680414	−	0.117851i
$55$	1.70202	+	2.94799i	0.229501	+	0.397507i
$56$	1.74790	+	3.02744i	0.233572	+	0.404559i
$57$	1.20202	−	2.08197i	0.159212	−	0.275763i
$58$	−4.35817	+	7.54858i	−0.572256	+	0.991177i
$59$	−6.19781	+	10.7349i	−0.806887	+	1.39757i	0.108123	+	0.994138i	$0.465516\pi$
$59$	−6.19781	+	10.7349i	−0.806887	+	1.39757i	−0.915010	+	0.403431i	$0.867817\pi$
$60$	1.00000			0.129099
$61$	−0.454128	−	0.786572i	−0.0581451	−	0.100710i	0.835488	−	0.549509i	$-0.185185\pi$
$61$	−0.454128	−	0.786572i	−0.0581451	−	0.100710i	−0.893633	+	0.448799i	$0.851852\pi$
$62$	−5.40405	+	9.36008i	−0.686315	+	1.18873i
$63$	−3.49579			−0.440428
$64$	1.00000			0.125000
$65$	0.500000	−	0.866025i	0.0620174	−	0.107417i
$66$	−3.40405			−0.419009
$67$	−6.65194	−	11.5215i	−0.812664	−	1.40758i	−0.910993	−	0.412422i	$-0.864683\pi$
$67$	−6.65194	−	11.5215i	−0.812664	−	1.40758i	0.0983289	−	0.995154i	$-0.468650\pi$
$68$	6.49579			0.787730
$69$	−0.0917445	−	0.158906i	−0.0110447	−	0.0191300i
$70$	−1.74790	−	3.02744i	−0.208913	−	0.361849i
$71$	2.83964	+	4.91840i	0.337003	+	0.583707i	0.983868	−	0.178898i	$-0.0572533\pi$
$71$	2.83964	+	4.91840i	0.337003	+	0.583707i	−0.646864	+	0.762605i	$0.723920\pi$
$72$	−0.500000	+	0.866025i	−0.0589256	+	0.102062i
$73$	4.80809			0.562745			0.281372	−	0.959599i	$-0.409210\pi$
$73$	4.80809			0.562745			0.281372	+	0.959599i	$0.409210\pi$
$74$	2.11028	−	5.70497i	0.245315	−	0.663190i
$75$	−1.00000			−0.115470
$76$	−1.20202	+	2.08197i	−0.137882	+	0.238818i
$77$	5.94992	+	10.3056i	0.678056	+	1.17443i
$78$	0.500000	+	0.866025i	0.0566139	+	0.0980581i
$79$	−8.58754	−	14.8740i	−0.966173	−	1.67346i	−0.706429	−	0.707784i	$-0.749695\pi$
$79$	−8.58754	−	14.8740i	−0.966173	−	1.67346i	−0.259744	−	0.965677i	$-0.583638\pi$
$80$	−1.00000			−0.111803
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	5.71635			0.631265
$83$	−2.34385	+	4.05967i	−0.257271	+	0.445606i	−0.965510	−	0.260367i	$-0.916157\pi$
$83$	−2.34385	+	4.05967i	−0.257271	+	0.445606i	0.708239	+	0.705973i	$0.249490\pi$
$84$	3.49579			0.381422
$85$	−6.49579			−0.704568
$86$	3.49579	−	6.05489i	0.376961	−	0.652915i
$87$	4.35817	+	7.54858i	0.467245	+	0.809293i
$88$	3.40405			0.362873
$89$	0.495791	−	0.858736i	0.0525538	−	0.0910258i	−0.838552	−	0.544822i	$-0.816597\pi$
$89$	0.495791	−	0.858736i	0.0525538	−	0.0910258i	0.891106	+	0.453796i	$0.149931\pi$
$90$	0.500000	−	0.866025i	0.0527046	−	0.0912871i
$91$	1.74790	−	3.02744i	0.183229	−	0.317362i
$92$	0.0917445	+	0.158906i	0.00956502	+	0.0165671i
$93$	5.40405	+	9.36008i	0.560374	+	0.970595i
$94$	−1.61028	+	2.78909i	−0.166088	+	0.287672i
$95$	1.20202	−	2.08197i	0.123325	−	0.213605i
$96$	0.500000	−	0.866025i	0.0510310	−	0.0883883i
$97$	2.00000			0.203069			0.101535	−	0.994832i	$-0.467625\pi$
$97$	2.00000			0.203069			0.101535	+	0.994832i	$0.467625\pi$
$98$	−2.61028	−	4.52114i	−0.263678	−	0.456704i
$99$	−1.70202	+	2.94799i	−0.171060	+	0.296284i
$100$	1.00000			0.100000
$101$	8.67928			0.863621			0.431810	−	0.901964i	$-0.357875\pi$
$101$	8.67928			0.863621			0.431810	+	0.901964i	$0.357875\pi$
$102$	3.24790	−	5.62552i	0.321590	−	0.557010i
$103$	−10.3039			−1.01527			−0.507636	−	0.861572i	$-0.669481\pi$
$103$	−10.3039			−1.01527			−0.507636	+	0.861572i	$0.669481\pi$
$104$	−0.500000	−	0.866025i	−0.0490290	−	0.0849208i
$105$	−3.49579			−0.341154
$106$	−3.94992	−	6.84146i	−0.383650	−	0.664501i
$107$	9.75801	+	16.9014i	0.943343	+	1.63392i	0.759036	+	0.651049i	$0.225671\pi$
$107$	9.75801	+	16.9014i	0.943343	+	1.63392i	0.184307	+	0.982869i	$0.440996\pi$
$108$	0.500000	+	0.866025i	0.0481125	+	0.0833333i
$109$	−7.17048	+	12.4196i	−0.686807	+	1.18958i	0.286058	+	0.958212i	$0.407655\pi$
$109$	−7.17048	+	12.4196i	−0.686807	+	1.18958i	−0.972865	+	0.231373i	$0.925678\pi$
$110$	−3.40405			−0.324563
$111$	−3.88551	−	4.68004i	−0.368797	−	0.444210i
$112$	−3.49579			−0.330321
$113$	2.86238	−	4.95779i	0.269270	−	0.466390i	−0.699403	−	0.714727i	$-0.746551\pi$
$113$	2.86238	−	4.95779i	0.269270	−	0.466390i	0.968674	+	0.248337i	$0.0798841\pi$
$114$	1.20202	+	2.08197i	0.112580	+	0.194994i
$115$	−0.0917445	−	0.158906i	−0.00855522	−	0.0148181i
$116$	−4.35817	−	7.54858i	−0.404646	−	0.700868i
$117$	1.00000			0.0924500
$118$	−6.19781	−	10.7349i	−0.570555	−	0.988230i
$119$	−22.7079			−2.08163
$120$	−0.500000	+	0.866025i	−0.0456435	+	0.0790569i
$121$	0.587536			0.0534124
$122$	0.908256			0.0822296
$123$	2.85817	−	4.95050i	0.257713	−	0.446372i
$124$	−5.40405	−	9.36008i	−0.485298	−	0.840560i
$125$	−1.00000			−0.0894427
$126$	1.74790	−	3.02744i	0.155715	−	0.269706i
$127$	−0.839640	+	1.45430i	−0.0745060	+	0.129048i	−0.900871	−	0.434086i	$-0.857071\pi$
$127$	−0.839640	+	1.45430i	−0.0745060	+	0.129048i	0.826365	+	0.563134i	$0.190405\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	−3.49579	−	6.05489i	−0.307787	−	0.533103i
$130$	0.500000	+	0.866025i	0.0438529	+	0.0759555i
$131$	0.206232	−	0.357204i	0.0180186	−	0.0312091i	−0.856876	−	0.515523i	$-0.827598\pi$
$131$	0.206232	−	0.357204i	0.0180186	−	0.0312091i	0.874894	+	0.484314i	$0.160931\pi$
$132$	1.70202	−	2.94799i	0.148142	−	0.256590i
$133$	4.20202	−	7.27812i	0.364362	−	0.631093i
$134$	13.3039			1.14928
$135$	−0.500000	−	0.866025i	−0.0430331	−	0.0745356i
$136$	−3.24790	+	5.62552i	−0.278505	+	0.482384i
$137$	5.10016			0.435736			0.217868	−	0.975978i	$-0.430090\pi$
$137$	5.10016			0.435736			0.217868	+	0.975978i	$0.430090\pi$
$138$	0.183489			0.0156196
$139$	10.0833	−	17.4648i	0.855257	−	1.48135i	−0.0211500	−	0.999776i	$-0.506733\pi$
$139$	10.0833	−	17.4648i	0.855257	−	1.48135i	0.876407	−	0.481572i	$-0.159934\pi$
$140$	3.49579			0.295448
$141$	1.61028	+	2.78909i	0.135610	+	0.234883i
$142$	−5.67928			−0.476595
$143$	−1.70202	−	2.94799i	−0.142330	−	0.246523i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	4.35817	+	7.54858i	0.361927	+	0.626875i
$146$	−2.40405	+	4.16393i	−0.198960	+	0.344609i
$147$	−5.22056			−0.430584
$148$	3.88551	+	4.68004i	0.319387	+	0.384697i
$149$	−7.90826			−0.647870			−0.323935	−	0.946079i	$-0.605006\pi$
$149$	−7.90826			−0.647870			−0.323935	+	0.946079i	$0.605006\pi$
$150$	0.500000	−	0.866025i	0.0408248	−	0.0707107i
$151$	−0.587536	−	1.01764i	−0.0478130	−	0.0828145i	0.841128	−	0.540835i	$-0.181892\pi$
$151$	−0.587536	−	1.01764i	−0.0478130	−	0.0828145i	−0.888941	+	0.458021i	$0.848558\pi$
$152$	−1.20202	−	2.08197i	−0.0974970	−	0.168870i
$153$	−3.24790	−	5.62552i	−0.262577	−	0.454796i
$154$	−11.8998			−0.958916
$155$	5.40405	+	9.36008i	0.434064	+	0.751820i
$156$	−1.00000			−0.0800641
$157$	10.7121	−	18.5540i	0.854922	−	1.48077i	−0.0217955	−	0.999762i	$-0.506938\pi$
$157$	10.7121	−	18.5540i	0.854922	−	1.48077i	0.876717	−	0.481006i	$-0.159728\pi$
$158$	17.1751			1.36638
$159$	−7.89984			−0.626498
$160$	0.500000	−	0.866025i	0.0395285	−	0.0684653i
$161$	−0.320720	−	0.555503i	−0.0252762	−	0.0437797i
$162$	1.00000			0.0785674
$163$	−9.65194	+	16.7177i	−0.755999	+	1.30943i	0.188878	+	0.982001i	$0.439515\pi$
$163$	−9.65194	+	16.7177i	−0.755999	+	1.30943i	−0.944876	+	0.327427i	$0.893818\pi$
$164$	−2.85817	+	4.95050i	−0.223186	+	0.386569i
$165$	−1.70202	+	2.94799i	−0.132502	+	0.229501i
$166$	−2.34385	−	4.05967i	−0.181918	−	0.315091i
$167$	−5.60186	−	9.70271i	−0.433485	−	0.750818i	0.563686	−	0.825989i	$-0.309383\pi$
$167$	−5.60186	−	9.70271i	−0.433485	−	0.750818i	−0.997171	+	0.0751713i	$0.976050\pi$
$168$	−1.74790	+	3.02744i	−0.134853	+	0.233572i
$169$	6.00000	−	10.3923i	0.461538	−	0.799408i
$170$	3.24790	−	5.62552i	0.249102	−	0.431458i
$171$	2.40405			0.183842
$172$	3.49579	+	6.05489i	0.266552	+	0.461681i
$173$	5.26222	−	9.11444i	0.400079	−	0.692958i	−0.593656	−	0.804719i	$-0.702316\pi$
$173$	5.26222	−	9.11444i	0.400079	−	0.692958i	0.993735	+	0.111761i	$0.0356492\pi$
$174$	−8.71635			−0.660785
$175$	−3.49579			−0.264257
$176$	−1.70202	+	2.94799i	−0.128295	+	0.222213i
$177$	−12.3956			−0.931713
$178$	0.495791	+	0.858736i	0.0371611	+	0.0643650i
$179$	12.9916			0.971037			0.485518	−	0.874227i	$-0.338631\pi$
$179$	12.9916			0.971037			0.485518	+	0.874227i	$0.338631\pi$
$180$	0.500000	+	0.866025i	0.0372678	+	0.0645497i
$181$	3.18349	+	5.51396i	0.236627	+	0.409850i	0.959744	−	0.280875i	$-0.0906248\pi$
$181$	3.18349	+	5.51396i	0.236627	+	0.409850i	−0.723117	+	0.690725i	$0.757291\pi$
$182$	1.74790	+	3.02744i	0.129563	+	0.224409i
$183$	0.454128	−	0.786572i	0.0335701	−	0.0581451i
$184$	−0.183489			−0.0135270
$185$	−3.88551	−	4.68004i	−0.285669	−	0.344084i
$186$	−10.8081			−0.792488
$187$	−11.0560	+	19.1495i	−0.808494	+	1.40035i
$188$	−1.61028	−	2.78909i	−0.117442	−	0.203415i
$189$	−1.74790	−	3.02744i	−0.127141	−	0.220214i
$190$	1.20202	+	2.08197i	0.0872040	+	0.151042i
$191$	15.7163			1.13720			0.568598	−	0.822616i	$-0.307486\pi$
$191$	15.7163			1.13720			0.568598	+	0.822616i	$0.307486\pi$
$192$	0.500000	+	0.866025i	0.0360844	+	0.0625000i
$193$	17.2584			1.24229			0.621143	−	0.783697i	$-0.286668\pi$
$193$	17.2584			1.24229			0.621143	+	0.783697i	$0.286668\pi$
$194$	−1.00000	+	1.73205i	−0.0717958	+	0.124354i
$195$	1.00000			0.0716115
$196$	5.22056			0.372897
$197$	11.7079	−	20.2787i	0.834156	−	1.44480i	−0.0605604	−	0.998165i	$-0.519289\pi$
$197$	11.7079	−	20.2787i	0.834156	−	1.44480i	0.894716	−	0.446635i	$-0.147378\pi$
$198$	−1.70202	−	2.94799i	−0.120958	−	0.209505i
$199$	−14.3123			−1.01457			−0.507286	−	0.861778i	$-0.669351\pi$
$199$	−14.3123			−1.01457			−0.507286	+	0.861778i	$0.669351\pi$
$200$	−0.500000	+	0.866025i	−0.0353553	+	0.0612372i
$201$	6.65194	−	11.5215i	0.469192	−	0.812664i
$202$	−4.33964	+	7.51648i	−0.305336	+	0.528858i
$203$	15.2353	+	26.3883i	1.06931	+	1.85209i
$204$	3.24790	+	5.62552i	0.227398	+	0.393865i
$205$	2.85817	−	4.95050i	0.199624	−	0.345758i
$206$	5.15194	−	8.92343i	0.358953	−	0.621725i
$207$	0.0917445	−	0.158906i	0.00637668	−	0.0110447i
$208$	1.00000			0.0693375
$209$	−4.09174	−	7.08711i	−0.283032	−	0.490226i
$210$	1.74790	−	3.02744i	0.120616	−	0.208913i
$211$	21.5791			1.48557			0.742784	−	0.669531i	$-0.233505\pi$
$211$	21.5791			1.48557			0.742784	+	0.669531i	$0.233505\pi$
$212$	7.89984			0.542563
$213$	−2.83964	+	4.91840i	−0.194569	+	0.337003i
$214$	−19.5160			−1.33409
$215$	−3.49579	−	6.05489i	−0.238411	−	0.412940i
$216$	−1.00000			−0.0680414
$217$	18.8914	+	32.7209i	1.28243	+	2.22124i
$218$	−7.17048	−	12.4196i	−0.485646	−	0.841164i
$219$	2.40405	+	4.16393i	0.162450	+	0.281372i
$220$	1.70202	−	2.94799i	0.114750	−	0.198754i
$221$	6.49579			0.436954
$222$	5.99579	−	1.02493i	0.402411	−	0.0687889i
$223$	13.6162			0.911807			0.455904	−	0.890029i	$-0.349316\pi$
$223$	13.6162			0.911807			0.455904	+	0.890029i	$0.349316\pi$
$224$	1.74790	−	3.02744i	0.116786	−	0.202280i
$225$	−0.500000	−	0.866025i	−0.0333333	−	0.0577350i
$226$	2.86238	+	4.95779i	0.190403	+	0.329788i
$227$	−3.65615	−	6.33264i	−0.242667	−	0.420312i	0.718806	−	0.695211i	$-0.244689\pi$
$227$	−3.65615	−	6.33264i	−0.242667	−	0.420312i	−0.961473	+	0.274899i	$0.911356\pi$
$228$	−2.40405			−0.159212
$229$	−2.45413	−	4.25067i	−0.162173	−	0.280892i	0.773475	−	0.633827i	$-0.218517\pi$
$229$	−2.45413	−	4.25067i	−0.162173	−	0.280892i	−0.935648	+	0.352935i	$0.885184\pi$
$230$	0.183489			0.0120989
$231$	−5.94992	+	10.3056i	−0.391476	+	0.678056i
$232$	8.71635			0.572256
$233$	11.7794			0.771697			0.385848	−	0.922562i	$-0.373909\pi$
$233$	11.7794			0.771697			0.385848	+	0.922562i	$0.373909\pi$
$234$	−0.500000	+	0.866025i	−0.0326860	+	0.0566139i
$235$	1.61028	+	2.78909i	0.105043	+	0.181940i
$236$	12.3956			0.806887
$237$	8.58754	−	14.8740i	0.557820	−	0.966173i
$238$	11.3540	−	19.6656i	0.735968	−	1.27473i
$239$	0.202023	−	0.349915i	0.0130678	−	0.0226341i	−0.859418	−	0.511274i	$-0.829174\pi$
$239$	0.202023	−	0.349915i	0.0130678	−	0.0226341i	0.872485	+	0.488640i	$0.162507\pi$
$240$	−0.500000	−	0.866025i	−0.0322749	−	0.0559017i
$241$	9.88551	+	17.1222i	0.636782	+	1.10294i	0.986135	+	0.165947i	$0.0530681\pi$
$241$	9.88551	+	17.1222i	0.636782	+	1.10294i	−0.349353	+	0.936991i	$0.613599\pi$
$242$	−0.293768	+	0.508821i	−0.0188841	+	0.0327083i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	−0.454128	+	0.786572i	−0.0290726	+	0.0503551i
$245$	−5.22056			−0.333529
$246$	2.85817	+	4.95050i	0.182231	+	0.315633i
$247$	−1.20202	+	2.08197i	−0.0764829	+	0.132472i
$248$	10.8081			0.686315
$249$	−4.68770			−0.297071
$250$	0.500000	−	0.866025i	0.0316228	−	0.0547723i
$251$	−8.02865			−0.506764			−0.253382	−	0.967366i	$-0.581543\pi$
$251$	−8.02865			−0.506764			−0.253382	+	0.967366i	$0.581543\pi$
$252$	1.74790	+	3.02744i	0.110107	+	0.190711i
$253$	−0.624605			−0.0392686
$254$	−0.839640	−	1.45430i	−0.0526837	−	0.0912509i
$255$	−3.24790	−	5.62552i	−0.203391	−	0.352284i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	15.6705	−	27.1421i	0.977498	−	1.69308i	0.306063	−	0.952011i	$-0.400988\pi$
$257$	15.6705	−	27.1421i	0.977498	−	1.69308i	0.671434	−	0.741064i	$-0.265679\pi$
$258$	6.99158			0.435277
$259$	−13.5829	−	16.3605i	−0.844003	−	1.01659i
$260$	−1.00000			−0.0620174
$261$	−4.35817	+	7.54858i	−0.269764	+	0.467245i
$262$	0.206232	+	0.357204i	0.0127411	+	0.0220682i
$263$	14.6162	+	25.3160i	0.901273	+	1.56105i	0.825844	+	0.563899i	$0.190699\pi$
$263$	14.6162	+	25.3160i	0.901273	+	1.56105i	0.0754290	+	0.997151i	$0.475967\pi$
$264$	1.70202	+	2.94799i	0.104752	+	0.181436i
$265$	−7.89984			−0.485283
$266$	4.20202	+	7.27812i	0.257643	+	0.446250i
$267$	0.991583			0.0606839
$268$	−6.65194	+	11.5215i	−0.406332	+	0.703788i
$269$	−18.0034			−1.09769			−0.548843	−	0.835925i	$-0.684932\pi$
$269$	−18.0034			−1.09769			−0.548843	+	0.835925i	$0.684932\pi$
$270$	1.00000			0.0608581
$271$	−4.84385	+	8.38979i	−0.294243	+	0.509644i	−0.974808	−	0.223044i	$-0.928401\pi$
$271$	−4.84385	+	8.38979i	−0.294243	+	0.509644i	0.680566	+	0.732687i	$0.261734\pi$
$272$	−3.24790	−	5.62552i	−0.196933	−	0.341097i
$273$	3.49579			0.211575
$274$	−2.55008	+	4.41687i	−0.154056	+	0.266833i
$275$	−1.70202	+	2.94799i	−0.102636	+	0.177771i
$276$	−0.0917445	+	0.158906i	−0.00552237	+	0.00956502i
$277$	−2.22477	−	3.85341i	−0.133673	−	0.231529i	0.791417	−	0.611277i	$-0.209344\pi$
$277$	−2.22477	−	3.85341i	−0.133673	−	0.231529i	−0.925090	+	0.379748i	$0.876011\pi$
$278$	10.0833	+	17.4648i	0.604758	+	1.04747i
$279$	−5.40405	+	9.36008i	−0.323532	+	0.560374i
$280$	−1.74790	+	3.02744i	−0.104457	+	0.180924i
$281$	0.312303	−	0.540924i	0.0186304	−	0.0322688i	−0.856560	−	0.516048i	$-0.827403\pi$
$281$	0.312303	−	0.540924i	0.0186304	−	0.0322688i	0.875190	+	0.483779i	$0.160736\pi$
$282$	−3.22056			−0.191781
$283$	−9.56020	−	16.5587i	−0.568295	−	0.984315i	−0.996735	−	0.0807452i	$-0.974270\pi$
$283$	−9.56020	−	16.5587i	−0.568295	−	0.984315i	0.428440	−	0.903570i	$-0.359063\pi$
$284$	2.83964	−	4.91840i	0.168502	−	0.291853i
$285$	2.40405			0.142403
$286$	3.40405			0.201286
$287$	9.99158	−	17.3059i	0.589784	−	1.02154i
$288$	1.00000			0.0589256
$289$	−12.5977	−	21.8198i	−0.741038	−	1.28352i
$290$	−8.71635			−0.511842
$291$	1.00000	+	1.73205i	0.0586210	+	0.101535i
$292$	−2.40405	−	4.16393i	−0.140686	−	0.243676i
$293$	9.08333	+	15.7328i	0.530654	+	0.919119i	0.999360	+	0.0357652i	$0.0113868\pi$
$293$	9.08333	+	15.7328i	0.530654	+	0.919119i	−0.468707	+	0.883354i	$0.655280\pi$
$294$	2.61028	−	4.52114i	0.152235	−	0.263678i
$295$	−12.3956			−0.721701
$296$	−5.99579	+	1.02493i	−0.348498	+	0.0595729i
$297$	−3.40405			−0.197523
$298$	3.95413	−	6.84875i	0.229056	−	0.396737i
$299$	0.0917445	+	0.158906i	0.00530572	+	0.00918978i
$300$	0.500000	+	0.866025i	0.0288675	+	0.0500000i
$301$	−12.2206	−	21.1666i	−0.704381	−	1.22002i
$302$	1.17507			0.0676178
$303$	4.33964	+	7.51648i	0.249306	+	0.431810i
$304$	2.40405			0.137882
$305$	0.454128	−	0.786572i	0.0260033	−	0.0450390i
$306$	6.49579			0.371340
$307$	28.7913			1.64320			0.821602	−	0.570062i	$-0.193081\pi$
$307$	28.7913			1.64320			0.821602	+	0.570062i	$0.193081\pi$
$308$	5.94992	−	10.3056i	0.339028	−	0.587214i
$309$	−5.15194	−	8.92343i	−0.293084	−	0.507636i
$310$	−10.8081			−0.613858
$311$	3.26222	−	5.65033i	0.184984	−	0.320401i	−0.758587	−	0.651571i	$-0.774110\pi$
$311$	3.26222	−	5.65033i	0.184984	−	0.320401i	0.943571	+	0.331170i	$0.107443\pi$
$312$	0.500000	−	0.866025i	0.0283069	−	0.0490290i
$313$	11.3039	−	19.5789i	0.638933	−	1.10667i	−0.346734	−	0.937964i	$-0.612709\pi$
$313$	11.3039	−	19.5789i	0.638933	−	1.10667i	0.985667	−	0.168702i	$-0.0539574\pi$
$314$	10.7121	+	18.5540i	0.604521	+	1.04706i
$315$	−1.74790	−	3.02744i	−0.0984828	−	0.170577i
$316$	−8.58754	+	14.8740i	−0.483087	+	0.836731i
$317$	−2.67469	+	4.63269i	−0.150225	+	0.260198i	−0.931310	−	0.364227i	$-0.881333\pi$
$317$	−2.67469	+	4.63269i	−0.150225	+	0.260198i	0.781085	+	0.624425i	$0.214667\pi$
$318$	3.94992	−	6.84146i	0.221500	−	0.383650i
$319$	29.6709			1.66125
$320$	0.500000	+	0.866025i	0.0279508	+	0.0484123i
$321$	−9.75801	+	16.9014i	−0.544639	+	0.943343i
$322$	0.641439			0.0357460
$323$	15.6162			0.868908
$324$	−0.500000	+	0.866025i	−0.0277778	+	0.0481125i
$325$	1.00000			0.0554700
$326$	−9.65194	−	16.7177i	−0.534572	−	0.925905i
$327$	−14.3410			−0.793057
$328$	−2.85817	−	4.95050i	−0.157816	−	0.273346i
$329$	5.62920	+	9.75006i	0.310348	+	0.537538i
$330$	−1.70202	−	2.94799i	−0.0936933	−	0.162282i
$331$	−1.73948	+	3.01287i	−0.0956104	+	0.165602i	−0.909863	−	0.414908i	$-0.863814\pi$
$331$	−1.73948	+	3.01287i	−0.0956104	+	0.165602i	0.814253	+	0.580510i	$0.197147\pi$
$332$	4.68770			0.257271
$333$	2.11028	−	5.70497i	0.115643	−	0.312631i
$334$	11.2037			0.613040
$335$	6.65194	−	11.5215i	0.363434	−	0.629487i
$336$	−1.74790	−	3.02744i	−0.0953555	−	0.165161i
$337$	10.8127	+	18.7281i	0.589005	+	1.02019i	0.994363	+	0.106028i	$0.0338134\pi$
$337$	10.8127	+	18.7281i	0.589005	+	1.02019i	−0.405358	+	0.914158i	$0.632853\pi$
$338$	6.00000	+	10.3923i	0.326357	+	0.565267i
$339$	5.72477			0.310927
$340$	3.24790	+	5.62552i	0.176142	+	0.305087i
$341$	36.7913			1.99236
$342$	−1.20202	+	2.08197i	−0.0649980	+	0.112580i
$343$	6.22056			0.335879
$344$	−6.99158			−0.376961
$345$	0.0917445	−	0.158906i	0.00493936	−	0.00855522i
$346$	5.26222	+	9.11444i	0.282899	+	0.489995i
$347$	−34.2037			−1.83615			−0.918076	−	0.396404i	$-0.870258\pi$
$347$	−34.2037			−1.83615			−0.918076	+	0.396404i	$0.870258\pi$
$348$	4.35817	−	7.54858i	0.233623	−	0.404646i
$349$	6.18349	−	10.7101i	0.330995	−	0.573299i	−0.651713	−	0.758466i	$-0.725949\pi$
$349$	6.18349	−	10.7101i	0.330995	−	0.573299i	0.982707	+	0.185167i	$0.0592825\pi$
$350$	1.74790	−	3.02744i	0.0934290	−	0.161824i
$351$	0.500000	+	0.866025i	0.0266880	+	0.0462250i
$352$	−1.70202	−	2.94799i	−0.0907182	−	0.157128i
$353$	−1.70623	+	2.95528i	−0.0908136	+	0.157294i	−0.907854	−	0.419287i	$-0.862280\pi$
$353$	−1.70623	+	2.95528i	−0.0908136	+	0.157294i	0.817040	+	0.576581i	$0.195613\pi$
$354$	6.19781	−	10.7349i	0.329410	−	0.570555i
$355$	−2.83964	+	4.91840i	−0.150712	+	0.261042i
$356$	−0.991583			−0.0525538
$357$	−11.3540	−	19.6656i	−0.600916	−	1.04082i
$358$	−6.49579	+	11.2510i	−0.343313	+	0.594636i
$359$	10.0371			0.529736			0.264868	−	0.964285i	$-0.414672\pi$
$359$	10.0371			0.529736			0.264868	+	0.964285i	$0.414672\pi$
$360$	−1.00000			−0.0527046
$361$	6.61028	−	11.4493i	0.347909	−	0.602597i
$362$	−6.36698			−0.334641
$363$	0.293768	+	0.508821i	0.0154188	+	0.0267062i
$364$	−3.49579			−0.183229
$365$	2.40405	+	4.16393i	0.125834	+	0.217950i
$366$	0.454128	+	0.786572i	0.0237376	+	0.0411148i
$367$	−0.385512	−	0.667727i	−0.0201236	−	0.0348551i	0.855788	−	0.517326i	$-0.173073\pi$
$367$	−0.385512	−	0.667727i	−0.0201236	−	0.0348551i	−0.875912	+	0.482471i	$0.839739\pi$
$368$	0.0917445	−	0.158906i	0.00478251	−	0.00828355i
$369$	5.71635			0.297581
$370$	5.99579	−	1.02493i	0.311706	−	0.0532837i
$371$	−27.6162			−1.43376
$372$	5.40405	−	9.36008i	0.280187	−	0.485298i
$373$	−12.9100	−	22.3607i	−0.668452	−	1.15779i	−0.978337	−	0.207019i	$-0.933624\pi$
$373$	−12.9100	−	22.3607i	−0.668452	−	1.15779i	0.309885	−	0.950774i	$-0.399710\pi$
$374$	−11.0560	−	19.1495i	−0.571692	−	0.990199i
$375$	−0.500000	−	0.866025i	−0.0258199	−	0.0447214i
$376$	3.22056			0.166088
$377$	−4.35817	−	7.54858i	−0.224457	−	0.388772i
$378$	3.49579			0.179804
$379$	−1.16036	+	2.00980i	−0.0596037	+	0.103237i	−0.894288	−	0.447493i	$-0.852317\pi$
$379$	−1.16036	+	2.00980i	−0.0596037	+	0.103237i	0.834684	+	0.550729i	$0.185650\pi$
$380$	−2.40405			−0.123325
$381$	−1.67928			−0.0860321
$382$	−7.85817	+	13.6108i	−0.402059	+	0.696387i
$383$	−4.38130	−	7.58864i	−0.223874	−	0.387761i	0.732107	−	0.681190i	$-0.238537\pi$
$383$	−4.38130	−	7.58864i	−0.223874	−	0.387761i	−0.955981	+	0.293428i	$0.905204\pi$
$384$	−1.00000			−0.0510310
$385$	−5.94992	+	10.3056i	−0.303236	+	0.525220i
$386$	−8.62920	+	14.9462i	−0.439215	+	0.760742i
$387$	3.49579	−	6.05489i	0.177701	−	0.307787i
$388$	−1.00000	−	1.73205i	−0.0507673	−	0.0879316i
$389$	5.23909	+	9.07437i	0.265633	+	0.460089i	0.967729	−	0.251993i	$-0.0810859\pi$
$389$	5.23909	+	9.07437i	0.265633	+	0.460089i	−0.702097	+	0.712082i	$0.747753\pi$
$390$	−0.500000	+	0.866025i	−0.0253185	+	0.0438529i
$391$	0.595953	−	1.03222i	0.0301386	−	0.0522017i
$392$	−2.61028	+	4.52114i	−0.131839	+	0.228352i
$393$	0.412464			0.0208061
$394$	11.7079	+	20.2787i	0.589837	+	1.02163i
$395$	8.58754	−	14.8740i	0.432086	−	0.748395i
$396$	3.40405			0.171060
$397$	13.5875			0.681939			0.340969	−	0.940074i	$-0.389245\pi$
$397$	13.5875			0.681939			0.340969	+	0.940074i	$0.389245\pi$
$398$	7.15615	−	12.3948i	0.358705	−	0.621296i
$399$	8.40405			0.420729
$400$	−0.500000	−	0.866025i	−0.0250000	−	0.0433013i
$401$	17.8830			0.893035			0.446517	−	0.894775i	$-0.352664\pi$
$401$	17.8830			0.893035			0.446517	+	0.894775i	$0.352664\pi$
$402$	6.65194	+	11.5215i	0.331769	+	0.574640i
$403$	−5.40405	−	9.36008i	−0.269195	−	0.466259i
$404$	−4.33964	−	7.51648i	−0.215905	−	0.373959i
$405$	0.500000	−	0.866025i	0.0248452	−	0.0430331i
$406$	−30.4705			−1.51223
$407$	−20.4100	+	3.48892i	−1.01168	+	0.172939i
$408$	−6.49579			−0.321590
$409$	−0.408256	+	0.707119i	−0.0201869	+	0.0349648i	−0.875942	−	0.482416i	$-0.839759\pi$
$409$	−0.408256	+	0.707119i	−0.0201869	+	0.0349648i	0.855755	+	0.517381i	$0.173093\pi$
$410$	2.85817	+	4.95050i	0.141155	+	0.244488i
$411$	2.55008	+	4.41687i	0.125786	+	0.217868i
$412$	5.15194	+	8.92343i	0.253818	+	0.439626i
$413$	−43.3325			−2.13225
$414$	0.0917445	+	0.158906i	0.00450900	+	0.00780981i
$415$	−4.68770			−0.230110
$416$	−0.500000	+	0.866025i	−0.0245145	+	0.0424604i
$417$	20.1667			0.987565
$418$	8.18349			0.400268
$419$	−1.68770	+	2.92318i	−0.0824494	+	0.142807i	−0.904302	−	0.426894i	$-0.859608\pi$
$419$	−1.68770	+	2.92318i	−0.0824494	+	0.142807i	0.821852	+	0.569701i	$0.192941\pi$
$420$	1.74790	+	3.02744i	0.0852886	+	0.147724i
$421$	−23.0917			−1.12542			−0.562711	−	0.826653i	$-0.690242\pi$
$421$	−23.0917			−1.12542			−0.562711	+	0.826653i	$0.690242\pi$
$422$	−10.7896	+	18.6881i	−0.525228	+	0.909721i
$423$	−1.61028	+	2.78909i	−0.0782944	+	0.135610i
$424$	−3.94992	+	6.84146i	−0.191825	+	0.332251i
$425$	−3.24790	−	5.62552i	−0.157546	−	0.272878i
$426$	−2.83964	−	4.91840i	−0.137581	−	0.238297i
$427$	1.58754	−	2.74969i	0.0768262	−	0.133067i
$428$	9.75801	−	16.9014i	0.471671	−	0.816959i
$429$	1.70202	−	2.94799i	0.0821745	−	0.142330i
$430$	6.99158			0.337164
$431$	−12.7395	−	22.0654i	−0.613639	−	1.06285i	−0.990622	−	0.136634i	$-0.956372\pi$
$431$	−12.7395	−	22.0654i	−0.613639	−	1.06285i	0.376983	−	0.926220i	$-0.376962\pi$
$432$	0.500000	−	0.866025i	0.0240563	−	0.0416667i
$433$	29.9832			1.44090			0.720449	−	0.693507i	$-0.243936\pi$
$433$	29.9832			1.44090			0.720449	+	0.693507i	$0.243936\pi$
$434$	−37.7828			−1.81363
$435$	−4.35817	+	7.54858i	−0.208958	+	0.361927i
$436$	14.3410			0.686807
$437$	0.220558	+	0.382018i	0.0105507	+	0.0182744i
$438$	−4.80809			−0.229740
$439$	−9.23948	−	16.0032i	−0.440976	−	0.763793i	0.556786	−	0.830656i	$-0.312034\pi$
$439$	−9.23948	−	16.0032i	−0.440976	−	0.763793i	−0.997762	+	0.0668627i	$0.978701\pi$
$440$	1.70202	+	2.94799i	0.0811408	+	0.140540i
$441$	−2.61028	−	4.52114i	−0.124299	−	0.215292i
$442$	−3.24790	+	5.62552i	−0.154487	+	0.267579i
$443$	−36.6540			−1.74149			−0.870743	−	0.491739i	$-0.836361\pi$
$443$	−36.6540			−1.74149			−0.870743	+	0.491739i	$0.836361\pi$
$444$	−2.11028	+	5.70497i	−0.100149	+	0.270746i
$445$	0.991583			0.0470055
$446$	−6.80809	+	11.7920i	−0.322373	+	0.558366i
$447$	−3.95413	−	6.84875i	−0.187024	−	0.323935i
$448$	1.74790	+	3.02744i	0.0825803	+	0.143033i
$449$	−2.18349	−	3.78191i	−0.103045	−	0.178480i	0.809893	−	0.586578i	$-0.199525\pi$
$449$	−2.18349	−	3.78191i	−0.103045	−	0.178480i	−0.912938	+	0.408099i	$0.866192\pi$
$450$	1.00000			0.0471405
$451$	−9.72936	−	16.8517i	−0.458138	−	0.793518i
$452$	−5.72477			−0.269270
$453$	0.587536	−	1.01764i	0.0276048	−	0.0478130i
$454$	7.31230			0.343183
$455$	3.49579			0.163885
$456$	1.20202	−	2.08197i	0.0562899	−	0.0974970i
$457$	11.3123	+	19.5935i	0.529167	+	0.916544i	0.999421	+	0.0340134i	$0.0108289\pi$
$457$	11.3123	+	19.5935i	0.529167	+	0.916544i	−0.470254	+	0.882531i	$0.655838\pi$
$458$	4.90826			0.229348
$459$	3.24790	−	5.62552i	0.151599	−	0.262577i
$460$	−0.0917445	+	0.158906i	−0.00427761	+	0.00740904i
$461$	4.50459	−	7.80219i	0.209800	−	0.363384i	−0.741851	−	0.670564i	$-0.766052\pi$
$461$	4.50459	−	7.80219i	0.209800	−	0.363384i	0.951651	+	0.307180i	$0.0993854\pi$
$462$	−5.94992	−	10.3056i	−0.276815	−	0.479458i
$463$	12.5143	+	21.6754i	0.581590	+	1.00734i	0.995291	+	0.0969307i	$0.0309025\pi$
$463$	12.5143	+	21.6754i	0.581590	+	1.00734i	−0.413701	+	0.910413i	$0.635764\pi$
$464$	−4.35817	+	7.54858i	−0.202323	+	0.350434i
$465$	−5.40405	+	9.36008i	−0.250607	+	0.434064i
$466$	−5.88972	+	10.2013i	−0.272836	+	0.472566i
$467$	−14.4040			−0.666540			−0.333270	−	0.942831i	$-0.608152\pi$
$467$	−14.4040			−0.666540			−0.333270	+	0.942831i	$0.608152\pi$
$468$	−0.500000	−	0.866025i	−0.0231125	−	0.0400320i
$469$	23.2538	−	40.2768i	1.07376	−	1.85981i
$470$	−3.22056			−0.148553
$471$	21.4243			0.987179
$472$	−6.19781	+	10.7349i	−0.285278	+	0.494115i
$473$	−23.7997			−1.09431
$474$	8.58754	+	14.8740i	0.394439	+	0.683188i
$475$	2.40405			0.110305
$476$	11.3540	+	19.6656i	0.520408	+	0.901373i
$477$	−3.94992	−	6.84146i	−0.180854	−	0.313249i
$478$	0.202023	+	0.349915i	0.00924034	+	0.0160047i
$479$	−10.3956	+	18.0058i	−0.474988	+	0.822704i	−0.999590	−	0.0286439i	$-0.990881\pi$
$479$	−10.3956	+	18.0058i	−0.474988	+	0.822704i	0.524601	+	0.851348i	$0.324214\pi$
$480$	1.00000			0.0456435
$481$	3.88551	+	4.68004i	0.177164	+	0.213392i
$482$	−19.7710			−0.900546
$483$	0.320720	−	0.555503i	0.0145932	−	0.0252762i
$484$	−0.293768	−	0.508821i	−0.0133531	−	0.0231282i
$485$	1.00000	+	1.73205i	0.0454077	+	0.0786484i
$486$	0.500000	+	0.866025i	0.0226805	+	0.0392837i
$487$	−32.7542			−1.48423			−0.742117	−	0.670270i	$-0.766178\pi$
$487$	−32.7542			−1.48423			−0.742117	+	0.670270i	$0.766178\pi$
$488$	−0.454128	−	0.786572i	−0.0205574	−	0.0356065i
$489$	−19.3039			−0.872952
$490$	2.61028	−	4.52114i	0.117920	−	0.204244i
$491$	12.1835			0.549833			0.274917	−	0.961468i	$-0.411350\pi$
$491$	12.1835			0.549833			0.274917	+	0.961468i	$0.411350\pi$
$492$	−5.71635			−0.257713
$493$	−28.3098	+	49.0340i	−1.27501	+	2.20838i
$494$	−1.20202	−	2.08197i	−0.0540816	−	0.0936721i
$495$	−3.40405			−0.153001
$496$	−5.40405	+	9.36008i	−0.242649	+	0.420280i
$497$	−9.92679	+	17.1937i	−0.445277	+	0.771243i
$498$	2.34385	−	4.05967i	0.105030	−	0.181918i
$499$	2.56441	+	4.44168i	0.114799	+	0.198837i	0.917699	−	0.397276i	$-0.130044\pi$
$499$	2.56441	+	4.44168i	0.114799	+	0.198837i	−0.802901	+	0.596113i	$0.796711\pi$
$500$	0.500000	+	0.866025i	0.0223607	+	0.0387298i
$501$	5.60186	−	9.70271i	0.250273	−	0.433485i
$502$	4.01433	−	6.95302i	0.179168	−	0.310328i
$503$	−3.51853	+	6.09428i	−0.156884	+	0.271731i	−0.933743	−	0.357943i	$-0.883478\pi$
$503$	−3.51853	+	6.09428i	−0.156884	+	0.271731i	0.776860	+	0.629674i	$0.216811\pi$
$504$	−3.49579			−0.155715
$505$	4.33964	+	7.51648i	0.193111	+	0.334479i
$506$	0.312303	−	0.540924i	0.0138835	−	0.0240470i
$507$	12.0000			0.532939
$508$	1.67928			0.0745060
$509$	−6.60607	+	11.4420i	−0.292809	+	0.507160i	−0.974473	−	0.224506i	$-0.927923\pi$
$509$	−6.60607	+	11.4420i	−0.292809	+	0.507160i	0.681664	+	0.731665i	$0.261257\pi$
$510$	6.49579			0.287638
$511$	8.40405	+	14.5562i	0.371773	+	0.643930i
$512$	1.00000			0.0441942
$513$	1.20202	+	2.08197i	0.0530706	+	0.0919210i
$514$	15.6705	+	27.1421i	0.691195	+	1.19719i
$515$	−5.15194	−	8.92343i	−0.227022	−	0.393213i
$516$	−3.49579	+	6.05489i	−0.153894	+	0.266552i
$517$	10.9629			0.482149
$518$	20.9600	−	3.58295i	0.920931	−	0.157426i
$519$	10.5244			0.461972
$520$	0.500000	−	0.866025i	0.0219265	−	0.0379777i
$521$	10.9083	+	18.8937i	0.477899	+	0.827746i	0.999679	−	0.0253343i	$-0.00806503\pi$
$521$	10.9083	+	18.8937i	0.477899	+	0.827746i	−0.521780	+	0.853080i	$0.674732\pi$
$522$	−4.35817	−	7.54858i	−0.190752	−	0.330392i
$523$	6.70793	+	11.6185i	0.293317	+	0.508041i	0.974592	−	0.223987i	$-0.0719074\pi$
$523$	6.70793	+	11.6185i	0.293317	+	0.508041i	−0.681275	+	0.732028i	$0.738574\pi$
$524$	−0.412464			−0.0180186
$525$	−1.74790	−	3.02744i	−0.0762844	−	0.132128i
$526$	−29.2324			−1.27459
$527$	−35.1036	+	60.8012i	−1.52914	+	2.64854i
$528$	−3.40405			−0.148142
$529$	−22.9663			−0.998536
$530$	3.94992	−	6.84146i	0.171574	−	0.297174i
$531$	−6.19781	−	10.7349i	−0.268962	−	0.465856i
$532$	−8.40405			−0.364362
$533$	−2.85817	+	4.95050i	−0.123801	+	0.214430i
$534$	−0.495791	+	0.858736i	−0.0214550	+	0.0371611i
$535$	−9.75801	+	16.9014i	−0.421876	+	0.730710i
$536$	−6.65194	−	11.5215i	−0.287320	−	0.497653i
$537$	6.49579	+	11.2510i	0.280314	+	0.485518i
$538$	9.00170	−	15.5914i	0.388091	−	0.672193i
$539$	−8.88551	+	15.3902i	−0.382726	+	0.662901i
$540$	−0.500000	+	0.866025i	−0.0215166	+	0.0372678i
$541$	9.27523			0.398773			0.199387	−	0.979921i	$-0.436105\pi$
$541$	9.27523			0.398773			0.199387	+	0.979921i	$0.436105\pi$
$542$	−4.84385	−	8.38979i	−0.208061	−	0.360372i
$543$	−3.18349	+	5.51396i	−0.136617	+	0.236627i
$544$	6.49579			0.278505
$545$	−14.3410			−0.614299
$546$	−1.74790	+	3.02744i	−0.0748030	+	0.129563i
$547$	18.8654			0.806626			0.403313	−	0.915062i	$-0.367859\pi$
$547$	18.8654			0.806626			0.403313	+	0.915062i	$0.367859\pi$
$548$	−2.55008	−	4.41687i	−0.108934	−	0.188679i
$549$	0.908256			0.0387634
$550$	−1.70202	−	2.94799i	−0.0725745	−	0.125703i
$551$	−10.4773	−	18.1471i	−0.446346	−	0.773094i
$552$	−0.0917445	−	0.158906i	−0.00390490	−	0.00676349i
$553$	30.0202	−	51.9966i	1.27659	−	2.21112i
$554$	4.44953			0.189043
$555$	2.11028	−	5.70497i	0.0895764	−	0.242163i
$556$	−20.1667			−0.855257
$557$	5.18349	−	8.97807i	0.219631	−	0.380413i	−0.735064	−	0.677998i	$-0.762848\pi$
$557$	5.18349	−	8.97807i	0.219631	−	0.380413i	0.954695	+	0.297585i	$0.0961812\pi$
$558$	−5.40405	−	9.36008i	−0.228772	−	0.396244i
$559$	3.49579	+	6.05489i	0.147856	+	0.256094i
$560$	−1.74790	−	3.02744i	−0.0738621	−	0.127933i
$561$	−22.1120			−0.933569
$562$	0.312303	+	0.540924i	0.0131737	+	0.0228175i
$563$	−17.8459			−0.752117			−0.376058	−	0.926596i	$-0.622721\pi$
$563$	−17.8459			−0.752117			−0.376058	+	0.926596i	$0.622721\pi$
$564$	1.61028	−	2.78909i	0.0678050	−	0.117442i
$565$	5.72477			0.240843
$566$	19.1204			0.803690
$567$	1.74790	−	3.02744i	0.0734047	−	0.127141i
$568$	2.83964	+	4.91840i	0.119149	+	0.206372i
$569$	9.14905			0.383548			0.191774	−	0.981439i	$-0.438576\pi$
$569$	9.14905			0.383548			0.191774	+	0.981439i	$0.438576\pi$
$570$	−1.20202	+	2.08197i	−0.0503472	+	0.0872040i
$571$	9.28535	−	16.0827i	0.388580	−	0.673040i	−0.603679	−	0.797228i	$-0.706299\pi$
$571$	9.28535	−	16.0827i	0.388580	−	0.673040i	0.992259	+	0.124188i	$0.0396324\pi$
$572$	−1.70202	+	2.94799i	−0.0711652	+	0.123262i
$573$	7.85817	+	13.6108i	0.328280	+	0.568598i
$574$	9.99158	+	17.3059i	0.417041	+	0.722336i
$575$	0.0917445	−	0.158906i	0.00382601	−	0.00662684i
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	12.9786	−	22.4795i	0.540305	−	0.935836i	−0.458581	−	0.888652i	$-0.651642\pi$
$577$	12.9786	−	22.4795i	0.540305	−	0.935836i	0.998886	−	0.0471832i	$-0.0150245\pi$
$578$	25.1953			1.04799
$579$	8.62920	+	14.9462i	0.358617	+	0.621143i
$580$	4.35817	−	7.54858i	0.180963	−	0.313438i
$581$	−16.3872			−0.679856
$582$	−2.00000			−0.0829027
$583$	−13.4457	+	23.2887i	−0.556864	+	0.964518i
$584$	4.80809			0.198960
$585$	0.500000	+	0.866025i	0.0206725	+	0.0358057i
$586$	−18.1667			−0.750458
$587$	−23.1351	−	40.0712i	−0.954888	−	1.65391i	−0.734624	−	0.678474i	$-0.762641\pi$
$587$	−23.1351	−	40.0712i	−0.954888	−	1.65391i	−0.220264	−	0.975440i	$-0.570692\pi$
$588$	2.61028	+	4.52114i	0.107646	+	0.186449i
$589$	−12.9916	−	22.5021i	−0.535309	−	0.927182i
$590$	6.19781	−	10.7349i	0.255160	−	0.441950i
$591$	23.4159			0.963200
$592$	2.11028	−	5.70497i	0.0867319	−	0.234473i
$593$	−26.8628			−1.10312			−0.551561	−	0.834135i	$-0.685968\pi$
$593$	−26.8628			−1.10312			−0.551561	+	0.834135i	$0.685968\pi$
$594$	1.70202	−	2.94799i	0.0698349	−	0.120958i
$595$	−11.3540	−	19.6656i	−0.465467	−	0.806213i
$596$	3.95413	+	6.84875i	0.161967	+	0.280536i
$597$	−7.15615	−	12.3948i	−0.292882	−	0.507286i
$598$	−0.183489			−0.00750342
$599$	3.73948	+	6.47697i	0.152791	+	0.264642i	0.932252	−	0.361808i	$-0.117841\pi$
$599$	3.73948	+	6.47697i	0.152791	+	0.264642i	−0.779462	+	0.626450i	$0.784507\pi$
$600$	−1.00000			−0.0408248
$601$	3.28956	−	5.69768i	0.134184	−	0.232413i	−0.791101	−	0.611685i	$-0.790492\pi$
$601$	3.28956	−	5.69768i	0.134184	−	0.232413i	0.925285	+	0.379272i	$0.123825\pi$
$602$	24.4411			0.996146
$603$	13.3039			0.541776
$604$	−0.587536	+	1.01764i	−0.0239065	+	0.0414073i
$605$	0.293768	+	0.508821i	0.0119434	+	0.0206865i
$606$	−8.67928			−0.352572
$607$	−8.47726	+	14.6830i	−0.344081	+	0.595966i	−0.985186	−	0.171487i	$-0.945143\pi$
$607$	−8.47726	+	14.6830i	−0.344081	+	0.595966i	0.641105	+	0.767453i	$0.278476\pi$
$608$	−1.20202	+	2.08197i	−0.0487485	+	0.0844349i
$609$	−15.2353	+	26.3883i	−0.617364	+	1.06931i
$610$	0.454128	+	0.786572i	0.0183871	+	0.0318474i
$611$	−1.61028	−	2.78909i	−0.0651449	−	0.112834i
$612$	−3.24790	+	5.62552i	−0.131288	+	0.227398i
$613$	−1.40826	+	2.43917i	−0.0568789	+	0.0985172i	−0.893063	−	0.449932i	$-0.851448\pi$
$613$	−1.40826	+	2.43917i	−0.0568789	+	0.0985172i	0.836184	+	0.548449i	$0.184782\pi$
$614$	−14.3956	+	24.9340i	−0.580960	+	1.00625i
$615$	5.71635			0.230505
$616$	5.94992	+	10.3056i	0.239729	+	0.415223i
$617$	17.9457	−	31.0829i	0.722467	−	1.25135i	−0.237541	−	0.971378i	$-0.576341\pi$
$617$	17.9457	−	31.0829i	0.722467	−	1.25135i	0.960008	−	0.279972i	$-0.0903253\pi$
$618$	10.3039			0.414483
$619$	−35.0581			−1.40910			−0.704552	−	0.709653i	$-0.748852\pi$
$619$	−35.0581			−1.40910			−0.704552	+	0.709653i	$0.748852\pi$
$620$	5.40405	−	9.36008i	0.217032	−	0.375910i
$621$	0.183489			0.00736316
$622$	3.26222	+	5.65033i	0.130803	+	0.226558i
$623$	3.46637			0.138877
$624$	0.500000	+	0.866025i	0.0200160	+	0.0346688i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	11.3039	+	19.5789i	0.451794	+	0.782530i
$627$	4.09174	−	7.08711i	0.163409	−	0.283032i
$628$	−21.4243			−0.854922
$629$	13.7079	−	37.0583i	0.546571	−	1.47761i
$630$	3.49579			0.139276
$631$	5.19322	−	8.99492i	0.206739	−	0.358082i	−0.743947	−	0.668239i	$-0.767048\pi$
$631$	5.19322	−	8.99492i	0.206739	−	0.358082i	0.950685	+	0.310157i	$0.100382\pi$
$632$	−8.58754	−	14.8740i	−0.341594	−	0.591658i
$633$	10.7896	+	18.6881i	0.428846	+	0.742784i
$634$	−2.67469	−	4.63269i	−0.106225	−	0.183988i
$635$	−1.67928			−0.0666402
$636$	3.94992	+	6.84146i	0.156624	+	0.271282i
$637$	5.22056			0.206846
$638$	−14.8354	+	25.6957i	−0.587340	+	1.01730i
$639$	−5.67928			−0.224669
$640$	−1.00000			−0.0395285
$641$	−19.5745	+	33.9041i	−0.773147	+	1.33913i	0.162683	+	0.986678i	$0.447985\pi$
$641$	−19.5745	+	33.9041i	−0.773147	+	1.33913i	−0.935830	+	0.352452i	$0.885348\pi$
$642$	−9.75801	−	16.9014i	−0.385118	−	0.667044i
$643$	−24.7534			−0.976180			−0.488090	−	0.872793i	$-0.662306\pi$
$643$	−24.7534			−0.976180			−0.488090	+	0.872793i	$0.662306\pi$
$644$	−0.320720	+	0.555503i	−0.0126381	+	0.0218899i
$645$	3.49579	−	6.05489i	0.137647	−	0.238411i
$646$	−7.80809	+	13.5240i	−0.307205	+	0.532095i
$647$	−10.4815	−	18.1544i	−0.412069	−	0.713724i	0.583047	−	0.812438i	$-0.301860\pi$
$647$	−10.4815	−	18.1544i	−0.412069	−	0.713724i	−0.995116	+	0.0987142i	$0.968527\pi$
$648$	−0.500000	−	0.866025i	−0.0196419	−	0.0340207i
$649$	−21.0977	+	36.5422i	−0.828155	+	1.43441i
$650$	−0.500000	+	0.866025i	−0.0196116	+	0.0339683i
$651$	−18.8914	+	32.7209i	−0.740413	+	1.28243i
$652$	19.3039			0.755999
$653$	−16.8544	−	29.1926i	−0.659562	−	1.14239i	−0.980729	−	0.195372i	$-0.937409\pi$
$653$	−16.8544	−	29.1926i	−0.659562	−	1.14239i	0.321167	−	0.947022i	$-0.395925\pi$
$654$	7.17048	−	12.4196i	0.280388	−	0.485646i
$655$	0.412464			0.0161163
$656$	5.71635			0.223186
$657$	−2.40405	+	4.16393i	−0.0937908	+	0.162450i
$658$	−11.2584			−0.438898
$659$	16.1978	+	28.0554i	0.630977	+	1.09288i	0.987352	+	0.158542i	$0.0506792\pi$
$659$	16.1978	+	28.0554i	0.630977	+	1.09288i	−0.356375	+	0.934343i	$0.615987\pi$
$660$	3.40405			0.132502
$661$	−7.12881	−	12.3475i	−0.277279	−	0.480261i	0.693429	−	0.720525i	$-0.256099\pi$
$661$	−7.12881	−	12.3475i	−0.277279	−	0.480261i	−0.970707	+	0.240264i	$0.922766\pi$
$662$	−1.73948	−	3.01287i	−0.0676068	−	0.117098i
$663$	3.24790	+	5.62552i	0.126138	+	0.218477i
$664$	−2.34385	+	4.05967i	−0.0909590	+	0.157546i
$665$	8.40405			0.325895
$666$	3.88551	+	4.68004i	0.150561	+	0.181348i
$667$	−1.59935			−0.0619272
$668$	−5.60186	+	9.70271i	−0.216743	+	0.375409i
$669$	6.80809	+	11.7920i	0.263216	+	0.455904i
$670$	6.65194	+	11.5215i	0.256987	+	0.445114i
$671$	−1.54587	−	2.67753i	−0.0596777	−	0.103365i
$672$	3.49579			0.134853
$673$	12.4457	+	21.5566i	0.479747	+	0.830946i	0.999730	−	0.0232305i	$-0.00739515\pi$
$673$	12.4457	+	21.5566i	0.479747	+	0.830946i	−0.519983	+	0.854176i	$0.674062\pi$
$674$	−21.6254			−0.832978
$675$	0.500000	−	0.866025i	0.0192450	−	0.0333333i
$676$	−12.0000			−0.461538
$677$	−30.9487			−1.18946			−0.594728	−	0.803927i	$-0.702740\pi$
$677$	−30.9487			−1.18946			−0.594728	+	0.803927i	$0.702740\pi$
$678$	−2.86238	+	4.95779i	−0.109929	+	0.190403i
$679$	3.49579	+	6.05489i	0.134156	+	0.232365i
$680$	−6.49579			−0.249102
$681$	3.65615	−	6.33264i	0.140104	−	0.242667i
$682$	−18.3956	+	31.8622i	−0.704405	+	1.22007i
$683$	14.1120	−	24.4427i	0.539980	−	0.935273i	−0.458925	−	0.888475i	$-0.651765\pi$
$683$	14.1120	−	24.4427i	0.539980	−	0.935273i	0.998904	−	0.0467973i	$-0.0149015\pi$
$684$	−1.20202	−	2.08197i	−0.0459605	−	0.0796060i
$685$	2.55008	+	4.41687i	0.0974336	+	0.168760i
$686$	−3.11028	+	5.38716i	−0.118751	+	0.205683i
$687$	2.45413	−	4.25067i	0.0936308	−	0.162173i
$688$	3.49579	−	6.05489i	0.133276	−	0.230840i
$689$	7.89984			0.300960
$690$	0.0917445	+	0.158906i	0.00349265	+	0.00604945i
$691$	−9.82663	+	17.0202i	−0.373823	+	0.647480i	−0.990150	−	0.140010i	$-0.955286\pi$
$691$	−9.82663	+	17.0202i	−0.373823	+	0.647480i	0.616327	+	0.787490i	$0.288620\pi$
$692$	−10.5244			−0.400079
$693$	−11.8998			−0.452037
$694$	17.1019	−	29.6213i	0.649178	−	1.12441i
$695$	20.1667			0.764965
$696$	4.35817	+	7.54858i	0.165196	+	0.286128i
$697$	37.1322			1.40648
$698$	6.18349	+	10.7101i	0.234049	+	0.405384i
$699$	5.88972	+	10.2013i	0.222770	+	0.385848i
$700$	1.74790	+	3.02744i	0.0660642	+	0.114427i
$701$	8.02734	−	13.9038i	0.303188	−	0.525138i	−0.673668	−	0.739034i	$-0.735282\pi$
$701$	8.02734	−	13.9038i	0.303188	−	0.525138i	0.976856	+	0.213897i	$0.0686155\pi$
$702$	−1.00000			−0.0377426
$703$	9.34095	+	11.2510i	0.352301	+	0.424341i
$704$	3.40405			0.128295
$705$	−1.61028	+	2.78909i	−0.0606466	+	0.105043i
$706$	−1.70623	−	2.95528i	−0.0642149	−	0.111223i
$707$	15.1705	+	26.2760i	0.570545	+	0.988212i
$708$	6.19781	+	10.7349i	0.232928	+	0.403443i
$709$	15.4992			0.582084			0.291042	−	0.956710i	$-0.405998\pi$
$709$	15.4992			0.582084			0.291042	+	0.956710i	$0.405998\pi$
$710$	−2.83964	−	4.91840i	−0.106570	−	0.184584i
$711$	17.1751			0.644116
$712$	0.495791	−	0.858736i	0.0185806	−	0.0321825i
$713$	−1.98317			−0.0742701
$714$	22.7079			0.849823
$715$	1.70202	−	2.94799i	0.0636521	−	0.110249i
$716$	−6.49579	−	11.2510i	−0.242759	−	0.420471i
$717$	0.404047			0.0150894
$718$	−5.01853	+	8.69236i	−0.187290	+	0.324396i
$719$	−5.29836	+	9.17703i	−0.197596	+	0.342246i	−0.947748	−	0.319019i	$-0.896647\pi$
$719$	−5.29836	+	9.17703i	−0.197596	+	0.342246i	0.750153	+	0.661265i	$0.229980\pi$
$720$	0.500000	−	0.866025i	0.0186339	−	0.0322749i
$721$	−18.0101	−	31.1944i	−0.670732	−	1.16174i
$722$	6.61028	+	11.4493i	0.246009	+	0.426100i
$723$	−9.88551	+	17.1222i	−0.367646	+	0.636782i
$724$	3.18349	−	5.51396i	0.118313	−	0.204925i
$725$	−4.35817	+	7.54858i	−0.161859	+	0.280347i
$726$	−0.587536			−0.0218055
$727$	−13.9815	−	24.2166i	−0.518544	−	0.898144i	−0.999768	−	0.0215466i	$-0.993141\pi$
$727$	−13.9815	−	24.2166i	−0.518544	−	0.898144i	0.481224	−	0.876598i	$-0.340192\pi$
$728$	1.74790	−	3.02744i	0.0647813	−	0.112205i
$729$	1.00000			0.0370370
$730$	−4.80809			−0.177956
$731$	22.7079	−	39.3313i	0.839883	−	1.45472i
$732$	−0.908256			−0.0335701
$733$	13.1894	+	22.8447i	0.487162	+	0.843789i	0.999891	−	0.0147617i	$-0.00469896\pi$
$733$	13.1894	+	22.8447i	0.487162	+	0.843789i	−0.512730	+	0.858550i	$0.671366\pi$
$734$	0.771025			0.0284590
$735$	−2.61028	−	4.52114i	−0.0962816	−	0.166765i
$736$	0.0917445	+	0.158906i	0.00338175	+	0.00585736i
$737$	−22.6435	−	39.2197i	−0.834085	−	1.44468i
$738$	−2.85817	+	4.95050i	−0.105211	+	0.182231i
$739$	−44.9025			−1.65176			−0.825882	−	0.563843i	$-0.809322\pi$
$739$	−44.9025			−1.65176			−0.825882	+	0.563843i	$0.809322\pi$
$740$	−2.11028	+	5.70497i	−0.0775754	+	0.209719i
$741$	−2.40405			−0.0883149
$742$	13.8081	−	23.9163i	0.506911	−	0.877996i
$743$	8.05140	+	13.9454i	0.295377	+	0.511608i	0.975073	−	0.221886i	$-0.0712214\pi$
$743$	8.05140	+	13.9454i	0.295377	+	0.511608i	−0.679695	+	0.733494i	$0.737888\pi$
$744$	5.40405	+	9.36008i	0.198122	+	0.343157i
$745$	−3.95413	−	6.84875i	−0.144868	−	0.250919i
$746$	25.8199			0.945334
$747$	−2.34385	−	4.05967i	−0.0857569	−	0.148535i
$748$	22.1120			0.808494
$749$	−34.1120	+	59.0837i	−1.24642	+	2.15887i
$750$	1.00000			0.0365148
$751$	−28.3528			−1.03461			−0.517304	−	0.855802i	$-0.673064\pi$
$751$	−28.3528			−1.03461			−0.517304	+	0.855802i	$0.673064\pi$
$752$	−1.61028	+	2.78909i	−0.0587208	+	0.101707i
$753$	−4.01433	−	6.95302i	−0.146290	−	0.253382i
$754$	8.71635			0.317431
$755$	0.587536	−	1.01764i	0.0213826	−	0.0370358i
$756$	−1.74790	+	3.02744i	−0.0635704	+	0.110107i
$757$	−25.8729	+	44.8132i	−0.940366	+	1.62876i	−0.175592	+	0.984463i	$0.556184\pi$
$757$	−25.8729	+	44.8132i	−0.940366	+	1.62876i	−0.764774	+	0.644299i	$0.777149\pi$
$758$	−1.16036	−	2.00980i	−0.0421462	−	0.0729993i
$759$	−0.312303	−	0.540924i	−0.0113359	−	0.0196343i
$760$	1.20202	−	2.08197i	0.0436020	−	0.0755208i
$761$	2.36238	−	4.09177i	0.0856363	−	0.148326i	−0.820026	−	0.572326i	$-0.806041\pi$
$761$	2.36238	−	4.09177i	0.0856363	−	0.148326i	0.905662	+	0.424000i	$0.139374\pi$
$762$	0.839640	−	1.45430i	0.0304170	−	0.0526837i
$763$	−50.1330			−1.81494
$764$	−7.85817	−	13.6108i	−0.284299	−	0.492420i
$765$	3.24790	−	5.62552i	0.117428	−	0.203391i
$766$	8.76261			0.316606
$767$	12.3956			0.447580
$768$	0.500000	−	0.866025i	0.0180422	−	0.0312500i
$769$	23.9006			0.861878			0.430939	−	0.902381i	$-0.358182\pi$
$769$	23.9006			0.861878			0.430939	+	0.902381i	$0.358182\pi$
$770$	−5.94992	−	10.3056i	−0.214420	−	0.371387i
$771$	31.3410			1.12872
$772$	−8.62920	−	14.9462i	−0.310572	−	0.537926i
$773$	0.253805	+	0.439603i	0.00912872	+	0.0158114i	0.870554	−	0.492073i	$-0.163761\pi$
$773$	0.253805	+	0.439603i	0.00912872	+	0.0158114i	−0.861425	+	0.507885i	$0.830428\pi$
$774$	3.49579	+	6.05489i	0.125654	+	0.217638i
$775$	−5.40405	+	9.36008i	−0.194119	+	0.336224i
$776$	2.00000			0.0717958
$777$	7.37710	−	19.9434i	0.264652	−	0.715465i
$778$	−10.4782			−0.375661
$779$	−6.87119	+	11.9012i	−0.246186	+	0.426406i
$780$	−0.500000	−	0.866025i	−0.0179029	−	0.0310087i
$781$	9.66627	+	16.7425i	0.345886	+	0.599093i
$782$	0.595953	+	1.03222i	0.0213112	+	0.0369121i
$783$	−8.71635			−0.311497
$784$	−2.61028	−	4.52114i	−0.0932243	−	0.161469i
$785$	21.4243			0.764665
$786$	−0.206232	+	0.357204i	−0.00735605	+	0.0127411i
$787$	7.22975			0.257713			0.128856	−	0.991663i	$-0.458869\pi$
$787$	7.22975			0.257713			0.128856	+	0.991663i	$0.458869\pi$
$788$	−23.4159			−0.834156
$789$	−14.6162	+	25.3160i	−0.520350	+	0.901273i
$790$	8.58754	+	14.8740i	0.305531	+	0.529195i
$791$	20.0126			0.711566
$792$	−1.70202	+	2.94799i	−0.0604788	+	0.104752i
$793$	−0.454128	+	0.786572i	−0.0161265	+	0.0279320i
$794$	−6.79377	+	11.7672i	−0.241102	+	0.417601i
$795$	−3.94992	−	6.84146i	−0.140089	−	0.242642i
$796$	7.15615	+	12.3948i	0.253643	+	0.439323i
$797$	22.5707	−	39.0936i	0.799495	−	1.38477i	−0.120450	−	0.992719i	$-0.538434\pi$
$797$	22.5707	−	39.0936i	0.799495	−	1.38477i	0.919945	−	0.392047i	$-0.128233\pi$
$798$	−4.20202	+	7.27812i	−0.148750	+	0.257643i
$799$	−10.4600	+	18.1173i	−0.370049	+	0.640945i
$800$	1.00000			0.0353553
$801$	0.495791	+	0.858736i	0.0175179	+	0.0303419i
$802$	−8.94150	+	15.4871i	−0.315735	+	0.546870i
$803$	16.3670			0.577578
$804$	−13.3039			−0.469192
$805$	0.320720	−	0.555503i	0.0113039	−	0.0195789i
$806$	10.8081			0.380699
$807$	−9.00170	−	15.5914i	−0.316875	−	0.548843i
$808$	8.67928			0.305336
$809$	13.6877	+	23.7078i	0.481234	+	0.833521i	0.999768	−	0.0215354i	$-0.00685547\pi$
$809$	13.6877	+	23.7078i	0.481234	+	0.833521i	−0.518534	+	0.855057i	$0.673522\pi$
$810$	0.500000	+	0.866025i	0.0175682	+	0.0304290i
$811$	−6.84976	−	11.8641i	−0.240528	−	0.416606i	0.720337	−	0.693624i	$-0.243987\pi$
$811$	−6.84976	−	11.8641i	−0.240528	−	0.416606i	−0.960865	+	0.277018i	$0.910654\pi$
$812$	15.2353	−	26.3883i	0.534653	−	0.926046i
$813$	−9.68770			−0.339762
$814$	7.18349	−	19.4200i	0.251781	−	0.680671i
$815$	−19.3039			−0.676186
$816$	3.24790	−	5.62552i	0.113699	−	0.196933i
$817$	8.40405	+	14.5562i	0.294020	+	0.509258i
$818$	−0.408256	−	0.707119i	−0.0142743	−	0.0247238i
$819$	1.74790	+	3.02744i	0.0610764	+	0.105787i
$820$	−5.71635			−0.199624
$821$	−26.2412	−	45.4511i	−0.915823	−	1.58625i	−0.805691	−	0.592336i	$-0.798206\pi$
$821$	−26.2412	−	45.4511i	−0.915823	−	1.58625i	−0.110132	−	0.993917i	$-0.535127\pi$
$822$	−5.10016			−0.177889
$823$	13.0434	−	22.5918i	0.454663	−	0.787500i	−0.544006	−	0.839082i	$-0.683093\pi$
$823$	13.0434	−	22.5918i	0.454663	−	0.787500i	0.998669	+	0.0515820i	$0.0164263\pi$
$824$	−10.3039			−0.358953
$825$	−3.40405			−0.118514
$826$	21.6663	−	37.5271i	0.753866	−	1.30573i
$827$	18.2769	+	31.6566i	0.635551	+	1.10081i	0.986398	+	0.164374i	$0.0525605\pi$
$827$	18.2769	+	31.6566i	0.635551	+	1.10081i	−0.350847	+	0.936433i	$0.614106\pi$
$828$	−0.183489			−0.00637668
$829$	3.03325	−	5.25374i	0.105349	−	0.182470i	−0.808532	−	0.588453i	$-0.799737\pi$
$829$	3.03325	−	5.25374i	0.105349	−	0.182470i	0.913881	+	0.405983i	$0.133071\pi$
$830$	2.34385	−	4.05967i	0.0813562	−	0.140913i
$831$	2.22477	−	3.85341i	0.0771763	−	0.133673i
$832$	−0.500000	−	0.866025i	−0.0173344	−	0.0300240i
$833$	−16.9558	−	29.3684i	−0.587485	−	1.01755i
$834$	−10.0833	+	17.4648i	−0.349157	+	0.604758i
$835$	5.60186	−	9.70271i	0.193860	−	0.335776i
$836$	−4.09174	+	7.08711i	−0.141516	+	0.245113i
$837$	−10.8081			−0.373582
$838$	−1.68770	−	2.92318i	−0.0583005	−	0.100980i
$839$	26.5375	−	45.9642i	0.916175	−	1.58686i	0.111002	−	0.993820i	$-0.464594\pi$
$839$	26.5375	−	45.9642i	0.916175	−	1.58686i	0.805172	−	0.593041i	$-0.202073\pi$
$840$	−3.49579			−0.120616
$841$	46.9747			1.61982
$842$	11.5459	−	19.9980i	0.397897	−	0.689178i
$843$	0.624605			0.0215125
$844$	−10.7896	−	18.6881i	−0.371392	−	0.643270i
$845$	12.0000			0.412813
$846$	−1.61028	−	2.78909i	−0.0553625	−	0.0958907i
$847$	1.02695	+	1.77873i	0.0352865	+	0.0611180i
$848$	−3.94992	−	6.84146i	−0.135641	−	0.234937i
$849$	9.56020	−	16.5587i	0.328105	−	0.568295i
$850$	6.49579			0.222804
$851$	1.10016	−	0.188064i	0.0377131	−	0.00644674i
$852$	5.67928			0.194569
$853$	17.7854	−	30.8051i	0.608959	−	1.05475i	−0.382454	−	0.923975i	$-0.624921\pi$
$853$	17.7854	−	30.8051i	0.608959	−	1.05475i	0.991412	−	0.130773i	$-0.0417459\pi$
$854$	1.58754	+	2.74969i	0.0543244	+	0.0940926i
$855$	1.20202	+	2.08197i	0.0411083	+	0.0712017i
$856$	9.75801	+	16.9014i	0.333522	+	0.577677i
$857$	−2.54969			−0.0870959			−0.0435480	−	0.999051i	$-0.513866\pi$
$857$	−2.54969			−0.0870959			−0.0435480	+	0.999051i	$0.513866\pi$
$858$	1.70202	+	2.94799i	0.0581061	+	0.100643i
$859$	43.0951			1.47039			0.735194	−	0.677857i	$-0.237091\pi$
$859$	43.0951			1.47039			0.735194	+	0.677857i	$0.237091\pi$
$860$	−3.49579	+	6.05489i	−0.119205	+	0.206470i
$861$	19.9832			0.681024
$862$	25.4790			0.867817
$863$	−25.4100	+	44.0113i	−0.864965	+	1.49816i	0.00211701	+	0.999998i	$0.499326\pi$
$863$	−25.4100	+	44.0113i	−0.864965	+	1.49816i	−0.867082	+	0.498165i	$0.834007\pi$
$864$	0.500000	+	0.866025i	0.0170103	+	0.0294628i
$865$	10.5244			0.357842
$866$	−14.9916	+	25.9662i	−0.509435	+	0.882367i
$867$	12.5977	−	21.8198i	0.427839	−	0.741038i
$868$	18.8914	−	32.7209i	0.641217	−	1.11062i
$869$	−29.2324	−	50.6320i	−0.991640	−	1.71757i
$870$	−4.35817	−	7.54858i	−0.147756	−	0.255921i
$871$	−6.65194	+	11.5215i	−0.225392	+	0.390391i
$872$	−7.17048	+	12.4196i	−0.242823	+	0.420582i
$873$	−1.00000	+	1.73205i	−0.0338449	+	0.0586210i
$874$	−0.441116			−0.0149210
$875$	−1.74790	−	3.02744i	−0.0590897	−	0.102346i
$876$	2.40405	−	4.16393i	0.0812252	−	0.140686i
$877$	30.1751			1.01894			0.509470	−	0.860488i	$-0.329842\pi$
$877$	30.1751			1.01894			0.509470	+	0.860488i	$0.329842\pi$
$878$	18.4790			0.623635
$879$	−9.08333	+	15.7328i	−0.306373	+	0.530654i
$880$	−3.40405			−0.114750
$881$	−10.0371	−	17.3847i	−0.338157	−	0.585706i	0.645929	−	0.763398i	$-0.276470\pi$
$881$	−10.0371	−	17.3847i	−0.338157	−	0.585706i	−0.984086	+	0.177692i	$0.943137\pi$
$882$	5.22056			0.175785
$883$	1.23948	+	2.14684i	0.0417118	+	0.0722469i	0.886128	−	0.463441i	$-0.153386\pi$
$883$	1.23948	+	2.14684i	0.0417118	+	0.0722469i	−0.844416	+	0.535688i	$0.820052\pi$
$884$	−3.24790	−	5.62552i	−0.109239	−	0.189207i
$885$	−6.19781	−	10.7349i	−0.208337	−	0.360851i
$886$	18.3270	−	31.7433i	0.615708	−	1.06644i
$887$	28.6246			0.961120			0.480560	−	0.876962i	$-0.340433\pi$
$887$	28.6246			0.961120			0.480560	+	0.876962i	$0.340433\pi$
$888$	−3.88551	−	4.68004i	−0.130389	−	0.157052i
$889$	−5.87041			−0.196887
$890$	−0.495791	+	0.858736i	−0.0166190	+	0.0287849i
$891$	−1.70202	−	2.94799i	−0.0570199	−	0.0987614i
$892$	−6.80809	−	11.7920i	−0.227952	−	0.394824i
$893$	−3.87119	−	6.70509i	−0.129544	−	0.224377i
$894$	7.90826			0.264492
$895$	6.49579	+	11.2510i	0.217130	+	0.376081i
$896$	−3.49579			−0.116786
$897$	−0.0917445	+	0.158906i	−0.00306326	+	0.00530572i
$898$	4.36698			0.145728
$899$	94.2071			3.14198
$900$	−0.500000	+	0.866025i	−0.0166667	+	0.0288675i
$901$	−25.6579	−	44.4407i	−0.854787	−	1.48053i
$902$	19.4587			0.647905
$903$	12.2206	−	21.1666i	0.406675	−	0.704381i
$904$	2.86238	−	4.95779i	0.0952015	−	0.164894i
$905$	−3.18349	+	5.51396i	−0.105823	+	0.183290i
$906$	0.587536	+	1.01764i	0.0195196	+	0.0338089i
$907$	4.82493	+	8.35702i	0.160209	+	0.277490i	0.934944	−	0.354796i	$-0.115450\pi$
$907$	4.82493	+	8.35702i	0.160209	+	0.277490i	−0.774734	+	0.632287i	$0.782116\pi$
$908$	−3.65615	+	6.33264i	−0.121334	+	0.210156i
$909$	−4.33964	+	7.51648i	−0.143937	+	0.249306i
$910$	−1.74790	+	3.02744i	−0.0579422	+	0.100359i
$911$	−46.8115			−1.55093			−0.775467	−	0.631388i	$-0.782486\pi$
$911$	−46.8115			−1.55093			−0.775467	+	0.631388i	$0.782486\pi$
$912$	1.20202	+	2.08197i	0.0398030	+	0.0689408i
$913$	−7.97857	+	13.8193i	−0.264052	+	0.457352i
$914$	−22.6246			−0.748355
$915$	0.908256			0.0300260
$916$	−2.45413	+	4.25067i	−0.0810867	+	0.140446i
$917$	1.44189			0.0476153
$918$	3.24790	+	5.62552i	0.107197	+	0.185670i
$919$	18.4790			0.609565			0.304782	−	0.952422i	$-0.401416\pi$
$919$	18.4790			0.609565			0.304782	+	0.952422i	$0.401416\pi$
$920$	−0.0917445	−	0.158906i	−0.00302473	−	0.00523898i
$921$	14.3956	+	24.9340i	0.474352	+	0.821602i
$922$	4.50459	+	7.80219i	0.148351	+	0.256951i
$923$	2.83964	−	4.91840i	0.0934679	−	0.161891i
$924$	11.8998			0.391476
$925$	2.11028	−	5.70497i	0.0693855	−	0.187578i
$926$	−25.0287			−0.822493
$927$	5.15194	−	8.92343i	0.169212	−	0.293084i
$928$	−4.35817	−	7.54858i	−0.143064	−	0.247794i
$929$	−5.31230	−	9.20118i	−0.174291	−	0.301881i	0.765625	−	0.643288i	$-0.222430\pi$
$929$	−5.31230	−	9.20118i	−0.174291	−	0.301881i	−0.939916	+	0.341407i	$0.889097\pi$
$930$	−5.40405	−	9.36008i	−0.177206	−	0.306929i
$931$	12.5505			0.411325
$932$	−5.88972	−	10.2013i	−0.192924	−	0.334155i
$933$	6.52444			0.213601
$934$	7.20202	−	12.4743i	0.235657	−	0.408171i
$935$	−22.1120			−0.723139
$936$	1.00000			0.0326860
$937$	10.2993	−	17.8389i	0.336463	−	0.582771i	−0.647302	−	0.762234i	$-0.724103\pi$
$937$	10.2993	−	17.8389i	0.336463	−	0.582771i	0.983765	+	0.179463i	$0.0574359\pi$
$938$	23.2538	+	40.2768i	0.759264	+	1.31508i
$939$	22.6078			0.737777
$940$	1.61028	−	2.78909i	0.0525215	−	0.0909699i
$941$	−8.80639	+	15.2531i	−0.287080	+	0.497238i	−0.973112	−	0.230335i	$-0.926018\pi$
$941$	−8.80639	+	15.2531i	−0.287080	+	0.497238i	0.686031	+	0.727572i	$0.259351\pi$
$942$	−10.7121	+	18.5540i	−0.349020	+	0.604521i
$943$	0.524444	+	0.908363i	0.0170782	+	0.0295804i
$944$	−6.19781	−	10.7349i	−0.201722	−	0.349392i
$945$	1.74790	−	3.02744i	0.0568591	−	0.0984828i
$946$	11.8998	−	20.6111i	0.386897	−	0.670125i
$947$	−0.697815	+	1.20865i	−0.0226759	+	0.0392759i	−0.877141	−	0.480233i	$-0.840552\pi$
$947$	−0.697815	+	1.20865i	−0.0226759	+	0.0392759i	0.854465	+	0.519509i	$0.173885\pi$
$948$	−17.1751			−0.557820
$949$	−2.40405	−	4.16393i	−0.0780387	−	0.135167i
$950$	−1.20202	+	2.08197i	−0.0389988	+	0.0675479i
$951$	−5.34937			−0.173465
$952$	−22.7079			−0.735968
$953$	−3.48699	+	6.03964i	−0.112955	+	0.195643i	−0.916960	−	0.398978i	$-0.869365\pi$
$953$	−3.48699	+	6.03964i	−0.112955	+	0.195643i	0.804006	+	0.594622i	$0.202698\pi$
$954$	7.89984			0.255767
$955$	7.85817	+	13.6108i	0.254285	+	0.440434i
$956$	−0.404047			−0.0130678
$957$	14.8354	+	25.6957i	0.479561	+	0.830625i
$958$	−10.3956	−	18.0058i	−0.335868	−	0.581740i
$959$	8.91455	+	15.4405i	0.287866	+	0.498598i
$960$	−0.500000	+	0.866025i	−0.0161374	+	0.0279508i
$961$	85.8149			2.76822
$962$	−5.99579	+	1.02493i	−0.193312	+	0.0330451i
$963$	−19.5160			−0.628895
$964$	9.88551	−	17.1222i	0.318391	−	0.551469i
$965$	8.62920	+	14.9462i	0.277784	+	0.481136i
$966$	0.320720	+	0.555503i	0.0103190	+	0.0178730i
$967$	−19.4642	−	33.7131i	−0.625928	−	1.08414i	−0.988361	−	0.152129i	$-0.951387\pi$
$967$	−19.4642	−	33.7131i	−0.625928	−	1.08414i	0.362433	−	0.932010i	$-0.381946\pi$
$968$	0.587536			0.0188841
$969$	7.80809	+	13.5240i	0.250832	+	0.434454i
$970$	−2.00000			−0.0642161
$971$	−21.5875	+	37.3907i	−0.692777	+	1.19992i	0.278147	+	0.960538i	$0.410280\pi$
$971$	−21.5875	+	37.3907i	−0.692777	+	1.19992i	−0.970924	+	0.239387i	$0.923054\pi$
$972$	−1.00000			−0.0320750
$973$	70.4984			2.26008
$974$	16.3771	−	28.3660i	0.524756	−	0.908904i
$975$	0.500000	+	0.866025i	0.0160128	+	0.0277350i
$976$	0.908256			0.0290726
$977$	−13.0375	+	22.5815i	−0.417105	+	0.722447i	−0.995647	−	0.0932055i	$-0.970289\pi$
$977$	−13.0375	+	22.5815i	−0.417105	+	0.722447i	0.578542	+	0.815653i	$0.303622\pi$
$978$	9.65194	−	16.7177i	0.308635	−	0.534572i
$979$	1.68770	−	2.92318i	0.0539390	−	0.0934252i
$980$	2.61028	+	4.52114i	0.0833823	+	0.144422i
$981$	−7.17048	−	12.4196i	−0.228936	−	0.396528i
$982$	−6.09174	+	10.5512i	−0.194395	+	0.336703i
$983$	−9.68770	+	16.7796i	−0.308990	+	0.535186i	−0.978142	−	0.207940i	$-0.933324\pi$
$983$	−9.68770	+	16.7796i	−0.308990	+	0.535186i	0.669152	+	0.743126i	$0.266657\pi$
$984$	2.85817	−	4.95050i	0.0911153	−	0.157816i
$985$	23.4159			0.746091
$986$	−28.3098	−	49.0340i	−0.901568	−	1.56156i
$987$	−5.62920	+	9.75006i	−0.179179	+	0.310348i
$988$	2.40405			0.0764829
$989$	1.28288			0.0407932
$990$	1.70202	−	2.94799i	0.0540939	−	0.0936933i
$991$	−20.9369			−0.665083			−0.332541	−	0.943089i	$-0.607906\pi$
$991$	−20.9369			−0.665083			−0.332541	+	0.943089i	$0.607906\pi$
$992$	−5.40405	−	9.36008i	−0.171579	−	0.297183i
$993$	−3.47896			−0.110401
$994$	−9.92679	−	17.1937i	−0.314859	−	0.545351i
$995$	−7.15615	−	12.3948i	−0.226865	−	0.392942i
$996$	2.34385	+	4.05967i	0.0742677	+	0.128635i
$997$	−19.7955	+	34.2868i	−0.626929	+	1.08587i	0.361236	+	0.932475i	$0.382355\pi$
$997$	−19.7955	+	34.2868i	−0.626929	+	1.08587i	−0.988164	+	0.153398i	$0.950978\pi$
$998$	−5.12881			−0.162350
$999$	5.99579	−	1.02493i	0.189698	−	0.0324274i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.i.o.121.3	✓	6
37.26	even	3	inner	1110.2.i.o.211.3	yes	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.i.o.121.3	✓	6	1.1	even	1	trivial
1110.2.i.o.211.3	yes	6	37.26	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} -1.00000 q^{6} +(1.74790 + 3.02744i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(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} +(1.74790 + 3.02744i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} -1.00000 q^{10} +3.40405 q^{11} +(0.500000 - 0.866025i) q^{12} +(-0.500000 - 0.866025i) q^{13} -3.49579 q^{14} +(-0.500000 + 0.866025i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-3.24790 + 5.62552i) q^{17} +(-0.500000 - 0.866025i) q^{18} +(-1.20202 - 2.08197i) q^{19} +(0.500000 - 0.866025i) q^{20} +(-1.74790 + 3.02744i) q^{21} +(-1.70202 + 2.94799i) q^{22} -0.183489 q^{23} +(0.500000 + 0.866025i) q^{24} +(-0.500000 + 0.866025i) q^{25} +1.00000 q^{26} -1.00000 q^{27} +(1.74790 - 3.02744i) q^{28} +8.71635 q^{29} +(-0.500000 - 0.866025i) q^{30} +10.8081 q^{31} +(-0.500000 - 0.866025i) q^{32} +(1.70202 + 2.94799i) q^{33} +(-3.24790 - 5.62552i) q^{34} +(-1.74790 + 3.02744i) q^{35} +1.00000 q^{36} +(-5.99579 + 1.02493i) q^{37} +2.40405 q^{38} +(0.500000 - 0.866025i) q^{39} +(0.500000 + 0.866025i) q^{40} +(-2.85817 - 4.95050i) q^{41} +(-1.74790 - 3.02744i) q^{42} -6.99158 q^{43} +(-1.70202 - 2.94799i) q^{44} -1.00000 q^{45} +(0.0917445 - 0.158906i) q^{46} +3.22056 q^{47} -1.00000 q^{48} +(-2.61028 + 4.52114i) q^{49} +(-0.500000 - 0.866025i) q^{50} -6.49579 q^{51} +(-0.500000 + 0.866025i) q^{52} +(-3.94992 + 6.84146i) q^{53} +(0.500000 - 0.866025i) q^{54} +(1.70202 + 2.94799i) q^{55} +(1.74790 + 3.02744i) q^{56} +(1.20202 - 2.08197i) q^{57} +(-4.35817 + 7.54858i) q^{58} +(-6.19781 + 10.7349i) q^{59} +1.00000 q^{60} +(-0.454128 - 0.786572i) q^{61} +(-5.40405 + 9.36008i) q^{62} -3.49579 q^{63} +1.00000 q^{64} +(0.500000 - 0.866025i) q^{65} -3.40405 q^{66} +(-6.65194 - 11.5215i) q^{67} +6.49579 q^{68} +(-0.0917445 - 0.158906i) q^{69} +(-1.74790 - 3.02744i) q^{70} +(2.83964 + 4.91840i) q^{71} +(-0.500000 + 0.866025i) q^{72} +4.80809 q^{73} +(2.11028 - 5.70497i) q^{74} -1.00000 q^{75} +(-1.20202 + 2.08197i) q^{76} +(5.94992 + 10.3056i) q^{77} +(0.500000 + 0.866025i) q^{78} +(-8.58754 - 14.8740i) q^{79} -1.00000 q^{80} +(-0.500000 - 0.866025i) q^{81} +5.71635 q^{82} +(-2.34385 + 4.05967i) q^{83} +3.49579 q^{84} -6.49579 q^{85} +(3.49579 - 6.05489i) q^{86} +(4.35817 + 7.54858i) q^{87} +3.40405 q^{88} +(0.495791 - 0.858736i) q^{89} +(0.500000 - 0.866025i) q^{90} +(1.74790 - 3.02744i) q^{91} +(0.0917445 + 0.158906i) q^{92} +(5.40405 + 9.36008i) q^{93} +(-1.61028 + 2.78909i) q^{94} +(1.20202 - 2.08197i) q^{95} +(0.500000 - 0.866025i) q^{96} +2.00000 q^{97} +(-2.61028 - 4.52114i) q^{98} +(-1.70202 + 2.94799i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{2} + 3 q^{3} - 3 q^{4} + 3 q^{5} - 6 q^{6} - q^{7} + 6 q^{8} - 3 q^{9}+O(q^{10}) \) 6 * q - 3 * q^2 + 3 * q^3 - 3 * q^4 + 3 * q^5 - 6 * q^6 - q^7 + 6 * q^8 - 3 * q^9	\( 6 q - 3 q^{2} + 3 q^{3} - 3 q^{4} + 3 q^{5} - 6 q^{6} - q^{7} + 6 q^{8} - 3 q^{9} - 6 q^{10} + 3 q^{12} - 3 q^{13} + 2 q^{14} - 3 q^{15} - 3 q^{16} - 8 q^{17} - 3 q^{18} + 3 q^{19} + 3 q^{20} + q^{21} + 4 q^{23} + 3 q^{24} - 3 q^{25} + 6 q^{26} - 6 q^{27} - q^{28} + 14 q^{29} - 3 q^{30} + 24 q^{31} - 3 q^{32} - 8 q^{34} + q^{35} + 6 q^{36} - 13 q^{37} - 6 q^{38} + 3 q^{39} + 3 q^{40} + 2 q^{41} + q^{42} + 4 q^{43} - 6 q^{45} - 2 q^{46} + 4 q^{47} - 6 q^{48} - 8 q^{49} - 3 q^{50} - 16 q^{51} - 3 q^{52} - 2 q^{53} + 3 q^{54} - q^{56} - 3 q^{57} - 7 q^{58} - 4 q^{59} + 6 q^{60} - 4 q^{61} - 12 q^{62} + 2 q^{63} + 6 q^{64} + 3 q^{65} - 8 q^{67} + 16 q^{68} + 2 q^{69} + q^{70} + 3 q^{71} - 3 q^{72} - 12 q^{73} + 5 q^{74} - 6 q^{75} + 3 q^{76} + 14 q^{77} + 3 q^{78} - 26 q^{79} - 6 q^{80} - 3 q^{81} - 4 q^{82} - 23 q^{83} - 2 q^{84} - 16 q^{85} - 2 q^{86} + 7 q^{87} - 20 q^{89} + 3 q^{90} - q^{91} - 2 q^{92} + 12 q^{93} - 2 q^{94} - 3 q^{95} + 3 q^{96} + 12 q^{97} - 8 q^{98}+O(q^{100}) \) 6 * q - 3 * q^2 + 3 * q^3 - 3 * q^4 + 3 * q^5 - 6 * q^6 - q^7 + 6 * q^8 - 3 * q^9 - 6 * q^10 + 3 * q^12 - 3 * q^13 + 2 * q^14 - 3 * q^15 - 3 * q^16 - 8 * q^17 - 3 * q^18 + 3 * q^19 + 3 * q^20 + q^21 + 4 * q^23 + 3 * q^24 - 3 * q^25 + 6 * q^26 - 6 * q^27 - q^28 + 14 * q^29 - 3 * q^30 + 24 * q^31 - 3 * q^32 - 8 * q^34 + q^35 + 6 * q^36 - 13 * q^37 - 6 * q^38 + 3 * q^39 + 3 * q^40 + 2 * q^41 + q^42 + 4 * q^43 - 6 * q^45 - 2 * q^46 + 4 * q^47 - 6 * q^48 - 8 * q^49 - 3 * q^50 - 16 * q^51 - 3 * q^52 - 2 * q^53 + 3 * q^54 - q^56 - 3 * q^57 - 7 * q^58 - 4 * q^59 + 6 * q^60 - 4 * q^61 - 12 * q^62 + 2 * q^63 + 6 * q^64 + 3 * q^65 - 8 * q^67 + 16 * q^68 + 2 * q^69 + q^70 + 3 * q^71 - 3 * q^72 - 12 * q^73 + 5 * q^74 - 6 * q^75 + 3 * q^76 + 14 * q^77 + 3 * q^78 - 26 * q^79 - 6 * q^80 - 3 * q^81 - 4 * q^82 - 23 * q^83 - 2 * q^84 - 16 * q^85 - 2 * q^86 + 7 * q^87 - 20 * q^89 + 3 * q^90 - q^91 - 2 * q^92 + 12 * q^93 - 2 * q^94 - 3 * q^95 + 3 * q^96 + 12 * q^97 - 8 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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