LMFDB - Embedded newform 570.2.x.a.217.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(103,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 9, 2]))

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

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

chi := DirichletCharacter("570.103");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.x (of order $12$, degree $4$, 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:	$4.55147291521$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			217.8
Character	$\chi$	$=$	570.217
Dual form			570.2.x.a.373.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.258819 + 0.965926i) q^{2} +(-0.965926 + 0.258819i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(-0.809185 + 2.08452i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(-3.60529 - 3.60529i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.866025 - 0.500000i) q^{9} +O(q^{10})$	\(q+(0.258819 + 0.965926i) q^{2} +(-0.965926 + 0.258819i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(-0.809185 + 2.08452i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(-3.60529 - 3.60529i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.866025 - 0.500000i) q^{9} +(-2.22292 - 0.242099i) q^{10} +2.76087 q^{11} +(0.707107 - 0.707107i) q^{12} +(1.37677 - 5.13819i) q^{13} +(2.54933 - 4.41557i) q^{14} +(0.242099 - 2.22292i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-3.93757 + 1.05507i) q^{17} +(0.707107 + 0.707107i) q^{18} +(4.32144 - 0.570220i) q^{19} +(-0.341485 - 2.20984i) q^{20} +(4.41557 + 2.54933i) q^{21} +(0.714566 + 2.66680i) q^{22} +(6.48095 + 1.73656i) q^{23} +(0.866025 + 0.500000i) q^{24} +(-3.69044 - 3.37352i) q^{25} +5.31945 q^{26} +(-0.707107 + 0.707107i) q^{27} +(4.92492 + 1.31963i) q^{28} +(-1.54892 - 2.68280i) q^{29} +(2.20984 - 0.341485i) q^{30} +0.810201i q^{31} +(0.965926 + 0.258819i) q^{32} +(-2.66680 + 0.714566i) q^{33} +(-2.03823 - 3.53033i) q^{34} +(10.4327 - 4.59796i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(-2.19015 + 2.19015i) q^{37} +(1.66926 + 4.02661i) q^{38} +5.31945i q^{39} +(2.04616 - 0.901798i) q^{40} +(-9.40889 - 5.43223i) q^{41} +(-1.31963 + 4.92492i) q^{42} +(-2.71012 - 10.1143i) q^{43} +(-2.39099 + 1.38044i) q^{44} +(0.341485 + 2.20984i) q^{45} +6.70957i q^{46} +(2.53715 - 9.46876i) q^{47} +(-0.258819 + 0.965926i) q^{48} +18.9963i q^{49} +(2.30342 - 4.43782i) q^{50} +(3.53033 - 2.03823i) q^{51} +(1.37677 + 5.13819i) q^{52} +(1.18314 - 4.41554i) q^{53} +(-0.866025 - 0.500000i) q^{54} +(-2.23406 + 5.75509i) q^{55} +5.09866i q^{56} +(-4.02661 + 1.66926i) q^{57} +(2.19050 - 2.19050i) q^{58} +(2.60356 - 4.50949i) q^{59} +(0.901798 + 2.04616i) q^{60} +(-2.92319 - 5.06311i) q^{61} +(-0.782594 + 0.209695i) q^{62} +(-4.92492 - 1.31963i) q^{63} +1.00000i q^{64} +(9.59660 + 7.02766i) q^{65} +(-1.38044 - 2.39099i) q^{66} +(-2.00042 - 0.536010i) q^{67} +(2.88250 - 2.88250i) q^{68} -6.70957 q^{69} +(7.14145 + 8.88713i) q^{70} +(4.86063 + 2.80628i) q^{71} +(-0.965926 - 0.258819i) q^{72} +(-3.08260 - 11.5044i) q^{73} +(-2.68238 - 1.54867i) q^{74} +(4.43782 + 2.30342i) q^{75} +(-3.45737 + 2.65455i) q^{76} +(-9.95376 - 9.95376i) q^{77} +(-5.13819 + 1.37677i) q^{78} +(3.78472 - 6.55532i) q^{79} +(1.40065 + 1.74303i) q^{80} +(0.500000 - 0.866025i) q^{81} +(2.81193 - 10.4943i) q^{82} +(-3.75772 + 3.75772i) q^{83} -5.09866 q^{84} +(0.986910 - 9.06168i) q^{85} +(9.06825 - 5.23555i) q^{86} +(2.19050 + 2.19050i) q^{87} +(-1.95223 - 1.95223i) q^{88} +(-2.32243 - 4.02257i) q^{89} +(-2.04616 + 0.901798i) q^{90} +(-23.4884 + 13.5610i) q^{91} +(-6.48095 + 1.73656i) q^{92} +(-0.209695 - 0.782594i) q^{93} +9.80278 q^{94} +(-2.30821 + 9.46954i) q^{95} -1.00000 q^{96} +(4.15072 + 15.4907i) q^{97} +(-18.3490 + 4.91660i) q^{98} +(2.39099 - 1.38044i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 8 q^{5} - 20 q^{6} - 8 q^{7}+O(q^{10}) $ 40 * q - 8 * q^5 - 20 * q^6 - 8 * q^7	$ 40 q - 8 q^{5} - 20 q^{6} - 8 q^{7} - 12 q^{10} + 8 q^{11} - 24 q^{13} + 20 q^{16} + 8 q^{17} + 12 q^{21} + 24 q^{22} + 16 q^{23} - 16 q^{25} + 32 q^{26} + 4 q^{28} + 16 q^{30} - 24 q^{33} - 4 q^{35} - 20 q^{36} - 8 q^{38} - 36 q^{41} + 4 q^{42} - 4 q^{43} + 8 q^{47} - 24 q^{52} - 16 q^{55} - 8 q^{57} + 16 q^{58} + 12 q^{60} - 8 q^{61} - 16 q^{62} - 4 q^{63} - 4 q^{66} - 36 q^{67} - 16 q^{68} + 48 q^{70} + 72 q^{71} - 16 q^{73} - 8 q^{76} + 24 q^{77} + 24 q^{78} + 8 q^{80} + 20 q^{81} - 24 q^{82} - 40 q^{83} - 48 q^{85} + 16 q^{87} - 72 q^{91} - 16 q^{92} + 16 q^{93} - 16 q^{95} - 40 q^{96} + 36 q^{97} - 48 q^{98}+O(q^{100}) $ 40 * q - 8 * q^5 - 20 * q^6 - 8 * q^7 - 12 * q^10 + 8 * q^11 - 24 * q^13 + 20 * q^16 + 8 * q^17 + 12 * q^21 + 24 * q^22 + 16 * q^23 - 16 * q^25 + 32 * q^26 + 4 * q^28 + 16 * q^30 - 24 * q^33 - 4 * q^35 - 20 * q^36 - 8 * q^38 - 36 * q^41 + 4 * q^42 - 4 * q^43 + 8 * q^47 - 24 * q^52 - 16 * q^55 - 8 * q^57 + 16 * q^58 + 12 * q^60 - 8 * q^61 - 16 * q^62 - 4 * q^63 - 4 * q^66 - 36 * q^67 - 16 * q^68 + 48 * q^70 + 72 * q^71 - 16 * q^73 - 8 * q^76 + 24 * q^77 + 24 * q^78 + 8 * q^80 + 20 * q^81 - 24 * q^82 - 40 * q^83 - 48 * q^85 + 16 * q^87 - 72 * q^91 - 16 * q^92 + 16 * q^93 - 16 * q^95 - 40 * q^96 + 36 * q^97 - 48 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	0.258819	+	0.965926i	0.183013	+	0.683013i
$2$	0.258819	+	0.965926i	0.183013	+	0.683013i
$3$	−0.965926	+	0.258819i	−0.557678	+	0.149429i
$3$	−0.965926	+	0.258819i	−0.557678	+	0.149429i
$4$	−0.866025	+	0.500000i	−0.433013	+	0.250000i
$5$	−0.809185	+	2.08452i	−0.361878	+	0.932225i
$5$	−0.809185	+	2.08452i	−0.361878	+	0.932225i
$6$	−0.500000	−	0.866025i	−0.204124	−	0.353553i
$7$	−3.60529	−	3.60529i	−1.36267	−	1.36267i	−0.870494	−	0.492179i	$-0.836201\pi$
$7$	−3.60529	−	3.60529i	−1.36267	−	1.36267i	−0.492179	−	0.870494i	$-0.663799\pi$
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	0.866025	−	0.500000i	0.288675	−	0.166667i
$10$	−2.22292	−	0.242099i	−0.702950	−	0.0765585i
$11$	2.76087			0.832434			0.416217	−	0.909265i	$-0.363356\pi$
$11$	2.76087			0.832434			0.416217	+	0.909265i	$0.363356\pi$
$12$	0.707107	−	0.707107i	0.204124	−	0.204124i
$13$	1.37677	−	5.13819i	0.381849	−	1.42508i	−0.461227	−	0.887282i	$-0.652590\pi$
$13$	1.37677	−	5.13819i	0.381849	−	1.42508i	0.843075	−	0.537796i	$-0.180743\pi$
$14$	2.54933	−	4.41557i	0.681337	−	1.18011i
$15$	0.242099	−	2.22292i	0.0625097	−	0.573956i
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	−3.93757	+	1.05507i	−0.955000	+	0.255892i	−0.702483	−	0.711701i	$-0.747925\pi$
$17$	−3.93757	+	1.05507i	−0.955000	+	0.255892i	−0.252518	+	0.967592i	$0.581259\pi$
$18$	0.707107	+	0.707107i	0.166667	+	0.166667i
$19$	4.32144	−	0.570220i	0.991406	−	0.130817i
$19$	4.32144	−	0.570220i	0.991406	−	0.130817i
$20$	−0.341485	−	2.20984i	−0.0763584	−	0.494135i
$21$	4.41557	+	2.54933i	0.963555	+	0.556309i
$22$	0.714566	+	2.66680i	0.152346	+	0.568563i
$23$	6.48095	+	1.73656i	1.35137	+	0.362099i	0.860641	−	0.509213i	$-0.170063\pi$
$23$	6.48095	+	1.73656i	1.35137	+	0.362099i	0.490730	+	0.871312i	$0.336730\pi$
$24$	0.866025	+	0.500000i	0.176777	+	0.102062i
$25$	−3.69044	−	3.37352i	−0.738088	−	0.674704i
$26$	5.31945			1.04323
$27$	−0.707107	+	0.707107i	−0.136083	+	0.136083i
$28$	4.92492	+	1.31963i	0.930723	+	0.249386i
$29$	−1.54892	−	2.68280i	−0.287627	−	0.498184i	0.685616	−	0.727963i	$-0.259533\pi$
$29$	−1.54892	−	2.68280i	−0.287627	−	0.498184i	−0.973243	+	0.229779i	$0.926200\pi$
$30$	2.20984	−	0.341485i	0.403460	−	0.0623464i
$31$			0.810201i			0.145516i	0.997350	+	0.0727582i	$0.0231801\pi$
$31$			0.810201i			0.145516i	−0.997350	+	0.0727582i	$0.976820\pi$
$32$	0.965926	+	0.258819i	0.170753	+	0.0457532i
$33$	−2.66680	+	0.714566i	−0.464230	+	0.124390i
$34$	−2.03823	−	3.53033i	−0.349554	−	0.605446i
$35$	10.4327	−	4.59796i	1.76344	−	0.777196i
$36$	−0.500000	+	0.866025i	−0.0833333	+	0.144338i
$37$	−2.19015	+	2.19015i	−0.360059	+	0.360059i	−0.863835	−	0.503775i	$-0.831944\pi$
$37$	−2.19015	+	2.19015i	−0.360059	+	0.360059i	0.503775	+	0.863835i	$0.331944\pi$
$38$	1.66926	+	4.02661i	0.270790	+	0.653202i
$39$			5.31945i			0.851793i
$40$	2.04616	−	0.901798i	0.323526	−	0.142587i
$41$	−9.40889	−	5.43223i	−1.46942	−	0.848371i	−0.470010	−	0.882661i	$-0.655750\pi$
$41$	−9.40889	−	5.43223i	−1.46942	−	0.848371i	−0.999412	+	0.0342894i	$0.989083\pi$
$42$	−1.31963	+	4.92492i	−0.203623	+	0.759932i
$43$	−2.71012	−	10.1143i	−0.413290	−	1.54242i	−0.788237	−	0.615372i	$-0.789006\pi$
$43$	−2.71012	−	10.1143i	−0.413290	−	1.54242i	0.374947	−	0.927046i	$-0.377661\pi$
$44$	−2.39099	+	1.38044i	−0.360455	+	0.208109i
$45$	0.341485	+	2.20984i	0.0509056	+	0.329423i
$46$			6.70957i			0.989272i
$47$	2.53715	−	9.46876i	0.370081	−	1.38116i	−0.490320	−	0.871542i	$-0.663120\pi$
$47$	2.53715	−	9.46876i	0.370081	−	1.38116i	0.860401	−	0.509618i	$-0.170213\pi$
$48$	−0.258819	+	0.965926i	−0.0373573	+	0.139419i
$49$			18.9963i			2.71376i
$50$	2.30342	−	4.43782i	0.325752	−	0.627603i
$51$	3.53033	−	2.03823i	0.494345	−	0.285410i
$52$	1.37677	+	5.13819i	0.190924	+	0.712539i
$53$	1.18314	−	4.41554i	0.162517	−	0.606521i	−0.835827	−	0.548993i	$-0.815011\pi$
$53$	1.18314	−	4.41554i	0.162517	−	0.606521i	0.998344	−	0.0575281i	$-0.0183219\pi$
$54$	−0.866025	−	0.500000i	−0.117851	−	0.0680414i
$55$	−2.23406	+	5.75509i	−0.301240	+	0.776017i
$56$			5.09866i			0.681337i
$57$	−4.02661	+	1.66926i	−0.533337	+	0.221099i
$58$	2.19050	−	2.19050i	0.287627	−	0.287627i
$59$	2.60356	−	4.50949i	0.338954	−	0.587086i	−0.645282	−	0.763945i	$-0.723260\pi$
$59$	2.60356	−	4.50949i	0.338954	−	0.587086i	0.984236	+	0.176858i	$0.0565934\pi$
$60$	0.901798	+	2.04616i	0.116422	+	0.264158i
$61$	−2.92319	−	5.06311i	−0.374276	−	0.648264i	0.615943	−	0.787791i	$-0.288775\pi$
$61$	−2.92319	−	5.06311i	−0.374276	−	0.648264i	−0.990218	+	0.139527i	$0.955442\pi$
$62$	−0.782594	+	0.209695i	−0.0993895	+	0.0266313i
$63$	−4.92492	−	1.31963i	−0.620482	−	0.166258i
$64$			1.00000i			0.125000i
$65$	9.59660	+	7.02766i	1.19031	+	0.871674i
$66$	−1.38044	−	2.39099i	−0.169920	−	0.294310i
$67$	−2.00042	−	0.536010i	−0.244390	−	0.0654840i	0.134545	−	0.990908i	$-0.457043\pi$
$67$	−2.00042	−	0.536010i	−0.244390	−	0.0654840i	−0.378935	+	0.925423i	$0.623709\pi$
$68$	2.88250	−	2.88250i	0.349554	−	0.349554i
$69$	−6.70957			−0.807737
$70$	7.14145	+	8.88713i	0.853567	+	1.06222i
$71$	4.86063	+	2.80628i	0.576850	+	0.333045i	0.759881	−	0.650063i	$-0.225257\pi$
$71$	4.86063	+	2.80628i	0.576850	+	0.333045i	−0.183030	+	0.983107i	$0.558591\pi$
$72$	−0.965926	−	0.258819i	−0.113835	−	0.0305021i
$73$	−3.08260	−	11.5044i	−0.360791	−	1.34649i	−0.873038	−	0.487652i	$-0.837854\pi$
$73$	−3.08260	−	11.5044i	−0.360791	−	1.34649i	0.512248	−	0.858838i	$-0.328813\pi$
$74$	−2.68238	−	1.54867i	−0.311820	−	0.180030i
$75$	4.43782	+	2.30342i	0.512436	+	0.265976i
$76$	−3.45737	+	2.65455i	−0.396587	+	0.304497i
$77$	−9.95376	−	9.95376i	−1.13434	−	1.13434i
$78$	−5.13819	+	1.37677i	−0.581786	+	0.155889i
$79$	3.78472	−	6.55532i	0.425814	−	0.737532i	−0.570682	−	0.821171i	$-0.693321\pi$
$79$	3.78472	−	6.55532i	0.425814	−	0.737532i	0.996496	+	0.0836396i	$0.0266544\pi$
$80$	1.40065	+	1.74303i	0.156598	+	0.194877i
$81$	0.500000	−	0.866025i	0.0555556	−	0.0962250i
$82$	2.81193	−	10.4943i	0.310526	−	1.15890i
$83$	−3.75772	+	3.75772i	−0.412463	+	0.412463i	−0.882596	−	0.470133i	$-0.844206\pi$
$83$	−3.75772	+	3.75772i	−0.412463	+	0.412463i	0.470133	+	0.882596i	$0.344206\pi$
$84$	−5.09866			−0.556309
$85$	0.986910	−	9.06168i	0.107045	−	0.982877i
$86$	9.06825	−	5.23555i	0.977854	−	0.564564i
$87$	2.19050	+	2.19050i	0.234846	+	0.234846i
$88$	−1.95223	−	1.95223i	−0.208109	−	0.208109i
$89$	−2.32243	−	4.02257i	−0.246177	−	0.426391i	0.716285	−	0.697808i	$-0.245841\pi$
$89$	−2.32243	−	4.02257i	−0.246177	−	0.426391i	−0.962462	+	0.271417i	$0.912508\pi$
$90$	−2.04616	+	0.901798i	−0.215684	+	0.0950578i
$91$	−23.4884	+	13.5610i	−2.46225	+	1.42158i
$92$	−6.48095	+	1.73656i	−0.675685	+	0.181049i
$93$	−0.209695	−	0.782594i	−0.0217444	−	0.0811512i
$94$	9.80278			1.01108
$95$	−2.30821	+	9.46954i	−0.236817	+	0.971554i
$96$	−1.00000			−0.102062
$97$	4.15072	+	15.4907i	0.421442	+	1.57284i	0.771572	+	0.636142i	$0.219471\pi$
$97$	4.15072	+	15.4907i	0.421442	+	1.57284i	−0.350131	+	0.936701i	$0.613863\pi$
$98$	−18.3490	+	4.91660i	−1.85353	+	0.496652i
$99$	2.39099	−	1.38044i	0.240303	−	0.138739i
$100$	4.88278	+	1.07634i	0.488278	+	0.107634i
$101$	1.92111	+	3.32747i	0.191158	+	0.331095i	0.945634	−	0.325232i	$-0.105442\pi$
$101$	1.92111	+	3.32747i	0.191158	+	0.331095i	−0.754476	+	0.656327i	$0.772109\pi$
$102$	2.88250	+	2.88250i	0.285410	+	0.285410i
$103$	−2.51460	−	2.51460i	−0.247770	−	0.247770i	0.572285	−	0.820055i	$-0.306057\pi$
$103$	−2.51460	−	2.51460i	−0.247770	−	0.247770i	−0.820055	+	0.572285i	$0.806057\pi$
$104$	−4.60678	+	2.65972i	−0.451732	+	0.260807i
$105$	−8.88713	+	7.14145i	−0.867295	+	0.696934i
$106$	4.57130			0.444004
$107$	0.316498	−	0.316498i	0.0305971	−	0.0305971i	−0.691643	−	0.722240i	$-0.743113\pi$
$107$	0.316498	−	0.316498i	0.0305971	−	0.0305971i	0.722240	+	0.691643i	$0.243113\pi$
$108$	0.258819	−	0.965926i	0.0249049	−	0.0929463i
$109$	−2.96976	+	5.14377i	−0.284451	+	0.492684i	−0.972476	−	0.233003i	$-0.925145\pi$
$109$	−2.96976	+	5.14377i	−0.284451	+	0.492684i	0.688025	+	0.725687i	$0.258478\pi$
$110$	−6.13721	−	0.668405i	−0.585160	−	0.0637299i
$111$	1.54867	−	2.68238i	0.146994	−	0.254600i
$112$	−4.92492	+	1.31963i	−0.465361	+	0.124693i
$113$	2.21370	+	2.21370i	0.208247	+	0.208247i	0.803522	−	0.595275i	$-0.202957\pi$
$113$	2.21370	+	2.21370i	0.208247	+	0.208247i	−0.595275	+	0.803522i	$0.702957\pi$
$114$	−2.65455	−	3.45737i	−0.248621	−	0.323812i
$115$	−8.86418	+	12.1045i	−0.826589	+	1.12875i
$116$	2.68280	+	1.54892i	0.249092	+	0.143813i
$117$	−1.37677	−	5.13819i	−0.127283	−	0.475026i
$118$	5.02969	+	1.34770i	0.463020	+	0.124066i
$119$	17.9999	+	10.3923i	1.65005	+	0.952657i
$120$	−1.74303	+	1.40065i	−0.159117	+	0.127862i
$121$	−3.37758			−0.307053
$122$	4.13401	−	4.13401i	0.374276	−	0.374276i
$123$	10.4943	+	2.81193i	0.946235	+	0.253543i
$124$	−0.405100	−	0.701654i	−0.0363791	−	0.0630104i
$125$	10.0184	−	4.96299i	0.896075	−	0.443903i
$126$		−	5.09866i		−	0.454224i
$127$	8.68032	+	2.32588i	0.770254	+	0.206389i	0.622484	−	0.782633i	$-0.286124\pi$
$127$	8.68032	+	2.32588i	0.770254	+	0.206389i	0.147770	+	0.989022i	$0.452790\pi$
$128$	−0.965926	+	0.258819i	−0.0853766	+	0.0228766i
$129$	5.23555	+	9.06825i	0.460965	+	0.798415i
$130$	−4.30442	+	11.0885i	−0.377522	+	0.972525i
$131$	−2.25085	+	3.89859i	−0.196658	+	0.340621i	−0.947443	−	0.319926i	$-0.896342\pi$
$131$	−2.25085	+	3.89859i	−0.196658	+	0.340621i	0.750785	+	0.660547i	$0.229675\pi$
$132$	1.95223	−	1.95223i	0.169920	−	0.169920i
$133$	−17.6359	−	13.5243i	−1.52922	−	1.17270i
$134$		−	2.07098i		−	0.178906i
$135$	−0.901798	−	2.04616i	−0.0776144	−	0.176105i
$136$	3.53033	+	2.03823i	0.302723	+	0.174777i
$137$	−3.84474	+	14.3488i	−0.328478	+	1.22590i	0.582291	+	0.812981i	$0.302157\pi$
$137$	−3.84474	+	14.3488i	−0.328478	+	1.22590i	−0.910769	+	0.412917i	$0.864510\pi$
$138$	−1.73656	−	6.48095i	−0.147826	−	0.551695i
$139$	−11.2043	+	6.46881i	−0.950338	+	0.548678i	−0.893186	−	0.449688i	$-0.851535\pi$
$139$	−11.2043	+	6.46881i	−0.950338	+	0.548678i	−0.0571518	+	0.998365i	$0.518202\pi$
$140$	−6.73596	+	9.19827i	−0.569293	+	0.777396i
$141$			9.80278i			0.825543i
$142$	−1.45264	+	5.42132i	−0.121903	+	0.454947i
$143$	3.80110	−	14.1859i	0.317864	−	1.18628i
$144$		−	1.00000i		−	0.0833333i
$145$	6.84572	−	1.05786i	0.568506	−	0.0878509i
$146$	10.3146	−	5.95512i	0.853640	−	0.492849i
$147$	−4.91660	−	18.3490i	−0.405514	−	1.51340i
$148$	0.801652	−	2.99181i	0.0658954	−	0.245925i
$149$	−3.70625	−	2.13980i	−0.303628	−	0.175300i	0.340444	−	0.940265i	$-0.389423\pi$
$149$	−3.70625	−	2.13980i	−0.303628	−	0.175300i	−0.644071	+	0.764965i	$0.722756\pi$
$150$	−1.07634	+	4.88278i	−0.0878824	+	0.398677i
$151$		−	11.2943i		−	0.919114i	−0.888148	−	0.459557i	$-0.848008\pi$
$151$		−	11.2943i		−	0.919114i	0.888148	−	0.459557i	$-0.151992\pi$
$152$	−3.45893	−	2.65251i	−0.280556	−	0.215147i
$153$	−2.88250	+	2.88250i	−0.233036	+	0.233036i
$154$	7.03837	−	12.1908i	0.567168	−	0.982364i
$155$	−1.68888	−	0.655602i	−0.135654	−	0.0526592i
$156$	−2.65972	−	4.60678i	−0.212948	−	0.368837i
$157$	−5.92528	+	1.58767i	−0.472889	+	0.126710i	−0.487390	−	0.873185i	$-0.662051\pi$
$157$	−5.92528	+	1.58767i	−0.472889	+	0.126710i	0.0145006	+	0.999895i	$0.495384\pi$
$158$	7.31151	+	1.95911i	0.581673	+	0.155859i
$159$			4.57130i			0.362528i
$160$	−1.32113	+	1.80406i	−0.104444	+	0.142623i
$161$	−17.1049	−	29.6265i	−1.34805	−	2.33490i
$162$	0.965926	+	0.258819i	0.0758903	+	0.0203347i
$163$	−12.2110	+	12.2110i	−0.956437	+	0.956437i	−0.999090	−	0.0426525i	$-0.986419\pi$
$163$	−12.2110	+	12.2110i	−0.956437	+	0.956437i	0.0426525	+	0.999090i	$0.486419\pi$
$164$	10.8645			0.848371
$165$	0.668405	−	6.13721i	0.0520352	−	0.477781i
$166$	−4.60224	−	2.65711i	−0.357203	−	0.206231i
$167$	−20.8018	−	5.57383i	−1.60969	−	0.431316i	−0.661741	−	0.749733i	$-0.730182\pi$
$167$	−20.8018	−	5.57383i	−1.60969	−	0.431316i	−0.947951	+	0.318417i	$0.896849\pi$
$168$	−1.31963	−	4.92492i	−0.101812	−	0.379966i
$169$	−13.2472	−	7.64826i	−1.01901	−	0.588328i
$170$	9.00834	−	1.39205i	0.690908	−	0.106766i
$171$	3.45737	−	2.65455i	0.264391	−	0.202998i
$172$	7.40419	+	7.40419i	0.564564	+	0.564564i
$173$	−0.254907	+	0.0683021i	−0.0193802	+	0.00519292i	−0.268496	−	0.963281i	$-0.586527\pi$
$173$	−0.254907	+	0.0683021i	−0.0193802	+	0.00519292i	0.249116	+	0.968474i	$0.419860\pi$
$174$	−1.54892	+	2.68280i	−0.117423	+	0.203383i
$175$	1.14258	+	25.4677i	0.0863713	+	1.92517i
$176$	1.38044	−	2.39099i	0.104054	−	0.180227i
$177$	−1.34770	+	5.02969i	−0.101299	+	0.378055i
$178$	3.28441	−	3.28441i	0.246177	−	0.246177i
$179$	−0.0897580			−0.00670883			−0.00335441	−	0.999994i	$-0.501068\pi$
$179$	−0.0897580			−0.00670883			−0.00335441	+	0.999994i	$0.501068\pi$
$180$	−1.40065	−	1.74303i	−0.104399	−	0.129918i
$181$	19.7637	−	11.4106i	1.46903	−	0.848143i	0.469630	−	0.882864i	$-0.344387\pi$
$181$	19.7637	−	11.4106i	1.46903	−	0.848143i	0.999397	+	0.0347206i	$0.0110541\pi$
$182$	−19.1782	−	19.1782i	−1.42158	−	1.42158i
$183$	4.13401	+	4.13401i	0.305595	+	0.305595i
$184$	−3.35478	−	5.81066i	−0.247318	−	0.428367i
$185$	−2.79318	−	6.33766i	−0.205359	−	0.465954i
$186$	0.701654	−	0.405100i	0.0514478	−	0.0297034i
$187$	−10.8711	+	2.91291i	−0.794975	+	0.213013i
$188$	2.53715	+	9.46876i	0.185040	+	0.690580i
$189$	5.09866			0.370873
$190$	−9.74428	+	0.221339i	−0.706924	+	0.0160576i
$191$	21.3086			1.54184			0.770919	−	0.636934i	$-0.219797\pi$
$191$	21.3086			1.54184			0.770919	+	0.636934i	$0.219797\pi$
$192$	−0.258819	−	0.965926i	−0.0186787	−	0.0697097i
$193$	14.9237	−	3.99879i	1.07423	−	0.287839i	0.322000	−	0.946740i	$-0.395645\pi$
$193$	14.9237	−	3.99879i	1.07423	−	0.287839i	0.752230	+	0.658901i	$0.228978\pi$
$194$	−13.8886	+	8.01858i	−0.997142	+	0.575700i
$195$	−11.0885	−	4.30442i	−0.794063	−	0.308246i
$196$	−9.49814	−	16.4513i	−0.678439	−	1.17509i
$197$	4.38695	+	4.38695i	0.312557	+	0.312557i	0.845900	−	0.533342i	$-0.179064\pi$
$197$	4.38695	+	4.38695i	0.312557	+	0.312557i	−0.533342	+	0.845900i	$0.679064\pi$
$198$	1.95223	+	1.95223i	0.138739	+	0.138739i
$199$	5.73567	−	3.31149i	0.406591	−	0.234745i	−0.282733	−	0.959199i	$-0.591241\pi$
$199$	5.73567	−	3.31149i	0.406591	−	0.234745i	0.689324	+	0.724453i	$0.257908\pi$
$200$	0.224095	+	4.99498i	0.0158459	+	0.353198i
$201$	2.07098			0.146076
$202$	−2.71687	+	2.71687i	−0.191158	+	0.191158i
$203$	−4.08799	+	15.2566i	−0.286921	+	1.07080i
$204$	−2.03823	+	3.53033i	−0.142705	+	0.247172i
$205$	18.9371	−	15.2173i	1.32263	−	1.06283i
$206$	1.77809	−	3.07974i	0.123885	−	0.214575i
$207$	6.48095	−	1.73656i	0.450457	−	0.120700i
$208$	−3.76142	−	3.76142i	−0.260807	−	0.260807i
$209$	11.9309	−	1.57431i	0.825281	−	0.108897i
$210$	−9.19827	−	6.73596i	−0.634741	−	0.464826i
$211$	16.5022	+	9.52752i	1.13606	+	0.655902i	0.945451	−	0.325765i	$-0.105622\pi$
$211$	16.5022	+	9.52752i	1.13606	+	0.655902i	0.190605	+	0.981667i	$0.438955\pi$
$212$	1.18314	+	4.41554i	0.0812584	+	0.303260i
$213$	−5.42132	−	1.45264i	−0.371463	−	0.0995332i
$214$	0.387630	+	0.223798i	0.0264978	+	0.0152985i
$215$	23.2765	+	2.53505i	1.58744	+	0.172889i
$216$	1.00000			0.0680414
$217$	2.92101	−	2.92101i	0.198291	−	0.198291i
$218$	−5.73713	−	1.53726i	−0.388568	−	0.104116i
$219$	5.95512	+	10.3146i	0.402410	+	0.696994i
$220$	−0.942797	−	6.10108i	−0.0635634	−	0.411335i
$221$			21.6846i			1.45866i
$222$	2.99181	+	0.801652i	0.200797	+	0.0538034i
$223$	6.81189	−	1.82524i	0.456158	−	0.122227i	−0.0234214	−	0.999726i	$-0.507456\pi$
$223$	6.81189	−	1.82524i	0.456158	−	0.122227i	0.479579	+	0.877499i	$0.340789\pi$
$224$	−2.54933	−	4.41557i	−0.170334	−	0.295027i
$225$	−4.88278	−	1.07634i	−0.325518	−	0.0717557i
$226$	−1.56532	+	2.71122i	−0.104124	+	0.180347i
$227$	6.02454	−	6.02454i	0.399862	−	0.399862i	−0.478322	−	0.878184i	$-0.658755\pi$
$227$	6.02454	−	6.02454i	0.399862	−	0.399862i	0.878184	+	0.478322i	$0.158755\pi$
$228$	2.65251	−	3.45893i	0.175667	−	0.229073i
$229$			1.79138i			0.118377i	0.998247	+	0.0591887i	$0.0188514\pi$
$229$			1.79138i			0.118377i	−0.998247	+	0.0591887i	$0.981149\pi$
$230$	−13.9862	−	5.42928i	−0.922224	−	0.357996i
$231$	12.1908	+	7.03837i	0.802097	+	0.463091i
$232$	−0.801779	+	2.99228i	−0.0526393	+	0.196453i
$233$	2.72051	+	10.1531i	0.178227	+	0.665150i	0.995980	+	0.0895812i	$0.0285528\pi$
$233$	2.72051	+	10.1531i	0.178227	+	0.665150i	−0.817753	+	0.575569i	$0.804780\pi$
$234$	4.60678	−	2.65972i	0.301154	−	0.173872i
$235$	17.6848	+	12.9507i	1.15363	+	0.844811i
$236$			5.20712i			0.338954i
$237$	−1.95911	+	7.31151i	−0.127258	+	0.474934i
$238$	−5.37943	+	20.0763i	−0.348697	+	1.30135i
$239$			24.0812i			1.55768i	0.627221	+	0.778841i	$0.284192\pi$
$239$			24.0812i			1.55768i	−0.627221	+	0.778841i	$0.715808\pi$
$240$	−1.80406	−	1.32113i	−0.116451	−	0.0852783i
$241$	−12.4307	+	7.17686i	−0.800731	+	0.462302i	−0.843727	−	0.536773i	$-0.819643\pi$
$241$	−12.4307	+	7.17686i	−0.800731	+	0.462302i	0.0429956	+	0.999075i	$0.486310\pi$
$242$	−0.874182	−	3.26249i	−0.0561946	−	0.209721i
$243$	−0.258819	+	0.965926i	−0.0166032	+	0.0619642i
$244$	5.06311	+	2.92319i	0.324132	+	0.187138i
$245$	−39.5981	−	15.3715i	−2.52983	−	0.982049i
$246$			10.8645i			0.692692i
$247$	3.01975	−	22.9895i	0.192142	−	1.46278i
$248$	0.572898	−	0.572898i	0.0363791	−	0.0363791i
$249$	2.65711	−	4.60224i	0.168387	−	0.291655i
$250$	7.38684	+	8.39253i	0.467185	+	0.530790i
$251$	−8.38708	−	14.5268i	−0.529388	−	0.916926i	−0.999413	−	0.0342732i	$-0.989088\pi$
$251$	−8.38708	−	14.5268i	−0.529388	−	0.916926i	0.470025	−	0.882653i	$-0.344245\pi$
$252$	4.92492	−	1.31963i	0.310241	−	0.0831288i
$253$	17.8931	+	4.79443i	1.12493	+	0.301423i
$254$			8.98653i			0.563865i
$255$	1.39205	+	9.00834i	0.0871738	+	0.564124i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−11.5977	−	3.10759i	−0.723445	−	0.193846i	−0.121737	−	0.992562i	$-0.538846\pi$
$257$	−11.5977	−	3.10759i	−0.723445	−	0.193846i	−0.601708	+	0.798716i	$0.705513\pi$
$258$	−7.40419	+	7.40419i	−0.460965	+	0.460965i
$259$	15.7923			0.981286
$260$	−11.8247	−	1.28783i	−0.733338	−	0.0798681i
$261$	−2.68280	−	1.54892i	−0.166061	−	0.0958756i
$262$	−4.34831	−	1.16513i	−0.268639	−	0.0719817i
$263$	−1.70344	−	6.35734i	−0.105039	−	0.392010i	0.893311	−	0.449440i	$-0.148376\pi$
$263$	−1.70344	−	6.35734i	−0.105039	−	0.392010i	−0.998350	+	0.0574293i	$0.981710\pi$
$264$	2.39099	+	1.38044i	0.147155	+	0.0849600i
$265$	8.24690	+	6.03926i	0.506603	+	0.370989i
$266$	8.49892	−	20.5353i	0.521102	−	1.25910i
$267$	3.28441	+	3.28441i	0.201003	+	0.201003i
$268$	2.00042	−	0.536010i	0.122195	−	0.0327420i
$269$	−0.869056	+	1.50525i	−0.0529873	+	0.0917766i	−0.891302	−	0.453409i	$-0.850208\pi$
$269$	−0.869056	+	1.50525i	−0.0529873	+	0.0917766i	0.838315	+	0.545186i	$0.183541\pi$
$270$	1.74303	−	1.40065i	0.106078	−	0.0852411i
$271$	6.83546	−	11.8394i	0.415224	−	0.719190i	−0.580228	−	0.814454i	$-0.697036\pi$
$271$	6.83546	−	11.8394i	0.415224	−	0.719190i	0.995452	+	0.0952645i	$0.0303697\pi$
$272$	−1.05507	+	3.93757i	−0.0639729	+	0.238750i
$273$	19.1782	−	19.1782i	1.16072	−	1.16072i
$274$	−14.8549			−0.897419
$275$	−10.1888	−	9.31387i	−0.614410	−	0.561647i
$276$	5.81066	−	3.35478i	0.349760	−	0.201934i
$277$	−7.27122	−	7.27122i	−0.436885	−	0.436885i	0.454077	−	0.890962i	$-0.349969\pi$
$277$	−7.27122	−	7.27122i	−0.436885	−	0.436885i	−0.890962	+	0.454077i	$0.849969\pi$
$278$	−9.14828	−	9.14828i	−0.548678	−	0.548678i
$279$	0.405100	+	0.701654i	0.0242527	+	0.0420069i
$280$	−10.6282	−	4.12575i	−0.635159	−	0.246561i
$281$	22.4127	−	12.9400i	1.33703	−	0.771933i	0.350662	−	0.936502i	$-0.385956\pi$
$281$	22.4127	−	12.9400i	1.33703	−	0.771933i	0.986366	+	0.164568i	$0.0526232\pi$
$282$	−9.46876	+	2.53715i	−0.563856	+	0.151085i
$283$	3.64938	+	13.6197i	0.216933	+	0.809604i	0.985477	+	0.169808i	$0.0543147\pi$
$283$	3.64938	+	13.6197i	0.216933	+	0.809604i	−0.768544	+	0.639797i	$0.779019\pi$
$284$	−5.61257			−0.333045
$285$	−0.221339	−	9.74428i	−0.0131110	−	0.577201i
$286$	14.6863			0.868420
$287$	14.3371	+	53.5066i	0.846289	+	3.15840i
$288$	0.965926	−	0.258819i	0.0569177	−	0.0152511i
$289$	−0.331165	+	0.191198i	−0.0194803	+	0.0112469i
$290$	2.79362	+	6.33866i	0.164047	+	0.372219i
$291$	−8.01858	−	13.8886i	−0.470057	−	0.814163i
$292$	8.42181	+	8.42181i	0.492849	+	0.492849i
$293$	17.4443	+	17.4443i	1.01911	+	1.01911i	0.999814	+	0.0192920i	$0.00614123\pi$
$293$	17.4443	+	17.4443i	1.01911	+	1.01911i	0.0192920	+	0.999814i	$0.493859\pi$
$294$	16.4513	−	9.49814i	0.959457	−	0.553943i
$295$	7.29337	+	9.07618i	0.424636	+	0.528436i
$296$	3.09735			0.180030
$297$	−1.95223	+	1.95223i	−0.113280	+	0.113280i
$298$	1.10764	−	4.13378i	0.0641641	−	0.239464i
$299$	17.8456	−	30.9095i	1.03204	−	1.78754i
$300$	−4.99498	+	0.224095i	−0.288385	+	0.0129381i
$301$	−26.6943	+	46.2359i	−1.53863	+	2.66499i
$302$	10.9094	−	2.92317i	0.627766	−	0.168209i
$303$	−2.71687	−	2.71687i	−0.156080	−	0.156080i
$304$	1.66690	−	4.02759i	0.0956030	−	0.230998i
$305$	12.9195	−	1.99645i	0.739771	−	0.114316i
$306$	−3.53033	−	2.03823i	−0.201815	−	0.116518i
$307$	−6.14569	−	22.9360i	−0.350753	−	1.30903i	−0.885746	−	0.464171i	$-0.846352\pi$
$307$	−6.14569	−	22.9360i	−0.350753	−	1.30903i	0.534993	−	0.844857i	$-0.320314\pi$
$308$	13.5971	+	3.64333i	0.774766	+	0.207598i
$309$	3.07974	+	1.77809i	0.175200	+	0.101152i
$310$	0.196149	−	1.80101i	0.0111405	−	0.102291i
$311$	4.86906			0.276099			0.138049	−	0.990425i	$-0.455917\pi$
$311$	4.86906			0.276099			0.138049	+	0.990425i	$0.455917\pi$
$312$	3.76142	−	3.76142i	0.212948	−	0.212948i
$313$	6.85672	+	1.83725i	0.387565	+	0.103848i	0.447340	−	0.894364i	$-0.352372\pi$
$313$	6.85672	+	1.83725i	0.387565	+	0.103848i	−0.0597747	+	0.998212i	$0.519038\pi$
$314$	−3.06715	−	5.31246i	−0.173089	−	0.299800i
$315$	6.73596	−	9.19827i	0.379529	−	0.518264i
$316$			7.56944i			0.425814i
$317$	14.0936	+	3.77636i	0.791574	+	0.212102i	0.631881	−	0.775065i	$-0.282283\pi$
$317$	14.0936	+	3.77636i	0.791574	+	0.212102i	0.159693	+	0.987167i	$0.448950\pi$
$318$	−4.41554	+	1.18314i	−0.247611	+	0.0663472i
$319$	−4.27636	−	7.40688i	−0.239430	−	0.414706i
$320$	−2.08452	−	0.809185i	−0.116528	−	0.0452348i
$321$	−0.223798	+	0.387630i	−0.0124912	+	0.0216354i
$322$	24.1900	−	24.1900i	1.34805	−	1.34805i
$323$	−16.4143	+	6.80469i	−0.913318	+	0.378623i
$324$			1.00000i			0.0555556i
$325$	−22.4147	+	14.3176i	−1.24334	+	0.794198i
$326$	−14.9553	−	8.63446i	−0.828299	−	0.478219i
$327$	1.53726	−	5.73713i	0.0850107	−	0.317264i
$328$	2.81193	+	10.4943i	0.155263	+	0.579448i
$329$	−43.2848	+	24.9905i	−2.38637	+	1.37777i
$330$	6.10108	−	0.942797i	0.335854	−	0.0518993i
$331$		−	35.4767i		−	1.94998i	−0.222256	−	0.974988i	$-0.571342\pi$
$331$		−	35.4767i		−	1.94998i	0.222256	−	0.974988i	$-0.428658\pi$
$332$	1.37542	−	5.13313i	0.0754859	−	0.281717i
$333$	−0.801652	+	2.99181i	−0.0439303	+	0.163950i
$334$		−	21.5356i		−	1.17838i
$335$	2.73603	−	3.73617i	0.149485	−	0.204129i
$336$	4.41557	−	2.54933i	0.240889	−	0.139077i
$337$	0.962870	+	3.59348i	0.0524508	+	0.195749i	0.987180	−	0.159612i	$-0.0510244\pi$
$337$	0.962870	+	3.59348i	0.0524508	+	0.195749i	−0.934729	+	0.355362i	$0.884358\pi$
$338$	3.95903	−	14.7753i	0.215343	−	0.803671i
$339$	−2.71122	−	1.56532i	−0.147253	−	0.0850166i
$340$	3.67615	+	8.34110i	0.199367	+	0.452360i
$341$			2.23686i			0.121133i
$342$	3.45893	+	2.65251i	0.187037	+	0.143432i
$343$	43.2501	−	43.2501i	2.33529	−	2.33529i
$344$	−5.23555	+	9.06825i	−0.282282	+	0.488927i
$345$	5.42928	−	13.9862i	0.292303	−	0.752993i
$346$	−0.131950	−	0.228543i	−0.00709365	−	0.0122866i
$347$	−19.7489	+	5.29170i	−1.06018	+	0.284073i	−0.746451	−	0.665440i	$-0.768244\pi$
$347$	−19.7489	+	5.29170i	−1.06018	+	0.284073i	−0.313726	+	0.949514i	$0.601577\pi$
$348$	−2.99228	−	0.801779i	−0.160403	−	0.0429798i
$349$		−	22.8777i		−	1.22461i	−0.790620	−	0.612307i	$-0.790241\pi$
$349$		−	22.8777i		−	1.22461i	0.790620	−	0.612307i	$-0.209759\pi$
$350$	−24.3041	+	7.69517i	−1.29911	+	0.411324i
$351$	2.65972	+	4.60678i	0.141966	+	0.245892i
$352$	2.66680	+	0.714566i	0.142141	+	0.0380865i
$353$	−6.58822	+	6.58822i	−0.350656	+	0.350656i	−0.860353	−	0.509698i	$-0.829757\pi$
$353$	−6.58822	+	6.58822i	−0.350656	+	0.350656i	0.509698	+	0.860353i	$0.329757\pi$
$354$	−5.20712			−0.276755
$355$	−9.78290	+	7.86127i	−0.519222	+	0.417233i
$356$	4.02257	+	2.32243i	0.213196	+	0.123089i
$357$	−20.0763	−	5.37943i	−1.06255	−	0.284710i
$358$	−0.0232311	−	0.0866996i	−0.00122780	−	0.00458222i
$359$	9.36029	+	5.40417i	0.494017	+	0.285221i	0.726240	−	0.687442i	$-0.241266\pi$
$359$	9.36029	+	5.40417i	0.494017	+	0.285221i	−0.232222	+	0.972663i	$0.574600\pi$
$360$	1.32113	−	1.80406i	0.0696294	−	0.0950822i
$361$	18.3497	−	4.92834i	0.965774	−	0.259387i
$362$	16.1370	+	16.1370i	0.848143	+	0.848143i
$363$	3.26249	−	0.874182i	0.171236	−	0.0458827i
$364$	13.5610	−	23.4884i	0.710790	−	1.23113i
$365$	26.4756	+	2.88346i	1.38579	+	0.150927i
$366$	−2.92319	+	5.06311i	−0.152797	+	0.264653i
$367$	1.50560	−	5.61897i	0.0785916	−	0.293308i	−0.915432	−	0.402472i	$-0.868151\pi$
$367$	1.50560	−	5.61897i	0.0785916	−	0.293308i	0.994024	+	0.109165i	$0.0348176\pi$
$368$	4.74438	−	4.74438i	0.247318	−	0.247318i
$369$	−10.8645			−0.565581
$370$	5.39878	−	4.33831i	0.280669	−	0.225538i
$371$	−20.1849	+	11.6537i	−1.04795	+	0.605032i
$372$	0.572898	+	0.572898i	0.0297034	+	0.0297034i
$373$	−13.6596	−	13.6596i	−0.707268	−	0.707268i	0.258692	−	0.965960i	$-0.416709\pi$
$373$	−13.6596	−	13.6596i	−0.707268	−	0.707268i	−0.965960	+	0.258692i	$0.916709\pi$
$374$	−5.62731	−	9.74678i	−0.290981	−	0.503994i
$375$	−8.39253	+	7.38684i	−0.433389	+	0.381455i
$376$	−8.48946	+	4.90139i	−0.437810	+	0.252770i
$377$	−15.9173	+	4.26502i	−0.819781	+	0.219660i
$378$	1.31963	+	4.92492i	0.0678744	+	0.253311i
$379$	−0.147193			−0.00756079			−0.00378040	−	0.999993i	$-0.501203\pi$
$379$	−0.147193			−0.00756079			−0.00378040	+	0.999993i	$0.501203\pi$
$380$	−2.73580	−	9.35497i	−0.140344	−	0.479900i
$381$	−8.98653			−0.460394
$382$	5.51508	+	20.5825i	0.282176	+	1.05309i
$383$	4.12694	−	1.10581i	0.210877	−	0.0565043i	−0.151834	−	0.988406i	$-0.548518\pi$
$383$	4.12694	−	1.10581i	0.210877	−	0.0565043i	0.362711	+	0.931902i	$0.381851\pi$
$384$	0.866025	−	0.500000i	0.0441942	−	0.0255155i
$385$	28.8032	−	12.6944i	1.46795	−	0.646965i
$386$	7.72507	+	13.3802i	0.393196	+	0.681035i
$387$	−7.40419	−	7.40419i	−0.376376	−	0.376376i
$388$	−11.3400	−	11.3400i	−0.575700	−	0.575700i
$389$	−23.1677	+	13.3759i	−1.17465	+	0.678184i	−0.954771	−	0.297344i	$-0.903899\pi$
$389$	−23.1677	+	13.3759i	−1.17465	+	0.678184i	−0.219878	+	0.975527i	$0.570566\pi$
$390$	1.28783	−	11.8247i	0.0652120	−	0.598768i
$391$	−27.3514			−1.38322
$392$	13.4324	−	13.4324i	0.678439	−	0.678439i
$393$	1.16513	−	4.34831i	0.0587728	−	0.219343i
$394$	−3.10204	+	5.37289i	−0.156279	+	0.270683i
$395$	10.6022	+	13.1938i	0.533453	+	0.663851i
$396$	−1.38044	+	2.39099i	−0.0693695	+	0.120152i
$397$	−10.6739	+	2.86006i	−0.535707	+	0.143542i	−0.516522	−	0.856274i	$-0.672774\pi$
$397$	−10.6739	+	2.86006i	−0.535707	+	0.143542i	−0.0191847	+	0.999816i	$0.506107\pi$
$398$	4.68315	+	4.68315i	0.234745	+	0.234745i
$399$	20.5353	+	8.49892i	1.02805	+	0.425478i
$400$	−4.76678	+	1.50925i	−0.238339	+	0.0754627i
$401$	18.0055	+	10.3955i	0.899150	+	0.519124i	0.876924	−	0.480629i	$-0.159592\pi$
$401$	18.0055	+	10.3955i	0.899150	+	0.519124i	0.0222254	+	0.999753i	$0.492925\pi$
$402$	0.536010	+	2.00042i	0.0267337	+	0.0997717i
$403$	4.16297	+	1.11546i	0.207372	+	0.0555652i
$404$	−3.32747	−	1.92111i	−0.165548	−	0.0955790i
$405$	1.40065	+	1.74303i	0.0695991	+	0.0866121i
$406$	−15.7948			−0.783882
$407$	−6.04674	+	6.04674i	−0.299726	+	0.299726i
$408$	−3.93757	−	1.05507i	−0.194939	−	0.0522336i
$409$	1.02098	+	1.76839i	0.0504843	+	0.0874413i	0.890163	−	0.455642i	$-0.150590\pi$
$409$	1.02098	+	1.76839i	0.0504843	+	0.0874413i	−0.839679	+	0.543083i	$0.817257\pi$
$410$	19.6001	+	14.3533i	0.967981	+	0.708859i
$411$		−	14.8549i		−	0.732740i
$412$	3.43500	+	0.920406i	0.169230	+	0.0453451i
$413$	−25.6446	+	6.87146i	−1.26189	+	0.338123i
$414$	3.35478	+	5.81066i	0.164879	+	0.285578i
$415$	−4.79234	−	10.8737i	−0.235247	−	0.533770i
$416$	2.65972	−	4.60678i	0.130404	−	0.225866i
$417$	9.14828	−	9.14828i	0.447993	−	0.447993i
$418$	4.60862	+	11.1170i	0.225415	+	0.543748i
$419$		−	24.8231i		−	1.21269i	−0.795203	−	0.606343i	$-0.792636\pi$
$419$		−	24.8231i		−	1.21269i	0.795203	−	0.606343i	$-0.207364\pi$
$420$	4.12575	−	10.6282i	0.201316	−	0.518605i
$421$	−6.16031	−	3.55666i	−0.300235	−	0.173341i	0.342313	−	0.939586i	$-0.388790\pi$
$421$	−6.16031	−	3.55666i	−0.300235	−	0.173341i	−0.642548	+	0.766245i	$0.722123\pi$
$422$	−4.93181	+	18.4058i	−0.240077	+	0.895979i
$423$	−2.53715	−	9.46876i	−0.123360	−	0.460387i
$424$	−3.95886	+	2.28565i	−0.192259	+	0.111001i
$425$	18.0907	+	9.38980i	0.877526	+	0.455472i
$426$		−	5.61257i		−	0.271930i
$427$	−7.71504	+	28.7929i	−0.373357	+	1.39339i
$428$	−0.115846	+	0.432345i	−0.00559965	+	0.0208982i
$429$			14.6863i			0.709062i
$430$	3.57573	+	23.1395i	0.172437	+	1.11588i
$431$	1.05773	−	0.610681i	0.0509491	−	0.0294154i	−0.474309	−	0.880358i	$-0.657302\pi$
$431$	1.05773	−	0.610681i	0.0509491	−	0.0294154i	0.525258	+	0.850943i	$0.323969\pi$
$432$	0.258819	+	0.965926i	0.0124524	+	0.0464731i
$433$	−2.06463	+	7.70531i	−0.0992199	+	0.370294i	−0.997625	−	0.0688732i	$-0.978060\pi$
$433$	−2.06463	+	7.70531i	−0.0992199	+	0.370294i	0.898406	+	0.439167i	$0.144726\pi$
$434$	3.57749	+	2.06547i	0.171725	+	0.0991456i
$435$	−6.33866	+	2.79362i	−0.303915	+	0.133944i
$436$		−	5.93952i		−	0.284451i
$437$	28.9972	+	3.80889i	1.38713	+	0.182204i
$438$	−8.42181	+	8.42181i	−0.402410	+	0.402410i
$439$	5.08089	−	8.80036i	0.242498	−	0.420018i	−0.718927	−	0.695085i	$-0.755367\pi$
$439$	5.08089	−	8.80036i	0.242498	−	0.420018i	0.961425	+	0.275067i	$0.0887000\pi$
$440$	5.64918	−	2.48975i	0.269314	−	0.118694i
$441$	9.49814	+	16.4513i	0.452293	+	0.783394i
$442$	−20.9457	+	5.61238i	−0.996285	+	0.266954i
$443$	16.5385	+	4.43147i	0.785766	+	0.210545i	0.629325	−	0.777142i	$-0.283331\pi$
$443$	16.5385	+	4.43147i	0.785766	+	0.210545i	0.156441	+	0.987687i	$0.449998\pi$
$444$			3.09735i			0.146994i
$445$	10.2644	−	1.58615i	0.486579	−	0.0751907i
$446$	3.52609	+	6.10737i	0.166965	+	0.289192i
$447$	4.13378	+	1.10764i	0.195521	+	0.0523898i
$448$	3.60529	−	3.60529i	0.170334	−	0.170334i
$449$	−4.78956			−0.226033			−0.113017	−	0.993593i	$-0.536051\pi$
$449$	−4.78956			−0.226033			−0.113017	+	0.993593i	$0.536051\pi$
$450$	−0.224095	−	4.99498i	−0.0105639	−	0.235465i
$451$	−25.9768	−	14.9977i	−1.22320	−	0.706214i
$452$	−3.02397	−	0.810270i	−0.142236	−	0.0381119i
$453$	2.92317	+	10.9094i	0.137342	+	0.512569i
$454$	7.37852	+	4.25999i	0.346291	+	0.199931i
$455$	−9.26177	−	59.9353i	−0.434199	−	2.80981i
$456$	4.02759	+	1.66690i	0.188609	+	0.0780595i
$457$	−20.3041	−	20.3041i	−0.949786	−	0.949786i	0.0490125	−	0.998798i	$-0.484393\pi$
$457$	−20.3041	−	20.3041i	−0.949786	−	0.949786i	−0.998798	+	0.0490125i	$0.984393\pi$
$458$	−1.73034	+	0.463642i	−0.0808533	+	0.0216646i
$459$	2.03823	−	3.53033i	0.0951367	−	0.164782i
$460$	1.62438	−	14.9149i	0.0757371	−	0.695409i
$461$	−10.6343	+	18.4192i	−0.495291	+	0.857868i	−0.999985	−	0.00542951i	$-0.998272\pi$
$461$	−10.6343	+	18.4192i	−0.495291	+	0.857868i	0.504695	+	0.863298i	$0.331605\pi$
$462$	−3.64333	+	13.5971i	−0.169503	+	0.632594i
$463$	4.42653	−	4.42653i	0.205718	−	0.205718i	−0.596726	−	0.802445i	$-0.703532\pi$
$463$	4.42653	−	4.42653i	0.205718	−	0.205718i	0.802445	+	0.596726i	$0.203532\pi$
$464$	−3.09783			−0.143813
$465$	1.80101	+	0.196149i	0.0835200	+	0.00909618i
$466$	−9.10300	+	5.25562i	−0.421689	+	0.243462i
$467$	11.0231	+	11.0231i	0.510086	+	0.510086i	0.914553	−	0.404467i	$-0.132543\pi$
$467$	11.0231	+	11.0231i	0.510086	+	0.510086i	−0.404467	+	0.914553i	$0.632543\pi$
$468$	3.76142	+	3.76142i	0.173872	+	0.173872i
$469$	5.27961	+	9.14456i	0.243790	+	0.422257i
$470$	−7.93226	+	20.4341i	−0.365888	+	0.942554i
$471$	5.31246	−	3.06715i	0.244785	−	0.141327i
$472$	−5.02969	+	1.34770i	−0.231510	+	0.0620330i
$473$	−7.48230	−	27.9243i	−0.344037	−	1.28396i
$474$	−7.56944			−0.347676
$475$	−17.8717	−	12.4741i	−0.820008	−	0.572351i
$476$	−20.7845			−0.952657
$477$	−1.18314	−	4.41554i	−0.0541723	−	0.202174i
$478$	−23.2606	+	6.23267i	−1.06392	+	0.285076i
$479$	1.03665	−	0.598508i	0.0473656	−	0.0273465i	−0.476130	−	0.879375i	$-0.657961\pi$
$479$	1.03665	−	0.598508i	0.0473656	−	0.0273465i	0.523496	+	0.852028i	$0.324628\pi$
$480$	0.809185	−	2.08452i	0.0369341	−	0.0951448i
$481$	8.23809	+	14.2688i	0.375624	+	0.650601i
$482$	−10.1496	−	10.1496i	−0.462302	−	0.462302i
$483$	24.1900	+	24.1900i	1.10068	+	1.10068i
$484$	2.92507	−	1.68879i	0.132958	−	0.0767632i
$485$	−35.6494	−	3.88258i	−1.61875	−	0.176299i
$486$	−1.00000			−0.0453609
$487$	6.55216	−	6.55216i	0.296907	−	0.296907i	−0.542894	−	0.839801i	$-0.682672\pi$
$487$	6.55216	−	6.55216i	0.296907	−	0.296907i	0.839801	+	0.542894i	$0.182672\pi$
$488$	−1.51315	+	5.64716i	−0.0684972	+	0.255635i
$489$	8.63446	−	14.9553i	0.390464	−	0.676303i
$490$	4.59898	−	42.2273i	0.207761	−	1.90763i
$491$	−6.26828	+	10.8570i	−0.282884	+	0.489969i	−0.972094	−	0.234593i	$-0.924624\pi$
$491$	−6.26828	+	10.8570i	−0.282884	+	0.489969i	0.689210	+	0.724562i	$0.257958\pi$
$492$	−10.4943	+	2.81193i	−0.473118	+	0.126772i
$493$	8.92951	+	8.92951i	0.402165	+	0.402165i
$494$	22.9877	−	3.03326i	1.03426	−	0.136473i
$495$	0.942797	+	6.10108i	0.0423756	+	0.274223i
$496$	0.701654	+	0.405100i	0.0315052	+	0.0181895i
$497$	−7.40651	−	27.6415i	−0.332227	−	1.23989i
$498$	5.13313	+	1.37542i	0.230021	+	0.0616340i
$499$	−6.88753	−	3.97652i	−0.308328	−	0.178013i	0.337850	−	0.941200i	$-0.390300\pi$
$499$	−6.88753	−	3.97652i	−0.308328	−	0.178013i	−0.646178	+	0.763187i	$0.723634\pi$
$500$	−6.19471	+	9.30729i	−0.277036	+	0.416234i
$501$	21.5356			0.962140
$502$	11.8611	−	11.8611i	0.529388	−	0.529388i
$503$	−22.5095	−	6.03141i	−1.00365	−	0.268927i	−0.280676	−	0.959803i	$-0.590559\pi$
$503$	−22.5095	−	6.03141i	−1.00365	−	0.268927i	−0.722974	+	0.690875i	$0.757225\pi$
$504$	2.54933	+	4.41557i	0.113556	+	0.196685i
$505$	−8.49071	+	1.31206i	−0.377831	+	0.0583861i
$506$			18.5243i			0.823504i
$507$	14.7753	+	3.95903i	0.656195	+	0.175827i
$508$	−8.68032	+	2.32588i	−0.385127	+	0.103194i
$509$	10.2217	+	17.7045i	0.453069	+	0.784739i	0.998575	−	0.0533680i	$-0.0169956\pi$
$509$	10.2217	+	17.7045i	0.453069	+	0.784739i	−0.545505	+	0.838107i	$0.683662\pi$
$510$	−8.34110	+	3.67615i	−0.369350	+	0.162783i
$511$	−30.3631	+	52.5905i	−1.34319	+	2.32646i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	−2.65251	+	3.45893i	−0.117111	+	0.152715i
$514$		−	12.0068i		−	0.529598i
$515$	7.27649	−	3.20695i	0.320641	−	0.141315i
$516$	−9.06825	−	5.23555i	−0.399207	−	0.230482i
$517$	7.00474	−	26.1420i	0.308068	−	1.14973i
$518$	4.08735	+	15.2542i	0.179588	+	0.670231i
$519$	0.228543	−	0.131950i	0.0100319	−	0.00579194i
$520$	−1.81651	−	11.7551i	−0.0796593	−	0.515496i
$521$		−	23.4276i		−	1.02638i	−0.858275	−	0.513190i	$-0.828464\pi$
$521$		−	23.4276i		−	1.02638i	0.858275	−	0.513190i	$-0.171536\pi$
$522$	0.801779	−	2.99228i	0.0350929	−	0.130968i
$523$	5.13269	−	19.1555i	0.224437	−	0.837610i	−0.758192	−	0.652031i	$-0.773917\pi$
$523$	5.13269	−	19.1555i	0.224437	−	0.837610i	0.982629	−	0.185579i	$-0.0594161\pi$
$524$		−	4.50170i		−	0.196658i
$525$	−7.69517	−	24.3041i	−0.335845	−	1.06072i
$526$	5.69983	−	3.29080i	0.248525	−	0.143486i
$527$	−0.854817	−	3.19022i	−0.0372364	−	0.138968i
$528$	−0.714566	+	2.66680i	−0.0310975	+	0.116058i
$529$	19.0684	+	11.0092i	0.829062	+	0.478659i
$530$	−3.69903	+	9.52897i	−0.160675	+	0.413912i
$531$		−	5.20712i		−	0.225970i
$532$	22.0352	+	2.89441i	0.955349	+	0.125489i
$533$	−40.8658	+	40.8658i	−1.77009	+	1.77009i
$534$	−2.32243	+	4.02257i	−0.100501	+	0.174073i
$535$	0.403641	+	0.915853i	0.0174509	+	0.0395958i
$536$	1.03549	+	1.79352i	0.0447264	+	0.0774684i
$537$	0.0866996	−	0.0232311i	0.00374136	−	0.00100250i
$538$	−1.67889	−	0.449856i	−0.0723819	−	0.0193947i
$539$			52.4463i			2.25902i
$540$	1.80406	+	1.32113i	0.0776343	+	0.0568522i
$541$	−8.09293	−	14.0174i	−0.347942	−	0.602654i	0.637942	−	0.770085i	$-0.279786\pi$
$541$	−8.09293	−	14.0174i	−0.347942	−	0.602654i	−0.985884	+	0.167431i	$0.946453\pi$
$542$	13.2051	+	3.53829i	0.567207	+	0.151983i
$543$	−16.1370	+	16.1370i	−0.692506	+	0.692506i
$544$	−4.07647			−0.174777
$545$	−8.31921	−	10.3528i	−0.356356	−	0.443464i
$546$	23.4884	+	13.5610i	1.00521	+	0.580358i
$547$	19.5235	+	5.23131i	0.834765	+	0.223675i	0.650791	−	0.759257i	$-0.274437\pi$
$547$	19.5235	+	5.23131i	0.834765	+	0.223675i	0.183974	+	0.982931i	$0.441104\pi$
$548$	−3.84474	−	14.3488i	−0.164239	−	0.612949i
$549$	−5.06311	−	2.92319i	−0.216088	−	0.124759i
$550$	6.35944	−	12.2523i	0.271167	−	0.522438i
$551$	−8.22334	−	10.7104i	−0.350326	−	0.456276i
$552$	4.74438	+	4.74438i	0.201934	+	0.201934i
$553$	−37.2789	+	9.98885i	−1.58526	+	0.424769i
$554$	5.14153	−	8.90538i	0.218443	−	0.378354i
$555$	4.33831	+	5.39878i	0.184151	+	0.229165i
$556$	6.46881	−	11.2043i	0.274339	−	0.475169i
$557$	10.1741	−	37.9704i	0.431092	−	1.60886i	−0.319157	−	0.947702i	$-0.603400\pi$
$557$	10.1741	−	37.9704i	0.431092	−	1.60886i	0.750249	−	0.661155i	$-0.229934\pi$
$558$	−0.572898	+	0.572898i	−0.0242527	+	0.0242527i
$559$	−55.7005			−2.35588
$560$	1.23438	−	11.3339i	0.0521621	−	0.478946i
$561$	9.74678	−	5.62731i	0.411509	−	0.237585i
$562$	18.2999	+	18.2999i	0.771933	+	0.771933i
$563$	14.3715	+	14.3715i	0.605687	+	0.605687i	0.941816	−	0.336129i	$-0.109118\pi$
$563$	14.3715	+	14.3715i	0.605687	+	0.605687i	−0.336129	+	0.941816i	$0.609118\pi$
$564$	−4.90139	−	8.48946i	−0.206386	−	0.357471i
$565$	−6.40579	+	2.82321i	−0.269494	+	0.118773i
$566$	−12.2110	+	7.05005i	−0.513269	+	0.296336i
$567$	−4.92492	+	1.31963i	−0.206827	+	0.0554192i
$568$	−1.45264	−	5.42132i	−0.0609514	−	0.227474i
$569$	25.5362			1.07053			0.535267	−	0.844683i	$-0.320211\pi$
$569$	25.5362			1.07053			0.535267	+	0.844683i	$0.320211\pi$
$570$	9.35497	−	2.73580i	0.391836	−	0.114590i
$571$	−10.0715			−0.421480			−0.210740	−	0.977542i	$-0.567587\pi$
$571$	−10.0715			−0.421480			−0.210740	+	0.977542i	$0.567587\pi$
$572$	3.80110	+	14.1859i	0.158932	+	0.593142i
$573$	−20.5825	+	5.51508i	−0.859848	+	0.230396i
$574$	−47.9727	+	27.6971i	−2.00234	+	1.15605i
$575$	−18.0592	−	28.2723i	−0.753121	−	1.17904i
$576$	0.500000	+	0.866025i	0.0208333	+	0.0360844i
$577$	25.7233	+	25.7233i	1.07088	+	1.07088i	0.997289	+	0.0735874i	$0.0234448\pi$
$577$	25.7233	+	25.7233i	1.07088	+	1.07088i	0.0735874	+	0.997289i	$0.476555\pi$
$578$	−0.270395	−	0.270395i	−0.0112469	−	0.0112469i
$579$	−13.3802	+	7.72507i	−0.556062	+	0.321043i
$580$	−5.39963	+	4.33900i	−0.224207	+	0.180167i
$581$	27.0953			1.12410
$582$	11.3400	−	11.3400i	0.470057	−	0.470057i
$583$	3.26650	−	12.1907i	0.135285	−	0.504889i
$584$	−5.95512	+	10.3146i	−0.246425	+	0.426820i
$585$	11.8247	+	1.28783i	0.488892	+	0.0532454i
$586$	−12.3350	+	21.3648i	−0.509553	+	0.882572i
$587$	−12.6425	+	3.38754i	−0.521811	+	0.139819i	−0.510104	−	0.860113i	$-0.670393\pi$
$587$	−12.6425	+	3.38754i	−0.521811	+	0.139819i	−0.0117068	+	0.999931i	$0.503726\pi$
$588$	13.4324	+	13.4324i	0.553943	+	0.553943i
$589$	0.461993	+	3.50123i	0.0190361	+	0.144266i
$590$	−6.87925	+	9.39394i	−0.283214	+	0.386742i
$591$	−5.37289	−	3.10204i	−0.221011	−	0.127601i
$592$	0.801652	+	2.99181i	0.0329477	+	0.122963i
$593$	−39.2047	−	10.5049i	−1.60994	−	0.431383i	−0.661917	−	0.749577i	$-0.730257\pi$
$593$	−39.2047	−	10.5049i	−1.60994	−	0.431383i	−0.948025	+	0.318194i	$0.896924\pi$
$594$	−2.39099	−	1.38044i	−0.0981033	−	0.0566400i
$595$	−36.2281	+	29.1119i	−1.48521	+	1.19347i
$596$	4.27961			0.175300
$597$	−4.68315	+	4.68315i	−0.191669	+	0.191669i
$598$	34.4751	+	9.23756i	1.40979	+	0.377752i
$599$	9.26120	+	16.0409i	0.378402	+	0.655412i	0.990830	−	0.135115i	$-0.0431403\pi$
$599$	9.26120	+	16.0409i	0.378402	+	0.655412i	−0.612428	+	0.790527i	$0.709807\pi$
$600$	−1.50925	−	4.76678i	−0.0616150	−	0.194603i
$601$		−	19.6073i		−	0.799797i	−0.916559	−	0.399899i	$-0.869045\pi$
$601$		−	19.6073i		−	0.799797i	0.916559	−	0.399899i	$-0.130955\pi$
$602$	−51.5694	−	13.8180i	−2.10181	−	0.563179i
$603$	−2.00042	+	0.536010i	−0.0814632	+	0.0218280i
$604$	5.64713	+	9.78111i	0.229778	+	0.397988i
$605$	2.73309	−	7.04063i	0.111116	−	0.286242i
$606$	1.92111	−	3.32747i	0.0780399	−	0.135169i
$607$	−16.1463	+	16.1463i	−0.655360	+	0.655360i	−0.954279	−	0.298919i	$-0.903374\pi$
$607$	−16.1463	+	16.1463i	−0.655360	+	0.655360i	0.298919	+	0.954279i	$0.403374\pi$
$608$	4.32177	+	0.567681i	0.175271	+	0.0230225i
$609$		−	15.7948i		−	0.640037i
$610$	5.27225	+	11.9626i	0.213467	+	0.484352i
$611$	−45.1592	−	26.0727i	−1.82695	−	1.05479i
$612$	1.05507	−	3.93757i	0.0426486	−	0.159167i
$613$	4.81164	+	17.9573i	0.194340	+	0.725289i	0.992437	+	0.122758i	$0.0391740\pi$
$613$	4.81164	+	17.9573i	0.194340	+	0.725289i	−0.798096	+	0.602530i	$0.794159\pi$
$614$	20.5639	−	11.8726i	0.829890	−	0.479137i
$615$	−14.3533	+	19.6001i	−0.578781	+	0.790353i
$616$			14.0767i			0.567168i
$617$	−1.44089	+	5.37746i	−0.0580079	+	0.216488i	−0.988846	−	0.148945i	$-0.952412\pi$
$617$	−1.44089	+	5.37746i	−0.0580079	+	0.216488i	0.930838	+	0.365433i	$0.119079\pi$
$618$	−0.920406	+	3.43500i	−0.0370241	+	0.138176i
$619$			20.2122i			0.812399i	0.913784	+	0.406199i	$0.133146\pi$
$619$			20.2122i			0.812399i	−0.913784	+	0.406199i	$0.866854\pi$
$620$	1.79041	−	0.276671i	0.0719047	−	0.0111114i
$621$	−5.81066	+	3.35478i	−0.233174	+	0.134623i
$622$	1.26020	+	4.70315i	0.0505296	+	0.188579i
$623$	−6.12949	+	22.8756i	−0.245573	+	0.916491i
$624$	4.60678	+	2.65972i	0.184419	+	0.106474i
$625$	2.23870	+	24.8996i	0.0895480	+	0.995983i
$626$			7.09860i			0.283717i
$627$	−11.1170	+	4.60862i	−0.443968	+	0.184051i
$628$	4.33761	−	4.33761i	0.173089	−	0.173089i
$629$	6.31312	−	10.9346i	0.251721	−	0.435993i
$630$	10.6282	+	4.12575i	0.423439	+	0.164374i
$631$	3.35327	+	5.80804i	0.133492	+	0.231214i	0.925020	−	0.379918i	$-0.124048\pi$
$631$	3.35327	+	5.80804i	0.133492	+	0.231214i	−0.791529	+	0.611132i	$0.790714\pi$
$632$	−7.31151	+	1.95911i	−0.290836	+	0.0779294i
$633$	−18.4058	−	4.93181i	−0.731563	−	0.196022i
$634$			14.5907i			0.579472i
$635$	−11.8723	+	16.2122i	−0.471139	+	0.643362i
$636$	−2.28565	−	3.95886i	−0.0906319	−	0.156979i
$637$	97.6066	+	26.1536i	3.86731	+	1.03624i
$638$	6.04769	−	6.04769i	0.239430	−	0.239430i
$639$	5.61257			0.222030
$640$	0.242099	−	2.22292i	0.00956981	−	0.0878688i
$641$	32.0129	+	18.4827i	1.26443	+	0.730022i	0.973929	−	0.226852i	$-0.0728433\pi$
$641$	32.0129	+	18.4827i	1.26443	+	0.730022i	0.290505	+	0.956873i	$0.406177\pi$
$642$	−0.432345	−	0.115846i	−0.0170633	−	0.00457210i
$643$	11.9974	+	44.7751i	0.473133	+	1.76576i	0.628407	+	0.777885i	$0.283707\pi$
$643$	11.9974	+	44.7751i	0.473133	+	1.76576i	−0.155274	+	0.987872i	$0.549626\pi$
$644$	29.6265	+	17.1049i	1.16745	+	0.674027i
$645$	−23.1395	+	3.57573i	−0.911115	+	0.140794i
$646$	−10.8212	−	14.0939i	−0.425753	−	0.554515i
$647$	22.8060	+	22.8060i	0.896597	+	0.896597i	0.995133	−	0.0985364i	$-0.0314161\pi$
$647$	22.8060	+	22.8060i	0.896597	+	0.896597i	−0.0985364	+	0.995133i	$0.531416\pi$
$648$	−0.965926	+	0.258819i	−0.0379452	+	0.0101674i
$649$	7.18809	−	12.4501i	0.282157	−	0.488711i
$650$	−19.6311	−	17.9453i	−0.769995	−	0.703872i
$651$	−2.06547	+	3.57749i	−0.0809520	+	0.140213i
$652$	4.46953	−	16.6805i	0.175040	−	0.653259i
$653$	−18.2786	+	18.2786i	−0.715299	+	0.715299i	−0.967639	−	0.252340i	$-0.918800\pi$
$653$	−18.2786	+	18.2786i	−0.715299	+	0.715299i	0.252340	+	0.967639i	$0.418800\pi$
$654$	5.93952			0.232253
$655$	−6.30533	−	7.84662i	−0.246369	−	0.306593i
$656$	−9.40889	+	5.43223i	−0.367356	+	0.212093i
$657$	−8.42181	−	8.42181i	−0.328566	−	0.328566i
$658$	−35.3419	−	35.3419i	−1.37777	−	1.37777i
$659$	−10.6736	−	18.4872i	−0.415783	−	0.720158i	0.579727	−	0.814811i	$-0.303159\pi$
$659$	−10.6736	−	18.4872i	−0.415783	−	0.720158i	−0.995510	+	0.0946530i	$0.969826\pi$
$660$	2.48975	+	5.64918i	0.0969133	+	0.219894i
$661$	−23.1737	+	13.3793i	−0.901353	+	0.520396i	−0.877639	−	0.479323i	$-0.840882\pi$
$661$	−23.1737	+	13.3793i	−0.901353	+	0.520396i	−0.0237139	+	0.999719i	$0.507549\pi$
$662$	34.2679	−	9.18205i	1.33186	−	0.356871i
$663$	−5.61238	−	20.9457i	−0.217967	−	0.813463i
$664$	5.31421			0.206231
$665$	42.4622	−	25.8187i	1.64662	−	1.00121i
$666$	−3.09735			−0.120020
$667$	−5.37959	−	20.0769i	−0.208299	−	0.777381i
$668$	20.8018	−	5.57383i	0.804846	−	0.215658i
$669$	−6.10737	+	3.52609i	−0.236125	+	0.136327i
$670$	4.31700	+	1.67581i	0.166780	+	0.0647421i
$671$	−8.07055	−	13.9786i	−0.311560	−	0.539638i
$672$	3.60529	+	3.60529i	0.139077	+	0.139077i
$673$	10.1750	+	10.1750i	0.392218	+	0.392218i	0.875477	−	0.483259i	$-0.160547\pi$
$673$	10.1750	+	10.1750i	0.392218	+	0.392218i	−0.483259	+	0.875477i	$0.660547\pi$
$674$	−3.22182	+	1.86012i	−0.124100	+	0.0716492i
$675$	4.99498	−	0.224095i	0.192257	−	0.00862543i
$676$	15.2965			0.588328
$677$	4.01327	−	4.01327i	0.154242	−	0.154242i	−0.625767	−	0.780010i	$-0.715214\pi$
$677$	4.01327	−	4.01327i	0.154242	−	0.154242i	0.780010	+	0.625767i	$0.215214\pi$
$678$	0.810270	−	3.02397i	0.0311182	−	0.116135i
$679$	40.8840	−	70.8131i	1.56898	−	2.71756i
$680$	−7.10543	+	5.70972i	−0.272481	+	0.218958i
$681$	−4.25999	+	7.37852i	−0.163243	+	0.282745i
$682$	−2.16064	+	0.578942i	−0.0827352	+	0.0221688i
$683$	6.54510	+	6.54510i	0.250441	+	0.250441i	0.821152	−	0.570710i	$-0.193332\pi$
$683$	6.54510	+	6.54510i	0.250441	+	0.250441i	−0.570710	+	0.821152i	$0.693332\pi$
$684$	−1.66690	+	4.02759i	−0.0637353	+	0.153999i
$685$	−26.7992	−	19.6252i	−1.02394	−	0.749842i
$686$	52.9704	+	30.5825i	2.02242	+	1.16764i
$687$	−0.463642	−	1.73034i	−0.0176890	−	0.0660164i
$688$	−10.1143	−	2.71012i	−0.385605	−	0.103322i
$689$	−21.0590	−	12.1584i	−0.802283	−	0.463198i
$690$	14.9149	+	1.62438i	0.567799	+	0.0618391i
$691$	−14.1102			−0.536778			−0.268389	−	0.963311i	$-0.586491\pi$
$691$	−14.1102			−0.536778			−0.268389	+	0.963311i	$0.586491\pi$
$692$	0.186605	−	0.186605i	0.00709365	−	0.00709365i
$693$	−13.5971	−	3.64333i	−0.516511	−	0.138399i
$694$	−10.2228	−	17.7064i	−0.388052	−	0.672125i
$695$	−4.41801	−	28.5901i	−0.167585	−	1.08448i
$696$		−	3.09783i		−	0.117423i
$697$	42.7795	+	11.4627i	1.62039	+	0.434182i
$698$	22.0982	−	5.92118i	0.836428	−	0.224120i
$699$	−5.25562	−	9.10300i	−0.198786	−	0.344307i
$700$	−13.7233	−	21.4843i	−0.518693	−	0.812032i
$701$	−4.98594	+	8.63590i	−0.188316	+	0.326174i	−0.944689	−	0.327967i	$-0.893636\pi$
$701$	−4.98594	+	8.63590i	−0.188316	+	0.326174i	0.756373	+	0.654141i	$0.226970\pi$
$702$	−3.76142	+	3.76142i	−0.141966	+	0.141966i
$703$	−8.21575	+	10.7135i	−0.309863	+	0.404067i
$704$			2.76087i			0.104054i
$705$	−20.4341	−	7.93226i	−0.769592	−	0.298746i
$706$	−8.06889	−	4.65858i	−0.303677	−	0.175328i
$707$	5.07032	−	18.9227i	0.190689	−	0.711661i
$708$	−1.34770	−	5.02969i	−0.0506497	−	0.189027i
$709$	15.9390	−	9.20241i	0.598603	−	0.345604i	−0.169889	−	0.985463i	$-0.554341\pi$
$709$	15.9390	−	9.20241i	0.598603	−	0.345604i	0.768492	+	0.639860i	$0.221008\pi$
$710$	−10.1254	−	7.41491i	−0.380000	−	0.278277i
$711$		−	7.56944i		−	0.283876i
$712$	−1.20218	+	4.48659i	−0.0450535	+	0.168142i
$713$	−1.40697	+	5.25087i	−0.0526913	+	0.196646i
$714$		−	20.7845i		−	0.777841i
$715$	26.4950	+	19.4025i	0.990856	+	0.725611i
$716$	0.0777327	−	0.0448790i	0.00290501	−	0.00167721i
$717$	−6.23267	−	23.2606i	−0.232763	−	0.868685i
$718$	−2.79740	+	10.4401i	−0.104398	+	0.389619i
$719$	−14.8026	−	8.54630i	−0.552044	−	0.318723i	0.197902	−	0.980222i	$-0.436587\pi$
$719$	−14.8026	−	8.54630i	−0.552044	−	0.318723i	−0.749946	+	0.661499i	$0.769921\pi$
$720$	2.08452	+	0.809185i	0.0776854	+	0.0301565i
$721$			18.1317i			0.675260i
$722$	9.50967	+	16.4489i	0.353913	+	0.612165i
$723$	10.1496	−	10.1496i	0.377468	−	0.377468i
$724$	−11.4106	+	19.7637i	−0.424071	+	0.734513i
$725$	−3.33431	+	15.1260i	−0.123833	+	0.561767i
$726$	1.68879	+	2.92507i	0.0626769	+	0.108560i
$727$	10.8238	−	2.90022i	0.401431	−	0.107563i	−0.0524543	−	0.998623i	$-0.516704\pi$
$727$	10.8238	−	2.90022i	0.401431	−	0.107563i	0.453885	+	0.891060i	$0.350038\pi$
$728$	26.1979	+	7.01970i	0.970958	+	0.260167i
$729$		−	1.00000i		−	0.0370370i
$730$	4.06717	+	26.3197i	0.150533	+	0.974136i
$731$	21.3426	+	36.9664i	0.789384	+	1.36725i
$732$	−5.64716	−	1.51315i	−0.208725	−	0.0559277i
$733$	33.1288	−	33.1288i	1.22364	−	1.22364i	0.257314	−	0.966328i	$-0.417163\pi$
$733$	33.1288	−	33.1288i	1.22364	−	1.22364i	0.966328	−	0.257314i	$-0.0828373\pi$
$734$	5.81718			0.214716
$735$	42.2273	+	4.59898i	1.55758	+	0.169636i
$736$	5.81066	+	3.35478i	0.214184	+	0.123659i
$737$	−5.52289	−	1.47986i	−0.203438	−	0.0545112i
$738$	−2.81193	−	10.4943i	−0.103509	−	0.386299i
$739$	−31.9240	−	18.4313i	−1.17434	−	0.678007i	−0.219644	−	0.975580i	$-0.570490\pi$
$739$	−31.9240	−	18.4313i	−1.17434	−	0.678007i	−0.954699	+	0.297573i	$0.903823\pi$
$740$	5.58779	+	4.09198i	0.205411	+	0.150424i
$741$	3.03326	+	22.9877i	0.111429	+	0.844474i
$742$	−16.4809	−	16.4809i	−0.605032	−	0.605032i
$743$	36.9897	−	9.91137i	1.35702	−	0.363613i	0.494300	−	0.869291i	$-0.335424\pi$
$743$	36.9897	−	9.91137i	1.35702	−	0.363613i	0.862722	+	0.505679i	$0.168758\pi$
$744$	−0.405100	+	0.701654i	−0.0148517	+	0.0257239i
$745$	7.45950	−	5.99425i	0.273295	−	0.219612i
$746$	9.65881	−	16.7295i	0.353634	−	0.612512i
$747$	−1.37542	+	5.13313i	−0.0503240	+	0.187812i
$748$	7.95821	−	7.95821i	0.290981	−	0.290981i
$749$	−2.28214			−0.0833876
$750$	−9.30729	−	6.19471i	−0.339854	−	0.226199i
$751$	4.72096	−	2.72565i	0.172270	−	0.0994603i	−0.411386	−	0.911461i	$-0.634955\pi$
$751$	4.72096	−	2.72565i	0.172270	−	0.0994603i	0.583656	+	0.812001i	$0.301622\pi$
$752$	−6.93161	−	6.93161i	−0.252770	−	0.252770i
$753$	11.8611	+	11.8611i	0.432243	+	0.432243i
$754$	−8.23939	−	14.2710i	−0.300061	−	0.519720i
$755$	23.5431	+	9.13914i	0.856821	+	0.332607i
$756$	−4.41557	+	2.54933i	−0.160593	+	0.0927182i
$757$	6.43059	−	1.72307i	0.233724	−	0.0626261i	−0.140056	−	0.990144i	$-0.544728\pi$
$757$	6.43059	−	1.72307i	0.233724	−	0.0626261i	0.373780	+	0.927517i	$0.378062\pi$
$758$	−0.0380963	−	0.142177i	−0.00138372	−	0.00516412i
$759$	−18.5243			−0.672388
$760$	8.32813	−	5.06383i	0.302093	−	0.183684i
$761$	−40.6613			−1.47397			−0.736986	−	0.675908i	$-0.763752\pi$
$761$	−40.6613			−1.47397			−0.736986	+	0.675908i	$0.763752\pi$
$762$	−2.32588	−	8.68032i	−0.0842579	−	0.314455i
$763$	29.2517	−	7.83796i	1.05898	−	0.283753i
$764$	−18.4538	+	10.6543i	−0.667635	+	0.385459i
$765$	−3.67615	−	8.34110i	−0.132912	−	0.301573i
$766$	2.13626	+	3.70011i	0.0771863	+	0.133691i
$767$	−19.5861	−	19.5861i	−0.707215	−	0.707215i
$768$	0.707107	+	0.707107i	0.0255155	+	0.0255155i
$769$	−11.1539	+	6.43969i	−0.402219	+	0.232221i	−0.687441	−	0.726240i	$-0.741266\pi$
$769$	−11.1539	+	6.43969i	−0.402219	+	0.232221i	0.285222	+	0.958461i	$0.407933\pi$
$770$	19.7166	+	24.5362i	0.710539	+	0.884225i
$771$	12.0068			0.432415
$772$	−10.9249	+	10.9249i	−0.393196	+	0.393196i
$773$	−5.89607	+	22.0044i	−0.212067	+	0.791445i	0.775112	+	0.631824i	$0.217694\pi$
$773$	−5.89607	+	22.0044i	−0.212067	+	0.791445i	−0.987178	+	0.159620i	$0.948973\pi$
$774$	5.23555	−	9.06825i	0.188188	−	0.325951i
$775$	2.73323	−	2.99000i	0.0981805	−	0.107404i
$776$	8.01858	−	13.8886i	0.287850	−	0.498571i
$777$	−15.2542	+	4.08735i	−0.547241	+	0.146633i
$778$	−18.9163	−	18.9163i	−0.678184	−	0.678184i
$779$	−43.7575	−	18.1099i	−1.56778	−	0.648855i
$780$	11.7551	−	1.81651i	0.420901	−	0.0650416i
$781$	13.4196	+	7.74779i	0.480190	+	0.277238i
$782$	−7.07905	−	26.4194i	−0.253146	−	0.944755i
$783$	2.99228	+	0.801779i	0.106935	+	0.0286532i
$784$	16.4513	+	9.49814i	0.587545	+	0.339219i
$785$	1.48511	−	13.6361i	0.0530058	−	0.486693i
$786$	4.50170			0.160570
$787$	−25.4235	+	25.4235i	−0.906249	+	0.906249i	−0.995967	−	0.0897183i	$-0.971403\pi$
$787$	−25.4235	+	25.4235i	−0.906249	+	0.906249i	0.0897183	+	0.995967i	$0.471403\pi$
$788$	−5.99268	−	1.60574i	−0.213481	−	0.0572019i
$789$	3.29080	+	5.69983i	0.117156	+	0.202919i
$790$	−10.0002	+	13.6557i	−0.355790	+	0.485848i
$791$		−	15.9621i		−	0.567546i
$792$	−2.66680	−	0.714566i	−0.0947606	−	0.0253910i
$793$	−30.0398	+	8.04914i	−1.06674	+	0.285833i
$794$	−5.52521	−	9.56995i	−0.196082	−	0.339625i
$795$	−9.52897	−	3.69903i	−0.337958	−	0.131191i
$796$	−3.31149	+	5.73567i	−0.117373	+	0.203295i
$797$	21.0678	−	21.0678i	0.746259	−	0.746259i	−0.227515	−	0.973775i	$-0.573060\pi$
$797$	21.0678	−	21.0678i	0.746259	−	0.746259i	0.973775	+	0.227515i	$0.0730601\pi$
$798$	−2.89441	+	22.0352i	−0.102461	+	0.780039i
$799$			39.9607i			1.41371i
$800$	−2.69156	−	4.21373i	−0.0951610	−	0.148978i
$801$	−4.02257	−	2.32243i	−0.142130	−	0.0820590i
$802$	−5.38108	+	20.0825i	−0.190013	+	0.709137i
$803$	−8.51066	−	31.7622i	−0.300335	−	1.12086i
$804$	−1.79352	+	1.03549i	−0.0632527	+	0.0365190i
$805$	75.5981	−	11.6821i	2.66448	−	0.411741i
$806$			4.30982i			0.151807i
$807$	0.449856	−	1.67889i	0.0158357	−	0.0590996i
$808$	0.994442	−	3.71131i	0.0349843	−	0.130563i
$809$		−	4.58393i		−	0.161162i	−0.996748	−	0.0805812i	$-0.974322\pi$
$809$		−	4.58393i		−	0.161162i	0.996748	−	0.0805812i	$-0.0256776\pi$
$810$	−1.32113	+	1.80406i	−0.0464196	+	0.0633882i
$811$	−2.54119	+	1.46716i	−0.0892332	+	0.0515188i	−0.543953	−	0.839116i	$-0.683073\pi$
$811$	−2.54119	+	1.46716i	−0.0892332	+	0.0515188i	0.454719	+	0.890635i	$0.349740\pi$
$812$	−4.08799	−	15.2566i	−0.143460	−	0.535402i
$813$	−3.53829	+	13.2051i	−0.124093	+	0.463123i
$814$	−7.40571	−	4.27569i	−0.259570	−	0.149863i
$815$	−15.5731	−	35.3349i	−0.545501	−	1.23773i
$816$		−	4.07647i		−	0.142705i
$817$	−17.4790	−	42.1630i	−0.611513	−	1.47510i
$818$	−1.44389	+	1.44389i	−0.0504843	+	0.0504843i
$819$	−13.5610	+	23.4884i	−0.473860	+	0.820750i
$820$	−8.79135	+	22.6472i	−0.307007	+	0.790873i
$821$	25.5684	+	44.2857i	0.892342	+	1.54558i	0.837061	+	0.547110i	$0.184272\pi$
$821$	25.5684	+	44.2857i	0.892342	+	1.54558i	0.0552811	+	0.998471i	$0.482394\pi$
$822$	14.3488	−	3.84474i	0.500471	−	0.134101i
$823$	26.7277	+	7.16167i	0.931670	+	0.249640i	0.692567	−	0.721354i	$-0.256480\pi$
$823$	26.7277	+	7.16167i	0.931670	+	0.249640i	0.239103	+	0.970994i	$0.423147\pi$
$824$			3.55617i			0.123885i
$825$	12.2523	+	6.35944i	0.426569	+	0.221407i
$826$	−13.2746	−	22.9924i	−0.461884	−	0.800007i
$827$	17.7926	+	4.76752i	0.618710	+	0.165783i	0.554541	−	0.832156i	$-0.312894\pi$
$827$	17.7926	+	4.76752i	0.618710	+	0.165783i	0.0641687	+	0.997939i	$0.479560\pi$
$828$	−4.74438	+	4.74438i	−0.164879	+	0.164879i
$829$	44.0421			1.52965			0.764823	−	0.644241i	$-0.222826\pi$
$829$	44.0421			1.52965			0.764823	+	0.644241i	$0.222826\pi$
$830$	9.26285	−	7.44337i	0.321518	−	0.258363i
$831$	8.90538	+	5.14153i	0.308924	+	0.178358i
$832$	5.13819	+	1.37677i	0.178135	+	0.0477311i
$833$	−20.0424	−	74.7992i	−0.694427	−	2.59164i
$834$	11.2043	+	6.46881i	0.387974	+	0.223997i
$835$	28.4512	−	38.8515i	0.984596	−	1.34451i
$836$	−9.54535	+	7.32886i	−0.330133	+	0.253474i
$837$	−0.572898	−	0.572898i	−0.0198023	−	0.0198023i
$838$	23.9772	−	6.42468i	0.828280	−	0.221937i
$839$	14.4829	−	25.0852i	0.500006	−	0.866037i	−0.499994	−	0.866029i	$-0.666664\pi$
$839$	14.4829	−	25.0852i	0.500006	−	0.866037i	1.00000		7.41500e-6i	$-2.36027e-6\pi$
$840$	11.3339	+	1.23438i	0.391057	+	0.0425902i
$841$	9.70171	−	16.8039i	0.334542	−	0.579443i
$842$	1.84106	−	6.87093i	0.0634471	−	0.236788i
$843$	−18.2999	+	18.2999i	−0.630281	+	0.630281i
$844$	−19.0550			−0.655902
$845$	26.6624	−	21.4251i	0.917214	−	0.737048i
$846$	8.48946	−	4.90139i	0.291873	−	0.168513i
$847$	12.1772	+	12.1772i	0.418413	+	0.418413i
$848$	−3.23240	−	3.23240i	−0.111001	−	0.111001i
$849$	−7.05005	−	12.2110i	−0.241957	−	0.419082i
$850$	−4.38765	+	19.9045i	−0.150495	+	0.682718i
$851$	−17.9976	+	10.3909i	−0.616950	+	0.356196i
$852$	5.42132	−	1.45264i	0.185732	−	0.0497666i
$853$	−10.9141	−	40.7320i	−0.373692	−	1.39464i	−0.855247	−	0.518221i	$-0.826594\pi$
$853$	−10.9141	−	40.7320i	−0.373692	−	1.39464i	0.481555	−	0.876416i	$-0.340072\pi$
$854$	−29.8086			−1.02003
$855$	2.73580	+	9.35497i	0.0935625	+	0.319933i
$856$	−0.447596			−0.0152985
$857$	4.81884	+	17.9842i	0.164609	+	0.614327i	0.998090	+	0.0617797i	$0.0196776\pi$
$857$	4.81884	+	17.9842i	0.164609	+	0.614327i	−0.833481	+	0.552548i	$0.813656\pi$
$858$	−14.1859	+	3.80110i	−0.484299	+	0.129767i
$859$	−8.71296	+	5.03043i	−0.297282	+	0.171636i	−0.641221	−	0.767356i	$-0.721572\pi$
$859$	−8.71296	+	5.03043i	−0.297282	+	0.171636i	0.343939	+	0.938992i	$0.388239\pi$
$860$	−21.4255	+	9.44282i	−0.730605	+	0.321998i
$861$	−27.6971	−	47.9727i	−0.943913	−	1.63491i
$862$	0.863633	+	0.863633i	0.0294154	+	0.0294154i
$863$	40.0726	+	40.0726i	1.36409	+	1.36409i	0.868635	+	0.495453i	$0.164998\pi$
$863$	40.0726	+	40.0726i	1.36409	+	1.36409i	0.495453	+	0.868635i	$0.335002\pi$
$864$	−0.866025	+	0.500000i	−0.0294628	+	0.0170103i
$865$	0.0638898	−	0.586628i	0.00217232	−	0.0199459i
$866$	−7.97713			−0.271074
$867$	0.270395	−	0.270395i	0.00918309	−	0.00918309i
$868$	−1.06916	+	3.99018i	−0.0362898	+	0.135435i
$869$	10.4491	−	18.0984i	0.354462	−	0.613947i
$870$	−4.33900	−	5.39963i	−0.147106	−	0.183065i
$871$	−5.50824	+	9.54056i	−0.186640	+	0.323269i
$872$	5.73713	−	1.53726i	0.194284	−	0.0520582i
$873$	11.3400	+	11.3400i	0.383800	+	0.383800i
$874$	3.82593	+	28.9950i	0.129414	+	0.980771i
$875$	−54.0124	−	18.2263i	−1.82595	−	0.616161i
$876$	−10.3146	−	5.95512i	−0.348497	−	0.201205i
$877$	−5.62721	−	21.0010i	−0.190017	−	0.709154i	−0.993501	−	0.113827i	$-0.963689\pi$
$877$	−5.62721	−	21.0010i	−0.190017	−	0.709154i	0.803483	−	0.595327i	$-0.202978\pi$
$878$	9.81553	+	2.63006i	0.331258	+	0.0887603i
$879$	−21.3648	−	12.3350i	−0.720617	−	0.416048i
$880$	3.86703	+	4.81230i	0.130357	+	0.162222i
$881$	0.171502			0.00577805			0.00288903	−	0.999996i	$-0.499080\pi$
$881$	0.171502			0.00577805			0.00288903	+	0.999996i	$0.499080\pi$
$882$	−13.4324	+	13.4324i	−0.452293	+	0.452293i
$883$	−0.272933	−	0.0731323i	−0.00918494	−	0.00246110i	0.254224	−	0.967145i	$-0.418180\pi$
$883$	−0.272933	−	0.0731323i	−0.00918494	−	0.00246110i	−0.263409	+	0.964684i	$0.584847\pi$
$884$	−10.8423	−	18.7794i	−0.364665	−	0.631619i
$885$	−9.39394	−	6.87925i	−0.315774	−	0.231244i
$886$			17.1219i			0.575221i
$887$	51.2503	+	13.7325i	1.72082	+	0.461092i	0.978035	−	0.208441i	$-0.0668390\pi$
$887$	51.2503	+	13.7325i	1.72082	+	0.461092i	0.742782	+	0.669533i	$0.233506\pi$
$888$	−2.99181	+	0.801652i	−0.100398	+	0.0269017i
$889$	−22.9096	−	39.6806i	−0.768363	−	1.33084i
$890$	4.18872	+	9.50412i	0.140406	+	0.318579i
$891$	1.38044	−	2.39099i	0.0462464	−	0.0801010i
$892$	−4.98665	+	4.98665i	−0.166965	+	0.166965i
$893$	5.56485	−	42.3654i	0.186221	−	1.41770i
$894$			4.27961i			0.143132i
$895$	0.0726308	−	0.187102i	0.00242778	−	0.00625414i
$896$	4.41557	+	2.54933i	0.147514	+	0.0851671i
$897$	−9.23756	+	34.4751i	−0.308433	+	1.15109i
$898$	−1.23963	−	4.62636i	−0.0413669	−	0.154383i
$899$	2.17361	−	1.25493i	0.0724939	−	0.0418544i
$900$	4.76678	−	1.50925i	0.158893	−	0.0503085i
$901$			18.6348i			0.620814i
$902$	7.76338	−	28.9733i	0.258492	−	0.964706i
$903$	13.8180	−	51.5694i	0.459834	−	1.71612i
$904$		−	3.13064i		−	0.104124i
$905$	7.79310	+	50.4312i	0.259051	+	1.67639i
$906$	−9.78111	+	5.64713i	−0.324956	+	0.187613i
$907$	9.26528	+	34.5785i	0.307649	+	1.14816i	0.930641	+	0.365932i	$0.119250\pi$
$907$	9.26528	+	34.5785i	0.307649	+	1.14816i	−0.622993	+	0.782227i	$0.714083\pi$
$908$	−2.20513	+	8.22967i	−0.0731799	+	0.273111i
$909$	3.32747	+	1.92111i	0.110365	+	0.0637193i
$910$	55.4960	−	24.4586i	1.83967	−	0.810794i
$911$		−	55.6416i		−	1.84349i	−0.387797	−	0.921745i	$-0.626764\pi$
$911$		−	55.6416i		−	1.84349i	0.387797	−	0.921745i	$-0.373236\pi$
$912$	−0.567681	+	4.32177i	−0.0187978	+	0.143108i
$913$	−10.3746	+	10.3746i	−0.343348	+	0.343348i
$914$	14.3572	−	24.8673i	0.474893	−	0.822538i
$915$	−11.9626	+	5.27225i	−0.395471	+	0.174295i
$916$	−0.895688	−	1.55138i	−0.0295944	−	0.0512589i
$917$	22.1705	−	5.94057i	0.732135	−	0.196175i
$918$	3.93757	+	1.05507i	0.129959	+	0.0348224i
$919$			47.0274i			1.55129i	0.631169	+	0.775645i	$0.282575\pi$
$919$			47.0274i			1.55129i	−0.631169	+	0.775645i	$0.717425\pi$
$920$	14.8271	−	2.29122i	0.488834	−	0.0755392i
$921$	11.8726	+	20.5639i	0.391214	+	0.677602i
$922$	−20.5440	−	5.50474i	−0.676579	−	0.181289i
$923$	21.1112	−	21.1112i	0.694884	−	0.694884i
$924$	−14.0767			−0.463091
$925$	15.4712	−	0.694101i	0.508689	−	0.0228219i
$926$	5.42137	+	3.13003i	0.178157	+	0.102859i
$927$	−3.43500	−	0.920406i	−0.112820	−	0.0302301i
$928$	−0.801779	−	2.99228i	−0.0263197	−	0.0982264i
$929$	5.79527	+	3.34590i	0.190137	+	0.109775i	0.592046	−	0.805904i	$-0.298320\pi$
$929$	5.79527	+	3.34590i	0.190137	+	0.109775i	−0.401910	+	0.915679i	$0.631654\pi$
$930$	0.276671	+	1.79041i	0.00907241	+	0.0587099i
$931$	10.8321	+	82.0913i	0.355007	+	2.69043i
$932$	−7.43257	−	7.43257i	−0.243462	−	0.243462i
$933$	−4.70315	+	1.26020i	−0.153974	+	0.0412572i
$934$	−7.79447	+	13.5004i	−0.255043	+	0.441747i
$935$	2.72473	−	25.0181i	0.0891083	−	0.818181i
$936$	−2.65972	+	4.60678i	−0.0869358	+	0.150577i
$937$	9.20482	−	34.3529i	0.300708	−	1.12226i	−0.635869	−	0.771797i	$-0.719358\pi$
$937$	9.20482	−	34.3529i	0.300708	−	1.12226i	0.936577	−	0.350462i	$-0.113975\pi$
$938$	−7.46650	+	7.46650i	−0.243790	+	0.243790i
$939$	−7.09860			−0.231654
$940$	−21.7908	−	2.37324i	−0.710738	−	0.0774067i
$941$	−43.8978	+	25.3444i	−1.43103	+	0.826205i	−0.997199	−	0.0747907i	$-0.976171\pi$
$941$	−43.8978	+	25.3444i	−1.43103	+	0.826205i	−0.433829	+	0.900995i	$0.642838\pi$
$942$	4.33761	+	4.33761i	0.141327	+	0.141327i
$943$	−51.5451	−	51.5451i	−1.67854	−	1.67854i
$944$	−2.60356	−	4.50949i	−0.0847386	−	0.146772i
$945$	−4.12575	+	10.6282i	−0.134211	+	0.345737i
$946$	25.0363	−	14.4547i	0.813999	−	0.469963i
$947$	47.1489	−	12.6335i	1.53213	−	0.410534i	0.608419	−	0.793616i	$-0.291804\pi$
$947$	47.1489	−	12.6335i	1.53213	−	0.410534i	0.923714	+	0.383082i	$0.125137\pi$
$948$	−1.95911	−	7.31151i	−0.0636291	−	0.237467i
$949$	−63.3559			−2.05662
$950$	7.42354	−	20.4912i	0.240851	−	0.664824i
$951$	−14.5907			−0.473137
$952$	−5.37943	−	20.0763i	−0.174348	−	0.650677i
$953$	32.5695	−	8.72697i	1.05503	−	0.282694i	0.310701	−	0.950508i	$-0.399436\pi$
$953$	32.5695	−	8.72697i	1.05503	−	0.282694i	0.744329	+	0.667813i	$0.232770\pi$
$954$	3.95886	−	2.28565i	0.128173	−	0.0740007i
$955$	−17.2426	+	44.4182i	−0.557958	+	1.43734i
$956$	−12.0406	−	20.8549i	−0.389421	−	0.674496i
$957$	6.04769	+	6.04769i	0.195494	+	0.195494i
$958$	0.846418	+	0.846418i	0.0273465	+	0.0273465i
$959$	65.5929	−	37.8701i	2.11811	−	1.22289i
$960$	2.22292	+	0.242099i	0.0717445	+	0.00781371i
$961$	30.3436			0.978825
$962$	−11.6504	+	11.6504i	−0.375624	+	0.375624i
$963$	0.115846	−	0.432345i	0.00373310	−	0.0139321i
$964$	7.17686	−	12.4307i	0.231151	−	0.400366i
$965$	−3.74046	+	34.3445i	−0.120410	+	1.10559i
$966$	−17.1049	+	29.6265i	−0.550341	+	0.953218i
$967$	−23.0252	+	6.16958i	−0.740440	+	0.198400i	−0.609274	−	0.792960i	$-0.708539\pi$
$967$	−23.0252	+	6.16958i	−0.740440	+	0.198400i	−0.131167	+	0.991360i	$0.541872\pi$
$968$	2.38831	+	2.38831i	0.0767632	+	0.0767632i
$969$	14.0939	−	10.8212i	0.452760	−	0.347626i
$970$	−5.47645	−	35.4395i	−0.175838	−	1.13789i
$971$	0.616054	+	0.355679i	0.0197701	+	0.0114143i	0.509852	−	0.860262i	$-0.329700\pi$
$971$	0.616054	+	0.355679i	0.0197701	+	0.0114143i	−0.490082	+	0.871676i	$0.663033\pi$
$972$	−0.258819	−	0.965926i	−0.00830162	−	0.0309821i
$973$	63.7168	+	17.0729i	2.04267	+	0.547331i
$974$	8.02472	+	4.63307i	0.257129	+	0.148453i
$975$	17.9453	−	19.6311i	0.574709	−	0.628699i
$976$	−5.84637			−0.187138
$977$	19.1483	−	19.1483i	0.612609	−	0.612609i	−0.331016	−	0.943625i	$-0.607392\pi$
$977$	19.1483	−	19.1483i	0.612609	−	0.612609i	0.943625	+	0.331016i	$0.107392\pi$
$978$	16.6805	+	4.46953i	0.533384	+	0.142920i
$979$	−6.41193	−	11.1058i	−0.204926	−	0.354943i
$980$	41.9787	−	6.48695i	1.34096	−	0.207218i
$981$			5.93952i			0.189634i
$982$	−12.1094	−	3.24470i	−0.386426	−	0.103543i
$983$	4.57822	−	1.22673i	0.146023	−	0.0391266i	−0.185067	−	0.982726i	$-0.559250\pi$
$983$	4.57822	−	1.22673i	0.146023	−	0.0391266i	0.331090	+	0.943599i	$0.392584\pi$
$984$	−5.43223	−	9.40889i	−0.173173	−	0.299945i
$985$	−12.6945	+	5.59483i	−0.404481	+	0.178266i
$986$	−6.31411	+	10.9364i	−0.201082	+	0.348285i
$987$	35.3419	−	35.3419i	1.12494	−	1.12494i
$988$	8.87955	+	21.4193i	0.282496	+	0.681440i
$989$		−	70.2566i		−	2.23403i
$990$	−5.64918	+	2.48975i	−0.179543	+	0.0791294i
$991$	38.3054	+	22.1156i	1.21681	+	0.702527i	0.964235	−	0.265050i	$-0.0853885\pi$
$991$	38.3054	+	22.1156i	1.21681	+	0.702527i	0.252577	+	0.967577i	$0.418722\pi$
$992$	−0.209695	+	0.782594i	−0.00665783	+	0.0248474i
$993$	9.18205	+	34.2679i	0.291384	+	1.08746i
$994$	24.7827	−	14.3083i	0.786058	−	0.453831i
$995$	2.26165	+	14.6357i	0.0716990	+	0.463983i
$996$			5.31421i			0.168387i
$997$	−13.4792	+	50.3051i	−0.426891	+	1.59318i	0.332868	+	0.942973i	$0.391984\pi$
$997$	−13.4792	+	50.3051i	−0.426891	+	1.59318i	−0.759759	+	0.650205i	$0.774683\pi$
$998$	2.05840	−	7.68204i	0.0651574	−	0.243171i
$999$		−	3.09735i		−	0.0979957i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.x.a.217.8	yes	40
5.3	odd	4	inner	570.2.x.a.103.7	✓	40
19.12	odd	6	inner	570.2.x.a.487.7	yes	40
95.88	even	12	inner	570.2.x.a.373.8	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.x.a.103.7	✓	40	5.3	odd	4	inner
570.2.x.a.217.8	yes	40	1.1	even	1	trivial
570.2.x.a.373.8	yes	40	95.88	even	12	inner
570.2.x.a.487.7	yes	40	19.12	odd	6	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:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.x (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.258819 + 0.965926i) q^{2} +(-0.965926 + 0.258819i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(-0.809185 + 2.08452i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(-3.60529 - 3.60529i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.866025 - 0.500000i) q^{9} +O(q^{10})\)	\(q+(0.258819 + 0.965926i) q^{2} +(-0.965926 + 0.258819i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(-0.809185 + 2.08452i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(-3.60529 - 3.60529i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.866025 - 0.500000i) q^{9} +(-2.22292 - 0.242099i) q^{10} +2.76087 q^{11} +(0.707107 - 0.707107i) q^{12} +(1.37677 - 5.13819i) q^{13} +(2.54933 - 4.41557i) q^{14} +(0.242099 - 2.22292i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-3.93757 + 1.05507i) q^{17} +(0.707107 + 0.707107i) q^{18} +(4.32144 - 0.570220i) q^{19} +(-0.341485 - 2.20984i) q^{20} +(4.41557 + 2.54933i) q^{21} +(0.714566 + 2.66680i) q^{22} +(6.48095 + 1.73656i) q^{23} +(0.866025 + 0.500000i) q^{24} +(-3.69044 - 3.37352i) q^{25} +5.31945 q^{26} +(-0.707107 + 0.707107i) q^{27} +(4.92492 + 1.31963i) q^{28} +(-1.54892 - 2.68280i) q^{29} +(2.20984 - 0.341485i) q^{30} +0.810201i q^{31} +(0.965926 + 0.258819i) q^{32} +(-2.66680 + 0.714566i) q^{33} +(-2.03823 - 3.53033i) q^{34} +(10.4327 - 4.59796i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(-2.19015 + 2.19015i) q^{37} +(1.66926 + 4.02661i) q^{38} +5.31945i q^{39} +(2.04616 - 0.901798i) q^{40} +(-9.40889 - 5.43223i) q^{41} +(-1.31963 + 4.92492i) q^{42} +(-2.71012 - 10.1143i) q^{43} +(-2.39099 + 1.38044i) q^{44} +(0.341485 + 2.20984i) q^{45} +6.70957i q^{46} +(2.53715 - 9.46876i) q^{47} +(-0.258819 + 0.965926i) q^{48} +18.9963i q^{49} +(2.30342 - 4.43782i) q^{50} +(3.53033 - 2.03823i) q^{51} +(1.37677 + 5.13819i) q^{52} +(1.18314 - 4.41554i) q^{53} +(-0.866025 - 0.500000i) q^{54} +(-2.23406 + 5.75509i) q^{55} +5.09866i q^{56} +(-4.02661 + 1.66926i) q^{57} +(2.19050 - 2.19050i) q^{58} +(2.60356 - 4.50949i) q^{59} +(0.901798 + 2.04616i) q^{60} +(-2.92319 - 5.06311i) q^{61} +(-0.782594 + 0.209695i) q^{62} +(-4.92492 - 1.31963i) q^{63} +1.00000i q^{64} +(9.59660 + 7.02766i) q^{65} +(-1.38044 - 2.39099i) q^{66} +(-2.00042 - 0.536010i) q^{67} +(2.88250 - 2.88250i) q^{68} -6.70957 q^{69} +(7.14145 + 8.88713i) q^{70} +(4.86063 + 2.80628i) q^{71} +(-0.965926 - 0.258819i) q^{72} +(-3.08260 - 11.5044i) q^{73} +(-2.68238 - 1.54867i) q^{74} +(4.43782 + 2.30342i) q^{75} +(-3.45737 + 2.65455i) q^{76} +(-9.95376 - 9.95376i) q^{77} +(-5.13819 + 1.37677i) q^{78} +(3.78472 - 6.55532i) q^{79} +(1.40065 + 1.74303i) q^{80} +(0.500000 - 0.866025i) q^{81} +(2.81193 - 10.4943i) q^{82} +(-3.75772 + 3.75772i) q^{83} -5.09866 q^{84} +(0.986910 - 9.06168i) q^{85} +(9.06825 - 5.23555i) q^{86} +(2.19050 + 2.19050i) q^{87} +(-1.95223 - 1.95223i) q^{88} +(-2.32243 - 4.02257i) q^{89} +(-2.04616 + 0.901798i) q^{90} +(-23.4884 + 13.5610i) q^{91} +(-6.48095 + 1.73656i) q^{92} +(-0.209695 - 0.782594i) q^{93} +9.80278 q^{94} +(-2.30821 + 9.46954i) q^{95} -1.00000 q^{96} +(4.15072 + 15.4907i) q^{97} +(-18.3490 + 4.91660i) q^{98} +(2.39099 - 1.38044i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 8 q^{5} - 20 q^{6} - 8 q^{7}+O(q^{10}) \) 40 * q - 8 * q^5 - 20 * q^6 - 8 * q^7	\( 40 q - 8 q^{5} - 20 q^{6} - 8 q^{7} - 12 q^{10} + 8 q^{11} - 24 q^{13} + 20 q^{16} + 8 q^{17} + 12 q^{21} + 24 q^{22} + 16 q^{23} - 16 q^{25} + 32 q^{26} + 4 q^{28} + 16 q^{30} - 24 q^{33} - 4 q^{35} - 20 q^{36} - 8 q^{38} - 36 q^{41} + 4 q^{42} - 4 q^{43} + 8 q^{47} - 24 q^{52} - 16 q^{55} - 8 q^{57} + 16 q^{58} + 12 q^{60} - 8 q^{61} - 16 q^{62} - 4 q^{63} - 4 q^{66} - 36 q^{67} - 16 q^{68} + 48 q^{70} + 72 q^{71} - 16 q^{73} - 8 q^{76} + 24 q^{77} + 24 q^{78} + 8 q^{80} + 20 q^{81} - 24 q^{82} - 40 q^{83} - 48 q^{85} + 16 q^{87} - 72 q^{91} - 16 q^{92} + 16 q^{93} - 16 q^{95} - 40 q^{96} + 36 q^{97} - 48 q^{98}+O(q^{100}) \) 40 * q - 8 * q^5 - 20 * q^6 - 8 * q^7 - 12 * q^10 + 8 * q^11 - 24 * q^13 + 20 * q^16 + 8 * q^17 + 12 * q^21 + 24 * q^22 + 16 * q^23 - 16 * q^25 + 32 * q^26 + 4 * q^28 + 16 * q^30 - 24 * q^33 - 4 * q^35 - 20 * q^36 - 8 * q^38 - 36 * q^41 + 4 * q^42 - 4 * q^43 + 8 * q^47 - 24 * q^52 - 16 * q^55 - 8 * q^57 + 16 * q^58 + 12 * q^60 - 8 * q^61 - 16 * q^62 - 4 * q^63 - 4 * q^66 - 36 * q^67 - 16 * q^68 + 48 * q^70 + 72 * q^71 - 16 * q^73 - 8 * q^76 + 24 * q^77 + 24 * q^78 + 8 * q^80 + 20 * q^81 - 24 * q^82 - 40 * q^83 - 48 * q^85 + 16 * q^87 - 72 * q^91 - 16 * q^92 + 16 * q^93 - 16 * q^95 - 40 * q^96 + 36 * q^97 - 48 * q^98

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