LMFDB - Embedded newform 546.2.bi.f.17.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(17,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1, 1]))

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

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

chi := DirichletCharacter("546.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bi (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$34$
Relative dimension:	$17$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			17.6
Character	$\chi$	$=$	546.17
Dual form			546.2.bi.f.257.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +(-0.889878 - 1.48597i) q^{3} +1.00000 q^{4} +(-2.84717 + 1.64381i) q^{5} +(-0.889878 - 1.48597i) q^{6} +(1.87202 + 1.86964i) q^{7} +1.00000 q^{8} +(-1.41623 + 2.64467i) q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +(-0.889878 - 1.48597i) q^{3} +1.00000 q^{4} +(-2.84717 + 1.64381i) q^{5} +(-0.889878 - 1.48597i) q^{6} +(1.87202 + 1.86964i) q^{7} +1.00000 q^{8} +(-1.41623 + 2.64467i) q^{9} +(-2.84717 + 1.64381i) q^{10} +(1.03510 + 1.79285i) q^{11} +(-0.889878 - 1.48597i) q^{12} +(3.53365 + 0.716460i) q^{13} +(1.87202 + 1.86964i) q^{14} +(4.97629 + 2.76802i) q^{15} +1.00000 q^{16} -1.12362 q^{17} +(-1.41623 + 2.64467i) q^{18} +(-0.505430 + 0.875431i) q^{19} +(-2.84717 + 1.64381i) q^{20} +(1.11237 - 4.44552i) q^{21} +(1.03510 + 1.79285i) q^{22} +3.50085i q^{23} +(-0.889878 - 1.48597i) q^{24} +(2.90424 - 5.03029i) q^{25} +(3.53365 + 0.716460i) q^{26} +(5.19019 - 0.248945i) q^{27} +(1.87202 + 1.86964i) q^{28} +(7.97573 + 4.60479i) q^{29} +(4.97629 + 2.76802i) q^{30} +(-1.86666 + 3.23315i) q^{31} +1.00000 q^{32} +(1.74301 - 3.13355i) q^{33} -1.12362 q^{34} +(-8.40328 - 2.24594i) q^{35} +(-1.41623 + 2.64467i) q^{36} -6.97226i q^{37} +(-0.505430 + 0.875431i) q^{38} +(-2.07988 - 5.88847i) q^{39} +(-2.84717 + 1.64381i) q^{40} +(-8.52566 - 4.92229i) q^{41} +(1.11237 - 4.44552i) q^{42} +(3.35600 + 5.81276i) q^{43} +(1.03510 + 1.79285i) q^{44} +(-0.315084 - 9.85784i) q^{45} +3.50085i q^{46} +(-1.05515 + 0.609193i) q^{47} +(-0.889878 - 1.48597i) q^{48} +(0.00888497 + 6.99999i) q^{49} +(2.90424 - 5.03029i) q^{50} +(0.999885 + 1.66967i) q^{51} +(3.53365 + 0.716460i) q^{52} +(5.05843 + 2.92049i) q^{53} +(5.19019 - 0.248945i) q^{54} +(-5.89421 - 3.40302i) q^{55} +(1.87202 + 1.86964i) q^{56} +(1.75064 - 0.0279705i) q^{57} +(7.97573 + 4.60479i) q^{58} -9.80909i q^{59} +(4.97629 + 2.76802i) q^{60} +(-0.209571 - 0.120996i) q^{61} +(-1.86666 + 3.23315i) q^{62} +(-7.59580 + 2.30301i) q^{63} +1.00000 q^{64} +(-11.2386 + 3.76878i) q^{65} +(1.74301 - 3.13355i) q^{66} +(-10.2316 + 5.90721i) q^{67} -1.12362 q^{68} +(5.20218 - 3.11533i) q^{69} +(-8.40328 - 2.24594i) q^{70} +(-3.94585 - 6.83441i) q^{71} +(-1.41623 + 2.64467i) q^{72} +(0.878160 - 1.52102i) q^{73} -6.97226i q^{74} +(-10.0593 + 0.160721i) q^{75} +(-0.505430 + 0.875431i) q^{76} +(-1.41426 + 5.29150i) q^{77} +(-2.07988 - 5.88847i) q^{78} +(-2.48977 - 4.31240i) q^{79} +(-2.84717 + 1.64381i) q^{80} +(-4.98856 - 7.49095i) q^{81} +(-8.52566 - 4.92229i) q^{82} -0.999900i q^{83} +(1.11237 - 4.44552i) q^{84} +(3.19914 - 1.84702i) q^{85} +(3.35600 + 5.81276i) q^{86} +(-0.254829 - 15.9494i) q^{87} +(1.03510 + 1.79285i) q^{88} +7.61879i q^{89} +(-0.315084 - 9.85784i) q^{90} +(5.27553 + 7.94788i) q^{91} +3.50085i q^{92} +(6.46548 - 0.103301i) q^{93} +(-1.05515 + 0.609193i) q^{94} -3.32333i q^{95} +(-0.889878 - 1.48597i) q^{96} +(-3.21628 - 5.57077i) q^{97} +(0.00888497 + 6.99999i) q^{98} +(-6.20743 + 0.198407i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q + 34 q^{2} + 6 q^{3} + 34 q^{4} + 9 q^{5} + 6 q^{6} + 4 q^{7} + 34 q^{8} + 4 q^{9}+O(q^{10}) $ 34 * q + 34 * q^2 + 6 * q^3 + 34 * q^4 + 9 * q^5 + 6 * q^6 + 4 * q^7 + 34 * q^8 + 4 * q^9	$ 34 q + 34 q^{2} + 6 q^{3} + 34 q^{4} + 9 q^{5} + 6 q^{6} + 4 q^{7} + 34 q^{8} + 4 q^{9} + 9 q^{10} + 9 q^{11} + 6 q^{12} + 8 q^{13} + 4 q^{14} - 17 q^{15} + 34 q^{16} + 12 q^{17} + 4 q^{18} - 5 q^{19} + 9 q^{20} - 7 q^{21} + 9 q^{22} + 6 q^{24} + 16 q^{25} + 8 q^{26} - 18 q^{27} + 4 q^{28} + 27 q^{29} - 17 q^{30} - q^{31} + 34 q^{32} + 12 q^{34} - 3 q^{35} + 4 q^{36} - 5 q^{38} - 10 q^{39} + 9 q^{40} - 3 q^{41} - 7 q^{42} - 3 q^{43} + 9 q^{44} + 9 q^{45} - 27 q^{47} + 6 q^{48} - 2 q^{49} + 16 q^{50} - 36 q^{51} + 8 q^{52} - 21 q^{53} - 18 q^{54} - 57 q^{55} + 4 q^{56} - 17 q^{57} + 27 q^{58} - 17 q^{60} - 51 q^{61} - q^{62} - 24 q^{63} + 34 q^{64} - 21 q^{65} - 21 q^{67} + 12 q^{68} + 30 q^{69} - 3 q^{70} - 15 q^{71} + 4 q^{72} - 19 q^{73} - 54 q^{75} - 5 q^{76} + 9 q^{77} - 10 q^{78} - 9 q^{79} + 9 q^{80} + 28 q^{81} - 3 q^{82} - 7 q^{84} - 42 q^{85} - 3 q^{86} - 81 q^{87} + 9 q^{88} + 9 q^{90} - 72 q^{91} - 17 q^{93} - 27 q^{94} + 6 q^{96} + 19 q^{97} - 2 q^{98} - 27 q^{99}+O(q^{100}) $ 34 * q + 34 * q^2 + 6 * q^3 + 34 * q^4 + 9 * q^5 + 6 * q^6 + 4 * q^7 + 34 * q^8 + 4 * q^9 + 9 * q^10 + 9 * q^11 + 6 * q^12 + 8 * q^13 + 4 * q^14 - 17 * q^15 + 34 * q^16 + 12 * q^17 + 4 * q^18 - 5 * q^19 + 9 * q^20 - 7 * q^21 + 9 * q^22 + 6 * q^24 + 16 * q^25 + 8 * q^26 - 18 * q^27 + 4 * q^28 + 27 * q^29 - 17 * q^30 - q^31 + 34 * q^32 + 12 * q^34 - 3 * q^35 + 4 * q^36 - 5 * q^38 - 10 * q^39 + 9 * q^40 - 3 * q^41 - 7 * q^42 - 3 * q^43 + 9 * q^44 + 9 * q^45 - 27 * q^47 + 6 * q^48 - 2 * q^49 + 16 * q^50 - 36 * q^51 + 8 * q^52 - 21 * q^53 - 18 * q^54 - 57 * q^55 + 4 * q^56 - 17 * q^57 + 27 * q^58 - 17 * q^60 - 51 * q^61 - q^62 - 24 * q^63 + 34 * q^64 - 21 * q^65 - 21 * q^67 + 12 * q^68 + 30 * q^69 - 3 * q^70 - 15 * q^71 + 4 * q^72 - 19 * q^73 - 54 * q^75 - 5 * q^76 + 9 * q^77 - 10 * q^78 - 9 * q^79 + 9 * q^80 + 28 * q^81 - 3 * q^82 - 7 * q^84 - 42 * q^85 - 3 * q^86 - 81 * q^87 + 9 * q^88 + 9 * q^90 - 72 * q^91 - 17 * q^93 - 27 * q^94 + 6 * q^96 + 19 * q^97 - 2 * q^98 - 27 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$	−0.889878	−	1.48597i	−0.513771	−	0.857927i
$3$	−0.889878	−	1.48597i	−0.513771	−	0.857927i
$4$	1.00000			0.500000
$5$	−2.84717	+	1.64381i	−1.27329	+	0.735135i	−0.975606	−	0.219529i	$-0.929548\pi$
$5$	−2.84717	+	1.64381i	−1.27329	+	0.735135i	−0.297686	+	0.954664i	$0.596215\pi$
$6$	−0.889878	−	1.48597i	−0.363291	−	0.606646i
$7$	1.87202	+	1.86964i	0.707555	+	0.706658i
$7$	1.87202	+	1.86964i	0.707555	+	0.706658i
$8$	1.00000			0.353553
$9$	−1.41623	+	2.64467i	−0.472078	+	0.881557i
$10$	−2.84717	+	1.64381i	−0.900353	+	0.519819i
$11$	1.03510	+	1.79285i	0.312095	+	0.540564i	0.978816	−	0.204744i	$-0.0656361\pi$
$11$	1.03510	+	1.79285i	0.312095	+	0.540564i	−0.666721	+	0.745307i	$0.732303\pi$
$12$	−0.889878	−	1.48597i	−0.256886	−	0.428964i
$13$	3.53365	+	0.716460i	0.980058	+	0.198710i
$13$	3.53365	+	0.716460i	0.980058	+	0.198710i
$14$	1.87202	+	1.86964i	0.500317	+	0.499683i
$15$	4.97629	+	2.76802i	1.28487	+	0.714700i
$16$	1.00000			0.250000
$17$	−1.12362			−0.272518			−0.136259	−	0.990673i	$-0.543508\pi$
$17$	−1.12362			−0.272518			−0.136259	+	0.990673i	$0.543508\pi$
$18$	−1.41623	+	2.64467i	−0.333810	+	0.623355i
$19$	−0.505430	+	0.875431i	−0.115954	+	0.200838i	−0.918161	−	0.396209i	$-0.870326\pi$
$19$	−0.505430	+	0.875431i	−0.115954	+	0.200838i	0.802207	+	0.597046i	$0.203659\pi$
$20$	−2.84717	+	1.64381i	−0.636646	+	0.367568i
$21$	1.11237	−	4.44552i	0.242739	−	0.970092i
$22$	1.03510	+	1.79285i	0.220684	+	0.382236i
$23$			3.50085i			0.729979i	0.931012	+	0.364989i	$0.118927\pi$
$23$			3.50085i			0.729979i	−0.931012	+	0.364989i	$0.881073\pi$
$24$	−0.889878	−	1.48597i	−0.181646	−	0.303323i
$25$	2.90424	−	5.03029i	0.580848	−	1.00606i
$26$	3.53365	+	0.716460i	0.693006	+	0.140509i
$27$	5.19019	−	0.248945i	0.998852	−	0.0479096i
$28$	1.87202	+	1.86964i	0.353778	+	0.353329i
$29$	7.97573	+	4.60479i	1.48106	+	0.855088i	0.999769	−	0.0214746i	$-0.00683611\pi$
$29$	7.97573	+	4.60479i	1.48106	+	0.855088i	0.481287	+	0.876563i	$0.340169\pi$
$30$	4.97629	+	2.76802i	0.908543	+	0.505369i
$31$	−1.86666	+	3.23315i	−0.335262	+	0.580691i	−0.983535	−	0.180717i	$-0.942158\pi$
$31$	−1.86666	+	3.23315i	−0.335262	+	0.580691i	0.648273	+	0.761408i	$0.275492\pi$
$32$	1.00000			0.176777
$33$	1.74301	−	3.13355i	0.303419	−	0.545480i
$34$	−1.12362			−0.192699
$35$	−8.40328	−	2.24594i	−1.42041	−	0.379633i
$36$	−1.41623	+	2.64467i	−0.236039	+	0.440778i
$37$		−	6.97226i		−	1.14623i	−0.819474	−	0.573116i	$-0.805734\pi$
$37$		−	6.97226i		−	1.14623i	0.819474	−	0.573116i	$-0.194266\pi$
$38$	−0.505430	+	0.875431i	−0.0819916	+	0.142014i
$39$	−2.07988	−	5.88847i	−0.333047	−	0.942910i
$40$	−2.84717	+	1.64381i	−0.450177	+	0.259910i
$41$	−8.52566	−	4.92229i	−1.33148	−	0.768733i	−0.345957	−	0.938250i	$-0.612446\pi$
$41$	−8.52566	−	4.92229i	−1.33148	−	0.768733i	−0.985527	+	0.169517i	$0.945779\pi$
$42$	1.11237	−	4.44552i	0.171643	−	0.685958i
$43$	3.35600	+	5.81276i	0.511785	+	0.886438i	0.999907	+	0.0136621i	$0.00434890\pi$
$43$	3.35600	+	5.81276i	0.511785	+	0.886438i	−0.488122	+	0.872776i	$0.662318\pi$
$44$	1.03510	+	1.79285i	0.156047	+	0.270282i
$45$	−0.315084	−	9.85784i	−0.0469700	−	1.46952i
$46$			3.50085i			0.516173i
$47$	−1.05515	+	0.609193i	−0.153910	+	0.0888599i	−0.574977	−	0.818170i	$-0.694989\pi$
$47$	−1.05515	+	0.609193i	−0.153910	+	0.0888599i	0.421067	+	0.907029i	$0.361656\pi$
$48$	−0.889878	−	1.48597i	−0.128443	−	0.214482i
$49$	0.00888497	+	6.99999i	0.00126928	+	0.999999i
$50$	2.90424	−	5.03029i	0.410722	−	0.711391i
$51$	0.999885	+	1.66967i	0.140012	+	0.233801i
$52$	3.53365	+	0.716460i	0.490029	+	0.0993551i
$53$	5.05843	+	2.92049i	0.694829	+	0.401160i	0.805419	−	0.592706i	$-0.201941\pi$
$53$	5.05843	+	2.92049i	0.694829	+	0.401160i	−0.110589	+	0.993866i	$0.535274\pi$
$54$	5.19019	−	0.248945i	0.706295	−	0.0338772i
$55$	−5.89421	−	3.40302i	−0.794775	−	0.458863i
$56$	1.87202	+	1.86964i	0.250159	+	0.249841i
$57$	1.75064	−	0.0279705i	0.231878	−	0.00370479i
$58$	7.97573	+	4.60479i	1.04727	+	0.604639i
$59$		−	9.80909i		−	1.27703i	−0.769607	−	0.638517i	$-0.779548\pi$
$59$		−	9.80909i		−	1.27703i	0.769607	−	0.638517i	$-0.220452\pi$
$60$	4.97629	+	2.76802i	0.642437	+	0.357350i
$61$	−0.209571	−	0.120996i	−0.0268328	−	0.0154919i	0.486524	−	0.873667i	$-0.338265\pi$
$61$	−0.209571	−	0.120996i	−0.0268328	−	0.0154919i	−0.513356	+	0.858176i	$0.671598\pi$
$62$	−1.86666	+	3.23315i	−0.237066	+	0.410611i
$63$	−7.59580	+	2.30301i	−0.956980	+	0.290152i
$64$	1.00000			0.125000
$65$	−11.2386	+	3.76878i	−1.39398	+	0.467459i
$66$	1.74301	−	3.13355i	0.214550	−	0.385713i
$67$	−10.2316	+	5.90721i	−1.24999	+	0.721680i	−0.971107	−	0.238645i	$-0.923297\pi$
$67$	−10.2316	+	5.90721i	−1.24999	+	0.721680i	−0.278880	+	0.960326i	$0.589963\pi$
$68$	−1.12362			−0.136259
$69$	5.20218	−	3.11533i	0.626268	−	0.375042i
$70$	−8.40328	−	2.24594i	−1.00438	−	0.268441i
$71$	−3.94585	−	6.83441i	−0.468286	−	0.811096i	0.531057	−	0.847336i	$-0.321795\pi$
$71$	−3.94585	−	6.83441i	−0.468286	−	0.811096i	−0.999343	+	0.0362405i	$0.988462\pi$
$72$	−1.41623	+	2.64467i	−0.166905	+	0.311677i
$73$	0.878160	−	1.52102i	0.102781	−	0.178022i	−0.810049	−	0.586363i	$-0.800559\pi$
$73$	0.878160	−	1.52102i	0.102781	−	0.178022i	0.912829	+	0.408341i	$0.133893\pi$
$74$		−	6.97226i		−	0.810509i
$75$	−10.0593	+	0.160721i	−1.16155	+	0.0185584i
$76$	−0.505430	+	0.875431i	−0.0579768	+	0.100419i
$77$	−1.41426	+	5.29150i	−0.161169	+	0.603023i
$78$	−2.07988	−	5.88847i	−0.235500	−	0.666738i
$79$	−2.48977	−	4.31240i	−0.280121	−	0.485183i	0.691294	−	0.722574i	$-0.257041\pi$
$79$	−2.48977	−	4.31240i	−0.280121	−	0.485183i	−0.971414	+	0.237391i	$0.923708\pi$
$80$	−2.84717	+	1.64381i	−0.318323	+	0.183784i
$81$	−4.98856	−	7.49095i	−0.554284	−	0.832328i
$82$	−8.52566	−	4.92229i	−0.941502	−	0.543576i
$83$		−	0.999900i		−	0.109753i	−0.998493	−	0.0548767i	$-0.982523\pi$
$83$		−	0.999900i		−	0.109753i	0.998493	−	0.0548767i	$-0.0174766\pi$
$84$	1.11237	−	4.44552i	0.121370	−	0.485046i
$85$	3.19914	−	1.84702i	0.346995	−	0.200338i
$86$	3.35600	+	5.81276i	0.361887	+	0.626806i
$87$	−0.254829	−	15.9494i	−0.0273206	−	1.70996i
$88$	1.03510	+	1.79285i	0.110342	+	0.191118i
$89$			7.61879i			0.807590i	0.914849	+	0.403795i	$0.132309\pi$
$89$			7.61879i			0.807590i	−0.914849	+	0.403795i	$0.867691\pi$
$90$	−0.315084	−	9.85784i	−0.0332128	−	1.03911i
$91$	5.27553	+	7.94788i	0.553025	+	0.833164i
$92$			3.50085i			0.364989i
$93$	6.46548	−	0.103301i	0.670439	−	0.0107118i
$94$	−1.05515	+	0.609193i	−0.108831	+	0.0628334i
$95$		−	3.32333i		−	0.340967i
$96$	−0.889878	−	1.48597i	−0.0908228	−	0.151662i
$97$	−3.21628	−	5.57077i	−0.326564	−	0.565626i	0.655264	−	0.755400i	$-0.272558\pi$
$97$	−3.21628	−	5.57077i	−0.326564	−	0.565626i	−0.981828	+	0.189775i	$0.939224\pi$
$98$	0.00888497	+	6.99999i	0.000897518	+	0.707106i
$99$	−6.20743	+	0.198407i	−0.623870	+	0.0199407i
$100$	2.90424	−	5.03029i	0.290424	−	0.503029i
$101$	9.66204	+	16.7351i	0.961409	+	1.66521i	0.718968	+	0.695043i	$0.244615\pi$
$101$	9.66204	+	16.7351i	0.961409	+	1.66521i	0.242441	+	0.970166i	$0.422052\pi$
$102$	0.999885	+	1.66967i	0.0990034	+	0.165322i
$103$	−7.86720	+	4.54213i	−0.775178	+	0.447549i	−0.834719	−	0.550677i	$-0.814370\pi$
$103$	−7.86720	+	4.54213i	−0.775178	+	0.447549i	0.0595405	+	0.998226i	$0.481036\pi$
$104$	3.53365	+	0.716460i	0.346503	+	0.0702547i
$105$	4.14049	+	14.4857i	0.404070	+	1.41366i
$106$	5.05843	+	2.92049i	0.491318	+	0.283663i
$107$		−	3.76351i		−	0.363832i	−0.983314	−	0.181916i	$-0.941770\pi$
$107$		−	3.76351i		−	0.363832i	0.983314	−	0.181916i	$-0.0582299\pi$
$108$	5.19019	−	0.248945i	0.499426	−	0.0239548i
$109$	−2.43945	−	1.40841i	−0.233657	−	0.134902i	0.378601	−	0.925560i	$-0.376405\pi$
$109$	−2.43945	−	1.40841i	−0.233657	−	0.134902i	−0.612258	+	0.790658i	$0.709739\pi$
$110$	−5.89421	−	3.40302i	−0.561991	−	0.324465i
$111$	−10.3606	+	6.20446i	−0.983384	+	0.588901i
$112$	1.87202	+	1.86964i	0.176889	+	0.176664i
$113$	−4.57774	+	2.64296i	−0.430637	+	0.248629i	−0.699618	−	0.714517i	$-0.746646\pi$
$113$	−4.57774	+	2.64296i	−0.430637	+	0.248629i	0.268981	+	0.963146i	$0.413313\pi$
$114$	1.75064	−	0.0279705i	0.163962	−	0.00261968i
$115$	−5.75475	−	9.96752i	−0.536633	−	0.929476i
$116$	7.97573	+	4.60479i	0.740528	+	0.427544i
$117$	−6.89928	+	8.33066i	−0.637839	+	0.770170i
$118$		−	9.80909i		−	0.903000i
$119$	−2.10344	−	2.10077i	−0.192822	−	0.192577i
$120$	4.97629	+	2.76802i	0.454271	+	0.252685i
$121$	3.35713	−	5.81473i	0.305194	−	0.528612i
$122$	−0.209571	−	0.120996i	−0.0189736	−	0.0109544i
$123$	0.272400	+	17.0491i	0.0245615	+	1.53727i
$124$	−1.86666	+	3.23315i	−0.167631	+	0.290346i
$125$			2.65798i			0.237737i
$126$	−7.59580	+	2.30301i	−0.676687	+	0.205169i
$127$	9.40084	−	16.2827i	0.834190	−	1.44486i	−0.0604988	−	0.998168i	$-0.519269\pi$
$127$	9.40084	−	16.2827i	0.834190	−	1.44486i	0.894688	−	0.446691i	$-0.147398\pi$
$128$	1.00000			0.0883883
$129$	5.65118	−	10.1596i	0.497559	−	0.894500i
$130$	−11.2386	+	3.76878i	−0.985692	+	0.330544i
$131$	1.45204	+	2.51500i	0.126865	+	0.219737i	0.922460	−	0.386092i	$-0.126175\pi$
$131$	1.45204	+	2.51500i	0.126865	+	0.219737i	−0.795595	+	0.605828i	$0.792842\pi$
$132$	1.74301	−	3.13355i	0.151710	−	0.272740i
$133$	−2.58291	+	0.693847i	−0.223967	+	0.0601642i
$134$	−10.2316	+	5.90721i	−0.883874	+	0.510305i
$135$	−14.3681	+	9.24048i	−1.23661	+	0.795294i
$136$	−1.12362			−0.0963497
$137$	21.1790			1.80945			0.904724	−	0.425999i	$-0.140077\pi$
$137$	21.1790			1.80945			0.904724	+	0.425999i	$0.140077\pi$
$138$	5.20218	−	3.11533i	0.442839	−	0.265195i
$139$	17.6205	−	10.1732i	1.49455	−	0.862878i	0.494568	−	0.869139i	$-0.335326\pi$
$139$	17.6205	−	10.1732i	1.49455	−	0.862878i	0.999980	+	0.00626156i	$0.00199313\pi$
$140$	−8.40328	−	2.24594i	−0.710207	−	0.189816i
$141$	1.84420	+	1.02582i	0.155310	+	0.0863898i
$142$	−3.94585	−	6.83441i	−0.331128	−	0.573531i
$143$	2.37318	+	7.07690i	0.198455	+	0.591800i
$144$	−1.41623	+	2.64467i	−0.118020	+	0.220389i
$145$	−30.2777			−2.51442
$146$	0.878160	−	1.52102i	0.0726770	−	0.125880i
$147$	10.3939	−	6.24234i	0.857274	−	0.514860i
$148$		−	6.97226i		−	0.573116i
$149$	6.62502	−	11.4749i	0.542743	−	0.940058i	−0.456003	−	0.889978i	$-0.650719\pi$
$149$	6.62502	−	11.4749i	0.542743	−	0.940058i	0.998745	−	0.0500793i	$-0.0159474\pi$
$150$	−10.0593	+	0.160721i	−0.821338	+	0.0131228i
$151$	−15.0137	−	8.66818i	−1.22180	−	0.705407i	−0.256499	−	0.966545i	$-0.582569\pi$
$151$	−15.0137	−	8.66818i	−1.22180	−	0.705407i	−0.965301	+	0.261138i	$0.915902\pi$
$152$	−0.505430	+	0.875431i	−0.0409958	+	0.0710068i
$153$	1.59131	−	2.97161i	0.128650	−	0.240240i
$154$	−1.41426	+	5.29150i	−0.113964	+	0.426401i
$155$		−	12.2738i		−	0.985852i
$156$	−2.07988	−	5.88847i	−0.166523	−	0.471455i
$157$	12.2223	+	7.05652i	0.975442	+	0.563172i	0.900891	−	0.434045i	$-0.142914\pi$
$157$	12.2223	+	7.05652i	0.975442	+	0.563172i	0.0745511	+	0.997217i	$0.476248\pi$
$158$	−2.48977	−	4.31240i	−0.198075	−	0.343076i
$159$	−0.161620	−	10.1156i	−0.0128173	−	0.802217i
$160$	−2.84717	+	1.64381i	−0.225088	+	0.129955i
$161$	−6.54534	+	6.55365i	−0.515845	+	0.516500i
$162$	−4.98856	−	7.49095i	−0.391938	−	0.588544i
$163$	−8.93321	−	5.15759i	−0.699703	−	0.403974i	0.107534	−	0.994201i	$-0.465705\pi$
$163$	−8.93321	−	5.15759i	−0.699703	−	0.403974i	−0.807237	+	0.590228i	$0.799038\pi$
$164$	−8.52566	−	4.92229i	−0.665742	−	0.384366i
$165$	0.188323	+	11.7869i	0.0146610	+	0.917610i
$166$		−	0.999900i		−	0.0776073i
$167$	12.1099	+	6.99167i	0.937094	+	0.541032i	0.889048	−	0.457813i	$-0.151367\pi$
$167$	12.1099	+	6.99167i	0.937094	+	0.541032i	0.0480461	+	0.998845i	$0.484701\pi$
$168$	1.11237	−	4.44552i	0.0858214	−	0.342979i
$169$	11.9734	+	5.06344i	0.921028	+	0.389495i
$170$	3.19914	−	1.84702i	0.245363	−	0.141660i
$171$	−1.59942	−	2.57651i	−0.122311	−	0.197031i
$172$	3.35600	+	5.81276i	0.255893	+	0.443219i
$173$	2.53897	−	4.39763i	0.193035	−	0.334346i	−0.753220	−	0.657769i	$-0.771500\pi$
$173$	2.53897	−	4.39763i	0.193035	−	0.334346i	0.946254	+	0.323423i	$0.104834\pi$
$174$	−0.254829	−	15.9494i	−0.0193186	−	1.20912i
$175$	14.8416	−	3.98690i	1.12192	−	0.301381i
$176$	1.03510	+	1.79285i	0.0780236	+	0.135141i
$177$	−14.5760	+	8.72889i	−1.09560	+	0.656104i
$178$			7.61879i			0.571053i
$179$	10.1439	−	5.85660i	0.758193	−	0.437743i	−0.0704536	−	0.997515i	$-0.522445\pi$
$179$	10.1439	−	5.85660i	0.758193	−	0.437743i	0.828647	+	0.559772i	$0.189111\pi$
$180$	−0.315084	−	9.85784i	−0.0234850	−	0.734760i
$181$		−	22.6731i		−	1.68528i	−0.538480	−	0.842638i	$-0.681001\pi$
$181$		−	22.6731i		−	1.68528i	0.538480	−	0.842638i	$-0.318999\pi$
$182$	5.27553	+	7.94788i	0.391048	+	0.589136i
$183$	0.00669590	+	0.419088i	0.000494975	+	0.0309798i
$184$			3.50085i			0.258086i
$185$	11.4611	+	19.8512i	0.842636	+	1.45949i
$186$	6.46548	−	0.103301i	0.474072	−	0.00757440i
$187$	−1.16306	−	2.01448i	−0.0850514	−	0.147313i
$188$	−1.05515	+	0.609193i	−0.0769549	+	0.0444299i
$189$	10.1815	+	9.23775i	0.740599	+	0.671948i
$190$		−	3.32333i		−	0.241100i
$191$	−22.3913	−	12.9276i	−1.62017	−	0.935408i	−0.986872	−	0.161503i	$-0.948366\pi$
$191$	−22.3913	−	12.9276i	−1.62017	−	0.935408i	−0.633302	−	0.773905i	$-0.718301\pi$
$192$	−0.889878	−	1.48597i	−0.0642214	−	0.107241i
$193$	18.8878	−	10.9049i	1.35957	−	0.784951i	0.370008	−	0.929029i	$-0.379355\pi$
$193$	18.8878	−	10.9049i	1.35957	−	0.784951i	0.989566	+	0.144078i	$0.0460216\pi$
$194$	−3.21628	−	5.57077i	−0.230916	−	0.399958i
$195$	15.6013	+	13.3465i	1.11723	+	0.955765i
$196$	0.00888497	+	6.99999i	0.000634641	+	0.500000i
$197$	3.51025	−	6.07993i	0.250095	−	0.433177i	−0.713457	−	0.700699i	$-0.752872\pi$
$197$	3.51025	−	6.07993i	0.250095	−	0.433177i	0.963552	+	0.267522i	$0.0862049\pi$
$198$	−6.20743	+	0.198407i	−0.441143	+	0.0141002i
$199$		−	15.0791i		−	1.06893i	−0.845191	−	0.534464i	$-0.820513\pi$
$199$		−	15.0791i		−	1.06893i	0.845191	−	0.534464i	$-0.179487\pi$
$200$	2.90424	−	5.03029i	0.205361	−	0.355695i
$201$	17.8828	+	9.94717i	1.26136	+	0.701619i
$202$	9.66204	+	16.7351i	0.679819	+	1.17748i
$203$	6.32139	+	23.5320i	0.443675	+	1.65162i
$204$	0.999885	+	1.66967i	0.0700060	+	0.116900i
$205$	32.3653			2.26049
$206$	−7.86720	+	4.54213i	−0.548134	+	0.316465i
$207$	−9.25860	−	4.95803i	−0.643517	−	0.344607i
$208$	3.53365	+	0.716460i	0.245015	+	0.0496776i
$209$	−2.09268			−0.144754
$210$	4.14049	+	14.4857i	0.285721	+	0.999606i
$211$	−10.2101	+	17.6845i	−0.702895	+	1.21745i	0.264550	+	0.964372i	$0.414776\pi$
$211$	−10.2101	+	17.6845i	−0.702895	+	1.21745i	−0.967446	+	0.253079i	$0.918557\pi$
$212$	5.05843	+	2.92049i	0.347415	+	0.200580i
$213$	−6.64443	+	11.9452i	−0.455269	+	0.818473i
$214$		−	3.76351i		−	0.257268i
$215$	−19.1102	−	11.0333i	−1.30330	−	0.752463i
$216$	5.19019	−	0.248945i	0.353147	−	0.0169386i
$217$	−9.53925	+	2.56252i	−0.647567	+	0.173955i
$218$	−2.43945	−	1.40841i	−0.165220	−	0.0953899i
$219$	−3.04165	+	0.0485974i	−0.205535	+	0.00328391i
$220$	−5.89421	−	3.40302i	−0.397387	−	0.229432i
$221$	−3.97048	−	0.805029i	−0.267084	−	0.0541521i
$222$	−10.3606	+	6.20446i	−0.695358	+	0.416416i
$223$	1.37326	−	2.37855i	0.0919602	−	0.159280i	−0.816376	−	0.577521i	$-0.804020\pi$
$223$	1.37326	−	2.37855i	0.0919602	−	0.159280i	0.908336	+	0.418241i	$0.137353\pi$
$224$	1.87202	+	1.86964i	0.125079	+	0.124921i
$225$	9.19037	+	14.8048i	0.612692	+	0.986989i
$226$	−4.57774	+	2.64296i	−0.304507	+	0.175807i
$227$		−	8.98000i		−	0.596024i	−0.954562	−	0.298012i	$-0.903676\pi$
$227$		−	8.98000i		−	0.596024i	0.954562	−	0.298012i	$-0.0963235\pi$
$228$	1.75064	−	0.0279705i	0.115939	−	0.00185239i
$229$	8.23500	+	14.2634i	0.544184	+	0.942554i	0.998658	+	0.0517940i	$0.0164939\pi$
$229$	8.23500	+	14.2634i	0.544184	+	0.942554i	−0.454474	+	0.890760i	$0.650173\pi$
$230$	−5.75475	−	9.96752i	−0.379457	−	0.657239i
$231$	9.12155	−	2.60725i	0.600154	−	0.171544i
$232$	7.97573	+	4.60479i	0.523633	+	0.302319i
$233$	−4.79194	+	2.76663i	−0.313931	+	0.181248i	−0.648684	−	0.761058i	$-0.724680\pi$
$233$	−4.79194	+	2.76663i	−0.313931	+	0.181248i	0.334753	+	0.942306i	$0.391347\pi$
$234$	−6.89928	+	8.33066i	−0.451020	+	0.544592i
$235$	2.00280	−	3.46895i	0.130648	−	0.226289i
$236$		−	9.80909i		−	0.638517i
$237$	−4.19253	+	7.53724i	−0.272334	+	0.489596i
$238$	−2.10344	−	2.10077i	−0.136346	−	0.136173i
$239$	4.33497			0.280406			0.140203	−	0.990123i	$-0.455224\pi$
$239$	4.33497			0.280406			0.140203	+	0.990123i	$0.455224\pi$
$240$	4.97629	+	2.76802i	0.321218	+	0.178675i
$241$	4.20698			0.270995			0.135498	−	0.990778i	$-0.456737\pi$
$241$	4.20698			0.270995			0.135498	+	0.990778i	$0.456737\pi$
$242$	3.35713	−	5.81473i	0.215805	−	0.373785i
$243$	−6.69214	+	14.0789i	−0.429301	+	0.903161i
$244$	−0.209571	−	0.120996i	−0.0134164	−	0.00774595i
$245$	−11.5320	−	19.9155i	−0.736751	−	1.27236i
$246$	0.272400	+	17.0491i	0.0173676	+	1.08701i
$247$	−2.41322	+	2.73135i	−0.153550	+	0.173791i
$248$	−1.86666	+	3.23315i	−0.118533	+	0.205305i
$249$	−1.48583	+	0.889789i	−0.0941604	+	0.0563881i
$250$			2.65798i			0.168105i
$251$	9.79168	+	16.9597i	0.618045	+	1.07049i	0.989842	+	0.142172i	$0.0454086\pi$
$251$	9.79168	+	16.9597i	0.618045	+	1.07049i	−0.371797	+	0.928314i	$0.621258\pi$
$252$	−7.59580	+	2.30301i	−0.478490	+	0.145076i
$253$	−6.27649	+	3.62374i	−0.394600	+	0.227822i
$254$	9.40084	−	16.2827i	0.589861	−	1.02167i
$255$	−5.59147	−	3.11021i	−0.350151	−	0.194769i
$256$	1.00000			0.0625000
$257$	17.9497			1.11967			0.559837	−	0.828603i	$-0.310864\pi$
$257$	17.9497			1.11967			0.559837	+	0.828603i	$0.310864\pi$
$258$	5.65118	−	10.1596i	0.351827	−	0.632507i
$259$	13.0356	−	13.0522i	0.809994	−	0.811023i
$260$	−11.2386	+	3.76878i	−0.696990	+	0.233730i
$261$	−23.4737	+	14.5717i	−1.45298	+	0.901967i
$262$	1.45204	+	2.51500i	0.0897072	+	0.155377i
$263$	−24.1161	+	13.9235i	−1.48707	+	0.858557i	−0.999891	−	0.0147476i	$-0.995306\pi$
$263$	−24.1161	+	13.9235i	−1.48707	+	0.858557i	−0.487174	+	0.873305i	$0.661972\pi$
$264$	1.74301	−	3.13355i	0.107275	−	0.192856i
$265$	−19.2029			−1.17963
$266$	−2.58291	+	0.693847i	−0.158369	+	0.0425425i
$267$	11.3213	−	6.77979i	0.692854	−	0.414917i
$268$	−10.2316	+	5.90721i	−0.624994	+	0.360840i
$269$	28.3069			1.72590			0.862951	−	0.505288i	$-0.168614\pi$
$269$	28.3069			1.72590			0.862951	+	0.505288i	$0.168614\pi$
$270$	−14.3681	+	9.24048i	−0.874415	+	0.562358i
$271$	25.3037			1.53709			0.768546	−	0.639795i	$-0.220981\pi$
$271$	25.3037			1.53709			0.768546	+	0.639795i	$0.220981\pi$
$272$	−1.12362			−0.0681295
$273$	7.11577	−	14.9119i	0.430666	−	0.902511i
$274$	21.1790			1.27947
$275$	12.0247			0.725118
$276$	5.20218	−	3.11533i	0.313134	−	0.187521i
$277$	−13.0935			−0.786713			−0.393356	−	0.919386i	$-0.628686\pi$
$277$	−13.0935			−0.786713			−0.393356	+	0.919386i	$0.628686\pi$
$278$	17.6205	−	10.1732i	1.05680	−	0.610147i
$279$	−5.90699	−	9.51560i	−0.353642	−	0.569684i
$280$	−8.40328	−	2.24594i	−0.502192	−	0.134220i
$281$	−16.5616			−0.987980			−0.493990	−	0.869468i	$-0.664462\pi$
$281$	−16.5616			−0.987980			−0.493990	+	0.869468i	$0.664462\pi$
$282$	1.84420	+	1.02582i	0.109821	+	0.0610868i
$283$	−15.9278	+	9.19594i	−0.946811	+	0.546642i	−0.892089	−	0.451860i	$-0.850761\pi$
$283$	−15.9278	+	9.19594i	−0.946811	+	0.546642i	−0.0547224	+	0.998502i	$0.517427\pi$
$284$	−3.94585	−	6.83441i	−0.234143	−	0.405548i
$285$	−4.93838	+	2.95736i	−0.292524	+	0.175179i
$286$	2.37318	+	7.07690i	0.140329	+	0.418466i
$287$	−6.75725	−	25.1545i	−0.398868	−	1.48483i
$288$	−1.41623	+	2.64467i	−0.0834524	+	0.155839i
$289$	−15.7375			−0.925734
$290$	−30.2777			−1.77797
$291$	−5.41591	+	9.73662i	−0.317486	+	0.570771i
$292$	0.878160	−	1.52102i	0.0513904	−	0.0890108i
$293$	−7.37759	+	4.25945i	−0.431003	+	0.248840i	−0.699774	−	0.714364i	$-0.746716\pi$
$293$	−7.37759	+	4.25945i	−0.431003	+	0.248840i	0.268771	+	0.963204i	$0.413383\pi$
$294$	10.3939	−	6.24234i	0.606185	−	0.364061i
$295$	16.1243	+	27.9281i	0.938793	+	1.62604i
$296$		−	6.97226i		−	0.405254i
$297$	5.81868	+	9.04752i	0.337634	+	0.524991i
$298$	6.62502	−	11.4749i	0.383777	−	0.664721i
$299$	−2.50822	+	12.3708i	−0.145054	+	0.715422i
$300$	−10.0593	+	0.160721i	−0.580774	+	0.00927922i
$301$	−4.58529	+	17.1561i	−0.264292	+	0.988861i
$302$	−15.0137	−	8.66818i	−0.863943	−	0.498798i
$303$	16.2699	−	29.2498i	0.934684	−	1.68036i
$304$	−0.505430	+	0.875431i	−0.0289884	+	0.0502094i
$305$	0.795576			0.0455546
$306$	1.59131	−	2.97161i	0.0909692	−	0.169875i
$307$	−21.3161			−1.21658			−0.608288	−	0.793716i	$-0.708143\pi$
$307$	−21.3161			−1.21658			−0.608288	+	0.793716i	$0.708143\pi$
$308$	−1.41426	+	5.29150i	−0.0805847	+	0.301511i
$309$	13.7503	+	7.64851i	0.782229	+	0.435109i
$310$		−	12.2738i		−	0.697103i
$311$	7.40693	−	12.8292i	0.420008	−	0.727476i	−0.575931	−	0.817498i	$-0.695361\pi$
$311$	7.40693	−	12.8292i	0.420008	−	0.727476i	0.995940	+	0.0900223i	$0.0286938\pi$
$312$	−2.07988	−	5.88847i	−0.117750	−	0.333369i
$313$	−22.7031	+	13.1077i	−1.28326	+	0.740889i	−0.977442	−	0.211203i	$-0.932262\pi$
$313$	−22.7031	+	13.1077i	−1.28326	+	0.740889i	−0.305814	+	0.952091i	$0.598929\pi$
$314$	12.2223	+	7.05652i	0.689742	+	0.398223i
$315$	17.8408	−	19.0431i	1.00521	−	1.07296i
$316$	−2.48977	−	4.31240i	−0.140060	−	0.242592i
$317$	−9.80532	−	16.9833i	−0.550722	−	0.953878i	−0.998223	−	0.0595945i	$-0.981019\pi$
$317$	−9.80532	−	16.9833i	−0.550722	−	0.953878i	0.447501	−	0.894283i	$-0.352314\pi$
$318$	−0.161620	−	10.1156i	−0.00906319	−	0.567253i
$319$			19.0657i			1.06747i
$320$	−2.84717	+	1.64381i	−0.159161	+	0.0918919i
$321$	−5.59247	+	3.34906i	−0.312141	+	0.186926i
$322$	−6.54534	+	6.55365i	−0.364758	+	0.365221i
$323$	0.567912	−	0.983652i	0.0315995	−	0.0547319i
$324$	−4.98856	−	7.49095i	−0.277142	−	0.416164i
$325$	13.8666	−	15.6945i	0.769179	−	0.870575i
$326$	−8.93321	−	5.15759i	−0.494765	−	0.285652i
$327$	0.0779417	+	4.87827i	0.00431019	+	0.269769i
$328$	−8.52566	−	4.92229i	−0.470751	−	0.271788i
$329$	−3.11423	−	0.832338i	−0.171693	−	0.0458883i
$330$	0.188323	+	11.7869i	0.0103669	+	0.648848i
$331$	22.5837	+	13.0387i	1.24131	+	0.716671i	0.969361	−	0.245641i	$-0.0789985\pi$
$331$	22.5837	+	13.0387i	1.24131	+	0.716671i	0.271949	+	0.962312i	$0.412332\pi$
$332$		−	0.999900i		−	0.0548767i
$333$	18.4393	+	9.87436i	1.01047	+	0.541112i
$334$	12.1099	+	6.99167i	0.662626	+	0.382567i
$335$	19.4207	−	33.6376i	1.06107	−	1.83782i
$336$	1.11237	−	4.44552i	0.0606849	−	0.242523i
$337$	−13.5184			−0.736394			−0.368197	−	0.929748i	$-0.620025\pi$
$337$	−13.5184			−0.736394			−0.368197	+	0.929748i	$0.620025\pi$
$338$	11.9734	+	5.06344i	0.651265	+	0.275415i
$339$	8.00099	+	4.45049i	0.434554	+	0.241717i
$340$	3.19914	−	1.84702i	0.173498	−	0.100169i
$341$	−7.72873			−0.418534
$342$	−1.59942	−	2.57651i	−0.0864866	−	0.139322i
$343$	−13.0708	+	13.1207i	−0.705759	+	0.708452i
$344$	3.35600	+	5.81276i	0.180943	+	0.313403i
$345$	−9.69044	+	17.4213i	−0.521716	+	0.937930i
$346$	2.53897	−	4.39763i	0.136496	−	0.236418i
$347$			33.5765i			1.80248i	0.433322	+	0.901239i	$0.357341\pi$
$347$			33.5765i			1.80248i	−0.433322	+	0.901239i	$0.642659\pi$
$348$	−0.254829	−	15.9494i	−0.0136603	−	0.854979i
$349$	11.8845	−	20.5845i	0.636161	−	1.10186i	−0.350107	−	0.936710i	$-0.613855\pi$
$349$	11.8845	−	20.5845i	0.636161	−	1.10186i	0.986268	−	0.165153i	$-0.0528118\pi$
$350$	14.8416	−	3.98690i	0.793318	−	0.213109i
$351$	18.5187	+	2.83887i	0.988453	+	0.151528i
$352$	1.03510	+	1.79285i	0.0551710	+	0.0955590i
$353$	−9.28444	+	5.36037i	−0.494161	+	0.285304i	−0.726299	−	0.687379i	$-0.758761\pi$
$353$	−9.28444	+	5.36037i	−0.494161	+	0.285304i	0.232138	+	0.972683i	$0.425428\pi$
$354$	−14.5760	+	8.72889i	−0.774708	+	0.463935i
$355$	22.4690	+	12.9725i	1.19253	+	0.688508i
$356$			7.61879i			0.403795i
$357$	−1.24988	+	4.99508i	−0.0661509	+	0.264368i
$358$	10.1439	−	5.85660i	0.536123	−	0.309531i
$359$	−7.26878	−	12.5899i	−0.383632	−	0.664469i	0.607947	−	0.793978i	$-0.291993\pi$
$359$	−7.26878	−	12.5899i	−0.383632	−	0.664469i	−0.991578	+	0.129508i	$0.958660\pi$
$360$	−0.315084	−	9.85784i	−0.0166064	−	0.519554i
$361$	8.98908	+	15.5695i	0.473110	+	0.819450i
$362$		−	22.6731i		−	1.19167i
$363$	−11.6280	+	0.185784i	−0.610310	+	0.00975113i
$364$	5.27553	+	7.94788i	0.276513	+	0.416582i
$365$			5.77412i			0.302231i
$366$	0.00669590	+	0.419088i	0.000350000	+	0.0219061i
$367$	−15.1524	+	8.74823i	−0.790948	+	0.456654i	−0.840296	−	0.542128i	$-0.817619\pi$
$367$	−15.1524	+	8.74823i	−0.790948	+	0.456654i	0.0493484	+	0.998782i	$0.484286\pi$
$368$			3.50085i			0.182495i
$369$	25.0922	−	15.5764i	1.30625	−	0.810877i
$370$	11.4611	+	19.8512i	0.595834	+	1.03201i
$371$	4.00920	+	14.9247i	0.208147	+	0.774849i
$372$	6.46548	−	0.103301i	0.335219	−	0.00535591i
$373$	5.93324	−	10.2767i	0.307211	−	0.532106i	−0.670540	−	0.741874i	$-0.733937\pi$
$373$	5.93324	−	10.2767i	0.307211	−	0.532106i	0.977751	+	0.209768i	$0.0672708\pi$
$374$	−1.16306	−	2.01448i	−0.0601404	−	0.104166i
$375$	3.94968	−	2.36528i	0.203961	−	0.122142i
$376$	−1.05515	+	0.609193i	−0.0544153	+	0.0314167i
$377$	24.8843	+	21.9860i	1.28161	+	1.13234i
$378$	10.1815	+	9.23775i	0.523682	+	0.475139i
$379$	10.9141	+	6.30127i	0.560620	+	0.323674i	0.753394	−	0.657569i	$-0.228415\pi$
$379$	10.9141	+	6.30127i	0.560620	+	0.323674i	−0.192774	+	0.981243i	$0.561748\pi$
$380$		−	3.32333i		−	0.170483i
$381$	−32.5613	+	0.520243i	−1.66817	+	0.0266528i
$382$	−22.3913	−	12.9276i	−1.14564	−	0.661433i
$383$	0.920885	+	0.531673i	0.0470550	+	0.0271672i	0.523343	−	0.852122i	$-0.324685\pi$
$383$	0.920885	+	0.531673i	0.0470550	+	0.0271672i	−0.476288	+	0.879289i	$0.658018\pi$
$384$	−0.889878	−	1.48597i	−0.0454114	−	0.0758308i
$385$	−4.67162	−	17.3906i	−0.238088	−	0.886305i
$386$	18.8878	−	10.9049i	0.961364	−	0.555044i
$387$	−20.1257	+	0.643275i	−1.02305	+	0.0326995i
$388$	−3.21628	−	5.57077i	−0.163282	−	0.282813i
$389$	2.28039	+	1.31658i	0.115620	+	0.0667534i	0.556695	−	0.830717i	$-0.312069\pi$
$389$	2.28039	+	1.31658i	0.115620	+	0.0667534i	−0.441075	+	0.897470i	$0.645403\pi$
$390$	15.6013	+	13.3465i	0.790003	+	0.675828i
$391$		−	3.93363i		−	0.198932i
$392$	0.00888497	+	6.99999i	0.000448759	+	0.353553i
$393$	2.44509	−	4.39574i	0.123339	−	0.221736i
$394$	3.51025	−	6.07993i	0.176844	−	0.306302i
$395$	14.1776	+	8.18542i	0.713351	+	0.411853i
$396$	−6.20743	+	0.198407i	−0.311935	+	0.00997033i
$397$	−4.27357	+	7.40204i	−0.214484	+	0.371498i	−0.953113	−	0.302615i	$-0.902140\pi$
$397$	−4.27357	+	7.40204i	−0.214484	+	0.371498i	0.738629	+	0.674113i	$0.235474\pi$
$398$		−	15.0791i		−	0.755846i
$399$	3.32952	+	3.22070i	0.166684	+	0.161237i
$400$	2.90424	−	5.03029i	0.145212	−	0.251515i
$401$	15.5754			0.777797			0.388898	−	0.921281i	$-0.372856\pi$
$401$	15.5754			0.777797			0.388898	+	0.921281i	$0.372856\pi$
$402$	17.8828	+	9.94717i	0.891914	+	0.496120i
$403$	−8.91255	+	10.0874i	−0.443966	+	0.502491i
$404$	9.66204	+	16.7351i	0.480705	+	0.832605i
$405$	26.5170	+	13.1277i	1.31764	+	0.652322i
$406$	6.32139	+	23.5320i	0.313725	+	1.16787i
$407$	12.5002	−	7.21699i	0.619612	−	0.357733i
$408$	0.999885	+	1.66967i	0.0495017	+	0.0826610i
$409$	10.8097			0.534504			0.267252	−	0.963627i	$-0.413884\pi$
$409$	10.8097			0.534504			0.267252	+	0.963627i	$0.413884\pi$
$410$	32.3653			1.59841
$411$	−18.8468	−	31.4715i	−0.929642	−	1.55237i
$412$	−7.86720	+	4.54213i	−0.387589	+	0.223775i
$413$	18.3395	−	18.3628i	0.902427	−	0.903573i
$414$	−9.25860	−	4.95803i	−0.455036	−	0.243674i
$415$	1.64365	+	2.84688i	0.0806836	+	0.139748i
$416$	3.53365	+	0.716460i	0.173251	+	0.0351273i
$417$	−30.7971	−	17.1307i	−1.50814	−	0.838892i
$418$	−2.09268			−0.102357
$419$	7.13932	−	12.3657i	0.348779	−	0.604102i	−0.637254	−	0.770654i	$-0.719930\pi$
$419$	7.13932	−	12.3657i	0.348779	−	0.604102i	0.986033	+	0.166551i	$0.0532632\pi$
$420$	4.14049	+	14.4857i	0.202035	+	0.706828i
$421$		−	31.1553i		−	1.51842i	−0.650848	−	0.759208i	$-0.725586\pi$
$421$		−	31.1553i		−	1.51842i	0.650848	−	0.759208i	$-0.274414\pi$
$422$	−10.2101	+	17.6845i	−0.497022	+	0.860867i
$423$	−0.116769	−	3.65329i	−0.00567753	−	0.177629i
$424$	5.05843	+	2.92049i	0.245659	+	0.141831i
$425$	−3.26326	+	5.65214i	−0.158292	+	0.274169i
$426$	−6.64443	+	11.9452i	−0.321924	+	0.578748i
$427$	−0.166101	−	0.618327i	−0.00803819	−	0.0299230i
$428$		−	3.76351i		−	0.181916i
$429$	8.40425	−	9.82406i	0.405761	−	0.474310i
$430$	−19.1102	−	11.0333i	−0.921575	−	0.532071i
$431$	−10.7951	−	18.6976i	−0.519981	−	0.900634i	−0.999730	−	0.0232279i	$-0.992606\pi$
$431$	−10.7951	−	18.6976i	−0.519981	−	0.900634i	0.479749	−	0.877406i	$-0.340728\pi$
$432$	5.19019	−	0.248945i	0.249713	−	0.0119774i
$433$	16.2009	−	9.35358i	0.778565	−	0.449505i	−0.0573567	−	0.998354i	$-0.518267\pi$
$433$	16.2009	−	9.35358i	0.778565	−	0.449505i	0.835921	+	0.548849i	$0.184934\pi$
$434$	−9.53925	+	2.56252i	−0.457899	+	0.123005i
$435$	26.9434	+	44.9918i	1.29184	+	2.15719i
$436$	−2.43945	−	1.40841i	−0.116828	−	0.0674508i
$437$	−3.06476	−	1.76944i	−0.146607	−	0.0846437i
$438$	−3.04165	+	0.0485974i	−0.145336	+	0.00232207i
$439$			14.3709i			0.685885i	0.939356	+	0.342943i	$0.111424\pi$
$439$			14.3709i			0.685885i	−0.939356	+	0.342943i	$0.888576\pi$
$440$	−5.89421	−	3.40302i	−0.280995	−	0.162233i
$441$	−18.5253	−	9.89014i	−0.882155	−	0.470959i
$442$	−3.97048	−	0.805029i	−0.188857	−	0.0382913i
$443$	−1.21594	+	0.702023i	−0.0577711	+	0.0333541i	−0.528607	−	0.848866i	$-0.677286\pi$
$443$	−1.21594	+	0.702023i	−0.0577711	+	0.0333541i	0.470836	+	0.882221i	$0.343952\pi$
$444$	−10.3606	+	6.20446i	−0.491692	+	0.294451i
$445$	−12.5239	−	21.6920i	−0.593688	−	1.02830i
$446$	1.37326	−	2.37855i	0.0650257	−	0.112628i
$447$	−22.9468	+	0.366629i	−1.08535	+	0.0173409i
$448$	1.87202	+	1.86964i	0.0884444	+	0.0883322i
$449$	−11.0266	−	19.0987i	−0.520379	−	0.901323i	−0.999719	−	0.0236937i	$-0.992457\pi$
$449$	−11.0266	−	19.0987i	−0.520379	−	0.901323i	0.479340	−	0.877629i	$-0.340876\pi$
$450$	9.19037	+	14.8048i	0.433238	+	0.697906i
$451$		−	20.3803i		−	0.959669i
$452$	−4.57774	+	2.64296i	−0.215319	+	0.124314i
$453$	0.479698	+	30.0236i	0.0225382	+	1.41063i
$454$		−	8.98000i		−	0.421453i
$455$	−28.0851	−	13.9570i	−1.31665	−	0.654313i
$456$	1.75064	−	0.0279705i	0.0819812	−	0.00130984i
$457$			42.3253i			1.97990i	0.141432	+	0.989948i	$0.454829\pi$
$457$			42.3253i			1.97990i	−0.141432	+	0.989948i	$0.545171\pi$
$458$	8.23500	+	14.2634i	0.384796	+	0.666486i
$459$	−5.83180	+	0.279720i	−0.272205	+	0.0130562i
$460$	−5.75475	−	9.96752i	−0.268317	−	0.464738i
$461$	−10.2913	+	5.94166i	−0.479312	+	0.276731i	−0.720130	−	0.693839i	$-0.755918\pi$
$461$	−10.2913	+	5.94166i	−0.479312	+	0.276731i	0.240818	+	0.970570i	$0.422584\pi$
$462$	9.12155	−	2.60725i	0.424373	−	0.121300i
$463$		−	3.56440i		−	0.165652i	−0.996564	−	0.0828258i	$-0.973605\pi$
$463$		−	3.56440i		−	0.165652i	0.996564	−	0.0828258i	$-0.0263945\pi$
$464$	7.97573	+	4.60479i	0.370264	+	0.213772i
$465$	−18.2385	+	10.9221i	−0.845790	+	0.506503i
$466$	−4.79194	+	2.76663i	−0.221983	+	0.128162i
$467$	3.56143	+	6.16858i	0.164803	+	0.285448i	0.936585	−	0.350439i	$-0.113968\pi$
$467$	3.56143	+	6.16858i	0.164803	+	0.285448i	−0.771782	+	0.635887i	$0.780634\pi$
$468$	−6.89928	+	8.33066i	−0.318919	+	0.385085i
$469$	−30.1981	−	8.07101i	−1.39442	−	0.372684i
$470$	2.00280	−	3.46895i	0.0923821	−	0.160011i
$471$	−0.390508	−	24.4414i	−0.0179937	−	1.12620i
$472$		−	9.80909i		−	0.451500i
$473$	−6.94759	+	12.0336i	−0.319451	+	0.553305i
$474$	−4.19253	+	7.53724i	−0.192569	+	0.346197i
$475$	2.93578	+	5.08492i	0.134703	+	0.233312i
$476$	−2.10344	−	2.10077i	−0.0964108	−	0.0962885i
$477$	−14.8877	+	9.24179i	−0.681659	+	0.423152i
$478$	4.33497			0.198277
$479$	−26.4547	+	15.2736i	−1.20875	+	0.697870i	−0.962485	−	0.271334i	$-0.912535\pi$
$479$	−26.4547	+	15.2736i	−1.20875	+	0.697870i	−0.246260	+	0.969204i	$0.579202\pi$
$480$	4.97629	+	2.76802i	0.227136	+	0.126342i
$481$	4.99535	−	24.6375i	0.227768	−	1.12337i
$482$	4.20698			0.191623
$483$	15.5631	+	3.89425i	0.708146	+	0.177195i
$484$	3.35713	−	5.81473i	0.152597	−	0.264306i
$485$	18.3146	+	10.5739i	0.831623	+	0.480138i
$486$	−6.69214	+	14.0789i	−0.303562	+	0.638632i
$487$			32.0202i			1.45098i	0.688235	+	0.725488i	$0.258386\pi$
$487$			32.0202i			1.45098i	−0.688235	+	0.725488i	$0.741614\pi$
$488$	−0.209571	−	0.120996i	−0.00948681	−	0.00547721i
$489$	0.285421	+	17.8641i	0.0129072	+	0.807844i
$490$	−11.5320	−	19.9155i	−0.520962	−	0.899693i
$491$	−13.0865	−	7.55549i	−0.590585	−	0.340975i	0.174744	−	0.984614i	$-0.444090\pi$
$491$	−13.0865	−	7.55549i	−0.590585	−	0.340975i	−0.765329	+	0.643639i	$0.777424\pi$
$492$	0.272400	+	17.0491i	0.0122807	+	0.768635i
$493$	−8.96170	−	5.17404i	−0.403615	−	0.233027i
$494$	−2.41322	+	2.73135i	−0.108576	+	0.122889i
$495$	17.3475	−	10.7688i	0.779710	−	0.484019i
$496$	−1.86666	+	3.23315i	−0.0838156	+	0.145173i
$497$	5.39121	−	20.1715i	0.241829	−	0.904813i
$498$	−1.48583	+	0.889789i	−0.0665814	+	0.0398724i
$499$	−4.18606	+	2.41682i	−0.187394	+	0.108192i	−0.590762	−	0.806846i	$-0.701173\pi$
$499$	−4.18606	+	2.41682i	−0.187394	+	0.108192i	0.403368	+	0.915038i	$0.367839\pi$
$500$			2.65798i			0.118868i
$501$	−0.386919	−	24.2168i	−0.0172863	−	1.08193i
$502$	9.79168	+	16.9597i	0.437024	+	0.756948i
$503$	−13.7946	−	23.8930i	−0.615073	−	1.06534i	−0.990372	−	0.138433i	$-0.955793\pi$
$503$	−13.7946	−	23.8930i	−0.615073	−	1.06534i	0.375299	−	0.926904i	$-0.377540\pi$
$504$	−7.59580	+	2.30301i	−0.338344	+	0.102584i
$505$	−55.0189	−	31.7652i	−2.44831	−	1.41353i
$506$	−6.27649	+	3.62374i	−0.279024	+	0.161095i
$507$	−3.13070	−	22.2980i	−0.139039	−	0.990287i
$508$	9.40084	−	16.2827i	0.417095	−	0.722429i
$509$		−	31.3889i		−	1.39129i	−0.718386	−	0.695645i	$-0.755119\pi$
$509$		−	31.3889i		−	1.39129i	0.718386	−	0.695645i	$-0.244881\pi$
$510$	−5.59147	−	3.11021i	−0.247594	−	0.137722i
$511$	4.48769	−	1.20553i	0.198524	−	0.0533293i
$512$	1.00000			0.0441942
$513$	−2.40534	+	4.66947i	−0.106198	+	0.206162i
$514$	17.9497			0.791728
$515$	14.9328	−	25.8644i	0.658019	−	1.13972i
$516$	5.65118	−	10.1596i	0.248779	−	0.447250i
$517$	−2.18438	−	1.26115i	−0.0960688	−	0.0554654i
$518$	13.0356	−	13.0522i	0.572753	−	0.573480i
$519$	−8.79414	+	0.140507i	−0.386020	+	0.00616757i
$520$	−11.2386	+	3.76878i	−0.492846	+	0.165272i
$521$	−0.178115	+	0.308505i	−0.00780338	+	0.0135159i	−0.869901	−	0.493227i	$-0.835817\pi$
$521$	−0.178115	+	0.308505i	−0.00780338	+	0.0135159i	0.862097	+	0.506743i	$0.169151\pi$
$522$	−23.4737	+	14.5717i	−1.02741	+	0.637787i
$523$		−	24.9103i		−	1.08925i	−0.838679	−	0.544626i	$-0.816672\pi$
$523$		−	24.9103i		−	1.08925i	0.838679	−	0.544626i	$-0.183328\pi$
$524$	1.45204	+	2.51500i	0.0634326	+	0.109868i
$525$	−19.1317	−	18.5064i	−0.834974	−	0.807686i
$526$	−24.1161	+	13.9235i	−1.05151	+	0.607092i
$527$	2.09742	−	3.63284i	0.0913650	−	0.158249i
$528$	1.74301	−	3.13355i	0.0758548	−	0.136370i
$529$	10.7440			0.467131
$530$	−19.2029			−0.834122
$531$	25.9418	+	13.8920i	1.12578	+	0.602860i
$532$	−2.58291	+	0.693847i	−0.111984	+	0.0300821i
$533$	−26.6001	−	23.5020i	−1.15218	−	1.01798i
$534$	11.3213	−	6.77979i	0.489922	−	0.293390i
$535$	6.18650	+	10.7153i	0.267466	+	0.463264i
$536$	−10.2316	+	5.90721i	−0.441937	+	0.255153i
$537$	−17.7296	−	9.86195i	−0.765089	−	0.425575i
$538$	28.3069			1.22040
$539$	−12.5407	+	7.26163i	−0.540167	+	0.312780i
$540$	−14.3681	+	9.24048i	−0.618305	+	0.397647i
$541$	17.5713	−	10.1448i	0.755447	−	0.436158i	−0.0722115	−	0.997389i	$-0.523006\pi$
$541$	17.5713	−	10.1448i	0.755447	−	0.436158i	0.827659	+	0.561232i	$0.189672\pi$
$542$	25.3037			1.08689
$543$	−33.6916	+	20.1763i	−1.44584	+	0.865846i
$544$	−1.12362			−0.0481748
$545$	9.26068			0.396684
$546$	7.11577	−	14.9119i	0.304527	−	0.638172i
$547$	−18.3443			−0.784344			−0.392172	−	0.919892i	$-0.628276\pi$
$547$	−18.3443			−0.784344			−0.392172	+	0.919892i	$0.628276\pi$
$548$	21.1790			0.904724
$549$	0.616794	−	0.382887i	0.0263241	−	0.0163412i
$550$	12.0247			0.512736
$551$	−8.06235	+	4.65480i	−0.343468	+	0.198301i
$552$	5.20218	−	3.11533i	0.221419	−	0.132597i
$553$	3.40176	−	12.7279i	0.144658	−	0.541243i
$554$	−13.0935			−0.556290
$555$	19.2994	−	34.6960i	0.819213	−	1.47276i
$556$	17.6205	−	10.1732i	0.747274	−	0.431439i
$557$	6.08906	+	10.5466i	0.258002	+	0.446872i	0.965707	−	0.259636i	$-0.0836026\pi$
$557$	6.08906	+	10.5466i	0.258002	+	0.446872i	−0.707705	+	0.706508i	$0.750269\pi$
$558$	−5.90699	−	9.51560i	−0.250063	−	0.402828i
$559$	7.69432	+	22.9447i	0.325435	+	0.970457i
$560$	−8.40328	−	2.24594i	−0.355103	−	0.0949082i
$561$	−1.95848	+	3.52092i	−0.0826872	+	0.148653i
$562$	−16.5616			−0.698608
$563$	−11.3717			−0.479262			−0.239631	−	0.970864i	$-0.577026\pi$
$563$	−11.3717			−0.479262			−0.239631	+	0.970864i	$0.577026\pi$
$564$	1.84420	+	1.02582i	0.0776549	+	0.0431949i
$565$	8.68905	−	15.0499i	0.365551	−	0.633153i
$566$	−15.9278	+	9.19594i	−0.669497	+	0.386534i
$567$	4.66673	−	23.3500i	0.195984	−	0.980607i
$568$	−3.94585	−	6.83441i	−0.165564	−	0.286766i
$569$		−	24.0497i		−	1.00822i	−0.863641	−	0.504108i	$-0.831821\pi$
$569$		−	24.0497i		−	1.00822i	0.863641	−	0.504108i	$-0.168179\pi$
$570$	−4.93838	+	2.95736i	−0.206846	+	0.123870i
$571$	3.64194	−	6.30802i	0.152410	−	0.263983i	−0.779703	−	0.626150i	$-0.784630\pi$
$571$	3.64194	−	6.30802i	0.152410	−	0.263983i	0.932113	+	0.362167i	$0.117963\pi$
$572$	2.37318	+	7.07690i	0.0992277	+	0.295900i
$573$	0.715414	+	44.7768i	0.0298868	+	1.87058i
$574$	−6.75725	−	25.1545i	−0.282042	−	1.04993i
$575$	17.6103	+	10.1673i	0.734401	+	0.424007i
$576$	−1.41623	+	2.64467i	−0.0590098	+	0.110195i
$577$	−2.11186	+	3.65785i	−0.0879179	+	0.152278i	−0.906631	−	0.421925i	$-0.861355\pi$
$577$	−2.11186	+	3.65785i	−0.0879179	+	0.152278i	0.818713	+	0.574203i	$0.194688\pi$
$578$	−15.7375			−0.654593
$579$	−33.0122	−	18.3628i	−1.37194	−	0.763131i
$580$	−30.2777			−1.25721
$581$	1.86945	−	1.87183i	0.0775581	−	0.0776566i
$582$	−5.41591	+	9.73662i	−0.224497	+	0.403596i
$583$			12.0920i			0.500799i
$584$	0.878160	−	1.52102i	0.0363385	−	0.0629402i
$585$	5.94935	−	35.0599i	0.245975	−	1.44955i
$586$	−7.37759	+	4.25945i	−0.304765	+	0.175956i
$587$	−39.5103	−	22.8113i	−1.63077	−	0.941523i	−0.983857	−	0.178954i	$-0.942729\pi$
$587$	−39.5103	−	22.8113i	−1.63077	−	0.941523i	−0.646908	−	0.762568i	$-0.723938\pi$
$588$	10.3939	−	6.24234i	0.428637	−	0.257430i
$589$	−1.88693	−	3.26827i	−0.0777498	−	0.134667i
$590$	16.1243	+	27.9281i	0.663827	+	1.14978i
$591$	−12.1583	+	0.194257i	−0.500126	+	0.00799068i
$592$		−	6.97226i		−	0.286558i
$593$	−21.1653	+	12.2198i	−0.869154	+	0.501807i	−0.867067	−	0.498191i	$-0.833998\pi$
$593$	−21.1653	+	12.2198i	−0.869154	+	0.501807i	−0.00208732	+	0.999998i	$0.500664\pi$
$594$	5.81868	+	9.04752i	0.238744	+	0.371224i
$595$	9.44210	+	2.52358i	0.387088	+	0.103457i
$596$	6.62502	−	11.4749i	0.271371	−	0.470029i
$597$	−22.4071	+	13.4185i	−0.917062	+	0.549184i
$598$	−2.50822	+	12.3708i	−0.102569	+	0.505879i
$599$	11.4214	+	6.59416i	0.466667	+	0.269430i	0.714843	−	0.699285i	$-0.246498\pi$
$599$	11.4214	+	6.59416i	0.466667	+	0.269430i	−0.248177	+	0.968715i	$0.579831\pi$
$600$	−10.0593	+	0.160721i	−0.410669	+	0.00656140i
$601$	34.6176	+	19.9865i	1.41208	+	0.815266i	0.995584	−	0.0938714i	$-0.0299242\pi$
$601$	34.6176	+	19.9865i	1.41208	+	0.815266i	0.416497	+	0.909137i	$0.363258\pi$
$602$	−4.58529	+	17.1561i	−0.186883	+	0.699230i
$603$	−1.13229	−	35.4252i	−0.0461103	−	1.44262i
$604$	−15.0137	−	8.66818i	−0.610900	−	0.352703i
$605$			22.0740i			0.897436i
$606$	16.2699	−	29.2498i	0.660922	−	1.18819i
$607$	−17.4747	−	10.0890i	−0.709275	−	0.409500i	0.101518	−	0.994834i	$-0.467630\pi$
$607$	−17.4747	−	10.0890i	−0.709275	−	0.409500i	−0.810793	+	0.585334i	$0.800964\pi$
$608$	−0.505430	+	0.875431i	−0.0204979	+	0.0355034i
$609$	29.3427	−	30.3340i	1.18902	−	1.22920i
$610$	0.795576			0.0322119
$611$	−4.16500	+	1.39670i	−0.168498	+	0.0565044i
$612$	1.59131	−	2.97161i	0.0643249	−	0.120120i
$613$	21.6006	−	12.4711i	0.872440	−	0.503703i	0.00428146	−	0.999991i	$-0.498637\pi$
$613$	21.6006	−	12.4711i	0.872440	−	0.503703i	0.868158	+	0.496288i	$0.165304\pi$
$614$	−21.3161			−0.860249
$615$	−28.8012	−	48.0940i	−1.16138	−	1.93934i
$616$	−1.41426	+	5.29150i	−0.0569820	+	0.213201i
$617$	1.22499	+	2.12175i	0.0493164	+	0.0854185i	0.889630	−	0.456682i	$-0.150962\pi$
$617$	1.22499	+	2.12175i	0.0493164	+	0.0854185i	−0.840313	+	0.542101i	$0.817629\pi$
$618$	13.7503	+	7.64851i	0.553119	+	0.307668i
$619$	−11.9145	+	20.6365i	−0.478883	+	0.829449i	−0.999707	−	0.0242147i	$-0.992291\pi$
$619$	−11.9145	+	20.6365i	−0.478883	+	0.829449i	0.520824	+	0.853664i	$0.325625\pi$
$620$		−	12.2738i		−	0.492926i
$621$	0.871522	+	18.1701i	0.0349730	+	0.729140i
$622$	7.40693	−	12.8292i	0.296991	−	0.514403i
$623$	−14.2444	+	14.2625i	−0.570690	+	0.571415i
$624$	−2.07988	−	5.88847i	−0.0832617	−	0.235728i
$625$	10.1520	+	17.5837i	0.406079	+	0.703350i
$626$	−22.7031	+	13.1077i	−0.907399	+	0.523887i
$627$	1.86223	+	3.10967i	0.0743704	+	0.124188i
$628$	12.2223	+	7.05652i	0.487721	+	0.281586i
$629$			7.83418i			0.312369i
$630$	17.8408	−	19.0431i	0.710794	−	0.758696i
$631$	−17.5516	+	10.1334i	−0.698718	+	0.403405i	−0.806870	−	0.590729i	$-0.798840\pi$
$631$	−17.5516	+	10.1334i	−0.698718	+	0.403405i	0.108152	+	0.994134i	$0.465507\pi$
$632$	−2.48977	−	4.31240i	−0.0990376	−	0.171538i
$633$	35.3645	−	0.565030i	1.40561	−	0.0224579i
$634$	−9.80532	−	16.9833i	−0.389419	−	0.674494i
$635$			61.8129i			2.45297i
$636$	−0.161620	−	10.1156i	−0.00640865	−	0.401109i
$637$	−4.98382	+	24.7419i	−0.197466	+	0.980310i
$638$			19.0657i			0.754818i
$639$	23.6630	−	0.756337i	0.936095	−	0.0299202i
$640$	−2.84717	+	1.64381i	−0.112544	+	0.0649774i
$641$		−	33.2647i		−	1.31388i	−0.753945	−	0.656938i	$-0.771851\pi$
$641$		−	33.2647i		−	1.31388i	0.753945	−	0.656938i	$-0.228149\pi$
$642$	−5.59247	+	3.34906i	−0.220717	+	0.132177i
$643$	−3.65734	−	6.33469i	−0.144231	−	0.249816i	0.784855	−	0.619680i	$-0.212738\pi$
$643$	−3.65734	−	6.33469i	−0.144231	−	0.249816i	−0.929086	+	0.369864i	$0.879404\pi$
$644$	−6.54534	+	6.55365i	−0.257923	+	0.258250i
$645$	0.610581	+	38.2155i	0.0240416	+	1.50473i
$646$	0.567912	−	0.983652i	0.0223442	−	0.0387013i
$647$	16.0186	+	27.7451i	0.629757	+	1.09077i	0.987600	+	0.156990i	$0.0501789\pi$
$647$	16.0186	+	27.7451i	0.629757	+	1.09077i	−0.357843	+	0.933782i	$0.616488\pi$
$648$	−4.98856	−	7.49095i	−0.195969	−	0.294272i
$649$	17.5862	−	10.1534i	0.690319	−	0.398556i
$650$	13.8666	−	15.6945i	0.543892	−	0.615590i
$651$	12.2966	+	11.8947i	0.481942	+	0.466192i
$652$	−8.93321	−	5.15759i	−0.349851	−	0.201987i
$653$		−	33.6453i		−	1.31664i	−0.752737	−	0.658321i	$-0.771267\pi$
$653$		−	33.6453i		−	1.31664i	0.752737	−	0.658321i	$-0.228733\pi$
$654$	0.0779417	+	4.87827i	0.00304776	+	0.190755i
$655$	−8.26839	−	4.77376i	−0.323073	−	0.186526i
$656$	−8.52566	−	4.92229i	−0.332871	−	0.192183i
$657$	2.77891	+	4.47656i	0.108416	+	0.174647i
$658$	−3.11423	−	0.832338i	−0.121405	−	0.0324479i
$659$	21.1966	−	12.2379i	0.825704	−	0.476720i	−0.0266755	−	0.999644i	$-0.508492\pi$
$659$	21.1966	−	12.2379i	0.825704	−	0.476720i	0.852379	+	0.522924i	$0.175159\pi$
$660$	0.188323	+	11.7869i	0.00733048	+	0.458805i
$661$	2.77785	+	4.81137i	0.108046	+	0.187141i	0.914979	−	0.403503i	$-0.132207\pi$
$661$	2.77785	+	4.81137i	0.108046	+	0.187141i	−0.806933	+	0.590643i	$0.798874\pi$
$662$	22.5837	+	13.0387i	0.877739	+	0.506763i
$663$	2.33699	+	6.61641i	0.0907613	+	0.256960i
$664$		−	0.999900i		−	0.0388037i
$665$	6.21343	−	6.22133i	0.240947	−	0.241253i
$666$	18.4393	+	9.87436i	0.714510	+	0.382624i
$667$	−16.1207	+	27.9219i	−0.624196	+	1.08114i
$668$	12.1099	+	6.99167i	0.468547	+	0.270516i
$669$	−4.75650	+	0.0759962i	−0.183897	+	0.00293818i
$670$	19.4207	−	33.6376i	0.750287	−	1.29953i
$671$		−	0.500970i		−	0.0193397i
$672$	1.11237	−	4.44552i	0.0429107	−	0.171490i
$673$	9.31475	−	16.1336i	0.359057	−	0.621905i	−0.628746	−	0.777610i	$-0.716432\pi$
$673$	9.31475	−	16.1336i	0.359057	−	0.621905i	0.987804	+	0.155705i	$0.0497649\pi$
$674$	−13.5184			−0.520709
$675$	13.8213	−	26.8311i	0.531981	−	1.03273i
$676$	11.9734	+	5.06344i	0.460514	+	0.194748i
$677$	13.4512	+	23.2982i	0.516972	+	0.895422i	0.999806	+	0.0197102i	$0.00627434\pi$
$677$	13.4512	+	23.2982i	0.516972	+	0.895422i	−0.482833	+	0.875712i	$0.660392\pi$
$678$	8.00099	+	4.45049i	0.307276	+	0.170920i
$679$	4.39440	−	16.4419i	0.168642	−	0.630981i
$680$	3.19914	−	1.84702i	0.122681	−	0.0708301i
$681$	−13.3440	+	7.99111i	−0.511345	+	0.306220i
$682$	−7.72873			−0.295948
$683$	40.7673			1.55992			0.779958	−	0.625831i	$-0.215240\pi$
$683$	40.7673			1.55992			0.779958	+	0.625831i	$0.215240\pi$
$684$	−1.59942	−	2.57651i	−0.0611553	−	0.0985154i
$685$	−60.3003	+	34.8144i	−2.30395	+	1.33019i
$686$	−13.0708	+	13.1207i	−0.499047	+	0.500951i
$687$	13.8669	−	24.9297i	0.529057	−	0.951127i
$688$	3.35600	+	5.81276i	0.127946	+	0.221609i
$689$	15.7823	+	13.9441i	0.601258	+	0.531230i
$690$	−9.69044	+	17.4213i	−0.368909	+	0.663217i
$691$	13.7971			0.524865			0.262432	−	0.964950i	$-0.415475\pi$
$691$	13.7971			0.524865			0.262432	+	0.964950i	$0.415475\pi$
$692$	2.53897	−	4.39763i	0.0965173	−	0.167173i
$693$	−11.9914	−	11.2342i	−0.455514	−	0.426754i
$694$			33.5765i			1.27454i
$695$	−33.4456	+	57.9295i	−1.26866	+	2.19739i
$696$	−0.254829	−	15.9494i	−0.00965928	−	0.604562i
$697$	9.57961	+	5.53079i	0.362854	+	0.209494i
$698$	11.8845	−	20.5845i	0.449833	−	0.779134i
$699$	8.37538	+	4.65874i	0.316786	+	0.176210i
$700$	14.8416	−	3.98690i	0.560961	−	0.150691i
$701$		−	9.30649i		−	0.351501i	−0.984435	−	0.175751i	$-0.943765\pi$
$701$		−	9.30649i		−	0.351501i	0.984435	−	0.175751i	$-0.0562352\pi$
$702$	18.5187	+	2.83887i	0.698942	+	0.107146i
$703$	6.10373	+	3.52399i	0.230207	+	0.132910i
$704$	1.03510	+	1.79285i	0.0390118	+	0.0675704i
$705$	−6.93701	+	0.110835i	−0.261263	+	0.00417428i
$706$	−9.28444	+	5.36037i	−0.349425	+	0.201740i
$707$	−13.2012	+	49.3930i	−0.496483	+	1.85762i
$708$	−14.5760	+	8.72889i	−0.547801	+	0.328052i
$709$	−2.68396	−	1.54958i	−0.100798	−	0.0581958i	0.448754	−	0.893656i	$-0.351868\pi$
$709$	−2.68396	−	1.54958i	−0.100798	−	0.0581958i	−0.549552	+	0.835460i	$0.685201\pi$
$710$	22.4690	+	12.9725i	0.843246	+	0.486848i
$711$	14.9310	−	0.477236i	0.559955	−	0.0178978i
$712$			7.61879i			0.285526i
$713$	−11.3188	−	6.53491i	−0.423892	−	0.244734i
$714$	−1.24988	+	4.99508i	−0.0467757	+	0.186936i
$715$	−18.3899	−	16.2481i	−0.687745	−	0.607643i
$716$	10.1439	−	5.85660i	0.379097	−	0.218871i
$717$	−3.85760	−	6.44166i	−0.144065	−	0.240568i
$718$	−7.26878	−	12.5899i	−0.271268	−	0.469851i
$719$	5.88702	−	10.1966i	0.219549	−	0.380270i	−0.735121	−	0.677936i	$-0.762875\pi$
$719$	5.88702	−	10.1966i	0.219549	−	0.380270i	0.954670	+	0.297666i	$0.0962082\pi$
$720$	−0.315084	−	9.85784i	−0.0117425	−	0.367380i
$721$	−23.2197	−	6.20590i	−0.864746	−	0.231120i
$722$	8.98908	+	15.5695i	0.334539	+	0.579438i
$723$	−3.74370	−	6.25146i	−0.139230	−	0.232494i
$724$		−	22.6731i		−	0.842638i
$725$	46.3269	−	26.7468i	1.72054	−	0.993353i
$726$	−11.6280	+	0.185784i	−0.431554	+	0.00689509i
$727$			13.8729i			0.514518i	0.966342	+	0.257259i	$0.0828194\pi$
$727$			13.8729i			0.514518i	−0.966342	+	0.257259i	$0.917181\pi$
$728$	5.27553	+	7.94788i	0.195524	+	0.294568i
$729$	26.8761	−	2.58415i	0.995409	−	0.0957091i
$730$			5.77412i			0.213710i
$731$	−3.77087	−	6.53134i	−0.139471	−	0.241570i
$732$	0.00669590	+	0.419088i	0.000247488	+	0.0154899i
$733$	21.6003	+	37.4129i	0.797827	+	1.38188i	0.921029	+	0.389495i	$0.127350\pi$
$733$	21.6003	+	37.4129i	0.797827	+	1.38188i	−0.123202	+	0.992382i	$0.539316\pi$
$734$	−15.1524	+	8.74823i	−0.559284	+	0.322903i
$735$	−19.3319	+	34.8586i	−0.713069	+	1.28578i
$736$			3.50085i			0.129043i
$737$	−21.1814	−	12.2291i	−0.780228	−	0.450465i
$738$	25.0922	−	15.5764i	0.923656	−	0.573377i
$739$	−29.5969	+	17.0878i	−1.08874	+	0.628585i	−0.933241	−	0.359251i	$-0.883032\pi$
$739$	−29.5969	+	17.0878i	−1.08874	+	0.628585i	−0.155500	+	0.987836i	$0.549699\pi$
$740$	11.4611	+	19.8512i	0.421318	+	0.729744i
$741$	6.20618	+	1.15542i	0.227990	+	0.0424456i
$742$	4.00920	+	14.9247i	0.147182	+	0.547901i
$743$	−15.6321	+	27.0755i	−0.573484	+	0.993304i	0.422720	+	0.906260i	$0.361075\pi$
$743$	−15.6321	+	27.0755i	−0.573484	+	0.993304i	−0.996204	+	0.0870439i	$0.972258\pi$
$744$	6.46548	−	0.103301i	0.237036	−	0.00378720i
$745$			43.5611i			1.59596i
$746$	5.93324	−	10.2767i	0.217231	−	0.376256i
$747$	2.64441	+	1.41609i	0.0967538	+	0.0518122i
$748$	−1.16306	−	2.01448i	−0.0425257	−	0.0736567i
$749$	7.03641	−	7.04534i	0.257105	−	0.257431i
$750$	3.94968	−	2.36528i	0.144222	−	0.0863676i
$751$	2.10325			0.0767488			0.0383744	−	0.999263i	$-0.487782\pi$
$751$	2.10325			0.0767488			0.0383744	+	0.999263i	$0.487782\pi$
$752$	−1.05515	+	0.609193i	−0.0384775	+	0.0222150i
$753$	16.4883	−	29.6422i	0.600865	−	1.08022i
$754$	24.8843	+	21.9860i	0.906233	+	0.800684i
$755$	56.9955			2.07428
$756$	10.1815	+	9.23775i	0.370299	+	0.335974i
$757$	16.8638	−	29.2089i	0.612924	−	1.06162i	−0.377821	−	0.925879i	$-0.623326\pi$
$757$	16.8638	−	29.2089i	0.612924	−	1.06162i	0.990745	−	0.135737i	$-0.0433402\pi$
$758$	10.9141	+	6.30127i	0.396419	+	0.228872i
$759$	10.9701	+	6.10202i	0.398189	+	0.221489i
$760$		−	3.32333i		−	0.120550i
$761$	−16.6410	−	9.60768i	−0.603235	−	0.348278i	0.167078	−	0.985944i	$-0.446567\pi$
$761$	−16.6410	−	9.60768i	−0.603235	−	0.348278i	−0.770313	+	0.637666i	$0.779900\pi$
$762$	−32.5613	+	0.520243i	−1.17957	+	0.0188464i
$763$	−1.93345	−	7.19746i	−0.0699956	−	0.260566i
$764$	−22.3913	−	12.9276i	−0.810087	−	0.467704i
$765$	0.354035	+	11.0765i	0.0128002	+	0.400471i
$766$	0.920885	+	0.531673i	0.0332729	+	0.0192101i
$767$	7.02782	−	34.6619i	0.253760	−	1.25157i
$768$	−0.889878	−	1.48597i	−0.0321107	−	0.0536205i
$769$	19.1381	−	33.1482i	0.690139	−	1.19536i	−0.281653	−	0.959516i	$-0.590883\pi$
$769$	19.1381	−	33.1482i	0.690139	−	1.19536i	0.971792	−	0.235840i	$-0.0757840\pi$
$770$	−4.67162	−	17.3906i	−0.168353	−	0.626712i
$771$	−15.9731	−	26.6728i	−0.575256	−	0.960598i
$772$	18.8878	−	10.9049i	0.679787	−	0.392475i
$773$		−	2.52422i		−	0.0907898i	−0.998969	−	0.0453949i	$-0.985545\pi$
$773$		−	2.52422i		−	0.0907898i	0.998969	−	0.0453949i	$-0.0144546\pi$
$774$	−20.1257	+	0.643275i	−0.723404	+	0.0231220i
$775$	10.8425	+	18.7797i	0.389473	+	0.674587i
$776$	−3.21628	−	5.57077i	−0.115458	−	0.199979i
$777$	−30.9953	−	7.75575i	−1.11195	−	0.278236i
$778$	2.28039	+	1.31658i	0.0817558	+	0.0472018i
$779$	8.61825	−	4.97575i	0.308781	−	0.178275i
$780$	15.6013	+	13.3465i	0.558616	+	0.477883i
$781$	8.16870	−	14.1486i	0.292299	−	0.506277i
$782$		−	3.93363i		−	0.140666i
$783$	42.5419	+	21.9142i	1.52032	+	0.783150i
$784$	0.00888497	+	6.99999i	0.000317320	+	0.250000i
$785$	−46.3984			−1.65603
$786$	2.44509	−	4.39574i	0.0872136	−	0.156791i
$787$	−1.76492			−0.0629126			−0.0314563	−	0.999505i	$-0.510014\pi$
$787$	−1.76492			−0.0629126			−0.0314563	+	0.999505i	$0.510014\pi$
$788$	3.51025	−	6.07993i	0.125047	−	0.216588i
$789$	42.1503	+	23.4458i	1.50059	+	0.834692i
$790$	14.1776	+	8.18542i	0.504415	+	0.291224i
$791$	−13.5110	−	3.61107i	−0.480395	−	0.128395i
$792$	−6.20743	+	0.198407i	−0.220572	+	0.00705009i
$793$	−0.653860	−	0.577705i	−0.0232193	−	0.0205149i
$794$	−4.27357	+	7.40204i	−0.151663	+	0.262689i
$795$	17.0883	+	28.5351i	0.606058	+	1.01203i
$796$		−	15.0791i		−	0.534464i
$797$	5.40206	+	9.35664i	0.191351	+	0.331429i	0.945698	−	0.325046i	$-0.105380\pi$
$797$	5.40206	+	9.35664i	0.191351	+	0.331429i	−0.754347	+	0.656476i	$0.772047\pi$
$798$	3.32952	+	3.22070i	0.117864	+	0.114012i
$799$	1.18559	−	0.684502i	0.0419432	−	0.0242159i
$800$	2.90424	−	5.03029i	0.102680	−	0.177848i
$801$	−20.1492	−	10.7900i	−0.711937	−	0.381246i
$802$	15.5754			0.549985
$803$	3.63594			0.128309
$804$	17.8828	+	9.94717i	0.630678	+	0.350810i
$805$	7.86270	−	29.4187i	0.277124	−	1.03687i
$806$	−8.91255	+	10.0874i	−0.313931	+	0.355315i
$807$	−25.1897	−	42.0633i	−0.886718	−	1.48070i
$808$	9.66204	+	16.7351i	0.339909	+	0.588740i
$809$	−14.3880	+	8.30689i	−0.505854	+	0.292055i	−0.731128	−	0.682241i	$-0.761006\pi$
$809$	−14.3880	+	8.30689i	−0.505854	+	0.292055i	0.225274	+	0.974295i	$0.427672\pi$
$810$	26.5170	+	13.1277i	0.931711	+	0.461261i
$811$	−7.44633			−0.261476			−0.130738	−	0.991417i	$-0.541735\pi$
$811$	−7.44633			−0.261476			−0.130738	+	0.991417i	$0.541735\pi$
$812$	6.32139	+	23.5320i	0.221837	+	0.825811i
$813$	−22.5172	−	37.6006i	−0.789713	−	1.31871i
$814$	12.5002	−	7.21699i	0.438132	−	0.252955i
$815$	33.9124			1.18790
$816$	0.999885	+	1.66967i	0.0350030	+	0.0584502i
$817$	−6.78489			−0.237373
$818$	10.8097			0.377951
$819$	−28.4909	+	2.69596i	−0.995553	+	0.0942044i
$820$	32.3653			1.13025
$821$	−3.42773			−0.119629			−0.0598143	−	0.998210i	$-0.519051\pi$
$821$	−3.42773			−0.119629			−0.0598143	+	0.998210i	$0.519051\pi$
$822$	−18.8468	−	31.4715i	−0.657356	−	1.09769i
$823$	39.6380			1.38169			0.690847	−	0.723001i	$-0.257238\pi$
$823$	39.6380			1.38169			0.690847	+	0.723001i	$0.257238\pi$
$824$	−7.86720	+	4.54213i	−0.274067	+	0.158233i
$825$	−10.7005	−	17.8684i	−0.372545	−	0.622098i
$826$	18.3395	−	18.3628i	0.638112	−	0.638923i
$827$	0.211856			0.00736695			0.00368347	−	0.999993i	$-0.498828\pi$
$827$	0.211856			0.00736695			0.00368347	+	0.999993i	$0.498828\pi$
$828$	−9.25860	−	4.95803i	−0.321759	−	0.172304i
$829$	27.2898	−	15.7558i	0.947815	−	0.547221i	0.0554133	−	0.998464i	$-0.482352\pi$
$829$	27.2898	−	15.7558i	0.947815	−	0.547221i	0.892401	+	0.451242i	$0.149019\pi$
$830$	1.64365	+	2.84688i	0.0570519	+	0.0988168i
$831$	11.6516	+	19.4566i	0.404190	+	0.674942i
$832$	3.53365	+	0.716460i	0.122507	+	0.0248388i
$833$	−0.00998334	−	7.86534i	−0.000345902	−	0.272518i
$834$	−30.7971	−	17.1307i	−1.06642	−	0.593186i
$835$	−45.9720			−1.59093
$836$	−2.09268			−0.0723770
$837$	−8.88344	+	17.2454i	−0.307057	+	0.596087i
$838$	7.13932	−	12.3657i	0.246624	−	0.427165i
$839$	−13.7645	+	7.94694i	−0.475204	+	0.274359i	−0.718416	−	0.695614i	$-0.755132\pi$
$839$	−13.7645	+	7.94694i	−0.475204	+	0.274359i	0.243212	+	0.969973i	$0.421799\pi$
$840$	4.14049	+	14.4857i	0.142860	+	0.499803i
$841$	27.9082	+	48.3384i	0.962352	+	1.66684i
$842$		−	31.1553i		−	1.07368i
$843$	14.7378	+	24.6101i	0.507596	+	0.847615i
$844$	−10.2101	+	17.6845i	−0.351448	+	0.608725i
$845$	−42.4135	+	5.26553i	−1.45907	+	0.181140i
$846$	−0.116769	−	3.65329i	−0.00401462	−	0.125603i
$847$	17.1561	−	4.60862i	0.589489	−	0.158354i
$848$	5.05843	+	2.92049i	0.173707	+	0.100290i
$849$	27.8387	+	15.4851i	0.955423	+	0.531446i
$850$	−3.26326	+	5.65214i	−0.111929	+	0.193867i
$851$	24.4089			0.836725
$852$	−6.64443	+	11.9452i	−0.227635	+	0.409237i
$853$	−8.80214			−0.301379			−0.150690	−	0.988581i	$-0.548149\pi$
$853$	−8.80214			−0.301379			−0.150690	+	0.988581i	$0.548149\pi$
$854$	−0.166101	−	0.618327i	−0.00568386	−	0.0211587i
$855$	8.78911	+	4.70662i	0.300581	+	0.160963i
$856$		−	3.76351i		−	0.128634i
$857$	−2.96296	+	5.13199i	−0.101213	+	0.175305i	−0.912185	−	0.409780i	$-0.865606\pi$
$857$	−2.96296	+	5.13199i	−0.101213	+	0.175305i	0.810972	+	0.585085i	$0.198939\pi$
$858$	8.40425	−	9.82406i	0.286916	−	0.335388i
$859$	21.0079	−	12.1289i	0.716781	−	0.413834i	−0.0967860	−	0.995305i	$-0.530856\pi$
$859$	21.0079	−	12.1289i	0.716781	−	0.413834i	0.813567	+	0.581472i	$0.197523\pi$
$860$	−19.1102	−	11.0333i	−0.651652	−	0.376231i
$861$	−31.3658	+	32.4256i	−1.06895	+	1.10506i
$862$	−10.7951	−	18.6976i	−0.367682	−	0.636844i
$863$	9.92236	+	17.1860i	0.337761	+	0.585019i	0.984011	−	0.178106i	$-0.0569971\pi$
$863$	9.92236	+	17.1860i	0.337761	+	0.585019i	−0.646250	+	0.763126i	$0.723664\pi$
$864$	5.19019	−	0.248945i	0.176574	−	0.00846930i
$865$			16.6944i			0.567626i
$866$	16.2009	−	9.35358i	0.550528	−	0.317848i
$867$	14.0044	+	23.3855i	0.475615	+	0.794212i
$868$	−9.53925	+	2.56252i	−0.323783	+	0.0869777i
$869$	5.15432	−	8.92754i	0.174848	−	0.302846i
$870$	26.9434	+	44.9918i	0.913467	+	1.52536i
$871$	−40.3871	+	13.5435i	−1.36847	+	0.458904i
$872$	−2.43945	−	1.40841i	−0.0826101	−	0.0476949i
$873$	19.2879	−	0.616494i	0.652795	−	0.0208652i
$874$	−3.06476	−	1.76944i	−0.103667	−	0.0598521i
$875$	−4.96946	+	4.97578i	−0.167999	+	0.168212i
$876$	−3.04165	+	0.0485974i	−0.102768	+	0.00164195i
$877$	−7.64550	−	4.41413i	−0.258170	−	0.149055i	0.365329	−	0.930878i	$-0.380956\pi$
$877$	−7.64550	−	4.41413i	−0.258170	−	0.149055i	−0.623500	+	0.781824i	$0.714290\pi$
$878$			14.3709i			0.484994i
$879$	12.8946	+	7.17251i	0.434923	+	0.241923i
$880$	−5.89421	−	3.40302i	−0.198694	−	0.114716i
$881$	−9.51336	+	16.4776i	−0.320513	+	0.555145i	−0.980594	−	0.196049i	$-0.937189\pi$
$881$	−9.51336	+	16.4776i	−0.320513	+	0.555145i	0.660081	+	0.751195i	$0.270522\pi$
$882$	−18.5253	−	9.89014i	−0.623778	−	0.333018i
$883$	−30.8587			−1.03848			−0.519239	−	0.854629i	$-0.673785\pi$
$883$	−30.8587			−1.03848			−0.519239	+	0.854629i	$0.673785\pi$
$884$	−3.97048	−	0.805029i	−0.133542	−	0.0270761i
$885$	27.1518	−	48.8129i	0.912697	−	1.64083i
$886$	−1.21594	+	0.702023i	−0.0408503	+	0.0235849i
$887$	−13.1419			−0.441262			−0.220631	−	0.975357i	$-0.570812\pi$
$887$	−13.1419			−0.441262			−0.220631	+	0.975357i	$0.570812\pi$
$888$	−10.3606	+	6.20446i	−0.347679	+	0.208208i
$889$	48.0414	−	12.9053i	1.61126	−	0.432831i
$890$	−12.5239	−	21.6920i	−0.419801	−	0.727116i
$891$	8.26646	−	16.6976i	0.276937	−	0.559391i
$892$	1.37326	−	2.37855i	0.0459801	−	0.0796399i
$893$		−	1.23162i		−	0.0412145i
$894$	−22.9468	+	0.366629i	−0.767456	+	0.0122619i
$895$	−19.2543	+	33.3494i	−0.643601	+	1.11475i
$896$	1.87202	+	1.86964i	0.0625397	+	0.0624603i
$897$	20.6147	−	7.28135i	0.688304	−	0.243117i
$898$	−11.0266	−	19.0987i	−0.367963	−	0.637331i
$899$	−29.7760	+	17.1912i	−0.993085	+	0.573358i
$900$	9.19037	+	14.8048i	0.306346	+	0.493494i
$901$	−5.68376	−	3.28152i	−0.189354	−	0.109323i
$902$		−	20.3803i		−	0.678589i
$903$	29.5738	−	8.45320i	0.984156	−	0.281305i
$904$	−4.57774	+	2.64296i	−0.152253	+	0.0879035i
$905$	37.2703	+	64.5540i	1.23891	+	2.14585i
$906$	0.479698	+	30.0236i	0.0159369	+	0.997468i
$907$	−24.3534	−	42.1813i	−0.808640	−	1.40061i	−0.913806	−	0.406151i	$-0.866871\pi$
$907$	−24.3534	−	42.1813i	−0.808640	−	1.40061i	0.105165	−	0.994455i	$-0.466463\pi$
$908$		−	8.98000i		−	0.298012i
$909$	−57.9427	+	1.85201i	−1.92184	+	0.0614273i
$910$	−28.0851	−	13.9570i	−0.931013	−	0.462669i
$911$		−	7.94598i		−	0.263262i	−0.991299	−	0.131631i	$-0.957979\pi$
$911$		−	7.94598i		−	0.263262i	0.991299	−	0.131631i	$-0.0420214\pi$
$912$	1.75064	−	0.0279705i	0.0579694	−	0.000926197i
$913$	1.79267	−	1.03500i	0.0593287	−	0.0342534i
$914$			42.3253i			1.40000i
$915$	−0.707966	−	1.18221i	−0.0234046	−	0.0390825i
$916$	8.23500	+	14.2634i	0.272092	+	0.471277i
$917$	−1.98392	+	7.42292i	−0.0655147	+	0.245126i
$918$	−5.83180	+	0.279720i	−0.192478	+	0.00923215i
$919$	13.5830	−	23.5265i	0.448062	−	0.776067i	−0.550198	−	0.835034i	$-0.685448\pi$
$919$	13.5830	−	23.5265i	0.448062	−	0.776067i	0.998260	+	0.0589679i	$0.0187810\pi$
$920$	−5.75475	−	9.96752i	−0.189728	−	0.328619i
$921$	18.9688	+	31.6752i	0.625042	+	1.04373i
$922$	−10.2913	+	5.94166i	−0.338925	+	0.195678i
$923$	−9.04667	−	26.9775i	−0.297775	−	0.887974i
$924$	9.12155	−	2.60725i	0.300077	−	0.0857721i
$925$	−35.0725	−	20.2491i	−1.15318	−	0.665787i
$926$		−	3.56440i		−	0.117133i
$927$	−0.870631	−	27.2389i	−0.0285953	−	0.894642i
$928$	7.97573	+	4.60479i	0.261816	+	0.151160i
$929$	20.5681	+	11.8750i	0.674816	+	0.389605i	0.797899	−	0.602791i	$-0.205945\pi$
$929$	20.5681	+	11.8750i	0.674816	+	0.389605i	−0.123083	+	0.992396i	$0.539278\pi$
$930$	−18.2385	+	10.9221i	−0.598064	+	0.358151i
$931$	−6.13250	−	3.53023i	−0.200985	−	0.115699i
$932$	−4.79194	+	2.76663i	−0.156965	+	0.0906240i
$933$	−25.6551	+	0.409900i	−0.839909	+	0.0134195i
$934$	3.56143	+	6.16858i	0.116534	+	0.201842i
$935$	6.62285	+	3.82371i	0.216591	+	0.125049i
$936$	−6.89928	+	8.33066i	−0.225510	+	0.272296i
$937$			44.8244i			1.46435i	0.681116	+	0.732175i	$0.261495\pi$
$937$			44.8244i			1.46435i	−0.681116	+	0.732175i	$0.738505\pi$
$938$	−30.1981	−	8.07101i	−0.986001	−	0.263528i
$939$	39.6806	+	22.0720i	1.29493	+	0.720294i
$940$	2.00280	−	3.46895i	0.0653240	−	0.113145i
$941$	−26.3318	−	15.2027i	−0.858393	−	0.495593i	0.00508113	−	0.999987i	$-0.498383\pi$
$941$	−26.3318	−	15.2027i	−0.858393	−	0.495593i	−0.863474	+	0.504394i	$0.831716\pi$
$942$	−0.390508	−	24.4414i	−0.0127234	−	0.796343i
$943$	17.2322	−	29.8471i	0.561159	−	0.971955i
$944$		−	9.80909i		−	0.319259i
$945$	−44.1737	−	9.56487i	−1.43697	−	0.311145i
$946$	−6.94759	+	12.0336i	−0.225886	+	0.391245i
$947$	8.01406			0.260422			0.130211	−	0.991486i	$-0.458435\pi$
$947$	8.01406			0.260422			0.130211	+	0.991486i	$0.458435\pi$
$948$	−4.19253	+	7.53724i	−0.136167	+	0.244798i
$949$	4.19286	−	4.74558i	0.136106	−	0.154048i
$950$	2.93578	+	5.08492i	0.0952493	+	0.164977i
$951$	−16.5112	+	29.6835i	−0.535413	+	0.962554i
$952$	−2.10344	−	2.10077i	−0.0681728	−	0.0680863i
$953$	4.48194	−	2.58765i	0.145184	−	0.0838222i	−0.425648	−	0.904889i	$-0.639954\pi$
$953$	4.48194	−	2.58765i	0.145184	−	0.0838222i	0.570833	+	0.821067i	$0.306621\pi$
$954$	−14.8877	+	9.24179i	−0.482006	+	0.299214i
$955$	85.0022			2.75061
$956$	4.33497			0.140203
$957$	28.3311	−	16.9661i	0.915815	−	0.548437i
$958$	−26.4547	+	15.2736i	−0.854712	+	0.493468i
$959$	39.6475	+	39.5972i	1.28028	+	1.27866i
$960$	4.97629	+	2.76802i	0.160609	+	0.0893375i
$961$	8.53115	+	14.7764i	0.275199	+	0.476658i
$962$	4.99535	−	24.6375i	0.161056	−	0.794346i
$963$	9.95323	+	5.33001i	0.320738	+	0.171757i
$964$	4.20698			0.135498
$965$	−35.8512	+	62.0960i	−1.15409	+	1.99894i
$966$	15.5631	+	3.89425i	0.500735	+	0.125296i
$967$			14.4231i			0.463816i	0.972738	+	0.231908i	$0.0744968\pi$
$967$			14.4231i			0.463816i	−0.972738	+	0.231908i	$0.925503\pi$
$968$	3.35713	−	5.81473i	0.107902	−	0.186892i
$969$	−1.96705	+	0.0314283i	−0.0631909	+	0.00100962i
$970$	18.3146	+	10.5739i	0.588046	+	0.339509i
$971$	0.714834	−	1.23813i	0.0229401	−	0.0397335i	−0.854327	−	0.519735i	$-0.826031\pi$
$971$	0.714834	−	1.23813i	0.0229401	−	0.0397335i	0.877268	+	0.480002i	$0.159364\pi$
$972$	−6.69214	+	14.0789i	−0.214651	+	0.451581i
$973$	52.0060	+	13.8996i	1.66723	+	0.445600i
$974$			32.0202i			1.02599i
$975$	−35.6612	−	6.63915i	−1.14207	−	0.212623i
$976$	−0.209571	−	0.120996i	−0.00670819	−	0.00387297i
$977$	−7.46343	−	12.9270i	−0.238776	−	0.413573i	0.721587	−	0.692324i	$-0.243413\pi$
$977$	−7.46343	−	12.9270i	−0.238776	−	0.413573i	−0.960363	+	0.278751i	$0.910080\pi$
$978$	0.285421	+	17.8641i	0.00912676	+	0.571232i
$979$	−13.6593	+	7.88621i	−0.436554	+	0.252044i
$980$	−11.5320	−	19.9155i	−0.368375	−	0.636179i
$981$	7.17962	−	4.45688i	0.229228	−	0.142297i
$982$	−13.0865	−	7.55549i	−0.417607	−	0.241106i
$983$	2.34938	+	1.35641i	0.0749334	+	0.0432628i	0.536999	−	0.843583i	$-0.319558\pi$
$983$	2.34938	+	1.35641i	0.0749334	+	0.0432628i	−0.462065	+	0.886846i	$0.652891\pi$
$984$	0.272400	+	17.0491i	0.00868379	+	0.543507i
$985$			23.0808i			0.735414i
$986$	−8.96170	−	5.17404i	−0.285399	−	0.164775i
$987$	1.53445	+	5.36835i	0.0488422	+	0.170876i
$988$	−2.41322	+	2.73135i	−0.0767749	+	0.0868957i
$989$	−20.3496	+	11.7489i	−0.647080	+	0.373592i
$990$	17.3475	−	10.7688i	0.551338	−	0.342253i
$991$	3.28838	+	5.69564i	0.104459	+	0.180928i	0.913517	−	0.406801i	$-0.133356\pi$
$991$	3.28838	+	5.69564i	0.104459	+	0.180928i	−0.809058	+	0.587729i	$0.800022\pi$
$992$	−1.86666	+	3.23315i	−0.0592665	+	0.102653i
$993$	−0.721561	−	45.1615i	−0.0228980	−	1.43316i
$994$	5.39121	−	20.1715i	0.170999	−	0.639800i
$995$	24.7872	+	42.9327i	0.785807	+	1.36106i
$996$	−1.48583	+	0.889789i	−0.0470802	+	0.0281941i
$997$			22.9904i			0.728114i	0.931377	+	0.364057i	$0.118609\pi$
$997$			22.9904i			0.728114i	−0.931377	+	0.364057i	$0.881391\pi$
$998$	−4.18606	+	2.41682i	−0.132508	+	0.0765033i
$999$	−1.73571	−	36.1873i	−0.0549155	−	1.14492i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bi.f.17.6	yes	34
3.2	odd	2		546.2.bi.e.17.12	✓	34
7.5	odd	6		546.2.bn.e.173.1	yes	34
13.10	even	6		546.2.bn.f.101.17	yes	34
21.5	even	6		546.2.bn.f.173.17	yes	34
39.23	odd	6		546.2.bn.e.101.1	yes	34
91.75	odd	6		546.2.bi.e.257.12	yes	34
273.257	even	6	inner	546.2.bi.f.257.6	yes	34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bi.e.17.12	✓	34	3.2	odd	2
546.2.bi.e.257.12	yes	34	91.75	odd	6
546.2.bi.f.17.6	yes	34	1.1	even	1	trivial
546.2.bi.f.257.6	yes	34	273.257	even	6	inner
546.2.bn.e.101.1	yes	34	39.23	odd	6
546.2.bn.e.173.1	yes	34	7.5	odd	6
546.2.bn.f.101.17	yes	34	13.10	even	6
546.2.bn.f.173.17	yes	34	21.5	even	6

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:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.bi (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +(-0.889878 - 1.48597i) q^{3} +1.00000 q^{4} +(-2.84717 + 1.64381i) q^{5} +(-0.889878 - 1.48597i) q^{6} +(1.87202 + 1.86964i) q^{7} +1.00000 q^{8} +(-1.41623 + 2.64467i) q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +(-0.889878 - 1.48597i) q^{3} +1.00000 q^{4} +(-2.84717 + 1.64381i) q^{5} +(-0.889878 - 1.48597i) q^{6} +(1.87202 + 1.86964i) q^{7} +1.00000 q^{8} +(-1.41623 + 2.64467i) q^{9} +(-2.84717 + 1.64381i) q^{10} +(1.03510 + 1.79285i) q^{11} +(-0.889878 - 1.48597i) q^{12} +(3.53365 + 0.716460i) q^{13} +(1.87202 + 1.86964i) q^{14} +(4.97629 + 2.76802i) q^{15} +1.00000 q^{16} -1.12362 q^{17} +(-1.41623 + 2.64467i) q^{18} +(-0.505430 + 0.875431i) q^{19} +(-2.84717 + 1.64381i) q^{20} +(1.11237 - 4.44552i) q^{21} +(1.03510 + 1.79285i) q^{22} +3.50085i q^{23} +(-0.889878 - 1.48597i) q^{24} +(2.90424 - 5.03029i) q^{25} +(3.53365 + 0.716460i) q^{26} +(5.19019 - 0.248945i) q^{27} +(1.87202 + 1.86964i) q^{28} +(7.97573 + 4.60479i) q^{29} +(4.97629 + 2.76802i) q^{30} +(-1.86666 + 3.23315i) q^{31} +1.00000 q^{32} +(1.74301 - 3.13355i) q^{33} -1.12362 q^{34} +(-8.40328 - 2.24594i) q^{35} +(-1.41623 + 2.64467i) q^{36} -6.97226i q^{37} +(-0.505430 + 0.875431i) q^{38} +(-2.07988 - 5.88847i) q^{39} +(-2.84717 + 1.64381i) q^{40} +(-8.52566 - 4.92229i) q^{41} +(1.11237 - 4.44552i) q^{42} +(3.35600 + 5.81276i) q^{43} +(1.03510 + 1.79285i) q^{44} +(-0.315084 - 9.85784i) q^{45} +3.50085i q^{46} +(-1.05515 + 0.609193i) q^{47} +(-0.889878 - 1.48597i) q^{48} +(0.00888497 + 6.99999i) q^{49} +(2.90424 - 5.03029i) q^{50} +(0.999885 + 1.66967i) q^{51} +(3.53365 + 0.716460i) q^{52} +(5.05843 + 2.92049i) q^{53} +(5.19019 - 0.248945i) q^{54} +(-5.89421 - 3.40302i) q^{55} +(1.87202 + 1.86964i) q^{56} +(1.75064 - 0.0279705i) q^{57} +(7.97573 + 4.60479i) q^{58} -9.80909i q^{59} +(4.97629 + 2.76802i) q^{60} +(-0.209571 - 0.120996i) q^{61} +(-1.86666 + 3.23315i) q^{62} +(-7.59580 + 2.30301i) q^{63} +1.00000 q^{64} +(-11.2386 + 3.76878i) q^{65} +(1.74301 - 3.13355i) q^{66} +(-10.2316 + 5.90721i) q^{67} -1.12362 q^{68} +(5.20218 - 3.11533i) q^{69} +(-8.40328 - 2.24594i) q^{70} +(-3.94585 - 6.83441i) q^{71} +(-1.41623 + 2.64467i) q^{72} +(0.878160 - 1.52102i) q^{73} -6.97226i q^{74} +(-10.0593 + 0.160721i) q^{75} +(-0.505430 + 0.875431i) q^{76} +(-1.41426 + 5.29150i) q^{77} +(-2.07988 - 5.88847i) q^{78} +(-2.48977 - 4.31240i) q^{79} +(-2.84717 + 1.64381i) q^{80} +(-4.98856 - 7.49095i) q^{81} +(-8.52566 - 4.92229i) q^{82} -0.999900i q^{83} +(1.11237 - 4.44552i) q^{84} +(3.19914 - 1.84702i) q^{85} +(3.35600 + 5.81276i) q^{86} +(-0.254829 - 15.9494i) q^{87} +(1.03510 + 1.79285i) q^{88} +7.61879i q^{89} +(-0.315084 - 9.85784i) q^{90} +(5.27553 + 7.94788i) q^{91} +3.50085i q^{92} +(6.46548 - 0.103301i) q^{93} +(-1.05515 + 0.609193i) q^{94} -3.32333i q^{95} +(-0.889878 - 1.48597i) q^{96} +(-3.21628 - 5.57077i) q^{97} +(0.00888497 + 6.99999i) q^{98} +(-6.20743 + 0.198407i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q + 34 q^{2} + 6 q^{3} + 34 q^{4} + 9 q^{5} + 6 q^{6} + 4 q^{7} + 34 q^{8} + 4 q^{9}+O(q^{10}) \) 34 * q + 34 * q^2 + 6 * q^3 + 34 * q^4 + 9 * q^5 + 6 * q^6 + 4 * q^7 + 34 * q^8 + 4 * q^9	\( 34 q + 34 q^{2} + 6 q^{3} + 34 q^{4} + 9 q^{5} + 6 q^{6} + 4 q^{7} + 34 q^{8} + 4 q^{9} + 9 q^{10} + 9 q^{11} + 6 q^{12} + 8 q^{13} + 4 q^{14} - 17 q^{15} + 34 q^{16} + 12 q^{17} + 4 q^{18} - 5 q^{19} + 9 q^{20} - 7 q^{21} + 9 q^{22} + 6 q^{24} + 16 q^{25} + 8 q^{26} - 18 q^{27} + 4 q^{28} + 27 q^{29} - 17 q^{30} - q^{31} + 34 q^{32} + 12 q^{34} - 3 q^{35} + 4 q^{36} - 5 q^{38} - 10 q^{39} + 9 q^{40} - 3 q^{41} - 7 q^{42} - 3 q^{43} + 9 q^{44} + 9 q^{45} - 27 q^{47} + 6 q^{48} - 2 q^{49} + 16 q^{50} - 36 q^{51} + 8 q^{52} - 21 q^{53} - 18 q^{54} - 57 q^{55} + 4 q^{56} - 17 q^{57} + 27 q^{58} - 17 q^{60} - 51 q^{61} - q^{62} - 24 q^{63} + 34 q^{64} - 21 q^{65} - 21 q^{67} + 12 q^{68} + 30 q^{69} - 3 q^{70} - 15 q^{71} + 4 q^{72} - 19 q^{73} - 54 q^{75} - 5 q^{76} + 9 q^{77} - 10 q^{78} - 9 q^{79} + 9 q^{80} + 28 q^{81} - 3 q^{82} - 7 q^{84} - 42 q^{85} - 3 q^{86} - 81 q^{87} + 9 q^{88} + 9 q^{90} - 72 q^{91} - 17 q^{93} - 27 q^{94} + 6 q^{96} + 19 q^{97} - 2 q^{98} - 27 q^{99}+O(q^{100}) \) 34 * q + 34 * q^2 + 6 * q^3 + 34 * q^4 + 9 * q^5 + 6 * q^6 + 4 * q^7 + 34 * q^8 + 4 * q^9 + 9 * q^10 + 9 * q^11 + 6 * q^12 + 8 * q^13 + 4 * q^14 - 17 * q^15 + 34 * q^16 + 12 * q^17 + 4 * q^18 - 5 * q^19 + 9 * q^20 - 7 * q^21 + 9 * q^22 + 6 * q^24 + 16 * q^25 + 8 * q^26 - 18 * q^27 + 4 * q^28 + 27 * q^29 - 17 * q^30 - q^31 + 34 * q^32 + 12 * q^34 - 3 * q^35 + 4 * q^36 - 5 * q^38 - 10 * q^39 + 9 * q^40 - 3 * q^41 - 7 * q^42 - 3 * q^43 + 9 * q^44 + 9 * q^45 - 27 * q^47 + 6 * q^48 - 2 * q^49 + 16 * q^50 - 36 * q^51 + 8 * q^52 - 21 * q^53 - 18 * q^54 - 57 * q^55 + 4 * q^56 - 17 * q^57 + 27 * q^58 - 17 * q^60 - 51 * q^61 - q^62 - 24 * q^63 + 34 * q^64 - 21 * q^65 - 21 * q^67 + 12 * q^68 + 30 * q^69 - 3 * q^70 - 15 * q^71 + 4 * q^72 - 19 * q^73 - 54 * q^75 - 5 * q^76 + 9 * q^77 - 10 * q^78 - 9 * q^79 + 9 * q^80 + 28 * q^81 - 3 * q^82 - 7 * q^84 - 42 * q^85 - 3 * q^86 - 81 * q^87 + 9 * q^88 + 9 * q^90 - 72 * q^91 - 17 * q^93 - 27 * q^94 + 6 * q^96 + 19 * q^97 - 2 * q^98 - 27 * q^99

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