LMFDB - Embedded newform 1110.2.l.b.697.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1110,2,Mod(43,1110)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1110, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("1110.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1110 = 2 \cdot 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1110.l (of order $4$, 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:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			697.14
Character	$\chi$	$=$	1110.697
Dual form			1110.2.l.b.43.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +(0.707107 + 0.707107i) q^{3} -1.00000 q^{4} +(0.215025 - 2.22571i) q^{5} +(-0.707107 + 0.707107i) q^{6} +(-1.35684 - 1.35684i) q^{7} -1.00000i q^{8} +1.00000i q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +(0.707107 + 0.707107i) q^{3} -1.00000 q^{4} +(0.215025 - 2.22571i) q^{5} +(-0.707107 + 0.707107i) q^{6} +(-1.35684 - 1.35684i) q^{7} -1.00000i q^{8} +1.00000i q^{9} +(2.22571 + 0.215025i) q^{10} -0.0194198i q^{11} +(-0.707107 - 0.707107i) q^{12} +0.159054i q^{13} +(1.35684 - 1.35684i) q^{14} +(1.72586 - 1.42177i) q^{15} +1.00000 q^{16} -4.04014 q^{17} -1.00000 q^{18} +(-4.58811 - 4.58811i) q^{19} +(-0.215025 + 2.22571i) q^{20} -1.91886i q^{21} +0.0194198 q^{22} -2.53621i q^{23} +(0.707107 - 0.707107i) q^{24} +(-4.90753 - 0.957166i) q^{25} -0.159054 q^{26} +(-0.707107 + 0.707107i) q^{27} +(1.35684 + 1.35684i) q^{28} +(-0.812030 + 0.812030i) q^{29} +(1.42177 + 1.72586i) q^{30} +(2.35628 + 2.35628i) q^{31} +1.00000i q^{32} +(0.0137318 - 0.0137318i) q^{33} -4.04014i q^{34} +(-3.31168 + 2.72817i) q^{35} -1.00000i q^{36} +(1.68369 - 5.84510i) q^{37} +(4.58811 - 4.58811i) q^{38} +(-0.112468 + 0.112468i) q^{39} +(-2.22571 - 0.215025i) q^{40} -8.21459i q^{41} +1.91886 q^{42} -4.36855i q^{43} +0.0194198i q^{44} +(2.22571 + 0.215025i) q^{45} +2.53621 q^{46} +(-5.16443 - 5.16443i) q^{47} +(0.707107 + 0.707107i) q^{48} -3.31797i q^{49} +(0.957166 - 4.90753i) q^{50} +(-2.85681 - 2.85681i) q^{51} -0.159054i q^{52} +(-4.20428 + 4.20428i) q^{53} +(-0.707107 - 0.707107i) q^{54} +(-0.0432227 - 0.00417574i) q^{55} +(-1.35684 + 1.35684i) q^{56} -6.48857i q^{57} +(-0.812030 - 0.812030i) q^{58} +(-3.16117 - 3.16117i) q^{59} +(-1.72586 + 1.42177i) q^{60} +(1.82280 + 1.82280i) q^{61} +(-2.35628 + 2.35628i) q^{62} +(1.35684 - 1.35684i) q^{63} -1.00000 q^{64} +(0.354008 + 0.0342007i) q^{65} +(0.0137318 + 0.0137318i) q^{66} +(-2.18514 + 2.18514i) q^{67} +4.04014 q^{68} +(1.79337 - 1.79337i) q^{69} +(-2.72817 - 3.31168i) q^{70} +4.70533 q^{71} +1.00000 q^{72} +(5.46673 + 5.46673i) q^{73} +(5.84510 + 1.68369i) q^{74} +(-2.79333 - 4.14696i) q^{75} +(4.58811 + 4.58811i) q^{76} +(-0.0263495 + 0.0263495i) q^{77} +(-0.112468 - 0.112468i) q^{78} +(4.93909 + 4.93909i) q^{79} +(0.215025 - 2.22571i) q^{80} -1.00000 q^{81} +8.21459 q^{82} +(6.36886 - 6.36886i) q^{83} +1.91886i q^{84} +(-0.868732 + 8.99216i) q^{85} +4.36855 q^{86} -1.14838 q^{87} -0.0194198 q^{88} +(-10.2334 + 10.2334i) q^{89} +(-0.215025 + 2.22571i) q^{90} +(0.215811 - 0.215811i) q^{91} +2.53621i q^{92} +3.33228i q^{93} +(5.16443 - 5.16443i) q^{94} +(-11.1983 + 9.22523i) q^{95} +(-0.707107 + 0.707107i) q^{96} +17.8376 q^{97} +3.31797 q^{98} +0.0194198 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 40 q^{4} - 4 q^{7}+O(q^{10}) $ 40 * q - 40 * q^4 - 4 * q^7	$ 40 q - 40 q^{4} - 4 q^{7} + 4 q^{14} + 40 q^{16} + 24 q^{17} - 40 q^{18} + 4 q^{19} + 8 q^{22} + 8 q^{25} + 8 q^{26} + 4 q^{28} + 28 q^{31} - 4 q^{33} + 20 q^{35} + 20 q^{37} - 4 q^{38} + 4 q^{39} + 16 q^{42} - 16 q^{47} + 16 q^{51} + 20 q^{53} + 16 q^{55} - 4 q^{56} - 4 q^{59} - 8 q^{61} - 28 q^{62} + 4 q^{63} - 40 q^{64} - 4 q^{65} - 4 q^{66} + 16 q^{67} - 24 q^{68} - 8 q^{69} + 12 q^{70} + 40 q^{71} + 40 q^{72} + 8 q^{73} - 8 q^{74} + 16 q^{75} - 4 q^{76} - 24 q^{77} + 4 q^{78} - 12 q^{79} - 40 q^{81} - 24 q^{82} - 8 q^{83} - 8 q^{85} + 8 q^{87} - 8 q^{88} + 12 q^{89} - 24 q^{91} + 16 q^{94} - 28 q^{95} + 40 q^{97} - 56 q^{98} + 8 q^{99}+O(q^{100}) $ 40 * q - 40 * q^4 - 4 * q^7 + 4 * q^14 + 40 * q^16 + 24 * q^17 - 40 * q^18 + 4 * q^19 + 8 * q^22 + 8 * q^25 + 8 * q^26 + 4 * q^28 + 28 * q^31 - 4 * q^33 + 20 * q^35 + 20 * q^37 - 4 * q^38 + 4 * q^39 + 16 * q^42 - 16 * q^47 + 16 * q^51 + 20 * q^53 + 16 * q^55 - 4 * q^56 - 4 * q^59 - 8 * q^61 - 28 * q^62 + 4 * q^63 - 40 * q^64 - 4 * q^65 - 4 * q^66 + 16 * q^67 - 24 * q^68 - 8 * q^69 + 12 * q^70 + 40 * q^71 + 40 * q^72 + 8 * q^73 - 8 * q^74 + 16 * q^75 - 4 * q^76 - 24 * q^77 + 4 * q^78 - 12 * q^79 - 40 * q^81 - 24 * q^82 - 8 * q^83 - 8 * q^85 + 8 * q^87 - 8 * q^88 + 12 * q^89 - 24 * q^91 + 16 * q^94 - 28 * q^95 + 40 * q^97 - 56 * q^98 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$371$	$631$	$667$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$4$	−1.00000			−0.500000
$5$	0.215025	−	2.22571i	0.0961622	−	0.995366i
$5$	0.215025	−	2.22571i	0.0961622	−	0.995366i
$6$	−0.707107	+	0.707107i	−0.288675	+	0.288675i
$7$	−1.35684	−	1.35684i	−0.512838	−	0.512838i	0.402557	−	0.915395i	$-0.368121\pi$
$7$	−1.35684	−	1.35684i	−0.512838	−	0.512838i	−0.915395	+	0.402557i	$0.868121\pi$
$8$		−	1.00000i		−	0.353553i
$9$			1.00000i			0.333333i
$10$	2.22571	+	0.215025i	0.703830	+	0.0679969i
$11$		−	0.0194198i		−	0.00585528i	−0.999996	−	0.00292764i	$-0.999068\pi$
$11$		−	0.0194198i		−	0.00585528i	0.999996	−	0.00292764i	$-0.000931898\pi$
$12$	−0.707107	−	0.707107i	−0.204124	−	0.204124i
$13$			0.159054i			0.0441137i	0.999757	+	0.0220569i	$0.00702148\pi$
$13$			0.159054i			0.0441137i	−0.999757	+	0.0220569i	$0.992979\pi$
$14$	1.35684	−	1.35684i	0.362631	−	0.362631i
$15$	1.72586	−	1.42177i	0.445614	−	0.367098i
$16$	1.00000			0.250000
$17$	−4.04014			−0.979877			−0.489939	−	0.871757i	$-0.662981\pi$
$17$	−4.04014			−0.979877			−0.489939	+	0.871757i	$0.662981\pi$
$18$	−1.00000			−0.235702
$19$	−4.58811	−	4.58811i	−1.05259	−	1.05259i	−0.998538	−	0.0540467i	$-0.982788\pi$
$19$	−4.58811	−	4.58811i	−1.05259	−	1.05259i	−0.0540467	−	0.998538i	$-0.517212\pi$
$20$	−0.215025	+	2.22571i	−0.0480811	+	0.497683i
$21$		−	1.91886i		−	0.418730i
$22$	0.0194198			0.00414031
$23$		−	2.53621i		−	0.528836i	−0.964408	−	0.264418i	$-0.914820\pi$
$23$		−	2.53621i		−	0.528836i	0.964408	−	0.264418i	$-0.0851799\pi$
$24$	0.707107	−	0.707107i	0.144338	−	0.144338i
$25$	−4.90753	−	0.957166i	−0.981506	−	0.191433i
$26$	−0.159054			−0.0311931
$27$	−0.707107	+	0.707107i	−0.136083	+	0.136083i
$28$	1.35684	+	1.35684i	0.256419	+	0.256419i
$29$	−0.812030	+	0.812030i	−0.150790	+	0.150790i	−0.778471	−	0.627681i	$-0.784004\pi$
$29$	−0.812030	+	0.812030i	−0.150790	+	0.150790i	0.627681	+	0.778471i	$0.284004\pi$
$30$	1.42177	+	1.72586i	0.259578	+	0.315097i
$31$	2.35628	+	2.35628i	0.423200	+	0.423200i	0.886304	−	0.463104i	$-0.153264\pi$
$31$	2.35628	+	2.35628i	0.423200	+	0.423200i	−0.463104	+	0.886304i	$0.653264\pi$
$32$			1.00000i			0.176777i
$33$	0.0137318	−	0.0137318i	0.00239041	−	0.00239041i
$34$		−	4.04014i		−	0.692878i
$35$	−3.31168	+	2.72817i	−0.559777	+	0.461145i
$36$		−	1.00000i		−	0.166667i
$37$	1.68369	−	5.84510i	0.276797	−	0.960928i
$37$	1.68369	−	5.84510i	0.276797	−	0.960928i
$38$	4.58811	−	4.58811i	0.744290	−	0.744290i
$39$	−0.112468	+	0.112468i	−0.0180093	+	0.0180093i
$40$	−2.22571	−	0.215025i	−0.351915	−	0.0339985i
$41$		−	8.21459i		−	1.28290i	−0.767164	−	0.641451i	$-0.778333\pi$
$41$		−	8.21459i		−	1.28290i	0.767164	−	0.641451i	$-0.221667\pi$
$42$	1.91886			0.296087
$43$		−	4.36855i		−	0.666197i	−0.942892	−	0.333099i	$-0.891906\pi$
$43$		−	4.36855i		−	0.666197i	0.942892	−	0.333099i	$-0.108094\pi$
$44$			0.0194198i			0.00292764i
$45$	2.22571	+	0.215025i	0.331789	+	0.0320541i
$46$	2.53621			0.373944
$47$	−5.16443	−	5.16443i	−0.753309	−	0.753309i	0.221786	−	0.975095i	$-0.428811\pi$
$47$	−5.16443	−	5.16443i	−0.753309	−	0.753309i	−0.975095	+	0.221786i	$0.928811\pi$
$48$	0.707107	+	0.707107i	0.102062	+	0.102062i
$49$		−	3.31797i		−	0.473995i
$50$	0.957166	−	4.90753i	0.135364	−	0.694029i
$51$	−2.85681	−	2.85681i	−0.400033	−	0.400033i
$52$		−	0.159054i		−	0.0220569i
$53$	−4.20428	+	4.20428i	−0.577502	+	0.577502i	−0.934214	−	0.356712i	$-0.883898\pi$
$53$	−4.20428	+	4.20428i	−0.577502	+	0.577502i	0.356712	+	0.934214i	$0.383898\pi$
$54$	−0.707107	−	0.707107i	−0.0962250	−	0.0962250i
$55$	−0.0432227	−	0.00417574i	−0.00582814	−	0.000563057i
$56$	−1.35684	+	1.35684i	−0.181316	+	0.181316i
$57$		−	6.48857i		−	0.859432i
$58$	−0.812030	−	0.812030i	−0.106625	−	0.106625i
$59$	−3.16117	−	3.16117i	−0.411549	−	0.411549i	0.470729	−	0.882278i	$-0.343991\pi$
$59$	−3.16117	−	3.16117i	−0.411549	−	0.411549i	−0.882278	+	0.470729i	$0.843991\pi$
$60$	−1.72586	+	1.42177i	−0.222807	+	0.183549i
$61$	1.82280	+	1.82280i	0.233385	+	0.233385i	0.814104	−	0.580719i	$-0.197228\pi$
$61$	1.82280	+	1.82280i	0.233385	+	0.233385i	−0.580719	+	0.814104i	$0.697228\pi$
$62$	−2.35628	+	2.35628i	−0.299248	+	0.299248i
$63$	1.35684	−	1.35684i	0.170946	−	0.170946i
$64$	−1.00000			−0.125000
$65$	0.354008	+	0.0342007i	0.0439093	+	0.00424207i
$66$	0.0137318	+	0.0137318i	0.00169027	+	0.00169027i
$67$	−2.18514	+	2.18514i	−0.266958	+	0.266958i	−0.827873	−	0.560916i	$-0.810449\pi$
$67$	−2.18514	+	2.18514i	−0.266958	+	0.266958i	0.560916	+	0.827873i	$0.310449\pi$
$68$	4.04014			0.489939
$69$	1.79337	−	1.79337i	0.215896	−	0.215896i
$70$	−2.72817	−	3.31168i	−0.326079	−	0.395822i
$71$	4.70533			0.558420			0.279210	−	0.960230i	$-0.409927\pi$
$71$	4.70533			0.558420			0.279210	+	0.960230i	$0.409927\pi$
$72$	1.00000			0.117851
$73$	5.46673	+	5.46673i	0.639832	+	0.639832i	0.950514	−	0.310682i	$-0.100557\pi$
$73$	5.46673	+	5.46673i	0.639832	+	0.639832i	−0.310682	+	0.950514i	$0.600557\pi$
$74$	5.84510	+	1.68369i	0.679479	+	0.195725i
$75$	−2.79333	−	4.14696i	−0.322546	−	0.478850i
$76$	4.58811	+	4.58811i	0.526293	+	0.526293i
$77$	−0.0263495	+	0.0263495i	−0.00300281	+	0.00300281i
$78$	−0.112468	−	0.112468i	−0.0127345	−	0.0127345i
$79$	4.93909	+	4.93909i	0.555690	+	0.555690i	0.928078	−	0.372387i	$-0.121461\pi$
$79$	4.93909	+	4.93909i	0.555690	+	0.555690i	−0.372387	+	0.928078i	$0.621461\pi$
$80$	0.215025	−	2.22571i	0.0240406	−	0.248841i
$81$	−1.00000			−0.111111
$82$	8.21459			0.907149
$83$	6.36886	−	6.36886i	0.699074	−	0.699074i	−0.265137	−	0.964211i	$-0.585417\pi$
$83$	6.36886	−	6.36886i	0.699074	−	0.699074i	0.964211	+	0.265137i	$0.0854172\pi$
$84$			1.91886i			0.209365i
$85$	−0.868732	+	8.99216i	−0.0942272	+	0.975336i
$86$	4.36855			0.471073
$87$	−1.14838			−0.123120
$88$	−0.0194198			−0.00207015
$89$	−10.2334	+	10.2334i	−1.08474	+	1.08474i	−0.0886823	+	0.996060i	$0.528266\pi$
$89$	−10.2334	+	10.2334i	−1.08474	+	1.08474i	−0.996060	+	0.0886823i	$0.971734\pi$
$90$	−0.215025	+	2.22571i	−0.0226656	+	0.234610i
$91$	0.215811	−	0.215811i	0.0226232	−	0.0226232i
$92$			2.53621i			0.264418i
$93$			3.33228i			0.345541i
$94$	5.16443	−	5.16443i	0.532670	−	0.532670i
$95$	−11.1983	+	9.22523i	−1.14893	+	0.946488i
$96$	−0.707107	+	0.707107i	−0.0721688	+	0.0721688i
$97$	17.8376			1.81114			0.905569	−	0.424198i	$-0.139444\pi$
$97$	17.8376			1.81114			0.905569	+	0.424198i	$0.139444\pi$
$98$	3.31797			0.335165
$99$	0.0194198			0.00195176
$100$	4.90753	+	0.957166i	0.490753	+	0.0957166i
$101$			0.190594i			0.0189648i	0.999955	+	0.00948241i	$0.00301839\pi$
$101$			0.190594i			0.0189648i	−0.999955	+	0.00948241i	$0.996982\pi$
$102$	2.85681	−	2.85681i	0.282866	−	0.282866i
$103$	−6.73625			−0.663743			−0.331871	−	0.943325i	$-0.607680\pi$
$103$	−6.73625			−0.663743			−0.331871	+	0.943325i	$0.607680\pi$
$104$	0.159054			0.0155966
$105$	−4.27082	−	0.412604i	−0.416790	−	0.0402660i
$106$	−4.20428	−	4.20428i	−0.408355	−	0.408355i
$107$	−6.22156	−	6.22156i	−0.601461	−	0.601461i	0.339239	−	0.940700i	$-0.389830\pi$
$107$	−6.22156	−	6.22156i	−0.601461	−	0.601461i	−0.940700	+	0.339239i	$0.889830\pi$
$108$	0.707107	−	0.707107i	0.0680414	−	0.0680414i
$109$	13.0168	+	13.0168i	1.24678	+	1.24678i	0.957132	+	0.289652i	$0.0935394\pi$
$109$	13.0168	+	13.0168i	1.24678	+	1.24678i	0.289652	+	0.957132i	$0.406461\pi$
$110$	0.00417574	−	0.0432227i	0.000398141	−	0.00412112i
$111$	5.32366	−	2.94256i	0.505299	−	0.279295i
$112$	−1.35684	−	1.35684i	−0.128209	−	0.128209i
$113$	−9.74000			−0.916262			−0.458131	−	0.888885i	$-0.651481\pi$
$113$	−9.74000			−0.916262			−0.458131	+	0.888885i	$0.651481\pi$
$114$	6.48857			0.607710
$115$	−5.64485	−	0.545349i	−0.526385	−	0.0508541i
$116$	0.812030	−	0.812030i	0.0753951	−	0.0753951i
$117$	−0.159054			−0.0147046
$118$	3.16117	−	3.16117i	0.291009	−	0.291009i
$119$	5.48182	+	5.48182i	0.502518	+	0.502518i
$120$	−1.42177	−	1.72586i	−0.129789	−	0.157548i
$121$	10.9996			0.999966
$122$	−1.82280	+	1.82280i	−0.165028	+	0.165028i
$123$	5.80859	−	5.80859i	0.523743	−	0.523743i
$124$	−2.35628	−	2.35628i	−0.211600	−	0.211600i
$125$	−3.18561	+	10.7169i	−0.284930	+	0.958548i
$126$	1.35684	+	1.35684i	0.120877	+	0.120877i
$127$	−12.3217	−	12.3217i	−1.09337	−	1.09337i	−0.995166	−	0.0982049i	$-0.968690\pi$
$127$	−12.3217	−	12.3217i	−1.09337	−	1.09337i	−0.0982049	−	0.995166i	$-0.531310\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	3.08903	−	3.08903i	0.271974	−	0.271974i
$130$	−0.0342007	+	0.354008i	−0.00299960	+	0.0310485i
$131$	2.08833	+	2.08833i	0.182458	+	0.182458i	0.792426	−	0.609968i	$-0.208818\pi$
$131$	2.08833	+	2.08833i	0.182458	+	0.182458i	−0.609968	+	0.792426i	$0.708818\pi$
$132$	−0.0137318	+	0.0137318i	−0.00119520	+	0.00119520i
$133$			12.4507i			1.07961i
$134$	−2.18514	−	2.18514i	−0.188767	−	0.188767i
$135$	1.42177	+	1.72586i	0.122366	+	0.148538i
$136$			4.04014i			0.346439i
$137$	−3.35280	−	3.35280i	−0.286449	−	0.286449i	0.549225	−	0.835674i	$-0.314923\pi$
$137$	−3.35280	−	3.35280i	−0.286449	−	0.286449i	−0.835674	+	0.549225i	$0.814923\pi$
$138$	1.79337	+	1.79337i	0.152662	+	0.152662i
$139$	20.9597			1.77778			0.888889	−	0.458123i	$-0.151478\pi$
$139$	20.9597			1.77778			0.888889	+	0.458123i	$0.151478\pi$
$140$	3.31168	−	2.72817i	0.279888	−	0.230573i
$141$		−	7.30360i		−	0.615074i
$142$			4.70533i			0.394862i
$143$	0.00308880			0.000258298
$144$			1.00000i			0.0833333i
$145$	1.63273	+	1.98195i	0.135591	+	0.164592i
$146$	−5.46673	+	5.46673i	−0.452429	+	0.452429i
$147$	2.34616	−	2.34616i	0.193508	−	0.193508i
$148$	−1.68369	+	5.84510i	−0.138399	+	0.480464i
$149$			6.54196i			0.535938i	0.963427	+	0.267969i	$0.0863525\pi$
$149$			6.54196i			0.535938i	−0.963427	+	0.267969i	$0.913647\pi$
$150$	4.14696	−	2.79333i	0.338598	−	0.228074i
$151$		−	14.2779i		−	1.16192i	−0.813931	−	0.580961i	$-0.802677\pi$
$151$		−	14.2779i		−	1.16192i	0.813931	−	0.580961i	$-0.197323\pi$
$152$	−4.58811	+	4.58811i	−0.372145	+	0.372145i
$153$		−	4.04014i		−	0.326626i
$154$	−0.0263495	−	0.0263495i	−0.00212331	−	0.00212331i
$155$	5.75104	−	4.73772i	0.461935	−	0.380543i
$156$	0.112468	−	0.112468i	0.00900467	−	0.00900467i
$157$	−0.0829263	−	0.0829263i	−0.00661824	−	0.00661824i	0.703790	−	0.710408i	$-0.251490\pi$
$157$	−0.0829263	−	0.0829263i	−0.00661824	−	0.00661824i	−0.710408	+	0.703790i	$0.751490\pi$
$158$	−4.93909	+	4.93909i	−0.392933	+	0.392933i
$159$	−5.94574			−0.471528
$160$	2.22571	+	0.215025i	0.175957	+	0.0169992i
$161$	−3.44123	+	3.44123i	−0.271207	+	0.271207i
$162$		−	1.00000i		−	0.0785674i
$163$	−9.48615			−0.743012			−0.371506	−	0.928430i	$-0.621159\pi$
$163$	−9.48615			−0.743012			−0.371506	+	0.928430i	$0.621159\pi$
$164$			8.21459i			0.641451i
$165$	−0.0276104	−	0.0335157i	−0.00214946	−	0.00260920i
$166$	6.36886	+	6.36886i	0.494320	+	0.494320i
$167$	−14.9171			−1.15432			−0.577161	−	0.816630i	$-0.695840\pi$
$167$	−14.9171			−1.15432			−0.577161	+	0.816630i	$0.695840\pi$
$168$	−1.91886			−0.148043
$169$	12.9747			0.998054
$170$	−8.99216	−	0.868732i	−0.689667	−	0.0666287i
$171$	4.58811	−	4.58811i	0.350862	−	0.350862i
$172$			4.36855i			0.333099i
$173$	−7.09005	−	7.09005i	−0.539046	−	0.539046i	0.384203	−	0.923249i	$-0.374476\pi$
$173$	−7.09005	−	7.09005i	−0.539046	−	0.539046i	−0.923249	+	0.384203i	$0.874476\pi$
$174$		−	1.14838i		−	0.0870587i
$175$	5.36001	+	7.95746i	0.405179	+	0.601527i
$176$		−	0.0194198i		−	0.00146382i
$177$		−	4.47057i		−	0.336029i
$178$	−10.2334	−	10.2334i	−0.767029	−	0.767029i
$179$	−12.4815	+	12.4815i	−0.932912	+	0.932912i	−0.997887	−	0.0649750i	$-0.979303\pi$
$179$	−12.4815	+	12.4815i	−0.932912	+	0.932912i	0.0649750	+	0.997887i	$0.479303\pi$
$180$	−2.22571	−	0.215025i	−0.165894	−	0.0160270i
$181$	−3.65527			−0.271694			−0.135847	−	0.990730i	$-0.543376\pi$
$181$	−3.65527			−0.271694			−0.135847	+	0.990730i	$0.543376\pi$
$182$	0.215811	+	0.215811i	0.0159970	+	0.0159970i
$183$			2.57782i			0.190558i
$184$	−2.53621			−0.186972
$185$	−12.6474	−	5.00425i	−0.929858	−	0.367919i
$186$	−3.33228			−0.244335
$187$			0.0784585i			0.00573746i
$188$	5.16443	+	5.16443i	0.376655	+	0.376655i
$189$	1.91886			0.139577
$190$	−9.22523	−	11.1983i	−0.669268	−	0.812413i
$191$	6.33676	−	6.33676i	0.458512	−	0.458512i	−0.439655	−	0.898167i	$-0.644899\pi$
$191$	6.33676	−	6.33676i	0.458512	−	0.458512i	0.898167	+	0.439655i	$0.144899\pi$
$192$	−0.707107	−	0.707107i	−0.0510310	−	0.0510310i
$193$			13.0970i			0.942746i	0.881934	+	0.471373i	$0.156241\pi$
$193$			13.0970i			0.942746i	−0.881934	+	0.471373i	$0.843759\pi$
$194$			17.8376i			1.28067i
$195$	0.226138	+	0.274505i	0.0161941	+	0.0196577i
$196$			3.31797i			0.236998i
$197$	0.639639	+	0.639639i	0.0455724	+	0.0455724i	0.729526	−	0.683953i	$-0.239741\pi$
$197$	0.639639	+	0.639639i	0.0455724	+	0.0455724i	−0.683953	+	0.729526i	$0.739741\pi$
$198$			0.0194198i			0.00138010i
$199$	9.39994	−	9.39994i	0.666344	−	0.666344i	−0.290523	−	0.956868i	$-0.593829\pi$
$199$	9.39994	−	9.39994i	0.666344	−	0.666344i	0.956868	+	0.290523i	$0.0938294\pi$
$200$	−0.957166	+	4.90753i	−0.0676818	+	0.347015i
$201$	−3.09026			−0.217970
$202$	−0.190594			−0.0134102
$203$	2.20359			0.154662
$204$	2.85681	+	2.85681i	0.200017	+	0.200017i
$205$	−18.2832	−	1.76634i	−1.27696	−	0.123367i
$206$		−	6.73625i		−	0.469337i
$207$	2.53621			0.176279
$208$			0.159054i			0.0110284i
$209$	−0.0891001	+	0.0891001i	−0.00616318	+	0.00616318i
$210$	0.412604	−	4.27082i	0.0284724	−	0.294715i
$211$	2.64429			0.182041			0.0910203	−	0.995849i	$-0.470987\pi$
$211$	2.64429			0.182041			0.0910203	+	0.995849i	$0.470987\pi$
$212$	4.20428	−	4.20428i	0.288751	−	0.288751i
$213$	3.32717	+	3.32717i	0.227974	+	0.227974i
$214$	6.22156	−	6.22156i	0.425297	−	0.425297i
$215$	−9.72310	−	0.939348i	−0.663110	−	0.0640630i
$216$	0.707107	+	0.707107i	0.0481125	+	0.0481125i
$217$		−	6.39419i		−	0.434066i
$218$	−13.0168	+	13.0168i	−0.881609	+	0.881609i
$219$			7.73112i			0.522420i
$220$	0.0432227	+	0.00417574i	0.00291407	+	0.000281528i
$221$		−	0.642601i		−	0.0432260i
$222$	2.94256	+	5.32366i	0.197492	+	0.357301i
$223$	−20.2192	+	20.2192i	−1.35398	+	1.35398i	−0.472813	+	0.881163i	$0.656761\pi$
$223$	−20.2192	+	20.2192i	−1.35398	+	1.35398i	−0.881163	+	0.472813i	$0.843239\pi$
$224$	1.35684	−	1.35684i	0.0906578	−	0.0906578i
$225$	0.957166	−	4.90753i	0.0638110	−	0.327169i
$226$		−	9.74000i		−	0.647895i
$227$	15.0931			1.00177			0.500884	−	0.865515i	$-0.333008\pi$
$227$	15.0931			1.00177			0.500884	+	0.865515i	$0.333008\pi$
$228$			6.48857i			0.429716i
$229$			4.42655i			0.292514i	0.989247	+	0.146257i	$0.0467227\pi$
$229$			4.42655i			0.292514i	−0.989247	+	0.146257i	$0.953277\pi$
$230$	0.545349	−	5.64485i	0.0359593	−	0.372211i
$231$	−0.0372639			−0.00245178
$232$	0.812030	+	0.812030i	0.0533124	+	0.0533124i
$233$	0.899214	+	0.899214i	0.0589095	+	0.0589095i	0.735948	−	0.677038i	$-0.236737\pi$
$233$	0.899214	+	0.899214i	0.0589095	+	0.0589095i	−0.677038	+	0.735948i	$0.736737\pi$
$234$		−	0.159054i		−	0.0103977i
$235$	−12.6050	+	10.3840i	−0.822258	+	0.677378i
$236$	3.16117	+	3.16117i	0.205775	+	0.205775i
$237$			6.98492i			0.453719i
$238$	−5.48182	+	5.48182i	−0.355334	+	0.355334i
$239$	7.43447	+	7.43447i	0.480896	+	0.480896i	0.905418	−	0.424522i	$-0.139558\pi$
$239$	7.43447	+	7.43447i	0.480896	+	0.480896i	−0.424522	+	0.905418i	$0.639558\pi$
$240$	1.72586	−	1.42177i	0.111404	−	0.0917746i
$241$	18.1472	−	18.1472i	1.16897	−	1.16897i	0.186514	−	0.982452i	$-0.440281\pi$
$241$	18.1472	−	18.1472i	1.16897	−	1.16897i	0.982452	−	0.186514i	$-0.0597190\pi$
$242$			10.9996i			0.707083i
$243$	−0.707107	−	0.707107i	−0.0453609	−	0.0453609i
$244$	−1.82280	−	1.82280i	−0.116693	−	0.116693i
$245$	−7.38481	−	0.713446i	−0.471798	−	0.0455804i
$246$	5.80859	+	5.80859i	0.370342	+	0.370342i
$247$	0.729759	−	0.729759i	0.0464334	−	0.0464334i
$248$	2.35628	−	2.35628i	0.149624	−	0.149624i
$249$	9.00693			0.570791
$250$	−10.7169	−	3.18561i	−0.677796	−	0.201476i
$251$	−18.2937	−	18.2937i	−1.15469	−	1.15469i	−0.985601	−	0.169089i	$-0.945918\pi$
$251$	−18.2937	−	18.2937i	−1.15469	−	1.15469i	−0.169089	−	0.985601i	$-0.554082\pi$
$252$	−1.35684	+	1.35684i	−0.0854729	+	0.0854729i
$253$	−0.0492526			−0.00309648
$254$	12.3217	−	12.3217i	0.773130	−	0.773130i
$255$	−6.97270	+	5.74413i	−0.436647	+	0.359711i
$256$	1.00000			0.0625000
$257$	7.10286			0.443064			0.221532	−	0.975153i	$-0.428894\pi$
$257$	7.10286			0.443064			0.221532	+	0.975153i	$0.428894\pi$
$258$	3.08903	+	3.08903i	0.192315	+	0.192315i
$259$	−10.2154	+	5.64637i	−0.634752	+	0.350848i
$260$	−0.354008	−	0.0342007i	−0.0219546	−	0.00212104i
$261$	−0.812030	−	0.812030i	−0.0502634	−	0.0502634i
$262$	−2.08833	+	2.08833i	−0.129017	+	0.129017i
$263$	−15.7333	−	15.7333i	−0.970154	−	0.970154i	0.0294131	−	0.999567i	$-0.490636\pi$
$263$	−15.7333	−	15.7333i	−0.970154	−	0.970154i	−0.999567	+	0.0294131i	$0.990636\pi$
$264$	−0.0137318	−	0.0137318i	−0.000845137	−	0.000845137i
$265$	8.45345	+	10.2615i	0.519292	+	0.630359i
$266$	−12.4507			−0.763400
$267$	−14.4723			−0.885688
$268$	2.18514	−	2.18514i	0.133479	−	0.133479i
$269$			8.36958i			0.510302i	0.966901	+	0.255151i	$0.0821252\pi$
$269$			8.36958i			0.510302i	−0.966901	+	0.255151i	$0.917875\pi$
$270$	−1.72586	+	1.42177i	−0.105032	+	0.0865259i
$271$	2.13823			0.129888			0.0649441	−	0.997889i	$-0.479313\pi$
$271$	2.13823			0.129888			0.0649441	+	0.997889i	$0.479313\pi$
$272$	−4.04014			−0.244969
$273$	0.305203			0.0184717
$274$	3.35280	−	3.35280i	0.202550	−	0.202550i
$275$	−0.0185879	+	0.0953031i	−0.00112089	+	0.00574699i
$276$	−1.79337	+	1.79337i	−0.107948	+	0.107948i
$277$			8.76961i			0.526915i	0.964671	+	0.263457i	$0.0848628\pi$
$277$			8.76961i			0.526915i	−0.964671	+	0.263457i	$0.915137\pi$
$278$			20.9597i			1.25708i
$279$	−2.35628	+	2.35628i	−0.141067	+	0.141067i
$280$	2.72817	+	3.31168i	0.163040	+	0.197911i
$281$	−1.22380	+	1.22380i	−0.0730057	+	0.0730057i	−0.742667	−	0.669661i	$-0.766439\pi$
$281$	−1.22380	+	1.22380i	−0.0730057	+	0.0730057i	0.669661	+	0.742667i	$0.266439\pi$
$282$	7.30360			0.434923
$283$	11.8050			0.701734			0.350867	−	0.936425i	$-0.385887\pi$
$283$	11.8050			0.701734			0.350867	+	0.936425i	$0.385887\pi$
$284$	−4.70533			−0.279210
$285$	−14.4416	−	1.39521i	−0.855449	−	0.0826449i
$286$			0.00308880i			0.000182644i
$287$	−11.1459	+	11.1459i	−0.657921	+	0.657921i
$288$	−1.00000			−0.0589256
$289$	−0.677286			−0.0398403
$290$	−1.98195	+	1.63273i	−0.116384	+	0.0958773i
$291$	12.6131	+	12.6131i	0.739394	+	0.739394i
$292$	−5.46673	−	5.46673i	−0.319916	−	0.319916i
$293$	11.7733	−	11.7733i	0.687802	−	0.687802i	−0.273944	−	0.961746i	$-0.588328\pi$
$293$	11.7733	−	11.7733i	0.687802	−	0.687802i	0.961746	+	0.273944i	$0.0883283\pi$
$294$	2.34616	+	2.34616i	0.136831	+	0.136831i
$295$	−7.71556	+	6.35610i	−0.449217	+	0.370067i
$296$	−5.84510	−	1.68369i	−0.339739	−	0.0978626i
$297$	0.0137318	+	0.0137318i	0.000796803	+	0.000796803i
$298$	−6.54196			−0.378966
$299$	0.403395			0.0233289
$300$	2.79333	+	4.14696i	0.161273	+	0.239425i
$301$	−5.92743	+	5.92743i	−0.341651	+	0.341651i
$302$	14.2779			0.821604
$303$	−0.134770	+	0.134770i	−0.00774236	+	0.00774236i
$304$	−4.58811	−	4.58811i	−0.263146	−	0.263146i
$305$	4.44895	−	3.66506i	0.254746	−	0.209861i
$306$	4.04014			0.230959
$307$	5.74100	−	5.74100i	0.327656	−	0.327656i	−0.524038	−	0.851695i	$-0.675575\pi$
$307$	5.74100	−	5.74100i	0.327656	−	0.327656i	0.851695	+	0.524038i	$0.175575\pi$
$308$	0.0263495	−	0.0263495i	0.00150140	−	0.00150140i
$309$	−4.76325	−	4.76325i	−0.270972	−	0.270972i
$310$	4.73772	+	5.75104i	0.269085	+	0.326637i
$311$	4.78072	+	4.78072i	0.271090	+	0.271090i	0.829539	−	0.558449i	$-0.188603\pi$
$311$	4.78072	+	4.78072i	0.271090	+	0.271090i	−0.558449	+	0.829539i	$0.688603\pi$
$312$	0.112468	+	0.112468i	0.00636727	+	0.00636727i
$313$			2.04383i			0.115524i	0.998330	+	0.0577621i	$0.0183965\pi$
$313$			2.04383i			0.115524i	−0.998330	+	0.0577621i	$0.981604\pi$
$314$	0.0829263	−	0.0829263i	0.00467980	−	0.00467980i
$315$	−2.72817	−	3.31168i	−0.153715	−	0.186592i
$316$	−4.93909	−	4.93909i	−0.277845	−	0.277845i
$317$	−18.6699	+	18.6699i	−1.04861	+	1.04861i	−0.0498508	+	0.998757i	$0.515875\pi$
$317$	−18.6699	+	18.6699i	−1.04861	+	1.04861i	−0.998757	+	0.0498508i	$0.984125\pi$
$318$		−	5.94574i		−	0.333421i
$319$	0.0157694	+	0.0157694i	0.000882919	+	0.000882919i
$320$	−0.215025	+	2.22571i	−0.0120203	+	0.124421i
$321$		−	8.79861i		−	0.491091i
$322$	−3.44123	−	3.44123i	−0.191772	−	0.191772i
$323$	18.5366	+	18.5366i	1.03140	+	1.03140i
$324$	1.00000			0.0555556
$325$	0.152241	−	0.780563i	0.00844482	−	0.0432979i
$326$		−	9.48615i		−	0.525389i
$327$			18.4085i			1.01799i
$328$	−8.21459			−0.453575
$329$			14.0146i			0.772651i
$330$	0.0335157	−	0.0276104i	0.00184498	−	0.00151990i
$331$	2.59788	−	2.59788i	0.142792	−	0.142792i	−0.632097	−	0.774889i	$-0.717806\pi$
$331$	2.59788	−	2.59788i	0.142792	−	0.142792i	0.774889	+	0.632097i	$0.217806\pi$
$332$	−6.36886	+	6.36886i	−0.349537	+	0.349537i
$333$	5.84510	+	1.68369i	0.320309	+	0.0922657i
$334$		−	14.9171i		−	0.816229i
$335$	4.39362	+	5.33334i	0.240049	+	0.291392i
$336$		−	1.91886i		−	0.104683i
$337$	4.86472	−	4.86472i	0.264998	−	0.264998i	−0.562083	−	0.827081i	$-0.690000\pi$
$337$	4.86472	−	4.86472i	0.264998	−	0.264998i	0.827081	+	0.562083i	$0.190000\pi$
$338$			12.9747i			0.705731i
$339$	−6.88722	−	6.88722i	−0.374062	−	0.374062i
$340$	0.868732	−	8.99216i	0.0471136	−	0.487668i
$341$	0.0457584	−	0.0457584i	0.00247796	−	0.00247796i
$342$	4.58811	+	4.58811i	0.248097	+	0.248097i
$343$	−13.9998	+	13.9998i	−0.755920	+	0.755920i
$344$	−4.36855			−0.235536
$345$	−3.60590	−	4.37714i	−0.194135	−	0.235657i
$346$	7.09005	−	7.09005i	0.381163	−	0.381163i
$347$			3.00444i			0.161287i	0.996743	+	0.0806435i	$0.0256975\pi$
$347$			3.00444i			0.161287i	−0.996743	+	0.0806435i	$0.974302\pi$
$348$	1.14838			0.0615598
$349$		−	19.3862i		−	1.03772i	−0.854860	−	0.518859i	$-0.826357\pi$
$349$		−	19.3862i		−	1.03772i	0.854860	−	0.518859i	$-0.173643\pi$
$350$	−7.95746	+	5.36001i	−0.425344	+	0.286505i
$351$	−0.112468	−	0.112468i	−0.00600312	−	0.00600312i
$352$	0.0194198			0.00103508
$353$	17.9551			0.955651			0.477826	−	0.878455i	$-0.341425\pi$
$353$	17.9551			0.955651			0.477826	+	0.878455i	$0.341425\pi$
$354$	4.47057			0.237608
$355$	1.01176	−	10.4727i	0.0536989	−	0.555832i
$356$	10.2334	−	10.2334i	0.542371	−	0.542371i
$357$			7.75247i			0.410304i
$358$	−12.4815	−	12.4815i	−0.659668	−	0.659668i
$359$		−	14.6602i		−	0.773734i	−0.922136	−	0.386867i	$-0.873557\pi$
$359$		−	14.6602i		−	0.773734i	0.922136	−	0.386867i	$-0.126443\pi$
$360$	0.215025	−	2.22571i	0.0113328	−	0.117305i
$361$			23.1015i			1.21587i
$362$		−	3.65527i		−	0.192117i
$363$	7.77791	+	7.77791i	0.408234	+	0.408234i
$364$	−0.215811	+	0.215811i	−0.0113116	+	0.0113116i
$365$	13.3428	−	10.9918i	0.698394	−	0.575339i
$366$	−2.57782			−0.134745
$367$	−14.1413	−	14.1413i	−0.738172	−	0.738172i	0.234052	−	0.972224i	$-0.424801\pi$
$367$	−14.1413	−	14.1413i	−0.738172	−	0.738172i	−0.972224	+	0.234052i	$0.924801\pi$
$368$		−	2.53621i		−	0.132209i
$369$	8.21459			0.427634
$370$	5.00425	−	12.6474i	0.260158	−	0.657509i
$371$	11.4091			0.592329
$372$		−	3.33228i		−	0.172771i
$373$	13.0549	+	13.0549i	0.675958	+	0.675958i	0.959083	−	0.283125i	$-0.0913713\pi$
$373$	13.0549	+	13.0549i	0.675958	+	0.675958i	−0.283125	+	0.959083i	$0.591371\pi$
$374$	−0.0784585			−0.00405699
$375$	−9.83056	+	5.32542i	−0.507648	+	0.275004i
$376$	−5.16443	+	5.16443i	−0.266335	+	0.266335i
$377$	−0.129157	−	0.129157i	−0.00665191	−	0.00665191i
$378$			1.91886i			0.0986957i
$379$		−	23.0708i		−	1.18507i	−0.805545	−	0.592534i	$-0.798128\pi$
$379$		−	23.0708i		−	1.18507i	0.805545	−	0.592534i	$-0.201872\pi$
$380$	11.1983	−	9.22523i	0.574463	−	0.473244i
$381$		−	17.4255i		−	0.892734i
$382$	6.33676	+	6.33676i	0.324217	+	0.324217i
$383$		−	12.0188i		−	0.614132i	−0.951688	−	0.307066i	$-0.900653\pi$
$383$		−	12.0188i		−	0.614132i	0.951688	−	0.307066i	$-0.0993472\pi$
$384$	0.707107	−	0.707107i	0.0360844	−	0.0360844i
$385$	0.0529805	+	0.0643121i	0.00270014	+	0.00327765i
$386$	−13.0970			−0.666622
$387$	4.36855			0.222066
$388$	−17.8376			−0.905569
$389$	−0.966160	−	0.966160i	−0.0489862	−	0.0489862i	0.682189	−	0.731176i	$-0.261028\pi$
$389$	−0.966160	−	0.966160i	−0.0489862	−	0.0489862i	−0.731176	+	0.682189i	$0.761028\pi$
$390$	−0.274505	+	0.226138i	−0.0139001	+	0.0114509i
$391$			10.2466i			0.518195i
$392$	−3.31797			−0.167583
$393$			2.95334i			0.148976i
$394$	−0.639639	+	0.639639i	−0.0322246	+	0.0322246i
$395$	12.0550	−	9.93092i	0.606552	−	0.499679i
$396$	−0.0194198			−0.000975880
$397$	−2.34748	+	2.34748i	−0.117817	+	0.117817i	−0.763557	−	0.645740i	$-0.776549\pi$
$397$	−2.34748	+	2.34748i	−0.117817	+	0.117817i	0.645740	+	0.763557i	$0.276549\pi$
$398$	9.39994	+	9.39994i	0.471177	+	0.471177i
$399$	−8.80396	+	8.80396i	−0.440749	+	0.440749i
$400$	−4.90753	−	0.957166i	−0.245376	−	0.0478583i
$401$	25.6841	+	25.6841i	1.28260	+	1.28260i	0.939181	+	0.343421i	$0.111586\pi$
$401$	25.6841	+	25.6841i	1.28260	+	1.28260i	0.343421	+	0.939181i	$0.388414\pi$
$402$		−	3.09026i		−	0.154128i
$403$	−0.374776	+	0.374776i	−0.0186689	+	0.0186689i
$404$		−	0.190594i		−	0.00948241i
$405$	−0.215025	+	2.22571i	−0.0106847	+	0.110596i
$406$			2.20359i			0.109362i
$407$	−0.113510	−	0.0326969i	−0.00562650	−	0.00162073i
$408$	−2.85681	+	2.85681i	−0.141433	+	0.141433i
$409$	−2.09660	+	2.09660i	−0.103670	+	0.103670i	−0.757039	−	0.653369i	$-0.773355\pi$
$409$	−2.09660	+	2.09660i	−0.103670	+	0.103670i	0.653369	+	0.757039i	$0.273355\pi$
$410$	1.76634	−	18.2832i	0.0872335	−	0.902945i
$411$		−	4.74157i		−	0.233885i
$412$	6.73625			0.331871
$413$			8.57841i			0.422116i
$414$			2.53621i			0.124648i
$415$	−12.8057	−	15.5447i	−0.628609	−	0.763058i
$416$	−0.159054			−0.00779828
$417$	14.8207	+	14.8207i	0.725775	+	0.725775i
$418$	−0.0891001	−	0.0891001i	−0.00435803	−	0.00435803i
$419$			24.3693i			1.19052i	0.803534	+	0.595259i	$0.202951\pi$
$419$			24.3693i			1.19052i	−0.803534	+	0.595259i	$0.797049\pi$
$420$	4.27082	+	0.412604i	0.208395	+	0.0201330i
$421$	−20.8544	−	20.8544i	−1.01638	−	1.01638i	−0.999864	−	0.0165195i	$-0.994741\pi$
$421$	−20.8544	−	20.8544i	−1.01638	−	1.01638i	−0.0165195	−	0.999864i	$-0.505259\pi$
$422$			2.64429i			0.128722i
$423$	5.16443	−	5.16443i	0.251103	−	0.251103i
$424$	4.20428	+	4.20428i	0.204178	+	0.204178i
$425$	19.8271	+	3.86708i	0.961755	+	0.187581i
$426$	−3.32717	+	3.32717i	−0.161202	+	0.161202i
$427$		−	4.94649i		−	0.239377i
$428$	6.22156	+	6.22156i	0.300730	+	0.300730i
$429$	0.00218411	+	0.00218411i	0.000105450	+	0.000105450i
$430$	0.939348	−	9.72310i	0.0452994	−	0.468890i
$431$	15.2684	+	15.2684i	0.735455	+	0.735455i	0.971695	−	0.236240i	$-0.0759152\pi$
$431$	15.2684	+	15.2684i	0.735455	+	0.735455i	−0.236240	+	0.971695i	$0.575915\pi$
$432$	−0.707107	+	0.707107i	−0.0340207	+	0.0340207i
$433$	12.7638	−	12.7638i	0.613390	−	0.613390i	−0.330438	−	0.943828i	$-0.607196\pi$
$433$	12.7638	−	12.7638i	0.613390	−	0.613390i	0.943828	+	0.330438i	$0.107196\pi$
$434$	6.39419			0.306931
$435$	−0.246931	+	2.55596i	−0.0118395	+	0.122549i
$436$	−13.0168	−	13.0168i	−0.623392	−	0.623392i
$437$	−11.6364	+	11.6364i	−0.556645	+	0.556645i
$438$	−7.73112			−0.369407
$439$	−11.8601	+	11.8601i	−0.566050	+	0.566050i	−0.931020	−	0.364969i	$-0.881080\pi$
$439$	−11.8601	+	11.8601i	−0.566050	+	0.566050i	0.364969	+	0.931020i	$0.381080\pi$
$440$	−0.00417574	+	0.0432227i	−0.000199071	+	0.00206056i
$441$	3.31797			0.157998
$442$	0.642601			0.0305654
$443$	1.27875	+	1.27875i	0.0607553	+	0.0607553i	0.736832	−	0.676076i	$-0.236321\pi$
$443$	1.27875	+	1.27875i	0.0607553	+	0.0607553i	−0.676076	+	0.736832i	$0.736321\pi$
$444$	−5.32366	+	2.94256i	−0.252650	+	0.139648i
$445$	20.5762	+	24.9771i	0.975404	+	1.18403i
$446$	−20.2192	−	20.2192i	−0.957405	−	0.957405i
$447$	−4.62587	+	4.62587i	−0.218796	+	0.218796i
$448$	1.35684	+	1.35684i	0.0641047	+	0.0641047i
$449$	8.61386	+	8.61386i	0.406513	+	0.406513i	0.880521	−	0.474008i	$-0.157193\pi$
$449$	8.61386	+	8.61386i	0.406513	+	0.406513i	−0.474008	+	0.880521i	$0.657193\pi$
$450$	4.90753	+	0.957166i	0.231343	+	0.0451212i
$451$	−0.159525			−0.00751175
$452$	9.74000			0.458131
$453$	10.0960	−	10.0960i	0.474353	−	0.474353i
$454$			15.0931i			0.708357i
$455$	−0.433927	−	0.526737i	−0.0203428	−	0.0246938i
$456$	−6.48857			−0.303855
$457$	−22.6986			−1.06179			−0.530897	−	0.847436i	$-0.678145\pi$
$457$	−22.6986			−1.06179			−0.530897	+	0.847436i	$0.678145\pi$
$458$	−4.42655			−0.206839
$459$	2.85681	−	2.85681i	0.133344	−	0.133344i
$460$	5.64485	+	0.545349i	0.263193	+	0.0254270i
$461$	0.105452	−	0.105452i	0.00491138	−	0.00491138i	−0.704647	−	0.709558i	$-0.748895\pi$
$461$	0.105452	−	0.105452i	0.00491138	−	0.00491138i	0.709558	+	0.704647i	$0.248895\pi$
$462$		−	0.0372639i		−	0.00173367i
$463$			38.4038i			1.78478i	0.451270	+	0.892388i	$0.350971\pi$
$463$			38.4038i			1.78478i	−0.451270	+	0.892388i	$0.649029\pi$
$464$	−0.812030	+	0.812030i	−0.0376975	+	0.0376975i
$465$	7.41668	+	0.716525i	0.343940	+	0.0332280i
$466$	−0.899214	+	0.899214i	−0.0416553	+	0.0416553i
$467$	−18.3192			−0.847713			−0.423857	−	0.905729i	$-0.639324\pi$
$467$	−18.3192			−0.847713			−0.423857	+	0.905729i	$0.639324\pi$
$468$	0.159054			0.00735228
$469$	5.92978			0.273812
$470$	−10.3840	−	12.6050i	−0.478979	−	0.581424i
$471$		−	0.117276i		−	0.00540377i
$472$	−3.16117	+	3.16117i	−0.145505	+	0.145505i
$473$	−0.0848362			−0.00390077
$474$	−6.98492			−0.320828
$475$	18.1247	+	26.9079i	0.831619	+	1.23462i
$476$	−5.48182	−	5.48182i	−0.251259	−	0.251259i
$477$	−4.20428	−	4.20428i	−0.192501	−	0.192501i
$478$	−7.43447	+	7.43447i	−0.340045	+	0.340045i
$479$	−10.0271	−	10.0271i	−0.458149	−	0.458149i	0.439899	−	0.898047i	$-0.355014\pi$
$479$	−10.0271	−	10.0271i	−0.458149	−	0.458149i	−0.898047	+	0.439899i	$0.855014\pi$
$480$	1.42177	+	1.72586i	0.0648944	+	0.0787742i
$481$	0.929688	+	0.267798i	0.0423901	+	0.0122106i
$482$	18.1472	+	18.1472i	0.826584	+	0.826584i
$483$	−4.86664			−0.221440
$484$	−10.9996			−0.499983
$485$	3.83554	−	39.7013i	0.174163	−	1.80275i
$486$	0.707107	−	0.707107i	0.0320750	−	0.0320750i
$487$	1.88010			0.0851955			0.0425977	−	0.999092i	$-0.486437\pi$
$487$	1.88010			0.0851955			0.0425977	+	0.999092i	$0.486437\pi$
$488$	1.82280	−	1.82280i	0.0825141	−	0.0825141i
$489$	−6.70772	−	6.70772i	−0.303334	−	0.303334i
$490$	0.713446	−	7.38481i	0.0322302	−	0.333612i
$491$	3.90817			0.176373			0.0881867	−	0.996104i	$-0.471893\pi$
$491$	3.90817			0.176373			0.0881867	+	0.996104i	$0.471893\pi$
$492$	−5.80859	+	5.80859i	−0.261871	+	0.261871i
$493$	3.28071	−	3.28071i	0.147756	−	0.147756i
$494$	0.729759	+	0.729759i	0.0328334	+	0.0328334i
$495$	0.00417574	−	0.0432227i	0.000187686	−	0.00194271i
$496$	2.35628	+	2.35628i	0.105800	+	0.105800i
$497$	−6.38438	−	6.38438i	−0.286379	−	0.286379i
$498$			9.00693i			0.403610i
$499$	9.78694	−	9.78694i	0.438124	−	0.438124i	−0.453257	−	0.891380i	$-0.649738\pi$
$499$	9.78694	−	9.78694i	0.438124	−	0.438124i	0.891380	+	0.453257i	$0.149738\pi$
$500$	3.18561	−	10.7169i	0.142465	−	0.479274i
$501$	−10.5480	−	10.5480i	−0.471250	−	0.471250i
$502$	18.2937	−	18.2937i	0.816489	−	0.816489i
$503$		−	29.6653i		−	1.32271i	−0.750073	−	0.661355i	$-0.769982\pi$
$503$		−	29.6653i		−	1.32271i	0.750073	−	0.661355i	$-0.230018\pi$
$504$	−1.35684	−	1.35684i	−0.0604385	−	0.0604385i
$505$	0.424206	+	0.0409825i	0.0188769	+	0.00182370i
$506$		−	0.0492526i		−	0.00218954i
$507$	9.17450	+	9.17450i	0.407454	+	0.407454i
$508$	12.3217	+	12.3217i	0.546686	+	0.546686i
$509$	9.99725			0.443120			0.221560	−	0.975147i	$-0.428885\pi$
$509$	9.99725			0.443120			0.221560	+	0.975147i	$0.428885\pi$
$510$	−5.74413	−	6.97270i	−0.254354	−	0.308756i
$511$		−	14.8350i		−	0.656260i
$512$			1.00000i			0.0441942i
$513$	6.48857			0.286477
$514$			7.10286i			0.313294i
$515$	−1.44846	+	14.9929i	−0.0638269	+	0.660667i
$516$	−3.08903	+	3.08903i	−0.135987	+	0.135987i
$517$	−0.100292	+	0.100292i	−0.00441084	+	0.00441084i
$518$	−5.64637	−	10.2154i	−0.248087	−	0.448838i
$519$		−	10.0268i		−	0.440129i
$520$	0.0342007	−	0.354008i	0.00149980	−	0.0155243i
$521$		−	34.5888i		−	1.51536i	−0.652625	−	0.757681i	$-0.726332\pi$
$521$		−	34.5888i		−	1.51536i	0.652625	−	0.757681i	$-0.273668\pi$
$522$	0.812030	−	0.812030i	0.0355416	−	0.0355416i
$523$		−	26.2205i		−	1.14654i	−0.819366	−	0.573271i	$-0.805674\pi$
$523$		−	26.2205i		−	1.14654i	0.819366	−	0.573271i	$-0.194326\pi$
$524$	−2.08833	−	2.08833i	−0.0912291	−	0.0912291i
$525$	−1.83667	+	9.41687i	−0.0801588	+	0.410986i
$526$	15.7333	−	15.7333i	0.686003	−	0.686003i
$527$	−9.51969	−	9.51969i	−0.414684	−	0.414684i
$528$	0.0137318	−	0.0137318i	0.000597602	−	0.000597602i
$529$	16.5676			0.720332
$530$	−10.2615	+	8.45345i	−0.445731	+	0.367195i
$531$	3.16117	−	3.16117i	0.137183	−	0.137183i
$532$		−	12.4507i		−	0.539805i
$533$	1.30656			0.0565936
$534$		−	14.4723i		−	0.626276i
$535$	−15.1851	+	12.5096i	−0.656511	+	0.540836i
$536$	2.18514	+	2.18514i	0.0943837	+	0.0943837i
$537$	−17.6515			−0.761719
$538$	−8.36958			−0.360838
$539$	−0.0644341			−0.00277537
$540$	−1.42177	−	1.72586i	−0.0611830	−	0.0742691i
$541$	30.0077	−	30.0077i	1.29013	−	1.29013i	0.355429	−	0.934703i	$-0.384335\pi$
$541$	30.0077	−	30.0077i	1.29013	−	1.29013i	0.934703	−	0.355429i	$-0.115665\pi$
$542$			2.13823i			0.0918449i
$543$	−2.58467	−	2.58467i	−0.110919	−	0.110919i
$544$		−	4.04014i		−	0.173219i
$545$	31.7705	−	26.1726i	1.36090	−	1.12111i
$546$			0.305203i			0.0130615i
$547$		−	22.2754i		−	0.952429i	−0.879329	−	0.476214i	$-0.842009\pi$
$547$		−	22.2754i		−	0.952429i	0.879329	−	0.476214i	$-0.157991\pi$
$548$	3.35280	+	3.35280i	0.143225	+	0.143225i
$549$	−1.82280	+	1.82280i	−0.0777950	+	0.0777950i
$550$	−0.0953031	−	0.0185879i	−0.00406374	−	0.000792592i
$551$	7.45137			0.317439
$552$	−1.79337	−	1.79337i	−0.0763309	−	0.0763309i
$553$		−	13.4031i		−	0.569958i
$554$	−8.76961			−0.372585
$555$	−5.40455	−	12.4816i	−0.229410	−	0.529815i
$556$	−20.9597			−0.888889
$557$			6.61666i			0.280357i	0.990126	+	0.140178i	$0.0447676\pi$
$557$			6.61666i			0.280357i	−0.990126	+	0.140178i	$0.955232\pi$
$558$	−2.35628	−	2.35628i	−0.0997492	−	0.0997492i
$559$	0.694836			0.0293884
$560$	−3.31168	+	2.72817i	−0.139944	+	0.115286i
$561$	−0.0554786	+	0.0554786i	−0.00234231	+	0.00234231i
$562$	−1.22380	−	1.22380i	−0.0516228	−	0.0516228i
$563$		−	2.52225i		−	0.106300i	−0.998587	−	0.0531501i	$-0.983074\pi$
$563$		−	2.52225i		−	0.106300i	0.998587	−	0.0531501i	$-0.0169262\pi$
$564$			7.30360i			0.307537i
$565$	−2.09435	+	21.6784i	−0.0881098	+	0.912016i
$566$			11.8050i			0.496201i
$567$	1.35684	+	1.35684i	0.0569820	+	0.0569820i
$568$		−	4.70533i		−	0.197431i
$569$	30.3659	−	30.3659i	1.27301	−	1.27301i	0.328503	−	0.944503i	$-0.393456\pi$
$569$	30.3659	−	30.3659i	1.27301	−	1.27301i	0.944503	−	0.328503i	$-0.106544\pi$
$570$	1.39521	−	14.4416i	0.0584388	−	0.604894i
$571$	−18.8014			−0.786812			−0.393406	−	0.919365i	$-0.628703\pi$
$571$	−18.8014			−0.786812			−0.393406	+	0.919365i	$0.628703\pi$
$572$	−0.00308880			−0.000129149
$573$	8.96153			0.374373
$574$	−11.1459	−	11.1459i	−0.465220	−	0.465220i
$575$	−2.42757	+	12.4465i	−0.101237	+	0.519056i
$576$		−	1.00000i		−	0.0416667i
$577$	−24.0197			−0.999955			−0.499977	−	0.866039i	$-0.666658\pi$
$577$	−24.0197			−0.999955			−0.499977	+	0.866039i	$0.666658\pi$
$578$		−	0.677286i		−	0.0281714i
$579$	−9.26101	+	9.26101i	−0.384874	+	0.384874i
$580$	−1.63273	−	1.98195i	−0.0677955	−	0.0822958i
$581$	−17.2831			−0.717023
$582$	−12.6131	+	12.6131i	−0.522831	+	0.522831i
$583$	0.0816461	+	0.0816461i	0.00338143	+	0.00338143i
$584$	5.46673	−	5.46673i	0.226215	−	0.226215i
$585$	−0.0342007	+	0.354008i	−0.00141402	+	0.0146364i
$586$	11.7733	+	11.7733i	0.486349	+	0.486349i
$587$			4.20338i			0.173492i	0.996230	+	0.0867461i	$0.0276469\pi$
$587$			4.20338i			0.173492i	−0.996230	+	0.0867461i	$0.972353\pi$
$588$	−2.34616	+	2.34616i	−0.0967538	+	0.0967538i
$589$		−	21.6217i		−	0.890908i
$590$	−6.35610	−	7.71556i	−0.261677	−	0.317645i
$591$			0.904587i			0.0372097i
$592$	1.68369	−	5.84510i	0.0691993	−	0.240232i
$593$	23.2834	−	23.2834i	0.956134	−	0.956134i	−0.0429431	−	0.999078i	$-0.513673\pi$
$593$	23.2834	−	23.2834i	0.956134	−	0.956134i	0.999078	+	0.0429431i	$0.0136734\pi$
$594$	−0.0137318	+	0.0137318i	−0.000563425	+	0.000563425i
$595$	13.3797	−	11.0222i	0.548512	−	0.451866i
$596$		−	6.54196i		−	0.267969i
$597$	13.2935			0.544068
$598$			0.403395i			0.0164960i
$599$		−	16.5077i		−	0.674486i	−0.941418	−	0.337243i	$-0.890506\pi$
$599$		−	16.5077i		−	0.674486i	0.941418	−	0.337243i	$-0.109494\pi$
$600$	−4.14696	+	2.79333i	−0.169299	+	0.114037i
$601$	35.4824			1.44736			0.723679	−	0.690137i	$-0.242450\pi$
$601$	35.4824			1.44736			0.723679	+	0.690137i	$0.242450\pi$
$602$	−5.92743	−	5.92743i	−0.241584	−	0.241584i
$603$	−2.18514	−	2.18514i	−0.0889858	−	0.0889858i
$604$			14.2779i			0.580961i
$605$	2.36520	−	24.4819i	0.0961589	−	0.995332i
$606$	−0.134770	−	0.134770i	−0.00547467	−	0.00547467i
$607$			3.25209i			0.131998i	0.997820	+	0.0659992i	$0.0210235\pi$
$607$			3.25209i			0.131998i	−0.997820	+	0.0659992i	$0.978977\pi$
$608$	4.58811	−	4.58811i	0.186073	−	0.186073i
$609$	1.55817	+	1.55817i	0.0631404	+	0.0631404i
$610$	3.66506	+	4.44895i	0.148394	+	0.180133i
$611$	0.821424	−	0.821424i	0.0332313	−	0.0332313i
$612$			4.04014i			0.163313i
$613$	17.6613	+	17.6613i	0.713332	+	0.713332i	0.967231	−	0.253898i	$-0.0817129\pi$
$613$	17.6613	+	17.6613i	0.713332	+	0.713332i	−0.253898	+	0.967231i	$0.581713\pi$
$614$	5.74100	+	5.74100i	0.231688	+	0.231688i
$615$	−11.6792	−	14.1772i	−0.470951	−	0.571680i
$616$	0.0263495	+	0.0263495i	0.00106165	+	0.00106165i
$617$	13.8113	−	13.8113i	0.556021	−	0.556021i	−0.372151	−	0.928172i	$-0.621380\pi$
$617$	13.8113	−	13.8113i	0.556021	−	0.556021i	0.928172	+	0.372151i	$0.121380\pi$
$618$	4.76325	−	4.76325i	0.191606	−	0.191606i
$619$	3.58040			0.143909			0.0719543	−	0.997408i	$-0.477076\pi$
$619$	3.58040			0.143909			0.0719543	+	0.997408i	$0.477076\pi$
$620$	−5.75104	+	4.73772i	−0.230967	+	0.190272i
$621$	1.79337	+	1.79337i	0.0719655	+	0.0719655i
$622$	−4.78072	+	4.78072i	−0.191690	+	0.191690i
$623$	27.7703			1.11259
$624$	−0.112468	+	0.112468i	−0.00450234	+	0.00450234i
$625$	23.1677	+	9.39463i	0.926707	+	0.375785i
$626$	−2.04383			−0.0816879
$627$	−0.126007			−0.00503222
$628$	0.0829263	+	0.0829263i	0.00330912	+	0.00330912i
$629$	−6.80235	+	23.6150i	−0.271227	+	0.941592i
$630$	3.31168	−	2.72817i	0.131941	−	0.108693i
$631$	14.6097	+	14.6097i	0.581603	+	0.581603i	0.935344	−	0.353740i	$-0.115090\pi$
$631$	14.6097	+	14.6097i	0.581603	+	0.581603i	−0.353740	+	0.935344i	$0.615090\pi$
$632$	4.93909	−	4.93909i	0.196466	−	0.196466i
$633$	1.86980	+	1.86980i	0.0743177	+	0.0743177i
$634$	−18.6699	−	18.6699i	−0.741477	−	0.741477i
$635$	−30.0739	+	24.7749i	−1.19345	+	0.983163i
$636$	5.94574			0.235764
$637$	0.527736			0.0209097
$638$	−0.0157694	+	0.0157694i	−0.000624318	+	0.000624318i
$639$			4.70533i			0.186140i
$640$	−2.22571	−	0.215025i	−0.0879787	−	0.00849962i
$641$	−0.439539			−0.0173607			−0.00868037	−	0.999962i	$-0.502763\pi$
$641$	−0.439539			−0.0173607			−0.00868037	+	0.999962i	$0.502763\pi$
$642$	8.79861			0.347254
$643$	−21.2554			−0.838230			−0.419115	−	0.907933i	$-0.637660\pi$
$643$	−21.2554			−0.838230			−0.419115	+	0.907933i	$0.637660\pi$
$644$	3.44123	−	3.44123i	0.135604	−	0.135604i
$645$	−6.21105	−	7.53949i	−0.244560	−	0.296867i
$646$	−18.5366	+	18.5366i	−0.729313	+	0.729313i
$647$		−	19.6315i		−	0.771793i	−0.922542	−	0.385897i	$-0.873892\pi$
$647$		−	19.6315i		−	0.771793i	0.922542	−	0.385897i	$-0.126108\pi$
$648$			1.00000i			0.0392837i
$649$	−0.0613892	+	0.0613892i	−0.00240974	+	0.00240974i
$650$	0.780563	+	0.152241i	0.0306162	+	0.00597139i
$651$	4.52138	−	4.52138i	0.177207	−	0.177207i
$652$	9.48615			0.371506
$653$	−6.65486			−0.260425			−0.130212	−	0.991486i	$-0.541566\pi$
$653$	−6.65486			−0.260425			−0.130212	+	0.991486i	$0.541566\pi$
$654$	−18.4085			−0.719831
$655$	5.09705	−	4.19896i	0.199158	−	0.164067i
$656$		−	8.21459i		−	0.320726i
$657$	−5.46673	+	5.46673i	−0.213277	+	0.213277i
$658$	−14.0146			−0.546347
$659$	12.4367			0.484467			0.242233	−	0.970218i	$-0.422120\pi$
$659$	12.4367			0.484467			0.242233	+	0.970218i	$0.422120\pi$
$660$	0.0276104	+	0.0335157i	0.00107473	+	0.00130460i
$661$	23.3713	+	23.3713i	0.909039	+	0.909039i	0.996195	−	0.0871559i	$-0.0277778\pi$
$661$	23.3713	+	23.3713i	0.909039	+	0.909039i	−0.0871559	+	0.996195i	$0.527778\pi$
$662$	2.59788	+	2.59788i	0.100969	+	0.100969i
$663$	0.454388	−	0.454388i	0.0176470	−	0.0176470i
$664$	−6.36886	−	6.36886i	−0.247160	−	0.247160i
$665$	27.7115	+	2.67721i	1.07461	+	0.103818i
$666$	−1.68369	+	5.84510i	−0.0652417	+	0.226493i
$667$	2.05948	+	2.05948i	0.0797433	+	0.0797433i
$668$	14.9171			0.577161
$669$	−28.5942			−1.10552
$670$	−5.33334	+	4.39362i	−0.206045	+	0.169740i
$671$	0.0353983	−	0.0353983i	0.00136654	−	0.00136654i
$672$	1.91886			0.0740217
$673$	11.3601	−	11.3601i	0.437901	−	0.437901i	−0.453404	−	0.891305i	$-0.649790\pi$
$673$	11.3601	−	11.3601i	0.437901	−	0.437901i	0.891305	+	0.453404i	$0.149790\pi$
$674$	4.86472	+	4.86472i	0.187382	+	0.187382i
$675$	4.14696	−	2.79333i	0.159617	−	0.107515i
$676$	−12.9747			−0.499027
$677$	34.5887	−	34.5887i	1.32935	−	1.32935i	0.423417	−	0.905935i	$-0.360830\pi$
$677$	34.5887	−	34.5887i	1.32935	−	1.32935i	0.905935	−	0.423417i	$-0.139170\pi$
$678$	6.88722	−	6.88722i	0.264502	−	0.264502i
$679$	−24.2028	−	24.2028i	−0.928820	−	0.928820i
$680$	8.99216	+	0.868732i	0.344833	+	0.0333143i
$681$	10.6725	+	10.6725i	0.408970	+	0.408970i
$682$	0.0457584	+	0.0457584i	0.00175218	+	0.00175218i
$683$		−	14.2153i		−	0.543935i	−0.962306	−	0.271967i	$-0.912326\pi$
$683$		−	14.2153i		−	0.543935i	0.962306	−	0.271967i	$-0.0876743\pi$
$684$	−4.58811	+	4.58811i	−0.175431	+	0.175431i
$685$	−8.18328	+	6.74141i	−0.312667	+	0.257576i
$686$	−13.9998	−	13.9998i	−0.534516	−	0.534516i
$687$	−3.13004	+	3.13004i	−0.119419	+	0.119419i
$688$		−	4.36855i		−	0.166549i
$689$	−0.668708	−	0.668708i	−0.0254757	−	0.0254757i
$690$	4.37714	−	3.60590i	0.166635	−	0.137274i
$691$		−	38.8851i		−	1.47926i	−0.673015	−	0.739629i	$-0.735001\pi$
$691$		−	38.8851i		−	1.47926i	0.673015	−	0.739629i	$-0.264999\pi$
$692$	7.09005	+	7.09005i	0.269523	+	0.269523i
$693$	−0.0263495	−	0.0263495i	−0.00100094	−	0.00100094i
$694$	−3.00444			−0.114047
$695$	4.50686	−	46.6501i	0.170955	−	1.76954i
$696$			1.14838i			0.0435294i
$697$			33.1881i			1.25709i
$698$	19.3862			0.733777
$699$			1.27168i			0.0480994i
$700$	−5.36001	−	7.95746i	−0.202589	−	0.300764i
$701$	−26.6174	+	26.6174i	−1.00532	+	1.00532i	−0.00533868	+	0.999986i	$0.501699\pi$
$701$	−26.6174	+	26.6174i	−1.00532	+	1.00532i	−0.999986	+	0.00533868i	$0.998301\pi$
$702$	0.112468	−	0.112468i	0.00424484	−	0.00424484i
$703$	−34.5429	+	19.0930i	−1.30281	+	0.720106i
$704$			0.0194198i			0.000731910i
$705$	−16.2557	−	1.57046i	−0.612224	−	0.0591469i
$706$			17.9551i			0.675747i
$707$	0.258606	−	0.258606i	0.00972588	−	0.00972588i
$708$			4.47057i			0.168014i
$709$	15.4865	+	15.4865i	0.581609	+	0.581609i	0.935345	−	0.353736i	$-0.115089\pi$
$709$	15.4865	+	15.4865i	0.581609	+	0.581609i	−0.353736	+	0.935345i	$0.615089\pi$
$710$	10.4727	+	1.01176i	0.393033	+	0.0379708i
$711$	−4.93909	+	4.93909i	−0.185230	+	0.185230i
$712$	10.2334	+	10.2334i	0.383514	+	0.383514i
$713$	5.97602	−	5.97602i	0.223804	−	0.223804i
$714$	−7.75247			−0.290129
$715$	0.000664169	−	0.00687475i	2.48385e−5	−	0.000257101i
$716$	12.4815	−	12.4815i	0.466456	−	0.466456i
$717$			10.5139i			0.392650i
$718$	14.6602			0.547112
$719$		−	6.15628i		−	0.229591i	−0.993389	−	0.114795i	$-0.963379\pi$
$719$		−	6.15628i		−	0.229591i	0.993389	−	0.114795i	$-0.0366212\pi$
$720$	2.22571	+	0.215025i	0.0829471	+	0.00801352i
$721$	9.14002	+	9.14002i	0.340392	+	0.340392i
$722$	−23.1015			−0.859751
$723$	25.6641			0.954457
$724$	3.65527			0.135847
$725$	4.76231	−	3.20781i	0.176868	−	0.119135i
$726$	−7.77791	+	7.77791i	−0.288665	+	0.288665i
$727$			12.6971i			0.470911i	0.971885	+	0.235455i	$0.0756581\pi$
$727$			12.6971i			0.470911i	−0.971885	+	0.235455i	$0.924342\pi$
$728$	−0.215811	−	0.215811i	−0.00799850	−	0.00799850i
$729$		−	1.00000i		−	0.0370370i
$730$	10.9918	+	13.3428i	0.406826	+	0.493839i
$731$			17.6495i			0.652792i
$732$		−	2.57782i		−	0.0952791i
$733$	−6.22173	−	6.22173i	−0.229805	−	0.229805i	0.582806	−	0.812611i	$-0.301955\pi$
$733$	−6.22173	−	6.22173i	−0.229805	−	0.229805i	−0.812611	+	0.582806i	$0.801955\pi$
$734$	14.1413	−	14.1413i	0.521967	−	0.521967i
$735$	−4.71737	−	5.72633i	−0.174003	−	0.211219i
$736$	2.53621			0.0934859
$737$	0.0424349	+	0.0424349i	0.00156311	+	0.00156311i
$738$			8.21459i			0.302383i
$739$	−12.1182			−0.445774			−0.222887	−	0.974844i	$-0.571548\pi$
$739$	−12.1182			−0.445774			−0.222887	+	0.974844i	$0.571548\pi$
$740$	12.6474	+	5.00425i	0.464929	+	0.183960i
$741$	1.03203			0.0379127
$742$			11.4091i			0.418840i
$743$	13.3639	+	13.3639i	0.490273	+	0.490273i	0.908392	−	0.418119i	$-0.137310\pi$
$743$	13.3639	+	13.3639i	0.490273	+	0.490273i	−0.418119	+	0.908392i	$0.637310\pi$
$744$	3.33228			0.122167
$745$	14.5605	+	1.40669i	0.533455	+	0.0515370i
$746$	−13.0549	+	13.0549i	−0.477974	+	0.477974i
$747$	6.36886	+	6.36886i	0.233025	+	0.233025i
$748$		−	0.0784585i		−	0.00286873i
$749$			16.8833i			0.616903i
$750$	−5.32542	−	9.83056i	−0.194457	−	0.358961i
$751$			28.9598i			1.05676i	0.849009	+	0.528379i	$0.177200\pi$
$751$			28.9598i			1.05676i	−0.849009	+	0.528379i	$0.822800\pi$
$752$	−5.16443	−	5.16443i	−0.188327	−	0.188327i
$753$		−	25.8712i		−	0.942800i
$754$	0.129157	−	0.129157i	0.00470361	−	0.00470361i
$755$	−31.7785	−	3.07012i	−1.15654	−	0.111733i
$756$	−1.91886			−0.0697884
$757$	−5.84398			−0.212403			−0.106202	−	0.994345i	$-0.533869\pi$
$757$	−5.84398			−0.212403			−0.106202	+	0.994345i	$0.533869\pi$
$758$	23.0708			0.837970
$759$	−0.0348268	−	0.0348268i	−0.00126413	−	0.00126413i
$760$	9.22523	+	11.1983i	0.334634	+	0.406207i
$761$		−	9.14339i		−	0.331448i	−0.986172	−	0.165724i	$-0.947004\pi$
$761$		−	9.14339i		−	0.331448i	0.986172	−	0.165724i	$-0.0529960\pi$
$762$	17.4255			0.631258
$763$		−	35.3235i		−	1.27880i
$764$	−6.33676	+	6.33676i	−0.229256	+	0.229256i
$765$	−8.99216	−	0.868732i	−0.325112	−	0.0314091i
$766$	12.0188			0.434257
$767$	0.502797	−	0.502797i	0.0181550	−	0.0181550i
$768$	0.707107	+	0.707107i	0.0255155	+	0.0255155i
$769$	−4.69206	+	4.69206i	−0.169200	+	0.169200i	−0.786628	−	0.617428i	$-0.788175\pi$
$769$	−4.69206	+	4.69206i	−0.169200	+	0.169200i	0.617428	+	0.786628i	$0.288175\pi$
$770$	−0.0643121	+	0.0529805i	−0.00231765	+	0.00190928i
$771$	5.02248	+	5.02248i	0.180880	+	0.180880i
$772$		−	13.0970i		−	0.471373i
$773$	9.03929	−	9.03929i	0.325121	−	0.325121i	−0.525607	−	0.850728i	$-0.676162\pi$
$773$	9.03929	−	9.03929i	0.325121	−	0.325121i	0.850728	+	0.525607i	$0.176162\pi$
$774$			4.36855i			0.157024i
$775$	−9.30816	−	13.8189i	−0.334359	−	0.496388i
$776$		−	17.8376i		−	0.640334i
$777$	−11.2159	−	3.23077i	−0.402370	−	0.115903i
$778$	0.966160	−	0.966160i	0.0346385	−	0.0346385i
$779$	−37.6894	+	37.6894i	−1.35036	+	1.35036i
$780$	−0.226138	−	0.274505i	−0.00809703	−	0.00982885i
$781$		−	0.0913764i		−	0.00326970i
$782$	−10.2466			−0.366419
$783$		−	1.14838i		−	0.0410399i
$784$		−	3.31797i		−	0.118499i
$785$	−0.202401	+	0.166738i	−0.00722399	+	0.00595114i
$786$	−2.95334			−0.105342
$787$	−17.6370	−	17.6370i	−0.628690	−	0.628690i	0.319048	−	0.947738i	$-0.396637\pi$
$787$	−17.6370	−	17.6370i	−0.628690	−	0.628690i	−0.947738	+	0.319048i	$0.896637\pi$
$788$	−0.639639	−	0.639639i	−0.0227862	−	0.0227862i
$789$		−	22.2502i		−	0.792128i
$790$	9.93092	+	12.0550i	0.353326	+	0.428897i
$791$	13.2156	+	13.2156i	0.469894	+	0.469894i
$792$		−	0.0194198i		−	0.000690051i
$793$	−0.289923	+	0.289923i	−0.0102955	+	0.0102955i
$794$	−2.34748	−	2.34748i	−0.0833090	−	0.0833090i
$795$	−1.27849	+	13.2335i	−0.0453432	+	0.469343i
$796$	−9.39994	+	9.39994i	−0.333172	+	0.333172i
$797$		−	44.6488i		−	1.58154i	−0.612112	−	0.790771i	$-0.709680\pi$
$797$		−	44.6488i		−	1.58154i	0.612112	−	0.790771i	$-0.290320\pi$
$798$	−8.80396	−	8.80396i	−0.311657	−	0.311657i
$799$	20.8650	+	20.8650i	0.738151	+	0.738151i
$800$	0.957166	−	4.90753i	0.0338409	−	0.173507i
$801$	−10.2334	−	10.2334i	−0.361581	−	0.361581i
$802$	−25.6841	+	25.6841i	−0.906937	+	0.906937i
$803$	0.106163	−	0.106163i	0.00374639	−	0.00374639i
$804$	3.09026			0.108985
$805$	6.91922	+	8.39912i	0.243870	+	0.296030i
$806$	−0.374776	−	0.374776i	−0.0132009	−	0.0132009i
$807$	−5.91819	+	5.91819i	−0.208330	+	0.208330i
$808$	0.190594			0.00670508
$809$	−12.8315	+	12.8315i	−0.451130	+	0.451130i	−0.895730	−	0.444599i	$-0.853346\pi$
$809$	−12.8315	+	12.8315i	−0.451130	+	0.451130i	0.444599	+	0.895730i	$0.353346\pi$
$810$	−2.22571	−	0.215025i	−0.0782033	−	0.00755522i
$811$	17.5894			0.617646			0.308823	−	0.951120i	$-0.400065\pi$
$811$	17.5894			0.617646			0.308823	+	0.951120i	$0.400065\pi$
$812$	−2.20359			−0.0773309
$813$	1.51196	+	1.51196i	0.0530267	+	0.0530267i
$814$	0.0326969	−	0.113510i	0.00114603	−	0.00397854i
$815$	−2.03976	+	21.1134i	−0.0714497	+	0.739569i
$816$	−2.85681	−	2.85681i	−0.100008	−	0.100008i
$817$	−20.0434	+	20.0434i	−0.701230	+	0.701230i
$818$	−2.09660	−	2.09660i	−0.0733059	−	0.0733059i
$819$	0.215811	+	0.215811i	0.00754106	+	0.00754106i
$820$	18.2832	+	1.76634i	0.638479	+	0.0616834i
$821$	−34.8832			−1.21743			−0.608717	−	0.793388i	$-0.708315\pi$
$821$	−34.8832			−1.21743			−0.608717	+	0.793388i	$0.708315\pi$
$822$	4.74157			0.165381
$823$	36.7080	−	36.7080i	1.27956	−	1.27956i	0.338647	−	0.940914i	$-0.390031\pi$
$823$	36.7080	−	36.7080i	1.27956	−	1.27956i	0.940914	−	0.338647i	$-0.109969\pi$
$824$			6.73625i			0.234668i
$825$	−0.0805331	+	0.0542458i	−0.00280380	+	0.00188860i
$826$	−8.57841			−0.298481
$827$	28.8629			1.00366			0.501830	−	0.864966i	$-0.332660\pi$
$827$	28.8629			1.00366			0.501830	+	0.864966i	$0.332660\pi$
$828$	−2.53621			−0.0881394
$829$	−19.1753	+	19.1753i	−0.665985	+	0.665985i	−0.956784	−	0.290799i	$-0.906079\pi$
$829$	−19.1753	+	19.1753i	−0.665985	+	0.665985i	0.290799	+	0.956784i	$0.406079\pi$
$830$	15.5447	−	12.8057i	0.539564	−	0.444494i
$831$	−6.20105	+	6.20105i	−0.215112	+	0.215112i
$832$		−	0.159054i		−	0.00551421i
$833$			13.4050i			0.464457i
$834$	−14.8207	+	14.8207i	−0.513200	+	0.513200i
$835$	−3.20756	+	33.2011i	−0.111002	+	1.14897i
$836$	0.0891001	−	0.0891001i	0.00308159	−	0.00308159i
$837$	−3.33228			−0.115180
$838$	−24.3693			−0.841823
$839$	10.3671			0.357913			0.178956	−	0.983857i	$-0.442728\pi$
$839$	10.3671			0.357913			0.178956	+	0.983857i	$0.442728\pi$
$840$	−0.412604	+	4.27082i	−0.0142362	+	0.147357i
$841$			27.6812i			0.954525i
$842$	20.8544	−	20.8544i	0.718691	−	0.718691i
$843$	−1.73071			−0.0596089
$844$	−2.64429			−0.0910203
$845$	2.78989	−	28.8779i	0.0959751	−	0.993429i
$846$	5.16443	+	5.16443i	0.177557	+	0.177557i
$847$	−14.9247	−	14.9247i	−0.512820	−	0.512820i
$848$	−4.20428	+	4.20428i	−0.144375	+	0.144375i
$849$	8.34739	+	8.34739i	0.286482	+	0.286482i
$850$	−3.86708	+	19.8271i	−0.132640	+	0.680064i
$851$	−14.8244	−	4.27020i	−0.508174	−	0.146380i
$852$	−3.32717	−	3.32717i	−0.113987	−	0.113987i
$853$	−4.27814			−0.146481			−0.0732403	−	0.997314i	$-0.523334\pi$
$853$	−4.27814			−0.146481			−0.0732403	+	0.997314i	$0.523334\pi$
$854$	4.94649			0.169265
$855$	−9.22523	−	11.1983i	−0.315496	−	0.382975i
$856$	−6.22156	+	6.22156i	−0.212648	+	0.212648i
$857$	−1.58066			−0.0539944			−0.0269972	−	0.999636i	$-0.508595\pi$
$857$	−1.58066			−0.0539944			−0.0269972	+	0.999636i	$0.508595\pi$
$858$	−0.00218411	+	0.00218411i	−7.45642e−5	+	7.45642e-5i
$859$	−13.0806	−	13.0806i	−0.446303	−	0.446303i	0.447821	−	0.894123i	$-0.352200\pi$
$859$	−13.0806	−	13.0806i	−0.446303	−	0.446303i	−0.894123	+	0.447821i	$0.852200\pi$
$860$	9.72310	+	0.939348i	0.331555	+	0.0320315i
$861$	−15.7627			−0.537190
$862$	−15.2684	+	15.2684i	−0.520045	+	0.520045i
$863$	−12.1820	+	12.1820i	−0.414680	+	0.414680i	−0.883365	−	0.468685i	$-0.844728\pi$
$863$	−12.1820	+	12.1820i	−0.414680	+	0.414680i	0.468685	+	0.883365i	$0.344728\pi$
$864$	−0.707107	−	0.707107i	−0.0240563	−	0.0240563i
$865$	−17.3049	+	14.2558i	−0.588384	+	0.484712i
$866$	12.7638	+	12.7638i	0.433732	+	0.433732i
$867$	−0.478913	−	0.478913i	−0.0162647	−	0.0162647i
$868$			6.39419i			0.217033i
$869$	0.0959159	−	0.0959159i	0.00325372	−	0.00325372i
$870$	−2.55596	−	0.246931i	−0.0866553	−	0.00837176i
$871$	−0.347556	−	0.347556i	−0.0117765	−	0.0117765i
$872$	13.0168	−	13.0168i	0.440805	−	0.440805i
$873$			17.8376i			0.603713i
$874$	−11.6364	−	11.6364i	−0.393608	−	0.393608i
$875$	18.8635	−	10.2188i	0.637702	−	0.345457i
$876$		−	7.73112i		−	0.261210i
$877$	−12.5800	−	12.5800i	−0.424796	−	0.424796i	0.462055	−	0.886851i	$-0.347112\pi$
$877$	−12.5800	−	12.5800i	−0.424796	−	0.424796i	−0.886851	+	0.462055i	$0.847112\pi$
$878$	−11.8601	−	11.8601i	−0.400258	−	0.400258i
$879$	16.6499			0.561588
$880$	−0.0432227	−	0.00417574i	−0.00145704	−	0.000140764i
$881$		−	13.7250i		−	0.462408i	−0.972905	−	0.231204i	$-0.925733\pi$
$881$		−	13.7250i		−	0.462408i	0.972905	−	0.231204i	$-0.0742665\pi$
$882$			3.31797i			0.111722i
$883$	−50.0025			−1.68272			−0.841360	−	0.540475i	$-0.818244\pi$
$883$	−50.0025			−1.68272			−0.841360	+	0.540475i	$0.818244\pi$
$884$			0.642601i			0.0216130i
$885$	−9.95017	−	0.961285i	−0.334471	−	0.0323132i
$886$	−1.27875	+	1.27875i	−0.0429605	+	0.0429605i
$887$	−8.68575	+	8.68575i	−0.291639	+	0.291639i	−0.837728	−	0.546088i	$-0.816116\pi$
$887$	−8.68575	+	8.68575i	−0.291639	+	0.291639i	0.546088	+	0.837728i	$0.316116\pi$
$888$	−2.94256	−	5.32366i	−0.0987458	−	0.178650i
$889$			33.4371i			1.12144i
$890$	−24.9771	+	20.5762i	−0.837233	+	0.689715i
$891$			0.0194198i			0.000650587i
$892$	20.2192	−	20.2192i	0.676988	−	0.676988i
$893$			47.3900i			1.58584i
$894$	−4.62587	−	4.62587i	−0.154712	−	0.154712i
$895$	25.0963	+	30.4640i	0.838878	+	1.01830i
$896$	−1.35684	+	1.35684i	−0.0453289	+	0.0453289i
$897$	0.285243	+	0.285243i	0.00952399	+	0.00952399i
$898$	−8.61386	+	8.61386i	−0.287448	+	0.287448i
$899$	−3.82674			−0.127629
$900$	−0.957166	+	4.90753i	−0.0319055	+	0.163584i
$901$	16.9859	−	16.9859i	0.565881	−	0.565881i
$902$		−	0.159525i		−	0.00531161i
$903$	−8.38265			−0.278957
$904$			9.74000i			0.323948i
$905$	−0.785976	+	8.13556i	−0.0261267	+	0.270435i
$906$	10.0960	+	10.0960i	0.335418	+	0.335418i
$907$	−3.82232			−0.126918			−0.0634590	−	0.997984i	$-0.520213\pi$
$907$	−3.82232			−0.126918			−0.0634590	+	0.997984i	$0.520213\pi$
$908$	−15.0931			−0.500884
$909$	−0.190594			−0.00632161
$910$	0.526737	−	0.433927i	0.0174612	−	0.0143846i
$911$	−4.47777	+	4.47777i	−0.148355	+	0.148355i	−0.777383	−	0.629028i	$-0.783453\pi$
$911$	−4.47777	+	4.47777i	−0.148355	+	0.148355i	0.629028	+	0.777383i	$0.283453\pi$
$912$		−	6.48857i		−	0.214858i
$913$	−0.123682	−	0.123682i	−0.00409327	−	0.00409327i
$914$		−	22.6986i		−	0.750802i
$915$	5.73747	+	0.554297i	0.189675	+	0.0183245i
$916$		−	4.42655i		−	0.146257i
$917$		−	5.66706i		−	0.187143i
$918$	2.85681	+	2.85681i	0.0942887	+	0.0942887i
$919$	12.7583	−	12.7583i	0.420858	−	0.420858i	−0.464641	−	0.885499i	$-0.653817\pi$
$919$	12.7583	−	12.7583i	0.420858	−	0.420858i	0.885499	+	0.464641i	$0.153817\pi$
$920$	−0.545349	+	5.64485i	−0.0179796	+	0.186105i
$921$	8.11900			0.267530
$922$	0.105452	+	0.105452i	0.00347287	+	0.00347287i
$923$			0.748402i			0.0246340i
$924$	0.0372639			0.00122589
$925$	−13.8575	+	27.0734i	−0.455632	+	0.890168i
$926$	−38.4038			−1.26203
$927$		−	6.73625i		−	0.221248i
$928$	−0.812030	−	0.812030i	−0.0266562	−	0.0266562i
$929$	−54.9093			−1.80152			−0.900758	−	0.434322i	$-0.856988\pi$
$929$	−54.9093			−1.80152			−0.900758	+	0.434322i	$0.856988\pi$
$930$	−0.716525	+	7.41668i	−0.0234958	+	0.243202i
$931$	−15.2232	+	15.2232i	−0.498920	+	0.498920i
$932$	−0.899214	−	0.899214i	−0.0294547	−	0.0294547i
$933$			6.76097i			0.221344i
$934$		−	18.3192i		−	0.599424i
$935$	0.174626	+	0.0168706i	0.00571087	+	0.000551726i
$936$			0.159054i			0.00519885i
$937$	−7.14738	−	7.14738i	−0.233495	−	0.233495i	0.580655	−	0.814150i	$-0.302796\pi$
$937$	−7.14738	−	7.14738i	−0.233495	−	0.233495i	−0.814150	+	0.580655i	$0.802796\pi$
$938$			5.92978i			0.193614i
$939$	−1.44521	+	1.44521i	−0.0471625	+	0.0471625i
$940$	12.6050	−	10.3840i	0.411129	−	0.338689i
$941$	−17.1081			−0.557707			−0.278854	−	0.960334i	$-0.589954\pi$
$941$	−17.1081			−0.557707			−0.278854	+	0.960334i	$0.589954\pi$
$942$	0.117276			0.00382104
$943$	−20.8339			−0.678445
$944$	−3.16117	−	3.16117i	−0.102887	−	0.102887i
$945$	0.412604	−	4.27082i	0.0134220	−	0.138930i
$946$		−	0.0848362i		−	0.00275826i
$947$	−19.8405			−0.644729			−0.322364	−	0.946616i	$-0.604478\pi$
$947$	−19.8405			−0.644729			−0.322364	+	0.946616i	$0.604478\pi$
$948$		−	6.98492i		−	0.226860i
$949$	−0.869506	+	0.869506i	−0.0282254	+	0.0282254i
$950$	−26.9079	+	18.1247i	−0.873007	+	0.588043i
$951$	−26.4033			−0.856184
$952$	5.48182	−	5.48182i	0.177667	−	0.177667i
$953$	32.1571	+	32.1571i	1.04167	+	1.04167i	0.999093	+	0.0425778i	$0.0135570\pi$
$953$	32.1571	+	32.1571i	1.04167	+	1.04167i	0.0425778	+	0.999093i	$0.486443\pi$
$954$	4.20428	−	4.20428i	0.136118	−	0.136118i
$955$	−12.7412	−	15.4663i	−0.412295	−	0.500478i
$956$	−7.43447	−	7.43447i	−0.240448	−	0.240448i
$957$			0.0223013i			0.000720900i
$958$	10.0271	−	10.0271i	0.323960	−	0.323960i
$959$			9.09843i			0.293804i
$960$	−1.72586	+	1.42177i	−0.0557018	+	0.0458873i
$961$		−	19.8959i		−	0.641803i
$962$	−0.267798	+	0.929688i	−0.00863416	+	0.0299743i
$963$	6.22156	−	6.22156i	0.200487	−	0.200487i
$964$	−18.1472	+	18.1472i	−0.584483	+	0.584483i
$965$	29.1502	+	2.81620i	0.938377	+	0.0906565i
$966$		−	4.86664i		−	0.156582i
$967$	−16.2480			−0.522502			−0.261251	−	0.965271i	$-0.584135\pi$
$967$	−16.2480			−0.522502			−0.261251	+	0.965271i	$0.584135\pi$
$968$		−	10.9996i		−	0.353541i
$969$			26.2147i			0.842138i
$970$	39.7013	+	3.83554i	1.27473	+	0.123152i
$971$	−2.16831			−0.0695845			−0.0347923	−	0.999395i	$-0.511077\pi$
$971$	−2.16831			−0.0695845			−0.0347923	+	0.999395i	$0.511077\pi$
$972$	0.707107	+	0.707107i	0.0226805	+	0.0226805i
$973$	−28.4390	−	28.4390i	−0.911711	−	0.911711i
$974$			1.88010i			0.0602423i
$975$	0.659592	−	0.444291i	0.0211239	−	0.0142287i
$976$	1.82280	+	1.82280i	0.0583463	+	0.0583463i
$977$		−	6.78475i		−	0.217063i	−0.994093	−	0.108532i	$-0.965385\pi$
$977$		−	6.78475i		−	0.217063i	0.994093	−	0.108532i	$-0.0346149\pi$
$978$	6.70772	−	6.70772i	0.214489	−	0.214489i
$979$	0.198731	+	0.198731i	0.00635147	+	0.00635147i
$980$	7.38481	+	0.713446i	0.235899	+	0.0227902i
$981$	−13.0168	+	13.0168i	−0.415595	+	0.415595i
$982$			3.90817i			0.124715i
$983$	−7.20001	−	7.20001i	−0.229645	−	0.229645i	0.582900	−	0.812544i	$-0.301918\pi$
$983$	−7.20001	−	7.20001i	−0.229645	−	0.229645i	−0.812544	+	0.582900i	$0.801918\pi$
$984$	−5.80859	−	5.80859i	−0.185171	−	0.185171i
$985$	1.56119	−	1.28611i	0.0497436	−	0.0409789i
$986$	3.28071	+	3.28071i	0.104479	+	0.104479i
$987$	−9.90983	+	9.90983i	−0.315433	+	0.315433i
$988$	−0.729759	+	0.729759i	−0.0232167	+	0.0232167i
$989$	−11.0796			−0.352309
$990$	0.0432227	+	0.00417574i	0.00137371	+	0.000132714i
$991$	15.5914	+	15.5914i	0.495276	+	0.495276i	0.909964	−	0.414688i	$-0.136109\pi$
$991$	15.5914	+	15.5914i	0.495276	+	0.495276i	−0.414688	+	0.909964i	$0.636109\pi$
$992$	−2.35628	+	2.35628i	−0.0748119	+	0.0748119i
$993$	3.67395			0.116589
$994$	6.38438	−	6.38438i	0.202500	−	0.202500i
$995$	−18.9003	−	22.9427i	−0.599179	−	0.727333i
$996$	−9.00693			−0.285396
$997$	56.3695			1.78524			0.892621	−	0.450808i	$-0.148864\pi$
$997$	56.3695			1.78524			0.892621	+	0.450808i	$0.148864\pi$
$998$	9.78694	+	9.78694i	0.309800	+	0.309800i
$999$	2.94256	+	5.32366i	0.0930985	+	0.168433i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.l.b.697.14	yes	40
5.3	odd	4		1110.2.o.b.253.7	yes	40
37.6	odd	4		1110.2.o.b.487.7	yes	40
185.43	even	4	inner	1110.2.l.b.43.14	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.l.b.43.14	✓	40	185.43	even	4	inner
1110.2.l.b.697.14	yes	40	1.1	even	1	trivial
1110.2.o.b.253.7	yes	40	5.3	odd	4
1110.2.o.b.487.7	yes	40	37.6	odd	4

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.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +(0.707107 + 0.707107i) q^{3} -1.00000 q^{4} +(0.215025 - 2.22571i) q^{5} +(-0.707107 + 0.707107i) q^{6} +(-1.35684 - 1.35684i) q^{7} -1.00000i q^{8} +1.00000i q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +(0.707107 + 0.707107i) q^{3} -1.00000 q^{4} +(0.215025 - 2.22571i) q^{5} +(-0.707107 + 0.707107i) q^{6} +(-1.35684 - 1.35684i) q^{7} -1.00000i q^{8} +1.00000i q^{9} +(2.22571 + 0.215025i) q^{10} -0.0194198i q^{11} +(-0.707107 - 0.707107i) q^{12} +0.159054i q^{13} +(1.35684 - 1.35684i) q^{14} +(1.72586 - 1.42177i) q^{15} +1.00000 q^{16} -4.04014 q^{17} -1.00000 q^{18} +(-4.58811 - 4.58811i) q^{19} +(-0.215025 + 2.22571i) q^{20} -1.91886i q^{21} +0.0194198 q^{22} -2.53621i q^{23} +(0.707107 - 0.707107i) q^{24} +(-4.90753 - 0.957166i) q^{25} -0.159054 q^{26} +(-0.707107 + 0.707107i) q^{27} +(1.35684 + 1.35684i) q^{28} +(-0.812030 + 0.812030i) q^{29} +(1.42177 + 1.72586i) q^{30} +(2.35628 + 2.35628i) q^{31} +1.00000i q^{32} +(0.0137318 - 0.0137318i) q^{33} -4.04014i q^{34} +(-3.31168 + 2.72817i) q^{35} -1.00000i q^{36} +(1.68369 - 5.84510i) q^{37} +(4.58811 - 4.58811i) q^{38} +(-0.112468 + 0.112468i) q^{39} +(-2.22571 - 0.215025i) q^{40} -8.21459i q^{41} +1.91886 q^{42} -4.36855i q^{43} +0.0194198i q^{44} +(2.22571 + 0.215025i) q^{45} +2.53621 q^{46} +(-5.16443 - 5.16443i) q^{47} +(0.707107 + 0.707107i) q^{48} -3.31797i q^{49} +(0.957166 - 4.90753i) q^{50} +(-2.85681 - 2.85681i) q^{51} -0.159054i q^{52} +(-4.20428 + 4.20428i) q^{53} +(-0.707107 - 0.707107i) q^{54} +(-0.0432227 - 0.00417574i) q^{55} +(-1.35684 + 1.35684i) q^{56} -6.48857i q^{57} +(-0.812030 - 0.812030i) q^{58} +(-3.16117 - 3.16117i) q^{59} +(-1.72586 + 1.42177i) q^{60} +(1.82280 + 1.82280i) q^{61} +(-2.35628 + 2.35628i) q^{62} +(1.35684 - 1.35684i) q^{63} -1.00000 q^{64} +(0.354008 + 0.0342007i) q^{65} +(0.0137318 + 0.0137318i) q^{66} +(-2.18514 + 2.18514i) q^{67} +4.04014 q^{68} +(1.79337 - 1.79337i) q^{69} +(-2.72817 - 3.31168i) q^{70} +4.70533 q^{71} +1.00000 q^{72} +(5.46673 + 5.46673i) q^{73} +(5.84510 + 1.68369i) q^{74} +(-2.79333 - 4.14696i) q^{75} +(4.58811 + 4.58811i) q^{76} +(-0.0263495 + 0.0263495i) q^{77} +(-0.112468 - 0.112468i) q^{78} +(4.93909 + 4.93909i) q^{79} +(0.215025 - 2.22571i) q^{80} -1.00000 q^{81} +8.21459 q^{82} +(6.36886 - 6.36886i) q^{83} +1.91886i q^{84} +(-0.868732 + 8.99216i) q^{85} +4.36855 q^{86} -1.14838 q^{87} -0.0194198 q^{88} +(-10.2334 + 10.2334i) q^{89} +(-0.215025 + 2.22571i) q^{90} +(0.215811 - 0.215811i) q^{91} +2.53621i q^{92} +3.33228i q^{93} +(5.16443 - 5.16443i) q^{94} +(-11.1983 + 9.22523i) q^{95} +(-0.707107 + 0.707107i) q^{96} +17.8376 q^{97} +3.31797 q^{98} +0.0194198 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 40 q^{4} - 4 q^{7}+O(q^{10}) \) 40 * q - 40 * q^4 - 4 * q^7	\( 40 q - 40 q^{4} - 4 q^{7} + 4 q^{14} + 40 q^{16} + 24 q^{17} - 40 q^{18} + 4 q^{19} + 8 q^{22} + 8 q^{25} + 8 q^{26} + 4 q^{28} + 28 q^{31} - 4 q^{33} + 20 q^{35} + 20 q^{37} - 4 q^{38} + 4 q^{39} + 16 q^{42} - 16 q^{47} + 16 q^{51} + 20 q^{53} + 16 q^{55} - 4 q^{56} - 4 q^{59} - 8 q^{61} - 28 q^{62} + 4 q^{63} - 40 q^{64} - 4 q^{65} - 4 q^{66} + 16 q^{67} - 24 q^{68} - 8 q^{69} + 12 q^{70} + 40 q^{71} + 40 q^{72} + 8 q^{73} - 8 q^{74} + 16 q^{75} - 4 q^{76} - 24 q^{77} + 4 q^{78} - 12 q^{79} - 40 q^{81} - 24 q^{82} - 8 q^{83} - 8 q^{85} + 8 q^{87} - 8 q^{88} + 12 q^{89} - 24 q^{91} + 16 q^{94} - 28 q^{95} + 40 q^{97} - 56 q^{98} + 8 q^{99}+O(q^{100}) \) 40 * q - 40 * q^4 - 4 * q^7 + 4 * q^14 + 40 * q^16 + 24 * q^17 - 40 * q^18 + 4 * q^19 + 8 * q^22 + 8 * q^25 + 8 * q^26 + 4 * q^28 + 28 * q^31 - 4 * q^33 + 20 * q^35 + 20 * q^37 - 4 * q^38 + 4 * q^39 + 16 * q^42 - 16 * q^47 + 16 * q^51 + 20 * q^53 + 16 * q^55 - 4 * q^56 - 4 * q^59 - 8 * q^61 - 28 * q^62 + 4 * q^63 - 40 * q^64 - 4 * q^65 - 4 * q^66 + 16 * q^67 - 24 * q^68 - 8 * q^69 + 12 * q^70 + 40 * q^71 + 40 * q^72 + 8 * q^73 - 8 * q^74 + 16 * q^75 - 4 * q^76 - 24 * q^77 + 4 * q^78 - 12 * q^79 - 40 * q^81 - 24 * q^82 - 8 * q^83 - 8 * q^85 + 8 * q^87 - 8 * q^88 + 12 * q^89 - 24 * q^91 + 16 * q^94 - 28 * q^95 + 40 * q^97 - 56 * q^98 + 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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